• TABLE OF CONTENTS
HIDE
 Front Cover
 Dedication
 Acknowledgement
 Table of Contents
 List of Tables
 List of Figures
 Abstract
 Introduction
 Background
 Materials and methods
 Characterization and modification...
 Results
 Discussion
 Conclusions
 References
 Biographical sketch
 Back Cover














Title: Quantitative studies of the effects of interfacial bonding strength on the mechanical and rheological properties of polymer composites /
CITATION PDF VIEWER THUMBNAILS PAGE IMAGE ZOOMABLE
Full Citation
STANDARD VIEW MARC VIEW
Permanent Link: http://ufdc.ufl.edu/UF00097394/00001
 Material Information
Title: Quantitative studies of the effects of interfacial bonding strength on the mechanical and rheological properties of polymer composites /
Physical Description: xx, 337 leaves : ill. ; 28 cm.
Language: English
Creator: Shang, Shaye-Wen, 1957-
Publication Date: 1989
Copyright Date: 1989
 Subjects
Subject: Polymeric composites -- Mathematical models   ( lcsh )
Polymers -- Rheology   ( lcsh )
Polymeric composites -- Testing   ( lcsh )
Adhesion   ( lcsh )
Materials Science and Engineering thesis Ph. D
Dissertations, Academic -- Materials Science and Engineering -- UF
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
 Notes
Thesis: Thesis (Ph. D.)--University of Florida, 1989.
Bibliography: Includes bibliographical references (leaves 312-336)
Additional Physical Form: Also available on World Wide Web
Statement of Responsibility: by Shaye-Wen Shang.
General Note: Typescript.
General Note: Vita.
 Record Information
Bibliographic ID: UF00097394
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 - 001515136
oclc - 21969369
notis - AHC8161

Downloads

This item has the following downloads:

quantitativestud00shanrich ( PDF )


Table of Contents
    Front Cover
        Page i
        Page i-a
    Dedication
        Page ii
    Acknowledgement
        Page iii
    Table of Contents
        Page iv
        Page v
        Page vi
        Page vii
        Page viii
    List of Tables
        Page ix
    List of Figures
        Page x
        Page xi
        Page xii
        Page xiii
        Page xiv
        Page xv
        Page xvi
        Page xvii
        Page xviii
    Abstract
        Page xix
        Page xx
    Introduction
        Page 1
        Page 2
        Page 3
        Page 4
        Page 5
        Page 6
    Background
        Page 7
        Page 8
        Page 9
        Page 10
        Page 11
        Page 12
        Page 13
        Page 14
        Page 15
        Page 16
        Page 17
        Page 18
        Page 19
        Page 20
        Page 21
        Page 22
        Page 23
        Page 24
        Page 25
        Page 26
        Page 27
        Page 28
        Page 29
        Page 30
        Page 31
        Page 32
        Page 33
        Page 34
        Page 35
        Page 36
        Page 37
        Page 38
        Page 39
        Page 40
        Page 41
        Page 42
        Page 43
        Page 44
        Page 45
        Page 46
        Page 47
        Page 48
        Page 49
        Page 50
        Page 51
        Page 52
        Page 53
        Page 54
        Page 55
        Page 56
        Page 57
        Page 58
        Page 59
        Page 60
        Page 61
        Page 62
        Page 63
    Materials and methods
        Page 64
        Page 65
        Page 66
        Page 67
        Page 68
        Page 69
        Page 70
        Page 71
        Page 72
        Page 73
        Page 74
        Page 75
        Page 76
        Page 77
        Page 78
        Page 79
        Page 80
    Characterization and modification of surface of silica particles
        Page 81
        Page 82
        Page 83
        Page 84
        Page 85
        Page 86
        Page 87
        Page 88
        Page 89
        Page 90
        Page 91
        Page 92
        Page 93
        Page 94
        Page 95
        Page 96
        Page 97
        Page 98
        Page 99
        Page 100
        Page 101
        Page 102
        Page 103
        Page 104
        Page 105
        Page 106
        Page 107
        Page 108
        Page 109
        Page 110
        Page 111
        Page 112
        Page 113
        Page 114
        Page 115
        Page 116
        Page 117
        Page 118
        Page 119
        Page 120
        Page 121
        Page 122
        Page 123
        Page 124
        Page 125
        Page 126
        Page 127
        Page 128
        Page 129
        Page 130
        Page 131
        Page 132
        Page 133
        Page 134
        Page 135
        Page 136
    Results
        Page 137
        Page 138
        Page 139
        Page 140
        Page 141
        Page 142
        Page 143
        Page 144
        Page 145
        Page 146
        Page 147
        Page 148
        Page 149
        Page 150
        Page 151
        Page 152
        Page 153
        Page 154
        Page 155
        Page 156
        Page 157
        Page 158
        Page 159
        Page 160
        Page 161
        Page 162
        Page 163
        Page 164
        Page 165
        Page 166
        Page 167
        Page 168
        Page 169
        Page 170
        Page 171
        Page 172
        Page 173
        Page 174
        Page 175
        Page 176
        Page 177
        Page 178
        Page 179
        Page 180
        Page 181
        Page 182
        Page 183
        Page 184
        Page 185
        Page 186
        Page 187
        Page 188
        Page 189
        Page 190
        Page 191
        Page 192
        Page 193
        Page 194
        Page 195
        Page 196
        Page 197
        Page 198
        Page 199
        Page 200
        Page 201
        Page 202
        Page 203
        Page 204
        Page 205
        Page 206
        Page 207
        Page 208
        Page 209
        Page 210
        Page 211
        Page 212
        Page 213
        Page 214
        Page 215
        Page 216
        Page 217
        Page 218
        Page 219
        Page 220
        Page 221
        Page 222
        Page 223
        Page 224
        Page 225
        Page 226
        Page 227
        Page 228
        Page 229
        Page 230
        Page 231
        Page 232
        Page 233
        Page 234
        Page 235
        Page 236
        Page 237
        Page 238
        Page 239
        Page 240
        Page 241
        Page 242
        Page 243
        Page 244
        Page 245
        Page 246
        Page 247
        Page 248
        Page 249
        Page 250
        Page 251
        Page 252
        Page 253
        Page 254
        Page 255
    Discussion
        Page 256
        Page 257
        Page 258
        Page 259
        Page 260
        Page 261
        Page 262
        Page 263
        Page 264
        Page 265
        Page 266
        Page 267
        Page 268
        Page 269
        Page 270
        Page 271
        Page 272
        Page 273
        Page 274
        Page 275
        Page 276
        Page 277
        Page 278
        Page 279
        Page 280
        Page 281
        Page 282
        Page 283
        Page 284
        Page 285
        Page 286
        Page 287
        Page 288
        Page 289
        Page 290
        Page 291
        Page 292
        Page 293
        Page 294
        Page 295
        Page 296
        Page 297
        Page 298
    Conclusions
        Page 299
        Page 300
        Page 301
        Page 302
        Page 303
        Page 304
        Page 305
        Page 306
        Page 307
        Page 308
        Page 309
        Page 310
        Page 311
    References
        Page 312
        Page 313
        Page 314
        Page 315
        Page 316
        Page 317
        Page 318
        Page 319
        Page 320
        Page 321
        Page 322
        Page 323
        Page 324
        Page 325
        Page 326
        Page 327
        Page 328
        Page 329
        Page 330
        Page 331
        Page 332
        Page 333
        Page 334
        Page 335
        Page 336
    Biographical sketch
        Page 337
        Page 338
        Page 339
    Back Cover
        Page 340
        Page 341
Full Text




















