Group Title: experimental investigation of the rheological properties of various polystyrene composites /
Title: An Experimental investigation of the rheological properties of various polystyrene composites /
CITATION PDF VIEWER THUMBNAILS PAGE IMAGE ZOOMABLE
Full Citation
STANDARD VIEW MARC VIEW
Permanent Link: http://ufdc.ufl.edu/UF00098255/00001
 Material Information
Title: An Experimental investigation of the rheological properties of various polystyrene composites /
Physical Description: xvi, 112 leaves : ill. ; 28 cm.
Language: English
Creator: Small, James D., 1958-
Publication Date: 1989
Copyright Date: 1989
 Subjects
Subject: Polymers -- Rheology   ( lcsh )
Viscosity   ( lcsh )
Polymer melting   ( lcsh )
Chemical Engineering thesis Ph. D
Dissertations, Academic -- Chemical Engineering -- UF
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
 Notes
Thesis: Thesis (Ph. D.)--University of Florida, 1989.
Bibliography: Includes bibliographical references (leaves 107-110)
General Note: Typescript.
General Note: Vita.
Statement of Responsibility: by James D. Small, Jr.
 Record Information
Bibliographic ID: UF00098255
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: alephbibnum - 001485807
oclc - 21107681
notis - AGZ7922

Downloads

This item has the following downloads:

PDF ( 3 MBs ) ( PDF )


Full Text












AN LE..FEIillElTAL irJi. -_TIGATION OF THE
IRHEjLICAL FhjFEFTIE_ 'If VARIOUS POLYSTYRENE
A If,'- TES



















Jr.

.im.-z. C'. _,Tj],1 L, Jr .


A DIC'--:'F FAT[:r' PREL:ErJTElD TO THE GRADUATE SCHOOL
i.'F TEt U'JNi iE'lI 'rF FL:,hiD[A IN PARTIAL FULFILLMENT
'.'IF HE REU,,.i[:l ~IEr; l FR'F: THE DEGREE OF
L'I": T.:,i F FH i LOSOPHY

IrJl IE iT i.F FLORIDA

I ''? .'







































Copyright 1989

by

James D. Small, Jr.















ACKNOWLEDGMENTS


The author wishes to thank Dr. A.L. Fricke for his guidance and

friendship through the years required to obtain both the M.S. and Ph.D.

degrees. His example of the work ethic, his character, and his friend-

ship will always be an inspiration. He also wishes to thank Dr. G.A.

Campbell of Clarkson University who "bailed" the author out when his

first dissertation project proved unsuccessful after two years of

work. His enthusiasm for the subject and his friendship are truly

valued. The author would also like to thank Dr. C.L. Beatty whose

enthusiasm and spirit helped the author through some extremely bad times

during the course of this endeavor. He also wishes to express his

appreciation to Dr. G. Hoflund and Dr. M.O. Balaban for their willing-

ness to participate in the review and critique of this dissertation.

The author considers himself most fortunate to not only be able to claim

these gentlemen as his committee members, but to also be able to call

them friends.

The author would also like to express his appreciation to Debbie

Hitt, who prepared this manuscript, and to the Mobil Chemical Company

and the employees of the Fabrication Laboratory, who on extremely short

notice provided the necessary materials, processing equipment, and

expertise to accomplish this research. Finally, the author wishes to

express his gratitude to Miss JoEllen Kelly, the author's best friend

and the colleague who obtained the capillary viscometric data, to Mary


iii









Adams, who supplied the author with useful computer programs, and to

Mark Davidson, Ron Baxley and Tracy Lambert, who assisted the author in

solving the many electronic and mechanical problems that arose during

this work. The author thanks you all.
















TABLE OF CONTENTS


page

ACKNOWLEDGMENTS ............................................. iii

LIST OF SYMBOLS ............................................. vii

LIST OF TABLES .............................................. x

LIST OF FIGURES ............................................. xi

ABSTRACT .................................................... xv

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

PURPOSE OF INVESTIGATION .................................... 4

LITERATURE REVIEW ........................................... 5

Newton's Law of Viscosity ................................ 5
Parallel Disk Rheometry .................................. 6
Melt Rheology of Polymer Composites ...................... 13
Percolation Theory ....................................... 16
Rheological Models for Composite Systems ................. 19

EXPERIMENTAL ................................................ 24

Plan of Experimentation .................................. 24
Procedures ............................................... 26

RESULTS ..................................................... 35

DISCUSSION OF RESULTS ....................................... 83

Rheology of Filled Polystyrene ........................... 84
Effect of Concentration ............................... 85
Effect of Particle Size ............................... 86
Effect of Particle Size Distribution .................. 87
Effect of Filler Type ................................. 88
Effect of Temperature ................................. 89
Cox-Merz Approximation ................................. 90
Rheological Models for Composite Systems .............. 90
Phenomenological Interpretations ...................... 92
Limitations of Results ................................... 95

CONCLUSIONS ...................................... ........... 99

V









RECOMMENDATIONS ................................. ........ 101

APPENDIX .................................................... 103

REFERENCES .................................................. 107

BIOGRAPHICAL SKETCH ......................................... 111















LIST OF SYMBOLS

Symbol Definition

A Area, m2

A Filler specific surface area, m2/g composite

a Constant

Ea Activation energy, kcal/mol

F Force, N

G Complex modulus, Pa

G' Storage modulus, Pa

G" Loss modulus, Pa

GRo Reduced storage modulus at zero frequency, Pa
R ,o
H Distance between parallel disks, mm

i Index

N Number of particles in a cluster

P, Critical concentration of occupied squares in statistical

lattice

R Disk radius, mm

r Radial position

S Power-law slope

T Torque, N-m

t Time, s

V Velocity, m/s

v Velocity profile

w Angular velocity, rad/s








x Linear position

y Linear position

Y Distance between parallel plates, mm



Y Strain

Y Strain amplitude
0
YShear rate, s-

6 Phase shift

A Relaxation time, s

6 Circumferential position

pI Primary normal stress coefficient

I2 Secondary normal stress coefficient

p Newtonian viscosity, Pa-s

in p Adams model parameter

o Adams model parameter

n Apparent viscosity, Pa-s
*
n Complex viscosity, Pa-s

n' Real component of n Pa-s

n" Imaginary component of n Pa-s

n Zero shear rate viscosity, Pa-s
*
no Limiting frequency viscosity, Pa-s

n Relative viscosity

0 Filler volume fraction

Oc Critical filler volume fraction

Om Maximum filler packing fraction

T Shear stress, Pa








T Shear stress amplitude, Pa

w Frequency, rad/s















LIST OF TABLES

Table page

1 U.S. Consumption of Nonfibrous Extenders and
Reinforcing Agents ............................... 2

2 Experimental Plan ................................ 25

3 Sample Identification Coding System .............. 27

4 Extrusion Conditions Used to Compound the
PS Composites .................................... 29

5 Actual Volume Fractions of CaCO3 Filled Materials
(Determining from ashing) ........................ 73

6 Actual Volume Fractions of Bimodally Distributed
CaCO3 Filled Materials (Determined from ashing) .. 74

7 The Activation Energy for the Onset of Viscous
Flow for CaCO3 Filled PS Materials ............... 75

8 The Activation Energy for the Onset of Viscous
Flow for Rubber Filled PS Materials .............. 76

9 Viscosity Model Parameters for CaCO3 Filled PS
Materials ........................................ 77

10 Viscosity Model Parameters for Rubber Filled PS
Materials ........................................ 78

11 Reduced Storage Modulus Model Parameters for CaCO3
Filled PS Materials .............................. 79

12 Reduced Storage Modulus Model Parameters for
Rubber Filled PS Materials ....................... 80

13 Intrinsic Viscosities of Selected PS Composites .. 81

14 Residual Water Adsorbed on CaCO3 After Vacuum
Drying (Determined by ashing) .................... 82

15 Torque Calibration Data for RMS-800 with
2000 g-cm Transducer ............................. 96















LIST OF FIGURES


Figure page

1 Steady Laminar Flow Between Parallel Plates ....... 5

2 Steady Shear Flow in Parallel Disk Geometry ....... 7

3 Dynamic Oscillatory Shear Flow in Parallel
Disk Geometry ..................................... 8

4 Square Lattice .................................... 17

5 The Effect of Nominal Concentration of 20 Micron
CaCO3 on the Complex Viscosity of Polystyrene
Composites at 2100C. Included are the Adams
Model Predictions ( ). .......................... 36

6 The Effect of Nominal Concentration of 2 Micron
CaCO3 on the Complex Viscosity of Polystyrene
Composites at 2100C. Included are the Adams
Model Predictions ( ). .......................... 37

7 The Effect of Nominal Concentration of 0.8 Micron
CaCO3 on the Complex Viscosity of Polystyrene
Composites at 2100C. Included are the Adams
Model Predictions ( ). .......................... 38

8 The Effect of Nominal Concentration of 1.9 Micron
Rubber on the Complex Viscosity of Polystyrene
Composites at 2100C. Included are the Adams
Model Predictions ( ). .......................... 39

9 The Effect of CaCO3 Particle Size Distribution
on the Complex Viscosity of Polystyrene
Composites at 2100C. Nominal Concentrations
are 12 vol. %. .................................... 40

10 The Effect of CaCO3 Particle Size Distribution on
the Complex Viscosity of Polystyrene Composites
at 2100C. Nominal Concentrations are 20 vol. $.
Included are the Adams Model Predictions for
PS2020 ( ) and PS202 (---). ..................... 41

11 The Effect of Nominal Concentration of 20 Micron
CaCO3 on the Reduced Storage Modulus (G'/w ) of
Polystyrene Composites at 2100C. Included are
the Adams Model Predictions ( ). ................ 42








