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Assembly of Spherical, Sub-Micron Stöber Silica Spheres into Hexagonal Arrays in Ethoxylated Trimethylolpropane Triacrylate

Permanent Link: http://ufdc.ufl.edu/UFE0044002/00001

Material Information

Title: Assembly of Spherical, Sub-Micron Stöber Silica Spheres into Hexagonal Arrays in Ethoxylated Trimethylolpropane Triacrylate
Physical Description: 1 online resource (165 p.)
Language: english
Creator: Brubaker, Gill D
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2012

Subjects

Subjects / Keywords: colloids -- photonic-crystals -- self-assembled
Physics -- Dissertations, Academic -- UF
Genre: Physics thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: This dissertation will examine and explain the hexagonal ordering of spin coated Stöber silica particles in ethoxylated trimethylolpropane triacrylate (ETPTA) monomer. It will document the fact that these arrays are formed primarily by settling and self ordering to minimize their gravitational energy, constrained by monomer mediated interparticle repulsion. It will use the fact that these arrays partially self assemble to explain the ordering produced by spin coating of the Stöber silica-triacrylate suspensions. The final ordering produces vertically compact, horizontally non-close packed, simple hexagonal arrays of silica particles, in a polymer produced by ultraviolet light initiated, free radical polymerization of the ETPTA triacrylate monomer.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Gill D Brubaker.
Thesis: Thesis (Ph.D.)--University of Florida, 2012.
Local: Adviser: Tanner, David B.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2012
System ID: UFE0044002:00001

Permanent Link: http://ufdc.ufl.edu/UFE0044002/00001

Material Information

Title: Assembly of Spherical, Sub-Micron Stöber Silica Spheres into Hexagonal Arrays in Ethoxylated Trimethylolpropane Triacrylate
Physical Description: 1 online resource (165 p.)
Language: english
Creator: Brubaker, Gill D
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2012

Subjects

Subjects / Keywords: colloids -- photonic-crystals -- self-assembled
Physics -- Dissertations, Academic -- UF
Genre: Physics thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: This dissertation will examine and explain the hexagonal ordering of spin coated Stöber silica particles in ethoxylated trimethylolpropane triacrylate (ETPTA) monomer. It will document the fact that these arrays are formed primarily by settling and self ordering to minimize their gravitational energy, constrained by monomer mediated interparticle repulsion. It will use the fact that these arrays partially self assemble to explain the ordering produced by spin coating of the Stöber silica-triacrylate suspensions. The final ordering produces vertically compact, horizontally non-close packed, simple hexagonal arrays of silica particles, in a polymer produced by ultraviolet light initiated, free radical polymerization of the ETPTA triacrylate monomer.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Gill D Brubaker.
Thesis: Thesis (Ph.D.)--University of Florida, 2012.
Local: Adviser: Tanner, David B.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2012
System ID: UFE0044002:00001


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1 ASSEMBL Y OF SPHERICAL, SUBMICRON STBER SILICA SPHERES INTO HEXAGONAL ARRAYS IN ETHOXYLATED TRIMETHYLOLPROPANE TRIACRYLATE By GILL BRUBAKER 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 2012

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2 2012 Gill Brubaker

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3 To my mother for her support of her unemployed son, while he indulged his obsession to discover the mathematical re presentation of the dynamical structure of the universe

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4 ACKNOWLEDGMENTS I acknowledge the support of my mother who allowed me to stay home and study physics. I owe a debt of gratitude to Prof. Brian Scarlet t without whose help I would probably not have been admitted to the Ph.D. program. He was instrumental in forming my Ph.D. committee and was generally supportive of his students; we all miss him greatly Without help from Nic h olas Li nn I would have had to learn wafer fabrication techniques on my own. His experience, questions, observations and notes on the spin coating process were invaluable in starting my own wheels spinning. I appreciate the support of my committee chair, Prof. Tanner, without whose indulgence I would have no committee. I thank P rof. Jiang for allowing me to work on this project. Without Prof. Jiangs permission, I would not have a project to work on. I thank the rest of my committee for staying with me though the last five years; I need everyones support to continue in the Ph.D. program. I thank all those persons I work with for constantly telling me to write your dissertation. The constant nagging may be the most valuable of all, as I am forced to submit to peer pressure and would hate to let everyone down. Paul Carpinone has provided valuable discussion on surface modification involving hydrogen bonding and order formation. I am thankful for a warm winter, as I have no heat in my squalid trailer and it is hard to write when the temperature is in the teens, twenties, and thirti es; little hard in the forties as well. Im grateful that my supervisors at work who have allowed me to attend classes and such. Finally I am thankful to live in a civilization growing in science, technology, and decency It has allowed me to exist in an environment conducive to intellectual growth; for this, I am truly grateful

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5 TABLE OF CONTENTS page ACKNOWLEDGMENTS .................................................................................................. 4 LIST OF TABLES ............................................................................................................ 7 LIST OF FIGURES .......................................................................................................... 8 LIST OF ABBREVIATIONS ........................................................................................... 12 ABSTRACT ................................................................................................................... 15 CHAPTER 1 INTRODUCTION .................................................................................................... 16 Motivation to Study Colloidal Arrays ....................................................................... 16 Spin Coated Arrays of Na noparticles ...................................................................... 16 Objectives of This Study ......................................................................................... 23 2 MATERIALS AND SAMPLE PREPARATION ......................................................... 25 Overview of the Components of the St ber Triacrylate System ............................. 25 St ber Silica Particles ............................................................................................. 25 Ethoxylated Trimethyl olpropane Triacrylate ............................................................ 35 Overview of Wafer Preparation for Spin Coating .................................................... 41 Preparing Samples to Characterize Initial Conditions ............................................. 42 3 CHARACTERIZATION ........................................................................................... 45 Instruments and Measurements ............................................................................. 45 SEM .................................................................................................................. 45 Video ................................................................................................................ 45 Electrophoretic Mobility .................................................................................... 45 Density ............................................................................................................. 46 FTIR ................................................................................................................. 46 Results .................................................................................................................... 46 SEM .................................................................................................................. 46 Video ................................................................................................................ 63 Electrophoretic Mobility .................................................................................... 69 Density ............................................................................................................. 69 FTIR ................................................................................................................. 69 Discussion .............................................................................................................. 70 4 ANALYSIS OF ARRAY ORDER ............................................................................. 74

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6 Introduct ory Remark s.............................................................................................. 74 Particle Size Distributions ................................................................................. 74 Interparticle Spacing Analysis .......................................................................... 74 Translational and Rotational Order Analysis .................................................... 74 Particle Size, Interparticle Spacing, and Order Analysis ......................................... 80 Figure 31 and Figure 33 Ideal Array Order Analysis ...................................... 80 Figure 31 ......................................................................................................... 89 Figure 33 ......................................................................................................... 98 Figure 36 ....................................................................................................... 108 Figure 317 ..................................................................................................... 110 Figure 318 ..................................................................................................... 112 Figure 319 ..................................................................................................... 123 Figure 19 ....................................................................................................... 131 5 THEORY AND MODELS ...................................................................................... 133 Initial Theory Consid erations ................................................................................ 133 OrderedMonomer Mediated Interparticle Spacing ............................................... 134 Settling Into Simple Hexagonal Arrays Minimizes Gravitational Energy ............... 135 Hydrogen Bonding of Monomer to Particle Surface Initiates Order ...................... 135 Shear Ordering ..................................................................................................... 140 6 FUTURE RESEARCH POSSIBILITIES ................................................................ 144 Control of Spacing ................................................................................................ 144 Different Fluids ............................................................................................... 144 Different Particles ........................................................................................... 144 Different Conditions ........................................................................................ 146 Large Scale Arrays ............................................................................................... 148 7 CONCLUSIONS ................................................................................................... 149 APPENDIX A SPIN COATED WAFER PROCEDURE ................................................................ 151 B ELECTROPH ORETIC MOBILITY ......................................................................... 155 C PARTICLE DENSITY AND BOUYANT FORCE ................................................... 160 LIST OF REFERENCES ............................................................................................. 163 BIOGRAPHICAL SKETCH .......................................................................................... 165

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7 LIST OF TABLES Table page A 1 St ber suspension samples used in spin coating. ............................................ 154

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8 LIST OF FIGURES Figure page 1 1 Photonic crystals ................................................................................................ 17 1 2 A schematic planar waveguide ........................................................................... 17 1 3 An ordered array of silic a particles in a polymer matrix ...................................... 18 1 4 An ordered macro porous array .......................................................................... 18 1 5 Metallic Nanohole array ...................................................................................... 19 1 6 Metallic 2D surface grating ................................................................................. 19 1 7 Fabrication of an attoliter array. .......................................................................... 20 1 8 Fabrication of a variety of arrays. ....................................................................... 20 1 9 Two layers of a simple hexagonal, nonclose packed array ............................... 21 1 10 Typical hcp fcc close packed silica particles ....................................................... 22 1 11 Hexagonal arrays produced by spin coating ....................................................... 23 2 1 The siliconoxygen tetrahedron. ......................................................................... 27 2 2 An amorphous network of polysiloxane polymers ............................................... 28 2 3 Tetraethylorthosilicate (TEOS). .......................................................................... 32 2 4 Ethoxylated trimethylolpropane triacrylate (ETPTA) ........................................... 35 2 5 A xenon lamp spectrum compared to the solar spectrum ................................... 37 2 6 Ciba Darocur 1173. ......................................................................................... 37 2 7 Ciba Irgacure 2959 free radical generation ..................................................... 38 2 8 Free radical chain propagation of ETPTA polymerization. .................................. 39 2 9 A hypothetical network of polymerized ETPTA molecules. ................................. 40 3 1 SEM image from the top of a zerohour settled array ......................................... 49 3 2 SEM image of 20hour top, 2.7kX. ...................................................................... 49 3 3 SEM image of 20hour top, 8kX. ......................................................................... 50

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9 3 4 SEM image of zero hours, 80 m cross section, 950X magnification. ................. 51 3 5 SEM image of zerohour, m cross section, 1.7kX. ........................................ 52 3 6 SEM image of zerohour, c ross section, 4.5kX. .................................................. 53 3 7 SEM image of zerohour, cross section, 4.3kX. .................................................. 53 3 8 SEM image of zerohour, thin cross section,14kX ............................................. 54 3 9 SEM image of 20hour, cross section, 4.5kX. ..................................................... 54 3 10 SEM image of 20hour, enlarged cross section, 4.5kX. ...................................... 55 3 11 SEM image of 20hour, thin cross section, 8kX. ................................................. 56 3 12 SEM image of 20hour particlemonomer wafer interface, 8.5kX. ...................... 5 6 3 13 SEM image of 20hour, vertical ordering at 4kX. This image shows well defined cubic, hexagonal, and transitional vertical order. ................................... 58 3 14 SEM image of 20hour, vertical ordering ............................................................ 59 3 15 SEM image of 20hour, vertical ordering at 6.5kX magnification. ....................... 59 3 16 SEM imag e of calcined 500 nm GelTech St ber particles, 2kX. ......................... 60 3 17 SEM image of calcined 500 nm GelTech St ber particles at 4kX ....................... 61 3 18 SEM image of 24hour, freeze dried, LLC St ber particles,17kX. ...................... 62 3 19 SEM image of 24hour, freeze dried, LLC St ber particles, 8kX. ....................... 62 3 20 Initial condition of a wafer prepared as in Chapter 2. .......................................... 64 3 21 Snap shots of a spinning wafer. .......................................................................... 66 3 22 FTIR spect ra of St ber polymer system. ............................................................ 70 4 1 Disk overlay images. ......................................................................................... 76 4 2 Reference areas for calculating the masked area %. ......................................... 78 4 3 Masked% vs. translation.. ................................................................................... 79 4 4 Translation images of the ideal mask over Figure 41B ...................................... 83 4 5 Plot of the masked% for the rotation of the ideal mask over the ideal sample. ... 84

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10 4 6 Rotation overlays of ideal mask over ideal sample based .................................. 89 4 7 Fig 3 1 SEM particle size distribution ................................................................. 90 4 8 Analysis of Fig. 3 1 interparticle spacing relative to diameter of 378 nm ............ 91 4 9 Translational analysis of the ideal mask of Fig. 33 ............................................ 92 4 10 Rotational analysis of the ideal mask of Fig. 33. ............................................... 93 4 11 Translational overlay images of the ideal mask created from Fig. 33 ................ 95 4 12 Masked images of Fig 3 1 as function of mask rotation ...................................... 97 4 13 Disk representation of SEM image Fig.3 3. ........................................................ 98 4 14 Particle size distributions of Fig. 3 3 ................................................................... 98 4 15 Fig. 3 3 nearest neighbor spacing analysis ...................................................... 100 4 16 Fig. 3 3 Masked % vs. Translation ................................................................... 101 4 17 Rotational analy sis of masked % vs, angular rotation of ideal array over disk representation of sample array ......................................................................... 101 4 18 Translational overlay images of the ideal mask created from Fig. 33. ............. 104 4 19 Masked images of Fig 3 3 as function of mask rotation .................................... 108 4 20 Disk representation of Figure 3 6 ..................................................................... 109 4 21 Particle size distributions of Fig.3 6. ................................................................. 109 4 22 Nearest neighbor interparticle spacing analysis of Fig 3 6 ............................... 110 4 23 Disk representation of Fig. 317 ........................................................................ 111 4 24 Particle size distribution measured from the SEM image ................................. 111 4 25 In terparticle spacing analysis for Fig. 317 ....................................................... 112 4 26 Representative image used to measure mean particle size for the Particle Solutions, LLC Stober silica particles used in Figures 318 and 3 1 9 ............... 113 4 27 Disk representation of Figure 3 18. Compare to Figure 435. ........................... 115 4 28 Interparticle spacing analysis of Figure 3 18. ................................................... 115

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11 4 29 Translational and rotational masked% graphs from the ideal mask and array generated from Figure 319. ............................................................................. 116 4 30 Translati onal and rotational masked% graphs for Figure 3 18 ......................... 117 4 31 Overlay of ideal and sample translation and rotation masked% ....................... 117 4 3 2 Translational masked% images for Figure 318 ............................................... 119 4 33 Rotational masked percent of Figure 3 18 ........................................................ 123 4 34 Interparticle spacing results for Figure 319.. .................................................... 124 4 35 Disk representation of Fig. 319 ........................................................................ 124 4 36 Fig. 3 19 translational and rotational masked% ................................................ 125 4 37 Overlay of Fig. 3 19 ideal and sample masked% ............................................. 125 4 38 Fig 3 19 translational masked% images ........................................................... 127 4 39 Fig 3 19 rotational mask% images ................................................................... 131 4 40 ANOVA diagram for particle size and spacing of Figure 19. ............................ 132 5 1 Radial divergence of order. ............................................................................... 137 5 2 Radial divergence of order to scale .................................................................. 137 5 3 ETPTA monomer hydrogen bonding to SiOH groups of the silica surface ....... 139 5 4 ETPTA monomer hydrogen bonding to SiOH groups of the silica surface. ...... 140 5 5 Initial condition model. Fluid flow is represented by yellow arrows; rotation of the particles is represented by the black circular arrows. ................................. 141 5 6 Particle organization during spin coating .......................................................... 142 A 1 Ethoxylated trimethylolpropane triacrylate (ETPTA). ........................................ 151 A 2 Darocur 1173, 2Hydroxy 2 methyl 1 phenyl 1 propanone. ........................... 152 A 3 Silane primer: 3acryloxypropyl trichlorosilane ................................................. 153 B 1 Schematic of a phase analysis light scattering (PALS) set up. ......................... 158 C 1 Schematic of a helium pycnometer. .................................................................. 161

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12 LIST OF ABBREVIATION S ACPTS Primer; 3 acryloxypropyl trichlorosilane (Figure A 3). ANOVA Analysis of variance. BIC Brookhaven Instruments Corporation. C Coulomb. cc Cubic centimeter. cm Centimeter = 1 0 2 meter. cP Centipoise = 10 3kg*m/sec. Darocur 1173 Photoinitiator; 2 Hydroxy 2 methyl 1 phenyl 1 propanone ( Figure 2 6). e Elementary charge, + 1.602*10-19 C. EBSD Electron backscatter diffraction. ETPTA Monomer; SR 454@, Ethoxylated trimethylolpropane triacrylate (Figure 21). Et O H Ethanol, H3C CH2OH eV electron volt = 0.16*10 Joule. fcc Face centered cubic FIB Focused ion beam milling. fNt Femto Newton =10 15 Newton. FTIR Fourier transform infrared spectroscopy. H Hydrogen. H2O Water, oxidane. h cp Hexagonal close packed. HF Hydrofluoric acid. hncp Hexagonal nonclose packed.

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13 kJ/mol kilo Joule per mole = 103 Joule per mole = 10.36*10 3 eV/bond =10.36 meV/event .. kg Kilogram = 1000 grams. L L iter m Meter, though sometimes mass, as specified in context. Me Methane; CH4. me Electron mass. MeOEtOAc Methoxy Ethoxy Acetate; one leg of the ETPTA monomer. MeOH Methanol; HO CH3. meV milli eV = 10 3 eV mL M illiliter = 10 3 liter = 1 cc mm Millimeter = 10 6 meter. m M icrometer = 10 6 meter. mV milli Volt nm N anometer = 10 9 meter. np Nanoparticle. Nt Newton =1kg*meter/second2. nNt NanoNewton = 10 9 Newton. O Oxygen OH hydroxide, hydroxyl. PALS Phase analysis light scattering. pc Photonic crystal. PEG polyethylene glycol. pm Picometer = 10 12 meter. psi Pounds per square inch of pressure.

