Citation
Sol-gel derived silica optics

Material Information

Title:
Sol-gel derived silica optics
Creator:
Wang, Shi-Ho
Publisher:
[s.n.]
Publication Date:
Language:
English
Physical Description:
vii, 252 leaves : ill. (some col.) ; 28 cm.

Subjects

Subjects / Keywords:
Chemicals ( jstor )
Gels ( jstor )
Ions ( jstor )
Ligands ( jstor )
Light refraction ( jstor )
Orbitals ( jstor )
Porosity ( jstor )
Silica gel ( jstor )
Silica glass ( jstor )
Water temperature ( jstor )
Dissertations, Academic -- Materials Science and Engineering -- UF
Materials Science and Engineering thesis Ph.D ( lcsh )
Quartz fibers ( lcsh )
Silica gel ( lcsh )
Silica, Vitreous ( lcsh )
Genre:
bibliography ( marcgt )
non-fiction ( marcgt )

Notes

Thesis:
Thesis (Ph. D.)--University of Florida, 1988.
Bibliography:
Includes bibliographical references.
General Note:
Typescript.
General Note:
Vita.
Statement of Responsibility:
by Shi-Ho Wang.

Record Information

Source Institution:
University of Florida
Holding Location:
University of Florida
Rights Management:
Copyright [name of dissertation author]. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Resource Identifier:
023644220 ( ALEPH )
19299381 ( OCLC )

Downloads

This item has the following downloads:


Full Text










SOL-GEL DERIVED SILICA OPTICS


By
SHI-HO WANG






















A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA


1988








ACKNOWLEDGMENTS

I am deeply honored to acknowledge several persons who have helped me during the

time of my research as a graduate student at the University of Florida and as a scientist

at GelTech Inc., Alachua, Florida.

I am grateful to my advisor Professor Larry L. Hench who has shared my dream of

creating a new method for manufacturing high-tech silica optical monoliths, including

high power glass lasers for nuclear fusion which might contribute to freeing mankind

from energy and pollution crisises. This dream has been partially realized by this

research and I greatly appreciate his guidance and support.

Dennis A. LeSage, Candace E. Campbell, and Grib Murphy of GelTech Inc., and Dr.

Jon West, Guy LaTorre, and Martin Wilson of the Advanced Materials Research Center of

University of Florida assisted me directly or indirectly in this work. I give each of them,

my friends, sincere thanks. My appreciation is also extended to Linton E. Floyd, III, and

the Glass Fab Inc. for arranging and performing the gel-silica optical property proving

tests, and to Professor Stephen F. Jacobs in Optical Sciences Center of the University of

Arizona for the low temperature gel-silica thermal expansion test.

Financial support from the U.S Air Force Office of Scientific Research through

contract no. F49620-83-0072, GelTech Inc. and the Department of Materials Science

and Engineering were very important to me and made the research and this manuscript

possible. I am grateful to Dr. Donald R. Ulrich of the AFOSR for his understanding and

contributions to my success.

Special thanks are given to Professor Gholamreza J. Abbaschian, Chairman of the

Department of Materials Science and Engineering, and Professor John Staudhammer of

the Department of Electrical Engineering for their unforgettable assistance and

encouragement at a very critical moment in September 1987.

I greatly appreciate the members of my supervisory committee, Professors

Vellayan Ramaswamy of the Department of Electrical Engineering, Joseph H. Simmons,









David E. Clark and Gholamreza J. Abbaschian of the Department of Materials Science and

Engineering for their advice and recommendations regarding this dissertation. The

responsibility for any remaining errors or shortcomings is, of course, mine.

Words are insufficient to express gratitude to my parents for their constant

support and to my brothers and sisters for their consideration in Taiwan. I am also

particularly indebted to my wife, Sue-Ling, not only for her great backup but also for

her scientific discussions, and to my daughter, Jean, for understanding why we couldn't

have much fun together while this work was being finished.









TABLE OF CONTENTS



ACKNOW LEDGM ENTS ..................................................................................... i i

ABSTRACT ...................................................................................................... v i

CHAPTERS

1 INTRODUCTION TO SOL-GEL DERIVED SIUCA GLASS TECHNOLOGY ......... 1

2 SOL-GEL TRANSFORMATION AND EXPERIMENTAL PROCEDURES ........... 12

Introduction .............................................................................................. 12
Literature Review of Sol-Gel Transformation Modeling ........................ 12
Experimental Procedure ......................................................................... 48
Results ...................................................................................................... 57
Conclusions ............................................................................................... 64

3 PHYSICAL PROPERTIES OF PARTIALLY DENSIFIED SIUCA XEROGEL ...... 67

Introduction ............................................................................................. 67
Review of the Literature .......................................................................... 68
Experimental Procedure ......................................................................... 73
Results and Discussions ............................................................................ 81
Conclusions ............................................................................................... 1 26

4 DEHYDRATION OF SOL-GEL DERIVED SIUCA OPTICS .............................. 128

Introduction .............................................................................................. 128
Review of the Uterature Regarding Dehydration ................................. 130
Experimental Procedure ....................................................................... 139
Results and Discussions ............................................................................ 1 45
Conclusions ............................................................................................... 157

5 OPTICAL PROPERTIES OF FULLY DEHYDRATED SIUCA GEL GLASS ......... 160

Introduction .............................................................................................. 1 60
Literature Review Regarding Optical Properties of Silica Glass ............. 1 61
Experimental Procedure ....................................................................... 178
Results and Discussions ............................................................................ 185
Conclusions ............................................................................................... 203

6 SILICA GEL OPTICAL FILTERS USING TRANSITION-METAL COMPOUNDS 206

Introduction .............................................................................................. 206
Review of the Literature ....................................*.** .**............ 207









Experimental Procedure ................................................................. ......... 229
Results and Discussions ............................................................................ 230
Conclusions ............................................................................................... 238

7 CONCLUSIONS AND RECOMMENDATIONS ........................ ...................... 239

REFERENCES ................................................................................................... 244

BIOGRAPHICAL SKETCH ................................................ ............. ........... .......... 252














Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy


SOL-GEL DERIVED SILICA OPTICS


By

SHI-HO WANG


April 1988


Chairman: Dr. Larry L. Hench
Major Department: Materials Science and Engineering

Large monolithic xerogel silica glasses were successfully made from tetramethyl-

orthosilicate and distilled water using the combination of an acidic drying control

chemical additive (DCCA) and a specially designed drying chamber. The acidic DCCA

increases the gel strength by formation of a fibrillar ultrastucture, and the drying

chamber reduces the catastrophic capillary forces inside the wet gel body.

Partially densified monolithic gels up to 850C were routinely made for physical

property tests and compared to commercial fused silicas. Although the mechanical

properties of the porous gel-silica monoliths such as microhardness, Young's modulus,

toughness, flexural strength, density are relatively lower than fused silica, the optically

transparent porous gel silica has a uv cut-off ranging from 250-300 nm. Such a porous

gel with excellent optical transmission and a highly uniform pore radius of 10-50 A

offers a unique, chemically stable matrix for impregnation with a second phase of

optically active organic or inorganic compounds.

The processing and properties of Types I and II fused quartz optics and Types III and

IV synthetic fused silica optics are compared with the new organometallic sol-gel









derived gel-silica optics. Fully dehydrated and densified gel-silica has excellent

transmission from 165 nm to 4400 nm with no OH absorption peaks. This optical

transmission is equivalent to the best type IV fused silica. The other physical properties

and structural characteristics of the dehydrated dense gel-silica are similar to fused

quartz and fused silica. However, the dense gel-silica has a lower coefficient of thermal

expansion of 2.0 x10-7 cm/cm compared with 5.5 x 10"7 cm/cm for standard vitreous

silicas. The CTE value is temperature independent from 80 K to 500 K. Sol-gel silica

optics can be made as complex shapes by casting of the sol into inexpensive plastic molds.

Monolithic silica gel optical filters were produced by chemical doping with various

transition-metal ions (e.g., cobalt, copper, nickel). Color changes occurred with

various sintering temperature indicating a unique method to control light wavelength

filtration in the visible range. For instance, the observed color or spectral (major peak

of absorption) shifts for the 160C, the 850C, and the 900C Col ion doped gels were

reddish pink (505 nm), deep blue (660 nm), and greenish black (670 nm)

respectively. The optical absorption spectra of the chemically doped-silica are

interpreted in terms of ligand-field and molecular orbital theories.














CHAPTER 1
INTRODUCTION TO SOL-GEL DERIVED SIUCA GLASS TECHNOLOGY

One of the world's most pervasive chemical compounds is silicon dioxide (SiO2).

This compound can exist in many forms crystalline or amorphous, hydroxylated or

dehydroxylated but is most often called "silica" as a generic name.

Silica-based compounds have been fabricated and utilized by mankind for tens of

thousands of years, although only in the past few decades have significant strides been

made in understanding the variables that control silica chemistry [1-7].

Application of this knowledge has produced many useful materials worth billions of

dollars per year; however, today's rapidly accelerating technology demands even greater

performance of silicate materials as well as the need to create new materials. The

objective of this study is to produce a number of new materials using sol-gel silica

processing, including (1) ultraporous gel monoliths for optical and chemical matrices,

(2) ultrapure monolithic gel-glasses with ultralow optical absorption, and (3)

chemically doped gel glass monoliths for optical filters with low expansion coefficients

and high softening points.

Traditional silica glasses are manufactured by melting natural quartz minerals or

synthetic silica, or by flame or plasma vapor-deposition methods. Generally, four types

of commercial vitreous silica are recognized and identified: Type I is obtained by electric

melting of natural quartz in vacuum. Type II is made by flame fusion of quartz. Type III

is made by vapor-phase hydrolysis of pure silicon tetrachloride carried out in a flame.

Type IV is made by oxidation of pure silicon tetrachloride which is subsequently fused

electrically or by means of a plasma. Types I and II are called fused quartz, whereas

Types III and IV are called synthetic fused silica.









Fused quartz is melted at temperatures above its liquidus (1713C) from crushed

natural crystalline quartz powders of mixed particle size, well above micrometers in

diameter [8]. The initial size of these particles, millions of times larger than a silica

molecule, limits the control over the resulting structure and in part determines the

temperature necessary for melting, homogenization, and fabrication. Glass products

from this method have numerous deficiencies; impurities, inhomogeneities, seeds and

bubbles, a high energy requirement for raw material crushing, melting and

homogenization, as well as premature phase separation and crystallization.

Chemical reactions used to produce synthetic fused silica by flame hydrolysis of

silica tetrachloride (type III) and by vacuum plasma oxidation of silica tetrachloride

(type IV) are shown in equations #1 and #2:

Type III hydrolysiss)

SiCI4 + 02 + 2H2 ----> SiO2 + 4HCI (1)

Type IV (oxidation)

SiCl4 + 02 --.... > SiO2 + 2C12 (2)

In fact, it is very difficult to have a complete reaction for either of these two

equations. Consequently, water contents of several thousand ppm are present in type III
silicas, and SiCI4 in few hundred ppm is retained as an unreacted residual in both type

III and IV silicas. In addition to these two intrinsic impurities, the resultant glasses

from type III and IV processes have extrinsic impurities in the range of few parts per

million (ppm) due to the contamination of raw materials and crucibles at high

temperatures (about 1900C).

Table 1-1 [9] lists the dominant characteristics of commercial brands of silica

corresponding to these four types. Their transmission curves are summarized in Figure

1-1 and Table 1-2 [10]. Type I and II glasses have more impurities (Table 1-1) which

make uv transmission curves cut off at higher wavelengths (curves 2 and 3 in Fig. 1-1)

than that of type III and IV glasses (curve 1 in Fig. 1-1). The amount of water (Table 1-














Table 1-1
Preparation and characteristics of four types of vitreous silica


Type


Electromelted
Quartz

IR-Vitreosila
Infrasilb


Flame-fused
Quartz


Herasilb
Homosilb


Hydrolyzed
SiCl4

7940C
Dynasild
Spectrosila
Suprasilb


Oxidized
SiCI4


Spectrosil WFa
7943C
Suprasil-Wb


Impurity (ppm):


400-1500
<1
<0.1
0
3
0.4
0
0
0
1
0
0
1.5
1
0
0.2
0
0.005
<1
5
2
0.0006
0
0


-1000
<0.2
<0.1
<0.02
0.1
<0.1
100
0.03
0.0001
<1
<0.02
<0.1
<0.2
0
0
<0.02
<0.1
<0.001
0.1
<0.1
0
0
<0.1
0


-0(<0.4)
<0.2
<0.1
<0.02
0.1
<0.1
up to 200
0.03
0.0001
<1
<0.02
<0.1
<0.2
0
0
<0.02
<0.1
<0.001
0.1
<0.1
0
0
<0.1
0


a: Thermal Syndicate, England. b: Heraus Amersil, Heraeus, Sayreville, NJ.
c: Corning Glass Work, Corning, NY. d: Dynasil; Berlin, NJ.


Process


Example


<5
30-100
<0.3
0
4
16
0
0.1
0
1
0
0
7
7
4
1
0
0.01
6
9
3
0
0
3














100 I I I





S60I



-40 / I ,
C 3 B





20
.r





160 240 320 400 1000 3000 5000






Wavelength nm


Figure 1-1 Transmission curves for commercial vitreous silica
10mm thick
E A


~40



20


0
160 240 320 400 1000 3000 5000
Wavelength nmn


Figure 1-1 Transmission curves for commercial vitreous silica
10mm thick














Table 1-2
identification of transmission curves of silica glasses


Manufacturer


Amersil, Inc.
(Heraeus)




Coming Glass
Works

Dynasil Corp. of
America

Thermal Syndicate
Ltd.


Product name


Herasil
Infrasil
Homosil
Suprasil
Suprasil-W

Code 7940
Code 7943

Dynasil-1000


Spectrosil
Spectrosil WF
IR-vitreosil


Type


UV curve
in Fig. 1-1


IR curve
in Fig. 1-1









1) in silica glass depends on which type of process is used. For example, Spectrosil WF

(type IV) in Table 1-1 has a water content less than 0.4 ppm compare to 1200 ppm for

Suprasil (type 111). It is observed that there is no significant shift in the uv cut off

between type III and IV silicas due to the increased water content if the other impurities

are constant. However, in the infrared range, water (type III, curve A in Fig. 1-1)

noticeably gives a strong absorption. These shortcomings can limit the use of glass

products made by the traditional techniques described above, as summarized in Table 1-

3.

Sol-gel processing has been used for many years, although the principal chemical

and physical mechanisms are still not clearly understood [11-14]. In recent years

special applications require silica optical components that meet very stringent

requirements. The sol-gel method offers new hope in that structural manipulation is

possible on an extremely fine scale, within the nanometer range, thereby allowing

production of a new generation of silica materials. The outstanding features of these

silicas include very high homogeneity, very high purity, potentially extremely low

optical loss, ease of chemical doping, and near net shape casting. These features make

sol-gel silicas potentially applicable to a wide range of optical products including lenses,

mirrors, wavequides, optical fibers, integrated optoelectronics, and host materials for

filters, lasers, and non-linear optical elements or compounds.

The sol-gel process as it relates to silicas is summarized briefly. A sol is defined

as a dispersion of colloids in a solvent. Silica colloids are solid particles with diameters

ranging from 1nm to 100 nm which depend upon the type and amount of drying control

chemical additive (DCCA) in the solution [15-19]. In this study all colloidal particles

are synthesized by the hydrolysis of tetramethylorthosilicate (TMOS) [Si(OCH3)4]

followed by the growth of the hydrolyzed species [Si(OCH3)4.n(OH)n with 0_
20].


















Type


Table 1-3
Limits for the four types of silica fabrication processes


Fabrication Limits

(1) Bad homogeneity (granular microstructure and bubbles)
(2) Noticeable water content -- few tens to hundreds ppm.
(3) High impurities -- in the range of few ppm from nature
quartz mineral.
(4) Micrometer scale structural manipulation -- quartz is
ground to few micrometers before sintering.
(5) High sintering temperature (above 1700C) --
(a) High energy cost;
(b) React with crucible, thus impurities;
(c) Possible initiate crystallization.


(1) High water content(above 1000 ppm).
(2) High sintering temperature (above 2000C)--
(a) High energy cost;
(b) React with crucible, thus impurities;
(c) Possible initiate crystallization.


(1) Detectable water content (around 1 ppm).
(2) High sintering temperature (above 2000C)--
(a) High energy cost;
(b) React with crucible, thus impurities;
(c) Possible initiate crystallization.


Type I & II














Type III







Type IV









This over-saturated sol is never chemically stable in the presence of the DCCA

and/or under thermally activated conditions; however, after some time and with the

addition of thermal energy a sufficient concentration of colloids that are within an

appropriate size distribution is reached and a zero surface charge is obtained [21]. At

this point the colloids become randomly linked together in fibrillar chains with

thermally activated Brownian motion in the presence of a Van der Waals attractive force

and a base catalyst [see p. 224 in ref. 4]. As the chains grow they form three-

dimensional irregular structures throughout the liquid phase. A network develops with

the liquid phase localized within the solid gel skeleton and microscopically confined by

it. The "sol" has lost its freedom of movement and now becomes a "gel"; this is described

as the gelation point.

Solids tend to decrease their interfacial area so as to minimize surface energy.

Therefore, after the gelation point has been reached the weakly connected spherical-

particle chains tend to minimize surface energy by particle rearrangement, thereby

forming a strong fibrillar-shaped ultrastructure. This phenomenon continues during the

aging process (also termed syneresis), in which liquid is expelled from the gel body and

the weak gel shrinks and becomes stronger.

In this study the first goal, described in Chapter 2, is the production of silica-

based monolithic dried xerogels composed of (a) pure silica and (b) doped with

transition-metal elements. A xerogel is defined as a gel from which the liquid phase has

been evacuated under ambient pressures. The net size and porosity of a xerogel is

minimized, at least to some degree, by surface energy as the liquid is removed. However,

without the help of the DCCA in controlling the colloidal particle size, this can not be

realized because of cracking during drying.

In the amorphous form of silica, a tetrahedral arrangement is primarily favored

by the radius ratios of the silicon to the oxygen ions and by the bonding of sp3 hybrid

orbitals in SiO2. X-ray diffraction studies by Mozzi, Warren and Uhlmann [22, 23]









have shown that silicon forms bonds with oxygen of variable bond angles that are 10%

within the 144 maximum in the distribution of Si-O-Si angles. Various arrangements

of these SiO2 tetrahedra are possible in noncrystalline silica gels. Bonding oxygens at the

corners of two silica tetrahedra can be easily disconnected in the presence of uneven

hydrostatic stresses and water [24]. DCCA's can be used to minimize the particle size

within the polymerized chain, thereby improving the strength of the gel structure so

that during the critical drying process the gel can endure differential evaporation

without initiating cracking.

The processing and physical properties of dried monolithic silica xerogels, heated

from 150C to 900C, are discussed in Chapter 3. This ultraporous material has

densities ranging from 0.7 g/cm3 to 2.10 g/cm3 depending on the initial conditions of

the sol, such as the variation of DCCA and/or the amount of water used, as well as the

aging and drying temperatures.

Two types of water exist within the dried xerogel structure chemical water and

physical water [25], which must be removed to achieve monolithic optical components.

Water in solution can hydrolyze the silicon-oxygen-silicon bond. The hydroxyl ion's

oxygen is covalently bonded to silicon, whereas the hydrogen ion forms an ionic bond to

the oxygen. Consequently, chemical water results with hydroxyl groups strongly

attached to the gel's surface. The physical water associated with hydrogen-bonding of

surface hydroxyl groups exists within the ultraporous space of the gel body.

A major problem with monolithic silica xerogels, especially for high-

transmittance optical components, is the removal of chemically bonded water, also called

a silanol group. The chemically bonded silanols give rise to the fundamental vibration of

hydroxyl ions occurring at a wavelength of 2669.4 nm. Also present are vibrational

overtones and combinations of this ion and associated water occurring at the following

wavelengths: 2919.7 nm, 2768.9 nm, 2698.3 nm, 2262.5 nm, 2207.5 nm, 1890.4

nm, 1459.9 nm, 1408.5 nm, 1366.1 nm, 1237.9 nm, 1131.2 nm, 939.0 nm, 704.2









nm. These IR absorptions are the result of electromagnetic vibrational interactions with

the electrons, atoms, and molecules of the gel water. Selectively absorbed light energy,

such as this, is mostly converted into heat. Consequently it is important to reduce the

hydroxyl groups to nondetectable levels in order to minimize absorption loss, especially

for optical lenses, optoelectronic signal processors, optical fiber, filters, and laser

resonant host systems. Therefore, monitoring the IR absorption peaks is a primary

method for determining the degree of dehydration achieved during densification [26,

27].

Consequently, the second goal of this study is to dehydrate and densify monolithic

silica xerogels; this is described in Chapter 4. Two methods are investigated: (1)

sintering samples in an air atmosphere and (2) chemical treatment and sintering in a

controlled gas atmosphere (e.g., carbon tetrachloride). At sufficient temperatures these

gases can react with the hydroxyl groups to form hydrogen chloride which escapes freely

from the unclosed ultrapores [28]. The dehydrated xerogel samples are then exposed to a

higher temperature for full sintering.

The third goal is to determine the physical properties of monolithic fully

dehydrated gel-silica glasses. In Chapter 5 various physical properties of the dense gel-

silica glasses are compared with commercial melt/cast vitreous silica glasses (fused

quartz) and other high-quality optical silica glasses (synthetic fused silica).

The fourth goal of this study is to develop the technology for fabrication of

transition-element doped xerogels. This is described in Chapter 6. Optical color filters

that selectively transmit part of the visible spectrum can be made from xerogels doped

with transition metal compounds. Transition elements, having unpaired electrons in

their d-orbitals, can absorb light by ligand field-controlled transitions that do not

involve variable valence states. The energy level scheme is controlled by the number and

symmetry of the ligands and the strength of the ligand field [29]. The doped xerogels

processed at different temperatures exhibit different densities and slight changes in






11


bonding strength which can produce a dramatic shift in their color response. For

example, a 160C silica xerogel containing 0.25% cobalt is a reddish-orange color,

whereas the 850C sample is a deep blue, and the 900C sample has a greenish-black

color.

Finally, a summary (Chapter 7) is presented which reviews the present state of

sol-gel processing science as applied to gel-silica optical monoliths and the properties

of these unique materials. Questions still to be answered by future investigations are

also included in the summary chapter.














CHAPTER 2
SOL-GEL TRANSFORMATION AND EXPERIMENTAL PROCEDURES


Introduction

During recent years many researchers have attempted to produce large monolithic

dried xerogels; however, a reliable process had not yet been established at the time this

work began [30-36]. Difficulties associated with this sol-gel processing method arise

during all phases of aging, drying, and densification, clearly indicating insufficient

understanding of basic changes in the ultrastructure during the sol-gel transformation

and in the chemical reactions of the solvents, precursors, and catalysts involved. In

general, crack formation during drying is a result of strong hydrostatic stresses within

a relatively weak gel structure. Catastrophic failure can be avoided by adjusting the

mechanical strength of the gel structure to exceed that of the hydrostatic force and/or by

decreasing the hydrostatic stress relative to the gel's strength.

The object of this chapter is to describe the principal mechanisms of the sol-gel

method by which monolithic xerogels may be reliably produced. Four factors are used to

describe the sol-gel transformation up to the gelation point: (1) the isoelectric point

(iep), (2) the point of zero surface charge (pzc), (3) thermally activated particle

movement (Brownian motion), and (4) Van der Waals force. Three kinds of dried

monolithic gel samples were routinely prepared to aid in this study: pure silica, silica

doped with transition elements, and silica doped with rare earth elements.


Literature Review of Sol-Gei Transformation Modeling

Dr. Ralph K. Iler's pioneering work in the investigation of silica chemistry is the

foundation of many of the ideas discussed in this chapter. HIer found that silica gels can be









obtained from supersaturated aqueous solutions produced by one of the following

methods:

(i) Concentrating an unsaturated silica solution by evaporating its solvent.

(ii) Cooling a hot saturated silica solution.

(i i i) Lowering the pH of an aqueous solution of a soluble silicate below 10.7.
(iv) Hydrolyzing Si(OR)4 -- (where R is CH3, C2H5, or C3H7).

In this study all of the monomers were produced by chemically hydrolyzing

tetramethylorthosilicate (TMOS), as indicated in method (iv). The amount of monomer

generated within a given period of time depends on temperature and the relative amounts

of DCCA, water, and TMOS. When a solution of monomer, Si(OH)4, is formed at a

concentration greater than the solubility of the solid phase of amorphous gel silica in

water, and in the absence of a solid phase on which the soluble silica might be deposited,

the monomers then polymerize by condensation to form dimers (two silicons), then

tetramers (four silicons), then particles (eight or more silicons). For most alkoxide

syntheses, a polymerization reaction occurs before hydrolysis is completed (as

evidenced by 29Si NMR studies [37, 38]). As shown in Figures 2-1 and 2-2, the

particle's size at any moment of growth is controlled by the Ostwald ripening mechanism

[see p. 175-220 in ref. 4] and essentially is determined by the pH of the DCCA/silicic

acid solution.

Vysotskii and Strazhesko [39] describe that in the presence of a given acid, the

growth of monomers is governed by the chemical equilibrium kinetics of the sol and is

minimized at the isoelectric point (iep). This implies that the monomers grow to some

certain size before the solution reaches its own iep. The iep occurs when the net

electrical mobility of surface ions on the silica particles is zero and at a pH at which

there is no charge outside the hydroelectric slip plane (outside this plane the liquid is

free to move, inside the plane the liquid molecules are held too tightly to move) [see p.











H

I
0
H-0-Si -0-H


H H
I
o 0
0 0
H I

H H
Sdimer


monomer


H

-0O-Si -0 --H


-O0-Si -0 --H
0
I


cyclic tetramer


particle (less than 10 A)


particle size
smaller than 50 A


particle size
larger than 50 A


Figure 2-1 Particle growth in solution


H
0
H -O --Si

9
H-O-Si

0
H










100


90


80 o


70 -
0o .amount of Si(OH)4
g 60 generated
--
CZ
_. ............/...-.....-.....-....-....................................-.....-.

0
o 30 ,/
o40


i- /
CD
a)
0 30


o 20
5 amount of Si(OH)4
10 polymerized into particles

0
0 0msce
relative time scale


Figure 2-2 Polymerization reaction occurs before hydrolysis is completed









660 in ref. 4]. Below are equations related to particle growth under two different pH

conditions, and will be described as two models in the following paragraph.

0 < pH < 2, [H+] as a catalyst

SinOa(OH)b+ +Si(OH)3 + OH- -> SinOa(OH)b-lOSi(OH)3 + H20 (1)

2 < pH < 7, [OH-] as a catalyst

SinOa(OH)b + -OSi(OH)3 + H+ -> SinOa(OH)b-1OSi(OH)3 + H20 (2)

SinOa(OH)b is a surface hydrolyzed silica particle, where "n" can be 2, 4, 8, 40, 311,

1438, etc. [see p. 8 in ref. 4]. The number of anhydrous oxygens within a particle is

represented by "a"; "b" is the number of surface hydroxyl groups per particle.

In an extensive study of silica polymerization, Linsen, Okkerse, Vysotskii and

Strazhesko [39, 40], found the iep to be between pH of 1.0 and 2.0. Condensation is

slowest in this pH range, thereby producing a minimum gelation rate. Gelation occurring

at the iep results in gel structures of maximum specific surface area and maximum

strength. These structures occur because the rate of aggregation is minimal as is the

growth rate of the ultimate particles from the monomer. Consequently, the ultimate

particles are smallest when the gel is formed at the iep.


Strong Acid Model

Figure 2-3 represents experimental data of relative gelation time versus solution

acidity found by many researchers [39, 41, 42]; the corresponding relative surface

area curve is shown in Figure 2-4. These two figures show that the longest gelation time

results in the highest surface area when the solution was prepared at pH=2. This is

because the rate of polymerization reaction depends on a catalytic effect which is at a

minimum at pH-2. From these data a model is developed describing the gelation

phenomenon in a strongly acidic solution, in which the pH is less than 2.0.

The very high hydrogen ion concentration at pH<2.0 results in a rapid reaction

among monomers to form dimers, cyclic tetramers, and very small particles, producing








































0 1 2 3 4


Figure 2-3 Relative gelation time versus solution acidity















































1 2 3


Figure 2-4 Relative surface area versus solution acidity









a significant amount of free water (equation #1) which dynamically reduces the

hydrogen ion concentration. This dilution slows the reaction between monomer and the

particle surface causing a build up of monomers around the particle while the total

hydrogen concentration in solution is reduced. This causes the pH to be increased to the

isoelectric point with a pH approximately equal to 2.0. This implies that the stronger

initial acidic solution (pH < 2) allows the monomers to grow to relatively larger

particles before the iep is achieved and results in a relatively smaller surface area, as

measured. As soon as the iep is reached, the particle size is nearly determined, the slip

plane of the electrical double layer is formed, no electric charge outside the slipping

plane can be measured, and particles are then homogeneously distributed in the solution.

As shown in Figure 2-5, the particle surface has a slight negative charge in the

presence of the positively charged monomer (equation #1). The monomers confined

within the slip plane of the electrical double layer [see p. 358-378 in ref. 4] will

gradually react with the particle surface under the influence of the hydrogen ion

concentration and thermal energy, resulting in slight particle growth. Free water is

released, diluting the hydrogen ion concentration while particle growth decreases. As the

confined monomers are consumed, the electrical double layer and slip plane is

eliminated. Formation of an electrically neutral particle surface, referred to as the

point of zero surface charge (pzc), at pH = 2.5 [41] marks the beginning of gelation

under the influence of thermally activated Brownian motion and Van der Waals attractive

force from this strongly acidic sol.


Weak Acid Model

The mechanism for gelation in a weaker acid solution (pH 2.0 pH 7.0) is

somewhat different from that of a strong acid solution, as shown in Figure 2-6. The

reduction in hydrogen ion concentration effectively weakens its strength as an acid

catalyst preventing the hydrogen ion from attracting the hydroxyl group from the











monomers expose their positively charged
electric cloud toward particle surface.


electrical double layer


Figure 2-5 Particles in strong acidic solution. pH










particles surface exposes positively charged electric
cloud toward negatively charged monomer in the weak
acid solution.


electrical double layer


Figure 2-6 Particles in weak acidic solution. pH>iep (pH 2.0 pH 7.0).









monomers around the particle and exposing the negatively charged -OSi(OH)3 molecules

(equation #2) which can react with the particle's positively charged surface. Rather,

the negatively charged oxygen of the hydroxyl ions in solution can attract a hydrogen

from the monomer. This forms free water and leaves the negatively charged oxygen as a

site now available to react with the positively charged silicon on the particle surface,

thereby regenerating this basic catalyst as a hydroxyl ion is released. With the

production of free water, the hydroxyl concentration is reduced, decreasing the pH as

well as the hydroxyl ion's ability to act as catalyst which causes a build-up of monomers

surrounding the particle surface. As the concentration of these monomers within the slip

plane reaches a maximum, at about pH = 2.0, the isoelectric point (iep) is attained. At

this pH the hydrogen ion acts as a catalyst promoting the reaction between the monomers

and the surface hydroxyl groups which facilitates particle growth. Free water is a by-

product of this reaction, reducing the hydrogen ion concentration and increasing the pH.

This process continues until the monomer concentration inside the slip plane is

exhausted and the electrical double layer eliminated. Thus, the point of zero surface

charge (pzc) has been reached and gelation begins under the influences of thermally

activated Brownian motion and Van der Waals attractive force.


Brownian Motion. Van der Waals. and Interparticle Bonding Models

When monomers come together to form very small (10 A 50 A) [43], uniform,

uncharged (pzc) particles, their motion is essentially governed by thermal diffusion as

described by the diffusion equation below.

D = KT/(37 T d) (3)

where

D is the diffusion coefficient

'r is viscosity

d is the effective instantaneous diameter of the polymerized cluster









K is Boltzmann's constant

T is absolute temperature

The average displacement X of a particle from time zero (@ pzc) to any point in

time t is:

X = (2Dt)1/2 (4)

Prior to reaching the pzc, the viscosity of the sol increases only slightly, as shown in

Figure 2-7 [44]. At the point (pzc) is achieved the small particles are homogeneously

distributed throughout the solvent, as shown in Figure 2-8. Governed by Brownian

motion (equation #4), these thermally activated, hydroxyl ion-catalyzed particles

randomly collide under the aid of Van der Waals attractive forces and a base catalyst, as

shown in Figure 2-9, to form long spherical-particle chains. As these chains continue to

form, the viscosity increases until there exists a three dimensional network throughout

the volume of the sol, as shown in Figure 2-10. This is described as the gelation point. A

sol takes a specific time to reach its own gelation point.

Gelation time is then defined as at the moment the sol is prepared to the moment the

sol loses its freedom to move. The length of gelation time is a function of the temperature

and the relative amounts of acidic DCCA, water, and TMOS in a sol. Figures 2-11, 2-12,

2-13, and 2-14 show that the gelation time can be exponential curve fitted with one of

the four variables (i.e. temperature, oxalic acid (DCCA), water, and TMOS) in which the

other three are kept constants. Increasing the sol temperature promotes the thermally

activated Brownian motion and thus decreases the gelation time as shown in Figure 2-

11. A decreased amount of oxalic acid concentration weakens the catalytic effect among

particles and therefore increases the gelation time as shown in Figure 2-12. An

increased TMOS content in water results in an increased concentration of particles and a

decreased distance between particles, which consequently, shortens the gelation time as

shown in Figures 2-13 and 2-14.






24







0
'*6
T
I I


!! I c
!~ i-=-

I
EU


3:o
0 C i
02 70 .
*> L CD
o -o .

% iep formation region i "-

I

IPZC


relative time scale

*tg is the gelation time


Figure 2-7 Relative viscosity versus time



















0


particle
sol i



0s.


100 A


Figure 2-8 Homogeneous particle distribution throughout the solvent.









(a) Brownian motion and Van der Waals forces


(b) base catalyst


IYiO
HO
HO
0oH



[OH-]


0rA
0
0

UOH,
0


(c) vacancies are created
in the neck area


Figure 2-9 Particles collide randomly with the help of Van der Waals
attractive forces, Brownian motion and base catalyst.














100oo A


Figure 2-10 Acid catalyzed particles constitute fibrillar chains throughout
the volume of sol.







28








3000 -



2500

DI water 400 cc

,- 2000- oxalic acid 8 grams
.C TMOS 200 cc
E
a,
E1 1500-

C)
(5

1000



500


0'
20 40 60 80 100

Temperature (C)


Figure 2-11 Gelation time versus temperature.















1200



1000 -

TMOS 200 cc
800 Dl water 400 cc

,.' temperature (C)
E 600

0

00
o 400 -\


200-



0 5 10 15

oxalic acid (gram)


Figure 2-12 Gelation time versus oxalic acid content.













































0 100 200 300 400

DI water (cc)


Figure 2-13 Gelation time versus water content.


400





300
'C


E
200
0



100
100


500















800-





600 DI water 400 cc
oxalic acid 8 grams
temperature 550C

E
E 400
c0
.9.


200-





0 100 200 300 400 500

TMOS (cc)


Figure 2-14 Gelation time versus TMOS content.









Characterization of Gelation

Professor Paul Flory's theory of gel formation [45, 46], with which Her agrees

[see p. 176 in ref. 4], notes that the silica monomer has four polymerization functional

groups (f=4). The degree of polymerization (DP) obtainable in a system is therefore

described by the equation:

DP = 1/(1-pf/2) (5)

in which "p" is the percentage of reacting monomers (that is the fraction of the total

concentration of monomer which is the reaction product from TMOS) and "f" is the

number of polymerization functional groups. At the gelation point the degree of

polymerization approaches infinity, therefore (1-pf/2) must equal zero. For f=4 the

percentage of total concentration of monomer going into gel phase must equal 50%. Since

equal amounts of monomer exist in the liquid as well as in the gel, no refractive index

change is observed at the gelation point. Consequently, the xerogel remain optically

transparent throughout gelation.


Aging Mechanism

Aging is a process by which the gel structure is reinforced via surface area

minimization of the spherical particle chains; this is shown in Figure 2-15. The surface

area can be minimized by four possible mechanisms: (1) condensation of surface silanol

groups (zipper effect) which creates stress and then results in vacancies in the neck

area between particles, (2) thermally activated transportation of silica molecules from

the volume or from the particle neck boundary to vacancies, (3) deposition of monomers

from the liquid into the negative curvature area of two weakly connected spherical

particles, and (4) dissolution of monomer from the particles' area of positive curvature

into the pore liquid, as shown in Figure 2-16.

The first, third, and fourth mechanisms do not result in gel shrinkage; the second

of these mechanisms does [47]. The particle rearrangement involved in the second










(a) No surface area minimization
of gelation point.


at the time


(b) surface minimzed after aging.


-I d2 [-


do= dI + d2


Figure 2-15 Surface minimization in the neck area.









(a) at the time of gelation point (tg =0)





L.---- do-----

(b) the first mechanism: formation of
vacancies in the necks of chain, the total
length do does not change







(c) the second mechanism: migration of vacanices
from neck area out of gel body, the total length do
shrinks.




-d--

(d) silanol groups depart from the positive
curvature area of particle's surface (the third
mechanism) and deposit on the negative curvature
area (the fourth mechanism). monomers

I .._ '- ,. Fi |deposit


silanol group depart
"siljanol group depart


Figure 2-16 Surface minimization during aging.









mechanism is initiated by thermal energy. Therefore, the higher the aging temperature,

the faster is the rate of matter migration to vacancies and the more rapid is gel

shrinkage, as shown in Figure 2-17. About the same maximum shrinkage (=28%) is

associated with each aging temperature. It is possible that the same amount of vacancies

are quickly created inside the necks between particles during the first stage, mechanism

No.1, for all identical gels. Subsequently, all of these vacancies are annealed out of the

gel body in the second stage, mechanism No. 2, and then equal shrinkage is obtained. The

same maximum shrinkage in the aging stage is probably predetermined by the

processing characteristics of each gel (e.g. pH, water, DCCA, TMOS ratio). The gel

shrinkage kinetics can also be monitored by the time at which 28% maximum gel

shrinkage is observed at each temperature, as shown in Figure 2-18. Shrinkage

improves gel strength; therefore, a relatively hard and dense gel can be obtained as a

result of optimizing the aging process. Figure 2-19 shows the increase in gel

microhardness with percentage of shrinkage. It is this increase in mechanical strength

with aging that makes it possible to obtain dried monolithic xerogels.



Drying Modeling

Control of drying is critical; without a full understanding of the gel's drying

mechanism and the development of a suitable method to deal with it achieving a dried

xerogel without cracking is very difficult. Drying control involves both chemical and

physical aspects. Chemically, the use of an acidic DCCA in the sol minimizes the particle

size which results in an increased gel strength and a more homogeneous particle-size

distribution, thereby diminishing uneven pore stresses. Physically, the use of a drying

control chamber decreases the effect of differential pressures on the gel body which

could lead to stress fracturing.














40




30




U)
E 20
0
E20




4-
S10
a)
20



0


30 60 90 120 150

time (hr)

*time starts from the gelation point.







Figure 2-17 Shrinkage of silica gel inside 100 cc polystyrene cylinder
as a function of aging time.














80




60 -



S40
240

CL)
E
CD)
I -I

20 -






0 0 30 60 90 120 150
time (hr)






Figure 2-18 The time silica gels shrink to 72% of original volume versus
aging temperatures inside 100 cc polystyrene cylinder.





































-


I I I I I
1 5 10 15 20 25 3

Percent of shrinkage


Figure 2-19 Microhardness of aged gel versus percentage of shrinkage.


z
C 6

C)
Co
CO
10-


CO4
2
0

2









A silica gel is defined as "dried" when the physically adsorbed water is

completely evacuated and no significant weight loss is observed at increased

temperatures.

Cracking during the drying process is essentially the result of differential

evaporation of pore liquid, Figure 2-20, as discussed in detail by J. Zarzycki [48]. The

Laplace equation is used:

APvi = P1 Pv = 2yvl cose /R (6)

where APvl is the differential capillary vapor pressure between the surface of the vapor

phase (in which vapor pressure = Pv) and the liquid phase (in which vapor pressure =

P1), within a very small pore of radius R. In equation (6) yvl is the specific surface

energy, and 0 is the contact angle.

Theoretically, to prevent shattering of the gel body during drying, the capillary

vapor pressure in the liquid phase (which is transmitted to the wall of the pore channel)

must be offset by the capillary vapor pressure in the vapor phase. For APvi to equal

zero, the cosine of the contact angle must also equal zero (@ 0=90), as the radius (R)

and the surface energy (-'l) at the liquid-vapor interface will always have some value.

Young's equation for the equilibrium of a solid (s) liquid (I) vapor (v) system is

derived by balancing the horizontal components of the specific surface energies, ysl,

Ysv, yv1 of the system. The equilibrium equation is given as:

Ysv =Ysl + Yvl cos (7)
As cosine 0 becomes zero, this equation simplifies to y'sv = Ysl. This means that the

work required of the liquid to act on the wall of the solid is the same as the work

required of the vapor to act on the wall of the solid.

cos 0=O0

Ysv = Ysl
Asv Asl

YsvdAsv=YsldAsl













stress initiated crack lines


Figure 2-20 Differential evaporation.









PsvdVsv= dwsv = YsvdAsv

PsidVsi = dwsi = YsldAsi

APvI=Psv-Psl=O

PV = nRT (for ideal system)

PV = W/M XT (for real system)

PsvdVsv = XTsvd(W/M) PsldVsl = XTsvd(W/M)

where

W = weight of vaporized liquid

M = molecular weight of liquid

X = vapor constant

The actual pressure of the vapor phase per unit area of pore wall is the same as the

actual pressure of the liquid phase per unit area of pore wall; this is called the

saturation point or equilibrium vapor pressure [49]. When APvl is zero, there is no

difference in the liquid level within the capillary pore channels regardless of the pore

radius, as shown in Figure 2-21.

However, for the case of drying actual xerogels the differential pressure APvi can

be minimized to zero with the use of a proprietary device. This device keeps the vapor

pressure in the vapor phase, Pv, at a value the same as that of the vapor pressure in the

liquid phase, PI, in the gel. As a result, APvl is zero and gel remains intact. The vapor

pressure within this device is controlled by the temperature which must be carefully

maintained. At temperatures higher than the boiling point temperature of the gel pore

liquid, the vapor pressure in the liquid phase, PI, exceeds one atmosphere (Pv will

never be higher than 1 atm in this device because it is not an autoclave system). Thus

the system will equalize as gas escapes from the device, i.e., APvl is not zero, which

would cause a differential vapor pressure APvi between the liquid and the vapor phases

sufficient to shatter the gels, as shown in Figures 2-20 and 2-22(a).















get structure


Figure 2-21 No differential evaporation.


pore






43

P(air) = one atmosphere (1 atm)


vapor out


S) z .-.;.

* ;- ;.: ",..,,o '.::
,.... '. o *,.


P(vapor) > P(air)


P(air) = one atmosphere (1 atm)


air in


P(air) > P(vapor)


Figure 2-22 Gel cracks inside nonequivalent evaporation containers.


vapor out


air in


Pk4'apor)









At temperatures lower than the boiling point of the gel pore liquid the vapor

pressure in the liquid phase (Pi) is less than one atmosphere; therefore, air will enter

the device to establish a vapor phase pressure (Pv) equal to 1 atm, resulting in a

differential vapor pressure (APvl) which is not zero (Figures 2-20 and 2-22(b)).

However, by maintaining a zero differential pressure the capillary force is eliminated

(Figure 2-23), thereby significantly removing the differential hydrostatic stresses

within the gel body and retaining the gel's monolithic shape.


Structural Characterization

The gel consists of a three-dimensional network of silica particles rigidly linked

together. If the structure of the gel is relatively coarse, the gel body is fragile and likely

to shatter. If the structure of the gel is relatively fine, consisting of fibrillar chains of

very tiny particles, and therefore somewhat flexible, the gel will be strong enough to

shrink considerably without cracking. However, the shrinkage of a silica gel is

irreversible. Shrinkage occurs as the gel dries due to the surface tension of the liquid

within the pores. As drying occurs it is probable that certain bonds on the necks between

particles break, which allows portions of this area to be dissolved into the pore liquid

and transported to areas of negative curvature, as shown in Figure 2-24. This is because

solids minimize surface area so as to reduce surface energy to a minimum.

An equation relating the solubility of a curved solid surface in water to the radius

of curvature was derived by Ostwald and Freundlich [see p. 50-51 in ref. 4]:

Log(Sr/Si) = KE/Tr (8)

where Sr is the solubility of a particle having a radius of curvature r; Si is the

solubility of a flat surface with a radius of curvature of infinity in that water; E is the

surface energy of the solid; T is the temperature; and K is Boltzmann's constant. The

meaning of this equation is schematically illustrated by Iler in Figure 2-25. As





45







P(air) = one atmosphere (1 atm)


Patm(air) ~ Pvapor = Pliquid


Figure 2-23 Situation to avoid cracking.


i


















silica fibrillar structure


monomers depart and
old bond broken


shear stress &P
-


-i
shear stress AP


monomers deposit
and new bond formed


Figure 2-24 Redeposition of monomers from the broken neck area to the area of
negative curvature.




















increasing negative


100


-10 -5 0 5 10
diameter of curvature nanometers
Figure 2-25 Solubility of silica in neutral water at 25C varies with the radius of
curvature of the surface according to the Ostwald-Freundlich equation.


curvature


.... .. .










shown, when an acidic silica gel is sufficiently dried to contain pores (negative

curvature in left side of the figure) that are only a few nm in diameter a small decrease

in pore size results in sudden elimination of the pores. Table 2-1 confirms that the

remaining uniform pores stay unchanged in diameter but decrease in total volume and

surface area as the sintering temperature increases.

A mechanism was suggested by HIer [47] that in a densification process, gel

shrinkage is the results of sudden decomposition of pores into vacancies in the gel

structure and traveling vacancies which migrate to the outside of the gel body along the

surface of the pore network and do not remain in the pores to enlarge them [50].


Experimental Procedure

Large scale monolithic dried silica gel samples (up to 10 cm x 8 cm x 2 cm), as in

Figure 2-26, have been routinely produced by applying the concepts and mechanisms

stated in Section II of this chapter. Several kinds of standardized samples were made for

characterization in this study including pure silica gels, cobalt- copper- and nickel-

doped silica gels, neodymium- and erbium-doped silica gels. The two examples described

below detail the procedure used to produce both pure silica and doped silica samples. Six

steps are generally needed to produce the sol-gel derived monolithic silica gel-glass

samples, as shown in Figure 2-27. The drying control chemical additive (DCCA) is

introduced in Step 1; this makes it possible to control each of the five subsequent steps

and prevent gel shattering.
















Table 2-1
Oxalic acid (5.0 grams) as DCCA in 200 cc


Temperature 200C 450C 7500C


Surface area
(m2/g) 651.12 612.10 413.25


Total pore volume
(cc/g) 0.36 0.33 0.22


Average pore radius
(A) 11.02 11.03 11.06


H20/1 00 cc TMOS


8000C 8300C



385.47 335.40



0.20 0.18


11.03 11.05





























































-

-


~-


Figure 2-26 Picture of a large scale 160C dried silica gel sample.











Step 1






Step 2






Step 3





Step 4




Step 5





Step 6


Figure 2-27 Procedure for producing pure silica gels and gel-glasses.










Example one:

Production of dried pure silica gel monolith from oxalic acid DCCA



Step 1: Mixing

Tetramethylorthosilicate (TMOS) is used as a precursor for silica monomers to

form Si-O-Si bonds in the gel structure. The mixing of water with TMOS forms a silica

sol via the following simplified hydrolysis and polymerization reactions:

Si(OCH3)4 + 4 H20 ----> Si(OH)4 + 4 CH3OH

-Si-OH + OH-Si- --- > -Si-O-Si- + H20

The specific standard procedure followed in Step 1 is:

(a) Pour 300 cc of water into a clean 800 cc beaker.

(b) Place the beaker on a hot-stirring plate.

(c) Mix 6 grams of oxalic acid with water using a PTFE coated magnetic bar;

control via the hot-stirring plate.

(d) Stir for 5 minutes to get a homogeneous solution.

(e) Add 150 cc TMOS to the acid solution, while continuing to stir

vigorously for approximately 50 minutes.

(f) Immediately increase the temperature from 25C to 85C by raising the

temperature on the hot-stirring plate to maximum.

(g) If feasible, carefully place ice water in a three-layer polystyrene

thin film on top of the beaker to condense the hot vapor and return

it to its solution.

(h) Continue stirring and heating for approximately 50 minutes before

casting.










Step 2: Casting -

(a) The intimately mixed sol is cast from its heated vessel into a mold (20 mm H x

100 mm D) that corresponds to the final desired shape. For best surface results,

polystyrene is the selected mold material.

(b) The duration of the casting operation is not critical since gelation does not

occur until after casting is completed.



Step 3: Gelation

Gelation occurs in the mold with the resulting solid object taking the shape and

surface finish of the mold. Gelation times with oxalic acid are typically 20 hours at 250C

and 4 hours at 70C, depending on the relative concentrations of water, TMOS, and DCCA,

as shown in Figures 2-11, 2-12, 2-13, and 2-14.



Step 4: Aging

The solidified gel is then placed into an aging oven at a temperature ranging from

50C to 80C for a times ranging from 20 to 48 hours to achieve maximum shrinkage.



Step 5: Drying

Prior to Step 5, control of the gel ultrastructure is governed by the DCCA which

allows removal of the pore liquid without cracking the gel. Typically this is done by first

removing the excess liquid present after gel shrinkage in Step 4. The pore liquid is then

removed, consistent with the theory stated in Section II of this chapter, by confined

evaporation over a temperature range from 70C to 160C for times ranging from 18 to

90 hours. An example of a typical heating program is shown in Figure 2-28.















200-

180

160

.- 140
0
0) 120
S100-0-E

80
E
I-- I

60

40

20
20-

0 25 50 75 100 125 150 175 200

Time (hr)


Figure 2-28 Drying program for wet gel.









Step 6: Densification

The ultraporous dried silica gels are converted to partially dense monoliths by

heating from 150C up to 900C over a period of 3 to 6 days; samples are taken out of

the furnace at the end of the heating program. An example is shown in Figure 2-29.


Example two:

Production of dried transition and rare earth element doped silica gels from nitric acid

DCCA.



Step 1: Mixing
(a) Add 60 cc (1N) HNO3 (nitric acid) to 340 cc of distilled water at room

temperature and mix for 5 minutes with a magnetic stirrer.

(b) Add 200 cc TMOS to the nitric acid water solution while continuing to mix

vigorously, increasing the solution temperature to 85C for no more than 60 minutes.



Step 2: Casting

The intimately mixed sol (60 cc) is cast from its heated vessel into a polystyrene

mold (20 mm H x 100 mm D) at room temperature. The length of time for casting

should be no more than 110 minutes since gelation will take place during prolonged

casting operation.



Step 3: Gelation

Gelation occurs in the mold at 55C in 115 minutes with the resulting solid object

taking the shape and surface finish of the mold.















1000



800

j
0
6oo
(D
.. 600-


E
-- 400




200




0 25 50 75 100 125 150

Time (hr)


Figure 2-29 An example of a silica gel-glass densification program.










Step 4: Aging

The solid is aged in the mold initially at 55C for 10 hours, followed by an increase

to 80C for 15 hours.

Step 5: Drying

The aged pure-silica gel is removed from the mold and dried with a controlled

evaporation rate, as described in Section II of this chapter, initially at 700C, gradually

increasing the temperature to 160C during a 90 hour period.

Step 6: Impregnation

(a) One gram-percent of transition metal element (i.e., cobalt nitrate, nickel

nitrate, copper nitrate) or three gram-percent of rare earth element (i.e., neodymium

nitrate, erbium nitrate) in deionized (Dl) water is prepared for doping, or

impregnating, the completely dried gel. The dried gel is immersed into the solution,

whereby the interface between the liquid and the voids migrates from the exterior into

the center of the gel body in the rate of 0.5 cm/hour, as shown in Figure 2-30.

(b) The doped gel is then placed in the drying oven at 200C for 12 hours to

remove the pore solvent.



Step 7: Densification

(a) The fully dried silica gel doped with transition metal or rare earth elements is

heated to 40000C to eliminated any residual nitrates via conversion to its gaseous oxides.

(b) Additional densification can be achieved by heating from 400C to 1000C.


Results

Monolithic samples of pure silica gel, transition metal element doped silica gel, and

rare earth element doped silica gel were routinely produced following these procedures;

some are shown in Figures 2-31 to 2-35. The physical and optical properties of these

samples will be discussed in succeeding chapters.





58



!1 hr
3 hr


top view 5 hr
10 hr


i I,




g i imm
I I i 5 i '
: iii i
i !
I I ,I I

i I I I 6mm
I I I .........
I Ii iI :




5 cm


Figure 2-30 Sample immersion into transition metal or rare earth nitrate/water solution.





















K8e-


Figure 2-31 Picture of a 160C dried silica gel.

















M17


Figure 2-32 Picture of a cobalt nitrate-doped silica gel which was stabilized at
7500C and redried at 1600C.





61









M14

























Figure 2-33 Picture of nickel nitrate-doped silica gel which was stabilized at 750C
and redried at 160C.















M3


Figure 2-34 Picture of copper nitrate-doped silica gel which was stabilized at 750C
and redried at 160C.








63



">...4, m ..I. : ,# .:


















~' II






















..,..... : 4'. '..


r.4i
i....g-4-'r"
















Fiue : 2 35 Picture o n i t d a bt o l s
wcwealea 5Cnri a10
:. ";': .'.": -". .':"."5:4
,,W
: .. :. .:.:







Figure 2A35 Picture of neodymium nitrate-doped and erbium nitrate-doped silica gels
which were stabilized at 750C and redried at 1600C.







64

Conclusions

It was not found necessary to add methanol to this xerogel system, though this is the

practice of many researchers [51-56].

Addition of oxalic acid or nitric acid as DCCAs is necessary in the mixing step of

both Examples #1 and #2 as an acidic DCCA controls the radius of the individual silica

particles to a few nanometers that form during the early stage of monomer growth and

the subsequent fiber-like polymerization.

The particles are made uniform due to Ostwald ripening at any moment of growth.

As soon as particle growth stops at the pzc (point of zero surface charge), an electrically

neutral particle surface forms; therefore, thermally activated Brownian motion, Van

der Waals attractive forces and base catalytic effects among particles in the sol become

the driving forces to form particle chains which reach the gelation point.

During aging, the reinforcement and the shrinkage of the fibrillar network of a gel

proceeds as a result of growth of interparticle necks and migration of vacancies to the

exterior of the gel. The rate of aging shrinkage is primarily determined by the rate of

thermally activated vacancy migration.

After aging, the interparticle necks comprise a very large fraction of the gel

fibrillar structure and become relatively flexible (like glass fibers are flexible).

Consequently, the gel can endure certain hydrostatic stresses and shrink considerably in

the drying stage without cracking, as illustrated in Figure 2-36.

Differential vapor pressure (APvl) is the stress which shatters the relatively

weak gel into pieces in the drying stage. A gel can be dried without cracking by using a

drying device which eliminates the differential vapor pressure between vapor phase

(Pv) and liquid phase (PI) inside the capillary pores.


















stress


in presence
of water


rigid gel structure


broken
neck


M1 =M2


stress


flexible gel
structure


Figure 2-36 Fibrillar gel structure is relatively flexible compare to coarse gel structure.


M2 1









Monolithic gels with an optimal ultrastructure and high resistance to drying

stresses, which are chemically controlled (by adding acidic DCCA) and physically

stabilized (by introducing a drying device), are identified by a change in visible light

scattering during the drying process. The optical sequence for a drying gel is as follows:

complete transparency with a very slight blue tone, followed by an opaque stage,

followed by transparency. These changes in optical properties can be used to monitor the

drying process and therefore offer the potential to be used in a feedback loop to optimize

drying. Monitoring weight loss can also help to achieve the final stage of drying; when

the theoretical molecular weight of silica is reached, drying is finished. This process can

be automated and used with computer aided processing.

The fully dried gels can be modified by liquid phase impregnation of various

chemical species (e.g., compounds of transition or rare earth elements) into the dried

gel. Because of the extremely small size (10 A 100 A) of the ultrapores in the gel, it

is possible to introduce a very homogeneous ion distribution within the gel matrix. For

measurements the physical properties presented in Chapter 3, the ultraporous dried

silica gels are converted to partially dense monoliths by heating from 150C to 900C

over times ranging from one day to one week.













CHAPTER 3
PHYSICAL PROPERTIES OF PARTIALLY DENSIFIED SIULICA XEROGELS


Introduction

Monolithic, noncrystalline, dried xerogels of pure silica, hereafter simply called

gels, have been made by the procedure stated in Example #1 of Chapter 2. These samples

are heated to 150C (the temperature at which the gels are free from physical water) to

become standard dried gels.

The physical properties of the fully dried gel are a function of the internal

structure which depends on the various chemical and physical conditions during every

step of processing (i.e., the relative amounts of water/DCCA/TMOS, temperature,

pressure, and time for aging and drying).

At sufficiently high temperatures thermal energy provides the driving force for

ultrastructural rearrangement which decreases surface area and thereby minimizes

surface tension inside the gel structure. This is the primary mechanism for

densification [see p. 469-490 in ref. 23].

A large reduction in pore volume is accompanied by the decomposition of residual

organic compounds into carbon dioxide (between 250 and 450C) and also by the

combining of surface hydroxyl groups resulting in some degree of dehydration. Both of

these phenomena may cause thermally induced stress fracturing in the densification

stage. However, by controlling the rates of these reactions silica gel monoliths that are

crack-free, partially densified and shrunk, can be successfully made at various

temperatures, ranging from 200C to 850C.

This chapter presents a study of the physical properties of partially dense silica-

gel monoliths. Data were obtained from numerous measurements including structural,

optical, thermal, and mechanical testing. Structural information was provided by










Fourier-transform-infrared (FTIR) spectroscopy, ultraviolet-visible-near-infrared
spectroscopy (UV-VIS-NIR), N2 adsorption-desorption isotherms interpreted using

Brunauer, Emmett, Teller (BET) analysis which includes specific measurements of

surface area, pore size distribution, pore volume, and pore radius, as well as large angle

X-ray diffraction. Optical information was obtained solely using an index of refraction

test. Thermal data were collected from differential scanning calorimetry (DSC),

differential thermal analysis (DTA), thermogravimetric analysis (TGA), and

thermomechanical analysis (TMA). Mechanical properties (gel strength) were

determined using flexural strength, compressive strength, microhardness, fracture

toughness and density measurements.


Review of the Literature

Three mechanisms of densification are summarized by Zarzycki, et al. and

Brinker, et al. [25, 57]: (1) polymerization reactions which serve to crosslink the

network and partially release the surface hydroxyl groups, thereby forming free water;

(2) structural rearrangements that occurs when segments of interparticle necks are

broken and other neck segments become connected; and (3) viscous sintering

accompanied by the combination of surface hydroxyl groups. The first two mechanisms

cause a slight density increase; the third mechanism is a result of high temperature

viscous flow which eliminates the pores so that the bulk density approaches that of fused

silica. No gel can be completely dehydrated and converted into a fully dense glass (i.e.,

without foaming) in an ordinary air-atmosphere furnace; but fortunately, the gel can be

partially sintered to a desired temperature, below the foaming point, and cooled to room

temperature while remaining intact.

Any material can give rise to absorption or emission of radiation within the

allowed transitional, vibrational, and/or rotational energy levels. Infrared spectroscopy









(FTIR) can provide vibrational information on changes occurring in the gel structure

during sintering [58].

Water terminates the bridging silicon-oxygen-silicon bonds on the particle's

surface inside the porous gel, as shown in Figures 3-1 and 3-2. Water's disruption of

the Si-O-Si bridging bond is similar to that of sodium ions within a dense soda silicate

glass. This gives rise to absorption in the ultraviolet (UV) region of the optical

spectrum. The UV-VIS-NIR spectra technique is an easier and more sensitive tool than

the infrared method for understanding the evolution of bonding and identifying the

species inside the gel structure in the densification process [59].

The measured surface area, obtained from BET analysis, of a standard dried gel is

about 750 m2/g at 200C. The particle size is calculated from Havard, Wilson's model

[60] where the diameter is equal to a constant (2750) divided by the surface area. The

particle diameter for a gel made by Example #1 in Chapter 2 is 3.6 nm at 200C. The

measured surface area is somewhat less than actual since nitrogen molecules, used in the

BET analysis, cannot completely penetrate the negative curvature area between all the

connected particles. However, the BET surface area measurement also includes the

surface hydroxyl groups which increases the particles' measured surface area value;

this increase is less significant than the decrease resulting from incomplete nitrogen

penetration.

Silica gel is essentially a special form of porous glass. Previous x-ray diffraction

studies by Mozzi, Warren, Uhlmann and Wicks [22, 23] have established in detail the

tetrahedral bonding arrangements in vitreous silica. The maximum in the distribution of

Si-O-Si angles in amorphous silica is at 144, with most angles being within 10% of

this maximum. There is no evidence for a preference in fused silica for edge-to-face

sharing of tetrahedra, which is often found in crystalline silicates. X-ray diffraction

patterns generally exhibit a relatively broad peak for gels indicating the absence of

atomic periodicity or long-range structural ordering compare to that of quartz.













































cut-off profile magnified in Figure 3-2


Figure 3-1 Random sampling profile of gel skeleton.










A profile of gel skeleton


T ,n H

0.5nm


Oxygen atom Q

Silicon atom *


Gel fibrillar structure cut off profile


Figure 3-2 Water terminates the Si-O-Si bridging bond on the particle's surface.









Consequently, a random edge-to-edge sharing of silica tetrahedra with variable Si-O-Si

angles described above is proposed for silica gel fibrillar structures.

The magnitude of index of refraction (n) indicates the extent of change of the speed

of light by the electromagnetic field of a transparent dense material. The index of

refraction can be expressed by Snell's law n(glass)/n(vacuum) = sin 0(vacuum)/sin

O(glass) = V(vacuum)/V(glass), where n(glass), V(glass), and 0(glass) are the refractive

index, the velocity, and the angle of refraction of glass respectively, n(vacuum),

V(vacuum) are constants, and 9(vacuum) is the angle of incidence of light in vacuum.

Index of refraction is a dependence of (1) the density, (2) the polarizability of the

glass, and (3) the wavelength (X) of monochromatic radiation [61]. In this chapter

partially densified silica gels are discussed where the chemical compositions are

essentially SiC2 and chemical bonded surface -SiOH groups. The nonbridging hydrogen

ions (H+, a proton) of these silanol groups contribute very little effect on oncoming

light [see p. 660 in ref. 23], thus, the polarizability of these partially densified silica

gels can be assumed to be a constant. Consequently, the variation of refractive index with

density described by the Lorentz-Lorenz equation [see p. 658 in ref. 23] can be

simplified as will be discussed in the Results and Discussions Section of this chapter.

Differential scanning calorimetry (DSC) is used to measure the temperatures

associated with transitions in materials, including boiling points, melting points,

liquid-crystal transitions, heats of reaction, specific heat capacity, oxidative and

thermal stability, purity, glass transitions, and reaction kinetics.

Differential thermal analysis (DTA) gives the same qualitative information as DSC,

but is used primarily for studies involving high temperatures which exceed the range of

the DSC cell (700C).

Thermogravimetric analysis measures weight change as a function of temperature,

and provides derivative TGA data used to quantify the chemical changes in a gel during

thermal processing.









Thermomechanical analysis (TMA) measures the thermal expansion coefficient,

glass transition temperature, softening temperature and provides data for gel shrinkage

analysis [62].

Flexural (FLEX) and compressive (COMP) tests are performed to determine the

material's strength under external mechanical loads.

A Vickers microhardness test, which yields a value for the diamond pyramid

microhardness number (DPN), is used to measure the mechanical resistance of a gel and

gel-glass to diamond pyramid plastic indentation in a microscopic area of the surface

[63]. The fracture toughness is obtained directly from the crack length which extends

outside the diagonal of diamond pyramid indentation during the Vickers microhardness

measurement [64].

Bulk density measurements are used to monitor the change in gel structure during

sintering; it also gives useful information for interpreting variations in refractive

index.



Experimental Procedure

Samples, fabricated by the procedure stated in Example #1 of Chapter 2, were

heated to various programmed temperatures in an ambient air furnace, as shown in

Figure 3-3. The following tests, listed in Table 3-1, were performed on these samples.

The infrared spectra were recorded on a Nicolet MX-1 FTIR spectrometer

equipped with a diffusion reflection stage and a microcomputer for data storage. The

diffusion reflection stage in which the infrared passes into the bulk (about 0.5 mm deep

and 20 mm2 area) of the gel, undergoes reflection, refraction, scattering and absorption

in varying degrees before returning back at the sample surface. The radiation reflected

out from the gel is distributed in all directions of the surrounding hemisphere and

corrected to form spectra by a highly reflective semispherical mirror. Chemical species

and bonding information can be interpreted in terms of the position and intensity of IR

















1000




800




600



a,.
o

S400

1L
0)
a-
E

200




0


0 50 100


Time (hr)


Figure 3-3 Heating programs for various samples















Table 3-1
Physical property measurements


SAMPLE SHAPE


HEATED TEMP. (C)


Structural information tests:


FTIR
UV-VIS-NIR
BET
X-Ray


flat piece (smooth surface)
flat piece (smooth surface)
powder (course ground)
powder (fine ground)


Optical information test:


Index of refraction polished flat piece


150, 450, 750, 800, 830


Thermal information tests:


DSC
DTA
TGA
TMA


broken piece
broken piece
broken piece
smooth cylinder's ends


Mechanical information tests:


FLEX
COMP
DPN
Toughness
Density


rectangular piece
rectangular piece
unpolished gel surface
unpolished gel surface
broken piece


TEST


150,
150,
200,
200,


250,
350,
450,
450,


500,
500,
750,
750,


800
800
830, 860
800, 850


150
150
150,
150,


740
540


150,
150,
150,
150,
150,


450,
450,
250,
250,
250,


750,
750,
450,
450,
450,


830
830
750,
750,
750,


800, 830
800, 830
800, 830









peaks in the sample's spectra. A dried gel was installed in a hot stage inside the FTIR

sample chamber and heated to the temperatures designed in Table 3-1 for IR analysis. A

heating rate of 3.3C/min from room temperature to 800C was used.

The ultraviolet-visible-near infrared spectra were obtained from a Perkin-Elmer

Lamda 9 UV/VIS/NIR spectrophotometer. This instrument consists of a high performance

double-beam, double-monochromator and a superior signal-to-noise energy optimized

optical system [65] throughout the entire 185 to 3200 nm wavelength range; it is

integrated with microcomputer electronics, video display, soft key operating system and

printer. Gels heated to the temperatures designated in Table 3-1 and cooled to room

temperature with heating programs shown in Figure 3-3 were taken out immediately

from the furnace for testing. Subsequently, the thickness of the gels was measured and

they were scanned at a rate of 120nm/min through a required wavelength range in

either transmission or absorption mode after background correction had been made.

The surface area, total pore volume, average pore radius, and pore size

distribution were determined by the nitrogen adsorption-desorption isotherm BET

method, using an automatic Quantachrome Autosorb-6 sorption system [66].

Specific surface area (A) of the gels is obtained from a series of data management

and calculations performed in the microcomputer of the Autosorb-6 system. The

calculations involve: (1) a BET equation, 1/{W[(Po/P)-l]=l/(WmC)+[(C-

1)/(WmC)]x(P/Po) in which W is the weight of gas adsorbed at a relative pressure

P/Po (pressure ratio of N2 gas in He gas), Wm is the weight of adsorbate constituting a

monolayer of N2 on surface, and the constant C is related to the energy of adsorption in

the first layer. (2) a linear plot of 1/{W[(Po/P)-1]} vs P/Po to yield values of slope

s=(C-1)/(WmC) and intercept i=l/(WmC). (3) the weight of a monolayer Wm obtained

by equation Wm=l/(s+i). (4) At=(WmNAcs)/M where At is total surface area of the

sample measured and N is Avogadro's number. For N2 at 77 K, the cross-sectional area,









Acs is 16.2 A2 and M is the molecular weight of N2. (5) A=At/W in which A is specific

surface area of sample and W is the sample weight.

The total pore volume (Vliq) is derived from the amount of N2 adsorbed at a

relative pressure close to unity, by assuming that the pores are all filled with liquidized

N2 of a volume Vliq which can be calculated using equation (Vliq/Vm)RT=PaVads where

Vm is the molar volume of the liquid N2, Pa is ambient pressure, and Vads is vaporized

pore liquid (N2).

The average pore size can be estimated from the pore volume, by assuming

cylindrical pore geometry; then the average pore radius rp can be derived as rp =

2Vliq/A. The pore size distribution is calculated using the method proposed by Barrett,

Joyner and Halenda [67].

Samples heated to the temperatures designated in Table 3-1 and cooled to room

temperature with the heating program shown in Figure 3-3 were ground into powder

and weighed to around 0.6 gram in the pellet cells before installing in the Autosorb-6

system for outgassing and preheating to eliminate the water moisture. The outgassing

and preheating was held for 15 hours at 2000C in N2 gas atmosphere. Consequently,

samples were transferred to the ports of the system for nitrogen adsorption-desorption

isotherm measurements. Data were automatically accumulated in the mirocomputer and

the results printed out.

The X-ray diffraction analysis was obtained using a Philips diffractometer at room

temperature with a 40Kv CuKa radiation and a nickel filter. The samples heated to the

temperatures designed in Table 3-1 and cooled to room temperature with heating

programs shown in Figure 3-3 were ground and scanned at a rate of 6/min from 28

angles of 10 up to 50.

The index of refraction was obtained using a Pulfrich refractometer and a HeNe

laser light source which wavelength is 632.8 nm. The principle of the refractometer is

based on the measurement of the critical angle tc, which is the angle of the interface









between the unknown gel sample of index n and a prism of known index n'. Since n' is

greater than n, the two must be interchanged in the standard equation, sin *c = n/n'

[68]. The beam is oriented such that some of its rays just graze the surface as shown in

Figure 3-4, so that the transmitted light has a sharp boundary occurs which allows one

to compute the value of Oc and hence of n.

DSC, DTA, TGA, and TMA analyses were obtained with a DuPont 1090 thermal

analysis system. In The DSC system, the gel sample and a reference were placed in pans

which sat on a disk. Heat was transferred through the disk into the gel sample and

reference. The differential heat flow to the sample and reference was monitored by the

junction of a constantan disc and the chromel wafer which covers the underside of each

platform. Chromel and alumel wires were connected to the underside of the chromel

wafers, and the resultant wire-thermocouples were used to monitor the sample

temperature. Therefore, heat transfer and temperature of the sample and reference

could be recorded. The temperature range of the DSC cell is from room temperature to

600C.

Differential thermal analysis (DTA) measures the temperatures at which heat-

related phenomena occur in materials. DTA provides the same qualitative information as

DSC, and can provide semiquantitative calorimetric measurements. The temperature

range of the DTA cell is from ambient to 1200C.

The high temperature 1200C DTA cell consist of a platinum sample and reference

cups resting on the tops of two insulated thermocouple pedestals. The sample and

reference were located 6 mm apart surrounded by a programmable furnace.

Thermocouples located in the pedestals measured both the presence of transitions and the

temperatures at which they occur. DTA cells complement the DSC to offer appropriate

measurements over a wide temperature range.

The thermogravimetric analyzer measures changes in weight as a function of

temperature, and provides derivative TGA data. These data can be used to measure the





















incident HeNe laser beam
wavelength: 0.6328pm


Sin e0 = n/n'


Figure 3-4 Refraction in the prism of a Pulfrich refractometer.









changing in moisture and volatiles (oxidation reaction) when gel is in the heating

process.

A thermomechanical analyzer (TMA) can be used as a dilatometer to measure gel

volume shrinkage, or glass expansion coefficient from room temperature to 800C. The

sample was installed in a programmable furnace in which a thermocouple in direct

contact with the sample measured the sample temperature. A movable-core linear

variable differential transformer (LVDT) whose output is proportional to the linear

displacement of its core is used. The dimensional change of the sample with temperature

can be monitored using this LVDT core displacement technique.

Flexural strength tests were performed under guidelines of the ASTM D 790M-84

standard [69]. Samples heated to the various temperatures (see Table 3-1) and cooled

with the thermal schedule shown in Figure 3-3 were cut with a diamond watering blade

and polished carefully with 600 SiC grit paper into a size of length x width x thickness

(46 mm x 10 mm x 5 mm). All samples were dried at 150C for 3 hours immediately

prior to measurements to eliminate absorbed moisture. Subsequently, the samples with

a span : width : thickness ratio of about 7:2:1 were loaded in three-point bending in

ambient conditions at a strain rate of 3.5 x 10-3 s-1 using an Instron model 1122. In

this experiment a set of five identical samples were heated at same time in a furnace to

each temperature.

The compressive strength tests were carried out under the guidelines of the ASTM

C158-80 standard [70]. Samples heated to the designated temperatures (see Table 3-1)

and cooled with heating programs shown in Figure 3-3 were cut into a rectangular shape

of length x width x thickness (14 mm x 7.5 mm x 5 mm). All samples were dried at

1500C for 3 hours immediately prior to measurements to eliminate absorbed moisture.

Subsequently, samples were loaded in an Instron model 1122 such that the length was

parallel to the axis of the applied stress applied at a strain rate of 3 x 10-4 s-1. The










same number of samples and processing temperatures were used as that of flexural

strength test.

Microhardness values were obtained using a 136 diamond pyramid indenter at a

50 gram load with the Micro Hardness Tester, model M-400 F (Leco Co. Japan).

Samples were heated to the designated temperatures (see Table 3-1) and cooled with

heating programs shown in Figure 3-3. Then, the samples were placed under the

indenter and applied with the 50 gram load. Two diagonals of the indenter were produced

on the surface of the sample. The DPN can be calculated by measuring the average length

of two diagonals through the microscope on the instrument. In this test five indentations

were performed on each sample to obtain the data.

Fracture toughness values were calculated using the extended crack lengths from

the two stamped diagonals created by the diamond indenter on the surface of gel during

the Vickers microhardness test. The calculations used to convert indentation length to

fracture toughness are described by Anstis' relationship (Equation #16) [64] in the

Results and Discussions of this chapter.

Density of the samples was determined using a simple mercury displacement

technique. Samples followed the heat treatments shown in Table 3-1 and Figure 3-3

were immersed into a pycnometer. By knowing the sample weight, the corresponding

weight of mercury displacement, and the density of mercury, the density of the sample

was calculated.



Results and Discussions

Figure 3-5 shows the FTIR spectra for the partially densified gels heat-treated at

various temperatures. The samples were scanned between 200 cm"1 (50000 nm) and

5600 cm-1 (1786 nm). The results show that the Si-O-Si molecular stretching











































4400 3200 2000 1400 800 200
Wavenumbers


Figure 3-5 FTIR hot stage data from 250C to 800C of pure silica gel


5600










vibration is observed at 1120 cm-1 (8928.6 nm), even in the low temperature sample.

