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Dispersion of ceramic particles in polymer melts

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Dispersion of ceramic particles in polymer melts
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Dow, Joan-Huey, 1959-
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vi, 342 leaves : ill., photos ; 29 cm.

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Additives ( jstor )
Agglomerates ( jstor )
Diameters ( jstor )
Particulate materials ( jstor )
Polyethylenes ( jstor )
Polymers ( jstor )
Silanes ( jstor )
Torque ( jstor )
Viscosity ( jstor )
Wetting ( jstor )
Dissertations, Academic -- Materials Science and Engineering -- UF
Materials Science and Engineering thesis Ph. D
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Thesis (Ph. D.)--University of Florida, 1992.
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Includes bibliographical references (leaves 329-341)
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Typescript.
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Vita.
Statement of Responsibility:
by Joan-Huey Dow.

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DISPERSION OF CERAMIC PARTICLES IN POLYMER MELTS


By

JOAN-HUEY DOW
















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

1992


UNIVERSITY OF FLORIDA LIBRARIES














ACKNOWLEDGEMENTS


I am grateful to Dr. M. D. Sacks for his guidance and support on the research

work. Support from the Department of Energy, Office of Basic Energy Sciences,

Division of Materials Sciences (DE-FG05-85ER45202) is gratefully acknowledged.

The advice from Dr. P. H. Holloway is appreciated. Thanks should also go to

Drs. C. D. Batich, E. D. Whitney, and G. B. Westermann-Clark for their suggestions

on this dissertation.

I would like to thank Dr. A. V. Shenoy, G. W. Scheiffele, C. Khadilkar, T.-

S. Yeh, H. W. Lee, S. Vora, R. Raghunathan, M. Saleem, A. Bagwell, and Dr. A.

Fradkin for their assistance in carrying out various experiments and editing this

dissertation.

This dissertation is dedicated to my parents for their love, understanding, and

encouragement.














TABLE OF CONTENTS




ACKNOWLEDGEMENTS ................................. ii

ABSTRACT ......................................... v

CHAPTERS

1 INTRODUCTION ................................... 1

2 BACKGROUND .................................. 5

2.1 Evaluation of the State of Particulate Dispersion by
Non-rheological Techniques ................. ........ 6
2.2 Rheology of Fluids and Particle/Fluid Mixtures ............ 11
2.2.1 Overview ............................... 11
2.2.2 Polymer Melts ............................ 16
2.2.3 Particle/Fluid Mixtures ...................... 17
2.3 Particle/Fluid Mixing ............................ 22
2.4 Particle/Fluid Wetting ........................... 25
2.5 Characteristics of Alumina Surfaces with Adsorbed Water and
Hydroxyl Groups .............................. 30
2.6 Effects of Moisture on Ceramic/Polymer Composites ........ 32
2.7 Chemical Additives .................. ........... 34
2.7.1 Structures ................................ 35
2.7.2 Effects of Chemical Additives on Rheological Properties 40

3 EXPERIMENTAL ................................. 42

3.1 Materials and Materials Preparation .................. 42
3.1.1 Starting Materials .......................... 42
3.1.2 Treatment of Alumina Powder ................. 46
3.2 Characterization of Ceramic Powders, Powder Compacts,
and Polymers ................................ 49
3.2.1 Alumina Powder Characterization ................ 49
3.2.2 Alumina Powder Compact Characterization ........... 53









3.2.3 Polymer Characterization ........ ............ 54
3.3 Mixing of Ceramic Powders and Polymers ............... 54
3.4 Characterization of Ceramic Powder/Polymer Mixtures ....... 57
3.4.1 Rheology ............................. 57
3.4.2 Quantitative Microscopy ...................... 62
3.4.3 Ceramic/Polymer Wetting Behavior ............... 63
3.4.4 Elemental Analysis .............. .......... 67
3.4.5 Characterization via FTIR .................... 68
3.4.6 Analysis for Iron Content .................. 68
3.4.7 Microhardness Measurements ............. 68

4 RESULTS AND DISCUSSION ......................... 69

4.1 Effects of Mixing Conditions ....................... 69
4.1.1 Single-Segment Mixing Schedules ................ 69
4.1.1.1 Effects of mixing temperature on theological and
wetting behavior ...................... 70
4.1.1.2 Quantitative microscopy ............. 94
4.1.1.3 Effects of rotor speed ................... 134
4.1.1.4 Effects of mixing time .................. 136
4.1.2 Multi-Segment Mixing Schedules ................. 136
4.1.2.1 Mixing with change in temperature .......... 146
4.1.2.2 Mixing with change in rotor speed ........... 154
4.2 Effects of Ceramic Powder Characteristics ................ 159
4.2.1 Calcination Effect ....................... 160
4.2.2 Aging Phenomenon ........................ 210
4.3 Effects of Polymer Characteristics .................... 227
4.3 Effects of Chemical Additives ...................... 248
4.4.1 Coupling Agents ........................... 248
4.4.2 Surfactants ............... .............. 275
4.4.3 Lubricants ................. ............ 288

5 SUMMARY ...................................... 322

REFERENCES ......................................... 329

BIOGRAPHICAL SKETCH ................................. 342














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

DISPERSION OF CERAMIC PARTICLES IN POLYMER MELTS

By

Joan-Huey Dow

May, 1992


Chairperson: Dr. Michael D. Sacks
Major Department: Materials Science and Engineering

The effects of mixing conditions, powder and polymer characteristics, and

chemical additives on dispersion of ceramic particles in polymer melts were investigated.

Fine-sized alumina powder and low-molecular-weight polyethylene (PE) were used in

most experiments. Samples were prepared using a high-shear bowl mixer and the mixing

operation was monitored by torque rheometry. The state of dispersion was evaluated

using theological and quantitative microscopic measurements. Ceramic/polymer melt

wetting behavior was evaluated by the sessile drop and polymer penetration methods.

Further understanding of mixing and dispersion behavior was developed by using particle

size and surface area measurements, infrared spectroscopy, mercury porosimetry,

microhardness measurements, gravimetric analysis, etc.

Samples mixed at lower temperatures and higher rotor speeds had better

particulate dispersion (i.e., due to increased agglomerate breakdown rates and decreased









coagulation rates). Mixed batches prepared with heat-treated powders (100-1000C)

showed relatively poor particulate dispersion. This was due to changes in the

physicochemical characteristics of the heat-treated powders (i.e., due to removal of water

and hydroxyl groups on powder surfaces at low temperatures and interparticle neck

growth at higher temperatures). Samples prepared with heat-treated powders were also

highly susceptible to aging effects due to absorption of moisture from the ambient air

atmosphere. Mixed batches prepared with polyethylene or ethylene-acrylic acid

copolymer showed relatively good dispersion compared to batches prepared with

ethylene-vinyl acetate copolymer. Further investigation is needed to understand the

reason for this behavior. Particulate dispersion in mixed batches was also highly

dependent upon the presence of chemical additives (i.e., coupling agents, a surfactant,

and a lubricant). In some cases, it was possible to establish correlations between the

state of dispersion in the suspensions used to coat powders with additives, the peak

torques generated during powder/polymer mixing, and the state of dispersion in the

mixed batches.














CHAPTER 1
INTRODUCTION


The state of particulate dispersion and the theological properties of ceramic

powder/polymer melt mixtures are important for ceramic shape forming processes such

as injection molding [Edi86, Ino89, Man82, Man83, Schw49, Tay62]. The first major

step in the process is to mix ceramic powder with polymer melt at an elevated

temperature to form a plastic mass. The ceramic/polymer mixture should have suitable

fluidity in order to fill the die completely and uniformly without leaving any defects in

the shaped parts. Usually, chemical additives are used to improve the processibility of

the mixtures. After the shape forming step, the parts are heated to remove polymer and

then sintered to form the final products.

The state of dispersion of the ceramic powder in the polymer melt, i.e., the

distribution and packing of ceramic particles in the polymer, determines the fluidity of

the ceramic/polymer mixture and thus controls the flow pattern of the mixture in the die

during injection molding. It also has a strong effect on the maximum solids loading (i.e.,

volume fraction of ceramic powder in the mixture) that can be achieved. In general, a

high solids loading is desired in order to minimize the polymer amount to be removed

and to reduce the amount of shrinkage during sintering. During the polymer burnout

step, transport of polymer molecules is influenced by the pore size and size distribution

formed by the packing arrangement of the ceramic particles and, thus, the polymer

1








2

removal process is indirectly dependent on the dispersion state. Furthermore, the

densification rate and the grain growth rate during sintering are strongly affected by the

particle packing arrangement in the ceramic powder compact. Therefore, it is important

to examine the dispersion of ceramic powders in polymer melts since it strongly

influences each step in the processing sequence and ultimately affects the microstructure

and properties of the final product.

Information about dispersion and rheology is also crucial in processing of polymer

composites in which inorganic particles or fibers are incorporated into polymers, either

to reduce the cost or to tailor the composite properties [Han74, HesW82, Utr82]. For

example, the existence of porous particle agglomerates in a polymer matrix (i.e., poor

dispersion) can significantly reduce the mechanical strength of the composites. In

addition to affecting physical properties, the energy consumption during processing of

the composites is much less for a well-dispersed mixture since the viscosity is lower.

The state of dispersion in ceramic/polymer mixtures is dependent on the mixing

conditions and the properties of the starting materials (i.e., ceramic powders, polymers,

and chemical additives). The present study addresses the following four areas:

Mixing conditions. The effect of mixing variables, including time, temperature,

and rotor speed, on the dispersion of alumina in polyethylene was investigated. The

study was confined to a simple two-phase ceramic/polymer mixture without any chemical

additives. Rheological flow measurements, torque rheometry, ceramic/polymer melt

wetting behavior, and quantitative microscopic analysis were used to evaluate the effect

of mixing variables on the state of dispersion.








3

Ceramic powder characteristics. Ceramic/polymer injection molding is affected

by ceramic powder properties, such as particle size, size distribution, particle shape, etc.

To some extent, these variables have been studied [Big84b, Wil78]. However, the effect

of ceramic surface hydroxylation and adsorbed molecular water on particle dispersion has

not been investigated. In this part of the study, alumina powders were calcined at

temperatures in the range of 100-1000C prior to mixing with polyethylene (i.e., in order

to remove surface hydroxyl groups and adsorbed water). The effects of calcination on

dispersion and aging behavior were evaluated using theological flow measurements,

torque rheometry, infrared spectroscopy, hardness tests, particle size and specific surface

area measurements, ceramic/polymer melt wetting behavior, and qualitative and

quantitative microscopic analysis.

Polymer characteristics. The ceramic/polymer theological behavior can be altered

significantly by varying polymer properties. In this part of the study, experiments were

carried out using polymers with different functional groups: polyethylene (PE), ethylene-

acrylic acid (EAA), and ethylene-vinyl acetate (EVA). The influence of polymer

chemistry on the ceramic/polymer mixture properties were investigated by theological

flow measurements of polymer melts and ceramic/polymer mixtures, ceramic/polymer

melt wetting behavior, quantitative microscopic analysis, and torque rheometry.

Chemical additives. Chemical additives can be used to modify the

ceramic/polymer interface and thereby alter the state of dispersion and composite

properties [Big83, Zha88]. In this part of the study, several coupling agents, surfactants,

and fatty acids were used to modify the alumina dispersion in polyethylene. The role of









4

these chemical additives was investigated using torque rheometry, theological flow

measurements, ceramic/polymer melt wetting behavior, and quantitative microscopic

analysis.













CHAPTER 2
BACKGROUND


The dispersion of particles in polymer melts is important in ceramic injection

molding and the processing of ceramic/polymer composites. There have been many

methods developed to evaluate the state of particulate dispersion. Non-rheological

techniques (e.g., qualitative and quantitative microscopy) are discussed in section 2.1,

while theological measurements are discussed in section 2.2. The latter section includes

a brief description of basic concepts of rheology, followed by descriptions of the

theological properties of polymer melts and particle/fluid mixtures.

Ceramic powder/polymer melt wetting and mixing behavior are crucial in

determining the state of particulate dispersion. The mixing process and the effects of

mixing variables on the state of dispersion are reviewed in section 2.3. Section 2.4

discusses methods used to evaluate the wetting behavior of polymer melts on ceramic

substrates and powders.

The state of particulate dispersion in polymer melts is also affected by other

factors, including particle properties, polymer characteristics, atmospheric moisture,

addition of chemical additives, etc. Since alumina powder was used for most of the work

in this study, the surface characteristics of alumina (i.e., especially when adsorbed water

and hydroxyl groups are present) are discussed in section 2.5. The effect of atmospheric

moisture on properties of polymer composites is reviewed in section 2.6 Finally, the








6

structures of chemical additives and their effects on rheological properties are discussed

in section 2.7.

2.1 Evaluation of the State of Particulate Dispersion by Non-rheological Techniques

It has been well established that the breakdown of agglomerates and uniform

dispersion of particles in the matrix phase can significantly improve mechanical

properties of composites. Many studies of dispersion in powder/polymer mixtures have

been carried out for carbon black/rubber composites. Carbon black dispersion greatly

affects the mechanical properties of such mixtures [Boo63a, HesW82, Med78]. For

example, strength is adversely affected in composites with poor dispersion, as porous

agglomerates cannot support the load and act as structural flaws. Carbon black is also

added to polyethylene as an ultraviolet absorber for outdoor applications [Bes59, Wal50].

The protection efficiency and the useful lifetime depend on the state of dispersion of the

carbon black.

Early studies of dispersion of powders in polymer matrices were restricted to

qualitative analysis. Researchers used visual methods (either by the naked eye or by

optical microscope) to compare the size of agglomerates on cross-sections of

particle/polymer mixtures. Later analyses evolved to a semi-quantitative or quantitative

level due to the development of more sophisticated technologies, such as the electron

microscope, high-speed computers, and image analyzers.

A simple method to evaluate particle dispersion involves inspection of the sample

surface directly by light microscopy or electron microscopy [Boo63a, Chap57, For63,

Hes62, HesB63, HesF63, Veg78]. Samples with poor dispersion clearly show large









7

agglomerates, whereas well-dispersed samples have smaller primary particles distributed

homogeneously throughout the entire matrix. The specimens are prepared either by

tearing or by cutting to expose the inner structure. Using optical microscopy to examine

torn surfaces has the advantages of easy and quick operation with minimal equipment

cost. However, only large agglomerates can be identified due to the limitations imposed

by low magnification and roughness of the sample surface. In fact, this is still a valuable

evaluation method in the rubber industry because the most damaging agglomerates are

those in the range of 10 j/m or greater. To compare samples with smaller-sized

agglomerates, a tedious process of microtomy becomes necessary to prepare thin sections

[AST82, Chap57, Hes62, HesB63, Lei56]. Samples are first frozen in dry ice or liquid

nitrogen to increase hardness and then the frozen samples are cut by a glass or steel

knife. For optical microscopy, sections with 2 jim thickness allow suitable light

transmission. Sample thickness should be less than 0.1 Cjm for good electron

transmission.

A visual inspection method has been adopted as an ASTM standard for qualitative

rating of particle dispersion of carbon black or other fillers in rubber [AST82]. The

samples are cut or torn by a sharp knife or a razor blade to reveal fresh surfaces which

are then inspected by a hand lens or a binocular microscope. The observed particle

dispersion is compared with a series of five photographic standards which are assigned

numbers from 1 to 5. A rating of 5 indicates that the best possible dispersion is

achieved, whereas a rating of 1 indicates the poorest dispersion (Table 2.1). This

method is applicable only for samples containing larger-sized particles. Bell Laboratories











Table 2.1 The relation between visual dispersion rating (by visual inspection
method) with the particle dispersion quality [AST82].


has developed a similar type of microscopic standard with three photographs designated

alphabetically from A (satisfactory dispersion) to C (poor dispersion). This standard also

has been used very often to rate carbon black dispersion [Wal50].

In addition to the qualitative rating methods described above, carbon black

dispersion has been quantitatively evaluated using a numerical scale that is related to a

measured percentage of well-dispersed particles. Experimentally, this is done by

counting the number of agglomerates larger than a certain arbitrarily defined threshold

size [AST82, HesB3a, Kad74, Lei56]. The samples are first microtomed into thin

sections (2 to 3 t/m thick) in order to allow light transmission for observation of the

agglomerates. A ruled grid is attached in one of the microscope eyepieces and the

number of squares covered by agglomerates that are larger than half a square is counted.

For example, in a grid with 10 x 10 14m squares, the number of agglomerates larger than

50 pim is counted. From the agglomerate count and the volume fraction of carbon

black, the degree of dispersion is calculated and expressed as "percent dispersion" or

"dispersion coefficient." The meaning of the dispersion rating is listed in Table 2.2.


Visual Dispersion Rating Classification

4 to 5 High
3 to 4 Intermediate
2 to 3 Low
1 to 2 Very low











Table 2.2 The relation between dispersion percentage (by agglomerate count
method) with the particle dispersion quality [AST82].


Dispersion % Classification

Above 99 Very high
97 to 99 High
95 to 97 Intermediate
92 to 95 Low
below 92 Very low


The methods described above utilize either microscopy or the naked eye to

examine the size and the distribution of particles in the polymer matrix. There are other

methods that measure properties of the composite which are sensitive to the state of

particle dispersion. For example, sample density and surface roughness are recorded at

different sample locations and the fluctuations of the properties reflect the homogeneity

of the particle distribution. The advantage of these methods is that they are less time-

consuming and are easy to operate; therefore, they are commonly used in industry.

The microdensitometer has been used as an instrument to evaluate particle

dispersion [Bes59, Eic61]. The principle of the microdensitometer is that the optical

absorbance of two-phase mixtures is dependent on the quantity and size of the dispersed

phase, i.e., the light transmitted through a sample reflects the particle distribution in the

polymer matrix. In one common method, test samples are prepared in the form of 1 mil

thick films. A light with a 10 tim diameter passes through the film and the intensity of

the light is recorded as a function of position on a strip chart. Well-dispersed samples

have light intensity profiles varying within a comparatively small range, whereas poorly









10

dispersed samples have significant variations in the light intensity profile (Figure 2.1).

Densitometers have been improved over the years [Eic61] so that the transmitted light

intensities at different locations are converted to light intensity "distribution" functions

automatically. Furthermore, a dimensionless number (i.e., a uniformity index) is

calculated statistically from the light intensity distribution function. This index

quantitatively describes the particle dispersion and has been shown to be consistent with

dispersion ratings obtained by using light microscopy [Wal50].


litA

EI hi 1 ill HillA i I ilt P. 1 1
111! 11 i r'' c/I m pV m 1 1 I I A A n1 rti l
IN ____ -1 11 "' '- "--iV-i' LAW -1 .l' 1


CURVE A
POOR DISPERSION


LENGTH OF SCAN


Figure 2.1


Light intensity curves for two carbon black/polyethylene mixtures with
different states of particulate dispersion [Bes59].








11

As noted earlier, surface roughness is another useful property to reveal the

differences in particle dispersion among samples [HesC80, HesS84, HesW82, Veg78].

Test samples are often similar in size to standard stress-strain slabs (i.e., -2.5 x 1.5

cm). The surface for roughness testing is freshly created using a razor blade. A stylus-

type tester is then moved along the cut surface and the resulting surface profile is

recorded on a strip chart or by a computer. Poorly dispersed samples show significant

fluctuations in the roughness profiles, whereas well-dispersed samples produce minor

fluctuations. The "dispersion index" is then calculated based on the frequency and the

average height of the peaks on the roughness traces. The results are usually consistent

with measurements made by microscopy methods [HesS84, HesW82]. Even though this

method is simple and quick, it is necessary to cut samples carefully without creating any

inherent difference in roughness. If there are pores or bubbles on the cut surface, the

test results may yield misleading information.

2.2 Rheology of Fluids and Particle/Fluid Mixtures

2.2.1 Overview

Rheology is the science dealing with the deformation and flow of materials.

Rheological measurements are experimentally conducted either by applying a known

magnitude of deformation while monitoring the stress value that develops, or by applying

a certain level of stress while measuring the deformation that occurs. The tests can be

either shear, tensile, or compressive. Shear tests are commonly used in studying fine

particle suspensions or ceramic particle/polymer melt mixtures. Commercially available

equipment for fluid theological measurements includes cone-and-plate, parallel plate,









12

concentric-cylinder, and capillary viscometers [Dea82, Eir60]. These viscometers differ

in the geometries of the sensor systems, measurable viscosity levels, and operating shear-

rate ranges.

Rheological measurements are often made using a steady-shear mode. For

example, measurements are made by rotating one part of the sensor system (e.g., plate,

cone, or cylinder) at controlled shear rate, while the torque generated is measured by a

transducer attached to another part of the sensor system. The shear stress is then

calculated from the measured torque value and the geometrical configuration of the

sensor system. The sample viscosity is calculated from the shear stress (a) and the shear

rate (i) values. The viscosity is defined as apparent viscosity ()J or true viscosity (in):


a (2.1)




Sdo (2.2)
d



The apparent viscosity n, is more commonly used when reporting theological data.

Several typical theological flow curves (i.e., shear stress vs. shear rate behavior) and

viscosity vs. shear rate curves are shown in Figure 2.2. The different flow curves may

reflect differences in fluid characteristics (e.g., molecular structure), particle

characteristics (e.g., size, shape, concentration, etc.), fluid/particle interfacial

characteristics, and/or particle-particle interactions [Chaf77, Dea82, Eir60, Far68,

Goo75, Lew68, Sac86]. Flow behaviors in which viscosities decrease with increasing




















Bingham plastic



Pseudoplastic


0

m
$i



















'>
0









0
O












Figure 2.2


Newtonian (A)



Dilatant




Shear rate ( )




Bingham plastic



Pseudoplastic
+ (B)

Newtonian




Dilatant



Shear rate (f)


stress vs. shear rate and (B) viscosity vs. shear rate
of materials.


Plots of (A) shear
for different types








14

shear rate (i.e., pseudoplastic and Bingham plastic flow) are also referred to as "shear

thinning." This behavior will be discussed in more detail later since it is very common

in highly concentrated particle/fluid mixtures, such as investigated in this study.

It is not adequate to use steady-shear measurements alone to describe the

theological properties of ceramic/polymer mixtures because they are viscoelastic in

nature. When deformed, viscous materials dissipate energy while elastic materials store

energy. As a result, dynamic-shear measurements are used extensively to characterize

ceramic/polymer mixtures because information on both the viscous and elastic properties

can be obtained simultaneously. Dynamic measurements are performed by applying a

sinusoidal deformation (i.e., strain -) with controlled amplitude (i.e., maximum strain

y0) and frequency (w). Due to the viscoelastic properties of the sample, the responding

stress also has a sinusoidal form but with a phase difference represented by an angle 5.

Figure 2.3 provides graphical and mathematical descriptions of the strain, strain rate, and

stress functions and also illustrates the relationship of these functions to the storage

modulus, loss modulus, and loss tangent. The storage modulus (G') shows the capability

of the sample to store energy that will be released after the deformation is recovered.

The loss modulus (G") represents the energy dissipated as heat when the sample is

deformed. Usually, the viscous property is expressed by dynamic viscosity (O' = G"/o)

or complex viscosity (n* = [(G'/o)2 + (G"/1)21n). For a completely viscous fluid like

water, the storage modulus is negligible compared to the loss modulus, and the stress

function is 90" out of phase from the deformation function. In contrast, the stress and

deformation sinusoidal functions are exactly in phase (6 = 0) for a perfectly elastic















\\SZ/ \ Strain

Time IG Stress

Stress out of phase .
Stress in phase



Strain = y = o sin at

Strain rate y = w Yo cos wt

Stress = a = a sin (wt + 6)

= Y (G' sin wt + G" cos wt)

Storage modulus = G' = (ao/y) cos 6

Loss modulus = G" = (ao/yo) sin 6

Loss tangent = tan 6 = G"/G




Figure 2.3 Graphical and mathematical descriptions of several variables used in
dynamic-shear measurement.



sample. Viscoelastic materials are characterized by a phase difference 6 that is

somewhere between 0 and 90.

The theological properties of particle/polymer mixtures depend not only on

characteristics of particles (e.g., solids loading, particle shape, particle size, and state of









16

dispersion), but the polymer rheology as well. Therefore, the rheology of polymer melts

and particle/fluid mixtures will be discussed in the following two sections.

2.2.2 Polymer Melts

Polymer melts are typical viscoelastic fluids due to the complex structures, i.e.,

long molecular chains with side branches [Alk72, Fer80, Len78]. The main molecular

chains tend to coil or entangle together because of various types of intermolecular and

intramolecular forces. Polymers can store energy when the coiled chains are stretched

under an applied shear stress. Energy can also be dissipated as heat by the friction

between molecules.

Viscoelasticity of polymers is dependent on many factors, including molecular

weight distribution, molecular structure, chemical composition, and temperature of

measurement. The dependence of polymer rheology on these variables has been studied

by both steady- and dynamic-measurements [Fer80, Han71, HanK83, HanL82, HanY71,

Tan81]. For example, capillary viscometry has been used to investigate the effect of

molecular structure on the theological properties of polyethylene [Han71]. Polymers

with broad molecular weight distributions have lower viscosities and higher elasticities

than those with narrow molecular weight distribution. Polymers with long-chain

branching are more elastic and less viscous than the linear polymers [Han71]. The effect

of temperature on polymer rheology has been studied extensively for polyethylene,

polystyrene, poly(methyl methacrylate), and polybutadiene [HanJ86, HanL82]. For a

given polymer, both viscosity and elasticity increase as temperature decreases, but the

G'/G" ratio is relatively insensitive to temperature variation.








17

Correlations between steady- and dynamic-shear theological behavior have been

observed in simple viscoelastic samples such as polymer melts or solutions. A certain

degree of similarity is recognized between the shear rate (i) dependence of steady

viscosity (n) and the frequency (w) dependence of dynamic viscosity (,q') [Cox58, Kul80,

Schu80]. At extremely low deformation rates, the viscosity values for many polymeric

fluids approach the same value for steady- and dynamic-shear measurements:


lim v (') = lim Q'(o) (2.3)
5.<0 &-.0


For most cases, these two functions (q vs. and 7' vs. w) have the same shape or can

be superimposed to form a single curve. For example, two polystyrene melts were tested

and compared using a capillary extrusion rheometer for steady shear and an

elastoviscometer for dynamic measurement [Cox58]. The apparent viscosity %, matched

better with the complex viscosity qr*, but the true viscosity 7, fit well with the dynamic

viscosity q'. The former relation (i, with q*) is often referred to as the Cox-Merz rule:


*(0) = 7(5y) Ii=. (2.4)


The rule was also found to be applicable for polystyrene and polyacrylamide solutions

over a wide range of concentrations and molecular weights at relatively high shear rates

and frequencies [Kul80].

2.2.3 Particle/Fluid Mixtures

The theological behavior of particle/fluid mixtures is of major research interest

because it controls both processability and energy consumption in areas such as ceramic









18

or metal injection molding and manufacturing of filled polymer composites.

Unfortunately, there are still no rigorous theoretical models predicting the theological

behavior of particle/fluid mixtures with high solids contents. Einstein derived the most

rigorous expression describing the effect of particle additions on fluid viscosity:


'r = ( 1 + 2.5 4) (2.5)


where i,, is the relative viscosity which is defined as the viscosity of the particle/fluid

mixture divided by the fluid viscosity, and 4) is the particle volume percentage.

However, the Einstein relation has limited applicability since it is derived with several

restrictive assumptions, i.e., (1) there are no particle-particle interactions, (2) particles

are spherical in shape, (3) particles are nondeformable, (4) particles are monosized, etc.

Consequently, it is valid only for very dilute suspensions prepared with rigid monosized

spheres. A large number of other equations have been used to describe the relation

between relative viscosity and the particle (solids) loading for more concentrated

suspensions containing nonspherical, nonmonosized particles. These equations are

usually empirical and contain one or two adjustable parameters for achieving good data

fits. Typical equations include those due to Farris (Eq. 2.6), Maron and Pierce (Eq.

2.7), and Mooney (Eq. 2.8) [Far68, Man83, Mil71, Utr82]:


(2.6)


S, = (1 4 )-












S= ( 1- )-2 (2.7)



f"4 (2.8)
Sr = exp( )-s (2.



where k (Eq. 2.6) ranges from 3 for broad size distribution up to 21 for monomodal size

particles, 40 (Eq. 2.7) is the maximum solids loading, and f and s (Eq. 2.8) are

adjustable variables. Figure 2.4 plots the dependence of relative viscosity (r,) as a

function of solids loading (4) for these models. The models give similar predictions at

low solids loadings, but large differences in relative viscosity are observed in the high

solids loading region. As empirical equations, they are limited utility in predicting the

viscosity of real systems.

As illustrated in Figure 2.2, the viscosity of concentrated particle/fluid mixtures

is often dependent on shear rate (or, in the case of dynamic shear measurements, on

oscillation frequency). Shear-thinning flow behavior (i.e., decreases in viscosity as the

shear rate increases) is often observed in samples with higher solids loading because of

extensive particle-particle interactions [Big82, Sai86, Sain86]. At low shear rates, the

presence of both (1) isolated agglomerates and/or floes and (2) extensive three-

dimensional particulate network structures increase the resistance of the particle/fluid

suspensions to flow and, therefore, the measured viscosity is high. As the shear rate is

increased, both particle network structures, agglomerates, and/or floes are broken down

and resistance to flow is greatly reduced (because the liquid occluded in those networks












o











0 4










-
0

















\ c
U)



















>
III










Co
t> 0 0





- II II\ h o

0 0
a N S o

O- O0 O \
























bA4








21

and agglomerates is now released). Thus, the measured viscosity decreases, i.e., shear-

thinning behavior is observed. (In some cases, shear thinning behavior also results from

the characteristics of the polymer, as described in section 2.2.2) Bigg studied the

dynamic theological behavior of polyethylene samples containing relatively large (- 15

pm) steel spheres (to avoid the complexities caused by particle shape irregularity and

particle agglomerates) and irregular-shaped relatively fine (- 0.6 pm) alumina powders

[Big82, Big83, Big84b]. The dynamic viscosities of the sample containing 60 vol% steel

spheres were strongly shear-dependent over the measured shear frequency range (0.1-100

rad/sec) even though the polyethylene (PE) melts were Newtonian at the same frequency

range, indicating the existence of the particulate structure in the suspension. For the

samples containing alumina powders, agglomerates and/or flocs were formed and highly

shear-thinning behavior was also observed. By treating alumina with appropriate

chemical additives, it was possible to improve particulate dispersion in the PE melts, thus

decreasing the viscosity and allowing mixtures with higher solids loading (from 57 vol%

to 64 vol%) to be prepared.

The storage modulus (G') determined from dynamic shear measurements is

indicative of the elasticity of a particle/fluid mixture. In general, the G' values increase

with increasing shear rate. Adding particles to a polymer has the effect of increasing G'

values [Big82, Big83, Big84b, Ron88, Sai86, Sher68]. As the solids loading increases,

the slope of a G' vs. shear rate curve decreases due to the increased particulate network

structure of the mixture (i.e., as samples develop a more elastic character). In the case

of the steel sphere/polyethylene mixtures described above, the storage modulus values









22

still increased with increasing frequency at 60 vol% of solids loading [Big82]. However,

if fine alumina or zirconia particles were used, which tended to form agglomerates and/or

flocs easily, the storage modulus curves were relatively flat over the entire frequency

range at solids loading as low as 50 vol% [Alt83, Big83].

The strain values used in dynamic-shear measurements also affect the theological

properties for particle/polymer mixtures. Bigg investigated the effect of strain for a

polyethylene sample containing 50 vol% steel spheres [Big83]. The theological

properties of pure polyethylene (without steel spheres) were independent of strain values.

However, both dynamic viscosity and storage modulus decreased by about two orders of

magnitude when the strain was increased from 1 to 25 %, suggesting that the particle

networks dominated the theological response of mixtures.

2.3 Particle/Fluid Mixing

Dispersion of particles in a polymeric fluid consists of three major steps: wetting,

deagglomeration, and stabilization [Fun86, Hee69, Nak84]. First, the polymer wets the

outer surface of large particle lumps and penetrates into the interstitial space of the

agglomerates. In the second step, high shear force is applied to break down the particle

lumps into smaller units. In the last step, re-agglomeration and de-agglomeration reach

dynamic equilibrium. It should be emphasized that the various aspects of dispersing a

powder in a fluid do not really occur in successive stages, but in fact occur in a

simultaneous manner [Hee69].

Mixing of particle/polymer batches is often carried out in internal mixers with

variable-speed rotors of different geometries. A transducer is sometimes attached to the








23

mixer to monitor the torque required to maintain the rotors at a specified mixing speed.

The torque vs. time function provides information related to the extent the mixing and

the properties of the mixes. For example, consider the case in which

alumina/polyethylene samples were mixed by preheating a portion of powder to the

desired temperature, adding polymer all at once, and then adding the remaining portion

of powder [Alt83, Big84a]. During the initial stage of mixing, a large torque peak was

observed which was attributed to wetting of the powder (by the polymer), incorporation

of the powder into the polymers, and deagglomeration of the powder. Torque values

subsequently decreased (after the peak) and tended to maintain a steady value, suggesting

that no further improvements in dispersion were likely to occur with continued mixing.

Usually, a high shear stress is required in order to break down the powder

agglomerates in the starting powders. The shear stress generated during mixing is

dependent on the rotor speed. As a result, samples mixed at higher rotor speeds have

better particulate dispersion than those mixed at lower rotor speeds [Dan52, Frea85,

HesS84, Moh59, Sha84]. This conclusion has been supported by experiments using

various techniques to evaluate the state of particulate dispersion, including electrical

resistance and quantitative microscopy for carbon black/rubber samples [Dan52], and

viscosity measurement for cement/water suspensions [Sha84].

High shear mixers are generally used to incorporate powders into polymer melts.

The breakdown of agglomerates is generally maximized within a few minutes of mixing

and prolonged mixing times generally do not result in further decreases in the amount

or size of the agglomerates [Dan52]. This conclusion has been reached from many









24

studies with carbon black/rubber mixtures in which the properties and microstructure

were evaluated as a function of mixing time [Boo63a, Boo63b, Dan52, Lei56].

Particulate dispersion may be affected by mixing temperature because of its effect

on polymer viscosity and polymer/particle wetting behavior. Since polymers have higher

viscosities at lower temperatures, high shear stresses are generated if mixing is carried

out at lower mixing temperatures [Frea85, Gar85, LeeM84, Moh59]. As a result,

agglomerate breakdown may be enhanced if samples are mixed at lower temperatures.

The effect of temperature on polymer/particle wetting behavior has received less

attention. Cotton studied the effects of mixing temperature on dispersion of carbon

black/rubber mixtures and found that samples mixed at higher temperatures had lower

electrical resistance, indicating that better particulate dispersion was achieved [Cot84].

He suggested that this was due to the improvement in rubber/carbon black wetting at

higher temperatures, although direct measurements of wetting behavior were not carried

out.

When a low mixing temperature is used, it becomes more difficult to remove the

voids created during mixing due to the high polymer viscosity. The mechanical strength

may be reduced even though the particulate dispersion may be improved. To solve this

type of problem, Lee used a cyclic temperature schedule to mix carbon black with

elastomer in a two-roll mixer to improve the degree of mixing and the mechanical

strength [LeeM84]. The mixing temperature profile, shown in Figure 2.5, combined the

heating and cooling steps with different time lengths in each segment. In the heating

cycle, voids were removed more effectively due to the lower rubber viscosity at higher



















140 -
120 -
S100
s 80
I 60 1
40 -
20

2 min 4 min 3 min 1 min
Neoprene + Fillers + Curatives
Rubber
Mixing Time Period (min)


Figure 2.5 A cyclic mixing schedule with the combination of heating and cooling
and steps [LeeM84].



temperature. In the cooling cycle, the efficiency of dispersing carbon black was greatly

increased due to the higher rubber viscosity. The mechanical strength of the cyclically

mixed mixtures was higher than the conventionally mixed mixtures (i.e., in which mixing

was carried out at a constant temperature). By examining the cryogenically fracture

surface, the cyclically mixed sample clearly showed fewer voids and a better particulate

dispersion.

2.4 Particle/Fluid Wetting

Wetting behavior can be understood from Young's equation (see Figure 2.6).

Spontaneous wetting is defined as the case when the contact angle, 0, is < 90'. The

contact angle can be simply evaluated by the sessile drop method, which is based on










/ Vapor

YLV

Liquid
-Ysv 7s--s

Solid


Ysv YSL
Young's Equation: cosO =
YLV

Figure 2.6 Contact angle for a liquid droplet deposited on a solid substrate and
Young's equation.



using the geometry of a liquid droplet deposited on a solid substrate (Figure 2.6).

Measurements are made of the angle formed by a line along the solid-liquid interface and

a line tangent to the droplet surface which passes through the three-phase intersection

point (Figure 2.6) [Cari75, Com89, Her70]. Sessile drop measurements are generally

carried out on bulk solid (dense) substrates. However, in some cases, contact angles can

also be measured for fluid droplets deposited on powder compact surfaces [Buc86,

Fel79]. The method is restricted to cases in which penetration of fluid into pores of the

powder compact is negligible (e.g., when the fluid is non-wetting, the fluid viscosity is

high, etc.).

Another method for determining fluid/powder contact angles is to measure the

penetration rate of the fluid through the powder compact. The correlation between








27

penetration time and penetration distance is expressed by the Washburn equation

[Was21]:


I2 = ( r cos 0) ( ) t (2.9)
2

where 1 = penetration depth
r = pore radius of the alumina compact
0 = contact angle
= surface tension of the fluid
= viscosity of the fluid
t = penetration time


This equation is based on the following assumptions: (i) the pores in the powder

compacts are cylindrical in shape; (ii) there are no closed pores or enlargements in the

pore structure; (iii) the pore size is much greater than the molecular diameter of the

liquid; (iv) gravity is neglected; and (v) there is no chemical reaction between liquid and

powder. The powder compact can be made either by compaction of the powder at a

constant pressure or by compaction of a fixed weight of powder into a fixed volume

[Che83, CroV67, Stu55]. Application of Eq. 2.9 requires knowledge of parameters 7,

71, and r. Both y and q can be readily measured with considerable accuracy. However,

r can not be assigned a single value since real powder compacts have a wide range of

pore sizes and pore shapes. To address this problem, it is necessary to find a reference

liquid which has zero contact angle (i.e., cos 0. = 1) [Buc85, Stu55] for the powder

under investigation. The times required for the reference and test fluids to penetrate a

fixed distance into the powder compact are defined as to and ti, respectively. The same

type of powder compact is used for each penetration experiment, so that pore radii, r.








28

and ri, can be considered to be the same. Consequently, the contact angle of the test

fluid, Oi, can be calculated from the following equation (which is derived from the

Washburn equation):


cos = (To ) ( ) = H ( )
l t t10 (2.10)

H = (T"i)
.Yi ^10

where 00, o0, and To = contact angle, viscosity, and surface tension of the
reference fluid, respectively
0O, T7i, and 7, = contact angle, viscosity, and surface tension of the
test fluid, respectively


For more accurate results, many penetration rate (1 vs. t) data points are collected

for each sample, and the contact angle is calculated by linear regression. By taking

logarithmic values on both sides, the Washburn equation is transformed to the following

linear equation:



2 2 )] 2+ (2.11)
log l --- -2 log [ (r cos 6 ) ( '. 1/ 2 (.11)

= K + m log t
where m = slope of log 1 vs. log t curve
K = intercept of log 1 vs. log t curve


If Eq. 2.11 applies, a plot of logarithm of penetration distance vs. logarithm of

penetration time should give a slope of 0.5. From linear regression, the best fit K and

m values for a test fluid and a reference liquid can be found. Then, the contact angle

of the test liquid is calculated from the following equations:












K. = *log [(r, cos ) ( )]
S 2 2 C

1 7o
K log [(ro cos 0,) ( )
2 2 t. (2.12)

cos 0, = ( ) exp [ 2 (K,-K) ]
7yi 0 o

=H exp [ 2 (,-K) ]


It should be noted that the plot of log 1 vs. log t does not always give a slope equal to

0.5. Furthermore, log 1 vs. log t plots are not always linear. These effects have been

attributed to non-uniformities in powder packing, as well as the range of pore sizes and

pore shapes in real powder compacts [Carl79, Coo77].

If a reference liquid with zero contact angle is not available, it is still possible to

identify differences in wetting behavior by determining the contact angle ratio for

different powder/fluid systems. By assuming the pore structures in the powder compacts

are the same, the contact angle ratio can be calculated.


(cos 0), t
R (C 0) H ( 2 (2.13)
(cos 0)2 tl


R. Cos ) H exp [2 (K--Kz)] (2.14)
(cos 0)2


where RI. 0 = Contact angle ratio between conditions 1 and 2
(cos 0), = Cosine of contact angle at condition 1
(cos 0)2 = Cosine of contact angle at condition 2








30

The parameters H, K, and K2 are obtained from Eqs. 2.10 and 2.11. If only one

penetration data point is taken for each sample, Eq. 2.13 should be used. Eq. 2.14 will

give higher accuracy if many data points are taken for each sample.

2.5 Characteristics of Alumina Surfaces with Adsorbed Water and Hydroxyl Groups

When alumina powders are treated at high temperatures, the surface hydroxyl

groups and the adsorbed molecular water are removed gradually. This effect can change

the alumina/polymer wetting behavior, mixing behavior, and the state of particulate

dispersion. In this study, infrared spectroscopy (IR) and gravimetric analysis were used

to examine the change in alumina surface characteristics after heat treatment. IR gives

information on the chemical bonding at alumina surface, while gravimetric analysis gives

information about the weight of molecules that are adsorbed or removed from the

alumina surface.

In general, alumina surface OH groups and molecular water show stretching and

bending bands at 3000-3800 cm-' and 960-1700 cm-1, respectively. Five IR peaks for

isolated OH groups on dehydrated alumina surface have been identified [Hai67, Per65b].

These peaks are at located at 3700, 3733, 3744, 3780, and 3800 cm-', which correspond

to the sites with different numbers of nearest oxide neighbors. The theoretical model of

these OH groups is schematically illustrated in Figure 2.7, and the assigned OH

stretching frequencies are listed in Table 2.3. The exact location of these IR peaks for

any specific powder may shift slightly depending on particle size, surface structure, and

state of hydration. In fact, these IR peaks for isolated OH groups cannot be observed

unless alumina is heated to a very high temperature (e.g., 1000C). At room
































Isolated hydroxyl groups on alumina surface (+ donates Al3 in lower
layer) [Per65b].


Table 2.3 Isolated hydroxyl groups
spectra [Per65b].


on alumina surface observed in infrared


Figure 2.7


OH group Wave #(cm-') Number of nearest oxide neighbors

A 3800 4
B 3744 2
C 3700 0
D 3780 3
E 3733 1








32

temperature, alumina adsorbs molecular water which gives wide bands centered at 3300

and 1650 cm1 regions and the OH peaks are concealed [Hai67, PerH60]. As the

temperature is increased (- 100-400"C), the intensities of these two bands are reduced

as molecular water is removed. At even higher temperatures (e.g., in the range of 650

and 700C), molecular water and some hydrogen-bonded hydroxyl groups are removed

and sharp OH peaks become evident. Due to condensation of OH groups, trace amounts

of water continue to evolve up to very high temperatures (> 1000C).

The amount of water adsorbed on alumina surface has been studied by gravimetric

measurement [Cor55, DeBF63]. The water molecules bound directly by surface

hydroxyl groups are referred to as chemisorbed water which cannot be expelled by heat

treatment at 120"C. The term chemisorbedd" is justified based on the strength of the

bond and the activation energy for dehydration. Above the chemisorbed water layer is

the physisorbed water which has a multilayered structure and can be described by the

BET equation. The amount of water on the alumina surface is actually dependent on

temperature, pressure, and treatment of the alumina powders. These variables have been

investigated by adsorption-desorption experiments [Cor55, Per65a, PerH60].

2.6 Effects of Moisture on Ceramic/Polymer Composites

It is well-known that the properties of polymer/ceramic composite may be affected

by exposure to water or by storage in a humid environment [Col86, Roy76, Tra76].

Moisture can diffuse either through the polymer matrix or along the ceramic/polymer

interface into the inner structure of the composites. Diffusion of moisture into samples

was confirmed by weight change measurements [Col86, Shi78, Spr81]. Sample weights








33

increased initially and then levelled off after a long period of time. Generally, moisture

diffusion rates and final moisture contents increased with increasing humidity and

temperature. If there were microvoids in the composites, the final equilibrium moisture

content became greater than expected because the microvoids could accumulate a

considerable amount of water. In addition, abnormally high initial rates or continuously

increasing weight gains for long times have been observed. These effects are due to

cracks in the sample, especially cracks on sample surfaces [Bro78].

The effect of moisture on the properties of fiber-reinforced thermosetting

composites have been investigated extensively. Usually, experiments were carried out

by storing samples in environments with controlled moisture contents and temperatures,

and the properties were measured periodically [Put82, Spr81, Sto90]. For example,

significant reduction in yield stress and ultimate strength were observed for glass

fiber/epoxy composites in a four-point bending test [Sto90]. In a vibration test,

absorption of moisture reduced the dynamic modulus for graphite/epoxy samples, but it

had little effect on damping coefficients [Put82]. In tensile tests, reduction of ultimate

tensile strength of fiber reinforced composites depended on the orientation of fibers and

moisture content [Shen81].

Many hypotheses have been proposed to explain the mechanisms of aging in

samples which absorb moisture. For example, it has been suggested that water might act

as a plasticizer [Bro78, CorF78, Sto90, Tra76] to decrease the glass transition

temperatures (Tg) of the polymer matrices. The Tg values for epoxy and nylon

composites have been shown to decrease with increasing moisture content [Bro78,








34

Luo83, Whi82]. Under this circumstance, the ability of the polymer to support the

reinforcing fiber and to transfer loads to the fiber may be reduced. It has also been

proposed that absorbed water may cause polymer swelling that might induce internal

stress and initiate cracks inside polymer composites. As a result, the mechanical strength

could be significantly reduced. Unfortunately, these is still no conclusive evidence to

support these hypotheses even though this type of aging phenomenon has been well

recognized.

2.7 Chemical Additives

For almost all ceramic/polymer mixtures used in industry, chemical additives are

indispensable ingredients for various purposes, including reducing flow resistance during

processing and enhancing adhesion between two components. Numerous chemical

additives are available commercially which are generally classified as lubricants,

plasticizers, wetting agents, coupling agents, etc. These conventional classifications are

made according to chemical structures and their intended functions. The expected

effects, however, may not indeed occur in practical applications. For example, a

coupling agent may actually act as a particulate dispersing agent, with no real coupling

(i.e., chemical bonding) between the polymer and particles [Luo83, Mon74]. Such a

result demonstrates the complexity in selecting a proper chemical additive to achieve the

desired goal and the difficulty in predicting the performance of any specific chemical

additive. This section reviews the structure of some additives (including coupling agents,

surfactants, and lubricants) and analyzes their influence on the theological properties for

ceramic/polymer mixtures.











2.7.1 Structures

Coupling agents are the molecules designed to form chemical bonds between two

components with different natures. The general formula of a coupling agent is expressed

as


R M (O-R') (2.15)


In the above formula, O-R' is a hydrolyzable group, such as methoxyl (OCH3) or ethoxyl

(OCzH,), that can react with water or a hydroxyl group on the ceramic surface, R is an

organic part with different functional groups, and M is a metal atom. The parameters

m and n vary from 1 to 4 for most coupling agents. Depending on the center atom M

(e.g., Si, Ti, or Al), the coupling agents are classified as silane, titanate, or aluminate.

Silanes have received the most research attention and have extensive applications [Big82,

HanV81, InoK75, LeeM87, Luo83, Plu70, Plu78, Plu82, PluS78, Sain85, Zha88].

The commonly used silanes have three hydrolyzable groups (n=3) and their chemical

structures are listed in Table 2.4. Titanates can be classified according to the number

of hydrolyzable groups and the structures of the R groups. Table 2.5 gives chemical

descriptions of some popularly used titanates [Bre85, HanS78, HanV81, Luo83, Mon78,

Mon84a, Mon84b, Mon84c]. However, the exact formula for titanates and some other

coupling agents are not available from the manufacturers.

To have a real coupling effect, the OR' groups should be hydrolyzed and a strong

bond between the ceramic surface and the polymer matrix should be formed. The ideal

mechanism can be described by the following reactions, using silane as an example:














-(- 4 00 00
. oo eo


at a o I I









m0 0




C 4 U
u 0o


Uu u u
r au =O .


u U U J Z Z :
4 f r C4 U t 4

u u u u x u
r020


o 0



I 4 E
i| 0 I sl I
0 |1 EI I iII
| uS <- 23: U 2 ^



S. i tN:


m .











Table 2.5 Commonly used titanate coupling agents [Mon78a, Mon84a].


Titanate type Chemical description

Monoalkoxy (m= 1, n=3)'
KR TTS Isopropyl, triisostearoyl titanate
KR 6 Isopropyl, methacryl diisostearoyl titanate
KR 9S Isopropyl, tridodecylbenzenesulfonyl titanate
KR 12 Isopropyl, tri(dioctylphosphato) titanate
KR 38S Isopropyl, tri(dioctylpyrophosphato) titanate
KR 44 Isopropyl, tri(N ethylamino-ethlamino) titanate
Monoalkoxy (m= 1, n=3)
LICA 01 Neoalkoxy, triisostearoyl titanate
LICA 09 Neoalkoxy, dodecylbenzenesulfonyl titanate
LICA 12 Neoalkoxy, tri(dioctylphosphato) titanate
LICA 38 Neoalkoxy, tri(dioctylpyrophosphato) titanate
LICA 44 Neoalkoxy, tri(N ethylamino-ethlamino) titanate
Chelate (m= 1, n=2)
KR 112 Titanium di(dioctylphosphate) oxyacetate
KR 138S Titanium di(dioctylpyrophosphate) oxyacetate
KR 238S Di(dioctylpyrophosphato) ethylene titanate
Coordinate (m=4, n=2)
KR 41B Tetraisopropyl di(dioctylphosphito) titanate
KR 46B Tetraoctyloxytitanium di(ditridecylphosphite)

See EQ (2.23) in the text for the chemical formula of coupling agent.