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14 rpm Revolutions per minute. sec Second. SEM Scanning electron microscope. UV Ultraviolet (light). Zeta potential

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15 Abstract of Dissertation Presented to the Graduate School of the University o f Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy ASSEMBLY OF SPHERICAL, SUBMICRON STBER SILICA SPHERES INTO HEXAGONAL ARRAYS IN ETHOXYLATED TRIMETHYLOLPROPANE TRIACRYLATE By G ill B rubaker August 2012 Chair: David Tanner Major: Physics This dissertation will examine and explain the hexagonal ordering of spin coated St ber silica particles in e thoxylated t rimethylolpropane t riacrylate (ETPTA) monomer. It will document the fact that these arrays are formed primarily by settling and self ordering to minimize their gravitational energy constrained by monomer mediated interparticle repulsion. It will use th e fact that these arrays partially self assemble to explain the ordering produced by spin c oating of the St ber silica triacrylate suspensions The final ordering produces vertically compact, horizontally non close packed, simple hexagonal arrays of silica particles in a polymer produced by ultraviolet light in itiated, free radical polymerizati on of the ETPTA triacrylate monomer

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16 CHAPTER 1 INTRODUCTION M otivation to Study Colloidal Arrays Arrays of colloidal particles have several possible uses and exhibit interesting and useful interactions with light. Such arrays are referred to as photonic crystals. Photonic crystals are arrays with periodic dielectric structure ( Figure 11 A ) [2]. These crystals have forbidden propagation frequencies for light that depend on lattice spacing, particle size and dielectric functions of particles and media ( Fig ure 11 B ) [2]. Such crystals are seen in nature, such as opal, insect coloring, pearls, and mother of pearl. Photonic crystals are used as reflective coatings or dielectric mirrors [2]. Properties of photonic crystals include [1] supp ression or enhancement of spontaneous emission [3 6] low threshold lasing [7 11] lossless planar wave guiding ( Figure 12 ) [12 13 ], and quantum information processing [14 15 ]. These properties enable all optical circuit ry for optical computing [16 2 ], negative Poissons r atio [17], and superprism effect [18 19 ] Spin Coated Arrays of Nanoparticles Spin coat crystals can be used to develop three dimensional ordered arrays of nano particles ( Figure 13 ) macroporous polymers ( Figure 14 ) sub wavelength nanohole arrays ( Fi gure 15 ) metallic surface gratings ( Figure 1 6 ) attoliter void arrays ( Figure 17 ) periodic magnetic nanodots and other interesting and potentially useful structures ( Figure 18 ) [1] A promising application of nonclose packed arrays of particles, wh ose diameters and spacing are on the order of the wavelengths of visible light, is the enhancement of solar energy collection efficiency. Reactive ion etching of spin coated arrays of silica particles on silicon erodes the silicon into pillars under the

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17 pr otective silica particles. Such pillar arrays can reduce the reflectivity of smooth (100) silicon wafer from 30% to less than 2.5% [20] The spin coating process used in this study was designed to produce planes of hexagonally ordered silica particles wit h only a few layers of planes in the final product. F igure 1 1. Photonic crystals A ) 1, 2, and 3 dimensional photonic crystals. Different colors represent materials with different refractive indices The different regions may be air, fluid, or polymer and embedded structures. The dimensions of the regions are on the order of the wavelengths of visible light. B ) Band gap diagram for a photonic crystal. Frequency versus wave vector: regions in red represent combinations of frequency and crystal momentum that will not propagate in the crystal like cavity modes (Adapted from [2].) Figure 12. A schematic planar waveguide using photonic band gap to mold the flow of light around a 6 0 degree bend in a photonic crystal. By having the light beam impact a region whose dielectric structure forbids propagation in the forward direction, the beam is forced to make a 6 0o turn. (Adapted from [2].)

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18 Figure 13. An ordered array of silica particles in a polymer matrix produced by spin coating [1]. Notice both the horizontal and vertical order, and the protrusion of particles into the surface. ( Source: Prof. Peng Jiang used by permission) A B Figure 14. An ordered macro porous array produced by dissolving silica particles from a polymer matrix produced by spin coating [1]. A) Silica particles in polystyrene were dissolved away by hydrofluoric acid (HF) from a polystyrene matrix, B) similar to A, but in a polymethylmethacry late matrix. Note that the channels are interconnected because the vertical layers have collapsed during the spin process. This happens as the particles shear monomer from between vertical layers as they migrate outward towards the edge of the spinning waf er, causing them to settle into gravitational minima between particles in nonclose packed simple hexagonal arrays in the layer below. ( Source: Prof. Peng Jiang, used by permission)

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19 Figure 15. Metallic Nanohole array. ( Source: P. Jiang and M. McFarland J. Am. Chem. Soc. 127 3710 (200 5) u sed by permission). Figure 16. Metallic 2D surface grating from a spin coated array of silica particles in a polymer matrix [1]. Note the six armed diffraction star characteristic of simple hexagonal order. ( Source: P. Jiang, Angew. Chem. Int. Ed 43, 5625, 2004, used by permission)

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20 Figure 17 Fabrication of an attoliter array from a spin coated array of nanoparticles in a polymer matrix (Source: P. Jiang, Chem. Commun., 1699, 2005, u sed by permission). Figur e 18. Fabrication of a variety of arrays from spin coated arrays of silica particles in a polymer matrix [1]. (Source: P. Jiang, Chem. Commun., 1699, 2005, u sed by permission).

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21 For photonic crystals to be useful in advanced applications, their dielectric function must be periodic in three dimensions (Figure 11 A ) [2]. The spincoating technique and surrounding technologies enable construction of three dimensional photonic ba nd gap arrays including defect channels necessary for wave guide application (Figure 12). Spin coating these arrays produce simple hexagonal, nonclose packed geometry ( Figure 19 ) It is the mechanism of the formation of these structures that is the focus of this study. In Figure 19 we see two layers of particles, in which the polymer matrix has been etched away by oxygen plasma etching. Note the center to center interparticle spacing is approximately equal to the square root of two, times the particle d iameter; this is a typical result characteristic of particles from about 70 nm to around 600 nm [1]. Please see Figure 4 4 0 for a detailed analysis of the interparticle spacing and particle size of the particles in this figure. Note that if another layer is added to this, the resulting array can be either hexagonal or face centered cubic. If the next layer covers the deep void (blue circles), the resulting structure is face centered cubic looking along the (111) axis, if the next layer covers the red circl es, the structure is hexagonal [ 21] Figure 19. Two layers of a simple hexagonal, nonclose packed array of silica particles produced by spin coating. Clarity of particles is due to oxygen plasma etching of the polymer matrix to reveal particles [1]. (Source: Prof. Peng Jiang, used by permission).

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22 In Figure 110 we see an example of evaporative self assembly which produces close packed arrays T he close packed nature of these arrays makes them difficult to modify and characterize their internal order However, this array is a good example of a self assembled, regular array. This array appears to be face centered cubic (fcc) as can be seen from the cubic structures in the forward edges of the image, althou gh it is possible that both hexagonal close packed (hcp) and fcc domains as well as disordered domains may exist. T echniques such as focused ion beam milling (FIB) and electron backscatter diffraction (EBSD) can be used to look at crystalline grains of pol ycrystalline material at the atomic level Th e FIB technique exposes and smooths the surface of a structure, and images them by EBSD. As the electron beam scans the sample, the different crystal orientations exhibit Bragg diffraction which can be correlated with the crystal planes probed and is specific to the region scanned. This results in a map of the crystal domains exposed on the surface of the sample. M illing successive surfaces and mapping crystalline structure generates a three dimensional tomograph of the crystal P robing photonic crystal s in this way requires visible light sources with wavelengths similar to the size of the structural elements of the photonic crystal Figure 110. Typical hcp fcc close packed silica particles, obtained by dry ing an aqueous suspension of colloidal silica [1]. (Source: Prof. Peng Jiang, used by permission).

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23 Additionally, three dimensional, closed packed arrays are difficult to modify and time consuming to make. The evaporative process can take many days. Spincoating can make monolayer arrays or arrays with a few layers that can be modified and layered much like electronic circuit fabrication. Although the spin coating process can be completed in a few minutes, t he overall wafer preparation has required three days. The wafer preparation process is outlined in Appendix A. Objectives of This Study The initial objective of this study was to answer two questions. 1. Why do hexagonal nonclose packed arrays of colloidal particles form during spin coating (Figure 111 A ) [1]? 2. Can we control the geometry of spincoated arrays (Figure 111B ) [1]? A B Figure 1 11. Hexagonal arrays produced by spin coat ing. A ) Non close packed array showing two layer s of a simple hexagonal array of silica particles [1], B ) variations in particle size and organization of a monolayer simple hexagonal array [1] (Source: Prof. Peng Jiang, used by permission). Figure 111A shows a section of a horizontal plane of simple hexagonally ordered St ber silica particles produced by spin coating. The structure and synthesis of St ber silica particles will be discussed in Chapter 2. Note that there are appear to be two layers of particles and that the upper layer is centered over the interparticle spaces in the layer below. This indicates that the layers are minimizing their gravitational energy.

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24 Horizontal layers are touching vertically, but remain well spaced in the horizontal plane. The clarity of the particles in both figures is due to the fact that the polymer matrix has been etched away by oxygen plasma etch. Figure 111 B show s a monolayer of St ber particles, demonstrating variations in particle sizes and interparticle spacing. The waviness of the lines of particles and the fact that not all the particles are the same size is obvious. Please see the discussion of Figure 4 4 0 for a n analysis of particle size and interparticle spacing averages and standard deviation of Figure 19. F igure 1 11B represents the possible difficulty in producing ideal arrays with variations less than some critical application dependent specification. The question of control over array geometry includes analysis of variance (ANOVA) of interparticle spacing, particle size and particle shape, with the possibility of unavoidable variations in array geometry

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25 CHAPTER 2 MATERIALS AND SAMPLE PREPARAT ION Overview of the Components of the S t ber Triacrylate System I will first outline the principa l components in the system of St ber silica particles in triacrylate monomer. Then each of the components will be discussed in a bit more detail. St ber silic a particles in this study were essentially spherical and prepared by the St ber process as described in the next section. These particles had diameters in the range of about 70 nm to 600 nm. The triacrylate monomers I UPAC name is ethoxylated trimethylolpropane triacrylate abbreviated ETPTA and will be described in the section following the discussion of St ber silica. St ber Silica Particles Since this study involves St ber silica particles, it seems relevant to discuss their synthesis, structure, and properties. Especially important to the dynamics of the system under study is the molecular structure of the surface of St ber silica particles as well as the geometry of the particle as a whole. Much of this discussion is based on the eight hundred page vo lume by Iler [ 2 2 ]. Judging from the size of the referenced volume and the amount of literature concerning silica, it is clear that this is a huge subject. It is therefore not appropriate to indulge a detailed treatise on the chemistry of silica, but some u nderstanding of silic a chemistry and resulting silic a based structures is necessary to understand the dynamics of the assembly of these particles into the regular arrays seen in this study. Of particular importance to my interpretation of the results of th is study, is the role of the interaction of hydroxyl (O H) groups on the surface of Stober silica particles with ether (R O R) and carbonyl ( RR C=O) groups of the ETPTA monomer ( Figure 2 4 ).

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26 The structure of St ber silica particles is said to be amorphous ( Figure 22 ) that is, Stber silica particles do not have regular crystalline structure. A common form of amorphous silica is silica glass. A common form of crystalline silica is quartz. This study is focused on amorphous silica so a brief discussion of the chemistry of amorphous silica will be relevant First, what is silica? It is the most common chemical species in the earths crust, and as mentioned above can be crystalline or amorphous. In either case, the basic building block is silicon dioxide, SiO2. That is, two oxygen atoms per silicon atom. The bond structure suggested by the chemical formula SiO2, is not the same as carbon dioxide, CO2 (O=C=O). CO2 is stable, linear, and involves bonds between the oxygen and carbon atoms. Although silicon species with bonds to silicon and other atoms have been isolated, silicon does not as readily form stable bonds due to the weaker strength of the Si=Si bond compared to the C=C bond; The C=C bond is about twice as strong as the Si=Si bond. In fact disilenes are only readily isolated at low temperatures in the neighborhood of from 10K to 220K [ 2 3 ]. Pauling has discussed the nature of the silicon oxygen bonds and presented reasonable evidence to suggest a certain fraction of ionic as well as resonant bonding with sp3d2 silicon hybridization and delocalization. This he claims allows silicon to form two single and two double bonds resonating between the four oxygen atoms of the oxygen tetrahedron [ 2 4 ]. As an aside, this is a reason why silicon might not make a good backbone atom for biological structures, as the instability of the Si=Si bond precludes the stereo specific structures observed in carbon based biological structures. Therefore, the chemical formula for silica, SiO2 is really based on an overall

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27 stoicheiometric ratio for large silicon oxide structures whose basic structural element is a silicon oxygen tetrahedron as shown in Figure 21 Keep in mind that the oxygen valence will be c ompleted, since free radical oxygen is very reactive and wants to fill its valence structure. T he silica oxygen tetrahedr on is represented in Figure 2 1 Silicon is in the center of a tetrahedron formed by four oxygen atoms. The bond length is approximat ely 1.61 and the bond angle approximately 110o. These dimensions can vary depending on the overall structure in which this subunit participates [ 2 4 ]. Figure 21 The silicon oxygen tetrahedron. Figure 22 is a computer generated image of amorphous silica based on molecular dynamics simulations [ 25 ] This shows hydroxyl groups on the surface. Silicon atoms are orange spheres, oxygen is red in the interior, and purple on the surface, hydrogen is white. Each silicon atom is bonded to four oxygens. The free purple oxygen may be charged in a resonant double bond with silicon, or be a free radical.

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28 A B Figure 22. An a morphous network of polysiloxane polymers comprising a thin glass slab A) slab viewed perpendicularly to the plane of the surface, B) slab viewed edge on, displaying apparent increase in atomic density and showing surface hydroxyl groups extending outward from the surface [25]. (Source http://biot.alfred.edu/~lewis/Cormack_Lab/Du.htm l Prof. A. Cormack, Alfred University In am o ri School of Engineering, Alfred, NY used by permission )

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29 The figure represents a glass surface; the upper figure is looking perpendicular to the plane of the glass, the lower figure represents the upper figure viewed edge on, which is why the density of atoms appears greater than the surface view. This network can be extended indefinitely, by filling the silicon valences with more siloxane groups. It is the unfilled silicon valences on the outer surface of these networks that can be filled with hydroxyl groups, to form surface silanol groups, Si OH. The molecular dynamics on which this figure is based suggests that hydroxylation reduces bond strain, but m ore than 4.5 hydroxyls per square nanometer are not energetically favored [ 25] The hydroxylated surface allows hydrogen bonding with polar molecules. Not all of the surface silicon atoms are terminated with hydroxyl groups; many are closed with other surf ace silicon atoms with an oxygen bridge to form siloxane bonds. The siloxane bonds render the surface hydrophobic and may not participate in hydrogen bonding. However, since the Si O Si structure is similar to an ether bond, C O C the siloxane bond may ex hibit dipolar character The Si O Si bond angle on the surface siloxanes can vary from about 120 to 180 degrees with a broad peak from 140 to 160 degrees [ 25 ]. In the case of calcined silica particles, the hydroxyl groups have been removed to create Si O S i surface structure and liberate one water molecule per siloxane bond formed. Experimental results indicate that even if the siloxane bonds have dipolar structure, calcined particles do not form ordered arrays in the ETPTA monomer. This result will be discussed and documented in Chapter 3 in the results section. Stber silica particles can be considered to be polysiloxane polymers. A siloxane involves Si O with added groups to fill out the valences of the silicon and oxygen atoms. Building block precursors for amorphous polysiloxane polymers can be derived from a

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30 number of siloxane molecules. The systematic and popular nomenclature makes this field a bit confusing. A polysiloxane polymer has a backbone chain of the form O (Si O)nSi with various side c hains to fill out the valence of the silicon atoms. The side chains may be other siloxane chains which will form the amorphous structures of colloidal silica. Polysiloxanes include the silicones like poly dimethyl siloxane, where the added groups are methyl groups, CH3. T he nature of these polymers depends on the side chains of the siloxane monomers ; this is analogous to protein and lipid structures in biology The side chains of interest in this case will be other Si O chains, with the excepti on that some of the silicon free valences will be filled by hydroxyl groups, OH. It is the hydroxyl groups that can interact with ether oxygen atoms, R O R, where R and R usually represent organic molecules, or carbonyl oxygen atoms, (RR) C=O [ 2 2 ] The ether oxygens and carbonyl oxygens of the ETPTA monomer can hydrogen bond with the hydroxyl g roups on the surface of the Stober silica particles. This interaction will give rise to the principle hypothesis regarding the formation of the non close packed si mple hexagonal arrays observed in the spin coated samples ( Figures 1 9 and 1 1 1 ) Co lloidal silica particles are assembled as the polymer chains grow. The growing chains are compacted into spheres to minimize their surface energy in the solvent, i.e., are phase separated from the solvent. These small spheres may be only a few nanometers in diameter, and can condense into larger particles by eliminating adsorbed solvent and hydroxyl groups from their surface. The energetics of this process [22] is describ ed by Iler in terms of changes in free energy change per decrease of 1000 meter2 of silica surface area. The free energy is assumed due to heat liberated in the

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31 process and neglect s entropy changes assumed small. The energetics includes displacing solvent molecules from the surface of the silica particles, mostly water, and hydroxyl groups to form siloxane bonds. The displacement of water requires 1.2 eV/ nm2 of work Dehydration of two hydroxyls liberates one water molecule and forms a siloxane bond and re quires 810 to 470 meV/ nm2 of work depending on the number of hydroxyls per square nanometer of surface area. T he energy released when the t iny silica particles aggregate i s 1.65 eV/ nm2. Th e dehydration energy depends on the number of silanol groups on the surface; the higher value corresponds to 8 OH/nm2. The total energy balance is U = W = ( 1200 + (810 to 470)) meV/ nm2 + 1.65 eV/ nm2 = 366 meV/ nm2 to 26 meV/ nm2, correspond ing to 8 OH / nm2 and 4.6 OH / nm2 of silica surface respectively. Thus the overall internal change is small and negative, which is required for spontaneous transformations That is, the work done lowers the internal energy if there is no heat in or out of the system. The number of hydroxyls per surface area of silica particles will be discussed in the next paragraphs, and equations will be presented to allow cal culation of the hydroxyl populations on the particle surface. See the discussion on page 3 3 for more on this issue. Silicic acid is the basic building block of polysiloxane polymers Although t etraethyl orthosilicate (TEOS) is used as a precursor in the formation of the polysiloxane polymers, it is converted to silicic acid or silanols during the reaction, as described below. Silicic acid is tetrahedral as in Figure 2 1 with a hydrogen atom attached to each of the oxygen atoms. Silicic acid can also be call ed a silanol in the same manner as methanol. Interestingly, the carbon analogue of this silanol, methanetetraol if it exists, is highly unstable and would decay into carbonic acid plus water, i.e., C(OH)4 O=C -

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32 (OH)2 +H2O [ 26]. The molecule used to make th e Stber particles in this study is t etraethyl orthosilicate (TEOS) TEOS is tetrahedral as in Figure 2 1 with an ethyl group, CH2CH3, attached to each oxygen atom ( Figure 23 ) Silicon (red) is at the center of the tetrahedron, with an ethyl (H3C CH2 ) group bound to each oxygen (blue), carbon is represented by black circles, hydrogen by green circles. In the polymerization, the TEOS will be hydrolyzed to produce silanols ( n Si(OH)4 + nEthanol), which condense to polysiloxanes by removing water from between two Si OH groups to form Si O Si + H2O. The symbolizing three other groups attached to the silicon atom to complete its valence. The condensation reaction is facilitated by the presence of ammonium, ( H3NH)+(OH ) [ 27]. This is presumably due to ( H3NH)+ withdrawing an electron from the sigma bond between the carbon and oxygen in the Si O CH2 CH3 molecule, as the Si O bond is stronger than the C O bond by about 1eV/bond [2 8 2 9 ]. Figure 23 Tetraethylorthosilicate (TEOS). Silicon (red) is at th e center of the tetrahedron, with an eth y l (H3C CH2) group bound to each oxygen ( blue ) carbon is represented by black circles, hydrogen by green circles Next consider the chemical formula for polysiloxane [22] which includes hydroxyl side groups and a calculation to estimate the number of hydroxyl groups expressed on

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33 the surface of St ber silica particles. The chemical formula for condensed polysiloxanes is [ SinO(2n nx/2)(OH)nx]+mSi(OH)4 [ Sin+mO(2n nx/2+2m(2 p))(OH)nx+4m p]+2pmH2O n is the number if silicon atoms in the molecule on the left side of the equation, x is the number of OH groups per silicon atom in the molecule on the left, m is the number of silicic acid molecules added to the polymer, and p is the fraction of hydroxyl groups per silic ic acid molecule converted to water The above formula can be written in simplified form as SinOa(OH)b. Without proof [22] the numbers n, a, and b, are related to the anhydrous i.e., dried diameter d, of the particle in nano meters (nm) where n = 11.5d3, is the number of silicon atoms, a = 23d312.3d2+8.8d2.09, is the number of oxygens not in hydroxyl groups b = 24d217.6d+4.18, is the number of hydroxyl groups. The number of hydroxyls per unit surface area is approximately b/( d2). For d =10 nm for instance, this formula predicts about 7.28 hydroxyls per nm2. As d goes to infinity, the number of hydroxyls per unit surface area goes to about 7.82 per nm2. However, as pointed out by Iler [ 2 2 ] since the hydroxyl groups lay above and below the average surface, the effective number of exposed hydroxyls is more likely to be around 4.6 per nm2. This number is also reported by Du, Cormack and others though some authors suggest numbers as high as eight hydroxyls per nm2 [ 25]. Iler reports 4.6 hydroxyls per nm2 as the commonly measured value. These numbers are surely approximate, and the number of exposed hydroxyl groups is likely to be variable. This variability could well affect the strength of interaction between the particle surface and the monomer by hy drogen bonding and final ordering of the fixed, spin coated array.