12 The Effect of Nominal Concentration of 2 Micron
CaCO3 on the Reduced Storage Modulus (G'/w ) of
Polystyrene Composites at 2100C. Included are
the Adams Model Predictions ( ). ................ 43

13 The Effect of Nominal Concentration of 0.82Micron
CaCO3 on the Reduced Storage Modulus (G'/m ) of
Polystyrene Composites at 2100C. Included are
the Adams Model Predictions ( ). ................ 44

14 The Effect of Nominal Concentration of 1.9 Micron
Rubber on the Reduced Storage Modulus (G'/w ) of
Polystyrene Composites at 2100C. Included are the
Adams Model Predictions ( ). ................... 45

15 The Effect of CaCO3 Particle Size Distribution
on the Reduced Storage Modulus (G'/w ) of Poly-
styrene Composites at 2100C. Nominal Concentra-
tions 12 vol. %. ................................... 46

16 The Effect of CaCO3 Particle Size2Distribution on
the Reduced Storage Modulus (G'/w ) of Polystyrene
Composites at 210C. Nominal Concentrations are
20 vol. %. Included are the Adams Model Predic-
tions for PS2020 (---) and PS202 ~ ). ........... 47

17 The Effect of Nominal Concentration of 20 Micron
CaCO3 on the Reduced Loss Modulus (G"/w) of
Polystyrene Composites at 2100C. .................. 49

18 The Effect of Nominal Concentration of 2 Micron
CaCO3 on the Reduced Loss Modulus (G"/u) of
Polystyrene Composites at 210C. .................. 50

19 The Effect of Nominal Concentration of 0.8 Micron
CaCO3 on the Reduced Loss Modulus (G"/w) of
Polystyrene Composites at 2100C. .................. 51

20 The Effect of Nominal Concentration of 1.9 Micron
Rubber on the Reduced Loss Modulus (G"'/) of
Polystyrene Composites at 2100C. .................. 52

21 The Effect of CaCO Particle Size Distribution on
the Reduced Loss Modulus (G"/w) of Polystyrene
Composites at 2100C. Nominal Concentrations are
12 vol. %. ........................................ 53

22 The Effect of CaCO3 Particle Size Distribution on
the Reduced Loss Modulus (G"/I) of Polystyrene
Composites at 2100C. Nominal Concentrations are
20 vol. %. ........................................ 54


xii








23 The Effect of CaCO Particle Size on the Complex
Viscosity of Polystyrene Composites at 2100C.
Nominal Concentrations are 10 vol. % ............ 55

24 The Effect of Both CaCO3 and Rubber Particle Size
on the Complex Viscosity of Polystyrene Composites
at 2100C. Nominal Concentration are 25 vol. %. ... 56

25 The Effect of Concentration of 20 Micron CaCO3
on the Reduced Viscosity (at limiting frequency)
of Polystyrene Composites at 2100C. Included are
the Campbell and Forgacs Model Predictions at m
= 0.74 (---) and at m = 0.524 ( ). ............. 57

26 The Effect of Concentration of 2 Micron CaCO on
the Reduced Viscosity (at limiting frequency) of
Polystyrene Composites at 2100C. Included are
the Campbell and Forgacs Model Predictions at
4m = 0.74 (---) and at Om = 0.524 ( ). ........... 58

27 The Effect of Concentration of 0.8 Micron CaCO3
on the Reduced Viscosity (at limiting frequency)
of Polystyrene Composites at 2100C. Included are
the Campbell and Forgacs Model Predictions at
m = 0.74 (---) and at 0m 0.524 ( ). ........... 59

28 The Effect of Concentration of 1.9 Micron Rubber
on the Reduced Viscosity (at limiting frequency)
of Polystyrene Composites at 2100C. Included are
the Campbell and Forgacs Model Predictions at
4m = 0.74 (---) and at $m = 0.524 ( ). ........... 60

29 The Effect of Filler Specific Surface Area on the
Reduced Viscosity (at limiting frequency as pre-
dicted by the Adams Model) of Polystyrene Compo-
sites at 2100C. Fillers are 2 Micron CaCO3
(---) and 0.8 Micron CaCO3 (_).................. 61

30 The Effect of Filler Specific Surface Area on the
Adams Model Parameter, in u, for 2 Micron CaCO3
(---) and 0.8 Micron CaCO ( ) Filled Poly-
styrene Composites at 210C. .................... 62

31 The Effect of Filler Specific Surface Area on the
Adams Model Parameter, sigma, for 2 Micron CaCO3
(---) and 0.8 Micron CaCO ( ) Filled Poly-
styrene Composites at 210C. ..................... 63

32 A Comparison of the Cox-Merz Approximation for
PS2520 at 2100C. (Complex Viscosity -
Apparent Viscosity ---). ........................ 64









33 A Comparison of the Cox-Merz Approximation for
PS2508 at 2100C. (Complex Viscosity =
Apparent Viscosity = ---). ....................... 65

34 The Temperature Dependence of the Complex
Viscosity of PS2520. (Temperatures in OC). ....... 66

35 The Effect of Oxidative Degradation on the
Complex Viscosity of Polystyrene at 2100C ( )
and at 2600C (---) .............................. 67

36 The Effect of Oxidative Degradation on the
Complex Viscosity of PS2020 at 2100C ( ) and
at 2600C (---). ................................... 68

37 SEM Micrographs of PS2520 ......................... 69

38 SEM Micrographs of PS252 .......................... 70

39 SEM Micrographs of PS2508 ......................... 71















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

AN EXPERIMENTAL INVESTIGATION OF THE
RHEOLOGICAL PROPERTIES OF VARIOUS
POLYSTYRENE COMPOSITES

By

James D. Small, Jr.

May 1989

Chairman: Arthur L. Fricke
Major Department: Chemical Engineering


The understanding of the effects of the addition of a second phase

into a polymer matrix on the melt theological properties of the result-

ing composite system is of vital industrial importance. This investiga-

tion was initiated to provide the necessary experimental data to develop

quantitative relationships between the melt flow properties of various

polystyrene composites and the characteristic properties of the filled

systems such as filler type, concentration, particle size and particle

size distribution. Polystyrene-calcium carbonate and high impact poly-

styrene (rubber filled) were compounded using a commercially available

polystyrene resin with a weight average molecular weight of 220,000

molecular weight units. The average particle sizes of the calcium

carbonate fillers were 0.8, 2.0, and 20 microns, and the average size of

the rubber domains in the impact modified polystyrene was approximately

1.9 microns. The concentration of these fillers in the resulting compo-

site was varied between 5 and 30 volume percent, and several composites

containing bimodal filler distributions were also prepared.

xv









Rheological testing was accomplished by using a Rheometrics Mechan-

ical Spectrometer in dynamic oscillatory mode over a temperature range

of 210-260C in a nitrogen environment. Limited steady shear viscosity

data were obtained by using the Rheometrics Mechanical Spectrometer in

steady shear mode, and these results combined with reported results

obtained by capillary rheometry proved the validity of the Cox-Merz

approximation for most of the experimental systems over a range of

frequencies or shear rate of 0.01 to 10,000 s1.

The viscoelastic properties were found to be strongly dependent on

filler concentration, filler particle size and particle size distribu-

tion, filler type (i.e., rubber or calcium carbonate), frequency, and

temperature. The total specific surface area of the filler was shown to

significantly affect the flow properties, and in fact, only at values of

the total filler specific surface area greater than 2.7 m2/g composite

was the Cox-Merz approximation proved unreliable. A stochastic model

for the viscosity of polymer melts was modified to represent filled

systems and was able to predict viscoelastic results with excellent

reproducibility.

Finally, percolation theory was found to be useful in semi-quanti-

tatively describing the theological behavior of the composite systems.

The results suggest that the critical percolation concentration (that

concentration where a macroscopic interconnected cluster of filler

particles is formed) was between 15 and 20 volume percent as predicted

by theory.


xvi















INTRODUCTION


The economic and efficient processing of polymer melts is of tre-

mendous industrial importance. During 1987, total U.S. polymer resin

consumption increased 9% and has surpassed the 50 billion pounds per

year level (1). Remarkably, of the twenty-three specific resin categor-

ies tabulated in Modern Plastics (1), each shared in the record growth.

In the U.S. plastics industry, there is a growing trend toward the

modification of polymers, through the incorporation of various addi-

tives, to improve physical properties and/or oost competitiveness. With

the demand for many polymer resins approaching the current supply levels

(1), inexpensive fillers and extenders are becoming increasingly impor-

tant. The use of nonfibrous fillers and extenders is increasing at a

rate of approximately 4.5% annually (2), and as can be seen in Table 1,

carbonates (calcium carbonate, chalk, and limestone) currently comprise

more than 70% of the market. Other common additives include such items

as antioxidants, flame retardants, processing aids, reinforcing agents,

and coloring pigments or concentrates. As new filled systems are being

developed, the need for reliable theological information increases. All

of the major melt processing operations are strongly dependent on the

theological properties of the polymeric material being processed. The

addition of fillers and additives can significantly change the flow

properties of the resulting composite, and therefore the processing of

these composite systems can vary drastically.















Table 1. U.S. Consumption of Nonfibrous Extenders and Reinforcing
Agents


Material

Carbonates

Kaolin

Mica

Microspheres

Minerals

Organics

Silica

Talc

Others


Consumption, million lbs.
1985 1986 1987

2710 2820 2950

170 190 210

22 25 30

18 20 23

380 400 415

190 190 198

95 100 105

142 150 160

8 9 11


3904 4102


TOTAL









Obviously, it is extremely important to understand how the addition

of a second phase into a polymer matrix affects the subsequent rheologi-

cal properties. As expected, the flow behavior of composites may be

influenced by the type of filler (i.e., rigid versus elastic), concen-

tration of the filler, filler shape (sphere versus fiber), degree of

matrix-particle bonding and interaction, filler particle size and dis-

tribution, temperature, deformation rate, and a myriad of other

factors. It is highly impractical to perform complete theological

testing on all possible combinations of resins and additives.