R-Si(-OR')3 + 3 H20 R-Si(-OH)3 + 3 HOR'

R-Si(-OH)3 + HOM(,Cf) R(OH)2-Si-O-M(,f.+ H20


(2.16)

(2.17)


The above reaction is applicable in cases where the coupling agent is applied to the

ceramic as a water-containing solution. Coupling agents can also react directly with the


surface hydroxyl groups if nonaqueous solvents are used:









38

R-Si(-OR')3 + HOM(m,^) R(OH)2-Si-O-M(..,+ HOR' (2.18)


In aqueous solutions, condensation between OH groups of hydrolyzed silane coupling

agent molecules can result in monolayers of silanoxanes on ceramic surfaces. The step-

by-step mechanism is illustrated in Figure 2.8 [LeeL68]. In fact, this is an idealized

model for monolayer coverage. The hydrolyzed silane R-Si(OH)3 actually starts to

condense even in the solution and the polymerization rate is dependent on pH values of

the solution, concentration of coupling agent, composition of the R group, and

temperature [Plu69, Plu82]. Coupling agent solutions turn hazy when extensive

polymerization occurs and molecules are large enough to scatter light. Consequently, a

simple way to experimentally monitor the stability of hydrolyzed silane solutions is to

determine the amount of time required for the solutions to turn hazy. Some silane

coupling agent solution (e.g., hydrolyzed aminofunctional silane solutions) have

extraordinarily high stability. This has been attributed to be formation of stable (low

molecular weight) cyclic structures as illustrated in Figure 2.9.


R R R
RO-Si-O HO-Si-ON "-t HO-Si-OH

TRIALKOXYSILAMES STABLE SILANETRILS Si ASS SURFACE
NIOvO(m- | IgW pi


Io I Ii
4r l R 0
-HO-- "-0 -Si--OH
,>S ^ J' /,-, \ o- 0-

GLASS SURFACE CLASS SURFACE

Figure 2.8 Formation of a monolayer of polysiloxane on silicate glass surface
[LeeL68].













-0 CH2-CH,

S CH2 (A)
/ \ /
--0 O' ,- +NH2






-0 CH2-CH2

Si CH2 (B)
/\ /
--0 O'-~-- +NH2

NH2-CH2-CH2


Figure 2.9 Cyclic structures of (A) aminosilane and (B) diaminosilane coupling
agents in solution [Plu69].



Surfactants (surface active agents) are chemicals with the capability of modifying

the interfacial energy by adsorption at interface. A surfactant has two distinct parts in

the molecular structure: a hydrophilic (lyophobic) head group and a hydrophobic

(lyophilic) tail. According to the structure of the hydrophobic groups, surfactants are

classified as hydrocarbon, silicone, and fluorocarbon. Among these, hydrocarbons with

8 to 20 carbon atoms are used most extensively. Fluorocarbons have very low surface

energies and exceptional resistance to thermal and chemical attack.

Surfactants are usually applied by solution treatment of the powder (or fiber) in

order to achieve homogeneous coatings in an efficient manner. The amount and








40

orientation of surfactant adsorbed on solid surfaces are controlled by many factors,

including the nature of surfactant, property of solid surface, solution concentration,

solvent, etc.

A lubricant is an interfacial phase that is used to reduce the resistance to sliding

between two phases [Ree88]. The lubricants commonly used in ceramic processing

include paraffin wax, stearic acid, oleic acid, polyglycols, silicone oil, etc. Stearic acid

and its salts are effective lubricants because the carboxyl end of the molecule may be

strongly bonded to an oxide surface, and the shear resistance between the first oriented

adsorbed layer and successive layers is low. Lubricants can be applied either as additives

to a batch formulation [Edi86, Sto90, Zha88] or as coated films on surfaces (of molds,

dies, extrusion chambers, etc.) in contact with the batch during shape forming operations

[Dim83, Str77]. The term "internal lubricant" is applied to the former case, while the

term "external lubricant" is used in the latter case. In the case of external lubrication,

it is well-documented that the shear stress generated during processing at the interface

between batch and the coated surface may be greatly reduced by the presence of a

lubricant.

2.7.2 Effects of Chemical Additives on Rheological Properties

The incorporation of small amounts of chemical additives (such as coupling

agents, surfactants, lubricants, etc.) in ceramic/polymer batches may significantly affect

the properties of the mixture, including the theological properties. These additives can

modify particle-particle, particle-polymer, and polymer-polymer interactions depending

on nature of chemical additives, polymer properties, ceramic characteristics, and the









41

method by which the chemical additive is applied. It is important to consider all these

types of interactions in understanding the mechanism by which the additive influence

batch properties.

It has been suggested that a chemical additive can increase viscosity and modulus

values if chemical bonding occurs between the ceramic surface and the polymer [Big82,

Big84b] or if ceramic/polymer adhesion is improved [HanV81]. In such cases, enhanced

bonding or adhesion at the interface is indicated by changes in fracture mode (i.e., cracks

propagate through the polymer matrix and not along the ceramic/polymer interface

[HanV81]).

Chemical additives may also affect viscosity and modulus values by altering the

state of particulate dispersion. Reductions in viscosity and modulus values are observed

when the state of particulate dispersion is improved (e.g., when agglomerates are broken

down) [Big83]. It should be noted that some coupling agents may also act as wetting

agents or dispersing agents (i.e., as opposed to forming strong bonding between ceramic

particles (or fibers) and polymer matrices [Big83, Boa77, HanS78, HanV81, Luo83,

Mon84c, Sain85]).

Reduction in viscosity and modulus can be caused by a lubricating effect at the

particle-polymer interface or plasticization of the polymer matrix [Alt83, Big83, Big84a,

Big84b, Sain85, Mon74, Mon78, Mon84c, Sain85]. An effective lubricant should also

result in lower shear stress developed during mixing (i.e., lower mixing torque value)

[Big83].














CHAPTER 3
EXPERIMENTAL


3.1 Materials and Materials Preparation

3.1.1 Starting Materials

Most of the experimental work was carried out with a high purity aluminum oxide

powder' (RCHP alumina) which had a median Stokes diameter 0.4 pm and a specific

surface area3 of 7.3 m2/g. A few experiments were carried out with a glass powder

(median Stokes diameter2 =2.7 Am) which had major constituents SiO2-Al203-MgO

(approximate weight ratio of 57:21:18 as determined by wavelength dispersive

spectroscopy4) and trace amounts of Ca and P. Another grade of high purity aluminum

oxide powder5 (AKP alumina) with median Stokes diameter2 -0.9 Am was also used

in some experiments.






1 RCHP-DBM, Reynolds Metals Co., Chemical Division, Little Rock, AR. Nominal
purity >99.98% A1203.
2 Sedi-Graph Particle Size Analyzer, Micromeritics Instrument Corp., Norcross, GA.

3 Model OS-7, Quantachrome Corp., NY.

4 Superprobe 733, Japan Electron Optics Co., Ltd., Tokyo, Japan.

5 AKP-15, Sumitomo Chemical America, Inc., New York, NY. Nominal purity
> 99.99% A12O3.









43

bet Most of the experimental work was carried out using a relatively low molecular

weight, low density polyethylene6 (PE A-C' 9). Copolymers ethylene-acrylic acid6

(EAA A-C" 5120 and 540) and ethylene-vinyl acetate6 (EVA A-C' 400 and 405T) and

a high molecular weight, high density polyethylene (PE Sclair 29157) were also used in

some experiments. The physical properties obtained from the manufacturers for these

polymers are listed in Table 3.1. The chemical compositions of these different polymers

are shown in Figure 3.1.


EAA


EVA


H H H H


(-C-C-) (-C-C-)
I m2C=O

H H H C=0


O-H


HH HH



HH HO
H H HO


C=O


CH3


Where 1, ml, m2, nl, and n2 are integers.


Figure 3.1


Chemical compositions of polyethylene (PE), ethylene-acrylic acid
(EAA), and ethylene-vinyl acetate (EVA) polymers.


6 Allied Corp., Morristown, NJ.

7 DuPont Canada Inc., Plastics Division, Toronto, Canada.


H H


(-C-C-)

H H










44




J4)



0 x
4.u








O cc





z II
S' |So -







i o oo oo a I>


- I S II
in 0 4 + V









10 "0
-- a c + c C -


Co '



el ) U
|? tn VS Va




1- c> a, ^^




.0n t










Chemical additives used in this study are listed below:

(1) Silane coupling agent Z-60208 has the formula NH2(CH2)2NH(CH2)3Si(OCH3)3 and

is designated --(f3-aminoethyl)--y-aminopropyltrimethoxysilane. It is a clear, light straw-

to-yellow colored liquid with specific gravity of 1.02.

(2) Silane coupling agent Z-6076' has the formula C1(CH2)3Si(OCH3)3 and is designated

y-chloropropyltrimethoxysilane. It is a colorless liquid with specific gravity of 1.08.

(3) Titanate coupling agent9 Ken-React LICA 12 has formula ROTi[OP(O)(OCH17)2]3

and is designated neoalkoxy, tri(dioctylphosphato) titanate. (The R in the formula is a

neoalkoxy group, but the manufacture does not provide information on the exact

structure.) It is a clear, red-orange colored liquid with a mild alcoholic odor and specific

gravity of 1.02.

(4) Zircoaluminate coupling agent CAVCO MOD APGo1 is an amino functional

zircoaluminate having an inorganic polymer backbone dissolved in propylene glycol. It

is a colorless liquid with specific gravity of 1.15.

(5) Surfactant Fluorad FC-740u is a nonionic fluorinated alkyl ester liquid with specific

gravity of 1.01.







8 Dow Coming Corp., Midland, MI.

9 Kenrich Petrochemicals, Inc., Bayonne, NJ.

10 Cavedon Chemical Co., Inc., Woonsocket, RI.

n Commercial Chemical Division/3M, St. Paul, MN.









46

(6) Stearic acid" is a solid which has the chemical formula CH3(CH2)3COOH and a

specific gravity of 0.85.

The chemical compositions of silanes, titanate, and stearic acid are shown in Figure 3.2.

Unfortunately, the compositions for zircoaluminate coupling agent and Fluorad FC-740

are not available from the manufacturers.

3.1.2 Treatment of Alumina Powder

Alumina powder calcination. Alumina powders were heated to temperatures in

the range 300-1000IC in a box furnace13 at a rate of 10C/min and subsequently held

at the desired temperatures for 4 hr. Furnace power was turned off at the end of the 4

hr hold period. Powders were cooled in the furnace to 150C and then were immediately

transferred to a desiccator in order to avoid moisture absorption as powders cooled to

room temperature. Calcined powders were kept in the desiccator for at least 12 hr

before performing mixing experiments. Experiments were also carried out with alumina

powder that was calcined at 100C for 4 hr using a convection oven14. The alumina

powder was transferred to a desiccator immediately after the heat treatment was finished.

The same experimental procedures were used for heat treatment of alumina

powder compacts. These compacts were subsequently used in contact angle and

microhardness measurements.





12 Fisher Scientific Co., Fair Lawn, NJ.

13 Model DT-31, Deltech, Inc., Denver, CO.
14 Fisher Isotemp' Oven, Model 126G, Fisher Scientific Co., Fair Lawn, NJ.

















Silane Z-6020


O-CH3
I
NH2- (CH2) 2-NH- (CH2) 3-Si-O-CH3
I
O-CH3



Silane Z-6076

O-CH3

Cl- (CH2) 3-Si-O-CH3

O-CH3



Titanate LICA 12

R-O-Ti-[O-P- (O-CH17) 2) 3]
II
O

Where R is a neoalkoxy group (The composition is not
revealed by the manufacturer).


Stearic Acid

CH3- (CH2)16-C-OH
II
0


Figure 3.2 Chemical structures of some chemical additives.









48

Mixing with chemical additives. Coupling agents (1.25 g) were added to

deionized water (125 cc) in 250 cc bottles. The bottles were shaken by hand for a few

sec and then placed on a low-speed (- 30 rpm) rotary mixer for 1 hr. Alumina powder

(125 g) was added into the bottles and mixing on the low-speed rotary mixer was

continued for 22 hr. The theological flow properties of the suspensions were then

characterized using a steady-shear viscometer". Samples were then transferred to 250

cc glass beakers which were placed on a hot plate (-900C)/stirrer. Water was

evaporated from the suspension under constant stirring until dry powder cakes were

obtained. (This step took -24 hr to insure that the solvent was completely removed.)

The cakes were crushed by a mortar and pestle to powders with as fine a size as

possible. Powders were stored in a vacuum desiccator prior to mixing with polymer.

This procedure was used for mixing other chemical additives with the alumina powder,

but the solvents were changed to heptane for additions of Fluorad FC-740 and carbon

disulfide for additions of stearic acid. The drying temperature was reduced to -40C

for carbon disulfide because it had a boiling temperature of 46.5C. (Heptane had a

boiling temperature of 98.40C and so the drying temperature was kept at 90"C.) Also,

the amounts of Fluorad and stearic acid added were varied in the range of 0.063-3.75 cc.

Compaction. Alumina powder compacts were made by three methods: pressing

dry powders, slip casting, and pouring powder/water suspension on a glass plate. Dry

pressed powder compacts were formed by uniaxial compaction at 35 MPa (- 5100 psi)


15 Model RV 20/CV 100, Haake, Inc., Saddle Brook, NJ.









49

of 2 g of dry powder in a 2.54 cm diameter cylindrical steel die. The powder compacts

were -2 mm thick and had a relative density of 53%16 (as determined by mercury

porosimetry). Slip cast powder compacts (thickness -3 mm) with different packing

densities were made from aqueous suspensions (30 vol% solids) having either pH 4

or pH 9. The initial preparation of the suspensions involved mixing alumina powder

and deionized water by hand for 1 min, followed by 1 hr of sonication in order to

break down powder agglomerates. Suspensions were then poured into plastic tubes

sitting on blocks of plaster of Paris. Thin alumina powder compacts (thickness 1 mm)

were also made by pouring pH -4 suspension (30 vol% solids) on a 30 x 30 cm glass

plate. The suspensions were the same as those used in preparing slip cast compacts.

Suspensions were poured on the glass plate and allowed to spread out naturally. Water

was allowed to evaporate at room temperature for 24 hr and thin pieces (-2-10 cm2) of

consolidated powder (i.e., green compacts) were subsequently collected for

microhardness and contact angle measurements.

3.2 Characterization of Ceramic Powders.

Powder Compacts. and Polymers

3.2.1 Alumina Powder Characterization

Weight loss. The amount of weight loss during calcination was determined by

measuring the powder weights before and after heat treatment.


16 Autoscan-60, Model SP-20LV, Quantachrome Corp., Syosset, NY.









50

Specific surface area. The specific surface areas of as-received (uncalcined) and

calcined alumina powders were measured by nitrogen gas adsorption7 (multipoint BET

method). Powders were outgassed at 2000C for 3 hr under a flowing nitrogen

atmosphere just before making the measurements.

Particle size distribution for as-received ceramic powders. The particle size

distributions of ceramic powders were measured either by x-ray sedimentation18 or by

centrifugal photosedimentation19. In order to prepare well-dispersed suspensions,

alumina powders were mixed with water at pH = 4 (i.e., to develop a high positive

surface charge) and subsequently sonicated to break down agglomerates. For x-ray

sedimentation, the suspensions were prepared with 2 vol% solids and sonicated for 1 hr.

For centrifugal photosedimentation, 0.1 vol% alumina suspensions were prepared,

sonicated for 30 min, and diluted to the appropriate concentration (-0.01-0.03 vol%)

before measurement. The magnesium aluminum silicate glass powder was characterized

by x-ray sedimentation using a suspension which was prepared with 3 vol% solids in

methanol and sonicated for 1 hr. (Methanol was used as the suspension liquid because

of concerns regarding possible chemical reactions between water and the glass powder.)

Particle size distribution for calcined alumina powders. The particle size

distributions of calcined alumina powders were measured in order to determine if

interparticle bonding (agglomerate formation) occurred during heat treatment. Some of


17 ASAP 2000, Micromeritics Instrument Corp., Norcross, GA.

8 Sedi-Graph Particle Size Analyzer, Micromeritics Instrument Corp., Norcross,
GA.

1 CAPA-700, Horiba Instruments, Inc., Irvine, CA.









51

the measurements were carried out by the x-ray sedimentation and/or centrifugal

photosedimentation methods using the same procedures as described above for the

characterization of as-received powders. However, in other experiments, centrifugal

photosedimentation measurements were carried out on suspensions prepared with either

no sonication or with only 15 sec sonication. Of course, this procedure resulted in

incomplete breakdown of powder agglomerates and, thus, the measured size distributions

were shifted to larger sizes compared to results obtained using well-sonicated

suspensions. However, these measurements were useful in providing information about

the strength of the agglomerates that formed when powders were calcined at various

temperatures. Powders with weaker agglomerates will disperse more completely with

short sonication times and, therefore, the measured distributions show smaller apparent

particle sizes. In contrast, powders containing stronger agglomerates tend to resist

breakdown during sonication and, therefore, the measured size distributions show larger

apparent particle sizes.

Surface characterization via FTIR. The effect of calcination on the alumina

powder surface characteristics was analyzed by diffuse reflectance2 Fourier Transform

Infrared Spectroscopy21 (FTIR). Samples were scanned over the range from 400 to

4000 cm' at a rate of 200 scans per minute. Generally, 500 scans were collected for

reference materials (potassium bromide, Kbr) and 200 scans for other samples. A hot





20 DRA-2C6, Harrick Scientific Corp. Ossining, NY.

21 Model 60SX, Nicolet Analytical Co., Madison, WI.








52

stage22 was used for in-situ FTIR measurements at elevated temperatures. In one

experiment, spectra were collected as alumina powder was heated from room temperature

to 100C in 15 min and subsequently held at 100C for 4 hr. In another experiment,

spectra were collected every 100TC as the powder was heated from room temperature to

600"C at 10C/min.

Analysis for Iron content. Iron (either elemental or ionic state) contamination in

alumina powders was extracted into aqueous solution and concentrations were determined

by inductively coupled plasma spectrometry' (ICP). Alumina powders (10 g) were

boiled in 200 cc of 1 N HC1 for 2 hr with stirring. After cooling down to room

temperature, the alumina powders were removed from suspension using filter paper24.

The filtrates were then concentrated to 20 cc for the ICP measurement.

Scanning electron microscopy and optical microscopy. The as-received and

calcined alumina powders were observed by scanning electron microscope (SEM")

using 25 KeV accelerating voltage. Alumina powders or bulk substrates treated with

coupling agents were also examined at high magnification using SEM and at low

magnification using optical microscopy6.



22 HVC-DRP, Harrick Scientific Corp. Ossining, NY.

2 Plasma II Emission Spectrometer, Model 5800, Perkin-Elmer Corp., Norwalk,
CT.

4 No. 3. qualitative filter paper, Whatman International Ltd., Maidsone, England.

2 Model JSM-35CF, Japan Electron Optics Co., Ltd., Tokyo, Japan.

26 Nikon Inverted Microscopy, EPIPHIT-TIME, Nippon Kogaku K. K., Tokyo,
Japan.










3.2.2 Alumina Powder Compact Characterization

Pore size analysis. The pore size distributions and total porosity of alumina

powder compacts were measured by mercury porosimetry2. Plots of intruded volume

vs. applied pressure were obtained up to a maximum applied pressure of 414 MPa

(60,000 psi). The pore channel radius distribution was obtained using standard values

for the mercury surface energy (484 erg/cm2) and the contact angle (1400) under the

assumption that the pores are cylindrical. The pore radius distribution was then

calculated using the following relation:


Pore radius (nm) 735 (3.1)
P (MPa)



The median pore radius was calculated from the pressure corresponding to 50% of the

maximum intruded volume (V). The total porosity (P) was calculated using the equation:


P (%) = W_ 100 (3.2)
+V
P


where W is the weight of the sample and p is the theoretical density of the powder. The

relative density of the powder compact is equal to 1-P.

Microhardness measureinents. Hardness measurements were made on the thin

(- 1 mm) alumina powder compacts which were prepared by casting pH = 4 suspensions

onto glass plates (see section 3.1.2). Measurements were carried out on both uncalcined


" Autoscan-60, Model SP-20LV, Quantachrome Corp., Syosset, NY.









54

and calcined alumina (1 hr at temperature) compacts using a microhardness tester28 with

a 10 g load. Five readings were taken for each sample and the average hardness value

was reported.

3.2.3 Polymer Characterization

Rheological properties of polymers were determined by a viscometer2 in a

dynamic oscillatoryy) mode under conditions of controlled temperature, strain, and

frequency (or shear rate). A cone-and-plate test fixture with 25 mm radius and 0.04 rad

cone angle was used. A detailed discussion of the procedures used in measuring

theological properties is given in section 3.4.1.

3.3 Mixing of Ceramic Powders and Polymers

The ceramic/polymer mixtures were prepared using a high-shear bowl mixer

which was equipped with variable-speed roller blades and attached to a torque

rheometer30. The conditions chosen for mixing 50 vol% RCHP alumina with

polyethylene (A-C 9) are listed in Table 3.2. For experimental Run Nos. 1-6 (single-

segment mixing schedules), the temperature and rotor speed were kept constant

throughout the entire mixing period. The following procedure was used to prepare the

ceramic/polymer mixtures: (1) the mixer was heated to the desired temperature and the

roller blades were set rotating at the desired speed, (2) polyethylene was added to the

mixing bowl and -2 min were allowed for the polymer to melt and reach the pre-set



28 Micromet II, Buehler Ltd., Lake Bluff, IL.

29 Model RDS-II, Rheometrics, Inc., Piscataway, NJ.

30 Rheomix 500/Rheocord System 40, Haake, Inc., Saddle Brook, NJ.
















Table 3.2 Mixing conditions used
polyethylene mixtures.


to prepare 50 vol% alumina/50 vol%


Run # Temperature Rotor Speed Total Mixing Time
(C) (rpm) (min)
Single-segment mixing schedules
1 125 200 30
2 150 200 30
3 175 200 30
4 220 200 30
5 150 10 30
6 150 200 10
Multi-segment mixing schedules
Mixing with temperature change
7 150(30) 220(10)' 200 45+
8 220(10) 150(30)' 200 45+
Mixing with rotor speed change
9 150 200(30)- 10(10)' 40
10 150 10(20) 200(30)' 50

SNumbers in parentheses are the mixing times in minutes for each segment.
+ Total mixing time includes 5 min heating (Run #7) or cooling (Run #8) period
between 150 and 2200C.









56
mixing temperature, (3) alumina powder was gradually added (over an -4 min period)

to polymer melt, and (4) mixing was continued for a fixed period of time (usually 30 min

for the entire mixing operation). Run #5 was an exception to the above procedure. The

powder incorporation rate at the low rotor speed (10 rpm) was so slow that step (3) alone

required 20 min. For Run Nos. 7-10 listed in Table 3.2 (multi-segment mixing

schedules), steps (1) to (3) were the same as described above. However, either mixing

temperature or rotor speed was varied during an extended mixing period. Run #7 was

similar to Run #2 (mixed at 1500C), but the temperature was raised from 150 to 220C

over a five min period, and mixing was continued for an additional 10 min. The initial

part of Run #8 was similar to Run #4 (mixed at 220C), but the sample was mixed only

10 min, the temperature was then lowered from 220 to 150C over a five min period, and

mixing was continued for an additional 30 min. The mixing time for Run Nos. 7 and

8 totaled 45 min due to the extra 5 min needed for heating or cooling between segments

at 150 and 220C. For the last two experiments, the mixing speed was either reduced

from 200 rpm to 10 rpm (Run #9), or raised from 10 rpm to 200 rpm (Run #10). In

each case, the 200 rpm mixing segment was carried out for 30 min. The 10 rpm

segment was carried out for 10 min in Run #9, but Run #10 required a 20 min mixing

time at 10 rpm because of the slow rate of incorporation of the alumina. In contrast to

multi-segment experiments involving a temperature change, the transition times between

segments in Runs Nos. 9 and 10 were very short (a few seconds) because the rotor speed

could be changed mechanically within a few seconds.








57

A standard mixing procedure was used to prepare all other ceramic

powder/polymer samples in this study. The mixing temperature, time, and rotor speed

were 150C, 30 min, and 200 rpm, respectively.

3.4 Characterization of Ceramic Powder/Polymer Mixtures

3.4.1 Rheology

Rheological properties of ceramic/polymer mixtures were determined using a

parallel-plate viscometer" which was operated in dynamic-shear oscillatoryy) or steady-

shear modes under conditions of controlled temperature, strain, and frequency (or shear

rate). The test fixtures had a circular plate geometry with either 25 mm radius (for

lower viscosity samples) or 12.5 mm radius (for higher viscosity samples).

The test fixture was heated up to the desired temperature (usually 125'C) and kept

for 1 hr to reach thermal equilibrium. Gap calibration was performed before starting

theological measurements. A sufficient amount of sample was placed on the lower plate

of the test fixture. After 10 min of heating, the sample softened and the upper part of

the test fixture was then moved down to the appropriate gap distance. The gap was 0.05

mm for the cone-and-plate fixture. For the parallel-plate fixture, the gap was in the

range of 0.25-2.5 mm, although a value of 0.6 mm was used most of the time. Low

viscosity samples flowed easily and filled up the gap space when the upper plate was

moved downwards. However, samples with high viscosity or high elasticity did not flow

easily and a significant normal force developed on the transducer attached to the upper

plate. The upper plate was automatically immobilized to prevent further movement when

the normal force exceeded 70% of the maximum transducer load (2000 g).








58

Consequently, a larger gap (typically between 1 to 2 mm) was used for the latter

samples. A sufficient quantity of sample was used to ensure that gap space between

plates was completely filled. As described below, the viscometer was operated in several

deformation modes for this study.

Dynamic rate (frequency) sweep. The lower plate of the test fixture oscillated

sinusoidally at programmed oscillating frequencies (w, rad/sec) and maximum strain (y0,

dimensionless). The shearing angle (0, rad) of the oscillating plate was calculated

according to the equation 0 = 7 -(H/R), where R and H were the radius of the test

fixture and the gap between parallel plates, respectively. In this mode, the maximum

strain was kept constant (7y = 100%) and the frequency was increased logarithmically

from 0.01 to 100 rad/sec. Data were collected at ten frequencies per decade. The

torque value was measured by a transducer attached to the upper plate and the theological

properties were calculated using Eqs. 3.3-3.5 given below.

Transient (thixotropic loop). The rotation speed of the lower plate of the test

fixture was first increased linearly (over 6 min interval) to a maximum shear rate (25 or

50 sec -). Upon reaching the final speed, the rotation speed was decreased linearly to

zero over the same time interval. The torque values were measured and stored 1024

times during each 6 min interval. It should be noted that maximum shear rates were

limited to values noted above because some samples were ejected from the test fixture

at higher rotation speeds. Thus, torque readings taken at higher rotation speeds were

considered to be unreliable.









59

Transient (step strain, or relaxation). In stress relaxation experiments, the lower

plate is first rotated instantly in a clockwise direction to a pre-selected strain value (i.e.,

the sample is subjected to a step strain). (In this study, the step strain was always

100%.) At the same time, torque values are measured as a function of time, i.e., the

relaxation of the stress is monitored over time. The torque values corresponding to the

step strain were recorded at 512 evenly spaced intervals during four sequential time

zones. The time periods of these four zones were kept as 1, 9, 90, and 900 sec in order

to get the best resolution for the relaxation curve. For most samples, the torque values

diminished to values below the detection limit of the transducer (i.e., 2 g-cm) within the

first or the second zone and the experiments were terminated. However, in some

samples (i.e., those with high viscosity and/or high storage modulus), significant torque

values were still observed even at the end of the fourth zone. It should be noted that the

pre-selected strain value (100%) could not be applied on the sample instantly; in reality,

it takes 0.02-0.03 sec to reach the strain value. The instrument starts to collect torque

values before the strain reaches 100%. Consequently, the stress vs. time curve always

shows an initial increase in stress (during the initial 0.01-0.02 sec), followed by the

relaxation of the stress.

The transducer in the viscometer detects the torque generated in response to the

imposed strain on the sample. Using the equations listed below, theological properties

are then calculated from the measured torque values, the geometrical constants for the

test fixtures, and the input parameters (i.e., rotational frequency, strain, etc.).











Rheological properties


M K/i
K (M,)'
K -(M)"
[ (G') + (G")2 ]12
G"/ c
G'/Iw
[ (7,)2 + (7")2 ]11 = G* /
G"/G' = n'/tn"


Cone-and-plate fixture geometry equations (Figure 3.3)

K = 0.1 [3 980.7 ] / [ (R/10 2r ]
to = 0o/f
l- t= o0/

Parallel-plate fixture geometry equations (Figure 3.3)


0.1 [ (2H/10) 980.7] / [ (R/10) ]
- R/H
0 -R/H


Viscosity in steady-shear mode (Pa-s)
Storage modulus (Pa)
Loss modulus (Pa)
Complex modulus (Pa)
Dynamic viscosity (Pa-s)
Imaginary component of complex viscosity (Pa-s)
Complex viscosity (Pa-s)
Loss angle (rad)
Geometric scaling constant dimensionlesss)
Radius of the test fixture (mm)
Cone angle of the con-and-plate fixture(rad)
Height of sample or gap between parallel plates (mm)
Rotational rate in steady-shear mode (rad/sec)
Shear rate in steady-shear mode (sec-')
Maximum strain in dynamic-shear mode dimensionlesss)
Oscillating frequency in dynamic-shear mode (rad/sec)
Shearing angle or oscillating amplitude in dynamic-shear mode (rad)
Transducer torque (g-cm)
Component of torque in phase with strain (g-cm)
Component of torque 90W out of phase with strain (or in phase with
the strain rate) (g-cm)


17
G'
G"
G*

Tan
Tan 6


(3.3)


(3.4)


(3.5)


where q7
G'
G"
G*
7'
7"
7r*

K
R

H



To(
0
M
(Mo)'
(MO)"















Cone-and-plate fixture


Liii-izz


.#.- 0 -~'


Parallel-plate fixture


R
RI I


0 I
#


Geometry of a cone-and-plate and a parallel-plate viscometer.


Figure 3.3










3.4.2 Quantitative Microscopy

Quantitative microscopy (QM) was used to evaluate the state of particle dispersion

in the polymer matrix at room temperature. QM analysis is usually carried out on a

polished cross-section of the material [DeH68, Und70]. However, in this study, it was

not possible to prepare polished sections because of the extreme difference in hardness

between the alumina particles and the low molecular weight polymers. Consequently,

a new sample preparation technique was developed which allowed for microscopic

assessment of the state of dispersion in ceramic/polymer mixtures. Experimental

procedures are given below, but more detailed information on the development of this

method are described in section 4.1.

Alumina/PE samples were mixed in the usual manner in the high-shear bowl

mixer. At the end of the mixing cycle, samples were immediately transferred onto

aluminum foil. The surfaces of the samples that formed directly on the aluminum foil

had relatively good flatness; however, the surface region consisted mostly of a thin layer

of polymer. In order to expose the alumina particles for QM analysis, plasma etching"

was used to remove much of the polymer from the surface. The plasma reaction

chamber was a glass tube (16 mm x 150 mm) which was pumped down to 50 mTorr.

The residual air inside the glass tube was excited with a radio frequency power supply

to produce an oxygen plasma containing excited atoms, molecules, and ions. These

active species reacted with the polyethylene to produce low molecular weight volatile

products (e.g., CO, CO2, and H20) which were carried out of the reaction chamber by


31 Harrick Plasma Cleaner, Harrick Scientific Corp., Ossining, NY.









63

the vacuum pumping system. Plasma etching was normally performed at power level 5

(controlled by a switch selector) for 30 min. Etched surfaces were observed at 20,000

magnification using a scanning electron microscope (SEM2) with a 25 KeV accelerating

voltage. A grid with 10x10 lines was placed on top of SEM micrographs. A template

with circles of varying diameter was then used to measure the equivalent projection

circumscribing diameter (Dpc) of each alumina particle. Particles were selected only if

a cross point of the grid overlaid on the particle and if its perimeter was clear. For each

mixed batch, five different pieces were etched and two SEM micrographs for each piece

were taken. The total number of particles collected in these ten micrographs was 600.

The rationale for collecting particle size (Dpc) distributions as a measure for assessing

the state of particulate dispersion is discussed in much detail in section 4.1.

3.4.3 Ceramic/Polymer Wetting Behavior

Sessile drop method. Measurement of contact angles by the sessile drop method

was carried out using a contact angle goniometer32 equipped with a controlled

temperature environmental chamber. The contact angles of polyethylene melts (PE A-C

9) on sintered alumina substrates were recorded as a function of time at various

temperatures. The following procedure was used: (1) the alumina substrate was heated

in the environmental chamber to the desired temperature for -5 min, (2) a polymer

pellet was placed on the center of the alumina substrate and allowed to melt completely,

and (3) contact angle values were measured as soon as melting was completed and were

recorded periodically thereafter.


32 NRL Model 100, Rame-Hart, Inc., Mountain Lakes, NJ.








64

Contact angle measurements were also made for polyethylene melts on alumina

powder compacts. In these experiments, a high density, high molecular weight

polyethylene (Sclair 2915) was used (i.e., instead of PE A-C 9) in order to avoid rapid

penetration of polymer melt into the pore channels of the alumina compacts. (Even at

temperatures as low as 125"C, the low viscosity polyethylene (PE A-C 9) penetrates into

the porous compacts within seconds, thereby making it impossible to get reliable contact

angle values.) The alumina powder compacts used in these experiments were prepared

by casting pH = 4 suspensions (on glass plates) according to the procedure described in

section 3.1.2.

Penetration method. Polyethylene melt/alumina powder wetting behavior was

assessed by measuring the penetration rate of the melt through powder compacts. The

experimental steps for this method are described below:

(1) Preparation of polymer disks. Polymer was formed into a disk shape (- 1 mm and

-20 mm diameter) by melting -0.4 g of polymer in a 10 cm3 glass beaker at 150"C in

the environmental chamber attached to the contact angle goniometer. Upon complete

melting, the low viscosity, free-flowing polymer quickly conformed to the cylindrical

shape of the beaker. The beaker was then removed from the environmental chamber and

cooled to room temperature. The solidified polymer disk was then removed from the

beaker.

(2) Preparation of alumina powder compacts. Alumina powder compacts (-25 mm

diameter) were formed by dry pressing according to the procedure described in section

3.1.2.









65
(3) Penetration of polymer melt through powder compacts. An alumina powder compact

was heated in the environmental chamber to the testing temperature and heated at the

temperature for 5 min. A preformed polymer disk was then placed on top of the

compact at the center. It took about 1 min for the edge of the polymer disk to melt and

15 sec more for the center portion to melt. When the polymer disk melted completely,

a stop watch was pressed to start counting the penetration time. After 5 min of

penetration, the alumina compact was quickly taken out of the environmental chamber

(and cooled to room temperature) in order to "freeze" the polymer and prevent further

penetration. Penetration of the polymer melt was repeated (with new compacts) using

different penetration times (10, 16, 25, and 40 min).

(4) Measurement of polymer penetration depth. The unpenetrated part of the alumina

compact (bottom portion) was washed off under running water. Small squares (about 2x2

mm2) were cut from the center of the polymer-penetrated powder compacts. The

penetration distance was determined using a vertical control mechanism on the contact

angle goniometer stage which allowed adjustments in increments as small as 0.02 mm.

A cross-hair built into the ocular was initially placed on the top surface of polymer-

penetrated powder compacts (i.e., at the original powder compact/polymer disk

interface). The distance penetrated was then determined by moving the sample on the

adjustable stage, which was calibrated with a micrometer, until the cross-hair was lined

up with the bottom plane of polymer penetration inside the powder compact.

Measurements were taken from each side of the cut squares (i.e., four per sample) and









66

an average penetration depth was calculated. The average penetration depth was then

recorded as a function of penetration time.

As discussed in detailed in Chapter 2 (section 2.4), contact angles can be

determined by measuring the penetration rate of a liquid through a porous compact. If

the Washburn equation is applicable (see Eq. 3.6 below), a plot of the logarithm of the

penetration distance, 1, vs. the logarithm of the penetration time, t, should give a straight

line with slope = 0.5.


1 )]+ 1 logt (3.6)
log = log [(r cosO) ( ) + *logt (3.6)
2 2.r 2
= K + m log t

where 1 = penetration depth
r = pore radius of the alumina compact
0 = contact angle
y = surface tension of the fluid
71 = viscosity of the fluid
t = penetration time
m = slope of log 1 vs. log t curve
K = intercept of log 1 vs. log t curve


The best fit values for m and K were obtained by linear regression. In general, the data

fit well to a straight line with slopes in the range of 0.49-0.52 (correlation coefficients

> 0.992). Therefore, the slope of the straight line was fixed at 0.5 and the intercept

values, K, were obtained from the least square method. Absolute values of the contact

angle could not be calculated from Eq. 3.6 because of the complex pore geometry of the

powder compacts. Therefore, the relative wetting behavior under different conditions

was assessed by calculating a contact angle ratio, R0, according to the following

equation:











R. (cos 0), (2 ) [ exp[2 (KI -1()] (3.7)
(cos 0)2 7Y '72

where R,. = Contact angle ratio between conditions 1 and 2
(cos 0), = Cosine of contact angle at condition 1
(cos 0)2 = Cosine of contact angle at condition 2
K, = Intercepts obtained by EQ 2.19 at condition 1
K2 = Intercepts obtained by EQ 2.19 at condition 2


According to equation 2.22, R, > 1 means that condition 1 gives a lower

contact angle (i.e., better wetting) than condition 2. In order to apply Eq. 3.7, it was

necessary to determine surface tension and viscosity values for the polymer at the

appropriate temperature for the polymer penetration experiments. Viscosity values of the

polymer melts were measured with the parallel-plate viscometer" in an oscillatory mode

at 100% strain and 10-100 rad/sec frequency. The surface tension values of polymer

melts were measured by a tensiometer" employing the Wilhelmy Plate principle.

3.4.4 Elemental Analysis

Semi-quantitative elemental analyses for Al, 0, and C at the surface of

alumina/polyethylene mixtures were carried out by Electron Spectroscopy for Chemical

Analysis3 (ESCA, also called XPS for X-ray Photoelectron Spectroscopy). This

technique gives compositional information from only a thin surface layer (- 10-30 A) of

the material. Samples were in the form of thin plates (-1 mm thick) which were

prepared by melting the alumina/PE mixtures at 1250C (in the environmental chamber




3 RosanoOCr Surface Tensiometer, Federal Pacific Electric Co., Newark, NJ.

" Model XSAM 800, Kratos Scientific Instruments, Manchester, England.









68
attached to the contact angle goniometer) between two glass slides. The thin plates were

cut into 1 cm x 1 cm squares and then plasma etched for various lengths of time by the

method described in section 3.4.2. Samples were stored in a desiccator before ESCA

analysis.

3.4.5 Characterization via FTIR

Mixtures of alumina/polyethylene were analyzed by diffuse reflectance FTIR at

room temperature using the same operating conditions as described in section 3.2.1 for

the alumina powders. Samples were ground to powders as fine as possible at room

temperature using an A1203 mortar and pestle.

3.4.6 Analysis for Iron Content

Iron content was determined for alumina/PE mixtures using the same method

described in section 3.2.1 for the analysis of the alumina powders. The only differences

were that (1) the mixtures were ground to fine powders before mixing with the boiling

HCI solution and (2) 20 g samples were used.

3.4.7 Microhardness Measurements

The hardnesses of pure polymer and ceramic/polymer mixtures were measured

by a microhardness tester" using loads in the range from 25 to 100 g. Samples were

formed into thin plates (-2 mm thick) by melting and pressing between two glass slides

at 125C in the environmental chamber attached to the contact angle goniometer. Five

hardness readings were taken for each sample and the average hardness value was

reported.


3s Micromet 3, Buehler Ltd., Lake Bluff, IL.














CHAPTER 4
RESULTS AND DISCUSSION


4.1 Effects of Mixing Conditions

In this section, the effects of mixing variables (temperature, time, and rotor

speed) on the ceramic particulate dispersion in polymer melts are reported. The mixing

conditions include single-segment and multi-segment mixing schedules, which were

previously described in Chapter 3 (see Table 3.2). In single-segment mixing (section

4.1.1), mixing temperature and rotor speed were kept constant throughout the entire

mixing process. In multi-segment mixing (section 4.1.2), either temperature or rotor

speed was changed during mixing. Samples of 50 vol% alumina/50 vol% polyethylene

(PE A-C' 9) were used unless noted otherwise.

4.1.1 Single-Segment Mixing Schedules

The effects of three mixing variables -- temperature, time, and rotor speed -- were

studied by changing one variable and keeping the other two constant. The state of

particulate dispersion was evaluated by using steady and dynamic theological

measurements, which were carried out at an elevated temperature (1250C). Quantitative

microscopy (QM) was also used to evaluate the state of dispersion and to establish

correlations between elevated temperature theological measurements and QM

measurements made on samples at room temperature.










4.1.1.1 Effects of mixing temperature on theological and wetting behavior

Alumina was mixed with polyethylene at four different temperatures (125, 150,

175 and 220C) at a constant mixing speed (200 rpm) for 30 min. Figure 4.1 shows

plots of dynamic viscosity, storage modulus, loss modulus, and tangent delta as functions

of oscillation frequency for samples measured at 125C(. The sample mixed at 220C had

the highest viscosity values and the largest decrease in viscosity over the measured

oscillation frequency range (0.1-100 rad/sec). The sample mixed at 175C showed

similar behavior to the 220C sample, although the viscosity values were slightly lower

and the decrease in viscosity with increasing frequency was smaller. The decrease in

dynamic viscosity with increasing oscillation frequency is analogous to shear thinning

flow behavior in steady shear measurement and suggests that the ceramic/polymer

mixture has an extensive particle-particle network structure. (It should be noted that the

polymer alone has Newtonian flow behavior at the measuring temperature, as shown in

Figure 4.2 and, thus, the polymer flow characteristics are not responsible for the

observed decreases in viscosity with increasing frequency.) Samples mixed at 1500C

showed further reductions in viscosity (i.e., compared to the 175 and 220C samples).

Furthermore, a relatively small decrease in viscosity was observed over the measured

frequency range. These results indicated that the particulate dispersion was improved by

lowering the mixing temperature. A further decrease in mixing temperature (to 1250C)

resulted in little change in theological properties, indicating that the state of dispersion

was similar to that obtained by mixing at 150C. It should be noted that the lowest










71
10000

C 50 vol% A1203
220oC



> 1000
S: ,175'C

(A)

1509C



1250C



10
1 0 I I I I I II I I I I I III I I I I I

0.1 1 10 100

FREQUENCY (rad/s)


1000

S220C




,.J
100
175*C


-u 150oc

M 10-
0


1 C 50 vol% AI203
125oC

1 t e n ar l I f I l 1 I I I I fi ll
0.1 1 10 100

FREQUENCY (rad/s)




Figure 4.1 Plots of (A) dynamic viscosity, (B) storage modulus, (C) loss modulus,
and (D) tangent delta vs. frequency for 50 vol% alumina/50 vol%
polyethylene samples prepared at the mixing temperatures indicated.




































1 10 100


FREQUENCY (rad/s)


50 voIX Al203


1 10 100
FREQUENCY (rod/s)


Figure 4.1 (Continued)


10000


10L
0.1


a 125 C
0 150 C
0
S175 C
0 220C














1.2


1.0


0.8


0.6


0.4


0.2'


0.0


POLYETHYLENE
o 125C
v 150C
175eC
220C






I-0--0-0--0-0--0---0


S1& a 1 A -- --- --

0I I 100
0 100


FREQUENCY (rad/s)


Plots of dynamic viscosity vs. frequency for polyethylene at the
temperatures indicated.


mixing temperature used in this study was very close to the drop temperature' of the

polymer (117C).

The storage and loss modulus values increased as the mixing temperature

increased (Figure 4.1B). The moduli also became less frequency dependent as the



1 Drop point is defined as the temperature at which the sample, suspended in a
cylindrical cup with a 6.35 mm hole in the bottom, flows downward a distance of 19 mm
to interrupt a light beam, as the sample is heated at a linear rate in air [AST77].


Figure 4.2









74
mixing temperature increased. Similar changes in theological behavior have been

observed in previous investigations in which the particle solids loadings were increased

in powder/polymer mixtures [Big82, Big83, Big84b, Ron88, Sain86, Sher68]. In

general, samples with higher powder solids loading experience greater resistance to flow

because of the more extensive particle-particle interactions and the presence of particulate

network structures. Hence, higher viscosity and modulus values are observed. In the

case of poorly dispersed samples, the void space within agglomerates is filled with

polymer, thereby reducing the amount of polymer available for flow during shear motion.

Thus, samples have a higher effective solids loading and viscosity and modulus values

are more similar to those measured for well-dispersed samples with higher true solids

loading. Therefore, the poor dispersion caused by using higher mixing temperatures (175

and 220'C) can be viewed as having a similar effect as increasing the true solids loading

in well-dispersed mixtures. This is demonstrated in Figure 4.3, which shows the

dynamic viscosities, moduli, and tangent delta for alumina/polyethylene samples with

different true solids loading (38, 50, 59 vol%). The viscosity and modulus values

increased with increasing solids loading. The frequency dependence of both moduli also

decreased with increasing solids loading.

Other theological measurements were consistent with those shown in Figures 4.1

and 4.3. The steady shear stress vs. shear rate flow behavior is shown in Figure 4.4 for

samples prepared with different mixing temperatures (125-2200C). The flow curves for

the 125 and 150C samples show low yield stress and very little hysteresis, thereby

suggesting good dispersion of the alumina particles in the polymer matrix. In contrast,









10000


1 10 100


FREQUENCY (rad/s)


Plots of (A) dynamic viscosity, (B) storage modulus, (C) loss modulus,
and (D) tangent delta vs. frequency for alumina/polyethylene samples at
the solids loading indicated.


59 vol% A1203







50 vol% A1203







38 vol% Al2 03


I I1 l l til I i i 11 l I 1 1 1i 1111
.1 1 10 100

FREQUENCY (rad/s)


1000




100




10


10000


1000



100



10


0.1 -
0.1


Figure 4.3


































.1


10

FREQUENCY (rad/i)


FREQUENCY (rod/s)


Figure 4.3 (Continued)


10000



1000



100



10


1



0.1
0,


59vol%Al03





50 vo% A1203







38 vol% AI2O


i i m. 1 1 !! 1 1 i u I I 1 11111


(C)


0 38 vol% AI203
O 50 vol% AI203
A 59 vol% Al203


I I I I i .. .









2000

50 vol% AI203
1600
0
a.
a 1200


800 150C


400
125C

0 r I *I *- *- -* I


2000
50 vol% A1203

1600
0 220eC
a-
U) 1200
i

800


400 175'C


0 I* I I _1 I I I .
0 5 10 15 20 25 30 35 40 45 50
SHEAR RATE (1/s)
Figure 4.4 Plots of shear stress vs. shear rate for 50 vol% alumina/50 vol%
polyethylene samples prepared at the mixing temperatures indicated.








78

high yield stresses and extensive thixotropy were observed for the 175 and 220C

samples. These characteristics are typical for samples having a three-dimensional particle

network structure. The highly shear-thinning behavior in the 220C sample reflects a

breakdown of the network structure. (As noted earlier, the pure polymer had a

Newtonian flow curve over the frequency range for which measurements could be made,

i.e., 10 to 100 rad/sec. The non-Newtonian behavior of the mixed alumina/polyethylene

samples must have resulted from changes in particle structure under shear.) The concept

of a poorly-dispersed sample as having a higher effective solids loading was again

supported by the flow curves for alumina/polyethylene mixtures with different tue solids

loading (Figure 4.5). The 38 vol% sample had almost Newtonian flow behavior,

whereas the 59 vol% sample showed a very high yield stress and a high degree of

thixotropy.

Stress relaxation measurements were also consistent with the other theological

data. Figure 4.6 shows residual stress as a function of time for samples prepared using

different mixing temperatures ranging from 125-220C. Short relaxation times were

observed for the 125 and 150C samples because the particles were relatively well

dispersed in polymer melts. In contrast, stress relaxation for the other two samples (175

and 220C) took place much more slowly, which was consistent with the occurrence of

a solid-like particle network structure in these samples. Figure 4.7 shows the stress

relaxation curves for samples with different solids loading. As expected, stress

relaxation occurred more slowly as solids loading increased. Again, this supports the

view that poorly-dispersed samples have a higher effective solids loading.
















































SHEAR RATE (s1)


Plots of shear stress vs. shear rate for alumina/polyethylene samples at the
solids loading indicated.


2000



1600


1200



800


400



0










Figure 4.5
























10000








1000




in
w
cI-

100








10
0.0








Figure 4.6


1 0.1 1.
TIME (s)


Plots of residual stress vs. time for 50 vol% alumina/50 vol%
polyethylene samples prepared at the temperatures indicated.









81



10000






S : / ^ 59 vol% AI203



1000

_E 50 vol% AI203

38 vol% AI2 03

10 I I I I I 1 1 I I

0.01 0.1 1
TIME (s)


Figure 4.7 Plots of residual stress vs. time for alumina/polyethylene at the solids
loading indicated.



The effects of mixing temperature on the state of dispersion and theological

behavior were also observed for alumina/polyethylene samples prepared with different

solids loading. Figures 4.8 and 4.9 show dynamic viscosity, storage and loss moduli,

and tangent delta vs. frequency plots for samples of 59 vol% alumina/41 vol%

polyethylene and 38 vol% alumina/62 vol% polyethylene, respectively. As expected,

viscosity and modulus values were considerably lower for the samples mixed at 1500C

than for those at 220C. In addition, steady shear flow curves for the 38 vol% alumina






























1 10 100
FREQUENCY (rad/s)


100


FREQUENCY (rad/s)
Plots of (A) dynamic viscosity, (B) storage modulus, (C) loss modulus,
and (D) tangent delta vs. frequency for 59 vol% alumina/41 vol%
polyethylene samples prepared at 150 and 220"C.


100000




a 10000




100
0
g 1000




E 100


10 L
0.1


100000





10000


0


1000
0
U-
U)


59 vol% Al20
v 220 C
O 150C














S .. I ....I I


100 L
0.


1


Figure 4.8










100000


10000





1000


100
0.

100 r


1
O.


100


1 10
FREQUENCY (rad/s)


1 10 100
FREQUENCY (rad/s)


Figure 4.8 (Continued)


59 vol% Al,03

v 220C
0 150C












I I .I I ,, .Ii1
-S




























1 10 100
FREQUENCY (rad/s)


1 10 100
FREQUENCY (rad/s)


Plots of (A) dynamic viscosity, (B) storage modulus, (C) loss modulus,
and (D) tangent delta vs. frequency for 38 vol% alumina/62 vol%
polyethylene samples prepared at 150 and 220C.


1000


100





10


1 -
0.1


1000


100



10



1


0.1 I-
0.1


Figure 4.9





























1 10 100
FREQUENCY (rad/s)


1 10 100
FREQUENCY (rad/s)


Figure 4.9 (Continued)


1000


100





10


1 -
0.1

100








10








1
0.1








86
samples (Figure 4.10) showed exactly the same trend as that observed in 50 vol%

alumina samples (see Figures 4.4), indicating that better dispersion was achieved by

using a lower mixing temperature. However, there was very little difference in the

relaxation curves (Figure 4.11) for these two samples. This probably reflects the low

true solids loading of the samples, such that even the poorly dispersed 220C sample does

not have sufficient particle network structure to significantly increase the stress relaxation

time.