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34 Finally Ill summarize some of the discussion in Iler [ 2 2 ] regarding hydrogen bonding of hydroxylated silica surfaces with various molecules, a little about the hydrogen bond itself and the interaction of the ETPTA monomer with the silica surface. First, what is a hydrogen bond? A hydrogen bond involves a hydrogen atom, bonded to an electronegative atom, such as oxygen, nitrogen, fluorine etc. The electronegative atom pulls electron dens ity from the hydrogen, leaving the hydrogen partially positive in charge. This creates a dipole moment, which can attract other charge densities by inducing an oppositely charged dipole, such as those present in ether bonds. These dipoledipole bonds can b e somewhat strong, with bond energies for OH O = hydrogen bonds from about 300 to 1000 meV/bond [ 30, 31 ] The theory of hydrogen bonding is an ongoing research effort and the dynamics of hydrogen bonds are not fully known after 100 years [ 31 ] I n particul ar the ethers, R O R strongly hydrogen bond to silica surface hydroxyl groups [ 20] The monomer and resulting polymer can be regarded as polyethers, as there are six ether bonds in each monomer molecule ( Figure 24 ). As documented in Iler, the ability to form hydrogen bonded structures with hydroxylated silica is reduced if the hydroxyl groups are ionized. Using a ZetaReader MK21 to look for electrophoretic mobility of fresh Stober particles in the ETPTA monomer, we observed no sign of particle migration up to 100 volts of driving potential. This implies that the silica is not charged in the EPTA monomer, enabling the formation of hydrogen bonded complexes of the particles and monomer. Since the monomer can hydrogen bond with 6 ethers and 3 carbonyl groups the minimum energy conformation would involve all the groups hydrogen bonded to the

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35 particle surface, with the all the monomer arms bound to the silica surface, so the monomer lies flat on the particle surface ( Figure 5 3 ). Ethoxylated Trimethylolpro pane Triacrylate Ethoxylated trimethylolpropane triacrylate, abbreviated ETPTA ( Figure 2 4 ) is the principle fluid component involved in the formation of arrays of Stober silica particles in this study. Therefore a brief discussion of its structure is in order to understand its role in array formation. In particular, the organization of ether bonds RO R and carbonyl groups, RRC=O, should be considered in light of their potential to hydrogen bond with hydroxyl groups on silica surfaces. H ydrogen bonding is hypothesized to be the principle reason for the ordering of the silica particles into simple hexagonal arrays. Figure 24 Ethoxylated trimethylolpropane triacrylate (ETPTA), the triacrylate monomer. The oxygen atoms in red, are involved in two types of bond: ether bonds, R O R and carbonyl bonds, RR C=O. The ether and carbonyl oxygen atoms can hydrogen bond to surface hydroxyl (OH) groups on the St ber silica particle surface. R and R represent the molecules bound directly to the ether oxygens, or to the carbon of the carbonyl (C=O) oxygen atom. Additionally, it is hypothesized that the presumed ordering of the monomer imposed at the surface of the particle is propagated outward from the surface to a distance

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36 dependent on the curvature of the par ticle surface. These considerations will be further discussed in Chapter 4 on theories and models. One reason for choosing this monomer [1], is that the refractive index and dielectric constant of ETPTA and Stober silica particles are nearly the same. The value of refractive index, n, is n [22] and for ETPTA is 1.4989 [1]. Since the van der Wa a ls force between two particles in a fluid is proportional to the difference in the dielectric constants of the fluid and particles [ 32] matching the dielectric constants minimizes the van der Waals attraction between the St ber silica particles. Thus refractive index matching helps assure that the particles will not aggregate by van der Waals forces in the particle monomer suspension. Th is assumes of course that the zero frequency dielectric constants of particle and monomer are also approximately the same. Since the calcined particles (Chapter 3) neither order nor aggregate, the assumption of approximately equal dielectric constants is n ot unwarranted based on the van der Waals theory [ 32]. Finally, consider the mechanism of polymerization and its possible effect on the generation of array variance. The mechanism of polymerization is photoinduced free radical polymerization. The polymeriz ation is initiated with an initiator molecule, in this case Ciba Darocur to be discussed below. The light source for this photoinitiation is a Xenon Corporation model RC 742 pulsed xenon lamp, which is a broad spectrum ultraviolet light source ( Figure 25 ). Note the increased amount of ultra violet intensity of the xenon spectrum with respect to the solar spectrum. Note especially the intensity spikes in the 200 to 300 nm range. It is energies in this range that excite atomic transitions. For

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37 instance a 250 nm photon has energy of nearly 5 eV, sufficient to excite many atomic states A free radical is an atom or molecule with an open valence, that is, one or more unpaired binding electrons. Carbon atoms have four free radical electrons for instance. Free radical polymerization involves the propagation of free radicals as polymerization proceeds. The initial free radical or initiator in this case, is produced by photo induced free radical generation of an initiator molecule. The initiator in this system is called a photoinitiator, and is the Ciba Darocur 1173 molecule represented in Figure 2 6 Figure 25. A xenon lamp spectrum compared to the solar spectrum. (Source: Xenon Corporation. Used by permission). Figure 26. Ciba Darocur 1173, 2 Hydro xy 2 methyl 1 phenyl 1 propan1 one Key: carbon is black, oxygen is red, and hydrogen is blue.

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38 The mechanism of photoinitiation of a very similar photoinitiator [3 3 ] Ciba Irgacure 2959, and a proposed similarity to Darocur 1173 photoinitiation is represented in Figure 2 7 Figure 27 Ciba Irgacure 2959 free radical generation and its proposed relation to Darocur free radical generation [ 33] Green circles represent unpaired binding electrons, i.e., free radical electrons. The molecular species are neutrally charged. T he UV photon, h represented by the blue wavy line, excites the indicated carboncarbon sigma bond to produce a pair of reactive free radical electron species by photolysis. The free radical electrons are depicted as green ci rcles. The free radical electrons can withdraw electrons from the pi bonds of the vinyl groups ( H2C =CH3) at the end of the triacrylate monomer arms, and form sigma bonds with the vinyl group. The b ond formed between the free radical Darocur species and t he vinyl group produces another free radical on the inner carbon atom of the vinyl group. The free radical on the vinyl group can now extract and bind with another electron from another

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39 vinyl group. This reaction is propagated to bind the monomers together into the finished polymer to form polymer chains as in methyl methacrylate [ 34 ] This process is represented in Figure 28. Figure 28. Free radical chain propagation of ETPTA polymerization. Only one of the acrylate arms of each ETPTA molecule are shown enlarged. Note that if a free radical species of the photolysed Darocur combines with the free radical end of the ETPTA molecule, the polymerization will be terminated. Finally Figure 2 9 shows a hypothetical network of polymerized monomer molecules. The red ovals in Figure 2 9 represent the covalent bonds formed in the free radical polymerization. The ETPTA molecules are represented by simple line drawings. However, the constituents of the ETPTA legs are singly bonded and have free rotation about their bonds. This means the monomer can adopt random configurations before polymerizing. As I have discussed though, the layer of monomer closest to the particle surface is hypothesized to be ordered tangentially to the particle surface by hydrogen

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40 bonds and initiates a longer range order of the monomer around the particles. It would be desirable to be able to image such order by transmission electron microscopy (TEM). Indications are that this would be quite difficult, as the features of interest, namely incr eased porosity of the polymer away from the particle surface are on the order of angstroms and irregular, making TEM and X ray images difficult. Figure 29. A hypothetical network of polymerized ETPTA molecules. The polymer network can be extended int o three dimensions forming an amorphous matrix embedding the particles. It is not expected that the monomer will covalently bond to the particle, as there are no double bonds in the silica particle. If the surface of the silica particle were functionalized with a small vinyl bearing molecule, it would be possible to bind with monomer, creating a stronger overall structure. Evidence from fracturing samples for viewing in the SEM, indicates that the polymer matrix does not bind to the particles. This is because there seems to be no polymer adhered to the particles in the fracture cross sections ( Figures 31 3 3 1 4 and 3 1 5 ).

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41 I t seems that the polymerization process c ould induce internal stress and resulting strain in the polymerized matrix. This strain could well influence the final array geometry and be a significant source of variance of interparticle spacing. However, in the discussion of Figure 4 40 an analysis of the variance of interparticle spacing indicates no statistically significant variance of in terparticle spacing based on hexagonal direction. As a final note, the polymerization process is strongly influenced by the concentration of Darocur For films of 2 to 20 microns thick a concentration of 2 to 4 weight percent Darocur is recommended by C iba. For films of from 20 to 2 000 microns thick, a concentration of 1 to 3 weight percent Darocur is recommended by Ciba. The film thickness of the wafer films ranges from about 1 to 80 microns as shown in Figures 3 4 and 38. The concentration of Darocur used in these samples was about 2 weight percent as discussed in Appendix A According to Ciba, the best results, as defined by the strength of the fixed polymer are a matter of trial and error. This being the case, a careful study of the amount of Daro cur would be necessary to arrive at the polymer of maximum strength. If too little initiator is added, the polymerization will not be complete because of insufficient initiation. I f too much initiator is added, the polymerization may be terminated by bind ing with free a free radical initiator species causing incomplete polymerization. This could be a significant source of variance of interparticle spacing by leaving weak spots or regions of fluid monomer, allowing particles to shift their positions with ti me. Overview of Wafer Preparation for Spin Coating The wafer monomer preparation process in Professor Jiangs laboratory has been a three step, three day process [ 35 ] For much of this section I am indebted to Nic h olas L i nn, one of Prof. Jiangs graduate students. Nick was engaged in the preparation and

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42 characterization of the arrays made by the spincoating technique. He helped me prepare samples and provided m e with extensive notes on the fabrication of their spin coated wafers. The following observations and procedures are adapted from those notes. First, the monomer particle suspension is prepared and bottled. The bottled suspension is stored in the dark, loosely capped, for approximately 24 hours to allow residual ethanol to evaporate from the suspen sion On day two, the wafer is prepared in a clean room to reduce contamination. T he wafer surface is cleaned and primed with a thin layer of 3 acryloxypropyl trichlorosilane ( ACPTS ) ( F igure A 3 ) This primer serves to hold the monomer to the spinning waf er. Without the adhesive interface provided by the primer between wafer and monomer, the monomer suspension will be spun off the wafer at low rpm. T he particle monomer suspension is then poured onto the primed wafer. The wafer and suspension are placed in a wafer cassette to prevent dust settling on the wafer. The prepared wafer is transported from the clean room to the spin lab and allowed to settle overnight in its cassette. On day three, wafer and suspension are put on the spinner and subjected to various spin programs. For a complete checklist of the preparation of the particle monomer suspension, its application to the wafer, and spin programs ( Appendix A ) Preparing Samples to Characterize Initial Conditions Samples of fresh and calcined St ber particl es in monomer were prepared and placed on centimeter square pieces of wafer Several samples were fixed in the UV lamp as soon as they were placed of the wafer; several other samples were fixed in the UV lamp after 20 hours.

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43 The first samples I made were prepared to examine the initial conditions of the particlemonomer wafer system The idea here was to make small samples and after various settling times, fix them with the xenon lamp. T hen these samples would be imaged with the SEM These samples were prepared along with Nic h olas Li nn as he prepared several wafers for spinning. Therefore, this sample preparation proceeded exactly as specified above through priming the wafer. The purpose of this exercise was to look at the organization of the particles as they settled by gravity. Knowledge of the initial organization would be needed to completely solve any differential equations of motion of the system. After priming the wafer, the wafer was scribed and broken into roughly rectangular pieces of a centimeter or so in area, and a drop of particlemonomer suspension was placed on several pieces of primed wafer. The particle size used was about 440 nm. The particlemonomer suspension was then rotated around, as previously described, to spread a uniform coating on the wafer pieces. Two pieces of these wafers were immediately fixed in the xenon UV lamp. Although several samples were made, with the intention of fixing them at regular intervals, an explosion in another lab caused us to have to vacate the building T herefore, the next samples were fixed 20 hours after placing a drop on each of the wafer pieces This is however, about the usual time to wait from the final wafer preparation step until spinning the wafer. Subsequent samples were prepared on silicon wafer pieces without priming. Samples made with 500 nm calcined GelTech silica were prepared, as well as samples made with fresh, fre eze dried St ber silica particles prepared as in the Day 1

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44 procedure. These fresh St ber particles were from a different supplier than those represented in Table 31. These particles were prov ided by Particle Solutions, LLC (LLC particles) The diameter of these St ber silica particles was about 300 nm. Although the solids loading of the LLC particles was different from those in Table A 1, the appropriate amount of suspension was centrifuged to produce a 20 volume percent particle monomer suspension. These samples were not prepared in clean room conditions. Calcination was accomplished on freeze dried LLC particles at 900 C in a Thermolyne 6000 muffle furnace for 6 hours. The calcined samples were mixed with monomer at the same volume fraction of particles as the fresh St ber samples as per Table 3 1, i.e., around 20 volume percent particles

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45 CHAPTER 3 CHARACTERIZATION Instruments and Measurements The principle characterizations were to generate SEM images, compare the e lectrophoretic mobility of calcined and fresh St ber particles measure the density of the Stober silica particles and probe particle monomer suspensions for signs of hydrogen bonding of monomer to particle surface wi th FTIR SEM The SEM used was a JOEL 6335F, housed at the Particle Engineering Research Center. SEM images reveal the interparticle spacing and vertical organization of spin coated and simply settled arrays. Selected images were analyzed by image analysi s to collect data on variance of interparticle spacing, particle size and order analysis. Video A Sony HDR SR12 was used to video record a particle monomer prepared wafer during the spin coating process. Snap shots of the characteristic times and RPMs of the spin program will be shown in the results section below. Electrophoretic M obility Charge on the particles is inferred from electrophoretic mobility measurements, using a Brookhaven Instruments Corporation (BIC) ZetaPlus zeta potential analyzer, utili zing their Zeta PALS method. Please see Appendix B for more discussion on this method concerning the data collection and calculation of the charge on a particle. Charge on the particles is an indication of possible hydrogen bonding sites as discussed in C h apter 2 on materials and sample preparation. The relation between particle charge and array order will also be discussed in C hapter 5 on t heory and m odels.

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46 Density Density of the particles is measured using a Quantachrome ULTRPYC 1000 helium pycnometer. D ensity of the particles is needed to calculate the buoyant force on the particle in monomer which is balanced by the forces maintaining the vertical interparticle spacing observed in simply settled arrays Please see Appendix C for a description of the density measurement and calculating the buoyant force. FTIR Gary Scheiffele the FTIR spectroscopist at the Particle Engineering Research Center at the University of Florida performed these measurements. A Nicolet Magna 760 FTIR was used with a diffuse reflec tance Infrared Fourier transform (DRIFT) sample module. The MCT A liquid nitrogen chilled detector was used to reduce thermal detector noise. The number of scans was 128 with 4 wave number resolution. A relatively sharp peak at around 3600 cm is characteristic of unconfined hydroxyl groups and broadening of this peak in the range of 3700 to 3000 cm is an indication of restriction of hydroxyl oscillations due to hydrogen bonding [ 36] Results SEM SEM images of simply settled arrays reveal ed that fresh Stober particles display regions of simple hexagonal ordering in horizontal planes ( Figure s 3 2, 3 3 3 18 and 3 19) but calcined particles showed no signs of ordering ( Figures 316 and 3 17 ) These images are the most important results of this study, as they clearly show the initial organization of the particles before spin coating. There are three types of image, views from the top of the horizontal sample surface, views of the bottom of the samples, and views of the cross section edges of fractured samples.

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47 The issue of representing an entire disk with a few SEM images requires some discussion. A wafer has an area of about 81 cm2, and a typical image such as Fig 3 1 covers an area of about 5.78*10 cm2. It requires about one minute to capture the image, and so would require about 26.7 years to image the entire disk. Clearly it is impractical to image the entire wafer. Additionally, many such wafers prepared in the same way would have to be analyzed to gain a complete picture of these samples Also, the wafer would have to be analyzed not only from the top, but perhaps more importantly, from the bottom of the samples peeled from the wafer. Then the samples should be cross sectioned to characterize the vertical organization. Finally, as will be seen from the video analysis, many wafers would have to be prepared and stopped at various times in the spin coating process and analyzed by SEM and associated image analysis techniques to completely characterize this system; a daunting challenge indeed! Therefore, we will have to content ourselves with a few, hopefully representative images and analyses. I n C hapter 4, I will present an analysis of the ordering of a selected set of SEM images. For Figs. 3 1, 3 3, 3 18, and 319, an analysis of the particle size distribution, analysis of the frequency of particle spacing of nearest neighbors, and a novel correlation function to compare the sample arrays with ideal arrays created from the samples will be presented. For Figs. 36, 3 14, 3 15, and 3 17 p article size and nearest neighbor spacing analysis will be presented. For the initial batch of samples, Nicolas Lynn operated the SEM and took the initial pictures. Samples fixed immediately i.e., at zero hours and at 20 hours were imaged. Representative images from this session are displayed in Figures 31 through 3 14.