Thus this investigation was initiated to provide the necessary

experimental data to develop quantitative relationships between the melt

flow properties of various polystyrene (PS) composites and the charac-

teristic properties of the filled systems such as filler type, concen-

tration, particle size, and particle size distribution. The models

developed should predict the viscoelastic data over a wide range of

frequency and/or shear rate with reliability. A major objective of the

modelling was to relate the model parameters to physical properties of

the filled systems. It is hoped that, such a model can be easily and

methodically adapted to fit a wide variety of filled systems.

It should be noted that this investigation is part of a joint

program, between the University of Florida and Clarkson University,

established to study the interactions between composite melt rheology,

subsequent processing, and final part properties. The theological

testing is being accomplished at the University of Florida, and Clarkson

University Is responsible for the processing (extrusion and injection

molding) studies to follow. Both universities are jointly investigating

the solid molded part properties.
















PURPOSE OF INVESTIGATION


Since as previously described, a comprehensive investigation of all

of the factors that influence the theological behavior of filled systems

would be most unwieldy, the main objective of this investigation was to

systematically and quantitatively determine the effects of filler type,

concentration, particle size, and particle size distribution on the

theological properties of PS composites. Additionally, the effects of

temperature and shear rate or frequency were to be determined. The

results could be used to help interpret future processing experiments,

to aid in the planning of future theological studies, and to discern the

utility of available theological models and predictive equations.

The second major objective of this study was to use the results of

the proposed experimental work to test the adaptability of new theoreti-

cally based correlations that correctly predict the frequency or shear

rate dependence of the viscosity of polymer melts to filled polymer

systems. Data from at least two different composite systems will be

used to test the newly developed models. It is hoped that by basing the

models on measurable polymer and filler parameters, it will be proved

generally useful in predicting flow properties of composite systems.















LITERATURE REVIEW


Newton's Law of Viscosity


For steady laminar flow, consider the parallel plate system pre-

sented in Figure 1.


1,
x


Figure 1. Steady Laminar Flow Between Parallel Plates



The lower plate moves in the x-direction at a constant velocity V, and

at steady state the velocity profile, vx(y), is established. At steady

state, a constant force F is required to maintain the motion of the

lower plate and is expressed as


F V
A Y


-0 V









The proportionality constant j is called the viscosity of the fluid.

Equation (1) may be rewritten as


dv
Tyx dy (2)



where T is the shear stress exerted in the x-direction on a fluid in
yx
the region of lesser y, and vx is the x-component of the fluid velocity

vector. This is known as Newton's law of viscosity.



Parallel Disk Rheometry



The parallel disk rheometer is commonly used to study the visco-

metric functions of both polymeric and non-polymeric fluids. It is

especially useful in the study of composites where the influence of the

disks on the solid filler particles can be reduced by setting the gap

between the disks such that it is much larger than the average filler

particle size. The rheometer can usually be operated in either steady

shear or dynamic oscillatory mode. Schematic representations of steady

shear flow and oscillatory shear flow in the parallel disk geometry are

shown in Figures 2 and 3, respectively.



Steady Shear Operation

During the steady shear operation of the parallel disk rheometer,

the lower disk is rotated at a constant angular velocity W while the

upper disk is held stationary. The assumptions used in the mathematical

analysis of the parallel disk systems are




7







k-------- z


N
T
\
\^


Figure 2. Steady Shear Flow in Parallel Disk Geometry




8







N

y\
I N
iiD


Figure 3. Dynamic Oscillatory Shear Flow in Parallel Disk Geometry








(1) steady-state laminar flow

(2) incompressible fluid

(3) isothermal system (constant physical properties)

(4) negligible inertial effects

(5) no slip condition at the disk surface



With these assumptions, the equations of continuity and motion given by

Bird et al. (3) can be solved to yield the fundamental equations for the

system. The shear rate, Yz6, is a function only of radial position and

is given by



Yze (3)
zG H


In order to determine the steady shear viscosity of the sample, the

total torque required to maintain the stationary position of the upper

disk must be measured. The total torque T can be expressed as


2s R
T = f (-rr z)rdrdo (4)
0 0


The shear stress, Tze, may be rewritten as



Tz nYz (5)



where n = apparent viscosity



and this expression may then be substituted into equation (4). However,

because of the inhomogeneity of the shear field in the parallel disk









geometry, the apparent viscosity is not an explicit function of the

applied torque as shown in equation (6)


R
T = 2s f nir2dr (6)
0


Fortunately, by changing the variable of integration and by applying the

Leibnitz rule for differentiation of a definite integral, the viscosity

may be determined explicitly as a function of the shear rate and the

applied torque by


n( R (T/2R 3) + d n(T/2 R3) (7)
SR d Ln Y


where Y is the shear rate at r = R.

The parallel disk rheometer can also be used to determine normal

stresses that may be present in viscoelastic samples. The total force F

that must be applied to maintain a constant gap between the disks has

been shown by Bird et al. (3) to be related to the difference in primary

and secondary normal stress coefficients, I1 and p2 respectively, as


1 F d tn(F/R2) )
- (- ) [2 + d] (8)
1 2 12 7T2 d in Y


Dynamic Oscillatory Operation

In order to utilize the parallel disk rheometer to determine the

unsteady response of a sample in small-amplitude oscillatory shear flow

as shown in Figure 3, the bottom disk is oscillated sinusoidally with

angular frequency w, and the torque required to maintain the stationary

position of the top disk is measured. This applied torque also varies









sinusoidally with frequency w, but depending on the nature of the

sample, it may or may not be in phase with the applied strain. The

strain as a function of time is given by



Y = Y sin(wt) (9)
o



where N = sinusoidal strain

Y = strain amplitude

t = time



If the strain amplitude is sufficiently small, the shear stress can be

written as



T = T sin (wt + 6) (10)



where t = shear stress amplitude

6 = phase shift relative to the strain



Experimentally, the displacement of the bottom disk is proportional to

the strain, and the torque is proportional to the stress, so the ratio

of torque amplitude to displacement amplitude is equivalent to the ratio

of stress amplitude to stain amplitude. The phase angle between the

stress and strain is related to the response of the fluid. For a purely

elastic material, 6 = 0, and the stress is in phase with the strain.

For a purely viscous material, 6 = 900, and the stress lags the strain

by 90. Most materials are neither purely viscous nor purely elastic

but are what is termed viscoelastic, and for these materials, 0 < 6 <

90.









Using trigonometric identities and the stress strain phasors, the

material functions can be calculated for a given frequency from



G' = (T /Y ) cos 6 (11)
o 0



G" = (y /Y ) sin 6 (12)



The quantities G' and G" are called the storage modulus and the loss

modulus respectively. The storage modulus is related to the energy

stored elastically in the material upon deformation, whereas the loss

modulus represents the energy lost (converted to heat through molecular

friction) due to viscous dissipation within the material.

The complex modulus G is defined as the magnitude of the vector

sum of the in-phase and out-of-phase moduli:



G* = IG*| = [(G')2 + (G"')2]1/2 (13)



The complex modulus gives an indication of the total energy required to

deform a material.

The complex modulus and its components can be used to determine the
*
complex viscosity n and its real and imaginary components, n' and n",

respectively, as follows:


S= ()
p = C/W (1~4)


n' = G"/w








n" = G'/m (16)



It can be seen from equation (15) that the dynamic viscosity n' is

proportional to the loss modulus, and thus n' also gives an indication

of the energy dissipation that occurs during flow. Similarly, n" is

indicative of the energy stored by the fluid elastically upon deforma-

tion.



Melt Rheology of Polymer Composites



There exist in the literature many experimental studies involving

the viscoelastic behavior of molten, amorphous polymer composites (4-45

e.g.). These investigations include a wide variety of thermoplastic

resins in conjunction with both fibrous and non-fibrous fillers; how-

ever, there are numerous experimental discrepancies in the reported

literature which make many of the results questionable. Common flaws in

experimental procedures reported include the use of cone and plate

geometries in obtaining theological properties of filled systems, the

assumption of negligible end effects in capillary rheometry, and the

failure to report experimental errors in the measurements due to lack of

replication, temperature control, and thermal stability of the composite

sample. In all fairness, many of the assumptions used by previous

investigators were employed to alleviate the costs associated with

accounting for the possible problems.

Most of the work to date has focused mainly on the effect of filler

concentration on the flow properties, while choosing to neglect the

Influence of the particle size and particle size distribution of the









solid phase. In fact, in a majority of the reported studies, only one

filler particle size was actually investigated, thus eliminating any

possibility of determining size effects. A few investigations are

notable exceptions (12,13,14,15 and 27). Chapman and Lee (12) noted

that the viscosity of talc filled polypropylene increased with increas-

ing filler surface area; however, the two talc fillers used had equiva-

lent average particle sizes and only slightly different particle size

distributions. Kitano et al. (13) and Kataoka et al. (15) observed an

increase in the reduced viscosity of polymers filled with smaller cal-

cium carbonate particles, but their results were confounded by using

different types of calcium carbonate with differing degrees of surface

roughness. Kataoka et al. (14) investigated the effects of particle

size of various types and sizes of glass fillers on the viscosity of

both polyethylene and polystyrene composites. They noted that the melt

theological properties were strongly influenced by the glass concentra-

tion but were not appreciably affected by changes in the glass particle

size. This may be attributed to the relatively larger filler particle

sizes used in their work (> 30 microns). Suetsugu and White (27)

observed increases in viscosity and yield stress with decreasing parti-

cle size for PS/CaCO3 compounds at 30 vol. %; however, their emphasis in

reporting centered on the yield phenomena in both steady shear and

elongation. White and Crowder (45) observed that the melt viscosity

increased dramatically as the filler particle size was decreased to less

than 0.04 microns for various elastomers filled with carbon black.