The peak at 1250 cm-1 (8000 nm) is an artifact of the diffuse reflection stage. The

primary difference between these curves is that peaks corresponding to organic

residuals in the range between 1400cm-1 (7142.9 nm) and 2600 cm-1 (3846.2 nm)

are absent in the high temperature sample. The spectrum of the 800C silica sample is

nearly the same as that for fused silica, with the exception of a small shift in the

absorption edge near 1400 cm-1 (7142.9 nm) to lower wavenumbers.

The temperature-dependent changes in intensity of the characteristic absorption

band at 950 cm-1 (10526.3 nm) have been attributed to the stretching vibration of the

Si-O-H nonbridging oxygen (NBO) groups. With increasing temperatures, the

concentration of silanol groups is decreased to a nondetectable level and the

characteristic 950 cm-1 (10526.3 nm) peak disappears. The extent of hydroxyl

absorption bands at 3500 cm-1 (2857.1 nm) to 4000 cm-1 (2500 nm) is also

diminished for the higher temperature samples. This does not mean that the gel is

completely free (zero ppm) from all types of water, but rather that the FTIR technique

is not sensitive enough in this region (950 cm-1) to detect the residual hydroxyl bonds

to fully understand and monitor the water associated with gel structure. Overtone and

combination frequencies should be investigated [71].

These results show that the only significant "impurity" in the ultrapure silica gel

is water. The amount of water determines the extent of non-bridging oxygen (NBO)

content, which prevents complete densification. Water content can also be observed

easily using a UV-VIS-NIR spectrophotometer. Figure 3-6 shows the intensity of free

water peaks at 1363.3 nm, 1891.1 nm, and 2212.4 nm decreasing with increasing

processing temperature. It indicates that the densification is due to the combination of

silanol groups on the surface of particles which form free water and escape;

consequently, the surface chemical water is reduced and the absorption peaks are

diminished.


















2.00


1.60


1.20
CD

,-0.80
o
0
VI)
(n


0.40


0.00 -
200


800 1400 2000 2600
Wavelength (nm)


Figure 3-6 The absorptance peaks of water decreasing with increasing temperature.


3200









Samples heated to different temperatures are compared with a pure silica melt

glass (Dynasil) in terms of the cut-off wavelength, as shown in Figure 3-7. Increasing

the temperature of the thermal treatment increases the optical transmission near the UV

absorption end and shifts the uv cut-off to the short wavelength for the pure silica gels,

apparently as the result of a decreased water content in the high temperature samples.

As Sigel concludes [72], the introduction of one electron valent elements (i.e. H,

Li, Na, K, Rb, Cs, Fr, F, Cl, Br, I) produces a noticeable shift of the uv edge to longer

wavelengths. This shift is because these elements terminate the bridging oxygens (BO)

into nonbridging oxygens (NBO) and provide lower energy exciton levels for photo-

electron excitations. More water-related phenomena will be discussed in detail in the

dehydration study in Chapter 4.

Another important analytical technique for understanding the ultrastructure of

partially densified gels is the N2 adsorption-desorption isotherm analyses. The results

include analysis of the variation of average pore radius, pore radius distribution,

specific surface area, and pore volume with densification temperature, as shown in

Figures 3-8, 3-9, 3-10, and 3-11. There was no significant change in pore size

(Figures 3-8 and 9) while the total pore volume and surface area decreased (Figures 3-

10 and 3-11) with temperatures up to 860C. An assumption is that the pores decrease

in number and force the entire gel body to contract. This is because the pores are very

small (in this study, the mean pore diameter is only 2.2 nm). Consequently, they

essentially obey the mechanism presented by the Ostwald-Freundlich equation,

log(Sr/Si) = KE/Tr, stated in Chapter 2 Equation #8 and illustrated in Figure 2-21.

Once the pores start to decrease in size, the rate of decrease becomes very fast and they

immediately fill and disappear under the assistance of the migration of silanol groups

along the interior surface and/or migration of vacancies through the structure to the

exterior of the gel. Therefore, the gel shrinks as the temperature increases as a result of


















g60 : 0
6o i B linesc
S/ / / Dash lines indicate the cut-off
// ii / / / wavelengths
"40 /
I- i n B


o I l I
5000C
20*


200 250 300 350 400 450
Wavelength (nm)


Figure 3-7 Transmission cut-off of pure silica gel










































0 200 400 600 800


Temperature (C)


Figure 3-8 Pore radius vs. temperature


1000
















40



30


E
o 20
E

0
0
0i 10


5 10 15 20 25
Pore radius (A)


Figure 3-9 pore size distribution vs. pore volume at various temperatures.
























.------------------
? 0.25

0.)
E 0.2 0 -------------... .. ..


0
0 -------------------------------
- -------------



0.05- -

0.00' -_ ------___- -------_ ------ -------___--
0.00
0 200 400 600 800 1000

Temperature (C)


Figure 3-10 Total pore volume versus temperature.















600


500-

S400 ...... --------..
S400---------------------------------------- .... ---------------
0E


o) 300- ------
*-----------------
C.)
*I 2 0 0 --------- ................. .. ..... .. ........ .... ..
. \
,oo --------- ..------------------------- \- ------

o-------------- JL -
1 00-

0



0 200 400 600 800 1000
Temperature (0C)

Figure 3-11 Specific surface area versus temperature.










the total pore volume decrease. It can also be reasonably assumed that the decrease of the

surface area is linearly proportional to the disappearance of the number of pores.

When a gel is heated higher than its foaming temperature, free water is formed

from the dissociated surface hydroxyl groups inside the fully densified gel structure.

Immediately, these free water molecules follow the idea gas law in Equation #1 to create

new pores:

pv=nRT (1)
where p is internal pressure of a closed-pore volume v, n is a mole number of gaseous

water molecules within an instantaneously created closed-pore v, v = 4tr3/3 where r

is the closed-pore radius, and T is gel body temperature at the moment foaming occurs.

If N is the total molar number of gaseous water molecules in total of such created pores

of V per unit volume of matter, then N/n is the total number of pores per unit volume of

silica, and V = Nv/n is total pore volume (Vvoid) per unit volume of silica (Vsolid).

Consequently, equations #2 and #3 can be written:

pV=NRT (2)

V=(N/n) x v = (N/n) x 4nr3/3 = (1- p)/p (3)
where p, the relative density, is equal to Pa/pr, Pa= msolid/(Vsolid+Vvoid) is the

apparent density of the foamed silica gel and Pr = msolid/Vsolid is the fully densified

silica gel. Therefore, from Equations (2) and (3), we get:

p = 3nRT/4nr3 = NRTp/ (1- p) (4)

When temperature exceeds the pore closing temperature, the gel immediately foams as

soon as the surface water is released.

The gel foaming mechanism is explored by J. Phalippou, T. Woignier, and J.

Zarzycki [73]. They use the concept that the rate of total energy input to the gel

sintering system equals the rate of total energy output from the system. The total energy

input includes the surface energy of silica gel (dWa/dt = 8nradr/dt) where r is the

pore radius, a is surface tension, and t is time and the external pressure energy is









dWb/dt -PdV = -P x 41r2dr/dt, where P is external pressure. The total energy

output includes the energy for viscous flow (dWc/dt = 16m1rp(dr/dt)2) where iq is the

viscosity of silica gel at the temperature of foaming, p is the relative density of the gel

and the energy for varying the pore radius is dWd/dt = -pdV = -p x 4 Ar2dr/dt. The

equation for this system is thus:
dWa/dt + dWb/dt = dWc/dt + dWd/dt (5)

By replacing ail the items, we get:

-2 a r(P-p) = 4 Tip(dr/dt) (6)

and by combining with Equation #3 yields,

2 a(1-p)2/3 p1/3 x (4Nn/3n)1/3 + (P-p)(1- p)=4 Ti/3(dp/dt) (7)

when we assume gel is sintered in conventional pressure, P=0, the equation becomes:

dp/dt= (1- p)(3 a/2 qir 3p/4 "j) (8)

If there is no escape of gaseous water from the closed-pores, then combine Equation #4

dp/dt= (1- p)(3 cr/2 Tr) 3 NRTp/4 iq (9)
and let dp/dt= 0, and use Equation #3, then a critical pore radius rmin is obtained:

rmin = (3nRT/87 a)1/2 (10)

By substituting Equation #10 into Equation #9, then, an expression for the maximum

value of density (Pmax) is achieved:

Pmax = 1/[(NRT/4 a )(3nRT/8nc)112 + 1] (11)
These two equations (#10,11) show that a maximum value Pmax and a corresponding

critical pore radius rmin can be predicted in terms of the sintering temperature (T),

surface tension (a), the amount of free water in a pore (n) and the number of pores per

unit volume of silica (N/n). From this study the conclusion is reached that whenever the

residual surface water is released after the collapse or closing of the original open-

pores, then the free water in the gel structure follows the idea gas law at higher

temperatures to create closed-pores. Consequently, foaming of the gel happens and the

average radii of the pores increases significantly when temperature is just above 860C










(see Figure 3-9). At 860C the pore radius suddenly increases from a 1.1 nm open-

pore radius to a 5.4 nm closed-pore radius.

X-ray diffraction patterns from fused silica generally exhibit a broad peak

centered around the second strongest peak in the diffraction pattern of quartz (Figure 3-

12). The partially densified silica gels made in this study have broader diffraction

patterns than that of fused silica, as shown in Figure 3-12. The broadening of the gel

diffraction peak decreases with increasing temperature, indicating an increase in the

ordering inside the gel [74]. The BET data in Table 2-1 using Havard, Wilson, Iler's

particle size model described in Section Il also suggest that the effective particle

diameter of the gels increases with temperature; e.g. 2000C (3.6 nm), 7500C (6.6

nm), 8000C (7.1 nm) and 8600C (15.7 nm) [75]. These values can be compared to the

diameter around 100 nm of fully densified silica. These results imply that very short-

range-ordering is taken place inside the structure forming crystallites. The size of a

single silica tetrahedron is about 0.3 nm. Therefore, the structure of the gel crystallites

is composed of only few silica tetrahedra. The gel preheated to 2000C is estimated to be

about 8 tetrahedra, at 7500C it is about 15 tetrahedra, at 800C it is about 17

tetrahedra, and at 8600C the gel has about 35 tetrahedra along the diameter of the gel

fibrillar structure. As a result, x-ray diffraction produces a relatively broader peak

for this relatively short-range-ordering than is observed for fused silica.

This observation led to the suggestion that the silica gel is composed of a randomly

oriented fibrillar structure (random-network model [23]) in which the silica

molecules are relatively ordered crystallites crystallitee model [23]). This

phenomenon is similar to a "mosaic structure" in an imperfect crystal in which the

lattice is broken up into a number of tiny blocks (about 1000 A), each slightly

disoriented one from another [74]. The overall observed gel structure is amorphous.

Based upon the above results, the structure of porous gel in which the

temperature-independent pore diameter is always around 2.2 nm (see Table 2-1) is




Full Text
9
have shown that silicon forms bonds with oxygen of variable bond angles that are 10%
within the 144 maximum in the distribution of Si-O-Si angles. Various arrangements
of these SiOg tetrahedra are possible in noncrystalline silica gels. Bonding oxygens at the
corners of two silica tetrahedra can be easily disconnected in the presence of uneven
hydrostatic stresses and water [24]. DCCA's can be used to minimize the particle size
within the polymerized chain, thereby improving the strength of the gel structure so
that during the critical drying process the gel can endure differential evaporation
without initiating cracking.
The processing and physical properties of dried monolithic silica xerogels, heated
from 150-C to 9Q0C, are discussed in Chapter 3. This ultraporous material has
densities ranging from 0.7 g/cm3 to 2.10 g/cm3 depending on the initial conditions of
the sol, such as the variation of DCCA and/or the amount of water used, as well as the
aging and drying temperatures.
Two types of water exist within the dried xerogel structure chemical water and
physical water [25], which must be removed to achieve monolithic optical components.
Water in solution can hydrolyze the silicon-oxygen-silicon bond. The hydroxyl ion's
oxygen is covalently bonded to silicon, whereas the hydrogen ion forms an ionic bond to
the oxygen. Consequently, chemical water results with hydroxyl groups strongly
attached to the gel's surface. The physical water associated with hydrogen-bonding of
surface hydroxyl groups exists within the ultraporous space of the gel body.
A major problem with monolithic silica xerogels, especially for high-
transmittance optical components, is the removal of chemically bonded water, also called
a silanol group. The chemically bonded silanols give rise to the fundamental vibration of
hydroxyl ions occurring at a wavelength of 2669.4 nm. Also present are vibrational
overtones and combinations of this ion and associated water occurring at the following
wavelengths: 2919.7 nm, 2768.9 nm, 2698.3 nm, 2262.5 nm, 2207.5 nm, 1890.4
nm, 1459.9 nm, 1408.5 nm, 1366.1 nm, 1237.9 nm, 1131.2 nm, 939.0 nm, 704.2


141
Wavelength nm
v
1
Figure 4-7 Transmission curve from Melles Griot Co. commercial UV grage optical
melt silica Code UVGSFS. Thickness 10 mm.


195
The stress birefringence test showed that through the faces of the six, 30 mm x 3
mm (diameter x thickness), fully densified gel-silica glass samples no stress or strain
could be measured. Through the ends (30 mm length) strain was observed which
computed to 4 millimicrons (nanometers) per centimeter. For comparison, normal
optical glass, per MIL-G-174 [111], should have less than 10 millimicrons per
centimeter. The birefringence constant (R) of 4 nm/cm determined for the gel-silica
glass is nearly equivalent to the values of 3.54 nm/cm and 5 nm/cm of Corning 7940
and NSG-ES samples, respectively.
The strain associated with partially densified gel-silica glass samples, using two
plane polarized films, is shown in Figure 5-15. The strain present in partially
densified gel-silica is eliminated by the densificaron process (Figure 5-16). This
effect can perhaps be characterized as "precision annealling".
The six control samples tested showed no evidence of bubbles or inclusions. All of
the silica gel glasses exhibited bubbles approximately one micrometer in size. The so-
called "bubbles" are really optical diffraction points. They appear more like "stars" than
"bubbles". They are closed micropores created by the freed chlorine gas inside densified
gel glass, as discussed in Section II of this chapter. Since the tested samples vary in
quantity of these diffraction points, they seem directly related to thermal process
parameters and should, therefore, be able to be eliminated by optimization of the
thermal-chemical processing. Due to these defects the first generation gel silica samples
would not acceptable for certain precision optical applications. Further analysis of the
test results shows the spacing between points to be fairly homogeneous at a distance of
about 75-125 microns.
Impurity tests by neutron activation analysis show a significant chlorine content at
about 0.1 wt.% with the other impurities in the ten to hundred ppb. No hydroxyl groups
were detected. Except for the chlorine content, all impurity levels were below the levels
of commercially available Types III and IV fused silica.


Dimension change (LA) x 10'4
103
Temperature (C)
Figure 3-19 Thermal mechanical analysis of a unfired sample and a preheated sample.


97
random orientation of
relatively ordered crystallite
20nm
1.1,
silanol group or nonbonding oxygen on the
surface of relatively ordered crystallites
Figure 3-14 A proposed scheme of sintered silica gel in which silanol groups
terminate briding bonds on the surface of crystallites.


Density (g/cc)
112
Figure 3-25 Density versus temperature.


39
A silica gel is defined as "dried" when the physically adsorbed water is
completely evacuated and no significant weight loss is observed at increased
temperatures.
Cracking during the drying process is essentially the result of differential
evaporation of pore liquid, Figure 2-20, as discussed in detail by J. Zarzycki [48], The
Laplace equation is used:
APV| = P| Pv = 2yv| COS 0/R (6)
where APV| is the differential capillary vapor pressure between the surface of the vapor
phase (in which vapor pressure = Pv) and the liquid phase (in which vapor pressure =
Pi), within a very small pore of radius R. In equation (6) yvl is the specific surface
energy, and 6 is the contact angle.
Theoretically, to prevent shattering of the gel body during drying, the capillary
vapor pressure in the liquid phase (which is transmitted to the wall of the pore channel)
must be offset by the capillary vapor pressure in the vapor phase. For APV| to equal
zero, the cosine of the contact angle must also equal zero (@ e=90), as the radius (R)
and the surface energy [y^\) at the liquid-vapor interface will always have some value.
Young's equation for the equilibrium of a solid (s) liquid (I) vapor (v) system is
derived by balancing the horizontal components of the specific surface energies, ysl,
Ysv. tVI of the system. The equilibrium equation is given as:
Ysv = Ysl + Yvl cose (7)
As cosine 9 becomes zero, this equation simplifies to ySv = Ysl- This means that the
work required of the liquid to act on the wall of the solid is the same as the work
required of the vapor to act on the wall of the solid,
cos 0 = o
Ysv = Ysl
As v = As|
YsvdAsv=YsldAs|


optical density (OD)
233
1.0
0.8
0.6
0.4
0.2
0.0
200 300 400 500 600
wavelength (nm)
700
800 900
Figure 6-16 Spectra of 160C Co^-doped silica gel samples and some Co"-doped
melted glasses.


193
Table 5-6
Reference indices and Abbe values of silica glasses
Test No. ID. No.
Reference index (nd)
Abbe Value
Corning #7940, Control Samples:
1} CGW-1
1.45848
67.72
2) CGW-2
1.45848
67.52
3) CGW-3
1.45848
67.72
Statistical Value:
1.45848
67.65
()
0.00000
0.11
NSG-ES, Control Samples:
4) NSG-I
1.45847
67.72
5) NSG-2
1.45848
67.72
6) NSG-3
4.45846
67.52
Statistical Value:
1.45848
67.65
()
0.00001
0.11
Gel Glass Test Samples:
7} N34
1.46317
66.64
8) Q34
1.46276
66.49
9) Q27
1.46326
65.90
10) P37
1.46281
66.21
11) G11
1.46334
66.38
12) Q30
1.46319
66.55
Statistical Value:
1.46309
66.36
()
0.00024
0.27


178
Finally, impurities such as alkali and alkali earth elements, transition-metal
elements, and halogen elements terminate the bridging oxygen bonds, create light
interaction centers and degrade the optical performance of a silica glass. All of the above
physical and structure factors must be determined to characterize the quality of the gel-
silica glass produced herein.
Experimental Procedure
Glass Fab, Inc. of Rochester, New York was selected to evaluate these first
generation ultrapure silica gel glass, produced as described in Chapter 4, as potential
optical components. They were contracted to perform optical performance
characteristics and properties tests on six gel-silica glass samples. Several
commercially available, high quality type III optical silica glasses were used for
comparison. The samples were three high purity fused silica samples (Corning 7940)
and three synthetic optical quartz samples (NSG quartz type ES). Comparative optical
transmission and stress birefringence data were also obtained at the Advanced Materials
Research Center (AMRC) of University of Florida. The tests performed on these samples
are fisted in Tabie 5-2.
Prior to Glass Fab's transmission testing they polished all samples simultaneously
to 0.5 wavelength of red helium light (706.5188 nm). After polishing, the samples
were tested for flatness on two surfaces to 0.5 wavelength flatness. Samples were then
cut into 20 mm squares and two surfaces were polished to a 90 degree angle.
Vacuum ultraviolet (VUV) transmission tests, in the 160 nm to 200 nm range,
were performed by Giass Fab on an Acton Research Corporation, 0.2 meter (focal
length), Model VM-502 with an uncertainty of 2%.
Transmission in the UV-VIS-NIR range, 200 nm to 2600 nm, was measured by
Glass Fab using a double-beam Perkin-Elmer spectrophotometer, slit width 2-10 nm,
with an uncertainty of 1%. Transmission measurements were made in the 186 nm to


Trensmission %
143
160 240 320 400 1000 3000 5000
Wavelength nm
Figure 4-9 Transmission curve from Quartz Science Inc. commercial UV grage optical
melt silica. Thickness 10 mm.


181
Table 5-3
Optical dispersion wavelengths
Designation Wavelength (nm) Spectral Line
r
c
d
e
f
h
706.5188
656.2725
587.5618
546.0740
486.1327
404.6561
red helium line
red hydrogen line
yellow helium line
green mercury line
blue hydrogen line
violet mercury line


Gelation time (min)
30
Figure 2-13 Gelation time versus water content.


22
monomers around the particle and exposing the negatively charged 'OSi(OH)3 molecules
(equation #2) which can react with the particle's positively charged surface. Rather,
the negatively charged oxygen of the hydroxyl ions in solution can attract a hydrogen
from the monomer. This forms free water and leaves the negatively charged oxygen as a
site now available to react with the positively charged silicon on the particle surface,
thereby regenerating this basic catalyst as a hydroxyl ion is released. With the
production of free water, the hydroxyl concentration is reduced, decreasing the pH as
well as the hydroxyl ion's ability to act as catalyst which causes a build-up of monomers
surrounding the particle surface. As the concentration of these monomers within the slip
plane reaches a maximum, at about pH = 2.0, the isoelectric point (iep) is attained. At
this pH the hydrogen ion acts as a catalyst promoting the reaction between the monomers
and the surface hydroxyl groups which facilitates particle growth. Free water is a by
product of this reaction, reducing the hydrogen ion concentration and increasing the pH.
This process continues until the monomer concentration inside the slip plane is
exhausted and the electrical double layer eliminated. Thus, the point of zero surface
charge (pzc) has been reached and gelation begins under the influences of thermally
activated Brownian motion and Van der Waals attractive force.
Brownian Motion, Van tterJflteals^aprf ioteipariiola Bonding Models
When monomers come together to form very small (10 50 ) [43], uniform,
uncharged (pzc) particles, their motion is essentially governed by thermal diffusion as
described by the diffusion equation below.
D = KT/(3rc t| d) (3)
where
D is the diffusion coefficient
n is viscosity
d is the effective instantaneous diameter of the polymerized cluster


127
processing temperature approaching the values of vitreous silica. The low toughness, K|C
and Kic/p, values of the partially densified gels are comparable to those of Type I-IV
vitreous silicas. The interesting point is the 150C gel sample has a higher K\Jp value
than fused silica confirming that the fibrillar ultrastructure of the gel can absorb
relatively high energy before rupture occur. The presence of surface water is suggested
to be a major deteriorating factor for the mechanical properties, and is especially
severe in the lower temperature gels.


53
Step 2: Casting -
(a) The intimately mixed sol is cast from its heated vessel into a mold (20 mm H x
100 mm D) that corresponds to the final desired shape. For best surface results,
polystyrene is the selected mold material
(b) The duration of the casting operation is not critical since gelation does not
occur until after casting is completed.
Step 3: Gelation
Gelation occurs in the mold with the resulting solid object taking the shape and
surface finish of the mold. Gelation times with oxalic acid are typically 20 hours at 25C
and 4 hours at 70C, depending on the relative concentrations of water, TMOS, and DCCA,
as shown in Figures 2-11, 2-12, 2-13, and 2-14.
Step 4: Aging
The solidified gel is then placed into an aging oven at a temperature ranging from
50C to 80C for a times ranging from 20 to 48 hours to achieve maximum shrinkage.
Step 5: Drying
Prior to Step 5, control of the gel ultrastructure is governed by the DCCA which
allows removal of the pore liquid without cracking the gel. Typically this is done by first
removing the excess liquid present after gel shrinkage in Step 4. The pore liquid is then
removed, consistent with the theory stated in Section II of this chapter, by confined
evaporation over a temperature range from 70G to 160C for times ranging from 18 to
90 hours. An example of a typical heating program is shown in Figure 2-28.


208
have a fully filled noble gas electron shell. Consequently, no incoming photon with lower
energy than 7.6 eV can excite these strongly bonded electrons to higher quantum levels;
as a result pure silica gel glass is transparent and colorless to human eyes.
Coloring is one of the most important arts in human life. Artists since ancient
China have tried successfully to preserve their masterpieces forever using vivid colors
in porcelain ceramic glazes. The coloring constituents and molecular ratios of the glazes
are trade secrets since they can only be developed by way of trial and error.
The most common coloring ingredients found in ceramic arts are the transition
metal ions characterized by an incomplete d electron shell, particularly V, Cr, Mn, Fe,
Co, Ni, Cu. Rare earth elements, such as Nd, Er and characterized by an incomplete f
shell, are less frequently used due to their cost and rareness. Insoluble metallic
colorants such as Au are also used but will not be considered in this chapter since the
chemistry is so dissimilar to that of the transition-metal ions.
Ligand-field theory, which is a special case of the most general molecular orbital
theory, is an alternative to crystal-field theory [114-116] to explain the color
formation of transition metal doped silica glasses. In crystal field theory, bonding is
treated as electrostatic, derived from the electric field of the ligands viewed as purely
ionic species. Thus, in a crystal field method the chemical compound of a transition metal
ion is considered as an aggregate of ions and/or dipolar molecules which symmetrically
interact with each other electrostatically but do not exchange electrons. Consequently,
when any covalency is involved, a pure crystal field theory can not explain the
experimental data very well.
The advantage of the ligand field theory is the mixing between the electrons of the
central ion and the ligands. This feature of mixed ionic-covalency successfully explains
the coloring phenomena for most situations involving transition elements. In this
theory, a ligand presents a negatively charged, nonspherical, partially covalent bonded,
distorted coordination complex towards the positive central transition-metal ion.


CHAPTER?
CONCLUSIONS AND RECOMMENDATIONS
Sol-ge! processing offers a new manufacturing method for high technology
ceramics and glasses since it allows structural manipulation down to the molecular scale
in the nanometer range. Thus, ultrahigh purity and extreme molecular homogeneity of a
material may be achieved.
Two major chemical reactions, hydrolysis and polymerization, are involved in sol-
gel ulfrastructure processing. Hydrolysis enables the organometallic chemical
precursor to react to form a monomer on the atomic scale, which is composed of a
positive metallic ion surrounded by an anionic complex (e.g., Si+4(OH)4, Ti+4(OH')4,
AI+3(OH")3, Si+4(CH3)4 etc..). This step is followed by a polymerization based
growth process which links the monomers together.
In recent years special optical applications require silica components that meet
very stringent requirements. Sol-gel processing applied to silica offers the potential for
producing a new generation of silica glasses to meet these requirements for optical and
electro-optical applications. The quality of gel-silica glasses expected to meet these
stringent requirements are (1) very high purity, (2) extremely low optical signal
loss, (3) very high chemically homogeneous doping, (4) very high optical homogeneity.
These features make gel-silicas able to upgrade the optical performance in a wide range
of precise optical apparatus including lenses, mirrors, waveguides, optical fibers,
integrated optoelectronics, and host materials for filters, lasers, and non-linear optical
elements or compounds. Therefore, achieving a chemically optimized sol-gel processing
for silica optical monoliths was the focus of this study.
239


Index of refraction (n)
192
Wavelength (nm)
Figure 5-13 Dispersion data comparison of optical silicas.


optical density (OD)
234
200 300 400 500 600 700 800 900
wavelength (nm)
Figure 6-17 Spectra of 850C, 900C CoiS-sHica gel samples and two Con-doped
melted glasses.


209
For example, in a free ion of a transition metal the five equivalent d orbitals are
depicted spatially as shown in Figure 6-1. The energy level diagram of the five orbitals
in a free transition metal ion is also illustrated in Figure 6-2(a). The electrons can be
found with equal probability in any of these five orbitals (Figs. 6-1, 6-2(a)). When
this positive transition metal ion with partly filled d-orbitals is placed at the center of a
regular (undistorted crystal field) octahedron of ligands, represented as point negative
charges, the configuration is as shown in Figure 6-3. An interaction of the d orbitals of
the central ion with the six ligands in the octahedral field is expected. The two lobes of
the dz2 orbital point exactly at the two ligands in the +Z and -Z directions; similarly,
the four lobes of the dx2-y2 orbital point exactly at the four ligands in the plus and
minus directions of the X and Y axes. The electrostatic interaction of these two d shells
with the negative ligands at the corners of the octahedron is repulsive, consequently,
there is a splitting and raising of the energy of these two of the five d energy levels of the
system. This leads to the two upper eg levels for the octahedral ligand field configuration
as shown in Figure 6-2(b).
The remaining three sets of d orbitals of Figure 6-1, the dxy, dy2 and d2X
orbitals, have orientations which protrude halfway between the ligands as shown in
Figure 6-4. Because there is no repulsive interactions with the ligands these orbitals
will have lower energy levels than the eg set. Thus, the dxy, dy2 and dzx orbitals are
shown as the three equal energy i2g levels in Figure 6-2(b).
The energy difference between the eg and t2g levels called the crystal field
splitting, is designated A0. Since the overall energy does not change, the upward and
downward movements are inversely proportional to the number of equal energy levels;
e.g.e the degeneracy. Thus in Figure 6-2(b), the triply degenerate lower energy t2g
level moves down 0.4 A0, while the upper doubly degenerate eg level moves up 0.6 A0
compared to the unsplit free ion levels (Figure 6-2(b)).


CHAPTER 2
SOL-GEL TRANSFORMATION AND EXPERIMENTAL PROCEDURES
Introduction
During recent years many researchers have attempted to produce large monolithic
dried xerogels; however, a reliable process had not yet been established at the time this
work began [30-36]. Difficulties associated with this sol-gel processing method arise
during all phases of aging, drying, and densification, clearly indicating insufficient
understanding of basic changes in the ultrastructure during the sol-gel transformation
and in the chemical reactions of the solvents, precursors, and catalysts involved. In
general, crack formation during drying is a result of strong hydrostatic stresses within
a relatively weak gel structure. Catastrophic failure can be avoided by adjusting the
mechanical strength of the gel structure to exceed that of the hydrostatic force and/or by
decreasing the hydrostatic stress relative to the gel's strength.
The object of this chapter is to describe the principal mechanisms of the sol-gel
method by which monolithic xerogels may be reliably produced. Four factors are used to
describe the sol-gel transformation up to the gelation point: (1) the isoelectric point
(iep), (2) the point of zero surface charge (pzc), (3) thermally activated particle
movement (Brownian motion), and (4) Van der Waals force. Three kinds of dried
monolithic gel samples were routinely prepared to aid in this study: pure silica, silica
doped with transition elements, and silica doped with rare earth elements.
literature Review of Sol-Gel Transformation Modeling
Dr. Ralph K. Iler's pioneering work in the investigation of silica chemistry is the
foundation of many of the ideas discussed in this chapter. Her found that silica gels can be
12


171
Consequently, the stretching vibration of a Si-O-Si bond is at a higher energy, at around
1130 cm'1 than the rocking vibration which is at 480 cm'1.
As the temperature decreases below a certain point (Tc) the stretching vibration
can no longer contribute to a dimensional change due to the onset of symmetry of the
Morse curve, as shown below point (Tc) in Figure 5-6(b) curve (1).
It is also reasonable to propose that as the temperature continuously decreases
below Tc the strong transverse bending vibration of silica starts to reduce its amplitude.
This consequently increases the interatomic distance as shown in Figure 5-6(b), curve
(2), and thus changes the dimensions as shown in Figure 5-6(a) and curve (3) of
Figure 5-6(b).
The corresponding coefficient of thermal expansion curve of vitreous silica is
shown in Figure 5-6(c). Thus, both the large interatomic space and the decrease of
amplitude of bending vibrations with temperature below Tc contribute to the unusual
thermal expansion behavior in silica glass. As will be shown later, this "anomolous" CTE
behavior of vitreous silica is dramatically different for a sol-gel derived silica.
The optical properties are not solely determined by the chemical composition of the
silica gel glass, but are also influenced by the densification procedure. Since the
refractive index of glass is related to both chemical composition and density, it can be
altered by changes in two interrelated intrinsic properties, the electronic
polarizabilities of negatively charged chemical species (e.g., oxygen ion, chlorine ion)
and density. The electronic polarizability, ae, is an inverse function of the
electronegativity [105]. The electronegativity of an oxygen ion (O'2) is higher than that
of a chlorine ion (Cl'1). Consequently, the polarizability of a chlorine ion is higher than
that of oxygen ion.
The index of refraction (n) is proportional to the summation of the
polarizability of all the chemical species in a glass. Because of the higher polarizability
of the anions, n is primarily dependent on the summation of the anionic


42
ge! structure
pore
Figure 2-21 No differential evaporation.


CHAPTER 6
SILICA GEL OPTICAL FILTERS USING TRANSITION-METAL COMPOUNDS
introduction
Large, monolithic pure silica gels have been made rapidly and reliably from
tetramethylorthosilicate (TMOS) using drying control chemical additives (DCCA). In
this chapter attention is shifted to using the TMOS-DCCA method to make silica gels with
optical filter characteristics by introducing transition-metal ions into the transparent
and colorless matrix. When the impurity is added, five incomplete but equal energy
levels are split by the ligand field of the matrix. Ions with incomplete, split d electronic
excitational and associated vibrational levels are responsible for absorbing light in
characteristic ranges of wavelength in the gel matrix. Color observed in the gel glass
containing transition-metal ions is the complementary color to the region of optical
absorption due to these excitational and vibrational electron transitions. For instance
Cr3+ in a distorted octahedral ligand field of crystalline alumina (ruby) absorbs the
violet and green-yeiiow from the spectra, thus giving ruby its beautiful red color with a
slight purple overtone.
If an optical absorption is simply due to an electronic transition between two
electronic levels, then the absorption bands should be very sharp. However, for glass
containing transition-metal ions the band widths are very broad. This implies that the
associated vibrational ieveis of an excitational state interact with each other in the
presence of the ligand field, and also indicates that by altering the composition of the
glass, the ligand field strengh can be changed. Consequently, variations of bonding
strength may shift the absorption spectra and alter the band width. Unlike transition-
metal ions, the ligand field is effectively shielded by the outer s and p orbitals of a rare
206


31
Figure 2-14 Gelation time versus TMOS content.


82
Figure 3-5 FTIR hot stage data from 25C to 800C of pure silica gel


170
(a)
(b)
Figure 5-5 Thermal expansion depends on bonding strength


115
slope of the curve in Figure 3-26 becomes very sharp at about 700C indicating a
significant structural change in gels.
Fracture toughness indicates the amount of energy absorbed by a material during
failure. This is in contrast to flexural strength (cmax), which is a measure of the stress
required to break a material. A tougher material can absorb more energy within the
structure before rupture occurs. The critical stress intensity factor, K|C, can be
estimated from the length of the plastic zone ahead of the crack tip. A simple testing
procedure and economical method, using a Vickers diamond pyramid indenter, was
introduced by S. Palmqvist [77] and evaluated by Anstis [64], Although the
determination of K|c by this method is not unique, the experimental relationship
established by Anstis is given below:
K|c = 0.016 (E/H)1/2 p2/(c/2)3/2 (16)
where
E : elastic modulus in pascals,
H : microhardness in Kg/cm3 = 2P2 sin 687d2 [see p. 143-149 in ref. 63],
P2 : indentation load in kg,
68: the half angle between opposite faces of the four-sided pyramid of
diamond indender.
d: diamond point indentation diagonal length, mm,
c : extended crack length, pm.
The experimental data (density, Young's modulus, microhardness and extended
crack length) and the calculated results (K¡c and Kjc/p) are compared to the values of
vitreous silica, as listed in Table 3-4. The low K|c value (0.72 MPa-m1/2) of fused
silica glass indicates its brittle character. None of the silica gel samples has a higher K|C
value than fused silica. This shows that the gel samples are even more brittle and easier
to break than fused silica. Surpringly, the 150C gel (0.49 MPa-m1/2) is fairly
tougher than the 830C gel (0.40 MPa-m1/2). If the K|C value is divided by the density


142
160 240 320 400 1000 3000 5000
Wavelength nm
Figure 4-8 Transmission curve from Dynast! Co. commercial UV grage optical
melt silica Code 1000. Thickness 10 mm.


percent of volume shrinkage
36
40
*time starts from the gelation point.
Figure 2-17 Shrinkage of silica gel inside 100 cc polystyrene cylinder
as a function of aging time.


Relative gelation time
17
pH
Figure 2-3 Relative gelation time versus solution acidity


120
Density (g/cc)
Figure 3-29 Flexura! strength versus density.


210
z z
Figure 6-1 Electron distribution shapes of the five equivalent d obritals.


60
Figure 2-32 Picture of a cobalt nitrate-doped silica gel which was stabilized at
750C and redried at 160C.


95
proposed as shown in Figure 3-13. The ultrastructure of a densified gel is also proposed
as shown in Figure 3-14.
The data obtained show that the index of refraction of the gel monoliths increases
with the pyrolysis temperature as wel! as density. The measured index of refraction
ranged from n = 1.27 0.03 to n =1.35 0.04 for the sample heated from 150C to
830C, and the corresponding density varied from 1.40 0.02 g/cm3 to 1.80 0.02
g/cm3. Within experimental error the results shown in Figure 3-15 are reasonably
well predicted by the Lorentz-Lorenz equation [see p. 658 in ref. 23]:
a = [3 e0(n2-1) M]/[No(n2+2)p] (12)
Rearranging equation #12 yields:
(ni2-1)/[(ni2+2)P1] = (n22-1 )/[(n22 + 2)P2] (13)
where the constants are:
a is polarizability of a silica molecule,
e0 is the dielectric constant of a vacuum,
M is the molecular weight of silica,
N0 is Avogadro's number,
and the variables are:
n is index of refraction, p is density,
ni is index of refraction of the gel and n2 is that of fused silica,
P1 is density of the gel and p2 is that of fused silica.
The results of Figure 3-15 show that it is possible that silica gel optics can be
heated to specific temperatures to obtain a required combination of density and index of
refraction. It is also possible that lenses can be obtained by controlling the temperature
gradient in the silica gel to produce a refractive index gradient of refraction in a flat
silica gel.
The differential scanning calorimeter (DSC) data, shown in Figure 3-16, indicate
an endothermic desorption of physical water at a maximum 100C in the 27.7C to


Maximum strain to rupture (AL/L x E6)
108
Figure 3-22 Maximum strain to rupture versus temperature.


61
Figure 2-33 Picture of nickel nitrate-doped silica gel which was stabilized at 750C
and redried at 160C.


4
160 240 320 400 1000 3000 5000
Wavelength nm
Figure 1-1 Transmission curves for commercial vitreous silica
10mm thick


29
oxalic acid (gram)
Figure 2-12 Gelation time versus oxalic acid content.


96
Surface silanol groups are not shown
Figure 3-13 A proposed ge! structural model.


?><.
"^*v


DPN (Kg/mm*2)
114
Figure 3-26 Microhardness vs. temperature


215
negative charged ligand
Figure 6-5 Interaction of the dz2 and d x2.y2 orbitals of a central ion with four
ligands in a tetrahedral field.


217
Use of the subscript g designates the presence of a change in sign of the wave
function on inversion through a center of symmetry. A subscript 1 refers to the
presence of mirror planes parallel to the symmetry axis and a subscript 2 refers to
mirror planes normal to this axis. Upper case designations such as 2A2g, 1Bi, 2Eg, 2T2g
are generally used to represent the energy levels in the atom, ion, or molecule, with the
prefix superscript as the (2S + 1) multiplicity.
The energy states that can accommodate undisturbed or excited electrons in free
transition-metal ions having incomplete d orbitals (d1 to d9), based on Russell-
Saunders coupling [see p. 381-408 in ref. 102], are named to be S, P, D, F, G, H and I
corresponding to the quantum number L equal to 0, 1, 2, 3, 4, 5, and 6. These states are
listed in Table 6-1 for various transition metals.
In a ligand field the tetrahedral d9 or d4 configuration can be viewed as containing
one hole; i.e., one electron missing from a full d or half full d shell. This configuration
provides a strong analogy with one electron added to an octahedral empty d shell (d1) or
a half filled d shell (d6) and, conversely, so do the octahedral d9 or d4 and the
tetrahedral d1 or d6 configurations, as shown in Figure 6-7, except that the highest
rather than the lowest split orbital is being occupied. The same applies to all other
configurations. For example, the tetrahedral d2 or d7 configuration has the same
sequence of levels as the octahedral d8 or d3 and, conversely, so do the octahedral d2 or
d7 and the tetrahedral d8 or d3 configurations. These similarities are shown in Figure
6-8. Consequently, the splitting scheme of dn (octahedral) configurations is equivalent
to that of d(10'n) (tetrahedral) or vice versa. The d and d10 configurations
corresponding to completely empty or completely full d orbitals cannot show color
directly derived from d electronic transitions.
An s1 orbital is completely symmetrical and hence is unaffected by ligands in an
octahedral field such as 2S or Aig. The p1 orbitals are not split by octahedral fields such
as 2P or 2T-|g since all interact equally as illustrated in Figures 6-9 and 6-10. In an


130
chlorosilanes, such as CISi(CH3)3, Cl2S¡(CH3)2, CI3SKCH3), silica tetrachloride
(SCI4), chlorine (CI2) and carbon tetrachloride (CICI4) can completely react with
surface hydroxyl groups to form hydrochloric acid, which then desorbs from the gel
body at a temperature range (400C to 800C) where the pores are still interconnected.
In this study, carbon tetrachloride is used successfully to achieve complete dehydration
of ultrapure gel-silica monoliths.
Review of the Literature Regarding Dehydration
The quality of silica gel can be significantly reduced by impurities. By far the most
troublesome impurity, "water", is present in two forms: free water within the
ultraporous gel structure (i.e., physical water), and hydroxyl groups associated with
the gel surface (i.e., chemical water). The amount of physical water adsorbed to the
silica particles is directly related to the number of hydroxyl groups existing on the
surface of silica. During the 1950's and 1960's, researchers Young, Fripiat, Benesi and
Jones, Hockey and Pethica, Kiselev, McDonald, et al. [87-91] contributed much
information regarding the hydration/dehydration characteristics of the silica gel/water
system, as summarized below:
1. The physical water can be eliminated and surface silanol (Si-O-H) groups
condensed starting at about 170C, as shown in Figure 4-1. Thermal analyses, such as
TGA and DSC, confirmed this process in our silica gel system, as shown in Chapter 3.
2. The dehydration is completely reversible, up to about 400C, as shown in
Figure 4-2. Decomposition of organic residuals, up to 400C, was also confirmed using
DSC and TGA for our TMOS derived silica gels, as presented in Chapter 3.
3. Above 400C, the dehydration process is irreversible as a result of
shrinkage and sintering across pores, as shown in Figure 4-3. Thus, the amount of
existing hydroxyl groups on the gel surface is an inverse function of the temperature of


optical density (OD)
237
350 550 750 950 .1150 1350
wavelength (nm)
Figure 6-19 Absorption spectra of Cul!-doped silica gel sample and three
Cu^-doped sodium-borate glasses.


Temperature difference (C)
101
Figure 3-17 The differential thermal analysis (DTA) data of a dried gel.


74
Figure 3-3 Heating programs
for various
samples


80
changing in moisture and volatiles (oxidation reaction) when gel is in the heating
process.
A thermomechanical analyzer (TMA) can be used as a dilatometer to measure gel
volume shrinkage, or glass expansion coefficient from room temperature to 800C. The
sample was installed in a programmable furnace in which a thermocouple in direct
contact with the sample measured the sample temperature. A movable-core linear
variable differential transformer (LVDT) whose output is proportional to the linear
displacement of Its core is used. The dimensional change of the sample with temperature
can be monitored using this LVDT core displacement technique.
Flexural strength tests were performed under guidelines of the ASTM D 790M-84
standard [69]. Samples heated to the various temperatures (see Table 3-1) and cooled
with the thermal schedule shown in Figure 3-3 were cut with a diamond watering blade
and polished carefully with 600 SiC grit paper into a size of length x width x thickness
(46 mm x 10 mm x 5 mm). All samples were dried at 150C for 3 hours immediately
prior to measurements to eliminate absorbed moisture. Subsequently, the samples with
a span : width : thickness ratio of about 7:2:1 were loaded in three-point bending in
ambient conditions at a strain rate of 3.5 x 10'3 S'1 using an Instron model 1122. In
this experiment a set of five identical samples were heated at same time in a furnace to
each temperature.
The compressive strength tests were carried out under the guidelines of the ASTM
C158-80 standard [70]. Samples heated to the designated temperatures (see Table 3-1)
and cooled with heating programs shown in Figure 3-3 were cut into a rectangular shape
of length x width x thickness (14 mm x 7.5 mm x 5 mm). All samples were dried at
150C for 3 hours immediately prior to measurements to eliminate absorbed moisture.
Subsequently, samples were loaded in an Instron model 1122 such that the length was
parallel to the axis of the applied stress applied at a strain rate of 3 x 104 s'1. The


152
Carbon tetrachloride treated samples were removed from the tube furnace after
reaching various temperatures (850C, 950C, 1050C, 1150C) and then analyzed to
determine their characteristic UV-VIS-NIR absorption spectra, as shown in Figures 4-
15, 4-16, 4-17(a) and (d). Absorption peaks were visible at 2890.1 nm, 2768.9 nm,
2698.9 nm, 2668.8 nm, 2207.5 nm, 1897.6 nm for the 850C sample; and at 2884.3
nm, 2765.4 nm, 2698.3 nm, 2669.4 nm, 2207.5 nm, 1897.6 nm for the 950C
sample.
Stretching vibrations of the adsorbed physical water gives rise to typical broad
absorption peaks at 2890.1 nm and 2884.3nm which are shifted from 2919.70 nm (0)4)
within a broad range from 2700 nm to 3200 nm. Absorption peaks at 2698.3 nm and
2698.9 nm are suggested to be the result of the stretching vibrations of hydrogen-
oxygen bonds of adjacent silanol groups. The 2768.9 nm and 2765.4 nm peaks are
proposed to be the result of stretching of the hygrogen bonds to the neighboring silanol
oxygens, as shown in Figure 4-2. These two kinds of absorption peaks in general can not
be distinguished and thus form the combined broad peak at 2732.24 nm which is
observed by many researchers [91, 93, 98, 99]. The sharp peaks at 2668.8 nm and
2669.4 nm are identified to be caused by vibrating surface isolated silanol groups (i.e.,
free hydroxyl groups).
The intensity of all absorption peaks decreases as the temperature increases. The
spectrum from the 1050C sample shows only one peak, as shown in Figure 4-17 (a),
occurring at 2668.8 nm (01), which is caused by isolated hydroxyl groups. The sample
heated to 1150C has a spectrum in which the water peaks have been eliminated, as
shown in Figures 4-17 (b) and 4-18. The absorption loss due to water is estimated to
approach zero as no water or hydroxyl absorption peaks are present at any wavelength.
The quality of optical transmittance of this sample is significantly higher than that of
traditional fused silica glass.


129
The intrinsic fundamental vibrations of the ultrapure silica molecules result in
resonance with the incoming light at an infrared absorption peak of 8333 nm (1200
cm'1, 0.149 eV); however, weak combination and overtone bands exist at 3200 nm
(3125 cm"1, 0.39 eV) and 3800 nm (2632 cm'1, 0.33 eV), and strong bands occur at
4400 nm (2273 cm-1, 0.28 eV). The infrared absorption tail of ultrapure silica, like
its UV absorption tail, is also caused by phonons. These combinations and overtones
influence the infrared absorption tail down to 1300 nm (7692 cm'1, 0.95 eV) [82].
Extrinsic absorption of light in silica gel in the 140 nm to 8333 nm range has
been detected and interpreted as essentially the result of surface hydroxyl groups and
their associated free water; only one ppm of hydroxyl ions in glass can produce 30
dB/km loss at 1390 nm [83]. All other types of impurities have been reduced to very
low levels (only several parts per billion) by a chemical refining system during TMOS
synthesis, thereby contributing no significant absorption effects in these gels.
Thus, a major problem in producing gel-silica optics is that gel surface hydroxyl
groups and hydrogen-bonded pore water give rise to atomic vibrational energy
absorption in almost the entire range of ultraviolet to infrared wavelengths (160 nm to
4500 nm). This absorption greatly decreases the optical applications of a silica-gel
monolith. Consequently, in order to achieve the full theoretical performance of silica
complete dehydration is imperative. The degree of dehydration of gel-silica optics is
monitored by analyzing the light absorption spectra in a broad range; the Perkin-Elmer
UV-VIS-NIR spectrophotometer covers the range from 184.5 nm (54200 cm'1) to
3200 nm (3125 cm'1) and the Nicolet FTIR covers the range from 2083 nm (4800
cm'1) to 50,000 nm (200 cm'1).
After extensive experimentation a reliable method was found that completely
eliminates the surface chemical hydroxyl groups and associated pore water in gel-silica
monoliths. By applying the concepts of fundamental silica surface chemistry [84-86],
it was found that many chlorine compounds some of these include methylated


188
Wavelength (nm)
Figure 5-12 Infrared transmission of optical silicas
sample thickness: 3 mm.


221
negative charged ligand
Figure 6-9 All interaction between ligands and 4S1 are equal,
therefore, no splitting results.


ACKNOWLEDGMENTS
I am deeply honored to acknowledge several persons who have helped me during the
time of my research as a graduate student at the University of Florida and as a scientist
at GelTech Inc., Alachua, Florida.
I am grateful to my advisor Professor Larry L. Hench who has shared my dream of
creating a new method for manufacturing high-tech silica optical monoliths, including
high power glass lasers for nuclear fusion which might contribute to freeing mankind
from energy and pollution crisises. This dream has been partially realized by this
research and I greatly appreciate his guidance and support.
Dennis A. LeSage, Candace E. Campbell, and Grib Murphy of GelTech Inc., and Dr.
Jon West, Guy LaTorre, and Martin Wilson of the Advanced Materials Research Center of
University of Florida assisted me directly or indirectly in this work. I give each of them,
my friends, sincere thanks. My appreciation is also extended to Linton E. Floyd, III, and
the Glass Fab Inc. for arranging and performing the gel-silica optical property proving
tests, and to Professor Stephen F. Jacobs in Optical Sciences Center of the University of
Arizona for the low temperature gel-silica thermal expansion test.
Financial support from the U.S Air Force Office of Scientific Research through
contract no. F49620-83-0072, GelTech Inc. and the Department of Materials Science
and Engineering were very important to me and made the research and this manuscript
possible. I am grateful to Dr. Donald R. Ulrich of the AFOSR for his understanding and
contributions to my success.
Special thanks are given to Professor Gholamreza J. Abbaschian, Chairman of the
Department of Materials Science and Engineering, and Professor John Staudhammer of
the Department of Electrical Engineering for their unforgettable assistance and
encouragement at a very critical moment in September 1987.
I greatly appreciate the members of my supervisory committee, Professors
Vellayan Ramaswamy of the Department of Electrical Engineering, Joseph H. Simmons,


78
between the unknown gel sample of index n and a prism of known index n'. Since n' is
greater than n, the two must be interchanged in the standard equation, sin <|>c = n/n'
[68]. The beam is oriented such that some of its rays just graze the surface as shown in
Figure 3-4, so that the transmitted light has a sharp boundary occurs which allows one
to compute the value of and hence of n.
DSC, DTA, TGA, and TMA analyses were obtained with a DuPont 1090 thermal
analysis system. In The DSC system, the gel sample and a reference were placed in pans
which sat on a disk. Heat was transferred through the disk into the gel sample and
reference. The differential heat flow to the sample and reference was monitored by the
junction of a constantan disc and the chromel wafer which covers the underside of each
platform. Chromel and alumel wires were connected to the underside of the chromel
wafers, and the resultant wire-thermocouples were used to monitor the sample
temperature. Therefore, heat transfer and temperature of the sample and reference
could be recorded. The temperature range of the DSC cell is from room temperature to
600C.
Differential thermal analysis (DTA) measures the temperatures at which heat-
related phenomena occur in materials. DTA provides the same qualitative information as
DSC, and can provide semiquantitative calorimetric measurements. The temperature
range of the DTA cell is from ambient to 1200C.
The high temperature 1200C DTA cell consist of a platinum sample and reference
cups resting on the tops of two insulated thermocouple pedestals. The sample and
reference were located 6 mm apart surrounded by a programmable furnace.
Thermocouples located in the pedestals measured both the presence of transitions and the
temperatures at which they occur. DTA cells complement the DSC to offer appropriate
measurements over a wide temperature range.
The thermogravimetric analyzer measures changes in weight as a function of
temperature, and provides derivative TGA data. These data can be used to measure the


CHAPTER 5
OPTICAL PROPERTIES OF FULLY DEHYDRATED SIUCA GEL GLASS
Introduction
The initial approach towards producing high optical quality, pure silica gel glass
monoliths via a chemically treated, thermal densification process was achieved, as
described in Chapter 4. The purpose of this chapter is to investigate the optical
properties of these samples and to compare them with those of traditional, high-purity,
commercial type III and type IV silica glasses.
Silica glass, whether produced by the traditional method or by the low-
temperature sol-gel route, can be described as a solidified supercooled silica liquid of
randomly packed silica tetrahedra in which a relatively stress free, short-range-
ordered structure has been formed, as discussed in Chapter 3 Section IV. This solid
appears to have a complete lack of periodicity and a tendency to "order" only in the sense
that a few silica tetrahedra are fairly tightly packed together with a statistical
preference for a particular interatomic distance, as indicated by x-ray scattering. For
optical applications, silica glass usually is required to be an amorphous, isotropic,
homogeneous, transparent, dielectric, insulating material.
An ideal silica glass, defined as silica glass without nonbridging oxygen bonds or
cation or anion impurities, does not exist in the real world. However, like an ideal gas an
ideal silica glass can be approached. The sol-gel fabrication technique developed herein
is a step forward to this goal since the new low-temperature route results in no
absorption toss due to hydroxyl (OH) ions and minimal other ionic impurities in the
ppb range.
160


162
which determines the degree of shift to higher wavelengths in the 150 nm to 200 nm
range; (c) significantly higher wavelength shifts, from 200 nm to 350 nm, which are
induced by impurities (e.g. transition elements, alkali, alkaline-earth and halogen
elements) in the ppm range, as listed in Tables 1-1, 1-2 and shown in Figure 1-1.
Refinement of the soi-gel precursor, for exampie TEOS (tetraethylorthosilicate)
reduces the metallic impurities to a minimal ppb level, as listed in Table 5-1, which
makes it possible to produce a glass having a very high quality of light transmission in
the VUV and UV. The elimination of physical and chemical water (also considered
impurities) associated with the gel has been described in Chapter 4. An absolutely
impurity-free silica glass should exhibit a VUV absorption edge of approximately 150
nm, as indicated in factor (a) above.
Silica glass is capable of being used as an "optical window" between the vacuum
ultraviolet and infrared absorption (160 nm to 4400 nm) regions. The subregion from
600 nm to 1100 nm is the portion of the electromagnetic spectrum of interest for
present day long distance optical fiber communication systems [103]. However, the
"window" from 600 1100 nm is not usually perfect since a number of material
absorption and scattering losses are present. Loss mechanisms, including fundamental
UV and IR absorption tails, overtone and combination peaks of hydroxyl groups, and
Rayleigh scattering are shown in Figure 5-1.
Rayleigh scattering is due to density and compositional variations in the material.
Today, type IV silica is developed and produced commercially for making optical
wavequides (fibers) which require extremely low signal loss for long distance use in
optical communication cable systems. The best quality of silica optical fiber (type IV)
has been achieved with an infernal attenuation value around 0.2 dB/Km (10 dB = 1 OD
optical density absorbance = 10% transmission, OD = Log [lo/l] where lo is the incident
intensity, I is the transmitted intensity) at 1550 nm in single-mode operation [see p.
32 in ref. 83]. Silica gel-glass optical fiber with no hydroxyl groups and minimal


144
Sample
Figure 4-10 A mixed vapor(CCi¡4 and He) atmosphere within the tubing of a furnace.


107
Figure 3-21 Flexural strength versus temperature.


Klc/density
123
Density (g/cc)
Figure 3-32 Toughness versus density.


161
Interactions between electromagnetic radiation and glass, based on both quantum
mechanics and classical treatments, has been well established in the literature [80,
100, 101] and is the basis for interpreting the results presented in this chapter.
Optica! properties of gel glass are determined not only by intrinsic chemical
aspects (e.g. electronic energy gap, interatomic bond strength, ionic mass, and impurity
levels), but also by extrinsic physical aspects of the processing (e.g. thermal history,
thermal gradients, structural arrangement, and degree of isotropy) developed during
densification process.
The physical properties of a glass are always interrelated; for example, molecular
vibrations are responsible for light absorption, resonance, heat dissipation,
fluorescence, phosphorescence and thermal expansion [102]. Refractive index is a
function of density and electronic polarizability, etc. The optical properties to be
examined in this chapter include vacuum ultraviolet (VUV) transmission, ultraviolet
(UV) transmission, visible (VIS) and near infrared (NIR) transmission, infrared (IR)
spectra, index of refraction (n), and dispersion (u). In addition, the optical quality of
the gel silica monoliths is tested by measurements of homogeneity, stress birefringence,
striae, bubbles, inclusions, and impurities. This information along with coefficient of
thermal expansion (CTE), density and microhardness (Knoop hardness, DPN) data are
used to compare and characterize the gel-silica glasses.
literature Review Regarding Optical Properties of Silica Glass
Classification of the ultraviolet cutoff wavelength of commercially available high
purity fused silica has been made by Sige! [72]. He suggests that the location of the VUV
(vacuum ultraviolet) absorption edge can be attributed to three factors: (a) a
completely stoichiometric Si-0 network, with its strong O-Si-O bridging bonds, which
provides the minimum absorption wavelength at about 150 nm; (b) a small amount of
terminal Si-0 bonds (e.g. silanol groups), also called non-bridging oxygen (NBO) bonds,


47
Figure 2-25 Solubility of silica in neutral water at 25C varies with the radius of
curvature of the surface according to the Ostwald-Freundlich eqiation.


54
Time (hr)
Figure 2-28 Drying program for wet gel.


230
The examples used for this investigation were Co11, Ni11 and Cu11 colored silica
monoliths. The first step involved mixing 60 cc (1N) nitric acid DCCA with 340 cc of
distilled water for 5 minutes at room temperature, followed by adding to the nitric acid
water solution 2Q0cc of TMOS with mixing at 85C for no more than 60 minutes. This
well mixed sol was then cast into a polystyrene mode (20 mm H x 100 mm D, a disk
shape) at room temperature. Gelation occurred in the mold at 55C in about 115
minutes, followed by aging at 55C for 10 hours and followed by aging at 80C for 15
hours. The aged silica gel was taken from the molds and dried with a controlled
evaporation rate, as described in Section II of Chapter 2. The drying was initially at
70C with the temperature gradually increasing to 160C during a 90 hour period.
Before impregnation, the gel was stabilized to 800C at 10C/hour to increase the
strength and density and make it possible to perform a nondestructive doping process.
The stabilized gel was then immersed into a 0.25 gram-percent Co11 nitrate or a 0.30
gram-percent Ni11 nitrate oran one gram-percent Cu11 nitrate water solution for 24
hours. The solution doping followed by drying at 160C for 12 hours to remove the pore
solvent. Subsequent thermal treatments to 850C and 900C were done in ambient air.
The transmission spectra of the 160C Co11 and Cu11 doped silica gel glasses and
the 85DC,. 900C Co11 doped silica gel glasses were obtained in the visible range from
200 nm to 900 nm using a Perkin-Elmer UV-VIS spectrophotometer model 552. The
transmission spectra of the 160C Nii! doped silica gel glass was performed in the UV-
VIS-NIR range from 200 nm to 1300 nm using a Perkin-Elmer Lambda 9 UV-VIS-NIR
spectrophotometer.
Results and Discussions
The silica gel samples containing 0.25% Co were heated to certain temperatures.
The color of the 160C Co" gel is reddish pink. The color of the 850C sample is deep
blue, and the 900C sample has a greenish black color. The UV-Visible spectra


243
There is no difficulty for the sol-gel process to prepare an extremely Intimate and
chemically homogeneous sol to form a molecularly uniform gel. The optical homogeneity
problem due to localized density and chlorine fluctuations could be improved by
developing further optimization of the thermal dehydration densification process. This
will require modification of the atmosphere control system of the furnace.
Use of the chemical doping technique for porous gel-silica could lead to produce a
new category of multicomponent glasses. For instance, a colorful and fascinating world in
the transition-metal and rare earth elements doped gel-glasses is waiting for further
exploration. Oxidation states and ligand fields can be stabilized within the gel-silica
matrix that are not possible using traditional high temperature melt derived glasses.


151
vibrational peaks are observed at 704.22 nm, 938.95 nm, 1131.21 nm, 1237.85 nm,
1366.12 nm, 1408.44 nm, 1459.85 nm, 1890.35 nm, 2207.51 nm. A very strong,
broad absorption band occurs between 2400 nm and 3200 nm. None of these peaks have
been eliminated by heating, instead they have only decreased in intensity with increasing
temperatures. Clearly, the gel is not completely dehydrated, even when heated to the
point of full densification; further heating results in a foaming problem.
Data obtained in this study show that a combination vibration is identified at
2207.5 nm, resulting from the adjacent silanol stretching vibration at 2732.24 nm
(x>2) and the out-of-plane hydroxyl ion deformation vibration at 11494.25 nm (uqh
(bend)). The peak at 1890.35 nm is a combination vibration of 2816.88 nm (\>3) plus
two times the bending frequency (2uoh (bend)). The peak at 1459.85 nm (2v4) seems
to be the first overtone of the 2919.70 nm (U4). The peak at 1408.44 nm (2^3)
observed is the first overtone at 2816.88 nm (1)3); whereas the 1366.12 nm (22)
peak is exactly from the first overtone of the fundamental hydroxyl stretching vibration
observed at 2732.24 nm (\>2).
The peak observed at 1237.85 nm is presumed to be an overlap from the
contribution of two type of combinations which are 1221.00 nm (2v2 + uoh (bend))
and 1254.70 nm (2^3 + uoh (bend)). A tiny peak at 1131.21 nm is believed to be 2^3
+ 2dqh (bend) and a small peak at 938.95 nm is presumed to be a second overtone of
2816.88 nm (3^3). There is a very tiny peak at 704.22 nm which is a third overtone
of 2816.88 nm (4v>3) as shown in Figure 4-14 curve d.
These results show that for critical optical applications where complete
transmission over a broad range of wavelength is important, densification in an air
atmosphere is obviously a failure. The resulting quality of this gel can not compete with
that of fused silica (see Chapter 1), and it will never reach the point of complete
dehydration.


202
Table 5-9
Knoop hardness
TEST
SAMPLE NO.
SAMPLE
ID No. 100 gm Load, Kg / mmH2
Gel Glass Sample:
No. Q 11
456 Standard Deviation: 16.6
Corning #7940:
No. CGW-3
508
Standard Deviation: 11.2
For reference only:
Following are the Knoop Hardness characteristics of various materials based
upon published data (100 gm Load):
1. Fused Silica (Synthetic) 600 630
2. Fused Quartz (Natural) 590 620
Notes:
It should be noted that the Knoop hardness of the control sample of Corning
fused silica measured lower than published data. Other Corning published data
on the same material is lower than was measured.


224
(a)octahedral field
d2 (V3+)
d7 (Co2+)
(b)tetrahedral field
d3 (V2+, Cr3-*")
d8 (Ni2+)
octahedral field:
d1 (Ti3+)
d6 (Fe2+ Co3+)
tetrahedral field:
d4 (Cr2+, Mn3*)
d9 (Cu2+)
Figure 6-11 The splitting of d orbitals (a), (b) for P, F states,
(c)for D state in octahedral and tetrahedral ligand field.


222
negative charged ligand
Figure 6-10 Ail interaction between ligands and 4P1 are equal,
therefore, no splitting results.


(a) Brownian motion and Van der Waals forces
(b) base catalyst
[OH" ]
Figure 2-9 Particles collide randomly with the help of Van der Waals
attractive forces, Brownian motion and base catalyst.


76
peaks in the sample's spectra. A dried gel was installed in a hot stage inside the FUR
sample chamber and heated to the temperatures designed in Table 3-1 for IR analysis. A
heating rate of 3.3C/min from room temperature to 800C was used.
The uttraviolet-visible-near infrared spectra were obtained from a Perkin-Elmer
Lamda 9 UV/VIS/NIR spectrophotometer. This instrument consists of a high performance
double-beam, double-monochromator and a superior signal-to-noise energy optimized
optical system [65] throughout the entire 185 to 3200 nm wavelength range; it is
integrated with microcomputer electronics, video display, soft key operating system and
printer. Gels heated to the temperatures designated in Table 3-1 and cooled to room
temperature with heating programs shown in Figure 3-3 were taken out immediately
from the furnace for testing. Subsequently, the thickness of the gels was measured and
they were scanned at a rate of 120nm/min through a required wavelength range in
either transmission or absorption mode after background correction had been made.
The surface area, total pore volume, average pore radius, and pore size
distribution were determined by the nitrogen adsorption-desorption isotherm BET
method, using an automatic Quantachrome Autosorb-6 sorption system [66].
Specific surface area (A) of the gels is obtained from a series of data management
and calculations performed in the microcomputer of the Autosorb-6 system. The
calculations involve: (1) a BET equation, 1/{W[(P0/P)-1 ] = 1 /(WmC) + [(C-
1)/(WmC)]x(P/P0) in which W is the weight of gas adsorbed at a relative pressure
P/P0 (pressure ratio of N2 gas in He gas), Wm is the weight of adsorbate constituting a
monolayer of N2 on surface, and the constant C is related to the energy of adsorption in
the first layer. (2) a linear plot of 1/{W[(Po/P)-1]} vs P/P0 to yield values of slope
s=(C-1)/(WmC) and intercept i=1/(WmC). (3) the weight of a monolayer Wm obtained
by equation Wm=1/(s+i). (4) At=(WmNAcs)/M where At is total surface area of the
sample measured and N is Avogadro's number. For N2 at 77 K, the cross-sectional area,


116
Table 3-4
Fracture toughness (K|C) and K|C/p ratio of partially densifiedsilica gels, data
obtained from diamond indentation cracks.
(0.05 Kg load)
Temp.
Density
Modulus
Microhardness
T
P
E
H
(C)
(*g/cm3)
(MPa)
(***Kg/cm2)
150
1.40 0.05
7925
11300 2700
250
1.42 0.05
9148
12500 3800
450
1.46 0.05
12035
14000 4300
750
1.71 0.05
28539
19600 5200
800
1.74 0.05
32413
22000 3500
830
1.80 0.05
36803
24500 9800
fused silica
2.20
73089
71000
Temperature
Extended Crack Length
Toughness
T
c
K|c
K|c/p
(C)
** pm
*** MPa-m1/2
150
24.3 5.8
0.49
0.35
250
27.0 3.8
0.43
0.30
450
30.6 3.2
0.39
0.27
750
32.2 5.1
0.47
0.27
800
35.0 9.7
0.42
0.24
830
35.9 4.3
0.40
0.22
fused silica
21.5
0.72
0.33
1Kg = 1000 g.
' 1 pm = 10'6m
= 10 '4cm = 103mm,
*'*10.194 Kg/cm2 = 1 MPa =145 psi.


173
polarizabilities. This relationship is described by the Lorentz Lorenz equation:
a= 3 e0(n2 1)M/[N0(n2 + 2)p] (1)
Therefore n is directly proportional to a as the other items in the equation above
are constants: i.e.
N0 is Avogadros number
e0 is the dielectric constant of vacuum
M is the molecular weight of silica
p is the density of silica
The second important effect to consider is density. Since a is constant for silica, on
condition that other anionic impurities are negligible, the density is proportional to (n2
- 1)/(n2 + 1). Thus, as density increases the index of refraction increases.
Susa, Matsuyama, Satoh, and Suganuma at Hitachi Ltd. Japan [106], reported on
the effect of chlorine content in sol-gel derived silica glass. They observed that the
refractive index of the gel glass increases in proportion to the chlorine content. These
findings are correct according to the larger chlorine ion polarizability discussed above.
However, in their report the chlorine content of selected gel glass samples was
determined by nephelometry, which is a method to measure the concentration of a
suspension or substance or a second phase (e.g., bubbles, inclusions) by comparing the
brightness of light passed through a sample with that passed through a standard and is
incapable of directly measuring a colorless ionic solution (e.g., NaCI in water, or Cl'1 in
glass). All the samples they produced had been heated to 1300C, consequently, those
with a higher initial chlorine (Cl"1) ion concentration were likely to have
proportionally freed more chlorine gas (Cfe) to create more closed micropores. This
structural change would decrease the brightness of incident light in the measurement and
lower the apparent density. In addition the equilibrium of 2CI'1 <-> CI2 + 2e"1
should be a constant, K = [Cl2]/[CI'1]2, at that temperature for all samples having
various chlorine contents. Therefore, samples with a higher initial surface area were


199
Table 5-7
Coefficient of thermal expansion of fully dense gel silica
Temp
Temp
Penn
C
K
Orton
State
150
225
25
298
0.4 x
10*7
-1.0 x 10-7
100
373
1.1 X
10-7
-1.0 x 10-7
200
473
1.4 x
10-7
3.1 x 10*7
300
573
1.9 x
10-7
3.1 x 10-7
400
673
1.0 x
10-7
3.1 x 10-7
500
773
2.4 x
IQ'7
3.1 X 10-7
(a)/C
Univ. of
Arizona
2 x 10-7
2 x 10-7
2 x 10-7
2 x 10-7
2 x 10-7


231
characteristic of these three Co^-silica gel samples are shown in Figure 6-15. There is
a totally different absorption curve for the 160C pink sample than for the 850C blue
sample and the 900C green sample. Since the color of transition ions such as cobalt in
silicate glasses depends primarily on the outer d valence orbitals, it means that the color
and absorption spectra depends on the oxidation state and coordination number of the ion.
The temperature sensitivity of the Co^-silica gel absorption spectra indicates a shift in
oxidation state and coordination number (CN). The low-temperature gel shows evidence
of a sixfold CN similar to that reported for Co11 in metaphosphate glasses [117] and 10
mol% Na20-borate glass [see p. 241 in ref. 112], as shown in Figure 6-16. Thus, it is
reasonable to assume that the Co11 ion in the silica gel in octahedral symmetry.
The major absorption band of the Con ion is due to the 4Ti(F) to 4Ti(P)
transition (see Figure 6-16). The high energy shoulder at 470 nm is a consequence of
spin-orbit couping in the 4T-|(P) state [9]. The 4T-¡(F) to 4T2(F) transition occurs in
the infrared region around 1250 nm and does not contribute to color formation. The
4Ti(F) to 4A2(F) transition is expected to be at 555 nm. However, this transition is
very weak because it involves the forbidden two-electron jump [118]. This weakness
combined with the closeness of the major 4Ti(F) to 4Ti(P) transition makes the 4T1 (F)
to 4A2(F) transition unresolved.
In contrast, the high-temperature (850C and 900C) CoM doped gels appear to
have a CN of 4. This fourfold coordination is more equivalent to that of a standard
vitreous Silicate glass [119] (see Figure 6-17), that is,
Co5S06(pink) A]_ > Col!04(blue).
The main absorption band in 550 nm to 700 nm range of this tetrahedral Co11 ion
is due to the 4A2(F) to 4T-|(P) transition. As shown in Figure 6-17, the Co11 doped high-
temperature gel shows evidence of a fourfold CN simlliar to that for Co11 ion in fused


113
Table 3-3
Microhardness data of partially densified silica gel
(0.05 Kg load)
Temperature
Indentation Diagonal length
Microhardness
(C)
d, (mm)
DPN (kg/mm2)
150
0.0202

0.0040
113 27
250
0.0193
+
0.0054
125 38
450
0.0182

0.0032
140 43
750
0.0154

0.0024
196 52
800
0.0145

0.0025
220 35
830
0.0138

0.0030
245 49
***Vickers' hardness number for silica is 710 kg/mm2 [see p. 144 in ref. 63].


Index of refraction (nd)
98
Figure 3-15 index of refraction vs. density for silica gels, gel-glass, and
crystallines phases.


246
30. L. C. Klein and G. J. Garvey, Monolithic Dried Gels, Journal of Non-Crystalline
Solids, Vol. 48, 1982, p. 97-104.
31. M. Decottignies, J. Phalippou and J. Zarzycki, Synthesis of Glasses by Hot-
Pressing of Gels, Journal of Materials Science, Vol. 13, 1978, p. 2605-2618.
32. J. Phalippou, M. Prassas and J. Zarzycki, Crystallization of Gels and Glasses
Made from Hot-Pressed Gels, Journal of Non-Crystalline Solids, Vol. 48, 1982,
p. 17-30.
33. R. Roy, Gel Route to Homogeneous Glass Preparation, Journal of American
Ceramic Society, Vol. 52, 1969, p. 344-345.
34. B. E. Yoldas, Monolithic Glass Formation by Chemical Polymerization, Journal of
Materials Science, Vol. 14, 1979, p. 1843-1849.
35. G. Carturan, V. Gottardi and M. Graziani, Physical and Chemical Evolutions
Occurring in Glass Formation from Alkoxides of Silicon, Aluminum and Sodium,
Journal of Non-Crystalline Solids, Vol. 29, 1978, p. 41-47.
36. M. Yamane, S. Aso, S. Okano and T. Sakaino, Preparation of a Gel from Metal
Alkoxide and Its Properties as A Precursor of Oxide Glass. Journal of Materials
Science, Vol. 13, 1978, p. 865-871.
37. L. L. Hench and Gerard Orcel, Physical-Chemical and Biochemical Factors in
Silica Sol-Gels, Journal of Non-Crystalline Solids, Vol. 82, 1986, p. 1-10.
38. Gerard Orcel, The Chemistry of Silica Sol-Gel, Ph. D. Dissertation, University of
Florida, Gainesville, Florida, 1987.
39. Z. Z. Vysotskii and D. N. Strazhesko, The Role of Polymerization and
Depolymerization Reactions of Silicic Acid, etc., in D. N. Strazhesko, ed.,
Adsorption and Adsorbents. John Wiley & Sons, Inc., New York, 1974, p. 55-75.
40. C. Okkerse, Chapter 5: Porous Silica, in Physical and Chemical Aspects of
Adsorbents and Cafalysts. B. G. Linsen, ed., Academic, New York, 1970, p. 214-
219.
41. S. G. De Bussetti, M. Tschapek, and A. K. Helmy, Calorimetric Determination of
the Point of Zero Charge, Journal of Electroanalytical Chemistry and Interfacial
Electrochemistry, Vol. 36, 1972, p. 507-511.
42. Ralph K. Her, Polymerization of Silica Acid: Retarding Effect of Chromate Ion,
Journal of Physical Chemistry, Vol. 56, 1952, p. 678-679.
43. Ralph K, Her, Chapter 2: Dissolution and Polymerization of Silica, in Surface and
Colloid Science. Vol. 6, E. Matijevic, ed., John Wiley & Sons, Inc., New York,
1973, p. 4-15.
44. Michael D. Sacks and Rong-Shenq Sheu, Rheological Characterization During the
Sol-Gel Transition, in Science of Ceramic Chemical Processing. L. L. Hench and D.
R. Ulrich, eds. John Wiley & Sons, Inc., New York, 1986, p.100-107.


213
negative charged ligand
this presents one of dxy, dyz dzx orbitals
Figure 6-4 Less interaction of the dxy dy2 d2X orbitals of a centra! ion with six
ligands in a octahedral field.