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48 Figure 3 1 Figure 31 is an image of the top surface of one of the samples fixed with the xenon lamp immediately after spreading the particlemonomer suspension onto the wafer square, i. e., a 0 hour sample. Wafer squares were about one square centimeter in area. These wafer pieces were primed with the silane primer, 3 acryloxypropyl trichlorosilane (Figure A 3). The particles are distinct, and as will be seen in the images of the edges, close to the surface. Calcined particles will sink deeper in the polymer and will be difficult to see as fixed, i.e., without etching away the polymer. The important thing to appreciate in this image is the lack of definite order, but the somewhat uniform spacing which indicates a uniform interparticle force. There are local areas of simple hexagonal order, but no long range order. Figure 31. SEM image from the top of a zerohour settled array. Figure 3 2 Figure 32 is an image of one of the samples fixed at 20 hours after spreading the particlemonomer suspension onto the wafer square. The important observation here is essentially the answer to the first question posed in the objectives to this study: the particles are already hexagonally ordered. This image shows the existence of long range, simple hexagonal order. However around 40 percent of the

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49 image contains particles in square (cubic) order. There are also bands of transition from cubic to simple hexagonal order as one line of particles shears r elative to adjacent lines. The red hexagons and squares all have the same edge length. Based on the scale of 10 microns, these lines represent interparticle spacing (S) of approximately 650 nm, the red disks represent an apparent particle size of about 380 to 400 nm. The 2*Diameter ( 2D) spacing based on those diameters would be about 550 to 580 nm, so the spacing in this case is a bit larger than the often observed 2D. However Figure 36 allows a much better measurement and shows a diameter of about 450 nm, so the 650 nm spacing is consistent with 2D spacing. The hexagonal form contains more particles per unit area than the cubic, as the area of the square containing 9 particles is 4S2, while the area of the parallelogram outlined in red, containing 9 particles is 2 3S2<4S2. Thus the hexagonal packing allows more particles to settle into lower gravitational wells, minimizing the gravitational energy of the array. Figure 32. SEM image of 20hour top, 2.7kX. Figure 3 3. Figure 33 is a close up at 8000 magnification of a top view of the sample fixed at 20 hours. Simple hexagonal order as well as cubic (square) and

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50 transitional order are easily seen. Again, the interparticle spacing is uniform, except that in the cubic portions, the diagonal spacing is larger than the interparticle spacing of particles on the vertices of the squares. When domains of square array are sheared into hexagonal order, the i nterparticle spacing becomes approximately the same, i.e., 2D If this wafer was being spun, the cubic layers could be sheared into hexagonal order. It is also possible that hexagonal domains could shear into cubic domains, which could account for the observation of transient, 4 armed diffraction stars. The particle size is very subjective, as the SEM image is not well focused due to imaging through polymer, and at high magnification of the image analyzer, Microsoft Visio the particles are extremely fuzzy. However, in Figure 36 a much better measurement of the particle size gives a diameter of about 450 nm, so the interparticle spacing here is consistent with 2D spacing. Figure 33. SEM image of 20hour top, 8kX. Figure 3 4. Figure 34 is an image of a fracture surface through a vertical plane of the fixed particlemonomer suspension taken at zero hours of settling. The image spans

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51 the full cross section of the sample from wafer surface at the bottom of the image to the free surface of the sample. No particular order is observed. It can be seen that there appears to be a greater volume of free polymer on the upper right of the image versus on the left. The sample thickness is about 80 microns. In subsequent images, the sample thickness will decline to less than one micron. This image was taken towards the point where the particlemonomer suspension was applied to the wafer with a 100 micro liter pipette tip. Recall that the finished spun wafer typically is spun down to a few layers of particles. Thus this condition represents a typical starting point for a spun wafer. Figure 34. SEM image of z ero hours 80 m cross section 950X magnification. Figure 3 5. Figure 35 is an other zero hour image taken farther away from the point of particlemonomer application. The sample thickness here is about 37 microns. There does not seem to be any sign of organizat ion. There appear to be fewer particles in the upper 3 microns of the sample, indicating settling of the particles into the

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52 m onomer. The large blobs are presumably contaminants. The wafer is at the bottom of the image. Figure 35. SEM image of z ero hour m cross section 1.7kX Figure 3 6. Figure 36 shows a close up at 4500X of the zero hour settled sample cross section. The wafer surface is at the bottom of the image. The particles are distinct and a give a good idea of the particle diameter of about 450 nm. This allows a revised 2D interparticle spacing of S= 2D=630 nm, consistent with the spacing calculated from Figure 32. Once again there is little sign of order though very few of the particles are touching. That the particles are not touching i s an indication of monomer mediated interparticle repulsive forces. Note that the particles are not generally touching the wafer surface either. Figure 3 7. Figure 37 is similar to Figure 3 6, but shows the upper surface of the sample. The low density of particles in the upper 2 to 3 microns of the sample is evident. Again, there is no sign of order, but it should be noted that very few of the

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53 particles are touching each other, as an indication of monomer mediated interparticle repulsive forces. Figure 3 6. SEM image of z ero hour cross section, 4.5kX Figure 37. SEM image of z ero hour cross section, 4.3kX

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54 Figure 38. SEM image of z ero hour thin cross section 14kX Figure 3 8. Figure 38 is an image at the thin edge of the poured sample. There is no free monomer at the upper edge of these and a high density of particles. Particles are actually removed, it is the hemispherical voids remaining where particles have been pulled out where the sample was fractured that are imaged. There is no order observed, and the particles would appear to have been in a random jumble. Figure 39. SEM image of 20hour cross section, 4.5kX

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55 Figure 3 9. Figure 39 shows a fracture cross section of a 20 hour settled sample. Unfortunately, these cross secti ons have curved surfaces and it is difficult to see vertical order. Most notably however is the regular patterning of the top layer. Although it is difficult to see cubic and hexagonal order directly due to the angle, the regular lines of particles indicat e regular ordering. It is clear from this image that there is no void layer at the top of the sample; it is fully occupied with particles. Figure 310. SEM image of 20hour enlarged cross section, 4.5kX. Figure 3 10. Figure 310 is an artificially enla rged and cropped version of Figure 3 9 above. The red circles outline two particles embedded in the surface layer corresponding to the raised surface details. The pullout voids do not seem to carry portions of raised polymer and so do not show that it is t he particles that cause the raised surface details. Figure 3 11. Figure 311 is another fracture edge and surface, showing the regular variations of surface detail. There is some indication that there are regular lines of particles in horizontal planes as well.

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56 Figure 3 12. Figure 312 shows an interface between particlemonomer suspension and wafer surface. The contact angle of the suspension is about 90 degrees. There appears to be free fixed monomer with contact angle about zero degrees in the red circle s indicating strong adherence to the wafer surface. Figure 311. SEM image of 20hour thin cross section 8kX Figure 31 2 SEM image of 20hour particle monomer wafer interface, 8.5kX

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57 Figures 313, 3 14, and 3 15 are fracture edges of t he 20hour fixed samples. They all exhibit some amount of regular ordering. The edges exhibit signs of hexagonal, cubic, and transitional order in horizontal bands distributed vertically. I define transitional order as neither cubic nor hexagonal, but as t he lines of particles shear past one another in the horizontal plane, they may form hexagonal or cubic order. For instance, some of the horizontal line of particles forms a parallelogram type of array structure with angles just away from 90 degrees. As these lines shift with respect to each other, the angle increases so that hexagons will be formed. The ordering is not close packed, indicating a repulsive force between the particles, balanced by the particles buoyant weight. As discussed in the section on Stober particle synthesis the repulsive force is mediated by the monomer interacting with hydroxyl groups on the particle surface through hydrogen bonding. This is discussed in the sections on electrophoretic mobility, and theory and models, where electrophoretic mobility and surface charge is correlated with the number of surface hydroxyl groups. Figure 3 13 and 3 14 Figure 3 13 shows regions of well defined cubic, hexagonal, and transitional vertical order. I am defining transitional order as consisting of at least three lines of particles that are neither in squarecubic or hexagonal order, but that if the lines of particles are differentially sheared with respect to each other, they will assemble into square or hexagonal order. Figure 314 is a close up of Figure 31 3. Figure 3 15. Figure 315 shows organization that appears to be somewhat cubic along the diagonal of the image, although some regions can be seen to be hexagonal As discussed in Chapter 5 on theories and models that as these particles migrate

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58 outward from the wafer center they shear monomer from between hexagonally ordered horizontal arrays and settle into spaces between particles in layers below them. Since it has been demonstrated that horizontal planes of particles are in simple hexagonal order, the shear induced settling enforces the final three dimensional hexagonal ordering seen in the final spincoated arrays. These samples were prepared by scribing the silicon wafer and snapping it to reveal an edge containing vertical planes of particles. Note that some of the particles remain in the sample, while others were apparently retained by the other half of the sectioned sample. In this case in obtaining particle size distributions from the SEM images, the small dimples that remain look like small particles to image analyzers, and must be excluded from sizing analysis when a disk representation of the image is created for sizing analysis. Please see Chapter 4 for more on this issue. Figure 31 3 SEM image of 20hour vertical ordering at 4kX This image shows well defined cubic hexagonal, and transitional vertical order

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59 Figure 31 4 SEM image of 20hour vertical ordering at 6.5kX magnification. This is a higher magnification of Figure 31 3 Compare the triple pullout in the two ima ges circled in red. Figure 31 5 SEM image of 20hour vertical ordering at 6.5kX magnification.

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60 Pictures I made of the calcined St ber particles appear in Figures 3 1 6 and 31 7 The important result here is that there is no discernable order of the pa rticle positions in fixed monomer. Figure 3 16. Figure 316 is an image is of simply settled, calcined 500 nm GelTech Stber particles in ETPTA polymer. The important point of this image is the complete lack of regular array order. It is my theory that th is is due to the lack of sufficient hydroxyl groups on the particle surface to induce monomer ordering, which is hypothesized to build the repulsive cushion around the particles that enforces hexagonal order on fresh Stber particles. Figure 317 is an image of the same sample at twice the magnification of Figure 316. Again there is no sign of ordering, but neither is there any sign of aggregation of clustering of the particles. The lack of clustering indicates there is no attractive force between these particles, consistent with the neutralization of the van der Walls forces by refractive index matching. Figure 31 6 SEM image of c alcined 500 nm GelTech St ber particles 2kX

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61 Figure 31 7 SEM image of c alcined 500 nm GelTech St ber particles at 4kX This is at twice the magnification of Figure 3 16. T here is no sign of ordering or clustering the interparticle spacing is random. Pictures I took of samples made recently with fresh, freeze dried St ber particles, from Particle Solutions, LLC, are disp layed in Figures 318 and 3 19. The simple hexagonal order is obvious in both micrographs. This is the most important result of this study. It demonstrates repeatability of hexagonal self organization of fresh St ber particles in ETPTA monomer, at least in horizontal planes. Figure 3 18. Figure 318 is an image from the bottom of the sample. These samples were applied to unprimed silicon wafer and were easily peeled of to make SEM samples. The lack of clarity of this image is presumed due to the thickness of the polymer layer over the particles. In the next image, Figure 3 19, taken from the top of

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62 the sample, the particles are much more distinct, indicating they are much closer to the polymer surface than the particles on the bottom of the sample. Figur e 31 8 SEM image of 24hour, freeze dried, LLC St ber particles,17kX. Figure 31 9 SEM image of 24hour, freeze dried, LLC St ber particles, 8kX.

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63 Figure 3 19. Figure 319 is an image taken from the top of the sample. This is a particularly excellent micrograph, which is somewhat surprising as the particles are not relieved by plasma etching. It appears that there is less ETPTA polymer over these particles than appears in the images of the bottom of the sample as seen in Figure 318 This is evident i n the clarity of the image from the top versus that from the bottom. This does not appear to be a problem with SEM filament contamination, as the bottom images were taken before the top images. This indicates the particles are held up from the bottom, cushioned by monomer If the particles in Fig 3 19 are protruding into the surface, as in Figs. 39 through 3 12, this could help explain the clarity of the particles in Fig. 3 19. A simple analysis of the spacing of the edges of the red hexagon, and the part icle diameters indicated by the red circles indicates the particles have a diameter of about 290 nm and an interparticle spacing of about 410 nm. This spacing is exactly the often observed 2D spacing. Note also the regularity of the array, comparable to t hat of spun samples. There is no cubic order in this image. Video The following notes and observations on the spin coating process were adapted from notes prepared by Nicholas Linn, to whom I am much indebted for his time to write them up for me [ 35]. My comments are listed as Discussion. without reference. These notes are highlighted and supplemented by still images captured from one of the video recordings we made of a spin program.

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64 Figure 32 0 shows the wafer as prepared. Note the apparent surface roughness and the colorful radiance characteristic of photonic crystals ; h owever there are no initial diffraction stars. Figure 32 0 I nitial condition of a wafer prepared as in Chapter 2. Observation 1 The proper spin coating condition to use depends on the desired result a single layer or multilayer colloidal crystal and on the size of the particles used in day 1 [ 35 ]. Observation 2 After a time at 8000 rpm, Bragg diffraction disappears and does not return [ 35 ]. Discussion This indicates that hexagonal order is lost, or there are not enough layers for diffraction. SEM images of finished wafers exhibit nonclose packed simple

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65 hexagonal order with a few layers of particles, it must be that there are not enough planes of particles to generate sufficient scattering intensity to produce diffraction stars. Observation 3 In general, the larger the particle size, the less time required before all signs of ordering disappear [ 35] Discussion L arger more massive particles have larger inertia than small part icles. This requires more force to hold larger particles to the wafer, however the wafer to particle force is independent of particle size, as van der Waals forces have been reduced by index matching, so the larger particles migrate radially more quickly t han smaller particles. This also indicates the role of particle mass in increasing the flow of suspension radially from the disk center. That is, the particles drag fluid with them. Observation 4 The arrangement of particles on the wafer can be deduced in situ by shining a light on the wafer during the spin coating and observing the Bragg diffraction pattern by looking at the wafer from an appropriate angle. The presence of six bands indicates hexagonal ordering, and four bands indicate a square, gridlik e array. The thickness and length of the bands indicates the number of layers present, a monolayer sample will have very thin bands only visible at the center of the wafer. It is also possible to observe a transition between layers in situ when the number of layers is small (maybe <5). As spin coating proceeds, layer after layer of particles are removed, eventually resulting in a monolayer. When watching the spin coating at layers less than 5, the diffraction bands will appear to shrink and broaden, th e wafer becomes a grayish color the bands reemerge and grow gradually for a couple seconds. With practice, it is

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66 possible to stop the spin coating at a desired number of layers just by watching the change in the diffraction patterns on the wafer [ 35] A) 200 rpm, 1 min, B ) 300 rpm, 3 min, C ) 1000 rpm, 4:30 min, D ) 3000 rpm, 5:19 min, E ) 6000 rpm, 5:34 min, F ) 8000 rpm, 6:05 min, G ) 8000 rpm, 6:17 min, H ) 8000 rpm, 6:34 min, I ) Final, 0 rpm 7:41 min. Figure 32 1 Snap shots of a sp inning wafer. Discussion Figure 32 0 is an image of the initial condition of the wafer spun in Figure 32 1 A through 3 2 1 I. The spin program was 2 minutes at 200 rpm, 2 minutes at 300 rpm, 1 minute at 1000 rpm, 30 seconds at 3000 rpm, 20 seconds at 6000 rpm, and about 2 minutes at 8000 rpm (Appendix A)

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67 Figure 32 1 A shows the wafer half way through the spin program at 200 rpm. The initial wafer quickly makes a transitio n to the state shown in Figure 32 1 A and remains steady until the next transition to 300 rpm. Similar behavior is observed during each spin segment represented in each of the Figures 32 1 B through 321 E ; the wafer makes a quick transition and remains approximately steady until the next spin step. The notable observation here is the six armed diffraction stars produced by the three sets of Bragg planes of the simple hexagonal structure intersecting at the center of the wafer. As rpm are increased, suspension can be seen being ejected from the edge of the wafer. This reduces the amount of suspension on the wafer and the thickness of the suspension on the wafer The desired end result is a few layers of particles on the wafer. Figures 32 1 F through 32 1 I show t ransitions during the 8000 rpm spin segment. Most notably is the appearance of a final diffraction star in the center of the wafer shown in Figure 32 1 G The final diffraction star begins a little after the transition to 8000 rpm at 6:05 minutes and peaks in clarity and intensity at around 6:17 minutes, then smears out into a butterfly shape at 6:34 minutes to approximate uniformity until the end of the spin program at 7:41 seen in Figure 32 1 I It is possible that the butterfly shape is interpreted as resu lting from cubic order, but since this occurs at the end of the program and the final arrays are hexagonal, it seems likely this is a result of too few layers for distinct diffraction stars. The final emergence of a diffraction star at 8000 rpm occurs betw een 6:05 and 6:25 minutes of total spin time. Th is star is probably due to suspension near the center

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68 of the wafer flowing suddenly outwards, resulting in a burst of order and sufficient depth to generate diffraction; a yield stress condition exhibited at the highest rpm. Observation 5 Finally some observations on particle size, rpm, spin times, and final number of particle layers. 600nm particles seem to reach an endpoint immediately if 8000RPM is reached, therefore the time at 6000 RPM should be adjusted. Measurement of the time required to produce a given number of layers reveals significant variance between samples of the same particle size, for example producing monolayer wafers with 400nm particles. If left to spin at a low speed, e.g., 600 RPM overn ight, the wafer will eventually reach some equilibrium thickness, it will not spin down to a monolayer. Generally during the spin coating process it has not been possible to generate an equilibrium state of predicable number of layers. That is it has not been possible to establish a repeatable spin program to produce the exact same array structure for a given particle diameter [ 35] Discussion It would be desirable to construct a laser scan and image program to monitor the number of layers by diffraction and feed back to the spin program to control the final number of layers. There may be too any sources of variance, such as temperature, wobble and vibration of the wafer on the spinner, initial distribution of suspension on the wafer, settling time of the suspension on the wafer before spinning, and sampling suspensions to load wafers to control final geometry precisely I t is clear there will be a lenticular structure to the monomer on the wafer as it spins; suspension will be thicker towards the center, as the radial force is weakest there. This structure could be a significant source of variance as the yield stress and resulting radial flow of suspension and its

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69 final distribution over the wafer surface will influence the final number of layers. Without a direct way to monitor and control the evolving array structure by controlling the spin program it may be impossible to precisely control final geometry. Electrophoretic M obility Next is the discussion of electrophoretic mobility data. Please see Appendix B for a discussion of this technique. The 30 run average electrophoretic mobility of fresh, freeze dried LLC Stber particles was measured to be 4.68, while the mobility of the same particles calcined was only 1.36. This implies there are on the order of 4.687/1.36 = 3.44 times more hydroxyl groups on the fresh St bers than on the calcined particles. This difference is correlated with the difference in order between calcined and freeze dried St ber particles. Density Finally, density of the freeze dr ied particles was consistently 2.2 grams per centimeter cubed. Please see Appendix C for a discussion of this technique. It is possible that the freeze drying has removed water molecules from the porosity of the particles. It may be that with the preparat ion for spin coating that a certain amount of ethanol remains in the porosity of the particle. Fluid retained in the porosity would lower the effective density allowing the particle to float a little higher from the wafer surface, and to increase the average vertical separation. FTIR FTIR results show there is little if any sign of hydroxyl groups or hydrogen bo nding between calcined particles and monomer The increased absorption from 3800 to 3000 cm for the freeze dried top sample indicates increases surface hydroxylation of the