QUANTITATIVE STUDIES OF THE EFFECTS
OF INTERFACIAL BONDING STRENGTH ON THE
MECHANICAL AND RHEOLOGICAL PROPERTIES OF POLYMER COMPOSITES











BY


SHAYE-WEN SHANG


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


1989






























































UNIVERSITY OF FLORIDA


3 1262 08552 3180
































TO MY FAMILY











ACKNOWLEDGEMENTS


I would like to express my sincerest gratitude and

appreciation to my advisors professor Christopher D. Batich

and Dr. Jerry J. Williams in 3M for their invaluable

guidance and understanding during the course of this work.

I am also grateful to professor Robert T. DeHoff for

the discussion of the model proposed in this study, and to

professor Eugene P. Goldberg and professor Denish O. Shah

for their helpful comments and kind assistance, and to

professor Kevis S. Jones for the help with the TEM

micrograph, and to professor Michael D. Sacks for his kind

assistance with the Rheometrics Dynamic Spectrometer.

Special thanks are given to professor Karl-Johan M.

Soderholm of the Department of Dental Biomaterials for his

introducing me to the art of thorough scientific

investigation and for his unforgettable assistance as well

as encouragement during the time of my research as a

graduate student.

Meanwhile, I would like to express my gratitude to my

parents and sister for their constant support, without

their backup, this work cannot be done.


iii














TABLE OF CONTENTS


Page

ACKNOWLEDGEMENTS... .....................................iii

LIST OF TABLES...........................................ix

LISTS OF FIGURES................................................

ABSTRACT.............................................. ... xix

CHAPTERS

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

1.1 General. ........................................ 1
1.2 Outline of This Study.............................. 2

2. BACKGROUND............................................7

2.1 Effect of Filler Particles in Polymer Matrix......7
2.2 Interfacial Bonding ...............................7
2.2.1 Bonding and Force across an Interface....... 8
2.2.1.1 Aided Bonding by Coupling Agents....8
2.2.1.2 Direct Intermolecular Interactions..9
2.2.2 Ways to Characterize Forces at the
Interface............... ................... 15
2.2.2.1 Work of Adhesion and Wetting........15
2.2.2.2 Relationship between Work of
Adhesion and Force Attraction
Constant........................... 18
2.2.2.3 Work of Adhesion and Surface
Energy .............................19
2.2.2.3.1 Harmonic-Mean Approach...20
2.2.2.3.2 Geometric-Mean Approach..20
2.2.2.4 Surface Energy......................21
2.2.2.4.1 Surface Energy and
Contact Angle............21
2.2.2.4.2 Surface Energy and
Cohesive Energy Density..23
2.2.2.4.3 Hamilton Methods ........24
2.2.2.4.4 Captive Air Bubble
Technique.................26
2.2.2.5 Work of Adhesion and Acid-Base
Interaction........................27