145
Densification in an air atmosphere was carried out using the heating program
shown in Figure 4-11. These samples were heated to designated temperatures (150C,
450C, 750C, 800C, 850C), cooled to room temperature, and then subjected to
density and optical absorption measurements. The UV-VIS-NIR and FTIR spectra were
used to monitor the fundamental, overtone, and combination vibrations of hydroxyl
groups within the ranges of 900 nm to 3200 nm and 2083 nm to 50,000 nm,
respectively.
The heating program for densification of samples dehydrated in a carbon
tetrachloride/helium atmosphere in a tube furnace is shown in Figure 4-12. During the
dehydration process carbon tetrachloride was consumed at a rate of 4 cc/hour. The
samples were removed at various temperatures during the heating program (850C,
950C, 1050C, 1150C), Density measurements of the samples were taken, followed
by the UV-VIS-NIR and FTIR spectra measurements within the previously stated ranges.
Results and Discussions
The density measurements at various sintering temperatures for samples with or
without chlorination are shown in Figure 4-13, in which the density of the water-rich
(without chlorination) gel sample reaches a maximum (= 2.2 g/cc) at a lower
temperature about 860C, and the density of the water-free (with chlorination) gel
sample has its maximum (~ 2.2 g/cc) at a relatively higher temperature of about
1100C. This indicates that the hydroxyl groups significantly decrease the sintering
temperature by lowering the surface energy of silica.
The important absorption peaks and bands found in this dehydration study are
summarized in Table 4-1. These peaks and bands are identical to those discovered by
previous researchers stated in Section II of this Chapter.
Curves a, b, c, and d in Figure 4-14 show the UV-VIS-NIR spectra of gels heated in
ambient air at various temperatures up to about 850C. Overtone and combination


Gel Time (min)
28
Figure 2-11 Gelation time versus temperature.


10
nm. These IR absorptions are the result of electromagnetic vibrational interactions with
the electrons, atoms, and molecules of the gel water. Selectively absorbed light energy,
such as this, is mostly converted into heat. Consequently it is important to reduce the
hydroxyl groups to nondetectable levels in order to minimize absorption loss, especially
for optical lenses, optoelectronic signal processors, optical fiber, filters, and laser
resonant host systems. Therefore, monitoring the IR absorption peaks is a primary
method for determining the degree of dehydration achieved during densification [26,
27],
Consequently, the second goal of this study is to dehydrate and density monolithic
silica xerogels; this is described in Chapter 4. Two methods are investigated: (1)
sintering samples in an air atmosphere and (2) chemical treatment and sintering in a
controlled gas atmosphere (e.g., carbon tetrachloride). At sufficient temperatures these
gases can react with the hydroxyl groups to form hydrogen chloride which escapes freely
from the unclosed ultrapores [28]. The dehydrated xerogel samples are then exposed to a
higher temperature for full sintering.
The third goal is to determine the physical properties of monolithic fully
dehydrated gel-silica glasses. In Chapter 5 various physical properties of the dense gel-
silica glasses are compared with commercial melt/cast vitreous silica glasses (fused
quartz) and other high-quality optical silica glasses (synthetic fused silica).
The fourth goal of this study is to develop the technology for fabrication of
transition-element doped xerogels. This is described in Chapter 6. Optical color filters
that selectively transmit part of the visible spectrum can be made from xerogels doped
with transition metal compounds. Transition elements, having unpaired electrons in
their d-orbitals, can absorb light by ligand field-controlled transitions that do not
involve variable valence states. The energy level scheme is controlled by the number and
symmetry of the ligands and the strength of the ligand field [29], The doped xerogels
processed at different temperatures exhibit different densities and slight changes in


optical density (OD)
232
Figure 6-15 Spectra of three Co!S-doped silica gel samples at 160C, 850C, and 900C.


92
dWb/dt = -PdV = -P x 4nr2dr/dt, where P is external pressure. The total energy
output includes the energy for viscous flow (dWc/dt = 16jrnrp(dr/dt)2) where ti is the
viscosity of silica gel at the temperature of foaming, p is the relative density of the gel
and the energy for varying the pore radius is dWp/dt = -pdV = -px4 7cr2dr/dt. The
equation for this system is thus:
dWa/dt + dWb/dt = dWo/dt + dWd/dt (5)
By replacing ail the items, we get:
-2 a r(P-p) = 4 Tip(dr/dt) (6)
and by combining with Equation #3 yields,
2o(1-p)2/3p1/3 x (4Nn/3n)1/3 + (P-p)(1- p)=4 ri/3(dp/dt) (7)
when we assume gel is sintered in conventional pressure, P=0, the equation becomes:
dp/dt= (1- p)(3 a/2 Tjr 3p/4 r\) (8)
If there is no escape of gaseous water from the closed-pores, then combine Equation #4
dp/dt= (1- p)(3 a/2 nr) 3 NRTp/4 r\ (9)
and let dp/dt= 0, and use Equation #3, then a critical pore radius rm¡n is obtained:
rmin = (3nRT/8n a)1/2 (10)
By substituting Equation #10 into Equation #9, then, an expression for the maximum
value of density (pmax) is achieved:
pmax = 1/[(NRT/4 a )(3nRT/8rca)1/2 + 1] (11)
These two equations (#10,11) show that a maximum value pmax and a corresponding
critical pore radius rm¡n can be predicted in terms of the sintering temperature (T),
surface tension (a), the amount of free water in a pore (n) and the number of pores per
unit volume of silica (N/n). From this study the conclusion is reached that whenever the
residual surface water is released after the collapse or closing of the original open-
pores, then the free water in the gel structure follows the idea gas law at higher
temperatures to create closed-pores. Consequently, foaming of the gel happens and the
average radii of the pores increases significantly when temperature is just above 860C


248
58. Gerard Orcel, J. Phalippou, and L. L. Hench, Structural Changes of Silica
Xerogels During Low Temperature Dehydration, Journal of Non-Crystalline
Solids, Vol. 88, 1986, p. 114-130.
59. T. Izawa and S. Sudo, Optical Fibers: Materials and Fabrication. KTK Scientific
Publishers, sold by Kluwer Academic Publishers, Norwell, Massachusetts,
1987, p. 33.
60. D. C. Havard and R. Wilson, Pore Measurements on the SCi/IUPAC/NPL Meso-
Porous Silica Surface Area Standard, Journal of Colloid and Interface Science,
Voi. 57, 1976, p. 276-288.
61. Clarence L. Babcock, Refractive Index and Dispersion, in Silicate Glass
Technology Methods. John Wiley & Sons, Inc., New York, 1977, p. 87-114.
62. Du Pont Company, Du Pont 1090 Thermal Analysis System Manual. Du Pont Co.,
Wilmington, Delaware, 1983.
63. D. G. Holloway, The Physical Properties of Glass. Wykeham Publications Ltd.,
London, 1973, p. 143-149.
64. G. R. Anstis, P. Chantikul, B. R. Lawn, and D. B. Marshall, A Critical Evaluation of
Indentation Techniques for Measuring Fracture Toughness: I and II, Direct Crack
Measurements, Journal of American Ceramic Society, Vol. 64, 1981, p. 533-
543.
65. Perkin-Elmer Company, Perkin-Elmer Lambda 9 UV/VIS/NIR Spectrometer
Manual. Perkin-Elmer Co., West Germany, 1986.
66. Quantachrome Corporation, Autosorb-6 Manual. Quantachrome Corp., Syosset,
New York, 1985.
67. E. P. Barrett, L. G. Joyner and P. P. Halenda, The Determination of Pore Volume
and Area Distributions in Porous Substances, I: Computations from Nitrogen
Isotherms,Journal of the American Chemical Society, Vol. 73, 1951, p. 373-
380.
68. Jenkins and White, Fundamental of Optics. 3rd ed., McGraw-Hill, New York,
1957.
69. ASTM D790M-84, in Annual Book of ASTM Standards. 1986.
70. ASTM C158-80, in Annual Book of ASTM Standards. 1986.
71. D. B. Keck, R. D. Maurer and P. C. Schultz, On the Ultimate Low Limit of
Attenuation in Glass Optical Waveguides, Applied Physics Letters, Vol. 22, 1973,
p. 307-309.
72. G. H. Sigel, Ultraviolet Spectra of Silica Glasses: A Review of Some Experimental
Evidence, Journal of Non-Crystalline Solids, Vol.13, 1973/1974, p. 378-398.


191
Table 5-5
Refractive index measurements of the gel-silica glass and fused silica glasses
Test No. Index of refraction (n):
ID No. red e f h
Corning # 7940 Control Samples:
1)
CGW-1
1.45518
1.45639
1.45848
1.46010
1.46316
1.46965
2)
CGW-2
1.45516
1.45638
1.45848
1.46010
1.46317
1.46968
3)
CGW-3
1.45517
1.45639
1.45848
1.46010
1.46316
1.46965
Statistical Value:
1.45517
1.45638
1.45848
1.46010
1.46316
1.46966
()
0.00001
0.00001
0.00000
0.00000
0.00001
0.00002
NSG
"ES" Control Samples:
4)
MSG-1
1.45516
1.45638
1.45847
1.46009
1.46315
1.46965
5)
MSG-2
1.45517
1.45638
1.45848
1.46009
1.46315
1.46965
6)
NSG-3
1.45514
1.45636
1.45846
1.46008
1.46315
1.46967
Statistical Value:
1.45516
1.45637
1.45847
1.46009
1.46315
1.46966
()
0.00001
0.00001
0.00001
0.00001
0.00000
0.00001
Gel-Glass Samples:
7)
N34
1.45978
1.46102
1.46317
1.46483
1.46797
1.47464
8)
Q34
1.45936
1.46061
1.46276
1.46443
1.46057
1.47426
9)
Q27
1.45983
1.46109
1.46326
1.46448
1.46764
1.47435
11)
Q11
1.45994
1.46119
1.46334
1.46501
1.46817
1.47487
12)
Q30
1.45979
1.45104
1.46319
1.46485
1.46800
1.47468
Statistical Value
;
1.45968
1.46093
1.46309
1 .46476
1.46791
1.47461
()
0.00024
0.00024
0.00024
0.00024
0.00024
0.00024


198
The physical characteristics of silica glass, which generally include optical,
thermal, and mechanical properties, are interrelated. For example, in the gel glass
samples, having a large number of diffraction points or "microvoids", lower densities
were measured, and lower Knoop hardness values were obtained. Also, the degree of
inhomogeneity observed directly relates to the degree of refractive index variation
measured. These data are supported by the Lorentz Lorenz relationship, which
indicates that refractive index variation is the result of density gradients and/or
chlorine gradients within the gel glass.
Coefficient of thermal expansion (CTE) measurements from three testing
laboratories are listed in Table 5-7. Figure 5-17 presents that data collected by the
Optical Sciences Center of the University of Arizona, courtesy of Dr. Steve Jacobs.
Statistically, gel silica has a CTE value about two times lower and a more stable CTE over
a wide range of temperatures than ail five of the commercial glasses tested. As discussed
earlier the possible reason for the gel silica glass CTE behavior is the lower
concentration of cation impurities and a larger intermolecular space between the silica
structural units.
Density measurements made on three gel silica samples and two control samples
(Corning 7940, NSG-ES) are shown in Table 5-8. The densities of the gel glass
measured, on an average, 0.016 g/cm3 lower than the control samples. Micropores are
responsible for these somewhat lower density measurements.
Knoop hardness values were measured on one gel silica sample and one control
sample (Corning 7940) with the results shown in Table 5-9. The gel silica measured
lower than the control sample; however, the control sample measured significantly
lower than it's published data. Corning Engineering Laboratory Services reperformed
their tests and support those results. Though inconclusive, these data are an indication
that the first generation gel silica has a lower hardness than fused silica which is


106
Table 3-2
Mechanical properties of partially densified silica gels and fused silica
Temperature
C
Flexural strength
CTmax (MPa)
Maximum strain
Emaxi (AL/L x10')
Young's modulus
MPa
150
08.4
0.5
1060 201
07925
250
09.8
0.7
1071 178
09148
450
11.8
1.2
980 94
12035
750
25.0
2.3
876 157
28539
800
27.0
2.6
833 150
32413
830
30.4
3.6
826 121
36803
***For reference [76]:
fused silica
58.9
806
73089


44
At temperatures lower than the boiling point of the gel pore liquid the vapor
pressure in the liquid phase (P|) is less than one atmosphere; therefore, air will enter
the device to establish a vapor phase pressure (Pv) equal to 1 atm, resulting in a
differential vapor pressure (APV|) which is not zero (Figures 2-20 and 2-22(b)).
However, by maintaining a zero differential pressure the capillary force is eliminated
(Figure 2-23), thereby significantly removing the differential hydrostatic stresses
within the gel body and retaining the gels monolithic shape.
Structural Characterization
The gel consists of a three-dimensional network of silica particles rigidly linked
together. If the structure of the gel is relatively coarse, the gel body is fragile and likely
to shatter. If the structure of the gel is relatively fine, consisting of fibrillar chains of
very tiny particles, and therefore somewhat flexible, the gel will be strong enough to
shrink considerably without cracking. However, the shrinkage of a silica gel is
irreversible. Shrinkage occurs as the gel dries due to the surface tension of the liquid
within the pores. As drying occurs it is probable that certain bonds on the necks between
particles break, which allows portions of this area to be dissolved into the pore liquid
and transported to areas of negative curvature, as shown in Figure 2-24. This is because
solids minimize surface area so as to reduce surface energy to a minimum.
An equation relating the solubility of a curved solid surface in water to the radius
of curvature was derived by Ostwald and Freundlich [see p. 50-51 in ref. 4]:
Log(Sr/S¡) = KE/Tr (8)
where Sr is the solubility of a particle having a radius of curvature r; S¡ is the
solubility of a flat surface with a radius of curvature of infinity in that water; E Is the
surface energy of the solid; T is the temperature; and K is Boltzmann's constant. The
meaning of this equation is schematically illustrated by Her in Figure 2-25. As


186
Wavelength (nm)
Figure 5-10 Vacuum ultraviolet transmission of optical silicas
sample thickness: 3 mm.


177
Internal stress in glass can be produced by many factors such as mechanical stress,
thermal quenching, phase separation, crystallization, etc.. For example, If a piece of
glass quenched from high temperature has residual stresses (tension and compression)
and if light is propagated through such a glass the difference in refractive index between
the regions of stress results in stress birefringence. The birefringence is defined as the
numerical difference between the two refractive indices (e go) or a measure of path
difference, T, per sample thickness, L. Consequently, the birefringence can be expressed
as the retardation of light which is e a> = T/L where T is bXI2n, 5 is the phase
difference, and X is wavelength of incident light [see p. 339-341 in ref. 100].
To examine the stress induced birefringence the addition of two polarizing filters
and a rotatable stage converts a laboratory microscope into an polarizing microscope. If
a piece of strain-free glass is placed on the stage between these two crossed polarizers,
the glass remains dark no matter how the stage is turned; such a glass is isotropic.
Anisotropic glass, in contrast, has four positions of maximum extinction, 90 apart,
when the stage is rotated. The phase difference, 8, can be determined by measuring the
angle of rotation to give compensation.
To be optically useful a silica glass must be able to transmit electromagnetic waves
efficiently within the region in which it is to be used, i.e., it must exhibit a very low
scattering. For uniform interaction between light and glass, the glass should not only
have a homogeneous index of refraction but also be free of excessive striae, bubbles and
inclusions. In traditional melt glasses, these three types of defects are often found if the
thermal processes are inadequate. Striae result from incomplete homogenization and
high temperature mixing in the liquid phase prior to casting. Bubbles from chemical
reaction of raw materials and inclusions from unmelted high-temperature impurities on
the scale of micrometers to millimeters, and even larger, are formed and trapped during
an improper melting and cooling process. Consequently, it is necessary to examine
whether such imperfections are present in a gel glass.


I certify that I have read this study and that in my opinion it conforms to
acceptable standards of scholarly presentation and is fully adequate, in scope and
quality, as a dissertation for the degree of Doctor of Philosophy.
Larry L. Hench/Chairman
Graduate Research Professor of
Materials Science and Engineering
1 certify that I have read this study and that in my opinion it conforms to
acceptable standards of scholarly presentation and is fully adequate, in scope and
quality, as a dissertation for the degree of Doctor of Philosophy.
Professor of Materials Science
and Engineering
I certify that I have read this study and that in my opinion it conforms to
acceptable standards of scholarly presentation and is fully adequate, in scope and
quality, as a dissertation for the degree of Doctor of Philosophy.
Vellayan Ramaswamy
Professor of Electrical Engineering
I certify that I have read this study and that in my opinion it conforms to
acceptable standards of scholarly presentation and is fully adequate, in scope and
quality, as a dissertation for the degree of Doctor of Philosophy.
Gholamreza J. Abbaschian
Professor of Materials
Science and Engineering


182
Stress birefringence was qualitatively determined at the AMRC on "as cast",
partially dense (-60%) and fully dense gel-silica glass samples using two plane
polarized laminated plastic sheets.
Bubbles and inclusions were examined by Glass Fab using a Nomarski phase-
contrast microscope. In this test the magnification is set at 400X and the resolution is 1
micrometer. The number of bubbles and inclusions were counted in a volume 0.02 mm3.
Volumes were randomly selected in each quadrant and at the center of the samples. The
sampling volume was defined by a 0.5 mm diameter field of view and a 0.1 mm sweep
inside the sample about 0.5 mm from a polished face, as shown in Figure 5-8.
Impurity levels were measured in a gel glass sample by the Department of Nuclear
Engineering, North Carolina State University using a neutron activation analysis
technique [108] to measure the number and energy of gamma and x-rays emitted by the
radioactive isotopes produced in the sample matrix. This method involves irradiation of
the test sample with thermal neutrons from a nuclear reactor at a selected time period.
Quantitative analysis was obtained by comparing the number of characteristic x- or
gamma rays detected from the gel glass with the number determined for appropriate
standards.
Other physical properties measured included coefficient of thermal expansion,
specific gravity and knoop hardness.
Coefficient of thermal expansion (CTE) values from room temperature to 773 K
were measured on one gel glass sample by the Materials Research Laboratory,
Pennsylvania State University using a laser speckle dilatometer and on one gel glass
sample by Orton Jr. Ceramic Foundation, Ohio, using an automatic recording dilatometer.
The new laser speckle method [109] was based on the movement of a laser beam
reflected from a probe bar caused by thermal expansions of the sample and reference
rods as shown in Figure 5-9. The reflected laser beam was observed with a small
photodetector. A minute change in the laser beam position thus results in a precision


216
negative charged ligand
Figure 6-6 Interaction of one of the dxy dyz dzx orbitals of a central ion with four
ligands in a tetrahedral field.


184
Figure 5-9 Schematic diagram of a laser speckle diiatometer


40
stress initiated crack lines
Figure 2-20 Differential evaporation.


163
Table 5-1
Impurity levels in TEOS (ppb).
Al = 20
Li < 10
Cu < 10
Fe
Ca =50
Mn < 10
Ti < 20
Mg
Co < 50
Na = 30
Cr < 50
Zn
K = 100
Ni < 100
= 1000
= 100
< 50


Tensile stress in surface
104
P
Compression
Tension
Figure 3-20 A three-point bending test.


250
89. J. A. Hockey and B. A. Pethica, Surface Hydration of Silicas, Transactions of
Faraday Society, Vol. 57, 1961, p. 2247-2262.
90. A. V. Kiselev, Structure and Properties of Porous Materials, Colston Papers, Vol.
10, Butterworth, London, 1958, p. 195.
91. R. S. McDonald, Surface Functionality of Amorphous Silica by Infrared
Spectroscopy, Journal of Physical Chemistry, Vol. 62, 1958, p. 1168-1178.
92. J. H. Anderson Jr. and K. A Wickersheim, Near Infrared Characterization of
Water and Hydroxyl Groups on Silica Surfaces, Surface Science, Vol. 2, 1964, p.
252-259.
93. J. B. Peri, Infrared Study of OH and NH2 Groups on the Surface of a Dry Silica
Aerogel, Journal of Physical Chemistry, Vol. 70, 1966, p. 2937-2945.
94. N. W. Cant and L. H. Little, The Infrared Spectrum of Ammonia Adsorbed on
Cab-O-Sil Silica Powder, Canadian Journal of Chemistry, Vol. 43, 1965, p.
1252-1254.
95. N. W. Cant and L. H. Little, An Infrared Study of the Absorption of Ammonia on
Porous Vycor Glass, Canadian Journal of Chemistry, Vol. 42, 1964, p. 802-
809.
96. M. L. Hair and I. D. Chapman, Surface Composition of Porous Glass, Journal of
the American Ceramic Society, Vol. 49, 1966, p. 651-654.
97. T. H. Elmer, I. D. Chapman and M. E. Nordberg, Changes in Length and Infrared
Transmittance During Thermal Dehydration of Porous Glass at Temperatures Up
to 1200C, Journal of Physical Chemistry, Vol. 66, 1962, p. 1517-1519.
98. M. R. Basila, Hydrogen Bonding Interaction between Absrbate Molecules and
Surface Hydroxyl Groups on Silica, Journal of chemical physics, Vol. 35, 1961,
p.1151-1158.
99. V. Y. Davydov, L. T. Zhuravlev and A. V. Kiselev, Study of the Surface and Bulk
Hydroxyl Groups of Silica by Infrared Spectra and D20-Exchange, Transactions
of Faraday Society, Vol. 60, 1964, p. 2254-2264.
100. Jurgen R. Meyer-Arendt, Introduction to Classical and Modern Optics. Prentice-
Hall, Inc., New Jersey, 1984.
101. Ivan Fanderlik, Optical Properties of Glass. Glass Science and Technology 5.
Elsevier, New York, 1983.
102. Kurt Nassau, Part II: Color Involving Vibrations and Simple Excitations, in The
Physics and Chemistry of Color-The Fifteen Causes of Color. Wiley-lnterscience
Publication John Wiley & Sons, inc., New York, 1983, p. 65-76.
103. G. William Tasker and William G. French, Low-Loss Optical Waveguides with
Pure Fused Si02 Cores, IEEE, Vol. 62, 1974, p. 1281-1282.


77
Acs is 16.2 2 and M is the molecular weight of N2. (5) A=At/W In which A is specific
surface area of sample and W is the sample weight.
The total pore volume (V|¡q) is derived from the amount of N2 adsorbed at a
relative pressure close to unity, by assuming that the pores are all filled with liquidized
N2 of a volume Vliq which can be calculated using equation (V|jq/Vm)RT=PaVads where
Vm is the molar volume of the liquid N2, Pa is ambient pressure, and Vacjs is vaporized
pore liquid (N2).
The average pore size can be estimated from the pore volume, by assuming
cylindrical pore geometry; then the average pore radius rp can be derived as rp =
2V|¡q/A. The pore size distribution is calculated using the method proposed by Barrett,
Joyner and Halenda [67].
Samples heated to the temperatures designated in Table 3-1 and cooled to room
temperature with the heating program shown in Figure 3-3 were ground into powder
and weighed to around 0.6 gram in the pellet cells before installing in the Autosorb-6
system for outgassing and preheating to eliminate the water moisture. The outgassing
and preheating was held for 15 hours at 200C in N2 gas atmosphere. Consequently,
samples were transferred to the ports of the system for nitrogen adsorption-desorption
isotherm measurements. Data were automatically accumulated in the mirocomputer and
the results printed out .
The X-ray diffraction analysis was obtained using a Philips diffractometer at room
temperature with a 40Kv CuKa radiation and a nickel filter. The samples heated to the
temperatures designed in Table 3-1 and cooled to room temperature with heating
programs shown in Figure 3-3 were ground and scanned at a rate of 6/min from 29
angles of 10 up to 50.
The index of refraction was obtained using a Pulfrich refractometer and a HeNe
laser light source which wavelength is 632.8 nm. The principle of the refractometer is
based on the measurement of the critical angle 4>c. which is the angle of the interface


Attenuation dB/Km
164
700 800 900 1000 1100 1200 1300 1400 1500 1600
Wavelength (nm)
Figure 5-1 Typicai spectra! loss curves of silica optica! fibers.


220
b: (2 holes) d3, d8 in octahedral field
(2 electrons) d2, d7 in tetrahedral field
a: (2 electrons)
(2 holes)
d2,d7 in octahedral field
d3, d8 in tetrahedral field
Figure 6-8 Two lowest energy levels for d2, d3, d7, d8 splitting configurations in
octahedral and tetrahedral fields.


176
nm), the blue hydrogen f line (486.1337 nm), and the red hydrogen c line (656.2725
nm). The numerical difference between the two indices of refraction at the f and c lines
is called the mean dispersion (nf nc). The ratio (nf nc)/(nd 1) is the dispersive
power. Its inverse is called Abbe's value, (rtd -1}/ (nf nc). The dispersion of the gel
derived silica glasses developed herein is described in a later section.
Examination of the homogeneity of a piece of glass for optical applications is very
important since the wavefront of incident light can be distorted by any variations of
index of refraction in a nonhomogeneous glass. Index variations can be caused by
localized thermal gradients which induce density gradients. Such inhomogeneities can
result from either an improper sintering process or impurity fluctuations within the
densified glass. Consequently, careful control of both densification and the dehydration
process is necessary to provide a uniform refractive index throughout the gel glass body.
Interferometry is a precision measurement which can be used to examine the
quality of a material surface, to metrology, to the alignment of optical and mechanical
components, or to examine the differences in optical path length (S = Ln where S is
optica! length, L is sample thickness, n is index of refraction) in a glass. The path
difference, T, is the difference between two such path lengths, T = S2 Si = L (n2 -
n 1), where thickness L is constant. From Young's double-slit experiment, T can be
expressed as T =mA. where m is the order of interference or the number of fringes.
By rearranging the two equations above we have m = L(n2 n-|)/k[see p. 187-
204 in ref. 100]. Consequently, for a piece of glass with two perfectly parallel surfaces
and constant thickness, any internal irregular variation of refractive index results in an
irregular fringe shift pattern on an interferogram. An interferogram always shows
alternative dark bands and white bands with one fringe corresponding to one pair of
white and dark bands. This is the method used to examine optical homogeneity in the
densified gel-glass samples.


165
metallic ion impurities has been made by Susa showing a low-loss 5.9 dB/km at 850 nm
[104]. The gel-glass monoliths developed herein should have equivalent or even better
quality.
The infrared absorption (IR) spectrum of a glass can be used as a tool to understand
the chemical composition, molecular vibrations and the molecular bonding within the
material. According to both classical and quantum theories, as two atoms with partially
filled outer electron orbital approach each other the energy will either increase or
decrease. For example, if two outer electrons, one from each atom, have parallel
oriented spins, the result will be repulsion and the energy will increase. The closer they
move together, the higher the repulsive force, consequently, the atoms will move apart
resulting in an antibonding molecular orbital arrangement. If the spins are antiparallel,
the result will be attraction and the energy will decrease. The lowest energy is achieved
when the bonding takes place as the two orbitals overlap and electrons are shared by two
atoms. If the atoms come too close together, the repulsive force rises due to two
positively charged nuclei. The energy curves of this bonding (Morse curve) and
antibonding system is shown in Figure 5-2 [see p. 381-408 in ref. 102].
Atoms in a molecule can vibrate harmonically but not symmetrically with the
atoms moving together and moving apart as a stretching mode. This vibration of a bonding
molecule can be expressed as a horizontal line at a certain temperature within the
bonding cun/e of Figure 5-3. As shown in quantum theory, the vibration levels are not
continuous and always have many rotational levels associated with a vibration level and a
lowest possible energy level, called zero point energy, must exist even at 0K. The
higher energy level of a stretching vibration results in a larger average displacement
between two nuclei. Any vibration energy higher than the destruction of the bonding
energy will move atoms apart. The vibration frequencies of all molecules is so low that
the energy involved is too small to interact directly with visible light; however, the
absorption due to vibrational transitions between the vibrational ground state and


13
obtained from supersaturated aqueous solutions produced by one of the following
methods:
(I) Concentrating an unsaturated silica solution by evaporating its solvent.
(11) Cooling a hot saturated silica solution.
(I i i) Lowering the pH of an aqueous solution of a soluble silicate below 10.7.
(Iv) Hydrolyzing SI(OR)4 -- (where R is CH3, C2H5, or C3H7).
In this study all of the monomers were produced by chemically hydrolyzing
tetramethylorthoslllcate (TMOS), as indicated in method (lv). The amount of monomer
generated within a given period of time depends on temperature and the relative amounts
of DCCA, water, and TMOS. When a solution of monomer, Si(OH)4, is formed at a
concentration greater than the solubility of the solid phase of amorphous gel silica in
water, and In the absence of a solid phase on which the soluble silica might be deposited,
the monomers then polymerize by condensation to form dimers (two silicons), then
tetramers (four silicons), then particles (eight or more silicons). For most alkoxide
syntheses, a polymerization reaction occurs before hydrolysis is completed (as
evidenced by 29Si NMR studies [37, 38]). As shown in Figures 2-1 and 2-2, the
particle's size at any moment of growth is controlled by the Ostwald ripening mechanism
[see p. 175-220 in ref. 4] and essentially is determined by the pH of the DCCA/silicic
acid solution.
Vysotskii and Strazhesko [39] describe that in the presence of a given acid, the
growth of monomers is governed by the chemical equilibrium kinetics of the sol and is
minimized at the isoelectric point (iep). This implies that the monomers grow to some
certain size before the solution reaches its own iep. The iep occurs when the net
electrical mobility of surface ions on the silica particles is zero and at a pH at which
there is no charge outside the hydroelectric slip plane (outside this plane the liquid is
free to move, inside the plane the liquid molecules are held too tightly to move) [see p.


204
Table 5-10
Preparation and characteristics of five types of silica glass
Type of Silica l II
III
IV
V
Electromelted Flame-Fused
Hydrolyzed
Oxidized
Dense
Quartz Quartz
Tradenames
SiCI4
SiCI4
Gel-Silica
Vitreosil-IRa Homosilb
lnfrasilb NSG-OXe
Optosilb
Total Cation:
7940c
1000d
Suprasilb
NSG-ES
Spectrosil WFa Gelsilf
7943c
Suprasil-Wb
(ppm) 30-200 1 0-30
OH'1 group:
1-2
1-2
1 -2
(ppm) <5 150-1500
Cl'1:
600-1000
0.4-5
<1
(ppm) 0 0
UV 50% transmission:
100
< 200
< 1000
(nm) 212-223 210-220
Thermal Expansion Coefficient:
165-188
165-180
165-168
(x107) 5.4 5.5
Bubbles and Inclusions:
5.5-5.7
5.5
2.0
(# / i n 3) 0-8 0-5
Strain:
0-3
0-2
0
(nm/cm) 5-10 5-10
Refractive index:
5-10
1 0-40
5
(nd) 1.458 1.458
Dispersion:
1.458
1.458
1.458-1.463
(ud) 67.8 67.8
Density:
67.8
67.8
66.4 -67.8
(g/cm3) 2.21 2.21
2.20
2.20
2.20
a = Thermal American Fused Quartz; Montville, NJ.
b =Heraus Amersil; Sayrevilie, NJ. c = Coming Glass Work; Corning, NY.
d = Dynasil; Berlin, NJ e NSG quartz; Japan,
f = Material Engineering & Science, University of Florida & GelTech, Inc.; Alachua, FI.


Temperature (C)
37
Figure 2-18 The time silica gels shrink to 72% of original volume versus
aging temperatures inside 100 cc polystyrene cylinder.


180
3200 nm range at the AMRC on approximately 50 unpolished gel-silica glass samples
using a double-beam Perkin-Elmer Lamda 9 UV/VIS/NIR spectrophotometer, Model 33,
slit width 1 nm, with an uncertainty of 1%.
Infrared transmittance was also measured in the 2500 nm to 5000 nm range by
Glass Fab using the spectrophotometer previously mentioned.
Refractive indices were measured by Glass Fab on a Pulfrix Abbe Refractometer
using four special light sources, isolating the six spectral lines at which the tests were
conducted, as listed in Table 3. Calibration was accomplished by use of a standard index
sample certified by the National Bureau of Standards (NBS) accurate to 1 x 10'5.
Dispersion (dn/c&) values were calculated from refractive indices at different testing
wavelengths in according with the Abbe's value vd = (nd 1)/ (nf nc) defined in
Section II of this chapter.
Homogeneity of the gel glass and control samples was checked for wavefront
distortion by Glass Fab on a Zygo Zapp Interferometer. Samples were examined and then
additionally tested using oiled-on master plates to eliminate any effects of polishing.
Striae tests were made by Glass Fab using a pin hole arc lamp to project an image
10 time size onto a projection screen. In this test any striae in a glass appear as fine
lines on the screen.
Stress birefringence tests were performed by Glass Fab using a Fridel Polariscope,
Polarmetrics Model 35 polarimeter. Prior to cutting, polished samples were examined
in two directions. Any visible strain appeared as a field change (a twist of the polarized
length). Using a rotating eyepiece, the field was rotated until the field change was
reversed. This angle change was used to determine the retardation level, R, (strain)
using the formula: R = 3.3 A/T, where A is angle of rotation to give compensation, and T
is thickness of sample.


137
More importantly, Hair mentioned that when the silica gel has been completely
dehydrated, there are no surface hydroxyl groups to adsorb the free water; in other
words, the surface is essentially hydrophobic. Clearly, it is the realization of this
critical point that is the focus for this study.
The vibrational overtones and combinations of hydroxyl groups and their associated
molecular water, occurring in the 1250 nm to 3000 nm range, have been studied by
Anderson and Wickersheim [92]. Evaluation of a partially dehydrated (800C) silica gel
shows an absorption peak at 01 = 2668.80 nm (see Fig. 4-5), surely due to the
fundamental stretching vibration of hydroxyl groups on the gel surface. These singular,
or free, hydroxyl groups are also referred to as "isolated silanol groups". The
symmetrical appearance of this peak indicates that these singular hydroxyl groups have
no interaction with water molecules. The band at 1366.12 nm {2x>2) is the first
overtone of the adjacent silanol group vibration U2 = 2732.24 nm (see Fig. 4-2). The
1366.12 nm peak becomes less intense as the gel is heated and disappears with complete
dehydration. The combination peak at 2207.51 nm (x>2 + uoh (bend)) is the result of
the hydroxyl ion's stretching and bending vibrations, where doh is a bending wavelength
between 11494.25 nm and 12345.67 nm. Researcher Peri [93] suggests that this
combination band is due to the Si-O-H stretching vibration and an out-of-plane O-H
displacement (bending) vibration. This type of hydroxyl group is labeled an OH(2)
group.
The adjacent hydroxyl groups also interact with free water (03, see Fig. 4-4) to
form hydrogen bonds; this effect causes a change in both the fundamental stretching
vibration and its associated overtones and combinations. Therefore, the hydroxyl groups
associated with water show a new combination peak at 2262.44 nm (u3 + uoh (bend));
this kind of hydroxyl group is called QH(3). The energy calculations, by Benesi and
Jones [88], predict that the fundamental stretching vibration of OH(3) at 03 = 2816.88
nm is a value shifted about 148.08 nm from the vibration of the free hydroxyl group at


205
The gel glass coefficient of thermal expansion is linear over a wide temperature
range and lower than that of any previous fused silica. Less impurities and/or a larger
intermolecular volume may account for both the low and anomalous thermal expansion
behavior.
Elimination of the density variations, microvoids and micropores can be
accomplished with a final optimization of the sol-gel process. More precise control of
the thermal program and the dehydration technique in densificaron process will make it
possible for gel silica glass to approach the theoretical optical performance of an ideal
silica glass.


183
gel glass sample
Figure 5-8 Volume for counting "bubbles or stars"


90
80
70
60
50
40
30
20
10
0
relative time scale
Figure 2-2 Polymerization reaction occurs before hydrolysis is completed


P(air) = one atmosphere (1 atm)
^atm(air) ^vapor ^liquid
Figure 2-23 Situation to avoid cracking.


134
densification. It is shown in Chapter 3, based upon UV-VIS-NIR data, that the reduction
of surface hydroxyl groups occurs above 400C.
4. Viscous flow occurs above 850C with the exact temperature depending on the
particle size of a specific gel. The singular hydroxyl groups on the gel surface react with
each other bringing particles together, thereby eliminating voids within the gel. Some
surface water, which is unable to be desorbed prior to pore closure, is trapped inside
the densified gel.
Young, in his early work, found that the decrease in surface area of the silica gel at
high temperatures is a function of the time and temperature of the heat treatment. This
supports the concept that the sintering mechanism is essentially the result of viscous
flow, rather than surface diffusion. Impurities (i.e., surface water) effectively lower
surface energy and thereby the sintering temperature, presumably by facilitating
viscous flow; Zarzycki, et al. [73] confirmed this point.
Hair [see p. 87 in ref. 27] also proved that heating silica gel in the 170C to
400C range causes reversible dehydration via elimination of surface water and the
formation of both single and adjacent surface hydroxyl groups, as illustrated in Figure
4-2. Hair found that at 400C, no more than half of the surface hydroxyl groups had
been desorbed and that most of the remaining surface hydroxyl groups were adjacent to
each other and therefore situated for preferential water adsorption, shown in Figure 4-
4. He stated that heating the gel above 400C causes a drastic, irreversible elimination
of adjacent hydroxyl groups, as shown in Figure 4-3, until at about 800C, only single
hydroxyl groups remain, as shown In Figure 4-5. As the temperature increases, single
hydroxyl groups depart from the gel surface until the gel is densified; this occurs in the
850C to 1000C range. However, some single hydroxyl groups are still unable to
escape from the gel surface and therefore can contribute to foaming of the gel as the
temperature increases.


absorptance
155
Wavelength (nm)
0.40 r
(b) 1150C sample
0.20 -
0.00 fi I i I i I i I i
200 800 1400 2000 2600 3200
Wavelength (nm)
Figure 4-17 Absorption curves of gels partically densified in controlled CCI4
atmosphere tor a 1050C sample of 3.6 mm thickness and
a 1150C sample of 3.4 mm thickness.


66
Monolithic gels with an optimal ultrastructure and high resistance to drying
stresses, which are chemically controlled (by adding acidic DCCA) and physically
stabilized (by introducing a drying device), are identified by a change in visible light
scattering during the drying process. The optical sequence for a drying gel is as follows:
complete transparency with a very slight blue tone, followed by an opaque stage,
followed by transparency. These changes in optical properties can be used to monitor the
drying process and therefore offer the potential to be used in a feedback loop to optimize
drying. Monitoring weight loss can also help to achieve the final stage of drying: when
the theoretical molecular weight of silica is reached, drying is finished. This process can
be automated and used with computer aided processing.
The fully dried gels can be modified by liquid phase impregnation of various
chemical species (e.g., compounds of transition or rare earth elements) into the dried
gel. Because of the extremely small size (10 100 ) of the ultrapores in the gel, it
is possible to introduce a very homogeneous ion distribution within the gel matrix. For
measurements the physical properties presented in Chapter 3, the ultraporous dried
silica gels are converted to partially dense monoliths by heating from 150C to 900C
over times ranging from one day to one week.


140
Wavelength nm
Figure 4-6 Transmission curve from Corning Glass Co. commercial UV grage optical
melt silica Code 7940. Thickness 10 mm.


Temperature (C)
Figure 3-11 Specific surface area versus temperature.


68
Fourier-transform-infrared (FTIR) spectroscopy, ultraviolet-visible-near-infrared
spectroscopy (UV-VIS-NIR), N2 adsorption-desorption isotherms interpreted using
Brunauer, Emmett, Teller (BET) analysis which includes specific measurements of
surface area, pore size distribution, pore volume, and pore radius, as well as large angle
X-ray diffraction. Optical information was obtained soiely using an index of refraction
test. Thermal data were collected from differential scanning calorimetry (DSC),
differential thermal analysis (DTA), thermogravimetric analysis (TGA), and
thermomechanical analysis (TMA). Mechanical properties (gel strength) were
determined using flexural strength, compressive strength, microhardness, fracture
toughness and density measurements.
Review of the Literature
Three mechanisms of densification are summarized by Zarzycki, et al. and
Brinker, et al. [25, 57]: (1) polymerization reactions which serve to crosslink the
network and partially release the surface hydroxyl groups, thereby forming free water;
(2) structural rearrangements that occurs when segments of interparticle necks are
broken and other neck segments become connected; and (3) viscous sintering
accompanied by the combination of surface hydroxyl groups. The first two mechanisms
cause a slight density increase; the third mechanism is a result of high temperature
viscous flow which eliminates the pores so that the bulk density approaches that of fused
silica. No gel can be completely dehydrated and converted into a fully dense glass (i.e.,
without foaming) in an ordinary air-atmosphere furnace; but fortunately, the gel can be
partially sintered to & desired temperature, below the foaming point, and cooled to room
temperature while remaining intact.
Any material can give rise to absorption or emission of radiation within the
allowed transitional, vibrational, and/or rotational energy levels. Infrared spectroscopy


21
particles surface exposes positively charged electric
cloud toward negatively charged monomer in the weak
acid solution.
electrical double layer
Figure 2-6 Particles in weak acidic solution. pH>iep (pH 2.0 pH 7.0).


219
(hole) d4, d9 in octahedral field b: (electron) d1, d6 in octahedral field
(electron) d1, d6 in tetrahedral field (hole) d4, d9 in tetrahedral field
Figure 6-7 Three lowest energy levels for d1, d6, d4, d9 splitting configurations in
octahedral and tetrahedral fields.


Experimental Procedure 229
Results and Discussions 230
Conclusions 238
7 CONCLUSIONS AND RECOMMENDATIONS 239
REFERENCES 244
BIOGRAPHICAL SKETCH 252
v


Young's modulus (MPa)
121
80000
60000
40000
20000
1.2 1.4
1.6
1.8 2.0 2.2
Density (g/cc)
Figure 3-30 Young's modulus versus density.


absorptance
150
0.00 l_ I l L I I I L
200 800 1400 2000 2600
Wavelength (nm)
curve a is the spectrum of 150C sample
curve b is the spectrum of 750C sample
curve c is the spectrum of 800C sample
curve d is the spectrum of 850C sample
j
3200
Figure 4-14 Absorption curves of partially densified gels in air.


105
under the stress. Samples can be loaded and stressed up to the proportional limit
(rupture point at a maximum tensile stress amax). Elastic strain is directly
proportional to the applied tensile stress, a, by following the Hooke's law (a = E e where
a is tensile stress, E is Young's modulus of elasticity for bending test, e is elastic strain.
See ASTM D 790M 84) and is recoverable below cmax. In this test, the load to failure
was calculated using the equation [see p. 156-158 in ref. 63]:
o 3Pi L/2bd2 0 cr < CTmax (14)
where
a : tensile stress on the outer surface at midspan, pascal (newton/m2),
Pi : load at a given point on the load-deflection curve, N (newton),
L : support span distance, m,
b : width of specimen, m, and
d : thickness of specimen, m.
the elastic strain before or at fracture was obtained using equation [69]:
e = Zt = 6Rtd/L2 = 6Dd/L2 0 where
e : strain, mm/mm, emax is the maximum strain at amax
Z : strain rate, mm/sec,
t : time, sec,
R : rate of crosshead motion, mm/min,
D : midspan deflection, mm.
The variation of maximum flexural strength (amax), maximum strain (emax).
Young's modulus of elasticity (E = omax^max) with standard deviations for each set of
five samples prepared at different temperatures are listed in Table 3-2 and shown in
Figures 3-21, 3-22, 3-23. A large increase in flexural strength was noted above
700C (Table 3-2, Fig. 3-21). The specimen heated to 830C has a value of about 30.4
MPa which is about half the value of fused silica glass (58.9 MPa) [76]. The obtained


8
This over-saturated sol is never chemically stable in the presence of the DCCA
and/or under thermally activated conditions; however, after some time and with the
addition of thermal energy a sufficient concentration of colloids that are within an
appropriate size distribution is reached and a zero surface charge is obtained [21]. At
this point the colloids become randomly linked together in fibrillar chains with
thermally activated Brownian motion in the presence of a Van der Waals attractive force
and a base catalyst [see p. 224 in ref. 4]. As the chains grow they form three-
dimensional irregular structures throughout the liquid phase. A network develops with
the liquid phase localized within the solid gel skeleton and microscopically confined by
it. The "sol" has lost its freedom of movement and now becomes a "gel; this is described
as the gelation point.
Solids tend to decrease their interfacial area so as to minimize surface energy.
Therefore, after the gelation point has been reached the weakly connected spherical-
particle chains tend to minimize surface energy by particle rearrangement, thereby
forming a strong fibrillar-shaped ultrastructure. This phenomenon continues during the
aging process (also termed syneresis), in which liquid is expelled from the gel body and
the weak gel shrinks and becomes stronger.
In this study the first goal, described in Chapter 2, is the production of silica-
based monolithic dried xerogels composed of (a) pure silica and (b) doped with
transition-metal elements. A xerogel is defined as a gel from which the liquid phase has
been evacuated under ambient pressures. The net size and porosity of a xerogel is
minimized, at least to some degree, by surface energy as the liquid is removed. However,
without the help of the DCCA in controlling the colloidal particle size, this can not be
realized because of cracking during drying.
in the amorphous form of silica, a tetrahedral arrangement is primarily favored
by the radius ratios of the silicon to the oxygen ions and by the bonding of sp3 hybrid
orbitals in SO2. X-ray diffraction studies by Mozzi, Warren and Uhlmann [22, 23]


157
Samples which had been heated to 1050C in the tube furnace were aged for
various durations in air: 1 day, 2 days, 4 days, and 7 days. The density, surface area,
total pore volume, and pore radius measured were 1.89 g/cm3, 187.23 m2/g, 0.14%,
and 11.07 respectively. The resulting absorption spectra from each of these samples
indicates the readsorpfion of molecular water with the corresponding reappearance of a
broad absorption peak in the 2863.2 nm to 2898.5 nm range and shows no overtone or
combination peak, as shown in Figure 4-19(a), (b), (c), and (d).
On the other hand, the samples which were heated to 1150C in the tube furnace
and aged in air for 7 days, 14 days, and 30 days showed no evidence of readsorption as
shown in Figure 4-20(a), (b), and (c). Consequently, the dehydration and densification
of gel-silica monoliths as developed in this study results in an optical material
equivalent to the best Type IV silica. However, the temperature of densification has been
reduced to 1150C.
Conclusions
The second goal of this study, which was to achieve dehydration of monolithic
xerogels, has been accomplished. All the absorption peaks and bands in the range from
200 nm to 4400 nm due to the presence of pore water and surface hydroxyl groups were
identified. Monolithic gel-glasses were routinely produced by this sol-gel method in
conjunction with the carbon tetrachloride treatment. These completely dehydrated
samples were able to reach and maintain a completely hydrophobic surface. Further
evidence that these samples were completely densified is supported by mercury-
displacement density measurements, with a resulting average value of 2.2 g/cm3-the
density of fused silica glass of Types I, II, III, IV. The optical properties of these fully
dehydrated gel-glasses will be evaluated in Chapter 5.


131
Figure 4-1 Physical water decreases and silanol groups condense
in the range of room temperature and 170C.


81
same number of samples and processing temperatures were used as that of flexural
strength test.
Microhardness values were obtained using a 136 diamond pyramid indenter at a
50 gram load with the Micro Hardness Tester, model M-40Q F (Leco Co. Japan).
Samples were heated to the designated temperatures (see Table 3-1) and cooled with
heating programs shown in Figure 3-3. Then, the samples were placed under the
indenter and applied with the 50 gram load. Two diagonals of the indenter were produced
on the surface of the sample. The DPN can be calculated by measuring the average length
of two diagonals through the microscope on the instrument. In this test five Indentations
were performed on each sample to obtain the data.
Fracture toughness values were calculated using the extended crack lengths from
the two stamped diagonals created by the diamond indenter on the surface of gel during
the Vickers microhardness test. The calculations used to convert indentation length to
fracture toughness are described by Anstis' relationship (Equation #16) [64] in the
Results and Discussions of this chapter.
Density of the samples was determined using a simple mercury displacement
technique. Samples followed the heat treatments shown in Table 3-1 and Figure 3-3
were immersed into a pycnometer. By knowing the sample weight, the corresponding
weight of mercury displacement, and the density of mercury, the density of the sample
was calculated.
Results and Discussions
Figure 3-5 shows the FUR spectra for the partially densified gels heat-treated at
various temperatures. The samples were scanned between 200 cnr1 (50000 nm) and
5600 cm'1 (1786 nm). The results show that the Si-O-Si molecular stretching


147
1200
F'9ure 4-12 Fr,
2FOUrh^ogram
IS for controlled
a,mWre,umace


227
(b)
Figure 6-13 Ligand group orbital and central matching atomic orbitals
of the bonding symmestry.


bonding strength which can produce a dramatic shift in their color response. For
example, a 160C silica xerogel containing 0.25% cobalt Is a reddish-orange color,
whereas the 850C sample is a deep blue, and the 900C sample has a greenish-black
color.
Finally, a summary (Chapter 7) is presented which reviews the present state of
sol-gel processing science as applied to gel-silica optical monoliths and the properties
of these unique materials. Questions still to be answered by future investigations are
also included in the summary chapter.


Total pore volume (cm*3/g)
89
Temperature (C)
Figure 3-10 Total pore volume versus temperature.


Pore radius ()
87
£
i
x, ;
T '
3
V 1
0 200 400 600 800 1000
Temperature (C)
Figure 3-8 Pore radius vs. temperature


optical density (OD)
236
350 550 750 950 1150 1350
wavelength (nm)
Figure 6-18 Absorption spectra of a Ni^-doped silica gel sample, a Ni" water
solution and a Ni^-doped 16.2 mol% K2O-B2O3 glass.


71
A profile of gel skeleton
Figure 3-2 Water terminates the Si-O-Si bridging bond on the particle's surface.


85
Samples heated to different temperatures are compared with a pure silica melt
glass (Dynasil) in terms of the cut-off wavelength, as shown in Figure 3-7. Increasing
the temperature of the thermal treatment increases the optica! transmission near the UV
absorption end and shifts the uv cut-off to the short wavelength for the pure silica gels,
apparently as the result of a decreased water content in the high temperature samples.
As Sigel concludes [72], the introduction of one electron valent elements (i.e. H,
Li, Na, K, Rb, Cs, Fr, F, Cl, Br, I) produces a noticeable shift of the uv edge to longer
wavelengths. This shift is because these elements terminate the bridging oxygens (BO)
into nonbridging oxygens (NBO) and provide lower energy exciton levels for photo
electron excitations. More water-related phenomena will be discussed in detail in the
dehydration study in Chapter 4.
Another important analytical technique for understanding the ultrastructure of
partially densified gels is the N2 adsorption-desorption isotherm analyses. The results
include analysis of the variation of average pore radius, pore radius distribution,
specific surface area, and pore volume with densificaron temperature, as shown in
Figures 3-8, 3-9, 3-10, and 3-11. There was no significant change in pore size
(Figures 3-8 and 9) while the total pore volume and surface area decreased (Figures 3-
10 and 3-11) with temperatures up to 860C. An assumption is that the pores decrease
in number and force the entire gel body to contract. This is because the pores are very
small (in this study, the mean pore diameter is only 2.2 nm). Consequently, they
essentially obey the mechanism presented by the Ostwaid-Freundlich equation,
log(Sr/S¡) = KE/Tr, stated in Chapter 2 Equation #8 and illustrated in Figure 2-21.
Once the pores start to decrease in size, the rate of decrease becomes very fast and they
immediately fill and disappear under the assistance of the migration of silanol groups
along the interior surface and/or migration of vacancies through the structure to the
exterior of the gel. Therefore, the gel shrinks as the temperature increases as a result of


146
Time (hour)
Figure 4-11 Heating cycles for air atmosphere furnace.


211
Ligand configurations:
dx2.y2
(a) five unspilt d orbitals in a free ion.
(b) five splitfeet d orbitals in an octahedral field.
(c) five splitfed-d orbitals in a tetrahedral field.
(d) five splitfed d orbitals in a tetragonally
distorted octahedral field.
(e) same as (d) but relatively strong distorted.
(f) five splifted d orbitals in a square planar
ligand field.
*
B
dx2.y2 .
dx2-y2 /
eg: dx2.y2 dz2 y* 2iL
,p-fi y.
4 <
dxy dyz c!zx
L0
/____
|o.6V'
i *
L_i/
dx2.y2 diz2
dxy dyz dzx \
*^ = 4/9 4,
ft
ft
ft
I
0.6^
t__
' 0.44a
d,2 \
xy /'
V
/v
4 \
* \
*2g: dXy dyz dzx \
d,2\
.ft. .
ft
ft
dzx dyz 'sx
dzx dyz
\ ^zx dyz
dz2
(C)
(a)
(b)
(d)
(e)
(f)
Figure 6-2 Spotting of the five d orbitals in various types of ligand fields.


70
V y
cut-off profile magnified in Figure 3-2
Figure 3-1 Random sampling profile of gel skeleton.


251
104. K. Susa, S. Satoh, I. Matsuyama, and T. Suganuma, New Optical Fiber Fabrication
Method, Electron. Lett., Vol.18, No. 12, 1982, p. 499-500.
105. Table of Periodic Properties of the Elements, Sargent-Welch Scientific Co.,
Skokie, Illinois.
106. Kenzo Susa, Iwao Matsuyama, Shin Satoh and Tsuneo Suganuma, Reduction of
Chlorine Content in Sol-Gel Derived Silica Glass, Journal of Non-Crystalline
Solids, Vol.79, 1986, p. 165-176.
107. Handbook of Chemistry and Physics, 64th ed., CRC Press, Inc., Boca Raton,
Florida,1983-1984, p. B-135.
108. Neutron Activation Analysis of Trace Elements, Department of Nuclear
Engineering North Carolina State University, Raleigh, North Carolina.
109. C.S. Vikram, D. K. Agrawal, R. Roy and H. A. Mckinstry, A Simple Laser Speckle
Dilatometer for Thermal Expansion Measurements, Material Letters, Vol. 3,
No. 12, 1985, p. 482-484.
110. ASTM C-730, in Annual Book of ASTM Standards. 1976.
111. Naval Publications and Forms Center, Departments and Agencies of the
Department of Defense, Military Specification, Glass, Optical, MIL-G-174,
Amendment 2, Philadelphia, 25 June 1974.
112. A. Paul, Coloured Glasses, in Chemistry of Glasses. Chapman and Hall Ltd.,
New York, 1982, p. 204-270.
113. S. Hufner. Chapter 1. in Optical Spectra of Transparent Rare Earth Compounds.
Academic Press, New York, 1978, p. 1-13.
114. L. E. Orgel, Introduction to Transition Metal Chemistry Ligand Field Theory. John
Wiley & Sons, Inc., New York, 1960.
115. W. A. Weyl, Coloured Glasses. Society of Glass Technology, Sheffield, England
1951.
116. T. Bates, Ligand Fieid Theory and Absorption Spectra of Transition-Metal Ions in
Glasses, in Modern Aspects of the Vitreous State. Vol. 2. J. D. Mackenzie ed.,
Butterworth, Inc., Washington DC, 1962, p. 195-254.
117. Foster L. Harding, The Development of Colors in Glass. Brockway Glass Co., Inc.,
Brockway, Pennsylvania.
118. F. A. Cotton and C. Wilkinson, Advanced Inorganic Chemistry. 4th ed., John Wiley
& Sons, Inc., New York, 1980.
119. P. C. Schultz, Optical Absorption of the Transition Elements in Vitreous Silica,
Journal of the American Ceramic Society, Vol. 57, July 1974, p. 309-313.
120. O. G. Holmes and D. S. McClure, Optical Spectra of Hydrated Ions of the Transition
Metals, Journal of Chemical Physics, Vol. 26, 1957, p. 1686-1694.


27
100
Figure 2-10 Acid catalyzed particles constitute fibrillar chains throughout
the volume of sol.


32
Characterization of Gelation
Professor Paul Flory's theory of gel formation [45, 46], with which Her agrees
[see p. 176 in ref. 4], notes that the silica monomer has four polymerization functional
groups (f=4). The degree of polymerization (DP) obtainable in a system is therefore
described by the equation:
DP = 1/(1-pf/2) (5)
in which "p" is the percentage of reacting monomers (that is the fraction of the total
concentration of monomer which is the reaction product from TMOS) and T is the
number of polymerization functional groups. At the gelation point the degree of
polymerization approaches infinity, therefore (1 -pf/2) must equal zero. For f=4 the
percentage of total concentration of monomer going into gel phase must equal 50%. Since
equal amounts of monomer exist in the liquid as well as in the gel, no refractive index
change is observed at the gelation point. Consequently, the xerogel remain optically
transparent throughout gelation.
Aging Mechanism
Aging is a process by which the gel structure is reinforced via surface area
minimization of the spherical particle chains: this is shown in Figure 2-15. The surface
area can be minimized by four possible mechanisms: (1) condensation of surface silanol
groups (zipper effect) which creates stress and then results in vacancies in the neck
area between particles, (2) thermally activated transportation of silica molecules from
the volume or from the particle neck boundary to vacancies, (3) deposition of monomers
from the liquid into the negative curvature area of two weakly connected spherical
particles, and (4) dissolution of monomer from the particles' area of positive curvature
into the pore liquid, as shown in Figure 2-16.
The first, third, and fourth mechanisms do not result in gel shrinkage: the second
of these mechanisms does [47]. The particle rearrangement involved in the second


Index of Refraction
175
True Density (g/cc)
Figure 5-7 Index of Refraction versus True Density


102
Temperature (C)
Figure 3-18 Thermogravimetric analysis (TGA) curve of a dried gel.


136
H
T
Figure 4-5 Only single hydroxyl groups remain at temperature above 800C


Step 1
Step 2
Step 3
Step 4
Step 5
Step 6
Figure 2-27 Procedure for producing pure silica gels and gel-glasses.


174
expected to have a higher structural chlorine (Cl-1) residual attaching to the silica
matrix which would contribute to a higher refractive index (freed CI2 gas which boiling
point is -34.6C, the index of refraction is 1.000768). It is thus reasonable to conclude
that the measured refractive index in the report of Susa, et al. was mainly proportional
to the concentration of micropores rather than to that of chlorine (Ci*1) and the obtained
apparent density decreased as the chlorine gas, C2, content increased.
According to the Lorentz Lorenz relation, the refractive index is linearly
proportional to the true density of silica (SO2) as shown in Figure 5-7 [107].
Consequently any changes in short-range-ordering, crystallization or structural
transformations of vitreous silica that increases the density will also increase the
refractive index. The true density can be varied in a sintering process by controlling the
thermal history in the glass transition range of temperatures. Unfortunately, such phase
changes or structural rearrangements in small scale (below 2 wt.%) is unable to be
detected using x-ray diffraction. In addition, a small amount of a second phase
(microvoids) found in gel dried at 160C using a microscope, is x-ray undetectable by
x-ray diffraction.
The true density of a dehydrated gel glass with microvoids and closed micropores is
difficult to determine. The apparent density, which has a value around 2.184 gm/cm3
comparing to 2.202 gm/cm3 ((2.202 2.184)72.202 = 0.8 wt.%) of fused silica,
shows the effect of a very small volume fraction of micropores. Thus, differences in
refractive index can be due to either an increase of chlorine content or an increase in
density. When both factors are present it requires a measurement other than
nephelometry to separate them.
The index of refraction of a material usually decreases as the wavelength (X) of
light increases. This change with wavelength is called the dispersion of the index of
refraction and is defined as dn/dX. However, most practical measurements are made by
using the index of refraction at fixed wavelengths at the yellow helium d line (587.0740


Pore volume (cm3/g)
88
Figure 3-9 pore size distribution vs. pore volume at various temperatures.


41
PsvdVsv= dwsv = YsvdAsv
PsldVsi = dwS| = YsldAS|
APv|=Psv'Psl=0
PV = nRT (for ideal system)
PV = W/M XT (for real system)
PsvdVsv = XTsvd(VWM) = Ps|dVS| = XTsvd(W/M)
where
W = weight of vaporized liquid
M = molecular weight of liquid
X = vapor constant
The actual pressure of the vapor phase per unit area of pore wall is the same as the
actual pressure of the liquid phase per unit area of pore wall; this is called the
saturation point or equilibrium vapor pressure [49]. When APV| is zero, there is no
difference in the liquid level within the capillary pore channels regardless of the pore
radius, as shown in Figure 2-21.
However, for the case of drying actual xerogels the differential pressure APV| can
be minimized to zero with the use of a proprietary device. This device keeps the vapor
pressure in the vapor phase, Pv, at a value the same as that of the vapor pressure in the
liquid phase, P|, in the gel. As a result, APV| is zero and gel remains intact. The vapor
pressure within this device is controlled by the temperature which must be carefully
maintained. At temperatures higher than the boiling point temperature of the gel pore
liquid, the vapor pressure in the liquid phase, P|, exceeds one atmosphere (Pv will
never be higher than 1 atm in this device because it is not an autoclave system). Thus
the system will equalize as gas escapes from the device, i.e., APV| is not zero, which
would cause a differential vapor pressure APV| between the liquid and the vapor phases
sufficient to shatter the gels, as shown in Figures 2-20 and 2-22(a).


Fractional Young's elastic modulus
125
0.0 0.2 0.4 0.6 0.8 1.0
Volume fraction pores
Figure 3-33 Relative Young's modulus versus porosity.


154
Figure 4-16 Absorption curve of gel partically densified in controlled CCI4 atmosphere
for a 950C sample of 3.8 mm thickness.


CHAPTER 1
INTRODUCTION TO SOL-GEL DERIVED SILICA GLASS TECHNOLOGY
One of the world's most pervasive chemical compounds is silicon dioxide (Si02).
This compound can exist in many forms crystalline or amorphous, hydroxylated or
dehydroxylated but is most often called "silica" as a generic name.
Silica-based compounds have been fabricated and utilized by mankind for tens of
thousands of years, although only in the past few decades have significant strides been
made in understanding the variables that control silica chemistry [1-7].
Application of this knowledge has produced many useful materials worth billions of
dollars per year; however, today's rapidly accelerating technology demands even greater
performance of silicate materials as well as the need to create new materials. The
objective of this study is to produce a number of new materials using sol-gel silica
processing, including (1) ultraporous gel monoliths for optical and chemical matrices,
(2) ultrapure monolithic gel-glasses with ultralow optical absorption, and (3)
chemically doped gel glass monoliths for optical filters with low expansion coefficients
and high softening points.
Traditional silica glasses are manufactured by melting natural quartz minerals or
synthetic silica, or by flame or plasma vapor-deposition methods. Generally, four types
of commercial vitreous silica are recognized and identified: Type I is obtained by electric
melting of natural quartz in vacuum. Type II is made by flame fusion of quartz. Type III
is made by vapor-phase hydrolysis of pure silicon tetrachloride carried out in a flame.
Type IV is made by oxidation of pure silicon tetrachloride which is subsequently fused
electrically or by means of a plasma. Types I and II are called fused quartz, whereas
Types III and IV are called synthetic fused silica.
1


159
Wavelength (nm)
Wavelength (nm)
200 800 1400 2000 2600 3200
Wavelength (nm)
Figure 4-20 Absorption curve ot 1150C sample aged in air for various times.


196
Figure 5-15 Observed strain in a partially dense gel-silica glass


245
15. L. L. Hench, Use of Drying Control Chemical Additives (DCCAs) in Controlling
Sol-Gel Processing, in Science of Ceramic Chemical Processing. L. L. Hench and
D. R. Ulrich, eds., John Wiley & Sons, Inc., New York, 1986, p. 52-63.
16. G. Orcel and L. L. Hench, Effect of the Use of a Drying-Control Chemical Additive
(DCCA) on the Crystallization and Thermal Behavior of Soda Silicate and Soda
Borosilicate, Proceedings of the 8th Annual Conference on Composites and
Advanced Ceramic Materials, Cocoa Beach, Florida, January 15-18, 1984.
17. S. Wallace and L. L. Hench, Metal Organic Derived 20L Gel Monoliths,
Proceedings of the 8th Annual Conference on Composites and Advanced Ceramic
Materials, Cocoa. Beach, Florida, January 15-18, 1984.
18. Donald R. Ulrich, Chemical Science's Impact on Future Glass Research, Ceramic
Bulletin, Vof. 64, No. 11, 1985, p. 1444-1448.
19. S. H. Wang and L. L. Hench, Drying Control Additives for Rapid Production of
Large Sol-Gel Monoliths Containing Transition and Rare Earth Elements, patent
pending, Serial No. 704917, 1985.
20. Gerard Orcel and L. L. Hench, Effect of Formamide Additive on the Chemistry of
Silica Sol-Gels, Journal of Non-Crystalline Solids, Vol. 79, 1986, p. 177-194.
21. J. Lyklema, The Determination of the IEP and the PZC in Silicic Solution, Faraday
Discussions of the Chemical Society, No. 52, 1971, p. 318-325.
22. R. L. Mozzi and B. E. Warren, Structure of Vitreous Silica, Journal of Appl.
Cryst., Vol. 2, 1969, p.164 -172 .
23. W. D. Kingery, H. K. Bowen and D. R. Uhlmann, Introduction to Ceramics. 2nd
ed., John Wiley & Sons, Inc., New York, 1976, p. 95-108.
24. D. E. Clark, C. G. Pantano and L. L. Hench, Corrosion of Glass. Books for Industry,
Div. of Magazines for Industry, New York, 1979.
25. M. Prassas, J. Phalippou and J. Zarzycki, Sintering of Monolithic Silica
Aerogels, in Science of Ceramic Chemical Processing. L. L. Hench and D. R.
Ulrich, eds., John Wiley & Sons, Inc., New York, 1986, p. 156-167.
26. J. Wong and C. A. Angel, Glass Structure bv Spectroscopy, Marcel Dekker, Inc.,
New York, 1976.
27. Michael L. Hair, Infrared Spectroscopy in Surface Chemistry. Marcel Dekker,
Inc., New York, 1967.
28. E. M. Rabinovich, D. L. Wood, D. W. Johnson Jr, D. A. Fleming, S. M. Vincent and
J. B. MacChesney, Elimination of CI2 and H2O in Gel Glasses, Journal of Non-
Crystalline Solids, Vol. 82, 1986, p. 42-49.
29. B. N. Figgis, Introduction to Ligand Fields. John Wiley & Sons, Inc., New York,
1966. '


72
Consequently, a random edge-to-edge sharing of silica tetrahedra with variable Si-O-Si
angles described above is proposed for silica gel fibrillar structures.
The magnitude of index of refraction (n) indicates the extent of change of the speed
of light by the electromagnetic field of a transparent dense material. The Index of
refraction can be expressed by Snell's law n(giass)/ri(vacuum) = sin 6(vacuum)/sin
0(glass) = V(vacuum)/V{giass). where n(g|ass), V(g|ass), and 0(giass) are the refractive
Index, the velocity, and the angle of refraction of glass respectively, n(vacuum),
v(vacuum) are constants, and 0(vacuum) is the angle of incidence of light in vacuum.
Index of refraction is a dependence of (1) the density, (2) the polarizability of the
glass, and (3) the wavelength (X) of monochromatic radiation [61]. In this chapter
partially densified silica gels are discussed where the chemical compositions are
essentially SiC>2 and chemical bonded surface -SiOH groups. The nonbridging hydrogen
ions (H+, a proton) of these silanol groups contribute very little effect on oncoming
light [see p. 660 in ref. 23], thus, the polarizability of these partially densified silica
gels can be assumed to be a constant. Consequently, the variation of refractive index with
density described by the Lorentz-Lorenz equation [see p. 658 in ref. 23] can be
simplified as will be discussed in the Results and Discussions Section of this chapter.
Differential scanning calorimetry (DSC) is used to measure the temperatures
associated with transitions in materials, including boiling points, melting points,
liquid-crystai transitions, heats of reaction, specific heat capacity, oxidative and
thermal stability, purity, giass transitions, and reaction kinetics.
Differential thermal analysis (DTA) gives the same qualitative information as DSC,
but is used primarily for studies involving high temperatures which exceed the range of
the DSC cell (700C).
Thermogravimetric analysis measures weight change as a function of temperature,
and provides derivative TGA data used to quantify the chemical changes in a gel during
thermal processing.


223
octahedral field the d1 and d9 (2D) orbitals, as discussed before, split into T2g (dxy,
dyz, dzx) and Eg (dx2.y2 or dz2) levels. The f1 orbitals are split into three levels in an
octahedral field: a 2Tig level at 1/3 A below, a 2T2g level at 1/9 A above, and a 2A2g
level 2/3 A above the presplitted F orbital as shown in Figure 6-11(a).
The two split low-energy states 3F and 3P from either the d2 or the d8
configuration behave in an octahedral field exactly as the F and P states arising from the
1f and 1p as discussed above. Consequently, the 3F state is split into 3T-|g(F), 3T2g(F)
and 3A2g(F) states and the unsplit 3P becomes the 3Tig(P) state. The d3 or d7 state has
4P and 4F orbitals. Under a ligand field the 4F splits into 4T-|g(F), 4T2g(F) and 4A2g(F)
states and the unspiit 4P becomes the 4Ti(P) state, as shown in Figures 6-8 and 6-
11(b). The d4 and d6 configurations have a low-energy state 5D which splits into 5T2g
(dXy, dyz, dzx) and 5Eg (dx2.y2 or dz2) in an octahedral field (Figures 6-7 and 6-
11(c)). The d5 state has an unsplit 6S or 6Ai level in the octahedral field.
As mentioned above, ligand field theory describes the bonding occurring between
center transition-metal ion and the ligands. Molecular orbital theory, which develop the
combination of the atomic orbitals of the atoms to form the molecule, is used to explain
this bonding phenomenon.
The condition for two atoms to form: (1) a bonding molecular orbital (vb). (2) a
nonbonding molecular orbital, or (3) an antibonding molecular orbital (ya) depends on
S, the wave function overlap integral JxyaVbdt of the probability equation (\j/b2dt = J
VA^t + J VB2dt + J vAVBdt, where \j/a and wb are the wave functions of atoms A and B)
for finding an electron within the space. Bonding takes place only when the value of S is
positive (S > 0) and the bonding strength (energy) is proportional to the extent of the
overlap of the atomic orbitals. The bonding energy level is reduced relative to the level
of the free atoms by the same amount as the energy is increased for the antibonding level.
In the case of 3d transition-metal ions in an octahedral field, the dx2.y2 and dz2
configurations are in the direction of the ligands. This results in a positive overlap and a


241
The thermal information tests indicate that the decomposition and evaporation
weight losses due to loss of residual organic compounds and water take place below
450C, Dimensional shrinkage occurs throughout the entire heating program.
The results of mechanical information tests show that the compressive strength,
maximum strain to fracture, flexural strength, Young's modulus, and microhardness are
linearly proportional to the gel density. These values show a tendency to approach the
values of fused silica as the gel densification temperature increases. The K|c/density data
obtained show the 160C gel has a greater toughness than the value for fused silica
proving the fibrillar gel structure can absorb higher impact energy than fused silica
before cracking.
The second major difficulty to be overcome in producing large monolithic gel glass
for optical components was the surface silanol groups inside the porous silica gel which
terminated the -O-Si-O- bridging bonds and degenerated the optical performance
significantly. A dehydration thermal treatment using carbon tetrachloride was
accomplished. Monolithic samples of fully dehydrated and densified monolithic pure
silica gel-glass were routinely reproduced.
The tests of the dehydrated densified gel-silica monoliths yielded very important
results. A very high optical transmission was achieved throughout the entire spectral
range between 165 nm and 4400 nm in the VUV-UV-VIS-NIR spectra. The vuv cut-off
wavelength was at 162 nm. These results were equivalent to the very best Type IV
commercial silicas. The CTE data of the gel-silica had almost three times lower (2.0 x
10-7) values than that of Corning 7940 pure silica (5.5 x 107). Thus, the monolithic
gel-silica glass greatly improved the optica! transmission and significantly lowered
thermal expansion of traditional Type l-!V silica glasses. Equivalent or superior levels
of homogeneity, strain, bubbles and striae were also achieved. The second goal of this
study was reached.


118
CO
Q-
o>
c
CD
CD
>
co
CO
CD
SfUIW
Q.
E
o
O
Density (g/cc)
Figure 3-27 Compressive strength versus density.


Young's modulus (MPa)
10S
Figure 3-23 Young's modulus versus temperature.


91
the total pore volume decrease. It can also be reasonably assumed that the decrease of the
surface area is linearly proportional to the disappearance of the number of pores.
When a gel is heated higher than its foaming temperature, free water is formed
from the dissociated surface hydroxyl groups inside the fully densified gel structure.
Immediately, these free water molecules follow the idea gas law in Equation #1 to create
new pores:
pv=nRT (1)
where p is internal pressure of a closed-pore volume v, n is a mole number of gaseous
water molecules within an instantaneously created closed-pore v, v = 47^/3 where r
is the closed-pore radius, and T is gel body temperature at the moment foaming occurs.
If N is the total molar number of gaseous water molecules in total of such created pores
of V per unit volume of matter, then N/n is the total number of pores per unit volume of
silica, and V = Nv/n is total pore volume (Vvo¡d) per unit volume of silica (VSolid)-
Consequently, equations #2 and #3 can be written:
pV=NRT (2)
V=(N/n) x v = (N/n) x 4nr3/3 = (1- p)/p (3)
where p, the relative density, is equal to pa/pr, pa= mSolid/(VSolid+Vvoid) is the
apparent density of the foamed silica gel and pr = mS0|¡d/VS0i¡d is the fully densified
silica gel. Therefore, from Equations (2) and (3), we get:
p = 3nRT/4jtr3 = NRTp/ (1- p) (4)
When temperature exceeds the pore closing temperature, the gel immediately foams as
soon as the surface water is released.
The gel foaming mechanism is explored by J. Phalippou, T. Woignier, and J.
Zarzycki [73]. They use the concept that the rate of total energy input to the gel
sintering system equals the rate of total energy output from the system. The total energy
input includes the surface energy of silica gel (dWa/dt = 87trcdr/dt) where r is the
pore radius, a is surface tension, and t is time and the external pressure energy is


16
660 in ref. 4]. Below are equations related to particle growth under two different pH
conditions, and will be described as two models in the following paragraph.
0 < pH < 2, [H+] as a catalyst
SinOa(OH)b+ +Si(OH)3 + OH- ~> SinOa(OH)b-i OSi(OH)3 + H20 (1)
2 < pH < 7, [OH-] as a catalyst
SinOa(OH)b+ -OSi(OH)3 + H+ -> SinOa(OH)b-iOSi(OH)3 + H20 (2)
SinOa(OH)b is a surface hydrolyzed silica particle, where "n" can be 2, 4, 8, 40, 311,
1438, etc. [see p. 8 in ref. 4]. The number of anhydrous oxygens within a particle is
represented by "a"; "b" is the number of surface hydroxyl groups per particle.
In an extensive study of silica polymerization, Linsen, Okkerse, Vysotskii and
Strazhesko [39, 40], found the iep to be between pH of 1.0 and 2.0. Condensation is
slowest in this pH range, thereby producing a minimum gelation rate. Gelation occurring
at the iep results in gel structures of maximum specific surface area and maximum
strength. These structures occur because the rate of aggregation is minimal as is the
growth rate of the ultimate particles from the monomer. Consequently, the ultimate
particles are smallest when the gel is formed at the iep.
Strong Acid Model
Figure 2-3 represents experimental data of relative gelation time versus solution
acidity found by many researchers [39, 41, 42]; the corresponding relative surface
area curve is shown in Figure 2-4. These two figures show that the longest gelation time
results in the highest surface area when the solution was prepared at pH=2. This is
because the rate of polymerization reaction depends on a catalytic effect which is at a
minimum at pH=2. From these data a model is developed describing the gelation
phenomenon in a strongly acidic solution, in which the pH is less than 2.0.
The very high hydrogen ion concentration at pH<2.0 results in a rapid reaction
among monomers to form dimers, cyclic tetramers, and very small particles, producing


Energy
167
Figure 5-3 The vibration levels ai various temperatures.