1200
38 vol% AI203



a, 800
(n 220OC



1 400


150C


0 5 10 15 20 25 30 35 40 45 50
SHEAR RATE (1/s)

Figure 4.10 Plots of shear stress vs. shear rate for 38 vol% alumina/62 vol%
polyethylene samples prepared at 150 and 2200C.











10000
38 vol% A1203




1000



bJ

100 220C


150AC


10
0.01 0.1 1
TIME (s)

Figure 4.11 Plots of residual stress vs. time for 38 vol% alumina/62 vol%
polyethylene samples prepared at 150 and 220(C.


Torque rheometry was helpful in understanding the reason for the effect of mixing

temperature on the dispersion of alumina in polyethylene. Figure 4.12 shows the mixing

torque curves (i.e., measured torque during mixing as a function of time) for samples

processed at temperatures in the range of 125-220C. The peak torque value during

mixing represents the force developed during the process of incorporation of the alumina

particles into the polyethylene melts; the final "equilibrium" torque value tends to be
















































50 vol% AI203
Mixing Conditions: 1750C, 200 rpm


I I I i I I I I


zUU
50 vol% Al203
100- Mixing Conditions: 220C, 200 rpm
o- ----r-^^n__________


5


1 I
10


15


I I
20


25


30


TIME (min)


Figure 4.12


Plots of torque vs. mixing time for 50 vol% alumina/50 vol%
polyethylene samples prepared at the temperatures indicated.


E 500

w
LU
) 400-

0
1- 300


S300-

200-
CC.
-- 100-

0-

E 200-

D 100-
0
1- 0-










89

representative of the mixture's viscosity (and state of dispersion) after the powder has

been incorporated into the polymer melt. Both values are highly dependent on the

viscosity of the polymer matrix, which, in turn, is highly dependent upon the mixing

temperature. As expected, the polymer viscosity decreased with increasing temperature

(Figure 4.13). Thus, the peak torque developed during mixing decreased as the

temperature increased, i.e., as the polyethylene viscosity decreased. At higher

temperatures (175 and 220"C), the polymer viscosity was too low to support and transfer

the force necessary for breakdown of the agglomerates in the starting powder. In

contrast, a high mixing torque was developed at lower mixing temperatures (125 and




1.0

0.8 POLYETHYLENE

S 0.6-

>-
0.4 -
U)
0










1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6
1 0.2




0 .1 I I i i I i I i I i I
1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6


103 (OK-)



Figure 4.13 Plot of dynamic viscosity of polyethylene (A-C 9) vs. temperature.








90

150C) and consequently powder dispersion was greatly improved. These observations

were consistent with results reported for dispersion of carbon blacks in rubber [Frea85,

HesS84, LeeM84]. In rubber compounding, the high shear force needed to obtain good

dispersion state is usually achieved either by lowering the mixing temperature or by using

higher viscosity polymers (e.g., high molecular weight). A high shear stress is also

required when incorporating other solid particles (e.g., pigment) into polymer matrices

[Gar85, Moh59].

Figure 4.12 shows that the peak torque generated during mixing at 1250C was

considerably higher than that at 150C, yet there was not much difference in theological

data (see Figures 4.1, 4.4, and 4.6). This may indicate that near-optimum dispersion has

been achieved in both samples. It is also possible, however, that the benefit derived

from the increased mixing torque at 1250C may have been partially offset by poorer

wetting of the particles caused by the polymer melt at this mixing temperature. This is

suggested from measurements of penetration rates of the polyethylene melt into alumina

powder compacts heated to various temperatures. Figure 4.14 shows the penetration

depth as a function of time at different temperatures and Figure 4.15 shows the calculated

values of relative contact angle, 0, as a function of temperature. The R0 is defined

as the cos0 value at the testing temperature divided by the cos0 value at the reference

temperature (i.e., 220C). (The measured values of the polyethylene surface tension and

viscosity are given in Table 4.1, as are the penetration rates for the different

temperatures.) It is evident from Figure 4.15 that wetting of the alumina powder by the

polyethylene melt became poorer (i.e., the contact angle increased) as the temperature














































1000

TIME (SEC)


Figure 4.14


Plots of penetration depth vs. time for polyethylene melts into alumina
powder compacts at the temperatures indicated.


1000


100


10
10


A 220C
o 175C
v 150C
o 125C














* .


0


10000


--


- --


. I






























125 150 175 200 225


TEMPERATURE (C)


Figure 4.15


Plot of the contact angle ratio for polyethylene melt on alumina powder
vs. temperature. (Measured by polymer penetration method).


Table 4.1 Results for polyethylene
different temperatures.


penetration into alumina powder compacts at


1.00


0.95-


0.90-


0.85


0.80
100


Polyethylene/A2 03





0I


250


Mixing temperature (C) 125 150 175 220
Polymer viscosity (Pa-s) 0.65 0.43 0.26 0.13
Surface tension (erg/cm2) 28.8 27.5 25.8 23.9
Penetration depth x 100 (mm)
at 5 min 25.6 29.5 38.7 54.9
at 10 min 33.8 40.9 51.4 69.8
at 16 min 43.5 52.6 65.4 90.7
at 25 min 54.9 63.4 79.5 110.3
at 40 min 65.1 84.9 98.3 153.6









93

decreased. The wetting between alumina and polyethylene melt was also evaluated by

the sessile drop method. In this experiment, the contact angle values of polyethylene

melts on sintered alumina substrates were recorded as a function of time and temperature

(Figure 4.16). The contact angle decreased as the temperature increased, i.e., better

wetting behavior at higher temperatures. This result was consistent with data obtained

from the polymer penetration method. These results indicate that the mixing temperature

must be optimized in order to achieve maximum dispersion. The mixing temperature


0 10 20 30 40 50

TIME (min)


60 70 80 90


Figure 4.16 Plots of the contact angle for polyethylene melts on sintered alumina
substrates vs. time at the temperatures indicated.









94

should be low enough to develop large shear forces that can break down agglomerates,

but high enough so that wetting of the powder by the polymer melt is not adversely

affected. The theological data suggests that mixing in the range of 125-150C is suitable

for achieving good dispersion in alumina/polyethylene mixtures.

4.1.1.2 Quantitative microscopy

Development of quantitative microscopy technique for assessing dispersion

Quantitative measurements of microstructural features are usually carried out on

polished cross-sections of the materials [DeH68, Und70]. In the present investigation,

it was not possible to prepare polished sections due to the extreme difference in hardness

between the alumina particles (very hard) and the low molecular weight polyethylene

(very soft). Several different polishing methods (i.e., manual and automated2) and

polishing materials3 were evaluated for their ability to produce flat surfaces. None of

the polishing conditions was particularly successful. An example of one of best

"polished" surface is shown in Figure 4.17. Although this samples contains -50 vol%

alumina, relatively few particles are observed on the surface, presumably due to smearing

(flow) of the soft polymer over the surface.

Effort were also made to prepare thin sections of the alumina/polyethylene

composite using microtomy4. (As noted in Chapter 2.1, this technique has been used



2 Ecomet'lI, Minimet, and Vibromet' I, Buehler Ltd., Lake Bluff, II.

3 The polishing materials used included SiC paper, SiC powder/water slurries on
glass plates, and alumina powder/water slurries on microcloth.

4 Rotary Microtome, Reichert-Jung, Buffalo, NY, and Porter-Blum Microtome, Ivan
Sorvall, Inc., Norwalk, CT.




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PAGE 351

81,9(56,7< 2) )/25,'$


DISPERSION OF CERAMIC PARTICLES IN POLYMER MELTS
By
JOAN-HUEY DOW
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
1992
UNIVERSITY OF FLORIDA LIBRARIES

ACKNOWLEDGEMENTS
I am grateful to Dr. M. D. Sacks for his guidance and support on the research
work. Support from the Department of Energy, Office of Basic Energy Sciences,
Division of Materials Sciences (DE-FG05-85ER45202) is gratefully acknowledged.
The advice from Dr. P. H. Holloway is appreciated. Thanks should also go to
Drs. C. D. Batich, E. D. Whitney, and G. B. Westermann-Clark for their suggestions
on this dissertation.
I would like to thank Dr. A. V. Shenoy, G. W. Scheiffele, C. Khadilkar, T.-
S. Yeh, H. W. Lee, S. Vora, R. Raghunathan, M. Saleem, A. Bagwell, and Dr. A.
Fradkin for their assistance in carrying out various experiments and editing this
dissertation.
This dissertation is dedicated to my parents for their love, understanding, and
encouragement.
11

TABLE OF CONTENTS
Page
ACKNOWLEDGEMENTS ii
ABSTRACT v
CHAPTERS
1 INTRODUCTION 1
2 BACKGROUND 5
2.1 Evaluation of the State of Particulate Dispersion by
Non-rheological Techniques 6
2.2 Rheology of Fluids and Particle/Fluid Mixtures 11
2.2.1 Overview 11
2.2.2 Polymer Melts 16
2.2.3 Particle/Fluid Mixtures 17
2.3 Particle/Fluid Mixing 22
2.4 Particle/Fluid Wetting 25
2.5 Characteristics of Alumina Surfaces with Adsorbed Water and
Hydroxyl Groups 30
2.6 Effects of Moisture on Ceramic/Polymer Composites 32
2.7 Chemical Additives 34
2.7.1 Structures 35
2.7.2 Effects of Chemical Additives on Rheological Properties . . 40
3 EXPERIMENTAL 42
3.1 Materials and Materials Preparation 42
3.1.1 Starting Materials 42
3.1.2 Treatment of Alumina Powder 46
3.2 Characterization of Ceramic Powders, Powder Compacts,
and Polymers 49
3.2.1 Alumina Powder Characterization 49
3.2.2 Alumina Powder Compact Characterization 53
iii

3.2.3Polymer Characterization 54
3.3 Mixing of Ceramic Powders and Polymers 54
3.4 Characterization of Ceramic Powder/Polymer Mixtures 57
3.4.1 Rheology 57
3.4.2 Quantitative Microscopy 62
3.4.3 Ceramic/Polymer Wetting Behavior 63
3.4.4 Elemental Analysis 67
3.4.5 Characterization via FTIR 68
3.4.6 Analysis for Iron Content 68
3.4.7 Microhardness Measurements 68
4 RESULTS AND DISCUSSION 69
4.1 Effects of Mixing Conditions 69
4.1.1 Single-Segment Mixing Schedules 69
4.1.1.1 Effects of mixing temperature on rheological and
wetting behavior 70
4.1.1.2 Quantitative microscopy 94
4.1.1.3 Effects of rotor speed 134
4.1.1.4 Effects of mixing time 136
4.1.2 Multi-Segment Mixing Schedules 136
4.1.2.1 Mixing with change in temperature 146
4.1.2.2 Mixing with change in rotor speed 154
4.2 Effects of Ceramic Powder Characteristics 159
4.2.1 Calcination Effect 160
4.2.2 Aging Phenomenon 210
4.3 Effects of Polymer Characteristics 227
4.3 Effects of Chemical Additives 248
4.4.1 Coupling Agents 248
4.4.2 Surfactants 275
4.4.3 Lubricants 288
5 SUMMARY 322
REFERENCES 329
BIOGRAPHICAL SKETCH 342
IV

Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
DISPERSION OF CERAMIC PARTICLES IN POLYMER MELTS
By
Joan-Huey Dow
May, 1992
Chairperson: Dr. Michael D. Sacks
Major Department: Materials Science and Engineering
The effects of mixing conditions, powder and polymer characteristics, and
chemical additives on dispersion of ceramic particles in polymer melts were investigated.
Fine-sized alumina powder and low-molecular-weight polyethylene (PE) were used in
most experiments. Samples were prepared using a high-shear bowl mixer and the mixing
operation was monitored by torque rheometry. The state of dispersion was evaluated
using rheological and quantitative microscopic measurements. Ceramic/polymer melt
wetting behavior was evaluated by the sessile drop and polymer penetration methods.
Further understanding of mixing and dispersion behavior was developed by using particle
size and surface area measurements, infrared spectroscopy, mercury porosimetry,
microhardness measurements, gravimetric analysis, etc.
Samples mixed at lower temperatures and higher rotor speeds had better
particulate dispersion (i.e., due to increased agglomerate breakdown rates and decreased
v

coagulation rates). Mixed batches prepared with heat-treated powders (100-1000°C)
showed relatively poor particulate dispersion. This was due to changes in the
physicochemical characteristics of the heat-treated powders (i.e., due to removal of water
and hydroxyl groups on powder surfaces at low temperatures and interparticle neck
growth at higher temperatures). Samples prepared with heat-treated powders were also
highly susceptible to aging effects due to absorption of moisture from the ambient air
atmosphere. Mixed batches prepared with polyethylene or ethylene-acrylic acid
copolymer showed relatively good dispersion compared to batches prepared with
ethylene-vinyl acetate copolymer. Further investigation is needed to understand the
reason for this behavior. Particulate dispersion in mixed batches was also highly
dependent upon the presence of chemical additives (i.e., coupling agents, a surfactant,
and a lubricant). In some cases, it was possible to establish correlations between the
state of dispersion in the suspensions used to coat powders with additives, the peak
torques generated during powder/polymer mixing, and the state of dispersion in the
mixed batches.
vi

CHAPTER 1
INTRODUCTION
The state of particulate dispersion and the rheological properties of ceramic
powder/polymer melt mixtures are important for ceramic shape forming processes such
as injection molding [Edi86, Ino89, Man82, Man83, Schw49, Tay62]. The first major
step in the process is to mix ceramic powder with polymer melt at an elevated
temperature to form a plastic mass. The ceramic/polymer mixture should have suitable
fluidity in order to fill the die completely and uniformly without leaving any defects in
the shaped parts. Usually, chemical additives are used to improve the processibility of
the mixtures. After the shape forming step, the parts are heated to remove polymer and
then sintered to form the final products.
The state of dispersion of the ceramic powder in the polymer melt, i.e., the
distribution and packing of ceramic particles in the polymer, determines the fluidity of
the ceramic/polymer mixture and thus controls the flow pattern of the mixture in the die
during injection molding. It also has a strong effect on the maximum solids loading (i.e.,
volume fraction of ceramic powder in the mixture) that can be achieved. In general, a
high solids loading is desired in order to minimize the polymer amount to be removed
and to reduce the amount of shrinkage during sintering. During the polymer burnout
step, transport of polymer molecules is influenced by the pore size and size distribution
formed by the packing arrangement of the ceramic particles and, thus, the polymer
1

2
removal process is indirectly dependent on the dispersion state. Furthermore, the
densification rate and the grain growth rate during sintering are strongly affected by the
particle packing arrangement in the ceramic powder compact. Therefore, it is important
to examine the dispersion of ceramic powders in polymer melts since it strongly
influences each step in the processing sequence and ultimately affects the microstructure
and properties of the final product.
Information about dispersion and rheology is also crucial in processing of polymer
composites in which inorganic particles or fibers are incorporated into polymers, either
to reduce the cost or to tailor the composite properties [Han74, HesW82, Utr82]. For
example, the existence of porous particle agglomerates in a polymer matrix (i.e., poor
dispersion) can significantly reduce the mechanical strength of the composites. In
addition to affecting physical properties, the energy consumption during processing of
the composites is much less for a well-dispersed mixture since the viscosity is lower.
The state of dispersion in ceramic/polymer mixtures is dependent on the mixing
conditions and the properties of the starting materials (i.e., ceramic powders, polymers,
and chemical additives). The present study addresses the following four areas:
Mixing conditions. The effect of mixing variables, including time, temperature,
and rotor speed, on the dispersion of alumina in polyethylene was investigated. The
study was confined to a simple two-phase ceramic/polymer mixture without any chemical
additives. Rheological flow measurements, torque rheometry, ceramic/polymer melt
wetting behavior, and quantitative microscopic analysis were used to evaluate the effect
of mixing variables on the state of dispersion.

3
Ceramic powder characteristics. Ceramic/polymer injection molding is affected
by ceramic powder properties, such as particle size, size distribution, particle shape, etc.
To some extent, these variables have been studied [Big84b, Wil78]. However, the effect
of ceramic surface hydroxylation and adsorbed molecular water on particle dispersion has
not been investigated. In this part of the study, alumina powders were calcined at
temperatures in the range of 100-1000°C prior to mixing with polyethylene (i.e., in order
to remove surface hydroxyl groups and adsorbed water). The effects of calcination on
dispersion and aging behavior were evaluated using rheological flow measurements,
torque rheometry, infrared spectroscopy, hardness tests, particle size and specific surface
area measurements, ceramic/polymer melt wetting behavior, and qualitative and
quantitative microscopic analysis.
Polymer characteristics. The ceramic/polymer rheological behavior can be altered
significantly by varying polymer properties. In this part of the study, experiments were
carried out using polymers with different functional groups: polyethylene (PE), ethylene-
acrylic acid (EAA), and ethylene-vinyl acetate (EVA). The influence of polymer
chemistry on the ceramic/polymer mixture properties were investigated by rheological
flow measurements of polymer melts and ceramic/polymer mixtures, ceramic/polymer
melt wetting behavior, quantitative microscopic analysis, and torque rheometry.
Chemical additives. Chemical additives can be used to modify the
ceramic/polymer interface and thereby alter the state of dispersion and composite
properties [Big83, Zha88]. In this part of the study, several coupling agents, surfactants,
and fatty acids were used to modify the alumina dispersion in polyethylene. The role of

4
these chemical additives was investigated using torque rheometry, rheological flow
measurements, ceramic/polymer melt wetting behavior, and quantitative microscopic
analysis.

CHAPTER 2
BACKGROUND
The dispersion of particles in polymer melts is important in ceramic injection
molding and the processing of ceramic/polymer composites. There have been many
methods developed to evaluate the state of particulate dispersion. Non-rheological
techniques (e.g., qualitative and quantitative microscopy) are discussed in section 2.1,
while rheological measurements are discussed in section 2.2. The latter section includes
a brief description of basic concepts of rheology, followed by descriptions of the
rheological properties of polymer melts and particle/fluid mixtures.
Ceramic powder/polymer melt wetting and mixing behavior are crucial in
determining the state of particulate dispersion. The mixing process and the effects of
mixing variables on the state of dispersion are reviewed in section 2.3. Section 2.4
discusses methods used to evaluate the wetting behavior of polymer melts on ceramic
substrates and powders.
The state of particulate dispersion in polymer melts is also affected by other
factors, including particle properties, polymer characteristics, atmospheric moisture,
addition of chemical additives, etc. Since alumina powder was used for most of the work
in this study, the surface characteristics of alumina (i.e., especially when adsorbed water
and hydroxyl groups are present) are discussed in section 2.5. The effect of atmospheric
moisture on properties of polymer composites is reviewed in section 2.6 Finally, the
5

6
structures of chemical additives and their effects on rheological properties are discussed
in section 2.7.
2.1 Evaluation of the State of Particulate Dispersion by Non-rheological Techniques
It has been well established that the breakdown of agglomerates and uniform
dispersion of particles in the matrix phase can significantly improve mechanical
properties of composites. Many studies of dispersion in powder/polymer mixtures have
been carried out for carbon black/rubber composites. Carbon black dispersion greatly
affects the mechanical properties of such mixtures [Boo63a, HesW82, Med78]. For
example, strength is adversely affected in composites with poor dispersion, as porous
agglomerates cannot support the load and act as structural flaws. Carbon black is also
added to polyethylene as an ultraviolet absorber for outdoor applications [Bes59, Wal50].
The protection efficiency and the useful lifetime depend on the state of dispersion of the
carbon black.
Early studies of dispersion of powders in polymer matrices were restricted to
qualitative analysis. Researchers used visual methods (either by the naked eye or by
optical microscope) to compare the size of agglomerates on cross-sections of
particle/polymer mixtures. Later analyses evolved to a semi-quantitative or quantitative
level due to the development of more sophisticated technologies, such as the electron
microscope, high-speed computers, and image analyzers.
A simple method to evaluate particle dispersion involves inspection of the sample
surface directly by light microscopy or electron microscopy [Boo63a, Chap57, For63,
Hes62, HesB63, HesF63, Veg78]. Samples with poor dispersion clearly show large

7
agglomerates, whereas well-dispersed samples have smaller primary particles distributed
homogeneously throughout the entire matrix. The specimens are prepared either by
tearing or by cutting to expose the inner structure. Using optical microscopy to examine
tom surfaces has the advantages of easy and quick operation with minimal equipment
cost. However, only large agglomerates can be identified due to the limitations imposed
by low magnification and roughness of the sample surface. In fact, this is still a valuable
evaluation method in the rubber industry because the most damaging agglomerates are
those in the range of 10 /¿m or greater. To compare samples with smaller-sized
agglomerates, a tedious process of microtomy becomes necessary to prepare thin sections
[AST82, Chap57, Hes62, HesB63, Lei56]. Samples are first frozen in dry ice or liquid
nitrogen to increase hardness and then the frozen samples are cut by a glass or steel
knife. For optical microscopy, sections with 2 /xm thickness allow suitable light
transmission. Sample thickness should be less than 0.1 ^m for good electron
transmission.
A visual inspection method has been adopted as an ASTM standard for qualitative
rating of particle dispersion of carbon black or other fillers in rubber [AST82]. The
samples are cut or tom by a sharp knife or a razor blade to reveal fresh surfaces which
are then inspected by a hand lens or a binocular microscope. The observed particle
dispersion is compared with a series of five photographic standards which are assigned
numbers from 1 to 5. A rating of 5 indicates that the best possible dispersion is
achieved, whereas a rating of 1 indicates the poorest dispersion (Table 2.1). This
method is applicable only for samples containing larger-sized particles. Bell Laboratories

Table 2.1 The relation between visual dispersion rating (by visual inspection
method) with the particle dispersion quality [AST82].
8
Visual Dispersion Rating
Classification
4 to 5
High
3 to 4
Intermediate
2 to 3
Low
1 to 2
Very low
has developed a similar type of microscopic standard with three photographs designated
alphabetically from A (satisfactory dispersion) to C (poor dispersion). This standard also
has been used very often to rate carbon black dispersion [Wal50].
In addition to the qualitative rating methods described above, carbon black
dispersion has been quantitatively evaluated using a numerical scale that is related to a
measured percentage of well-dispersed particles. Experimentally, this is done by
counting the number of agglomerates larger than a certain arbitrarily defined threshold
size [AST82, HesB3a, Kad74, Lei56]. The samples are first microtomed into thin
sections (2 to 3 /xm thick) in order to allow light transmission for observation of the
agglomerates. A ruled grid is attached in one of the microscope eyepieces and the
number of squares covered by agglomerates that are larger than half a square is counted.
For example, in a grid with 10 x 10 /xm squares, the number of agglomerates larger than
50 /xm2 is counted. From the agglomerate count and the volume fraction of carbon
black, the degree of dispersion is calculated and expressed as "percent dispersion" or
"dispersion coefficient." The meaning of the dispersion rating is listed in Table 2.2.

9
Table 2.2 The relation between dispersion percentage (by agglomerate count
method) with the particle dispersion quality [AST82].
Dispersion %
Classification
Above 99
Very high
97 to 99
High
95 to 97
Intermediate
92 to 95
Low
below 92
Very low
The methods described above utilize either microscopy or the naked eye to
examine the size and the distribution of particles in the polymer matrix. There are other
methods that measure properties of the composite which are sensitive to the state of
particle dispersion. For example, sample density and surface roughness are recorded at
different sample locations and the fluctuations of the properties reflect the homogeneity
of the particle distribution. The advantage of these methods is that they are less time-
consuming and are easy to operate; therefore, they are commonly used in industry.
The microdensitometer has been used as an instrument to evaluate particle
dispersion [Bes59, Eic61]. The principle of the microdensitometer is that the optical
absorbance of two-phase mixtures is dependent on the quantity and size of the dispersed
phase, i.e., the light transmitted through a sample reflects the particle distribution in the
polymer matrix. In one common method, test samples are prepared in the form of 1 mil
thick films. A light with a 10 ¿tm diameter passes through the film and the intensity of
the light is recorded as a function of position on a strip chart. Well-dispersed samples
have light intensity profiles varying within a comparatively small range, whereas poorly

10
dispersed samples have significant variations in the light intensity profile (Figure 2.1).
Densitometers have been improved over the years [Eic61] so that the transmitted light
intensities at different locations are converted to light intensity "distribution" functions
automatically. Furthermore, a dimensionless number (i.e., a uniformity index) is
calculated statistically from the light intensity distribution function. This index
quantitatively describes the particle dispersion and has been shown to be consistent with
dispersion ratings obtained by using light microscopy [Wal50].
LENGTH OF SCAN
Figure 2.1 Light intensity curves for two carbon black/polyethylene mixtures with
different states of particulate dispersion [Bes59].

11
As noted earlier, surface roughness is another useful property to reveal the
differences in particle dispersion among samples [HesC80, HesS84, HesW82, Veg78].
Test samples are often similar in size to standard stress-strain slabs (i.e., ~2.5 x 1.5
cm). The surface for roughness testing is freshly created using a razor blade. A stylus-
type tester is then moved along the cut surface and the resulting surface profile is
recorded on a strip chart or by a computer. Poorly dispersed samples show significant
fluctuations in the roughness profiles, whereas well-dispersed samples produce minor
fluctuations. The "dispersion index" is then calculated based on the frequency and the
average height of the peaks on the roughness traces. The results are usually consistent
with measurements made by microscopy methods [HesS84, HesW82]. Even though this
method is simple and quick, it is necessary to cut samples carefully without creating any
inherent difference in roughness. If there are pores or bubbles on the cut surface, the
test results may yield misleading information.
2.2 Rheology of Fluids and Particle/Fluid Mixtures
2.2.1 Overview
Rheology is the science dealing with the deformation and flow of materials.
Rheological measurements are experimentally conducted either by applying a known
magnitude of deformation while monitoring the stress value that develops, or by applying
a certain level of stress while measuring the deformation that occurs. The tests can be
either shear, tensile, or compressive. Shear tests are commonly used in studying fine
particle suspensions or ceramic particle/polymer melt mixtures. Commercially available
equipment for fluid rheological measurements includes cone-and-plate, parallel plate,

12
concentric-cylinder, and capillary viscometers [Dea82, Eir60], These viscometers differ
in the geometries of the sensor systems, measurable viscosity levels, and operating shear-
rate ranges.
Rheological measurements are often made using a steady-shear mode. For
example, measurements are made by rotating one part of the sensor system (e.g., plate,
cone, or cylinder) at controlled shear rate, while the torque generated is measured by a
transducer attached to another part of the sensor system. The shear stress is then
calculated from the measured torque value and the geometrical configuration of the
sensor system. The sample viscosity is calculated from the shear stress (a) and the shear
rate (7) values. The viscosity is defined as apparent viscosity (77 J or true viscosity (17
V, =
do
dy
(2.2)
The apparent viscosity 77, is more commonly used when reporting rheological data.
Several typical rheological flow curves (i.e., shear stress vs. shear rate behavior) and
viscosity vs. shear rate curves are shown in Figure 2.2. The different flow curves may
reflect differences in fluid characteristics (e.g., molecular structure), particle
characteristics (e.g., size, shape, concentration, etc.), fluid/particle interfacial
characteristics, and/or particle-particle interactions [Chaf77, Dea82, Eir60, Far68,
Goo75, Lew68, Sac86]. Flow behaviors in which viscosities decrease with increasing

Viscosity (rj) Shear stress (a)
13
Figure 2.2 Plots of (A) shear stress vs. shear rate and (B) viscosity vs. shear rate
for different types of materials.

14
shear rate (i.e., pseudoplastic and Bingham plastic flow) are also referred to as "shear
thinning." This behavior will be discussed in more detail later since it is very common
in highly concentrated particle/fluid mixtures, such as investigated in this study.
It is not adequate to use steady-shear measurements alone to describe the
rheological properties of ceramic/polymer mixtures because they are viscoelastic in
nature. When deformed, viscous materials dissipate energy while elastic materials store
energy. As a result, dynamic-shear measurements are used extensively to characterize
ceramic/polymer mixtures because information on both the viscous and elastic properties
can be obtained simultaneously. Dynamic measurements are performed by applying a
sinusoidal deformation (i.e., strain 7) with controlled amplitude (i.e., maximum strain
70) and frequency (go). Due to the viscoelastic properties of the sample, the responding
stress also has a sinusoidal form but with a phase difference represented by an angle 5.
Figure 2.3 provides graphical and mathematical descriptions of the strain, strain rate, and
stress functions and also illustrates the relationship of these functions to the storage
modulus, loss modulus, and loss tangent. The storage modulus (G’) shows the capability
of the sample to store energy that will be released after the deformation is recovered.
The loss modulus (G") represents the energy dissipated as heat when the sample is
deformed. Usually, the viscous property is expressed by dynamic viscosity (tj’= G7go)
or complex viscosity (7?* = [(G’/gj)2 + (G'Vgj)2]1'2 ). For a completely viscous fluid like
water, the storage modulus is negligible compared to the loss modulus, and the stress
function is 90° out of phase from the deformation function. In contrast, the stress and
deformation sinusoidal functions are exactly in phase (5 = 0°) for a perfectly elastic

15
Strain = y = y0 sin cut
Strain rate y = cu y0 cos cut
Stress = a = o0 sin (cut + <5)
= y0 (G‘ • sin cut + G" • cos cut)
Storage modulus = G' = (a0/y0) cos ó
Loss modulus = G" = (<70/y0) sin <5
Loss tangent = tan <5 = G"/G'
Figure 2.3 Graphical and mathematical descriptions of several variables used in
dynamic-shear measurement.
sample. Viscoelastic materials are characterized by a phase difference 5 that is
somewhere between 0 and 90°.
The rheological properties of particle/polymer mixtures depend not only on
characteristics of particles (e.g., solids loading, particle shape, particle size, and state of

16
dispersion), but the polymer rheology as well. Therefore, the rheology of polymer melts
and particle/fluid mixtures will be discussed in the following two sections.
2.2.2 Polymer Melts
Polymer melts are typical viscoelastic fluids due to the complex structures, i.e.,
long molecular chains with side branches [Alk72, Fer80, Len78]. The main molecular
chains tend to coil or entangle together because of various types of intermolecular and
intramolecular forces. Polymers can store energy when the coiled chains are stretched
under an applied shear stress. Energy can also be dissipated as heat by the friction
between molecules.
Viscoelasticity of polymers is dependent on many factors, including molecular
weight distribution, molecular structure, chemical composition, and temperature of
measurement. The dependence of polymer rheology on these variables has been studied
by both steady- and dynamic-measurements [Fer80, Han71, HanK83, HanL82, HanY71,
Tan81]. For example, capillary viscometry has been used to investigate the effect of
molecular structure on the rheological properties of polyethylene [Han71]. Polymers
with broad molecular weight distributions have lower viscosities and higher elasticities
than those with narrow molecular weight distribution. Polymers with long-chain
branching are more elastic and less viscous than the linear polymers [Han71]. The effect
of temperature on polymer rheology has been studied extensively for polyethylene,
polystyrene, poly(methyl methacrylate), and polybutadiene [HanJ86, HanL82], For a
given polymer, both viscosity and elasticity increase as temperature decreases, but the
G7G" ratio is relatively insensitive to temperature variation.

17
Correlations between steady- and dynamic-shear rheological behavior have been
observed in simple viscoelastic samples such as polymer melts or solutions. A certain
degree of similarity is recognized between the shear rate (7) dependence of steady
viscosity (77) and the frequency (w) dependence of dynamic viscosity (77’) [Cox58, Kul80,
Schu80]. At extremely low deformation rates, the viscosity values for many polymeric
fluids approach the same value for steady- and dynamic-shear measurements:
lim 77 (7) = lim 77’(w) (2-3)
-p*0 or-*0
For most cases, these two functions (77 vs. 7 and 77’ vs. 00) have the same shape or can
be superimposed to form a single curve. For example, two polystyrene melts were tested
and compared using a capillary extrusion rheometer for steady shear and an
elastoviscometer for dynamic measurement [Cox58]. The apparent viscosity 77, matched
better with the complex viscosity 77*, but the true viscosity T7t fit well with the dynamic
viscosity 77’. The former relation (77, with 77*) is often referred to as the Cox-Merz rule:
77*(w) = 77,(7) U— (2-4)
The rule was also found to be applicable for polystyrene and polyacrylamide solutions
over a wide range of concentrations and molecular weights at relatively high shear rates
and frequencies [Kul80].
2.2.3 Particle/Fluid Mixtures
The rheological behavior of particle/fluid mixtures is of major research interest
because it controls both processability and energy consumption in areas such as ceramic

18
or metal injection molding and manufacturing of filled polymer composites.
Unfortunately, there are still no rigorous theoretical models predicting the rheological
behavior of particle/fluid mixtures with high solids contents. Einstein derived the most
rigorous expression describing the effect of particle additions on fluid viscosity:
Vr = ( 1 + 2.5 • 4>) (2.5)
where t)x is the relative viscosity which is defined as the viscosity of the particle/fluid
mixture divided by the fluid viscosity, and is the particle volume percentage.
However, the Einstein relation has limited applicability since it is derived with several
restrictive assumptions, i.e., (1) there are no particle-particle interactions, (2) particles
are spherical in shape, (3) particles are nondeformable, (4) particles are monosized, etc.
Consequently, it is valid only for very dilute suspensions prepared with rigid monosized
spheres. A large number of other equations have been used to describe the relation
between relative viscosity and the particle (solids) loading for more concentrated
suspensions containing nonspherical, nonmonosized particles. These equations are
usually empirical and contain one or two adjustable parameters for achieving good data
fits. Typical equations include those due to Farris (Eq. 2.6), Marón and Pierce (Eq.
2.7), and Mooney (Eq. 2.8) [Far68, Man83, MÍ171, Utr82]:
7,
( 1 -4>Y*
(2.6)

19
v, - (i - 4- )'2 <2-7>
Q0
r] = exp ( —/ ‘ ) (2.8)
1 - s •
where k (Eq. 2.6) ranges from 3 for broad size distribution up to 21 for monomodal size
particles, „ (Eq. 2.7) is the maximum solids loading, and f and s (Eq. 2.8) are
adjustable variables. Figure 2.4 plots the dependence of relative viscosity (r?r) as a
function of solids loading () for these models. The models give similar predictions at
low solids loadings, but large differences in relative viscosity are observed in the high
solids loading region. As empirical equations, they are limited utility in predicting the
viscosity of real systems.
As illustrated in Figure 2.2, the viscosity of concentrated particle/fluid mixtures
is often dependent on shear rate (or, in the case of dynamic shear measurements, on
oscillation frequency). Shear-thinning flow behavior (i.e., decreases in viscosity as the
shear rate increases) is often observed in samples with higher solids loading because of
extensive particle-particle interactions [Big82, Sai86, Sain86]. At low shear rates, the
presence of both (1) isolated agglomerates and/or floes and (2) extensive three-
dimensional particulate network structures increase the resistance of the particle/fluid
suspensions to flow and, therefore, the measured viscosity is high. As the shear rate is
increased, both particle network structures, agglomerates, and/or floes are broken down
and resistance to flow is greatly reduced (because the liquid occluded in those networks

Relative Viscosity (rjr)
1
a
7, = exp (
f - - ), f =
1 - S • 1p
T
7r = ( 1 -
T >' ’•
= 0.44
104
* 0
V
7, = ( 1 -
$â– )-*, to
= 0.68
to
â– 
•
7r = ( 1 -
t y\ k =
5
103
o
7, = ( 1 +
2-5 •

102 r
101
10D
Solids Loading ( 100
Figure 2.4 Plots of relative viscosity vs. solids loading by different models.
to
o

21
and agglomerates is now released). Thus, the measured viscosity decreases, i.e., shear¬
thinning behavior is observed. (In some cases, shear thinning behavior also results from
the characteristics of the polymer, as described in section 2.2.2) Bigg studied the
dynamic rheological behavior of polyethylene samples containing relatively large (~ 15
nm) steel spheres (to avoid the complexities caused by particle shape irregularity and
particle agglomerates) and irregular-shaped relatively fine ( — 0.6 ^m) alumina powders
[Big82, Big83, Big84b]. The dynamic viscosities of the sample containing 60 vol% steel
spheres were strongly shear-dependent over the measured shear frequency range (0.1-100
rad/sec) even though the polyethylene (PE) melts were Newtonian at the same frequency
range, indicating the existence of the particulate structure in the suspension. For the
samples containing alumina powders, agglomerates and/or floes were formed and highly
shear-thinning behavior was also observed. By treating alumina with appropriate
chemical additives, it was possible to improve particulate dispersion in the PE melts, thus
decreasing the viscosity and allowing mixtures with higher solids loading (from 57 vol%
to 64 vol%) to be prepared.
The storage modulus (G’) determined from dynamic shear measurements is
indicative of the elasticity of a particle/fluid mixture. In general, the G’ values increase
with increasing shear rate. Adding particles to a polymer has the effect of increasing G’
values [Big82, Big83, Big84b, Ron88, Sai86, Sher68]. As the solids loading increases,
the slope of a G’ vs. shear rate curve decreases due to the increased particulate network
structure of the mixture (i.e., as samples develop a more elastic character). In the case
of the steel sphere/polyethylene mixtures described above, the storage modulus values

22
still increased with increasing frequency at 60 vol% of solids loading [Big82]. However,
if fine alumina or zirconia particles were used, which tended to form agglomerates and/or
floes easily, the storage modulus curves were relatively flat over the entire frequency
range at solids loading as low as 50 vol% [Alt83, Big83].
The strain values used in dynamic-shear measurements also affect the rheological
properties for particle/polymer mixtures. Bigg investigated the effect of strain for a
polyethylene sample containing 50 vol% steel spheres [Big83]. The rheological
properties of pure polyethylene (without steel spheres) were independent of strain values.
However, both dynamic viscosity and storage modulus decreased by about two orders of
magnitude when the strain was increased from 1 to 25 %, suggesting that the particle
networks dominated the rheological response of mixtures.
2.3 Particle/Fluid Mixing
Dispersion of particles in a polymeric fluid consists of three major steps: wetting,
deagglomeration, and stabilization [Fun86, Hee69, Nak84]. First, the polymer wets the
outer surface of large particle lumps and penetrates into the interstitial space of the
agglomerates. In the second step, high shear force is applied to break down the particle
lumps into smaller units. In the last step, re-agglomeration and de-agglomeration reach
dynamic equilibrium. It should be emphasized that the various aspects of dispersing a
powder in a fluid do not really occur in successive stages, but in fact occur in a
simultaneous manner [Hee69].
Mixing of particle/polymer batches is often carried out in internal mixers with
variable-speed rotors of different geometries. A transducer is sometimes attached to the

23
mixer to monitor the torque required to maintain the rotors at a specified mixing speed.
The torque vs. time function provides information related to the extent the mixing and
the properties of the mixes. For example, consider the case in which
alumina/polyethylene samples were mixed by preheating a portion of powder to the
desired temperature, adding polymer all at once, and then adding the remaining portion
of powder [Alt83, Big84a]. During the initial stage of mixing, a large torque peak was
observed which was attributed to wetting of the powder (by the polymer), incorporation
of the powder into the polymers, and deagglomeration of the powder. Torque values
subsequently decreased (after the peak) and tended to maintain a steady value, suggesting
that no further improvements in dispersion were likely to occur with continued mixing.
Usually, a high shear stress is required in order to break down the powder
agglomerates in the starting powders. The shear stress generated during mixing is
dependent on the rotor speed. As a result, samples mixed at higher rotor speeds have
better particulate dispersion than those mixed at lower rotor speeds [Dan52, Frea85,
HesS84, Moh59, Sha84], This conclusion has been supported by experiments using
various techniques to evaluate the state of particulate dispersion, including electrical
resistance and quantitative microscopy for carbon black/rubber samples [Dan52], and
viscosity measurement for cement/water suspensions [Sha84],
High shear mixers are generally used to incorporate powders into polymer melts.
The breakdown of agglomerates is generally maximized within a few minutes of mixing
and prolonged mixing times generally do not result in further decreases in the amount
or size of the agglomerates [Dan52]. This conclusion has been reached from many

24
studies with carbon black/rubber mixtures in which the properties and microstructure
were evaluated as a function of mixing time [Boo63a, Boo63b, Dan52, Lei56].
Particulate dispersion may be affected by mixing temperature because of its effect
on polymer viscosity and polymer/particle wetting behavior. Since polymers have higher
viscosities at lower temperatures, high shear stresses are generated if mixing is carried
out at lower mixing temperatures [Frea85, Gar85, LeeM84, Moh59]. As a result,
agglomerate breakdown may be enhanced if samples are mixed at lower temperatures.
The effect of temperature on polymer/particle wetting behavior has received less
attention. Cotton studied the effects of mixing temperature on dispersion of carbon
black/rubber mixtures and found that samples mixed at higher temperatures had lower
electrical resistance, indicating that better particulate dispersion was achieved [Cot84].
He suggested that this was due to the improvement in rubber/carbon black wetting at
higher temperatures, although direct measurements of wetting behavior were not carried
out.
When a low mixing temperature is used, it becomes more difficult to remove the
voids created during mixing due to the high polymer viscosity. The mechanical strength
may be reduced even though the particulate dispersion may be improved. To solve this
type of problem, Lee used a cyclic temperature schedule to mix carbon black with
elastomer in a two-roll mixer to improve the degree of mixing and the mechanical
strength [LeeM84]. The mixing temperature profile, shown in Figure 2.5, combined the
heating and cooling steps with different time lengths in each segment. In the heating
cycle, voids were removed more effectively due to the lower rubber viscosity at higher

25
Rubber
Mixing Time Period (min)
Figure 2.5 A cyclic mixing schedule with the combination of heating and cooling
and steps [LeeM84],
temperature. In the cooling cycle, the efficiency of dispersing carbon black was greatly
increased due to the higher rubber viscosity. The mechanical strength of the cyclically
mixed mixtures was higher than the conventionally mixed mixtures (i.e., in which mixing
was carried out at a constant temperature). By examining the cryogenically fracture
surface, the cyclically mixed sample clearly showed fewer voids and a better particulate
dispersion.
2.4 Particle/Fluid Wetting
Wetting behavior can be understood from Young’s equation (see Figure 2.6).
Spontaneous wetting is defined as the case when the contact angle, 0, is < 9(P. The
contact angle can be simply evaluated by the sessile drop method, which is based on

26
ysv ' 7sl
Young’s Equation: cos# =
yLV
Figure 2.6 Contact angle for a liquid droplet deposited on a solid substrate and
Young’s equation.
using the geometry of a liquid droplet deposited on a solid substrate (Figure 2.6).
Measurements are made of the angle formed by a line along the solid-liquid interface and
a line tangent to the droplet surface which passes through the three-phase intersection
point (Figure 2.6) [Cari75, Com89, Her70]. Sessile drop measurements are generally
carried out on bulk solid (dense) substrates. However, in some cases, contact angles can
also be measured for fluid droplets deposited on powder compact surfaces [Buc86,
Fel79]. The method is restricted to cases in which penetration of fluid into pores of the
powder compact is negligible (e.g., when the fluid is non-wetting, the fluid viscosity is
high, etc.).
Another method for determining fluid/powder contact angles is to measure the
penetration rate of the fluid through the powder compact. The correlation between

27
penetration time and penetration distance is expressed by the Washburn equation
[Was21]:
/2 = ( r • cos 6 ) • ( ~y~ ) • t (2.9)
2 rj
where 1 = penetration depth
r = pore radius of the alumina compact
d = contact angle
7 = surface tension of the fluid
t) = viscosity of the fluid
t = penetration time
This equation is based on the following assumptions: (i) the pores in the powder
compacts are cylindrical in shape; (ii) there are no closed pores or enlargements in the
pore structure; (iii) the pore size is much greater than the molecular diameter of the
liquid; (iv) gravity is neglected; and (v) there is no chemical reaction between liquid and
powder. The powder compact can be made either by compaction of the powder at a
constant pressure or by compaction of a fixed weight of powder into a fixed volume
[Che83, CroV67, Stu55]. Application of Eq. 2.9 requires knowledge of parameters 7,
r], and r. Both y and 77 can be readily measured with considerable accuracy. However,
r can not be assigned a single value since real powder compacts have a wide range of
pore sizes and pore shapes. To address this problem, it is necessary to find a reference
liquid which has zero contact angle (i.e., cos 0o = 1) [Buc85, Stu55] for the powder
under investigation. The times required for the reference and test fluids to penetrate a
fixed distance into the powder compact are defined as ^ and t*, respectively. The same
type of powder compact is used for each penetration experiment, so that pore radii, r„

28
and r¡, can be considered to be the same. Consequently, the contact angle of the test
fluid, 0¡, can be calculated from the following equation (which is derived from the
Washburn equation):
y • v t
cos et = ( ).(-£)
7i • Va
(2.10)
where 60, -q0, and 70 = contact angle, viscosity, and surface tension of the
reference fluid, respectively
0¡, T7¡, and 7¡ = contact angle, viscosity, and surface tension of the
test fluid, respectively
For more accurate results, many penetration rate (1 vs. t) data points are collected
for each sample, and the contact angle is calculated by linear regression. By taking
logarithmic values on both sides, the Washburn equation is transformed to the following
linear equation:
log / = 1 log [ ( r • cos 6 ) • ( 7 ) ] + ^ • log /
2 2 • rj 2
(2.11)
= K + m • log t
where m = slope of log 1 vs. log t curve
K = intercept of log 1 vs. log t curve
If Eq. 2.11 applies, a plot of logarithm of penetration distance vs. logarithm of
penetration time should give a slope of 0.5. From linear regression, the best fit K and
m values for a test fluid and a reference liquid can be found. Then, the contact angle
of the test liquid is calculated from the following equations:

29
K¡ = ^ ' log [ ( r{ • cos 6t ) • ( ) ]
Z Z •
^ * log [ ( ro • cos 0O ) • ( 7o ) ]
2 2 • 7<,
cos 0,. = ( 2f_L_üí ) • exp [ 2 • (AT -AT^) ]
7,- • V0
= H • exp [ 2 • (K.-/Q ]
(2.12)
It should be noted that the plot of log 1 vs. log t does not always give a slope equal to
0.5. Furthermore, log 1 vs. log t plots are not always linear. These effects have been
attributed to non-uniformities in powder packing, as well as the range of pore sizes and
pore shapes in real powder compacts [Carl79, Coo77],
If a reference liquid with zero contact angle is not available, it is still possible to
identify differences in wetting behavior by determining the contact angle ratio for
different powder/fluid systems. By assuming the pore structures in the powder compacts
are the same, the contact angle ratio can be calculated.
R
cos 6
(cos 8). L
- li = H • ( 2 )
(cos 0)2 q
(2.13)
R.
cos 6
(cos 0),
(cos 0)2
H • exp [ 2 • (AT,-Ay ]
(2.14)
where e = Contact angle ratio between conditions 1 and 2
(cos 0), = Cosine of contact angle at condition 1
(cos 0)2 = Cosine of contact angle at condition 2

30
The parameters H, K, and K2 are obtained from Eqs. 2.10 and 2.11. If only one
penetration data point is taken for each sample, Eq. 2.13 should be used. Eq. 2.14 will
give higher accuracy if many data points are taken for each sample.
2.5 Characteristics of Alumina Surfaces with Adsorbed Water and Hydroxyl Groups
When alumina powders are treated at high temperatures, the surface hydroxyl
groups and the adsorbed molecular water are removed gradually. This effect can change
the alumina/polymer wetting behavior, mixing behavior, and the state of particulate
dispersion. In this study, infrared spectroscopy (IR) and gravimetric analysis were used
to examine the change in alumina surface characteristics after heat treatment. IR gives
information on the chemical bonding at alumina surface, while gravimetric analysis gives
information about the weight of molecules that are adsorbed or removed from the
alumina surface.
In general, alumina surface OH groups and molecular water show stretching and
bending bands at 3000-3800 cm'1 and 960-1700 cm'1, respectively. Five IR peaks for
isolated OH groups on dehydrated alumina surface have been identified [Hai67, Per65b].
These peaks are at located at 3700, 3733, 3744, 3780, and 3800 cm'1, which correspond
to the sites with different numbers of nearest oxide neighbors. The theoretical model of
these OH groups is schematically illustrated in Figure 2.7, and the assigned OH
stretching frequencies are listed in Table 2.3. The exact location of these IR peaks for
any specific powder may shift slightly depending on particle size, surface structure, and
state of hydration. In fact, these IR peaks for isolated OH groups cannot be observed
unless alumina is heated to a very high temperature (e.g., 1000°C). At room

31
Figure 2.7 Isolated hydroxyl groups on alumina surface (+ donates Al+3 in lower
layer) [Per65b].
Table 2.3 Isolated hydroxyl groups on alumina surface observed in infrared
spectra [Per65b].
OH group
Wave ^(cm'1)
Number of nearest oxide neighbors
A
3800
4
B
3744
2
C
3700
0
D
3780
3
E
3733
1

32
temperature, alumina adsorbs molecular water which gives wide bands centered at 3300
and 1650 cm'1 regions and the OH peaks are concealed [Hai67, PerH60]. As the
temperature is increased (~ 100-400°C), the intensities of these two bands are reduced
as molecular water is removed. At even higher temperatures (e.g., in the range of 650
and 700°C), molecular water and some hydrogen-bonded hydroxyl groups are removed
and sharp OH peaks become evident. Due to condensation of OH groups, trace amounts
of water continue to evolve up to very high temperatures (> 1000PC).
The amount of water adsorbed on alumina surface has been studied by gravimetric
measurement [Cor55, DeBF63]. The water molecules bound directly by surface
hydroxyl groups are referred to as chemisorbed water which cannot be expelled by heat
treatment at 120°C. The term "chemisorbed" is justified based on the strength of the
bond and the activation energy for dehydration. Above the chemisorbed water layer is
the physisorbed water which has a multilayered structure and can be described by the
BET equation. The amount of water on the alumina surface is actually dependent on
temperature, pressure, and treatment of the alumina powders. These variables have been
investigated by adsorption-desorption experiments [Cor55, Per65a, PerH60].
2.6 Effects of Moisture on Ceramic/Polymer Composites
It is well-known that the properties of polymer/ceramic composite may be affected
by exposure to water or by storage in a humid environment [Col86, Roy76, Tra76].
Moisture can diffuse either through the polymer matrix or along the ceramic/polymer
interface into the inner structure of the composites. Diffusion of moisture into samples
was confirmed by weight change measurements [Col86, Shi78, Spr81]. Sample weights

33
increased initially and then levelled off after a long period of time. Generally, moisture
diffusion rates and final moisture contents increased with increasing humidity and
temperature. If there were microvoids in the composites, the final equilibrium moisture
content became greater than expected because the microvoids could accumulate a
considerable amount of water. In addition, abnormally high initial rates or continuously
increasing weight gains for long times have been observed. These effects are due to
cracks in the sample, especially cracks on sample surfaces [Bro78].
The effect of moisture on the properties of fiber-reinforced thermosetting
composites have been investigated extensively. Usually, experiments were carried out
by storing samples in environments with controlled moisture contents and temperatures,
and the properties were measured periodically [Put82, Spr81, Sto90]. For example,
significant reduction in yield stress and ultimate strength were observed for glass
fiber/epoxy composites in a four-point bending test [Sto90]. In a vibration test,
absorption of moisture reduced the dynamic modulus for graphite/epoxy samples, but it
had little effect on damping coefficients [Put82]. In tensile tests, reduction of ultimate
tensile strength of fiber reinforced composites depended on the orientation of fibers and
moisture content [Shen81].
Many hypotheses have been proposed to explain the mechanisms of aging in
samples which absorb moisture. For example, it has been suggested that water might act
as a plasticizer [Bro78, CorF78, Sto90, Tra76] to decrease the glass transition
temperatures (Tg) of the polymer matrices. The Tg values for epoxy and nylon
composites have been shown to decrease with increasing moisture content [Bro78,

34
Luo83, Whi82]. Under this circumstance, the ability of the polymer to support the
reinforcing fiber and to transfer loads to the fiber may be reduced. It has also been
proposed that absorbed water may cause polymer swelling that might induce internal
stress and initiate cracks inside polymer composites. As a result, the mechanical strength
could be significantly reduced. Unfortunately, these is still no conclusive evidence to
support these hypotheses even though this type of aging phenomenon has been well
recognized.
2.7 Chemical Additives
For almost all ceramic/polymer mixtures used in industry, chemical additives are
indispensable ingredients for various purposes, including reducing flow resistance during
processing and enhancing adhesion between two components. Numerous chemical
additives are available commercially which are generally classified as lubricants,
plasticizers, wetting agents, coupling agents, etc. These conventional classifications are
made according to chemical structures and their intended functions. The expected
effects, however, may not indeed occur in practical applications. For example, a
coupling agent may actually act as a particulate dispersing agent, with no real coupling
(i.e., chemical bonding) between the polymer and particles [Luo83, Mon74]. Such a
result demonstrates the complexity in selecting a proper chemical additive to achieve the
desired goal and the difficulty in predicting the performance of any specific chemical
additive. This section reviews the structure of some additives (including coupling agents,
surfactants, and lubricants) and analyzes their influence on the rheological properties for
ceramic/polymer mixtures.