2.3 Quantitative Evaluation of Interfacial Bonding
Strength of Polymer Composites...................29
2.4 Mechanical Properties of Particulate Filled
Polymer Composite.................................32
2.4.1 Effect of Properties of Interface/
Interphase on a Polymer Composite..........34
2.4.2 Effect of Volume Fraction and Particle
Size on the Modulus of a Composite.........36
2.4.3 Effect of Volume Fraction and Particle Size
on the Tensile Strength of a composite.....42
2.4.4 Effect of Temperature and Testing Rate on
the Mechanical Properties of a composite...46
2.5 Rheological Properties of Particulate Filled
Polymer Melts.....................................48
2.5.1 Effect of Volume Fraction, Particle Size
and Size Distribution of Filler on
Polymer Melts ..............................49
2.5.2 Effect of Testing Rate and Temperature.....52
2.6 Dispersion of Filler Particles in the Polymer
Matrices. ...................................... .54
2.7 Friction in a Filled Polymer System..............56
2.7.1 Coefficient of Friction ....................56
2.7.1.1 Effect of Polar Functional Groups
on the Coefficient of Friction..... 58
2.7.1.2 Effect of Temperature on the
Coefficient of Friction............58
2.7.2 Friction Factor ............................ 59
2.7.2.1 Types of Friction Factor in
a Polymer System....................61
2.7.2.2 Segmental Friction of an
Unfilled Polymer Matrix............61
2.7.2.3 Surface Skin and Form Friction on
Particulate Filled Polymer Melts...62

3. MATERIALS AND METHODS ...............................64

3.1 Materials. ....................................... 64
3.1.1 Filler......................................64
3.1.1.1 Stober Silica ......................64
3.1.1.2 Cab-O-Sil Silica ...................64
3.1.1.3 Quartz Plates ......................65
3.1.2 Polymer..................................... 65
3.1.3 Chemical for Surface Modification..........66
3.2 Techniques.......................................67
3.2.1 Preparation of Stober Silica...............67
3.2.2 Surface Modification on Silica Particle....68
3.2.2.1 Heat Treatment .....................68
3.2.2.2 Chemical Treatment by
Trimethylchlorosilane (TMCS).......69
3.2.3 Contact Angle Measurement................. 69
3.2.4 Titration by Indicator Dye................. 71
3.2.5 Diffuse Reflectance Infrared Fourier
Transform (DRIFT) Spectrometry.............72






3.2.6 Thermogravimetric Analysis (TGA)...........74
3.2.7 Polymer Adsorption on the Silica
Surface.....................................75
3.2.8 Preparation of Polymer Composites..........76
3.2.9 Mechanical and Rheological Measurements....77
3.2.10 Scanning Electron Microscopy (SEM) and
Scanning Transmission Electron
Microscopy (STEM) Studies.................79

4. CHARACTERIZATION AND MODIFICATION OF SURFACE OF
SILICA PARTICLES.....................................81

4.1 Characterization of Silica Particles.............81
4.1.1 Stober Silica ..............................81
4.1.2 Cab-O-Sil Silica ...........................84
4.2 Modification of the Silica Surface...............88
4.2.1 Contact Angles on Amorphous Fused
Quartz Plates......................... ..... 88
4.2.2 Fourier Transform Infrared (FTIR) and
Thermogravity Analysis (TGA) Studies
of Silica Particles ........................89
4.2.2.1 Heat Treatment......................89
4.2.2.2 Chemical Treatment.................96
4.2.2.2.1 Cab-O-Sil Silica......... 97
4.2.2.2.2 Stober Silica ............99
4.3 Concentration of Hydroxyl Groups on the
Silica Surface...................................102
4.4 Polymer Adsorption on Silica Surface............104
4.4.1 Evidence of Hydrogen Bonding Studied
by FTIR.................................... 105
4.4.2 Effect of Hydrogen Bonding on the
Polymer Adsorption..........................107
4.4.3 Ratio of Hydrogen-Bonded to Non-
Hydrogen-Bonded Carbonyl Group............115
4.5 Temperature Dependence of the Interfacial
Bonding.............................................. 122
4.5.1 Heating Effect on the Silica-Surface-
Adsorbed Polymer...........................122
4.5.2 Cooling Effect on the Silica-Surface-
Adsorbed Polymer ..........................128
4.5.3 Quasi-Equilibrium Constant of Hydrogen
Bonding ...................................131
4.5.3.1 Thermodynamic Approach............131
4.5.3.2 Temperature Dependence of Quasi-
Equilibrium Constant of Hydrogen
Bonding at the Interface..........132

5. RESULTS.............................................137

5.1 Work of Adhesion between Silica Particles
and E-Va Copolymer ..............................137
5.1.1 Work of Adhesion of Weak
Interfacial Bonding........................137