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70 particles and hydrogen bonding with the polymer vs. the other samples [ 36 ] The St ber ETPTA suspensions were applied to glass slide s and fixed after 24 hrs. Samples were r emoved from the slide and probed with the DRIFT stage. T he bottom surface (closest to the slide) of the sample and the top surface of the sample were probed. The fact that only the top surface of the freeze dried particles showed signs of hydroxylation and hydrogen bonding with the polymer indicates the particles are close to the surface of the polymer as indicated in Figures 3 9 through 312, and that the calcined particles have little hydroxylation and signs of hydrogen bonding with the polymer. Fig. 3 22. FTIR spectr a of St ber polymer system. These spectra show increased hydroxylation and hydrogen bonding (dark blue curve) in the top surface of the freeze dried St ber polymer system vs. the calcined St ber polymer system or t he bottom surface of the freeze dried St ber polymer system. Discussion The SEM images of the initial conditions, showing the simple hexagonal ordering of the particles in the monomer stimulates the insight needed to answer the question of how the arrays f orm. The SEM images revealed that fresh Stober particles in monomer Control DRIFT -1 -H2O-CO2-BLC Calcined Top DRIFT -2 -H2O-CO2-BLC Calcined Bottom DRIFT -2 -H2O-CO2-BLC FD Top DRIFT -2 -H2O-CO2-BLC FD Bottom DRIFT -2 -H2O-CO2-BLC 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24 0.26 0.28 Log(1/R) 2500 3000 3500 cm-1

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71 were approximately organized into simple hexagonal arrays initially before the spin process began! Spinning has a definite effect on array formation though and will be further discussed i n C hapter 5 on theories and models The mobility results indicate fresh Stber particles have about 3.5 times as many hydroxyl sites as calcined Stber particles as it is the surface hydroxyl groups of silica particles that become charged in polar fluid [ 2 2 ]. Since charge is related to mobility =V/E, by the steady state equation Neb 3.5 times the mobility indicates 3.5 times the charge, if the diameter of the particles is the same, and hence 3.5 times the number of hydroxyl groups See Appendix B for details and definitions of the variables Density of the particles is needed to calculate the buoyant force on the particle in monomer. This force will be bal a nced by the repulsive forces between particles since a s indicated by the S EM images; vertical layers are not touching in the simply settled arrays. This indicates repulsion between particles balanced with the gravitational or buoyant force. The relation between particle and fluid density in calculating the buoyant force is discu ssed in Appendix C With the values of monomer and particle density I calculate a buoyant force of 0. 15x 10-15 Newtons = 0.15 fNt a very small force indeed. Total internal reflection microscopy (TIRM) can measure these tiny forces by using light scatterin g intensity fluctuations to measure the equilibrium distance of a particle from a surface as well as its excursions around the equilibrium position. From this data the force between particle and surface can be inferred. This technique is at least 4 orders of magnitude more sensitive than atomic force microscopy [ 32 ]. Anot her possible way to probe the dynamics of these interparticle forces might be optical tweezers, in which a particle is trapped in the focal point of a laser. The trapping force can be calc ulated, and

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72 displacement from the equilibrium position in the focal point can be correlated with the interparticle forces giving rise to the displacement. Unfortunately, I do not have access to such instrumentation. The question has been posed as to whether the monomer has been polymerizing prematurely during the settling process. Such premature fixing of the matrix would impede the formation of hexagonal arrays, which does not appear to be the case, s ince an increase in order was observed from the 0hour sample to the 20 hour sample. Further, the monomer photoinitiator solution appears to remain liquid and fixable after many months storage in the dark. The batch I am using was mixed with Darocur in June of 2010 and at the time of this writing had been stored for 17 months. It was still liquid and was fixable to make fresh samples. Since the samples are settled in the dark, it seems likely that premature polymerization is not a factor in array formation. However, it is prudent to consider this as a possible source of array variance from batch to batch. Reasons could include inadvertent dosing of UV in a lab environment, differences in photoinitiator concentration, or perhaps interaction with the particle surface. It is possible that free radical oxygen could exist on the particle surface, inducing free radical polymerization of ETPTA at the particle surface. The ETPTA bottle carr ies a polymerization haz ard warning, and is kept in opaque brown bottles in a closed cabinet to prevent exposure to light. The ETP TA as delivered from the manufacturer includes a polymerization inhibitor, which if evaporated or insufficient could influence the overall process and final results. I n Chapter 4 an analysis of Fig. 1 9 for interparticle spacing as a function of lattice d irection indicates no statistically significant difference in interparticle spacing as a function of lattice direction, suggesting no lattice distortion on

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73 polymerization. However one such analysis does not preclude the possibility that premature polymeriz ation for one reason or another may be present and influence final results.

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74 CHAPTER 4 ANALYSIS OF ARRAY OR DER Introduct ory Remarks Particle Size Distributions Particle size distributions will be shown from the direct analysis of the SE M images as measured by the ImagePro image analysis software as well as from a disk representation of the SEM image generated by using the MS Visio drawing program to overlay each particle represented in the SEM image with a disk that just covers each particle. Interparticle Spacing Analysis An analysis of nearest neighbor spacing frequency is shown from an analysis of the particle positions generated by ImagePro in the course of particle size analysis of the disk representations of the SEM images. ImagePro picks up too many artifacts from the SEM images to be useful in this analysis. The spacing frequency analysis was performed by Paul Carpinone, a fellow graduate student at the University of Florida Material s Science department. His programming experti se was indispensable for this analysis. The principal criterion for this analysis was to restrict the consideration of interparticle spaces to be less than three mean particle diameters. Translational and Rotational Order Analysis The correlation analysis proceeds in two basic steps. First, a disk representation of the SEM image is generated by using the MS Visio drawing program to overlay each particle represented in the SEM image with a disk that just covers each particle. An ideal array mask is generated with MS Visio by using a regular hexagon call out sized to span representative ordered regions of the disk representation of the SEM

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75 image. The callout aspect ratio is locked to prevent distortion of the hexagon. There is a certain amount of subjectiv ity to sizing the hexagon to the sample lattice that could perhaps be automated and optimized. This is due to the fact that the sample lattices are not ideal. The vertices of the regular hexagon are then populated with disks that span representative partic les of the SEM image. The populated hexagons are magnified to 2000 times in the MS Visio program and check lines drawn to ensure equality of the hexagon edge lengths. Then a center is identified by drawing lines between opposing vertices, and a disk is pl aced at the center of the hexagon. Then all lines are deleted, disks grouped, and the aspect ratio of the base structure locked. These base hexagons are copied and pasted together and aligned at 2000 magnification to ensure best alignment. In spite of the above precautions, a certain amount of spacing error propagates, so that the resulting ideal, simple hexagonal array does not align itself perfectly if copied and pasted over its self. With the lattices pasted over each other, the upper, movable lattice is colored white, and the lower, fixed lattice is colored black. If the upper lattice is translated by a lattice constant in the direction of a primitive lattice vector over the lower or fixed lattice, and if the upper lattice completely obscures the lower lattice initially it will not completely obscure the lower lattice after the shift. This is especially noticeable if the upper lattice is rotated by 60 degrees over the lower, as unobscured crescents appear at the periphery of the resulting structure. How ever in the following analysis the agreement with ideal expectations is true within about 4 %. That is, the uncovered area of the fixed array should be zero after rotation of the covering mask, but in fact is not zero. Also, the image analysis program, Imag ePro picks up small areas of the

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76 obscured fixed or sample array and so generates a small amount of uncovered area, even for the directly copied and pasted mask over mask in the initial configuration. Thus there are variances introduced with these software programs that could perhaps be fixed with more sophisticated software. It is hoped that the analysis is reasonable and suggestive of an interesting technique to characterize various types of partially ordered arrays. A plot of the ideal array translation data is presented with one obtained by deriving the mathematically ideal plot. The resulting fit is good to around 4 % at the limit of complete coverage, corresponding to zero translation of the mask with respect to the sample. After the ideal array is com pletely tiled to span the sample area, two types of image are created. One image has the ideal array copied and pasted over its self, the other pastes the ideal array over the disk representation of the SEM image. Figures 41A and 41B below show the disk representation of Figure 31 and the ideal array generated from Figure 33. The overlaid and translated ideal arrays are seen in Figures 4 6A through 4 6K. Fig. 4 1. Disk overlay images. A) Disk representation of Fig 3 1, B) Ideal array based on F ig 3 3. A B

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77 The upper array was stepped through its lattice constant in ten steps, and the angles stepped through 2, 3, or 6 degree increments depending on the sample. This was done for Figs. 31, 3 3, 3 18, and 319. Mask over mask analysis was done for the ideal arrays appropriate to Figs. 3 1 and 33, and Figs. 318 and 3 19; there is one of these for each set of two images The mask over mask analysis tells us what an ideal array should look like, and is to be compared to the mask over sample analysis to give an idea of the ideality of the sample arrays. An order factor M% was defined in terms of the percentage of the unmasked area of the fixed sample array overlaid by the mask, divided by the total area of the disks of the sample array whether the ideal sample or the disk representation of the SEM i m age as appropriate This parameter is defined as the masked percent, M % = (1 unm asked area/total sample area)*100%. The M% factor is then plotted as a function of the lattice displacement in nanometers or mas k rotation angle as appropriate. The ideal array plots tell us what an ideal array should look like with this characterization. The plots will depend on the particle size and spacing. We will see that the Fig. 31 ideal array plot ranges from ~ 100% to 0% while the Fig. 319 ideal array plot ranges from ~ 100% to only ~ 35%. This is because the sample in the Fig. 3 1 ideal is completely unmasked at the lattice constant translation, whereas the sample in the Fig 3 19 ideal is always masked to some extent due to particle size relative to the spacing. Thus the shape and depth of the curves is indicative of the order, particle size, and spacing of the ideal arrays. If the particle size was much less than the lattice spacing, the M % curves would d rop quickly to zero and look like an inverted square

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78 wave If the sample was close packed, the M % curve would have a maximum depth of ~78%. Another issue about this analysis is the calibration of ImagePro for particle size to use in the measurement of areas obscured. It is really irrelevant what size is used as long as the same calibration is used for each set of images, e.g., the 32 images analyzed for Fig. 31, since the ratio of areas is invariant to a gauge transformation of the form r ar. That is i fi ( ari)2 / i ( ari)2 = i fi ( ri)2 / i ( ri)2. However, I used a particle diameter of 378 nm for Figs 3 1 and 3 3, and 280 nm for Figs 3 18 and 3 19. It is important to be consistent from image to image when measuring the unmasked area. The lattice constant was t aken from the MS Visio disk representations of the SEM images using the above particle sizes as reference for each set of images analyzed The lattice constant used for Figures 31 and 3 3 was 796.7 nm and 440.7 nm for Figures 318 and 3 19. The functional form of the resulting plot of M % can be derived from the area of a sector of a disk by referring to Figure 4 2 Figure 42 Reference areas for calculating the masked area % as a function of mask translation X

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79 Area of part of disk contained in angle is R 2 s1 A= 2 Area of disk = R 2 dA. Area of black triangle is [sin()][cos()]sin() bhRR R 211 1 2 22222 A= Small area of disk bounded by triangle is sin() RR 2211 22sdA. M asked area = grey lenticular area = [sin()]sdAR 22 cos()cos() XX RR 12 222 where X = the mask translation [sin()] % *{cos()sin[cos()]} R XXM RR R 2 11 2100 1002 2 22 ImagePro measures unmasked area, so experimentally M%=100UM%. The plot of this derived M%, over laid with the plot of the measured M% of the ideal array vs. translation appears in Figure 4 3 below. Ideal Masked % vs. Lattice Displacement Derived: Red Measured: Blue 0 10 20 30 40 50 60 70 80 90 100 0 100 200 300 400 500 600 700 800 Displacement (nm) Masked% Figure 43 Masked% vs. translation. Red curve is derived, blue is experimental.

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80 Finally, it should be pointed out that particle size analysis from SEM images is affected by artifact s in generating SEM images. One such artifact is that when the electron beam encounters a nearly vertical surface as the vertical surface of a sphere, its effective sample volume for ejecting secondary electrons used in the imaging process is increased by 1/cos( where is the angle between the beam and surface normal, over that of a horizontal surface [ 37] This brightens and artificially enlarges the vertical edges. Also in this case, particles are embedded in polymerized ETPTA. This expands the apparent par ticle size. Sizes used for the order analysis of Fig s 3 1 and 3 3 were taken from Fig. 36, as this image is of a fracture cross section which clearly reveal s particles not ostensibly covered with monomer. However, some polymer may still be bound to these particles, so some degree of uncertainty still exists with the particle sizes used in the analysis of Figs. 3 1 through 315. Once again, the diameter used in these analyses was 378 nm. For Figs. 318 and 319, dedicated SEM images of dried Stober silica particles were sized, giving a mean diameter of about 280 nm ( Fig. 4 40) The images of Fig. 4 40 also had to be circled with MS Visio, otherwise ImagePro lumps all the particles together, as it cannot separate particles that are touching. An unfortunate artifact of drying particles on a piece of silicon wafer is that the particles aggregate by capillary forces as the solvent evaporates. It is a fairly standard technique to separate such aggregates using drawing programs for particle size image analysis. I n all there was a good deal of variance with the particle size measurements. Particle Size Interparticle Spacing, and Order Analysis Figure 3 1 and Figure 3 3 Ideal Array Order Analysis Translation To begin the analysis for this section, I will show the 11 images generated from MS Visio by translating the mask over the ideal array of Figure 41B

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81 though a lattice constant of 796.7 nanometers in 1/10 increments. The graph for this has already been shown in Figure 43. Then the 31 images for the rotation of the mask in 2 degree increments over the ideal array of Figure 41B will be shown, followed by the graph of the masked area%. Then images and graphs for translation and rotation of the mask over the sample image of Figure 41A with M % graphs will be displayed. F inally overlay the M% graphs for the Figure 4 1 A and 4 1 B translations and rotations to compare the sample with the ideal s. A black background has been added to aid visualization; ImagePro sees only white over black.

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83 Figure 44 Translation images of the ideal mask over Figure 4 1 B The increments are in 10ths of the lattice constant set to 796.7 nm. A) Initial translation X =0 nm M%~100% B) X= 79.7 nm, C) X=159.3 nm, D) X=239 nm, E) X=318.7 nm, F) X=398.3 nm M%=0 G) X=478 nm, H) X=557.7 nm, I) X=637.4 nm, J) X= X=717 nm, and K) X=796.7 nm one lattice constant translation, M%~100% The mask% plot, Fig. 4 3 shows that initially the sample particles are approximately 96% covered by the mask as measured by ImagePro and that after 10 tenths of lattice translations the mask% returns (approximately) to its initial value as it should. Regardless of the underlying sample, an ideal lattice displaced by any number of lattice constants in a primitive direction will be indistingui shable from its initial configuration and have the same coverage as its starting position. Since the particle spacing is large enough relative to the particle diameter a fter 5 of 10 lattice translations as seen in Figure 44 F, the sample is completely ex posed and the masked% drops to 0%, i.e., the sample is completely uncovered. Rotation Analysis. Next display the angle rotations over the ideal lattice. Here we expect to see periodic variations with angle as different crystal planes of the sample are mas ked and unmasked by the mask; the plot should and will be symmetric around 30 degrees. I will display the plot first, as it is the more interesting of the plots, then the list of images in order of rotation angle in 2 degree increments. The rotation is plotted from

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84 two degrees to 58 degrees, since at 0 and 60 degrees, the masked% is 100% and quickly drops to around 20%. At full scale the interesting detail from 2 to 58 degrees is lost to scaling. Note the interesting patterns generated in the Figure 4 6 ima ges Fig ure 4 5 Plot of the masked% for the rotation of the ideal mask over the ideal sample. Note the symmetry around 30 degrees of rotation. If the mask was perfect, the symmetry would be perfect.

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89 Figure 46 Rotation overlays of ideal mask over ideal sample based on Fig 3 3, in 2 degree increments Figures 46 A through 46 DD show the patterns generated for each rotation step. Note the symmetry around 30 degrees in Figure 4 6 P. Symmetry of Fig 4 6 B is the same as Fig 4 6 CC, symmetry of Fig 4 6 C is the same as Fig 46 BB and so on. Figure 3 1 Next the analysis of the disk representation of Fig 31 will be presented. First Ill show the particle size distribution from the SEM image and the dis k representation. Then the spacing analysis will be shown, and finally the ideal mask over sample correlation analysis. The correlation analysis will first examine the linear lattice displacement, then the rotations in 6 degree increments.

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90 Particle size. Particle size distributions for Figure 31 based on the SEM image and the disk representation of the SEM image are presented below in Figures 47 A and 4 7 B respectively. The results are a bit different in both cases and different from the particle size dis tribution obtained from the disk representation of Figure 36. Note the number of particles counted in the Figure 31 SEM image is nearly identical to the disk representation. This is surprising since ImagePro tends to pick up speckles and artifacts that increase the apparent number of particles. The width of the particle size distributions is quite different however. Once again, the particle size used in the spacing analysis is taken from Figure 36. The average of the disk representation is 405 nm, which is close to the Figure 3 6 average, much more so than the SEM average. Figure 47 A) Fig 3 1 SEM particle size distribution, B) Fig. 31 disk representation particle size distribution. Interparticle spacing. The graph of the interparticle spacing analysis for Figure 31 is presented below in Figure 4 8 The Gaussian structure from 1.53 to 2.23 diameters indicates some order, but the rise of spacing frequency after 2.53 diameters indicates lack of order. This should be compared to the similar analysis for Figure 317, which is the most randoml y spaced of the samples presented. The spacing analysis for Figure 317 shows a very uniform distribution of spacing out to 3 diameters. Although there is

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91 bimodality in the spacing graph of Figure 317, the depth of the intermodal well is only about 15 particles based on a rough average peak to valley distance, while the depth here is closer to 80 particles. Fig 4 8 Analysis of Fig. 3 1 interparticle spacing relative to diameter of 378 nm (Source: Paul Carpi none, University of Florida, Particle Engineering Research Center, used by permission). Order analysis. First the translational graphs will be shown with the sample graph of the Fig. 31 disk representation overlaid with the ideal array created from Fig. 3 3. Then the overlay of the sampleideal results with the ideal ideal results will be shown. This will be followed by the images used to generate the values for the graphical result. Similarly, the rotational graphs and images will be displayed next. Tran slation analysis. The results of the ImagePro measurements of the masked area% of Figure 31 overlaid with the ideal mask created from Figure 3 3 and

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92 translated through a lattice constant of 796.7 nm in 10th intervals is displayed in Figure 4 9 below. The principle feature of this result is that the masked area remains roughly constant with translation of the ideal mask. This is especially noticeable in the plot of the sample and ideal. This is expected, as the particles in Fig. 3 1 are not well ordered. Figure 49 Translational analysis of the ideal mask of Fig. 33 with the disk representation of Fig 31 and with itself A) Fig. 3 1 disk representation overlaid with Fig 33 ideal mask This show s the masked area percent as a function of translation of the ideal mask, B) Comparison of the translation of the ideal mask overlaid with itself and the translation of the ideal mask overlaid with the disk representation of Fig. 31. Ideal is the red curve; sample is blue. Rotation analysis. The resu lts of the ImagePro measurements of the masked area% of Figure 31 overlaid with the ideal mask created from Figure 3 3, and rotated through 60 degrees in 6 degree increments is displayed in Figure 41 0 below. This result is similar to the translational r esult, and the masked area remains roughly constant varying from around 19.8% to 21.6%, and does not display any particular symmetry as a function of the rotational angle.