35
2.7.1 Structures
Coupling agents are the molecules designed to form chemical bonds between two
components with different natures. The general formula of a coupling agent is expressed
as
Rm - M - ( 0-R’)n (2.15)
In the above formula, O-R’ is a hydrolyzable group, such as methoxyl (OCH3) or ethoxyl
(OC2H5), that can react with water or a hydroxyl group on the ceramic surface, R is an
organic part with different functional groups, and M is a metal atom. The parameters
m and n vary from 1 to 4 for most coupling agents. Depending on the center atom M
(e.g., Si, Ti, or Al), the coupling agents are classified as silane, titanate, or alumínate.
Silanes have received the most research attention and have extensive applications [Big82,
HanV81, InoK75, LeeM87, Luo83, Plu70, Plu78, Plu82, PluS78, Sain85, Zha88].
The commonly used silanes have three hydrolyzable groups (n=3) and their chemical
structures are listed in Table 2.4. Titanates can be classified according to the number
of hydrolyzable groups and the structures of the R groups. Table 2.5 gives chemical
descriptions of some popularly used titanates [Bre85, HanS78, HanV81, Luo83, Mon78,
Mon84a, Mon84b, Mon84c]. However, the exact formula for titanates and some other
coupling agents are not available from the manufacturers.
To have a real coupling effect, the OR’ groups should be hydrolyzed and a strong
bond between the ceramic surface and the polymer matrix should be formed. The ideal
mechanism can be described by the following reactions, using silane as an example:

Table 2.4 Commonly used silane coupling agents [Plu69, Plu78, Plu82].
Name
Chemical Stmcture
Identification*
7-[0(Vinyl benzylamino) ethylamino]
propyltrimethoxysilane
V.B.-NHCH2CH2NH(CH2)3Si(OCH3)3 • HC1‘*
Z-6032
Vinyl-tris(/3-methoxyethoxy)silane
CH2=CHSi(OCH2CH2OCH3)3
Z-6082, A-172
7-Methacryloxypropyltrimethoxysilane
CH2=C CO(CH2)3Si(OCH3)3
1 II
ch3 0
Z-6030, A-174
Vinyltriethoxysilane
CH2=CHSi(OC2H5)3
—
7-Aminopropyltriethoxysilane
NH2CH2CH2CH2Si(OC2H5)3
Z-6011, A-1100
7-(j8-Aminoethyl)-7-
amino-propyltrimethoxysilane
NH2CH2CH2NH(CH2)3Si(OCH3)3
Z-6020, A-1120
7-Glycidoxypropyltrimethoxysilane
CH2CHCH20(CH2)3Si(0CH3)3
\ /
0
Z-6040, A-187
7-Mercaptopropyltrimethoxysilane
HSCH2CH2CH2Si(OCH3)3
Z-6062, A-189
Triacetoxyvinylsilane
CH2=CHSi(OCCH3)3
II
0
Z-6075
7-Chloropropyltrimethoxysilane
ClCH2CH2CH2Si(OCH3)3
Z-6076, A-143
Series Z and A are commercial identifications from Dow Coming and Union Carbide respectively.
V.B. = Vinyl benzene
Os

37
Table 2.5 Commonly used titanate coupling agents [Mon78a, Mon84a].
Titanate type
Chemical description
Monoalkoxy (m = l, n=3)’
KR TTS
KR 6
KR 9S
KR 12
KR 38S
KR 44
Isopropyl, triisostearoyl titanate
Isopropyl, methacryl diisostearoyl titanate
Isopropyl, tridodecylbenzenesulfonyl titanate
Isopropyl, tri(dioctylphosphato) titanate
Isopropyl, tri(dioctylpyrophosphato) titanate
Isopropyl, tri(N ethylamino-ethlamino) titanate
Monoalkoxy (m = 1, n=3)
LICA 01
LICA 09
LICA 12
LICA 38
LICA 44
Neoalkoxy, triisostearoyl titanate
Neoalkoxy, dodecylbenzenesulfonyl titanate
Neoalkoxy, tri(dioctylphosphato) titanate
Neoalkoxy, tri(dioctylpyrophosphato) titanate
Neoalkoxy, tri(N ethylamino-ethlamino) titanate
Chelate (m = 1, n=2)
KR 112
KR 138S
KR 238S
Titanium di(dioctylphosphate) oxyacetate
Titanium di(dioctylpyrophosphate) oxyacetate
Di(dioctylpyrophosphato) ethylene titanate
Coordinate (m=4, n=2)
KR 41B
KR 46B
Tetraisopropyl di(dioctylphosphito) titanate
Tetraoctyloxytitanium di(ditridecylphosphite)
See EQ (2.23) in the text for the chemical formula of coupling agent.
R-Si(-OR’)3 + 3 H20 - R-Si(-OH)3 + 3 HOR’ (2.16)
R-Si(-OH)3 + HOM(surflce) - R(0H)2-Si-0-M(Iurflce)+ H20 (2.17)
The above reaction is applicable in cases where the coupling agent is applied to the
ceramic as a water-containing solution. Coupling agents can also react directly with the
surface hydroxyl groups if nonaqueous solvents are used:

38
R-Si(-OR’)3 + HOM(IurfKe) - R(0H)2-Si-0-M(lurflce) + HOR’ (2.18)
In aqueous solutions, condensation between OH groups of hydrolyzed silane coupling
agent molecules can result in monolayers of silanoxanes on ceramic surfaces. The step-
by-step mechanism is illustrated in Figure 2.8 [LeeL68]. In fact, this is an idealized
model for monolayer coverage. The hydrolyzed silane R-Si(OH)3 actually starts to
condense even in the solution and the polymerization rate is dependent on pH values of
the solution, concentration of coupling agent, composition of the R group, and
temperature [Plu69, Plu82]. Coupling agent solutions turn hazy when extensive
polymerization occurs and molecules are large enough to scatter light. Consequently, a
simple way to experimentally monitor the stability of hydrolyzed silane solutions is to
determine the amount of time required for the solutions to turn hazy. Some silane
coupling agent solution (e.g., hydrolyzed aminofunctional silane solutions) have
extraordinarily high stability. This has been attributed to be formation of stable (low
molecular weight) cyclic structures as illustrated in Figure 2.9.
ft
I
Rt) —Si—0R‘
I .
Oft
ft
I
MO-Si-OH
Ah
MO-Si-OH
TAWLKOXrSlLANES STABLE SILANETRIOLS /'¿Si''✓GLASS SURFACE✓
'/7 / ////////'.
mto»06Cii-
*>«0€9
R
I
--Si-
R
I
-Si-0
I
1
0>N ^VS.
tv&foiuriONi
-M70
*XTW£*lZAflO*
(Ouring drying
of I01»
)
GLASS SURFACE
R R
• .M, I
ho—sí—0. :o-sí-oh
I '* 1
GLASS SURFACE
Figure 2.8 Formation of a monolayer of polysiloxane on silicate glass surface
[LeeL68].

39
\ /
s
/ \
CH,—CH2
\
CH,
/
+NH,
(A)
/ \
\
ch2—ch2
\
ch2
/
— +nh2
nh2—ch2—ch2
(B)
Figure 2.9 Cyclic structures of (A) aminosilane and (B) diaminosilane coupling
agents in solution [Plu69].
Surfactants (surface active agents) are chemicals with the capability of modifying
the interfacial energy by adsorption at interface. A surfactant has two distinct parts in
the molecular structure: a hydrophilic (lyophobic) head group and a hydrophobic
(lyophilic) tail. According to the structure of the hydrophobic groups, surfactants are
classified as hydrocarbon, silicone, and fluorocarbon. Among these, hydrocarbons with
8 to 20 carbon atoms are used most extensively. Fluorocarbons have very low surface
energies and exceptional resistance to thermal and chemical attack.
Surfactants are usually applied by solution treatment of the powder (or fiber) in
order to achieve homogeneous coatings in an efficient manner. The amount and

40
orientation of surfactant adsorbed on solid surfaces are controlled by many factors,
including the nature of surfactant, property of solid surface, solution concentration,
solvent, etc.
A lubricant is an interfacial phase that is used to reduce the resistance to sliding
between two phases [Ree88]. The lubricants commonly used in ceramic processing
include paraffin wax, stearic acid, oleic acid, polyglycols, silicone oil, etc. Stearic acid
and its salts are effective lubricants because the carboxyl end of the molecule may be
strongly bonded to an oxide surface, and the shear resistance between the first oriented
adsorbed layer and successive layers is low. Lubricants can be applied either as additives
to a batch formulation [Edi86, Sto90, Zha88] or as coated films on surfaces (of molds,
dies, extrusion chambers, etc.) in contact with the batch during shape forming operations
[Dim83, Str77]. The term "internal lubricant" is applied to the former case, while the
term "external lubricant" is used in the latter case. In the case of external lubrication,
it is well-documented that the shear stress generated during processing at the interface
between batch and the coated surface may be greatly reduced by the presence of a
lubricant.
2.7.2 Effects of Chemical Additives on Rheological Properties
The incorporation of small amounts of chemical additives (such as coupling
agents, surfactants, lubricants, etc.) in ceramic/polymer batches may significantly affect
the properties of the mixture, including the rheological properties. These additives can
modify particle-particle, particle-polymer, and polymer-polymer interactions depending
on nature of chemical additives, polymer properties, ceramic characteristics, and the

41
method by which the chemical additive is applied. It is important to consider all these
types of interactions in understanding the mechanism by which the additive influence
batch properties.
It has been suggested that a chemical additive can increase viscosity and modulus
values if chemical bonding occurs between the ceramic surface and the polymer [Big82,
Big84b] or if ceramic/polymer adhesion is improved [HanV81]. In such cases, enhanced
bonding or adhesion at the interface is indicated by changes in fracture mode (i.e., cracks
propagate through the polymer matrix and not along the ceramic/polymer interface
[HanV81]).
Chemical additives may also affect viscosity and modulus values by altering the
state of particulate dispersion. Reductions in viscosity and modulus values are observed
when the state of particulate dispersion is improved (e.g., when agglomerates are broken
down) [Big83]. It should be noted that some coupling agents may also act as wetting
agents or dispersing agents (i.e., as opposed to forming strong bonding between ceramic
particles (or fibers) and polymer matrices [Big83, Boa77, HanS78, HanV81, Luo83,
Mon84c, Sain85]).
Reduction in viscosity and modulus can be caused by a lubricating effect at the
particle-polymer interface or plasticization of the polymer matrix [Alt83, Big83, Big84a,
Big84b, Sain85, Mon74, Mon78, Mon84c, Sain85]. An effective lubricant should also
result in lower shear stress developed during mixing (i.e., lower mixing torque value)
[Big83].

CHAPTER 3
EXPERIMENTAL
3.1 Materials and Materials Preparation
3.1.1 Starting Materials
Most of the experimental work was carried out with a high purity aluminum oxide
powder1 (RCHP alumina) which had a median Stokes diameter2 «0.4 ¿un and a specific
surface area3 of 7.3 m2/g. A few experiments were carried out with a glass powder
(median Stokes diameter2 «2.7 ¿un) which had major constituents Si02-Al203-Mg0
(approximate weight ratio of 57:21:18 as determined by wavelength dispersive
spectroscopy4) and trace amounts of Ca and P. Another grade of high purity aluminum
oxide powder5 (AKP alumina) with median Stokes diameter2 «0.9 ¿un was also used
in some experiments.
1 RCHP-DBM, Reynolds Metals Co., Chemical Division, Little Rock, AR. Nominal
purity >99.98% A1203.
2 Sedi-Graph Particle Size Analyzer, Micromeritics Instrument Corp., Norcross, GA.
3 Model OS-7, Quantachrome Corp., NY.
4 Superprobe 733, Japan Electron Optics Co., Ltd., Tokyo, Japan.
5 AKP-15, Sumitomo Chemical America, Inc., New York, NY. Nominal purity
>99.99% A1203.
42

43
bet Most of the experimental work was carried out using a relatively low molecular
weight, low density polyethylene6 (PE A-C* 9). Copolymers ethylene-acrylic acid6
(EAA A-C* 5120 and 540) and ethylene-vinyl acetate6 (EVA A-C* 400 and 405T) and
a high molecular weight, high density polyethylene (PE Sclair 29157) were also used in
some experiments. The physical properties obtained from the manufacturers for these
polymers are listed in Table 3.1. The chemical compositions of these different polymers
are shown in Figure 3.1.
PE
EAA
EVA
H H H H H H
(-C
:-c
'-) (“C
:-c
» -(-c
:-c
i
ml
H H H H H C=0
H H H H
(-C-C-) -(-C-C-)
n1 n2
H H HO
O-H
C=0
ch3
Where 1, ml, m2, nl, and n2 are integers.
Figure 3.1 Chemical compositions of polyethylene (PE), ethylene-acrylic acid
(EAA), and ethylene-vinyl acetate (EVA) polymers.
6 Allied Corp., Morristown, NJ.
7 DuPont Canada Inc., Plastics Division, Toronto, Canada.

Table 3.1 Physical properties for polyethylene (PE), ethylene-acrylic acid (EAA), and ethylene-vinyl
acetate (EAA).
Polymer
Drop pt.
(°C)
(ASTM D-3104)
Density
(g/cm3)
Viscosity
(Pas)
Number/Weight
Average
Molecular Weight
Acid Number
(mg KOH/g)
Vinyl Acetate
Content
(wt%)
PE A-C 9
117
0.94
0.45+
2100/5800
EAA A-C 5120
92
0.93
0.65 +
690/1200
120
EAA A-C 540
108
0.93
0.50+
1700/4500
40
EVA A-C 400
95
0.92
0.61 +
2400/7000
13
EVA A-C 405T
103
0.92
0.60+
3100/6800
6
PE Sclair 2915
123*
0.96
2.00*
14,000/40,000
Softening point (°C) according to ASTM D-1525.
+ Viscosity at 140°C using a Brookfield viscometer (reported by the manufacturer).
* Dynamic viscosity at 180°C (frequency = 1 rad/sec and strain = 100%) using a parallel-plate viscometer
(measured in this study).

45
Chemical additives used in this study are listed below:
(1) Silane coupling agent Z-60208 has the formula NH2(CH2)2NH(CH2)3Si(OCH3)3 and
is designated 7-(j8-aminoethyl)-7-aminopropyltrimethoxysilane. It is a clear, light straw-
to-yellow colored liquid with specific gravity of 1.02.
(2) Silane coupling agent Z-60768 has the formula Cl(CH2)3Si(OCH3)3 and is designated
7-chloropropyltrimethoxysilane. It is a colorless liquid with specific gravity of 1.08.
(3) Titanate coupling agent9 Ken-React LICA 12 has formula R0Ti[0P(0)(0CgH17)2]3
and is designated neoalkoxy, tri(dioctylphosphato) titanate. (The R in the formula is a
neoalkoxy group, but the manufacture does not provide information on the exact
structure.) It is a clear, red-orange colored liquid with a mild alcoholic odor and specific
gravity of 1.02.
(4) Zircoaluminate coupling agent CAVCO MOD APG10 is an amino functional
zircoaluminate having an inorganic polymer backbone dissolved in propylene glycol. It
is a colorless liquid with specific gravity of 1.15.
(5) Surfactant Fluorad FC-74011 is a nonionic fluorinated alkyl ester liquid with specific
gravity of 1.01.
8 Dow Coming Corp., Midland, MI.
9 Kenrich Petrochemicals, Inc., Bayonne, NJ.
10 Cavedon Chemical Co., Inc., Woonsocket, RI.
11 Commercial Chemical Division/3M, St. Paul, MN.

46
(6) Stearic acid12 is a solid which has the chemical formula CHjCCH^COOH and a
specific gravity of 0.85.
The chemical compositions of silanes, titanate, and stearic acid are shown in Figure 3.2.
Unfortunately, the compositions for zircoaluminate coupling agent and Fluorad FC-740
are not available from the manufacturers.
3.1.2 Treatment of Alumina Powder
Alumina powder calcination. Alumina powders were heated to temperatures in
the range 300-1000°C in a box furnace13 at a rate of 10°C/min and subsequently held
at the desired temperatures for 4 hr. Furnace power was turned off at the end of the 4
hr hold period. Powders were cooled in the furnace to 150°C and then were immediately
transferred to a desiccator in order to avoid moisture absorption as powders cooled to
room temperature. Calcined powders were kept in the desiccator for at least 12 hr
before performing mixing experiments. Experiments were also carried out with alumina
powder that was calcined at 100°C for 4 hr using a convection oven14. The alumina
powder was transferred to a desiccator immediately after the heat treatment was finished.
The same experimental procedures were used for heat treatment of alumina
powder compacts. These compacts were subsequently used in contact angle and
microhardness measurements.
12 Fisher Scientific Co., Fair Lawn, NJ.
13 Model DT-31, Del tech, Inc., Denver, CO.
14 Fisher Isotemp* Oven, Model 126G, Fisher Scientific Co., Fair Lawn, NJ.

47
Silane Z-6020
O-CH,
I
NH2- (CH2) 2-NH- (CH2) 3-SÍ-O-CH3
0-CH3
Silane Z-6076
O-CH,
I
Cl- (CH2) 3-SÍ-O-CH3
0-CH3
Titanate LICA 12
R-O-Ti- [O-P- (0-CgH17) 2) 3]
0
Where R is a neoalkoxy group (The composition is not
revealed by the manufacturer).
Stearic Acid
CH3-(CH2) 16-c-oh
0
Figure 3.2 Chemical structures of some chemical additives.

48
Mixing with chemical additives. Coupling agents (1.25 g) were added to
deionized water (125 cc) in 250 cc bottles. The bottles were shaken by hand for a few
sec and then placed on a low-speed (— 30 rpm) rotary mixer for 1 hr. Alumina powder
(125 g) was added into the bottles and mixing on the low-speed rotary mixer was
continued for 22 hr. The rheological flow properties of the suspensions were then
characterized using a steady-shear viscometer15. Samples were then transferred to 250
cc glass beakers which were placed on a hot plate (~ 90°C)/stirrer. Water was
evaporated from the suspension under constant stirring until dry powder cakes were
obtained. (This step took —24 hr to insure that the solvent was completely removed.)
The cakes were crushed by a mortar and pestle to powders with as fine a size as
possible. Powders were stored in a vacuum desiccator prior to mixing with polymer.
This procedure was used for mixing other chemical additives with the alumina powder,
but the solvents were changed to heptane for additions of Fluorad FC-740 and carbon
disulfide for additions of stearic acid. The drying temperature was reduced to ~40°C
for carbon disulfide because it had a boiling temperature of 46.5°C. (Heptane had a
boiling temperature of 98.4°C and so the drying temperature was kept at ~90°C.) Also,
the amounts of Fluorad and stearic acid added were varied in the range of 0.063-3.75 cc.
Compaction. Alumina powder compacts were made by three methods: pressing
dry powders, slip casting, and pouring powder/water suspension on a glass plate. Dry
pressed powder compacts were formed by uniaxial compaction at — 35 MPa ( — 5100 psi)
15
Model RV 20/CV 100, Haake, Inc., Saddle Brook, NJ.

49
of 2 g of dry powder in a 2.54 cm diameter cylindrical steel die. The powder compacts
were -2 mm thick and had a relative density of 53%16 (as determined by mercury
porosimetry). Slip cast powder compacts (thickness «3 mm) with different packing
densities were made from aqueous suspensions (30 vol% solids) having either pH «4
or pH «9. The initial preparation of the suspensions involved mixing alumina powder
and deionized water by hand for ~ 1 min, followed by 1 hr of sonication in order to
break down powder agglomerates. Suspensions were then poured into plastic tubes
sitting on blocks of plaster of Paris. Thin alumina powder compacts (thickness »1 mm)
were also made by pouring pH ~4 suspension (30 vol% solids) on a 30 x 30 cm glass
plate. The suspensions were the same as those used in preparing slip cast compacts.
Suspensions were poured on the glass plate and allowed to spread out naturally. Water
was allowed to evaporate at room temperature for 24 hr and thin pieces ( — 2-10 cm2) of
consolidated powder (i.e., green compacts) were subsequently collected for
microhardness and contact angle measurements.
3.2 Characterization of Ceramic Powders.
Powder Compacts, and Polymers
3.2.1 Alumina Powder Characterization
Weight loss. The amount of weight loss during calcination was determined by
measuring the powder weights before and after heat treatment.
16
Autoscan-60, Model SP-20LV, Quantachrome Corp., Syosset, NY.

50
Specific surface area. The specific surface areas of as-received (uncalcined) and
calcined alumina powders were measured by nitrogen gas adsorption17 (multipoint BET
method). Powders were outgassed at 200°C for 3 hr under a flowing nitrogen
atmosphere just before making the measurements.
Particle size distribution for as-received ceramic powders. The particle size
distributions of ceramic powders were measured either by x-ray sedimentation18 or by
centrifugal photosedimentation19. In order to prepare well-dispersed suspensions,
alumina powders were mixed with water at pH = 4 (i.e., to develop a high positive
surface charge) and subsequently sonicated to break down agglomerates. For x-ray
sedimentation, the suspensions were prepared with 2 vol% solids and sonicated for 1 hr.
For centrifugal photosedimentation, 0.1 vol% alumina suspensions were prepared,
sonicated for 30 min, and diluted to the appropriate concentration (-0.01-0.03 vol%)
before measurement. The magnesium aluminum silicate glass powder was characterized
by x-ray sedimentation using a suspension which was prepared with 3 vol% solids in
methanol and sonicated for 1 hr. (Methanol was used as the suspension liquid because
of concerns regarding possible chemical reactions between water and the glass powder.)
Particle size distribution for calcined alumina powders. The particle size
distributions of calcined alumina powders were measured in order to determine if
interparticle bonding (agglomerate formation) occurred during heat treatment. Some of
17 ASAP 2000, Micromeritics Instrument Corp., Norcross, GA.
18 Sedi-Graph Particle Size Analyzer, Micromeritics Instrument Corp., Norcross,
GA.
19
CAPA-700, Horiba Instruments, Inc., Irvine, CA.

51
the measurements were carried out by the x-ray sedimentation and/or centrifugal
photosedimentation methods using the same procedures as described above for the
characterization of as-received powders. However, in other experiments, centrifugal
photosedimentation measurements were carried out on suspensions prepared with either
no sonication or with only 15 sec sonication. Of course, this procedure resulted in
incomplete breakdown of powder agglomerates and, thus, the measured size distributions
were shifted to larger sizes compared to results obtained using well-sonicated
suspensions. However, these measurements were useful in providing information about
the strength of the agglomerates that formed when powders were calcined at various
temperatures. Powders with weaker agglomerates will disperse more completely with
short sonication times and, therefore, the measured distributions show smaller apparent
particle sizes. In contrast, powders containing stronger agglomerates tend to resist
breakdown during sonication and, therefore, the measured size distributions show larger
apparent particle sizes.
Surface characterization via FTIR. The effect of calcination on the alumina
powder surface characteristics was analyzed by diffuse reflectance20 Fourier Transform
Infrared Spectroscopy21 (FTIR). Samples were scanned over the range from 400 to
4000 cm'1 at a rate of 200 scans per minute. Generally, 500 scans were collected for
reference materials (potassium bromide, Kbr) and 200 scans for other samples. A hot
20 DRA-2C6, Harrick Scientific Corp. Ossining, NY.
21 Model 60SX, Nicolet Analytical Co., Madison, WI.

52
stage22 was used for in-situ FTIR measurements at elevated temperatures. In one
experiment, spectra were collected as alumina powder was heated from room temperature
to 100°C in 15 min and subsequently held at 100°C for 4 hr. In another experiment,
spectra were collected every 100°C as the powder was heated from room temperature to
600°C at 10°C/min.
Analysis for Iron content. Iron (either elemental or ionic state) contamination in
alumina powders was extracted into aqueous solution and concentrations were determined
by inductively coupled plasma spectrometry23 (ICP). Alumina powders (10 g) were
boiled in 200 cc of 1 N HC1 for 2 hr with stirring. After cooling down to room
temperature, the alumina powders were removed from suspension using filter paper24.
The filtrates were then concentrated to 20 cc for the ICP measurement.
Scanning electron microscopy and optical microscopy. The as-received and
calcined alumina powders were observed by scanning electron microscope (SEM25)
using 25 KeV accelerating voltage. Alumina powders or bulk substrates treated with
coupling agents were also examined at high magnification using SEM and at low
magnification using optical microscopy26.
22 HVC-DRP, Harrick Scientific Corp. Ossining, NY.
23 Plasma II Emission Spectrometer, Model 5800, Perkin-Elmer Corp., Norwalk,
CT.
24 No. 3. qualitative filter paper, Whatman International Ltd., Maidsone, England.
25 Model JSM-35CF, Japan Electron Optics Co., Ltd., Tokyo, Japan.
26 Nikon Inverted Microscopy, EPIPHIT-TIME, Nippon Kogaku K. K., Tokyo,
Japan.

53
3.2.2 Alumina Powder Compact Characterization
Pore size analysis. The pore size distributions and total porosity of alumina
powder compacts were measured by mercury porosimetry27. Plots of intruded volume
vs. applied pressure were obtained up to a maximum applied pressure of 414 MPa
(60,000 psi). The pore channel radius distribution was obtained using standard values
for the mercury surface energy (484 erg/cm2) and the contact angle (140°) under the
assumption that the pores are cylindrical. The pore radius distribution was then
calculated using the following relation:
Pore radius (run) = ——— (3.1)
P (MPa)
The median pore radius was calculated from the pressure corresponding to 50% of the
maximum intruded volume (V). The total porosity (P) was calculated using the equation:
P (%) = —. 100 n ~
W 17 (3-2)
— + V
P
where W is the weight of the sample and p is the theoretical density of the powder. The
relative density of the powder compact is equal to 1-P.
Microhardness measurements. Hardness measurements were made on the thin
(~ 1 mm) alumina powder compacts which were prepared by casting pH = 4 suspensions
onto glass plates (see section 3.1.2). Measurements were carried out on both uncalcined
27
Autoscan-60, Model SP-20LV, Quantachrome Corp., Syosset, NY.

54
and calcined alumina (1 hr at temperature) compacts using a microhardness tester28 with
a 10 g load. Five readings were taken for each sample and the average hardness value
was reported.
3.2.3 Polymer Characterization
Rheological properties of polymers were determined by a viscometer29 in a
dynamic (oscillatory) mode under conditions of controlled temperature, strain, and
frequency (or shear rate). A cone-and-plate test fixture with 25 mm radius and 0.04 rad
cone angle was used. A detailed discussion of the procedures used in measuring
rheological properties is given in section 3.4.1.
3.3 Mixing of Ceramic Powders and Polymers
The ceramic/polymer mixtures were prepared using a high-shear bowl mixer
which was equipped with variable-speed roller blades and attached to a torque
rheometer30. The conditions chosen for mixing 50 vol% RCHP alumina with
polyethylene (A-C 9) are listed in Table 3.2. For experimental Run Nos. 1-6 (single¬
segment mixing schedules), the temperature and rotor speed were kept constant
throughout the entire mixing period. The following procedure was used to prepare the
ceramic/polymer mixtures: (1) the mixer was heated to the desired temperature and the
roller blades were set rotating at the desired speed, (2) polyethylene was added to the
mixing bowl and ~ 2 min were allowed for the polymer to melt and reach the pre-set
28 Micromet II, Buehler Ltd., Lake Bluff, IL.
29 Model RDS-II, Rheometrics, Inc., Piscataway, NJ.
30 Rheomix 500/Rheocord System 40, Haake, Inc., Saddle Brook, NJ.

55
Table 3.2 Mixing conditions used to prepare 50 vol% alumina/50 vol%
polyethylene mixtures.
Run »
Temperature
(°C)
Rotor Speed Total Mixing Time
(rpm) (min)
Single-segment mixing schedules
1
125
200
30
2
150
200
30
3
175
200
30
4
220
200
30
5
150
10
30
6
150
200
10
Multi-segment mixing schedules
Mixing with temperature change
7
150(30) - 220(10)*
200
45+
8
220(10) - 150(30)*
200
45+
Mixing with rotor speed change
9
150
200(30) - 10(10)*
40
10
150
10(20) - 200(30)*
50
* Numbers in parentheses are the mixing times in minutes for each segment.
+ Total mixing time includes 5 min heating (Run #1) or cooling (Run #8) period
between 150 and 220°C.

56
mixing temperature, (3) alumina powder was gradually added (over an ~ 4 min period)
to polymer melt, and (4) mixing was continued for a fixed period of time (usually 30 min
for the entire mixing operation). Run #5 was an exception to the above procedure. The
powder incorporation rate at the low rotor speed (10 rpm) was so slow that step (3) alone
required 20 min. For Run Nos. 7-10 listed in Table 3.2 (multi-segment mixing
schedules), steps (1) to (3) were the same as described above. However, either mixing
temperature or rotor speed was varied during an extended mixing period. Run #7 was
similar to Run #2 (mixed at 150°C), but the temperature was raised from 150 to 220°C
over a five min period, and mixing was continued for an additional 10 min. The initial
part of Run #8 was similar to Run #4 (mixed at 220°C), but the sample was mixed only
10 min, the temperature was then lowered from 220 to 150°C over a five min period, and
mixing was continued for an additional 30 min. The mixing time for Run Nos. 7 and
8 totaled 45 min due to the extra 5 min needed for heating or cooling between segments
at 150 and 220°C. For the last two experiments, the mixing speed was either reduced
from 200 rpm to 10 rpm (Run #9), or raised from 10 rpm to 200 rpm (Run #10). In
each case, the 200 rpm mixing segment was carried out for 30 min. The 10 rpm
segment was carried out for 10 min in Run #9, but Run #10 required a 20 min mixing
time at 10 rpm because of the slow rate of incorporation of the alumina. In contrast to
multi-segment experiments involving a temperature change, the transition times between
segments in Runs Nos. 9 and 10 were very short (a few seconds) because the rotor speed
could be changed mechanically within a few seconds.

57
A standard mixing procedure was used to prepare all other ceramic
powder/polymer samples in this study. The mixing temperature, time, and rotor speed
were 150°C, 30 min, and 200 rpm, respectively.
3.4 Characterization of Ceramic Powder/Polymer Mixtures
3.4.1 Rheology
Rheological properties of ceramic/polymer mixtures were determined using a
parallel-plate viscometer29 which was operated in dynamic-shear (oscillatory) or steady-
shear modes under conditions of controlled temperature, strain, and frequency (or shear
rate). The test fixtures had a circular plate geometry with either 25 mm radius (for
lower viscosity samples) or 12.5 mm radius (for higher viscosity samples).
The test fixture was heated up to the desired temperature (usually 125°C) and kept
for 1 hr to reach thermal equilibrium. Gap calibration was performed before starting
rheological measurements. A sufficient amount of sample was placed on the lower plate
of the test fixture. After 10 min of heating, the sample softened and the upper part of
the test fixture was then moved down to the appropriate gap distance. The gap was 0.05
mm for the cone-and-plate fixture. For the parallel-plate fixture, the gap was in the
range of 0.25-2.5 mm, although a value of 0.6 mm was used most of the time. Low
viscosity samples flowed easily and filled up the gap space when the upper plate was
moved downwards. However, samples with high viscosity or high elasticity did not flow
easily and a significant normal force developed on the transducer attached to the upper
plate. The upper plate was automatically immobilized to prevent further movement when
the normal force exceeded 70% of the maximum transducer load (2000 g).

58
Consequently, a larger gap (typically between 1 to 2 mm) was used for the latter
samples. A sufficient quantity of sample was used to ensure that gap space between
plates was completely filled. As described below, the viscometer was operated in several
deformation modes for this study.
Dynamic rate (frequency) sweep. The lower plate of the test fixture oscillated
sinusoidally at programmed oscillating frequencies (a>, rad/sec) and maximum strain (70,
dimensionless). The shearing angle (0, rad) of the oscillating plate was calculated
according to the equation 6 = 70-(H/R), where R and H were the radius of the test
fixture and the gap between parallel plates, respectively. In this mode, the maximum
strain was kept constant (y0 = 100%) and the frequency was increased logarithmically
from 0.01 to 100 rad/sec. Data were collected at ten frequencies per decade. The
torque value was measured by a transducer attached to the upper plate and the rheological
properties were calculated using Eqs. 3.3-3.5 given below.
Transient (thixotropic loop). The rotation speed of the lower plate of the test
fixture was first increased linearly (over 6 min interval) to a maximum shear rate (25 or
50 sec'1). Upon reaching the final speed, the rotation speed was decreased linearly to
zero over the same time interval. The torque values were measured and stored 1024
times during each 6 min interval. It should be noted that maximum shear rates were
limited to values noted above because some samples were ejected from the test fixture
at higher rotation speeds. Thus, torque readings taken at higher rotation speeds were
considered to be unreliable.

59
Transient (step strain, or relaxation). In stress relaxation experiments, the lower
plate is first rotated instantly in a clockwise direction to a pre-selected strain value (i.e.,
the sample is subjected to a step strain). (In this study, the step strain was always
100%.) At the same time, torque values are measured as a function of time, i.e., the
relaxation of the stress is monitored over time. The torque values corresponding to the
step strain were recorded at 512 evenly spaced intervals during four sequential time
zones. The time periods of these four zones were kept as 1, 9, 90, and 900 sec in order
to get the best resolution for the relaxation curve. For most samples, the torque values
diminished to values below the detection limit of the transducer (i.e., 2 g-cm) within the
first or the second zone and the experiments were terminated. However, in some
samples (i.e., those with high viscosity and/or high storage modulus), significant torque
values were still observed even at the end of the fourth zone. It should be noted that the
pre-selected strain value (100%) could not be applied on the sample instantly; in reality,
it takes ~ 0.02-0.03 sec to reach the strain value. The instrument starts to collect torque
values before the strain reaches 100%. Consequently, the stress vs. time curve always
shows an initial increase in stress (during the initial 0.01-0.02 sec), followed by the
relaxation of the stress.
The transducer in the viscometer detects the torque generated in response to the
imposed strain on the sample. Using the equations listed below, rheological properties
are then calculated from the measured torque values, the geometrical constants for the
test fixtures, and the input parameters (i.e., rotational frequency, strain, etc.).

60
Rheological properties
V
=
M • K / 7
G’
=
K- (M,y
G"
=
K- (M,)"
G*
=
[ (G’)2 + (G")2 ]m
V
=
G" / 07
If"
=
G’ / 07
V*
=
[ (V)2 + Of)2 ]in = G* / 07
Tan 8
=
G" / G’ = 77’ / 77"
Cone-and-plate fixture geometry equations (Figure 3.3)
K = 0.1 •[ 3/3 • 980.7 ]/[ (R/10)3 • 2x ]
To =0/0 (3-4)
7 = n / 0
Parallel-plate fixture geometry equations (Figure 3.3)
K = 0.1 • [ (2H/10) • 980.7] / [ (R/10)4 • t ]
7o =6- R / H (3.5)
y = fi • R / H
where 77
G’
G"
G*
v'
v"
V*
8
K
R
0
H
0
7
To
07
0
M
(M„r
(H)"
Viscosity in steady-shear mode (Pa-s)
Storage modulus (Pa)
Loss modulus (Pa)
Complex modulus (Pa)
Dynamic viscosity (Pa-s)
Imaginary component of complex viscosity (Pa-s)
Complex viscosity (Pa-s)
Loss angle (rad)
Geometric scaling constant (dimensionless)
Radius of the test fixture (mm)
Cone angle of the con-and-plate fixture(rad)
Height of sample or gap between parallel plates (mm)
Rotational rate in steady-shear mode (rad/sec)
Shear rate in steady-shear mode (sec'1)
Maximum strain in dynamic-shear mode (dimensionless)
Oscillating frequency in dynamic-shear mode (rad/sec)
Shearing angle or oscillating amplitude in dynamic-shear mode (rad)
Transducer torque (g-cm)
Component of torque in phase with strain (g-cm)
Component of torque 90° out of phase with strain (or in phase with
the strain rate) (g-cm)

61
Cone-and-plate fixture
Parallel-plate fixture
Figure 3.3 Geometry of a cone-and-plate and a parallel-plate viscometer.

62
3.4.2 Quantitative Microscopy
Quantitative microscopy (QM) was used to evaluate the state of particle dispersion
in the polymer matrix at room temperature. QM analysis is usually carried out on a
polished cross-section of the material [DeH68, Und70]. However, in this study, it was
not possible to prepare polished sections because of the extreme difference in hardness
between the alumina particles and the low molecular weight polymers. Consequently,
a new sample preparation technique was developed which allowed for microscopic
assessment of the state of dispersion in ceramic/polymer mixtures. Experimental
procedures are given below, but more detailed information on the development of this
method are described in section 4.1.
Alumina/PE samples were mixed in the usual manner in the high-shear bowl
mixer. At the end of the mixing cycle, samples were immediately transferred onto
aluminum foil. The surfaces of the samples that formed directly on the aluminum foil
had relatively good flatness; however, the surface region consisted mostly of a thin layer
of polymer. In order to expose the alumina particles for QM analysis, plasma etching31
was used to remove much of the polymer from the surface. The plasma reaction
chamber was a glass tube (16 mm x 150 mm) which was pumped down to —50 mTorr.
The residual air inside the glass tube was excited with a radio frequency power supply
to produce an oxygen plasma containing excited atoms, molecules, and ions. These
active species reacted with the polyethylene to produce low molecular weight volatile
products (e.g., CO, C02, and H2Q) which were carried out of the reaction chamber by
31
Harrick Plasma Cleaner, Harrick Scientific Corp., Ossining, NY.

63
the vacuum pumping system. Plasma etching was normally performed at power level 5
(controlled by a switch selector) for 30 min. Etched surfaces were observed at 20,000
magnification using a scanning electron microscope (SEM25) with a 25 KeV accelerating
voltage. A grid with 10x10 lines was placed on top of SEM micrographs. A template
with circles of varying diameter was then used to measure the equivalent projection
circumscribing diameter (Dpc) of each alumina particle. Particles were selected only if
a cross point of the grid overlaid on the particle and if its perimeter was clear. For each
mixed batch, five different pieces were etched and two SEM micrographs for each piece
were taken. The total number of particles collected in these ten micrographs was ~ 600.
The rationale for collecting particle size (Dpc) distributions as a measure for assessing
the state of particulate dispersion is discussed in much detail in section 4.1.
3.4.3 Ceramic/Polymer Wetting Behavior
Sessile drop method. Measurement of contact angles by the sessile drop method
was carried out using a contact angle goniometer32 equipped with a controlled
temperature environmental chamber. The contact angles of polyethylene melts (PE A-C
9) on sintered alumina substrates were recorded as a function of time at various
temperatures. The following procedure was used: (1) the alumina substrate was heated
in the environmental chamber to the desired temperature for ~5 min, (2) a polymer
pellet was placed on the center of the alumina substrate and allowed to melt completely,
and (3) contact angle values were measured as soon as melting was completed and were
recorded periodically thereafter.
32
NRL Model 100, Rame-Hart, Inc., Mountain Lakes, NJ.

64
Contact angle measurements were also made for polyethylene melts on alumina
powder compacts. In these experiments, a high density, high molecular weight
polyethylene (Sclair 2915) was used (i.e., instead of PE A-C 9) in order to avoid rapid
penetration of polymer melt into the pore channels of the alumina compacts. (Even at
temperatures as low as 125°C, the low viscosity polyethylene (PE A-C 9) penetrates into
the porous compacts within seconds, thereby making it impossible to get reliable contact
angle values.) The alumina powder compacts used in these experiments were prepared
by casting pH = 4 suspensions (on glass plates) according to the procedure described in
section 3.1.2.
Penetration method. Polyethylene melt/alumina powder wetting behavior was
assessed by measuring the penetration rate of the melt through powder compacts. The
experimental steps for this method are described below:
(1) Preparation of polymer disks. Polymer was formed into a disk shape (~ 1 mm and
-20 mm diameter) by melting -0.4 g of polymer in a 10 cm3 glass beaker at 150°C in
the environmental chamber attached to the contact angle goniometer. Upon complete
melting, the low viscosity, free-flowing polymer quickly conformed to the cylindrical
shape of the beaker. The beaker was then removed from the environmental chamber and
cooled to room temperature. The solidified polymer disk was then removed from the
beaker.
(2) Preparation of alumina powder compacts. Alumina powder compacts (— 25 mm
diameter) were formed by dry pressing according to the procedure described in section
3.1.2.

65
(3) Penetration of polymer melt through powder compacts. An alumina powder compact
was heated in the environmental chamber to the testing temperature and heated at the
temperature for 5 min. A preformed polymer disk was then placed on top of the
compact at the center. It took about 1 min for the edge of the polymer disk to melt and
15 sec more for the center portion to melt. When the polymer disk melted completely,
a stop watch was pressed to start counting the penetration time. After 5 min of
penetration, the alumina compact was quickly taken out of the environmental chamber
(and cooled to room temperature) in order to "freeze" the polymer and prevent further
penetration. Penetration of the polymer melt was repeated (with new compacts) using
different penetration times (10, 16, 25, and 40 min).
(4) Measurement of polymer penetration depth. The unpenetrated part of the alumina
compact (bottom portion) was washed off under running water. Small squares (about 2x2
mm2) were cut from the center of the polymer-penetrated powder compacts. The
penetration distance was determined using a vertical control mechanism on the contact
angle goniometer stage which allowed adjustments in increments as small as 0.02 mm.
A cross-hair built into the ocular was initially placed on the top surface of polymer-
penetrated powder compacts (i.e., at the original powder compact/polymer disk
interface). The distance penetrated was then determined by moving the sample on the
adjustable stage, which was calibrated with a micrometer, until the cross-hair was lined
up with the bottom plane of polymer penetration inside the powder compact.
Measurements were taken from each side of the cut squares (i.e., four per sample) and

66
an average penetration depth was calculated. The average penetration depth was then
recorded as a function of penetration time.
As discussed in detailed in Chapter 2 (section 2.4), contact angles can be
determined by measuring the penetration rate of a liquid through a porous compact. If
the Washburn equation is applicable (see Eq. 3.6 below), a plot of the logarithm of the
penetration distance, 1, vs. the logarithm of the penetration time, t, should give a straight
line with slope = 0.5.
log / = 1 log [ ( r • cos0 ) • ( 7 ■ ) ] + ^ • log t
2 2 • r\ 2
= K + m • log t
where 1 = penetration depth
r = pore radius of the alumina compact
6 = contact angle
7 = surface tension of the fluid
77 = viscosity of the fluid
t = penetration time
m = slope of log 1 vs. log t curve
K = intercept of log 1 vs. log t curve
The best fit values for m and K were obtained by linear regression. In general, the data
fit well to a straight line with slopes in the range of 0.49-0.52 (correlation coefficients
> 0.992). Therefore, the slope of the straight line was fixed at 0.5 and the intercept
values, K, were obtained from the least square method. Absolute values of the contact
angle could not be calculated from Eq. 3.6 because of the complex pore geometry of the
powder compacts. Therefore, the relative wetting behavior under different conditions
was assessed by calculating a contact angle ratio, R^, according to the following
equation:

( 2lU!i ) . exp [ 2 • (KrK2) ]
7, * V2
67
(cos 0),
(cos d)2
(3.7)
where Rcotó
(cos 0)i
(cos d)2
K,
K2
Contact angle ratio between conditions 1 and 2
Cosine of contact angle at condition 1
Cosine of contact angle at condition 2
Intercepts obtained by EQ 2.19 at condition 1
Intercepts obtained by EQ 2.19 at condition 2
According to equation 2.22, > 1 means that condition 1 gives a lower
contact angle (i.e., better wetting) than condition 2. In order to apply Eq. 3.7, it was
necessary to determine surface tension and viscosity values for the polymer at the
appropriate temperature for the polymer penetration experiments. Viscosity values of the
polymer melts were measured with the parallel-plate viscometer29 in an oscillatory mode
at 100% strain and 10-100 rad/sec frequency. The surface tension values of polymer
melts were measured by a tensiometer33 employing the Wilhelmy Plate principle.
3.4.4 Elemental Analysis
Semi-quantitative elemental analyses for Al, O, and C at the surface of
alumina/polyethylene mixtures were carried out by Electron Spectroscopy for Chemical
Analysis34 (ESCA, also called XPS for X-ray Photoelectron Spectroscopy). This
technique gives compositional information from only a thin surface layer (~ 10-30 Á) of
the material. Samples were in the form of thin plates (—1 mm thick) which were
prepared by melting the alumina/PE mixtures at 125°C (in the environmental chamber
33 Rosano*â„¢5 Surface Tensiometer, Federal Pacific Electric Co., Newark, NJ.
34 Model XSAM 800, Kratos Scientific Instruments, Manchester, England.

68
attached to the contact angle goniometer) between two glass slides. The thin plates were
cut into 1 cm x 1 cm squares and then plasma etched for various lengths of time by the
method described in section 3.4.2. Samples were stored in a desiccator before ESCA
analysis.
3.4.5 Characterization via FTIR
Mixtures of alumina/polyethylene were analyzed by diffuse reflectance FTIR at
room temperature using the same operating conditions as described in section 3.2.1 for
the alumina powders. Samples were ground to powders as fine as possible at room
temperature using an A1203 mortar and pestle.
3.4.6 Analysis for Iron Content
Iron content was determined for alumina/PE mixtures using the same method
described in section 3.2.1 for the analysis of the alumina powders. The only differences
were that (1) the mixtures were ground to fine powders before mixing with the boiling
HC1 solution and (2) 20 g samples were used.
3.4.7 Microhardness Measurements
The hardnesses of pure polymer and ceramic/polymer mixtures were measured
by a microhardness tester35 using loads in the range from 25 to 100 g. Samples were
formed into thin plates (~2 mm thick) by melting and pressing between two glass slides
at 125°C in the environmental chamber attached to the contact angle goniometer. Five
hardness readings were taken for each sample and the average hardness value was
reported.
35
Micromet 3, Buehler Ltd., Lake Bluff, IL.

CHAPTER 4
RESULTS AND DISCUSSION
4.1 Effects of Mixing Conditions
In this section, the effects of mixing variables (temperature, time, and rotor
speed) on the ceramic particulate dispersion in polymer melts are reported. The mixing
conditions include single-segment and multi-segment mixing schedules, which were
previously described in Chapter 3 (see Table 3.2). In single-segment mixing (section
4.1.1), mixing temperature and rotor speed were kept constant throughout the entire
mixing process. In multi-segment mixing (section 4.1.2), either temperature or rotor
speed was changed during mixing. Samples of 50 vol% alumina/50 vol% polyethylene
(PE A-C* 9) were used unless noted otherwise.
4.1.1 Single-Segment Mixing Schedules
The effects of three mixing variables - temperature, time, and rotor speed - were
studied by changing one variable and keeping the other two constant. The state of
particulate dispersion was evaluated by using steady and dynamic rheological
measurements, which were carried out at an elevated temperature (125°C). Quantitative
microscopy (QM) was also used to evaluate the state of dispersion and to establish
correlations between elevated temperature rheological measurements and QM
measurements made on samples at room temperature.
69

70
4.1.1.1 Effects of mixing temperature on rheological and wetting behavior
Alumina was mixed with polyethylene at four different temperatures (125, 150,
175 and 220°C) at a constant mixing speed (200 rpm) for 30 min. Figure 4.1 shows
plots of dynamic viscosity, storage modulus, loss modulus, and tangent delta as functions
of oscillation frequency for samples measured at 125°C. The sample mixed at 220°C had
the highest viscosity values and the largest decrease in viscosity over the measured
oscillation frequency range (0.1-100 rad/sec). The sample mixed at 175°C showed
similar behavior to the 220°C sample, although the viscosity values were slightly lower
and the decrease in viscosity with increasing frequency was smaller. The decrease in
dynamic viscosity with increasing oscillation frequency is analogous to shear thinning
flow behavior in steady shear measurement and suggests that the ceramic/polymer
mixture has an extensive particle-particle network structure. (It should be noted that the
polymer alone has Newtonian flow behavior at the measuring temperature, as shown in
Figure 4.2 and, thus, the polymer flow characteristics are not responsible for the
observed decreases in viscosity with increasing frequency.) Samples mixed at 150°C
showed further reductions in viscosity (i.e., compared to the 175 and 220°C samples).
Furthermore, a relatively small decrease in viscosity was observed over the measured
frequency range. These results indicated that the particulate dispersion was improved by
lowering the mixing temperature. A further decrease in mixing temperature (to 125°C)
resulted in little change in rheological properties, indicating that the state of dispersion
was similar to that obtained by mixing at 150°C. It should be noted that the lowest

STORAGE MODULUS (Pa) DYNAMIC VISCOSITY (Pa-s)
71
FREQUENCY (rad/s)
(B)
Figure 4.1 Plots of (A) dynamic viscosity, (B) storage modulus, (C) loss modulus,
and (D) tangent delta vs. frequency for 50 vol% alumina/50 vol%
polyethylene samples prepared at the mixing temperatures indicated.