5.1.2 Work of Adhesion of Strong
Interfacial Bonding .......................139
5.1.3 Work of Adhesion and Surface Energy
of Silica Particles .......................142
5.1.4 The Hydrogen Bonding Component of
Work of Adhesion.......................... 144
5.2 The Mechanical Properties of Silica Filled
Filled Composites................................145
5.2.1 Effects of Particle Size and Volume
Fraction of Silica Filler..................145
5.2.2 Effect of Work of Adhesion.................149
5.2.2.1 Young's Modulus....................149
5.2.2.2 Extension of Guth-Smallwood
Equation ..........................154
5.2.2.3 Tensile Strength..................156
5.3 The Rheological Properties of Silica
Filled Composites................................160
5.3.1 Shear Storage Modulus of Polymer
Composites............................... 160
5.3.1.1 Dependence of Frequency and Solid
Loading on the Shear Modulus...... 160
5.3.1.1.1 Cab-O-Sil Silica
Filled Composites.......160
5.3.1.1.2 Stober Silica
Filled Composites........163
5.3.1.2 Dependence of Work of Adhesion
on the Shear Modulus..............163
5.3.1.2.1 Cab-O-Sil Silica
Filled Composites....... 163
5.3.1.2.2 St6ber Silica
Filled Composites...... 172
5.3.2 Melt Viscosity of Silica Filled
Polymer Melt............................... 186
5.3.2.1 Dependence of Frequency and Solid
Loading on the Melt Viscosity..... 186
5.3.2.1.1 Cab-O-Sil Silica
Filled Composites........186
5.3.2.1.2 Stober Silica
Filled Composites........ 187
5.3.2.2 Dependence of Work of Adhesion
on the Melt Viscosity............. 199
5.3.2.2.1 Cab-O-Sil Silica
Filled Composites........199
5.3.2.2.2 Stober Silica
Filled Composites........ 199
5.4 Effect of Temperature on the Viscosity of
Silica Filled Polymer Composites................213
5.5.1 Dependence of Volume Fraction
of Silica............................. ....215
5.5.2 Dependence of Silica Surface
Properties.. ....... ........................ 221
5.6 Dispersion of Silica Filler Particles in
the Polymer Matrix............................... 232


vii






6. DISCUSSION................................................ 256

6.1 Effective Silica Particle Size..................256
6.2 Interphase Dependence of Mechanical
Properties of Polymer Composites................260
6.2.1 Interphase Dependence of
Young's Modulus ...........................260
6.2.2 Interphase Dependence of
Tensile Strength ..........................262
6.3 Effect of Temperature on Work of Adhesion........268
6.3.1 Temperature Dependence of Weak
Interfacial Bonding .......................268
6.3.2 Temperature Dependence of Strong
Interfacial Bonding.......................269
6.3.3 Discussion of Temperature Dependence
of Work of Adhesion.......................270
6.4 Effect of Interphase on the Rheological
Properties of Silica Filled Polymer melt........272
6.4.1 Frequency Dependence of the
Effective Particle Size...................272
6.4.2 Interphase Dependence of
Shear Modulus .............................274
6.4.3 Interphase Dependence of
Melt Viscosity ............................275
6.4.3.1 Flow Process of a Filled
Polymer Melt ......................275
6.4.3.2 Effect of Friction Factor
on Melt Viscosity.................276
6.4.3.3 Low Frequency Dependence
of Surface Friction Factor........277
6.4.3.4 High Frequency Dependence
of Surface Friction Factor........280
6.5 Mathematical Model ..............................281
6.6 Effect of Frequency on the Activation
Energy of Polymer Melt ..........................290
6.7 The Extended Arrhenius Equation on the Melt
Viscosity of Silica Filled Polymer Melts........292

7. CONCLUSIONS.........................................299

8. FUTURE RESEARCH...................................... 303

REFERENCES... ...........................................312

BIOGRAPHICAL SKETCH ..................................... 337


viii












LIST OF TABLES


Tables Pages

2.1 Bond Types and Typical Bond Energy.................14

4.1 Contact Angles Versus Surface Modification on
Amorphous Fused Quartz Plates.......................91

4.2 Surface Hydroxyl Groups Per Unit Area.............103

4.3 Amount of Polymer Adsorbed on Unit Area of
Silica Surface.....................................110

4.4 Ratio of Hydrogen-Bonded to Non-Hydrogen-Bonded
Carbonyl Groups................................... 120

5.1 Surface Energy of Silica and E-Va Copolymer
Evaluated by Contact Angles.......................140

5.2 Calculated Work of Adhesion Between Silica
Surface and E-Va Copolymer........................141

5.3 Slopes of the Young's Modulus of Silica Filled
E-Va Copolymers..................................... 155

5.4 Slopes of the Tensile Strength of Silica Filled
E-Va Copolymers..................................... 159

5.5 Activation Energy of Viscosity of Stober Silica
Filled Ethylene-Vinyl Acetate Copolymer...........224












LIST OF FIGURES


Figures Pages

2.1 Relationship between Contact Angle and Young's
Equation....... ..................................... 17

2.2 Components of Surface Free Energy for the
Hamilton Technique.................................. 25

2.3 Components of Surface Free Energy for Air Bubble
Technique ......................................... 25

4.1 Shape and Size of Stober Silica by SEM.............82

4.2 The Three Dimensional Random Branching of the
Aggregates of Cab-O-Sil Silica.................... 85

4.3 The Isolated Individual Aggregates of Cab-O-Sil
Silica... ........................................... 86

4.4 The Individual Particles in the Aggregates of
Cab-O-Sil Silica.................................... 87

4.5 Contact Angles of Water on the Surface of the
Fused Quartz Plates Treated by Heat and/or TMCS....90

4.6 FTIR Spectrum of Stober Silica Heat Treated at
Different Temperatures.............................. 92

4.7 FTIR Spectrum of Cab-O-Sil Silica Heat Treated
at Different Temperatures........ ............... ......... 93

4.8 TGA Spectrum of the Weight Loss of Cab-O-Sil and
Stober Silica by the Heating Process...............95

4.9 FTIR Spectrum of Cab-O-Sil Silica at Different
Heat/TMCS Treatments................................ 98

4.10 FTIR Spectrum of Stober Silica at Different
Heat/TMCS Treatments..............................1. 00

4.11 The Wavenumber Shift of the Carbonyl Groups of
E-Va Copolymer after Hydrogen Bonding with the
Hydroxyl Groups on the Silica Surface..............106