However, since surface adsorption of rubber on carbon black and covalent

bonding between rubber and carbon black can occur in these systems,

their results may not represent filled thermoplastic systems very

well.









Equally scarce in the literature are detailed studies of the

effects of filler particle size distribution on the rheology of polymer

composites. Both Farris (35) and Chong et al. (30) observed that at

concentrations greater than approximately 20 volume percent, the visco-

sities of suspensions of multimodal particle sizes were significantly

lower than those of suspensions of unimodally dispersed particles at

equivalent loading levels. It is worth noting that in these studies the

concentration of smaller particles was always less than the concentra-

tion of the larger filler particles. There appear to be no data in the

literature relating the effects of higher concentrations of smaller

particles in multimodal systems, and the effects of particle size dis-

tribution on suspension viscosity in general are still neither well

documented nor understood.

In almost all of the reported work, the composite or suspension

viscosity increased with increased filler concentration over the entire

shear rate or frequency range investigated. Also observed by many

investigators was an increase in non-linear flow behavior with increas-

ing solids loading, which resulted in shifting the point at which pseud-

oplasticity began to lower shear rates. Since the slopes of the flow

curves in the fully developed power-law region were similar and rela-

tively unchanged by change in filler concentration, the viscosity curves

for different filler loadings, when superimposed, converged at higher

deformation rates. Thus the viscosities in the limiting shear region

showed much greater dependence on filler concentration than did the

viscosities In the power-law region.

There are currently two predominant theories used to explain the

observed influence of filler addition on the composite melt theological









properties. Utracki and Fisa (4) and Kataoka et al. (15) have proposed

that the increase in melt viscosity with increasing filler concentration

may be attributed to an interfacial boundary layer of polymer associated

with the filler particles. The mechanism assumes that the increase in

viscosity may be attributed to an increase in apparent volume of filler

attributed to the formation of a fixed layer of polymer on the filler

surface. Kataoka et al. (15) have estimated that the thickness of the

"fixed" polymer layer had to be at least 10% of the radius of the filler

particle to account for deviations between experimental results and

those predicted from various suspension models.

A second common explanation of the observed behavior previously

discussed was attributed to the formation of structure in the form of a

network within the filler domain (12). Agglomerating particles may form

a network-like structure within the melt at low shear rates or frequen-

cies, resulting in a large increase in relative viscosity. As the

deformation rate increases, the network structure is destroyed, and the

effect of filler content becomes negligible. The effect is a conver-

gence of the flow curves for filled systems at high deformation rates.



Percolation Theory



Percolation theory involves the transition from random processes to

processes where a macroscopic ordered structure develops. In order to

explain percolation, consider the array of squares shown in Figure 4.

Such an array, assumed to be sufficiently large so that effects from its

boundaries are negligible, is usually called a square lattice (46). As

seen in the figure, a certain fraction of the squares are occupied, and







































0 0 0






0 0



0 0



0


Figure 4. Square Lattice


0


0









the remainder are empty. Each of the occupied sites is filled randomly

with a probability which is independent of neighboring sites. A cluster

is defined as a group of occupied squares that share a common side, and

it is the interest in the number and the properties of these clusters

that constitutes percolation theory. At a critical concentration of

occupied squares, pc, the cluster percolates through the statistical

system as a macroscopic connected entity, and the formation of this

"infinite cluster" in real systems may have a dramatic effect on the

physical properties of the system (47).

Percolation theory has been used to describe many diverse phenomena

such as forest fires (48), diffusion in disordered media (49), and

conductive properties of disordered systems (50). Historically, Flory

(51) and Stockmayer (52) developed the theory of the Bethe lattice,

which is now called percolation theory, to describe the gelation of

macromolecules. This pioneering work led to the increased interest in

percolation theory and its usefulness in describing critical phenomena.

The application of percolation theory to composite systems has

focused mainly on the electrical transport phenomena in polymers filled

with conducting fillers (50, 53, and 54). Conductive particles dis-

persed in insulating polymer matrices exhibit bulk conductivity above a

critical concentration, while below the critical concentration, the

materials are insulating. In general, the experimentally determined

critical percolation concentrations are in good agreement with the

theoretically and numerically determined value (50,55,56) of 16 volume

percent.

No references regarding the use of percolation concepts to describe

theological properties of polymer composite systems were found, however









the *-,namic viscosity of various mIerjamui. r:Ln 5yte.- r1; teern *es3-

rLrDc- by percolation processes (56,57 and 58). At increased concen-

r.rLtion of the minor phase in emulsion systems, Stokes-Einstein predic-

Tr.r)Is for reduced viscosity fail (57). However, the observed transi-

tions at critical concentrations have been well predicted and described

by percolation concepts. Two studies involving the application of

percolation theory to describe the theological behavior of concentrated

suspensions were also discovered. Heyes (59) attributed the power-law

dependence of the shear modulus with packing fraction, for computer

simulated colloidal systems, to the onset of long range structural order

in the system. Campbell and Forgacs (47) used percolation concepts to

develop a stochastic model which predicted the limiting shear viscosity

of a suspension as a function of filler concentration. Their model was

used to predict slurry viscosities above the critical percolation con-

centration with excellent accuracy for several experimental systems.



Rheological Models for Composite Systems



Limiting Shear Viscosity

The development of theological models to describe the effect of the

addition of a second rigid phase to a fluid can be traced to the work of

Einstein (60) who noted that the viscosity of Newtonian suspensions of

rigid spheres was increased according to the following relationship:



nR 1 + 2.5 (17)


where nR = relative viscosity








= volume fraction of spheres



Since Einstein's equation is based on only single particle interactions,

its utility is restricted to very dilute systems (< 10 vol. %). Through

the years the Einstein equation has been extended to account for the

formation of multiple particle clusters (61 and 62), and in the result-

ing equations, the higher order terms represent the interactions of two

or more particles. All of these equations are of the form


N 1
T = a + E a 4 (18)
i=1


where N = number of particles in the cluster formation



In these models, the total energy dissipated during flow is determined

as a summation of the contributions from the particles and groups of

particles similar to the method used by Einstein.

Since the early theoretical work, many empirical and semi-empirical

models to predict the effect of particle concentration on slurry limit-

ing shear viscosity have been developed. An extensive review of these

developments was reported by Utracki and Fisa (4). Their results indi-

cate that most of the proposed models predict, within reasonable limits,

the increase in suspension viscosity with increase in concentration of

the second phase at concentrations well beyond the limits imposed on the

Einstein equation. However it should be noted that no matter how valid

the physical assumptions that were used to develop the theoretical

models of the form of equation (16), a power series equation would fit

the data, provided enough terms were used. This fact is manifested in









the result that for many of the proposed models, the reduced viscosity

does not approach infinity as the volume fraction of the rigid phase

approaches 1. Finally, it should also be noted that the overwhelming

majority of the work involving modelling of polymer composite systems

has historically consisted of extrapolating the slurry results by modi-

fying the available adjustable parameters without regard to the signifi-

cant physical differences in the two systems.

A more broad ranging phenomenalogical approach was employed by

Campbell and Forgacs (47) in their modelling work to determine the

effects of concentration on concentrated suspension viscosity. Their

approach involved the application of percolation theory to describe and

quantify the effect the addition of a second phase has on suspension

viscosity. The resulting stochastic equation


R -c
R exp(m -) 1 (19)



where im= maximum filler packing volume fraction

*c = critical volume fraction = 0.16



not only produced excellent prediction of available slurry data, but

also allowed justifiable extrapolation to filled macromolecular systems

since the concepts encompassed in percolation theory are not material

dependent. The only adjustable parameter in equation (19) is *m which

is determined from geometrical and probabilistic arguments. The criti-

cal percolation concentration is, to a very good approximation, indepen-

dent of material properties and has the value of 0.16 (50,55 and 56).









Shear Rate Dependent Viscosity

There are in the literature a myriad of constitutive equations

developed to describe the shear stress-shear rate behavior for pure

polymer systems. These range in complexity from the simple power-law

relationship to the eight constant Oldroyd model. An excellent review

of available theological models is found in Byrd et al. (3). These

models are all based on continuum mechanics and are developed for homo-

geneous systems. Farrington (63) recently reviewed the general state of

the art knowledge in molecularly based theological models of homogeneous

systems. Any of these models could be extended to heterophase systems,

by simply correlating the various parameters with the experimental

results for composite systems, to yield models whose parameters would

then depend on properties related to the filled system (e.g., filler

size and volume fraction). However, these models are quite unwieldy and

so it seems much easier and somewhat more applicable to start with a

model that lends itself to a clear simple extension to heterophase

systems. Such a stochastic model was presented by Adams (64). In her

model, the viscosity of a polymer is related to the numbers of molecules

of given sizes in the system, with the higher molecular weight "solvent"

molecules. Thus during flow at low shear rates, the higher molecular

weight larger molecules can deform quickly enough to move segments into

and out of available "holes" and therefore dissipate energy as molecular

friction. As the shear rate increases, the largest molecules become

trapped in certain configurations in the melt and cannot move into the

available holes fast enough and therefore cannot dissipate energy as

effectively. This phenomenon marks the onset of non-Newtonian flow.

Further increases in shear rate entrap more and more molecules until in








the limit only "solvent" molecules can effectively dissipate energy.