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93 Figure 410. Rotational analysis of the ideal mask of Fig. 33 with disk repre sentation of Fig 3 1 and with itself. A) Fig. 3 1 disk representation overlaid with Fig 33 ideal mask. This shows the masked area percent as a function of rotation of the ideal mask, B) Comparison of the rotation of the ideal mask overlaid with its self a nd the rotation of the ideal mask overlaid with the disk representation of Fig. 3 1. Ideal is the red curve; sample is blue. Translation images. These images were generated by first positioning the reference mask to try to obtain a maximum amount of coverage of the sample. However the coverage was never complete and the coverage as a function of translation and rotation remained about the same. The packing fraction of sample is about 0.21, which seems reasonable, as the packing is not close spaced. This is based on the MS Visio area containing the particles and the area of the particles measured by ImagePro.

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95 Figure 41 1 Translational overlay images of the ideal mask created from Fig. 33, scaled to the magnification of Fig. 31 mask ing the disk representation of Fig. 3 1. Figs. 4 11A through 4 11K are masked images in 10th lattice steps. The magnification of Fig. 31 is 4500 X; Fig. 3 3 is 8000 X. Figures 41 1 A through 4 1 1 K display the coverage of the mask over the sample in 1/10 st eps of 797 nm, starting with zero translation and ending with a lattice translation of 797 nm. Rotation images. The mask coverage images of Figure 31 as the mask rotat es over the sample in 6 degree steps are shown below in Figure 4 1 2

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97 Figure 41 2 Masked images of Fig 31 as function of mask rotation through 60 degrees in 6 degree increments. Figs. 4 12A through 4 11K are masked images in 10th lattice steps.

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98 Figure 3 3 Particle size. The particle size distributions measured from the SEM image and disk representation of Fig. 33 are shown in Figures 4 14A and 414B below. The result from the SEM images shows a lot of fines which are noise artifacts in the SEM image. The disk representation is mor e concise and has a standard deviation of one. This only indicates that all the disks used to cover the SEM image were the nearly same size. Once again, the particle size used in the order overlays was taken from the analysis of the disk representation of Fig. 36, which is shown in Figure 4 1 3 Packing fraction for this sample is about 0.1855. Figure 41 3 Disk representation of SEM image Fig.3 3. Figure 41 4 Particle size distributions of Fig. 33. A) Size distribution measured from the SEM image, B) Size distribution measured from the disk representation.

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99 Interparticle spacing. Nearest neighbor interparticle spacing analysis of the disk representation of Figure 33 shows definite signs of order. It is evident from looking at the micrograph that that there are relatively large regi ons of simple hexagonal order, as well as square order and transitional order as discussed previously. The graphical analysis shown in Figure 415 shows a strong Gaussian structure that trails off rapidly at about 2.8 particle diameters. This indicates nearest neighbor spacing is confined to a narrow set of nearest neighbor diameters consistent with regular structure. The mode of the peak occurs at 2.23 diameters. The mode here is larger than the mean interparticle spacing of spincoated arrays, which has been shown to be about 1.41 diameters [1]. This increase in spacing must be due in part to the regions of square and transitional order. This sample was settled for 20 hours before fixing, and has been used as an example as to how the spin coated arrays bec ome ordered. Although the ordering of the particles in this image is not completely simple hexagonal, it does exhibit regions of simple hexagonal order This suggest s that spincoating densifies the arrays, but that order is initiated by self assembly of t he particles in monomer, mediated by isotropic steric repulsion to force interparticle separations to be equal. The similar analysis of Figure 318 will be seen to be more concisely Gaussian; the particles in the Fig. 3 18 SEM image are obviously ordered. It must be pointed out though, that there are only 205 particles represented in Fig. 318. The analysis of Fig. 3 17 shows complete disorder, and the nearest neighbor results are very uniform out to three particle diameters. That is, the interparticle spacings are equally likely with no tendency for the spacings to cluster around a particular value, which is an indication of random ordering.

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100 Figure 41 5 Fig. 3 3 n earest neighbor spacing analysis. This shows strong ordering by the confinement of nearest neighbor spacings to a relatively small domain. More disorder e d arrays have a uniform distribution of spacings. (Source: Paul Carpinone, University of Florida, Particle Engineering Research Center, used by permission). Translation analysis. The results of the ImagePro measurements of the masked area% of Figure 33 overlaid with the ideal mask created from Figure 3 3, and translated through a lattice constant of 796.7 nm in 10th intervals is displayed in Figure 4 1 6 below. The shape of this plot is the similar to the ideal result shown in Fig 43. However, the depth of the plot is much less than ideal. This is due to the fact that it was not possible to completely mask the sample so that the mask could not cover the entire sample. Al so, the sample is never completely free of the mask and so the coverage does not go to zero as in the ideal case for Fig 33. However, t he similarity of shape can be interpreted as an indication of order in Fig. 33, which is obvious by looking at the SEM image. The fact that there is square and transitional order of the particles represented in Fig. 3 3 is of course the reason the sample is not ideal and the masking analysis reflects this fact.

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101 Figure 41 6 Fig. 3 3 Masked % vs. Translation. A) Sample M% B) Overlay of sample and ideal M %. Rotation analysis. The results of the ImagePro measurements of the masked area% of Figure 33 overlaid with the ideal mask created from Figure 3 3, and rotated through 60 degrees in 3 degree increments is displ ayed in Figure 41 7 below. The sample exhibits some symmetry about 30 degrees with dips around 6 and 54 degrees approximately like the ideal. However, as seen in Figure 41 7 B, the agreement between sample and ideal is far from exact. Figure 41 7 Rot ational analysis of masked % vs, angular rotation of ideal array over disk representation of sample array. A) Fig 3 3 masked%, B) Comparison plot of sample and ideal masked%.

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102 Translation images. The translation images are shown below in Figures 418 A through 4 18K. The masked images seem somewhat random, unlike the images of the ideal mask translated over it self. However, the plot of M% seems to indicate ordering, as can be seen by visual inspection of Fig. 33 and the resulting plot of the masked% in Figu re 41 6 A and 41 6 B. Figure 4 18A and 418K, the start and end points are in good agreement with each other as they should have the same coverage if the mask is ideal. This is also indicates by the plot, Fig 4 1 6 A and 41 6 B.

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104 Figure 4 1 8 Translational overlay images of the ideal mask created from Fig. 33, scaled to the magnification of Fig. 33 masking the disk representation of Fig. 3 3. Figures 41 8 A through 41 8 K are images of the ideal mask covering the sample in one tenth steps of the lattice constant taken as 796.7 nm. Rotation images. Figures 419A through 4 19U show the masking of Fig 3 3 by the ideal array mask created from Fig.3 3, rotated through 60 degrees in 3 degree increments. There are few signs of symmetry in these images like those in the images of the ideal mask over its self, although there is order evident in the micrograph.

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108 Figure 419. Masked images of Fig 33 Figs. 4 19A through 4 19S are masked images through 60 degrees in 3 degree increments. Figure 3 6 Particle size. The mean particle size from the size distribution analysis of Figure 3 6 was used in the analysis of Figures 31 and 33. Therefore this distribution will be displayed. As explained previously, since F ig 36 was a fracture edge, the particles are clearly visible and apparently not covered with polymer. Both the distribution obtained from the measurement of the SEM image Fig. 36, and its disk representation will be shown. The mean particle sized used in the analysis of Figures 3 1 and 33 was taken from the disk representation data. The small particles in the disk representation of Fig. 3 6 are from particles pulled out of the fracture edge, leaving only a small depression, and should be removed from t he analysis. This can be seen in the SEM image as apparent depressions ImagePro cannot distinguish these depressions from particles, so they must be removed from the size listing manually and the average recalculated. This is shown in Figure 420B in the bottom of the statistics panel. The small sizes were

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109 eliminated from the size listing and the mean particle diameter recalculated to be 377 nm. This is the diameter used in the spacing and order analysis of Figures 3 1 and 33. Only clearly defined partic les, identified from the micrograph, are used to calculate the mean diameter. Figure 420. Disk representation of Figure 36. Small particles are depressions left when particles are pulled out of the fracture face. Figure 421. Particle size distributions of Fig.3 6. A) SEM image analysis, B) Disk representation image analysis. Recalculated mean of 377.2 nm derived by removing fines from the size listing.

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110 Figure 422. Nearest neighbor interparticle spacing analysi s of Fig 3 6. This shows lack of concise order, which would be demonstrated if the curve dropped off after about 2 particle diameters. (Source: Paul Carpinone, University of Florida, Particle Engineering Research Center, used by permission). Interparticle spacing. The interparticle spacing analysis of Figure 36 is shown above in Figure 422 Much like the similar analysis of Fig 3 1, there is no concise order as indicated by the approximate uniformity of the spacing frequency. Since this is a zero hour fix ed sample, this is to be expected. Notice though that very few particles are touching, indicating that steric repulsion is active in the vertical plane. Particles that are touching have a relative spacing of one diameter. Figure 3 17 Particle size. The dis k representation of Figure 317 is shown in Figure 423 and the particle size distributions in Figures 424 A and 424 B. The stated size from the manufacturer, GelTech was nominal 500 nm. The disk average particle size of 469 nm is at least close to this va lue. The SEM image contains many speckles, which causes ImagePro to badly undersize the particles.

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111 Figure 423. Disk representation of Fig. 3 17 Fig 4 24 A) Particle size distribution measured from the SEM image, B) Particle size distribution measured from the disk representation of Fig. 317. Interparticle spacing. The interparticle spacing graph of Figure 317 is displayed below in Figure 4 25. These calcined particles formed the most disordered of the arrays. The interparticle spacing analysis indicates a uniformity of interparticle spacing consistent with random order. That is, any interparticle spacing is as equally likely as any other. The peak to valley distance here is only 15 particles. The Fig. 33 interparticle spacing peak to val ley distance is about 50 particles; the Fig. 3 1 peak to valley distance is about 80 particles. Note though that no particles are touching

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112 according to this analysis, which indicates the absence of an attractive van der Waals force between the particles. T here does in fact appear to be a certain amount of repulsive interaction, as the relative spacing begins at about 1.18 diameters. Figure 425. Interparticle spacing analysis for Fig. 317. The uniformity of spacing frequency is an indication of random order. Repulsion is indicated by rise of spacing frequency from about 1.18 diameters. Figure 3 1 8 Particle size. Pa rticles size for Figures 3 18 and 319 is taken from Figure 426 below. This sample was prepared by drying a suspension of the Particle Sol utions LLC Stober silica particles directly from the parent suspension. An artifact of such a procedure is that the particles aggregate on drying. This requires the particles to have a disk representation generated. First the particles Are circled as in Fi gure 4 26A. Then the circles are dragged off the image and filled in as disks. The disks are then grouped,

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113 copied and pasted on their own sheet along with the scale bar which is scaled at 100 nm by the SEM software. The disks are then separated and their s ize measured with ImagePro. The result is a mean particle size of 278 nm 9 nm. Since this is the particle size work up for Figures 318 and 3 19, I will forgo displaying the particle size distributions generated from the SEM and disked representations of these figures. As discussed previously, there are many artifacts generated from the SEM images of these particles embedded in polymer. It is unfortunate that I do not have any of the original particles used in this study, as it would reduce the uncertaint y in the particle sizes used. Figure 426. Representative image used to measure mean particle size for the Particle Solutions, LLC Stober silica particles used in Figures 318 and 3 19. A) SEM image with circles drawn around particle, B) Disks made fr om circles after dragging circles away from SEM image and pasting on their own sheet. Interparticle spacing. The interparticle spacing analysis for Figure 3 18 is displayed in Figure 42 8 below. An interesting feature of this plot is that there are partic les with relative spacing less than the mean diameter. This is of course a result of the fact that some of the particles are smaller than the 280 nm used to set the relative scale for this analysis. The remarkable feature of this plot is the very concise G aussian

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114 structure indicating tight clustering of the interparticle spacing. The standard deviation is 0.15 times 280 nm or 42 nm. It is obvious from the SEM image that these particles are well order ed in simple hexagonal array, but that there is also a good deal of variance in their spacing. This sheds light on the question of control of order in this system and suggests that there will be 10 to 20 percent variance in the interparticle spacing that is unavoidable. As mentioned before, there are only 205 par ticles in Fig. 3 18, so a larger sample, such as Fig. 319 might display a wider variance in spacing. However as will be seen shortly, the interparticle spacing analysis of Figure 319 reveals a standard deviation of only 0.1 diameters or 28 nm. Figure 318 is an image of the bottom of the fixed suspension, and as will be seen in the interparticle spacing analysis for Figure 319, the average interparticle spacing for Figure 318 appears to be larger than for Figure 319. Figure 3 19 is an image from the t op of the sample, so this result implies that the bottom layer is spread open by the upper layer particles pressing down on it. This could provide evidence that the spin coating helps drive the lower layers apart and allows them to be populated by particles from the higher layers densifying the final spin coated product. It is obvious from watching a spin coat process that particles separate axially as they progress radially down the wafer. This causes lines of particles to separate and allows particles from upper layers to populate layers below. Thus there appear to be at least two mechanisms operating to form the final spincoated product. One more point to support the difference in spacing from Figure 3 18 to 319 is that the lattice constants in these t wo images are different. The lattice constant for Fig ure 3 18 is 440 nm, while for Figure 419 it is 402 nm. The disk representation of

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115 Figure 318 is shown below in Figure 4 27. The spacing to diameter ratio for Figure 3 18 is S/D = 1.84, while S/D = 1.51 for Figure 319. That i s the spacing for Fig 3 18 is 1. 84 diameters, but only 1.51 diameters in Figure 3 19. This corresponds to the different lattice constants from the top image to the bottom image. Figure 427. Disk representation of Figure 318. C ompare to Figure 435. Figure 42 8 Interparticle spacing analysis of Figure 318.

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116 Order analysis. First the idea l array analysis of the mask derived from Figure 319 will be shown. It turns out to not be as interesting as the mask generated from Figure 3 3 due to the ratio of particle diameter to spacing. The ratio of diameter to spacing in Figure 319 is about 0.7, while for Figure 33 it is about 0. 47. The larger diameter to spacing ratio of Figure 319 causes the ideal sample to be always covered by the mask, where for Figure 3 3, the ideal sample can be completely exposed. Thus for Figure 319 ideal there results a translation curve of the same shape as the ideal translation curve for Figure 3 3, but only dips down to 35% coverage. The angular dis placements exhibit a much smoother behavior than the Figure 3 3 curve, as the sample retains a greater percentage of coverage. The symmetry of the Figure 33 ideal is not as evident for the Figure 319 ideal though symmetry is evident in the ideals and samples. T ranslational and rotational graphs for the ideal array sample, and overlay of ideal and sample for Figure 318 are shown below in Figures 42 9 through 43 1 The masked images are shown in Figures 4 3 2 and 43 3 The masked% is a maximum of 62%. A B Figure 42 9 Translational and rotational masked% graphs from the ideal mask and array generated from Figure 319. A) Translation, B) Rotation.

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117 A B Figure 430. Translational and rotational masked% graphs for Figure 318. A) Translation, B) Rotation. A B Figure 43 1 Overlay of ideal and sample translation and rotation masked%. A) Translation, B) Rotation.

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119 Figure 43 2 Translational masked% images for Figure 3 18. Figures 43 2 A through 43 2 K show masking% at 10t h intervals of the lattice constant of 440 nm.

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123 Figure 43 3 Rotational masked percent of Figure 318. Figure 43 3 A through 43 3 U shows the ideal mask coverage of the sample in 6 degree increments from zero to 60 deg rees. Figure 3 1 9 Particle size. P a rt icle size for this image has already been discussed for Figure 3 18. The particle size used in both these image analysis was 280 nm as previously stated. Interparticle spacing. The interparticle spacing analysis result s are shown in Figure 433. The results are well fit to a Gaussian distribution of numbers of particles versus interparticle spacing with a standard deviation of 28 nm. This is indicative of equality of interparticle spacing which is ensured by simple hexagonal packing. The curve begins concisely at 1.25 diameters and fall to zero at about 1.76 diameters with a mean at 1.53 diameters. The mean is not too different from the often observed 1.41 diameter spacing of the spin coated arrays [1]. There are a large number of simple hexagonal regions as can be seen by inspection of the SEM picture, Figure 319. This

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124 was the best image obtained in this study. The disk representation of this image is shown in Figure 4 34. The disk representation s w ere analyzed in ImagePro to obtain the particle positions, which were used to calculate the interparticle spacings. Nearest neighbor spacing was cut off at two diameters, but as is evident from the graph, the nearest neighbor spacing does not extend to even two diameters. Figure 43 4 Interparticle spacing results for Figure 3 19. The Gaussian fit is an indication of order, but perfect order would have a much smaller standard deviation, approaching a delta function. (Source: Paul Carpinone, University of Florida, Particle Eng i neering Research Center used by permission). Figure 43 5 Disk representation of Fig. 3 19. This image exhibits a great number of body centered hexagons demonstrating self assembly of freeze dried silica particles into approximate hexagonal arrays in ETPTA monomer

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125 Order analysis. Finally the translational and rotational graphs for Figure 319 sample, and overlay of ideal and sample for are shown in Figures 43 6 and 43 7 The translational and rotational mask images are shown in Figures 4 3 8 and 4 3 9 The sinusoidal structure of the sample mask% is unusual and certainly nothing like the ideal. The sample mask was tilted to conform to the lines of part icles and translated both in the X and Y directions. This will be seen in the masked images. The rotational graph does not quite return to its starting point; errors in the ideal array are most evident in the rotations. Starting and end coverage at 60 degr ees typically differ by about 6%. A B Figure 436. Fig. 319 translational and rotational masked%. A) Translation, B) Rotation. Figure 437. Overlay of Fig. 319 ideal and sample masked%. A) Translation, B) Rotation.

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127 Fig ure 438. Fig 3 19 translational masked% images. The mask was translated at 13 degrees from the horizontal Figures 4 38A through 438K are the mask images translated in 10th lattice constant steps. Lattice constant was 402 nm.

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131 Figure 439. Fig 3 19 rotational mask% images. Figures 439A through 439U are the masked images from zero degrees through 60 degrees in 3 degree increments. Figure 1 9 The image in Figure 4 4 0 shows the grid used to collect data on the vari ations in interparticle spacing and particle size. The Visio drawing program was used to infer the scale in nanometers from the dimension bar at the lower right of the micrograph.

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132 Figure 4 4 0 ANOVA diagram for particle size and spacing of Figure 19 (Source: Prof. Peng Jiang, used by permission). There does not seem to be a statistically significant difference in interparticle spacing due to the directions of the interparticle separation vectors in this image, i.e., vertical, positive slope, and negative slope; there are 52 separation lengths in each direction. The F value for this design is 0.44, which indicates there is no statistically significant difference in separation lengths with respect to direction, at least in the horizontal plane. This indicates there is no overall lattice distortion during polymerization. These calculations were carried out with DesignExpert 7.1.3, using a general factorial model with direction as blocks. The average of the vertical spacing is 424 nm 27 nm; the average particle diameter is 310 nm 16 nm. The 2D value based on an average particle size of 310 nm is 438 nm. These calculations were carried out with Microsoft Excel This image was adapted from Figure 19 [1].