4.12 Effects of Volume Concentrations of Polymer
Solution on the Extent of Polymer Adsorbed on
1100C and 7500C/TMCS Cab-O-Sil Silica Surfaces'....108

4.13 Effect of Silica Surface Properties on Polymer
Bonded and/or Adsorbed on the Cab-O-Sil Silica
Surface from 6% Volume of Polymer Solution........ 112

4.14 Effect of Silica Surface Properties on Polymer
Bonded and/or Adsorbed on the Cab-O-Sil Silica
Surface from 2% Volume of Polymer Solution........113

4.15 Effect of Silica Surface Properties and Volume
Concentration of Polymer Solution on the Extent
of Adsorbed Polymer per Unit Silica Surface....... 114

4.16 The Extent of Polymer Bonded and/or Adsorbed on
the Silica Surface versus Work of Adhesion from
Different Solution Concentrations.................116

4.17 Effect of Concentrations of Polymer Solution on
the Ratio of Hydrogen-Bonded to Non-Hydrogen-
Bonded Carbonyl Groups of 1100C Treated Silica.... 118

4.18 Effect of Concentrations of Polymer Solution on
the Ratio of Hydrogen-Bonded to Non-Hydrogen-
Bonded Carbonyl Groups of 7500C/TMCS Silica.......119

4.19 Effect of Environmental Temperature on the
Carbonyl Groups Bonded/Adsorbed on the
Cab-O-Sil Silica Treated at 110C .................123

4.20 Effect of Environmental Temperature on the
Intensity of Hydroxyl Groups of the Cab-O-Sil
Silica Treated at 110C ...........................125

4.21 Effect of Environmental Temperature on the
Carbonyl Groups Bonded/Adsorbed on the
Cab-O-Sil Silica Treated by 7500C/TMCS ............126

4.22 Effect of Environmental Temperature on the
Intensity of Hydroxyl Groups of the Cab-O-Sil
Silica Treated by 7500C/TMCS......................127

4.23 FTIR Spectrum of Temperature Cooling Process on
the Hydrogen-Bonded Carbonyl Groups Adsorbed on
the Cab-O-Sil Silica Treated at 110C .............129

4.24 FTIR Spectrum of Temperature Cooling Process on
the Hydrogen-Bonded Carbonyl Groups Adsorbed on
the Cab-O-Sil Silica Treated by 7500C/TMCS........ 130






4.25 Quasi-Equilibrium Constant between Hydrogen-
Bonded and Non-Hydrogen-Bonded Carbonyl Groups
at the Interface...................................134

4.26 Effect of Temperature on the Quasi-Equilibrium
Constant between Hydrogen-Bonded and Non-
Hydrogen-Bonded Carbonyl Groups at the Interface..136

5.1 Work of Adhesion versus Surface Energy of Silica..143

5.2 Hydrogen Component of Work of Adhesion versus
Hydrogen Component of Surface Energy of Silica.... 146

5.3 Effect of Volume Fraction and Surface Properties
of Stober Silica Filler Particles on the Modulus
of Polymer Composites..............................147

5.4 Effect of Volume Fraction and Surface Properties
of Cab-O-Sil Silica Filler Particles on the
Modulus of Polymer Composites.....................148

5.5 Effect of Volume Fraction and Surface Properties
of Stober Silica Filler on the Tensile Strength
of Polymer Composites.............................150

5.6 Effect of Volume Fraction and Surface Properties
of Cab-O-Sil Silica Filler on the Tensile
Strength of Polymer Composites....................151

5.7 Effect of Work of Adhesion, Volume Fraction and
Particle Size of Silica Filler on the Modulus
of Polymer Composites .............................153

5.8 Effect of Work of Adhesion, Volume Fraction and
Particle Size of Silica Filler on the Tensile
Strength of Polymer Composites....................157

5.9 Effect of Frequency and Surface Properties of
Silica on the Shear Modulus of 5% Volume
Cab-O-Sil Filled E-Va Copolymer...................161

5.10 Relative Shear Storage Modulus versus Frequency
of Various Surface Properties of 5% Volume
Cab-O-Sil Filled Copolymer........................162

5.11 Effect of Frequency and Surface Properties of
Silica on the Shear Modulus of 20% Volume
Stober Silica Filled Copolymer....................164

5.12 Effect of Frequency and Surface Properties of
Silica on the Shear Modulus of 15% Volume
Stober Silica Filled Copolymer....................165

xii





5.13 Effect of Frequency and Surface Properties of
Silica on the Shear Modulus of 10% Volume
Stober Silica Filled Copolymer....................166

5.14 Effect of Frequency and Surface Properties of
Silica on the Shear Modulus of 5% Volume
Stober Silica Filled Copolymer....................167

5.15 Relative Shear Modulus versus Frequency
of Various Surface Properties of 20% Volume
St6ber Silica Filled Copolymer....................168

5.16 Relative Shear Modulus versus Frequency
of Various Surface Properties of 15% Volume
Stober Silica Filled Copolymer....................169

5.17 Relative Shear Modulus versus Frequency
of Various Surface Properties of 10% Volume
Stober Silica Filled Copolymer....................170

5.18 Relative Storage Modulus versus Frequency
of Various Surface Properties of 5% Volume
Stober Silica Filled Copolymer....................171