Figure 4.1 (Continued)
TANGENT DELTA
o ^ o
o
FREQUENCY (rad/s)
LOSS MODULUS (Pa)
-*â–  o
K»

73
FREQUENCY (rad/s)
Figure 4.2 Plots of dynamic viscosity vs. frequency for polyethylene at the
temperatures indicated.
mixing temperature used in this study was very close to the drop temperature1 of the
polymer (117°C).
The storage and loss modulus values increased as the mixing temperature
increased (Figure 4. IB). The moduli also became less frequency dependent as the
1 Drop point is defined as the temperature at which the sample, suspended in a
cylindrical cup with a 6.35 mm hole in the bottom, flows downward a distance of 19 mm
to interrupt a light beam, as the sample is heated at a linear rate in air [AST77].

74
mixing temperature increased. Similar changes in rheological behavior have been
observed in previous investigations in which the particle solids loadings were increased
in powder/polymer mixtures [Big82, Big83, Big84b, Ron88, Sain86, Sher68]. In
general, samples with higher powder solids loading experience greater resistance to flow
because of the more extensive particle-particle interactions and the presence of particulate
network structures. Hence, higher viscosity and modulus values are observed. In the
case of poorly dispersed samples, the void space within agglomerates is filled with
polymer, thereby reducing the amount of polymer available for flow during shear motion.
Thus, samples have a higher effective solids loading and viscosity and modulus values
are more similar to those measured for well-dispersed samples with higher true solids
loading. Therefore, the poor dispersion caused by using higher mixing temperatures (175
and 220°C) can be viewed as having a similar effect as increasing the true solids loading
in well-dispersed mixtures. This is demonstrated in Figure 4.3, which shows the
dynamic viscosities, moduli, and tangent delta for alumina/polyethylene samples with
different true solids loading (38, 50, 59 vol%). The viscosity and modulus values
increased with increasing solids loading. The frequency dependence of both moduli also
decreased with increasing solids loading.
Other rheological measurements were consistent with those shown in Figures 4.1
and 4.3. The steady shear stress vs. shear rate flow behavior is shown in Figure 4.4 for
samples prepared with different mixing temperatures (125-220°C). The flow curves for
the 125 and 150°C samples show low yield stress and very little hysteresis, thereby
suggesting good dispersion of the alumina particles in the polymer matrix. In contrast,

STORAGE MODULUS (Pa) DYNAMIC VISCOSITY (Pa-s)
Figure 4.3 Plots of (A) dynamic viscosity, (B) storage modulus, (C) loss modulus,
and (D) tangent delta vs. frequency for alumina/polyethylene samples at
the solids loading indicated.

TANGENT DELTA LOSS MODULUS (Pa)
FREQUENCY (rad/a)
FREQUENCY (rod/s)
Figure 4.3 (Continued)

SHEAR STRESS (Pa) SHEAR STRESS (Pa)
77
SHEAR RATE (1/s)
Figure 4.4 Plots of shear stress vs. shear rate for 50 vol% alumina/50 vol%
polyethylene samples prepared at the mixing temperatures indicated.

78
high yield stresses and extensive thixotropy were observed for the 175 and 220°C
samples. These characteristics are typical for samples having a three-dimensional particle
network structure. The highly shear-thinning behavior in the 220°C sample reflects a
breakdown of the network structure. (As noted earlier, the pure polymer had a
Newtonian flow curve over the frequency range for which measurements could be made,
i.e., 10 to 100 rad/sec. The non-Newtonian behavior of the mixed alumina/polyethylene
samples must have resulted from changes in particle structure under shear.) The concept
of a poorly-dispersed sample as having a higher effective solids loading was again
supported by the flow curves for alumina/polyethylene mixtures with different true solids
loading (Figure 4.5). The 38 vol% sample had almost Newtonian flow behavior,
whereas the 59 vol% sample showed a very high yield stress and a high degree of
thixotropy.
Stress relaxation measurements were also consistent with the other rheological
data. Figure 4.6 shows residual stress as a function of time for samples prepared using
different mixing temperatures ranging from 125-220°C. Short relaxation times were
observed for the 125 and 150°C samples because the particles were relatively well
dispersed in polymer melts. In contrast, stress relaxation for the other two samples (175
and 220°C) took place much more slowly, which was consistent with the occurrence of
a solid-like particle network structure in these samples. Figure 4.7 shows the stress
relaxation curves for samples with different solids loading. As expected, stress
relaxation occurred more slowly as solids loading increased. Again, this supports the
view that poorly-dispersed samples have a higher effective solids loading.

SHEAR STRESS (Pa)
79
Figure 4.5
Plots of shear stress vs. shear rate for alumina/polyethylene samples at the
solids loading indicated.

STRESS (Pa)
80
Figure 4.6 Plots of residual stress vs. time for 50 vol% alumina/50 vol%
polyethylene samples prepared at the temperatures indicated.

81
Figure 4.7 Plots of residual stress vs. time for alumina/polyethylene at the solids
loading indicated.
The effects of mixing temperature on the state of dispersion and rheological
behavior were also observed for alumina/polyethylene samples prepared with different
solids loading. Figures 4.8 and 4.9 show dynamic viscosity, storage and loss moduli,
and tangent delta vs. frequency plots for samples of 59 vol% alumina/41 vol%
polyethylene and 38 vol% alumina/62 vol% polyethylene, respectively. As expected,
viscosity and modulus values were considerably lower for the samples mixed at 150°C
than for those at 220°C. In addition, steady shear flow curves for the 38 vol% alumina

82
(A)
(B)
Figure 4.8 Plots of (A) dynamic viscosity, (B) storage modulus, (C) loss modulus,
and (D) tangent delta vs. frequency for 59 vol% alumina/41 vol%
polyethylene samples prepared at 150 and 220°C.

TANGENT DELTA LOSS MODULUS (Pa)
Figure 4.8
(Continued)

STORAGE MODULUS (Pa) DYNAMIC VISCOSITY (P
84
Figure 4.9 Plots of (A) dynamic viscosity, (B) storage modulus, (C) loss modulus,
and (D) tangent delta vs. frequency for 38 vol% alumina/62 vol%
polyethylene samples prepared at 150 and 220°C.

TANGENT DELTA LOSS MODULUS (Pa)
85
FREQUENCY (rad/s)
Figure 4.9 (Continued)

86
samples (Figure 4.10) showed exactly the same trend as that observed in 50 vol%
alumina samples (see Figures 4.4), indicating that better dispersion was achieved by
usinp a lower mixing temperature. However, there was very little difference in the
relaxation curves (Figure 4.11) for these two samples. This probably reflects the low
true solids loading of the samples, such that even the poorly dispersed 220°C sample does
not have sufficient particle network structure to significantly increase the stress relaxation
time.
Figure 4.10 Plots of shear stress vs. shear rate for 38 vol% alumina/62 vol%
polyethylene samples prepared at 150 and 220°C.

87
TIME (s)
Figure 4.11 Plots of residual stress vs. time for 38 vol% alumina/62 vol%
polyethylene samples prepared at 150 and 220°C.
Torque rheometry was helpful in understanding the reason for the effect of mixing
temperature on the dispersion of alumina in polyethylene. Figure 4.12 shows the mixing
torque curves (i.e., measured torque during mixing as a function of time) for samples
processed at temperatures in the range of 125-220°C. The peak torque value during
mixing represents the force developed during the process of incorporation of the alumina
particles into the polyethylene melts; the final "equilibrium" torque value tends to be

TORQUE (g-m) TORQUE (g-m) TORQUE (g-m) TORQUE (g-m)
~ij— i i iiiiiiir
0 5 10 15 20 25 30
TIME (min)
Figure 4.12 Plots of torque vs. mixing time for 50 vol% alumina/50 vol%
polyethylene samples prepared at the temperatures indicated.

89
representative of the mixture’s viscosity (and state of dispersion) after the powder has
been incorporated into the polymer melt. Both values are highly dependent on the
viscosity of the polymer matrix, which, in turn, is highly dependent upon the mixing
temperature. As expected, the polymer viscosity decreased with increasing temperature
(Figure 4.13). Thus, the peak torque developed during mixing decreased as the
temperature increased, i.e., as the polyethylene viscosity decreased. At higher
temperatures (175 and 220°C), the polymer viscosity was too low to support and transfer
the force necessary for breakdown of the agglomerates in the starting powder. In
contrast, a high mixing torque was developed at lower mixing temperatures (125 and
Figure 4.13 Plot of dynamic viscosity of polyethylene (A-C 9) vs. temperature.

90
150°C) and consequently powder dispersion was greatly improved. These observations
were consistent with results reported for dispersion of carbon blacks in rubber [Frea85,
HesS84, LeeM84]. In rubber compounding, the high shear force needed to obtain good
dispersion state is usually achieved either by lowering the mixing temperature or by using
higher viscosity polymers (e.g., high molecular weight). A high shear stress is also
required when incorporating other solid particles (e.g., pigment) into polymer matrices
[Gar85, Moh59].
Figure 4.12 shows that the peak torque generated during mixing at 125°C was
considerably higher than that at 150°C, yet there was not much difference in rheological
data (see Figures 4.1, 4.4, and 4.6). This may indicate that near-optimum dispersion has
been achieved in both samples. It is also possible, however, that the benefit derived
from the increased mixing torque at 125°C may have been partially offset by poorer
wetting of the particles caused by the polymer melt at this mixing temperature. This is
suggested from measurements of penetration rates of the polyethylene melt into alumina
powder compacts heated to various temperatures. Figure 4.14 shows the penetration
depth as a function of time at different temperatures and Figure 4.15 shows the calculated
values of relative contact angle, Rcos¿, as a function of temperature. The Rcotó is defined
as the cost? value at the testing temperature divided by the cos0 value at the reference
temperature (i.e., 220°C). (The measured values of the polyethylene surface tension and
viscosity are given in Table 4.1, as are the penetration rates for the different
temperatures.) It is evident from Figure 4.15 that wetting of the alumina powder by the
polyethylene melt became poorer (i.e., the contact angle increased) as the temperature

PENETRATION DEPTH X 100 (MM)
91
TIME (SEC)
Figure 4.14 Plots of penetration depth vs. time for polyethylene melts into alumina
powder compacts at the temperatures indicated.

COS0T/COS0
92
TEMPERATURE (°C)
Figure 4.15 Plot of the contact angle ratio for polyethylene melt on alumina powder
vs. temperature. (Measured by polymer penetration method).
Table 4.1 Results for polyethylene penetration into alumina powder compacts at
different temperatures.
Mixing temperature (°C)
125
150
175
220
Polymer viscosity (Pa-s)
0.65
0.43
0.26
0.13
Surface tension (erg/cm2)
28.8
27.5
25.8
23.9
Penetration depth x 100 (mm)
at 5 min
25.6
29.5
38.7
54.9
at 10 min
33.8
40.9
51.4
69.8
at 16 min
43.5
52.6
65.4
90.7
at 25 min
54.9
63.4
79.5
110.3
at 40 min
65.1
84.9
98.3
153.6

93
decreased. The wetting between alumina and polyethylene melt was also evaluated by
the sessile drop method. In this experiment, the contact angle values of polyethylene
melts on sintered alumina substrates were recorded as a function of time and temperature
(Figure 4.16). The contact angle decreased as the temperature increased, i.e., better
wetting behavior at higher temperatures. This result was consistent with data obtained
from the polymer penetration method. These results indicate that the mixing temperature
must be optimized in order to achieve maximum dispersion. The mixing temperature
Figure 4.16 Plots of the contact angle for polyethylene melts on sintered alumina
substrates vs. time at the temperatures indicated.

94
should be low enough to develop large shear forces that can break down agglomerates,
but high enough so that wetting of the powder by the polymer melt is not adversely
affected. The rheological data suggests that mixing in the range of 125-150°C is suitable
for achieving good dispersion in alumina/polyethylene mixtures.
4.1.1.2 Quantitative microscopy
Development of quantitative microscopy technique for assessing dispersion
Quantitative measurements of microstructural features are usually carried out on
polished cross-sections of the materials [DeH68, Und70]. In the present investigation,
it was not possible to prepare polished sections due to the extreme difference in hardness
between the alumina particles (very hard) and the low molecular weight polyethylene
(very soft). Several different polishing methods (i.e., manual and automated2) and
polishing materials3 were evaluated for their ability to produce flat surfaces. None of
the polishing conditions was particularly successful. An example of one of best
"polished" surface is shown in Figure 4.17. Although this samples contains -50 vol%
alumina, relatively few particles are observed on the surface, presumably due to smearing
(flow) of the soft polymer over the surface.
Effort were also made to prepare thin sections of the alumina/polyethylene
composite using microtomy4. (As noted in Chapter 2.1, this technique has been used
2 Ecomet*III, Minimet, and Vibromet* I, Buehler Ltd., Lake Bluff, II.
3 The polishing materials used included SiC paper, SiC powder/water slurries on
glass plates, and alumina powder/water slurries on microcloth.
4 Rotary Microtome, Reichert-Jung, Buffalo, NY, and Porter-Blum Microtome, Ivan
Sorvall, Inc., Norwalk, CT.

95
Figure 4.17 SEM micrograph of the polished surface of a 50 vol% alumina/50
vol% polyethylene sample.
successfully for quantitative characterization of the dispersion of carbon blacks in rubber
compounds [AST82, Chap57, Hes62, HesB63, Lei56].) Microtomy was attempted using
several types of knives (i.e., glass, steel, and diamond). In addition, cryogenic
conditions5 were used to increase the hardness of the polymer. Nevertheless, it was still
not possible to obtain useful sections due to the difference in hardness between the
polymer and the alumina particles.
IEC Minotome Cryostat, International Equipment Co., Needham, MA.
5

96
Since useful flat sections could not be prepared by traditional polishing and
microtomy methods, a new sample preparation technique was developed for microscopic
assessment of state of dispersion in ceramic/polymer mixtures. As noted in Chapter 3.3,
alumina/polyethylene samples were mixed in a high-speed bowl mixer at temperatures
in the range of 125-220°C. Immediately upon the end of the mixing cycle, samples were
quickly transferred from the mixer onto aluminum foil . The surface of the
alumina/polyethylene sample that formed on the aluminum foil had relatively good
flatness. However, as in the case of samples prepared during the polishing experiments
described above, relatively few alumina particles were visible on the sample surfaces.
The sample surface consisted mostly of a thin polymer layer. Plasma etching, which will
be discussed in detail below, was used to remove much of this thin polymer layer,
thereby exposing the particulate structure in the alumina/polyethylene composite.
In many cases, a convenient way to quantitatively describe the particulate
structure in a composite material is in terms of the distribution of inter-particle spacings.
For example, consider the case of ceramic powder/polymer composites having the same
ratio of components, but different states of particulate dispersion. If the particles are
well-dispersed in the polymer matrix, there would be a narrower distribution of
interparticle spacings. In contrast, if the particles tend to form clusters (i.e.,
agglomerates) in the polymer matrix, there would be a broader distribution of
interparticle spacings. In the present investigation, the particulate structure in a ceramic
powder/polymer mixture was exposed by plasma etching of the thin layer of polymer at
the surface. The plasma-etched surface then appears (by observation in the SEM) to

97
have particle/pore structure. Therefore, it might seem appropriate to assess the state of
dispersion by measuring the distribution of (interparticle) pore spacings. In fact, pore
intercept distribution is not a good measure of dispersion in this particular case because
there is a tendency for some of the polymer to remain preferentially in the finest void
spaces (i.e., intra-agglomerate regions). (Experimental evidence supporting this
statement will be provided later in this section.) Therefore, an "apparent particle size"
measurement, Dpc, was used to assess the state dispersion. The rationale for using this
type of measurement can be explained by considering Figure 4.18. This figure
schematically illustrates two types of samples, one with good dispersion of particle (top)
and one with particle agglomerates (bottom). If we suppose that polymer remains
preferentially within the intra-agglomerate regions, then agglomerates would appear in
the SEM as large particles6. Therefore, larger values of the average "apparent particle
size" (Dpc) would be measured for samples with greater amounts of particle clusters (or
agglomerates). In the present study, the particle size measure used was the diameter of
the smallest circle which would circumscribe the projection of the "apparent particle."
This size measure is usually referred to as the equivalent projection circumscribing
diameter (Dpc). Experimental details regarding the measurement of Dpc have been given
previously in Chapter 3.
The remainder of this sub-section describes results of plasma etching experiments
and Dpc measurements on various samples. The main objective is to provide a more
6 There is extremely poor contrast between the ceramic and polymer phases.
Polymer films on particle surfaces or in intra-agglomerate regions cannot be
distinguished from the ceramic phase in the SEM.

98
O
o o
°_° o 0 °
0„ ° O
o o o
o O o ° - O
0-0
o
o
o
° °°° n
O o °
o o
o
o
o
° O O o o' O
O o O
o
O i Dpc
Dpc = Projection Circumscribing Diameter
Figure 4.18 Schematic illustration of (top) well-dispersed and (bottom) agglomerated
particles.

99
thorough understanding of the information obtained by Dpc measurements on plasma-
etched samples and to demonstrate the validity of Dpc measurements as a method for
assessing particulate dispersion in ceramic powder/polymer composites. In subsequent
portions of section 4.1, it is shown that Dpc measurements can be used to improve our
understanding of the effect of specific mixing variables (e.g., temperature, rotor speed)
on particulate dispersion.
The variables for plasma etching included etching time and radio frequency (RF)
power level. (The plasma etching machine is supplied with 25 watts of power. Power
level can be adjusted by a selector switch from a minimum of 1 to a maximum of 10.)
Samples from the same mixed batch (50 vol% alumina in polyethylene mixed at
150°C/200 rpm/30 min) were etched at RF power level 5 for varying lengths of time.
Figure 4.19 shows scanning electron microscopy (SEM) micrographs of samples etched
for 0 min, 0.5 min, 2 min, 10 min, 30 min, and 5 hr. Before etching, the alumina
particles were covered with a layer of polymer and the individual particles could not be
identified. In samples etched for 2 min, some of the alumina particles were exposed
completely, whereas some areas were still completely covered with a polymer film. For
etching times that were 10 min or longer, SEM observations did not reveal any polymer
at the surface or between particles. Of course, it became increasingly difficult to
distinguish residual polymer films by SEM as the total polymer amount decreased.
Electron spectroscopy for chemical analysis (ESCA) was employed for semi-quantitative
composition analysis of the etched sample surfaces. The information obtained was the
average composition over a large area (about 1 cm2). The mass concentrations of

Figure 4.19 SEM micrographs of 50 vol% alumina/50 vol% polyethylene sample
surfaces plasma etched for the lengths of times indicated.

101
Figure 4.19 (Continued)

102
carbon, oxygen, and aluminum in samples as a function of etching time are shown in
Figure 4.20. Before etching (0 min etching), the amounts of aluminum and oxygen on
the surface were negligible. This was consistent with the SEM observation which
showed that the surface was almost completely covered with a layer of polymer. The
oxygen and aluminum concentrations increased as the plasma etching proceeded in the
first 10 min, indicating that alumina particles gradually became exposed due to the
removal of polymer. After prolonged etching (3 hr), the elemental concentrations
remained similar to those at 10 min. The carbon concentration dropped to 42% in a very
short time of 2 min of plasma etching, and it decreased to 27% at 10 min of etching.
Prolonged etching (3 hr) did not further reduce carbon concentration, indicating that no
more polymer could be removed. The ESCA data thus demonstrated the actual removal
of polymer by plasma etching and the existence of residual polymer even after long time
etching treatments7. It should be noted that the experimental Al/O mass ratio 1.36 (at
3 hr of plasma etching) was higher than the theoretical value 1.12. This discrepancy
may be due to the use of inaccurate atomic sensitivity factors in calculating the elemental
weight percentages from the measured peak areas. These factors are dependent on
effective cross-section (i.e., the depth of sample from which photoelectrons can actually
escape and be collected by the detector), spectrometer detection efficiency, electron
kinetic energy, etc; the true values required for the alumina/polyethylene samples may
7 Part of the carbon detected after long etching times is probably due to hydrocarbon
contamination already present in the ESCA unit. The carbon concentration caused by
such contamination was not quantified because it changed with every experiment.
However, the carbon concentration in the long-time etched samples (27 mass%) was
much higher than typical concentrations arising from contamination.

MASS CONCENTRATION (X) MASS CONCENTRATION (X) MASS CONCENTRATION (X)
103
120
Figure 4.20 Plots of carbon, oxygen, and aluminum concentrations vs. etching time for
50 vol% alumina/50 vol% polyethylene samples.

104
be different from the standard values that were programmed in the ESCA software used
in this study.
A study of the effect of RF power was carried out by using different power levels
(levels 1, 5, and 9) to etch samples for a fixed amount of time (10 min). SEM
examination showed no obvious differences among the samples. Consequently, the RF
power was kept at level 5 for all further experiments.
As discussed in relation to Figure 4.18, it is believed that residual polymer
remains in the finest interparticle regions after plasma etching. To provide support for
this belief, an experiment was carried out in which the effect of varying the average size
of the interparticle region on plasma etching rate was investigated. The size of the
interparticle region was varied by altering the ceramic solids concentration. Experiments
were carried out with silicate glassVhigh density polyethylene9 mixtures containing 40
or 50 vol% ceramic solids. This material system was chosen for the following reasons:
(1) It was determined that mixed samples could be polished. This is because there was
less difference in hardness between these two components, i.e., compared to the
alumina/polyethylene mixtures. The high molecular weight PE (Sclair 2915) used in the
glass/polymer mixtures is considerably harder than the low molecular weight PE (A-C
9). In addition, the silicate glass is a softer material than alumina.
8 Magnesium aluminum silicate glass with the approximate composition of cordierite.
9 Grade Sclair 2915 with number and weight average molecular weight of 14,000 and
40,000, respectively.

105
(2) SEM observations were made more easily (i.e., at lower magnification) due to the
larger particle size of the glass powder (»2.7 ¿¿m median Stokes’ diameter) compared
to the particle size of the alumina powder (»0.4 ¿im median Stokes’ diameter). In
addition, the high molecular weight PE (Sclair 2915) did no! undergo local melting as
a result of electron beam heating during SEM observations.
(3) Plasma etching rates were relatively slow for glass/PE Sclair 2915 mixtures (e.g.,
compared to the alumina/PE A-C 9) due to the relatively high molecular weight of the
PE Sclair 2915. This was helpful in distinguishing differences in plasma etching rate for
various samples.
The polished surfaces of samples with 40 vol% glass/60 vol% PE and 50 vol%
glass/50 vol% PE were plasma etched for various times up to 24 hours. The SEM
micrographs in Figure 4.21 clearly show that etching occurred much more rapidly for
the samples with 40 vol% glass, i.e., the samples with larger interparticle regions. For
example, the polymer appeared to be mostly removed in the 40 vol% glass sample etched
for 3 hr; in contrast, a continuous polymer matrix is still evident in the 50 vol% glass
sample etched for 24 hr.
Additional experiments designed to evaluate the validity of a circumscribing
diameter (Dpc) as a practical measure of particulate dispersion were carried out using
alumina/PE A-C 9 mixtures. Based on the SEM observations (see Figure 4.19) and the
ESC A results (see Figure 4.20), a standard plasma etching time was chosen for most
experiments. The SEM micrographs in Figure 4.19 show that the ceramic particles (i.e.,
primary particles and agglomerates) appear as relatively well-defined units when samples

106
Figure 4.21 SEM micrographs of 40 vol% glass/60 vol% PE Sclair 2915 and 50 vol%
glass/50 vol% PE Sclair 2915 sample surfaces plasma etched for the
lengths of times indicated.

107
50 vol% Glass, 3 hr Etch
40 vol% Glass, 3 hr Etch
10 /¿m
10 ¡im
Figure 4.21 (Continued)

108
Figure 4.21 (Continued)
were etched for 10 min or longer. Thus, a circumscribing diameter could be selected
in a relatively unambiguous manner for these samples. However, since samples etched
for 10 min were just barely on the composition plateau shown in Figure 4.20, it was
decided that 30 min would be used as the standard plasma etching time. Longer etching
times were not considered necessary because the ESCA results (see Figure 4.20)
indicated that negligible polymer was removed with longer times. Furthermore,
measured Dpc values did not change after 30 min of etching. This was demonstrated by
Dpc measurements on the 50 vol% alumina/50 vol% PE A-C 9 samples shown in Figure
4.19 (i.e., samples etched both for 30 min and 5 hr, respectively). The Dpc histograms

109
for these two samples are shown in Figure 4.22. The distributions were very similar and
the average Dpc values (0.43 and 0.42 /xm, respectively) were the same (within
experimental error).
Several experiments were carried out to determine if Dpc measurements were
sensitive enough to detect differences in the state of particulate dispersion. As an initial
test, samples were prepared using a method that clearly resulted in a significant
difference in the state of particulate dispersion. Alumina/water suspensions were
prepared at two different pH values: 4 and 9. It is well known that aqueous alumina
suspensions prepared under acidic condition (pH=4) are well dispersed because the
alumina particles develop a large positive surface charge [Sac88]. In contrast,
suspensions prepared at pH=9 are highly flocculated because this pH is close to the
isoelectric point (point of zero zeta potential) for alumina [Sac88]. The two suspensions
were poured into plastic tubes that were set upon a glass plate and the particles were
allowed to settle under the influence of gravity. After sedimentation was complete,
supernatant liquid was withdrawn using a pipet, and samples were allowed to dry at room
temperature in air. The green compacts had very different porosity characteristics
because of the differences in the state of dispersion in the suspension state. Samples
formed from the well-dispersed suspension (pH=4) had a narrow distribution of fine
pores ( — 370 Á) and a high relative density (65%), whereas samples formed from the
flocculated suspension (pH=9) had a broader pore size distribution with larger average
pore size (-760 Á) and lower relative density (49%). Samples were removed from the
plastic tubes and put back on the glass plate. Polyethylene (PE A-C 9) was then placed

NUMBER PERCENT NUMBER PERCENT
EQUIVALENT DIAMETER (/¿m)
EQUIVALENT DIAMETER (/¿m)
Figure 4.22 Histogram plots of Dpc distributions for 50 vol% alumina/50 vol%
polyethylene samples plasma etched for 30 min and 5 hr, respectively.

Ill
on top of the compacts and the samples were heated to 150°C in order to melt the PE.
Due to low viscosity and good wetting behavior, the PE penetrated throughout the void
space of the sample within 1 hr and alumina/PE composites were produced. As a result
of different starting green compact structures for the pH=4 and pH=9 samples, the as-
produced composites had different spatial distributions of the alumina particles in the
polymer matrix. The "smooth" surfaces of the alumina/PE composites (i.e., the surfaces
contacting the glass plate) were then plasma etched for 30 min. The Dpc measurements
for these samples are given in Figure 4.23 and Table 4.2. The average Dpc values were
0.43 and 0.52 /¿m for the pH=4 and pH=9 samples, respectively. These results were
consistent with the hypothesis that polymer remains in the intra-agglomerate pores of the
pH=9 sample and suggest that Dpc measurements on plasma etched ceramic/polymer
samples are useful for assessing the state of particulate dispersion.
Table 4.2 Summary of Dpc results for RCHP and AKP alumina powder compacts.
Dpc (/zm)
Description 01 sa.mpies
Average
value
Standard
deviation
RCHP alumina, pH=4 polymer-infiltrated/plasma-etched
0.43
0.15
RCHP alumina, pH=9 polymer-infiltrated/plasma-etched
0.52
0.19
RCHP alumina, pH=4 as-dried green compact
0.38
0.13
RCHP alumina, pH=9 as-dried green compact
0.42
0.16
AKP alumina, pH=4 as-dried green compact
0.80
0.23
AKP alumina, pH=9 as-dried green compact
0.84
0.22
AKP alumina, pH=4 polished surface
0.75
0.23
AKP alumina, pH=9 polished surface
0.76
0.21

NUMBER PERCENT NUMBER PERCENT
20
18 -
16 -
14 -
12 -
10 -
8 -
6 -
4 -
2 -
0 -
0.00
112
RCHP Alumina pH=4
Polymer-Infiltrated/Plasma-Etched
J
llll
fill
UM
íííí
¡III
1111
u -
i i i i
Mean Diameter = 0.43 /xm
ill
0.20
0.40
0.60
0.80
q* ^a-njg—,
1.00
1.20
EQUIVALENT DIAMETER (/xm)
EQUIVALENT DIAMETER (/xm)
Figure 4.23 Histogram plots of Dpc distributions for polymer-infiltrated/plasma-etched
alumina powder compacts prepared from pH=4 and pH=9 suspensions,
respectively.

113
The Dpc measurements were also made on pH =4 and pH=9 green compacts that
had net been infiltrated with the PE melt. As-dried green compacts were removed from
sedimentation tubes and Dpc measurements were made on the "smooth" surface of the
compacts (i.e., the surface contacting the glass plate). The Dpc results for these samples
are shown in Figure 4.24 and Table 4.2. Several observations are noted:
(1) Both the as-dried pH =4 and pH=9 green compacts showed smaller Dpc values
compared to those of the corresponding polymer-infiltrated/plasma etched samples.
These values provide direct support for the contention that plasma etching results in
incomplete removal of the polymer.
(2) The pH=9 green compact showed slightly larger Dpc values compared to the Dpc
values in the pH=4 green compact.
The second observation was somewhat puzzling since it was initially thought that
the apparent particle size would be the same in green compacts containing no polymer.
To insure that the result was not simply due to experimental variations in Dpc
measurements, a similar experiment was carried out using larger (and, therefore, more
easily measurable) alumina particles. The samples were prepared with particles (AKP-
15) having approximately twice the average size of the standard alumina particles
(RCHP). The results of Dpc measurements on pH=4 and pH=9 as-dried green
compacts are shown in Figure 4.25 and Table 4.2. Once again, the green compact
prepared from the flocculated suspension (pH=9) showed slightly larger Dpc values
(Figure 4.25). Since the true particle size distribution was the same for green compacts
prepared at different pH values, the results suggested that the Dpc values (which are

NUMBER PERCENT NUMBER PERCENT
114
EQUIVALENT DIAMETER (/an)
EQUIVALENT DIAMETER (/an)
Figure 4.24 Histogram plots of Dpc distributions for as-dried RCHP alumina compacts
prepared from pH=4 and pH=9 suspensions, respectively.

NUMBER PERCENT NUMBER PERCENT
EQUIVALENT DIAMETER (fim)
EQUIVALENT DIAMETER (/¿m)
Figure 4.25 Histogram plots of Dpc distributions for as-dried AKP alumina compacts
prepared from pH=4 and pH=9 suspensions, respectively.

116
apparent diameters determined from two-dimensional micrographs) were affected by the
volume fraction of solids of the green compact. It should be evident that the two types
of green compacts differed not only in pore size distribution, but also in relative density
(volume fraction of solids). The relative densities for the pH=4 and pH=9 samples
were 65% and 49%, respectively (measured by mercury porosimetry). In compacts with
higher solids concentration (e.g., the pH=4 compact), there might be a greater amount
of particle-particle contacts and overlap. This could affect Dpc measurements, as
illustrated schematically in Figure 4.26. The first layer of particles of a plasma-etched
sample is schematically viewed in cross-section in Figure 4.26. If the particles are
crowded together (i.e., small average distance of separation), then the Dpc value for
Figure 4.26 Side view of particles on the top layer of an unpolished green compact.

117
particle C will be given by c’. If the particles, however, have a larger average distance
of separation (e.g., due to a lower solids loading in the compact), then the measured Dpc
value might be taken as a value closer to c. There is clearly a bias in Dpc measurement
as it depends on the amount of particle-particle overlap that occurs. Thus, it is not
surprising that the pH=9 green compact (with a much lower solids content of 49.4%)
has slightly higher Dpc values. It should be noted that this problem associated with Dpc
measurement arises because measurements were carried out on green compacts having
"rough" surfaces. This bias in Dpc measurement would be eliminated if a polished
section was used. To illustrate this point, the pH=4 and pH=9 samples were lightly
sintered10 to provide sufficient handling strength so that polished section could be
prepared. As shown in Figure 4.27, Dpc values for the two samples are now the same
(within experimental error). The Dpc values are also smaller for the polished samples
compared to the as-dried (unpolished) green compacts. This is because the measurements
are no longer biased toward larger size, as illustrated in Figure 4.28.
It should be emphasized that the effect of solids loading on Dpc values for the
pH=4 and pH=9 as-dried RCHP green compacts (see Figure 4.24 and Table 4.2) only
accounted for a portion of the difference in Dpc values of the corresponding samples that
were infiltrated with PE (see Figure 4.23 and Table 4.2). Thus, it appears that Dpc
values are still sensitive to changes in the state of particulate dispersion (i.e., due to the
residual polymer in intra-agglomerate regions). Based on the model experiments
10 Sintering was carried out at 1300°C/0.5 hr for pH=4 green compact and 1340°C/1
hr for pH=9 green compact. After slight sintering, the relatively density became
77.2 and 66.4%, respectively. No grain growth occurred during sintering [Yeh89].

NUMBER PERCENT NUMBER PERCENT
20
18 -
16 -
14 -
12 -
10 -
8 -
6 -
4 -
2 -
0 -
■V» T
0.20
AKP Alumina pH=4
Polished Surface
Mean Diameter = 0.75 /¿m
tl
II
% Z % Z Z Z
| | | v | i
mm
0.40
0.60
0.80
1.00
EQUIVALENT DIAMETER (Aim)
1.20
1.40
20
18 -
16 -
14 -
12 -
10 -
8
6
4 -
2 -
0
0.20
AKP Alumina pH=9
Polished Surface
Mean Diameter - 0.76 nm
i
mlmlmlm
iiniiiiiii
0.40
0.60
0.80
1
Â¥
1.00
EP EP Ep
1.20
1.40
EQUIVALENT DIAMETER (jim)
118
Figure 4.27 Histogram plots of Dpc distributions for polished AKP alumina compacts
prepared from pH=4 and pH=9 suspensions, respectively.

119
Polished
Surface
Dpc measured from an unpolished surface: A, B, C, and D.
Dpc measured from a polished surface: a, b, c, and d.
Figure 4.28 Comparison between Dpc values measured from an unpolished surface and
a polished surface.
described above, however, the effects of processing variables (e.g., mixing temperature)
on particulate dispersion are best evaluated using samples with constant solids loading.
Effect of mixing temperature on dispersion as assessed by OM
The state of particle dispersion assessed by QM for 50 vol% alumina/50 vol%
polyethylene mixtures prepared at 125-220°C was consistent with the rheological data

120
discussed in section 4.1.1.1. The SEM micrographs for 150 and 220°C samples with 30
min of plasma etching are shown in Figure 4.29; a greater amount of larger particles
(i.e., clusters of primary particles, or agglomerates, with residual polymer) is observed
in the 220°C sample. The Dpc histograms for samples mixed at 125-220°C are shown
in Figure 4.30. Data are also summarized in Table 4.3. The increase in average Dpc
value at higher mixing temperatures (i.e., above 150°C) indicates the presence of more
agglomerates. This is consistent with the increases in viscosities, moduli, and relaxation
times observed in Figures 4.1 and 4.6 as the mixing temperature increased. The Dpc
values are essentially the same (within experimental error) for the 125 and 150°C
samples. This is consistent with the similar rheological properties of these samples
(Figures 4.1, 4.4, and 4.6).
Table 4.3 Summary of Dpc results for 50 vol% alumina/50 vol% polyethylene
samples prepared at different temperatures.
Mixing variables
Dpc (¿un)
Percentage of
each category*
Temp
(°C)
Speed
(rpm)
Time
(min)
Average
value
Standard
deviation
Small
Medium
Large
125
200
30
0.41
0.15
46.5
44.7
8.8
150
200
30
0.43
0.16
40.6
47.7
11.7
175
200
30
0.48
0.18
29.0
51.6
19.4
220
200
30
0.52
0.19
24.0
51.4
24.6
* Small if Dpc <0.4 ¿un; medium if 0.4 ¿un< Dpc <0.6 ¿un; and large if Dpc >0.6
¿un.

121
Figure 4.29 SEM micrographs of plasma etched 50 vol% alumina/50 vol%
polyethylene samples prepared at 150 and 220°C, respectively.

NUMBER PERCENT NUMBER PERCENT
122
EQUIVALENT DIAMETER (¿zm)
EQUIVALENT DIAMETER (/im)
Figure 4.30 Histogram plots of Dpc distributions for 50 vol% alumina/50 vol%
polyethylene samples prepared at the temperatures indicated.

NUMBER PERCENT NUMBER PERCENT
123
EQUIVALENT DIAMETER (jim)
Figure 4.30 (Continued)

124
The Dpc histograms for 150 and 220°C samples shown in Figure 4.30 and Table
4.3 are actually average values taken from three sets of measurements. These
measurements were performed to assure the reproducibility of the QM measurements
within the same batch and between different batches. Each Dpc data set was based on
measurements of at least 600 particles from 10 SEM micrographs. Figures 4.31 and
4.32 show Dpc histograms for 150 and 220°C samples, respectively. The Dpc results
are also summarized in Table 4.4. The first two sets of data were collected from two
different samples from the same mixed batch. The third set of data was from a sample
taken from a different mixed batch. The differences in Dpc distributions were relatively
small. These results gave confidence that the differences in Dpc values between 150 and
220°C samples reflected true differences in the state of particulate dispersion.
Table 4.4 Summary of Dpc results for 50 vol% alumina/50 vol% polyethylene
samples prepared at 150 and 220°C, respectively, for reproducibility
examination.
Mixing
temp
(°C)
Mixing
batch
Dpc (/xm)
Percentage of
each category*
Average
value
Standard
deviation
Small
Medium
Large
1st batch
0.43
0.15
41.5
49.3
9.2
150
1st batch
0.45
0.16
36.3
50.3
13.4
2nd batch
0.42
0.17
44.4
43.4
12.2
Average values:
0.43
0.16
40.6
47.7
11.7
1st batch
0.52
0.18
23.8
49.5
26.7
220
1st batch
0.52
0.19
23.1
51.9
25.0
2nd batch
0.50
0.19
25.1
52.8
22.1
Average values:
0.52
0.19
24.0
51.4
24.6
* Small if Dpc <0.4 /xm; medium if 0.4 /xm< Dpc <0.6 /xm; and large if Dpc >0.6
/x m.

NUMBER PERCENT NUMBER PERCENT NUMBER PERCENT
125
I
III I
50 vol% A1203
Mixing Condition: 150°C, 200 rpm
First Mixing Batch
First Measurement
Up
nil
I III
Mean Diameter = 0.43 ¿un
, ,
)
•I | | P
HU
ÍÍÍÍ
IIII
lili
50 vol% A1203
Mixing Condition: 150°C, 200 rpm
First Mixing Batch
Second Measurement
Mean Diameter = 0.45 ¿un
Eft m ap-
T 1 1—r—r
ft p
m m
• lili lili
Til iliIUl
50 vol% AI203
Mixing Condition: 150°C, 200 rpm
Second Mixing Batch
First Measurement
Mean Diameter = 0.42 ¿un
I lié
0.4
1
0.6
^ -]—i
0.8
1.0
1.2
EQUIVALENT DIAMETER (¿un)
Figure 4.31 Histogram plots of Dpc distributions for 50 vol% alumina/50 vol%
polyethylene samples prepared at 150°C for reproducibility examination.

20
18
16
14
12
10
8
6
4
2
0
20
18
16
14
12
10
8
6
4
2
0
20
18
16
14
12
10
8
6
4
2
0
I
4.2
126
50 vol% AljOj
Mixing Condition: 220°C, 200 rpm
First Mixing Batch
-9-
P|
ilili
First Measurement
I
I
Mean Diameter = 0.52 ¿¿m
^ iff
-r f -p
H
50 volS ALO,
Mixing Condition: 220 C, 200 rpm
First Mixing Batch
Second Measurement
Mean Diameter â– =â–  0.52 /xm
fTT ? j
50 vol% A1203
Mixing Condition: 220°C, 200 rpm
Second Mixing Batch
0.2 0.4 0.6 0.8 1.0 1.2
EQUIVALENT DIAMETER (jim)
Histogram plots of Dpc distributions for 50 vol% alumina/50 vol%
polyethylene samples prepared at 220°C for reproducibility examination.

127
Rheological data reported earlier in this section (Figure 4.1-4.11) showed that the
mixing temperature had a similar effect on the state of dispersion for samples prepared
at various solids loading (38, 50 and 59 vol% alumina). Dpc measurements were
consistent with these results. Figures 4.33 and 4.34 show the Dpc histograms of 38 and
59 vol% alumina samples, respectively, which were mixed at both 150 and 220PC. Dpc
results for the 38, 50, and 59 vol% alumina samples are also summarized in Table 4.5.
As expected, the 220°C samples always had higher Dpc values than did the 150°C
samples at any given solids loading.
It was shown earlier in this section that polymer is not completely removed from
the sample surface during plasma etching. Incomplete polymer removal accounted for
the higher Dpc values reported in Figure 4.23 for plasma-etched alumina/polymer
samples compared to the Dpc values reported in Figure 4.24 for alumina samples which
Table 4.5 Summary of Dpc results for alumina/polyethylene samples at different
solids loading.
Mixing variables
Dpc (¿un)
Percentage of
each category*
Temp
(°C)
Solids loading
(vol%)
Average
value
Standard
deviation
Small
Medium
Large
150
38
0.44
0.16
40.0
46.0
14.0
150
50
0.43
0.16
40.6
47.7
11.7
150
59
0.46
0.18
32.2
50.8
17.0
220
38
0.52
0.20
22.9
53.9
23.2
220
50
0.52
0.19
24.0
51.4
24.6
220
59
0.54
0.19
20.0
52.3
27.7
* Small if Dpc <0.4 ¿un; medium if 0.4 ¿un< Dpc <0.6 ¿un; and large if Dpc >0.6
¿un.

NUMBER PERCENT NUMBER PERCENT
EQUIVALENT DIAMETER (/xm)
128
Figure 4.33 Histogram plots of Dpc distributions for 38 vol% alumina/62 vol%
polyethylene samples prepared at 150 and 220°C, respectively.

NUMBER PERCENT NUMBER PERCENT
20
18 -
16
14 -
12 -
10 -
8 -
6 -
4 -
2 -
0
0.00
59 vol% AlgOg Plasma Etched
Mixing Condition: 150 C, 200 rpm
Mean Diameter = 0.46 /zm
-t-M-
If II
lili
fill
!fl!
lili
lili
I
Eft P t?a.
0.20
0.40 0.60 0.80
EQUIVALENT DIAMETER (¿un)
1.00
■*—I
1.20
129
EQUIVALENT DIAMETER (¿un)
Figure 4.34 Histogram plots of Dpc distributions for plasma etched 59 vol%
alumina/41 vol% polyethylene samples prepared at 150 and 220°C,
respectively.

130
had no polymer. The samples prepared with 59 vol% alumina also provided an
opportunity to demonstrate that plasma etching does not completely remove polymer.
The solids concentration in these mixtures was high enough11 so that the bulk samples
retained their structural integrity upon removal of the polymer (i.e., by heat treatment
at elevated temperature). Thus, Dpc measurements could be made on 59 vol% alumina
samples after "complete" removal of the polymer. In the present investigation, the
polymer was removed by heating the samples in air at l°C/min to 1000°C12. Under
oxidizing condition, polyethylene will show essentially complete pyrolysis under this heat
treatment schedule13. Figure 4.36 shows the Dpc histograms for the 59 vol%
alumina/PE samples mixed at 150 and 220°C after thermal burnout of the polymer. Dpc
data is also summarized and compared with values for plasma-etched samples in Table
4.6. As expected, samples subjected to the 1000°C heat treatment have lower measured
Dpc values. The 150 and 220°C heat-treated samples both have Dpc values of 0.41 ^m,
i.e., compared to 0.46 and 0.54 ^m, respectively, for the plasma-etched samples.
Again, this provides clear evidence that plasma etching does not result in complete
removal of the polymer.
11 The solids loading is high enough to produce a sufficiently rigid, particulate
network structure that can withstand the internal stresses that develop when the
polymer decomposes and forms volatile products. In contrast, samples prepared with
50 vol% alumina disintegrate during heat treatment.
12 The heating rate was reduced to 0.1°C/min at 400-500°C range because most
polymer removal occurred at this temperature range. Slight sintering (i.e., neck
growth) occurs for the alumina compact at 1000°C, but densification is minimal.
13 TGA analysis (Figure 4.35) of PE AC-9 under more rapid heating conditions
(3°C/min) shows that polymer pyrolysis is complete by ~550°C.

131
Table 4.6 Summary of Dpc results for 59 vol% alumina/41 vol% polyethylene
samples treated by plasma etching and thermal burnout, respectively.
Mixing Polymer
temp removing
(°C) method
Dpc (/on)
Percentage of
each category
•
Average
value
Standard
deviation
Small
Medium
Large
150
plasma etching
0.46
0.18
32.2
50.8
17.0
220
plasma etching
0.54
0.19
20.0
52.3
27.7
150
thermal burnout
0.41
0.16
47.3
43.2
9.5
220
thermal burnout
0.41
0.15
45.5
43.7
10.8
* Small if Dpc <0.4 /on; medium if 0.4 /im< Dpc <0.6 /¿m; and large if Dpc >0.6
/tm.

NUMBER PERCENT NUMBER PERCENT
20
132
18 -
16 -
14 -
12 -
10 -
8 -
6 -
4
2 H
0
59 vol?» AlgOj Thermal Burnout
Mixing Condition: 150°C, 200 rpm
f III!
Ill II
11111
I i 111
%«11111
lililí
Él
Mean Diameter = 0.41 /im
Mill
¡I III
ill wi
T ? T
0.00 0.20 0.40 0.60 0.80 1.00
EQUIVALENT DIAMETER (/xm)
■>—»—r~
1.20
EQUIVALENT DIAMETER (/xm)
Figure 4.36 Histogram plots of Dpc distributions for thermally burnout 59 vol%
alumina/41 vol% polyethylene samples prepared at 150 and 220°C,
respectively.

133
The fact that the heat-treated 150 and 220°C samples with 59 vol% alumina have
the same Dpc value (Figure 4.36) is also an important observation. Recall that pH=4
and pH=9 alumina green compacts prepared without polymer showed small differences
in Dpc values (Figures 4.24 and 4.25). The latter observation was attributed to a
measuring bias which occurs in samples with rough surfaces14 and differences in solids
loadings. (Recall that the effective solids contents were 65 and 49% for the pH=4 and
pH=9 samples, respectively.) The result in Figure 4.36 indicates that the effect of this
measuring bias on Dpc measurements is essentially eliminated when the samples have the
same solids loading. Thus, Dpc measurements are especially accurate in evaluating the
effects of processing variables on particulate dispersion when comparisons are carried out
at constant solids loading.
It is interesting to directly compare the Dpc values for samples prepared with
different alumina loadings (Table 4.6). For a given mixing temperature (150 or 220°C),
the Dpc values are very similar for each solids loading, although it is noted that the
values for both 59 vol% alumina samples are slightly larger than the corresponding 38
and 50 vol% alumina samples. It is not possible, however, to draw the conclusion that
this reflects differences in the degree of particulate dispersion in the samples. Based on
results presented earlier in this section, it is clear that solids loading influences
experimental aspects of the Dpc measuring process. This is because the average
interparticle spacing depends on the solids content in the sample. The results described
in Figures 4.23-4.25 indicate that samples with lower solids content tend toward higher
14
Figure 4.26 shows that this bias does not arise in polished samples.

134
Dpc values because the largest dimensions of each particle become more accessible for
measurement when the average interparticle spacing is increased. In contrast, the results
in Figure 4.21 indicate that decreases in interparticle spacing inhibit polymer removing
during plasma etching. This, in turn, is expected to result in higher measured Dpc
values. It appears that these two effects are in competition for the samples under
investigation in this study. For the 38 and 50 vol% alumina samples, the Dpc values are
very similar, suggesting that the two effects cancel out each other. In contrast, the slight
increase in Dpc values for the 59 vol% samples could reflect inhibition of polymer
removal during plasma etching due to the smaller average interparticle spacing. Of
course, it is also possible that agglomerates were not broken down as effectively during
mixing these highly loaded samples.
4.1.1.3 Effects of rotor speed
In addition to optimizing mixing temperature, the mixer rotor speed must be high
enough to develop sufficient torque for agglomerate breakdown. For example, the
maximum torque generated during mixing 50 vol% alumina/50 vol% polyethylene at 10
rpm (Figure 4.37) was only about 1/3 of the peak value obtained when mixing at 200
rpm rotor speed15. The final torque value decreased to zero during mixing at 10 rpm.
It should be emphasized that this does not indicate improved particle dispersion
(compared to samples mixed at 200 rpm), but instead reflects the low shear rates (and,
hence, low torque values) that are developed during mixing at low rotor speeds. Figure
15 The peak torque value was shifted to a much longer time for the sample mixed at
10 rpm because the alumina powder was fed into mixer over a much longer period
time (i.e., 20 min compared to 4 min for a standard mixing condition).

TORQUE (g-m) TORQUE (g-m)
135
Figure 4.37 Plots of torque vs. mixing time for 50 vol% alumina/50 vol%
polyethylene samples prepared at the rotor speeds indicated.