The result of her modelling effort was a predictive equation for the

shear rate and molecular weight dependence of viscosity as follows:



innR = [- i-LP erfc ([n2 n) 7 exp (- w2 )] (20)
20


where S = negative slope in the fully developed power law region of

the flow curve

o and U = model parameters



Equation (18) was obtained by twice integrating the negative log normal

distribution function used to represent the viscosity-shear rate curve,

and thus o and p are simply the distribution standard deviation and the

distribution mean respectively. These parameters were then related to

polymer properties such as molecular weight, polydispersity, and glass

transition temperature. The resulting set of equations are easily

manipulated (64).

Since this model has its foundation in structure formation, the

percolation concepts previously discussed are applicable. Therefore it

should be relatively easy to extend this model to composite systems, and

by utilizing similar arguments as the original author, determine the

effects of filler properties on the composite rheology.
















EXPERIMENTAL


Plan of Experimentation



In order to efficiently determine the relationship between filler

properties (type, concentration, particle size, and particle size dis-

tribution) and composite theological properties, the experimental plan

outlined in Table 2 was employed. The polymers used in this study were

commercially available PS and high impact polystyrene (HIPS) with

weight average molecular weights of approximately 220,000 molecular

weight units. The impact modified PS was available with approximately

30 volume % of 1.8-2.0 micron rubber filler. The rigid CaCO3 fillers

employed were obtained from OMYA, Inc., and the pertinent physical

properties and size distributions appear in Appendix I. The filler

particles were neither chemically altered nor surface treated.

As shown in Table 2, the experimental plan was divided into three

distinct groups, and the filler parameters (i.e., type, average particle

size, and concentration) that were used to compound the PS composite

samples are listed for each group. Results from the Group 1 samples

provided information elucidating the effects of filler particle size and

concentration on the composite viscoelastic properties. The Group 2

results were used to compare elastic and rigid fillers over broad ranges

of particle size and concentration, whereas the Group 3 samples were

used to test the effects of bimodal particle size distributions.
















Table 2. Experimental Plan


Average
Particle
Size, Microns


S20
2
0.8




1.9




20
2


*Concentrations of 80/20, 60/40, 50/50,
Ratios of 20/2 micron filler.


Nominal Filler
Concentration,
Volume %

5
10
15
20
25

6
12
18
24
30


12*
20*


40/60, 20/80.


Filler Type


Group 1:
CaCO3




Group 2:
Rubber




Group 3:


Temperature,
Oc


210
235
260



210
235
260


210
235
260








The theological properties of the samples comprising the experi-

mental plan were determined by using a Rheometrics RMS-800 mechanical

spectrometer, in both steady shear and dynamic oscillatory modes, since

the instrument allowed precise control of both sample temperature and

environment. The parallel plate geometry was employed throughout this

investigation so that the influence of viscometer tooling on the rigid

phase of the heterophase systems studied (i.e., "wall effects") was

minimized.



Procedures



Sample Identification

A coding was developed to simplify references to the specific

samples that were previously outlined in the experimental plan. The

sample identification procedure appears in Table 3, and this coding was

used throughout the remainder of this dissertation.



Preparation of Composite Samples

The various PS composite samples used in this study were prepared

with the assistance of the Research and Development department of the

Mobil Chemical Company in Edison, New Jersey. Polystyrene resin was

combined with each of the three different size CaCO3 fillers by mixing

the materials in a 25 lb. capacity Stewart-Bolling Banbury mixer. The

resulting masterbatches, PS2520, PS252 and PS1508, were then diluted

with pure polymer to achieve the necessary composition. It should be

noted that for the PS filled with 0.8 micron CaCO3, the maximum filler

concentration that could be processed using the Banbury mixer was 15















Table 3. Sample Identification Coding System


Groups 1 and 2


Coding: Resin Nominal Total Average Filler
Material Filler Concentration Particle Size


exs. PS2503: Polystyrene filled with 25 vol. % of
0.8 micron CaCO3

HIPS1000: High impact PS filled with 10 vol. % rubber


Group 3


Nominal Weight % of Weight % of
Resin Total Filler Total that is Total that is
Coding: Material Concentration 20 micron filler 2 micron filler


ex. PS122080: Polystyrene filled with 12 vol. % total filler.
20% of the CaCO3 is 20 micron and 80% is 2
micron.








vol. %, therefore PS2008 and PS2508 were compounded using a heated

Farrel roll mill. The roll mill consisted of twin 12 in. circumference

rolls heated with hot oil to temperatures of 235F (front) and 2250F

(rear) respectively. The front roll was rotated at a rate of 22 ft/min,

and the rear roll was rotated at 27 ft/min.

Dilution and mixing of master batches to form the experimental

samples outlined previously in Table 2, was accomplished by first mixing

the materials to be compounded in a portable cement mixer and then by

melt extruding the materials in a Werner-Pfleiderer ZSK50 corotating 30

mm twin screw extruder. The extrusion parameters used to accomplish the

sample compounding are given in Table 4. The extruded strands were

quenched in a water filled take-up trough and then fed to a pelle-

tizer. The resulting composite pellets were then remixed in the cement

mixer and reextruded, as before, to provide sufficient mixing. The HIPS

composites were prepared similarly by using the commercially available

HIPS 3000 as the masterbatch.



Test Sample Preparation

The samples used to perform the theological testing were prepared

by compression molding the individual composite samples using a Pasadena

Hydraulic Inc. model SPW225C press with electrically heated platens.

The composite pellets were first dried in a vacuum over at 800C for at

least 8 hours to remove any residual moisture. The dried pellets were

then poured into a 6" x 6" x 1/8" picture frame mold supported by a

steel plate covered with teflon coated aluminum foil to prevent adhe-

sion, and the plate and mold were placed onto the lower of the two

preheated press platens. The temperature of the platens was maintained
















Q0






S0 0

o)
o L C
2 AO
a, i




o 0


o ,


a)





cl
0. =r
S Q




o =
0 1o
o CL

w 0. 0 0
Sa,)
3 a-



O a)
I La
0 aN I
, 0a 0 0
O a,

Va a
0 a. 0 I0


0 ) 4 0



0 0

CO
o c




N N


w n

0
N -
0 c~j -a- c o
t- *- 0 ^
^^C-] *









at approximately 20000C. After the pellets had melted (approximately 15

minutes), the top plate, also covered with teflon coated aluminum foil,

was positioned such that the mold filled with the melted sample was

sandwiched between the two plates. The platens were then pressed to-

gether until a force of approximately 5,000 lbs. was obtained. The

pressure was then relieved momentarily to allow the release of any

entrapped gases, after which a force of 20,000 Ibs. was applied to the

mold. After 20 minutes at 2000C and 20,000 lbs. force, the mold was

cooled by circulating water through the platens, and when the mold

temperature reached approximately 750C, the pressure was relieved and

the molded sample removed.

The rheometer test samples were prepared by cutting the molded

composite samples to the appropriate sizes by using a band saw. These

test samples were also vacuum dried at 80C before using them in the

rheometer.



Data Collection

The theological data were obtained by using a Rheometrics RMS-800

mechanical spectrometer operated in both steady shear and dynamic oscil-

latory modes. The RMS-800 can be operated with a controlled sample

environment and over a temperature range of -150 to +350C. Detailed

diagrams of the test station and the environmental chamber can be found

in the operating manual. Two sets of disks were used during this inves-

tigation, and the respective radii were 12.5 and 25 mm. In order









to prevent oxidative degradation, liquid nitrogen was boiled in the

system dewar to provide a gaseous nitrogen atmosphere in the sample

chamber.

The general operation of the rheometer involved the motion (steady

or oscillatory) of the lower disk fixture through a servo motor. The

rotational rate and the position of the motor shaft, and subsequently

the lower disk, were measured by a tachometer and a rotational variable

differential capacitor (RCVD). The command motion of the lower disk was

transmitted through the sample to the upper disk which was connected to

a force rebalance transducer (FRT). The torque required to maintain the

position of the transducer shaft, and thus the upper disk, and the

normal force required to maintain a constant disk separation were deter-

mined.

Sample temperature in the RMS-800 was maintained through the use of

the gas convection oven with PID control. Heat was supplied via an

electric gun heater inserted into the environmental chamber. The oven

temperature was measured with a type J thermocouple located in the

chamber, and a PRT sensor, also located in the environmental chamber,

provided the temperature monitoring required for control. Additionally,

the lower tool temperature was measured by using a type J thermocouple

located on the lower surface of the tool, and it was this temperature

that was used to determine when the sample thermal equilibrium was

attained.

The precut, dried test samples were individually placed on the

lower plate of the instrument, and the upper plate and test station were

lowered until contact with the sample occurred. The oven halves were

then closed, and the sample and tooling were heated to the desired set









point temperature. When thermal equilibrium was achieved, the top plate

was lowered further until the desired gap between the plates was

obtained. At that time, the oven was opened, and the excess sample that

was squeezed from the gap was removed. The oven was then resealed, and

reheating was initiated. When the desired tool temperature reached

steady state (no change in tool temperature over a 3-4 minute period),

the particular theological test was initiated.



Auxilliary Procedures

Ashing procedure. The concentrations of the various composite

samples were experimentally determined by ashing the samples. Predried

sample pellets were loaded into dried, tared, ceramic ashing boats, and

the total weight was measured and recorded. The filled boats were then

placed in a Fisher Scientific model 184A muffle furnace at 4600C for at

least 2 hours. The remaining ash and weigh boat were weighed, and the

mass fraction of the filler was determined from the inorganic ash that

remained. Component densities were used to convert the inorganic frac-

tion to a volumetric basis, and the calculations accounted for the water

hydrated to the CaCO3 filler.

Ashing experiments were also employed to test possible filler

particle migration in the rheometer test sample during the loading

process. Samples of the extrudate squeezed from the gap between the

disks were ashed as previously outlined, and the remaining test disk was

also ashed after completion of the theological testing.