5.19 Effect of Work of Adhesion and Frequency on the
Relative Shear Modulus of 5% Volume Cab-O-Sil
Silica Filled E-Va Copolymer ......................173

5.20 Effect of Work of Adhesion and Frequency on the
Relative Shear Modulus of 20% Volume Stober
Silica Filled E-Va Copolymer......................174

5.21 Effect of Work of Adhesion and Frequency on the
Relative Shear Modulus of 15% Volume Stober
Silica Filled E-Va Copolymer......................176

5.22 Effect of Work of Adhesion and Frequency on the
Relative Shear Modulus of 10% Volume St6ber
Silica Filled E-Va Copolymer.......................177

5.23 Effect of Work of Adhesion and Frequency on the
Relative Shear Modulus of 5% Volume Stober
Silica Filled E-Va Copolymer......................178

5.24 Effect of Work of Adhesion and Volume Fraction
on the Relative Shear Modulus of Stober Silica
Filled E-Va Copolymer Measured at 0.1 rad/sec.....179

5.25 Effect of Work of Adhesion and Volume Fraction
on the Relative Shear Modulus of Stober Silica
Filled E-Va Copolymer Measured at 1.0 rad/sec..... 180


xiii






5.26 Effect of Work of Adhesion and Volume Fraction
on the Relative Shear Modulus of Stober Silica
Filled E-Va Copolymer Measured at 10 rad/sec......181

5.27 Effect of Volume Fraction of Stober Silica and
Frequency on the Apparent Surface Energy
Barrier of Shear Modulus............................183

5.28 Effect of Frequency on the Intercept Values
in Figure 5.27.....................................184

5.29 Effect of Frequency and Surface Properties of
Silica on the Melt Viscosity of 5% Volume
Cab-O-Sil Filled Copolymer........................188

5.30 Relative Melt Viscosity versus Frequency
of Various Surface Properties of 5% Volume
Cab-O-Sil Filled Copolymer........................189

5.31 Effect of Frequency and Surface Properties of
Silica on the Melt Viscosity of 20% Volume
St6ber Filled Copolymer............................191

5.32 Effect of Frequency and Surface Properties of
Silica on the Melt Viscosity of 15% Volume
Stober Filled Copolymer.... .......................192

5.33 Effect of Frequency and Surface Properties of
Silica on the Melt Viscosity of 10% Volume
Stober Filled Copolymer.............................193

5.34 Effect of Frequency and Surface Properties of
Silica on the Melt Viscosity of 5% Volume
Stober Filled Copolymer ...........................194

5.35 Relative Melt Viscosity versus Frequency
of Various Surface Properties of 20% Volume
Stober Filled Copolymer.............................195

5.36 Relative Melt Viscosity versus Frequency
of Various Surface Properties of 15% Volume
Stober Filled Copolymer.............................196

5.37 Relative Melt Viscosity versus Frequency
of Various Surface Properties of 10% Volume
St6ber Filled Copolymer............................197

5.38 Relative Melt Viscosity versus Frequency
of Various Surface Properties of 5% Volume
Stbber Filled Copolymer...........................198


xiv





5.39 Effect of Work of Adhesion and Frequency on the
Relative Viscosity of 5% Volume Cab-O-Sil
Silica Filled E-Va Copolymer.......................200

5.40 Effect of Work of Adhesion and Frequency on the
Relative Viscosity of 20% Volume Stober Silica
Filled E-Va Copolymer .............................201

5.41 Effect of Work of Adhesion and Frequency on the
Relative Viscosity of 15% Volume St6ber Silica
Filled E-Va Copolymer .............................203

5.42 Effect of Work of Adhesion and Frequency on the
Relative Viscosity of 10% Volume Stober Silica
Filled E-Va Copolymer .............................204

5.43 Effect of Work of Adhesion and Frequency on the
Relative Viscosity of 5% Volume Stober Silica
Filled E-Va Copolymer .............................205

5.44 Effect of Work of Adhesion and Volume Fraction
on the Relative Viscosity of Stober Silica
Filled E-Va Copolymer Measured at 0.1 rad/sec.....206

5.45 Effect of Work of Adhesion and Volume Fraction
on the Relative Viscosity of Stober Silica
Filled E-Va Copolymer Measured at 1.0 rad/sec..... 207

5.46 Effect of Work of Adhesion and Volume Fraction
on the Relative Viscosity of Stober Silica
Filled E-Va Copolymer Measured at 10 rad/sec...... 208

5.47 Effect of Volume Fraction of Stober Silica and
Frequency on the Apparent Surface Energy
Barrier of Melt Viscosity .........................210

5.48 Effect of Frequency on the Slope Values in
Figure 5.47..........................................211

5.49 Effect of Frequency and Temperature on the Melt
Viscosity of Polymer Filled by 20% Stober
Silica with 1100C Treatment .......................214

5.50 Effect of Frequency and Temperature on the Melt
Viscosity of Polymer Filled by 15% St6ber
Silica with 5000C Treatment .......................216

5.51 Effect of Frequency and Temperature on the Melt
Viscosity of Polymer Filled by 10% Stober
Silica with 5000C/TMCS Treatment ..................217





5.52 Effect of Frequency and Temperature on the Melt
Viscosity of Polymer Filled by 5% Stober
Silica with 1100C Treatment........................218