136
4.38 shows that viscosity and modulus values were much higher for the sample mixed
at the low rotor speed. These results clearly show that samples mixed at 10 rpm were
poorly dispersed. The Dpc measurements (Figure 4.39) also show that agglomerates
were not broken down effectively with low mixing speed. These results are consistent
with other studies which show that high shear rate mixing can result in improved
particulate dispersion [Sha84] and shorter mixing time [Dan52, Cot84].
4.1.1.4 Effects of mixing time
Powder/polymer mixing operations are usually terminated when the mixing torque
reaches a stable value [AU83, Sain85]. It is usually assumed that the maximum extent
of agglomerate breakdown is achieved when the torque value remains constant with time.
This was confirmed in the present study by comparing samples mixed at 150pC/200 rpm
for 10 min and 30 min. Figure 4.40 shows that final torque value is approximately the
same for these two mixing experiments. The rheological properties for these samples
(Figures 4.41-4.43) are the same (within experimental error), indicating that the same
degree of particulate dispersion was achieved for the two mixing times. This is also
indicated from the Dpc measurements (Figure 4.44). Consequently, it may be concluded
that the maximum level of dispersion is achieved by the time the torque reaches a
constant value.
4.1.2 Multi-Segment Mixing Schedules
In addition to agglomerate breakdown and powder/fluid wetting, another
consideration in the dispersion process is stabilization of the particles against re¬
agglomeration (coagulation). Particles dispersed in a fluid have a tendency to coagulate

STORAGE MODULUS (Pa) DYNAMIC VISCOSITY (Pa s
137
FREQUENCY (rad/s)
(A)
(B)
Figure 4.38 Plots of (A) dynamic viscosity, (B) storage modulus, (C) loss modulus,
and (D) tangent delta vs. frequency for 50 vol% alumina/50 vol%
polyethylene samples prepared at the rotor speeds indicated.

TANGENT DELTA LOSS MODULUS (Pa)
Figure 4.38 (continued)

Mixing Conditions: 150°C, 10 rpm
O
CM
fc
=1
[
o
!
in
d
E
o>
E
aj
E
E
(0
Q
EE
c
YZZZL
Q)
V////////////77777Z
t'/////////////7777777s
V/////////////////////////////////A
V///////////////////////////77, -
vzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz-
vzzzzzzzzzzzzzzzzzzzzzzzz
vzzzzzzzzzzzzzz
Y777777/
o
o
o
*T#
o
o
CM
JLN30d3d d3airjnN
EQUIVALENT DIAMETER (pm)
Mixing Conditions: 150°C, 200 rpm
E
n.
co
O'
o
II
0)
E
5
b
c
nj
0)
2
o
- P
[
c-
E-o
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o CO
CM T-
nr
o
~r
CM
O
O
d
E
n
<
Q
<
>
ZD
o
LU
!N30d3d d30WflN
Figure 4.39 Histogram plots of Dpc distributions for 50 vol% alumina/50 vol%
polyethylene samples prepared at the rotor speeds indicated.

500 -
400-
300-
200-
100
0
500
400
300
200
100-
0 •
í 4.4'
140
50 vol% Al203
Mixing Conditions: 150°Cf 200 rpm,
L
30 min
V
i r
-i 1 1 1 r
50 vol% Al203
Mixing Conditions: 150°C, 200 rpm,
10 min
i | l | l | i i i i i ¡
5 10 15 20 25 30
TIME (min)
Plots of torque vs. mixing time for 50 vol% alumina/50 vol%
polyethylene samples prepared at the lengths of times indicated.

STORAGE MODULUS (Pa) DYNAMIC VISCOSITY (Pa-s
141
FREQUENCY (rad/s)
(A)
(B)
Figure 4.41 Plots of (A) dynamic viscosity, (B) storage modulus, (C) loss modulus,
and (D) tangent delta vs. frequency for 50 vol% alumina/50 vol%
polyethylene samples prepared at the lengths of times indicated.

TANGENT DELTA LOSS MODULUS (Pa)
J I I I 1—1 -l.i-lJ L —I I I I—I—JL—i J l 1 .1 1 .11 I 11 —<
0.1 1 10 100
FREQUENCY (rad/s)
Figure 4.41 (Continued)

SHEAR STRESS (Pa)
143
Figure 4.42 Plots of shear stress vs. shear rate for 50 vol% alumina/50 vol%
polyethylene samples prepared at the lengths of times indicated.

STRESS (Pa)
144
TIME (s)
Figure 4.43 Plots of residual stress vs. time for 50 vol% alumina/50 vol%
polyethylene samples prepared at the lengths of times indicated.

NUMBER PERCENT NUMBER PERCENT
EQUIVALENT DIAMETER (/¿m)
EQUIVALENT DIAMETER (/jm)
Figure 4.44 Histogram plots of Dpc distributions for 50 vol% alumina/50 vol%
polyethylene samples prepared at the lengths of times indicated.

146
due to attractive van der Walls forces. The rate of coagulation is inversely proportional
to the viscosity of the liquid phase. Thus, coagulation is not much of a concern in
particle/polymer melt systems prepared with high molecular weight polymers because the
melt viscosity tends to be very high during processing. In suspensions prepared with low
viscosity fluids (e.g., common solvents or low molecular weight polymer melts),
however, rapid coagulation may occur. This is especially true for submicrometer
particles because coagulation rates have a strong inverse dependence on particle size.
Strong interparticle repulsive forces would be needed to stabilize fine-particle suspensions
prepared with low viscosity fluids. In the present system of alumina particles in a
polyethylene melt, the most common interparticle repulsion mechanisms, such as
electrostatic and "steric" repulsion are not operative. Therefore, it is expected that
dynamic equilibrium between agglomerate breakdown and coagulation will be established
during mixing. The dynamic equilibrium established between agglomerate breakdown
and particle coagulation should be dependent upon mixing temperature and rotor speed.
Thus, changes in temperature or rotor speed during the mixing operation are expected
to alter the final state of particulate dispersion in the mixed sample. Several
experimental results are described below which support these concepts.
4.1.2.1 Mixing with change in temperature
As discussed in section 4.1.1.1, agglomerate breakdown is accelerated by mixing
at low temperature because higher fluid viscosity leads to higher operative shear forces.
Lower mixing temperature is also likely to reduce coagulation rate, again because of high
fluid viscosity. A consequence of lowering the coagulation rate is an improvement in the

147
overall state of particle dispersion. To demonstrate this point, an experiment was carried
out in which the temperature was varied during the mixing operation. A 50 vol%
alumina/50 vol% polyethylene sample was initially mixed at 150°C for 30 min (i.e.,
conditions giving relatively good dispersion based on rheology and QM measurements).
The temperature was subsequently increased to 220°C over a 5 min period and mixing
was continued at 220°C for an additional 10 min. Figures 4.45 (A) and (B) show a
comparison of the torque-mixing time curves and temperature profiles for the multi¬
segment (150 then 220°C) and single-segment (150°C) mixing operations, respectively.
The initial 30 min of the two mixing curves are very similar, which demonstrates that
experimental reproducibility is good. In the multi-segment mixing operation (150 then
220°C), the torque level dropped upon heating to 220°C. This decrease was a
consequence of the lower viscosity of the fluid phase (and the two-phase mixture).
Figure 4.46 shows plots of dynamic viscosities, moduli, and tangent delta vs. frequency
for samples prepared with the different mixing conditions. Stress relaxation behavior for
these samples is shown in Figure 4.47. It is evident that dispersion was poorer for the
samples prepared by the multi-segment mixing operation. The same conclusion can be
reached from Dpc measurement (Figure 4.48A and Table 4.7). Since the samples had
equivalent breakdown of agglomerates during the first 30 min, it is clear that re-
agglomeration (coagulation) occurred during the last 15 min of mixing in the sample
heated to a higher temperature 220°C.
Another experiment was carried out in which the sample was initially mixed at
220°C for 10 min, the temperature was reduced to 150°C over 5 min period, and then

500
250
148
50 vol% AljOj
Figure 4.45 Plots of torque and temperature vs. mixing time for 50 vol%
alumina/50 vol% polyethylene samples prepared by multi-segment
mixing schedules with change in temperature.
TEMPERATURE <*C) TEMPERATURE (*C) TEMPERATURE (*C)

STORAGE MODULUS (Pa) DYNAMIC VISCOSITY (Pa-s
149
(A)
(B)
Figure 4.46 Plots of (A) dynamic viscosity, (B) storage modulus, (C) loss modulus,
and (D) tangent delta vs. frequency for alumina/polyethylene samples
prepared by multi-segment mixing schedules with change in
temperature.

TANGENT DELTA LOSS MODULUS (Pa)
150
Figure 4.46 (Continued)

STRESS (Pa)
151
TIME (s)
Figure 4.47 Plots of residual stress vs. time for 50 vol% alumina/50 vol%
polyethylene samples prepared by multi-segment mixing schedules with
change in temperature.

NUMBER PERCENT NUMBER PERCENT
EQUIVALENT DIAMETER (Aim)
20
16 -
16 -
14 -
12 -
10 -
8 -
6 -
4 -
2 -
0 -
50 vol% A1203
Mixing Condition: 220°C, Then 150°C; 200 rpm
lili
lililí!
Mean Diameter = 0.50 fim
0.00
A
0.20
p p p p p p p
ÍÍÍÍÍÍÍ
111 f 111
ii
111
11
cpu C^S -Ej2 j—ape -ojaa-
(B)
0.40 0.60 0.80
EQUIVALENT DIAMETER (/im)
1.00
1.20
Figure 4.48 Histogram plots of Dpc distributions for 50 vol% alumina/50 vol%
polyethylene samples prepared by multi-segment mixing schedules with
change in temperature.

153
Table 4.7 Summary of Dpc results for 50 vol% alumina/50 vol% polyethylene
samples prepared by multi-segment mixing schedules.
Mixing variables+
Dpc (¿un)
Percentage of
each category*
Temp
(°C)
Speed
(rpm)
Time
(min)
Average
value
Standard
deviation
Small
Medium
Large
150-200
200
45
0.53
0.17
17.5
54.2
28.3
220-150
200
45
0.50
0.18
26.6
51.5
21.9
150
200-10
40
0.47
0.16
27.6
55.8
16.6
150
10-200
50
0.46
0.17
34.2
49.9
15.9
+ Check Table 3.2 and text for detail.
* Small if Dpc <0.4 ¿un; medium if 0.4 ¿un < Dpc <0.6 ¿un; and large if Dpc >0.6
¿un.
mixing was continued for an additional 30 min at 150°C. The torque-mixing time curve
and temperature profile for this experiment are shown in Figure 4.45C. The sample
prepared with this mixing schedule had high viscosity and modulus values (Figure 4.46),
indicating that poor dispersion was achieved. The stress relaxation measurements (Figure
4.47) led to the same conclusion. This was also shown by the high Dpc value (Figure
4.48B and Table 4.7) compared to the sample mixed only at 150°C. The torque-mixing
time curve in Figure 4.45C shows a very low maximum torque, indicating that
agglomerates were not broken down well during the initial mixing stage at 220°C. The
fact that dispersion remained poor after lowering the mixing temperature to 150°C
suggests that agglomerates cannot be broken down effectively once they are coated with
a polymer film.

154
4.1.2.2 Mixing with change in rotor speed
The use of sufficiently high mixing rotor speed is also important in minimizing
re-agglomeration (coagulation) during mixing. This was illustrated by an experiment in
which the rotor speed was varied during mixing. A 50 vol% alumina/50 vol%
polyethylene sample was initially mixed for 30 min at 150°C using a rotor speed of 200
rpm. The rotor speed was then decreased to 10 rpm and mixing was continued for 10
min. Figure 4.49A shows that the torque level dropped below the level of detection
when the rotor speed was decreased to 10 rpm. The occurrence of re-agglomeration
(coagulation) during this period was indicated by the increased values of viscosity,
moduli, and Dpc compared to those values in the sample mixed only at 200 rpm (Figures
4.50 and 4.51 A, and Table 4.7). It is interesting to note, however, that better dispersion
was achieved (as indicated by the rheological and microscopy data) compared to the
sample in which the re-agglomeration rate was accelerated by increasing the mixing
temperature to 220°C (see Figure 4.46). This again illustrates that using the low mixing
temperature is beneficial because the higher viscosity of the polymer matrix results in
lower coagulation rates.
Another experiment was carried out in which the sample was initially mixed at
10 rpm for 20 min, the rotor speed was then increased rapidly to 200 rpm, and mixing
was continued for 30 min. The alumina powder was fed into the mixer over the 20 min
time period at 10 rpm mixing. The torque-time curve is shown in Figure 4.49C.
Rheological characterization (Figure 4.50) and QM measurements (Figure 4.5IB and
Table 4.7) indicate that the sample had poor particulate dispersion compared to the

TORQUE (g.m) TORQUE (g.m) TORQUE (g.m)
155
Figure 4.49 Plots of torque and rotor speed vs. mixing time for 50 vol%
alumina/50 vol% polyethylene samples prepared by multi-segment
mixing schedules with change in rotor speed.
SPEED (rpm) SPEED (rpm) SPEED (rpm)

STORAGE MODULUS (Pa) DYNAMIC VISCOSITY (Pa s)
156
(A)
(B)
Figure 4.50 Plots of (A) dynamic viscosity, (B) storage modulus, (C) loss modulus,
and (D) tangent delta vs. frequency for alumina/polyethylene samples
prepared by multi-segment mixing schedules with change in rotor
speed.

TANGENT DELTA LOSS MODULUS (Pa)
Figure 4.50 (Continued)

NUMBER PERCENT NUMBER PERCENT
158
(A)
0.00 0.20 0.40 0.60 0.80 1.00 1.20
EQUIVALENT DIAMETER (/im)
EQUIVALENT DIAMETER (/zm)
Figure 4.51 Histogram plots of Dpc distributions for 50 vol% alumina/50 vol%
polyethylene samples prepared by multi-segment mixing schedules with
change in rotor speed.

159
sample mixed only at 200 rpm. The reason for this behavior may be similar to the case
in which the mixing temperature was decreased from 220 to 150^ (Figures 4.45 and
4.46), i.e., it becomes difficult to break down agglomerates once they are coated with
polymer films. It should be noted, however, that the torque peak generated upon
increasing the rotor speed from 10 to 200 rpm at 150^ (Figure 4.49C) was considerably
greater than observed in Figure 4.45C for the case in which the temperature was
decrease form 220 to 150°C. It is speculated that both (1) powder incorporation into the
polymer and (2) wetting of the particles by the polymer are less complete in the former
case because of the combination of low rotor speed (10 rpm) and low temperature
(150°C) during the initial mixing segment. Therefore, it seems reasonable that a higher
peak torque would be generated in this experiment when the rotor speed was increased
to 200 rpm. The higher torque peak generated also suggests that improved agglomerate
breakdown may have been achieved in this sample. This is confirmed by comparing the
rheological (Figure 4.46 vs. Figure 4.50) and QM (Figure 4.48B vs.Figure 4.51B) data
for the two samples.
4.2 Effects of Ceramic Powder Characteristics
The dispersion of ceramic particles in polymer melts is strongly influenced by the
powder characteristics. In this study, the alumina powder characteristics were modified
(prior to the ceramic/polymer mixing operation) by calcination at temperatures in the
range of 100-1000°C. The effect of powder calcination was evaluated for its effect on
the (1) physical and chemical characteristics of the powders, (2) torque response during
mixing, (3) rheological properties of the mixed batches, (4) state of dispersion as

160
assessed by quantitative microscopy, and (5) wettability of the powders by the polymer
melt. These results are discussed in section 4.2.1. During the course of this
investigation, it was determined that some mixed batches underwent changes in
rheological properties with time. The results of an investigation of this aging behavior
are presented in section 4.2.2. Unless noted otherwise, all experiments were carried out
on 50 vol% alumina/50 vol% polyethylene (PE A-C* 9) batches that were mixed for 30
min at 150°C with a rotor speed of 200 rpm.
4.2.1 Calcination Effect
Figure 4.52 shows the dynamic viscosity, modulus, and tangent delta values for
various calcined alumina/polyethylene mixtures. All samples prepared with calcined
alumina had higher viscosities and moduli compared to the sample prepared with
uncalcined alumina. The viscosity values also decreased to a greater extent over the
measured oscillation frequency range (0.1-100 rad/sec) for the calcined samples. In
addition, the storage and loss moduli showed less dependence upon oscillation frequency.
All of these observations indicated that the samples with calcined powders were not as
well dispersed as the sample prepared with the uncalcined powder. Figure 4.52 shows
that significant changes in rheological properties occurred even when powders were
calcined at temperatures as low as 100°C. The dynamic viscosity, storage modulus, and
loss modulus values measured at 0.1 rad/sec for the 100°C-calcined sample were all
about one order of magnitude higher than the values measured for the uncalcined sample.
Viscosity and modulus values were nearly the same for samples prepared with powders
calcined at 300 or 450°C. However, for samples prepared with powders calcined at

DYNAMIC VISCOSITY (Pa-s) DYNAMIC VISCOSITY (Pa-s
161
(A)
FREQUENCY (rad/s)
(B)
Figure 4.52 Plots of (A & B) dynamic viscosity, (C & D) storage modulus, (E) loss
modulus, and (F) tangent delta vs. frequency for alumina/polyethylene
samples prepared with uncalcined and calcined alumina powders.

STORAGE MODULUS (Pa) STORAGE MODULUS (Pa)
162
FREQUENCY (rad/s)
Figure 4.52 (Continued)

TANGENT DELTA LOSS MODULUS (Pa)
163
(E)
(F)
Figure 4.52 (Continued)

164
higher temperatures (600-1000°C), the viscosities and moduli measured at 0.1 rad/sec
increased again by approximately a half order of magnitude. The rheological properties
were very similar for the three samples (600, 800, and 1000°C powder calcination)
investigated. The influence of powder calcination on the state of dispersion in mixed
batches was confirmed by quantitative microscopy (QM) measurements (Table 4.8 and
Figure 4.53). The average Dpc values were 0.46-0.47 ¿un for low temperature calcined
samples (100-450°C) and 0.50-0.51 ¿un for high temperature calcined samples (600-
1000°C). All of the samples prepared with calcined powders (lOO-KXXFC) had higher
Dpc values than that obtained for samples prepared with uncalcined powder (0.43 ¿un),
indicating that there were more agglomerates in the former mixtures. Thus, the QM
measurements were quite consistent with the rheological data in Figure 4.52.
Table 4.8 Summary of Dpc results for 50% alumina/50 vol% polyethylene
samples prepared with uncalcined and calcined alumina powders.
Temperature
of alumina
calcination
(°C)
Dpc (¿un)
Percentage of
each category*
average
value
standard
deviation
small
medium
large
without treatment
0.43
0.16
40.6
47.7
11.7
100
0.47
0.16
30.6
53.7
15.7
300
0.47
0.17
32.0
50.1
17.9
450
0.46
0.17
35.6
46.9
17.5
600
0.50
0.17
25.1
56.7
18.2
800
0.50
0.17
24.7
56.5
18.8
1000
0.51
0.18
23.7
52.1
24.2
’ Small if Dpc <0.4 ¿un; medium if 0.4 ¿im< Dpc <0.6 ¿un; and large if Dpc >0.6
¿un.

NUMBER PERCENT NUMBER PERCENT
165
EQUIVALENT DIAMETER (/¿m)
EQUIVALENT DIAMETER (/an)
Figure 4.53 Histogram plots of Dpc distributions for 50 vol% alumina/50 vol%
polyethylene samples prepared with uncalcined and calcined alumina
powders.

NUMBER PERCENT NUMBER PERCENT
166
EQUIVALENT DIAMETER (/xm)
Figure 4.53 (Continued)

NUMBER PERCENT NUMBER PERCENT
167
Figure 4.53 (Continued)

168
H
Z.
w
o
CK
w
cl
VC
w
m
a
20
18
16 -
14 -
12 -
10
8 -
6 -
4 -
2 -
0
50 volX AlgOjj 1000 C Calcined
Mixing Condition: 150°C, 200 rpm
â– 
Mean Diameter = 0.51 /¿m
m
i 1 r*
0.00 0.20
lililii
0.40 0.60 0.80
EQUIVALENT DIAMETER (/an)
1.00
1.20
Figure 4.53 (Continued)
The torque response during mixing and the polymer/powder wetting behavior
were monitored as part of an effort to understand the mechanism by which powder
calcination influenced the state of dispersion in the mixed batches. The torque rheometry
results are shown in Figure 4.54 for samples prepared with uncalcined and calcined (100-
1000°C) alumina powders. In addition, some important torque values are summarized
in Table 4.9. The peak torque value during mixing represents the maximum force
developed as the powder is incorporated into the polymer melt (and as agglomerates

TORQUE (g-m) TORQUE (g-m)
500
169
400-
50vol%AI2O3 Uncalclned
Mixing Conditions: 150°C,200 rpm
Figure 4.54 Plots of torque vs. mixing time for 50 vol% alumina/50 vol%
polyethylene samples prepared with uncalcined and calcined alumina
powders.

TORQUE (g-m) TORQUE (g-m)
500
400 -
300-
50vol% Al2 03 300°C Calcined
Mixing Conditions: 150°C, 200 rpm
200-
Figure 4.54 (Continued)

TORQUE (g-m)
500
50vol% Al2 03 600°C Calcined
Mixing Conditions: 150°C, 200 rpm
Figure 4.54 (Continued)

TORQUE (g-m)
Figure 4.54 (Continued)

173
Table 4.9 Summary of important torque values for mixing 50 vol% alumina/50
vol% polyethylene samples.
Alumina calcination
temperature (°C)
Peak torque
(g-m)
Torque at 15 min
(g-m)
Final torque
(g-m)
without treatment
370
80
70
100
170
100
90
300
160
100
80
450
250
100
90
600
290
160
160
800
350
160
130
1000
350
160
110
begin to break down during powder incorporation). The final torque value is
representative of the mixture’s viscosity and the state of particulate dispersion during
mixing. It should be emphasized, however, that measurements of the final torque value
during mixing may not be very sensitive to the state of dispersion. The experiments in
this study were carried out using a high rotor speed (200 rpm) which means that high
shear rates were generated in the mixer. Therefore, unless the agglomerates in a
calcined powder batch are very strong, a substantial portion of them will be broken down
under the high shear stresses and the final torque values recorded during the mixing
operation may not show significant variations for different powder samples.
For the samples prepared with uncalcined alumina, the peak torque is relatively
high, while the final torque is relatively low (Figure 4.54). As discussed in section 4.1,
these results (in conjunction with the rheological and QM data) indicate that sufficient
shear force is generated during mixing to effectively break down agglomerates and
achieve good dispersion. In contrast, the 100°C- and 300°C-calcined samples show much

174
lower torque peaks, indicating that less shear force is generated during powder
incorporation and agglomerate breakdown. The final torque values are slightly higher
which is consistent with the poorer dispersion compared to the uncalcined sample
(Figures 4.52 and 4.53). The 450°C-calcined sample showed an increase in the torque
peak, but the final torque value was similar to the 100 and 300°C-calcined samples. The
fact that the final torque values for the 100-450°C calcined samples are only slightly
higher than the uncalcined sample suggests that the agglomerates in these powders are
not particularly strong. (This is also suggested by the low peak torques observed for
these samples.) The torque rheometry results reinforce the point that differences in state
of dispersion are not readily detected from final torque values. Instead, particulate
dispersion is more easily assessed at low shear rates, i.e., under conditions where the
weaker agglomerates tend to remain unbroken. This is clearly indicated by reviewing
the viscosity and moduli data in Figure 4.52. The largest differences in rheological
properties between the uncalcined and calcined samples are observed at the lowest
oscillation frequencies, i.e., when the deformation stresses are too low to substantially
break down the particulate network structure in the powder/polymer mixtures.
The peak torque and final torque values are both increased in samples prepared
with powders calcined at higher temperatures (600-1000°C). The peak torque values
were close to that observed for the uncalcined samples, but the final torque values were
considerably higher. The latter observation is consistent with the much poorer dispersion
in the 600-1000°C calcined samples, as indicated by rheological and QM data (Figures
4.52 and 4.53). The fact that both peak and final torque values are high suggests that

175
powders calcined at these high temperatures have relatively large, strong agglomerates
which resist breakdown in the mixing operation. Indeed, it is well known that fine
alumina particles can undergo neck growth (i.e., sintering) at relatively low temperatures
(i.e., compared to temperatures used to achieve bulk densification of powder compacts)
[CobR84, CobW80, Nic65]. A variety of evidence will be presented later in this section
which shows that very hard agglomerates (i.e., aggregates) do indeed form in powders
calcined at temperatures in the range 600-1000°C.
The effect of powder calcination on wetting behavior was investigated by two
techniques: polymer penetration and sessile drop. Figure 4.55 shows the relative contact
angles (i.e., the contact angle for the uncalcined powder divided by the contact angle for
the calcined powder) as a function of calcination temperature, respectively. The relative
contact angles were determined by monitoring the rate of polymer (PE A-C 9)
penetration (at 150°C) into (porous) alumina powder compacts (Figure 4.56). Figure
4.55 shows that polymer/powder wetting is the same for the uncalcined and 300°C-
calcined samples, but then improves (i.e., the contact angle decreases) for samples
prepared at higher calcination temperatures (450 and 600°C). It should be noted that the
polymer penetration method can only be used to compare the wetting behavior of
different samples if the powder compact porosity characteristics (i.e., pore volume and
pore size distribution) are the same. Figure 4.57 shows mercury porosimetry results
which confirm that the uncalcined and 100-600°C powder compacts have very similar
porosity characteristics. In contrast, compacts prepared with the 800 and 1000°C
powders have larger pore volume and larger pore sizes. (As discussed in more detail

CONTACT ANGLE RATIO
176
Figure 4.55 Plot of the contact angle ratio vs. calcination temperature for polyethylene
melt (PE A-C 9) on uncalcined and calcined alumina powders. (Measured
by polymer penetration method).

PENETRATION DEPTH X 100 (MM)
177
TIME (SEC)
Figure 4.56 Plots of penetration depth vs. time for polyethylene melts into calcined
alumina powder compacts.

Specific Volume Frequency (cm /g nm) x 10
300 100 70 50 30 10
Radius (nm)
Figure 4.57 Mercury porosimetry data for dry pressed powder compacts prepared
from uncalcined and calcined alumina powders.

Normalized Volume (cc/g)
179
Radius (nm)
Figure 4.57 (Continued)

180
below, this is due the increased amount of hard agglomerates in these powders.) Thus,
the 800- and 1000°C-calcined powder compacts were not used for assessing wetting
behavior by the polymer penetration method.
Figure 4.58 shows the results of sessile drop measurements of contact angle as
a function time for samples prepared with uncalcined and calcined powders. In these
experiments, the contact angles were measured for molten polymer deposited on top of
alumina powder compacts. The alumina powder compacts were identical to those used
in polymer penetration experiments (Figures 4.55 and 4.56), but a different polymer (PE
Sclair 2915) was used in order to minimize penetration of the sessile drops into the
powder compacts. This polymer had considerably higher molecular weight (Mn =
14,000) and viscosity (r] = 2.00 Pa-s at 180°C) compared to the PE A-C 9 (M„ = 2,100
and 77 = 0.65 Pa-s at 125°C). Despite the differences in the polymer used and the
measuring temperature, the results shown in Figure 4.58 are very similar to the polymer
penetration results in Figure 4.55. Once again, the same wetting behavior is observed
for the uncalcined and 300°C-calcined samples. In addition, improved wetting (i.e.,
lower contact angles) is again observed as the powder calcination temperature increases
above 300°C.
The results in Figures 4.55 and 4.58 clearly indicate that the relatively poor
dispersion achieved in samples prepared with calcined powders (Figures 4.52 and 4.53)
cannot be attributed to poor wetting behavior. Instead, it is believed that the differences
in dispersion can be attributed to changes in powder agglomeration that occur during
calcination. For example, it was noted earlier that the increased pore volume and pore

CONTACT ANGLE (DEGREE)
181
Figure 4.58 Plots of the contact angle vs. time for polyethylene melts (Sclair 2915)
on uncalcined and calcined alumina powder compacts.

182
size (Figure 4.57) and the increased torque peaks (Figure 4.54) for 800- and 1000°C-
calcined samples suggest that hard agglomerates (aggregates) form during high
temperature powder calcination. Additional evidence for this will be given below.
Furthermore, it will be demonstrated that calcination at all temperatures (even as low as
100°C) affects the particle-particle bonding characteristics in the alumina powders. The
experimental results are organized and discussed below according to powder temperature
calcination.
100-450°C calcination
As noted above, the torque peaks for the samples prepared with (100-450PC)-
calcined powders were relatively low, indicating that the maximum shear stress generated
during powder incorporation and agglomerate breakdown was lower than in the case of
the sample prepared with uncalcined powder. The rheological and QM data (Figures
4.52 and 4.53) indicate that this reduction in peak stresses results in less complete
breakdown of the powder agglomerates in the (100-450°C)-calcined powders. The
question arises as to why the peak torques are lower. It is also unclear why the peak
torques begin to increase again for samples mixed with powders calcined above 300°C.
A reasonable hypothesis is that these effects occur because of differences in the nature
of the agglomerates in the powder. While the precise differences in the agglomerates of
the various powders could not be identified in this study, it will be demonstrated below
that heat treatment, even at low temperatures of 100-450°C, does affect the
physicochemical characteristics of the powders.

183
As a starting point for discussion, it is noted that fine (e.g., submicrometer)
powders usually have low packing densities due to the presence of multiple generations
of agglomerates (i.e., powders have hierarchical clustering). The first generation is a
cluster of primary particles or hard agglomerates (formed during powder synthesis),
while the second generation is a cluster of these clusters. Successive generation clusters,
if they exist, would consist of clusters of the preceding generation clusters. A schematic
illustration of a powder with multiple generations of agglomerates is shown in Figure
4.59. Note that the overall packing density of the powder decreases as the number of
generations increases. The size of the largest agglomerates that form depends largely
upon the interparticle forces that are operative. The early generations of clusters can be
held together by relatively weak forces, e.g., van der Waals bonding. Stronger bonding
(e.g., capillary forces, polymer bridging, etc.) is required to hold together higher
generations because the strength of the low-density agglomerates decreases and the forces
acting to break the agglomerates (i.e., inertial forces) increases as the size of the
agglomerates increases. In the present study, the first generation clusters are composed
of a mixture of primary particles and small aggregates. (Commercial alumina powders
invariably have a significant percentage of aggregates because the synthesis process
requires a high temperature (> 1000°C) processing step in order to produce the desired
alpha polymorph. The RCHP-DBM alumina used in the present study is milled (ground)
extensively by the manufacturer, but the powder still contains a substantial amount of
aggregates. Examples of aggregates are shown in Figure 4.60.) Two types of
interparticle forces are usually operative in creating both first generation and higher

184
Figure 4.59 Schematic illustration of
agglomerates.
a powder with multiple generations of

185
Figure 4.60 SEM micrographs of hard agglomerates in as-received alumina
powders.

186
generation clusters in an alumina powder: van der Waals and capillary. Van der Waals
forces are ubiquitous, while the occurrence of capillary forces requires that some liquid
(e.g., adsorbed water) be present on the particle surfaces. It is well-known that fine-size
(high specific surface area) oxide powders usually have a significant concentration of
water and/or hydroxyl groups on the surface (i.e., unless the powders are synthesized (or
treated) at high temperatures and subsequently stored in a water-free environment). For
colloidal particles, capillary forces due to adsorbed moisture are generally much stronger
than van der Waals forces.
The above considerations suggest a reason for the difference in mixing and
dispersion behavior for 100-450°C-calcined samples compared to uncalcined samples.
The uncalcined powder presumably has more adsorbed moisture and, hence, capillary
forces should be a more important in forming agglomerates in this powder. Since
capillary forces are stronger than van der Waals forces, the uncalcined powder should
have a greater amount of large, low-density agglomerates (i.e., multiple generation
agglomerates). This type of powder should be more difficult to initially incorporate in
the polymer melt. In fact, this is suggested by the high peak torque that develops
initially in the mixture prepared with the uncalcined powder. The high peak torque is
indicative of a high initial viscosity of the mixture. It is well-recognized that suspensions
containing agglomerates have higher viscosity than well-dispersed suspensions because
of the higher "effective" solids concentration in the former suspensions. Similarly,
suspensions which initially contain agglomerates of low particle packing density (i.e.,
higher pore volume) will have higher effective solids concentrations (and, hence, higher

187
viscosities) compared to suspensions prepared with agglomerates of higher particle
packing density. Therefore, it is suggested that a higher initial torque is developed in
the mix with the uncalcined powder because of larger, low-density agglomerates held
together by capillary forces. In turn, it is also suggested that the high stresses generated
during mixing this powder are more effective in eventually breaking down the
agglomerates more completely.
If the hypothesis presented above is correct, the amount of adsorbed moisture in
the uncalcined alumina powder should decrease upon heat treatment to 100°C. For
powders having specific surface areas greater than a few m2/g (e.g., the alumina used in
this study), the adsorbed water and hydroxyl concentrations are usually large enough to
be readily detected by TG analysis or by batch measurements of weight losses after heat
treatment at specific temperatures. The latter type of experiment was carried out on
alumina powder calcined for four hours at temperatures in the range 100-1000°C (Figure
4.61). The sample calcined at 100°C lost ~0.3 wt%, presumably due to the elimination
of adsorbed molecular water. Alumina powder was analyzed at 100°C by diffuse
reflectance Fourier transform infrared spectroscopy (FTIR) in an attempt to confirm the
loss of water. Figure 4.62 shows spectra for the alumina powder at room temperature
(i.e., uncalcined) and after heating in 15 min to 100°C (0 min spectra) and holding at this
temperature for times up to 4 hr. The broad absorption band in the range — 3050-3750
cm'1 is due to O-H bond stretching vibrations in molecular water and in hydroxyl groups
on the alumina powder surface (Al-OH). The intensity of the small shoulder in the
region of -3200-3400 cm'1 was slightly reduced upon heating to 100PC (0 min).

WEIGHT LOSS (X)
188
CALCINATION TEMPERATURE (°C)
Figure 4.61 Plot of weight loss vs. calcination temperature for alumina powders.

ñBSGRBBNCE
189
Figure 4.62 FTIR spectra for alumina powders heated at 100°C for the lengths of
times indicated.

190
However, there is little difference in the spectra at longer times. Apparently, the powder
surface still retains a significant amount of hydrogen-bonded molecular water at 100°C.
(As shown in Figure 4.61, the 100°C-calcined powder still loses an additional 0.25 wt%
after heat treatment to higher temperatures.) Further analysis by FTTR spectroscopy
clearly shows that there is a continued loss of molecular water above KXPC. Figure 4.63
shows spectra collected during heat treatment from room temperature to 600°C at a
heating rate of 5°C/min. There is a substantial reduction in the broad absorption band
at temperatures between 200 and 300°C. The 300°C spectra also shows a shoulder at
~ 3750 cm'1 which is associated with the development of isolated hydroxyl groups on the
alumina surface. There is continued loss of isolated and hydrogen-bonded hydroxyl
groups as the temperature increases. These results are consistent with previous studies
reported by other researchers using gravimetric and IR measurements [Cor55, DeBH62,
DeBF63, Fred54, Hai67, Per65a, PerH60]. If the adsorbed water is uniformly
distributed as a dense film on the alumina powder surfaces, the 0.3 wt% loss observed
upon heat treatment of the uncalcined powder to 100°C is equivalent to the removal of
— 4 layers of water molecules. Thus, a significant reduction in interparticle capillary
forces is certainly possible. However, this does not prove that the uncalcined powder
has large, low-density agglomerates. Efforts to characterize the agglomerates in the
uncalcined and calcined powders are discussed below.
In one experiment, powders were first added to a small vial which contained
pH=4 water (in order to develop high positive charge on the particle surfaces), the vial
was shaken gently, and the particle size distribution was measured by the centrifugal

ABSORBANCE
191
Figure 4.63 FTIR spectra for alumina powders heated to the temperatures indicated.

CUMULATIVE VOLUME PERCENT
192
photosedimentation method. By avoiding high shear during the preparation of the
suspension, it was hoped that the measurement would be representative of the large
agglomerates in the powder. The results, shown in Figure 4.64, are actually contrary
to what might be expected from the above discussion; the measured particle (i.e.,
agglomerate) size distributions shift to larger sizes with increasing calcination
temperature. However, the particles measured in Figure 4.64 are not necessarily
representative of the highest generation agglomerates in the powders. This is suggested
because the median particle size for the coarsest powder in Figure 4.64 (i.e., 450°C-
Figure 4.64 Centrifugal photosedimentation data for uncalcined and calcined
alumina powders without sonication.

193
calcined) is less than twice the median particle size obtained in well-sonicated suspensions
of the as-received (uncalcined) powder. It is likely that even the process of introducing
the powder into water with gentle shaking (i.e., in order to prepare a suitably
homogenous suspensions for particle size analysis) results in breakdown of the largest,
lowest-density agglomerates.
Although the results in Figure 4.64 do not provide insight into the specific cause
of the lower peak torque values generated during mixing the 100-450°C samples, they
do suggest that water and hydroxyl group removal during calcination influences the
response of the powder agglomerates to applied stresses. Several additional experiments
were carried out which confirm that some relatively strong agglomerates do form in the
300 and 450°C powders. Figure 4.65A shows particle size distributions that were
measured after subjecting the suspensions in Figure 4.64 to 15 sec of ultrasonication.
The distributions measured for all of the sonicated suspensions are shifted to smaller sizes
(i.e., relative to the corresponding distributions obtained without sonication of the
suspensions), indicating that some breakdown of agglomerates occurs in all samples.
However, the 300- and 450°C-calcined powders still show larger sizes than the
uncalcined and 100°C-calcined powders. In another experiment, microhardness
measurements were made on powder compacts (prepared with the uncalcined powder)
which were calcined at temperatures in the range 100-1000°C. Figure 4.66 shows that
the Vickers hardness of the compacts increases with increasing calcination temperature
above 100°C. The hardness of the 300 and 450°C samples increases -56% and
— 267%, respectively, compared to the uncalcined sample.

CUMULATIVE VOLUME PERCENT CUMULATIVE VOLUME PERCENT
194
(B)
Figure 4.65 Centrifugal photosedimentation data for uncalcined and calcined alumina
powders with (A) 15 sec and (B) 30 min of sonication.

195
Figure 4.66 Plot of Vickers hardness vs. calcination temperature for alumina green
compacts.
The observations in Figures 4.65 and 4.66 indicate that some stronger bonds form
between the alumina particles during calcination at 300 and 450°C. A possible bonding
mechanism is condensation reactions between isolated hydroxyl groups on different
alumina particles, thereby creating interparticle aluminoxane bonds:
Al-OH + HO-A1 - Al-O-Al (4.1)
This reaction is favorable for the 300 and 450°C calcined powders because (i) most of
the adsorbed water has been removed from the surface and (ii) isolated Al-OH groups

196
(i.e., instead of hydroxyl groups that are hydrogen-bonded to nearby neighbors) are
available. (These surface characteristics were evident from the FTIR spectra in Figure
4.63.)
Another possible interparticle bonding mechanism is neck growth via surface
diffusion. As discussed below, however, model calculations indicate that very little neck
growth can occur at temperatures <450°C. In addition, if neck growth occurred, a
decrease in powder specific surface area would be expected. However, gas adsorption
measurements show that the specific surface area is the same, within experimental error,
for the uncalcined and 450°C-calcined powders.
The microhardness data in Figure 4.66 suggest that the more extensive
interparticle bonding (i.e., via reaction 1) occurs when the calcination temperature is
increased from 300 to 450°C. Since powders are calcined in a "loose-stack" (i.e.,
uncompacted) arrangement, the 450°C powder is likely to have more large, low-density
agglomerates. This may explain why the peak torque during mixing (Figure 4.54) starts
to increases again as the calcination temperature is increased above the 100-300°C range.
The higher stresses generated during mixing apparently can break down some of the
stronger, larger agglomerates formed during calcination, but are not sufficient to achieve
as good dispersion as in the sample prepared with uncalcined powder. The agglomerates
formed by calcination at 450°C do not appear to be exceptionally strong, e.g., compared
to aggregates that are formed by sintering. This is indicated by measurements of the
particle size distribution (by the centrifugal photosedimentation method) after 30 min of
sonication. Figure 4.65 (B) shows that the uncalcined and (100-450pC)-calcined powders

197
all have virtually identical size distributions when suspensions are sonicated for 30 min.
(It is also noted that all of the distributions are shifted to smaller sizes compared to the
corresponding distributions in Figure 4.64, indicating that breakdown of agglomerates
occurs in all samples. However, the longer sonication time allows even the stronger
agglomerates, formed during calcination at 300 or 450°C, to be broken down.)
600°C Calcination
The rheological and QM data (Figures 4.52 and 4.53) indicate that there is a
significant change in dispersion for samples prepared with powders calcined at 600°C (or
higher). As suggested earlier in this section, it is believed that agglomerates formed
during calcination at 600°C (and higher temperatures) are stronger and larger than
agglomerates formed during calcination at lower temperatures. Most of these
agglomerates cannot be broken down during the mixing operation. This would account
not only for the poor dispersion indicated by Figures 4.52 and 4.53, but also for the high
peak and final torque values observed in these samples. Other results which clearly
demonstrate that hard aggregates form during calcination at 600°C are described below.
1. In Figure 4.65 (B), it was demonstrated that long sonication time (30 min) was
sufficient to break down the "strong" agglomerates in the 300- and 450°C-calcined
powders. Thus, the particle size distributions measured for these samples were the
same as for the uncalcined powder. In contrast, measurement of the óOÍTC-calcined
sample after 30 min sonication showed substantially larger particle sizes. Extended
sonication did result in some agglomerate breakdown (i.e., compared to the
distribution measured on a 600°C-calcined sample sonicated for 15 sec.), but it is

198
clear that the powder contains some very strong, or "hard," agglomerates (i.e.,
aggregates).
2. Figure 4.66 shows that the hardness of the powder compacts continues to increase
substantially as the heat treatment temperature increases. The hardness of the 600°C
sample is almost an order of magnitude higher than the uncalcined sample and more
than double that of the 450°C sample.
The FTIR results in Figure 4.63 show that dehydroxylation of the alumina powder
surface continues as the temperature is increased to 600°C. (Both the broad absorption
in the range ~ 3300-3650 cm'1 and the shoulder at ~ 3750 cm'1 diminish between 400-
600°C. It was noted earlier that the latter absorption, which is observed most clearly at
300 and 400°C, is due to the presence of isolated hydroxyl groups [Hai67, Per65a,
PerH60]. Thus, it is possible that continued strengthening of the agglomerates occurs
by the condensation mechanism given in reaction 1. However, the substantial increase
in agglomerate strength for the 600°C-calcined powder suggests that sintering has been
activated at the higher processing temperature. It is well-known that the temperatures
at which ceramic particles undergo "neck growth" (interparticle bonding via atomic
diffusion) can be considerably lower than the temperatures required for substantial bulk
densification of macroscopic powder compacts. In many cases, neck growth at low
temperatures occurs by surface diffusion. In general, neck growth can also occur by a
variety of other mechanisms including viscous flow, grain boundary diffusion, volume
diffusion, and evaporation-condensation. Viscous flow is important for amorphous
materials, while evaporation-condensation requires relatively high vapor pressures at the

199
sintering temperature. Hence, both of these mechanisms are unimportant for neck
growth of alpha alumina. Grain boundary and volume diffusion are important
mechanisms in densification of alumina powder compacts, but they have a considerably
higher activation energy than surface diffusion. Thus, at low temperatures, surface
diffusion is a more likely mechanism for neck growth.
Coblenz evaluated various models for the neck growth kinetics of alumina via the
surface diffusion path [CobR84, CobW80, Nic65]. Two applicable equations are given
below. The relevant neck geometry is shown in Figure 4.67.
25
¿ Ds Q r
R T a4
(4.2)
225
• (
3 Ds n T
RT a4
(4-3)
where: x
a
8
D.
0
Tsv
R
T
t
particle-particle neck radius
particle radius
thickness of region for surface diffusion
surface diffusion coefficient
molar volume
specific surface energy
gas constant
sintering temperature
sintering time
Coblenz found that Eq. 4.2 fit better for the case when 0.05 < x/a < 0.3, while the
other equation Eq. 4.3 was more applicable for the case of smaller neck sizes. These
equations were applied in the present study to determine the calcination temperatures at

200
Figure 4.67 Schematic illustration of particle necking (neck size = 2x and particle
radius = a) formed by surface diffusion mechanism.
which significant neck growth would be expected. The values for the gas constant R,
molar volume of alumina (25.6 cm3/g-mole), and calcination temperature T and time t
were readily plugged into the equations. The values for a, 7,v, 5, and D, were less
certain, as discussed below:
1. The alumina powders have a range of particle sizes. For simplicity, calculations
were made using the average particle size for the uncalcined alumina as determined
by the X-ray sedimentation and centrifugal photosedimentation techniques. (The
median Stokes diameter «0.4 /xm, so a «0.2 /im.)
2. The surface energy is a function of temperature [Kin76, Tas84]. For polycrystalline
alumina, the specific surface energy has been experimentally measured as 0.9 Jnr2
at 1850°C and theoretically estimated at 2.6 J-m'2 at absolute zero degree [Tas84].
This information was used to calculate by linear interpolation the specific surface
energies in the range of 450-1000pC. The values are listed in Table 4.10.
3. The most difficult parameters to estimate accurately are 5 and D,. Surface diffusion
data is generally reported as the product (5 DJ. Although data is available for

201
Table 4.10 Calculated alumina neck size formed by surface diffusion mechanism at
different temperatures.
Temperature
(°C)
Surface tension
7 (J/cm2)
Surface diffusivity
5-D, (cmVsec)
x/a from
Eq. 4.2
x/a from
Eq. 4.3
450
2.0 x 104
1 x 10-31
0.008
0.005
600
1.8 x 104
5 x 10-27
0.043
0.036
800
1.7 x 104
1 x 10"23
0.15
0.16
1000
1.6 x 104
1 x IQ'21
0.31
0.38
alumina, there are two major problems. First, 5-D, values at any given temperature
typically vary by about 2-3 orders of magnitude depending on the experimental
method used, type of sample (e.g., polycrystal or single crystal), impurities in the
alumina, etc. For example, 5-D, has been reported between 1044 and 1042 cm3-s4
at 1800°C and between 5 x 1049 and 1046 ernes'1 at 1200°C [Dyn80]. For the
present study, the lower-bound values reported by Dynys were used in calculations
in order to estimate the minimum neck size formed during calcination. Second,
surface diffusitivies for alumina have only been reported at relatively high
temperatures 1000-1900°C [Dyn80]. Values for 5-D, at low temperature can be
obtained by extrapolation, but this requires an accurate activation energy value.
Furthermore, the activation energy is strictly valid only over the temperature range
in which the data was collected. The activation energy may have a different value
at substantially lower temperatures. Despite these concerns, 5-D, values were
estimated (see Table 4.10) using an activation energy of «68 kcal/mole [Dyn80],

202
Table 4.10 lists the relative neck growth (x/a) values that were calculated from Eqs. 4.2
and 4.3 for various calcination temperatures (for 4 hours). The two models gave similar
results. Despite assuming a relatively low 5-D, value, the calculated neck size for the
600°C powder is still -4% of the particle radius (x/a = 0.04). Thus, the calculations
support the hypothesis that hard agglomerate (aggregate) formation occurs in 600°C-
calcined powder via surface diffusion. It is also evident from Table 4.10 that substantial
neck growth by diffusion is expected at the higher calcination temperatures (800 and
1000°C), but not at 450°C. (Substantial neck growth by bulk and/or grain boundary
diffusion may also occur at the higher calcination temperatures.)
In practice, the growth of necks between particles can be detected by a decrease
in the measured external surface area of the powder or powder compact. Table 4.11 lists
specific surface areas (determined by nitrogen gas adsorption) for uncalcined and calcined
powders. The 600°C-calcined powder shows an ~ 10% decrease in specific surface area
compared to the uncalcined powder, confirming that neck growth does indeed occur. As
expected, even larger decreases are observed at higher calcination temperatures.
Table 4.11 Specific surface area of uncalcined and calcined alumina powders.
Calcination temperature
(°C)
Specific surface area
(m2/g)
Uncalcined
7.7
450
7.6
600
6.9
800
5.9
1000
4.2

203
800 and 1000°C Calcination
The effect of high temperature (> 600°C) powder calcination on subsequent
dispersion behavior can be interpreted in a relatively straightforward manner. The poor
dispersion (Figures 4.52 and 4.53) clearly arises as a result of the formation of large
aggregates (i.e., hard agglomerates) during calcination which cannot be broken down
during the subsequent powder/polymer mixing operation. There is a variety of evidence
which shows that severe aggregate formation occurs during calcination at high
temperatures.
1. Figure 4.68 shows plots of the alumina particle size distribution for the uncalcined
powder and the 450°C-, 800°C- and 1000°C-calcined powders. The size distributions
were determined by the X-ray sedimentation method. As noted in the section
(3.2.5), these measurements were made on ~2 vol% alumina/water suspensions
which were prepared at pH=4 and sonicated for 60 min minutes to break up
relatively weak agglomerates. Figure 4.68 shows that the particle size distributions
shift to larger sizes for the calcined powders. (The data for the 450°C-calcined
powder shows some larger particles compared to the uncalcined powder, but the
difference may be within experimental error of the measurement.) It is evident that
some relatively large agglomerates form in the powder calcined at 800 and 1000°C.
For example, the 1000°C-calcined powder has ~ 14 wt% > 1 /xm dia. and ~4 wt%
>2 ¿an dia. In contrast, the uncalcined powder has only ~2 wt% > 1 /xm and ~0
wt% >2 /xm dia. The agglomerates formed by calcination at 800 and 1000°C are
considered to be aggregates (i.e., hard agglomerates) because they are not broken

204
EQUIVALENT SPHERICAL DIAMETER (|lm)
Figure 4.68 Gravitational x-ray sedimentation data for uncalcined and calcined
alumina powders.
down by the long sonication treatment that was carried out prior to the size
distribution measurement. The calculations in Table 4.10 show that extensive neck
growth via surface diffusion is possible at 800 and 1000°C. Specific surface area
measurements confirm that powders undergo sintering during heat treatment at high
temperature. Table 4.11 shows that the specific surface area is 23% less for the
800°C-calcined powder (5.9 m2/g) compared to the uncalcined powder (7.7 m2/g).

205
The specific surface area for 1000°C-calcined powder (4.2 m2/g) is 45 % less than the
unclacined powder.
2. Figure 4.69 shows the alumina particle size distribution curves for the uncalcined,
800°C-, and 1000°C-calcined powders, as determined by the centrifugal
photosedimentation method using suspensions which were sonicated for 30 min. The
results are consist with the X-ray sedimentation results shown in Figure 4.68.
3. Mercury porosimetry measurements (Figure 4.57) show that dry-pressed compacts
prepared with the 800- and 1000°C-calcined powders have larger pore volume and
Figure 4.69 Centrifugal photosedimentation data for uncalcined, 800°C-, and 1000°C-
calcined alumina powders with 30 min of sonication.