138
\)1 = 2668.80 nm (OH(1)). From actual absorption data, McDonald observed a peak at
2816.88 nm, indicating a strong interaction between free pore water and surface
hydroxyl groups.
When a dehydrated silica gel is exposed to a slightly humid air atmosphere, sharp
peaks appear at 2816.88 nm (u3), 2732.24 nm (^2), 1890.35 nm (d3 + 2\>oh
(bend)), 1459.85 nm (2104), and 1408.44 nm (2\>3). Hair [see p. 89 in ref. 27]
believes that the intensity changes upon adsorption of water indicate that all these bands
are connected with the hydroxyl group which is associated with physical pore water.
Further hydration results in a broadened band at about 1)4 = 2919.70 nm (see Fig. 4-4)
-characteristic of bulk water.
Cant and Little [94, 95], and Chapman and Hair [96], tend to agree that for silica
gel a sharp and slightly asymmetrical peak on the high-wavelength side, at 2668.80 nm
(t>l), together with a distinct band at 2732.24 nm (02), can be attributed to freely
vibrating surface silanol groups, and to hydrogen-bonded adjacent silanol groups,
respectively, in addition, a broad band at 2919.70 nm (^4) is due to the stretching of
molecular water.
Elmer, et al. [97], in their rehydrated study of porous silica showed that the
intensity of the peak at 2668.80 nm increases during rehydration. They also indicated
that physical water prefers to adsorb on adjacent hydroxyl groups rather than on the
singular hydroxyl groups.
Recent studies in optical fiber communication technology by D. B. Keck, R. D.
Maurer, and F. C. Schultz [71] found that the extrinsic hydroxyl groups also give rise
to some noticeable overtones and combinations occurring roughly at 725 nm, 880 nm,
950 nm, 1125 nm, 1230 nm, 1370 nm. These absorptions strongly degrade the
performance of optical fibers.
Most of the silica glasses manufactured by melt or synthetic methods (Type I to IV
silicas stated in Chapter 1), such as those produced by Corning, Melles Groit, Dynasil,


48
shown, when an acidic silica gel is sufficiently dried to contain pores (negative
curvature in left side of the figure) that are only a few nm in diameter a small decrease
in pore size results in sudden elimination of the pores. Table 2-1 confirms that the
remaining uniform pores stay unchanged in diameter but decrease in total volume and
surface area as the sintering temperature increases.
A mechanism was suggested by Her [47] that in a densification process, gel
shrinkage is the results of sudden decomposition of pores into vacancies in the gel
structure and traveling vacancies which migrate to the outside of the gel body along the
surface of the pore network and do not remain in the pores to enlarge them [50].
Experimental Procedure
Large scale monolithic dried silica gel samples (up to 10 cm x 8 cm x 2 cm), as in
Figure 2-26, have been routinely produced by applying the concepts and mechanisms
stated in Section II of this chapter. Several kinds of standardized samples were made for
characterization in this study including pure silica gels, cobalt- copper- and nickel-
doped silica gels, neodymium- and erbium-doped silica gels. The two examples described
below detail the procedure used to produce both pure silica and doped silica samples. Six
steps are generally needed to produce the sol-gel derived monolithic silica gel-glass
samples, as shown in Figure 2-27. The drying control chemical additive (DCCA) is
introduced in Step 1; this makes it possible to control each of the five subsequent steps
and prevent gel shattering.


249
73. J. Phappou, T. Woignier, and J. Zarzycki, Behavior of Monolithic Silica
Aerogels at Temperatures Above 1000C, in Ultrastructure Processinn of
Ceramics. Glasses and Composites. L. L. Hench and D. R. Ulrich, eds., John Wiley
& Sons, Inc., New York, 1984, p. 70-87.
74. B. D. Cullity, Elements of X-Rav Diffraction. 2nd ed., Addison-Wesley
Publishing Co., Inc., Reading, Massachusetts,1978, p. 99-105.
75. C. A. Mulder, J. G. Van Lierop and G. Frens, Densification of SiQ^Xerogels to
Glass by Ostwald Ripening, Journal of Non-Crystalline Solids, Vol. 82, 1986, p.
92-96.
76. Dynasil Corporation of America, Catalog 302-M of Dynasil Synthetic Fused
Silica, Dynasil Corp. of America, Berlin, New Jersey, 1987.
77. S. Palmqvist, Occurrence of Crack Formation During Vickers Indentation as a
Measure of the Toughness of Hard Metals, Arch. Eisenhuttenwes., Vol. 33, No. 6,
1962, p. 629-633.
78. F. Orgaz and H. Rawson, Characterization of Various Stages of the Sol-Gel
Process, Journal of Non-Crystalline Solids, Vol. 82, 1986, p. 57-68.
79. J. B. Peri and A. L. Hensley, Jr., The Surface Structure of Silica Gel,
Journal of Physical Chemistry, Vol. 72, [8],1968, p. 2926-2933.
80. George H. Sigel, Jr., Interaction with Electromagnetic Radiation, in Treatise on
Materials Science and Technology Volume 12-Glass I. Miknoru Tomozawa and
Robert H. Doremus, eds., Academic Press, Inc., New York, 1977, p. 14.
81. M. AN Omar, Elementary Solid State Phvsics. Addison-Wesley Publishing Co.,
Inc., Reading, Massachusetts, 1975, p. 86-133.
82. Allen H. Cherin, Fabrication of Optical Fibers, in An Introduction to Optical
Fibers. McGraw-Hill Book Co., New York, 1983, p. 147-153.
83. Siemens, Fiber Optic Cables. John Wiley & Sons, Inc., New York, 1987, p.
32.
84. Michael L. Hair and William Hertl, Reactions of Chlorosilanes with Silica
Surfaces, Journal of Physical Chemistry, Vol. 72, 1968, p. 2372-2378.
85. A. V. Kiselev and V. I. Lygin, Infrared Spectra of Surface Compounds. Keter
Publishing House Jerusalem Ltd., John Wiley & Sons, Inc., New York, 1975.
86. L. R. Snyder and J. W. Ward, The Surface Structure of Porous Silicas,
Journal of Physical Chemistry, Vol. 70, 1966, p. 3941-3952.
87. G. J. Young, Interaction of Water Vapor with Silica Surface, Journal of Colloid
Science, Vol. 13, 1958, p.67-85.
88. H. A. Benesi and A. C. Jones, An Infrared Study of the Water-Silica Gel System,
Journal of Physical Chemistry, Vol. 63, 1957, p.179-182.


Microhardness DPN (Kg/mm*2)
122
Density (g/cc)
Figure 3-31 Microhardness versus density.


Transmission (%)
187
Wavelength (nm)
Figure 5-11 UV-VIS-NIR transmission of optica! silicas
sample thickness: 3 mm.


38
a.
o
w
w
CD
c
p
ns
JC
2
o
Percent of shrinkage
Figure 2-19 Microhardness of aged gel versus percentage of shrinkage.


212
negative charged ligand
Figure 6-3 Head on interaction of the d22 and d x2.y2 orbitals of a central ion
with six ligands in a octahedral field.


Figure 2-8 Homogeneous particle distribution throughout the solvent.


I certify that I have read this study and that in my opinion it conforms to
acceptable standards of scholarly presentation and is fully adequate, in scope and
quality, as a dissertation for the degree of Doctor of Philosophy.
(SLJL-
David E. Clark
Professor of Materials
Science and Engineering
This dissertation was submitted to the Graduate Faculty of the College of Engineering
and to the Graduate School and was accepted as partial fulfillment of the requirements
for the degree of Doctor of Philosophy.
April 1988
d
Dean, College of E ineering
Dean, Graduate School


57
Step 4: Aging
The solid is aged in the mold initially at 55C for 10 hours, followed by an increase
to 80C for 15 hours.
Step 5: Drying
The aged pure-silica gel is removed from the mold and dried with a controlled
evaporation rate, as described in Section II of this chapter, initially at 70C, gradually
increasing the temperature to 160C during a 90 hour period.
Step 6: Impregnation
(a) One gram-percent of transition metal element (i.e., cobalt nitrate, nickel
nitrate, copper nitrate) or three gram-percent of rare earth element (i.e., neodymium
nitrate, erbium nitrate) in deionized (Dl) water is prepared for doping, or
impregnating, the completely dried gel. The dried gel is immersed into the solution,
whereby the interface between the liquid and the voids migrates from the exterior Into
the center of the gel body in the rate of 0.5 cm/hour, as shown in Figure 2-30.
(b) The doped gel is then placed in the drying oven at 200C for 12 hours to
remove the pore solvent.
Step 7: Densification
(a) The fully dried silica gel doped with transition metal or rare earth elements is
heated to 400C to eliminated any residual nitrates via conversion to its gaseous oxides.
(b) Additional densification can be achieved by heating from 400C to 1000C.
Results
Monolithic samples of pure silica gel, transition metal element doped silica gel, and
rare earth element doped silica gel were routinely produced following these procedures;
some are shown in Figures 2-31 to 2-35. The physical and optical properties of these
samples will be discussed in succeeding chapters.


58
top view
Figure 2-30 Sample immersion into transition metal or rare earth nitrate/water solution.


absorptance
84
Figure 3-6 The absorptance peaks of water decreasing with increasing temperature.


Relative energy scale
169
Figure 5-4 Possible energy transformation in a glass.


179
Table 5-2
Physical property measurements on fully densified gel-silica glasses
and fused silica glasses
Test Number of Samples measured
Source
Optical tests:
Transmittance
6 gel glass samples
6 control samples
Glass Fab
(1) Vacuum UV
(2) UV-VIS-NIR
(3) IR
Refractive index
6 gel glass samples
6 control samples
Glass Fab
Dispersion
6 gel glass samples
6 control samples
Glass Fab
Homogeneity
6 gel glass samples
6 control samples
Glass Fab
Striae
6 gel glass samples
6 control samples
Glass Fab
Stress birefringence
6 gel glass samples
6 control samples
Glass Fab
Bubbles and Inclusions
6 gel glass samples
6 control samples
Glass Fab
Impurity
1 gel glass sample
North Carolina
State University
Thermal and mechanical test:
Coefficient of thermal
(a) 1 gel glass sample
Penn State University
expansion
(b) 2 gel glass samples
University of Arizona
Specific gravity
3 gel glass samples
Corning Engineering
2 control samples
Lab Services
Knoop hardness
1 gel glass sample
Corning Engineering
1 control sample
Lab Services


TABLE OF CONTENTS
Page
ACKNOWLEDGMENTS ii
ABSTRACT vi
CHAPTERS
1 INTRODUCTION TO SOL-GEL DERIVED SILICA GLASS TECHNOLOGY 1
2 SOL-GEL TRANSFORMATION AND EXPERIMENTAL PROCEDURES 1 2
Introduction 12
Literature Review of Sol-Gel Transformation Modeling 12
Experimental Procedure 48
Results 57
Conclusions 64
3 PHYSICAL PROPERTIES OF PARTIALLY DENSIFIED SIUCA XEROGEL 67
Introduction 67
Review of the Literature 68
Experimental Procedure 73
Results and Discussions 81
Conclusions 1 26
4 DEHYDRATION OF SOL-GEL DERIVED SILICA OPTICS 128
Introduction 128
Review of the Literature Regarding Dehydration 130
Experimental Procedure 139
Results and Discussions 145
Conclusions 157
5 OPTICAL PROPERTIES OF FULLY DEHYDRATED SIUCA GEL GLASS 1 6 0
Introduction 1 60
Literature Review Regarding Optical Properties of Silica Glass 161
Experimental Procedure 178
Results and Discussions 1 85
Conclusions 203
6 SILICA GEL OPTICAL FILTERS USING TRANSITION-METAL COMPOUNDS- 206
Introduction 206
Review of the Literature 207
iv


relative viscosity
24
tg
relative time scale
*tg is the gelation time
Figure 2-7 Relative viscosity versus time


absorptance absorptance
158
Wavelength (nm)
$ 0.40
(b) 2 days
0.20
2668.8 nm
V
0.00
i I i l i I i I i
200 800 1400 2000 2600 3200
Wavelength (nm)
Wavelength (nm)
Figure 4-19 Absorption curves of 1050C samples aged in air for various times.


derived gel-silica optics. Fully dehydrated and densified gel-silica has excellent
transmission from 165 nm to 4400 nm with no OH absorption peaks. This optical
transmission is equivalent to the best type IV fused silica. The other physical properties
and structural characteristics of the dehydrated dense gel-silica are similar to fused
quartz and fused silica. However, the dense gel-silica has a lower coefficient of thermal
expansion of 2.0 x10-7 cm/cm compared with 5.5 x 10'7 cm/cm for standard vitreous
silicas. The CTE value is temperature independent from 80 K to 500 K. Sol-gel silica
optics can be made as complex shapes by casting of the sol into inexpensive plastic molds.
Monolithic silica gel optical filters were produced by chemical doping with various
transition-metal ions (e.g., cobalt, copper, nickel). Color changes occurred with
various sintering temperature indicating a unique method to control light wavelength
filtration in the visible range. For instance, the observed color or spectral (major peak
of absorption) shifts for the 160C, the 850C, and the 900C Co11 ion doped gels were
reddish pink (505 nm), deep blue (660 nm), and greenish black (670 nm)
respectively. The optical absorption spectra of the chemically doped-silica are
interpreted in terms of ligand-field and molecular orbital theories.


6
1) in silica glass depends on which type of process is used. For example, Spectrosii WF
(type IV) in Table 1-1 has a water content less than 0.4 ppm compare to 1200 ppm for
Suprasil (type III). It is observed that there is no significant shift in the uv cut off
between type III and IV silicas due to the increased water content if the other impurities
are constant. However, in the infrared range, water (type III, curve A in Fig. 1-1)
noticeably gives a strong absorption. These shortcomings can limit the use of glass
products made by the traditional techniques described above, as summarized in Table 1-
3.
Sol-gel processing has been used for many years, although the principal chemical
and physical mechanisms are still not clearly understood [11-14]. In recent years
special applications require silica optical components that meet very stringent
requirements. The sol-gel method offers new hope in that structural manipulation is
possible on an extremely fine scale, within the nanometer range, thereby allowing
production of a new generation of silica materials. The outstanding features of these
silicas include very high homogeneity, very high purity, potentially extremely low
optical loss, ease of chemical doping, and near net shape casting. These features make
sol-gel silicas potentially applicable to a wide range of optical products including lenses,
mirrors, wavequides, optical fibers, integrated optoelectronics, and host materials for
filters, lasers, and non-linear optical elements or compounds.
The sol-gel process as it relates to silicas is summarized briefly. A sol is defined
as a dispersion of colloids in a solvent. Silica colloids are solid particles with diameters
ranging from 1nm to 100 nm which depend upon the type and amount of drying control
chemical additive (DCCA) in the solution [15-19]. In this study all colloidal particles
are synthesized by the hydrolysis of tetramethylorthosilicate (TMOS) [Si(OCH3)4]
followed by the growth of the hydrolyzed species [Si(OCH3)4-n(OH)n with 0 20].


126
Conclusions
The determination of the physical properties of partially densified gels establishes
the nature of the porous gel ultrastructure and ultrastructural dependence of properties.
FTIR analysis showed a 950 cm'1 SiOH stretching vibration peak decreasing with
increasing temperature, indicating that the sample is becoming increasingly dehydrated.
The peaks of organic residuals in the range from 2000 cm'1 to 3000 cnr1 disappear as
temperature increases. The shift to lower UV cut-off wavelengths with increasing
temperature, noted in the UV-VIS-NIR data, also shows that the impurity (water) level
is reduced. A quantitative study on the change of water level during sintering is discussed
in Chapter 4.
X-ray diffraction of the gels showed no evidence of devitrification, confirming the
development of an amorphous glass phase from the gel. More important in this study, the
observation led to suggestion that silica gel is composed of random oriented fibrillar
structure (random-network model) in which the silica molecules are very well ordered
crystallites (crystallite model).
The index of refraction of silica gel varied with density as predicted by the
Lorentz-Lorenz relationship. This variation of refractive index with density can be
utilized to manufacture optical waveguides and lenses using localized index gradients.
BET data showed a uniform size distribution of porosity for all temperatures below
the fully densified temperature. The densificaron mechanism reduces the volume and
number of pores, as opposed to pores merging together without reduction In pore
volume.
The DSC, DTA, TGA, and TMA data provide information useful in monitoring
thermodynamic, weight loss, and dimensional changes during sintering. With these data
an optimized manufacture process can be achieved.
Mechanical properties, including flexural and compressive strength,
microhardness, together with density, showed an increase in values with increasing


David E. Clark and Gholamreza J. Abbaschian of the Department of Materials Science and
Engineering for their advice and recommendations regarding this dissertation. The
responsibility for any remaining errors or shortcomings is, of course, mine.
Words are insufficient to express gratitude to my parents for their constant
support and to my brothers and sisters for their consideration in Taiwan. I am also
particularly indebted to my wife, Sue-Ling, not only for her great backup but also for
her scientific discussions, and to my daughter, Jean, for understanding why we couldn't
have much fun together while this work was being finished.


23
K is Boltzmann's constant
T is absolute temperature
The average displacement X of a particle from time zero (@ pzc) to any point in
time t is:
X = (2Dt)1/2 (4)
Prior to reaching the pzc, the viscosity of the sol increases only slightly, as shown in
Figure 2-7 [44]. At the point (pzc) is achieved the small particles are homogeneously
distributed throughout the solvent, as shown in Figure 2-8. Governed by Brownian
motion (equation #4), these thermally activated, hydroxyl ion-catalyzed particles
randomly collide under the aid of Van der Waals attractive forces and a base catalyst, as
shown in Figure 2-9, to form long spherical-particle chains. As these chains continue to
form, the viscosity increases until there exists a three dimensional network throughout
the volume of the sol, as shown in Figure 2-10. This is described as the gelation point. A
sol takes a specific time to reach its own gelation point.
Gelation time is then defined as at the moment the sol is prepared to the moment the
sol loses its freedom to move. The length of gelation time is a function of the temperature
and the relative amounts of acidic DCCA, water, and TMOS in a sol. Figures 2-11, 2-12,
2-13, and 2-14 show that the gelation time can be exponential curve fitted with one of
the four variables (i.e. temperature, oxalic acid (DCCA), water, and TMOS) in which the
other three are kept constants. Increasing the sol temperature promotes the thermally
activated Brownian motion and thus decreases the gelation time as shown in Figure 2-
11. A decreased amount of oxalic acid concentration weakens the catalytic effect among
particles and therefore increases the gelation time as shown in Figure 2-12. An
increased TMOS content in water results in an increased concentration of particles and a
decreased distance between particles, which consequently, shortens the gelation time as
shown in Figures 2-13 and 2-14.


235
silica and a binary 30 mol% Na20-borate glass.
The splitting of the 4A2(F) to 4T1 (P) band is caused by spin-orbit coupling
which splits the 4T-|(P) states and allows the transitions to the neighboring doublet
states to gain in intensity [see p. 241-242 in ref. 112]. The two other transitions,
4A2(F) to 4T2(F) and 4A2(F) to 4T-|(F) which take place in the infrared region
contribute no color chromophores. In this study, none of the spectra for the Co11 doped
silica gels is identical to the silicate melt glass spectrum in detail. This indicates that the
ligand field strength (A) may be varied by the thermal history of the gels.
The spectrum of a 160C Ni11 doped silica gel is similar to that of a 16.2 wt.%
melt K20-borate glass containing Ni ion. It is also similar to that of a [Ni(H20)6]2+
octahedral complex in water [see p. 242-243 in ref. 112], as shown in Figure 6-18.
The absorption band at 700 nm of Ni2+ in an octahedral complex is assigned to the
3A-|(F) --> 3Ti (F) transition, and the one at about 400 nm is assigned to the 3A2(F) -
-> 3Ti(P) transition. Another band corresponding to a 3A2(F) ~> 3T2(F) transition is
observed in the infrared region at about 1180 nm. In this study, the spectra of these
three samples are almost the same except for the difference in absorption intensity. The
similarity in absorption bands of the three curves indicates that the same ligand field
strength acts on Ni2+ ion in these three samples.
The absorption spectrum of Cu11 in a 160C gel and three binary sodium-borate
Cu11 melt glasses [120] are shown in Figure 6-19. All the absorption spectra consist of
a broad band with a maximum at about 780 nm. This absorption is attributed to the
transition from 2E levels to 2T2 levels. The band is asymmetric and departs from
Gaussian symmetry since the 2T2 levels are split by a distorted low symmetry ligand
field component. No significant band shift and shape change is present in spite of the
variations of the surrounding ligand chemical composition of the ligands.


133
Figure 4-3 irreversible elimination of adjacent hydroxyl groups


19
a significant amount of free water (equation #1) which dynamically reduces the
hydrogen ion concentration. This dilution slows the reaction between monomer and the
particle surface causing a build up of monomers around the particle while the total
hydrogen concentration in solution is reduced. This causes the pH to be increased to the
isoelectric point with a pH approximately equal to 2.0. This implies that the stronger
initial acidic solution (pH < 2) allows the monomers to grow to relatively larger
particles before the iep is achieved and results in a relatively smaller surface area, as
measured. As soon as the iep is reached, the particle size is nearly determined, the slip
plane of the electrical double layer is formed, no electric charge outside the slipping
plane can be measured, and particles are then homogeneously distributed in the solution.
As shown in Figure 2-5, the particle surface has a slight negative charge in the
presence of the positively charged monomer (equation #1). The monomers confined
within the slip plane of the electrical double layer [see p. 358-378 in ref. 4] will
gradually react with the particle surface under the influence of the hydrogen ion
concentration and thermal energy, resulting in slight particle growth. Free water is
released, diluting the hydrogen ion concentration while particle growth decreases. As the
confined monomers are consumed, the electrical double layer and slip plane is
eliminated. Formation of an electrically neutral particle surface, referred to as the
point of zero surface charge (pzc), at pH = 2.5 [41] marks the beginning of gelation
under the influence of thermally activated Brownian motion and Van der Waals attractive
force from this strongly acidic sol.
Weak Acid Model
The mechanism for gelation in a weaker acid solution (pH 2.0 pH 7.0) is
somewhat different from that of a strong acid solution, as shown in Figure 2-6. The
reduction in hydrogen ion concentration effectively weakens its strength as an acid
catalyst preventing the hydrogen ion from attracting the hydroxyl group from the


228
Figure 6-14 Ligand group orbital of only o bonds and matching atomic orbitals
to form molecular orbitals.


139
and Quartz Scientific, Inc., result in impurities (e.g., water and/or metallic elements).
Three significant absorption peaks at 2732.24 nm (v2). 2207.51 nm (v2 +
uOH(bend)} and 1366.12 nm (2v2) are found to be the unique stretching vibration of
adjacent silamol groups and its overtone and combination, as shown in Figures 4-6, 4-7,
4-8, and 4-9. No singular silanol group (u-i) was found using high resolution UV-VIS-
NIR spectrophotometer.
The electrons of these impurity atoms can be easily excited by photons of lower
energy than those associated with the 8.9 eV UV band edge of theoretically pure silica,
thereby causing a shift in the ultraviolet absorption edge to longer wavelengths. These
excitations also cause additional absorption bands or peaks in the visible and near
infrared ranges. Without complete dehydration, the quality of silica gel-glasses is
significantly affected by the problem of water retention.
The highest quality of pure silica manufactured in the world today is that of optical
fibers fabricated by vapor phase reaction of pure oxygen with silicon tetrachloride
(Type IV silica). This process results in fibers of ultralow loss about 1.0 dB/km to
5.0 dB/km in the 900 nm to 1300 nm range. It is shown in Chapter 5 that the fully
dehydrated, completely densified, gel-glass monoliths developed in this dissertation are
of such a quality as to compare with optical fibers.
Experimental Procedure
The standard dried gels (150C), manufactured as per Example One in Chapter 2,
are used as the basis for preparing two sample sets for the following dehydration study.
One sample set was partially densified at designated temperatures in an ambient air
atmosphere; the other set was chemically and thermally treated prior to sintering in a
mixed vapor (carbon tetrachloride and helium) atmosphere within a special apparatus,
shown in Figure 4-10.


214
When the transition-metal ion is in tetrahedral symmetry as shown in Figures
6-5 and 6-6, the situation is reversed. The lobes of the dx2.y2 or dz2 orbitals now lie
in the direction between the ligands, while the lobes of dxy, dyz and dzx orbitals, though
not pointing directly towards the ligands, lie closer to them. Thus the t2g (dxy, dyz, dzx)
orbitals are destabilized with respect to the eg orbitals. For the same strength ligands,
the tetrahedral scheme At can be related to the A0 value of the degenerate orbitals by At
= 4/9 Aq, as shown in Figure 6-2(c).
Practically, octahedral arrangements of the ligands around the transition-metal
ion are often tetragonally distorted. In such a case the two +Z and -Z (dz2) ligands in
Figure 6-3 are gradually moving away from the central transition-metal ion, and new
energy differences among the d orbitals arise. The dz2 level will fall and dx2-y2 level
will arise equally at the same time. If the two Z ligands are completely removed, the dz2
level becomes the lowest energy level in the resulting square planar ligand arrangement,
since there are now no energy-raising ligands in that direction and the dx2.y2 becomes
the highest energy level, as shown in Figure 6-2{f). For a sequare planar ligand field
the location of the dyz and dzx levels will fall and that of the dxy level must rise two
times as much. The frequently observed tetragonaiiy distorted octahedral arrangements
are shown in Figure 6-2(d) and (e). Consequently, the kind of energy level arrangement
formed by the ligand fields depends on three crucial properties: (1) the orbitals of the
centra! transition-metal ion, (2) the surrounding arrangement of ligand fields, and (3)
the strength of the ligand fields.
For ligand fields, in dealing with individual orbitals of an atom, lower case
notations such as a-|g, b, eig, t2g are used. Either a or b indicates a nondegenerate orbital
with a presenting a wave function which is symmetric with respect to the rotation axis,
whereas b represents a wave function which is antisymmetric and changes sign during
rotation. The e and t orbitals are symmetrically doubly and triply degenerate. The energy
levels in e or t orbitals are equal.


CTE (x 10-8/K)
200
Figure 5-17 Coefficient of thermal expansion of gel silica compare with other fused glasses.


64
Conclusions
It was not found necessary to add methanol to this xerogel system, though this is the
practice of many researchers [51-56].
Addition of oxalic acid or nitric acid as DCCAs is necessary in the mixing step of
both Examples #1 and #2 as an acidic DCCA controls the radius of the individual silica
particles to a few nanometers that form during the early stage of monomer growth and
the subsequent fiber-like polymerization.
The particles are made uniform due to Ostwald ripening at any moment of growth.
As soon as particle growth stops at the pzc (point of zero surface charge), an electrically
neutral particle surface forms; therefore, thermally activated Brownian motion, Van
der Waals attractive forces and base catalytic effects among particles in the sol become
the driving forces to form particle chains which reach the gelation point.
During aging, the reinforcement and the shrinkage of the fibrillar network of a gel
proceeds as a result of growth of interparticle necks and migration of vacancies to the
exterior of the gel. The rate of aging shrinkage is primarily determined by the rate of
thermally activated vacancy migration.
After aging, the interparticfe necks comprise a very large fraction of the gel
fibrillar structure and become relatively flexible (like glass fibers are flexible).
Consequently, the gel can endure certain hydrostatic stresses and shrink considerably in
the drying stage without cracking, as illustrated in Figure 2-36.
Differential vapor pressure (APV|) is the stress which shatters the relatively
weak gel into pieces in the drying stage. A gel can be dried without cracking by using a
drying device which eliminates the differential vapor pressure between vapor phase
(Pv) and liquid phase (P|) inside the capillary pores.


Transmission (%)
86
Wavelength (nm)
Figure 3-7 Transmission cut-off of pure silica ge!


Density (g/cc)
148
2.4
1.2 I l I l I l
0 200 400 600 800 1000 1200
Temperature (C)
Figure 4-13 Density measurements at various temperatures for samples with or
without CC4 treatment.


absorptance
153
Figure 4-15 Absorption curve of gel partically densified in controlled CCI4 atmosphere for
a 850C sample of 4 mm thickness.


226
4p
empty
empty
4s
partially
3d filled
(a) free ion
orbitals
(b) central ion
orbitals
completely filled
ligand group orbitals
(d) ligand orbitals
tiu(3)
aig(1)
(c) molecular orbitals
Figure 6-12 Molecular orbital splitting levels for a d orbital ion in an octahedral
environment with ligands having only a bonds.


SOL-GEL DERIVED SILICA OPTICS
By
SHI-HO WANG
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1988


117
of samples, the 150C gel sample has a value 0.35 which is even greater than the value
of 0.33 of fused silica. The reason is probably due to the fibrillar ultrastructure of the
low temperature gel which is described in Figure 2-36, Chapter 2.
Mechanical properties of the silica gels and gel-glasses, including flexural
strength, compression strength, microhardness, and toughness, are all dependent on the
gel ultrastructure. The evolution of ultrastructure, monitored by N2 adsorption-
desorption isotherms, FTIR, uv-vis-nir, and x-ray diffraction techniques, proves that
the pore volume, the surface area, and the amount of nonbridging oxygens (surface
silanol group) decreases and the effective particle size increases with an increase in
pyrolysis temperature. Consequently, the overall bulk density increases with sintering
temperature, representative of the degree of ultrastructural rearrangement. In Figures
3-27, 3-28, 3-29, 3-30, 3-31, and 3-32, the experimental data of compressive
strength, maximum strain to failure, flexural strength, Young's modulus,
microhardness, and toughness are plotted as a function of density. The maximum density
of 2.2 g/cm3 represents the value of vitreous silica. Within experimental error, the
mechanical properties are linearly related to the density. A simple relationship is:
Xgel = Xs ( pge|/ps) (17)
where
Xgei : mechanical properties of the partially densified gel (i.e. compressive
and flexural strength, Young's modulus, and microhardness),
Xs : mechanical properties of vitreous silica,
Pgei : density of the partially densified gel,
ps : density of vitreous silica, 2.2 g/cm3.
Dashed lines drawn in Figure 3-27, 3-29, 3-30, and 3-31 were obtained from
the above relationship. Although the present experimental results do not fit those
predicted by equation 17, a linear relationship can still be applied to the present



PAGE 1

62/*(/ '(5,9(' 6,/,&$ 237,&6 %\ 6+,+2 :$1* $ ',66(57$7,21 35(6(17(' 72 7+( *5$'8$7( 6&+22/ 2) 7+( 81,9(56,7< 2) )/25,'$ ,1 3$57,$/ )8/),//0(17 2) 7+( 5(48,5(0(176 )25 7+( '(*5(( 2) '2&725 2) 3+,/2623+< 81,9(56,7< 2) )/25,'$

PAGE 2

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

PAGE 3

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nW KDYH PXFK IXQ WRJHWKHU ZKLOH WKLV ZRUN ZDV EHLQJ ILQLVKHG

PAGE 4

7$%/( 2) &217(176 3DJH $&.12:/('*0(176 LL $%675$&7 f§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

PAGE 5

([SHULPHQWDO 3URFHGXUH 5HVXOWV DQG 'LVFXVVLRQV &RQFOXVLRQV &21&/86,216 $1' 5(&200(1'$7,216 5()(5(1&(6 %,2*5$3+,&$/ 6.(7&+ Y

PAGE 6

$EVWUDFW RI 'LVVHUWDWLRQ 3UHVHQWHG WR WKH *UDGXDWH 6FKRRO RI WKH 8QLYHUVLW\ RI )ORULGD LQ 3DUWLDO )XOILOOPHQW RI WKH 5HTXLUHPHQWV IRU WKH 'HJUHH RI 'RFWRU RI 3KLORVRSK\ 62/*(/ '(5,9(' 6,/,&$ 237,&6 %\ 6+,+2 :$1* $SULO &KDLUPDQ 'U /DUU\ / +HQFK 0DMRU 'HSDUWPHQW 0DWHULDOV 6FLHQFH DQG (QJLQHHULQJ /DUJH PRQROLWKLF [HURJHO VLOLFD JODVVHV ZHUH VXFFHVVIXOO\ PDGH IURP WHWUDPHWK\O RUWKRVLLLFDWH DQG GLVWLOOHG ZDWHU XVLQJ WKH FRPELQDWLRQ RI DQ DFLGLF GU\LQJ FRQWURO FKHPLFDO DGGLWLYH '&&$f DQG D VSHFLDOO\ GHVLJQHG GU\LQJ FKDPEHU 7KH DFLGLF '&&$ LQFUHDVHV WKH JHO VWUHQJWK E\ IRUPDWLRQ RI D ILEULOODU XOWUDVWXFWXUH DQG WKH GU\LQJ FKDPEHU UHGXFHV WKH FDWDVWURSKLF FDSLOODU\ IRUFHV LQVLGH WKH ZHW JHO ERG\ 3DUWLDOO\ GHQVLILHG PRQROLWKLF JHOV XS WR r& ZHUH URXWLQHO\ PDGH IRU SK\VLFDO SURSHUW\ WHVWV DQG FRPSDUHG WR FRPPHUFLDO IXVHG VLOLFDV $OWKRXJK WKH PHFKDQLFDO SURSHUWLHV RI WKH SRURXV JHOVLOLFD PRQROLWKV VXFK DV PLFURKDUGQHVV
PAGE 7

GHULYHG JHOVLOLFD RSWLFV )XOO\ GHK\GUDWHG DQG GHQVLILHG JHOVLOLFD KDV H[FHOOHQW WUDQVPLVVLRQ IURP QP WR QP ZLWK QR 2+ DEVRUSWLRQ SHDNV 7KLV RSWLFDO WUDQVPLVVLRQ LV HTXLYDOHQW WR WKH EHVW W\SH ,9 IXVHG VLOLFD 7KH RWKHU SK\VLFDO SURSHUWLHV DQG VWUXFWXUDO FKDUDFWHULVWLFV RI WKH GHK\GUDWHG GHQVH JHOVLOLFD DUH VLPLODU WR IXVHG TXDUW] DQG IXVHG VLOLFD +RZHYHU WKH GHQVH JHOVLOLFD KDV D ORZHU FRHIILFLHQW RI WKHUPDO H[SDQVLRQ RI [ FPFP FRPSDUHG ZLWK [ n FPFP IRU VWDQGDUG YLWUHRXV VLOLFDV 7KH &7( YDOXH LV WHPSHUDWXUH LQGHSHQGHQW IURP WR 6ROJHO VLOLFD RSWLFV FDQ EH PDGH DV FRPSOH[ VKDSHV E\ FDVWLQJ RI WKH VRO LQWR LQH[SHQVLYH SODVWLF PROGV 0RQROLWKLF VLOLFD JHO RSWLFDO ILOWHUV ZHUH SURGXFHG E\ FKHPLFDO GRSLQJ ZLWK YDULRXV WUDQVLWLRQPHWDO LRQV HJ FREDOW FRSSHU QLFNHOf &RORU FKDQJHV RFFXUUHG ZLWK YDULRXV VLQWHULQJ WHPSHUDWXUH LQGLFDWLQJ D XQLTXH PHWKRG WR FRQWURO OLJKW ZDYHOHQJWK ILOWUDWLRQ LQ WKH YLVLEOH UDQJH )RU LQVWDQFH WKH REVHUYHG FRORU RU VSHFWUDO PDMRU SHDN RI DEVRUSWLRQf VKLIWV IRU WKH r& WKH r& DQG WKH r& &R LRQ GRSHG JHOV ZHUH UHGGLVK SLQN QPf GHHS EOXH QPf DQG JUHHQLVK EODFN QPf UHVSHFWLYHO\ 7KH RSWLFDO DEVRUSWLRQ VSHFWUD RI WKH FKHPLFDOO\ GRSHGVLOLFD DUH LQWHUSUHWHG LQ WHUPV RI OLJDQGILHOG DQG PROHFXODU RUELWDO WKHRULHV

PAGE 8

&+$37(5 ,1752'8&7,21 72 62/*(/ '(5,9(' 6,/,&$ */$66 7(&+12/2*< 2QH RI WKH ZRUOGnV PRVW SHUYDVLYH FKHPLFDO FRPSRXQGV LV VLOLFRQ GLR[LGH 6Lf 7KLV FRPSRXQG FDQ H[LVW LQ PDQ\ IRUPV f§ FU\VWDOOLQH RU DPRUSKRXV K\GUR[\ODWHG RU GHK\GUR[\ODWHG f§ EXW LV PRVW RIWHQ FDOOHG VLOLFD DV D JHQHULF QDPH 6LOLFDEDVHG FRPSRXQGV KDYH EHHQ IDEULFDWHG DQG XWLOL]HG E\ PDQNLQG IRU WHQV RI WKRXVDQGV RI \HDUV DOWKRXJK RQO\ LQ WKH SDVW IHZ GHFDGHV KDYH VLJQLILFDQW VWULGHV EHHQ PDGH LQ XQGHUVWDQGLQJ WKH YDULDEOHV WKDW FRQWURO VLOLFD FKHPLVWU\ >@ $SSOLFDWLRQ RI WKLV NQRZOHGJH KDV SURGXFHG PDQ\ XVHIXO PDWHULDOV ZRUWK ELOOLRQV RI GROODUV SHU \HDU KRZHYHU WRGD\nV UDSLGO\ DFFHOHUDWLQJ WHFKQRORJ\ GHPDQGV HYHQ JUHDWHU SHUIRUPDQFH RI VLOLFDWH PDWHULDOV DV ZHOO DV WKH QHHG WR FUHDWH QHZ PDWHULDOV 7KH REMHFWLYH RI WKLV VWXG\ LV WR SURGXFH D QXPEHU RI QHZ PDWHULDOV XVLQJ VROJHO VLOLFD SURFHVVLQJ LQFOXGLQJ f XOWUDSRURXV JHO PRQROLWKV IRU RSWLFDO DQG FKHPLFDO PDWULFHV f XOWUDSXUH PRQROLWKLF JHOJODVVHV ZLWK XOWUDORZ RSWLFDO DEVRUSWLRQ DQG f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

PAGE 9

)XVHG TXDUW] LV PHOWHG DW WHPSHUDWXUHV DERYH LWV OLTXLGXV r&f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f DQG E\ YDFXXP SODVPD R[LGDWLRQ RI VLOLFD WHWUDFKORULGH W\SH ,9f DUH VKRZQ LQ HTXDWLRQV DQG 7\SH ,,, K\GURO\VLVf 6L&8 2 + f§! 6L +&, f 7\SH ,9 R[LGDWLRQf 6&, 2 f§f§! 6 &, f ,Q IDFW LW LV YHU\ GLIILFXOW WR KDYH D FRPSOHWH UHDFWLRQ IRU HLWKHU RI WKHVH WZR HTXDWLRQV &RQVHTXHQWO\ ZDWHU FRQWHQWV RI VHYHUDO WKRXVDQG SSP DUH SUHVHQW LQ W\SH ,,, VLOLFDV DQG 6&, LQ IHZ KXQGUHG SSP LV UHWDLQHG DV DQ XQUHDFWHG UHVLGXDO LQ ERWK W\SH ,,, DQG ,9 VLOLFDV ,Q DGGLWLRQ WR WKHVH WZR LQWULQVLF LPSXULWLHV WKH UHVXOWDQW JODVVHV IURP W\SH ,,, DQG ,9 SURFHVVHV KDYH H[WULQVLF LPSXULWLHV LQ WKH UDQJH RI IHZ SDUWV SHU PLOOLRQ SSPf GXH WR WKH FRQWDPLQDWLRQ RI UDZ PDWHULDOV DQG FUXFLEOHV DW KLJK WHPSHUDWXUHV DERXW r&f 7DEOH _@ OLVWV WKH GRPLQDQW FKDUDFWHULVWLFV RI FRPPHUFLDO EUDQGV RI VLOLFD FRUUHVSRQGLQJ WR WKHVH IRXU W\SHV 7KHLU WUDQVPLVVLRQ FXUYHV DUH VXPPDUL]HG LQ )LJXUH DQG 7DEOH >@ 7\SH DQG ,, JODVVHV KDYH PRUH LPSXULWLHV 7DEOH f ZKLFK PDNH XY WUDQVPLVVLRQ FXUYHV FXW RII DW KLJKHU ZDYHOHQJWKV FXUYHV DQG LQ )LJ f WKDQ WKDW RI W\SH ,,, DQG ,9 JODVVHV FXUYH LQ )LJ f 7KH DPRXQW RI ZDWHU 7DEOH

PAGE 10

7DEOH 3UHSDUDWLRQ DQG FKDUDFWHULVWLFV RI IRXU W\SHV RI YLWUHRXV VLOLFD 7\SH ,, ,,, ,9 3URFHVV (OHFWURPHOWHG )ODPHIXVHG +\GURO\]HG 2[LGL]HG 4XDUW] 4XDUW] 6L&, 6L&, ([DPSOH ,59LWUHRVLOD +HUDVLOE F 6SHFWURVLO :)D ,PSXULW\ ,QIUDVLOE SSPf +RPRVLOE '\QDVLOG 6SHFWURVLOD 6XSUDVLOE F 6XSUDVLO:E 2+ af $ 6E $V % &D &O XS WR &U &R &X *D $X )H /L 0J 0Q +J 3 1D 7L 8 =Q =U D 7KHUPDO 6\QGLFDWH (QJODQG E +HUDXV $PHUVLO +HUDHXV 6D\UHYLOOH 1F &RUQLQJ *ODVV :RUN &RUQLQJ 1< G '\QDVLO %HUOLQ 1-

PAGE 11

:DYHOHQJWK QP )LJXUH 7UDQVPLVVLRQ FXUYHV IRU FRPPHUFLDO YLWUHRXV VLOLFD PP WKLFN

PAGE 12

7DEOH ,GHQWLILFDWLRQ RI WUDQVPLVVLRQ FXUYHV RI VLOLFD JODVVHV 0DQXIDFWXUHU 3URGXFW QDPH 7\SH 89 FXUYH LQ )LJ ,5 FXUYH LQ )LJ $PHUVLO ,QF +HUDVLO ,, % +HUDHXVf ,QIUDVLO & +RPRVLO ,, % 6XSUDVLO ,,, $ 6XSUDVLO: ,9 & &RUQLQJ *ODVV &RGH ,,, $ :RUNV &RGH ,9 & '\QDVLO &RUS RI $PHULFD '\QDVLO ,,, $ 7KHUPDO 6\QGLFDWH 6SHFWURVLO ,,, $ /WG 6SHFWURVLO :) ,9 & 5YLWUHRVLO &

PAGE 13

f LQ VLOLFD JODVV GHSHQGV RQ ZKLFK W\SH RI SURFHVV LV XVHG )RU H[DPSOH 6SHFWURVLL :) W\SH ,9f LQ 7DEOH KDV D ZDWHU FRQWHQW OHVV WKDQ SSP FRPSDUH WR SSP IRU 6XSUDVLO W\SH ,,,f ,W LV REVHUYHG WKDW WKHUH LV QR VLJQLILFDQW VKLIW LQ WKH XY FXW RII EHWZHHQ W\SH ,,, DQG ,9 VLOLFDV GXH WR WKH LQFUHDVHG ZDWHU FRQWHQW LI WKH RWKHU LPSXULWLHV DUH FRQVWDQW +RZHYHU LQ WKH LQIUDUHG UDQJH ZDWHU W\SH ,,, FXUYH $ LQ )LJ f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f LQ WKH VROXWLRQ >@ ,Q WKLV VWXG\ DOO FROORLGDO SDUWLFOHV DUH V\QWKHVL]HG E\ WKH K\GURO\VLV RI WHWUDPHWK\ORUWKRVLOLFDWH 7026f >6L2&+f@ IROORZHG E\ WKH JURZWK RI WKH K\GURO\]HG VSHFLHV >6L2&+fQ2+fQ ZLWK Q@ > @

PAGE 14

7\SH 7\SH t ,, 7\SH ,,, 7\SH ,9 7DEOH /LPLWV IRU WKH IRXU W\SHV RI VLOLFD IDEULFDWLRQ SURFHVVHV )DEULFDWLRQ /LPLWV f %DG KRPRJHQHLW\ JUDQXODU PLFURVWUXFWXUH DQG EXEEOHVf f 1RWLFHDEOH ZDWHU FRQWHQW IHZ WHQV WR KXQGUHGV SSP f +LJK LPSXULWLHV LQ WKH UDQJH RI IHZ SSP IURP QDWXUH TXDUW] PLQHUDO f 0LFURPHWHU VFDOH VWUXFWXUDO PDQLSXODWLRQ TXDUW] LV JURXQG WR IHZ PLFURPHWHUV EHIRUH VLQWHULQJ f +LJK VLQWHULQJ WHPSHUDWXUH DERYH r&f Df +LJK HQHUJ\ FRVW Ef 5HDFW ZLWK FUXFLEOH WKXV LPSXULWLHV Ff 3RVVLEOH LQLWLDWH FU\VWDOOL]DWLRQ f +LJK ZDWHU FRQWHQWDERYH SSPf f +LJK VLQWHULQJ WHPSHUDWXUH DERYH r&f Df +LJK HQHUJ\ FRVW Ef 5HDFW ZLWK FUXFLEOH WKXV LPSXULWLHV Ff 3RVVLEOH LQLWLDWH FU\VWDOOL]DWLRQ f 'HWHFWDEOH ZDWHU FRQWHQW DURXQG SSPf f +LJK VLQWHULQJ WHPSHUDWXUH DERYH r&f Df +LJK HQHUJ\ FRVW Ef 5HDFW ZLWK FUXFLEOH WKXV LPSXULWLHV Ff 3RVVLEOH LQLWLDWH FU\VWDOOL]DWLRQ

PAGE 15

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f WKLV LV GHVFULEHG DV WKH JHODWLRQ SRLQW 6ROLGV WHQG WR GHFUHDVH WKHLU LQWHUIDFLDO DUHD VR DV WR PLQLPL]H VXUIDFH HQHUJ\ 7KHUHIRUH DIWHU WKH JHODWLRQ SRLQW KDV EHHQ UHDFKHG WKH ZHDNO\ FRQQHFWHG VSKHULFDO SDUWLFOH FKDLQV WHQG WR PLQLPL]H VXUIDFH HQHUJ\ E\ SDUWLFOH UHDUUDQJHPHQW WKHUHE\ IRUPLQJ D VWURQJ ILEULOODUVKDSHG XOWUDVWUXFWXUH 7KLV SKHQRPHQRQ FRQWLQXHV GXULQJ WKH DJLQJ SURFHVV DOVR WHUPHG V\QHUHVLVf LQ ZKLFK OLTXLG LV H[SHOOHG IURP WKH JHO ERG\ DQG WKH ZHDN JHO VKULQNV DQG EHFRPHV VWURQJHU ,Q WKLV VWXG\ WKH ILUVW JRDO GHVFULEHG LQ &KDSWHU LV WKH SURGXFWLRQ RI VLOLFD EDVHG PRQROLWKLF GULHG [HURJHOV FRPSRVHG RI Df SXUH VLOLFD DQG Ef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2 ;UD\ GLIIUDFWLRQ VWXGLHV E\ 0R]]L :DUUHQ DQG 8KOPDQQ > @

PAGE 16

KDYH VKRZQ WKDW VLOLFRQ IRUPV ERQGV ZLWK R[\JHQ RI YDULDEOH ERQG DQJOHV WKDW DUH b ZLWKLQ WKH r PD[LPXP LQ WKH GLVWULEXWLRQ RI 6L26L DQJOHV 9DULRXV DUUDQJHPHQWV RI WKHVH 6L2J WHWUDKHGUD DUH SRVVLEOH LQ QRQFU\VWDOOLQH VLOLFD JHOV %RQGLQJ R[\JHQV DW WKH FRUQHUV RI WZR VLOLFD WHWUDKHGUD FDQ EH HDVLO\ GLVFRQQHFWHG LQ WKH SUHVHQFH RI XQHYHQ K\GURVWDWLF VWUHVVHV DQG ZDWHU >@ '&&$nV FDQ EH XVHG WR PLQLPL]H WKH SDUWLFOH VL]H ZLWKLQ WKH SRO\PHUL]HG FKDLQ WKHUHE\ LPSURYLQJ WKH VWUHQJWK RI WKH JHO VWUXFWXUH VR WKDW GXULQJ WKH FULWLFDO GU\LQJ SURFHVV WKH JHO FDQ HQGXUH GLIIHUHQWLDO HYDSRUDWLRQ ZLWKRXW LQLWLDWLQJ FUDFNLQJ 7KH SURFHVVLQJ DQG SK\VLFDO SURSHUWLHV RI GULHG PRQROLWKLF VLOLFD [HURJHOV KHDWHG IURP & WR 4r& DUH GLVFXVVHG LQ &KDSWHU 7KLV XOWUDSRURXV PDWHULDO KDV GHQVLWLHV UDQJLQJ IURP JFP WR JFP GHSHQGLQJ RQ WKH LQLWLDO FRQGLWLRQV RI WKH VRO VXFK DV WKH YDULDWLRQ RI '&&$ DQGRU WKH DPRXQW RI ZDWHU XVHG DV ZHOO DV WKH DJLQJ DQG GU\LQJ WHPSHUDWXUHV 7ZR W\SHV RI ZDWHU H[LVW ZLWKLQ WKH GULHG [HURJHO VWUXFWXUH f§ FKHPLFDO ZDWHU DQG SK\VLFDO ZDWHU >@ ZKLFK PXVW EH UHPRYHG WR DFKLHYH PRQROLWKLF RSWLFDO FRPSRQHQWV :DWHU LQ VROXWLRQ FDQ K\GURO\]H WKH VLOLFRQR[\JHQVLOLFRQ ERQG 7KH K\GUR[\O LRQnV R[\JHQ LV FRYDOHQWO\ ERQGHG WR VLOLFRQ ZKHUHDV WKH K\GURJHQ LRQ IRUPV DQ LRQLF ERQG WR WKH R[\JHQ &RQVHTXHQWO\ FKHPLFDO ZDWHU UHVXOWV ZLWK K\GUR[\O JURXSV VWURQJO\ DWWDFKHG WR WKH JHOnV VXUIDFH 7KH SK\VLFDO ZDWHU DVVRFLDWHG ZLWK K\GURJHQERQGLQJ RI VXUIDFH K\GUR[\O JURXSV H[LVWV ZLWKLQ WKH XOWUDSRURXV VSDFH RI WKH JHO ERG\ $ PDMRU SUREOHP ZLWK PRQROLWKLF VLOLFD [HURJHOV HVSHFLDOO\ IRU KLJK WUDQVPLWWDQFH RSWLFDO FRPSRQHQWV LV WKH UHPRYDO RI FKHPLFDOO\ ERQGHG ZDWHU DOVR FDOOHG D VLODQRO JURXS 7KH FKHPLFDOO\ ERQGHG VLODQROV JLYH ULVH WR WKH IXQGDPHQWDO YLEUDWLRQ RI K\GUR[\O LRQV RFFXUULQJ DW D ZDYHOHQJWK RI QP $OVR SUHVHQW DUH YLEUDWLRQDO RYHUWRQHV DQG FRPELQDWLRQV RI WKLV LRQ DQG DVVRFLDWHG ZDWHU RFFXUULQJ DW WKH IROORZLQJ ZDYHOHQJWKV QP QP QP QP QP QP QP QP QP QP QP QP

PAGE 17

QP 7KHVH ,5 DEVRUSWLRQV DUH WKH UHVXOW RI HOHFWURPDJQHWLF YLEUDWLRQDO LQWHUDFWLRQV ZLWK WKH HOHFWURQV DWRPV DQG PROHFXOHV RI WKH JHO ZDWHU 6HOHFWLYHO\ DEVRUEHG OLJKW HQHUJ\ VXFK DV WKLV LV PRVWO\ FRQYHUWHG LQWR KHDW &RQVHTXHQWO\ LW LV LPSRUWDQW WR UHGXFH WKH K\GUR[\O JURXSV WR QRQGHWHFWDEOH OHYHOV LQ RUGHU WR PLQLPL]H DEVRUSWLRQ ORVV HVSHFLDOO\ IRU RSWLFDO OHQVHV RSWRHOHFWURQLF VLJQDO SURFHVVRUV RSWLFDO ILEHU ILOWHUV DQG ODVHU UHVRQDQW KRVW V\VWHPV 7KHUHIRUH PRQLWRULQJ WKH ,5 DEVRUSWLRQ SHDNV LV D SULPDU\ PHWKRG IRU GHWHUPLQLQJ WKH GHJUHH RI GHK\GUDWLRQ DFKLHYHG GXULQJ GHQVLILFDWLRQ > @ &RQVHTXHQWO\ WKH VHFRQG JRDO RI WKLV VWXG\ LV WR GHK\GUDWH DQG GHQVLW\ PRQROLWKLF VLOLFD [HURJHOV WKLV LV GHVFULEHG LQ &KDSWHU 7ZR PHWKRGV DUH LQYHVWLJDWHG f VLQWHULQJ VDPSOHV LQ DQ DLU DWPRVSKHUH DQG f FKHPLFDO WUHDWPHQW DQG VLQWHULQJ LQ D FRQWUROOHG JDV DWPRVSKHUH HJ FDUERQ WHWUDFKORULGHf $W VXIILFLHQW WHPSHUDWXUHV WKHVH JDVHV FDQ UHDFW ZLWK WKH K\GUR[\O JURXSV WR IRUP K\GURJHQ FKORULGH ZKLFK HVFDSHV IUHHO\ IURP WKH XQFORVHG XOWUDSRUHV >@ 7KH GHK\GUDWHG [HURJHO VDPSOHV DUH WKHQ H[SRVHG WR D KLJKHU WHPSHUDWXUH IRU IXOO VLQWHULQJ 7KH WKLUG JRDO LV WR GHWHUPLQH WKH SK\VLFDO SURSHUWLHV RI PRQROLWKLF IXOO\ GHK\GUDWHG JHOVLOLFD JODVVHV ,Q &KDSWHU YDULRXV SK\VLFDO SURSHUWLHV RI WKH GHQVH JHO VLOLFD JODVVHV DUH FRPSDUHG ZLWK FRPPHUFLDO PHOWFDVW YLWUHRXV VLOLFD JODVVHV IXVHG TXDUW]f DQG RWKHU KLJKTXDOLW\ RSWLFDO VLOLFD JODVVHV V\QWKHWLF IXVHG VLOLFDf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

PAGE 18

ERQGLQJ VWUHQJWK ZKLFK FDQ SURGXFH D GUDPDWLF VKLIW LQ WKHLU FRORU UHVSRQVH )RU H[DPSOH D r& VLOLFD [HURJHO FRQWDLQLQJ b FREDOW ,V D UHGGLVKRUDQJH FRORU ZKHUHDV WKH r& VDPSOH LV D GHHS EOXH DQG WKH r& VDPSOH KDV D JUHHQLVKEODFN FRORU )LQDOO\ D VXPPDU\ &KDSWHU f LV SUHVHQWHG ZKLFK UHYLHZV WKH SUHVHQW VWDWH RI VROJHO SURFHVVLQJ VFLHQFH DV DSSOLHG WR JHOVLOLFD RSWLFDO PRQROLWKV DQG WKH SURSHUWLHV RI WKHVH XQLTXH PDWHULDOV 4XHVWLRQV VWLOO WR EH DQVZHUHG E\ IXWXUH LQYHVWLJDWLRQV DUH DOVR LQFOXGHG LQ WKH VXPPDU\ FKDSWHU

PAGE 19

&+$37(5 62/*(/ 75$16)250$7,21 $1' (;3(5,0(17$/ 352&('85(6 ,QWURGXFWLRQ 'XULQJ UHFHQW \HDUV PDQ\ UHVHDUFKHUV KDYH DWWHPSWHG WR SURGXFH ODUJH PRQROLWKLF GULHG [HURJHOV KRZHYHU D UHOLDEOH SURFHVV KDG QRW \HW EHHQ HVWDEOLVKHG DW WKH WLPH WKLV ZRUN EHJDQ >@ 'LIILFXOWLHV DVVRFLDWHG ZLWK WKLV VROJHO SURFHVVLQJ PHWKRG DULVH GXULQJ DOO SKDVHV RI DJLQJ GU\LQJ DQG GHQVLILFDWLRQ FOHDUO\ LQGLFDWLQJ LQVXIILFLHQW XQGHUVWDQGLQJ RI EDVLF FKDQJHV LQ WKH XOWUDVWUXFWXUH GXULQJ WKH VROJHO WUDQVIRUPDWLRQ DQG LQ WKH FKHPLFDO UHDFWLRQV RI WKH VROYHQWV SUHFXUVRUV DQG FDWDO\VWV LQYROYHG ,Q JHQHUDO FUDFN IRUPDWLRQ GXULQJ GU\LQJ LV D UHVXOW RI VWURQJ K\GURVWDWLF VWUHVVHV ZLWKLQ D UHODWLYHO\ ZHDN JHO VWUXFWXUH &DWDVWURSKLF IDLOXUH FDQ EH DYRLGHG E\ DGMXVWLQJ WKH PHFKDQLFDO VWUHQJWK RI WKH JHO VWUXFWXUH WR H[FHHG WKDW RI WKH K\GURVWDWLF IRUFH DQGRU E\ GHFUHDVLQJ WKH K\GURVWDWLF VWUHVV UHODWLYH WR WKH JHOnV VWUHQJWK 7KH REMHFW RI WKLV FKDSWHU LV WR GHVFULEH WKH SULQFLSDO PHFKDQLVPV RI WKH VROJHO PHWKRG E\ ZKLFK PRQROLWKLF [HURJHOV PD\ EH UHOLDEO\ SURGXFHG )RXU IDFWRUV DUH XVHG WR GHVFULEH WKH VROJHO WUDQVIRUPDWLRQ XS WR WKH JHODWLRQ SRLQW f WKH LVRHOHFWULF SRLQW LHSf f WKH SRLQW RI ]HUR VXUIDFH FKDUJH S]Ff f WKHUPDOO\ DFWLYDWHG SDUWLFOH PRYHPHQW %URZQLDQ PRWLRQf DQG f 9DQ GHU :DDOV IRUFH 7KUHH NLQGV RI GULHG PRQROLWKLF JHO VDPSOHV ZHUH URXWLQHO\ SUHSDUHG WR DLG LQ WKLV VWXG\ SXUH VLOLFD VLOLFD GRSHG ZLWK WUDQVLWLRQ HOHPHQWV DQG VLOLFD GRSHG ZLWK UDUH HDUWK HOHPHQWV OLWHUDWXUH 5HYLHZ RI 6RO*HO 7UDQVIRUPDWLRQ 0RGHOLQJ 'U 5DOSK ,OHUnV SLRQHHULQJ ZRUN LQ WKH LQYHVWLJDWLRQ RI VLOLFD FKHPLVWU\ LV WKH IRXQGDWLRQ RI PDQ\ RI WKH LGHDV GLVFXVVHG LQ WKLV FKDSWHU +HU IRXQG WKDW VLOLFD JHOV FDQ EH

PAGE 20

REWDLQHG IURP VXSHUVDWXUDWHG DTXHRXV VROXWLRQV SURGXFHG E\ RQH RI WKH IROORZLQJ PHWKRGV ,f &RQFHQWUDWLQJ DQ XQVDWXUDWHG VLOLFD VROXWLRQ E\ HYDSRUDWLQJ LWV VROYHQW f &RROLQJ D KRW VDWXUDWHG VLOLFD VROXWLRQ L Lf /RZHULQJ WKH S+ RI DQ DTXHRXV VROXWLRQ RI D VROXEOH VLOLFDWH EHORZ ,Yf +\GURO\]LQJ 6,25f ZKHUH 5 LV &+ &+ RU &+f ,Q WKLV VWXG\ DOO RI WKH PRQRPHUV ZHUH SURGXFHG E\ FKHPLFDOO\ K\GURO\]LQJ WHWUDPHWK\ORUWKRVOOOFDWH 7026f DV LQGLFDWHG LQ PHWKRG OYf 7KH DPRXQW RI PRQRPHU JHQHUDWHG ZLWKLQ D JLYHQ SHULRG RI WLPH GHSHQGV RQ WHPSHUDWXUH DQG WKH UHODWLYH DPRXQWV RI '&&$ ZDWHU DQG 7026 :KHQ D VROXWLRQ RI PRQRPHU 6L2+f LV IRUPHG DW D FRQFHQWUDWLRQ JUHDWHU WKDQ WKH VROXELOLW\ RI WKH VROLG SKDVH RI DPRUSKRXV JHO VLOLFD LQ ZDWHU DQG ,Q WKH DEVHQFH RI D VROLG SKDVH RQ ZKLFK WKH VROXEOH VLOLFD PLJKW EH GHSRVLWHG WKH PRQRPHUV WKHQ SRO\PHUL]H E\ FRQGHQVDWLRQ WR IRUP GLPHUV WZR VLOLFRQVf WKHQ WHWUDPHUV IRXU VLOLFRQVf WKHQ SDUWLFOHV HLJKW RU PRUH VLOLFRQVf )RU PRVW DONR[LGH V\QWKHVHV D SRO\PHUL]DWLRQ UHDFWLRQ RFFXUV EHIRUH K\GURO\VLV LV FRPSOHWHG DV HYLGHQFHG E\ 6L 105 VWXGLHV > @f $V VKRZQ LQ )LJXUHV DQG WKH SDUWLFOHnV VL]H DW DQ\ PRPHQW RI JURZWK LV FRQWUROOHG E\ WKH 2VWZDOG ULSHQLQJ PHFKDQLVP >VHH S LQ UHI @ DQG HVVHQWLDOO\ LV GHWHUPLQHG E\ WKH S+ RI WKH '&&$VLOLFLF DFLG VROXWLRQ 9\VRWVNLL DQG 6WUD]KHVNR >@ GHVFULEH WKDW LQ WKH SUHVHQFH RI D JLYHQ DFLG WKH JURZWK RI PRQRPHUV LV JRYHUQHG E\ WKH FKHPLFDO HTXLOLEULXP NLQHWLFV RI WKH VRO DQG LV PLQLPL]HG DW WKH LVRHOHFWULF SRLQW LHSf 7KLV LPSOLHV WKDW WKH PRQRPHUV JURZ WR VRPH FHUWDLQ VL]H EHIRUH WKH VROXWLRQ UHDFKHV LWV RZQ LHS 7KH LHS RFFXUV ZKHQ WKH QHW HOHFWULFDO PRELOLW\ RI VXUIDFH LRQV RQ WKH VLOLFD SDUWLFOHV LV ]HUR DQG DW D S+ DW ZKLFK WKHUH LV QR FKDUJH RXWVLGH WKH K\GURHOHFWULF VOLS SODQH RXWVLGH WKLV SODQH WKH OLTXLG LV IUHH WR PRYH LQVLGH WKH SODQH WKH OLTXLG PROHFXOHV DUH KHOG WRR WLJKWO\ WR PRYHf >VHH S

PAGE 21

I 2 c + f§2 a6L f§2f§+ g 2 2 L + f§2f§6L f§2f§6L f§2f§+ L R L + PRQRPHU 2 O + GLPHU + 2 + L + f§2 f§6L f§2 f§6c f§2 f§+ + f§26L f§2f§6L f§2f§+ 2 + 2 F\FOLF WHWUDPHU SDUWLFLH VL]H SDUWLFOH VL]H VPDOOHU WKDQ ƒ ODUJHU WKDQ ƒ )LJXUH 3DUWLFOH JURZWK LQ VROXWLRQ

PAGE 22

UHODWLYH WLPH VFDOH )LJXUH 3RO\PHUL]DWLRQ UHDFWLRQ RFFXUV EHIRUH K\GURO\VLV LV FRPSOHWHG

PAGE 23

LQ UHI @ %HORZ DUH HTXDWLRQV UHODWHG WR SDUWLFOH JURZWK XQGHU WZR GLIIHUHQW S+ FRQGLWLRQV DQG ZLOO EH GHVFULEHG DV WZR PRGHOV LQ WKH IROORZLQJ SDUDJUDSK S+ >+@ DV D FDWDO\VW 6LQ2D2+fE 6L2+f 2+ a! 6LQ2D2+fEL 26L2+f + f S+ >2+@ DV D FDWDO\VW 6LQ2D2+fE 26L2+f + 6LQ2D2+fEL26L2+f + f 6LQ2D2+f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

PAGE 24

5HODWLYH JHODWLRQ WLPH S+ )LJXUH 5HODWLYH JHODWLRQ WLPH YHUVXV VROXWLRQ DFLGLW\

PAGE 25

5HODWLYH VXUIDFH DUHD S+ )LJXUH 5HODWLYH VXUIDFH DUHD YHUVXV VROXWLRQ DFLGLW\

PAGE 26

D VLJQLILFDQW DPRXQW RI IUHH ZDWHU HTXDWLRQ f ZKLFK G\QDPLFDOO\ UHGXFHV WKH K\GURJHQ LRQ FRQFHQWUDWLRQ 7KLV GLOXWLRQ VORZV WKH UHDFWLRQ EHWZHHQ PRQRPHU DQG WKH SDUWLFOH VXUIDFH FDXVLQJ D EXLOG XS RI PRQRPHUV DURXQG WKH SDUWLFOH ZKLOH WKH WRWDO K\GURJHQ FRQFHQWUDWLRQ LQ VROXWLRQ LV UHGXFHG 7KLV FDXVHV WKH S+ WR EH LQFUHDVHG WR WKH LVRHOHFWULF SRLQW ZLWK D S+ DSSUR[LPDWHO\ HTXDO WR 7KLV LPSOLHV WKDW WKH VWURQJHU LQLWLDO DFLGLF VROXWLRQ S+ f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f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f DW S+ >@ PDUNV WKH EHJLQQLQJ RI JHODWLRQ XQGHU WKH LQIOXHQFH RI WKHUPDOO\ DFWLYDWHG %URZQLDQ PRWLRQ DQG 9DQ GHU :DDOV DWWUDFWLYH IRUFH IURP WKLV VWURQJO\ DFLGLF VRO :HDN $FLG 0RGHO 7KH PHFKDQLVP IRU JHODWLRQ LQ D ZHDNHU DFLG VROXWLRQ S+ S+ f LV VRPHZKDW GLIIHUHQW IURP WKDW RI D VWURQJ DFLG VROXWLRQ DV VKRZQ LQ )LJXUH 7KH UHGXFWLRQ LQ K\GURJHQ LRQ FRQFHQWUDWLRQ HIIHFWLYHO\ ZHDNHQV LWV VWUHQJWK DV DQ DFLG FDWDO\VW SUHYHQWLQJ WKH K\GURJHQ LRQ IURP DWWUDFWLQJ WKH K\GUR[\O JURXS IURP WKH

PAGE 27

PRQRPHUV H[SRVH WKHLU SRVLWLYHO\ FKDUJHG HOHFWULF FORXG WRZDUG SDUWLFOH VXUIDFH HOHFWULFDO GRXEOH OD\HU )LJXUH 3DUWLFOHV LQ VWURQJ DFLGLF VROXWLRQ S+LHS af

PAGE 28

SDUWLFOHV VXUIDFH H[SRVHV SRVLWLYHO\ FKDUJHG HOHFWULF FORXG WRZDUG QHJDWLYHO\ FKDUJHG PRQRPHU LQ WKH ZHDN DFLG VROXWLRQ HOHFWULFDO GRXEOH OD\HU )LJXUH 3DUWLFOHV LQ ZHDN DFLGLF VROXWLRQ S+!LHS S+ S+ f

PAGE 29

PRQRPHUV DURXQG WKH SDUWLFOH DQG H[SRVLQJ WKH QHJDWLYHO\ FKDUJHG n26L2+f PROHFXOHV HTXDWLRQ f ZKLFK FDQ UHDFW ZLWK WKH SDUWLFOHnV SRVLWLYHO\ FKDUJHG VXUIDFH 5DWKHU WKH QHJDWLYHO\ FKDUJHG R[\JHQ RI WKH K\GUR[\O LRQV LQ VROXWLRQ FDQ DWWUDFW D K\GURJHQ IURP WKH PRQRPHU 7KLV IRUPV IUHH ZDWHU DQG OHDYHV WKH QHJDWLYHO\ FKDUJHG R[\JHQ DV D VLWH QRZ DYDLODEOH WR UHDFW ZLWK WKH SRVLWLYHO\ FKDUJHG VLOLFRQ RQ WKH SDUWLFOH VXUIDFH WKHUHE\ UHJHQHUDWLQJ WKLV EDVLF FDWDO\VW DV D K\GUR[\O LRQ LV UHOHDVHG :LWK WKH SURGXFWLRQ RI IUHH ZDWHU WKH K\GUR[\O FRQFHQWUDWLRQ LV UHGXFHG GHFUHDVLQJ WKH S+ DV ZHOO DV WKH K\GUR[\O LRQnV DELOLW\ WR DFW DV FDWDO\VW ZKLFK FDXVHV D EXLOGXS RI PRQRPHUV VXUURXQGLQJ WKH SDUWLFOH VXUIDFH $V WKH FRQFHQWUDWLRQ RI WKHVH PRQRPHUV ZLWKLQ WKH VOLS SODQH UHDFKHV D PD[LPXP DW DERXW S+ WKH LVRHOHFWULF SRLQW LHSf LV DWWDLQHG $W WKLV S+ WKH K\GURJHQ LRQ DFWV DV D FDWDO\VW SURPRWLQJ WKH UHDFWLRQ EHWZHHQ WKH PRQRPHUV DQG WKH VXUIDFH K\GUR[\O JURXSV ZKLFK IDFLOLWDWHV SDUWLFOH JURZWK )UHH ZDWHU LV D E\n SURGXFW RI WKLV UHDFWLRQ UHGXFLQJ WKH K\GURJHQ LRQ FRQFHQWUDWLRQ DQG LQFUHDVLQJ WKH S+ 7KLV SURFHVV FRQWLQXHV XQWLO WKH PRQRPHU FRQFHQWUDWLRQ LQVLGH WKH VOLS SODQH LV H[KDXVWHG DQG WKH HOHFWULFDO GRXEOH OD\HU HOLPLQDWHG 7KXV WKH SRLQW RI ]HUR VXUIDFH FKDUJH S]Ff KDV EHHQ UHDFKHG DQG JHODWLRQ EHJLQV XQGHU WKH LQIOXHQFHV RI WKHUPDOO\ DFWLYDWHG %URZQLDQ PRWLRQ DQG 9DQ GHU :DDOV DWWUDFWLYH IRUFH %URZQLDQ 0RWLRQ 9DQ WWHU-IOWHDOVADSUI LRWHLSDULLROD %RQGLQJ 0RGHOV :KHQ PRQRPHUV FRPH WRJHWKHU WR IRUP YHU\ VPDOO ƒ ƒf >@ XQLIRUP XQFKDUJHG S]Ff SDUWLFOHV WKHLU PRWLRQ LV HVVHQWLDOO\ JRYHUQHG E\ WKHUPDO GLIIXVLRQ DV GHVFULEHG E\ WKH GLIIXVLRQ HTXDWLRQ EHORZ .7UF W_ Gf f ZKHUH LV WKH GLIIXVLRQ FRHIILFLHQW ‘Q LV YLVFRVLW\ G LV WKH HIIHFWLYH LQVWDQWDQHRXV GLDPHWHU RI WKH SRO\PHUL]HG FOXVWHU

PAGE 30

. LV %ROW]PDQQnV FRQVWDQW 7 LV DEVROXWH WHPSHUDWXUH 7KH DYHUDJH GLVSODFHPHQW ; RI D SDUWLFOH IURP WLPH ]HUR # S]Ff WR DQ\ SRLQW LQ WLPH W LV ; 'Wf f 3ULRU WR UHDFKLQJ WKH S]F WKH YLVFRVLW\ RI WKH VRO LQFUHDVHV RQO\ VOLJKWO\ DV VKRZQ LQ )LJXUH >@ $W WKH SRLQW S]Ff LV DFKLHYHG WKH VPDOO SDUWLFOHV DUH KRPRJHQHRXVO\ GLVWULEXWHG WKURXJKRXW WKH VROYHQW DV VKRZQ LQ )LJXUH *RYHUQHG E\ %URZQLDQ PRWLRQ HTXDWLRQ f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f ZDWHU DQG 7026f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

PAGE 31

UHODWLYH YLVFRVLW\ WJ UHODWLYH WLPH VFDOH rWJ LV WKH JHODWLRQ WLPH )LJXUH 5HODWLYH YLVFRVLW\ YHUVXV WLPH

PAGE 32

)LJXUH +RPRJHQHRXV SDUWLFOH GLVWULEXWLRQ WKURXJKRXW WKH VROYHQW

PAGE 33

Df %URZQLDQ PRWLRQ DQG 9DQ GHU :DDOV IRUFHV Ef EDVH FDWDO\VW >2+ @ )LJXUH 3DUWLFOHV FROOLGH UDQGRPO\ ZLWK WKH KHOS RI 9DQ GHU :DDOV DWWUDFWLYH IRUFHV %URZQLDQ PRWLRQ DQG EDVH FDWDO\VW