5.53 Effect of Frequency and Temperature on the
Melt Viscosity of E-Va Copolymer..................219

5.54 Effect of Environmental Testing Temperature and
Solid Loading on the Melt Viscosity of Stober
Silica Filled Polymer Measured at 0.1 rad/sec.....220

5.55 Effect of Environmental Testing Temperature and
Solid Loading on the Melt Viscosity of Stober
Silica Filled Polymer Measured at 1.0 rad/sec..... 222

5.56 Effect of Environmental Testing Temperature and
Solid Loading on the Melt Viscosity of Stober
Silica Filled Polymer Measured at 10 rad/sec...... 223

5.57 Effect of Frequency and Solid Loading on the
Change of Melt Viscosity with Temperature.........225

5.58 Effect of Frequency and Temperature on the Melt
Viscosity of Polymer Filled by 20% St6ber
Silica with 1100C Treatment........................ 226

5.59 Effect of Frequency and Temperature on the Melt
Viscosity of Polymer Filled by 20% Stober
Silica with 5000C Treatment........................227

5.60 Effect of Frequency and Temperature on the Melt
Viscosity of Polymer Filled by 20% Stober
Silica with 7500C Treatment........................228

5.61 Effect of Frequency and Temperature on the Melt
Viscosity of Polymer Filled by 20% Stober
Silica with 7500C/TMCS Treatment..................229

5.62 Effect of Frequency and Temperature on the Melt
Viscosity of Polymer Filled by 20% Stober
Silica with 5000C/TMCS Treatment ..................230

5.63 Effect of Frequency and Temperature on the Melt
Viscosity of Polymer Filled by 20% St6ber
Silica with 1100C/TMCS Treatment ..................231

5.64 Effect of Temperature and Work of Adhesion on
the Melt Viscosity of 20% Volume Stober Filled
Polymer at 0.1 rad/sec.... ......................... 233


xvi





5.65 Effect of Temperature and Work of Adhesion on
the Melt Viscosity of 20% Volume Stober Filled
Polymer at 1.0 rad/sec ............................234

5.66 Effect of Temperature and Work of Adhesion on
the Melt Viscosity of 20% Volume Stober Filled
Polymer at 10 rad/sec .............................235

5.67 Effect of Testing Temperature on the Change of
Melt Viscosity with Work of Adhesion for 20%
Stober Silica Filled Polymer at 0.1 rad/sec....... 236

5.68 Effect of Testing Temperature on the Change of
Melt Viscosity with Work of Adhesion for 20%
Stober Silica Filled Polymer at 1.0 rad/sec....... 237

5.69 Effect of Testing Temperature on the Change of
Melt Viscosity with Work of Adhesion for 20%
Stober Silica Filled Polymer at 10 rad/sec........ 238

5.70 SEM Micrograph of the Brittle Fracture Surface
of 15% Volume Stober Silica Particles in E-Va
Copolymer Matrix. Silica Treated at 110C.........239

5.71 SEM Micrograph of the Brittle Fracture Surface
of 15% Volume Stober Silica Particles in E-Va
Copolymer Matrix. Silica Treated by 110C/TMCS.....241

5.72 SEM Micrograph of the Brittle Fracture Surface
of 15% Volume Stober Particles in E-Va Matrix.
Silica Treated at (a) 7500C (b) 7500C/TMCS......... 244

5.73 SEM Micrograph of the Tensile Fracture Surface
of 5% Volume Stober Particles in E-Va Matrix.
Silica Treated at (a) 110C (b) 1100C/TMCS........ 246

5.74 SEM Micrograph of the Tensile Fracture Surface
of 15% Volume Stober Particles in E-Va Matrix.
Silica Treated at (a) 750C (b) 7500C/TMCS........ 247

5.75 SEM Micrograph of the Brittle Fracture Surface
of 5% Volume Cab-O-Sil Silica in E-Va Matrix.
Silica Treated at 1100C ...........................248

5.76 SEM Micrograph of the Brittle Fracture Surface
of 5% Volume Cab-O-Sil Silica in E-Va Matrix.
Silica Treated by 1100C/TMCS......................249

5.77 TEM Micrographs of 5% Volume Cab-O-Sil Silica
in E-Va Matrix. Silica with Various Surface
Modification. (a) 1100C (b) 5000C (c) 7500C
(d) 7500C/TMCS (e) 5000C/TMCS (f) 110C/TMCS......252

xvii






5.78 TEM Micrographs of 5% Volume Cab-O-Sil Silica
in E-Va Matrix. Silica with Various Surface
Modification at High Magnification................255

6.1 Schematic Representation of the Interface Model
..................................................257

6.2 Effect of Work of Adhesion on the Gradient of
Properties of Polymer within the Interphase Layer.259

6.3 The Change of Effective Particle Size of Silica
with Frequency at Different Levels of Work of
Adhesion. ......................................... 273

6.4 The Apparent Surface Energy Barrier of Polymer
Flowing Through Different Surface Properties of
Silica Filler Particles ...........................283

8.1 DSC Spectrum of 20% Volume Stober Silica and 5%
Volume Cab-O-Sil Silica filled E-Va Copolymer.....308

8.2 DSC Spectrum of Unfilled and 20% Volume Stober
Silica Filled E-Va Copolymer......................309

8.3 DSC Spectrum of Unfilled and 5% Volume Cab-O-Sil
Silica Filled E-Va Copolymer......................310


xviii











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



QUANTITATIVE STUDIES OF THE EFFECTS
OF INTERFACIAL BONDING STRENGTH ON THE
MECHANICAL AND RHEOLOGICAL PROPERTIES OF POLYMER COMPOSITES


BY

SHAYE-WEN SHANG

August 1989


Chairman: Dr. Christopher D. Batich
Major Department: Materials Science and Engineering


The aims of this study are to develop a model polymer

composite system which will allow one to (1) quantify

interfacial bonding, (2) relate the interfacial bonding

strength quantitatively to the mechanical and theological

properties of polymer composites, and (3) interpret the

interfacial bonding at a molecular level.