Intrinsic viscosity measurements. The polymer intrinsic viscosi-

ties of several of the composite samples were determined to insure that

the preparation and processing of the samples had not resulted in any









significant polymer degradation. Predried composite samples were dis-

solved in a 50/50 methylethylketone/acetone solution. The resulting

solution was then centrifuged for 15-20 minutes at room temperature to

remove any CaCO3 present in the PS composite. The supernatant polymer

solution was separated from the CaCO3 precipitate by decanting the

liquid into filtered methanol. The polymer precipitate was then fil-

tered under suction and washed with methanol. Finally, the polymer was

dried in a vacuum oven at 50C until no solvent residue remained, and

the dry PS was then redissolved in filtered toluene at various concen-

trations. The viscosities of these solutions were then measured using

Canon-Fenske type capillary viscometers, and the intrinsic viscosities

were determined by extrapolating to zero polymer concentration as out-

lined by Hiemenz (65).

Scanning electron microscopic analyses. Scanning electron micros-

copy (SEM) was used to determine the degree of dispersion for several

selected composite samples. The predried samples were submitted to the

Materials Analytical Instrumentation Center at the University of Florida

and were freeze fractured and then gold coated under high vacuum. The

samples were then observed with a JEOL model JSM-35CF SEM and represen-

tative micrographs were obtained.

Modelling work. The model derived by Adams (64) was used to fit

the complex viscosity-frequency data obtained from both group 1 and

group 2 experiments at 2100C. Since the model has utility in predicting

similarly shaped functions, the reduced storage modulus-frequency data

at 2100C was used to further test the model. Detailed derivations of

the models used appear in (64). In both cases, the slope in the fully

developed power-law region was known and so a standard simplex routine,





34



obtained from Clarkson University, was modified for use with a personal

computer and used to determine the remaining model parameters. A copy

of the programs used is on file and can be obtained from Dr. Arthur

Fricke, University of Florida. The model was not applied to higher

temperature data since many of the flow curves at both 235 and 2600C

failed to reach the fully developed power-law region. Both models

require that either the power-law slope or the distribution standard

deviation be determined independently. It is possible to determine a

standard deviation by trial and error methods, however this approach was

considered to be more of a curve fitting technique than having at least

one known parameter value.
















RESULTS


The theological properties of PS composites containing from 2.5 to

30 volume % of both CaCO3 and rubber fillers were determined over a

temperature range of 210-2600C. Both unimodal and bimodal distributions

of particle sizes ranging from 0.8 to 20 microns were employed, and the

theological properties were determined over a frequency range of 0.1 to

100 rad/S. The amount of raw data obtained in this investigation was

considered to be too extensive to include in this dissertation, however

all of the data obtained may be obtained by contacting the Department of

Chemical Engineering at the University of Florida.

A recently developed stochastic model developed by Adams (64) to

describe the shear rate, molecular weight, and temperature dependence of

polymer melt viscosity was used to describe the frequency dependence of

both the complex viscosity and the reduced loss modulus (G /2 ) of the

various PS composites. Finally, the results of the study were analyzed

and semi-quantltatively described using concepts and a model (47)

derived from percolation theory.

Figures 5 through 10 display the frequency dependence of Groups 1,

2, and 3 composites at 2100C along with the Adams model predictions, and

Figures 11 through 14 show both the data and the model predictions of

the reduced storage moduli of Groups 1 and 2 materials as functions of

frequency also at 2100C. The effect of frequency on the reduced storage

modulus for the Group 3 samples are given in Figures 15 and 16, and





















- 0



a) W
-0

E -
0
.0
O





a







U*
0- a)
0
















OC
mu

























OC
O C:
z *H C


o
C L4 .
0 t4-1 4 -
0
u
0 0









E- >





= -H gH
o o ?.,


S-ed 'ALISODSIA X41doN03




















-.11 CC


I I I I I I I I


I111 I I I


o u)? LO 0


11l l I I I111 1 I III1111 1 I

1 0 0

S-Pd 'AIISOOSIA XtIcd'INOD


0


m
x E


E
00



4- i
0,0
C)

0
(-
uo








S 0 a
2 (1 C



Co

0 0g


,- 2





u v
0 u Q)








.r-I
0 I
> )
C *J 'O




E > U)
-- 4-4 --








U)



0




















I I 1 I


11111 I 1 1111111 I 1 III rI 1 1 111111 I

0 0I X 0

s-2d L'AIIS0OSIA X31cId0IO


11111 1 1 I l i l I I Il I I I





















C.4 -



















J 0 J J J
0000O0


O 4 O -


0




0 -

C-

z

a
Z
M
^>

o'
e=
L,


Cl(
SE
E -=I

aQ 4
O <


4-,
0)




0)





-o
0 a
1c 0




u L
*H







00 0




4- 44














ro
0 0



C C


4 aH
CE




0)0
u 0-
c

0)






0 *-





44
.c .4 0






*r
[.L


















I -7 I I


I1I I I I


1* 0






I Id


I I I I I I










//



























000000
> >>> >
0 0- 0C C0 0 0
rN C' J- -
*0 0 < <*


ii11 Iiliii I~

0 0 0


IISOOSIA


x diInD03


x

Q. E
E
o *o
U() <









) cc
1-1







.o ao




U







0 0
CJ

W 0

Z 0 0






u W
S0
QC
o





4-
00
Q 0
H _i .r
i-> (0 0







C
0 a






















I I I I I I I I


nl *


- *


*Dlo .
a OlGI *


004
1041


000
LO N
0 0

(D 1 .N



O < <


S-ed 'ALISODSIA X3IdWOD


-0 0
o

CI
0>
0
u t-
i-

ca

a)
O EO
0 60



Q)




H H

mH E









a -H
." .tj
K a
r- I -l
I-' CD *


I i I i I


i





















Jl ll I i I I


S O0


4 1 i I I


1 1 1 1 I I I II i I ? I i II li

S- 0 0 X

s-edj 'AKJISODSIA X'IdPHOD


II I I I I











7 "





























00000
00c 10 r C ER
00000
CN -J L CO 00 .J
000000
C" (N C0 (N CM >
W cn Vn cn V)
- Qa-- a_- o0
* 0 0 < q
maaomm


0

0 -
CJ>






O CN








CO
0 c

U) E









0O
C) (0





> u







o








lOE
C. 00





SoU



H OC
2 C U *H
(oo C o



_, mT] T
" l 0m








cn .-
0 E


S(





















ll l II I 1111111 1 I 1111111 I I Iflll I I -


0000

uon on o

* 0 al 4


iIIII I 1 11111 1 I


1LLll 1 ii ii I I I


S-Ud 'Sf1nJOIN 3DVUOIS UnDflH


a,








Oo




Oc
40






C o

u a

o 00
cz) 0 -0



0 0













vU
c(-



S0
H UU


<~y c o









-3



ECa




U3-C




00





















1111111 I I IIII II -I I IIIII IIII I I 1111 1I


0000

In 0o in
CNl C -

.* C 4


l lt I I I I i l I i IlI f il I I


'0 0 0 o



'Sfl1LCOW ZIDVHOIS Q339U31


. 1 I I I


m


C


s-Cd


M III I i i


-q C



CU
V U
0 C

ci



CN
0 *
u m


0






- 0 ^ 0 a
ZE





z 2








0-c4 w








oo
0 Q



f UZ






2 0O.C


V)4 i


1




*r-


11H I F I I If l l i l l I li f l i l I





















111 11 I i IIII I I 11 111 I I 111111IIIII I I I IIl11 l l I Il llli I


SR w R, Bw 9
_J -J _J _J J -j
0000 00


N C'- N-
S0 C < 4*


Iii 1 1 1 III1 1 1 4 I iii II
C


1I 1111 1111 1IIII I hut11
o a


Ow




0
a-t








co
Uac
c




0 C1



2 o



0 Q4-1







040
CO
















000

un
r. 0 0
S 00
S 0O
z .A



a-' 5 ^004


Sc -i
co
4 3 4









0c S


C- QC

1-4








CC


S-ed 'Sfna0I0W ZDVUHOS GE3Dna






















11111 1 I I lIl i ll I I


1111 l l I 1 1 I il l i I I I


0000
>> >>

0 co 00 N
rf (N -
* 0 0 <


I I 11111 1 I


0 0 0 0



'Sf11iUO0} 3DVHOIS G3O96103


4-ill I


0

UT
C O

0u





MC0
-0 -
U










-u
0c
0 -
o ,














-

CM
















0 0
-e-




a)
o o
'U *r





u C








c 0-


C -o


"0 CU ^





en CU




- u~-1 () d

N- 0J
M 3 -

J=r. t


sO

o-e


(1111111 i )1111111 1 1111111 1





















- H I I I I I


Ii l l I I I I I 11111 1 1 1 I I


C. -


ON
03MA
aI *




S**

EK I


* as


0000
0 (,D CC "
0000
(NM CC- ) (
NN NN

(/)(/)(/ (/)
*, o m


1111111 I I llll I Ii iI I 1 1111ll 1 II

S'S0 0



s-ed 'smnaoiU 3oVUOIS U30nfE3


0



a C
OU




u
S o3


(0 0




co














ud o 0
-e .








4UU




-I C )
a3 0









_r 01
0 0 X4
-




m 3






C









fc -





















4IIII I 111111 I


1111111 1 1 111 l1 1 I


111111 I 111111 I I


- Z.


* oCC/ 4


.0 4

*O ciy 4


' 0 44
@ 0 4 .


- C










11111 11 11111 1I 11111111


00000
C( t- ul to 0 _
000000
C( C- (N (N CN >
V) U) Lcn cV (n

0 D <







hlllli I IIIIIII I I Illi I I i


0 0
co
Oiu







MO-
20



ouo









m
0 0 C
N U Cu*H


d 0 O
- 0e-o







S00
ZO 0





-
cc





a
0 u n .