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133 CHAPTER 5 THEORY AND MODELS Initial Theory Considerations It w as assumed when I began this study, that the spin process and the resulting fluid flow and shear caused the particles to organize into hexagonal arrays. Initially I assumed this to be true. Thus I was led to consider development of complex fluid flow equations with a free boundary, variable shear as a function of the radial distance from the center of the wafer, in a viscous (60cP), possibly non Newtonian fluid, with 20 volume percent of spherical particles. This presented a formidable theoretical challenge that daunted me for s ome time. It is well known that models of fluid particle flows at high solids loading are not well established, even for otherwise simple laminar flows. In this case I was lead to consider not only the radial motion of the center of mass of the particles, but also their rotation. The particles should rotate, since they are subjected to a greater fluid velocity shear force on their surface closest to the free fluid boundary than the velocity shear force on their surface closest to the wafer surface. In addit ion, the hypothesis of a fixed layer of fluid at the wafer surface begins to break down at high rpm. At high rpm all the fluid can be removed from the wafer. During the spin process, the fluid probably begins to exhibit semi stick conditions and begins to migrate radially outward from the center of the wafer as rpm increases. Such conditions further complicate fluid flow models. In considering such models, the mathematics is typically second order in space and first or second order in time. Therefore, two boundary and one or two initial conditions must be given in order to completely specify the solution.

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134 It is apparent from the images in Figures 3 1 and 3 2 that the particles show simple hexagonal ordering, even for the immediately fixed (0hour) samples T he 20hour samples are beautifully ordered in the horizontal plane as shown in Figure 3 19. Additionally, there are signs of hexagonal and square order in the vertical planes for the 20hour samples as shown in Figures 3 13, 3 14, and 3 15. This then, provides a major clue to the answer of the first question posed in the objectives: why do hexagonal arrays form during spin coating? It is because they are already hexagonally ordered! Ordered Monomer Mediated Interparticle Spacing With evidence in hand that the particles are approximately ordered into simple hexagonal arrays before spinning, it remains to suggest a reason for this behavior. Why is the hexagonal ordering not close packed ? W hy does the center to center separation, S of the particles scale to their diameter as SD 2 (Figure 19) in horizontal planes. As discussed throughout this dissertation, t he principa l theory is that steric or entropic forces, due to monomer ordering by hydrogen bonding to the surface of fresh St ber particles, enforces simple hexagonal packing Hexagonal packing equalizes interparticle repulsion since the spacing between the particles is the same for all the particles. I f there is a force imbalance, the particles will be forced to a configuration of equal forces on and between all the particles ; this enforces simple hexagonal order Since the particles are spherical, the effective steric force field surrounding the particles is spherically symmetric, which enforces equal interparticle spacing in t he horizontal plane as well as vertically, although the horizontal and vertical spacings are different due to gravitational settling in the vertical direction Only simple hexagonal packing

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135 ensures equality of all the forces in this case. This is not true for covalently bound systems, where bonds are highly directional ; the forces involved here appear to be isotropic and very soft. Settling Into Simple Hexagonal Arrays Minimize s Gravitational Energy G ravitational energy is minimized by having as many part icles as low as possible in the gravitational field, consistent with the constraints o n the system e.g., the horizontal surface of the wafer and the confinement of the particles to the monomer The maximum number of spherical particles, of the same diamet er, that can be fit into a given volume is achieved with either hexagonal or face centered cubic packing. Hydrogen Bonding of Monomer to Particle Surface Initiates Order My theor y is that the monomer orders by hydrogen bonding of the monomer molecules to the hydroxyl groups on the surface of fresh St ber particles. This order is theorized to propagate outwards from the particle surface to a distance depending on the radius of the particle. This theory is motivated by the observation that calcined partic les do not become ordered, as mobility measurements suggest they do not have enough hydroxyl sites for hydrogen bonding. Since there are fewer binding sites on calcined St ber particles for strong (3090meV) hydrogen bonding, the particle fails to align the monomer molecules. Thus, the monomer remains in a random state and provides no entropic or steric structure to enforce the ordering observed with fresh St ber particles. Since the ether and carbonyl oxygens of the monomer are capable of forming hydrogen bonds with the hydroxyl groups on the surface of fresh St ber particles it seems likely that bonding could occur.

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136 This idea that order propagates outward from the particle surface can be used to suggest a reason why particle separation depends on partic le radius. An e xtremely simplified model of a state of such particlemonomer ordering is depicted in Figure 5 1 A fully extended monomer molecule may be loosely rep resented as a n oblate ellipsoid. Such molecules are represented as red ellipsoids in Figure 5 1 The diameter of the major axis is taken to be 2.2 nm. The diameter is approximately eight times the length of a carbon carbon bond, approximately 1.5 times the sine of one half the average bond angle taken as 110 degrees, plus the length of a carbon hydrogen bond, about 1.09 The diameter of the minor axis is, similarly about 6 This model imagines a stack of ordered monomer molecules crystallized by the monomer strongly bound to the St ber particle surface, represented by the blue half disk by hydrogen bonds. As can be seen from Figure 5 1, the radiation of the column of disk stacks is wide enough to admit a monomer molecule at maximum cross section, exactly one radius distance from the surface. The observed center to center interparticle spacing i s around 1.4 times the diameter. The distance between two spherical particle surfaces separated by S along a line between their centers, where the center to center distance is D 2 satisfies D 2 = S+D so that the distance to disorder from one surface is S /2 = 0.4R From Figure 5 1 we see that for monomer configurations that present less than the maximum cross section, they still have the ability to invade the order of the model monomer stacks, reduci ng the distance from the surface of well ordered monomer. Figure 5 1 is a great exaggeration of the typical diameters of the particles used; t o scale with monomer the particle in Figure 5 1 would be only 8.2 nm in diameter.

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137 Figure 5 1. Radial divergenc e of order. This figure is an exaggerated model of hypothetical stacks of monomer molecules diverging along radii, so that random phase monomer molecules can invade the ordered stacks. A more realistic depiction of this model, in terms of the particle di ameter involved, in this case 300 nm is shown in Figure 5 2. T he situation is probably more chaotic, but this simple model, with the assumption that the monomer is well aligned on the particle surface by hydrogen b onding, provides a plausible qualitative explanation for diameter dependent spacing. Figure 5 2. Radial divergence of order to scale.

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138 Figure 5 2 is to scale with the diameter of the spherical particle set to 300 nm. Monomer major diameter is scaled to 2.166 nm; minor diameter to 0.6 nm. The distance to disorder as discussed above is approximately 0.4R, where R is the radius of the particle. With the minor axis of the ETPTA molecule around 0.6 nm, it would require a stack of 200 monomer molecules in this image before disorder attenuates the in terparticle repulsive cushion. The number of monomer molecules in the in the stacks in this image only 17, not nearly high enough to admit the random monomer fluid phase. I t may be that the monomer is somewhat ordered in the random phase, as the molecules m a y tend to align with their major axes approximately parallel, on average. This could give rise to non Newtonian behavior at very low shear, less than say 100/sec. Such alignment would be conducive to forming a steric cushion There are nine atoms of ETPTA capable of hydrogen bonding to hydroxyl groups on the Stober particle surface (Figure s 5 3 and 5 4 ) There are approximately five hydroxyl groups per square nanometer as discussed in the section on materials and St ber particle synthesis Figure 5 3 re presents monomer hydrogen bonded to the surface of a Stober silica particle having five hydroxyl groups per square nanometer. The density of hydroxyl groups is represented by the squares containing five SiOH groups to indicate the distribution of these gro ups on a square nanometer and their potential hydrogen bonding with the ether and carbonyl groups of the monomer. The angular structure of the hydrogen bonds may be important, as it is known that hydrogen bonds have definite geometric structure [ 30].

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139 F igure 5 3. ETPTA monomer hydrogen bonding to SiOH groups of the silica surface. Key: Silicon green, Oxygen r ed, Hydrogen blue, Carbon black; squares represent 1 square nanometer of particle surface area. Depicted in Figure 5 4 is the same situation, but with the squares removed and an extra MeOEtOAc arm on the model particle surface. There is some evidence [22 ] that the hydrophobic hydrocarbon sections can interact with hydrophobic sections of the silica particle, i.e., the Si O Si siloxane chains. These bonds would be much weaker than hydrogen bonds, perhaps less than 1 meV/bond, although there could be as many as 18 bonds per monomer molecule. It may also be possible that some amount of hydrogen bonding with the ether like Si O Si siloxane bonds of the s urface exists. This was mentioned in the discussion of Figure 2 2, though these bonds by themselves do not induce hexagonal order as evidenced by lack of ordering of calcined particles. Such bonds could lend strength to the overall structure however.

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140 Fi gure 5 4. ETPTA monomer hydrogen bonding to SiOH groups of the silica surface. Shear Ordering Finally, it remains to provide a model for the collapse of vertical spacing that produces interlocking channel arrays observed on dissolving the silica particles from the fixed polymer matrix. The basic model is that r adial flow shears monomer from between the particles in the vertical direction, allowing horizontal layers to collapse onto each other (Figure 1 4 ). In Figure 1 4B, note that the spacing of the voids appears nearly close packed and that the polymer matrix is polymethylmethacrylate (PMMA), which appears to generate different spacing than ETPTA, suggesting that control of spacing may be accomplished with different monomers. I have modeled the situation in Figures 5 5 and 5 6. In Figure 5 5 I have represented an initial condition in which the particl es are not in a regular order in the vertical planes but that there is appreciable distance between horizontal planes of particles The yellow arrows represent fluid flow velocity vectors, whose magnitude parallel to the wafer surface, a distance z away from the wafer surface, increases with z

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141 Laminar flow typically increases as v = a z2 The axial arrows are meant to represent rotation of the particles. It is suspected that the particles will rotate, as there is a difference in flow velocity with z along the vertical diameter of the particle. Figure 5 5. Initial condition model. Fluid flow is represented by yellow arrows; rotation of the particles is r epresented by the black circular arrows. In Figure 5 5, I have modeled an almost initial condition in which the fluid flow is established, but the vertical organization of particles is irregular as shown in the SEM images of Figures 3 11, 12, and 13 As the particles and monomer move outward from the center of the wafer, the particles shear monomer from between horizontal planes of particles, removing the monomer mediated repulsive cushion in the z direction. This allows horizontal layers to collapse onto each other and settle into gravitational wells between particles in the layer below them Th e vertical collapse of the bottom layers is represented in Figure 5 6. Here the yellow wavy lines represent hypothetical trajectories of fluid and particles as t he horizontal planes converge vertically. The monomer mediated cushion still exists between particles in horizontal planes and maintains the 2D horizontal interparticle separation. The rotational and translational shear generated by the particle motion

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142 di sturbs the weak ordering of the monomer around the particles, stripping monomer from between particles. Thus the horizontal layers are compacted into interlocking simple hexagonal arrays as in Figure 1 4. Figure 5 6. Particle organization during spin c oating (fcc) Row 1 is foreground, row 2 is behind row 1, and row 3 is behind row 2. Rows 4 and 5 are not yet settled. In Figure 5 6, I have represented the condition in which the particles have sheared monomer from between horizontal planes. Plane two has settled into the gravitational wells generated by the simple hexagonal, non close packed array of horizontal layer one. Layers four, five and so on are settling into the layers below them. As the vertical distance between layers decreases, the fluid flow will be pinched off between horizontal layers. Here, the blue wavy line represents hypothetical trajectories of fluid and particle flow from the center of the wafer as the horizontal planes converge. The monomer mediated cushion still exists between part icles in horizontal planes and maintains the 2D, horizontal, interparticle separation. The rotational and translational shear generated by the particle motion disturbs the weak ordering of the monomer around the particles, shearing monomer from between particles. Thus the horizontal layers are compacted into interlocking simple hexagonal lattices that can form three dimensional

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143 hexagonal or face centered cubic arrays. The dashed green circle around the particles represents surface roughness and hydroxyl gr oups. It is evident from watching the video of the spin process of Figures 3 21 and 3 22, that suspension is being flung off the wafer as the spin program progresses. That it is the upper layers that are being removed is suggested by the hypothesis that the suspension velocities are greatest in the upper layers of the suspension. This is a typical fluid flow regime in which free streaml ines move faster than those close to a surface. T hus it seems that the upper suspension layers do not contribute to the final array which is typically only a few particle layers deep. This indicates the lowest particle layers move slowly, which would tend to maintain the initial hexagonal order as indicated in Chapter 3. However, since the final layers are close packed vertica lly the model of collapse of the layers by shearing monomer from between the layers seems valid. One further point about Figure 5 6, is that it is evident from Figures 39 through 311 that particles protrude into the surface, although covered by monomer Figure 5 6 expresses this fact by representing the boundary of the particlepolymer system as the upper most blue wavy dashed line. There is otherwise no free monomer represented here. In Figure 37, a 0 hour cross section there appears to be a low density of particles in the upper level. However in Figure 34, another 0 hour cross section, particles populate the upper levels and protrude into the surface. It is likely that the number of particles in the upper layer decreases and increase as particles s ettle and as monomer is flung from the wafer.

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144 CHAPTER 6 FUTURE RESEARCH POSSIBILITI ES Control of Spacing Future research on this system should include further study of the control of interparticle spacing. There are two dimensions to control of interpartic le spacing in the construction of these arrays. One is the horizontal spacing and two is the vertical spacing. Although the horizontal spacing sel f assembles readily in 20 hours the vertical spacing was a good deal less symmetric after 20 hours ( Figure s 3 13, 3 1 4, and 3 15 ). Some of the topics below could be used to control both dimensions of order, such as varying the structure of the fluid molecules; some may help with the vertical order, such as temperature and sonic vibration. Different Fluids T he use of monomers similar to ETPTA with different numbers of ethoxy groups in the triacrylate chains or longer hub groups than propane, e.g., butane, pentane, or functional groups such as amino acids, and so on could be considered for their effect on array form ation. As shown in Figure 1 4, the polymers were polystyrene and polymethylmethacrylate (PMMA). The spacing in the two polymers is noticeably different, with the PMMA producing close packed arrays in both dimensions. Different Particles Another possibility for controlling interparticle spacing may be to use different types of particles than fresh St ber silica spheres. Aspects of arbitrary particles include size, shape, chemistry, and surface structure. Particles of various shapes may well form arrays consi stent with their shape, in order to minimize their constrained gravitational energy For instance, cubic particles may align themselves under orderedmonomer

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145 mediated interparticle forces to form cubic arrays. Since the packing fraction of cubes is one for cubic arrays of aligned cubes, a cubic array of aligned cubes minimizes the arrays gravitational energy and interparticle, ordered monomer repulsion, just as hexagonal packing minimizes the gravitational energy of settling spheres. Irregular shapes would require the ordered monomer to conform to the surface of the particle to generate a force field with the same symmetry as the particle. This force field symmetry then facilitates the minimization of the ordered monomer mediated interparticle forces consist ent with the geometry of the particles. Particle surfaces can be functionalized by attaching various molecules This is currently a very active area of research in conjunction with medical imaging and therapeutics; theranostics. It would be interesting to functionalize the particle surface with molecules of various lengths, degrees of hydrophobicity, hydrophilicity, symmetries, and chemical reactivity with the fluid, under various conditions, such as temperature, pressure, artificial gravity, and solids loading, i.e., fraction of effective particle volume to suspension volume, and observe the effects on final array structure. In other words, molecules attached to the particle surfaces could be used to engineer the particle spacing with respect to the 2D spacing observed with fresh St ber particles in ETPTA. Functionalization could also produce some useful interactions with light. For instance neutralize a fraction of the hydroxyl sites of fresh St ber particles with a small hydrophobic molecule X i.e., S iOH + X OH SiO X + H2O and see what changes in array structure are generated. Another interesting possibility is to use distinctly different particle sizes in the same particlemonomer suspension, such that the smaller particles will fit in the interstices

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146 between the larger particles without disturbing the large particle array. This may produce arrays with distinctive photonic behavior around two different wavelengths. Different Conditions Since most of these studies have been carried out in ambient condit ions, it is appropriate to consider a broader range of conditions these systems may be subjected to. Such conditions include temperature, pressure, volume fraction of particles to suspension volume, electric and magnetic fields both static and time dependent as well as sonic excitation. S onic excitations may facilitate settling into the lowest energy state of the array consistent with fluid mediated interparticle forces. This could help better organize self assembled arrays in the vertical direction. Tem perature may be useful to increase or decrease viscosity Decreasing the viscosity could help in vertical organization. Issues here might include thermal agitation i.e., Brownian motion, that would generate a population of particles with sufficient kinetic energy to escape binding to gravitational wells. Increasing temperature increases monomer kinetic energy as well and would lead to increased disorder of the monomer on the particle surface. T his might produce a steady state of disorder I t would be intere sting to map the temperature dependence in terms of a disorder to order ratio and arrive at an optimum temperature to maximize order ( effective packing fraction) and minimize production time and cost That is, the number of particles not in an array divid ed by the number of particles i n an array structure as a function of time, temperature, and cost Depending on the fluid temperature could be increased or decreased from ambient, e.g. ETPTA versus water respectively, to control thermal motion and surfacefluid molecule ordering.

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147 Pressure has been shown to be an important variable in spontaneous colloidal phase transitions from disordered to ordered crystalline states [ 38 ]. Particle size mass and temperature have been shown to be a consideration. Many wafers have been prepared with different particle sizes at room temperature. However particles below about 70 nm do not form good arrays [ 1] presumably because of excessive thermal motion due to their smaller size and mass Therefore, lowering the temperature might allow particles below 70 nm to form arrays though it may require more settling time than for larger particles that settle quickly ; sonic pulses may facilitate settling Electrophoretic methods could be used to interact with charges or dipole mo ments on the particle o r fluid molecules By aligning dipoles, or migrating charges, more general arrays might be constructed Oscillating electric fields to stimulate decay to lower energy states, e.g., pulse relaxation techniques may help induce order P olarized, alternating polar pulses and various wave shapes c ould be applied. One question posed by Nic h olas L i nn was to try and predict the number of final layers as a function of the spin program. This could be done, but requires spin stations that can accurately monitor and record the actual behavior of the spin station as it runs its program. As discussed, it may be possible to correlate the number and structure of layers with light scattering measurements. Correlating these measurements with SEM analys is, should allow a fairly good predictive model, even if only on a statistical basis. Variables here include temperature and pressure, as well as solids loading. Variability in the particle surface properties might be the largest source of variance, follow ed by

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148 p ossible variations in monomer properties, s uch as premature polymerization, and adherence of the suspension to the wafer surface. Large Scale Arrays Future work on these arrays might also include constructing large arrays of self assembling particlefluid systems. Depending on an intended application, it would significantly reduce cost if these arrays could be produced in a normal environment and did not need to be spun to produce ordered arrays. Such arrays could be constructed by spraying or painting of a coating made with particles that self organize in their fluid matrix. Such arrays could be used to improve solar energy collection [ 20] or provide an artistically pleasing coating to an architectural structure, or both! These coatings would be re latively inexpensive as they should be easy to manufacture and apply much like paint. Although such arrays may not have the uniformity of a spin coated array, due to inhibited settling, some of the techniques discussed above can be considered to improve or dering for certain classes of arrays.