PAGE 34

ƒ )LJXUH $FLG FDWDO\]HG SDUWLFOHV FRQVWLWXWH ILEULOODU FKDLQV WKURXJKRXW WKH YROXPH RI VRO

PAGE 35

*HO 7LPH PLQf )LJXUH *HODWLRQ WLPH YHUVXV WHPSHUDWXUH

PAGE 36

R[DOLF DFLG JUDPf )LJXUH *HODWLRQ WLPH YHUVXV R[DOLF DFLG FRQWHQW

PAGE 37

*HODWLRQ WLPH PLQf )LJXUH *HODWLRQ WLPH YHUVXV ZDWHU FRQWHQW

PAGE 38

)LJXUH *HODWLRQ WLPH YHUVXV 7026 FRQWHQW

PAGE 39

&KDUDFWHUL]DWLRQ RI *HODWLRQ 3URIHVVRU 3DXO )ORU\nV WKHRU\ RI JHO IRUPDWLRQ > @ ZLWK ZKLFK +HU DJUHHV >VHH S LQ UHI @ QRWHV WKDW WKH VLOLFD PRQRPHU KDV IRXU SRO\PHUL]DWLRQ IXQFWLRQDO JURXSV I f 7KH GHJUHH RI SRO\PHUL]DWLRQ '3f REWDLQDEOH LQ D V\VWHP LV WKHUHIRUH GHVFULEHG E\ WKH HTXDWLRQ '3 SIf f LQ ZKLFK S LV WKH SHUFHQWDJH RI UHDFWLQJ PRQRPHUV WKDW LV WKH IUDFWLRQ RI WKH WRWDO FRQFHQWUDWLRQ RI PRQRPHU ZKLFK LV WKH UHDFWLRQ SURGXFW IURP 7026f DQG 7 LV WKH QXPEHU RI SRO\PHUL]DWLRQ IXQFWLRQDO JURXSV $W WKH JHODWLRQ SRLQW WKH GHJUHH RI SRO\PHUL]DWLRQ DSSURDFKHV LQILQLW\ WKHUHIRUH SIf PXVW HTXDO ]HUR )RU I WKH SHUFHQWDJH RI WRWDO FRQFHQWUDWLRQ RI PRQRPHU JRLQJ LQWR JHO SKDVH PXVW HTXDO b 6LQFH HTXDO DPRXQWV RI PRQRPHU H[LVW LQ WKH OLTXLG DV ZHOO DV LQ WKH JHO QR UHIUDFWLYH LQGH[ FKDQJH LV REVHUYHG DW WKH JHODWLRQ SRLQW &RQVHTXHQWO\ WKH [HURJHO UHPDLQ RSWLFDOO\ WUDQVSDUHQW WKURXJKRXW JHODWLRQ $JLQJ 0HFKDQLVP $JLQJ LV D SURFHVV E\ ZKLFK WKH JHO VWUXFWXUH LV UHLQIRUFHG YLD VXUIDFH DUHD PLQLPL]DWLRQ RI WKH VSKHULFDO SDUWLFOH FKDLQV WKLV LV VKRZQ LQ )LJXUH 7KH VXUIDFH DUHD FDQ EH PLQLPL]HG E\ IRXU SRVVLEOH PHFKDQLVPV f FRQGHQVDWLRQ RI VXUIDFH VLODQRO JURXSV ]LSSHU HIIHFWf ZKLFK FUHDWHV VWUHVV DQG WKHQ UHVXOWV LQ YDFDQFLHV LQ WKH QHFN DUHD EHWZHHQ SDUWLFOHV f WKHUPDOO\ DFWLYDWHG WUDQVSRUWDWLRQ RI VLOLFD PROHFXOHV IURP WKH YROXPH RU IURP WKH SDUWLFOH QHFN ERXQGDU\ WR YDFDQFLHV f GHSRVLWLRQ RI PRQRPHUV IURP WKH OLTXLG LQWR WKH QHJDWLYH FXUYDWXUH DUHD RI WZR ZHDNO\ FRQQHFWHG VSKHULFDO SDUWLFOHV DQG f GLVVROXWLRQ RI PRQRPHU IURP WKH SDUWLFOHVn DUHD RI SRVLWLYH FXUYDWXUH LQWR WKH SRUH OLTXLG DV VKRZQ LQ )LJXUH 7KH ILUVW WKLUG DQG IRXUWK PHFKDQLVPV GR QRW UHVXOW LQ JHO VKULQNDJH WKH VHFRQG RI WKHVH PHFKDQLVPV GRHV >@ 7KH SDUWLFOH UHDUUDQJHPHQW LQYROYHG LQ WKH VHFRQG

PAGE 40

Df 1R VXUIDFH DUHD PLQLPL]DWLRQ DW WKH WLPH RI JHODWLRQ SRLQW G Ef VXUIDFH PLQLP]HG DIWHU DJLQJ )LJXUH 6XUIDFH PLQLPL]DWLRQ LQ WKH QHFN DUHD

PAGE 41

DfDW WKH WLPH RI JHODWLRQ SRLQW W f \ EfWKH ILUVW PHFKDQLVP IRUPDWLRQ RI YDFDQFLHV LQ WKH QHFNV RI FKDLQ WKH WRWDO OHQJWK G GRHV QRW FKDQJH FfWKH VHFRQG PHFKDQLVP PLJUDWLRQ RI YDFDQLFHV IURP QHFN DUHD RXW RI JHO ERG\ WKH WRWDO OHQJWK G VKULQNV GfVLODQRO JURXSV GHSDUW IURP WKH SRVLWLYH FXUYDWXUH DUHD RI SDUWLFOHnV VXUIDFH WKH WKLUG PHFKDQLVPf DQG GHSRVLW RQ WKH QHJDWLYH FXUYDWXUH DUHD WKH IRXUWK PHFKDQLVPf Y n PRQRPHUV GHSRVLW )LJXUH 6XUIDFH PLQLPL]DWLRQ GXULQJ DJLQJ

PAGE 42

PHFKDQLVP LV LQLWLDWHG E\ WKHUPDO HQHUJ\ 7KHUHIRUH WKH KLJKHU WKH DJLQJ WHPSHUDWXUH WKH IDVWHU LV WKH UDWH RI PDWWHU PLJUDWLRQ WR YDFDQFLHV DQG WKH PRUH UDSLG LV JHO VKULQNDJH DV VKRZQ LQ )LJXUH $ERXW WKH VDPH PD[LPXP VKULQNDJH bf LV DVVRFLDWHG ZLWK HDFK DJLQJ WHPSHUDWXUH ,W LV SRVVLEOH WKDW WKH VDPH DPRXQW RI YDFDQFLHV DUH TXLFNO\ FUHDWHG LQVLGH WKH QHFNV EHWZHHQ SDUWLFOHV GXULQJ WKH ILUVW VWDJH PHFKDQLVP 1R IRU DOO LGHQWLFDO JHOV 6XEVHTXHQWO\ DOO RI WKHVH YDFDQFLHV DUH DQQHDOHG RXW RI WKH JHO ERG\ LQ WKH VHFRQG VWDJH PHFKDQLVP 1R DQG WKHQ HTXDO VKULQNDJH LV REWDLQHG 7KH VDPH PD[LPXP VKULQNDJH LQ WKH DJLQJ VWDJH LV SUREDEO\ SUHGHWHUPLQHG E\ WKH SURFHVVLQJ FKDUDFWHULVWLFV RI HDFK JHO HJ S+ ZDWHU '&&$ 7026 UDWLRf 7KH JHO VKULQNDJH NLQHWLFV FDQ DOVR EH PRQLWRUHG E\ WKH WLPH DW ZKLFK b PD[LPXP JHO VKULQNDJH LV REVHUYHG DW HDFK WHPSHUDWXUH DV VKRZQ LQ )LJXUH 6KULQNDJH LPSURYHV JHO VWUHQJWK WKHUHIRUH D UHODWLYHO\ KDUG DQG GHQVH JHO FDQ EH REWDLQHG DV D UHVXOW RI RSWLPL]LQJ WKH DJLQJ SURFHVV )LJXUH VKRZV WKH LQFUHDVH LQ JHO PLFURKDUGQHVV ZLWK SHUFHQWDJH RI VKULQNDJH ,W LV WKLV LQFUHDVH LQ PHFKDQLFDO VWUHQJWK ZLWK DJLQJ WKDW PDNHV LW SRVVLEOH WR REWDLQ GULHG PRQROLWKLF [HURJHOV 'U\LQJ 0RGHOLQJ &RQWURO RI GU\LQJ LV FULWLFDO ZLWKRXW D IXOO XQGHUVWDQGLQJ RI WKH JHOn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

PAGE 43

SHUFHQW RI YROXPH VKULQNDJH rWLPH VWDUWV IURP WKH JHODWLRQ SRLQW )LJXUH 6KULQNDJH RI VLOLFD JHO LQVLGH FF SRO\VW\UHQH F\OLQGHU DV D IXQFWLRQ RI DJLQJ WLPH

PAGE 44

7HPSHUDWXUH r&f )LJXUH 7KH WLPH VLOLFD JHOV VKULQN WR b RI RULJLQDO YROXPH YHUVXV DJLQJ WHPSHUDWXUHV LQVLGH FF SRO\VW\UHQH F\OLQGHU

PAGE 45

D R Z Z &' F S QV -& R 3HUFHQW RI VKULQNDJH )LJXUH 0LFURKDUGQHVV RI DJHG JHO YHUVXV SHUFHQWDJH RI VKULQNDJH

PAGE 46

$ VLOLFD JHO LV GHILQHG DV GULHG ZKHQ WKH SK\VLFDOO\ DGVRUEHG ZDWHU LV FRPSOHWHO\ HYDFXDWHG DQG QR VLJQLILFDQW ZHLJKW ORVV LV REVHUYHG DW LQFUHDVHG WHPSHUDWXUHV &UDFNLQJ GXULQJ WKH GU\LQJ SURFHVV LV HVVHQWLDOO\ WKH UHVXOW RI GLIIHUHQWLDO HYDSRUDWLRQ RI SRUH OLTXLG )LJXUH DV GLVFXVVHG LQ GHWDLO E\ =DU]\FNL >@ 7KH /DSODFH HTXDWLRQ LV XVHG $39_ 3_ 3Y \Y_ &26 5 f ZKHUH $39_ LV WKH GLIIHUHQWLDO FDSLOODU\ YDSRU SUHVVXUH EHWZHHQ WKH VXUIDFH RI WKH YDSRU SKDVH LQ ZKLFK YDSRU SUHVVXUH 3Yf DQG WKH OLTXLG SKDVH LQ ZKLFK YDSRU SUHVVXUH 3Lf ZLWKLQ D YHU\ VPDOO SRUH RI UDGLXV 5 ,Q HTXDWLRQ f \YO LV WKH VSHFLILF VXUIDFH HQHUJ\ DQG LV WKH FRQWDFW DQJOH 7KHRUHWLFDOO\ WR SUHYHQW VKDWWHULQJ RI WKH JHO ERG\ GXULQJ GU\LQJ WKH FDSLOODU\ YDSRU SUHVVXUH LQ WKH OLTXLG SKDVH ZKLFK LV WUDQVPLWWHG WR WKH ZDOO RI WKH SRUH FKDQQHOf PXVW EH RIIVHW E\ WKH FDSLOODU\ YDSRU SUHVVXUH LQ WKH YDSRU SKDVH )RU $39_ WR HTXDO ]HUR WKH FRVLQH RI WKH FRQWDFW DQJOH PXVW DOVR HTXDO ]HUR # H rf DV WKH UDGLXV 5f DQG WKH VXUIDFH HQHUJ\ >\A?f DW WKH OLTXLGYDSRU LQWHUIDFH ZLOO DOZD\V KDYH VRPH YDOXH
PAGE 47

VWUHVV LQLWLDWHG FUDFN OLQHV )LJXUH 'LIIHUHQWLDO HYDSRUDWLRQ

PAGE 48

3VYG9VY GZVY @ :KHQ $39_ LV ]HUR WKHUH LV QR GLIIHUHQFH LQ WKH OLTXLG OHYHO ZLWKLQ WKH FDSLOODU\ SRUH FKDQQHOV UHJDUGOHVV RI WKH SRUH UDGLXV DV VKRZQ LQ )LJXUH +RZHYHU IRU WKH FDVH RI GU\LQJ DFWXDO [HURJHOV WKH GLIIHUHQWLDO SUHVVXUH $39_ FDQ EH PLQLPL]HG WR ]HUR ZLWK WKH XVH RI D SURSULHWDU\ GHYLFH 7KLV GHYLFH NHHSV WKH YDSRU SUHVVXUH LQ WKH YDSRU SKDVH 3Y DW D YDOXH WKH VDPH DV WKDW RI WKH YDSRU SUHVVXUH LQ WKH OLTXLG SKDVH 3_ LQ WKH JHO $V D UHVXOW $39_ LV ]HUR DQG JHO UHPDLQV LQWDFW 7KH YDSRU SUHVVXUH ZLWKLQ WKLV GHYLFH LV FRQWUROOHG E\ WKH WHPSHUDWXUH ZKLFK PXVW EH FDUHIXOO\ PDLQWDLQHG $W WHPSHUDWXUHV KLJKHU WKDQ WKH ERLOLQJ SRLQW WHPSHUDWXUH RI WKH JHO SRUH OLTXLG WKH YDSRU SUHVVXUH LQ WKH OLTXLG SKDVH 3_ H[FHHGV RQH DWPRVSKHUH 3Y ZLOO QHYHU EH KLJKHU WKDQ DWP LQ WKLV GHYLFH EHFDXVH LW LV QRW DQ DXWRFODYH V\VWHPf 7KXV WKH V\VWHP ZLOO HTXDOL]H DV JDV HVFDSHV IURP WKH GHYLFH LH $39_ LV QRW ]HUR ZKLFK ZRXOG FDXVH D GLIIHUHQWLDO YDSRU SUHVVXUH $39_ EHWZHHQ WKH OLTXLG DQG WKH YDSRU SKDVHV VXIILFLHQW WR VKDWWHU WKH JHOV DV VKRZQ LQ )LJXUHV DQG Df

PAGE 49

JH VWUXFWXUH SRUH )LJXUH 1R GLIIHUHQWLDO HYDSRUDWLRQ

PAGE 50

Df 3DcUf RQH DWPRVSKHUH DWPf Ef 3DLUf RQH DWPRVSKHUH DWPf DLU LQ 3DLUf 3&YDSRUf )LJXUH *HO FUDFNV LQVLGH QRQHTXLYDOHQW HYDSRUDWLRQ FRQWDLQHUV

PAGE 51

$W WHPSHUDWXUHV ORZHU WKDQ WKH ERLOLQJ SRLQW RI WKH JHO SRUH OLTXLG WKH YDSRU SUHVVXUH LQ WKH OLTXLG SKDVH 3_f LV OHVV WKDQ RQH DWPRVSKHUH WKHUHIRUH DLU ZLOO HQWHU WKH GHYLFH WR HVWDEOLVK D YDSRU SKDVH SUHVVXUH 3Yf HTXDO WR DWP UHVXOWLQJ LQ D GLIIHUHQWLDO YDSRU SUHVVXUH $39_f ZKLFK LV QRW ]HUR )LJXUHV DQG Eff +RZHYHU E\ PDLQWDLQLQJ D ]HUR GLIIHUHQWLDO SUHVVXUH WKH FDSLOODU\ IRUFH LV HOLPLQDWHG )LJXUH f WKHUHE\ VLJQLILFDQWO\ UHPRYLQJ WKH GLIIHUHQWLDO K\GURVWDWLF VWUHVVHV ZLWKLQ WKH JHO ERG\ DQG UHWDLQLQJ WKH JHOf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cf .(7U f ZKHUH 6U LV WKH VROXELOLW\ RI D SDUWLFOH KDYLQJ D UDGLXV RI FXUYDWXUH U 6c LV WKH VROXELOLW\ RI D IODW VXUIDFH ZLWK D UDGLXV RI FXUYDWXUH RI LQILQLW\ LQ WKDW ZDWHU ( ,V WKH VXUIDFH HQHUJ\ RI WKH VROLG 7 LV WKH WHPSHUDWXUH DQG LV %ROW]PDQQnV FRQVWDQW 7KH PHDQLQJ RI WKLV HTXDWLRQ LV VFKHPDWLFDOO\ LOOXVWUDWHG E\ +HU LQ )LJXUH $V

PAGE 52

3DLUf RQH DWPRVSKHUH DWPf ADWPDLUf f AYDSRU f AOLTXLG )LJXUH 6LWXDWLRQ WR DYRLG FUDFNLQJ

PAGE 53

VLOLFD ILEULOODU VWUXFWXUH )LJXUH 5HGHSRVLWLRQ RI PRQRPHUV IURP WKH EURNHQ QHFN DUHD WR WKH DUHD RI QHJDWLYH FXUYDWXUH

PAGE 54

)LJXUH 6ROXELOLW\ RI VLOLFD LQ QHXWUDO ZDWHU DW r& YDULHV ZLWK WKH UDGLXV RI FXUYDWXUH RI WKH VXUIDFH DFFRUGLQJ WR WKH 2VWZDOG)UHXQGOLFK HTLDWLRQ

PAGE 55

VKRZQ ZKHQ DQ DFLGLF VLOLFD JHO LV VXIILFLHQWO\ GULHG WR FRQWDLQ SRUHV QHJDWLYH FXUYDWXUH LQ OHIW VLGH RI WKH ILJXUHf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f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f LV LQWURGXFHG LQ 6WHS WKLV PDNHV LW SRVVLEOH WR FRQWURO HDFK RI WKH ILYH VXEVHTXHQW VWHSV DQG SUHYHQW JHO VKDWWHULQJ

PAGE 56

7DEOH 2[DOLF DFLG JUDPVf DV '&&$ LQ FF +2,22 FF 7026 7HPSHUDWXUH r& r& r& r& r& 6XUIDFH DUHD PJf 7RWDO SRUH YROXPH FFJf $YHUDJH SRUH UDGLXV ƒf

PAGE 57

)LJXUH 3LFWXUH RI D ODUJH VFDOH r& GULHG VLOLFD JHO VDPSOH

PAGE 58

6WHS 6WHS 6WHS 6WHS 6WHS 6WHS )LJXUH 3URFHGXUH IRU SURGXFLQJ SXUH VLOLFD JHOV DQG JHOJODVVHV

PAGE 59

([DPSOH RQH 3URGXFWLRQ RI GULHG SXUH VLOLFD JHO PRQROLWK IURP R[DOLF DFLG '&&$ 6WHS 0L[LQJ 7HWUDPHWK\ORUWKRVLOLFDWH 7026f LV XVHG DV D SUHFXUVRU IRU VLOLFD PRQRPHUV WR IRUP 6L26L ERQGV LQ WKH JHO VWUXFWXUH 7KH PL[LQJ RI ZDWHU ZLWK 7026 IRUPV D VLOLFD VRO YLD WKH IROORZLQJ VLPSOLILHG K\GURO\VLV DQG SRO\PHUL]DWLRQ UHDFWLRQV 6L2&+f +2 6L2+f &+2+ 6L2+ 2+6L 6L26L +2 7KH VSHFLILF VWDQGDUG SURFHGXUH IROORZHG LQ 6WHS LV Df 3RXU FF RI ZDWHU LQWR D FOHDQ FF EHDNHU Ef 3ODFH WKH EHDNHU RQ D KRWVWLUULQJ SODWH Ff 0L[ JUDPV RI R[DOLF DFLG ZLWK ZDWHU XVLQJ D 37)( FRDWHG PDJQHWLF EDU FRQWURO YLD WKH KRWVWLUULQJ SODWH Gf 6WLU IRU PLQXWHV WR JHW D KRPRJHQHRXV VROXWLRQ Hf $GG FF 7026 WR WKH DFLG VROXWLRQ ZKLOH FRQWLQXLQJ WR VWLU YLJRURXVO\ IRU DSSUR[LPDWHO\ PLQXWHV If ,PPHGLDWHO\ LQFUHDVH WKH WHPSHUDWXUH IURP r& WR r& E\ UDLVLQJ WKH WHPSHUDWXUH RQ WKH KRWVWLUULQJ SODWH WR PD[LPXP Jf ,I IHDVLEOH FDUHIXOO\ SODFH LFH ZDWHU LQ D WKUHHOD\HU SRO\VW\UHQH WKLQ ILOP RQ WRS RI WKH EHDNHU WR FRQGHQVH WKH KRW YDSRU DQG UHWXUQ LW WR LWV VROXWLRQ Kf &RQWLQXH VWLUULQJ DQG KHDWLQJ IRU DSSUR[LPDWHO\ PLQXWHV EHIRUH FDVWLQJ

PAGE 60

6WHS &DVWLQJ Df 7KH LQWLPDWHO\ PL[HG VRO LV FDVW IURP LWV KHDWHG YHVVHO LQWR D PROG PP + [ PP 'f WKDW FRUUHVSRQGV WR WKH ILQDO GHVLUHG VKDSH )RU EHVW VXUIDFH UHVXOWV SRO\VW\UHQH LV WKH VHOHFWHG PROG PDWHULDO Ef 7KH GXUDWLRQ RI WKH FDVWLQJ RSHUDWLRQ LV QRW FULWLFDO VLQFH JHODWLRQ GRHV QRW RFFXU XQWLO DIWHU FDVWLQJ LV FRPSOHWHG 6WHS *HODWLRQ *HODWLRQ RFFXUV LQ WKH PROG ZLWK WKH UHVXOWLQJ VROLG REMHFW WDNLQJ WKH VKDSH DQG VXUIDFH ILQLVK RI WKH PROG *HODWLRQ WLPHV ZLWK R[DOLF DFLG DUH W\SLFDOO\ KRXUV DW r& DQG KRXUV DW r& GHSHQGLQJ RQ WKH UHODWLYH FRQFHQWUDWLRQV RI ZDWHU 7026 DQG '&&$ DV VKRZQ LQ )LJXUHV DQG 6WHS $JLQJ 7KH VROLGLILHG JHO LV WKHQ SODFHG LQWR DQ DJLQJ RYHQ DW D WHPSHUDWXUH UDQJLQJ IURP r& WR r& IRU D WLPHV UDQJLQJ IURP WR KRXUV WR DFKLHYH PD[LPXP VKULQNDJH 6WHS 'U\LQJ 3ULRU WR 6WHS FRQWURO RI WKH JHO XOWUDVWUXFWXUH LV JRYHUQHG E\ WKH '&&$ ZKLFK DOORZV UHPRYDO RI WKH SRUH OLTXLG ZLWKRXW FUDFNLQJ WKH JHO 7\SLFDOO\ WKLV LV GRQH E\ ILUVW UHPRYLQJ WKH H[FHVV OLTXLG SUHVHQW DIWHU JHO VKULQNDJH LQ 6WHS 7KH SRUH OLTXLG LV WKHQ UHPRYHG FRQVLVWHQW ZLWK WKH WKHRU\ VWDWHG LQ 6HFWLRQ ,, RI WKLV FKDSWHU E\ FRQILQHG HYDSRUDWLRQ RYHU D WHPSHUDWXUH UDQJH IURP r* WR r& IRU WLPHV UDQJLQJ IURP WR KRXUV $Q H[DPSOH RI D W\SLFDO KHDWLQJ SURJUDP LV VKRZQ LQ )LJXUH

PAGE 61

7LPH KUf )LJXUH 'U\LQJ SURJUDP IRU ZHW JHO

PAGE 62

6WHS 'HQVLILFDURQ 7KH XOWUDSRURXV GULHG VLOLFD JHOV DUH FRQYHUWHG WR SDUWLDOO\ GHQVH PRQROLWKV E\ KHDWLQJ IURP r& XS WR r& RYHU D SHULRG RI WR GD\V VDPSOHV DUH WDNHQ RXW RI WKH IXUQDFH DW WKH HQG RI WKH KHDWLQJ SURJUDP $Q H[DPSOH LV VKRZQ LQ )LJXUH ([DPSOH WZR 3URGXFWLRQ RI GULHG WUDQVLWLRQ DQG UDUH HDUWK HOHPHQW GRSHG VLOLFD JHOV IURP QLWULF DFLG '&&$ 6WHS 0L[LQJ Df $GG FF 1f +12 QLWULF DFLGf WR FF RI GLVWLOOHG ZDWHU DW URRP nL m WHPSHUDWXUH DQG PL[ IRU PLQXWHV ZLWK D PDJQHWLF VWLUUHU Ef $GG FF 7026 WR WKH QLWULF DFLG ZDWHU VROXWLRQ ZKLOH FRQWLQXLQJ WR PL[ YLJRURXVO\ LQFUHDVLQJ WKH VROXWLRQ WHPSHUDWXUH WR r& IRU QR PRUH WKDQ PLQXWHV 6WHS &DVWLQJ 7KH LQWLPDWHO\ PL[HG VRO FFf LV FDVW IURP LWV KHDWHG YHVVHO LQWR D SRO\VW\UHQH PROG PP + [ PP 'f DW URRP WHPSHUDWXUH 7KH OHQJWK RI WLPH IRU FDVWLQJ VKRXOG EH QR PRUH WKDQ PLQXWHV VLQFH JHODWLRQ ZLOO WDNH SODFH GXULQJ SURORQJHG FDVWLQJ RSHUDWLRQ 6WHS *HODWLRQ *HODWLRQ RFFXUV LQ WKH PROG DW r& LQ PLQXWHV ZLWK WKH UHVXOWLQJ VROLG REMHFW WDNLQJ WKH VKDSH DQG VXUIDFH ILQLVK RI WKH PROG

PAGE 63

7HPSHUDWXUH r&f 7LPH KUf )LJXUH $Q H[DPSOH RI D VLOLFD JHOJODVV GHQVLILFDURQ SURJUDP

PAGE 64

6WHS $JLQJ 7KH VROLG LV DJHG LQ WKH PROG LQLWLDOO\ DW r& IRU KRXUV IROORZHG E\ DQ LQFUHDVH WR r& IRU KRXUV 6WHS 'U\LQJ 7KH DJHG SXUHVLOLFD JHO LV UHPRYHG IURP WKH PROG DQG GULHG ZLWK D FRQWUROOHG HYDSRUDWLRQ UDWH DV GHVFULEHG LQ 6HFWLRQ ,, RI WKLV FKDSWHU LQLWLDOO\ DW r& JUDGXDOO\ LQFUHDVLQJ WKH WHPSHUDWXUH WR r& GXULQJ D KRXU SHULRG 6WHS ,PSUHJQDWLRQ Df 2QH JUDPSHUFHQW RI WUDQVLWLRQ PHWDO HOHPHQW LH FREDOW QLWUDWH QLFNHO QLWUDWH FRSSHU QLWUDWHf RU WKUHH JUDPSHUFHQW RI UDUH HDUWK HOHPHQW LH QHRG\PLXP QLWUDWH HUELXP QLWUDWHf LQ GHLRQL]HG 'Of ZDWHU LV SUHSDUHG IRU GRSLQJ RU LPSUHJQDWLQJ WKH FRPSOHWHO\ GULHG JHO 7KH GULHG JHO LV LPPHUVHG LQWR WKH VROXWLRQ ZKHUHE\ WKH LQWHUIDFH EHWZHHQ WKH OLTXLG DQG WKH YRLGV PLJUDWHV IURP WKH H[WHULRU ,QWR WKH FHQWHU RI WKH JHO ERG\ LQ WKH UDWH RI FPKRXU DV VKRZQ LQ )LJXUH Ef 7KH GRSHG JHO LV WKHQ SODFHG LQ WKH GU\LQJ RYHQ DW r& IRU KRXUV WR UHPRYH WKH SRUH VROYHQW 6WHS 'HQVLILFDWLRQ Df 7KH IXOO\ GULHG VLOLFD JHO GRSHG ZLWK WUDQVLWLRQ PHWDO RU UDUH HDUWK HOHPHQWV LV KHDWHG WR r& WR HOLPLQDWHG DQ\ UHVLGXDO QLWUDWHV YLD FRQYHUVLRQ WR LWV JDVHRXV R[LGHV Ef $GGLWLRQDO GHQVLILFDWLRQ FDQ EH DFKLHYHG E\ KHDWLQJ IURP r& WR r& 5HVXOWV 0RQROLWKLF VDPSOHV RI SXUH VLOLFD JHO WUDQVLWLRQ PHWDO HOHPHQW GRSHG VLOLFD JHO DQG UDUH HDUWK HOHPHQW GRSHG VLOLFD JHO ZHUH URXWLQHO\ SURGXFHG IROORZLQJ WKHVH SURFHGXUHV VRPH DUH VKRZQ LQ )LJXUHV WR 7KH SK\VLFDO DQG RSWLFDO SURSHUWLHV RI WKHVH VDPSOHV ZLOO EH GLVFXVVHG LQ VXFFHHGLQJ FKDSWHUV

PAGE 65

WRS YLHZ )LJXUH 6DPSOH LPPHUVLRQ LQWR WUDQVLWLRQ PHWDO RU UDUH HDUWK QLWUDWHZDWHU VROXWLRQ

PAGE 66

O )LJXUH 3LFWXUH RI D r& GULHG VLOLFD JHO

PAGE 67

)LJXUH 3LFWXUH RI D FREDOW QLWUDWHGRSHG VLOLFD JHO ZKLFK ZDV VWDELOL]HG DW r& DQG UHGULHG DW r&

PAGE 68

)LJXUH 3LFWXUH RI QLFNHO QLWUDWHGRSHG VLOLFD JHO ZKLFK ZDV VWDELOL]HG DW r& DQG UHGULHG DW r&

PAGE 69

)LJXUH 3LFWXUH RI FRSSHU QLWUDWHGRSHG VLOLFD JHO ZKLFK ZDV VWDELOL]HG DW r& DQG UHGULHG DW r&

PAGE 70

)LJXUH 3LFWXUH RI QHRG\PLXP QLWUDWHGRSHG DQG HUELXP QLWUDWHGRSHG VLOLFD JHOV ZKLFK ZHUH VWDELOL]HG DW r& DQG UHGULHG DW r&

PAGE 71

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f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f &RQVHTXHQWO\ WKH JHO FDQ HQGXUH FHUWDLQ K\GURVWDWLF VWUHVVHV DQG VKULQN FRQVLGHUDEO\ LQ WKH GU\LQJ VWDJH ZLWKRXW FUDFNLQJ DV LOOXVWUDWHG LQ )LJXUH 'LIIHUHQWLDO YDSRU SUHVVXUH $39_f LV WKH VWUHVV ZKLFK VKDWWHUV WKH UHODWLYHO\ ZHDN JHO LQWR SLHFHV LQ WKH GU\LQJ VWDJH $ JHO FDQ EH GULHG ZLWKRXW FUDFNLQJ E\ XVLQJ D GU\LQJ GHYLFH ZKLFK HOLPLQDWHV WKH GLIIHUHQWLDO YDSRU SUHVVXUH EHWZHHQ YDSRU SKDVH 3Yf DQG OLTXLG SKDVH 3_f LQVLGH WKH FDSLOODU\ SRUHV

PAGE 72

L 0 0 P VWUHVV IOH[LEOH JHO VWUXFWXUH )LJXUH )LEULOODU JHO VWUXFWXUH LV UHODWLYHO\ IOH[LEOH FRPSDUH WR FRDUVH JHO VWUXFWXUH

PAGE 73

0RQROLWKLF JHOV ZLWK DQ RSWLPDO XOWUDVWUXFWXUH DQG KLJK UHVLVWDQFH WR GU\LQJ VWUHVVHV ZKLFK DUH FKHPLFDOO\ FRQWUROOHG E\ DGGLQJ DFLGLF '&&$f DQG SK\VLFDOO\ VWDELOL]HG E\ LQWURGXFLQJ D GU\LQJ GHYLFHf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f LQWR WKH GULHG JHO %HFDXVH RI WKH H[WUHPHO\ VPDOO VL]H ƒ ƒf RI WKH XOWUDSRUHV LQ WKH JHO LW LV SRVVLEOH WR LQWURGXFH D YHU\ KRPRJHQHRXV LRQ GLVWULEXWLRQ ZLWKLQ WKH JHO PDWUL[ )RU PHDVXUHPHQWV WKH SK\VLFDO SURSHUWLHV SUHVHQWHG LQ &KDSWHU WKH XOWUDSRURXV GULHG VLOLFD JHOV DUH FRQYHUWHG WR SDUWLDOO\ GHQVH PRQROLWKV E\ KHDWLQJ IURP r& WR r& RYHU WLPHV UDQJLQJ IURP RQH GD\ WR RQH ZHHN

PAGE 74

&+$37(5 3+<6,&$/ 3523(57,(6 2) 3$57,$//< '(16,),(' 6,/,&$ ;(52*(/6 ,QWURGXFWLRQ 0RQROLWKLF QRQFU\VWDOOLQH GULHG [HURJHOV RI SXUH VLOLFD KHUHDIWHU VLPSO\ FDOOHG JHOV KDYH EHHQ PDGH E\ WKH SURFHGXUH VWDWHG LQ ([DPSOH RI &KDSWHU 7KHVH VDPSOHV DUH KHDWHG WR r& WKH WHPSHUDWXUH DW ZKLFK WKH JHOV DUH IUHH IURP SK\VLFDO ZDWHUf WR EHFRPH VWDQGDUG GULHG JHOV 7KH SK\VLFDO SURSHUWLHV RI WKH IXOO\ GULHG JHO DUH D IXQFWLRQ RI WKH LQWHUQDO VWUXFWXUH ZKLFK GHSHQGV RQ WKH YDULRXV FKHPLFDO DQG SK\VLFDO FRQGLWLRQV GXULQJ HYHU\ VWHS RI SURFHVVLQJ LH WKH UHODWLYH DPRXQWV RI ZDWHU'&&$7026 WHPSHUDWXUH SUHVVXUH DQG WLPH IRU DJLQJ DQG GU\LQJf $W VXIILFLHQWO\ KLJK WHPSHUDWXUHV WKHUPDO HQHUJ\ SURYLGHV WKH GULYLQJ IRUFH IRU XOWUDVWUXFWXUDO UHDUUDQJHPHQW ZKLFK GHFUHDVHV VXUIDFH DUHD DQG WKHUHE\ PLQLPL]HV VXUIDFH WHQVLRQ LQVLGH WKH JHO VWUXFWXUH 7KLV LV WKH SULPDU\ PHFKDQLVP IRU GHQVLILFDWLRQ >VHH S LQ UHI @ $ ODUJH UHGXFWLRQ LQ SRUH YROXPH LV DFFRPSDQLHG E\ WKH GHFRPSRVLWLRQ RI UHVLGXDO RUJDQLF FRPSRXQGV LQWR FDUERQ GLR[LGH EHWZHHQ r DQG r&f DQG DOVR E\ WKH FRPELQLQJ RI VXUIDFH K\GUR[\O JURXSV UHVXOWLQJ LQ VRPH GHJUHH RI GHK\GUDWLRQ %RWK RI WKHVH SKHQRPHQD PD\ FDXVH WKHUPDOO\ LQGXFHG VWUHVV IUDFWXULQJ LQ WKH GHQVLILFDWLRQ VWDJH +RZHYHU E\ FRQWUROOLQJ WKH UDWHV RI WKHVH UHDFWLRQV VLOLFD JHO PRQROLWKV WKDW DUH FUDFNIUHH SDUWLDOO\ GHQVLILHG DQG VKUXQN FDQ EH VXFFHVVIXOO\ PDGH DW YDULRXV WHPSHUDWXUHV UDQJLQJ IURP r& WR r& 7KLV FKDSWHU SUHVHQWV D VWXG\ RI WKH SK\VLFDO SURSHUWLHV RI SDUWLDOO\ GHQVH VLOLFD JHO PRQROLWKV 'DWD ZHUH REWDLQHG IURP QXPHURXV PHDVXUHPHQWV LQFOXGLQJ VWUXFWXUDO RSWLFDO WKHUPDO DQG PHFKDQLFDO WHVWLQJ 6WUXFWXUDO LQIRUPDWLRQ ZDV SURYLGHG E\

PAGE 75

)RXULHUWUDQVIRUPLQIUDUHG )7,5f VSHFWURVFRS\ XOWUDYLROHWYLVLEOHQHDULQIUDUHG VSHFWURVFRS\ 899,61,5f 1 DGVRUSWLRQGHVRUSWLRQ LVRWKHUPV LQWHUSUHWHG XVLQJ %UXQDXHU (PPHWW 7HOOHU %(7f DQDO\VLV ZKLFK LQFOXGHV VSHFLILF PHDVXUHPHQWV RI VXUIDFH DUHD SRUH VL]H GLVWULEXWLRQ SRUH YROXPH DQG SRUH UDGLXV DV ZHOO DV ODUJH DQJOH ;UD\ GLIIUDFWLRQ 2SWLFDO LQIRUPDWLRQ ZDV REWDLQHG VRLHO\ XVLQJ DQ LQGH[ RI UHIUDFWLRQ WHVW 7KHUPDO GDWD ZHUH FROOHFWHG IURP GLIIHUHQWLDO VFDQQLQJ FDORULPHWU\ '6&f GLIIHUHQWLDO WKHUPDO DQDO\VLV '7$f WKHUPRJUDYLPHWULF DQDO\VLV 7*$f DQG WKHUPRPHFKDQLFDO DQDO\VLV 70$f 0HFKDQLFDO SURSHUWLHV JHO VWUHQJWKf ZHUH GHWHUPLQHG XVLQJ IOH[XUDO VWUHQJWK FRPSUHVVLYH VWUHQJWK PLFURKDUGQHVV IUDFWXUH WRXJKQHVV DQG GHQVLW\ PHDVXUHPHQWV 5HYLHZ RI WKH /LWHUDWXUH 7KUHH PHFKDQLVPV RI GHQVLILFDWLRQ DUH VXPPDUL]HG E\ =DU]\FNL HW DO DQG %ULQNHU HW DO > @ f SRO\PHUL]DWLRQ UHDFWLRQV ZKLFK VHUYH WR FURVVOLQN WKH QHWZRUN DQG SDUWLDOO\ UHOHDVH WKH VXUIDFH K\GUR[\O JURXSV WKHUHE\ IRUPLQJ IUHH ZDWHU f VWUXFWXUDO UHDUUDQJHPHQWV WKDW RFFXUV ZKHQ VHJPHQWV RI LQWHUSDUWLFOH QHFNV DUH EURNHQ DQG RWKHU QHFN VHJPHQWV EHFRPH FRQQHFWHG DQG f YLVFRXV VLQWHULQJ DFFRPSDQLHG E\ WKH FRPELQDWLRQ RI VXUIDFH K\GUR[\O JURXSV 7KH ILUVW WZR PHFKDQLVPV FDXVH D VOLJKW GHQVLW\ LQFUHDVH WKH WKLUG PHFKDQLVP LV D UHVXOW RI KLJK WHPSHUDWXUH YLVFRXV IORZ ZKLFK HOLPLQDWHV WKH SRUHV VR WKDW WKH EXON GHQVLW\ DSSURDFKHV WKDW RI IXVHG VLOLFD 1R JHO FDQ EH FRPSOHWHO\ GHK\GUDWHG DQG FRQYHUWHG LQWR D IXOO\ GHQVH JODVV LH ZLWKRXW IRDPLQJf LQ DQ RUGLQDU\ DLUDWPRVSKHUH IXUQDFH EXW IRUWXQDWHO\ WKH JHO FDQ EH SDUWLDOO\ VLQWHUHG WR t GHVLUHG WHPSHUDWXUH EHORZ WKH IRDPLQJ SRLQW DQG FRROHG WR URRP WHPSHUDWXUH ZKLOH UHPDLQLQJ LQWDFW $Q\ PDWHULDO FDQ JLYH ULVH WR DEVRUSWLRQ RU HPLVVLRQ RI UDGLDWLRQ ZLWKLQ WKH DOORZHG WUDQVLWLRQDO YLEUDWLRQDO DQGRU URWDWLRQDO HQHUJ\ OHYHOV ,QIUDUHG VSHFWURVFRS\

PAGE 76

)7,5f FDQ SURYLGH YLEUDWLRQDO LQIRUPDWLRQ RQ FKDQJHV RFFXUULQJ LQ WKH JHO VWUXFWXUH GXULQJ VLQWHULQJ >@ :DWHU WHUPLQDWHV WKH EULGJLQJ VLOLFRQR[\JHQVLOLFRQ ERQGV RQ WKH SDUWLFOHnV VXUIDFH LQVLGH WKH SRURXV JHO DV VKRZQ LQ )LJXUHV DQG :DWHUfV GLVUXSWLRQ RI WKH 6L26L EULGJLQJ ERQG LV VLPLODU WR WKDW RI VRGLXP LRQV ZLWKLQ D GHQVH VRGD VLOLFDWH JODVV 7KLV JLYHV ULVH WR DEVRUSWLRQ LQ WKH XOWUDYLROHW 89f UHJLRQ RI WKH RSWLFDO VSHFWUXP 7KH 899,61,5 VSHFWUD WHFKQLTXH LV DQ HDVLHU DQG PRUH VHQVLWLYH WRRO WKDQ WKH LQIUDUHG PHWKRG IRU XQGHUVWDQGLQJ WKH HYROXWLRQ RI ERQGLQJ DQG LGHQWLI\LQJ WKH VSHFLHV LQVLGH WKH JHO VWUXFWXUH LQ WKH GHQVLILFDWLRQ SURFHVV >@ 7KH PHDVXUHG VXUIDFH DUHD REWDLQHG IURP %(7 DQDO\VLV RI D VWDQGDUG GULHG JHO LV DERXW PJ DW r& 7KH SDUWLFOH VL]H LV FDOFXODWHG IURP +DYDUG :LOVRQnV PRGHO >@ ZKHUH WKH GLDPHWHU LV HTXDO WR D FRQVWDQW f GLYLGHG E\ WKH VXUIDFH DUHD 7KH SDUWLFOH GLDPHWHU IRU D JHO PDGH E\ ([DPSOH LQ &KDSWHU LV QP DW r& 7KH PHDVXUHG VXUIDFH DUHD LV VRPHZKDW OHVV WKDQ DFWXDO VLQFH QLWURJHQ PROHFXOHV XVHG LQ WKH %(7 DQDO\VLV FDQQRW FRPSOHWHO\ SHQHWUDWH WKH QHJDWLYH FXUYDWXUH DUHD EHWZHHQ DOO WKH FRQQHFWHG SDUWLFOHV +RZHYHU WKH %(7 VXUIDFH DUHD PHDVXUHPHQW DOVR LQFOXGHV WKH VXUIDFH K\GUR[\O JURXSV ZKLFK LQFUHDVHV WKH SDUWLFOHVn PHDVXUHG VXUIDFH DUHD YDOXH WKLV LQFUHDVH LV OHVV VLJQLILFDQW WKDQ WKH GHFUHDVH UHVXOWLQJ IURP LQFRPSOHWH QLWURJHQ SHQHWUDWLRQ 6LOLFD JHO LV HVVHQWLDOO\ D VSHFLDO IRUP RI SRURXV JODVV 3UHYLRXV [UD\ GLIIUDFWLRQ VWXGLHV E\ 0R]]L :DUUHQ 8KOPDQQ DQG :LFNV > @ KDYH HVWDEOLVKHG LQ GHWDLO WKH WHWUDKHGUDO ERQGLQJ DUUDQJHPHQWV LQ YLWUHRXV VLOLFD 7KH PD[LPXP LQ WKH GLVWULEXWLRQ RI 6L26L DQJOHV LQ DPRUSKRXV VLOLFD LV DW r ZLWK PRVW DQJOHV EHLQJ ZLWKLQ b RI WKLV PD[LPXP 7KHUH LV QR HYLGHQFH IRU D SUHIHUHQFH LQ IXVHG VLOLFD IRU HGJHWRIDFH VKDULQJ RI WHWUDKHGUD ZKLFK LV RIWHQ IRXQG LQ FU\VWDOOLQH VLOLFDWHV ;UD\ GLIIUDFWLRQ SDWWHUQV JHQHUDOO\ H[KLELW D UHODWLYHO\ EURDG SHDN IRU JHOV LQGLFDWLQJ WKH DEVHQFH RI DWRPLF SHULRGLFLW\ RU ORQJUDQJH VWUXFWXUDO RUGHULQJ FRPSDUH WR WKDW RI TXDUW]

PAGE 77

9 \ FXWRII SURILOH PDJQLILHG LQ )LJXUH )LJXUH 5DQGRP VDPSOLQJ SURILOH RI JHO VNHOHWRQ

PAGE 78

$ SURILOH RI JHO VNHOHWRQ )LJXUH :DWHU WHUPLQDWHV WKH 6L26L EULGJLQJ ERQG RQ WKH SDUWLFOHnV VXUIDFH

PAGE 79

&RQVHTXHQWO\ D UDQGRP HGJHWRHGJH VKDULQJ RI VLOLFD WHWUDKHGUD ZLWK YDULDEOH 6L26L DQJOHV GHVFULEHG DERYH LV SURSRVHG IRU VLOLFD JHO ILEULOODU VWUXFWXUHV 7KH PDJQLWXGH RI LQGH[ RI UHIUDFWLRQ Qf LQGLFDWHV WKH H[WHQW RI FKDQJH RI WKH VSHHG RI OLJKW E\ WKH HOHFWURPDJQHWLF ILHOG RI D WUDQVSDUHQW GHQVH PDWHULDO 7KH ,QGH[ RI UHIUDFWLRQ FDQ EH H[SUHVVHG E\ 6QHOOnV ODZ QJLDVVfULYDFXXPf VLQ YDFXXPfVLQ JODVVf 9YDFXXPf9^JLDVVf ZKHUH QJ_DVVf 9J_DVVf DQG JLDVVf DUH WKH UHIUDFWLYH ,QGH[ WKH YHORFLW\ DQG WKH DQJOH RI UHIUDFWLRQ RI JODVV UHVSHFWLYHO\ QYDFXXPf YYDFXXPf DUH FRQVWDQWV DQG YDFXXPf LV WKH DQJOH RI LQFLGHQFH RI OLJKW LQ YDFXXP ,QGH[ RI UHIUDFWLRQ LV D GHSHQGHQFH RI f WKH GHQVLW\ f WKH SRODUL]DELOLW\ RI WKH JODVV DQG f WKH ZDYHOHQJWK ;f RI PRQRFKURPDWLF UDGLDWLRQ >@ ,Q WKLV FKDSWHU SDUWLDOO\ GHQVLILHG VLOLFD JHOV DUH GLVFXVVHG ZKHUH WKH FKHPLFDO FRPSRVLWLRQV DUH HVVHQWLDOO\ 6L&! DQG FKHPLFDO ERQGHG VXUIDFH 6L2+ JURXSV 7KH QRQEULGJLQJ K\GURJHQ LRQV + D SURWRQf RI WKHVH VLODQRO JURXSV FRQWULEXWH YHU\ OLWWOH HIIHFW RQ RQFRPLQJ OLJKW >VHH S LQ UHI @ WKXV WKH SRODUL]DELOLW\ RI WKHVH SDUWLDOO\ GHQVLILHG VLOLFD JHOV FDQ EH DVVXPHG WR EH D FRQVWDQW &RQVHTXHQWO\ WKH YDULDWLRQ RI UHIUDFWLYH LQGH[ ZLWK GHQVLW\ GHVFULEHG E\ WKH /RUHQW]/RUHQ] HTXDWLRQ >VHH S LQ UHI @ FDQ EH VLPSOLILHG DV ZLOO EH GLVFXVVHG LQ WKH 5HVXOWV DQG 'LVFXVVLRQV 6HFWLRQ RI WKLV FKDSWHU 'LIIHUHQWLDO VFDQQLQJ FDORULPHWU\ '6&f LV XVHG WR PHDVXUH WKH WHPSHUDWXUHV DVVRFLDWHG ZLWK WUDQVLWLRQV LQ PDWHULDOV LQFOXGLQJ ERLOLQJ SRLQWV PHOWLQJ SRLQWV OLTXLGFU\VWDL WUDQVLWLRQV KHDWV RI UHDFWLRQ VSHFLILF KHDW FDSDFLW\ R[LGDWLYH DQG WKHUPDO VWDELOLW\ SXULW\ JLDVV WUDQVLWLRQV DQG UHDFWLRQ NLQHWLFV 'LIIHUHQWLDO WKHUPDO DQDO\VLV '7$f JLYHV WKH VDPH TXDOLWDWLYH LQIRUPDWLRQ DV '6& EXW LV XVHG SULPDULO\ IRU VWXGLHV LQYROYLQJ KLJK WHPSHUDWXUHV ZKLFK H[FHHG WKH UDQJH RI WKH '6& FHOO r&f 7KHUPRJUDYLPHWULF DQDO\VLV PHDVXUHV ZHLJKW FKDQJH DV D IXQFWLRQ RI WHPSHUDWXUH DQG SURYLGHV GHULYDWLYH 7*$ GDWD XVHG WR TXDQWLI\ WKH FKHPLFDO FKDQJHV LQ D JHO GXULQJ WKHUPDO SURFHVVLQJ

PAGE 80

7KHUPRPHFKDQLFDO DQDO\VLV 70$f PHDVXUHV WKH WKHUPDO H[SDQVLRQ FRHIILFLHQW JODVV WUDQVLWLRQ WHPSHUDWXUH VRIWHQLQJ WHPSHUDWXUH DQG SURYLGHV GDWD IRU JHO VKULQNDJH DQDO\VLV >@ )OH[XUDO )/(;f DQG FRPSUHVVLYH &203f WHVWV DUH SHUIRUPHG WR GHWHUPLQH WKH PDWHULDOnV VWUHQJWK XQGHU H[WHUQDO PHFKDQLFDO ORDGV $ 9LFNHUV PLFURKDUGQHVV WHVW ZKLFK \LHOGV D YDOXH IRU WKH GLDPRQG S\UDPLG PLFURKDUGQHVV QXPEHU '31f LV XVHG WR PHDVXUH WKH PHFKDQLFDO UHVLVWDQFH RI D JHO DQG JHOJODVV WR GLDPRQG S\UDPLG SODVWLF LQGHQWDWLRQ LQ D PLFURVFRSLF DUHD RI WKH VXUIDFH >@ 7KH IUDFWXUH WRXJKQHVV LV REWDLQHG GLUHFWL\ IURP WKH FUDFN OHQJWK ZKLFK H[WHQGV RXWVLGH WKH GLDJRQDO RI GLDPRQG S\UDPLG LQGHQWDWLRQ GXULQJ WKH 9LFNHUV PLFURKDUGQHVV PHDVXUHPHQW >@ %XON GHQVLW\ PHDVXUHPHQWV DUH XVHG WR PRQLWRU WKH FKDQJH LQ JHO VWUXFWXUH GXULQJ VLQWHULQJ LW DOVR JLYHV XVHIXO LQIRUPDWLRQ IRU LQWHUSUHWLQJ YDULDWLRQV LQ UHIUDFWLYH LQGH[ ([SHULPHQWDO 3URFHGXUH 6DPSOHV IDEULFDWHG E\ WKH SURFHGXUH VWDWHG LQ ([DPSOH RI &KDSWHU ZHUH KHDWHG WR YDULRXV SURJUDPPHG WHPSHUDWXUHV LQ DQ DPELHQW DLU IXUQDFH DV VKRZQ LQ )LJXUH 7KH IROORZLQJ WHVWV OLVWHG LQ 7DEOH ZHUH SHUIRUPHG RQ WKHVH VDPSOHV 7KH LQIUDUHG VSHFWUD ZHUH UHFRUGHG RQ D 1LFROHW 0; )7,5 VSHFWURPHWHU HTXLSSHG ZLWK D GLIIXVLRQ UHIOHFWLRQ VWDJH DQG D PLFURFRPSXWHU IRU GDWD VWRUDJH 7KH GLIIXVLRQ UHIOHFWLRQ VWDJH LQ ZKLFK WKH LQIUDUHG SDVVHV LQWR WKH EXON DERXW PP GHHS DQG PP DUHDf RI WKH JHO XQGHUJRHV UHIOHFWLRQ UHIUDFWLRQ VFDWWHULQJ DQG DEVRUSWLRQ LQ YDU\LQJ GHJUHHV EHIRUH UHOXPLQJ EDFN DW WKH VDPSOH VXUIDFH 7KH UDGLDWLRQ UHIOHFWHG RXW IURP WKH JHO LV GLVWULEXWHG LQ DOO GLUHFWLRQV RI WKH VXUURXQGLQJ KHPLVSKHUH DQG FRUUHFWHG WR IRUP VSHFWUD E\ D KLJKO\ UHIOHFWLYH VHPLVSKHULFDO PLUURU &KHPLFDO VSHFLHV DQG ERQGLQJ LQIRUPDWLRQ FDQ EH LQWHUSUHWHG LQ WHUPV RI WKH SRVLWLRQ DQG LQWHQVLW\ RI ,5

PAGE 81

)LJXUH +HDWLQJ SURJUDPV IRU YDULRXV VDPSOHV

PAGE 82

7DEOH 3K\VLFDO SURSHUW\ PHDVXUHPHQWV 7(67 6$03/( 6+$3( +($7(' 7(03 r&f 6WUXFWXUDO LQIRUPDWLRQ WHVWV )7,5 IODW SLHFH VPRRWK VXUIDFHf 899,61,5 IODW SLHFH ^VPRRWK VXUIDFHf %(7 SRZGHU FRXUVH JURXQGf ;5D\ SRZGHU ILQH JURXQGf 2SWLFDO LQIRUPDWLRQ WHVW ,QGH[ RI UHIUDFWLRQ SROLVKHG IODW SLHFH 7KHUPDO LQIRUPDWLRQ WHVWV '6& EURNHQ SLHFH '7$ EURNHQ SLHFH 7*$ EURNHQ SLHFH 70$ VPRRWK F\OLQGHUnV HQGV 0HFKDQLFDO LQIRUPDWLRQ WHVWV )/(; UHFWDQJXODU SLHFH &203 UHFWDQJXODU SLHFH '31 XQSROLVKHG JHO VXUIDFH 7RXJKQHVV XQSROLVKHG JHO VXUIDFH 'HQVLW\ EURNHQ SLHFH

PAGE 83

SHDNV LQ WKH VDPSOHnV VSHFWUD $ GULHG JHO ZDV LQVWDOOHG LQ D KRW VWDJH LQVLGH WKH )85 VDPSOH FKDPEHU DQG KHDWHG WR WKH WHPSHUDWXUHV GHVLJQHG LQ 7DEOH IRU ,5 DQDO\VLV $ KHDWLQJ UDWH RI r&PLQ IURP URRP WHPSHUDWXUH WR r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f RI WKH JHOV LV REWDLQHG IURP D VHULHV RI GDWD PDQDJHPHQW DQG FDOFXODWLRQV SHUIRUPHG LQ WKH PLFURFRPSXWHU RI WKH $XWRVRUE V\VWHP 7KH FDOFXODWLRQV LQYROYH f D %(7 HTXDWLRQ ^:>33f @ :P&f >& f:P&f@[33f LQ ZKLFK : LV WKH ZHLJKW RI JDV DGVRUEHG DW D UHODWLYH SUHVVXUH 33 SUHVVXUH UDWLR RI 1 JDV LQ +H JDVf :P LV WKH ZHLJKW RI DGVRUEDWH FRQVWLWXWLQJ D PRQROD\HU RI 1 RQ VXUIDFH DQG WKH FRQVWDQW & LV UHODWHG WR WKH HQHUJ\ RI DGVRUSWLRQ LQ WKH ILUVW OD\HU f D OLQHDU SORW RI ^:>3R3f@` YV 33 WR \LHOG YDOXHV RI VORSH V &f:P&f DQG LQWHUFHSW L :P&f f WKH ZHLJKW RI D PRQROD\HU :P REWDLQHG E\ HTXDWLRQ :P VLf f $W :P1$FVf0 ZKHUH $W LV WRWDO VXUIDFH DUHD RI WKH VDPSOH PHDVXUHG DQG 1 LV $YRJDGURnV QXPEHU )RU 1 DW r. WKH FURVVVHFWLRQDO DUHD

PAGE 84

$FV LV ƒ DQG 0 LV WKH PROHFXODU ZHLJKW RI 1 f $ $W: ,Q ZKLFK $ LV VSHFLILF VXUIDFH DUHD RI VDPSOH DQG : LV WKH VDPSOH ZHLJKW 7KH WRWDO SRUH YROXPH 9_cTf LV GHULYHG IURP WKH DPRXQW RI 1 DGVRUEHG DW D UHODWLYH SUHVVXUH FORVH WR XQLW\ E\ DVVXPLQJ WKDW WKH SRUHV DUH DOO ILOOHG ZLWK OLTXLGL]HG 1 RI D YROXPH 9OLT ZKLFK FDQ EH FDOFXODWHG XVLQJ HTXDWLRQ 9_MT9Pf57 3D9DGV ZKHUH 9P LV WKH PRODU YROXPH RI WKH OLTXLG 1 3D LV DPELHQW SUHVVXUH DQG 9DFMV LV YDSRUL]HG SRUH OLTXLG 1f 7KH DYHUDJH SRUH VL]H FDQ EH HVWLPDWHG IURP WKH SRUH YROXPH E\ DVVXPLQJ F\OLQGULFDO SRUH JHRPHWU\ WKHQ WKH DYHUDJH SRUH UDGLXV US FDQ EH GHULYHG DV US 9_cT$ 7KH SRUH VL]H GLVWULEXWLRQ LV FDOFXODWHG XVLQJ WKH PHWKRG SURSRVHG E\ %DUUHWW -R\QHU DQG +DOHQGD >@ 6DPSOHV KHDWHG WR WKH WHPSHUDWXUHV GHVLJQDWHG LQ 7DEOH DQG FRROHG WR URRP WHPSHUDWXUH ZLWK WKH KHDWLQJ SURJUDP VKRZQ LQ )LJXUH ZHUH JURXQG LQWR SRZGHU DQG ZHLJKHG WR DURXQG JUDP LQ WKH SHOOHW FHOOV EHIRUH LQVWDOOLQJ LQ WKH $XWRVRUE V\VWHP IRU RXWJDVVLQJ DQG SUHKHDWLQJ WR HOLPLQDWH WKH ZDWHU PRLVWXUH 7KH RXWJDVVLQJ DQG SUHKHDWLQJ ZDV KHOG IRU KRXUV DW r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rPLQ IURP DQJOHV RI r XS WR r 7KH LQGH[ RI UHIUDFWLRQ ZDV REWDLQHG XVLQJ D 3XOIULFK UHIUDFWRPHWHU DQG D +H1H ODVHU OLJKW VRXUFH ZKLFK ZDYHOHQJWK LV QP 7KH SULQFLSOH RI WKH UHIUDFWRPHWHU LV EDVHG RQ WKH PHDVXUHPHQW RI WKH FULWLFDO DQJOH !F ZKLFK LV WKH DQJOH RI WKH LQWHUIDFH

PAGE 85

EHWZHHQ WKH XQNQRZQ JHO VDPSOH RI LQGH[ Q DQG D SULVP RI NQRZQ LQGH[ Qn 6LQFH Qn LV JUHDWHU WKDQ Q WKH WZR PXVW EH LQWHUFKDQJHG LQ WKH VWDQGDUG HTXDWLRQ VLQ _!F QQn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r& 'LIIHUHQWLDO WKHUPDO DQDO\VLV '7$f PHDVXUHV WKH WHPSHUDWXUHV DW ZKLFK KHDW UHODWHG SKHQRPHQD RFFXU LQ PDWHULDOV '7$ SURYLGHV WKH VDPH TXDOLWDWLYH LQIRUPDWLRQ DV '6& DQG FDQ SURYLGH VHPLTXDQWLWDWLYH FDORULPHWULF PHDVXUHPHQWV 7KH WHPSHUDWXUH UDQJH RI WKH '7$ FHOO LV IURP DPELHQW WR r& 7KH KLJK WHPSHUDWXUH r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

PAGE 86

)LJXUH 5HIUDFWLRQ LQ WKH SULVP RI D 3XOIULFK UHIUDFWRPHWHU

PAGE 87

FKDQJLQJ LQ PRLVWXUH DQG YRODWLOHV R[LGDWLRQ UHDFWLRQf ZKHQ JHO LV LQ WKH KHDWLQJ SURFHVV $ WKHUPRPHFKDQLFDO DQDO\]HU 70$f FDQ EH XVHG DV D GLODWRPHWHU WR PHDVXUH JHO YROXPH VKULQNDJH RU JODVV H[SDQVLRQ FRHIILFLHQW IURP URRP WHPSHUDWXUH WR r& 7KH VDPSOH ZDV LQVWDOOHG LQ D SURJUDPPDEOH IXUQDFH LQ ZKLFK D WKHUPRFRXSOH LQ GLUHFW FRQWDFW ZLWK WKH VDPSOH PHDVXUHG WKH VDPSOH WHPSHUDWXUH $ PRYDEOHFRUH OLQHDU YDULDEOH GLIIHUHQWLDO WUDQVIRUPHU /9'7f ZKRVH RXWSXW LV SURSRUWLRQDO WR WKH OLQHDU GLVSODFHPHQW RI ,WV FRUH LV XVHG 7KH GLPHQVLRQDO FKDQJH RI WKH VDPSOH ZLWK WHPSHUDWXUH FDQ EH PRQLWRUHG XVLQJ WKLV /9'7 FRUH GLVSODFHPHQW WHFKQLTXH )OH[XUDO VWUHQJWK WHVWV ZHUH SHUIRUPHG XQGHU JXLGHOLQHV RI WKH $670 0 VWDQGDUG >@ 6DPSOHV KHDWHG WR WKH YDULRXV WHPSHUDWXUHV VHH 7DEOH f DQG FRROHG ZLWK WKH WKHUPDO VFKHGXOH VKRZQ LQ )LJXUH ZHUH FXW ZLWK D GLDPRQG ZDWHULQJ EODGH DQG SROLVKHG FDUHIXOO\ ZLWK 6L& JULW SDSHU LQWR D VL]H RI OHQJWK [ ZLGWK [ WKLFNQHVV PP [ PP [ PPf $OO VDPSOHV ZHUH GULHG DW r& IRU KRXUV LPPHGLDWHO\ SULRU WR PHDVXUHPHQWV WR HOLPLQDWH DEVRUEHG PRLVWXUH 6XEVHTXHQWO\ WKH VDPSOHV ZLWK D VSDQ ZLGWK WKLFNQHVV UDWLR RI DERXW ZHUH ORDGHG LQ WKUHHSRLQW EHQGLQJ LQ DPELHQW FRQGLWLRQV DW D VWUDLQ UDWH RI [ n 6n XVLQJ DQ ,QVWURQ PRGHO ,Q WKLV H[SHULPHQW D VHW RI ILYH LGHQWLFDO VDPSOHV ZHUH KHDWHG DW VDPH WLPH LQ D IXUQDFH WR HDFK WHPSHUDWXUH 7KH FRPSUHVVLYH VWUHQJWK WHVWV ZHUH FDUULHG RXW XQGHU WKH JXLGHOLQHV RI WKH $670 & VWDQGDUG >@ 6DPSOHV KHDWHG WR WKH GHVLJQDWHG WHPSHUDWXUHV VHH 7DEOH f DQG FRROHG ZLWK KHDWLQJ SURJUDPV VKRZQ LQ )LJXUH ZHUH FXW LQWR D UHFWDQJXODU VKDSH RI OHQJWK [ ZLGWK [ WKLFNQHVV PP [ PP [ PPf $OO VDPSOHV ZHUH GULHG DW r& IRU KRXUV LPPHGLDWHO\ SULRU WR PHDVXUHPHQWV WR HOLPLQDWH DEVRUEHG PRLVWXUH 6XEVHTXHQWO\ VDPSOHV ZHUH ORDGHG LQ DQ ,QVWURQ PRGHO VXFK WKDW WKH OHQJWK ZDV SDUDOOHO WR WKH D[LV RI WKH DSSOLHG VWUHVV DSSOLHG DW D VWUDLQ UDWH RI [ f Vn 7KH

PAGE 88

VDPH QXPEHU RI VDPSOHV DQG SURFHVVLQJ WHPSHUDWXUHV ZHUH XVHG DV WKDW RI IOH[XUDO VWUHQJWK WHVW 0LFURKDUGQHVV YDOXHV ZHUH REWDLQHG XVLQJ D r GLDPRQG S\UDPLG LQGHQWHU DW D JUDP ORDG ZLWK WKH 0LFUR +DUGQHVV 7HVWHU PRGHO 04 ) /HFR &R -DSDQf 6DPSOHV ZHUH KHDWHG WR WKH GHVLJQDWHG WHPSHUDWXUHV VHH 7DEOH f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n UHODWLRQVKLS (TXDWLRQ f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f DQG FPn QPf 7KH UHVXOWV VKRZ WKDW WKH 6L26L PROHFXODU VWUHWFKLQJ

PAGE 89

)LJXUH )7,5 KRW VWDJH GDWD IURP r& WR r& RI SXUH VLOLFD JHO

PAGE 90

YLEUDWLRQ LV REVHUYHG DW FQU QPf HYHQ LQ WKH ORZ WHPSHUDWXUH VDPSOH 7KH SHDN DW FPn QPf LV DQ DUWLIDFW RI WKH GLIIXVH UHIOHFWLRQ VWDJH 7KH SULPDU\ GLIIHUHQFH EHWZHHQ WKHVH FXUYHV LV WKDW SHDNV FRUUHVSRQGLQJ WR RUJDQLF UHVLGXDOV LQ WKH UDQJH EHWZHHQ FPn QPf DQG FPn QPf DUH DEVHQW LQ WKH KLJK WHPSHUDWXUH VDPSOH 7KH VSHFWUXP RI WKH r& VLOLFD VDPSOH LV QHDUO\ WKH VDPH DV WKDW IRU IXVHG VLOLFD ZLWK WKH H[FHSWLRQ RI D VPDOO VKLIW LQ WKH DEVRUSWLRQ HGJH QHDU FP QUQf WR ORZHU ZDYHQXPEHUV 7KH WHPSHUDWXUHGHSHQGHQW FKDQJHV LQ LQWHQVLW\ RI WKH FKDUDFWHULVWLF DEVRUSWLRQ EDQG DW FP QPf KDYH EHHQ DWWULEXWHG WR WKH VWUHWFKLQJ YLEUDWLRQ RI WKH 6L2+ QRQEULGJLQJ R[\JHQ 1%2f JURXSV :LWK LQFUHDVLQJ WHPSHUDWXUHV WKH FRQFHQWUDWLRQ RI VLODQRO JURXSV LV GHFUHDVHG WR D QRQGHWHFWDEOH OHYHO DQG WKH FKDUDFWHULVWLF FPn QPf SHDN GLVDSSHDUV 7KH H[WHQW RI K\GUR[\O DEVRUSWLRQ EDQGV DW FPn QPf WR FPn QPf LV DOVR GLPLQLVKHG IRU WKH KLJKHU WHPSHUDWXUH VDPSOHV 7KLV GRHV QRW PHDQ WKDW WKH JHO LV FRPSOHWHO\ IUHH ]HUR SSPf IURP DOO W\SHV RI ZDWHU EXW UDWKHU WKDW WKH )7,5 WHFKQLTXH LV QRW VHQVLWLYH HQRXJK LQ WKLV UHJLRQ FPnf WR GHWHFW WKH UHVLGXDO K\GUR[\O ERQGV WR IXOO\ XQGHUVWDQG DQG PRQLWRU WKH ZDWHU DVVRFLDWHG ZLWK JHO VWUXFWXUH 2YHUWRQH DQG FRPELQDWLRQ IUHTXHQFLHV VKRXOG EH LQYHVWLJDWHG >@ 7KHVH UHVXOWV VKRZ WKDW WKH RQO\ VLJQLILFDQW LPSXULW\ LQ WKH XOWUDSXUH VLOLFD JHO LV ZDWHU 7KH DPRXQW RI ZDWHU GHWHUPLQHV WKH H[WHQW RI QRQEULGJLQJ R[\JHQ 1%2f FRQWHQW ZKLFK SUHYHQWV FRPSOHWH GHQVLILFDWLRQ :DWHU FRQWHQW FDQ DOVR EH REVHUYHG HDVLO\ XVLQJ D 899,61,5 VSHFWURSKRWRPHWHU )LJXUH VKRZV WKH LQWHQVLW\ RI IUHH ZDWHU SHDNV DW QP QP DQG QP GHFUHDVLQJ ZLWK LQFUHDVLQJ SURFHVVLQJ WHPSHUDWXUH ,W LQGLFDWHV WKDW WKH GHQVLILFDWLRQ LV GXH WR WKH FRPELQDWLRQ RI VLODQRO JURXSV RQ WKH VXUIDFH RI SDUWLFOHV ZKLFK IRUP IUHH ZDWHU DQG HVFDSH FRQVHTXHQWO\ WKH VXUIDFH FKHPLFDO ZDWHU LV UHGXFHG DQG WKH DEVRUSWLRQ SHDNV DUH GLPLQLVKHG

PAGE 91

DEVRUSWDQFH )LJXUH 7KH DEVRUSWDQFH SHDNV RI ZDWHU GHFUHDVLQJ ZLWK LQFUHDVLQJ WHPSHUDWXUH

PAGE 92

6DPSOHV KHDWHG WR GLIIHUHQW WHPSHUDWXUHV DUH FRPSDUHG ZLWK D SXUH VLOLFD PHOW JODVV '\QDVLOf LQ WHUPV RI WKH FXWRII ZDYHOHQJWK DV VKRZQ LQ )LJXUH ,QFUHDVLQJ WKH WHPSHUDWXUH RI WKH WKHUPDO WUHDWPHQW LQFUHDVHV WKH RSWLFD WUDQVPLVVLRQ QHDU WKH 89 DEVRUSWLRQ HQG DQG VKLIWV WKH XY FXWRII WR WKH VKRUW ZDYHOHQJWK IRU WKH SXUH VLOLFD JHOV DSSDUHQWO\ DV WKH UHVXOW RI D GHFUHDVHG ZDWHU FRQWHQW LQ WKH KLJK WHPSHUDWXUH VDPSOHV $V 6LJHO FRQFOXGHV >@ WKH LQWURGXFWLRQ RI RQH HOHFWURQ YDOHQW HOHPHQWV LH + /L 1D 5E &V )U ) &O %U ,f SURGXFHV D QRWLFHDEOH VKLIW RI WKH XY HGJH WR ORQJHU ZDYHOHQJWKV 7KLV VKLIW LV EHFDXVH WKHVH HOHPHQWV WHUPLQDWH WKH EULGJLQJ R[\JHQV %2f LQWR QRQEULGJLQJ R[\JHQV 1%2f DQG SURYLGH ORZHU HQHUJ\ H[FLWRQ OHYHOV IRU SKRWRn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f ZKLOH WKH WRWDO SRUH YROXPH DQG VXUIDFH DUHD GHFUHDVHG )LJXUHV DQG f ZLWK WHPSHUDWXUHV XS WR r& $Q DVVXPSWLRQ LV WKDW WKH SRUHV GHFUHDVH LQ QXPEHU DQG IRUFH WKH HQWLUH JHO ERG\ WR FRQWUDFW 7KLV LV EHFDXVH WKH SRUHV DUH YHU\ VPDOO LQ WKLV VWXG\ WKH PHDQ SRUH GLDPHWHU LV RQO\ QPf &RQVHTXHQWO\ WKH\ HVVHQWLDOO\ REH\ WKH PHFKDQLVP SUHVHQWHG E\ WKH 2VWZDLG)UHXQGOLFK HTXDWLRQ ORJ6U6cf .(7U VWDWHG LQ &KDSWHU (TXDWLRQ DQG LOOXVWUDWHG LQ )LJXUH 2QFH WKH SRUHV VWDUW WR GHFUHDVH LQ VL]H WKH UDWH RI GHFUHDVH EHFRPHV YHU\ IDVW DQG WKH\ LPPHGLDWHO\ ILOO DQG GLVDSSHDU XQGHU WKH DVVLVWDQFH RI WKH PLJUDWLRQ RI VLODQRO JURXSV DORQJ WKH LQWHULRU VXUIDFH DQGRU PLJUDWLRQ RI YDFDQFLHV WKURXJK WKH VWUXFWXUH WR WKH H[WHULRU RI WKH JHO 7KHUHIRUH WKH JHO VKULQNV DV WKH WHPSHUDWXUH LQFUHDVHV DV D UHVXOW RI

PAGE 93

7UDQVPLVVLRQ bf :DYHOHQJWK QPf )LJXUH 7UDQVPLVVLRQ FXWRII RI SXUH VLOLFD JH

PAGE 94

3RUH UDGLXV ƒf e L [ f 7 n 9 7HPSHUDWXUH r&f )LJXUH 3RUH UDGLXV YV WHPSHUDWXUH

PAGE 95

3RUH YROXPH FPJf )LJXUH SRUH VL]H GLVWULEXWLRQ YV SRUH YROXPH DW YDULRXV WHPSHUDWXUHV

PAGE 96

7RWDO SRUH YROXPH FPrJf 7HPSHUDWXUH r&f )LJXUH 7RWDO SRUH YROXPH YHUVXV WHPSHUDWXUH

PAGE 97

7HPSHUDWXUH r&f )LJXUH 6SHFLILF VXUIDFH DUHD YHUVXV WHPSHUDWXUH

PAGE 98

WKH WRWDO SRUH YROXPH GHFUHDVH ,W FDQ DOVR EH UHDVRQDEO\ DVVXPHG WKDW WKH GHFUHDVH RI WKH VXUIDFH DUHD LV OLQHDUO\ SURSRUWLRQDO WR WKH GLVDSSHDUDQFH RI WKH QXPEHU RI SRUHV :KHQ D JHO LV KHDWHG KLJKHU WKDQ LWV IRDPLQJ WHPSHUDWXUH IUHH ZDWHU LV IRUPHG IURP WKH GLVVRFLDWHG VXUIDFH K\GUR[\O JURXSV LQVLGH WKH IXOO\ GHQVLILHG JHO VWUXFWXUH ,PPHGLDWHO\ WKHVH IUHH ZDWHU PROHFXOHV IROORZ WKH LGHD JDV ODZ LQ (TXDWLRQ WR FUHDWH QHZ SRUHV SY Q57 f ZKHUH S LV LQWHUQDO SUHVVXUH RI D FORVHGSRUH YROXPH Y Q LV D PROH QXPEHU RI JDVHRXV ZDWHU PROHFXOHV ZLWKLQ DQ LQVWDQWDQHRXVO\ FUHDWHG FORVHGSRUH Y Y A ZKHUH U LV WKH FORVHGSRUH UDGLXV DQG 7 LV JHO ERG\ WHPSHUDWXUH DW WKH PRPHQW IRDPLQJ RFFXUV ,I 1 LV WKH WRWDO PRODU QXPEHU RI JDVHRXV ZDWHU PROHFXOHV LQ WRWDO RI VXFK FUHDWHG SRUHV RI 9 SHU XQLW YROXPH RI PDWWHU WKHQ 1Q LV WKH WRWDO QXPEHU RI SRUHV SHU XQLW YROXPH RI VLOLFD DQG 9 1YQ LV WRWDO SRUH YROXPH 9YRcGf SHU XQLW YROXPH RI VLOLFD 96ROLGf &RQVHTXHQWO\ HTXDWLRQV DQG FDQ EH ZULWWHQ S9 157 f 9 1Qf [ Y 1Qf [ QU SfS f ZKHUH S WKH UHODWLYH GHQVLW\ LV HTXDO WR SDSU SD P6ROLG96ROLG9YRLGf LV WKH DSSDUHQW GHQVLW\ RI WKH IRDPHG VLOLFD JHO DQG SU P6_cG96LcG LV WKH IXOO\ GHQVLILHG VLOLFD JHO 7KHUHIRUH IURP (TXDWLRQV f DQG f ZH JHW S Q57MWU 157S Sf f :KHQ WHPSHUDWXUH H[FHHGV WKH SRUH FORVLQJ WHPSHUDWXUH WKH JHO LPPHGLDWHO\ IRDPV DV VRRQ DV WKH VXUIDFH ZDWHU LV UHOHDVHG 7KH JHO IRDPLQJ PHFKDQLVP LV H[SORUHG E\ 3KDOLSSRX 7 :RLJQLHU DQG =DU]\FNL >@ 7KH\ XVH WKH FRQFHSW WKDW WKH UDWH RI WRWDO HQHUJ\ LQSXW WR WKH JHO VLQWHULQJ V\VWHP HTXDOV WKH UDWH RI WRWDO HQHUJ\ RXWSXW IURP WKH V\VWHP 7KH WRWDO HQHUJ\ LQSXW LQFOXGHV WKH VXUIDFH HQHUJ\ RI VLOLFD JHO G:DGW WUFGUGWf ZKHUH U LV WKH SRUH UDGLXV D LV VXUIDFH WHQVLRQ DQG W LV WLPH DQG WKH H[WHUQDO SUHVVXUH HQHUJ\ LV