Lo o -0



a- a




U 0l
0 0 0!



00
10 --0i



(N*



= 40 0
L- Cu 0)
C rt l
F-S a1C.
r- ^>0N
r2-^ CO rlv
fc 0 0


L
c^ 6 C


0 0 0 0 0S


S-Ud 'SfflfllOIOJ, DVJOS EL3DflQZIU









similarly, the frequency dependence of the reduced loss modulus for all

three groups of materials are contained in Figures 17 through 22.

The flow curves depicting the effects of particle size and type of

filler at 2100C and at filler concentrations both above and below the

theoretical critical percolation concentration are shown in Figures 23

and 24. The effect of filler concentration on the limiting frequency

reduced complex viscosity of both CaCO3 and rubber filled PS composites

at 2100C appear in Figures 25 through 28. Included in these figures are

the Campbell and Forgacs model predictions for both hexagonal and cubic

maximum packing geometries. The various modelling parameters determined

from the Adams model fit of the complex viscosity-frequency data at

210C are shown as functions of the filler specific surface area in

Figures 29 through 31. A comparison of the Cox-Merz (66) approximation

for selected materials appear in Figures 32 and 33. The steady shear

viscosities in these figures were determined by using an Instron capil-

lary rheometer (ICR) model 3211. The ICR results were determined in a

separate project by Kelly (67).

The typical temperature dependence of the composite flow curves is

shown in Figure 34, and the effects of oxidative degradation of the

theological test sample on the theological measurements for a selected

composite and the neat polymer appear in Figures 35 and 36. Finally,

the quality of the compounding and the dispersion of various composites

was investigated using SEM, and the micrographs appear in Figures 37

through 39.

The actual volume fractions of the various CaCO3 composites used

are given in Tables 5 and 6. These results were obtained by ashing the

composite samples as previously described. It should be noted that the



































O O <4

0 0 0<4

0 0 1 4
S D <4
0 O O 0'






o o '14
S 0 0 <<4

0 0 <14


0 D '4








O '14





0 0000 0
>>>>> >

o ono o )
fl L0fO u 0
) N l
*00 04:


II i 1 1 I I I I


s-ri 'SnnAOIIOW SSO'I UI3lUniaH


u

U


ac




0 0
rJ







"0
U-t








00 C




0.











o


E-
0-




w
- N a













." 0













CIO-
CS
S0-




-(-0


SillI I 1 I I1 111111i 1 1 1i 1111 1 1 1 1111111 IIII 11111111 i





















SI I I I I I


0 t.1



0 O

0 4< <

0 40 0
0 O~ C








0 40*
o 4





0 4 <


0 C

0 <1 0 4<1
0 a


0 4

_J _1 _J 1 1- 1 -
000000

m oo 0 L in 0
SC'JC- K


s-11 1 '1 I i s lli I i111 I



s-ed 'SifiQOI SSOI U3OfHIZL


-11 I


u

QJ
-t


0U





04
U
c
U)









0 u
0,-
o"
















0







m
D










0 -
U c
















-w X
z *'P*(
r ruJO-
1- W O>
I-s V4)







*g ^
Lr


11 1 l l I I



















I I I I


O 0 4 4

o a
000

Sno n

0 0


0 00

0 in C

4 3
oco I


I I I l i i I I Iil i I I I iiii r


C


'Sfi flUI ON


0


ssor


C


U3oflU3a?


I i i i. l i l 1 l ll I i| i I I i -

















0 0 04 C0
0 0 4

0 0 O


0 0 04
o 0 0 0


0 0 4 0
S o 04


S 0 4 4

o 4 4

0 04 4

0 04 4


0

s-ecd


h


n


*u
0
U








*O









0


oa








ac
o 0



o




.NC
o0
S on

































*-
- Ca CO


oa


0 C










C-

CEO
0


o -



zuC
F--i










o
cco
Ezi






















11 l l I I I I


*. C


0004
alle

.cas




OCO <4<

o00 < <*

.00 <4.



0 0O <4.

00 << *
S0 0 << *

0 <<*

O <3< *
0 0 <4. 4


000000
S0 o 4 >> >>>>

O O D O
0 a ,i *<


11 1il1 1 1 1 11 i 1 1i i I


0 0 0


S-ed 'SWIflflOT SSOcI QIOBUZNH


Ill I I I


11 I I II I I


*1





0
.o
m0









U-
0












3
C:






0 o
0
O ega


0
0 -i om








0)
4J
0





ra "-






S00

0 --





0-i






Z 0





Lxa


III I I




















-I I I I I I


C .

Co .


D60


000

o oo
O 00
a- LO CO


0_ 0 0-
O [3 ,


I i Sil I I II I I H

0 0


s-Pd 'SfnlloI^ SScn O aI3DnflUU


I I I I I I I


0 r;

U


r o

CO
0 -

0
ac 0
r
7-













C C) -











83 >
0 a -0
ooC)



U Q )












Wj 0
-a .2 .






o e
00





















o a



















II I I iI,.. .. . .


O 04 4


O 04 4



0 04
04 4


0 D4

.0 04 4

0 3 44 4



O 0D 4
.0 04 4

.0 04

*0 0 4 <
So 0 .4
C 4


00
-0 0 ( 4


000

N


000
L n i- C, t
000
0 o) _oo
0000
CL. C NL O>
W00
14 -I 10


I l I I l l ( 1 ) I !


~J I lrT 1 I 1


0 0


s-Pd 'SfYIf1UOIkT


sO'1 ElJ llaHa


1111 1 1 1 I


I I I I I I I


illij l 1 1 I


o-




(0
0 C







S r-
u a
C






k ~o0
0






aC



o
7r 1 CL





a00






0
U 0
0
0 0

0- 0
CCj

C) 0






c'J

0 0
I-
=Jl C -


I I I I 1 I I





















I I I I


I11111 I I I


= OO
S 0
* o 0


0 0



0 0


.0 0


-0 0

.0 0

.0 0

S0 0

S0 0


S I I I I I I I Ii II I I


0


s-8d 'AIlSO3SIA XnI1M0IO3


0.









0S


0 .

S Qo



U)



0 Q)
00




C)
C, 1



















OE
u-I<





















..O
0





U CD



o







C N
00
O
Or 0


















O O
o .




























o 3
-,u (
Q)a


0





















I I 111 1 I I li i I I I J i ill I II


40 <
S 0 <

S 0 <



4 0o .



4 O 0




0 0 a


4 o0






4 O 0

O 0 CC
4 0 <0
4 0 0.



4 0 0. *
OC


E E
4 o0


III1 1 I I I


C
cc


0E
0

* <


I1111 I I Iiiii i I I I IIIiil I I


s-'ed 'AIISOOSIA X3TId 0


0 .,-4

00
u 0

> .











0
a







- oJE
HO
> r.,




















0
0 c





z E
E
c-i



















0.
m4-
Sc





0 u







0





CO
to


-2
^D "
(- o ;-
^-- c f
r c1ff










t-1






















I I I I I I I


AJISOoSIA QI OIUGnP


O

0











- o

Z
O0


0















ac'9
0











0
0




-o











O0





0




-*O


O o



> (0


CU I
0*I
00o -v

C N r-
ca
c- u E






0.W r=
C>H





oa ,




Su m



c" 0 0)











co0


00
o L
o o UU











- m
(c (












u 00
r- a, .












a 'T
00u
o E E
*H 0 )
S14











O o0-v
00






UL
c-


I I


I I I


I i







58












0
U I i I l i I Ii- I I I I -.



4) ca
0
o -


c3 0





S00 .








o- 0o 0) 0
- 0








0
C) w at


o












0 \0 ( a














\d O I (*H B. l
00
\0 t


\ c 0))







0 0. -
0 -






o cE

0 -*



0i AD UC CO lDi





















11,1 I I


I I I I I i I i l i I I I I


0



,LISODSIA UaI DofnUa


1111 1 1 I | J


SI I I I I I


l l I I I I


o
0












O
o

o



o






o




o










o
C\,
C









o

o









o
- o
- o


o o





0 U
o I
ci *a









C II
> u





o c
(1) Q)
roo











0 04
C II




















ca
EE *




0) -H
o c
Coo
C 0 C
*3 C U





0 00

C 0C



4- '-
n ^^






60











0 0
S I IIl I I I I l i l I I I I
-o )
O "n


U C
"-c




S o~ o

r O II
-0 1 I








ul
0 a






S\ooo
E u





S0







O-



O ,O
\O r\ ,...
o \
\ -
\0 0 e

\ 0 0 EH
r. 0
CD 0 00




\U a) ) C)








I4-I | I
\O0 co E
0 \ -


-a r c o E _






co

SI ISDS IA (IfI CHf 0.






















I 1111I I I I


r


AIJISOOSIA (I30nD(IH


0


0 -C C
m 0


0o 0 w,



U .




c-o

o- 0c 0





0 m
U


0-01

















c) 10 I




L ~C *L




-0





E0 01-

w,


I I I I I I I I I I, L





















) I I I I I I I I j I I I I I I I I I I I I I I I I I I I I I


QI

0 0












O
0a .)


S0

(0)--



0
uo 0




"0 C




SE
CC'
P. U









c c
o 0
44U 44





00
C")en
oCo
c-i
00 r
C-.


n ui UHaLHIIVVd a(mOW





















SI I I I l l l l l I i I I I I I l l I I


1 1 ||I I I 1 1 1 C | C |I I1 l 1 |1C

0 0
0 0


utins LAJIIVVd iACIOI,


Ea





co
r-I


O



c 0



U



C
co







u
U





0ul
0E
0 CC
Cu o


S00
C3



<004


u mo




EC0
uU
u -e
- 00 0










EUI









[1-



















I lI I I


1111 11 11111 11 I I


111 1 1 I I I 1111 1 I I 111i1ii I I I IIII I I Ii


d I


S-10d 'AIISODSIA 1NM3?VddV


0


*io XaTdKcO3


111111 1 I


0






U




Eo





< u
0N 0
C I























co 0)
U






O E
lo
r .)