206
large pore sizes compared to compacts prepared with the uncalcined powder. This
is attributed to the low relative density of the aggregates that form during high
temperature calcination. (Recall that powders have a loose-stack, or uncompacted,
arrangement during calcination.) The pressure applied during the dry pressing
operation (i.e., 35 ~Mpa) is insufficient to break down these low density
aggregates. In contrast, some of the larger, weaker agglomerates in the uncalcined
powders can be broken down during the powder compaction and consolidation
operation, resulting in higher relative density and smaller pore sizes.
4. Figure 4.66 shows that the Vickers hardness of powder compacts continues to
increase substantially as the calcination temperature is increased to 800 and 1000°C.
This is indicative of the substantial increase in interparticle bonding via sintering.
In addition to the poor state of particulate dispersion, the sample prepared with
the 1000°C-calcined powder turned a gray color during the mixing operation. This color
change was also observed in samples prepared by mixing ethylene-acrylic acid (EAA A-
C 5120) or ethylene-vinyl acetate (EVA A-C 400) co-polymers with the 1000°C-calcined
alumina. (All other ceramic/polymer mixtures prepared in this study had white colors.)
Several other important observations were made for 1000°C-calcined alumina/PE A-C
9 mixtures:
1. Fracture surfaces showed many large white chunks, which were apparently alumina
aggregates.

207
2. No color change was observed in a sample prepared by adding the calcined powder
to a beaker of molten polymer (on a hot plate) and stirring the mixture with a glass
rod.
3. The alumina powder had a slightly pinkish color after the polymer was thermally
burned out (by heating to 1200°C in air).
These observations suggested two possible explanations for the color change: (1)
The high shear stresses generated during incorporation of the highly aggregated powder
into the PE matrix may have affected the physicochemical structure of the polymer. If
a change in polymer structure was responsible for the color change during mixing, then
thermal burnout would be expected to eliminate the gray color. (2) The large, hard
alumina aggregates may have abraded the walls of the bowl mixer and caused
contamination of the mixtures with finely divided, gray-colored steel particles. The
alumina aggregates (observed on a fracture surface) would remain white because the steel
particles would not be expected to penetrate the fine pore structure of the aggregates.
Furthermore, samples would remain white during hand-mixing in a glass beaker because
of the absence of steel contamination. Finally, heat treatment in air could eliminate the
color due to oxidation of the steel particles.
The first possibility was investigated by comparing FTIR spectra for samples
prepared with uncalcined and 1000°C-calcined samples. Figure 4.70 shows that the
spectra are very similar. Of course, the broad O-H stretching absorption band (-3500
cm'1) is considerably reduced in the calcined sample due to the loss of adsorbed
molecular water and hydroxyl groups during heat treatment. However, no differences

208
Figure 4.70 FTIR spectra for 50 vol% alumina/50 vol% polyethylene samples
prepared with uncalcined and 1000°C calcined alumina powders.
were observed in IR peaks associated with the polyethylene. The second possibility was
investigated by analyzing samples for iron content. As discussed in the section 3.2.5,
iron was extracted from alumina or ground alumina/PE mixtures by boiling in IN HC1
solutions. Concentrations were determined by using inductively coupled plasma (ICP)
spectroscopy. Table 4.12 shows that the iron concentration was about two orders of
magnitude higher for the 1000°C-calcined alumina/PE sample compared to the sample
prepared with the uncalcined powder. Iron concentrations were also determined for the

209
Table 4.12 Iron concentration extracted by HC1 solution for various alumina/PE
mixtures and alumina powders (milled and un-milled).
Description
of sample
Iron concentration*
measured (ppm)
Iron concentration
ratio
1000°C-calcined alumina/PE mixture
228
76 : 1
uncalcined alumina/PE mixture
3
1000°C-calcined alumina powder, milled
22
7.3 : 1
1000°C-calcined alumina powder, un-milled 3
uncalcined alumina powder, milled
3
1 : 1
uncalcined alumina powder, un-milled
3
* Iron concentration for 20 cc solutions extracted from 20 g of mixtures or 10 g of
alumina powders.
uncalcined and 1000°C-calcined alumina powders before mixing with the polymer. Both
powders showed the same low iron concentration (3 ppm) as observed for the uncalcined
alumina/PE mixture, again confirming that the contamination resulted from abrasion of
the steel mixer. Finally, iron concentrations were also determined for alumina powder
samples which were "milled" at 200 rpm for 30 min in the bowl mixer. Although the
torque levels generated during the "milling" experiments were below the limit of
detection for the rheometer, the 1000°C-calcined alumina still showed an approximately
seven-fold increase in iron concentration compared to an uncalcined powder "milled"
under the same conditions. This again confirms that contamination arises from the
abrasive action of the large, hard agglomerates in the powder.

210
4.2.2 Aging Phenomenon
Alumina/PE samples prepared with calcined powders were highly susceptible to
aging effects when stored under ambient atmospheric conditions (i.e., in air at room
temperature). This is illustrated in Figure 4.71 which shows plots of dynamic viscosity
(at frequency = 0.1 rad/sec) vs. aging time for samples prepared with both uncalcined
and calcined powders. Figures 4.72-4.74 show more detailed results of rheological
characterization at various aging times for samples prepared with the 300PC-, 450°C-, and
Figure 4.71 Plots of dynamic viscosity (at 0.1 rad/sec and 100% strain) vs. aging
time for 50 vol% alumina/50 vol% polyethylene samples aged in
normal atmospheric conditions.

STORAGE MODULUS (Pa) DYNAMIC VISCOSITY (Pa-s
211
100000
10000
1000
100
10
c
10000
1000
100
10
1
(
Figure 4.72
(A)
(B)
Plots of (A) dynamic viscosity, (B) storage modulus, (C) loss modulus,
and (D) tangent delta vs. frequency for alumina (300°C
calcined)/polyethylene aged in normal atmospheric conditions.

TANGENT DELTA LOSS MODULUS (Pa)
Figure 4.72 (Continued)

STORAGE MODULUS (Pa) DYNAMIC VISCOSITY (Pa-
213
FREQUENCY (rad/s)
(B)
Figure 4.73 Plots of (A) dynamic viscosity, (B) storage modulus, (C) loss modulus,
and (D) tangent delta vs. frequency for alumina (450°C
calcined)/polyethylene samples aged in normal atmospheric conditions.

TANGENT DELTA LOSS MODULUS (Pa)
214
’ 0.1 1 10 100
(C)
(D)
FREQUENCY (rad/s)
Figure 4.73 (Continued)

STORAGE MODULUS (Pa) DYNAMIC VISCOSITY (Pa*
215
(A)
(B)
Figure 4.74 Plots of (A) dynamic viscosity, (B) storage modulus, (C) loss modulus,
and (D) tangent delta vs. frequency for alumina (600 °C
calcined)/polyethylene samples aged in normal atmospheric conditions.

TANGENT DELTA LOSS MODULUS (Pa)
0.1 1 10 100
216
(C)
(D)
FREQUENCY (rad/s)
Figure 4.74 (Continued)

217
600°C-calcined powders, respectively. As described in section 4.2.1 (see Figure 4.52),
samples prepared with calcined powders show/higher initial viscosities and moduli
compared to samples prepared with uncalcined powder. The latter samples show no
significant changes in rheological properties during aging. In contrast, samples prepared
with calcined powders show decreases in viscosity and modulus values during the early
stages of aging (i.e., first two or three days), followed by large increases in these values
as the aging time is increased (see Figures 4.72-4.74). At long aging times, the
rheological data (viscosity, modulus, and tangent delta values) also show some
irregularities (i.e., less smooth increases or decreases) as the measuring frequency
changes. (This is particularly noticeable in the tangent delta data.)
Since the mixed samples were stored under an ambient air atmosphere, it was
suspected that the aging effects observed in Figures 4.71-4.74 were caused by moisture
absorption. As noted in section 2.6, it has been demonstrated in many studies that
atmospheric moisture can induce dramatic changes in the properties of filled polymer
composites [CroF78, Mor80, Shen81, Sto90]. In the present study, the importance of
moisture absorption on rheological properties was investigated by comparing the aging
behavior for samples that were stored under two extreme conditions: in water and in
vacuum. An alumina/PE batch (with 450°C-calcined powder) was prepared under the
usual conditions, but immediately divided into two samples after mixing. One sample
was stored in a desiccator under vacuum in order to minimize contact with water vapor,
while the other sample was stored directly in distilled water. As expected, the sample
stored in vacuum showed no significant changes in rheological properties as a function

218
of aging time. This is illustrated in Figure 4.75 which show plots of dynamic viscosity
and storage modulus values (at 0.1 rad/sec) vs. aging time. In contrast, the sample
stored in water shows dramatic changes in rheological properties with aging, as
illustrated in Figure 4.75. The results in Figures 4.75 and 4.76 show a similar trend as
observed in Figures 4.71 and 4.73 for the 450°C-calcined sample stored under ambient
air conditions, except that the aging phenomena (i.e., initial decrease in viscosity and
modulus values, followed by significant increases with longer aging times) was
considerably accelerated for the sample stored directly in water. (It is presumed that the
rate of moisture absorption is accelerated in the latter case.)
The absorption of moisture by alumina/polyethylene mixtures during storage in
water was confirmed by gravimetric measurements. Figure 4.77 shows the change in
weight for the 450°C-calcined alumina/polyethylene sample as a function of aging time
in water. The sample weight continuously increased during a 456 hour aging study.
Figure 4.77 also shows that pure polyethylene (i.e., a sample with no alumina particles)
gains no weight (within experimental error) during prolonged aging in water. These
results indicate that water absorption in the alumina/PE samples occurs by diffusion along
the ceramic/polymer interface, as opposed to diffusion through the polymer matrix.
Although the results in Figure 4.77 confirm that moisture absorption was
responsible for the changes in rheological properties during storage under atmospheric
conditions, the results provide limited insight into the detailed mechanism by which the
rheological properties were altered. In previous cases described in this study, differences
in rheological properties have reflected differences in the state of particulate dispersion

STORAGE MODULUS (Pa) DYNAMIC VISCOSITY (Pa s)
219
Figure 4.75 Plots of (A) dynamic viscosity and (B) storage modulus (at 0.1 rad/sec
and 100% strain) vs. aging time for alumina (450PC
calcined)/polyethylene samples aged in vacuum and in water.

STORAGE MODULUS (Pa) DYNAMIC VISCOSITY (Pa-
220
FREQUENCY (rad/s)
Figure 4.76 Plots of (A) dynamic viscosity, (B) storage modulus, (C) loss modulus,
and (D) tangent delta vs. frequency for alumina (450°C
calcined)/polyethylene samples aged in water.

TANGENT DELTA LOSS MODULUS (Pa)
Figure 4.76 (Continued)

222
Figure 4.77 Plots of weight gain vs. time for 450°C calcined alumina/polyethylene
sample and pure polyethylene aged in water.
in the samples. However, it would seem unlikely that such an explanation would be
applicable in the present case because the samples were not subjected to shear forces or
elevated temperatures during aging. Without shearing action or melting of the polymer,
it is unlikely that the changes in particulate dispersion would occur during aging. This
was confirmed by QM measurements on the 450°C-calcined alumina/PE samples stored

223
in water and in vacuum. Figure 4.78 shows Dpc histograms for samples that were aged
for 6 days. As expected, the two samples showed essentially the same Dpc distributions
and average Dpc values (within experimental error). Furthermore, the Dpc values were
also essentially the same as in the unaged sample (see Figure 4.53).
Other explanations were sought to understand the large changes in rheological
properties during aging for samples prepared with calcined powders. The pattern of an
initial decrease in viscosity, followed by an increase in viscosity with longer aging times,
suggested that more than one mechanism was responsible for the changes in rheological
properties. Because of the relatively large amount of water adsorbed at longer aging
times, it was suspected that the large increases in viscosity and modulus values were
caused by the formation of water vapor bubbles inside the alumina/PE samples during
testing. It should be recalled rheological measurements were carried out at an elevated
temperature (125°C), i.e., above the normal boiling point for water. (Before starting a
rheological measurement, the alumina/PE mixture was first softened at the 125°C for 10
min and then the sample was compressed in the test fixture in order to completely fill the
space between the two parallel plates.) The formation of large bubbles in the alumina/PE
samples was confirmed by SEM observations on fracture surfaces of a 450°C-calcined
alumina/poly ethylene sample which had been stored in water for 6 days. Before heat
treatment, no bubbles were found in the sample (Figure 4.79, top). In contrast, a sample
heated at 125°C for 10 min showed many large bubbles (Figure 4.79, bottom). These
bubbles remained in the sample after continued heat treatment (at 125°C for 2 hr). The
addition of bubbles to the particle/polymer mixture is expected to increase the viscosity

NUMBER PERCENT NUMBER PERCENT
224
Figure 4.78 Histogram plots of Dpc distributions for 50 vol% alumina (450°C
calcined)/50 vol% polyethylene samples aged in vacuum and in water,
respectively.

225
Figure 4.79 SEM micrographs of the fracture surfaces of 450°C calcined
alumina/polyethylene samples aged in water for 6 days, (top) before
and (bottom) after heat treatment at 125°C for 10 min.

226
and modulus values for the sample. The bubbles acts as a second dispersed phase (i.e.,
in addition to the alumina particles) in the polymer matrix. Thus, the samples have a
higher effective volume fraction of particulate (non-fluid) phase. The effect of bubbles
on the rheological properties of the alumina/PE samples is similar to the effect observed
in simple air bubble/liquid (i.e., foam) systems; higher viscosities are observed as the
volume fraction of air bubbles increases [Mat53, Pri86, Sher68]. The presence of water
vapor bubbles in the alumina/PE mixtures may also explain the irregular data (i.e., less
smooth changes in viscosity, modulus, and tangent delta values with changing frequency)
that was described earlier for samples with long aging times (Figures 4.72-4.74 and
4.76). It is possible that bubble sizes and concentrations varied under the shear forces
applied during the rheological measurements.
The reason for the decreases in viscosity and modulus values during the early
stage of aging in calcined alumina/PE samples (Figures 4.71-4.76) is not clear. It has
been suggested that absorbed water may act as a plasticizer and/or a lubricant in filled
polymer composites [CroF78, Fla84, Whi82], resulting in decreases in viscosity and/or
modulus. In the present case for alumina/PE samples, water is not absorbed directly by
the polymer (see Figure 4.77) so it seems unlikely that water acts as a plasticizer. As
noted earlier, the weight gain results (Figure 4.77) indicate that water diffuses along
alumina/PE interfaces. Thus, it is suggested that water re-adsorbs on the calcined
alumina particle surfaces and imparts a lubricating effect at the polymer/ceramic interface
which is responsible for the observed decreases in viscosity and modulus values.
Unfortunately, direct evidence supporting this hypothesis is not available.

227
4.3 Effects of Polymer Characteristics
This section focuses on the influence of the chemical composition of polymers on
the state of alumina particle dispersion in polymer melts. The polymer used in the
previous sections is polyethylene (PE), a nonpolar polymer composed of carbon and
hydrogen atoms only. By incorporating a controlled amount of acrylic acid or vinyl
acetate, copolymers ethylene-acrylic acid (EAA) and ethylene-vinyl acetate (EVA) are
formed. The chemical structures of these three types of polymers were illustrated in
Figure 3.1. According to the Brdnsted-Lowry definition, EAA is an acidic polymer
because the carboxylic acid group can react with bases (e.g., as potassium hydroxide)
[Mcm86]. Most polymers, except for saturated hydrocarbons such as polyethylene or
polypropylene, have functional sites that are electron donors (Lewis bases) or electron
acceptors (Lewis acids) [Fow89]. EVA is a basic polymer because of the existence of
the lone pairs of available electrons on the oxygen atom of the vinyl acetate group. The
purpose of using these copolymers is to modify ceramic/polymer interfacial
characteristics through the different functional groups in the polymer structure.
Five different grades of polymers were used. Their physical properties (obtained
from the manufacturer) were given in Table 3.1. The acidity of ethylene-acrylic acid
copolymer was characterized by an acid number (mg KOH/g) which was the amount of
potassium hydroxide required to neutralize 1 g of EAA. The EAA A-C 5120 and EAA
A-C 540 had acid numbers (reported by the manufacturer) of 120 and 40, respectively,
that correspond to 15 and 5 wt% of acrylic acid contents, respectively. Ethylene-vinyl
acetate copolymers, EVA A-C 400 and EVA A-C 405T, had 13 and 6 wt% vinyl acetate

228
contents (reported by the manufacturer), respectively. In order to isolate the effect of
the polymer side group functionality on the processing behavior and properties of
ceramic/polymer mixtures, an effort was made to select polymers in which other
characteristics (e.g., molecular weight, melt viscosity, etc.) were similar (see Table 3.1).
Of course, it was not possible to keep these other characteristics exactly constant and this
should be taken into account in the data analysis. All experiments were carried out with
50 vol% alumina/50 vol% polymer mixtures (mixed at 150°C/200 rpm/30 min).
Plots of dynamic viscosity, modulus, and tangent delta vs. measuring frequency
are shown in Figure 4.80 for samples prepared with 50 vol% alumina in PE, EAA, and
EVA polymers. Both alumina/EAA mixtures had very similar rheological behavior, but
they had slightly higher viscosities and moduli than the alumina/PE mixture. The
dynamic viscosities decreased and the moduli increased with increasing frequency. The
dynamic viscosities and moduli for alumina/EVA mixtures were higher than those for PE
and EAA samples, especially at low frequencies. The rheological behavior of the various
polymer/ceramic mixtures were also compared by plotting the relative dynamic viscosity
as a function of frequency (Figure 4.81). The relative viscosities were obtained by
dividing suspension viscosities (Figure 4.80) by measured polymer viscosities (Figure
4.82). When plotted on a relative basis, it is evident that samples prepared with PE and
EAA have similar rheological characteristics, while samples prepared with EVA still
have higher viscosity values (especially at low frequencies). These results suggest that
the state of particulate dispersion achieved during mixing was similar for the PE and
EAA samples, but that samples prepared with EVA were not as well dispersed.

STORAGE MODULUS (Pa) DYNAMIC VISCOSITY (Pa-s
229
(A)
(B)
Figure 4.80 Plots of (A) dynamic viscosity, (B) storage modulus, (C) loss modulus,
and (D) tangent delta vs. frequency for 50 vol% alumina/50 vol%
polymer samples prepared with the polymers indicated.

TANGENT DELTA LOSS MODULUS (Pa)
230
(C)
(D)
Figure 4.80 (Continued)

RELATIVE VISCOSITY
231
FREQUENCY (rad/s)
Figure 4.81 Plots of relative (dynamic) viscosity vs. frequency for 50 vol%
alumina/50 vol% polymer samples prepared with the polymers
indicated.

DYNAMIC VISCOSITY (Pa-s) DYNAMIC VISCOSITY (Pa-s)
Figure 4.82 Plots of dynamic viscosity vs. frequency at 125 and 150°C,
respectively, for the polymers indicated.

233
Table 4.13 Summary of Dpc results for 50 vol% alumina in polyethylene (PE),
ethylene-acrylic acid (EAA) and ethylene-vinyl acetate (EVA).
Sample
Dpc (fim)
Percentage of
each category*
average
value
standard
deviation
small
medium
large
Uncalcined Alumina:
PE A-C 9
0.43
0.16
40.6
47.7
11.7
EAA A-C 5120
0.42
0.15
43.6
47.9
8.5
EAA A-C 540
0.42
0.15
43.8
47.0
9.2
EVA A-C 400
0.47
0.18
36.3
46.4
17.3
EVA A-C 405T
0.47
0.18
32.9
48.4
18.7
300°C Calcined Alumina:
PE A-C 9
0.47
0.17
32.0
50.1
17.9
EVA A-C 400
0.46
0.16
32.3
53.3
14.4
’ Small if Dpc <0.4 ¿xm; medium if 0.4 ¿xm< Dpc <0.6 /xm; and large if Dpc >0.6
H m.
QM measurements are consistent with the rheological data. The Dpc histograms
are shown in Figure 4.83 and results are also summarized in Table 4.13. The average
Dpc values are in the range 0.42-0.43 /xm for the EAA and PE samples and the
differences among the three samples were within experimental error. In combination
with the results reported in section 4.1, it can be concluded that good particulate
dispersion is achieved in alumina/EAA mixtures. In contrast, the Dpc distributions for
EVA samples shift towards larger values and the average Dpc values, 0.47 /¿m, are also
larger, confirming that these samples are not dispersed as well as the PE and EAA
samples.

NUMBER PERCENT NUMBER PERCENT NUMBER PERCENT
20 -y
18 -
16 -
14 -
12 -
10 -
8 -
6 -
4 -
2 -
0 -
20
l|.
50 vol% AlgOg/50 vol% PE A-C 9
,||
% ú 4, Mean Diameter = 0.43 urn
I | I ral
i lililí
II Ipil
¡¡fililí
, , , ,
18
16 -
14 -
12 -
10 -
8 -
6 -
4 -
2 -
0
20
50 vol% Al„0_/50 vol% EAA A-C 5120
b 3
.
1
Mean Diameter = 0.42 /zm
||TTT
18 -
16 -
14 -
12 -
10 -
8 -
6 -
4 -
2 -
0 -
50 vol% Al203/50 vol% EAA A-C 540
W§mm
j
pppppp
lililí
% % % % % V
x
§
Mean Diameter - 0.42 /zm
11 „
fillip , T„
0.0 0.2 0.4 0.6 0.8
EQUIVALENT DIAMETER (/xm)
1.0
1.2
Figure 4.83 Histogram plots of Dpc distributions for 50 vol% alumina/50 vol%
polymer samples prepared with the polymers indicated.

235
18 -
h 16-
w 14 -
u
g 12 H
io -
os
w a _
6
4 -
2 -
0
55
50 vol% Al203/50 vol% EVA A-C 400
ll
!
p
i
i
m
111
111
4 | | KS
4 4 4â„¢
yean Diameter = 0.47 /xm
| | | 4, 4
Ilf fill f
Figure 4.83 (Continued)
It is evident from the above results that the type of functional side group has an
important effect on the state of dispersion achieved. However, for the limited range of
chemical compositions investigated, the amount of the functional side group in the
polymer has little effect on the state of dispersion achieved. For example, the two
EAA/alumina samples, which both have good particulate dispersion, show very similar
rheological and QM data. The two EVA/alumina samples, which both have poorer

236
dispersion, also show very similar rheological and QM data. As discussed in section 4.1,
one factor which influences the degree of particulate dispersion achieved in
polymer/powder batches is the amount of torque generated during the mixing operation.
In the case of samples prepared at different temperatures (section 4.1), significant
differences were observed in the mixing torques (Figure 4.12) because the polymer (and
polymer/powder suspension) viscosities were highly dependent on temperature. Recall
that samples mixed at lower temperatures (i.e., higher polymer viscosities) developed
larger peak torque values and improved agglomerate breakdown during mixing. In the
present case (with EVA and EAA polymers), however, it does not appear that differences
in particulate dispersion can be attributed to differences in the peak torques generated
during mixing. First, the polymer viscosities for all five samples were not substantially
different (Figure 4.82). Second, the peak torque values observed during mixing (Figure
4.84) were similar for the EAA and EVA samples, despite the significant differences in
the state of dispersion achieved after mixing. Even when the peak torque values are
compared on a relative basis (i.e., by dividing the peak torque values by the polymer
viscosities, Table 4.14), there is no obvious correlation with the state of dispersion
achieved during mixing. (Table 4.14 shows that the "relative peak torque" values are
similar for samples prepared with the EAA A-C 5120, EAA A-C 540, and EVA A-C
400, while considerably higher values are observed for samples prepared with PE A-C
9 and EVA A-C 405T.)
Table 4.14 also lists the final torque values observed during mixing samples with
the EAA, EVA, and PE polymers. These values show a modest correlation with the

TORQUE (g-m) TORQUE (g-m) TORQUE (g-m) TORQUE (gm) TORQUE (g-m)
237
Figure 4.84 Plots of torque vs. mixing time for 50 vol% alumina/50 vol% polymer
samples prepared with the polymers indicated.

238
Table 4.14 Summary of important torque values for mixing 50% alumina with
polyethylene (PE), ethylene-acrylic acid (EAA) and ethylene-vinyl
acetate (EVA).
Sample
Peak
torque
(g-m)
Final
torque
(g-m)
Polymer
viscosity
at 150°C
(Pas)
Relative
peak
torque
(g-m)/(Pa-s)
Relative
final
torque
(g-m)/(Pa-s)
Uncalcined Alumina:
PE A-C 9
370
70
0.43
860
163
EAA A-C 5120
155
85
0.62
250
137
EAA A-C 540
180
108
0.59
305
184
EVA-400
180
125
0.60
300
208
EVA-405T
225
80
0.37
608
216
300°C Calcined Alumina:
PE A-C 9 160
80
0.43
372
186
EVA-400
315
150
0.60
525
250
state of dispersion achieved during mixing if the values are compared on a relative basis
(i.e., by dividing the final torque values by the polymer viscosities.). Table 4.14 shows
that the "relative final torque" values are slightly higher for the two EVA samples
compared to the EAA and PE samples. However, the differences are relatively small.
This is not surprising since the polymer/particle suspensions have fairly similar viscosity
values at the high shear rates (Figure 4.80). (Note that viscosities at high shear rates
should be considered because the torque data is collected at a relatively high shear rate
(200 rpm rotor speed). The fact that viscosities and moduli for the various samples
approach similar values at higher frequencies (Figure 4.80) presumably reflects the
breakdown of particulate structures when measurements are carried out at higher
frequencies. The largest differences in rheological properties are observed at the lowest

239
oscillation frequencies, i.e., when the deformation stresses are too low to substantially
break down the particulate network structure in the powder/polymer mixtures.)
It is evident from the above discussion that correlations between mixing torque
curves and the state of dispersion achieved in polymer/particle mixtures are not always
straightforward. The overall torque curves produced during the mixing operation reflect
the initial incorporation of the alumina powder in the polymer, the breakdown of powder
agglomerates, and the development of a specific state of dispersion of the particles in the
polymer melt as the mixing operation is continued. It is presumed that these phenomena
are dependent not only upon powder and polymer characteristics (such as those discussed
in sections 4.1 and 4.2), but also on the interactions between the polymer and powder,
and also possible interactions at the interface between the mixer and the polymer/powder
batch.
In terms of the latter consideration, it is possible that the polymer (EAA, EVA,
and PE) could affect the "macroscopic" wetting and/or adhesion between the
powder/polymer batch and the mixer surfaces (i.e., roller blades and mixing bowl walls).
In turn, this could affect the torque response measured during mixing. (For example,
in forming ceramic powder compacts by dry pressing, it is well known that die wall
lubrication reduces frictional forces between the powder and die walls and improves
pressure transmission during the compaction operation [Dim83, Ree88, Str77],
Similarly, die wall lubricants are used in extrusion operations to improve flow behavior
[Lev89, Ree88].) Whether or not similar effects occur in the present study was not
determined.

240
Table 4.15 Summary of wetting results for polyethylene (PE), ethylene-acrylic acid
(EAA) and ethylene-vinyl acetate (EVA) melts on alumina powder
measured by polymer penetration method.
Sample
Viscosity
(Pas)
Surface tension
(erg/cm2)
k-cos0 x 107
(cm)
wetting ratio*
Uncalcined Alumina:
PE A-C 9
0.43
27.5
9.0
1.00
EAA A-C 5120
0.62
28.8
9.4
1.04
EAA A-C 540
0.59
27.5
9.1
1.02
EVA A-C 400
0.60
27.7
7.7
0.86
EVA A-C 405T
0.67
28.6
8.6
0.95
300°C Calcined Alumina:
PE A-C 9
0.43
27.5
9.0
1.00
EVA A-C 400
0.60
27.7
8.6
0.96
The wetting ratio is the sample’s k-cos0 divided by PE A-C 9’s k-cos0.
It is also possible that the selection of the polymer influences "microscopic"
wetting and/or adhesion between the alumina particles and the polymer melt during
mixing. Wetting and/or adhesion behavior is dependent upon the specific intermolecular
interactions between the polymer functional side groups and the alumina surface groups.
The adhesion and bonding mechanism between the alumina particles and the various
polymers (PE, EAA, and EVA) was not assessed in this study; however, wetting
behavior was evaluated using the polymer penetration method. The polymer penetration
depth values vs. time are shown in Figure 4.85. The results (shown in Table 4.15) are
reported as a "wetting ratio," i.e., the value of (k-cos0) for the polymer/alumina sample
divided by the value of (k-cos0) for the PE/alumina sample. The EAA samples show
similar wetting behavior compared to PE. In contrast, wetting by the EVA samples is
slightly worse than PE, especially for the EVA A-C 400. This may be a factor, at least

241
TIME (SEC)
Figure 4.85 Plots of penetration depth vs. time for polymer melts into alumina
powder compacts.
in part, which contributes to the poorer particulate dispersion in EVA/alumina samples.
However, this data alone cannot does not provide a conclusive explanation for the
differences in dispersion behavior, especially since the differences in wetting behavior
are relatively minor. Furthermore, the wetting data does not provide any insight into the
reason for the differences in the mixing torque curves shown in Figure 4.84.
The difficulty in correlating mixing torque curves with dispersion and wetting
behavior was also illustrated in an experiment carried out with a calcined alumina
powders. Figure 4.86 shows torque rheometry results for PE and EVA A-C 400 samples
prepared with alumina powder that was heat treated at 300PC. The EVA A-C 400

TORQUE (g-m) TORQUE (g m)
242
Figure 4.86 Plots of torque vs. mixing time for 50 vol% alumina (300°C
calcined)/50 vol% polymer samples prepared with the polymers
indicated.

243
sample shows considerably increased peak and final torque values compared to the PE
sample (Figure 4.86). In addition, comparison with Figure 4.84 shows that these torque
values are also higher than corresponding values for the EVA A-C 400 sample prepared
with uncalcined alumina. Despite these significant differences in torque response during
mixing, the three samples develop similar states of particulate dispersion. The
rheological and QM data for the PE and EVA-400 samples prepared with the 300°C-
calcined powder are shown in Figures 4.87-4.88 and Table 4.13. Relative dynamic
viscosity comparisons are also shown in Figure 4.89. These results show that particulate
dispersion is essentially the same for the two samples. Furthermore, comparison with
Figures 4.80-4.83 and Table 4.13 shows that particulate dispersion for these samples is
essentially the same as in the EVA sample prepared with uncalcined powder.
As noted earlier, correlating mixing behavior with dispersion behavior is difficult
because the torque response during mixing can be influenced by many variables factors.
It was illustrated in section 4.2, for example, that heat treatment at temperatures as low
as 100°C can affect the physicochemical properties of the powder and, in turn, this can
dramatically alter the torque response during powder/polymer mixing. In regards to the
results shown in Figures 4.87-4.89 and Table 4.13, heat treatment of the alumina powder
not only affects physical properties of the agglomerates, but may also influence
subsequent polymer/powder adhesion as a result of the removal of molecular water and
bound hydroxyl groups on the alumina surface. Clearly, additional work is needed to
determine the importance of ceramic/polymer adhesion and bonding on mixing and
dispersion behavior.

STORAGE MODULUS (Pa) DYNAMIC VISCOSITY (Pa-
244
(A)
(B)
Figure 4.87 Plots of (A) dynamic viscosity, (B) storage modulus, (C) loss modulus,
and (D) tangent delta vs. frequency for alumina (300°C
calcined)/polymer samples prepared with the polymers indicated.

TANGENT DELTA LOSS MODULUS (Pa)
245
(C)
(D)
Figure 4.87 (Continued)

NUMBER PERCENT NUMBER PERCENT
246
20
18
16
14
12
10
8
6
4
2
0
20
18
16
14
12
10
8
6
4
2
0
0.00 0.20 0.40 0.60 0.80 1.00 1.20
EQUIVALENT DIAMETER (/zm)
50 vol% A1„0_ (300 C Calcined)/50 vol% PE A-C 9
2 o
Mean Diameter = 0.47 /xm
I.
II
i|
'4
Y4
ill
i I—T
50 vol* A1203 (300°C Calcined)/50 vol% EVA A-C 400
¡II
I
lili
liilii
11
¿ ^ ^
iiii
Mean Diameter = 0.46 /xm
t ~T—r
Figure 4.88 Histogram plots of Dpc distributions for 50 vol% alumina (SOO’C
calcined)/50 vol% polymer samples prepared with the polymers
indicated.

RELATIVE VISCOSITY
247
Figure 4.89 Plots of relative (dynamic) viscosity vs. frequency for 50 vol% alumina
(300°C calcined)/50 vol% polymer samples prepared with the polymers
indicated.

248
It should be noted that these issues are relevant to the development of economical
mixing operations. By understanding the effect of polymer/ceramic interactions of
mixing and dispersion behavior, it may be possible to reduce the amount of energy
required during mixing to achieve a given state of particulate dispersion. For example,
it is noted that the area under the torque vs. time curve (which reflects the power
consumed during mixing) is considerably larger for the EVA/calcined alumina sample
(Figure 4.86) compared to the two EVA/uncalcined alumina samples (Figure 4.84) or the
PE/calcined alumina sample (Figure 4.86), despite the fact that the particulate dispersion
achieved during mixing is essentially the same for these samples.
4.4 Effects of Chemical Additives
As discussed in section 2.7, there are many possible mechanisms by which
chemical additives can affect mixing behavior, particulate dispersion, rheological
properties, and wetting behavior in polymer/powder systems. Small additions of various
common "processing aids" (i.e., surfactants, dispersants, coupling agents, lubricants,
etc.) may affect the properties of the ceramic powders, the polymer melt, and/or the
ceramic/polymer interface. In this study, experiments were directed toward providing
insight into the mechanisms by which specific additives influence the processing behavior
and properties of the polyethylene/alumina mixtures.
4.4.1 Coupling Agents
Coupling Agent/Water Mixtures
As described in section 3.1.2, coupling agents (1.25 g) and DI water (125 cc)
were initially mixed together for 1 hr before adding alumina powder. There were

249
obvious visual differences in the four coupling agent/water mixtures. The zircoaluminate
(grade CAVCO MOD APG) and silane Z-6020 coupling agents dissolved completely in
the DI water, as clear solutions were formed. In contrast, the silane Z-6076 and titanate
(grade LICA 12) coupling agents apparently formed emulsions, as small droplets
suspended in water were visible to the naked eye. According to information obtained
from the coupling agent manufacturers, the aqueous solubilities were ~ 1 wt% for the
silane Z-6076 coupling agent and < 1 wt% for the titanate coupling agent. In contrast,
the zircoaluminate and silane Z-6020 coupling agents showed much greater solubility.
(No specific solubility values were reported by the manufacturers). Due to these
differences, it is possible that the alumina powders were not coated as homogeneously
by the coupling agents with poorer solubility. This could not be confirmed conclusively
by SEM observations on coated (and dried) powders. However, deposition of coupling
agent/water mixtures on bulk alumina substrates did provide some evidence that less
uniform coatings may form with the less soluble mixtures. In these experiments, the
alumina substrates were dipped in — 1 wt% coupling agent/water mixtures for 22 hr and
subsequently dried for ~24 hr at 90°C. (Substrates were tilted during drying in order
to drain excess solution.) High magnification SEM micrographs of the coated substrates
are shown in Figure 4.90. The substrates treated with the zircoaluminate and silane Z-
6020 coupling agents looked the same as untreated substrates, indicating that coatings
were relatively thin and uniformly distributed. In contrast, regions with varying
thickness (i.e., less homogeneous coatings) were observed for substrates treated with the
silane Z-6076 and titanate coupling agents. This was also evident from low

Figure 4.90 SEM micrographs of alumina substrates treated with the coupling
agents indicated.

251
magnification optical micrographs (Figure 4.91). The micrographs of the substrates with
the zircoaluminate and silane Z-6020 coupling agents were relatively featureless, while
micrographs of the samples with the silane Z-6076 and titanate coupling agents showed
residues which indicated that large, discreet droplets had dried on the surface. This is
consistent with the visual observations that the low-solubility coupling agents (silane Z-
6076 and titanate) formed emulsions when mixed with DI water.
Coupling Agent/Water/Alumina Suspensions
As described in section 3.1.2, "coating suspensions" were prepared with 20 vol%
alumina powder and 80 vol% coupling agent/water "solution."16 The suspensions
contained 1 wt% of coupling agent based on the amount of alumina powder. The
rheological properties of these coating suspensions are of interest because the alumina
powder characteristics produced after liquid (i.e., water) removal are directly related to
the state of dispersion in the original suspension. It is well known that consolidation of
well-dispersed suspensions results in powder compacts (i.e., dried powder cakes) with
higher particle packing density and smaller pore sizes, while consolidation of flocculated
suspensions results in compacts with lower packing density and larger pore sizes [Roj88,
Sac88, Yeh89]. In this study, the dried powder cakes were broken up using a mortar
and pestle. Nevertheless, the crushed powder still consists of relatively large
agglomerates which are expected to retain essentially the same primary particle packing
and porosity characteristics of the original powder cake. This is of interest in the present
study because agglomerate characteristics can influence the torque response during
16 As discussed above, some of the coupling agents did not dissolve completely in water.

252
Untreated
Silane Z-6020
200 /xm
Zircoaluminate CAVCO MOD APG
200 /xm
.¡3 £ ,
V I
200 jim
Silane Z-6076
' ■ *i- **i \ i 1 * * * ^9' > ^ fc ■ * * . » w
• ,'y m. j
' ;>v • • ■«. • * . V «V
9HI Titanate LICA 12 ' % ^
* r-» * * * *
»
m
• * ' V % 1
HGfisiiljúiKl'S*'. * . * % j • “ ■ • J ■ ^ ■ k
a • w ^ j. Mm
• V . • V'lfll
■KsL,;': V • í•, i* --A ..‘r.'iV;: ' v ** * ** -•
, * • '9* * f j Jf
Hi ' ■ . s .•■•■•'.' .S, » W ^ *. fl
% ••• v -V ■ *
• “ .» ? >r *.# l_Lj
" ?
. ;* ¿
* j ;.
- ' â–  -
IS^?y % 2 00 Min ^
•3
■ •
2 00 yLiin
Figure 4.91 Optical micrographs of alumina substrates treated with the coupling
agents indicated.

253
study because agglomerate characteristics can influence the torque response during
polymer melt/powder mixing, as well as the state of particulate dispersion and the
rheological properties of the mixed batch. (For example, it was demonstrated in section
4.2 that heat treatment can affect powder agglomerate characteristics and thereby
influence mixing behavior, particulate dispersion, and rheological properties.)
Figure 4.92 shows plots of shear stress vs. shear rate for the coating suspensions
prepared with alumina powder and various coupling agents. The suspension with the
zircoaluminate coupling agent is well-dispersed, as indicated by the Newtonian flow
behavior (Figure 4.92) and low suspension viscosity (~2.8 mPa-s). Good dispersion is
also indicated by the fact that the rheological properties are essentially the same as
observed for electrostatically-stabilized alumina suspensions prepared at pH=4 with no
chemical additives (Figure 4.93). In contrast, large yield stresses, high viscosities, and
highly thixotropic flow behavior are observed for suspensions with the silane Z-6076 and
titanate coupling agents. (Note that the shear stress scale is 40 times larger than the one
used for the zircoaluminate coupling agent suspension.) These results indicate that the
two suspensions are extremely flocculated. (The particle network (floe) structure may
be more extensive for the suspension with titanate coupling agent, as a larger yield stress
and higher viscosities at high shear rates are observed.) The suspension prepared with
the silane Z-6020 coupling agent is also not as well-dispersed as the suspension with
zircoaluminate coupling agent; however, the relatively low yield stress, low viscosities,
and absence of thixotropy indicates vastly improved dispersion compared to the
suspensions with silane Z-6076 and titanate coupling agents.

160
120
80
40
0
160
120
80
40
0
254
20 vol% A1203 in Water
N Silane Z-6020
50 100 150
32
Zircoaluminate CAVCO MOD APG_
V
50 100 150 200 250 300
SHEAR RATE (l/s)
of shear stress vs. shear rate for the coating suspensions prepared
20 vol% alumina and the coupling agents indicated.

255
Figure 4.93 Plots of shear stress vs. shear rate for 20 vol% alumina suspensions in
pH =4 DI water and in zircoaluminate coupling agent solution.
Evidence that the silane Z-6076 and titanate coupling agents produce more
flocculated suspensions was also provided by particle size distributions (PSD)
measurements (centrifugal sedimentation method). Figure 4.94A shows distributions
obtained using suspensions which were sonicated for only 15 sec.17 The PSD’s for
samples prepared with the silane Z-6076 and titanate coupling agents show larger sizes.
17 Suspensions were prepared by mixing the coupling agent-treated (dried) alumina
powders with DI water (0.1 vol% solids). The suspensions were mixed by hand for a
few seconds and then subjected to sonication. The pH values of the suspensions were
close to that for the DI water (~6) because no acid/base additions were made and the
solids concentrations were low.

CUMULATIVE VOLUME PERCENT CUMULATIVE VOLUME PERCENT
100
80 -
60 -
40 -
20
Sonication Time: 15 sec
No Additive
Silane Z—6020
Silane Z-6076
Zircoaluminate
CAVCO MOD APG
Titanate LICA 12
256
(A)
0.0 0.2 0.4 0.6 0.8
1.0
1.2
100
80
60
40
20
Sonication Time: 30
No Additive
Silane Z-6020
Silane Z-6076
Zircoaluminate
CAVCO MOD APG
Titanate LICA 12
(B)
0.0 0.2 0.4 0.6 0.8 1.0
EQUIVALENT SPHERICAL DIAMETER (^m)
1.2
Figure 4.94 Centrifugal photosedimentation data for coupling agent treated alumina
powders with (A) 15 sec and (B) 30 min of sonication.

257
In contrast, samples prepared with the silane Z-6020 and zircoaluminate coupling agents
have essentially the same PSD (within experimental error) as the pH=4 suspension
prepared without any coupling agent. The PSD for the sample prepared with the titanate
coupling agent shows essentially no change after extended sonication (30 min), Figure
4.94B. This suggests that the suspension prepared with the titanate coupling agent has
very poor stability against flocculation.18 The PSD’s do shift to smaller sizes for the
other samples shown in Figure 4.94B. This presumably reflect some additional
breakdown of powder agglomerates during the long (30 min) sonication period. The
particles sizes decrease only slightly for the untreated sample and the samples with the
silane Z-6020 and zircoaluminate coupling agents, while a greater change is observed for
the sample with the silane Z-6076 coupling agent. This suggests that the first-generation
agglomerates may be somewhat stronger in the latter sample (i.e., since less agglomerate
breakdown occurred during the first 15 sec of sonication compared to the other samples).
Treated Alumina Powder/Polymer Mixtures
The effect of coupling agents on particulate dispersion in alumina/polymer
mixtures was assessed using both QM and rheological measurements. The Dpc
histograms are shown in Figure 4.95 and the results are also summarized in Table 4.16.
The samples prepared with the silane Z-6020 and zircoaluminate coupling agents have
low average Dpc values, indicating that the alumina particles are well dispersed. Within
18 It might also be argued that this result indicates that the powder agglomerates are
strong enough to resist break down under the stresses applied during extended sonication.
However, the results in section 4.2 showed that 30 min sonication was very effective in
breaking down agglomerates, except for hard aggregates formed by sintering.

NUMBER PERCENT NUMBER PERCENT NUMBER PERCENT
20 -j-
18 -
16 -
14 -
12 -
10 -
8 -
6 -
4 -
2 -
0 --
20
!!
III
III
ÍIÍ
50 vol% A1803
No Additive
Mean Diameter - 0.43 /xm
‘y-ni* t
258
18 -
16 -
14 -
12 -
10 -
8 -
6 -
4 -
2 -
0 -
20
¡I
I I I III
50 vol% A1203
Silane Z—6020
Mean Diameter - 0.42 /xm
iippp
lllllllll
f-
|—r—i—p—|-
18 -
16 -
14 -
12 -
10 -
8 -
6 -
4 -
2 -
0 -
-CP-
I
50 vol% A1203
SUane Z-6078
Mean Diameter => 0.46 /xm
plplplplplplpppl
mwmmm,
o.o
0.2
i ' i • • '
0.4 0.6 0.8
EQUIVALENT DIAMETER (/xm)
1.0
1.2
Figure 4.95 Histogram plots of Dpc distributions for 50 vol% alumina/50 vol%
polyethylene samples prepared with the coupling agents indicated.

259
T-^
¡
III
| |
1
||
50 vol% A1203
Zircoaluminate CAVCO MOD APG
yean Diameter = 0.42 /xm
*r~i r
50 vol% AIz03
Titanate LICA 12
PIP
P P P
y y y
Mean Diameter = 0.51 /xm
0.00
0.20
0.40
ww
tAyAy,
0.60
EQUIVALENT DIAMETER (¿un)
Figure 4.95 (continued)
experimental error, the Dpc values are the same as observed for samples prepared with
untreated alumina powder. In contrast, samples prepared with the silane Z-6076 and
titanate coupling agents have larger Dpc values (especially in the latter case), indicating
that particles are more poorly dispersed.

260
Table 4.16 Summary of Dpc results for 50 vol% alumina/50 vol% polyethylene
samples prepared with different coupling agents.
Sample
Dpc (/tm)
Percentage of
each category*
average
value
standard
deviation
small
medium
large
No Additive
0.43
0.16
40.6
47.7
11.7
Silane Z-6020
0.42
0.16
46.6
40.7
12.7
Silane Z-6076
0.46
0.18
34.7
47.9
17.4
Zircoaluminate
0.42
0.16
44.6
44.8
10.6
CAVCO MOD APG
Titanate LICA 12
0.51
0.19
22.7
53.1
24.2
* Small if Dpc <0.4 ^m; medium if 0.4 ^m< Dpc <0.6 /¿m; and large if Dpc >0.6
¿¿m.
Particulate dispersion was also assessed from dynamic-shear rheological
measurements and the results were generally consistent with the QM results. Figure 4.96
shows plots of dynamic viscosity, modulus, and tangent delta vs. measuring frequency
for mixtures prepared with untreated and coupling agent-treated powders. Lower
viscosity and modulus values were observed for the samples with untreated powder and
powders treated with the silane Z-6020 and zircoaluminate coupling agents; this is
consistent with the lower Dpc values for these samples. Higher viscosity and modulus
values (particularly at low measuring frequencies) were observed for the samples with
the silane Z-6076 and titanate coupling agents; this is consistent with the higher Dpc
values for these samples. It should be noted that Figure 4.96 shows comparisons of
suspension viscosity and modulus values for samples prepared with various coupling
agents, i.e., instead of comparisons based on relative viscosity and relative modulus
values. This still allows direct comparisons of the various samples, however, because

STORAGE MODULUS (Pa) DYNAMIC VISCOSITY (Pa-s
261
10000 e
50 vol% A1203
1000 r
â–¡ Silane Z-6076
O Tiianate LICA 12
o No Additive
v Silane Z-6020
a Zircoaluminate
CAVCO MOD APG
100
10 r
i i i i 11111 i i i i i i i â–  i 1111
1000
1 10
FREQUENCY (rad/s)
100
50 vol% A1203
100
1 s
0.1
â–¡ Silane Z-6076
o Titanate UCA 12
o No Additive
v Silane Z-6020
a Zircoaluminate
CAVCO MOD APG
i i—i i i «iiii
0.1
1 10
FREQUENCY (rad/s)
100
(A)
(B)
Figure 4.96 Plots of (A) dynamic viscosity, (B) storage modulus, (C) loss modulus,
and (D) tangent delta vs. frequency for 50 vol% alumina/50 vol%
polyethylene samples prepared with the coupling agents indicated.

TANGENT DELTA LOSS MODULUS (Pa)
10000
50 vol% A1203
1000 r
100 r
â–¡ Silane Z-6076
O Titanate LICA 12
o No Additive
v Silane Z—6020
a Zircoaluminate
CAVCO MOD APG
_J I I I L-J. I.J
-I I I L-LLU
_l I I I
0.1
10
1 10
FREQUENCY (rad/s)
100
50 vol% A1203
1 -
0.1
â–¡ Silane Z-6076
O Titanate LICA 12
o No Additive
v Silane Z-6020
a Zircoaluminate
CAVCO MOD APG
-l J- .1.. 1 l-l .
_l I I L-l AOJ
..». - i—i i ml
0.1
1 10
FREQUENCY (rad/s)
100
Figure 4.96 (Continued)

263
the coupling agents had very little effect on the rheological properties of the polymer.
For example, Figure 4.97 shows that ~4.2 wt% (based on the weight of polymer)
additions of the various coupling agents resulted in very small changes in dynamic
viscosities of PE melts. (The alumina/PE/coupling agent ratio in mixed batches is
89.1/20.9/0.89 by weight. Consequently, samples in Figure 4.97 were prepared with
polymer/coupling agent ratios of 20.9/0.89 by weight.)
An interesting observation in Figure 4.96 is that the lowest viscosity and modulus
values were consistently observed for the sample with the zircoaluminate coupling agent.
1.2
'In 1.0
É 0.8
co
o
o
CO
^ 0.6
o
0.4
0.2
POLYETHYLENE
o
No Additive
—
V
Silane Z—6020
a
Silane Z-6076
—
A
Zircolauminate
CAVCO MOD APG
o
Titanate LICA 12
=*=*£3*—<
4—5-—o—o—n
_J 1
1 1 L_L_jJ
10
100
FREQUENCY (rad/s)
Figure 4.97 Plots of dynamic viscosity vs. frequency for polyethylene with the
coupling agents indicated.

264
This may indicate that particulate dispersion is improved in this samples (i.e., relative
to the samples with untreated alumina). However, Dpc measurements are not sensitive
enough to confirm this. (The Dpc values are slightly smaller for the sample with the
zircoaluminate coupling agent, but the differences are within the range of experimental
error for the measurements.) Aside from changes in particulate dispersion, it is not
obvious why the sample prepared with the zircoaluminate coupling agent would have
lower viscosity and modulus values. In some instances, decreases in viscosity and
modulus values have been attributed to "lubricating effects" [Big82, Sain85]. For
example, it has been suggested that chemical additives may modify particle/fluid
interfacial characteristics and thereby reduce suspension viscosities [Big82].
Alternatively, it is possible that lubricating effects at the interface between the
polymer/powder mixture and viscometer rotor result in slip at the interface and, hence,
measurement of anomalously low torque values. No clear evidence in support or in
dispute of such lubricating effects has been obtained in the course of this study. It was
noted, however, that polymer wetting behavior was improved when coupling agents were
used. Table 4.17 shows that all the samples with coupling agents had significantly higher
wetting ratios compared to the sample with the untreated alumina powder. (The polymer
penetration rates are shown in Figure 4.98.) This observation certainly does not prove
that lubricating effects are important in samples prepared with the zircoaluminate
coupling agent. However, if such effects did occur, it is likely that they would be
accompanied by improved wetting.