PAGE 99

G:EGW 3G9 3 [ QUGUGW ZKHUH 3 LV H[WHUQDO SUHVVXUH 7KH WRWDO HQHUJ\ RXWSXW LQFOXGHV WKH HQHUJ\ IRU YLVFRXV IORZ G:FGW MUQUSGUGWff ZKHUH WL LV WKH YLVFRVLW\ RI VLOLFD JHO DW WKH WHPSHUDWXUH RI IRDPLQJ S LV WKH UHODWLYH GHQVLW\ RI WKH JHO DQG WKH HQHUJ\ IRU YDU\LQJ WKH SRUH UDGLXV LV G:SGW SG9 S[ FUGUGW 7KH HTXDWLRQ IRU WKLV V\VWHP LV WKXV G:DGW G:EGW G:RGW G:GGW f %\ UHSODFLQJ DLO WKH LWHPV ZH JHW D U3Sf 7LSGUGWf f DQG E\ FRPELQLQJ ZLWK (TXDWLRQ \LHOGV RSfS [ 1QQf 3Sf Sf ULGSGWf f ZKHQ ZH DVVXPH JHO LV VLQWHUHG LQ FRQYHQWLRQDO SUHVVXUH 3 WKH HTXDWLRQ EHFRPHV GSGW Sf D 7MU S U?f f ,I WKHUH LV QR HVFDSH RI JDVHRXV ZDWHU IURP WKH FORVHGSRUHV WKHQ FRPELQH (TXDWLRQ GSGW Sf D QUf 157S U? f DQG OHW GSGW DQG XVH (TXDWLRQ WKHQ D FULWLFDO SRUH UDGLXV UPcQ LV REWDLQHG UPLQ Q57Q Df f %\ VXEVWLWXWLQJ (TXDWLRQ LQWR (TXDWLRQ WKHQ DQ H[SUHVVLRQ IRU WKH PD[LPXP YDOXH RI GHQVLW\ SPD[f LV DFKLHYHG SPD[ >157 D fQ57UFDf @ f 7KHVH WZR HTXDWLRQV f VKRZ WKDW D PD[LPXP YDOXH SPD[ DQG D FRUUHVSRQGLQJ FULWLFDO SRUH UDGLXV UPcQ FDQ EH SUHGLFWHG LQ WHUPV RI WKH VLQWHULQJ WHPSHUDWXUH 7f VXUIDFH WHQVLRQ Df WKH DPRXQW RI IUHH ZDWHU LQ D SRUH Qf DQG WKH QXPEHU RI SRUHV SHU XQLW YROXPH RI VLOLFD 1Qf )URP WKLV VWXG\ WKH FRQFOXVLRQ LV UHDFKHG WKDW ZKHQHYHU WKH UHVLGXDO VXUIDFH ZDWHU LV UHOHDVHG DIWHU WKH FROODSVH RU FORVLQJ RI WKH RULJLQDO RSHQ SRUHV WKHQ WKH IUHH ZDWHU LQ WKH JHO VWUXFWXUH IROORZV WKH LGHD JDV ODZ DW KLJKHU WHPSHUDWXUHV WR FUHDWH FORVHGSRUHV &RQVHTXHQWO\ IRDPLQJ RI WKH JHO KDSSHQV DQG WKH DYHUDJH UDGLL RI WKH SRUHV LQFUHDVHV VLJQLILFDQWO\ ZKHQ WHPSHUDWXUH LV MXVW DERYH r&

PAGE 100

VHH )LJXUH f $W r& WKH SRUH UDGLXV VXGGHQO\ LQFUHDVHV IURP D QP RSHQ SRUH UDGLXV WR D QP FORVHGSRUH UDGLXV ;UD\ GLIIUDFWLRQ SDWWHUQV IURP IXVHG VLOLFD JHQHUDOO\ H[KLELW D EURDG SHDN FHQWHUHG DURXQG WKH VHFRQG VWURQJHVW SHDN LQ WKH GLIIUDFWLRQ SDWWHUQ RI TXDUW] )LJXUH f 7KH SDUWLDOO\ GHQVLILHG VLOLFD JHOV PDGH LQ WKLV VWXG\ KDYH EURDGHU GLIIUDFWLRQ SDWWHUQV WKDQ WKDW RI IXVHG VLOLFD DV VKRZQ LQ )LJXUH 7KH EURDGHQLQJ RI WKH JHO GLIIUDFWLRQ SHDN GHFUHDVHV ZLWK LQFUHDVLQJ WHPSHUDWXUH LQGLFDWLQJ DQ LQFUHDVH LQ WKH RUGHULQJ LQVLGH WKH JHO >@ 7KH %(7 GDWD LQ 7DEOH XVLQJ +DYDUG :LOVRQ OOHUnV SDUWLFOH VL]H PRGHO GHVFULEHG LQ 6HFWLRQ ,, DOVR VXJJHVW WKDW WKH HIIHFWLYH SDUWLFOH GLDPHWHU RI WKH JHOV LQFUHDVHV ZLWK WHPSHUDWXUH HJ r& QPf r& QPf r& QPf DQG r& QPf >@ 7KHVH YDOXHV FDQ EH FRPSDUHG WR WKH GLDPHWHU DURXQG QP RI IXOO\ GHQVLILHG VLOLFD 7KHVH UHVXOWV LPSO\ WKDW YHU\ VKRUW UDQJHRUGHULQJ LV WDNHQ SODFH LQVLGH WKH VWUXFWXUH IRUPLQJ FU\VWDOOLWHV 7KH VL]H RI D VLQJOH VLOLFD WHWUDKHGURQ LV DERXW QP 7KHUHIRUH WKH VWUXFWXUH RI WKH JHO FU\VWDOOLWHV LV FRPSRVHG RI RQO\ IHZ VLOLFD WHWUDKHGUD 7KH JHO SUHKHDWHG WR r& LV HVWLPDWHG WR EH DERXW WHWUDKHGUD DW r& LW LV DERXW WHWUDKHGUD DW r& LW LV DERXW WHWUDKHGUD DQG DW r& WKH JHO KDV DERXW WHWUDKHGUD DORQJ WKH GLDPHWHU RI WKH JHO ILEULOODU VWUXFWXUH $V D UHVXOW [UD\ GLIIUDFWLRQ SURGXFHV D UHODWLYHO\ EURDGHU SHDN IRU WKLV UHODWLYHO\ VKRUWUDQJHRUGHULQJ WKDQ LV REVHUYHG IRU IXVHG VLOLFD 7KLV REVHUYDWLRQ OHG WR WKH VXJJHVWLRQ WKDW WKH VLOLFD JHL LV FRPSRVHG RI D UDQGRPO\ RULHQWHG ILEULOODU VWUXFWXUH UDQGRPQHWZRUN PRGHO >@f LQ ZKLFK WKH VLOLFD PROHFXOHV DUH UHODWLYHO\ RUGHUHG FU\VWDOOLWHV FU\VWDOOLWH PRGHO >@f 7KLV SKHQRPHQRQ LV VLPLODU WR D PRVDLF VWUXFWXUH LQ DQ LPSHUIHFW FU\VWDO LQ ZKLFK WKH ODWWLFH LV EURNHQ XS LQWR D QXPEHU RI WLQ\ EORFNV DERXW ƒf HDFK VOLJKWO\ GLVRULHQWHG RQH IURP DQRWKHU >@ 7KH RYHUDOO REVHUYHG JHO VWUXFWXUH LV DPRUSKRXV %DVHG XSRQ WKH DERYH UHVXOWV WKH VWUXFWXUH RI SRURXV JHO LQ ZKLFK WKH WHPSHUDWXUHLQGHSHQGHQW SRUH GLDPHWHU LV DOZD\V DURXQG QP VHH 7DEOH f LV

PAGE 101

,QWHQVLW\ H )LJXUH ;UD\ SDWWHUQV RI VLOLFD JHOV DW GLIIHUHQW WHPSHUDWXUHV FRPSDUH WR WKDW RI IXVHG VLOLFD

PAGE 102

SURSRVHG DV VKRZQ LQ )LJXUH 7KH XOWUDVWUXFWXUH RI D GHQVLILHG JHO LV DOVR SURSRVHG DV VKRZQ LQ )LJXUH 7KH GDWD REWDLQHG VKRZ WKDW WKH LQGH[ RI UHIUDFWLRQ RI WKH JHO PRQROLWKV LQFUHDVHV ZLWK WKH S\URO\VLV WHPSHUDWXUH DV ZHO DV GHQVLW\ 7KH PHDVXUHG LQGH[ RI UHIUDFWLRQ UDQJHG IURP Q s WR Q s IRU WKH VDPSOH KHDWHG IURP r& WR r& DQG WKH FRUUHVSRQGLQJ GHQVLW\ YDULHG IURP s JFP WR s JFP :LWKLQ H[SHULPHQWDO HUURU WKH UHVXOWV VKRZQ LQ )LJXUH DUH UHDVRQDEO\ ZHOO SUHGLFWHG E\ WKH /RUHQW]/RUHQ] HTXDWLRQ >VHH S LQ UHI @ D > HQf 0@>1RQfS@ f 5HDUUDQJLQJ HTXDWLRQ \LHOGV QLf>QLf3@ Q f>Q f3@ f ZKHUH WKH FRQVWDQWV DUH D LV SRODUL]DELOLW\ RI D VLOLFD PROHFXOH H LV WKH GLHOHFWULF FRQVWDQW RI D YDFXXP 0 LV WKH PROHFXODU ZHLJKW RI VLOLFD 1 LV $YRJDGURn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f GDWD VKRZQ LQ )LJXUH LQGLFDWH DQ HQGRWKHUPLF GHVRUSWLRQ RI SK\VLFDO ZDWHU DW D PD[LPXP r& LQ WKH r& WR

PAGE 103

6XUIDFH VLODQRO JURXSV DUH QRW VKRZQ )LJXUH $ SURSRVHG JH VWUXFWXUDO PRGHO

PAGE 104

UDQGRP RULHQWDWLRQ RI UHODWLYHO\ RUGHUHG FU\VWDOOLWH QP ‘ VLODQRO JURXS RU QRQERQGLQJ R[\JHQ RQ WKH VXUIDFH RI UHODWLYHO\ RUGHUHG FU\VWDOOLWHV )LJXUH $ SURSRVHG VFKHPH RI VLQWHUHG VLOLFD JHO LQ ZKLFK VLODQRO JURXSV WHUPLQDWH EULGLQJ ERQGV RQ WKH VXUIDFH RI FU\VWDOOLWHV

PAGE 105

,QGH[ RI UHIUDFWLRQ QGf )LJXUH LQGH[ RI UHIUDFWLRQ YV GHQVLW\ IRU VLOLFD JHOV JHOJODVV DQG FU\VWDOOLQHV SKDVHV

PAGE 106

+HDW )ORZ P:f )LJXUH 7KH GLIIHUHQWLDO VFDQQLQJ FDORULPHWHU '6&f GDWD RI D GULHG VLOLFD JHO

PAGE 107

r& UDQJH DQG DQ H[RWKHUPLF GHFRPSRVLWLRQ DQGRU R[LGDWLRQ RI R[DOLF DFLG DW D PD[LPXP r& LQ WKH r& WR r& UDQJH 7KH '7$ GDWD DUH FROOHFWHG YLD WKH VDPH PHWKRG DV WKH '6& GDWD EXW '7$ KDV DQ LQFUHDVHG WHVWLQJ UDQJH WR r& DV VKRZQ LQ )LJXUH 7KHUH LV VLJQLILFDQW HQGRWKHUPLF GHVRUSWLRQ RI SK\VLFDO ZDWHU ZLWKLQ WKH SRUHV $ YHU\ ODUJH H[RWKHUPLF GHFRPSRVLWLRQ DQGRU R[LGDWLRQ RI R[DOLF DFLG LV DOVR REVHUYHG ZLWK '7$ 1R IXUWKHU WKHUPDO VRUSWLRQ LV REVHUYHG LQ WKH UDQJH EHWZHHQ r& DQG r& 7KXV WKH GULHG DQG GHVRUEHG JHOV DUH VWDEOH IURP r& RQZDUGV $ WKHUPRJUDYLPHWULF DQDO\]HU 7*$f ZDV DOVR XVHG WR DQDO\]H WKH GULHG JHO VDPSOH DV VKRZQ LQ )LJXUH ,Q WKLV FDVH WKH GLIIHUHQWLDO ZHLJKW ORVV VKRZV D YHU\ KLJK SHDN DW r& LQ WKH r& WR r& UDQJH LQGLFDWLQJ WKH PD[LPXP ORVV RI SK\VLFDO ZDWHU 7KHUH LV D VLJQLILFDQW ZHLJKW ORVV RI R[DOLF DFLG DW r& LQ WKH r& WR r& WHPSHUDWXUH UDQJH QR IXUWKHU ZHLJKW ORVV ZDV REVHUYHG IURP r& WR r& 7KLV 7*$ REVHUYDWLRQ WRJHWKHU ZLWK '6& RU '7$ GDWD REWDLQHG GXULQJ VLQWHULQJ FOHDUO\ LQGLFDWHV WKDW WZR SKHQRPHQD DUH SUHVHQW f WKH HQGRWKHUPLF ZDWHU HYDSRUDWLRQ LQ WKH UDQJH RI r& WR r& DQG f WKH H[RWKHUPLF R[LGDWLRQ RI R[DOLF DFLG LQ WKH r& WR r& UDQJH )LJXUH LOOXVWUDWHV WZR 70$ FXUYHV RQH RI DQ XQILUHG VWDQGDUG VLOLFD JHO VDPSOH DQG RQH RI D ILUHG r&f VDPSOH WKH FXUYH RI WKH XQILUHG VDPSOH KDV D VLJQLILFDQW GHFUHDVH LQ OLQHDU GLPHQVLRQ IURP r& WR r& 7KH SUHKHDWHG r& VDPSOH VKRZV RQO\ D VOLJKW GLPHQVLRQDO GHFUHDVH bf ZKHQ UHKHDWHG WR r& :KHQ KHDWHG DERYH r& WKH GLPHQVLRQV GHFUHDVHV QRWLFHDEO\ 7KHVH UHVXOWV VKRZ WKDW WKH VWUXFWXUH RI WKH ILUHG VDPSOH KDV DOUHDG\ XQGHUJRQH UHDUUDQJHPHQW DQG WKDW LW LV LUUHYHUVLEOH ,Q D SRLQW EHQGLQJ WHVW D EHDP ORDGHG KDV WHQVLOH VWUHVVHV RQ RQH VXUIDFH DQG FRPSUHVVLYH VWUHVV RQ WKH RWKHU DV VKRZQ LQ )LJXUH )OH[XUDO VWUHQJWK LV D PHDVXUH RI WKH OHYHO RI WKH WHQVLOH VWUHVV RQ WKH VXUIDFH UHTXLUHG WR PDNH D PDWHULDO IDLO $ SDUWLDOO\ GHQVLILHG JHO LV OLNH IXOO\ GHQVLILHG JODVV ZKLFK VKRZV QR SODVWLF GHIRUPDWLRQ

PAGE 108

7HPSHUDWXUH GLIIHUHQFH r&f )LJXUH 7KH GLIIHUHQWLDO WKHUPDO DQDO\VLV '7$f GDWD RI D GULHG JHO

PAGE 109

7HPSHUDWXUH r&f )LJXUH 7KHUPRJUDYLPHWULF DQDO\VLV 7*$f FXUYH RI D GULHG JHO

PAGE 110

'LPHQVLRQ FKDQJH /$f [ n 7HPSHUDWXUH r&f )LJXUH 7KHUPDO PHFKDQLFDO DQDO\VLV RI D XQILUHG VDPSOH DQG D SUHKHDWHG VDPSOH

PAGE 111

7HQVLOH VWUHVV LQ VXUIDFH 3 &RPSUHVVLRQ 7HQVLRQ )LJXUH $ WKUHHSRLQW EHQGLQJ WHVW

PAGE 112

XQGHU WKH VWUHVV 6DPSOHV FDQ EH ORDGHG DQG VWUHVVHG XS WR WKH SURSRUWLRQDO OLPLW UXSWXUH SRLQW DW D PD[LPXP WHQVLOH VWUHVV DPD[f (ODVWLF VWUDLQ LV GLUHFWO\ SURSRUWLRQDO WR WKH DSSOLHG WHQVLOH VWUHVV D E\ IROORZLQJ WKH +RRNHnV ODZ D ( H ZKHUH D LV WHQVLOH VWUHVV ( LV VHH S LQ UHI @ R f§ 3L /EG £ FU &7PD[ f ZKHUH D WHQVLOH VWUHVV RQ WKH RXWHU VXUIDFH DW PLGVSDQ SDVFDO QHZWRQPf 3L ORDG DW D JLYHQ SRLQW RQ WKH ORDGGHIOHFWLRQ FXUYH 1 QHZWRQf / VXSSRUW VSDQ GLVWDQFH P E ZLGWK RI VSHFLPHQ P DQG G WKLFNQHVV RI VSHFLPHQ P WKH HODVWLF VWUDLQ EHIRUH RU DW IUDFWXUH ZDV REWDLQHG XVLQJ HTXDWLRQ >@ H =W 5WG/ 'G/ HHPD[ f ZKHUH H VWUDLQ PPPP HPD[ LV WKH PD[LPXP VWUDLQ DW DPD[ = VWUDLQ UDWH PPVHF W WLPH VHF 5 UDWH RI FURVVKHDG PRWLRQ PPPLQ PLGVSDQ GHIOHFWLRQ PP 7KH YDULDWLRQ RI PD[LPXP IOH[XUDO VWUHQJWK DPD[f PD[LPXP VWUDLQ HPD[f @ 7KH REWDLQHG

PAGE 113

7DEOH 0HFKDQLFDO SURSHUWLHV RI SDUWLDOO\ GHQVLILHG VLOLFD JHOV DQG IXVHG VLOLFD 7HPSHUDWXUH r& )OH[XUDO VWUHQJWK &7PD[ 03Df 0D[LPXP VWUDLQ (PD[L $// [npf @ IXVHG VLOLFD

PAGE 114

)LJXUH )OH[XUDO VWUHQJWK YHUVXV WHPSHUDWXUH

PAGE 115

0D[LPXP VWUDLQ WR UXSWXUH $// [ (f )LJXUH 0D[LPXP VWUDLQ WR UXSWXUH YHUVXV WHPSHUDWXUH

PAGE 116


PAGE 117

PD[LPXP VWUDLQ WR WKH SRLQW RI UXSWXUH IRU WKH JHL VDPSOHV GHFUHDVH WR DSSURDFK WKH YDOXH [ f RI YLWUHRXV VLOLFD 7DEOH )LJ f ,W LV FRQFOXGHG WKDW WKH JHOV KDYH KLJKHU HODVWLF GHIRUPDELOLW\ WKDQ IXVHG VLOLFD VLQFH WKH ILEULOODU JHO VWUXFWXUH FDQ HQGXUH UHODWLYHO\ KLJKHU GLPHQVLRQDO GHIRUPDWLRQ EHIRUH UXSWXUH %HFDXVH RI WKH ORZ GHQVLWLHV RI WKH SRURXV JHOV WKH @ YDOXH RI IXVHG VLOLFD +RZHYHU WKH @ 7KH GHQVLW\ RI WKH VLOLFD JHOV DQG JHOJODVVHV DUH SORWWHG DV D IXQFWLRQ RI ILULQJ WHPSHUDWXUH LQ )LJXUHV ZLWK GHQVLW\ LQFUHDVLQJ DV WKH GHQVLILFDWLRQ WHPSHUDWXUH LQFUHDVHV 2QO\ VPDOO FKDQJHV LQ GHQVLW\ ZHUH REVHUYHG EHORZ r& KRZHYHU DERYH r& WKH GHQVLW\ LQFUHDVHG FRQVLGHUDEO\ ZLWK SURFHVVLQJ WHPSHUDWXUH 7KLV LQGLFDWHV WKDW YLVFRXV VLQWHULQJ LV LQLWLDWHG DERYH WKLV WHPSHUDWXUH 7KH GHQVLW\ RI WKH VDPSOHV KHDWHG WR r& LV DERXW s JFP DSSUR[LPDWHO\ b WKH GHQVLW\ RI IXVHG VLOLFD JODVV 7KH WHPSHUDWXUH UHTXLUHG WR UHDFK D GHQVLW\ HTXLYDOHQW WR W\SH O,9 VLOLFD LV D IXQFWLRQ RI WKH XOWUDVWUXFWXUH RI WKH JHO LWVHOI UDQJLQJ IURP r& WR r& GHSHQGLQJ RQ SDUWLFOH VL]H DQG WKH UHVLGXDO ZDWHU FRQWHQW RI WKH VROLG 7KH UHVXOWV RI D GLDPRQG SRLQW PLFURKDUGQHVV WHVW IRU VLOLFD JHO DV D IXQFWLRQ RI S\URO\VLV WHPSHUDWXUHV DUH JLYHQ LQ 7DEOH DQG )LJXUH )RU D FRQVWDQW ORDG .Jf WKH OHQJWK RI WKH LQGHQWDWLRQ GLDJRQDO GHFUHDVHV DV WKH WHPSHUDWXUH DQG WKH PLFURKDUGQHVV LQFUHDVHV 7KH r& JHO VDPSOH KDV D PLFURKDUGQHVV YDOXH RI .JPP ZKLFK LV DERXW WKUHH WLPHV OHVV WKDQ WKH .JPP YDOXH RI IXVHG VLOLFD 7KH

PAGE 118

)LJXUH &RPSUHVVLYH VWUHQJWK YHUVXV WHPSHUDWXUH

PAGE 119

'HQVLW\ JFFf )LJXUH 'HQVLW\ YHUVXV WHPSHUDWXUH

PAGE 120

7DEOH 0LFURKDUGQHVV GDWD RI SDUWLDOO\ GHQVLILHG VLOLFD JHO .J ORDGf 7HPSHUDWXUH ,QGHQWDWLRQ 'LDJRQDO OHQJWK 0LFURKDUGQHVV r&f G PPf '31 NJPPf s s s s s s s s s s s rrr9LFNHUVn KDUGQHVV QXPEHU IRU VLOLFD LV NJPP >VHH S LQ UHI @

PAGE 121

'31 .JPPrf )LJXUH 0LFURKDUGQHVV YV WHPSHUDWXUH

PAGE 122

VORSH RI WKH FXUYH LQ )LJXUH EHFRPHV YHU\ VKDUS DW DERXW r& LQGLFDWLQJ D VLJQLILFDQW VWUXFWXUDO FKDQJH LQ JHOV )UDFWXUH WRXJKQHVV LQGLFDWHV WKH DPRXQW RI HQHUJ\ DEVRUEHG E\ D PDWHULDO GXULQJ IDLOXUH 7KLV LV LQ FRQWUDVW WR IOH[XUDO VWUHQJWK FPD[f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f SFf f ZKHUH ( HODVWLF PRGXOXV LQ SDVFDOV + PLFURKDUGQHVV LQ .JFP 3 VLQ G >VHH S LQ UHI @ 3 LQGHQWDWLRQ ORDG LQ NJ r WKH KDOI DQJOH EHWZHHQ RSSRVLWH IDFHV RI WKH IRXUVLGHG S\UDPLG RI GLDPRQG LQGHQGHU G GLDPRQG SRLQW LQGHQWDWLRQ GLDJRQDO OHQJWK PP F H[WHQGHG FUDFN OHQJWK SP 7KH H[SHULPHQWDO GDWD GHQVLW\
PAGE 123

7DEOH )UDFWXUH WRXJKQHVV ._&f DQG ._&S UDWLR RI SDUWLDOO\ GHQVLILHGVLOLFD JHOV GDWD REWDLQHG IURP GLDPRQG LQGHQWDWLRQ FUDFNV .J ORDGf 7HPS 'HQVLW\ 0RGXOXV 0LFURKDUGQHVV 7 3 ( + r&f rJFPf 03Df rrr.JFPf s s s s s s s s s s s s IXVHG VLOLFD 7HPSHUDWXUH ([WHQGHG &UDFN /HQJWK 7RXJKQHVV 7 F ._F ._FS r&f rr SP rrr 03DP s s s s s s IXVHG VLOLFD .J J n SP nP nFP fPP rnr .JFP 03D SVL

PAGE 124

RI VDPSOHV WKH r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f GHFUHDVHV DQG WKH HIIHFWLYH SDUWLFOH VL]H LQFUHDVHV ZLWK DQ LQFUHDVH LQ S\URO\VLV WHPSHUDWXUH &RQVHTXHQWO\ WKH RYHUDOO EXON GHQVLW\ LQFUHDVHV ZLWK VLQWHULQJ WHPSHUDWXUH UHSUHVHQWDWLYH RI WKH GHJUHH RI XOWUDVWUXFWXUDO UHDUUDQJHPHQW ,Q )LJXUHV DQG WKH H[SHULPHQWDO GDWD RI FRPSUHVVLYH VWUHQJWK PD[LPXP VWUDLQ WR IDLOXUH IOH[XUDO VWUHQJWK
PAGE 125

&2 4 R! F &' &' fFR &2 &' 6I8,: 4 ( R 2 'HQVLW\ JFFf )LJXUH &RPSUHVVLYH VWUHQJWK YHUVXV GHQVLW\

PAGE 126

'HQVLW\ JFFf )LJXUH 0D[LPXP VWUHQJWK WR IDLOXUH YHUVXV GHQVLW\

PAGE 127

'HQVLW\ JFFf )LJXUH )OH[XUD VWUHQJWK YHUVXV GHQVLW\

PAGE 128


PAGE 129

0LFURKDUGQHVV '31 .JPPrf 'HQVLW\ JFFf )LJXUH 0LFURKDUGQHVV YHUVXV GHQVLW\

PAGE 130

.OFGHQVLW\ 'HQVLW\ JFFf )LJXUH 7RXJKQHVV YHUVXV GHQVLW\

PAGE 131

H[SHULPHQW 6HYHUDO PRGHOV >VHH S LQ UHI @ KDYH EHHQ GHYHORSHG WR SUHGLFW WKH @ $V WKH JHO EHFRPHV GHQVHU WKH QXPEHU RI SRUHV GHFUHDVHV DQG WKH VXUIDFH ZDWHU LV UHGXFHG 7KHUHIRUH LQ WKH KLJKHU GHQVLW\ UHJLRQ WKH H[SHULPHQWDO GDWD EHFRPH FORVHU WR WKH YDOXHV WKH DERYH HTXDWLRQ SUHGLFWV

PAGE 132

)UDFWLRQDO
PAGE 133

&RQFOXVLRQV 7KH GHWHUPLQDWLRQ RI WKH SK\VLFDO SURSHUWLHV RI SDUWLDOO\ GHQVLILHG JHOV HVWDEOLVKHV WKH QDWXUH RI WKH SRURXV JHO XOWUDVWUXFWXUH DQG XOWUDVWUXFWXUDO GHSHQGHQFH RI SURSHUWLHV )7,5 DQDO\VLV VKRZHG D FPn 6L2+ VWUHWFKLQJ YLEUDWLRQ SHDN GHFUHDVLQJ ZLWK LQFUHDVLQJ WHPSHUDWXUH LQGLFDWLQJ WKDW WKH VDPSOH LV EHFRPLQJ LQFUHDVLQJO\ GHK\GUDWHG 7KH SHDNV RI RUJDQLF UHVLGXDOV LQ WKH UDQJH IURP FPn WR FQU GLVDSSHDU DV WHPSHUDWXUH LQFUHDVHV 7KH VKLIW WR ORZHU 89 FXWRII ZDYHOHQJWKV ZLWK LQFUHDVLQJ WHPSHUDWXUH QRWHG LQ WKH 899,61,5 GDWD DOVR VKRZV WKDW WKH LPSXULW\ ZDWHUf OHYHO LV UHGXFHG $ TXDQWLWDWLYH VWXG\ RQ WKH FKDQJH RI ZDWHU OHYHO GXULQJ VLQWHULQJ LV GLVFXVVHG LQ &KDSWHU ;UD\ GLIIUDFWLRQ RI WKH JHOV VKRZHG QR HYLGHQFH RI GHYLWULILFDWLRQ FRQILUPLQJ WKH GHYHORSPHQW RI DQ DPRUSKRXV JODVV SKDVH IURP WKH JHO 0RUH LPSRUWDQW LQ WKLV VWXG\ WKH REVHUYDWLRQ OHG WR VXJJHVWLRQ WKDW VLOLFD JHO LV FRPSRVHG RI UDQGRP RULHQWHG ILEULOODU VWUXFWXUH UDQGRPQHWZRUN PRGHOf LQ ZKLFK WKH VLOLFD PROHFXOHV DUH YHU\ ZHOO RUGHUHG FU\VWDOOLWHV FU\VWDOOLWH PRGHOf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

PAGE 134

SURFHVVLQJ WHPSHUDWXUH DSSURDFKLQJ WKH YDOXHV RI YLWUHRXV VLOLFD 7KH ORZ WRXJKQHVV ._& DQG .LFS YDOXHV RI WKH SDUWLDOO\ GHQVLILHG JHOV DUH FRPSDUDEOH WR WKRVH RI 7\SH ,,9 YLWUHRXV VLOLFDV 7KH LQWHUHVWLQJ SRLQW LV WKH r& JHO VDPSOH KDV D KLJKHU .?-S YDOXH WKDQ IXVHG VLOLFD FRQILUPLQJ WKDW WKH ILEULOODU XOWUDVWUXFWXUH RI WKH JHO FDQ DEVRUE UHODWLYHO\ KLJK HQHUJ\ EHIRUH UXSWXUH RFFXU 7KH SUHVHQFH RI VXUIDFH ZDWHU LV VXJJHVWHG WR EH D PDMRU GHWHULRUDWLQJ IDFWRU IRU WKH PHFKDQLFDO SURSHUWLHV DQG LV HVSHFLDOO\ VHYHUH LQ WKH ORZHU WHPSHUDWXUH JHOV

PAGE 135

&+$37(5 '(+<'5$7,21 2) 62/*(/ '(5,9(' 6,/,&$ 237,&6 ,QWURGXFWLRQ $Q DPRUSKRXV VLOLFD JHO FDQ EH FKDUDFWHUL]HG E\ D UDQGRP SDFNLQJ RI 6L WHWUDKHGUD ZKLFK JLYHV ULVH WR D QRQSHULRGLF VROLG ILEULOODU VWUXFWXUH ZLWK PDQ\ YRLGV DQG D YHU\ ODUJH VXUIDFH DUHD 7KH VXUIDFH DUHD UDQJHV IURP PJ WR PJ GHSHQGLQJ RQ WKH ORZ WHPSHUDWXUH VROJHO SURFHVVLQJ VFKHGXOH %DVHG RQ OOHUnV VWXG\ VLOLFD JHO FRQVLVWV RI FRQQHFWHG VSKHULFDO SDUWLFOHV WKH LQWHULRU RI WKH SDUWLFOHV KDYH D GHQVLW\ RI JFP PDGH HQWLUHO\ RI DQK\GURXV 26L 26L EULGJLQJ ERQGV /RFDWHG RQ WKH SDUWLFOHn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ff 7KXV WKH 89 DEVRUSWLRQ SHDN IRU XOWUDSXUH VLOLFD VKRXOG RFFXU DW DSSUR[LPDWHO\ QP DQG LWV 89 DEVRUSWLRQ WDLO ZKLFK LV DVVRFLDWHG ZLWK WKHUPDOO\ DFWLYDWHG SKRQRQV >@ EHFRPHV QHJOLJLEOH LQ WKH YLVLEOH LQIUDUHG SRUWLRQ RI WKH VSHFWUXP

PAGE 136

7KH LQWULQVLF IXQGDPHQWDO YLEUDWLRQV RI WKH XOWUDSXUH VLOLFD PROHFXOHV UHVXOW LQ UHVRQDQFH ZLWK WKH LQFRPLQJ OLJKW DW DQ LQIUDUHG DEVRUSWLRQ SHDN RI QP FPn H9f KRZHYHU ZHDN FRPELQDWLRQ DQG RYHUWRQH EDQGV H[LVW DW QP FP H9f DQG QP FPn H9f DQG VWURQJ EDQGV RFFXU DW QP FP H9f 7KH LQIUDUHG DEVRUSWLRQ WDLO RI XOWUDSXUH VLOLFD OLNH LWV 89 DEVRUSWLRQ WDLO LV DOVR FDXVHG E\ SKRQRQV 7KHVH FRPELQDWLRQV DQG RYHUWRQHV LQIOXHQFH WKH LQIUDUHG DEVRUSWLRQ WDLO GRZQ WR QP FPn H9f >@ ([WULQVLF DEVRUSWLRQ RI OLJKW LQ VLOLFD JHO LQ WKH QP WR QP UDQJH KDV EHHQ GHWHFWHG DQG LQWHUSUHWHG DV HVVHQWLDOO\ WKH UHVXOW RI VXUIDFH K\GUR[\O JURXSV DQG WKHLU DVVRFLDWHG IUHH ZDWHU RQO\ RQH SSP RI K\GUR[\O LRQV LQ JODVV FDQ SURGXFH G%NP ORVV DW QP >@ $OO RWKHU W\SHV RI LPSXULWLHV KDYH EHHQ UHGXFHG WR YHU\ ORZ OHYHOV RQO\ VHYHUDO SDUWV SHU ELOOLRQf E\ D FKHPLFDO UHILQLQJ V\VWHP GXULQJ 7026 V\QWKHVLV WKHUHE\ FRQWULEXWLQJ QR VLJQLILFDQW DEVRUSWLRQ HIIHFWV LQ WKHVH JHOV 7KXV D PDMRU SUREOHP LQ SURGXFLQJ JHOVLOLFD RSWLFV LV WKDW JHO VXUIDFH K\GUR[\O JURXSV DQG K\GURJHQERQGHG SRUH ZDWHU JLYH ULVH WR DWRPLF YLEUDWLRQDO HQHUJ\ DEVRUSWLRQ LQ DOPRVW WKH HQWLUH UDQJH RI XOWUDYLROHW WR LQIUDUHG ZDYHOHQJWKV QP WR QPf 7KLV DEVRUSWLRQ JUHDWO\ GHFUHDVHV WKH RSWLFDO DSSOLFDWLRQV RI D VLOLFDJHO PRQROLWK &RQVHTXHQWO\ LQ RUGHU WR DFKLHYH WKH IXOO WKHRUHWLFDO SHUIRUPDQFH RI VLOLFD FRPSOHWH GHK\GUDWLRQ LV LPSHUDWLYH 7KH GHJUHH RI GHK\GUDWLRQ RI JHOVLOLFD RSWLFV LV PRQLWRUHG E\ DQDO\]LQJ WKH OLJKW DEVRUSWLRQ VSHFWUD LQ D EURDG UDQJH WKH 3HUNLQ(OPHU 899,61,5 VSHFWURSKRWRPHWHU FRYHUV WKH UDQJH IURP QP FPnf WR QP FPnf DQG WKH 1LFROHW )7,5 FRYHUV WKH UDQJH IURP QP FPnf WR QP FPnf $IWHU H[WHQVLYH H[SHULPHQWDWLRQ D UHOLDEOH PHWKRG ZDV IRXQG WKDW FRPSOHWHO\ HOLPLQDWHV WKH VXUIDFH FKHPLFDO K\GUR[\O JURXSV DQG DVVRFLDWHG SRUH ZDWHU LQ JHOVLOLFD PRQROLWKV %\ DSSO\LQJ WKH FRQFHSWV RI IXQGDPHQWDO VLOLFD VXUIDFH FKHPLVWU\ >@ LW ZDV IRXQG WKDW PDQ\ FKORULQH FRPSRXQGV VRPH RI WKHVH LQFOXGH PHWK\ODWHG

PAGE 137

FKORURVLODQHV VXFK DV &,6L&+f &O6c&+f &,6.&+f VLOLFD WHWUDFKORULGH 6&,f FKORULQH &,f DQG FDUERQ WHWUDFKORULGH &,&,f FDQ FRPSOHWHO\ UHDFW ZLWK VXUIDFH K\GUR[\O JURXSV WR IRUP K\GURFKORULF DFLG ZKLFK WKHQ GHVRUEV IURP WKH JHO ERG\ DW D WHPSHUDWXUH UDQJH r& WR r&f ZKHUH WKH SRUHV DUH VWLOO LQWHUFRQQHFWHG ,Q WKLV VWXG\ FDUERQ WHWUDFKORULGH LV XVHG VXFFHVVIXOO\ WR DFKLHYH FRPSOHWH GHK\GUDWLRQ RI XOWUDSXUH JHOVLOLFD PRQROLWKV 5HYLHZ RI WKH /LWHUDWXUH 5HJDUGLQJ 'HK\GUDWLRQ 7KH TXDOLW\ RI VLOLFD JHO FDQ EH VLJQLILFDQWO\ UHGXFHG E\ LPSXULWLHV %\ IDU WKH PRVW WURXEOHVRPH LPSXULW\ ZDWHU LV SUHVHQW LQ WZR IRUPV IUHH ZDWHU ZLWKLQ WKH XOWUDSRURXV JHO VWUXFWXUH LH SK\VLFDO ZDWHUf DQG K\GUR[\O JURXSV DVVRFLDWHG ZLWK WKH JHO VXUIDFH LH FKHPLFDO ZDWHUf 7KH DPRXQW RI SK\VLFDO ZDWHU DGVRUEHG WR WKH VLOLFD SDUWLFOHV LV GLUHFWO\ UHODWHG WR WKH QXPEHU RI K\GUR[\O JURXSV H[LVWLQJ RQ WKH VXUIDFH RI VLOLFD 'XULQJ WKH nV DQG nV UHVHDUFKHUV @ FRQWULEXWHG PXFK LQIRUPDWLRQ UHJDUGLQJ WKH K\GUDWLRQGHK\GUDWLRQ FKDUDFWHULVWLFV RI WKH VLOLFD JHOZDWHU V\VWHP DV VXPPDUL]HG EHORZ 7KH SK\VLFDO ZDWHU FDQ EH HOLPLQDWHG DQG VXUIDFH VLODQRO 6L2+f JURXSV FRQGHQVHG VWDUWLQJ DW DERXW r& DV VKRZQ LQ )LJXUH 7KHUPDO DQDO\VHV VXFK DV 7*$ DQG '6& FRQILUPHG WKLV SURFHVV LQ RXU VLOLFD JHO V\VWHP DV VKRZQ LQ &KDSWHU 7KH GHK\GUDWLRQ LV FRPSOHWHO\ UHYHUVLEOH XS WR DERXW r& DV VKRZQ LQ )LJXUH 'HFRPSRVLWLRQ RI RUJDQLF UHVLGXDOV XS WR r& ZDV DOVR FRQILUPHG XVLQJ '6& DQG 7*$ IRU RXU 7026 GHULYHG VLOLFD JHOV DV SUHVHQWHG LQ &KDSWHU $ERYH r& WKH GHK\GUDWLRQ SURFHVV LV LUUHYHUVLEOH DV D UHVXOW RI VKULQNDJH DQG VLQWHULQJ DFURVV SRUHV DV VKRZQ LQ )LJXUH 7KXV WKH DPRXQW RI H[LVWLQJ K\GUR[\O JURXSV RQ WKH JHO VXUIDFH LV DQ LQYHUVH IXQFWLRQ RI WKH WHPSHUDWXUH RI

PAGE 138

)LJXUH 3K\VLFDO ZDWHU GHFUHDVHV DQG VLODQRO JURXSV FRQGHQVH LQ WKH UDQJH RI URRP WHPSHUDWXUH DQG r&

PAGE 139

)LJXUH 6XUIDFH VLODQRO JURXSV DUH UHYHUVLEOH LQ WKH UDQJH RI r& WR r&

PAGE 140

)LJXUH LUUHYHUVLEOH HOLPLQDWLRQ RI DGMDFHQW K\GUR[\O JURXSV

PAGE 141

GHQVLILFDWLRQ ,W LV VKRZQ LQ &KDSWHU EDVHG XSRQ 899,61,5 GDWD WKDW WKH UHGXFWLRQ RI VXUIDFH K\GUR[\O JURXSV RFFXUV DERYH r& 9LVFRXV IORZ RFFXUV DERYH r& ZLWK WKH H[DFW WHPSHUDWXUH GHSHQGLQJ RQ WKH SDUWLFOH VL]H RI D VSHFLILF JHO 7KH VLQJXODU K\GUR[\O JURXSV RQ WKH JHO VXUIDFH UHDFW ZLWK HDFK RWKHU EULQJLQJ SDUWLFOHV WRJHWKHU WKHUHE\ HOLPLQDWLQJ YRLGV ZLWKLQ WKH JHO 6RPH VXUIDFH ZDWHU ZKLFK LV XQDEOH WR EH GHVRUEHG SULRU WR SRUH FORVXUH LV WUDSSHG LQVLGH WKH GHQVLILHG JHO @ FRQILUPHG WKLV SRLQW +DLU >VHH S LQ UHI @ DOVR SURYHG WKDW KHDWLQJ VLOLFD JHO LQ WKH r& WR r& UDQJH FDXVHV UHYHUVLEOH GHK\GUDWLRQ YLD HOLPLQDWLRQ RI VXUIDFH ZDWHU DQG WKH IRUPDWLRQ RI ERWK VLQJOH DQG DGMDFHQW VXUIDFH K\GUR[\O JURXSV DV LOOXVWUDWHG LQ )LJXUH +DLU IRXQG WKDW DW r& QR PRUH WKDQ KDOI RI WKH VXUIDFH K\GUR[\O JURXSV KDG EHHQ GHVRUEHG DQG WKDW PRVW RI WKH UHPDLQLQJ VXUIDFH K\GUR[\O JURXSV ZHUH DGMDFHQW WR HDFK RWKHU DQG WKHUHIRUH VLWXDWHG IRU SUHIHUHQWLDO ZDWHU DGVRUSWLRQ VKRZQ LQ )LJXUH +H VWDWHG WKDW KHDWLQJ WKH JHO DERYH r& FDXVHV D GUDVWLF LUUHYHUVLEOH HOLPLQDWLRQ RI DGMDFHQW K\GUR[\O JURXSV DV VKRZQ LQ )LJXUH XQWLO DW DERXW r& RQO\ VLQJOH K\GUR[\O JURXSV UHPDLQ DV VKRZQ ,Q )LJXUH $V WKH WHPSHUDWXUH LQFUHDVHV VLQJOH K\GUR[\O JURXSV GHSDUW IURP WKH JHO VXUIDFH XQWLO WKH JHO LV GHQVLILHG WKLV RFFXUV LQ WKH r& WR r& UDQJH +RZHYHU VRPH VLQJOH K\GUR[\O JURXSV DUH VWLOO XQDEOH WR HVFDSH IURP WKH JHO VXUIDFH DQG WKHUHIRUH FDQ FRQWULEXWH WR IRDPLQJ RI WKH JHO DV WKH WHPSHUDWXUH LQFUHDVHV

PAGE 142

)LJXUH 5HDEVRUSWLRQ RI SK\VLFDO ZDWHU EHORZ r&

PAGE 143

+ 7 )LJXUH 2QO\ VLQJOH K\GUR[\O JURXSV UHPDLQ DW WHPSHUDWXUH DERYH r&

PAGE 144

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r&f VLOLFD JHO VKRZV DQ DEVRUSWLRQ SHDN DW QP VHH )LJ f VXUHO\ GXH WR WKH IXQGDPHQWDO VWUHWFKLQJ YLEUDWLRQ RI K\GUR[\O JURXSV RQ WKH JHO VXUIDFH 7KHVH VLQJXODU RU IUHH K\GUR[\O JURXSV DUH DOVR UHIHUUHG WR DV LVRODWHG VLODQRO JURXSV 7KH V\PPHWULFDO DSSHDUDQFH RI WKLV SHDN LQGLFDWHV WKDW WKHVH VLQJXODU K\GUR[\O JURXSV KDYH QR LQWHUDFWLRQ ZLWK ZDWHU PROHFXOHV 7KH EDQG DW QP ^[!f LV WKH ILUVW RYHUWRQH RI WKH DGMDFHQW VLODQRO JURXS YLEUDWLRQ 8 QP VHH )LJ f 7KH QP SHDN EHFRPHV OHVV LQWHQVH DV WKH JHO LV KHDWHG DQG GLVDSSHDUV ZLWK FRPSOHWH GHK\GUDWLRQ 7KH FRPELQDWLRQ SHDN DW QP [! XRK EHQGff LV WKH UHVXOW RI WKH K\GUR[\O LRQnV VWUHWFKLQJ DQG EHQGLQJ YLEUDWLRQV ZKHUH GRK LV D EHQGLQJ ZDYHOHQJWK EHWZHHQ QP DQG QP 5HVHDUFKHU 3HUL >@ VXJJHVWV WKDW WKLV FRPELQDWLRQ EDQG LV GXH WR WKH 6L2+ VWUHWFKLQJ YLEUDWLRQ DQG DQ RXWRISODQH 2+ GLVSODFHPHQW EHQGLQJf YLEUDWLRQ 7KLV W\SH RI K\GUR[\O JURXS LV ODEHOHG DQ 2+f JURXS 7KH DGMDFHQW K\GUR[\O JURXSV DOVR LQWHUDFW ZLWK IUHH ZDWHU VHH )LJ f WR IRUP K\GURJHQ ERQGV WKLV HIIHFW FDXVHV D FKDQJH LQ ERWK WKH IXQGDPHQWDO VWUHWFKLQJ YLEUDWLRQ DQG LWV DVVRFLDWHG RYHUWRQHV DQG FRPELQDWLRQV 7KHUHIRUH WKH K\GUR[\O JURXSV DVVRFLDWHG ZLWK ZDWHU VKRZ D QHZ FRPELQDWLRQ SHDN DW QP X XRK EHQGff WKLV NLQG RI K\GUR[\O JURXS LV FDOOHG 4+f 7KH HQHUJ\ FDOFXODWLRQV E\ %HQHVL DQG -RQHV >@ SUHGLFW WKDW WKH IXQGDPHQWDO VWUHWFKLQJ YLEUDWLRQ RI 2+f DW QP LV D YDOXH VKLIWHG DERXW QP IURP WKH YLEUDWLRQ RI WKH IUHH K\GUR[\O JURXS DW

PAGE 145

?f QP 2+ff )URP DFWXDO DEVRUSWLRQ GDWD 0F'RQDOG REVHUYHG D SHDN DW QP LQGLFDWLQJ D VWURQJ LQWHUDFWLRQ EHWZHHQ IUHH SRUH ZDWHU DQG VXUIDFH K\GUR[\O JURXSV :KHQ D GHK\GUDWHG VLOLFD JHO LV H[SRVHG WR D VOLJKWO\ KXPLG DLU DWPRVSKHUH VKDUS SHDNV DSSHDU DW QP Xf QP Af QP G ?!RK EHQGff QP f DQG QP ?!f +DLU >VHH S LQ UHI @ EHOLHYHV WKDW WKH LQWHQVLW\ FKDQJHV XSRQ DGVRUSWLRQ RI ZDWHU LQGLFDWH WKDW DOO WKHVH EDQGV DUH FRQQHFWHG ZLWK WKH K\GUR[\O JURXS ZKLFK LV DVVRFLDWHG ZLWK SK\VLFDO SRUH ZDWHU )XUWKHU K\GUDWLRQ UHVXOWV LQ D EURDGHQHG EDQG DW DERXW f QP VHH )LJ f FKDUDFWHULVWLF RI EXON ZDWHU &DQW DQG /LWWOH > @ DQG &KDSPDQ DQG +DLU >@ WHQG WR DJUHH WKDW IRU VLOLFD JHO D VKDUS DQG VOLJKWO\ DV\PPHWULFDO SHDN RQ WKH KLJKZDYHOHQJWK VLGH DW QP W!Of WRJHWKHU ZLWK D GLVWLQFW EDQG DW QP ‘f FDQ EH DWWULEXWHG WR IUHHO\ YLEUDWLQJ VXUIDFH VLODQRO JURXSV DQG WR K\GURJHQERQGHG DGMDFHQW VLODQRO JURXSV UHVSHFWLYHO\ LQ DGGLWLRQ D EURDG EDQG DW QP Af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f VXFK DV WKRVH SURGXFHG E\ &RUQLQJ 0HOOHV *URLW '\QDVLO

PAGE 146

DQG 4XDUW] 6FLHQWLILF ,QF UHVXOW LQ LPSXULWLHV HJ ZDWHU DQGRU PHWDOOLF HOHPHQWVf 7KUHH VLJQLILFDQW DEVRUSWLRQ SHDNV DW QP Y}f QP Y X2+EHQGf` DQG QP Yf DUH IRXQG WR EH WKH XQLTXH VWUHWFKLQJ YLEUDWLRQ RI DGMDFHQW VLODPRO JURXSV DQG LWV RYHUWRQH DQG FRPELQDWLRQ DV VKRZQ LQ )LJXUHV DQG 1R VLQJXODU VLODQRO JURXS XLf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f 7KLV SURFHVV UHVXOWV LQ ILEHUV RI XOWUDORZ ORVV DERXW G%NP WR G%NP LQ WKH QP WR QP UDQJH ,W LV VKRZQ LQ &KDSWHU WKDW WKH IXOO\ GHK\GUDWHG FRPSOHWHO\ GHQVLILHG JHOJODVV PRQROLWKV GHYHORSHG LQ WKLV GLVVHUWDWLRQ DUH RI VXFK D TXDOLW\ DV WR FRPSDUH ZLWK RSWLFDO ILEHUV ([SHULPHQWDO 3URFHGXUH 7KH VWDQGDUG GULHG JHOV r&f PDQXIDFWXUHG DV SHU ([DPSOH 2QH LQ &KDSWHU DUH XVHG DV WKH EDVLV IRU SUHSDULQJ WZR VDPSOH VHWV IRU WKH IROORZLQJ GHK\GUDWLRQ VWXG\ 2QH VDPSOH VHW ZDV SDUWLDOO\ GHQVLILHG DW GHVLJQDWHG WHPSHUDWXUHV LQ DQ DPELHQW DLU DWPRVSKHUH WKH RWKHU VHW ZDV FKHPLFDOO\ DQG WKHUPDOO\ WUHDWHG SULRU WR VLQWHULQJ LQ D PL[HG YDSRU FDUERQ WHWUDFKORULGH DQG KHOLXPf DWPRVSKHUH ZLWKLQ D VSHFLDO DSSDUDWXV VKRZQ LQ )LJXUH

PAGE 147

:DYHOHQJWK QP )LJXUH 7UDQVPLVVLRQ FXUYH IURP &RUQLQJ *ODVV &R FRPPHUFLDO 89 JUDJH RSWLFDO PHOW VLOLFD &RGH 7KLFNQHVV PP

PAGE 148

:DYHOHQJWK QP Y )LJXUH 7UDQVPLVVLRQ FXUYH IURP 0HOOHV *ULRW &R FRPPHUFLDO 89 JUDJH RSWLFDO PHOW VLOLFD &RGH 89*6)6 7KLFNQHVV PP

PAGE 149

:DYHOHQJWK QP )LJXUH 7UDQVPLVVLRQ FXUYH IURP '\QDVW &R FRPPHUFLDO 89 JUDJH RSWLFDO PHOW VLOLFD &RGH 7KLFNQHVV PP

PAGE 150

7UHQVPLVVLRQ b :DYHOHQJWK QP )LJXUH 7UDQVPLVVLRQ FXUYH IURP 4XDUW] 6FLHQFH ,QF FRPPHUFLDO 89 JUDJH RSWLFDO PHOW VLOLFD 7KLFNQHVV PP

PAGE 151

6DPSOH )LJXUH $ PL[HG YDSRU&&Lc DQG +Hf DWPRVSKHUH ZLWKLQ WKH WXELQJ RI D IXUQDFH

PAGE 152

'HQVLILFDWLRQ LQ DQ DLU DWPRVSKHUH ZDV FDUULHG RXW XVLQJ WKH KHDWLQJ SURJUDP VKRZQ LQ )LJXUH 7KHVH VDPSOHV ZHUH KHDWHG WR GHVLJQDWHG WHPSHUDWXUHV r& r& r& r& r&f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r& r& r& r&f 'HQVLW\ PHDVXUHPHQWV RI WKH VDPSOHV ZHUH WDNHQ IROORZHG E\ WKH 899,61,5 DQG )7,5 VSHFWUD PHDVXUHPHQWV ZLWKLQ WKH SUHYLRXVO\ VWDWHG UDQJHV 5HVXOWV DQG 'LVFXVVLRQV 7KH GHQVLW\ PHDVXUHPHQWV DW YDULRXV VLQWHULQJ WHPSHUDWXUHV IRU VDPSOHV ZLWK RU ZLWKRXW FKORULQDWLRQ DUH VKRZQ LQ )LJXUH LQ ZKLFK WKH GHQVLW\ RI WKH ZDWHUULFK ZLWKRXW FKORULQDWLRQf JHO VDPSOH UHDFKHV D PD[LPXP JFFf DW D ORZHU WHPSHUDWXUH DERXW r& DQG WKH GHQVLW\ RI WKH ZDWHUIUHH ZLWK FKORULQDWLRQf JHO VDPSOH KDV LWV PD[LPXP a JFFf DW D UHODWLYHO\ KLJKHU WHPSHUDWXUH RI DERXW r& 7KLV LQGLFDWHV WKDW WKH K\GUR[\O JURXSV VLJQLILFDQWO\ GHFUHDVH WKH VLQWHULQJ WHPSHUDWXUH E\ ORZHULQJ WKH VXUIDFH HQHUJ\ RI VLOLFD 7KH LPSRUWDQW DEVRUSWLRQ SHDNV DQG EDQGV IRXQG LQ WKLV GHK\GUDWLRQ VWXG\ DUH VXPPDUL]HG LQ 7DEOH 7KHVH SHDNV DQG EDQGV DUH LGHQWLFDO WR WKRVH GLVFRYHUHG E\ SUHYLRXV UHVHDUFKHUV VWDWHG LQ 6HFWLRQ ,, RI WKLV &KDSWHU &XUYHV D E F DQG G LQ )LJXUH VKRZ WKH 899,61,5 VSHFWUD RI JHOV KHDWHG LQ DPELHQW DLU DW YDULRXV WHPSHUDWXUHV XS WR DERXW r& 2YHUWRQH DQG FRPELQDWLRQ

PAGE 153

7LPH KRXUf )LJXUH +HDWLQJ F\FOHV IRU DLU DWPRVSKHUH IXUQDFH

PAGE 154

)nXUH )U )28UKA}RJUDP ,6 IRU FRQWUROOHG DPr:rUHXPDFH

PAGE 155

'HQVLW\ JFFf O O O 7HPSHUDWXUH r&f )LJXUH 'HQVLW\ PHDVXUHPHQWV DW YDULRXV WHPSHUDWXUHV IRU VDPSOHV ZLWK RU ZLWKRXW && WUHDWPHQW

PAGE 156

7DEOH $EVRUSWLRQ SHDNV RI WKH SRUH ZDWHU DQG WKH VXUIDFH K\GUR[\O JURXSV RI JHOVLOLFD PRQROLWKV :DYHOHQJWK ^UWP` ,GHQWLILFDWLRQ REVHUYDWLRQ FRPPDQG rrrrrf D EURDG SHDN RQ D EURDG EDQG rrrr' D WLQ\ SHDN RQ D EURDG EDQG r r r D MRLQW RI WZR VPDOO SHDNV DW QP DQG QP rr' D YHU\ VKDUS V\PPHWULF SHDN 8 rf + D EURDG EDQG QR SHDN f Lf2+ D KLJK EURDG DV\PPHWULF SHDN GR+ D KLJK EURDG DV\PPHWULF SHDN Lf D WLQ\ SHDN RQ D EURDG EDQG G D VPDOO SHDN RQ D EURDG EDQG L! D YHU\ VKDUS V\PPHWULF SHDN ^>G GRK@ >Lf GRK@` D VPDOO SHDN Lf XRK D WLQ\ SHDN L! D VPDOO SHDN G 82+ QR SHDN REVHUYHG D WLQ\ SHDN rGTK DQ RXW RI SODQH EHQGLQJ YLEUDWLRQ RI 6L2+ ERQG rrXL VWUHWFKLQJ YLEUDWLRQ RI DQ LVRODWHG 6L2+ ERQG rrr [! VWUHWFKLQJ YLEUDWLRQ RI DQ DGMDFHQW 6L2+ ERQG rrrrL! VWUHWFKLQJ YLEUDWLRQ RI D 6L2+ ERQG ZKLFK LV K\GURJHQERQGHG WR ZDWHU rrfrf VWUHWFKLQJ YLEUDWLRQ RI DEVRUEHG ZDWHU

PAGE 157

DEVRUSWDQFH OB O / , / :DYHOHQJWK QPf FXUYH D LV WKH VSHFWUXP RI r& VDPSOH FXUYH E LV WKH VSHFWUXP RI r& VDPSOH FXUYH F LV WKH VSHFWUXP RI r& VDPSOH FXUYH G LV WKH VSHFWUXP RI r& VDPSOH M )LJXUH $EVRUSWLRQ FXUYHV RI SDUWLDOO\ GHQVLILHG JHOV LQ DLU

PAGE 158

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f DQG WKH RXWRISODQH K\GUR[\O LRQ GHIRUPDWLRQ YLEUDWLRQ DW QP XTK EHQGff 7KH SHDN DW QP LV D FRPELQDWLRQ YLEUDWLRQ RI QP ?!f SOXV WZR WLPHV WKH EHQGLQJ IUHTXHQF\ XRK EHQGff 7KH SHDN DW QP Yf VHHPV WR EH WKH ILUVW RYHUWRQH RI WKH QP 8f 7KH SHDN DW QP Af REVHUYHG LV WKH ILUVW RYHUWRQH DW QP ff ZKHUHDV WKH QP mf SHDN LV H[DFWO\ IURP WKH ILUVW RYHUWRQH RI WKH IXQGDPHQWDO K\GUR[\O VWUHWFKLQJ YLEUDWLRQ REVHUYHG DW QP ?!f 7KH SHDN REVHUYHG DW QP LV SUHVXPHG WR EH DQ RYHUODS IURP WKH FRQWULEXWLRQ RI WZR W\SH RI FRPELQDWLRQV ZKLFK DUH QP Y XRK EHQGff DQG QP A XRK EHQGff $ WLQ\ SHDN DW QP LV EHOLHYHG WR EH A GTK EHQGf DQG D VPDOO SHDN DW QP LV SUHVXPHG WR EH D VHFRQG RYHUWRQH RI QP Af 7KHUH LV D YHU\ WLQ\ SHDN DW QP ZKLFK LV D WKLUG RYHUWRQH RI QP Y!f DV VKRZQ LQ )LJXUH FXUYH G 7KHVH UHVXOWV VKRZ WKDW IRU FULWLFDO RSWLFDO DSSOLFDWLRQV ZKHUH FRPSOHWH WUDQVPLVVLRQ RYHU D EURDG UDQJH RI ZDYHOHQJWK LV LPSRUWDQW GHQVLILFDWLRQ LQ DQ DLU DWPRVSKHUH LV REYLRXVO\ D IDLOXUH 7KH UHVXOWLQJ TXDOLW\ RI WKLV JHO FDQ QRW FRPSHWH ZLWK WKDW RI IXVHG VLOLFD VHH &KDSWHU f DQG LW ZLOO QHYHU UHDFK WKH SRLQW RI FRPSOHWH GHK\GUDWLRQ

PAGE 159

&DUERQ WHWUDFKORULGH WUHDWHG VDPSOHV ZHUH UHPRYHG IURP WKH WXEH IXUQDFH DIWHU UHDFKLQJ YDULRXV WHPSHUDWXUHV r& r& r& r&f DQG WKHQ DQDO\]HG WR GHWHUPLQH WKHLU FKDUDFWHULVWLF 899,61,5 DEVRUSWLRQ VSHFWUD DV VKRZQ LQ )LJXUHV Df DQG Gf $EVRUSWLRQ SHDNV ZHUH YLVLEOH DW QP QP QP QP QP QP IRU WKH r& VDPSOH DQG DW QP QP QP QP QP QP IRU WKH r& VDPSOH 6WUHWFKLQJ YLEUDWLRQV RI WKH DGVRUEHG SK\VLFDO ZDWHU JLYHV ULVH WR W\SLFDO EURDG DEVRUSWLRQ SHDNV DW QP DQG QP ZKLFK DUH VKLIWHG IURP QP ff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f 7KH LQWHQVLW\ RI DOO DEVRUSWLRQ SHDNV GHFUHDVHV DV WKH WHPSHUDWXUH LQFUHDVHV 7KH VSHFWUXP IURP WKH r& VDPSOH VKRZV RQO\ RQH SHDN DV VKRZQ LQ )LJXUH Df RFFXUULQJ DW QP f ZKLFK LV FDXVHG E\ LVRODWHG K\GUR[\O JURXSV 7KH VDPSOH KHDWHG WR r& KDV D VSHFWUXP LQ ZKLFK WKH ZDWHU SHDNV KDYH EHHQ HOLPLQDWHG DV VKRZQ LQ )LJXUHV Ef DQG 7KH DEVRUSWLRQ ORVV GXH WR ZDWHU LV HVWLPDWHG WR DSSURDFK ]HUR DV QR ZDWHU RU K\GUR[\O DEVRUSWLRQ SHDNV DUH SUHVHQW DW DQ\ ZDYHOHQJWK 7KH TXDOLW\ RI RSWLFDO WUDQVPLWWDQFH RI WKLV VDPSOH LV VLJQLILFDQWO\ KLJKHU WKDQ WKDW RI WUDGLWLRQDO IXVHG VLOLFD JODVV

PAGE 160

DEVRUSWDQFH )LJXUH $EVRUSWLRQ FXUYH RI JHO SDUWLFDOO\ GHQVLILHG LQ FRQWUROOHG &&, DWPRVSKHUH IRU D r& VDPSOH RI PP WKLFNQHVV

PAGE 161

)LJXUH $EVRUSWLRQ FXUYH RI JHO SDUWLFDOO\ GHQVLILHG LQ FRQWUROOHG &&, DWPRVSKHUH IRU D r& VDPSOH RI PP WKLFNQHVV

PAGE 162

DEVRUSWDQFH :DYHOHQJWK QPf U Ef r& VDPSOH IL L L L L :DYHOHQJWK QPf )LJXUH $EVRUSWLRQ FXUYHV RI JHOV SDUWLFDOO\ GHQVLILHG LQ FRQWUROOHG &&, DWPRVSKHUH WRU D r& VDPSOH RI PP WKLFNQHVV DQG D r& VDPSOH RI PP WKLFNQHVV

PAGE 163

$EVRUEDQFH :DYHQXPEHUV FPf )LJXUH )7,5 DEVRUSWLRQ FXUYH RI IXOO\ GHQVLILHG JHOJODVV

PAGE 164

6DPSOHV ZKLFK KDG EHHQ KHDWHG WR r& LQ WKH WXEH IXUQDFH ZHUH DJHG IRU YDULRXV GXUDWLRQV LQ DLU GD\ GD\V GD\V DQG GD\V 7KH GHQVLW\ VXUIDFH DUHD WRWDO SRUH YROXPH DQG SRUH UDGLXV PHDVXUHG ZHUH JFP PJ b DQG ƒ UHVSHFWLYHO\ 7KH UHVXOWLQJ DEVRUSWLRQ VSHFWUD IURP HDFK RI WKHVH VDPSOHV LQGLFDWHV WKH UHDGVRUSILRQ RI PROHFXODU ZDWHU ZLWK WKH FRUUHVSRQGLQJ UHDSSHDUDQFH RI D EURDG DEVRUSWLRQ SHDN LQ WKH QP WR QP UDQJH DQG VKRZV QR RYHUWRQH RU FRPELQDWLRQ SHDN DV VKRZQ LQ )LJXUH Df Ef Ff DQG Gf 2Q WKH RWKHU KDQG WKH VDPSOHV ZKLFK ZHUH KHDWHG WR r& LQ WKH WXEH IXUQDFH DQG DJHG LQ DLU IRU GD\V GD\V DQG GD\V VKRZHG QR HYLGHQFH RI UHDGVRUSWLRQ DV VKRZQ LQ )LJXUH Df Ef DQG Ff &RQVHTXHQWO\ WKH GHK\GUDWLRQ DQG GHQVLILFDWLRQ RI JHOVLOLFD PRQROLWKV DV GHYHORSHG LQ WKLV VWXG\ UHVXOWV LQ DQ RSWLFDO PDWHULDO HTXLYDOHQW WR WKH EHVW 7\SH ,9 VLOLFD +RZHYHU WKH WHPSHUDWXUH RI GHQVLILFDWLRQ KDV EHHQ UHGXFHG WR r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

PAGE 165

DEVRUSWDQFH DEVRUSWDQFH :DYHOHQJWK QPf Ef GD\V QP 9 L L O L L L :DYHOHQJWK QPf :DYHOHQJWK QPf )LJXUH $EVRUSWLRQ FXUYHV RI r& VDPSOHV DJHG LQ DLU IRU YDULRXV WLPHV

PAGE 166

:DYHOHQJWK QPf :DYHOHQJWK QPf :DYHOHQJWK QPf )LJXUH $EVRUSWLRQ FXUYH RW r& VDPSOH DJHG LQ DLU IRU YDULRXV WLPHV

PAGE 167

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ff LRQV DQG PLQLPDO RWKHU LRQLF LPSXULWLHV LQ WKH SSE UDQJH

PAGE 168

,QWHUDFWLRQV EHWZHHQ HOHFWURPDJQHWLF UDGLDWLRQ DQG JODVV EDVHG RQ ERWK TXDQWXP PHFKDQLFV DQG FODVVLFDO WUHDWPHQWV KDV EHHQ ZHOO HVWDEOLVKHG LQ WKH OLWHUDWXUH > @ DQG LV WKH EDVLV IRU LQWHUSUHWLQJ WKH UHVXOWV SUHVHQWHG LQ WKLV FKDSWHU 2SWLFD SURSHUWLHV RI JHO JODVV DUH GHWHUPLQHG QRW RQO\ E\ LQWULQVLF FKHPLFDO DVSHFWV HJ HOHFWURQLF HQHUJ\ JDS LQWHUDWRPLF ERQG VWUHQJWK LRQLF PDVV DQG LPSXULW\ OHYHOVf EXW DOVR E\ H[WULQVLF SK\VLFDO DVSHFWV RI WKH SURFHVVLQJ HJ WKHUPDO KLVWRU\ WKHUPDO JUDGLHQWV VWUXFWXUDO DUUDQJHPHQW DQG GHJUHH RI LVRWURS\f GHYHORSHG GXULQJ GHQVLILFDWLRQ SURFHVV 7KH SK\VLFDO SURSHUWLHV RI D JODVV DUH DOZD\V LQWHUUHODWHG IRU H[DPSOH PROHFXODU YLEUDWLRQV DUH UHVSRQVLEOH IRU OLJKW DEVRUSWLRQ UHVRQDQFH KHDW GLVVLSDWLRQ IOXRUHVFHQFH SKRVSKRUHVFHQFH DQG WKHUPDO H[SDQVLRQ >@ 5HIUDFWLYH LQGH[ LV D IXQFWLRQ RI GHQVLW\ DQG HOHFWURQLF SRODUL]DELOLW\ HWF 7KH RSWLFDO SURSHUWLHV WR EH H[DPLQHG LQ WKLV FKDSWHU LQFOXGH YDFXXP XOWUDYLROHW 989f WUDQVPLVVLRQ XOWUDYLROHW 89f WUDQVPLVVLRQ YLVLEOH 9,6f DQG QHDU LQIUDUHG 1,5f WUDQVPLVVLRQ LQIUDUHG ,5f VSHFWUD LQGH[ RI UHIUDFWLRQ Qf DQG GLVSHUVLRQ Xf ,Q DGGLWLRQ WKH RSWLFDO TXDOLW\ RI WKH JHO VLOLFD PRQROLWKV LV WHVWHG E\ PHDVXUHPHQWV RI KRPRJHQHLW\ VWUHVV ELUHIULQJHQFH VWULDH EXEEOHV LQFOXVLRQV DQG LPSXULWLHV 7KLV LQIRUPDWLRQ DORQJ ZLWK FRHIILFLHQW RI WKHUPDO H[SDQVLRQ &7(f GHQVLW\ DQG PLFURKDUGQHVV .QRRS KDUGQHVV '31f GDWD DUH XVHG WR FRPSDUH DQG FKDUDFWHUL]H WKH JHOVLOLFD JODVVHV OLWHUDWXUH 5HYLHZ 5HJDUGLQJ 2SWLFDO 3URSHUWLHV RI 6LOLFD *ODVV &ODVVLILFDWLRQ RI WKH XOWUDYLROHW FXWRII ZDYHOHQJWK RI FRPPHUFLDOO\ DYDLODEOH KLJK SXULW\ IXVHG VLOLFD KDV EHHQ PDGH E\ 6LJH >@ +H VXJJHVWV WKDW WKH ORFDWLRQ RI WKH 989 YDFXXP XOWUDYLROHWf DEVRUSWLRQ HGJH FDQ EH DWWULEXWHG WR WKUHH IDFWRUV Df D FRPSOHWHO\ VWRLFKLRPHWULF 6L QHWZRUN ZLWK LWV VWURQJ 26L2 EULGJLQJ ERQGV ZKLFK SURYLGHV WKH PLQLPXP DEVRUSWLRQ ZDYHOHQJWK DW DERXW QP Ef D VPDOO DPRXQW RI WHUPLQDO 6L ERQGV HJ VLODQRO JURXSVf DOVR FDOOHG QRQEULGJLQJ R[\JHQ 1%2f ERQGV

PAGE 169

ZKLFK GHWHUPLQHV WKH GHJUHH RI VKLIW WR KLJKHU ZDYHOHQJWKV LQ WKH QP WR QP UDQJH Ff VLJQLILFDQWO\ KLJKHU ZDYHOHQJWK VKLIWV IURP QP WR QP ZKLFK DUH LQGXFHG E\ LPSXULWLHV HJ WUDQVLWLRQ HOHPHQWV DONDOL DONDOLQHHDUWK DQG KDORJHQ HOHPHQWVf LQ WKH SSP UDQJH DV OLVWHG LQ 7DEOHV DQG VKRZQ LQ )LJXUH 5HILQHPHQW RI WKH VRLJHO SUHFXUVRU IRU H[DPSLH 7(26 WHWUDHWK\ORUWKRVLOLFDWHf UHGXFHV WKH PHWDOOLF LPSXULWLHV WR D PLQLPDO SSE OHYHO DV OLVWHG LQ 7DEOH ZKLFK PDNHV LW SRVVLEOH WR SURGXFH D JODVV KDYLQJ D YHU\ KLJK TXDOLW\ RI OLJKW WUDQVPLVVLRQ LQ WKH 989 DQG 89 7KH HOLPLQDWLRQ RI SK\VLFDO DQG FKHPLFDO ZDWHU DOVR FRQVLGHUHG LPSXULWLHVf DVVRFLDWHG ZLWK WKH JHO KDV EHHQ GHVFULEHG LQ &KDSWHU $Q DEVROXWHO\ LPSXULW\IUHH VLOLFD JODVV VKRXOG H[KLELW D 989 DEVRUSWLRQ HGJH RI DSSUR[LPDWHO\ QP DV LQGLFDWHG LQ IDFWRU Df DERYH 6LOLFD JODVV LV FDSDEOH RI EHLQJ XVHG DV DQ RSWLFDO ZLQGRZ EHWZHHQ WKH YDFXXP XOWUDYLROHW DQG LQIUDUHG DEVRUSWLRQ QP WR QPf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f ZKLFK UHTXLUH H[WUHPHO\ ORZ VLJQDO ORVV IRU ORQJ GLVWDQFH XVH LQ RSWLFDO FRPPXQLFDWLRQ FDEOH V\VWHPV 7KH EHVW TXDOLW\ RI VLOLFD RSWLFDO ILEHU W\SH ,9f KDV EHHQ DFKLHYHG ZLWK DQ LQIHUQDO DWWHQXDWLRQ YDOXH DURXQG G%.P G% 2' RSWLFDO GHQVLW\ DEVRUEDQFH b WUDQVPLVVLRQ 2' /RJ >ORO@ ZKHUH OR LV WKH LQFLGHQW LQWHQVLW\ LV WKH WUDQVPLWWHG LQWHQVLW\f DW QP LQ VLQJOHPRGH RSHUDWLRQ >VHH S LQ UHI @ 6LOLFD JHOJODVV RSWLFDO ILEHU ZLWK QR K\GUR[\O JURXSV DQG PLQLPDO

PAGE 170

7DEOH ,PSXULW\ OHYHOV LQ 7(26 SSEf $O /L &X )H &D 0Q 7L 0J &R 1D &U =Q 1L

PAGE 171

$WWHQXDWLRQ G%.P :DYHOHQJWK QPf )LJXUH 7\SLFDL VSHFWUD ORVV FXUYHV RI VLOLFD RSWLFD ILEHUV

PAGE 172

PHWDOOLF LRQ LPSXULWLHV KDV EHHQ PDGH E\ 6XVD VKRZLQJ D ORZORVV G%NP DW QP >@ 7KH JHOJODVV PRQROLWKV GHYHORSHG KHUHLQ VKRXOG KDYH HTXLYDOHQW RU HYHQ EHWWHU TXDOLW\ 7KH LQIUDUHG DEVRUSWLRQ ,5f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f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r. 7KH KLJKHU HQHUJ\ OHYHO RI D VWUHWFKLQJ YLEUDWLRQ UHVXOWV LQ D ODUJHU DYHUDJH GLVSODFHPHQW EHWZHHQ WZR QXFOHL $Q\ YLEUDWLRQ HQHUJ\ KLJKHU WKDQ WKH GHVWUXFWLRQ RI WKH ERQGLQJ HQHUJ\ ZLOO PRYH DWRPV DSDUW 7KH YLEUDWLRQ IUHTXHQFLHV RI DOO PROHFXOHV LV VR ORZ WKDW WKH HQHUJ\ LQYROYHG LV WRR VPDOO WR LQWHUDFW GLUHFWO\ ZLWK YLVLEOH OLJKW KRZHYHU WKH DEVRUSWLRQ GXH WR YLEUDWLRQDO WUDQVLWLRQV EHWZHHQ WKH YLEUDWLRQDO JURXQG VWDWH DQG

