DISPERSION OF CERAMIC PARTICLES IN POLYMER MELTS
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
UNIVERSITY OF FLORIDA LIBRARIES
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
This dissertation is dedicated to my parents for their love, understanding, and
TABLE OF CONTENTS
ACKNOWLEDGEMENTS ................................. ii
ABSTRACT ......................................... v
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
184.108.40.206 Effects of mixing temperature on theological and
wetting behavior ...................... 70
220.127.116.11 Quantitative microscopy ............. 94
18.104.22.168 Effects of rotor speed ................... 134
22.214.171.124 Effects of mixing time .................. 136
4.1.2 Multi-Segment Mixing Schedules ................. 136
126.96.36.199 Mixing with change in temperature .......... 146
188.8.131.52 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
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
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
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.
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
these chemical additives was investigated using torque rheometry, theological flow
measurements, ceramic/polymer melt wetting behavior, and quantitative microscopic
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
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
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
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
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
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].
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
LENGTH OF SCAN
Light intensity curves for two carbon black/polyethylene mixtures with
different states of particulate dispersion [Bes59].
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
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,
concentric-cylinder, and capillary viscometers [Dea82, Eir60]. These viscometers differ
in the geometries of the sensor systems, measurable viscosity levels, and operating shear-
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):
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
Shear rate ( )
Shear rate (f)
stress vs. shear rate and (B) viscosity vs. shear rate
Plots of (A) shear
for different types
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
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
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
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.
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)
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
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]:
S, = (1 4 )-
S= ( 1- )-2 (2.7)
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
t> 0 0
- II II\ h o
a N S o
O- O0 O \
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
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
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
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
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
I 60 1
2 min 4 min 3 min 1 min
Neoprene + Fillers + Curatives
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
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
Young's Equation: cosO =
Figure 2.6 Contact angle for a liquid droplet deposited on a solid substrate and
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
Another method for determining fluid/powder contact angles is to measure the
penetration rate of the fluid through the powder compact. The correlation between
penetration time and penetration distance is expressed by the Washburn equation
I2 = ( r cos 0) ( ) t (2.9)
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.
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
cos = (To ) ( ) = H ( )
l t t10 (2.10)
H = (T"i)
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
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
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)
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
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
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
Table 2.3 Isolated hydroxyl groups
on alumina surface observed in infrared
OH group Wave #(cm-') Number of nearest oxide neighbors
A 3800 4
B 3744 2
C 3700 0
D 3780 3
E 3733 1
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
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,
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
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
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
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
C 4 U
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
I 4 E
i| 0 I sl I
0 |1 EI I iII
| uS <- 23: U 2 ^
S. i tN:
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
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:
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
S CH2 (A)
/ \ /
--0 O' ,- +NH2
Si CH2 (B)
--0 O'-~-- +NH2
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
orientation of surfactant adsorbed on solid surfaces are controlled by many factors,
including the nature of surfactant, property of solid surface, solution concentration,
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
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
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
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
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,
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)
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.
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.
H H H H
H H H C=0
H H HO
Where 1, ml, m2, nl, and n2 are integers.
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.
S' |So -
i o oo oo a I>
- I S II
in 0 4 + V
-- a c + c C -
el ) U
|? tn VS Va
1- c> a, ^^
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.
(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
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.
NH2- (CH2) 2-NH- (CH2) 3-Si-O-CH3
Cl- (CH2) 3-Si-O-CH3
Titanate LICA 12
R-O-Ti-[O-P- (O-CH17) 2) 3]
Where R is a neoalkoxy group (The composition is not
revealed by the manufacturer).
Figure 3.2 Chemical structures of some chemical additives.
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.
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.
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,
1 CAPA-700, Horiba Instruments, Inc., Irvine, CA.
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.
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,
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,
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)
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)
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.
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
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
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.
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.
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
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).
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.
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.).
[ (G') + (G")2 ]12
[ (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) ]
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)
.#.- 0 -~'
Geometry of a cone-and-plate and a parallel-plate viscometer.
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.
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.
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
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
(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) 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
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
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.
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
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
3s Micromet 3, Buehler Ltd., Lake Bluff, IL.
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.
184.108.40.206 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
C 50 vol% A1203
1 0 I I I I I II I I I I I III I I I I I
0.1 1 10 100
1 C 50 vol% AI203
1 t e n ar l I f I l 1 I I I I fi ll
0.1 1 10 100
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
50 voIX Al203
1 10 100
Figure 4.1 (Continued)
a 125 C
0 150 C
S1& a 1 A -- --- --
0I I 100
Plots of dynamic viscosity vs. frequency for polyethylene at the
mixing temperature used in this study was very close to the drop temperature' of the
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].
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,
1 10 100
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
Figure 4.3 (Continued)
50 vo% A1203
38 vol% AI2O
i i m. 1 1 !! 1 1 i u I I 1 11111
0 38 vol% AI203
O 50 vol% AI203
A 59 vol% Al203
I I I I i .. .
50 vol% AI203
0 r I *I *- *- -* I
50 vol% A1203
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.
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
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.
1 0.1 1.
Plots of residual stress vs. time for 50 vol% alumina/50 vol%
polyethylene samples prepared at the temperatures indicated.
S : / ^ 59 vol% AI203
_E 50 vol% AI203
38 vol% AI2 03
10 I I I I I 1 1 I I
0.01 0.1 1
Figure 4.7 Plots of residual stress vs. time for alumina/polyethylene at the solids
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
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.
59 vol% Al20
v 220 C
S .. I ....I I
1 10 100
Figure 4.8 (Continued)
59 vol% Al,03
I I .I I ,, .Ii1
1 10 100
1 10 100
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.
1 10 100
1 10 100
Figure 4.9 (Continued)
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
38 vol% AI203
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.
38 vol% A1203
0.01 0.1 1
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
50 vol% Al203
100- Mixing Conditions: 220C, 200 rpm
Plots of torque vs. mixing time for 50 vol% alumina/50 vol%
polyethylene samples prepared at the temperatures indicated.
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
1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6
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
Figure 4.13 Plot of dynamic viscosity of polyethylene (A-C 9) vs. temperature.
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
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
Plots of penetration depth vs. time for polyethylene melts into alumina
powder compacts at the temperatures indicated.
125 150 175 200 225
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
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
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
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.
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.
220.127.116.11 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.