265
Table 4.17 Summary of wetting results for polyethylene melts on alumina powders
treated with different coupling agents.
Sample
k-cos0 x 107
(cm)
wetting ratio*
No Additive
9.0
1.00
Silane Z-6020
12.9
1.44
Silane Z-6076
15.5
1.73
Zircoaluminate CAVCO MOD APG
12.5
1.39
Titanate LICA 12
14.7
1.64
’ k-cos0 value for each sample divided by that for the sample without additive.
TIME (SEC)
Figure 4.98 Plots of penetration depth vs. time for polyethylene melts into alumina
powder compacts treated with the coupling agents indicated.

266
Another interesting observation in Figures 4.95 and 4.96 is that the sample with
the titanate coupling agent had significantly higher Dpc values compared to the sample
with the silane Z-6076 coupling agent, but the viscosity and modulus values were very
similar. In comparison with other samples in this study that had high Dpc values (e.g.,
see Figures 4.1 and 4.30 in section 4.1.1 and Figures 4.52-53 in section 4.2.1), the
viscosity and modulus values for the sample with titanate coupling agent are somewhat
low. The reason(s) for this behavior are not known, but some possibilities include: (1)
differences in the agglomerate (particle-network) structure for the various samples and/or
(2) occurrence of "lubricating effects" (such as discussed in the previous paragraph) in
the sample with the titanate coupling agent.
Steady-shear rheological measurements were also carried out on samples with
coupling agents. Shear stress vs. shear rate and viscosity vs. shear rate plots for the
various samples are shown in Figure 4.99. The samples with titanate and silane Z-6076
coupling agents have obvious yield stresses and high viscosities at low shear rates. These
observations are indicative of relatively poor dispersion and are consistent with the
dynamic-shear rheological measurements and the Dpc measurements. In contrast,
samples prepared with untreated powder and with zircoaluminate and silane Z-6020
coupling agents show very low yield stresses and much lower viscosities at low shear
rates. These observations are consistent with Dpc and dynamic-shear measurements
which show that these samples have relatively good particulate dispersion. However,
there are several puzzling observations. First, the silane Z-6020 and zircoaluminate
coupling agents develop substantially lower viscosities (as the shear rate increases)

SHEAR STRESS (Pa) SHEAR STRESS (Pa)
267
1000
800
600
400
200
0
1000
800
600
400
200
0
Figure 4.99
Plots of shear stress vs. shear rate for 50 vol% alumina/50 vol%
polyethylene samples prepared with the coupling agents indicated.

VISCOSITY (Pa s) VISCOSITY (Pa s)
268
Figure 4.99 (Continued)

269
compared to the sample with the untreated powder. This is not expected from the
dynamic-shear measurements, especially for the sample with the silane Z-6020 coupling
agent. Second, samples with the silane Z-6076 and ti tanate coupling agents also develop
lower viscosities (at higher shear rates) compared to the sample with no coupling agent.
The cause for these effects is not known. However, it was noted in the experimental
section that the steady-shear rheological measurements tend to become unreliable at
higher shear rates because sample is ejected from the viscometer at increasing rotor
speeds. It was not determined if such effects were more important in samples prepared
with coupling agents. Recall, however, that coupling agents affect polymer/ceramic
wetting behavior and this in turn may have some influence on the steady-shear
rheological measurements. Although no firm conclusions can be drawn, the reliability
of the steady-shear measurements at high shear rates must be viewed with caution.
Stress relaxation measurements were also carried out on samples with coupling
agents. Figure 4.100 shows that samples with untreated alumina powder and with
zircoaluminate coupling agent have short relaxation times. This is expected for samples
having good particulate dispersion. In contrast, considerably longer relaxation times are
observed for the poorly-dispersed samples prepared with the silane Z-6076 and titanate
coupling agents. One surprising result, however, is the long stress relaxation time
observed for the sample with the silane Z-6020 coupling agent. In fact, the stress does
not relax to any appreciable extent, even after 100 sec. The reason for this behavior is
not understood, but available evidence suggests that the stress does not relax because the
sample adheres to the stainless steel rotor plate of the viscometer.

STRESS (Pa)
270
Figure 4.100 Plots of residual stress vs. time for 50 vol% alumina/50 vol%
polyethylene samples prepared with the coupling agents indicated.
Although some of the results described above are difficult to explain, the overall
conclusion from the Dpc and rheological data is that samples prepared with untreated
powder and with the silane Z-6020 and zircoaluminate coupling agents have relatively
good dispersion, while the samples prepared with the silane Z-6076 and titanate coupling
agents are more poorly dispersed. Of course, it is desirable to understand the reason(s)

271
for this behavior. A definitive explanation cannot be provided at this time, but some
potentially important information is found by examining the mixing torque curves for the
various samples (see Figure 4.101). Peak torque and final torque values for these
samples are listed in Table 4.18. Note that the peak torque values are highest for the
well-dispersed samples (untreated, zircoaluminate, and silane Z-6020), while the poorly-
dispersed samples (silane Z-6076 and titanate coupling agents) show the lowest peak
torque values during mixing. It should be recalled that many of the samples discussed
in sections 4.1 and 4.2 also showed good dispersion when high peak torques were
observed during mixing.19 In these cases, it was concluded that the large stresses
generated during mixing were effective in breaking down the powder agglomerates,
thereby resulting in polymer/powder mixtures with good dispersion. The same type of
effect may be operative in the present case for samples prepared with the various
coupling agents.
An interesting correlation is also observed between the peak torque values during
polymer/powder mixing and the degree of particulate dispersion observed in the "coating
suspensions" (i.e., the suspensions prepared for coating the alumina powders with
coupling agents). The samples prepared with no additive and with the zircoaluminate
coupling agent have the highest peak torques (Figure 4.101), while the corresponding
coating suspensions show the best dispersion (Figure 4.92). The peak torque is slightly
19 Exceptions to this observation were samples which were prepared using powder
calcined at high temperatures (>600°C). These samples showed high peak torques
during mixing, but poor dispersion in the final mixtures. This was because the powders
contained hard aggregates (formed by sintering) which could not be broken down under
the stresses generated during mixing.

TORQUE (g m) TORQUE (g-m) TORQUE (g-m)
400
272
Figure 4.101 Plots of torque vs. mixing time for 50 vol% alumina/50 vol%
polyethylene samples prepared with the coupling agents indicated.

TORQUE (g-m) TORQUE (g m)
Figure 4.101 (Continued)

274
Table 4.18 Summary of important torque values for mixing polyethylene with
alumina powders treated with different coupling agents.
Sample
Description
Peak torque
(g-m)
Final torque
(g-m)
No Additive
370
70
Silane Z-6020
305
60
Silane Z-6076
200
60
Zircoaluminate CAVCO MOD APG
425
15
Titanate LICA-12
170
50
lower for the sample mixed with the silane Z-6020 coupling agent (Figure 4.101) and
this, in turn, correlates with the slightly poorer dispersion observed for the coating
suspension (Figure 4.92). Finally, the torque peaks were substantially lower for samples
prepared with the silane Z-6076 and titanate coupling agents (Figure 4.101), while the
corresponding coating suspensions were highly flocculated (Figure 4.92). (Furthermore,
note that the slightly lower peak torque for the sample with titanate coupling agent
(Figure 4.101) also correlates with the slightly poorer dispersion in aqueous suspensions,
as indicated by rheological data (Figure 4.92) and PSD measurements (Figure 4.94)).
These correlations may be indicative of differences in the powder agglomerate
characteristics. (The porosity characteristics of dry powders and powder compacts are
often dependent upon the state of dispersion in the starting powder/liquid suspensions.)
In contrast to the observations concerning the peak torque values, no obvious
trends could be discerned regarding the final torque values (Figure 4.101 and Table
4.18). The final torque values do not show any clear correlation with the peak torque

275
values or with the characteristics of the coating suspensions. For example, despite the
relatively poor particulate dispersion, the samples with the titanate and silane Z-6076
coupling agents showed lower final torque values than the sample prepared with untreated
alumina powder. In addition, the sample with the zircoaluminate coupling agent showed
an extremely low final torque value, i.e., lower than expected based on the relatively
slight improvement in particulate dispersion compared to the sample with untreated
powder. The reason(s) for this behavior are not known. As discussed in section 4.3.,
the torque response during mixing depends on many factors, including powder and
polymer characteristics and the various interfacial properties of the system (i.e., the
ceramic powder/polymer interface and the batch/mixer interface). It was noted earlier
that all coupling agents appear to give significant improvements in powder/polymer
wetting (Table 4.17). However, it is unclear why this would result in low final torque
readings. Lubricating effects (i.e., friction-reducing effects at internal or external
interfaces) may be operative, but no supporting evidence was obtained in this study.
4.4.2 Surfactants
The term "surfactant" (i.e., surface active agent) usually refers to chemical
additives which adsorb at interfaces and thereby modify interfacial energies and
interfacial wetting behavior. The addition of small amounts of fluorocarbons to
appropriate solvents often results in reduced solid/liquid interfacial energies and enhanced
solid/liquid wetting. Hence, Fluorad FC-740 will be referred to as a surfactant in this
study, although its specific effect on interfacial properties was not determined for the
PE/alumina system used in this study.

276
As described in section 3.1.2, Fluorad FC-740 was initially dissolved in heptane
to form clear solutions. Suspensions were prepared with alumina (20 vol%) and Fluorad
FC-740/heptane solutions (80 vol%) using two different Fluorad FC-740 concentrations.
(These concentrations were 1.2 and 12.0 vol% based on the amount of alumina present.
However, after solvent evaporation, dried alumina/Fluorad FC-740 powders were mixed
with PE so that the alumina solids concentration was maintained at 50 vol%. Thus,
alumina/Fluorad/PE mixtures were prepared with volume ratios of 50.0/0.6/49.4 and
50.0/6.0/44.0. Hence, we refer to the samples as containing 0.6 and 6 vol% Fluorad
FC-740.) Figure 4.102 shows the shear stress vs. shear rate flow curves for these
SHEAR RATE (l/s)
Figure 4.102 Plots of shear stress vs. shear rate for the coating suspensions prepared
with 20 vol% alumina and indicated Fluorad FC 740 concentrations.

277
suspensions. As noted in the discussion concerning coupling agents, the rheological
properties of these coating suspensions are of interest because the alumina powder
characteristics produced after liquid (i.e., heptane) removal are directly related to the
state of dispersion in the original suspension. The suspension prepared with 0.6 vol%
Fluorad FC-740 shows Newtonian behavior and low viscosity (—1.6 mPa-s), indicating
that alumina particles are well-dispersed. Good dispersion is also indicated by the fact
that the rheological properties are very close to that observed for electrostatically-
stabilized alumina suspensions prepared at pH=4 with no chemical additives (Figure
4.103). In contrast, large yield stresses, high viscosities, and thixotropic flow behavior
are observed for the suspension prepared with 6.0 vol% Fluorad FC-740, indicating that
the suspension is highly flocculated.
As observed in the previous section on coupling agents, there was a correlation
between the peak torque values during polymer/powder mixing and the degree of
particulate dispersion observed in the "coating suspensions" (i.e., the suspensions
prepared for coating the alumina powders with Fluorad FC-740). The sample with 0.6
vol% Fluorad FC-740 had a high peak torque (Figure 4.104), while the corresponding
coating suspension showed good dispersion (Figure 4.102). In contrast, the sample with
6.0 vol% Fluorad FC-740 had a low peak torque (Figure 4.104), while the corresponding
coating suspension was highly flocculated. As discussed for the case of the samples
prepared with coupling agents, the differences in peak torque values may be due to
different porosity characteristics of dried powders.

RELATIVE VISCOSITY SHEAR STRESS (Pa)
1.0
278
20 vol% A1203
0 50 100 150 200 250 300
7
6
5
4
3
2
1
0
0 50 100 150 200 250 300
SHEAR RATE (l/a)
0.6 vol% Fluorad FC-740 in Heptane
pH=4 DI Water
20 vol% A1203
J . I . I . L
Figure 4.103 Plots of shear stress and relative viscosity vs. shear rate for 20 vol%
alumina in heptane with 0.6 vol% Fluorad FC 740 and in pH=4 DI
water.

TORQUE (g-m) TORQUE (gm) TORQUE (gm)
279
Figure 4.104 Plots of torque vs. mixing time for 50 vol% alumina/polyethylene
samples prepared with indicated Fluorad FC 740 concentrations.

280
As observed in many other parts of this study, there is a correlation between the
peak torque values observed during mixing and the state of particulate dispersion that
develops in the polymer/powder batch. QM and rheological data show that the sample
with 0.6 vol% Fluorad FC-740 (which has a high peak torque during mixing) develops
excellent particulate dispersion. In contrast, the sample with 6.0 vol% Fluorad FC-740
(which has low peak torque during mixing) is poorly dispersed. The Dpc histograms are
shown in Figure 4.105 and the results are also summarized in Table 4.19. The sample
with 0.6 vol% Fluorad has low Dpc values (i.e., essentially the same as the sample
prepared with untreated alumina), while the sample with 6.0 vol% Fluorad has
considerably higher Dpc values. Figure 4.106 shows plots of dynamic viscosity,
modulus, and tangent delta vs. measuring frequency for samples prepared with and
without the Fluorad FC-740 additions. Lower viscosity and modulus values are observed
for the samples with untreated powder and the powders treated with 0.6 vol% Fluorad
FC-740; this is consistent with the lower Dpc values for these samples. Higher viscosity
Table 4.19 Summary of Dpc results for 50 vol% alumina/polyethylene samples
prepared with different Fluorad FC 740 concentrations.
Sample
Dpc (¿un)
Percentage of
each category*
average
value
standard
deviation
small
medium
large
No Additive
0.43
0.16
40.6
47.7
11.7
0.6 vol% Fluorad
0.42
0.17
45.8
41.7
12.5
6 vol% Fluorad
0.49
0.16
27.4
54.2
18.4
* Small if Dpc <0.4 ^m; medium if 0.4 /xm< Dpc <0.6 ¿un; and large if Dpc >0.6
¿un.

NUMBER PERCENT NUMBER PERCENT NUMBER PERCENT
20
18 -
16 -
14 -
12 -
10 -
8 -
8 -
4 -
2 -
0 -
20
Jf
1
I
| | |
V, V, Vs
V, Vs V;
III
III
V V V
III
50 vol% A1203
No Additive
Mean Diameter = 0.43 /xm
¡ JL
in
Vs.
^ IP Ifl Ifl P Ep Z$L
“S” —|—i—i—i—(-
18 -
16 -
14 -
12 -
10 -
8 -
6 -
4 -
2 -
0 -
20
""II
llll
I I I; «
fill
II
V V V V,
I
111
!
ifl
50 vol% A1203
0.6 vol% Fluorad FC-740
Mean Diameter = 0.42 /xm
li
np -Oja—,—op>—, j-
18 -
16 -
14 -
12 -
10 -
8 -
6 -
4 -
2 -
0 -
ill
min
lililí im
50 vol% A1203
6 vol% Fluorad FC—740
Mean Diameter = 0.49 /xm
i
0.0 0.2 0.4 0.6 0.0
EQUIVALENT DIAMETER (/xm)
qa EP cp -i.
T—r
1.0
1.2
281
Figure 4.105 Histogram plots of Dpc distributions for 50 vol% alumina/polyethylene
samples prepared with indicated Fluorad FC 740 concentrations.

STORAGE MODULUS (Pa) DYNAMIC VISCOSITY (Pa-s
0.1 1 10 100
FREQUENCY (rad/s)
282
(A)
(B)
Figure 4.106 Plots of (A) dynamic viscosity, (B) storage modulus, (C) loss modulus,
and (D) tangent delta vs. frequency for 50 vol% alumina/polyethylene
samples prepared with indicated Fluorad FC 740 concentrations.

TANGENT DELTA LOSS MODULUS (Pa)
Figure 4.106 (Continued)

284
and modulus values (particularly at low measuring frequencies) are observed for the
sample with 6.0 vol% Fluorad FC-740; this is consistent with the higher Dpc values for
these samples. It should be noted that Figure 4.106 shows direct comparisons of
suspension viscosity and modulus values, i.e., instead of comparisons based on relative
dynamic viscosity and relative modulus values. However, these comparisons are valid
because the Fluorad FC-740 additions have very little effect on the rheological properties
of the polymer. For example, Figure 4.107 shows that Fluorad FC-740 additions
Figure 4.107 Plots of dynamic viscosity vs. frequency for polyethylene with indicated
Fluorad FC 740 concentrations.

285
produce only small changes in dynamic viscosity of PE melts. Figure 4.108 shows a plot
of relative dynamic viscosity vs. measured frequency for the alumina/PE mixtures with
and without the Fluorad additives.
Stress relaxation and steady-shear rheological measurements (Figures 4.109 and
4.110) are generally consistent with the conclusions drawn from the Dpc and dynamic-
shear rheological data. As expected, the sample with 0.6 vol% Fluorad FC-740 shows
a short relaxation time (which is almost identical to the sample with the untreated
FREQUENCY (rad/s)
Figure 4.108 Plots of relative (dynamic) viscosity vs. frequency for 50 vol%
alumina/polyethylene samples prepared with indicated Fluorad FC 740
concentrations.

STRESS (Pa)
286
TIME (s)
Figure 4.109 Plots of residual stress vs. time for 50 vol% alumina/polyethylene samples
prepared with indicated Fluorad FC 740 concentrations.

SHEAR STRESS (Pa) SHEAR STRESS (Pa)
1000
287
Figure 4.110 Plots of shear stress vs. shear rate for 50 vol% alumina/polyethylene
samples prepared with indicated Fluorad FC 740 concentrations.

288
powder). In contrast, the poorly-dispersed sample with 6.0 vol% Fluorad FC-740 shows
a much longer relaxation time. The steady-shear flow behavior for the sample with 0.6
vol% Fluorad FC-740 is slightly shear thinning and viscosities are relatively low, while
the sample with 6.0 vol% Fluorad FC-740 shows highly thixotropic flow behavior and
much higher viscosities (especially at low shear rates).
4.4.3. Lubricants
Fatty acids (hydrocarbon molecules with carboxylic acid end groups) are
commonly used as lubricants in ceramic processing operations. For example, lubrication
of steel dies with stearic acid or metal stearates has been shown to decrease wall stresses,
increase pressure transmission distances, and reduce ejection pressures during dry
compaction (i.e., dry pressing) of powders [Bow50, Dim83, Ree88, Str77]. Fatty acids
are also commonly used in extrusion and injection molding operations for similar reasons
[Edi86, Ste90, Zha88]. In some ceramic processing operations, the additive is used
solely as an "external lubricant," i.e., the bulk surfaces in contact with the powder or the
powder/fluid batch (i.e., die walls, extruder barrels, etc.) are coated with a lubricating
film [Dim83, Str77]. However, the fatty acids can also be mixed directly with the
ceramic powder or powder/fluid batch (i.e., prior to the shape-forming operation). In
these cases, it is sometimes suggested that the fatty acids (or other additives) can act as
an "internal lubricant" which reduces interparticle friction during mixing and shape
forming operation [Edi86, Ree88, Ste90, Zha88]. In the opinion of this author,
however, there is no evidence which directly demonstrates that chemical additives reduce
interparticle friction during such operations. Although stearic acid is commonly referred

289
to as a lubricant, its specific role in the processing of powder/polymer melt mixtures has
not been investigated in detail. Thus, the objective in this section is to improve our
understanding of the effect of stearic acid on mixing and dispersion behavior in
alumina/PE mixtures.
As described in section 3.1.2, one method (referred to as "pretreatment method")
for incorporating stearic acid into alumina/PE batches involved coating the powder prior
to the high-shear mixing operation. Stearic acid was initially dissolved in carbon
disulfide, CS2, (at various concentrations) to form clear solutions. Coating suspensions
were then prepared by mixing the alumina powder (20 vol%) with the stearic acid/CS2
solutions (80 vol%). (The concentrations listed are based on the volume ratios in the
alumina/stearic acid/PE mixtures that were eventually prepared. The latter mixtures
were prepared with 50 vol% alumina. Thus, a 0.6 vol% CS2 suspension had an
alumina/stearic acid volume ratio of 50/0.6, while the alumina/stearic acid/PE volume
ratio was 50/0.6/49.4.) Suspensions were then dried at 40°C for 22 hr to form coated
powders that were subsequently mixed with PE under the usual conditions (150°C/30
min/200 rpm). As discussed in section 4.4.1 and 4.4.2., the rheological properties of
the coating suspensions are of interest because the alumina powder characteristics
produced after liquid (i.e., CSj) removal are directly related to the state of dispersion in
the original suspension. However, carbon disulfide/alumina suspensions prepared with
0 and 0.2 vol% stearic acid flocculated so extensively that it was not possible to carry
out rheological measurements. (Large floes settled to the bottom of the suspension
within ~3 seconds.) Rheological measurements were carried out on suspensions

290
prepared with 0.6 and 2.0 vol% stearic acid (Figure 4.111). Both samples showed
extensive flocculation (as indicated by the yield stresses and thixotropic flow behavior),
although dispersion was worse in the sample with 2.0 vol% stearic acid. (Poor
dispersion for both suspensions was also indicated by comparison with the rheological
properties for the electrostatically-stabilized alumina suspensions prepared at pH=4 with
no chemical additives, Figure 4.111.)
In contrast to the results in sections 4.4.1. and 4.4.2., there is no clear correlation
between the characteristics of the coating suspensions and the peak torque values
Figure 4.111 Plots of shear stress vs. shear rate for 20 vol% alumina suspension (in
pH=4 DI water) and coating suspensions (in CS2) prepared with 20 vol%
alumina and indicated stearic acid concentrations.

291
observed during powder/polymer mixing. Although all of the suspensions prepared with
CS2 (0-2.0 vol% stearic acid) were highly flocculated, peak torque values showed
dramatic differences. Figure 4.112 shows that the peak torque during mixing the sample
with the CS2-treated alumina (0 vol% stearic acid) is approximately the same as observed
for the sample with untreated alumina. The peak torque values decreases significantly
for samples with stearic acid additions. In fact, the samples with 0.6 and 2.0 vol%
stearic acid have the lowest peak torque values observed in this entire study for mixing
operations carried out at 150°C.
The results in Figure 4.112 suggest the possibility that some type of lubricating
and/or wetting effect becomes operative when stearic acid is added. There is evidence
that wetting is improved by stearic acid additions or CS2 treatment (0 vol% stearic acid).
Figure 4.113 shows plots of contact angle vs. time for sessile drops of PE Sclair
deposited on dry pressed compacts that were prepared with coated alumina powders
having varying stearic acid concentration. Wetting is enhanced with CS2 treatment and
0.2 vol% stearic acid addition. Increasing the amount of stearic acid (0.6 and 2.0 vol%)
does not further improve the wetting behavior. The polymer penetration method was
also used to demonstrate improved wetting (Figure 4.114). The product (k-cos0) for PE
(AC-9) with a compact prepared with stearic acid-treated (0.6 vol%) powder is ~ 1.15
times the value for a compact prepared with untreated powder. The improved wetting
and faster polymer penetration with stearic acid additions could enhance polymer
penetration into powder agglomerate pore channels during mixing, thereby minimizing
the increase in suspension viscosity (and measured torque values) that occurs when

TORQUE (g m) TORQUE (g-m)
292
Figure 4.112 Plots of torque vs. mixing time for 50 vol% alumina/polyethylene samples
prepared with indicated stearic acid concentrations. (Pretreatment method).

TORQUE (gm) TORQUE (g m) TORQUE (gm)
Figure 4.112 (Continued)

294
15 20
TIME (MIN)
35
Figure 4.113 Plots of the contact angle vs. time for polyethylene melts (Sclair 2915) on
dry-pressed powder compacts prepared with stearic acid treated alumina
powders.

295
TIME (SEC)
Figure 4.114 Plots of penetration depth vs. time for polyethylene melts into stearic acid-
treated alumina powder compacts.
powder is incorporated into the polymer melt. However, this cannot be proved
conclusively since other phenomena (e.g., lubricating effects) might also be responsible
for the lower peak torque values observed in samples mixed with stearic acid. It is of
interest, for example, to determine if stearic acid reduces interparticle friction and/or
friction between the mixer (bowl and roller blade surfaces) and the powder/polymer
batch. The former effect was not be assessed in this study. In regards to the latter
effect, an experiment was carried out in which the rotor plates of the RDS viscometer

296
were coated with a thin film of stearic acid. Rheological measurements (dynamic-shear,
steady-shear, and stress relaxation) were then carried out on two samples which contained
no stearic acid additions (i.e., untreated alumina/PE samples mixed at 150 and 220°C).
Figures 4.115-4.117 show that slightly lower stresses (and, consequently, slightly lower
viscosities and moduli) were measured when the rotor plates were coated with stearic
acid. The largest effect was observed in the steady-shear measurements of the poorly-
dispersed 220°C sample (Figure 4.116).
The effect of stearic acid additions on particulate dispersion was investigated using
QM and rheological measurements. In contrast to other results in this study, the state
of dispersion in mixed batches did not correlate well with the peak torque values
observed during mixing. For example, consider the mixed alumina/PE samples prepared
with CS2-treated powders containing 0 and 0.2 vol% stearic acid. The average Dpc
value (0.51 /¿m) for these samples was substantially larger (indicating poorer dispersion)
than the value for the sample prepared with untreated alumina powder (0.43 /¿m). (The
Dpc histograms for all samples are shown in Figure 4.118 and the results are also
summarized in Table 4.20.)
This result is puzzling because the CS2-treated samples with 0 and 0.2 vol%
stearic acid had large peak torque values during mixing (especially for the former
sample). It is surprising that the Dpc values were lower (0.48 /im average) for the CS2-
treated sample with 0.6 vol% stearic acid, despite the much smaller peak torque value.
In addition, the Dpc values increase again (0.53 /im average) for the CS2-treated powder
with 2.0 vol% stearic acid, although there is little change in peak torque value. Despite

STORAGE MODULUS (Pa) DYNAMIC VISCOSITY (Pa-s
10000
1000 r
100 r
1 10
FREQUENCY (rad/s)
(B)
Figure 4.115 Plots of (A) dynamic viscosity, (B) storage modulus, (C) loss modulus,
and (D) tangent delta vs. frequency for alumina/polyethylene samples
with and without stearic acid coating on viscometer prior to
measurements.

TANGENT DELTA LOSS MODULUS (Pa)
Figure 4.115 (Continued)

1400
1200
1000
800
600
400
200
0
1400
1200
1000
800
600
400
200
0
re 4.11
299
50 volS Al203
150°C, W/O Stearic Acid ^
^150°C, W/Stearic Acid
220°C, W/O Stearic Acid ^
10 15
SHEAR RATE (1/s)
20
25
Plots of shear stress vs. shear rate for alumina/polyethylene samples
with and without stearic acid coating on viscometer prior to
measurements.

STRESS (Pa)
300
TIME (s)
Figure 4.117 Plots of residual stress vs. time for alumina/polyethylene samples with
and without stearic acid coating on viscometer prior to measurements.

NUMBER PERCENT NUMBER PERCENT NUMBER PERCENT
20
18 -
16 -
14 -
12 -
10 -
8 -
6 -
4 -
2 -
0 -
20
18 -
16 -
14 -
12 -
10 -
8 -
6 -
4 -
2 -
0 -
20
18 -
16 -
14 -
12 -
10 -
8 -
8 -
4 -
2 -
0 -
I
III
¡ I I
III
HI
50 vol% A1203
No Additive
Mean Diameter = 0.43 /xm
¡I
^ f? T T y
301
I
_j—r^i ÍP ^
!
50 vol% AIz03
0 vol% Stearic Acid
(Pretreatment)
Mean Diameter = 0.51 /xm
Hi!
1111
I I
1
1
7A VA njn
T" 1 r
IIP
I III
50 vol% A1203
0.2 vol/S Stearic Acid
(Pretreatment)
Mean Diameter = 0.51 /xm
nil
1
lllllllllllliiiil
0.0
0.2
I
0.4 0.6 0.8
EQUIVALENT DIAMETER (/xm)
%1 ^
1.0
1.2
Figure 4.118 Histogram plots of Dpc distributions for 50 vol% alumina/polyethylene
samples prepared with indicated stearic acid concentrations.
(Pretreatment method).

302
-S-
III
III
50 vo\% A1203
0.6 volJ. Stearic Acid
(Pretreatment)
Mean Diameter - 0.48 /¿m
-L
0.00
1
I!
1
50 volJS A1203
2.0 vol% Stearic Acid
(Pretreatment)
tlean Diameter - 0.53 ¿un
0.20
0.40 0.60
EQUIVALENT DIAMETER (¿mi)
1? , T
0.80 1.00 1.20
Figure 4.118 (Continued)
the poor correlation with peak torque values, it is interesting to note that the final state
of dispersion in the mixed polymer/powder batches still appears to correlate with the
state of dispersion in the coating suspensions. (The coating suspensions were all
flocculated and this is consistent with the high Dpc values in the final polymer/powder
mixes. In addition, the least flocculated coating suspension (0.6 vol% stearic acid) had
the lowest Dpc value.)

303
Table 4.20 Summary of Dpc results for 50 vol% alumina/polyethylene samples
prepared with different concentrations of stearic acid.
Sample
Dpc (/zm)
Percentage of
each category*
average
value
standard
deviation
small
medium
large
No Additive
0.43
0.16
40.6
47.7
11.7
Pretreatment with Stearic Acid:
0 vol%
0.51
0.17
22.0
54.7
23.3
0.2 vol%
0.51
0.18
25.5
51.8
22.7
0.6 vol%
0.48
0.18
30.7
49.8
19.4
2.0 vol%
0.53
0.19
20.4
53.1
26.5
Direct Addition with Stearic Acid:
0.2 vol%
0.48
0.15
26.8
57.9
15.3
0.6 vol%
0.49
0.15
24.5
59.9
15.6
2.0 vol%
0.50
0.16
24.2
55.5
20.3
Particulate dispersion in the powder/polymer mixtures was also assessed from
rheological data and results were generally consistent with the QM measurements.
Figure 4.119 shows plots of dynamic viscosity, modulus, and tangent delta vs. measuring
frequency for samples prepared with and without the stearic acid additions. Plots of
relative dynamic viscosity vs. frequency are shown in Figure 4.120. (These are obtained
by dividing suspension viscosities, Figure 4.119, by the appropriate polymer viscosities
in Figure 4.121.) As expected from the Dpc data, the lowest viscosity value is observed
for the sample prepared with untreated alumina powder. The viscosity values (at low
frequencies) increase for samples in the order 0.6 < 0.2 < 2.0 vol% stearic acid and
this correlates well with increasing Dpc values (Figure 4.118 and Table 4.20). The
sample prepared with 0 vol% stearic acid (CS2-treated alumina) deviates somewhat from

STORAGE MODULUS (Pa) DYNAMIC VISCOSITY (Pa-
304
FREQUENCY (rad/s)
(A)
(B)
Figure 4.119 Plots of (A) dynamic viscosity, (B) storage modulus, (C) loss modulus,
and (D) tangent delta vs. frequency for alumina/polyethylene samples
prepared with indicated stearic acid concentrations.

TANGENT DELTA LOSS MODULUS (Pa)
Figure 4.119 (Continued)

RELATIVE VISCOSITY
306
Figure 4.120 Plots of relative (dynamic) viscosity vs. frequency for 50 vol%
alumina/polyethylene samples prepared with indicated stearic acid
concentrations.

307
FREQUENCY (rad/s)
Figure 4.121 Plots of dynamic viscosity vs. frequency for polyethylene with indicated
stearic acid concentrations.
the trend expected from Dpc data. The viscosity and modulus values (Figure 4.119) are
somewhat lower than expected at low frequencies (e.g., compare to the sample with 0.2
vol% stearic acid), while the values are somewhat higher than expected at high
frequencies (e.g., compare to sample with 2.0 vol% stearic acid). (The sample with 0.2
vol% stearic acid also has slightly larger viscosity and modulus values (Figure 4.119) at
high frequency than expected from the Dpc data.) These results suggest the agglomerate
(particle network) characteristics may be different for the 0 and 0.2 vol% stearic acid

308
samples. For example, larger viscosity and moduli values at high frequencies suggest
that the particulate network structure is more deformation-resistant. This in turn may
have some relationship to the observation that the CS2-treated samples with 0 and 0.2
vol% stearic acid develop poor particulate dispersion despite the relatively large peak
torque values that develop during mixing. It is possible, for example, that the
agglomerates in CS2-treated alumina with 0 or 0.2 vol% stearic acid are stronger than
agglomerates in untreated alumina. This was investigated by measuring PSD’s on
aqueous (pH=4) alumina suspensions after sonication for various times (0 sec, 15 sec,
and 30 min). With no sonication, larger particle (i.e., agglomerate) sizes are measured
for the suspension prepared with CS2-treated alumina powders (0 vol% stearic acid), as
shown Figure 4.122. These agglomerates are apparently broken down within 15 sec of
sonication, as no significant differences were observed in PSD’s after the two samples
are subjected to sonication for 15 sec or 30 min (Figure 4.122). The results suggest that
CS2-treated powders have some stronger agglomerates, although the evidence is certainly
not conclusive.
Stress relaxation and steady-shear rheological measurements are generally
consistent with the conclusions drawn from the Dpc and dynamic-shear rheological data.
For example, samples with larger Dpc values have longer stress relaxation times (Figure
4.123). (The particulate network structure is more extensive in poorly-dispersed
samples.) Figure 4.124 shows shear stress vs. shear rate flow curves for the untreated
and treated samples. As expected, poorly-dispersed samples (0, 0.2, and 2.0 vol%
stearic acid) have high viscosities, large yield stresses, and highly shear thinning flow

CUMULATIVE VOLUME PERCENT CUMULATIVE VOLUME PERCENT
309
(A)
EQUIVALENT SPHERICAL DIAMETER (/mi)
(B)
EQUIVALENT SPHERICAL DIAMETER (/im)
Figure 4.122 Centrifugal photosedimentation data for stearic acid treated alumina
powders with (A) 15 sec and (B) 30 min of sonication.

STRESS (Pa)
310
TIME (s)
Figure 4.123 Plots of residual stress vs. time for 50 vol% alumina/50 vol%
polyethylene samples prepared with indicated stearic acid
concentrations. (Pretreatment method).

SHEAR STRESS (Pa) SHEAR STRESS (Pa)
311
0 5 10 15 20 25
SHEAR RATE (1/s)
Figure 4.124 Plots of shear stress vs. shear rate for 50 vol% alumina/polyethylene
samples prepared with indicated stearic acid concentrations.
(Pretreatment method).

312
Figure 4.124 (Continued)
behavior. However, the flow behavior for the sample with 0.6 vol% stearic acid is not
in line with expectations. The shear stresses are lower (i.e., viscosities are lower) at
most shear rates compared to the sample with untreated powder. This reason for this
behavior is unclear, although it may be indicative of wetting and/or lubricating effects
associated with the stearic acid addition. (For example, recall the small decreases in
shear stress values observed in Figure 4.115-4.117 when the rotor plates of the rheometer
were coated with a film of stearic acid.) However, it should also be re-emphasized that
some uncertainty exists in steady-shear measurement at higher shear rates because of the
tendency for material to be ejected from the gap between the rotors.

313
To this point, all of the chemical additives used in this study (coupling agents,
Fluorad, and stearic acid) have been added to the alumina powder prior to the
polymer/powder mixing operation. Thus, physicochemical characteristics of the as-
received alumina powder are modified by the suspension preparation and drying steps
used to incorporate the additives. For example, it was demonstrated that the porosity
characteristics of powder agglomerates may be significantly altered by such treatment.
To avoid such changes, an alternative processing strategy ("direct addition" method) was
adopted in which untreated alumina powder was added directly to polymer melts that
already contained stearic acid additions. Other than this modification, the usual
alumina/PE mixing procedure was followed.
Figure 4.125 shows plots of torque vs. mixing time for sample prepared by the
direct addition method. The mixing curves are very similar to those observed in Figure
4.112 for samples prepared used pretreated powders. Once again, peak torque values
decrease as the stearic acid concentration increases. As discussed below, these samples
also show relatively poor dispersion after mixing (i.e., compared to the sample prepared
with no stearic acid).
The mixing method had relatively minor effects on the Dpc values and rheological
properties. Perhaps the most significant difference was observed in the samples with 0.2
vol% stearic acid. Viscosity and modulus values at low frequencies (dynamic-shear),
yield stress (steady-shear), and stress relaxation time were all lower for the sample
prepared by the direct addition method (Figures 4.126-4.129). This correlated well with
lower Dpc values (Figure 4.130 and Table 4.20). The improved dispersion in this

TORQUE (g-m) TORQUE (g-m) TORQUE (g-m)
314
Figure 4.125 Plots of torque vs. mixing time for 50 vol% alumina/polyethylene samples
prepared with indicated stearic acid concentrations. (Direct addition
method).

315
sample tends to support earlier arguments that the CS2-treated samples (with 0 and 0.2
vol% stearic acid) formed strong agglomerates.
The mixing method also produced some differences in the samples prepared with
2.0 vol% stearic acid. The direct addition method gave slightly lower Dpc values. This
correlated with lower viscosities, moduli, and relaxation times for this sample. The only
data that appeared contradictory was the steady-shear measurements. For example, the
sample with 2.0 vol% stearic acid developed relatively low shear stress at high shear
rates, i.e., less than stresses measured for the samples with 0-0.6 vol% stearic acid. As
noted earlier in this section, there is some concern regarding the reliability of the steady-
shear data at high shear rates because of the tendency for material to be ejected from the
gap between the rotors. This may of be of greater concern for the samples with stearic
acid additions, since available evidence suggests that wetting and/or lubricating effects
may be enhanced with these samples.

STORAGE MODULUS (Pa) DYNAMIC VISCOSITY (Pa-
316
(A)
(B)
Figure 4.126 Plots of (A) dynamic viscosity, (B) storage modulus, (C) loss modulus,
and (D) tangent delta vs. frequency for 50 vol% alumina/polyethylene
samples prepared with indicated stearic acid concentrations.

TANGENT DELTA LOSS MODULUS (Pa)
317
(C)
(D)
Figure 4.126 (Continued)

RELATIVE VISCOSITY
318
FREQUENCY (rad/s)
Figure 4.127 Plots of relative (dynamic) viscosity vs. frequency for 50 vol%
alumina/polyethylene samples prepared with indicated stearic acid
concentrations. (Direct addition method).

SHEAR STRESS (Pa) SHEAR STRESS (Pa)
319
0 5 10 15 20 25
SHEAR RATE (1/s)
Figure 4.128 Plots of shear stress vs. shear rate for 50 vol% alumina/polyethylene
samples prepared with indicated stearic acid concentrations. (Direct
addition method).

STRESS (Pa)
320
TIME (s)
Figure 4.129 Plots of residual stress vs. time for 50 vol% alumina/polyethylene
samples prepared with indicated stearic acid concentrations. (Direct
addition method).

NUMBER PERCENT NUMBER PERCENT NUMBER PERCENT
20
18 -
16 -
14 -
12 -
10 -
8 -
6 -
4 -
2 -
0 -â– 
20
lililí
1
-v-
II I I A
Wmm
mtmtm
' I
50 vol% A1_0.
2 3
0.2 vol/J Stearic Acid
(Direct Addition)
Mean Diameter = 0.48 /xm
Hi
18 -
16 -
14
12 -
10 -
8 -
6 -
4 -
2 -
0
20
III
A i A
flflllflf
li
50 vol% A1 0
2 3
0.6 vol% Stearic Acid
(Direct Addition)
Mean Diameter = 0.49 /xm
ilililili
2
^ ^ ^ ^ 1^3 ^
18 -
16 -
14 -
12 -
10 -
8 -
6 -
4 -
2 -
0 -
0.0
50 vol% ALO,
2 vol% Stearic Acid
(Direct Addition)
J
I p I |fl
111 IIP
II 111 lili
ill 111 lili
ill 11 i llilll
Mean Diameter = 0.50 /xm
0.2
0.4 0.8 0.8
EQUIVALENT DIAMETER (/xm)
1.0
1.2
321
Figure 4.130 Histogram plots of Dpc distributions for 50 vol% alumina/polyethylene
samples prepared with indicated stearic acid concentrations. (Direct
addition method).

CHAPTER 5
SUMMARY
The state of ceramic particulate dispersion in polymer melts was significantly
influenced by mixing conditions and the characteristics of the starting materials (i.e.,
ceramic powders, polymers, and chemical additives). High purity (>99.98%), fine-
sized (-0.4 /xm Stokes diameter) alumina powder and low molecular weight (Mn
*2100), low density polyethylene were used for most of the experiments. Samples were
prepared using a high shear bowl mixer and the mixing operation was monitored by a
torque rheometer. The state of particulate dispersion was evaluated by rheological
measurements on samples heated to 125°C. In addition, a technique was developed to
evaluate the state of dispersion by quantitative microscopy on samples cooled to room
temperature. The method involved measurements of the equivalent projection
circumscribing diameter (Dpc) on plasma-etched surfaces. Ceramic/polymer melt wetting
behavior was evaluated by the sessile drop method and the polymer penetration method.
Important results are summarized below.
Mixing Conditions. Samples mixed at higher temperatures (175 and 220°C) had higher
viscosity and modulus values, higher yield stresses, extensive thixotropy, longer
relaxation times, and larger Dpc values. These characteristics were typical for samples
having extensive particulate network structure, indicating that samples were not dispersed
well. In contrast, samples mixed at lower temperatures (125 and 150°C) showed lower
322

323
viscosity and modulus values, lower yield stresses, limited thixotropy, shorter relaxation
times, and smaller Dpc values, indicating that the particulate dispersion was improved.
These differences were attributed primarily to the effect of mixing temperature on the
viscosity of the polymer matrix. As expected, the polymer viscosity increased with
decreasing temperature. This, in turn, resulted in the development of higher shear forces
during mixing. (This was indicated by higher torque values during mixing, as observed
by torque rheometry.) Thus, powder agglomerates were broken down more effectively
at lower mixing temperatures. It was observed, however, that polymer/powder wetting
became poorer with decreasing mixing temperature. Therefore, the optimum mixing
temperature should be low enough to develop large shear forces to break down
agglomerates, but high enough so that wetting of the powder by the polymer melt is not
adversely affected. In the present study, mixing temperature in the range HS-lSiFC
produced powder/polymer batches with good particulate dispersion.
It was also determined that the rotor speed used during mixing should be high
enough to develop sufficient torque for agglomerate breakdown. In addition, higher rotor
speed was helpful in stabilizing particles against re-agglomeration (coagulation). Multi¬
segment mixing experiments indicated that a dynamic equilibrium between agglomerate
breakdown and coagulation was established during the mixing operation. Higher rotor
speed (i.e., higher shear rate) and lower mixing temperature (i.e., higher polymer melt
viscosity) increased the agglomerate breakdown rate and decreased the coagulation rate,
thereby leading to improved particulate dispersion in mixed samples. It was also found
that the state of particulate dispersion could not be substantially improved (i.e., by

324
lowering the temperature or raising the rotor speed) once the powders were flocculated
and coated by the polymer melt.
Ceramic Powder Characteristics. Alumina powders were heat treated at temperatures in
the range 100-1000°C prior to mixing with polyethylene melts. Rheological and
quantitative microscopy measurements showed that the samples prepared with powders
heat treated in the range 100-450°C were poorly dispersed compared to a sample
prepared with uncalcined powder. Samples prepared with the heat treated powders
showed lower torque peaks during mixing, suggesting that agglomerates were not broken
down as effectively. Weight loss measurements and Fourier transform infrared spectra
showed that molecular water (and some hydroxyl groups) were gradually removed as the
alumina powders were heat treated in the range 100-450^. Particle size measurements
and powder compact microhardness measurements suggested that water removal altered
the alumina powder characteristics and, in turn, altered the powder/polymer mixing
behavior. However, the specific mechanism responsible for reducing the torque values
during mixing was not clearly identified.
Powders heat treated at higher temperatures (i.e., 600-1000°C) showed extremely
poor dispersion, as indicated by rheological and quantitative microscopy measurements.
Characterization of powders (i.e., by particle size measurements) and powder compacts
(i.e., by microhardness and mercury porosimetry measurements) showed that heat
treatment in the range 600-1000°C resulted in the formation of hard agglomerates by
solid state sintering. (Calculations showed that neck growth via surface diffusion was
likely, even at 600°C.) Despite the observation of high torque values during the mixing

325
powder/polymer mixing operation, the stresses generated were insufficient to break down
the hard agglomerates.
Aging Phenomena. Samples prepared with calcined powders were highly susceptible to
aging effects when stored under ambient atmospheric conditions (i.e., in air at room
temperature). Samples showed decreases in viscosity and modulus values during the
early stages of aging, followed by large increases in these values as the aging time
increased. Rheological and gravimetric measurements on samples stored in vacuum and
in water showed that the aging effects were due to moisture absorption. The initial
decrease in viscosity and modulus values was attributed to a lubricating effect at the
powder/polymer interface, although direct evidence in support of this mechanism was not
obtained. (However, it was shown that the effect could not be caused by plasticization
of the matrix phase, since a polymer sample containing no alumina powder showed no
weight gain when immersed in water.) The large increase in viscosity and modulus
values with longer aging times was caused by the formation of water vapor bubbles
inside the alumina/PE mixtures during the rheological test (which was carried out at
125°C). This was proven by SEM observations on the fracture surface of a sample aged
in water and then heated to 125°C for 10 min.
Polymer Characteristics. Alumina/polymer mixtures prepared with polyethylene (PE)
and ethylene-acrylic acid (EAA) had similar rheological properties and Dpc values, while
mixtures prepared with ethylene-vinyl acetate (EVA) had higher viscosity (especially at
low frequencies) and larger Dpc values. These results indicated that particulate
dispersion was similar for the PE and EAA samples, but EVA samples were not as well

326
dispersed. Based on the limited range of chemical compositions investigated, the amount
of the functional side group in the polymer had little effect on the state of dispersion
achieved. Instead, the type of functional side group had an important effect on the state
of dispersion achieved. The reason(s) for the difference in state of dispersion for
samples mixed with different polymers were not clear. Correlations between the mixing
torque curves, rheological properties, Dpc measurements, and ceramic/polymer wetting
behavior were not straightforward. It is suggested that more detailed characterization of
physicochemical interactions (e.g., adhesion and bonding) at the polymer/powder
interface and at the interface between the mixer and the polymer/powder batch is needed.
Chemical Additives. In most cases, the chemical additives (coupling agents, surfactants,
or lubricants) were added to the alumina powder prior to the polymer/powder mixing
operation. The physicochemical characteristics of alumina powders were modified by
the suspension preparation and drying steps used to incorporate the additives. The effects
of these additives on powder/polymer mixing, dispersion, and rheological behavior were
investigated.
Coupling agents. The coupling agents investigated in this study included a
zircoaluminate, a titanate, and two silanes (Z-6020 and Z-6076). The zircoaluminate and
silane Z-6020 coupling agents showed good solubility in water, while the others showed
relatively poor solubility. Coated alumina powders were prepared by mixing powders
with coupling agent/water "solutions." It appeared that alumina powders were not coated
as homogeneously by coupling agents which had poorer solubility in water (i.e., the
titanate and silane Z-6076). Furthermore, coating suspensions prepared with the titanate

327
and silane Z-6076 coupling agents were highly flocculated, while suspensions prepared
with the zircoalumínate and silane Z-6020 coupling agents were relatively well-dispersed.
This correlated with differences in mixing behavior of the coated (dry) powders with the
PE melts. Higher peak torques were observed in samples mixed with powders coated
with zircoaluminate and silane Z-6020 coupling agents. Rheological and quantitative
microscopy measurements indicated that improved particulate dispersion was achieved
in these samples after mixing. These results were consistent with previous observations
that high torque peaks generally correlated with improved breakdown of powder
agglomerates during mixing.
Surfactant. The surfactant investigated in this study was Fluorad FC-740.
Results were similar to those observed with the coupling agents in that good correlations
were observed between the state of dispersion in the coating suspensions, the peak torque
generated during polymer melt/coated powder mixing, and the state of dispersion in the
powder/polymer mixture. Coating suspensions prepared with 0.6 vol% Fluorad were
well-dispersed, while coating suspensions prepared with 6.0 vol% Fluorad were highly
flocculated. This correlated with the high peak torque value observed during mixing of
the alumina/PE melt sample with 0.6 vol% Fluorad and the low peak torque value
observed during mixing of the corresponding sample with 6.0 vol% Fluorad.
Rheological and quantitative microscopy measurements on mixed batches showed
relatively good dispersion for the former sample and relatively poor dispersion for the
latter sample.

328
Lubricant. The lubricant investigated in this study was stearic acid. In contrast
to results obtained with other chemical additives used in this study, there was a poor
correlation between the state of dispersion in the coating suspensions and the peak torque
values generated during mixing. In addition, there was a poor correlation between the
peak torque values generated during mixing and the state of dispersion (assessed by
rheological and quantitative microscopy measurements) that developed in the mixed
powder/polymer batches. Nevertheless, it was noted that the state of dispersion in these
batches was consistent with the state of dispersion in the coating suspensions. Additional
experiments concerning the mixing procedure and the wetting behavior were carried out,
but no definitive conclusions could be reached regarding the mechanisms by which stearic
acid affected mixing, dispersion, and rheological behavior.

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BIOGRAPHICAL SKETCH
The author was bom on July 17, 1959, in Taipei, Taiwan, Republic of China.
She received B.S. and M.S. degrees in chemical engineering from National Taiwan
University, R.O.C., in 1981 and 1983, respectively. In August 1983, she began her
doctoral work in chemical engineering at the University of Florida. She later switched
to materials science and engineering in May 1985 where she is now completing her
Ph.D. studies.
342

I certify that I have read this study and that in my opinion it conforms to
acceptable standards of scholarly presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
Michael D. Sacks, Chairman
Professor of Materials Science
and Engineering
I certify that I have read this study and that in my opinion it conforms to
acceptable standards of scholarly presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
Christopher D. Batich
Professor of Materials Science
and Engineering
I certify that I have read this study and that in my opinion it conforms to
acceptable standards of scholarly presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
Professor of Materials Science
and Engineering
I certify that I have read this study and that in my opinion it conforms to
acceptable standards of scholarly presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
E. Dow Whitney
Professor of Materials
and Engineering
cience

I certify that I have read this study and that in my opinion it conforms to
acceptable standards of scholarly presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
Gerald B. Westermann-Clark
Associate Professor of Chemical
Engineering
This dissertation was submitted to the Graduate Faculty of the College of
Engineering and to the Graduate School and was accepted as partial fulfillment of the
requirements for the degree of Doctor of Philosophy.
May 1992
¿^-'Winfred M. Philips
Dean, College of Engineering
Madelyn M. Lockhart
Dean, Graduate School

UNIVERSITY OF FLORIDA
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