PAGE 173

)LJXUH 7KH HQHUJ\ FXUYHV RI WKH DQWLERQGLQJ DQG ERQGLQJ PROHFXODU RUELWDOV

PAGE 174

(QHUJ\ )LJXUH 7KH YLEUDWLRQ OHYHOV DL YDULRXV WHPSHUDWXUHV

PAGE 175

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f WKH PHDQ SRVLWLRQ RI WKH FHQWHU RI PDVV RI WKH YLEUDWLQJ DWRPV ZLOO EH GLVSODFHG DV WKH DPSOLWXGH RI YLEUDWLRQ LQFUHDVHV DV VKRZQ LQ )LJXUHV DQG Df UHVXOWLQJ LQ WKHUPDO H[SDQVLRQ RI WKH PDWHULDO 7KH WKHUPDO H[SDQVLYLW\ LV GHWHUPLQHG E\ WKH DV\PPHWU\ LQ WKH SRWHQWLDO HQHUJ\ FXUYH DQG WKH GHHSHU WKH PLQLPXP WKH PRUH V\PPHWULFDO LV WKH FXUYH QHDU WKH ERWWRP DV VKRZQ LQ )LJXUH Ef $ VWURQJ ERQGLQJ PDWHULDO KDV D GHHSHU YDOOH\ RI KLJKHU V\PPHWU\ ZKLFK UHVXOWV LQ D VPDOOHU WKHUPDO H[SDQVLRQ +ROORZD\ LQ KLV ERRN 7KH 3K\VLFDO 3URSHUWLHV RI *ODVV >VHH S LQ UHI @ VWDWHV WKDW VLOLFD JODVV VKRZV DQ DQRPDORXV WKHUPDO H[SDQVLRQ EHKDYLRU WKH WKHUPDO H[SDQVLRQ FRHIILFLHQW &7(f IRU WKLV JODVV LV YHU\ PXFK ORZHU WKDQ IRU TXDUW] [ SDUDOOHO WR D[LV [ n SHUSHQGLFXODU WR D[LVf DQG LW EHFRPHV QHJDWLYH EHORZ DERXW r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

PAGE 176

5HODWLYH HQHUJ\ VFDOH )LJXUH 3RVVLEOH HQHUJ\ WUDQVIRUPDWLRQ LQ D JODVV

PAGE 177

Df Ef )LJXUH 7KHUPDO H[SDQVLRQ GHSHQGV RQ ERQGLQJ VWUHQJWK

PAGE 178

&RQVHTXHQWO\ WKH VWUHWFKLQJ YLEUDWLRQ RI D 6L26L ERQG LV DW D KLJKHU HQHUJ\ DW DURXQG FPn WKDQ WKH URFNLQJ YLEUDWLRQ ZKLFK LV DW FPn $V WKH WHPSHUDWXUH GHFUHDVHV EHORZ D FHUWDLQ SRLQW 7Ff WKH VWUHWFKLQJ YLEUDWLRQ FDQ QR ORQJHU FRQWULEXWH WR D GLPHQVLRQDO FKDQJH GXH WR WKH RQVHW RI V\PPHWU\ RI WKH 0RUVH FXUYH DV VKRZQ EHORZ SRLQW 7Ff LQ )LJXUH Ef FXUYH f ,W LV DOVR UHDVRQDEOH WR SURSRVH WKDW DV WKH WHPSHUDWXUH FRQWLQXRXVO\ GHFUHDVHV EHORZ 7F WKH VWURQJ WUDQVYHUVH EHQGLQJ YLEUDWLRQ RI VLOLFD VWDUWV WR UHGXFH LWV DPSOLWXGH 7KLV FRQVHTXHQWO\ LQFUHDVHV WKH LQWHUDWRPLF GLVWDQFH DV VKRZQ LQ )LJXUH Ef FXUYH f DQG WKXV FKDQJHV WKH GLPHQVLRQV DV VKRZQ LQ )LJXUH Df DQG FXUYH f RI )LJXUH Ef 7KH FRUUHVSRQGLQJ FRHIILFLHQW RI WKHUPDO H[SDQVLRQ FXUYH RI YLWUHRXV VLOLFD LV VKRZQ LQ )LJXUH Ff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f DQG GHQVLW\ 7KH HOHFWURQLF SRODUL]DELOLW\ DH LV DQ LQYHUVH IXQFWLRQ RI WKH HOHFWURQHJDWLYLW\ >@ 7KH HOHFWURQHJDWLYLW\ RI DQ R[\JHQ LRQ 2nf LV KLJKHU WKDQ WKDW RI D FKORULQH LRQ &Onf &RQVHTXHQWO\ WKH SRODUL]DELOLW\ RI D FKORULQH LRQ LV KLJKHU WKDQ WKDW RI R[\JHQ LRQ 7KH LQGH[ RI UHIUDFWLRQ Qf LV SURSRUWLRQDO WR WKH VXPPDWLRQ RI WKH SRODUL]DELOLW\ RI DOO WKH FKHPLFDO VSHFLHV LQ D JODVV %HFDXVH RI WKH KLJKHU SRODUL]DELOLW\ RI WKH DQLRQV Q LV SULPDULO\ GHSHQGHQW RQ WKH VXPPDWLRQ RI WKH DQLRQLF

PAGE 179

)LJXUH $ SURSRVHG FODVVLFDO VSULQJ PRGHO DQG WKHUPDO H[SDQVLRQ FXUYHV RI VLOLFD JODVV

PAGE 180

SRODUL]DELOLWLHV 7KLV UHODWLRQVKLS LV GHVFULEHG E\ WKH /RUHQW] /RUHQ] HTXDWLRQ D HQ f0>1Q fS@ f 7KHUHIRUH Q LV GLUHFWO\ SURSRUWLRQDO WR D DV WKH RWKHU LWHPV LQ WKH HTXDWLRQ DERYH DUH FRQVWDQWV LH 1 LV $YRJDGURfV QXPEHU H LV WKH GLHOHFWULF FRQVWDQW RI YDFXXP 0 LV WKH PROHFXODU ZHLJKW RI VLOLFD S LV WKH GHQVLW\ RI VLOLFD 7KH VHFRQG LPSRUWDQW HIIHFW WR FRQVLGHU LV GHQVLW\ 6LQFH D LV FRQVWDQW IRU VLOLFD RQ FRQGLWLRQ WKDW RWKHU DQLRQLF LPSXULWLHV DUH QHJOLJLEOH WKH GHQVLW\ LV SURSRUWLRQDO WR Q fQ f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f E\ FRPSDULQJ WKH EULJKWQHVV RI OLJKW SDVVHG WKURXJK D VDPSOH ZLWK WKDW SDVVHG WKURXJK D VWDQGDUG DQG LV LQFDSDEOH RI GLUHFWO\ PHDVXULQJ D FRORUOHVV LRQLF VROXWLRQ HJ 1D&, LQ ZDWHU RU &On LQ JODVVf $OO WKH VDPSOHV WKH\ SURGXFHG KDG EHHQ KHDWHG WR r& FRQVHTXHQWO\ WKRVH ZLWK D KLJKHU LQLWLDO FKORULQH &Of LRQ FRQFHQWUDWLRQ ZHUH OLNHO\ WR KDYH SURSRUWLRQDOO\ IUHHG PRUH FKORULQH JDV &IHf WR FUHDWH PRUH FORVHG PLFURSRUHV 7KLV VWUXFWXUDO FKDQJH ZRXOG GHFUHDVH WKH EULJKWQHVV RI LQFLGHQW OLJKW LQ WKH PHDVXUHPHQW DQG ORZHU WKH DSSDUHQW GHQVLW\ ,Q DGGLWLRQ WKH HTXLOLEULXP RI &,n f§! &, H VKRXOG EH D FRQVWDQW >&O@>&,n@ DW WKDW WHPSHUDWXUH IRU DOO VDPSOHV KDYLQJ YDULRXV FKORULQH FRQWHQWV 7KHUHIRUH VDPSOHV ZLWK D KLJKHU LQLWLDO VXUIDFH DUHD ZHUH

PAGE 181

H[SHFWHG WR KDYH D KLJKHU VWUXFWXUDO FKORULQH &Of UHVLGXDO DWWDFKLQJ WR WKH VLOLFD PDWUL[ ZKLFK ZRXOG FRQWULEXWH WR D KLJKHU UHIUDFWLYH LQGH[ IUHHG &, JDV ZKLFK ERLOLQJ SRLQW LV r& WKH LQGH[ RI UHIUDFWLRQ LV f ,W LV WKXV UHDVRQDEOH WR FRQFOXGH WKDW WKH PHDVXUHG UHIUDFWLYH LQGH[ LQ WKH UHSRUW RI 6XVD HW DO ZDV PDLQO\ SURSRUWLRQDO WR WKH FRQFHQWUDWLRQ RI PLFURSRUHV UDWKHU WKDQ WR WKDW RI FKORULQH &Lrf DQG WKH REWDLQHG DSSDUHQW GHQVLW\ GHFUHDVHG DV WKH FKORULQH JDV & FRQWHQW LQFUHDVHG $FFRUGLQJ WR WKH /RUHQW] /RUHQ] UHODWLRQ WKH UHIUDFWLYH LQGH[ LV OLQHDUO\ SURSRUWLRQDO WR WKH WUXH GHQVLW\ RI VLOLFD 62f DV VKRZQ LQ )LJXUH >@ &RQVHTXHQWO\ DQ\ FKDQJHV LQ VKRUWUDQJHRUGHULQJ FU\VWDOOL]DWLRQ RU VWUXFWXUDO WUDQVIRUPDWLRQV RI YLWUHRXV VLOLFD WKDW LQFUHDVHV WKH GHQVLW\ ZLOO DOVR LQFUHDVH WKH UHIUDFWLYH LQGH[ 7KH WUXH GHQVLW\ FDQ EH YDULHG LQ D VLQWHULQJ SURFHVV E\ FRQWUROOLQJ WKH WKHUPDO KLVWRU\ LQ WKH JODVV WUDQVLWLRQ UDQJH RI WHPSHUDWXUHV 8QIRUWXQDWHO\ VXFK SKDVH FKDQJHV RU VWUXFWXUDO UHDUUDQJHPHQWV LQ VPDOO VFDOH EHORZ ZWbf LV XQDEOH WR EH GHWHFWHG XVLQJ [UD\ GLIIUDFWLRQ ,Q DGGLWLRQ D VPDOO DPRXQW RI D VHFRQG SKDVH PLFURYRLGVf IRXQG LQ JHO GULHG DW r& XVLQJ D PLFURVFRSH LV [UD\ XQGHWHFWDEOH E\ [UD\ GLIIUDFWLRQ 7KH WUXH GHQVLW\ RI D GHK\GUDWHG JHO JODVV ZLWK PLFURYRLGV DQG FORVHG PLFURSRUHV LV GLIILFXOW WR GHWHUPLQH 7KH DSSDUHQW GHQVLW\ ZKLFK KDV D YDOXH DURXQG JPFP FRPSDULQJ WR JPFP f ZWbf RI IXVHG VLOLFD VKRZV WKH HIIHFW RI D YHU\ VPDOO YROXPH IUDFWLRQ RI PLFURSRUHV 7KXV GLIIHUHQFHV LQ UHIUDFWLYH LQGH[ FDQ EH GXH WR HLWKHU DQ LQFUHDVH RI FKORULQH FRQWHQW RU DQ LQFUHDVH LQ GHQVLW\ :KHQ ERWK IDFWRUV DUH SUHVHQW LW UHTXLUHV D PHDVXUHPHQW RWKHU WKDQ QHSKHORPHWU\ WR VHSDUDWH WKHP 7KH LQGH[ RI UHIUDFWLRQ RI D PDWHULDO XVXDOO\ GHFUHDVHV DV WKH ZDYHOHQJWK ;f RI OLJKW LQFUHDVHV 7KLV FKDQJH ZLWK ZDYHOHQJWK LV FDOOHG WKH GLVSHUVLRQ RI WKH LQGH[ RI UHIUDFWLRQ DQG LV GHILQHG DV GQG; +RZHYHU PRVW SUDFWLFDO PHDVXUHPHQWV DUH PDGH E\ XVLQJ WKH LQGH[ RI UHIUDFWLRQ DW IL[HG ZDYHOHQJWKV DW WKH \HOORZ KHOLXP G OLQH

PAGE 182

,QGH[ RI 5HIUDFWLRQ 7UXH 'HQVLW\ JFFf )LJXUH ,QGH[ RI 5HIUDFWLRQ YHUVXV 7UXH 'HQVLW\

PAGE 183

QPf WKH EOXH K\GURJHQ I OLQH QPf DQG WKH UHG K\GURJHQ F OLQH QPf 7KH QXPHULFDO GLIIHUHQFH EHWZHHQ WKH WZR LQGLFHV RI UHIUDFWLRQ DW WKH I DQG F OLQHV LV FDOOHG WKH PHDQ GLVSHUVLRQ QI QFf 7KH UDWLR QI QFfQG f LV WKH GLVSHUVLYH SRZHU ,WV LQYHUVH LV FDOOHG $EEHnV YDOXH UWG ` QI QFf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f LQ D JODVV 7KH SDWK GLIIHUHQFH 7 LV WKH GLIIHUHQFH EHWZHHQ WZR VXFK SDWK OHQJWKV 7 6 6L / Q Q f ZKHUH WKLFNQHVV / LV FRQVWDQW )URP VHH S LQ UHI @ &RQVHTXHQWO\ IRU D SLHFH RI JODVV ZLWK WZR SHUIHFWO\ SDUDOOHO VXUIDFHV DQG FRQVWDQW WKLFNQHVV DQ\ LQWHUQDO LUUHJXODU YDULDWLRQ RI UHIUDFWLYH LQGH[ UHVXOWV LQ DQ LUUHJXODU IULQJH VKLIW SDWWHUQ RQ DQ LQWHUIHURJUDP $Q LQWHUIHURJUDP DOZD\V VKRZV DOWHUQDWLYH GDUN EDQGV DQG ZKLWH EDQGV ZLWK RQH IULQJH FRUUHVSRQGLQJ WR RQH SDLU RI ZKLWH DQG GDUN EDQGV 7KLV LV WKH PHWKRG XVHG WR H[DPLQH RSWLFDO KRPRJHQHLW\ LQ WKH GHQVLILHG JHOJODVV VDPSOHV

PAGE 184

,QWHUQDO VWUHVV LQ JODVV FDQ EH SURGXFHG E\ PDQ\ IDFWRUV VXFK DV PHFKDQLFDO VWUHVV WKHUPDO TXHQFKLQJ SKDVH VHSDUDWLRQ FU\VWDOOL]DWLRQ HWF )RU H[DPSOH ,I D SLHFH RI JODVV TXHQFKHG IURP KLJK WHPSHUDWXUH KDV UHVLGXDO VWUHVVHV WHQVLRQ DQG FRPSUHVVLRQf DQG LI OLJKW LV SURSDJDWHG WKURXJK VXFK D JODVV WKH GLIIHUHQFH LQ UHIUDFWLYH LQGH[ EHWZHHQ WKH UHJLRQV RI VWUHVV UHVXOWV LQ VWUHVV ELUHIULQJHQFH 7KH ELUHIULQJHQFH LV GHILQHG DV WKH QXPHULFDO GLIIHUHQFH EHWZHHQ WKH WZR UHIUDFWLYH LQGLFHV H JRf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r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

PAGE 185

)LQDOO\ LPSXULWLHV VXFK DV DONDOL DQG DONDOL HDUWK HOHPHQWV WUDQVLWLRQPHWDO HOHPHQWV DQG KDORJHQ HOHPHQWV WHUPLQDWH WKH EULGJLQJ R[\JHQ ERQGV FUHDWH OLJKW LQWHUDFWLRQ FHQWHUV DQG GHJUDGH WKH RSWLFDO SHUIRUPDQFH RI D VLOLFD JODVV $OO RI WKH DERYH SK\VLFDO DQG VWUXFWXUH IDFWRUV PXVW EH GHWHUPLQHG WR FKDUDFWHUL]H WKH TXDOLW\ RI WKH JHO VLOLFD JODVV SURGXFHG KHUHLQ ([SHULPHQWDO 3URFHGXUH *ODVV )DE ,QF RI 5RFKHVWHU 1HZ
PAGE 186

7DEOH 3K\VLFDO SURSHUW\ PHDVXUHPHQWV RQ IXOO\ GHQVLILHG JHOVLOLFD JODVVHV DQG IXVHG VLOLFD JODVVHV 7HVW 1XPEHU RI 6DPSOHV PHDVXUHG 6RXUFH 2SWLFDO WHVWV 7UDQVPLWWDQFH JHO JODVV VDPSOHV FRQWURO VDPSOHV *ODVV )DE f 9DFXXP 89 f 899,61,5 f ,5 5HIUDFWLYH LQGH[ JHO JODVV VDPSOHV FRQWURO VDPSOHV *ODVV )DE 'LVSHUVLRQ JHO JODVV VDPSOHV FRQWURO VDPSOHV *ODVV )DE +RPRJHQHLW\ JHO JODVV VDPSOHV FRQWURO VDPSOHV *ODVV )DE 6WULDH JHO JODVV VDPSOHV FRQWURO VDPSOHV *ODVV )DE 6WUHVV ELUHIULQJHQFH JHO JODVV VDPSOHV FRQWURO VDPSOHV *ODVV )DE %XEEOHV DQG ,QFOXVLRQV JHO JODVV VDPSOHV FRQWURO VDPSOHV *ODVV )DE ,PSXULW\ JHO JODVV VDPSOH 1RUWK &DUROLQD 6WDWH 8QLYHUVLW\ 7KHUPDO DQG PHFKDQLFDO WHVW &RHIILFLHQW RI WKHUPDO Df JHO JODVV VDPSOH 3HQQ 6WDWH 8QLYHUVLW\ H[SDQVLRQ Ef JHO JODVV VDPSOHV 8QLYHUVLW\ RI $UL]RQD 6SHFLILF JUDYLW\ JHO JODVV VDPSOHV &RUQLQJ (QJLQHHULQJ FRQWURO VDPSOHV /DE 6HUYLFHV .QRRS KDUGQHVV JHO JODVV VDPSOH &RUQLQJ (QJLQHHULQJ FRQWURO VDPSOH /DE 6HUYLFHV

PAGE 187

QP UDQJH DW WKH $05& RQ DSSUR[LPDWHO\ XQSROLVKHG JHOVLOLFD JODVV VDPSOHV XVLQJ D GRXEOHEHDP 3HUNLQ(OPHU /DPGD 899,61,5 VSHFWURSKRWRPHWHU 0RGHO VOLW ZLGWK QP ZLWK DQ XQFHUWDLQW\ RI s b ,QIUDUHG WUDQVPLWWDQFH ZDV DOVR PHDVXUHG LQ WKH QP WR QP UDQJH E\ *ODVV )DE XVLQJ WKH VSHFWURSKRWRPHWHU SUHYLRXVO\ PHQWLRQHG 5HIUDFWLYH LQGLFHV ZHUH PHDVXUHG E\ *ODVV )DE RQ D 3XOIUL[ $EEH 5HIUDFWRPHWHU XVLQJ IRXU VSHFLDO OLJKW VRXUFHV LVRODWLQJ WKH VL[ VSHFWUDO OLQHV DW ZKLFK WKH WHVWV ZHUH FRQGXFWHG DV OLVWHG LQ 7DEOH &DOLEUDWLRQ ZDV DFFRPSOLVKHG E\ XVH RI D VWDQGDUG LQGH[ VDPSOH FHUWLILHG E\ WKH 1DWLRQDO %XUHDX RI 6WDQGDUGV 1%6f DFFXUDWH WR s [ n 'LVSHUVLRQ GQFtf YDOXHV ZHUH FDOFXODWHG IURP UHIUDFWLYH LQGLFHV DW GLIIHUHQW WHVWLQJ ZDYHOHQJWKV LQ DFFRUGLQJ ZLWK WKH $EEHnV YDOXH YG QG f QI QFf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f 8VLQJ D URWDWLQJ H\HSLHFH WKH ILHOG ZDV URWDWHG XQWLO WKH ILHOG FKDQJH ZDV UHYHUVHG 7KLV DQJOH FKDQJH ZDV XVHG WR GHWHUPLQH WKH UHWDUGDWLRQ OHYHO 5 VWUDLQf XVLQJ WKH IRUPXOD 5 $7 ZKHUH $ LV DQJOH RI URWDWLRQ WR JLYH FRPSHQVDWLRQ DQG 7 LV WKLFNQHVV RI VDPSOH

PAGE 188

7DEOH 2SWLFDO GLVSHUVLRQ ZDYHOHQJWKV 'HVLJQDWLRQ :DYHOHQJWK QPf 6SHFWUDO /LQH U F G H I K UHG KHOLXP OLQH UHG K\GURJHQ OLQH \HOORZ KHOLXP OLQH JUHHQ PHUFXU\ OLQH EOXH K\GURJHQ OLQH YLROHW PHUFXU\ OLQH

PAGE 189

6WUHVV ELUHIULQJHQFH ZDV TXDOLWDWLYHO\ GHWHUPLQHG DW WKH $05& RQ DV FDVW SDUWLDOO\ GHQVH bf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f YDOXHV IURP URRP WHPSHUDWXUH WR ZHUH PHDVXUHG RQ RQH JHO JODVV VDPSOH E\ WKH 0DWHULDOV 5HVHDUFK /DERUDWRU\ 3HQQV\OYDQLD 6WDWH 8QLYHUVLW\ XVLQJ D ODVHU VSHFNOH GLODWRPHWHU DQG RQ RQH JHO JODVV VDPSOH E\ 2UWRQ -U &HUDPLF )RXQGDWLRQ 2KLR XVLQJ DQ DXWRPDWLF UHFRUGLQJ GLODWRPHWHU 7KH QHZ ODVHU VSHFNOH PHWKRG >@ ZDV EDVHG RQ WKH PRYHPHQW RI D ODVHU EHDP UHIOHFWHG IURP D SUREH EDU FDXVHG E\ WKHUPDO H[SDQVLRQV RI WKH VDPSOH DQG UHIHUHQFH URGV DV VKRZQ LQ )LJXUH 7KH UHIOHFWHG ODVHU EHDP ZDV REVHUYHG ZLWK D VPDOO SKRWRGHWHFWRU $ PLQXWH FKDQJH LQ WKH ODVHU EHDP SRVLWLRQ WKXV UHVXOWV LQ D SUHFLVLRQ

PAGE 190

JHO JODVV VDPSOH )LJXUH 9ROXPH IRU FRXQWLQJ EXEEOHV RU VWDUV

PAGE 191

)LJXUH 6FKHPDWLF GLDJUDP RI D ODVHU VSHFNOH GLLDWRPHWHU

PAGE 192

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f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b

PAGE 193

:DYHOHQJWK QPf )LJXUH 9DFXXP XOWUDYLROHW WUDQVPLVVLRQ RI RSWLFDO VLOLFDV VDPSOH WKLFNQHVV PP

PAGE 194

7UDQVPLVVLRQ bf :DYHOHQJWK QPf )LJXUH 899,61,5 WUDQVPLVVLRQ RI RSWLFD VLOLFDV VDPSOH WKLFNQHVV PP

PAGE 195

:DYHOHQJWK QPf )LJXUH ,QIUDUHG WUDQVPLVVLRQ RI RSWLFDO VLOLFDV VDPSOH WKLFNQHVV PP

PAGE 196

7DEOH 9DFXXP XOWUDYLROHW WUDQVPLVVLRQ GDWD 6DPSOH ,' 1R QP 7UDQVPLVVLRQ bf DW :DYHOHQJWK RI QP QP QP QP QP *HO JODVV WHVW VDPSOHV PP WKLFN 4 1 3 &RUQLQJ &RQWURO 6DPSOH PP WKLFN &*:Df &RUQLQJ &RQWURO 6DPSOH &RQYHUWHG WR PP WKLFNQHVV &*: Df )URP UHIHUHQFH UHIOHFWLRQ ORVV SHU VLQJOH VXUIDFH 5 /RVV Ef 1RWHV Df $V QRWHG WKH &RUQLQJ VDPSOH PHDVXUHG ZDV PP WKLFN FRPSDUHG WR WKH PP WKLFN JHOJODVV WHVW VDPSOHV 7KLV GDWD ZDV FRQYHUWHG WR PP WKLFNQHVV IRU FRPSDULVRQ Ef 5HIOHFWLRQ ORVVHV VKRZQ DUH EDVHG RQ SXEOLVKHG GDWD IRU IXVHG VLOLFD DYDLODEOH IURP *ODVV )DE 6QF DQG LV SUHVHQWHG IRU UHIHUHQFH RQO\

PAGE 197

WUDQVPLVVLRQ DW WKH K\GUR[\O JURXS DEVRUSWLRQ SHDN RI QP FRPSDUHG WR b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f IURP VDPSOH WR VDPSOH RI JHO JODVV LQGLFDWHV WKDW WKLV FKDUDFWHULVWLF LV UHODWHG WR YDULDWLRQV LQ WKHUPDO SURFHVVLQJ $ KRPRJHQHLW\ WHVW RQ RQH JHO JODVV VDPSOH )LJXUH VKRZV DQ DSSUR[LPDWHO\ ZDYH SHDN WR YDOOH\ 39f UDWLR ZDYHIURQW GLVWRUWLRQ LQ WKH LQQHU PP DUHD ZKLFK FRPSDUHV WR WKH &RUQLQJ VDPSOHV ZLWK D 39 ZDYHIURQW GLVWRUWLRQ HTXDO WR WKH SRZHU RI WKH SROLVKHG VXUIDFHf +RZHYHU IXUWKHU H[DPLQDWLRQ RI WKH JHO JODVV VKRZV D UROO RII ZLWK WR ZDYHV 39 VLJQLILFDQW GLVWRUWLRQ DW WKH RXWHU PP 1R VWUDLQ ZDV HYLGHQFHG RQ WKH JHO JODVV HGJH WKHUHIRUH LW LV FOHDU WKDW WKH LQKRPRJHQHLW\ LQ WKH PDWHULDO DQG LWn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

PAGE 198

7DEOH 5HIUDFWLYH LQGH[ PHDVXUHPHQWV RI WKH JHOVLOLFD JODVV DQG IXVHG VLOLFD JODVVHV 7HVW 1R ,QGH[ RI UHIUDFWLRQ Qf ,' 1R UHG H I K &RUQLQJ &RQWURO 6DPSOHV f &*: f &*: f &*: 6WDWLVWLFDO 9DOXH sf 16* (6 &RQWURO 6DPSOHV f 06* f 06* f 16* 6WDWLVWLFDO 9DOXH sf *HO*ODVV 6DPSOHV f 1 f 4 f 4 f 4 f 4 6WDWLVWLFDO 9DOXH sf

PAGE 199

,QGH[ RI UHIUDFWLRQ Qf :DYHOHQJWK QPf )LJXUH 'LVSHUVLRQ GDWD FRPSDULVRQ RI RSWLFDO VLOLFDV

PAGE 200

7DEOH 5HIHUHQFH LQGLFHV DQG $EEH YDOXHV RI VLOLFD JODVVHV 7HVW 1R ,' 1R 5HIHUHQFH LQGH[ QGf $EEH 9DOXH &RUQLQJ &RQWURO 6DPSOHV ` &*: f &*: f &*: 6WDWLVWLFDO 9DOXH sf 16*(6 &RQWURO 6DPSOHV f 16*, f 16* f 16* 6WDWLVWLFDO 9DOXH sf *HO *ODVV 7HVW 6DPSOHV ` 1 f 4 f 4 f 3 f f 4 6WDWLVWLFDO 9DOXH sf

PAGE 201

)LJXUH +RPRJHQHLW\ WHVWV RI VLOLFD JHO JODVV VDPSOH DQG &RUQLQJ FRQWURO VDPSOH E\ =\JR =DSS ,QWHUIHURPHWHU 376

PAGE 202

7KH VWUHVV ELUHIULQJHQFH WHVW VKRZHG WKDW WKURXJK WKH IDFHV RI WKH VL[ PP [ PP GLDPHWHU [ WKLFNQHVVf IXOO\ GHQVLILHG JHOVLOLFD JODVV VDPSOHV QR VWUHVV RU VWUDLQ FRXOG EH PHDVXUHG 7KURXJK WKH HQGV PP OHQJWKf VWUDLQ ZDV REVHUYHG ZKLFK FRPSXWHG WR PLOOLPLFURQV QDQRPHWHUVf SHU FHQWLPHWHU )RU FRPSDULVRQ QRUPDO RSWLFDO JODVV SHU 0,/* >@ VKRXOG KDYH OHVV WKDQ PLOOLPLFURQV SHU FHQWLPHWHU 7KH ELUHIULQJHQFH FRQVWDQW 5f RI QPFP GHWHUPLQHG IRU WKH JHOVLOLFD JODVV LV QHDUO\ HTXLYDOHQW WR WKH YDOXHV RI QPFP DQG QPFP RI &RUQLQJ DQG 16*(6 VDPSOHV UHVSHFWLYHO\ 7KH VWUDLQ DVVRFLDWHG ZLWK SDUWLDOO\ GHQVLILHG JHOVLOLFD JODVV VDPSOHV XVLQJ WZR SODQH SRODUL]HG ILOPV LV VKRZQ LQ )LJXUH 7KH VWUDLQ SUHVHQW LQ SDUWLDOO\ GHQVLILHG JHOVLOLFD LV HOLPLQDWHG E\ WKH GHQVLILFDURQ SURFHVV )LJXUH f 7KLV HIIHFW FDQ SHUKDSV EH FKDUDFWHUL]HG DV SUHFLVLRQ DQQHDOOLQJ 7KH VL[ FRQWURO VDPSOHV WHVWHG VKRZHG QR HYLGHQFH RI EXEEOHV RU LQFOXVLRQV $OO RI WKH VLOLFD JHO JODVVHV H[KLELWHG EXEEOHV DSSUR[LPDWHO\ RQH PLFURPHWHU LQ VL]H 7KH VR FDOOHG EXEEOHV DUH UHDOO\ RSWLFDO GLIIUDFWLRQ SRLQWV 7KH\ DSSHDU PRUH OLNH VWDUV WKDQ EXEEOHV 7KH\ DUH FORVHG PLFURSRUHV FUHDWHG E\ WKH IUHHG FKORULQH JDV LQVLGH GHQVLILHG JHO JODVV DV GLVFXVVHG LQ 6HFWLRQ ,, RI WKLV FKDSWHU 6LQFH WKH WHVWHG VDPSOHV YDU\ LQ TXDQWLW\ RI WKHVH GLIIUDFWLRQ SRLQWV WKH\ VHHP GLUHFWO\ UHODWHG WR WKHUPDO SURFHVV SDUDPHWHUV DQG VKRXOG WKHUHIRUH EH DEOH WR EH HOLPLQDWHG E\ RSWLPL]DWLRQ RI WKH WKHUPDOFKHPLFDO SURFHVVLQJ 'XH WR WKHVH GHIHFWV WKH ILUVW JHQHUDWLRQ JHO VLOLFD VDPSOHV ZRXOG QRW DFFHSWDEOH IRU FHUWDLQ SUHFLVLRQ RSWLFDO DSSOLFDWLRQV )XUWKHU DQDO\VLV RI WKH WHVW UHVXOWV VKRZV WKH VSDFLQJ EHWZHHQ SRLQWV WR EH IDLUO\ KRPRJHQHRXV DW D GLVWDQFH RI DERXW PLFURQV ,PSXULW\ WHVWV E\ QHXWURQ DFWLYDWLRQ DQDO\VLV VKRZ D VLJQLILFDQW FKORULQH FRQWHQW DW DERXW ZWb ZLWK WKH RWKHU LPSXULWLHV LQ WKH WHQ WR KXQGUHG SSE 1R K\GUR[\O JURXSV ZHUH GHWHFWHG ([FHSW IRU WKH FKORULQH FRQWHQW DOO LPSXULW\ OHYHOV ZHUH EHORZ WKH OHYHOV RI FRPPHUFLDOO\ DYDLODEOH 7\SHV ,,, DQG ,9 IXVHG VLOLFD

PAGE 203

)LJXUH 2EVHUYHG VWUDLQ LQ D SDUWLDOO\ GHQVH JHOVLOLFD JODVV

PAGE 204

)LJXUH 6WUDLQ HOLPLQDWLRQ LQ D IXOO\ GHQVH JHOVLOLFD JODVV

PAGE 205

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f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f DUH VKRZQ LQ 7DEOH 7KH GHQVLWLHV RI WKH JHO JODVV PHDVXUHG RQ DQ DYHUDJH JFP ORZHU WKDQ WKH FRQWURO VDPSOHV 0LFURSRUHV DUH UHVSRQVLEOH IRU WKHVH VRPHZKDW ORZHU GHQVLW\ PHDVXUHPHQWV .QRRS KDUGQHVV YDOXHV ZHUH PHDVXUHG RQ RQH JHO VLOLFD VDPSOH DQG RQH FRQWURO VDPSOH &RUQLQJ f ZLWK WKH UHVXOWV VKRZQ LQ 7DEOH 7KH JHO VLOLFD PHDVXUHG ORZHU WKDQ WKH FRQWURO VDPSOH KRZHYHU WKH FRQWURO VDPSOH PHDVXUHG VLJQLILFDQWO\ ORZHU WKDQ LWnV SXEOLVKHG GDWD &RUQLQJ (QJLQHHULQJ /DERUDWRU\ 6HUYLFHV UHSHUIRUPHG WKHLU WHVWV DQG VXSSRUW WKRVH UHVXOWV 7KRXJK LQFRQFOXVLYH WKHVH GDWD DUH DQ LQGLFDWLRQ WKDW WKH ILUVW JHQHUDWLRQ JHO VLOLFD KDV D ORZHU KDUGQHVV WKDQ IXVHG VLOLFD ZKLFK LV

PAGE 206

7DEOH &RHIILFLHQW RI WKHUPDO H[SDQVLRQ RI IXOO\ GHQVH JHO VLOLFD 7HPS 7HPS 3HQQ r& r. 2UWRQ 6WDWH [ r [ ; [ [ [ r [ [ [ [ [ ,4n ; Dfr& 8QLY RI $UL]RQD [ [ [ [ [

PAGE 207

&7( [ r.f )LJXUH &RHIILFLHQW RI WKHUPDO H[SDQVLRQ RI JHO VLOLFD FRPSDUH ZLWK RWKHU IXVHG JODVVHV

PAGE 208

7DEH 'HQVLW\ PHDVXUHPHQWV RI JHOVLOLFD DQG IXVHG VLOLFD 7HVW 6DPSOH 6DPSOH 1R 'HQVLW\ ,' 1R 6SHFLILF *UDYLW\ JPFPf *HO *ODVV 6DPSOHV 6LOLFD 0DWHULDO 1R 1R 1R &RQWURO VDPSOH &RUQLQJ )XVHG 6LOLFD 1R &RQWURO 6DPSOH 16* (6 )XVHG 6LOLFD 1R 4 4 3 &*: 16*(6 )RU 5HIHUHQFH 2QO\ )ROORZLQJ DUH WKH GHQVLW\ VSHFLILF JUDYLW\f FKDUDFWHULVWLFV RI YDULRXV PDWHULDOV EDVHG XSRQ SXEOLVKHG GDWD JUDPV SHU FXELF FHQWLPHWHU )XVHG 6LOLFD &RUQLQJ 6DPH DV PHDVXUHGf )XVHG 6LOLFD 6\QWKHWLFf 16*(6 PHDVXUHG YDOXHf )XVHG 4XDUW] 1DWXUDOf 16*

PAGE 209

7DEOH .QRRS KDUGQHVV 7(67 6$03/( 12 6$03/( ,' 1R JP /RDG .J PP+ *HO *ODVV 6DPSOH 1R 4 6WDQGDUG 'HYLDWLRQ &RUQLQJ 1R &*: 6WDQGDUG 'HYLDWLRQ )RU UHIHUHQFH RQO\ )ROORZLQJ DUH WKH .QRRS +DUGQHVV FKDUDFWHULVWLFV RI YDULRXV PDWHULDOV EDVHG XSRQ SXEOLVKHG GDWD JP /RDGf )XVHG 6LOLFD 6\QWKHWLFf )XVHG 4XDUW] 1DWXUDOf 1RWHV ,W VKRXOG EH QRWHG WKDW WKH .QRRS KDUGQHVV RI WKH FRQWURO VDPSOH RI &RUQLQJ IXVHG VLOLFD PHDVXUHG ORZHU WKDQ SXEOLVKHG GDWD 2WKHU &RUQLQJ SXEOLVKHG GDWD RQ WKH VDPH PDWHULDO LV ORZHU WKDQ ZDV PHDVXUHG

PAGE 210

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f ,W ZDV VKRZQ WKDW WKH 989899,61,5,5 WUDQVPLVVLRQ RI JHO VLOLFD JODVV LV VXSHULRU WR WKDW RI IXVHG VLOLFD DV REVHUYHG IURP LWV EURDGHU WUDQVPLVVLRQ UDQJH DSSURDFKLQJ WKH WKHRUHWLFDO YDOXH RI LGHDO VLOLFD JODVV QP WR QP *HO VLOLFDn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

PAGE 211

7DEOH 3UHSDUDWLRQ DQG FKDUDFWHULVWLFV RI ILYH W\SHV RI VLOLFD JODVV 7\SH RI 6LOLFD O ,, ,,, ,9 9 (OHFWURPHOWHG )ODPH)XVHG +\GURO\]HG 2[LGL]HG 'HQVH 4XDUW] 4XDUW] 7UDGHQDPHV 6L&, 6L&, *HO6LOLFD 9LWUHRVLO,5D +RPRVLOE OQIUDVLOE 16*2;H 2SWRVLOE 7RWDO &DWLRQ F G 6XSUDVLOE 16*(6p 6SHFWURVLO :)D *HOVLOI F 6XSUDVLO:E SSPf 2+n JURXS SSPf &On SSPf 89 b WUDQVPLVVLRQ QPf 7KHUPDO ([SDQVLRQ &RHIILFLHQW [f %XEEOHV DQG ,QFOXVLRQV L Q f 6WUDLQ QPFPf 5HIUDFWLYH LQGH[ QGf 'LVSHUVLRQ XGf 'HQVLW\ JFPf D 7KHUPDO $PHULFDQ )XVHG 4XDUW] 0RQWYLOOH 1E +HUDXV $PHUVLO 6D\UHYLOLH 1F &RPLQJ *ODVV :RUN &RUQLQJ 1< G '\QDVLO %HUOLQ 1H 16* TXDUW] -DSDQ I 0DWHULDO (QJLQHHULQJ t 6FLHQFH 8QLYHUVLW\ RI )ORULGD t *HO7HFK ,QF $ODFKXD ),

PAGE 212

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

PAGE 213

&+$37(5 6,/,&$ *(/ 237,&$/ ),/7(56 86,1* 75$16,7,210(7$/ &203281'6 LQWURGXFWLRQ /DUJH PRQROLWKLF SXUH VLOLFD JHOV KDYH EHHQ PDGH UDSLGO\ DQG UHOLDEO\ IURP WHWUDPHWK\ORUWKRVLOLFDWH 7026f XVLQJ GU\LQJ FRQWURO FKHPLFDO DGGLWLYHV '&&$f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f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

PAGE 214

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nf WR WKH LQIUDUHG QP H9 FPnf DV GHVFULEHG LQ SUHYLRXV FKDSWHUV 7KH VLOLFD 26L2 ERQGLQJ HOHFWURQV

PAGE 215

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

PAGE 216

)RU H[DPSOH LQ D IUHH LRQ RI D WUDQVLWLRQ PHWDO WKH ILYH HTXLYDOHQW G RUELWDOV DUH GHSLFWHG VSDWLDOO\ DV VKRZQ LQ )LJXUH 7KH HQHUJ\ OHYHO GLDJUDP RI WKH ILYH RUELWDOV LQ D IUHH WUDQVLWLRQ PHWDO LRQ LV DOVR LOOXVWUDWHG LQ )LJXUH Df 7KH HOHFWURQV FDQ EH IRXQG ZLWK HTXDO SUREDELOLW\ LQ DQ\ RI WKHVH ILYH RUELWDOV )LJV Dff :KHQ WKLV SRVLWLYH WUDQVLWLRQ PHWDO LRQ ZLWK SDUWO\ ILOOHG GRUELWDOV LV SODFHG DW WKH FHQWHU RI D UHJXODU XQGLVWRUWHG FU\VWDO ILHOGf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f 7KH UHPDLQLQJ WKUHH VHWV RI G RUELWDOV RI )LJXUH WKH G[\ G\ DQG G; RUELWDOV KDYH RULHQWDWLRQV ZKLFK SURWUXGH KDOIZD\ EHWZHHQ WKH OLJDQGV DV VKRZQ LQ )LJXUH %HFDXVH WKHUH LV QR UHSXOVLYH LQWHUDFWLRQV ZLWK WKH OLJDQGV WKHVH RUELWDOV ZLOO KDYH ORZHU HQHUJ\ OHYHOV WKDQ WKH HJ VHW 7KXV WKH G[\ G\ DQG G][ RUELWDOV DUH VKRZQ DV WKH WKUHH HTXDO HQHUJ\ LJ OHYHOV LQ )LJXUH Ef 7KH HQHUJ\ GLIIHUHQFH EHWZHHQ WKH HJ DQG WJ OHYHOV FDOOHG WKH FU\VWDO ILHOG VSOLWWLQJ LV GHVLJQDWHG $ 6LQFH WKH RYHUDOO HQHUJ\ GRHV QRW FKDQJH WKH XSZDUG DQG GRZQZDUG PRYHPHQWV DUH LQYHUVHO\ SURSRUWLRQDO WR WKH QXPEHU RI HTXDO HQHUJ\ OHYHOV HJH WKH GHJHQHUDF\ 7KXV LQ )LJXUH Ef WKH WULSO\ GHJHQHUDWH ORZHU HQHUJ\ WJ OHYHO PRYHV GRZQ $ ZKLOH WKH XSSHU GRXEO\ GHJHQHUDWH HJ OHYHO PRYHV XS $ FRPSDUHG WR WKH XQVSOLW IUHH LRQ OHYHOV )LJXUH Eff

PAGE 217

] ] )LJXUH (OHFWURQ GLVWULEXWLRQ VKDSHV RI WKH ILYH HTXLYDOHQW G REULWDOV

PAGE 218

/LJDQG FRQILJXUDWLRQV G[\ Df ILYH XQVSLOW G RUELWDOV LQ D IUHH LRQ Ef ILYH VSOLWIHHW G RUELWDOV LQ DQ RFWDKHGUDO ILHOG Ff ILYH VSOLWIHGG RUELWDOV LQ D WHWUDKHGUDO ILHOG Gf ILYH VSOLWIHG G RUELWDOV LQ D WHWUDJRQDOO\ GLVWRUWHG RFWDKHGUDO ILHOG Hf VDPH DV Gf EXW UHODWLYHO\ VWURQJ GLVWRUWHG If ILYH VSOLIWHG G RUELWDOV LQ D VTXDUH SODQDU OLJDQG ILHOG r % G[\ G[\ HJ G[\ G] \r rL/ f§SIL \f§ ‘ G[\ G\] F][ / BBBB _R9n ‘ L r /BL G[\ GL] G[\ G\] G][ ? rA IW IW IW A WBB n D G ? [\ n 9 Y ? r ? rJ G;\ G\] G][ ? G? IW IW IW G][ G\] nV[ G][ G\] ? A][ G\] G] &f Df Ef Gf Hf If )LJXUH 6SRWWLQJ RI WKH ILYH G RUELWDOV LQ YDULRXV W\SHV RI OLJDQG ILHOGV

PAGE 219

QHJDWLYH FKDUJHG OLJDQG )LJXUH +HDG RQ LQWHUDFWLRQ RI WKH G DQG G [\ RUELWDOV RI D FHQWUDO LRQ ZLWK VL[ OLJDQGV LQ D RFWDKHGUDO ILHOG

PAGE 220

QHJDWLYH FKDUJHG OLJDQG WKLV SUHVHQWV RQH RI G[\ G\] G][ RUELWDOV )LJXUH /HVV LQWHUDFWLRQ RI WKH G[\ G\ G; RUELWDOV RI D FHQWUD LRQ ZLWK VL[ OLJDQGV LQ D RFWDKHGUDO ILHOG

PAGE 221

:KHQ WKH WUDQVLWLRQPHWDO LRQ LV LQ WHWUDKHGUDO V\PPHWU\ DV VKRZQ LQ )LJXUHV DQG WKH VLWXDWLRQ LV UHYHUVHG 7KH OREHV RI WKH G[\ RU G] RUELWDOV QRZ OLH LQ WKH GLUHFWLRQ EHWZHHQ WKH OLJDQGV ZKLOH WKH OREHV RI G[\ G\] DQG G][ RUELWDOV WKRXJK QRW SRLQWLQJ GLUHFWO\ WRZDUGV WKH OLJDQGV OLH FORVHU WR WKHP 7KXV WKH WJ G[\ G\] G][f RUELWDOV DUH GHVWDELOL]HG ZLWK UHVSHFW WR WKH HJ RUELWDOV )RU WKH VDPH VWUHQJWK OLJDQGV WKH WHWUDKHGUDO VFKHPH $W FDQ EH UHODWHG WR WKH $ YDOXH RI WKH GHJHQHUDWH RUELWDOV E\ $W $T DV VKRZQ LQ )LJXUH Ff 3UDFWLFDOO\ RFWDKHGUDO DUUDQJHPHQWV RI WKH OLJDQGV DURXQG WKH WUDQVLWLRQPHWDO LRQ DUH RIWHQ WHWUDJRQDOO\ GLVWRUWHG ,Q VXFK D FDVH WKH WZR = DQG = G]f OLJDQGV LQ )LJXUH DUH JUDGXDOO\ PRYLQJ DZD\ IURP WKH FHQWUDO WUDQVLWLRQPHWDO LRQ DQG QHZ HQHUJ\ GLIIHUHQFHV DPRQJ WKH G RUELWDOV DULVH 7KH G] OHYHO ZLOO IDOO DQG G[\ OHYHO ZLOO DULVH HTXDOO\ DW WKH VDPH WLPH ,I WKH WZR = OLJDQGV DUH FRPSOHWHO\ UHPRYHG WKH G] OHYHO EHFRPHV WKH ORZHVW HQHUJ\ OHYHO LQ WKH UHVXOWLQJ VTXDUH SODQDU OLJDQG DUUDQJHPHQW VLQFH WKHUH DUH QRZ QR HQHUJ\UDLVLQJ OLJDQGV LQ WKDW GLUHFWLRQ DQG WKH G[\ EHFRPHV WKH KLJKHVW HQHUJ\ OHYHO DV VKRZQ LQ )LJXUH ^If )RU D VHTXDUH SODQDU OLJDQG ILHOG WKH ORFDWLRQ RI WKH G\] DQG G][ OHYHOV ZLOO IDOO DQG WKDW RI WKH G[\ OHYHO PXVW ULVH WZR WLPHV DV PXFK 7KH IUHTXHQWO\ REVHUYHG WHWUDJRQDLL\ GLVWRUWHG RFWDKHGUDO DUUDQJHPHQWV DUH VKRZQ LQ )LJXUH Gf DQG Hf &RQVHTXHQWO\ WKH NLQG RI HQHUJ\ OHYHO DUUDQJHPHQW IRUPHG E\ WKH OLJDQG ILHOGV GHSHQGV RQ WKUHH FUXFLDO SURSHUWLHV f WKH RUELWDOV RI WKH FHQWUD WUDQVLWLRQPHWDO LRQ f WKH VXUURXQGLQJ DUUDQJHPHQW RI OLJDQG ILHOGV DQG f WKH VWUHQJWK RI WKH OLJDQG ILHOGV )RU OLJDQG ILHOGV LQ GHDOLQJ ZLWK LQGLYLGXDO RUELWDOV RI DQ DWRP ORZHU FDVH QRWDWLRQV VXFK DV D_J E HLJ WJ DUH XVHG (LWKHU D RU E LQGLFDWHV D QRQGHJHQHUDWH RUELWDO ZLWK D SUHVHQWLQJ D ZDYH IXQFWLRQ ZKLFK LV V\PPHWULF ZLWK UHVSHFW WR WKH URWDWLRQ D[LV ZKHUHDV E UHSUHVHQWV D ZDYH IXQFWLRQ ZKLFK LV DQWLV\PPHWULF DQG FKDQJHV VLJQ GXULQJ URWDWLRQ 7KH H DQG W RUELWDOV DUH V\PPHWULFDOO\ GRXEO\ DQG WULSO\ GHJHQHUDWH 7KH HQHUJ\ OHYHOV LQ H RU W RUELWDOV DUH HTXDO

PAGE 222

QHJDWLYH FKDUJHG OLJDQG )LJXUH ,QWHUDFWLRQ RI WKH G] DQG G [\ RUELWDOV RI D FHQWUDO LRQ ZLWK IRXU OLJDQGV LQ D WHWUDKHGUDO ILHOG

PAGE 223

QHJDWLYH FKDUJHG OLJDQG )LJXUH ,QWHUDFWLRQ RI RQH RI WKH G[\ G\] G][ RUELWDOV RI D FHQWUDO LRQ ZLWK IRXU OLJDQGV LQ D WHWUDKHGUDO ILHOG

PAGE 224

8VH RI WKH VXEVFULSW J GHVLJQDWHV WKH SUHVHQFH RI D FKDQJH LQ VLJQ RI WKH ZDYH IXQFWLRQ RQ LQYHUVLRQ WKURXJK D FHQWHU RI V\PPHWU\ $ VXEVFULSW UHIHUV WR WKH SUHVHQFH RI PLUURU SODQHV SDUDOOHO WR WKH V\PPHWU\ D[LV DQG D VXEVFULSW UHIHUV WR PLUURU SODQHV QRUPDO WR WKLV D[LV 8SSHU FDVH GHVLJQDWLRQV VXFK DV $J %L (J 7J DUH JHQHUDOO\ XVHG WR UHSUHVHQW WKH HQHUJ\ OHYHOV LQ WKH DWRP LRQ RU PROHFXOH ZLWK WKH SUHIL[ VXSHUVFULSW DV WKH 6 f PXOWLSOLFLW\ 7KH HQHUJ\ VWDWHV WKDW FDQ DFFRPPRGDWH XQGLVWXUEHG RU H[FLWHG HOHFWURQV LQ IUHH WUDQVLWLRQPHWDO LRQV KDYLQJ LQFRPSOHWH G RUELWDOV G WR Gf EDVHG RQ 5XVVHOO 6DXQGHUV FRXSOLQJ >VHH S LQ UHI @ DUH QDPHG WR EH 6 3 ) + DQG FRUUHVSRQGLQJ WR WKH TXDQWXP QXPEHU / HTXDO WR DQG 7KHVH VWDWHV DUH OLVWHG LQ 7DEOH IRU YDULRXV WUDQVLWLRQ PHWDOV ,Q D OLJDQG ILHOG WKH WHWUDKHGUDO G RU G FRQILJXUDWLRQ FDQ EH YLHZHG DV FRQWDLQLQJ RQH KROH LH RQH HOHFWURQ PLVVLQJ IURP D IXOO G RU KDOI IXOO G VKHOO 7KLV FRQILJXUDWLRQ SURYLGHV D VWURQJ DQDORJ\ ZLWK RQH HOHFWURQ DGGHG WR DQ RFWDKHGUDO HPSW\ G VKHOO Gf RU D KDOI ILOOHG G VKHOO Gf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f FRQILJXUDWLRQV LV HTXLYDOHQW WR WKDW RI GnQf WHWUDKHGUDOf RU YLFH YHUVD 7KH Gr DQG G FRQILJXUDWLRQV FRUUHVSRQGLQJ WR FRPSOHWHO\ HPSW\ RU FRPSOHWHO\ IXOO G RUELWDOV FDQQRW VKRZ FRORU GLUHFWO\ GHULYHG IURP G HOHFWURQLF WUDQVLWLRQV $Q V RUELWDO LV FRPSOHWHO\ V\PPHWULFDO DQG KHQFH LV XQDIIHFWHG E\ OLJDQGV LQ DQ RFWDKHGUDO ILHOG VXFK DV 6 RU $LJ 7KH S RUELWDOV DUH QRW VSOLW E\ RFWDKHGUDO ILHOGV VXFK DV 3 RU 7_J VLQFH DOO LQWHUDFW HTXDOO\ DV LOOXVWUDWHG LQ )LJXUHV DQG ,Q DQ

PAGE 225

7DEOH (QHUJ\ OHYHOV IRU WUDQVLWLRQPHWDO IUHH LRQV &RQILJXUDWLRQ ([DPSOH 7KH ORZHVW HQHUJ\ OHYHOV LQ D IUHH LRQ G G G 7L f m G&X f G m G G 9 f G 1Lf IGSJV G r G G &U 9f G )H &Rf I S J K 3 &2 &/ &2 4 &' G &U 0Q ` G 0Q )H &R f + 3 ) G G &U 0Q )H f 6 3 I

PAGE 226

KROHf G G LQ RFWDKHGUDO ILHOG E HOHFWURQf G G LQ RFWDKHGUDO ILHOG HOHFWURQf G G LQ WHWUDKHGUDO ILHOG KROHf G G LQ WHWUDKHGUDO ILHOG )LJXUH 7KUHH ORZHVW HQHUJ\ OHYHOV IRU G G G G VSOLWWLQJ FRQILJXUDWLRQV LQ RFWDKHGUDO DQG WHWUDKHGUDO ILHOGV

PAGE 227

E KROHVf G G LQ RFWDKHGUDO ILHOG HOHFWURQVf G G LQ WHWUDKHGUDO ILHOG D HOHFWURQVf KROHVf GG LQ RFWDKHGUDO ILHOG G G LQ WHWUDKHGUDO ILHOG )LJXUH 7ZR ORZHVW HQHUJ\ OHYHOV IRU G G G G VSOLWWLQJ FRQILJXUDWLRQV LQ RFWDKHGUDO DQG WHWUDKHGUDO ILHOGV

PAGE 228

QHJDWLYH FKDUJHG OLJDQG )LJXUH $OO LQWHUDFWLRQ EHWZHHQ OLJDQGV DQG 6 DUH HTXDO WKHUHIRUH QR VSOLWWLQJ UHVXOWV

PAGE 229

QHJDWLYH FKDUJHG OLJDQG )LJXUH $LO LQWHUDFWLRQ EHWZHHQ OLJDQGV DQG 3 DUH HTXDO WKHUHIRUH QR VSOLWWLQJ UHVXOWV

PAGE 230

RFWDKHGUDO ILHOG WKH G DQG G 'f RUELWDOV DV GLVFXVVHG EHIRUH VSOLW LQWR 7J G[\ G\] G][f DQG (J G[\ RU G]f OHYHOV 7KH I RUELWDOV DUH VSOLW LQWR WKUHH OHYHOV LQ DQ RFWDKHGUDO ILHOG D 7LJ OHYHO DW $ EHORZ D 7J OHYHO DW $ DERYH DQG D $J OHYHO $ DERYH WKH SUHVSOLWWHG ) RUELWDO DV VKRZQ LQ )LJXUH Df 7KH WZR VSOLW ORZHQHUJ\ VWDWHV ) DQG 3 IURP HLWKHU WKH G RU WKH G FRQILJXUDWLRQ EHKDYH LQ DQ RFWDKHGUDO ILHOG H[DFWO\ DV WKH ) DQG 3 VWDWHV DULVLQJ IURP WKH I DQG S DV GLVFXVVHG DERYH &RQVHTXHQWO\ WKH ) VWDWH LV VSOLW LQWR 7_J)f 7J)f DQG $J)f VWDWHV DQG WKH XQVSOLW 3 EHFRPHV WKH 7LJ3f VWDWH 7KH G RU G VWDWH KDV 3 DQG ) RUELWDOV 8QGHU D OLJDQG ILHOG WKH ) VSOLWV LQWR 7_J)f 7J)f DQG $J)f VWDWHV DQG WKH XQVSLLW 3 EHFRPHV WKH 7L3f VWDWH DV VKRZQ LQ )LJXUHV DQG Ef 7KH G DQG G FRQILJXUDWLRQV KDYH D ORZHQHUJ\ VWDWH ZKLFK VSOLWV LQWR 7J G;\ G\] G][f DQG (J G[\ RU G]f LQ DQ RFWDKHGUDO ILHOG )LJXUHV DQG Fff 7KH G VWDWH KDV DQ XQVSOLW 6 RU $L OHYHO LQ WKH RFWDKHGUDO ILHOG $V PHQWLRQHG DERYH OLJDQG ILHOG WKHRU\ GHVFULEHV WKH ERQGLQJ RFFXUULQJ EHWZHHQ FHQWHU WUDQVLWLRQPHWDO LRQ DQG WKH OLJDQGV 0ROHFXODU RUELWDO WKHRU\ ZKLFK GHYHORS WKH FRPELQDWLRQ RI WKH DWRPLF RUELWDOV RI WKH DWRPV WR IRUP WKH PROHFXOH LV XVHG WR H[SODLQ WKLV ERQGLQJ SKHQRPHQRQ 7KH FRQGLWLRQ IRU WZR DWRPV WR IRUP f D ERQGLQJ PROHFXODU RUELWDO YEf f D QRQERQGLQJ PROHFXODU RUELWDO RU f DQ DQWLERQGLQJ PROHFXODU RUELWDO \Df GHSHQGV RQ 6 WKH ZDYH IXQFWLRQ RYHUODS LQWHJUDO -[\D9EGW RI WKH SUREDELOLW\ HTXDWLRQ ?MEGW 9$AW 9%GW Y$9%GW ZKHUH ?MD DQG ZE DUH WKH ZDYH IXQFWLRQV RI DWRPV $ DQG %f IRU ILQGLQJ DQ HOHFWURQ ZLWKLQ WKH VSDFH %RQGLQJ WDNHV SODFH RQO\ ZKHQ WKH YDOXH RI 6 LV SRVLWLYH 6 f DQG WKH ERQGLQJ VWUHQJWK HQHUJ\f LV SURSRUWLRQDO WR WKH H[WHQW RI WKH RYHUODS RI WKH DWRPLF RUELWDOV 7KH ERQGLQJ HQHUJ\ OHYHO LV UHGXFHG UHODWLYH WR WKH OHYHO RI WKH IUHH DWRPV E\ WKH VDPH DPRXQW DV WKH HQHUJ\ LV LQFUHDVHG IRU WKH DQWLERQGLQJ OHYHO ,Q WKH FDVH RI G WUDQVLWLRQPHWDO LRQV LQ DQ RFWDKHGUDO ILHOG WKH G[\ DQG G] FRQILJXUDWLRQV DUH LQ WKH GLUHFWLRQ RI WKH OLJDQGV 7KLV UHVXOWV LQ D SRVLWLYH RYHUODS DQG D

PAGE 231

DfRFWDKHGUDO ILHOG G 9f G &Rf EfWHWUDKHGUDO ILHOG G 9 &Urf G 1Lf RFWDKHGUDO ILHOG G 7Lf G )H &Rf WHWUDKHGUDO ILHOG G &U 0Qrf G &Xf )LJXUH 7KH VSOLWWLQJ RI G RUELWDOV Df Ef IRU 3 ) VWDWHV FfIRU VWDWH LQ RFWDKHGUDO DQG WHWUDKHGUDO OLJDQG ILHOG

PAGE 232

UHGXFWLRQ HJ ERQGLQJf DQG DQ LQFUHDVH HrJ DQWLERQGLQJf LQ HQHUJ\ OHYHOV 7KH WJ G;\ G\= G][f OHYHOV DUH ORFDWHG EHWZHHQ WKH OLJDQGV DQG QR RYHUODS LV REVHUYHG $V D UHVXOW WKH HQHUJ\ OHYHOV RI WJ UHPDLQ XQFKDQJHG LQ WKH SUHVHQFH RI WKH OLJDQG ILHOG DV VKRZQ LQ )LJXUH Ff 7KH V RUELWDO RI WUDQVLWLRQPHWDO LRQV KDV D DLJf VSKHULFDO V\PPHWU\ DQG D FRUUHVSRQGLQJ OLJDQG JURXS RUELWDO WKDW LV FRPSRVHG RI VLJPD ERQGV ZKLFK DUH F\OLQGULFDO V\PPHWULFDO DERXW WKH LQWHUQXFOHDU D[LV )LJXUH f 7KH S WLX ERQGLQJ DQG Wr_8 DQWLERQGLQJf RUELWDOV ZLWK WKH UHODWHG OLJDQG JURXS RUELWDOV DUH VKRZQ LQ )LJXUH 7KH HOHFWURQV IURP WKH OLJDQG JURXS RUELWDOV DUH SHUIHFWO\ SDLUHG LQWR WKUHH ORZHVW HQHUJ\ PROHFXODU RUELWDOV ZKLFK DUH DLJf WLXf DQG HJf DV VKRZQ E\ WKH KHDY\ DUURZV LQ )LJXUH Ff &RQVHTXHQWO\ WKH G HOHFWURQV IURP WKH WUDQVLWLRQ PHWDO LRQV KDYH WR ILOO WKH WJf OHYHOV ILUVW LI WKHUH DUH DQ\ UHPDLQLQJ HOHFWURQV WKHQ WKH HrJf OHYHOV DYDLODEOH LI WKH HQHUJ\ JDS $ LV JUHDWHU WKDQ N7 ORZVSLQ FRQILJXUDWLRQV ZLOO EH IRUPHG 7KH JDS HQHUJ\ $ LV JHQHUDOO\ LQ WKH YLVLEOH UDQJH RI H9 1,5f WR H9 89f HQHUJ\ ,I HOHFWURPDJQHWLF UDGLDWLRQ KDV WKH VDPH DPRXQW RI HQHUJ\ DV WKH JDS HQHUJ\ LH $ KX SKRWRQ HQHUJ\f WKHQ WKH HOHFWURQLF WUDQVLWLRQV IURP WJf WR HrJf OHYHOV WDNHV SODFH 7KHVH WKHRULHV RI OLJDQG ILHOG DQG PROHFXODU RUELWDO WUDQVLWLRQV DUH WKH EDVLV IRU LQWHUSUHWLQJ WKH RSWLFDO VSHFWUD RI &R LRQ GRSHG 1L LRQ GRSHG DQG &X LRQ GRSHG VLOLFD JHOV 7KH SRVVLEOH HQHUJ\ OHYHO WUDQVLWLRQV IRU WKH &R LRQ LQ ERWK G RFWDKHGUDO DQG WHWUDKHGUDO V\PPHWULHV DUH DQDO\]HG E\ PHDQV RI )LJXUHV Df DQG Ef 7KH RFWDKHGUDO &R FRQILJXUDWLRQ LV SUHGLFWHG WR KDYH WKUHH VSLQDOORZHG WUDQVLWLRQV f 7L)f 7)f f 7L )f a! 7L 3f f 7 )f a! $)f 7KH WHWUDKHGUDO &R FRQILJXUDWLRQ LV H[SHFWHG WR KDYH WKUHH PDMRU WUDQVLWLRQV f $)f a! 7)f

PAGE 233

S HPSW\ HPSW\ V SDUWLDOO\ G ILOOHG Df IUHH LRQ RUELWDOV Ef FHQWUDO LRQ RUELWDOV FRPSOHWHO\ ILOOHG OLJDQG JURXS RUELWDOV Gf OLJDQG RUELWDOV WLXf DLJf Ff PROHFXODU RUELWDOV )LJXUH 0ROHFXODU RUELWDO VSOLWWLQJ OHYHOV IRU D G RUELWDO LRQ LQ DQ RFWDKHGUDO HQYLURQPHQW ZLWK OLJDQGV KDYLQJ RQO\ D ERQGV

PAGE 234

Ef )LJXUH /LJDQG JURXS RUELWDO DQG FHQWUDO PDWFKLQJ DWRPLF RUELWDOV RI WKH ERQGLQJ V\PPHVWU\

PAGE 235

)LJXUH /LJDQG JURXS RUELWDO RI RQO\ R ERQGV DQG PDWFKLQJ DWRPLF RUELWDOV WR IRUP PROHFXODU RUELWDOV

PAGE 236

f $)f a! 7)f f $)f 73f 7KH HQHUJ\ OHYHO GLDJUDP IRU WKH 1L LRQ LQ G WHWUDKHGUDO DQG RFWDKHGUDO V\PPHWULHV LV DOVR GHSLFWHG LQ )LJXUHV Df DQG Ef 7KH WHWUDKHGUDO 1L FRQILJXUDWLRQ KDV WKUHH VSLQDOORZHG WUDQVLWLRQV f 7L)f a! 7If f 7‘f )f D)f f 7)f 73f 7KH RFWDKHGUDO 1L V\PPHWU\ UHVXOWV LQ WKUHH PDMRU WUDQVLWLRQV f D)f W)f f $)f 7)f f $)f 7L 3f 7KH &X LRQ KDV D G FRQILJXUDWLRQ DQ LQYHUWHG G FRQILJXUDWLRQ DV VKRZQ LQ )LJXUH 7KH PDMRU WUDQVLWLRQ LV DWWULEXWHG WR ( 7 DV LV DOVR VKRZQ LQ )LJXUH Df ([SHULPHQWDO 3URFHGXUH 6HYHQ VWHSV DUH JHQHUDOO\ XVHG LQ PDNLQJ WKH PRQROLWKLF VLOLFD JHOV DQG JODVVHV FRQWDLQLQJ WUDQVLWLRQPHWDO HOHPHQWV f PL[LQJ f FDVWLQJ f JHODWLRQ f DJLQJ f GU\LQJ f LPSUHJQDWLRQ DQG f GHQVLILFDURQ GHVFULEHG LQ ([DPSOH 7ZR LQ &KDSWHU LQ WKH PL[LQJ VWDJH LW LV QHFHVVDU\ WR VHOHFW D VXLWDEOH GU\LQJ FRQWURO FKHPLFDO DGGLWLYHV VXFK DV IRUPDPLGH JO\FHURO QLWULF DFLG RU DQ RUJDQLF DFLG LQ RUGHU WR PDNH PRQROLWKV UDSLGO\ ZLWKRXW f SUHFLSLWDWLRQ f IRUPDWLRQ RI DQ LQKRPRJHQHRXV JHO RU f FU\VWDOOL]DWLRQ %\ XVH RI QLWULF DFLG LQ WKLV V\VWHP LW ZDV SRVVLEOH WR SURGXFH QRQFU\VWDOOLQH KRPRJHQHRXV RSWLFDO VLOLFD JHOV DQG JODVVHV 7R RXU NQRZOHGJH PRQROLWKLF JHLV FRQWDLQLQJ WKH WUDQVLWLRQ DQG UDUH HDUWK HOHPHQWV PHQWLRQHG LQ &KDSWHU KDYH QRW SUHYLRXVO\ EHHQ GHVFULEHG

PAGE 237

7KH H[DPSOHV XVHG IRU WKLV LQYHVWLJDWLRQ ZHUH &R 1L DQG &X FRORUHG VLOLFD PRQROLWKV 7KH ILUVW VWHS LQYROYHG PL[LQJ FF 1f QLWULF DFLG '&&$ ZLWK FF RI GLVWLOOHG ZDWHU IRU PLQXWHV DW URRP WHPSHUDWXUH IROORZHG E\ DGGLQJ WR WKH QLWULF DFLG ZDWHU VROXWLRQ 4FF RI 7026 ZLWK PL[LQJ DW r& IRU QR PRUH WKDQ PLQXWHV 7KLV ZHOO PL[HG VRO ZDV WKHQ FDVW LQWR D SRO\VW\UHQH PRGH PP + [ PP D GLVN VKDSHf DW URRP WHPSHUDWXUH *HODWLRQ RFFXUUHG LQ WKH PROG DW r& LQ DERXW PLQXWHV IROORZHG E\ DJLQJ DW r& IRU KRXUV DQG IROORZHG E\ DJLQJ DW r& IRU KRXUV 7KH DJHG VLOLFD JHO ZDV WDNHQ IURP WKH PROGV DQG GULHG ZLWK D FRQWUROOHG HYDSRUDWLRQ UDWH DV GHVFULEHG LQ 6HFWLRQ ,, RI &KDSWHU 7KH GU\LQJ ZDV LQLWLDOO\ DW r& ZLWK WKH WHPSHUDWXUH JUDGXDOO\ LQFUHDVLQJ WR r& GXULQJ D KRXU SHULRG %HIRUH LPSUHJQDWLRQ WKH JHO ZDV VWDELOL]HG WR r& DW r&KRXU WR LQFUHDVH WKH VWUHQJWK DQG GHQVLW\ DQG PDNH LW SRVVLEOH WR SHUIRUP D QRQGHVWUXFWLYH GRSLQJ SURFHVV 7KH VWDELOL]HG JHO ZDV WKHQ LPPHUVHG LQWR D JUDPSHUFHQW &R QLWUDWH RU D JUDPSHUFHQW 1L QLWUDWH RUDQ RQH JUDPSHUFHQW &X QLWUDWH ZDWHU VROXWLRQ IRU KRXUV 7KH VROXWLRQ GRSLQJ IROORZHG E\ GU\LQJ DW r& IRU KRXUV WR UHPRYH WKH SRUH VROYHQW 6XEVHTXHQW WKHUPDO WUHDWPHQWV WR r& DQG r& ZHUH GRQH LQ DPELHQW DLU 7KH WUDQVPLVVLRQ VSHFWUD RI WKH r& &R DQG &X GRSHG VLOLFD JHO JODVVHV DQG WKH 'r& r& &R GRSHG VLOLFD JHO JODVVHV ZHUH REWDLQHG LQ WKH YLVLEOH UDQJH IURP QP WR QP XVLQJ D 3HUNLQ(OPHU 899,6 VSHFWURSKRWRPHWHU PRGHO 7KH WUDQVPLVVLRQ VSHFWUD RI WKH r& 1LL GRSHG VLOLFD JHO JODVV ZDV SHUIRUPHG LQ WKH 89 9,61,5 UDQJH IURP QP WR QP XVLQJ D 3HUNLQ(OPHU /DPEGD 899,61,5 VSHFWURSKRWRPHWHU 5HVXOWV DQG 'LVFXVVLRQV 7KH VLOLFD JHO VDPSOHV FRQWDLQLQJ b &R ZHUH KHDWHG WR FHUWDLQ WHPSHUDWXUHV 7KH FRORU RI WKH r& &R JHO LV UHGGLVK SLQN 7KH FRORU RI WKH r& VDPSOH LV GHHS EOXH DQG WKH r& VDPSOH KDV D JUHHQLVK EODFN FRORU 7KH 899LVLEOH VSHFWUD

PAGE 238

FKDUDFWHULVWLF RI WKHVH WKUHH &RAVLOLFD JHO VDPSOHV DUH VKRZQ LQ )LJXUH 7KHUH LV D WRWDOO\ GLIIHUHQW DEVRUSWLRQ FXUYH IRU WKH r& SLQN VDPSOH WKDQ IRU WKH r& EOXH VDPSOH DQG WKH r& JUHHQ VDPSOH 6LQFH WKH FRORU RI WUDQVLWLRQ LRQV VXFK DV FREDOW LQ VLOLFDWH JODVVHV GHSHQGV SULPDULO\ RQ WKH RXWHU G YDOHQFH RUELWDOV LW PHDQV WKDW WKH FRORU DQG DEVRUSWLRQ VSHFWUD GHSHQGV RQ WKH R[LGDWLRQ VWDWH DQG FRRUGLQDWLRQ QXPEHU RI WKH LRQ 7KH WHPSHUDWXUH VHQVLWLYLW\ RI WKH &RAVLOLFD JHO DEVRUSWLRQ VSHFWUD LQGLFDWHV D VKLIW LQ R[LGDWLRQ VWDWH DQG FRRUGLQDWLRQ QXPEHU &1f 7KH ORZWHPSHUDWXUH JHO VKRZV HYLGHQFH RI D VL[IROG &1 VLPLODU WR WKDW UHSRUWHG IRU &R LQ PHWDSKRVSKDWH JODVVHV >@ DQG PROb 1DERUDWH JODVV >VHH S LQ UHI @ DV VKRZQ LQ )LJXUH 7KXV LW LV UHDVRQDEOH WR DVVXPH WKDW WKH &R LRQ LQ WKH VLOLFD JHO LQ RFWDKHGUDO V\PPHWU\ 7KH PDMRU DEVRUSWLRQ EDQG RI WKH &RQ LRQ LV GXH WR WKH 7L)f WR 7L3f WUDQVLWLRQ VHH )LJXUH f 7KH KLJK HQHUJ\ VKRXOGHU DW QP LV D FRQVHTXHQFH RI VSLQRUELW FRXSLQJ LQ WKH 7_3f VWDWH >@ 7KH 7c)f WR 7)f WUDQVLWLRQ RFFXUV LQ WKH LQIUDUHG UHJLRQ DURXQG QP DQG GRHV QRW FRQWULEXWH WR FRORU IRUPDWLRQ 7KH 7L)f WR $)f WUDQVLWLRQ LV H[SHFWHG WR EH DW QP +RZHYHU WKLV WUDQVLWLRQ LV YHU\ ZHDN EHFDXVH LW LQYROYHV WKH IRUELGGHQ WZRHOHFWURQ MXPS >@ 7KLV ZHDNQHVV FRPELQHG ZLWK WKH FORVHQHVV RI WKH PDMRU 7L)f WR 7L3f WUDQVLWLRQ PDNHV WKH 7 )f WR $)f WUDQVLWLRQ XQUHVROYHG ,Q FRQWUDVW WKH KLJKWHPSHUDWXUH r& DQG r&f &R0 GRSHG JHOV DSSHDU WR KDYH D &1 RI 7KLV IRXUIROG FRRUGLQDWLRQ LV PRUH HTXLYDOHQW WR WKDW RI D VWDQGDUG YLWUHRXV 6LOLFDWH JODVV >@ VHH )LJXUH f WKDW LV &R6SLQNf f§$@B &ROEOXHf 7KH PDLQ DEVRUSWLRQ EDQG LQ QP WR QP UDQJH RI WKLV WHWUDKHGUDO &R LRQ LV GXH WR WKH $)f WR 7_3f WUDQVLWLRQ $V VKRZQ LQ )LJXUH WKH &R GRSHG KLJK WHPSHUDWXUH JHO VKRZV HYLGHQFH RI D IRXUIROG &1 VLPOOLDU WR WKDW IRU &R LRQ LQ IXVHG