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149 CHAPTER 7 CONCLUSIONS The assembl y of arrays of particles in fluids by accelerations, controlled by fluid mediated interparticle forces appears to be a rich field capable of producing a variety of potential ly useful photonic products, as mentioned in the introduction. The fundamental phenomena involved in producing the arrays in this study appear to the interparticle forces mediated by the ETPTA monomer. It is theorized that the hydroxyl groups of the St be r particles hydrogen bond with the monomer molecules to force a close order of the monomer around the particle. This order decays in proportion to the radius of the particle due to the divergence of radial lines of organization away from the surface of the spherical particle. The distance over which these line diverge by an amount that can admit monomer molecules in the random phase to disrupt the radial order can account for the 2 D center to center separation of the particles in this monomer. The final or dering of the spin coated array is generated as the particles migrate from the center of the wafer, shearing monomer from between horizontal layers. This allows the horizontal layers to collapse onto each other, with layers settling into the gravitational wells in the interparticle spaces in the layers below. This allow s the formation of three dimensional arrays of hexagonal or face centered cubic structure. It appears that as the particles migrate from the center of the spinning wafer, they diverge axially and admit particles in layers above to populate opening layers below. It also appears that lower layers begin with a wider interparticle spacing, promoting the densification of the final product with the often observed 1.41 interparticle spacing. This

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150 occurs as particles populate lower, more open layers by forcing the lower level particles apart by shear and gravitational settling force.

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151 APPENDIX A SPIN COATED WAFER PROCEDU RE Day 1: Preparing the ParticleMonomer Suspension The particlemonomer suspensi on has been performed in nine steps for wafer spinning [ 35] For samples that were not spun, the particlemonomer suspension was prepared in the same way. Particles for these preparations were taken from suspensions listed in Table A 1. The nine steps are: 1. Shake a bottle of St ber suspension to suspend the silica particles. 2. Pour 50mL of St ber suspension into a 50mL centrifuge tube. 3. Centrifuge the suspension at 5000 rpm for 5 minutes. 4. Pour off the ethanol supernatant. 5. Add the specified quantity of e thoxylat ed t rimethyl ol propane t riacrylate ( ETPTA) (Figure A 1) monomer to the precipitate, according to Table A 1 [ 35]. Figure A 1. Ethoxylated trimethylolpropane triacrylate (ETPTA).

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152 6. Add 1 to 2 weight percent Darocur 1173 ( Figure A 2) photoinitiator to the t ube. Figure A 2. Darocur 1173, 2 Hydroxy 2 methyl 1 phenyl 1 propanone. 7. Vortex the silica particles, ETPTA monomer, and photoinitiator (Darocur 1173) until it appears that the particles have been completely dispersed. 8. Pour the blend into a syringe and pass it through a 5 m syringe filter into a scintillation vial. 9. Store the scintillation vial in the dark with the cap loosely screwed on. Polymerization is initiated by UV light; the blend must dry, i.e., allow remaining ethanol to evaporate from the particlemonomer suspension. Day 2: Preparing the Wafer for Spinning Wafers used were four inch silicon wafers. The wafers were obtained from Montco Silicon, cc030907 / lot# w34605. 1. The following steps were carried out in a clean room to reduce the risk of large particles contaminating the solution. 2. 3 silicon wafers per 50mL of original solution should be blown with air/N2 to remove dust. 3. The wafers will then be primed. 4. A thin layer of silane primer, 3 acryloxypropyl trichlorosilane ( APTCS) (Figure A 3), is applied to each wafer with a cleanroom swab. Figure A 3. Silane primer: 3 acryloxypropyl trichlorosilane

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153 5. After coating with APTCS, the wafer is covered with pure ethanol, then wiped with a cleanroom wipe. When the remaining ethanol film has evaporated, repeat this cleaning process two more times. 6. Place a wafer in the spin coater and allow it to spin for 1min at 3000RPM. During this time, rinse the wafer with four 3 second squirts of pure ethanol. The wafer should be completely dry before the 1min sp in ends. 7. Heat the wafer for 1min at 105C. 8. Repeat these steps until each wafer is primed. 9. Pour the particlemonomer suspension into a syringe and pass it through a 5 m syringe filter, allowing it to drip onto the wafers. Attempt to add the same amount of suspension to each wafer (it is hard to measure using the markings on the syringe because the filter chamber must be filled and wetted). 10. Spread the particle monomer suspension over the wafer evenly by hand without touching the suspension. That is, tilt the wafer in a wobbling fashion in small angles about the vertical, to distribute the suspension unifor ml y over the surface of the wafer. 11. Put the wafers in a wafer cassette and leave them in the dark overnight. They need to evaporate residual ethanol and the re should be no light induced polymerization. D ay 3: Spinning the Wafer 1. Load a wafer into the spin coater using a wafer aligner. 2. The following spin coating program was used for many samples, acceleration is left at default: 200 RPM 2 min 300 RPM 2 min 1000 RPM 1 min 3000 RPM 30 secs 6000 RPM 20 secs 8000 RPM for X secs

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154 Table A 1. St ber suspension samples used in spin coating. Important parameters are the particle diameter and volume fraction of particles in the parent suspension. The volume fraction of particles determines the amount of ETPTA monomer to add to the 50 mL of centrifuged St ber suspension in step 5 above. Samples Particle Diameter (n ano m eters ) Volume Fraction of Particles (Date) Quantity of ETPTA for 50 mL Solution ( g rams ) Quality A1#1 366 1.4% (1/24/07) 3.11 Very Good A1#2 ~600 1.2% (1/24/07) 2.71 Good A1#5 ~400 1.2% (1/24/07) 2.59 Good A1#7 ~500 1.4% (1/24/07) 3.17 Good A5#1 ~300 A8#1 ~300 1.0% (1/24/07) 2.24 Not Good A8#2 350 1.0% (1/24/07) 2.19 Very Good A8#3 ~300 1.0% (1/24/07) 2.12 Not Good A9#1 320 1.1% (1/24/07) 2.37 Very Good A9#2 327 1.2% (1/24/07) 2.54 Very Good A9#3 ~600 1.0% (1/24/07) 2.25 A10#1 315 1.2% (1/24/07) 2.61 Very Good A10#2 ~600 1.1% (1/24/07) 2.34 A10#3 ~650 1.3% (1/24/07) 2. 9 A11#1 ~70 0.94% (1/24/07) 2.07 A11#2 ~70 1.3% (1/24/07) 2.78 A12#1 297 0.97% (1/24/07) 2.14 Very Good A12#2 ~650 0.97% (1/24/07) 2.14 A12#3 ~800 0.97% (1/24/07) 2.12 A13#1 297 1.0% (1/24/07) 2.29 Ok A13#2 227 1.0% (1/24/07) 2.21 Ok A13#3 ~40 0 1.0% (1/24/07) 2.29 Very Good A14#1 ~70 1.3% (1/24/07) 2.96 A14#2 ~70 1.2% (1/24/07) 2.75 A15#1 ~300 1.0% (1/24/07) 2.26 A15#2 ~600 1.0% (1/24/07) 2.24 A15#3 ~800 1.0% (1/24/07) 2.19

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155 APPENDIX B ELECTROPHORETIC MOBI LITY To begin, the basics of this technique obey the equation mabVNeE (B 1) w here a particle of total charge Q = Ne and mass m, is assumed propelled through a still Newtonian fluid having viscosity by an electric field E to generate acceleration a, and velocity V The drag coefficient b, equals 3 d, where d is the particle diameter. For steady state electrophoresis the acceleration is zero so Eqn. B 1 becomes so that || || VNe bVNeE b E 0 (B 2) The quantity V/E defines the mobility, so that Eqn. B 2 can be written = Ne/b. Thus if the velocity can be measured and the electric field, fluid viscosity, and particle diameter are known, the total charge on the particle can be inferred. It will be assumed here that all the particles have the same diameter and total charge. In general, this will not be true, and ensemble averages over mobilities must be considered. The total charge on Stber silica particles in a polar fluid can be associated with the number of hydroxyl groups on the particle surface as discussed in Chapter 2. The important purpose of this investigation is to infer different numbers of hydroxyl groups on different types of particles, and the difference in the particles ability to form hydrogen bonds. Consider two types of Stber particle with the same diameter, one fresh, as synthesized, the other calcined to remove free hydroxyl groups. If these particles have different velocities in the same driving field E, then it can be inferred t hat the particles have different numbers of free surface hydroxyl groups. This assumes that the interaction of particles of the same diameter, but different surface properties interact

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156 with the fluid in the same way, as characterized by the viscosity. This assumption is usually valid if the first layer of fluid is bound to the particle, and subsequent fluid layers flow around the bound layer, with shear force characterized by This assumption is known as the stick boundary condition, or Prandtls hypothesis. This condition infers that the particles interaction with the fluid is characterized by the same viscosity coefficient independent of particle surface structure. The mobility of fresh Stber particles was measured to be about 3.44 times that of calci ned Stber particles. That is, the fresh Stober particles are inferred to have twice as many hydroxyl sites as calcined Stober particles. The charge on the particles was inferred from mobility measurements using a Brookhaven Instruments Corporation (BIC) Z etaPlus zeta potential analyzer, with their Zeta PALS method. ZetaPlus PALS measures the particle velocity in still fluid as the particle is forced to move sinusoidally between two parallel plate electrodes spaced about 1cm apart. By measuring the time dependence of the intensity due to Doppler shift ed frequency oscillations between the light scattered from the sample and a reference beam Since the Doppler shifted frequency depends on the relative velocity of the particle and detector, the velocity of the particle can be inferred. The phase shift between sample and reference beam depends on the velocity of the particle, which is caused to oscillate at around 2 Hz between the electrodes. The relativistic Doppler shift is given by Lorentz transform s, transfo rming the zeroth component of the wave 4vector from the rest frame of the scattering particle,

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157 moving with velocity V with respect to the detector into the rest frame of the detector This transformed frequency is [ 3 9 ] (Eqn. B-1) Where frequency of the scattered light at the detector, frequency of scattered light in the res t fr ()(cos)Dppppppp D pk 11 ame of the particle, velocity of the particle with respect to the detector, divided by the speed of l ight, wave vector of scattered light from the particle in direction of the d /pp p pc k 211 etector, and where is the detection angle. For velocities much less than Eqn B-1 reduces to (Eqn. B-2) cos() (cos)ppp Dppk c 1212 1 Th e moving particle sees a transverse Doppler shift of the incident beam, but since the particle velocity is much less than c, the frequency seen by the particle is essentially unshifted. Since the reference beam is up shifted by a piezo crystal by 250 Hz, the frequency difference between the reference beam and scattered beam is so that (cos) cos () () cosopiezoop piezoop piezo p ot Vtc 1 The measurement of intensity fluctuations in the time domain versus frequency domain makes the PALS technique one thousand times more sensitive than frequency domain measurement [ 40]. (B 3) (B 4) For velocitie s much less than c B 3 reduces to

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158 A schematic of the ZetaPALS set up is shown in Figure B 1. The 530 nm laser beam is split by a beam splitter (red line) into a reference beam and a sample beam. As the particles scatter light, the frequency of the scattered light is Doppler shifted. The Doppler shifted frequency depends on the relative velocity between the particle and detector. The reference beam frequency is up shifted 250 Hz by a piezoelectric crystal. The particle is forced to oscillate between the electr odes at about 2 Hz. The reference beam and scattered sample beam are combined (heterodyned), and the time oscillations of the resulting intensity are measured. Using the Doppler shift equation for light, the particle velocity, and hence mobility and charge can be inferred. Figure B 1 Schematic of a phase analysis light scattering (PALS) set up. There are also phase shifts and interference oscillations generated by coherent light scattering from many scattering centers moving both at random by Brownian motion and by the driving electric field. There are many particles in the interaction volume of the system. The beam diameter is about one millimeter ; scattering is observed at 15 degrees relative to the incident beam through a 200 m orifice. T h us th e sample volume is VolS ~ 0. 52 0.2mm3/sin( = 0.6mm3. The number of particles in this volum e is about 43*106, with volume fraction of particles and particle diameter

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159 of 300 nm. The scattering phase difference generated by the difference in particle positions due to collective motion imposed by the driving field cancels. The interference generated by the change in interparticle spacing due to Brownian motion can be used to work out particle size distributions by the method of correlation function theory [ 41]. The Brownian intensity fluctuations can be neglected, as they can be separated from the sinusoidal intensity fluctuations due to the driving field. Brownian fluctuations can be regarded as part of the noise spectrum. Since the wavelength is 530 nm, interactions with the particle can not be neglected in general. However for spherical parti cles, the scattering intensity does not depend on particle orientation and can be ignored. A simple equation for X (t) due to the sinusoidal driving field is which gives and The velocity is The RMS mobility is The ratio of RMS mobili () () ()Re[()] [cos()sin()] ()eit eoeo o o ee eee e RMS RMS eQE mXibXQE X XtXe mi d Ne VtXt tt dt m V Ne E m 2 22 222 ties for particles of the same diameter is =. N N 11 22 Thus the ratio of mobilities gives the ratio of charges if the diamet ers are approximately the same. This is the desired result to compare the surface charges on two types of particle whose only difference is their surface charge.

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160 APPENDIX C PARTICLE DENSITY AND BOUYANT FORCE Density of the particles is needed to calcul ate the buoyant force on the particle in monomer. The buoyant weight of the particles in monomer, balances apparent repulsion between particles that maintains the interparticle spacing. Density of the particles is measured using a Quantachrome ULTRPYC 1000 helium pycnometer. The ULTRAPYC was set to do 10 runs and average the last 7 runs, with a three minute helium purge and a thirty second pressure equilibration time. A pproximately one gram of freeze dried LLC Stober particles was used for the measurement. This technique is based on the ideal gas law, a sample cell of known volume, and an internal manifold of known volume. The set up is shown schematically in Figure C 1. Helium is pressured to flow through the sample cell and manifold by a high pressure tan k of ultra pure helium, regulated to a pressure of 20 psi. This flow purges the system of air, and w a s purged for three minutes. The inlet valve is closed, then the manifold valve is closed, and finally the outlet valve is closed as the pressure equilibrat es in each section to atmospheric pressure. Then the inlet valve is opened and the sample and sample cell is pressured to approximately 20 psi above atmospheric, the inlet valve closes, and the system equilibrates for 30 seconds, and records the pressure Then the manifold valve opens admitting the manifold volume. The effective volume increases and the pressure decreases according to the ideal gas law. This allows two equations in two unknowns : the volume displaced by the sample, and the number of moles of helium added to the system, times the ideal gas constant, times the temperature (nRT). Since

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161 no gas is added after the inlet valve closes, nRT can be eliminated and the sample volume can be solved for. The equations are ), and ).cellsample cellmanifoldsample(( PVVnRTPVVVnRT 12 Eliminating nRT gives ) ).cellsamplecellmanifoldsample(( PVVPVVV 12 Solving for the volume of sample gives .cellmanifold manifold sample cell() () () PPVPV PV VV PP PP 122 2 12 12 Dividing the sample volume into the sample weight obtained on a 5place analytical balance, calibrated to 10 mg, gives the apparent density. Apparent density may be different than the perfect crystalline density, if there are closed voids or porosity in the particles that are not accessible to the helium. This will result in a sample volume that is larger than the actual volume of material in the sample, thus reducing the ideal density to the apparent density. Figure C 1. Schematic of a helium pycnometer.

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162 Next calculate the buoyant force, or the net gravitational force the particle exerts on a particle or surface below it. With , the bouyant force is NewtonsfNt. ()() ... sec .* .bouyantsilicamonomerparticlesilicamonome rparticle silica monomer particle bF Volg dg g g meter d nmg cm cm F 3 33 2 156 22 111 30098 01510 015

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163 LIST OF REFERENCES [ 1] P. Jiang, (Unpublished). [2] J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding The Flow Of Light (Princeton University P ress, Princeton, 1995). [3] S. Noda, A. Chutinan, and M. Imada, Nature 407 608 (2000). [4] P. Lodahl, et al. Nature 430 654 (2004). [5] S. P. Ogawa, M. Imada, S. Yoshimoto, M. Okano, and S. Noda, Science 305, 227 (2004). [6] M. Fujita, S. Takahashi, Y. T anaka, T. Asano, and S. Noda, Science 308, 1296 (2005). [7] H. G. Park et al. Science 305, 1444 (2004). [8] R. Colombelli et al. Science 302, 1374 (2003). [9] K. J. Vahala, Nature 424 839 (2003). [10] S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mo chizuki, Science 293, 1123 (2001). [11] O. Painter, et al. Science 284, 1819 (1999). [12] T. A. Vlasov, M. O'Boyle, H. F. Hamann, and S. J. McNab, Nature 438 65 (2005). [13] S. Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, Science 282, 274 (1998). [14] A. Kuhn, M. Hennrich, and G. Rempe, Phys. Rev. Lett. 89, 067901 (2002). [15] P. Michler et al. Science 290, 2282 (2000). [16] J. D. Joannopoulos, P. R. Villeneuve, and S. H. Fan, Nature 386 143 (1997). [17] R. H. Baughman et al. Sci ence 288, 2018 (2000). [18] C. M. Soukoulis, M. Kafesaki, and E. N. Economou, Adv. Mater. 18, 1941 (2006). [19] T. Prasad, V. Colvin, and D. Mittleman, Phys. Rev. B 67 165103 (2003). [20] W. Min, B. Jiang, and P. Jiang, Adv. Mater. 20 3914 (2008). [21] N W. Ascroft and N. D. Mermin, Solid State Physics (Brooks/Cole, United States, 1976).

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165 BIOGRAPHICAL SKETCH He was born in 1948 in Olney, Maryland. H e lived on 300 acres outside of Washington, DC. His mothers step mother owned some cut stone hotels and a big mansion close to the National Zoologic al Park. One of his earliest memories was of a black snake in a barrel. His dad said, Gill, come look at this. That snake was the most fascinating thing he had ever seen, and his interest in nature was instantly awakened. It would be many years before h e gained the knowledge in mathematics, chemistry and physics to begin to understand how life works. He served four years in the Air Force from 1968 to 1972. After his discharge he started college at Santa Fe College in Gainesville, Florida. He transferred to the University of Florida (UF) in 1974. He majored in physics, with unofficial minors in mathematics and chemistry. He took a bit of graduate work on a GI bill extension and graduated in August of 1977 with a bachelors degree in physics. Since 1994 he has worked at UF and i n August of 2003 completed non thesis masters in physics. He received his Ph.D. in physics August 2012 Currently he is interested in gravitation and elementary particle physics, as well as aging research and a bit of robotics, with the exciting possibilities of the conquest of death, toil, and suffering. These are not only increasingly realizable technological goals, but propose a unifying ideal for ultimate human social development. As Mr. Spock often says, Live long and prosper, or as he says, Conquer death, toil, and suffering.