H c
0 C -










I-
S 0)
00
C 01
0 -H




















I l lI l l I I 1 I1 1 1 1 1 i I I I I I


SIll l I I ill SI I I III VdI V I X 11 1 I I




S-ejd 'ALIISO3SIA INMtEVddV ,'o X3idPV03


~ 1 ii I rl i


0
C








0>0
So
N, I




C.
U,) g'







0
Cu
o H>


co

Z C C



co"






0 E

2 .1
00
cE
.-H





U o
U



c m
n





















mmT1


1 1 1 1 I I I I ]


1 1 1 i I I I I


S 0
0 *

S 0 *

0 *

0

0 *

0

0

0 *

* 0 a

0


CD
0 O
c..


S11111 I 11 I I iI Illl 1 I I 1

S- 0 0X

S-Cd XAIISOJSJA XT^cJIO


C
N
v)
N N




0





>4

-0
o
O









-a *












a






E-
^3








Co









E
0 01






2

.CE
F---






67























0


0
U








Soo



(I

-)
0

U



to
C3 I





XC
:L1: -- -


4c oN







Sa 0


cn





S-ud 'AJJISOSIA l XT1dATOO



















I I 1111 1 I


-F-F -F F T- -


i i l i I I I I Sl l l i I I I

So0

S-Pd 'AIISOSIA X31dJNOD


0
N
O
N
CV







o








0
CMI
HCl




















o
rU o
z -io

















ca
c
0
T C o






o
H u










0n
(LI
U U
0 -


o a








Co..


/*





, 1
I





'-























I
























































Figure 37. SEM Micrographs of PS2520.























*8, 'pe 0001 pp O- p FS


Figure 38. SEM Micrographs of PS252.































J 8 '0 i 3 10


Figure 39. SEI Micrographs of PS2508.









volume fractions appearing in the figures previously described are

nominal values, and thus Tables 5 and 6 should be consulted to determine

the true respective composite filler concentration. The activation

energies for the onset of viscous flow were calculated for most of the

samples, and these results are given in Tables 7 and 8. Tables 9

through 12 contain the listings of the various model parameters that

were obtained from the Adams model fits to both complex viscosity and

reduced storage modulus data. Finally, an indication of the quality of

the compounding performed is evidenced from the intrinsic viscosity data

obtained from post compounded samples given in Table 13, and Table 14

displays the residual moisture remaining in the various size CaCO3

fillers after vacuum drying.















Table 5. Actual Volume Fractions of CaCO3 Filled Materials
(Determined from ashing).


Nominal Volume
Fraction

0.05
0.10
0.15
0.20
0.25
0.025
0.05
0.10
0.15
0.20
0.25
0.05
0.10
0.15
0.20
0.25


Measured Weight
Fraction

0.118
0.225
0.309
0.386
0.46
0.062
0.122
0.227
0.315
0.446
0.458
0.12
0.221
0.252
0.382
0.475


Actual Volume
Fraction

0.047
0.097
0.142
0.189
0.24
0.024
0.049
0.098
0.146
0.229
0.238
0.048
0.095
0.111
0.186
0.251


PS202 (molded)
PS202 (scrap)


Sample ID

PS520
PS1020
PS1520
PS2020
PS2520
PS0252
PS52
PS102
PS152
PS202
PS252
PS508
PS1008
PS1508
PS2008
PS2508


0.20
0.20


0.448
0.449


0.231
0.232















Table 6. Actual Volume Fractions of Bimodally Distributed
CaCO3 Filled Materials (Determined from ashing).


Nominal Volume
Sample ID Fraction


PS128020
PS126040
PS125050
PS124060
PS122080
PS208020
PS206040
PS205050
PS204060
PS202080


0.12
0.12
0.12
0.12
0.12
0.20
0.20
0.20
0.20
0.20


Measured Weight
Fraction

0.258
0.258
0.261
0.263
0.258
0.392
0.395
0.396
0.392
0.387


Actual Volume
Fraction

0.114
0.114
0.116
0.117
0.114
0.193
0.195
0.195
0.193
0.190















Table 7. The Activation Energy for the Onset of Viscous
Flow for CaCO3 Filled PS Materials.


Sample ID Frequency, rad/S. Activation Energy, kcal/nol


PS Resin and all 1 18.9 1.5%
CaCO3 Composites 10 14.6 3.0%
Except as Noted 100 9.1 5.0%
Below *




*Samples excluded include: PS2008, PS2508, PS202080, and PS204060
















Table 8. The Activation Energy for the Onset of Viscous
Flow for Rubber Filled PS Materials.


Sample ID Frequency, rad/S. Activation Energy, kcal/mol


HIPS500 100 9.3


1 23.3
HIPS1000 10 13.3
100 8.2


1 20.9
HIPS1500 10 11.8
100 6.6


10 10.8
HIPS2000 10 5.9


1 16.6
HIPS2500 10 9.4
100 5.1















Table 9. Viscosity Model Parameters for CaCO3 Filled PS Materials.



Sample ID inn en p o s





PS Resin 8.32 1.7 1.9 -0.64
PS520 8.30 1.8 1.9 -0.67
PS1020 8.36 1.9 1.9 -0.66
PS1520 8.56 1.9 1.85 -0.68
PS2020 8.92 1.6 2.2 -0.63
PS2520 9.15 1.5 2.0 -0.60


PS0252 8.33 1.7 2.0 -0.62
PS52 8.47 1.8 2.0 -0.68
PS102 8.69 1.7 2.0 -0.68
PS202 9.02 1.7 1.9 -0.60
PS252 11.51 -0.62 3.7 -0.65


PS508 8.30 2.0 1.8 -0.69
PS1008 8.84 1.5 2.1 -0.62
PS1508 9.41 0.9 2.5 -0.63
PS2008 10.57 0.3 3.0 -0.65















Table 10. Viscosity Model Parameters for Rubber Filled PS Materials.



Sample ID nno Sn p a s



PS Resin 8.32 1.7 1.9 -0.64
HIPS500 8.52 1.8 2.0 -0.72
HIPS1000 8.70 1.8 2.0 -0.75
HIPS1500 9.11 1.4 2.1 -0.77
HIPS2000 9.51 1.2 2.4 -0.80
HIPS2500 10.02 0.3 2.4 -0.72














Table 11. Reduced Storage Modulus Model Parameters
for CaCO3 Filled PS Materials.



Sample ID in (GR ,) n u' o' S'



PS Resin 7.74 0.67 2.3 -1.55


PS520 7.42 1.04 2.4 -1.62
PS1020 7.49 1.08 2.5 -1.61
PS1520 7.70 1.08 2.5 -1.63
PS2020 8.38 0.52 2.6 -1.54
PS2520 8.84 0.39 2.8 -1.55


PS0252 7.57 0.70 2.2 -1.54
PS52 7.87 0.85 2.5 -1.64
PS102 8.30 0.70 2.7 -1.64
PS202 8.50 0.62 2.6 -1.54
PS252 22.8 -7.3 8.6 -1.63


PS508 7.49 1.08 2.5 -1.63
PS1008 8.61 0.28 2.6 -1.54
PS1508 11.3 -0.84 4.3 -1.58.
PS2008 17.05 -3.89 6.7 -1.64















Table 12. Reduced Storage Modulus Model Parameters
for Rubber Filled PS Materials.


Sample ID Zn (GR~') in j' o' S'


PS Resin 7.74 0.67 2.3 -1.55


HIPS500 7.97 1.00 2.6 -1.66
HIPS1000 8.25 0.90 2.5 -1.70
HIPS1500 9.15 0.41 2.6 -1.73
HIPS2000 10.21 0.14 3.0 -1.77
HIPS2500 11.47 -0.83 3.0 -1.70




81









Table 13. Intrinsic Viscosities of Selected PS Composites.




Sample ID Intrinsic Viscosity, dl/g


PS Resin 0.89


PS 1508 0.90


PS2508 0.90
















Table 14. Residual Water Adsorbed on CaCO3 After

Vacuum Drying (Determined by ashing).


Average Particle
Size, microns


Percent Residual Moisture,
Weight %


20.0















DISCUSSION OF RESULTS


The theological properties of PS composites were determined as

functions of filler type, concentration, particle size, and particle

size distribution at temperatures ranging from 210-2600C and over a wide

range of frequency. The results were used to test models to describe

the frequency dependence of both the complex viscosity and the reduced

loss modulus for the unimodally distributed systems, and percolation

theory was determined to be useful in qualitatively explaining the

results.

The PS-rubber and PS-CaCO3 composites covering concentration ranges

of 2.5 to 30 volume % for both unimodal and bimodal particle size dis-

tributions of filler ranging in size from 0.8 to 20 microns were com-

pounded. Intrinsic viscosities of the compounded samples of PS1508 and

PS 2508 were determined, and the results indicated that the polymer

suffered no degradation during the compounding. The SEM micrographs of

the compression molded test samples revealed that the quality of disper-

sion was quite good, and the reproducibility of the theological results

indicated that composite uniformity was excellent. This fact was rein-

forced by the results of ashing experiments conducted on molded test

samples and on material trimmed from the tooling of the loaded rheo-

meter. A sample of the compression molded plaque of PS202 was ashed to

determine the filler concentration. Another sample of the same material

from the same plaque was loaded into the rheometer, the gap was adjusted




University of Florida Home Page
© 2004 - 2010 University of Florida George A. Smathers Libraries.
All rights reserved.

Acceptable Use, Copyright, and Disclaimer Statement
Last updated October 10, 2010 - - mvs