PAGE 239

RSWLFDO GHQVLW\ 2'f )LJXUH 6SHFWUD RI WKUHH &R6GRSHG VLOLFD JHO VDPSOHV DW r& r& DQG r&

PAGE 240

RSWLFDO GHQVLW\ 2'f ZDYHOHQJWK QPf )LJXUH 6SHFWUD RI r& &RAGRSHG VLOLFD JHO VDPSOHV DQG VRPH &RGRSHG PHOWHG JODVVHV

PAGE 241

RSWLFDO GHQVLW\ 2'f ZDYHOHQJWK QPf )LJXUH 6SHFWUD RI r& r& &RL6V+LFD JHO VDPSOHV DQG WZR &RQGRSHG PHOWHG JODVVHV

PAGE 242

VLOLFD DQG D ELQDU\ PROb 1DERUDWH JODVV 7KH VSOLWWLQJ RI WKH $)f WR 7 3f EDQG LV FDXVHG E\ VSLQRUELW FRXSOLQJ ZKLFK VSOLWV WKH 7_3f VWDWHV DQG DOORZV WKH WUDQVLWLRQV WR WKH QHLJKERULQJ GRXEOHW VWDWHV WR JDLQ LQ LQWHQVLW\ >VHH S LQ UHI @ 7KH WZR RWKHU WUDQVLWLRQV $)f WR 7)f DQG $)f WR 7_)f ZKLFK WDNH SODFH LQ WKH LQIUDUHG UHJLRQ FRQWULEXWH QR FRORU FKURPRSKRUHV ,Q WKLV VWXG\ QRQH RI WKH VSHFWUD IRU WKH &R GRSHG VLOLFD JHOV LV LGHQWLFDO WR WKH VLOLFDWH PHOW JODVV VSHFWUXP LQ GHWDLO 7KLV LQGLFDWHV WKDW WKH OLJDQG ILHOG VWUHQJWK $f PD\ EH YDULHG E\ WKH WKHUPDO KLVWRU\ RI WKH JHOV 7KH VSHFWUXP RI D r& 1L GRSHG VLOLFD JHO LV VLPLODU WR WKDW RI D ZWb PHOW .ERUDWH JODVV FRQWDLQLQJ 1L LRQ ,W LV DOVR VLPLODU WR WKDW RI D >1L+f@ RFWDKHGUDO FRPSOH[ LQ ZDWHU >VHH S LQ UHI @ DV VKRZQ LQ )LJXUH 7KH DEVRUSWLRQ EDQG DW QP RI 1L LQ DQ RFWDKHGUDO FRPSOH[ LV DVVLJQHG WR WKH $_)f 7L )f WUDQVLWLRQ DQG WKH RQH DW DERXW QP LV DVVLJQHG WR WKH $)f 7L3f WUDQVLWLRQ $QRWKHU EDQG FRUUHVSRQGLQJ WR D $)f a! 7)f WUDQVLWLRQ LV REVHUYHG LQ WKH LQIUDUHG UHJLRQ DW DERXW QP ,Q WKLV VWXG\ WKH VSHFWUD RI WKHVH WKUHH VDPSOHV DUH DOPRVW WKH VDPH H[FHSW IRU WKH GLIIHUHQFH LQ DEVRUSWLRQ LQWHQVLW\ 7KH VLPLODULW\ LQ DEVRUSWLRQ EDQGV RI WKH WKUHH FXUYHV LQGLFDWHV WKDW WKH VDPH OLJDQG ILHOG VWUHQJWK DFWV RQ 1L LRQ LQ WKHVH WKUHH VDPSOHV 7KH DEVRUSWLRQ VSHFWUXP RI &X LQ D r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

PAGE 243

RSWLFDO GHQVLW\ 2'f ZDYHOHQJWK QPf )LJXUH $EVRUSWLRQ VSHFWUD RI D 1LAGRSHG VLOLFD JHO VDPSOH D 1L ZDWHU VROXWLRQ DQG D 1LAGRSHG PROb .2%2 JODVV

PAGE 244

RSWLFDO GHQVLW\ 2'f ZDYHOHQJWK QPf )LJXUH $EVRUSWLRQ VSHFWUD RI &XOGRSHG VLOLFD JHO VDPSOH DQG WKUHH &XAGRSHG VRGLXPERUDWH JODVVHV

PAGE 245

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f GLVFXVVHG LQ WKLV FKDSWHU KDYH GHPRQVWUDWHG WKH SRVVLELOLWLHV RI SURGXFLQJ D YDULHW\ RI SURGXFWV LQFOXGLQJ VWUDWHJLF KLJKWHFK RSWLFDO JODVVHV ZLWK VSHFLILF ZDYHOHQJWK ILOWUDWLRQ FDSDELOLWLHV KLJKWHFK FRPPHUFLDO VXQ JODVVHV DQG WXQHDEOH ODVHU JODVVHV

PAGE 246

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ff 7L2+nf $,2+f 6L&+ff HWFf 7KLV VWHS LV IROORZHG E\ D SRO\PHUL]DWLRQ EDVHG JURZWK SURFHVV ZKLFK OLQNV WKH PRQRPHUV WRJHWKHU ,Q UHFHQW \HDUV VSHFLDO RSWLFDO DSSOLFDWLRQV UHTXLUH VLOLFD FRPSRQHQWV WKDW PHHW YHU\ VWULQJHQW UHTXLUHPHQWV 6ROJHO SURFHVVLQJ DSSOLHG WR VLOLFD RIIHUV WKH SRWHQWLDO IRU SURGXFLQJ D QHZ JHQHUDWLRQ RI VLOLFD JODVVHV WR PHHW WKHVH UHTXLUHPHQWV IRU RSWLFDO DQG HOHFWURRSWLFDO DSSOLFDWLRQV 7KH TXDOLW\ RI JHOVLOLFD JODVVHV H[SHFWHG WR PHHW WKHVH VWULQJHQW UHTXLUHPHQWV DUH f YHU\ KLJK SXULW\ f H[WUHPHO\ ORZ RSWLFDO VLJQDO ORVV f YHU\ KLJK FKHPLFDOO\ KRPRJHQHRXV GRSLQJ f YHU\ KLJK RSWLFDO KRPRJHQHLW\ 7KHVH IHDWXUHV PDNH JHOVLOLFDV DEOH WR XSJUDGH WKH RSWLFDO SHUIRUPDQFH LQ D ZLGH UDQJH RI SUHFLVH RSWLFDO DSSDUDWXV LQFOXGLQJ OHQVHV PLUURUV ZDYHJXLGHV RSWLFDO ILEHUV LQWHJUDWHG RSWRHOHFWURQLFV DQG KRVW PDWHULDOV IRU ILOWHUV ODVHUV DQG QRQOLQHDU RSWLFDO HOHPHQWV RU FRPSRXQGV 7KHUHIRUH DFKLHYLQJ D FKHPLFDOO\ RSWLPL]HG VROJHO SURFHVVLQJ IRU VLOLFD RSWLFDO PRQROLWKV ZDV WKH IRFXV RI WKLV VWXG\

PAGE 247

7KH ILUVW PDMRU GLIILFXOW\ IDFHG LQ SURGXFLQJ ODUJH PRQROLWKLF JHO JODVV IRU RSWLFDO FRPSRQHQWV ZDV FUDFNLQJ GXULQJ GU\LQJ ,Q WKLV VWXG\ WKH SUREOHP ZDV RYHUFRPH E\ XVH RI GU\LQJ FRQWURO FKHPLFDO DGGLWLYHV '&&$f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f JHOV DV ODUJH DV FP [ FP [ FP XS WR WKH FDSDELOLW\ RI WKH H[SHULPHQWDO IDFLOLW\f ZHUH URXWLQHO\ SURGXFHG 7KH ILUVW JRDO ZDV DFKLHYHG 7KH GULHG JHO PRQROLWKV ZHUH SDUWLDOO\ GHQVLILHG LQ DQ DPELHQW DLU IXUQDFH XS WR r& 7KH FKDUDFWHUL]DWLRQ RI WKHVH SDUWLDOO\ GHQVLILHG VLOLFD JHOV ZDV SHUIRUPHG E\ XVH RI f VWUXFWXUDO LQIRUPDWLRQ WHVWV [UD\ GLIIUDFWLRQ %(7f f 2SWLFDO LQIRUPDWLRQ WHVWV UHIUDFWLYH LQGH[ )7,5 899,61,5f f WKHUPDO LQIRUPDWLRQ WHVWV '6& '7$ 7*$ 70$f f PHFKDQLFDO LQIRUPDWLRQ WHVWV IOH[XUDO VWUHQJWK FRPSUHVVLYH VWUHQJWK PLFURKDUGQHVV WRXJKQHVV GHQVLW\f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

PAGE 248

7KH WKHUPDO LQIRUPDWLRQ WHVWV LQGLFDWH WKDW WKH GHFRPSRVLWLRQ DQG HYDSRUDWLRQ ZHLJKW ORVVHV GXH WR ORVV RI UHVLGXDO RUJDQLF FRPSRXQGV DQG ZDWHU WDNH SODFH EHORZ r& 'LPHQVLRQDO VKULQNDJH RFFXUV WKURXJKRXW WKH HQWLUH KHDWLQJ SURJUDP 7KH UHVXOWV RI PHFKDQLFDO LQIRUPDWLRQ WHVWV VKRZ WKDW WKH FRPSUHVVLYH VWUHQJWK PD[LPXP VWUDLQ WR IUDFWXUH IOH[XUDO VWUHQJWK
PAGE 249

$SSOLFDWLRQV DUH QHDUO\ XQOLPLWHG IRU XVH RI WKH VLOLFD VROJHO WHFKQRORJ\ GHYHORSHG KHUHLQ 7KH SRVVLELOLW\ RI XVLQJ WKH SRURXV JHO PRQROLWKV IRU VHFRQG SKDVH GRSLQJ ZDV WKH WKLUG JRDO SXUVXHG 0RQROLWKLF SDUWLDOO\ GHQVLILHG RSWLFDO VLOLFDJHO ILOWHUV LPSUHJQDWHG ZLWK WUDQVLWLRQPHWDO LRQV ^/H} *X 1L DQG &R LRQVf ZHUH VXFFHVVIXOO\ PDGH &RORU FKDQJHV RI WKHVH WUDQVLWLRQPHWDO LRQ GRSHG JHOV WKDW UHVXOWHG IURP GLIIHUHQW GHQVLILFDURQ WHPSHUDWXUH ZHUH LQWHUSUHWHG XVLQJ OLJDQG ILHOG DQG PROHFXODU RUELWDO WKHRULHV 7KH WKLUG JRDO LQ WKLV VWXG\ ZDV DFKLHYHG 7KH KLJKHVW TXDOLW\ RI SXUH VLOLFD PDGH LQ WKH ZRUOG WRGD\ LV WKDW RI RSWLFDO ILEHUV IDEULFDWHG E\ YDSRU SKDVH SODVPD UHDFWLRQ RI XOWUDSXUH R[\JHQ ZLWK XOWUDSXUH VLOLFRQ WHWUDFKORULGH 7\SH ,9 VLOLFDf 7KLV SURFHVV UHVXOWV LQ ILEHUV RI XOWUDORZ ORVV DERXW G%.P WR G%.Pf LQ WKH QP WR QP UDQJH ,W LV DOUHDG\ VKRZQ LQ WKLV VWXG\ WKDW WKH IXOO\ GHK\GUDWHG FRPSOHWHO\ GHQVLILHG JHOJODVV PRQROLWKV DUH RI VXFK D TXDOLW\ DV WR FRPSDUH ZLWK WKH EHVW 7\SH ,9 RSWLFDO VLOLFD ILEHUV +RZHYHU WKH WHPSHUDWXUH RI GHQVLILFDWLRQ KDV EHHQ UHGXFHG WR r& 7KH VROJHO VLOLFD SURFHVV KDV WKH DGGLWLRQDO DGYDQWDJH WKDW QHW VKDSH FDVWLQJ RI RSWLFDO FRPSRQHQWV LV YHU\ VLPSOH DOVR ORFDOL]HG GHQVLILFDWLRQ FDQ EH DFKLHYHG \LHOGLQJ D QHZ DSSURDFK IRU SURGXFLQJ ZDYHJXLGHV LQ D SXUH VLOLFD PDWUL[ LH LQWHJUDWHG RSWLFVf 7KH YXY FXWRII DW QP LQGLFDWHV WKDW WKH JHOJODVV LV QRW \HW DQ LGHDO VLOLFD JODVV 7HVW GDWD IURP QHXWURQ DFWLYDWLRQ DQDO\VLV VKRZHG WKDW WKH LPSXULW\ OHYHOV LQ WKH ILUVW JHQHUDWLRQ VLOLFD JHOJODVV ZHUH UHGXFHG WR VHYHUDO SSE RU HYHQ EHWWHU WKDQ WKDW RI 7\SH ,9 VLOLFD +RZHYHU D VLJQLILFDQW FKORULQH FRQWHQW DW D YDOXH ZWb ZDV SUHVHQW ZKLFK FDXVHG D VHULRXV SUREOHP RI WKH LQFUHDVLQJ RI LQGH[ RI UHIUDFWLRQ DQG IRDPLQJ RI D VLQWHUHG JHOJODVV DERYH r& ,Q DGGLWLRQ FKORULQH WHUPLQDWHV WKH EULGJLQJ R[\JHQ ERQG OLPLWV WKH WKHRUHWLFDO VLOLFD SHUIRUPDQFH DQG FUHDWH D SRVVLEOH RSWLFDO DEVRUSWLRQ FHQWHU IQ KLJK HQHUJ\ HOHFWURPDJQHWLF UDGLDWLRQ ILHOGV HJ [UD\ JDPPD UD\f (OLPLQDWLRQ RI WKH FKORULQH LPSXULW\ LV WKH PRVW LPSRUWDQW VXEMHFW IRU LPSURYHPHQWV LQ VROJHO SURFHVVLQJ LI WKH XOWLPDWH SHUIRUPDQFH LQ VLOLFD JODVV LV UHTXLUHG

PAGE 250

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

PAGE 251

5()(5(1&(6 % -LUJHQVRQV DQG 0 ( 6WUDXPDQLV &ROORLG &KHPLVWU\ 0DFPLOODQ &R 1HZ
PAGE 252

/ / +HQFK 8VH RI 'U\LQJ &RQWURO &KHPLFDO $GGLWLYHV '&&$Vf LQ &RQWUROOLQJ 6RO*HO 3URFHVVLQJ LQ 6FLHQFH RI &HUDPLF &KHPLFDO 3URFHVVLQJ / / +HQFK DQG 5 8OULFK HGV -RKQ :LOH\ t 6RQV ,QF 1HZ
PAGE 253

/ & .OHLQ DQG *DUYH\ 0RQROLWKLF 'ULHG *HOV -RXUQDO RI 1RQ&U\VWDOOLQH 6ROLGV 9RO S 0 'HFRWWLJQLHV 3KDOLSSRX DQG =DU]\FNL 6\QWKHVLV RI *ODVVHV E\ +RW 3UHVVLQJ RI *HOV -RXUQDO RI 0DWHULDOV 6FLHQFH 9RO S 3KDOLSSRX 0 3UDVVDV DQG =DU]\FNL &U\VWDOOL]DWLRQ RI *HOV DQG *ODVVHV 0DGH IURP +RW3UHVVHG *HOV -RXUQDO RI 1RQ&U\VWDOOLQH 6ROLGV 9RO S 5 5R\ *HO 5RXWH WR +RPRJHQHRXV *ODVV 3UHSDUDWLRQ -RXUQDO RI $PHULFDQ &HUDPLF 6RFLHW\ 9RO S % (
PAGE 254

2n ff  3DXO )ORU\ &RQGHQVDWLRQ 3RO\PHUL]DWLRQ DQG &RQVWLWXWLRQ RI &RQGHQVDWLRQ 3RO\PHUV LQ 5 ( %XUN DQG 2OLYHU *UXPPLWW HGV +LJK 0ROHFXODU :HLJKW 2UJDQLF &RPSRXQGV )URQWLHUV LQ &KHPLVWU\ 9RO 9,f ,QWHUVFLHQFH 3XEOLVKHUV 1HZ
PAGE 255

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t 6RQV ,QF 1HZ
PAGE 256

3KDSSRX 7 :RLJQLHU DQG =DU]\FNL %HKDYLRU RI 0RQROLWKLF 6LOLFD $HURJHOV DW 7HPSHUDWXUHV $ERYH r& LQ 8OWUDVWUXFWXUH 3URFHVVLQQ RI &HUDPLFV *ODVVHV DQG &RPSRVLWHV / / +HQFK DQG 5 8OULFK HGV -RKQ :LOH\ t 6RQV ,QF 1HZ @ S *HRUJH + 6LJHO -U ,QWHUDFWLRQ ZLWK (OHFWURPDJQHWLF 5DGLDWLRQ LQ 7UHDWLVH RQ 0DWHULDOV 6FLHQFH DQG 7HFKQRORJ\ 9ROXPH *ODVV 0LNQRUX 7RPR]DZD DQG 5REHUW + 'RUHPXV HGV $FDGHPLF 3UHVV ,QF 1HZ
PAGE 257

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r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
PAGE 258

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
PAGE 259

%,2*5$3+,&$/ 6.(7&+ 6KO+R :DQJ UHFHLYHG D % 6 LQ PLQHUDO DQG SHWUROHXP HQJLQHHULQJ IURP WKH 1DWLRQDO &KHQJ .XQJ 8QLYHUVLW\ 7DLQDQ 7DLZDQ LQ 8SRQ JUDGXDWLRQ KH ZDV UHTXLUHG WR VHUYH WKH QDWLRQ WZR \HDUV E\ ODZ DV D SROLWLFV DQG VFLHQFH LQVWUXFWRU OLHXWHQDQW LQ *XDQWLDUQ 6ROGLHU 7UDLQLQJ &HQWHU $UP\ 7DLQDQ 7DLZDQ $IWHU VHUYLQJ LQ WKH $UP\ KH ZDV ILUVW HPSOR\HG DV HQJLQHHU DQG SURPRWHG WR YLFH PDQDJHU RI WKH (QJLQHHULQJ 'HSDUWPHQW DW -RQJ 0HL 0LQHUDO 3URVSHFWLQJ t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nV HQFRXUDJHPHQW KH SDVVHG WKH GRFWRUDO TXDOLI\LQJ H[DPLQDWLRQ LQ WKH )DOO VHPHVWHU 2QH \HDU ODWHU KH ZDV D FRQVXOWDQW DQG ODWHU FKLHI UHVHDUFK DQG GHYHORSPHQW VFLHQWLVW DW *HO7HFK ,QF $ODFKXD )ORULGD 6LQFH 6HSWHPEHU KH KDV GHYRWHG IXOO WLPH DV D JUDGXDWH DVVRFLDWH WR FRPSOHWLQJ KLV GRFWRUDO GHJUHH LQ PDWHULDOV VFLHQFH DQG HQJLQHHULQJ

PAGE 260

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

PAGE 261

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

PAGE 262

"! ArY


242
Applications are nearly unlimited for use of the silica sol-gel technology developed
herein. The possibility of using the porous gel monoliths for second phase doping was the
third goal pursued. Monolithic partially densified optical silica-gel filters impregnated
with transition-metal ions {Le. Gu+2, Ni+2, and Co+2 ions) were successfully made.
Color changes of these transition-metal ion doped gels that resulted from different
densificaron temperature were interpreted using ligand field and molecular orbital
theories. The third goal in this study was achieved.
The highest quality of pure silica made in the world today is that of optical fibers
fabricated by vapor phase plasma reaction of ultrapure oxygen with ultrapure silicon
tetrachloride (Type IV silica). This process results in fibers of ultralow loss (about 1.0
dB/Km to 5.0 dB/Km) in the 900 nm to 1300 nm range. It is already shown in this
study that the fully dehydrated, completely densified, gel-glass monoliths are of such a
quality as to compare with the best Type IV optical silica fibers. However, the
temperature of densification has been reduced to 1150C. The sol-gel silica process has
the additional advantage that net shape casting of optical components is very simple, also
localized densification can be achieved yielding a new approach for producing waveguides
in a pure silica matrix (i.e., integrated optics)
The vuv cut-off at 162 nm indicates that the gel-glass is not yet an ideal silica
glass. Test data from neutron activation analysis showed that the impurity levels in the
first generation silica gel-glass were reduced to several ppb or even better than that of
Type IV silica. However, a significant chlorine content, at a value 0.1 wt%, was present
which caused a serious problem of the increasing of index of refraction and foaming of a
sintered gel-glass above 1300C. In addition, chlorine terminates the bridging oxygen
bond, limits the theoretical silica performance, and create a possible optical absorption
center fn high energy electromagnetic radiation fields (e.g., x-ray, gamma ray).
Elimination of the chlorine impurity is the most important subject for improvements in
sol-gel processing if the ultimate performance in silica glass is required.


46
silica fibrillar structure
Figure 2-24 Redeposition of monomers from the broken neck area to the area of
negative curvature.


225
reduction (eg, bonding) and an increase (e*g, antibonding) in energy levels. The t2g
(dXy, dyZ, dzx) levels are located between the ligands, and no overlap is observed. As a
result, the energy levels of t2g remain unchanged in the presence of the ligand field as
shown in Figure 6-12(c). The 4s orbital of transition-metal ions has a (aig) spherical
symmetry and a corresponding ligand group orbital that is composed of sigma bonds
which are cylindrical!/ symmetrical about the internuclear axis (Figure 6-13). The 4p
(t-iu bonding and t*-|U antibonding) orbitals with the related ligand group orbitals are
shown in Figure 6-14.
The 12 electrons from the ligand group orbitals are perfectly paired into three
lowest energy molecular orbitals which are aig(1), tiu(3) and eg(2), as shown by the
heavy arrows in Figure 6-12(c). Consequently, the d electrons from the transition-
metal ions have to fill the t2g(3) levels first, if there are any remaining electrons then
the e*g(2) levels available, if the energy gap, A, is greater than kT, low-spin
configurations will be formed. The gap energy A, is generally in the visible range of 1
eV (NIR) to 3 eV (UV) energy. If electromagnetic radiation has the same amount of
energy as the gap energy, i.e. A = hu (photon energy), then the electronic transitions
from t2g(3) to e*g(2) levels takes place.
These theories of ligand field and molecular orbital transitions are the basis for
interpreting the optical spectra of Co2+ ion doped, Ni2+ ion doped and Cu2+ ion doped
silica gels. The possible energy level transitions for the Co2+ ion in both d7 octahedral
and tetrahedral symmetries are analyzed by means of Figures 6-8(a) and (b). The
octahedral Co2+ configuration is predicted to have three spin-allowed transitions:
(1) 4Ti(F) -> 4T2(F),
(2) 4Ti (F) ~> 4Ti (P),
(3) 4T1 (F) ~> 4A2(F).
The tetrahedral Co2+ configuration is expected to have three major transitions:
(1) 4A2(F) ~> 4T2(F),


Relative surface area
15
pH
Figure 2-4 Relative surface area versus solution acidity


218
Table 6-1
Energy levels for transition-metal free ions
Configuration
Example
The lowest energy levels
in a free ion
3d1 3d9
3d1 (Ti3+ ) 3d9(Cu2+ )
2D
3d2 3d8
3d2 (V3+ ) = 3d8 (Ni2+)
3f<1d<3p<1g<1s
3d3 3d7
3d3 (Cr3+, V2+)
= 3d7 (Fe+ Co2+)
4f < 4p < 2g < 2h < 2P
CO
CL
11
CO
Q.
CD
3d4 (Cr2+, Mn3+ }
= 3d6 (Mn+ Fe2+, Co3+ )
5D < 3H < 3P < 3F < 3G < 11
3d5
3d5 (Cr+ Mn2+, Fe3+ )
6S < 4G < 4P < 4D < 2I < 4f


7
Type
Type I & II
Type III
Type IV
Table 1-3
Limits for the four types of silica fabrication processes
Fabrication Limits
(1) Bad homogeneity (granular microstructure and bubbles)
(2) Noticeable water content -- few tens to hundreds ppm.
(3) High impurities in the range of few ppm from nature
quartz mineral.
(4) Micrometer scale structural manipulation quartz is
ground to few micrometers before sintering.
(5) High sintering temperature (above 1700C) -
(a) High energy cost;
(b) React with crucible, thus impurities;
(c) Possible initiate crystallization.
(1) High water content(above 1000 ppm).
(2) High sintering temperature (above 2000C) --
(a) High energy cost;
(b) React with crucible, thus impurities;
(c) Possible initiate crystallization.
(1) Detectable water content (around 1 ppm).
(2) High sintering temperature (above 2000C) --
(a) High energy cost;
(b) React with crucible, thus impurities;
(c) Possible initiate crystallization.


197
Figure 5-16 Strain elimination in a fully dense gel-silica glass


Temperature (C)
56
Time (hr)
Figure 2-29 An example of a silica gel-glass densificaron program.


Absorbance
156
Wavenumbers (cm-1)
Figure 4-18 FTIR absorption curve of fully densified gel-glass.


52
Example one;
Production of dried pure silica gel monolith from oxalic acid DCCA
Step 1: Mixing
Tetramethylorthosilicate (TMOS) is used as a precursor for silica monomers to
form Si-O-Si bonds in the gel structure. The mixing of water with TMOS forms a silica
sol via the following simplified hydrolysis and polymerization reactions:
Si(OCH3)4 + 4 H2O --> Si(OH)4 + 4 CH3OH
-Si-OH + OH-Si > -Si-O-Si- + H2O
The specific standard procedure followed in Step 1 is:
(a) Pour 300 cc of water into a clean 800 cc beaker.
(b) Place the beaker on a hot-stirring plate.
(c) Mix 6 grams of oxalic acid with water using a PTFE coated magnetic bar;
control via the hot-stirring plate.
(d) Stir for 5 minutes to get a homogeneous solution.
(e) Add 150 cc TMOS to the acid solution, while continuing to stir
vigorously for approximately 50 minutes.
(f) Immediately increase the temperature from 25C to 85C by raising the
temperature on the hot-stirring plate to maximum.
(g) If feasible, carefully place ice water in a three-layer polystyrene
thin film on top of the beaker to condense the hot vapor and return
it to its solution.
(h) Continue stirring and heating for approximately 50 minutes before
casting.


43
(a)
P(a¡r) = one atmosphere (1 atm)
(b)
P(air) = one atmosphere (1 atm)
air in
P(air) > PCvapor)
Figure 2-22 Gel cracks inside nonequivalent evaporation containers.


75
Table 3-1
Physical property measurements
TEST SAMPLE SHAPE HEATED TEMP. (C)
Structural information tests:
FTIR
flat piece (smooth surface)
150,
250,
500,
800
UV-VIS-NIR
flat piece {smooth surface)
150,
350,
500,
800
BET
powder (course ground)
200,
450,
750,
830,
860
X-Ray
powder (fine ground)
200,
450,
750,
800,
850
Optical information test:
Index of refraction
polished flat piece
150,
450,
750,
800,
830
Thermal information tests:
DSC
broken piece
150
DTA
broken piece
150
TGA
broken piece
150,
740
TMA
smooth cylinder's ends
150,
540
Mechanical information
tests:
FLEX
rectangular piece
150,
450,
750,
830
COMP
rectangular piece
150,
450,
750,
830
DPN
unpolished gel surface
150,
250,
450,
750,
800,
830
Toughness
unpolished gel surface
150,
250,
450,
750,
800,
830
Density
broken piece
150,
250,
450,
750,
800,
830


65
"i
M1 = M2
m2
stress
flexible gel
structure
Figure 2-36 Fibrillar gel structure is relatively flexible compare to coarse gel structure.


Heat Flow (mW)
99
Figure 3-16 The differential scanning calorimeter (DSC) data of a dried silica gel.


190
transmission at the hydroxyl group absorption peak of 2730 nm, compared to 93%
transmission of gel-silica glass.
Precise refractive index measurements of the silica gel glass and control silica
samples are fisted in Table 5-5 as a function of measuring wavelength. The mean value
and its standard deviation of the index at each wavelength is also shown in Table 5-5. A
summary of the dispersion data is given in Figure 5-13. The size of data points in Figure
5-13 represents the variation of the data in Table 5-5.
The reference index nd and the calculated Abbe constant for each type of silica is
listed in Table 5-6. The variation in refractive index (d-line), from sample to sample
of gel glass, indicates that this characteristic is related to variations in thermal
processing.
A homogeneity test on one gel glass sample, Figure 5-14, shows an approximately
0.863 wave peak to valley (P/V) ratio wavefront distortion in the inner 25 mm area,
which compares to the Corning samples with a 0.529 P/V wavefront distortion (equal to
the power of the polished surface). However, further examination of the gel glass shows
a roll off with 4 to 5 waves P/V significant distortion at the outer 5 mm. No strain was
evidenced on the gel glass edge; therefore, it is clear that the inhomogeneity in the
material and it's edges is strictly due to changes in refractive index within the material.
This variation is quite pronounced and consistent at the ends, but appears to be better in
the middle. The localized variation in refractive index is a result of density gradients
caused by thermal gradients and/or chlorine impurity gradients.
No striae were visible during the striae test, indicating that there are no surface
irregularities, capillaries, or localized structural defects within the glass. This was
true for the six gei glass samples as well as the six control samples.


Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
SOL-GEL DERIVED SILICA OPTICS
By
SHI-HO WANG
April 1988
Chairman: Dr. Larry L. Hench
Major Department: Materials Science and Engineering
Large monolithic xerogel silica glasses were successfully made from tetramethyl-
orthosiiicate and distilled water using the combination of an acidic drying control
chemical additive (DCCA) and a specially designed drying chamber. The acidic DCCA
increases the gel strength by formation of a fibrillar ultrastucture, and the drying
chamber reduces the catastrophic capillary forces inside the wet gel body.
Partially densified monolithic gels up to 850C were routinely made for physical
property tests and compared to commercial fused silicas. Although the mechanical
properties of the porous gel-silica monoliths such as microhardness, Young's modulus,
toughness, flexural strength, density are relatively lower than fused silica, the optically
transparent porous gel silica has a uv cut-off ranging from 250-300 nm. Such a porous
gel with excellent optical transmission and a highly uniform pore radius of 10-50
offers a unique, chemically stable matrix for impregnation with a second phase of
optically active organic or inorganic compounds.
The processing and properties of Types I and II fused quartz optics and Types III and
IV synthetic fused silica optics are compared with the new organometallic sol-gel
VI


CHAPTER 4
DEHYDRATION OF SOL-GEL DERIVED SILICA OPTICS
Introduction
An amorphous silica gel can be characterized by a random packing of Si02
tetrahedra which gives rise to a nonperiodic, solid, fibrillar structure with many voids
and a very large surface area. The surface area ranges from 500 m2/g to 900 m2/g
depending on the low temperature sol-gel processing schedule.
Based on ller's study, silica gel consists of connected spherical particles; the
interior of the particles have a density of 2.2 g/cm3 made entirely of anhydrous -O-Si-
O-Si- bridging bonds. Located on the particle's surface are non-bridging terminal
oxygens, each having an attached hydroxyl ion; these are also referred to as silanol
groups. As a wet silica gel is dried, or partially densified, free water is removed from
the pores; however, the silanoi groups remain intact [78, 79].
Theoretically, for ultrapure silica without silanol groups the energy gap between
the valence and conduction bands is approximately 8.9 eV, as the oxygen ions have very
tightly bound electrons [80]. The high intrinsic absorption edge results from the
excitation of the valence band electrons within the bridging Si-0 network to unoccupied
higher energy states, such as exciton levels or conduction band levels [see p. 161-164
in ref. 26]. To excite these electrons requires ultraviolet photons of at least 140 nm
wavelength (or wavenumber 71428 cm1). Thus, the UV absorption peak for
ultrapure silica should occur at approximately 140 nm and its UV absorption tail, which
is associated with thermally activated phonons [81], becomes negligible in the visible-
infrared portion of the spectrum.
128


49
Table 2-1
Oxalic acid (5.0 grams) as DCCA in 200 cc H2O/IOO cc TMOS
Temperature
200C
450C
750C
800C
830C
Surface area
(m2/g)
651.12
612.10
413.25
385.47
335.40
Total pore volume
(cc/g) 0.36
Average pore radius
0.33
0.22
0.20
0.18
()
11.02
11.03
11.06
11.03
11.05


50
Figure 2-26 Picture of a large scale 160C dried silica gel sample.


79
Figure 3-4 Refraction in the prism of a Pulfrich refractometer.


100
200C range and an exothermic decomposition and/or oxidation of oxalic acid at a
maximum 362.5C in the 200C to 450C range. The DTA data are collected via the same
method as the DSC data, but DTA has an increased testing range to 1200C, as shown in
Figure 3-17. There is significant endothermic desorption of physical water within the
pores. A very large exothermic decomposition and/or oxidation of oxalic acid is also
observed with DTA. No further thermal sorption is observed in the range between 550C
and 1200C. Thus, the dried and desorbed gels are stable from 550C onwards.
A thermogravimetric analyzer (TGA) was also used to analyze the dried gel sample,
as shown in Figure 3-18. In this case, the differential weight loss shows a very high
peak at 124.0C in the 25C to 200C range, indicating the maximum loss of physical
water. There is a significant weight loss of oxalic acid at 361.3C in the 300C to 400C
temperature range; no further weight loss was observed from 450C to 800C. This TGA
observation, together with DSC or DTA data obtained during sintering, clearly indicates
that two phenomena are present; (1) the endothermic water evaporation in the range of
25C to 200C, and (2) the exothermic oxidation of oxalic acid in the 300C to 400C
range.
Figure 3-19 illustrates two TMA curves, one of an unfired standard silica gel
sample and one of a fired (540C) sample; the curve of the unfired sample has a
significant decrease in linear dimension from 200C to 750C. The preheated 540C
sample shows only a slight dimensional decrease (0.056%) when reheated to 540C.
When heated above 540C the dimensions decreases noticeably. These results show that
the structure of the fired sample has already undergone rearrangement and that it is
irreversible.
In a 3-point bending test, a beam loaded has tensile stresses on one surface and
compressive stress on the other, as shown in Figure 3-20. Flexural strength is a
measure of the level of the tensile stress on the surface required to make a material fail.
A partially densified gel is like fully densified glass which shows no plastic deformation


(a) No surface area minimization at the time
of gelation point.
d
0
(b) surface minimzed after aging.
Figure 2-15 Surface minimization in the neck area.


203
consistent with the density data. It is believed that these low microhardness
measurements are also related to the presence of micropores.
A summary of the property data for the commercial dense gel-silica made by a
modification of the process developed in this study is presented in Table 5-10. The gel-
glass is designated as a type V silica for comparing with the other four types of
traditional vitreous silicas.
Conclusions
Data from the characterization tests on the first generation of silica gel-glass
monoliths were compared to commercially available control samples of high quality
fused silica (type III). It was shown that the VUV-UV-VIS-NIR-IR transmission of gel
silica glass is superior to that of fused silica, as observed from its broader transmission
range approaching the theoretical value of ideal silica glass, 150 nm to 4400 nm. Gel-
silica's broad transmission spectra having no absorption peaks is conclusive evidence
that the major impurities, except chlorine, have been successfully reduced to ppb
levels. The variation in index of refraction from sample to sample indicates that the
chemical dehydration process and/or thermal process greatly influence the homogeneity
of the gel-silica optical material, and can thereby be controlled. Recent improvements in
thermal processing have elemininated most of this source of variation, as indicated in
Table 5-10. No stress birefringence or strain was observed, indicating that the samples
were well annealled; also no striae were found.
A significant number of microvoids were observed in the first generation gel silica
glass samples. These inhomogeneities resulted in a somewhat lower apparent density and
lower Knoop hardness value. Also density variations and/or chlorine gradients within
the gel silica glass induced a refractive index gradient, which seriously distorted the
incoming wavefront in the optical homogeneity tests.


110
maximum strain to the point of rupture for the gei samples decrease to approach the
value, 806 x 106 of vitreous silica (Table 3-2, Fig. 3-22). It is concluded that the
gels have higher elastic deformability than fused silica since the fibrillar gel structure
can endure relatively higher dimensional deformation before rupture. Because of the low
densities of the porous gels, the Young's moduli calculated from equation E = amax/£max
are much lower than the 73089 MPa [76] value of fused silica. However, the Young's
modulus increases and approaches the value of fused silica as the densification
temperature increases (Table 3-2, Fig. 3-23). We should also notice that it is very
difficult to achieve a highly polished surface for partially densified gel-glasses.
Consequently, relatively lower values with wider standard deviations are expected.
The test results (Figure 3-24) show that the compressive strength increases
gradually with temperature and reaches a value of 556 MPa at 830C, approximately
half the value of vitreous silica glass (1108 MPa) [76].
The density of the silica gels and gel-glasses are plotted as a function of firing
temperature in Figures 3-25, with density increasing as the densification temperature
increases. Only small changes in density were observed below 500C; however, above
700C the density increased considerably with processing temperature. This indicates
that viscous sintering is initiated above this temperature. The density of the samples
heated to 830C is about 1.80 0.05 g/cm3- approximately 82% the density of fused
silica glass. The temperature required to reach a density equivalent to type l-IV silica is
a function of the ultrastructure of the gel itself, ranging from 830C to 900C,
depending on particle size and the residual water content of the solid.
The results of a diamond point microhardness test for silica gel as a function of
pyrolysis temperatures are given in Table 3-3 and Figure 3-26. For a constant load
(0.05 Kg), the length of the indentation diagonal decreases as the temperature and the
microhardness increases. The 830C gel sample has a microhardness value of 245
Kg/mm2 which is about three times less than the 710 Kg/mm2 value of fused silica. The


62
Figure 2-34 Picture of copper nitrate-doped silica gel which was stabilized at 750C
and redried at 160C.


229
(2) 4A1(F) ~> 4T1(F),
(3) 4A2(F) -> 4T1(P).
The energy level diagram for the Ni2+ ion in d8 tetrahedral and octahedral
symmetries is also depicted in Figures 6-8(a) and (b). The tetrahedral Ni2+
configuration has three spin-allowed transitions:
(1) 3Ti(F) ~> 3T2(f),
(2) 3T) (F) -> 3a2(F),
(3) 3T1(F) -> 3T1(P).
The octahedral Ni2+ symmetry results in three major transitions:
(1) 3a2(F) --> 3t2(F),
(2) 3A1(F) -> 3T1(F),
(3) 3A2(F) -> 3Ti (P).
The Cu2+ ion has a 3d9 configuration, an inverted d1 configuration, as shown in
Figure 6-7. The major transition is attributed to 2E --> 2T2, as is also shown in Figure
6-7(a).
Experimental Procedure
Seven steps are generally used in making the monolithic silica gels and glasses
containing transition-metal elements: (1) mixing, (2) casting, (3) gelation, (4) aging,
(5) drying, (6) impregnation and (7) densificaron described in Example Two in
Chapter 2. in the mixing stage, it is necessary to select a suitable drying control
chemical additives, such as formamide, glycerol, nitric acid, or an organic acid, in order
to make monoliths rapidly without: (1) precipitation, (2) formation of an
inhomogeneous gel, or (3) crystallization. By use of nitric acid in this system it was
possible to produce non-crystalline homogeneous optical silica gels and glasses. To our
knowledge, monolithic geis containing the transition and rare earth elements mentioned
in Chapter 2 have not previously been described.


201
Tabe 5-8
Density measurements of gel-silica and fused silica
Test Sample
Sample No.
Density
ID No. (Specific Gravity, gm/cm3)
Gel Glass Samples, Silica Material:
No.
No.
No.
8
9
10
Control sample, Corning #7940, Fused Silica:
No. 1
Control Sample, NSG ES Fused Silica:
No. 4
Q 34 2.1829
Q 27 2.1835
P 37 2.1844
CGW-1 2.2020
NSG-ES 2.2002
For Reference Only:
Following are the density (specific gravity) characteristics of various materials
based upon published data, grams per cubic centimeter:
1. Fused Silica, Corning #7940: 2.202 (Same as measured)
2. Fused Silica (Synthetic) NSG-ES: 2.201 (> measured value)
3. Fused Quartz (Natural) NSG: 2.203


5
Table 1-2
Identification of transmission curves of silica glasses
Manufacturer
Product name
Type
UV curve
in Fig. 1-1
IR curve
in Fig. 1-1
Amersil, Inc.
Herasil
II
3
B
(Heraeus)
Infrasil
I
2
C
Homosil
II
3
B
Suprasil
III
1
A
Suprasil-W
IV
1
C
Corning Glass
Code 7940
III
1
A
Works
Code 7943
IV
3
C
Dynasil Corp. of
America
Dynasil-1 000
III
1
A
Thermal Syndicate
Spectrosil
III
1
A
Ltd.
Spectrosil WF
IV
1
C
I R-vitreosil
I
3
C


135
Figure 4-4 Reabsorption of physical water below 400C.


172
Figure 5-6 A proposed classical spring model and thermal expansion curves of silica glass


BIOGRAPHICAL SKETCH
Shl-Ho Wang received a B. S. in mineral and petroleum engineering from the
National Cheng Kung University, Tainan, Taiwan, in 1976. Upon graduation, he was
required to serve the nation two years by law as a politics and science instructor
lieutenant in Guantiarn Soldier Training Center, Army, Tainan, Taiwan. After serving in
the Army, he was first employed as engineer and promoted to vice manager of the
Engineering Department at Jong Mei Mineral Prospecting & Foundation Co., Taipei,
Taiwan, in 1978. His duties involved quantitative analysis of mineral components and
sampling design and engineering. Then he accepted a position as assistant engineer at the
Department of Mines, Ministry of Economic Affairs, Taipei, Taiwan, in 1980 where his
duties involved resolving the conflicts between domestic coke manufacturers and
Japanese coke import agents, as well as issuing mining rights.
For seeking a higher education, he was admitted to the Materials Science and
Engineering Department of University of Florida as a graduate student in the spring
semester of 1982. With his advisor Dr. Hench's encouragement, he passed the doctoral
qualifying examination in the Fall semester, 1985. One year later he was a consultant
and later chief research and development scientist at GelTech Inc., Alachua, Florida.
Since September 1987 he has devoted full time as a graduate associate to completing his
doctoral degree in materials science and engineering.
252


experiment.
Several models [see p. 773-777 in ref. 23] have been developed to predict the
Young's modulus of a two phase system, such as a partially sintered gel-glass. The first
is the Voigt model which assumes that the strain in each phase is the same; therefore, the
Young's modulus of this two phase system is expressed as EUpper bound = V2E2 + (1-
V2)E2 where V2 is the volume fraction of the phase with modulus E2 and E1 is the
modulus of the other phase. The second is the Reuss model which assumes that the stress
in each phase is the same; therefore, the modulus of this two phase system can be
expressed as 1/E|0wer bound = V2/E2 (1-V2)/E-|. Z. Hashin and S. Shtrikman have
established upper and lower limits for the moduli which are much narrower than the
Voigt and the Reuss models.
Ultimately, the second phase in a material can be considered as pore spaces that
have zero Young's modulus value. This model was developed at porosities (closed pores)
up to about 50% by J. K. Mackenzie and expressed as E/E0 = (1-1.9P + 0.9P2) where P
is porosity, and E0 is the modulus of the matrix phase. This is a much more reliable
model compared to the first three models in dealing with porous material. Porous gel can
be treated as a two-phase materia! in which the second phase is porosity. Consequently,
it seems reasonable to use this model to predict the Young's modulus of the porous gel.
The Young's modulus of the gels obtained from experiment are compared with the values
from Mackenzie's model as shown in Figure 3-33.
The experimental values of Young's moduli for the gels are generally lower than the
predicted values. The deviations between them at lower densities are larger than that at
higher densities. This may be due to the high surface water content in the lower density
gels which promotes crack propagation [24]. As the gel becomes denser, the number of
pores decreases and the surface water is reduced. Therefore, in the higher density
region, the experimental data become closer to the values the above equation predicts.


93
(see Figure 3-9). At 860C the pore radius suddenly increases from a 1.1 nm open-
pore radius to a 5.4 nm closed-pore radius.
X-ray diffraction patterns from fused silica generally exhibit a broad peak
centered around the second strongest peak in the diffraction pattern of quartz (Figure 3-
12). The partially densified silica gels made in this study have broader diffraction
patterns than that of fused silica, as shown in Figure 3-12. The broadening of the gel
diffraction peak decreases with increasing temperature, indicating an increase in the
ordering inside the gel [74], The BET data in Table 2-1 using Havard, Wilson, ller's
particle size model described in Section II also suggest that the effective particle
diameter of the gels increases with temperature; e.g. 200C (3.6 nm), 750C (6.6
nm), 800C (7.1 nm) and 860C (15.7 nm) [75]. These values can be compared to the
diameter around 100 nm of fully densified silica. These results imply that very short-
range-ordering is taken place inside the structure forming crystallites. The size of a
single silica tetrahedron is about 0.3 nm. Therefore, the structure of the gel crystallites
is composed of only few silica tetrahedra. The gel preheated to 200C is estimated to be
about 8 tetrahedra, at 750C it is about 15 tetrahedra, at 800C it is about 17
tetrahedra, and at 860C the gel has about 35 tetrahedra along the diameter of the gel
fibrillar structure. As a result, x-ray diffraction produces a relatively broader peak
for this relatively short-range-ordering than is observed for fused silica.
This observation led to the suggestion that the silica gei is composed of a randomly
oriented fibrillar structure (random-network model [23]) in which the silica
molecules are relatively ordered crystallites (crystallite model [23]). This
phenomenon is similar to a "mosaic structure" in an imperfect crystal in which the
lattice is broken up into a number of tiny blocks (about 1000 ), each slightly
disoriented one from another [74]. The overall observed gel structure is amorphous.
Based upon the above results, the structure of porous gel in which the
temperature-independent pore diameter is always around 2.2 nm (see Table 2-1) is


168
excited states are found in the energy range of the infrared spectrum, at least for silica
and silicate glasses.
A comprehensive simplified diagram of the molecular vibrational energy levels in
a ground state Morse curve and two excited state Morse curves is shown in Figure 5-4.
This diagram indicates that the iR absorption could possibly result in a series of possible
energy transformations in a silica glass which include resonance, heat dissipation by
internal conversion, fluorescence, heat dissipation by interstate crossing, and
phosphorescence.
Because of the asymmetry in the potential energy curve (Morse curve), the mean
position of the center of mass of the vibrating atoms will be displaced as the amplitude of
vibration increases, as shown in Figures 5-3 and 5-5(a), resulting in thermal
expansion of the material. The thermal expansivity is determined by the asymmetry in
the potential energy curve, and the deeper the minimum the more symmetrical is the
curve near the bottom, as shown in Figure 5-5(b). A strong bonding material has a
deeper valley of higher symmetry which results in a smaller thermal expansion.
D. G. Holloway, in his book The Physical Properties of Glass [see p. 36-41 in ref.
63], states that "silica glass shows an anomalous thermal expansion behavior: the
thermal expansion coefficient (CTE) for this glass is very much lower than for quartz
(80 x 10-7 parallel to axis 134 x 10'7 perpendicular to axis), and it becomes negative
below about -80C. This unusual behavior may be related to the very open structure of
the network, since the density of quartz is 2.66 g/cm3 and silica glass is 2.20 g/cm3,
and the consequent predominance of vibrational modes involving displacements of the
silicon and oxygen ions transverse to the bond direction".
It is reasonable to assume that the large interatomic space in vitreous silica
partially accommodates the dimensional increase with temperature due to stretching
vibrations and this reduces the thermal expansion effect. From the point of view of a
classical spring model, it is relative easier to bend than to stretch a spring.


132
Figure 4-2 Surface silanol groups are reversible in the range of 170C to 400C.


185
thermal expansion measurement. The Orton dilatometer was laboratory calibrated for
accuracy against platinum to help insure precise measurement of thermal length changes
of the get glass sample.
CTE values from 4 K to 473 K were obtained on two gel glass samples with five
control samples by the Optical Science Center, University of Arizona using a low
temperature laser interferometer dilatometer.
Precision apparent density measurements were obtained on three gel glass samples
with two control samples (Corning 7940 and NSG ES fused silicas) by Corning
Engineering Lab Services using a simple deionized water displacement buoyancy method.
Knoop Microhardness values of one gel glass sample and one control sample were
determined by Corning Engineering Lab Services using a 100 gram loaded knoop
hardness tester in accordance with ASTM C-730 testing procedure [110].
Results and Discussions
Transmission data of the six silica gel glass samples are separated into three
sections, according to their wavelength testing ranges, and compared with the traditional
glass control samples. The results shown in Figures 5 10, 11, 12 and Table 5-4. The
gel glass samples demonstrate a uniformly high transmittance in the 200 nm to 2600
nm range. In the vacuum ultraviolet region at 165 nm the gel glass has five times the
transmittance of the Corning 7940 sample and 2.5 times that of the NSG-ES samples.
The flat transmission spectra of the gel glass is evidence that cation impurity
contaminations have been minimized and water has been eliminated. In contrast,
transmission spectra for both control samples show significant water absorption peaks
at the wavelengths of 1370 nm and 2200 nm.
The gel-silica glass also shows substantially greater transmission than the
traditional type III silica glasses when tested in the far IR range from 2500 nm to 5000
nm, as shown in Figure 5-12. Corning 7940 and NSG-ES fused silica samples show 0%


59
l
Figure 2-31 Picture of a 160C dried silica gel.


111
Figure 3-24 Compressive strength versus temperature.


45.
O' )
4 /
Paul J. Flory, Condensation Polymerization and Constitution of Condensation
Polymers, in R. E. Burk and Oliver Grummitt, eds., High Molecular Weight
Organic Compounds (Frontiers in Chemistry, Vol. VI), Interscience Publishers,
New York, 1949, p. 211-283.
46. Paul J. Flory, Fundamental Principies of Condensation Polymerization, Chemical
Reviews, Vol. 39, 1946, p. 137-197.
47. Ralph K. Her, Inorganic Colloids for Forming Ultrastructures, in Science of
Ceramic Chemical Processing. L. L. Hench and D. R. Ulrich, eds., John Wiley &
Sons, fnc.t New York, 1986, p. 3-20.
48. J. Zarzycki, Monolithic Xero- and Aerogels for Gel-G!ass Processes, in
Ultrastructure Processing of Ceramics. Glasses and Composites. L. L. Hench and
D. R. Ulrich, eds., John Wiley & Sons, Inc., New York, 1984, p. 27- 42.
49. David R. Gaskell, Introduction to Metallurgical Thermodynamics. 2nd ed.
McGraw-Hill Book Co., New York, 1981.
50. J. F. Goodman and S. J. Gregg, The Production of Active Solids by Thermal
Decomposition, Part X: Heat Treatment of the Xerogels of Silica, Journal of
the Chemical Society, Vol. 1, 1959, p. 694-698.
51. S. Sakka and K. Kamiya, The Sol-Gel Transition in the Hydrolysis of Metal
Alkoxides in Relation to the Formation of Glass Fibers and Films, Journal of Non-
Crystaiiine Solids, Vol. 48, 1982, p. 31-46.
52. B. E. Yoldas, Effect of Molecular Separation on the Hydrolytic Polycondensation of
Si(OC2H5)4_ Journal of Non-Crystalline Solids, Vol. 82, 1986, p. 11-23.
53. Michel Prassas and L. L. Hench, Physical Chemical Factors in Sol-Gel
Processing, In Ultrastructure Processing of Ceramics. Glasses and Composites. L.
L. Hench and D. R. Ulrich, eds., John Wiley & Sons, Inc., New York, 1984, p.
100-125.
54. T. Kawaguchi, H. Hishikura, J. lura, and Y. Kokubu, Monolithic Dried Gels and
Silica Glass Prepared by the Sol-Gel Process, Journal of Non-Crystalline Solids,
Vol. 63, 1984, p. 61-69.
55. S. P. Mukherjee, Sol-Gel Processes in Glass Science and Technology, Journal of
Non-Crystalline Solids, Vol. 42, 1980, p. 477-488.
56. Iwao Matsuyama, Kenzo Susa, and Tsuneo Suganuma, Syntheses of High-Purity
Silica Glass by the Sol-Gei Method, American Ceramic Society Bulletin, Vol. 63,
No. 11, 1984, p. 1408-1411.
C. J. Brinker, E. P. Roth, D. R. Tallant, and G. W. Scherer, Relationships Between
Sol to Gel to Glass Conversions: Structure of Gels During Densificaron, in Science
of Ceramic Chemical Processing. L. L. Hench and D. R. Ulrich, eds., John Wiley &
Sons, Inc., New York, 1986, p. 37-51.
57.


149
Table 4-1
Absorption peaks of the pore water and the surface hydroxyl groups of gel-silica
monoliths
Wavelength
{rtm}
Identification
observation command
2919.70
*****1)4
a broad peak on a broad band
2816.88
****D3
a tiny peak on a broad band
2732.24
* * D 2
a joint of two small peaks at
2768.90 nm and 2698.90 nm
2668.80
**D1
a very sharp symmetric peak
2262.48
U3 + *1)0 H
a broad band, no peak
2207.51
1)2 + i)OH
a high broad asymmetric peak
1890.35
D3 + 2doH
a high broad asymmetric peak
1459.85
2i)4
a tiny peak on a broad band
1408.44
2d3
a small peak on a broad band
1366.12
2i>2
a very sharp symmetric peak
1237.85
{[2d3 + doh] +
[2i)2 + doh]}/2
a small peak
1131.21
2i)3 + 2uoh
a tiny peak
938.95
3i>3
a small peak
843.88
3d3 + UOH
no peak observed
704.22
41>3
a tiny peak
*dqh : an out of plane bending vibration of Si-O-H bond.
**ui : stretching vibration of an isolated Si-O-H bond.
*** x>2 : stretching vibration of an adjacent Si-O-H bond.
****i>3 : stretching vibration of a Si-O-H bond which is hydrogen-bonded to water.
***1)4 : stretching vibration of absorbed water.


20
monomers expose their positively charged
electric cloud toward particle surface.
electrical double layer
Figure 2-5 Particles in strong acidic solution. pH

83
vibration is observed at 1120 cnr1 (8928.6 nm), even in the low temperature sample.
The peak at 1250 cm'1 (8000 nm) is an artifact of the diffuse reflection stage. The
primary difference between these curves is that peaks corresponding to organic
residuals in the range between 1400cm'1 (7142.9 nm) and 2600 cm'1 (3846.2 nm)
are absent in the high temperature sample. The spectrum of the 800C silica sample is
nearly the same as that for fused silica, with the exception of a small shift in the
absorption edge near 1400 cm"1 (7142.9 nrn) to lower wavenumbers.
The temperature-dependent changes in intensity of the characteristic absorption
band at 950 cm-1 (10526.3 nm) have been attributed to the stretching vibration of the
Si-O-H nonbridging oxygen (NBO) groups. With increasing temperatures, the
concentration of silanol groups is decreased to a nondetectable level and the
characteristic 950 cm'1 (10526.3 nm) peak disappears. The extent of hydroxyl
absorption bands at 3500 cm'1 (2857.1 nm) to 4000 cm'1 (2500 nm) is also
diminished for the higher temperature samples. This does not mean that the gel is
completely free (zero ppm) from all types of water, but rather that the FTIR technique
is not sensitive enough in this region (950 cm'1) to detect the residual hydroxyl bonds
to fully understand and monitor the water associated with gel structure. Overtone and
combination frequencies should be investigated [71].
These results show that the only significant "impurity" in the ultrapure silica gel
is water. The amount of water determines the extent of non-bridging oxygen (NBO)
content, which prevents complete densification. Water content can also be observed
easily using a UV-VIS-NIR spectrophotometer. Figure 3-6 shows the intensity of free
water peaks at 1363.3 nm, 1891.1 nm, and 2212.4 nm decreasing with increasing
processing temperature. It indicates that the densification is due to the combination of
silanol groups on the surface of particles which form free water and escape;
consequently, the surface chemical water is reduced and the absorption peaks are
diminished.


63
Figure 2-35 Picture of neodymium nitrate-doped and erbium nitrate-doped silica gels
which were stabilized at 750C and redried at 160C.


35
mechanism is initiated by thermal energy. Therefore, the higher the aging temperature,
the faster is the rate of matter migration to vacancies and the more rapid is gel
shrinkage, as shown in Figure 2-17. About the same maximum shrinkage (=28%) is
associated with each aging temperature. It is possible that the same amount of vacancies
are quickly created inside the necks between particles during the first stage, mechanism
No.1, for all identical gels. Subsequently, all of these vacancies are annealed out of the
gel body in the second stage, mechanism No. 2, and then equal shrinkage is obtained. The
same maximum shrinkage in the aging stage is probably predetermined by the
processing characteristics of each gel (e.g. pH, water, DCCA, TMOS ratio). The gel
shrinkage kinetics can also be monitored by the time at which 28% maximum gel
shrinkage is observed at each temperature, as shown in Figure 2-18. Shrinkage
improves gel strength; therefore, a relatively hard and dense gel can be obtained as a
result of optimizing the aging process. Figure 2-19 shows the increase in gel
microhardness with percentage of shrinkage. It is this increase in mechanical strength
with aging that makes it possible to obtain dried monolithic xerogels.
Drying Modeling
Control of drying is critical; without a full understanding of the gel's drying
mechanism and the development of a suitable method to deal with it achieving a dried
xerogel without cracking is very difficult. Drying control involves both chemical and
physical aspects. Chemically, the use of an acidic DCCA in the soi minimizes the particle
size which results in an increased gel strength and a more homogeneous particle-size
distribution, thereby diminishing uneven pore stresses. Physically, the use of a drying
control chamber decreases the effect of differential pressures on the gel body which
could lead to stress fracturing.


189
Table 5-4
Vacuum ultraviolet transmission data
Sample
ID No.
165 nm
Transmission (%) at Wavelength of
170 nm 176 nm 180 nm 190 nm 200 nm
Gel glass test samples 3 mm thick:
Q 27
N 34
P 37
13.9
65.0
80.0
83.0
84.5
85.5
14.0
63.0
78.0
80.5
82.5
83.5
15 .0
64.0
78.5
80.5
83.0
84.0
Corning # 7940 Control Sample, 2 mm thick:
CGW-2(a) 08.0 60.0 76.0 83.0 88.0 91.0
Corning # 7940 Control Sample, Converted to 3 mm thickness:
CGW-2 (a) 03.0 47.0 67.0 77.0 82.5 87.0
From reference, reflection loss per single surface:
R Loss (b) 05.7 05.5 05.3 05.1 04.9 04.7
Notes:
a) As noted, the Corning #7940 sample measured was 2 mm thick compared to
the 3 mm thick gel-glass test samples. This data was converted to 3 mm thickness
for comparison.
b) Reflection losses shown are based on published data for fused silica available
from Glass Fab, Snc.. and is presented for reference only.


166
Figure 5-2 The energy curves of the antibonding and bonding molecular orbitals.


194
Figure 5-14 Homogeneity tests of silica gel glass sample and Corning #7940 control
sample by Zygo Zapp Interferometer.
3000 PTS


3
Table 1-1
Preparation and characteristics of four types of vitreous silica
Type
I
II
III
IV
Process
Electromelted
Flame-fused
Hydrolyzed
Oxidized
Quartz
Quartz
SiCI4
SiCI4
Example
IR-Vitreosila
Herasilb
7940c
Spectrosil WFa
Impurity
Infrasilb
(ppm):
Homosilb
Dynasild
Spectrosila
Suprasilb
7943c
Suprasil-Wb
OH
<5
400-1500
-1000
~0(<0.4)
A!
30-100
<1
<0.2
<0.2
Sb
<0.3
<0.1
<0.1
<0.1
As
0
0
<0.02
<0.02
B
4
3
0.1
0.1
Ca
16
0.4
<0.1
<0.1
Cl
0
0
100
up to 200
Cr
0.1
0
0.03
0.03
Co
0
0
0.0001
0.0001
Cu
1
1
<1
<1
Ga
0
0
<0.02
<0.02
Au
0
0
<0.1
<0.1
Fe
7
1.5
<0.2
<0.2
Li
7
1
0
0
Mg
4
0
0
0
Mn
1
0.2
<0.02
<0.02
Hg
0
0
<0.1
<0.1
P
0.01
0.005
<0.001
<0.001
K
6
<1
0.1
0.1
Na
9
5
<0.1
<0.1
Ti
3
2
0
0
U
0
0.0006
0
0
Zn
0
0
<0.1
<0.1
Zr
3
0
0
0
a: Thermal Syndicate, England. b: Heraus Amersil, Heraeus, Sayreville, NJ.
c: Corning Glass Work, Corning, NY. d: Dynasil; Berlin, NJ.


Intensity
94
2 e
Figure 3-12 X-ray patterns of silica gels at different temperatures
compare to that of fused silica.


240
The first major difficulty faced in producing large monolithic gel glass for optical
components was cracking during drying. In this study the problem was overcome by use
of drying control chemical additives (DCCA) and a special designed drying chamber
described in Chapter 2.
A fibrillar structure of a silica gel can be formed in the initial preparation of
silicic solution. Once the ratio of silica precursor, water and DCCA is fixed the fibrillar
structure of the gel is determined. Further evolution of the structure is a function of
time and temperature. A relatively strong gel was made using an acidic DCCA which
enabled the gel to endure the catastrophic capillary forces developed inside the gel during
drying. In addition, the introduction of special drying chamber for ambient atmosphere
control also reduced the capillary stress significantly. Monolithic dried (physical water
free) gels as large as 10 cm x 8 cm x 2.0 cm (up to the capability of the experimental
facility) were routinely produced. The first goal was achieved.
The dried gel monoliths were partially densified in an ambient air furnace up to
860C. The characterization of these partially densified silica gels was performed by use
of (1) structural information tests (x-ray diffraction, BET), (2) Optical information
tests (refractive index, FTIR, UV-VIS-NIR), (3) thermal information tests (DSC, DTA,
TGA, TMA), (4) mechanical information tests (flexural strength, compressive strength,
microhardness, toughness, density).
The results of structural information tests showed that the gels were an amorphous
phase with high a volume, and tremendous surface area of uniform open pores
throughout the entire body with chemisorbed hydroxyl groups being a function of
temperature.
The conclusion of optical information test proves that the index of refraction is a
function of sintering temperature and the index has a linear relationship with density as
predicted by the Lorentz-Lorenz equation. The -OH absorption bands and UV cut-off is
also a function of sintering temperature.


CHAPTER 3
PHYSICAL PROPERTIES OF PARTIALLY DENSIFIED SILICA XEROGELS
Introduction
Monolithic, noncrystalline, dried xerogels of pure silica, hereafter simply called
gels, have been made by the procedure stated in Example #1 of Chapter 2. These samples
are heated to 150C (the temperature at which the gels are free from physical water) to
become standard dried gels.
The physical properties of the fully dried gel are a function of the internal
structure which depends on the various chemical and physical conditions during every
step of processing (i.e., the relative amounts of water/DCCA/TMOS, temperature,
pressure, and time for aging and drying).
At sufficiently high temperatures thermal energy provides the driving force for
ultrastructural rearrangement which decreases surface area and thereby minimizes
surface tension inside the gel structure. This is the primary mechanism for
densification [see p. 469-490 in ref. 23].
A large reduction in pore volume is accompanied by the decomposition of residual
organic compounds into carbon dioxide (between 250 and 450C) and also by the
combining of surface hydroxyl groups resulting in some degree of dehydration. Both of
these phenomena may cause thermally induced stress fracturing in the densification
stage. However, by controlling the rates of these reactions silica gel monoliths that are
crack-free, partially densified and shrunk, can be successfully made at various
temperatures, ranging from 200C to 850C.
This chapter presents a study of the physical properties of partially dense silica-
gel monoliths. Data were obtained from numerous measurements including structural,
optical, thermal, and mechanical testing. Structural information was provided by
67


55
Step 6: Densificaron
The ultraporous dried silica gels are converted to partially dense monoliths by
heating from 150C up to 900C over a period of 3 to 6 days; samples are taken out of
the furnace at the end of the heating program. An example is shown in Figure 2-29.
Example two;
Production of dried transition and rare earth element doped silica gels from nitric acid
DCCA.
Step 1: Mixing
(a) Add 60 cc (1N) HNO3 (nitric acid) to 340 cc of distilled water at room
'i
temperature and mix for 5 minutes with a magnetic stirrer.
(b) Add 200 cc TMOS to the nitric acid water solution while continuing to mix
vigorously, increasing the solution temperature to 85C for no more than 60 minutes.
Step 2: Casting
The intimately mixed sol (60 cc) is cast from its heated vessel into a polystyrene
mold (20 mm H x 100 mm D) at room temperature. The length of time for casting
should be no more than 110 minutes since gelation will take place during prolonged
casting operation.
Step 3: Gelation
Gelation occurs in the mold at 55C in 115 minutes with the resulting solid object
taking the shape and surface finish of the mold.


2
Fused quartz is melted at temperatures above its liquidus (1713C) from crushed
natural crystalline quartz powders of mixed particle size, well above micrometers in
diameter [8J. The initial size of these particles, millions of times larger than a silica
molecule, limits the control over the resulting structure and in part determines the
temperature necessary for melting, homogenization, and fabrication. Glass products
from this method have numerous deficiencies; impurities, inhomogeneities, seeds and
bubbles, a high energy requirement for raw material crushing, melting and
homogenization, as well as premature phase separation and crystallization.
Chemical reactions used to produce synthetic fused silica by flame hydrolysis of
silica tetrachloride (type III) and by vacuum plasma oxidation of silica tetrachloride
(type IV) are shown in equations #1 and #2:
Type III (hydrolysis)
SiCU + O2 + 2 H2 -> Si02 + 4 HCI (1)
Type IV (oxidation)
SCI4 + O2 > S2 + 2 CI2 (2)
In fact, it is very difficult to have a complete reaction for either of these two
equations. Consequently, water contents of several thousand ppm are present in type III
silicas, and SCI4 in few hundred ppm is retained as an unreacted residual in both type
III and IV silicas. In addition to these two intrinsic impurities, the resultant glasses
from type III and IV processes have extrinsic impurities in the range of few parts per
million (ppm) due to the contamination of raw materials and crucibles at high
temperatures (about 1900C).
Table 1-1 |9] lists the dominant characteristics of commercial brands of silica
corresponding to these four types. Their transmission curves are summarized in Figure
1-1 and Table 1-2 [10]. Type I and II glasses have more impurities (Table 1-1) which
make uv transmission curves cut off at higher wavelengths (curves 2 and 3 in Fig. 1-1)
than that of type III and IV glasses (curve 1 in Fig. 1-1). The amount of water (Table 1-


14
f
O
¡
H O ~Si
I
OH
", ¥
O O
i I
H OSi OSi OH
8
i
o
i
H
monomer
O
l
H
dimer
H
I
O
H
i
H O Si O S¡ O H
9 9
H O-Si OSi OH
I
O
I
H
I
O
cyclic tetramer
particie size particle size
smaller than 50 larger than 50
Figure 2-1 Particle growth in solution


1200
1100
1000
900
800
700
119
Density (g/cc)
Figure 3-28 Maximum strength to failure versus density.


REFERENCES
1. B. Jirgensons and M. E. Straumanis, Colloid Chemistry. Macmillan Co., New
York, 1962.
2. Ralph K. Her, The Colloid Chemistry of Silica and Silicates. Cornell University
Press, Ithaca, New York, 1955.
3. P. J. Flory, Gels. A Introduction Lecture, Faraday Discussions of the Chemical
Society, Vol. 57, 1974, p. 7-18.
4. Ralph K. Her, The Chemistry of Silica. John Wiley & Sons, Inc., New York,
1979.
5. R. H. Doremus, Chemical Durability of Glass, in Treatise on Materials Science
and Technology Volume 17, Glass II. Miknoru Tomozawa and Robert H. Doremus,
eds., Academic Press, Inc., New York, 1979, p. 41-69.
6. C. J. Brinker, K. D. Keefer, D. W. Schaefer and C. S. Ashley, Sol-Gel Transition in
Simple Silicate, Journal of Non-Crystalline Solids, Vol. 48, 1982, p. 47-64.
7. L. C. Klein, Sol-Gel Glass Technology. A Review, Glass Ind., 1981, p. 14-16.
8. J. D. Mackenzie, Fusion of Quartz and Cristobaiite, Journal of the American
Ceramic Society, Vol. 43, 1960, p. 615-620.
9. Martin Grayson, ed., Encyclopedia of Glass, Ceramics, and Cement. John Wiley
& Sons, Inc., New York, 1985, p. 837-845.
10. N. J. Kreidl, Inorganic Glass-Forming Systems, Part I: Vitreous Silica, in Glass;
Science and Technology Vol. 1; Glass-Forming Systems. Academic Press, Inc.,
New York, 1983, p.107-121.
11. J. D. Mackenzie, Glasses from Melts and Glasses from Gels, A Comparsion,
Journal of Non-Crystalline Solids, Vol. 48, 1982, p. 1-10.
12. L. L Hench, Concepts of Ultrastructure Processing, in Ultrastructure Processing
of Ceramics. Glasses and Composites. L. L. Hench and D. R. Ulrich, eds., John
Wiley & Sons, Inc., New York, 1984, p. 3-5.
13. Sumi Sakka, Gel Method for Making Glass, in Treatise on Materials Science and
Technology Volume 22. Glass III. Miknoru Tomozawa and Robert H. Doremus,
eds., Academic Press, Inc., New York, 1982, p. 129-169.
14. !. Artaki, M. Bradley, T. Zerda, Jiri Jonas, G. Orcel, and L. L. Hench, NMR,
Raman Study of the Effect of Formamide on the Sol-Gel Process, in Science of
Ceramic Chemical Processing. L. L. Hench and D. R. Ulrich, eds. John Wiley &
Sons, Inc., New York, 1986, pp. 73-80.
244


238
Conclusions
Thermal history can alter the chemical environment and ligand-field around a
transition metal ion in a silica gel and have a marked effect on its optical absorption
characteristics and hence on the color produced. These results show that it is possible to
take advantage of low temperature sol-gel-glass techniques to manufacture various
optical filters using a silica matrix. The absorption spectra can be shifted by controlling
the thermal history of silica gels containing transition elements. The optical components
produced will have the unique physical properties of silica as discussed in previous
chapters, that is, low thermal expansion coefficients, extraordinarily high chemical
durability, and superb thermal shock resistance. In addition, depending upon the extent
of densification reached during thermal processing the density and index of refraction of
the optical component can be varied over wide ranges. The flexibility of the sol-gel
technique offers such new exciting processing methods in the production of a variety of
optical components. The silica gel glasses chemically doped with transition-metal ions
(Co, Ni, Cu ions) discussed in this chapter have demonstrated the possibilities of
producing a variety of products including strategic high-tech optical glasses with
specific wavelength filtration capabilities, high-tech commercial sun glasses, and
tuneable laser glasses.


73
Thermomechanical analysis (TMA) measures the thermal expansion coefficient,
glass transition temperature, softening temperature and provides data for gel shrinkage
analysis [62].
Flexural (FLEX) and compressive (COMP) tests are performed to determine the
material's strength under external mechanical loads.
A Vickers microhardness test, which yields a value for the diamond pyramid
microhardness number (DPN), is used to measure the mechanical resistance of a gel and
gel-glass to diamond pyramid plastic indentation in a microscopic area of the surface
[63]. The fracture toughness is obtained directiy from the crack length which extends
outside the diagonal of diamond pyramid indentation during the Vickers microhardness
measurement [64].
Bulk density measurements are used to monitor the change in gel structure during
sintering; it also gives useful information for interpreting variations in refractive
index.
Experimental Procedure
Samples, fabricated by the procedure stated in Example #1 of Chapter 2, were
heated to various programmed temperatures in an ambient air furnace, as shown in
Figure 3-3. The following tests, listed in Table 3-1, were performed on these samples.
The infrared spectra were recorded on a Nicolet MX-1 FTIR spectrometer
equipped with a diffusion reflection stage and a microcomputer for data storage. The
diffusion reflection stage in which the infrared passes into the bulk (about 0.5 mm deep
and 20 mm2 area) of the gel, undergoes reflection, refraction, scattering and absorption
in varying degrees before reluming back at the sample surface. The radiation reflected
out from the gel is distributed in all directions of the surrounding hemisphere and
corrected to form spectra by a highly reflective semispherical mirror. Chemical species
and bonding information can be interpreted in terms of the position and intensity of IR


207
earth element; thus the electron transitions taking place in inner f orbitals have less
ligand field effects. The resulting absorption peaks are much sharper and comparable to
that of a free ion.
Color formation in glass arises from excitation of unpaired electrons in the d or f
orbitals of the transition-metal ion or the rare earth element incorporated within the
glass networks. Colors of transition-metal ion doped materials are particularly subject
to change by the variation of the coordination numbers and the splitting of the outer five
d energy levels associated with the chemical bonding of the adjacent ions. Therefore the
colors in such materials are described as resulting from specific chromophores, which
are complex ions that produce a particular optical absorption effect [112]. In contrast,
rare earth colorants depending on electron transitions in the inner f shell are much less
subject to the local chemical environment of the coloring element; therefore, the change
in color with local chemical bonding is minima! [113].
in this chapter are discussed the variations in colors and spectral absorption due
to excitation of electrons in the silica gels and gel-glasses containing transition-metal
ions. The optical properties are interpreted using the ligand field theory of
chromophores. The theories of ligand field and molecular orbital transitions in d-shell
colorants are reviewed and applied to the optical spectra of the chemically doped gel
glasses. The transition metal elements investigated are Co, Cu, and Ni ion-doped silica
gels and gel-glasses. The effects of thermal history are also studied. The results are
compared with the spectra of the same elements in melt derived silicate and phosphate
glasses.
Review of Literature
Pure silica gel-glass has a very wide optical transmission range from the
vacuum ultraviolet, 163 nm (7.60 eV, 61347 cm'1) to the infrared, 4400 nm (0.28
eV, 2272 cm'1) as described in previous chapters. The silica O-Si-O bonding electrons


69
(FTIR) can provide vibrational information on changes occurring in the gel structure
during sintering [58].
Water terminates the bridging silicon-oxygen-silicon bonds on the particle's
surface inside the porous gel, as shown in Figures 3-1 and 3-2. Waters disruption of
the Si-O-Si bridging bond is similar to that of sodium ions within a dense soda silicate
glass. This gives rise to absorption in the ultraviolet (UV) region of the optical
spectrum. The UV-VIS-NIR spectra technique is an easier and more sensitive tool than
the infrared method for understanding the evolution of bonding and identifying the
species inside the gel structure in the densification process [59].
The measured surface area, obtained from BET analysis, of a standard dried gel is
about 750 m2/g at 200C. The particle size is calculated from Havard, Wilson's model
[60] where the diameter is equal to a constant (2750) divided by the surface area. The
particle diameter for a gel made by Example #1 in Chapter 2 is 3.6 nm at 200C. The
measured surface area is somewhat less than actual since nitrogen molecules, used in the
BET analysis, cannot completely penetrate the negative curvature area between all the
connected particles. However, the BET surface area measurement also includes the
surface hydroxyl groups which increases the particles' measured surface area value;
this increase is less significant than the decrease resulting from incomplete nitrogen
penetration.
Silica gel is essentially a special form of porous glass. Previous x-ray diffraction
studies by Mozzi, Warren, Uhlmann and Wicks [22, 23] have established in detail the
tetrahedral bonding arrangements in vitreous silica. The maximum in the distribution of
Si-O-Si angles in amorphous silica is at 144, with most angles being within 10% of
this maximum. There is no evidence for a preference in fused silica for edge-to-face
sharing of tetrahedra, which is often found in crystalline silicates. X-ray diffraction
patterns generally exhibit a relatively broad peak for gels indicating the absence of
atomic periodicity or long-range structural ordering compare to that of quartz.


34
(a)at the time of gelation point (t =0)
y
(b)the first mechanism: formation of
vacancies in the necks of chain, the total
length d0 does not change
(c)the second mechanism: migration of vacanices
from neck area out of gel body, the total length d0
shrinks.
(d)silanol groups depart from the positive
curvature area of particle's surface (the third
mechanism) and deposit on the negative curvature
area (the fourth mechanism).
v monomers
deposit
Figure 2-16 Surface minimization during aging.