The interfacial bonding strength is characterized in

terms of work of adhesion (Wa). Models used to evaluate

work of adhesion for strong and weak interfacial bonding

are proposed. The magnitude of the work of adhesion can be

controlled by modifying the surface properties of silica

filler particles.


xix






The value of Wa is increased with increasing

interfacial bonding strength. The calculated Wa ranges
-2 esl
from 63 to 301 erg cm2. The Young's modulus, tensile

strength, shear modulus and melt viscosity of composites

are directly proportional to the work of adhesion. The

relationship is exponential. Since hydrogen and/or polar

component of work of adhesion (Wah) varies significantly

when silica surface is modified, Wah is the main component

in determining the performance of polymer composites.

The effects of interfacial bonding on the mechanical

and theological properties of composites are studied at

different testing rates, temperatures, volume fractions of

filler, and particle sizes. At a constant temperature, Wa

has a greater effect on the melt viscosity of a filled

polymer measured at a low frequency. Wa has little effect,

however, on the change of melt viscosity with temperature

at a low volume fraction of silica filled polymers.

The effective particle size of filler is increased with

increasing work of adhesion. The thickness of the

interphase layer around filler surface has a great effect

on the performance of polymer composites. The idea of

friction factors is proposed, from a molecular level, to

interpret the importance of this interphase layer to

control the properties of composites. The skin friction

plays an important role from the flow process viewpoint.


xx











CHAPTER 1
INTRODUCTION

1.1. General

Most studies dealing with the effect of the interfacial

bonding on the mechanical and theological properties of

polymer composites have been qualitative rather than

quantitative (1-31). The effects of the interfacial

bonding are described as leading to either good adhesion or

poor adhesion. From the qualitative studies, it has been

concluded that the mechanical and physical properties of

particulate filled polymer composites can be improved by

optimizing the interfacial bonding between the filler

particles and polymer matrix (1-10). However, very few

quantitative studies relate the mechanical and theological

properties of polymer composites to the interfacial bonding

(15,16,30,31).

One of the reasons for this is that there is no

generally accepted method to evaluate the strength of

interfacial bonding. Therefore, it is important to develop

a quantitative and measurable technique to evaluate the

quality of the interface and relate this interface to the

composite properties. The effect of interfacial bonding on

the composite properties can then be systematically studied.








In general, the interactions at the filler-matrix

interface can be classified into three types: (a)

interactions due to intermolecular forces between the two

phases, (b) chemical bonding, and (c) physical bonding or

mechanical interlocking (17).

The interaction due to intermolecular forces between the

filler surface and polymer matrix is a simple case of

intermolecular interaction. These forces include dispersion

forces (Van der Waals), hydrogen bonding, dipole-dipole, and

dipole-induced dipole forces. Hydrogen bonding and/or polar

forces can be evaluated by using an acid-base concept

(18,19,20). A useful approach has been developed by Fowkes

et al. (18,21-25), based on acid-base concepts proposed by

Drago et al. (26,27).

The degree of intermolecular interaction can be

determined by controlling the surface properties of filler

particles through either heat or chemical treatment. The

polymer composites are prepared from these well-designed

filler surfaces. The mechanical and theological properties

of these polymer composites are then examined and correlated

with the strength of the interfacial interaction.

1.2. Outline of This Study

The specific objectives of this study are to develop a

model system which will allow one to (a) quantify

interfacial bonding, (b) relate interfacial bonding to the







mechanical and theological properties of filled polymers,

and (c) interpret interfacial bonding at a molecular level.

The materials used in the model study are silica filler

particles and ethylene-vinyl acetate (E-Va) copolymer.

This study focuses on the intermolecular interaction

between two phases in which a thermodynamic approach is used

to characterize the interfacial bonding. The strength of

the interfacial bonding is expressed in terms of the work of

adhesion (Wa).

Work of adhesion is defined as the change in free energy

when two surfaces are brought into contact. It has the same

numerical value but opposite sign as the amount of work

reversibly expended under equilibrium conditions to disrupt

the interface. In this study, the work of adhesion is

partitioned into two contributors (28,29). One contributor

comes from hydrogen bonding and/or polar forces. The other

comes from dispersion forces. The magnitude of work of

adhesion can be varied by modifying the surface properties

of the silica filler particles.

The surface silanol concentrations on the spherical

silica particles can be changed by heat and/or chemical

treatments. These silanol groups can form hydrogen bonds

with the carbonyl groups in the polymer molecular chain.

The hydrogen and/or polar contribution of work of adhesion

varies significantly with the concentration of surface








silanol groups. However, the dispersion component of work

of adhesion shows little change with these treatments.

The work of adhesion between the silica filler surface

and the E-Va copolymer matrix is examined by combinations of

measurement techniques: Fourier Transform Infrared

Spectroscopy (FTIR), contact angle measurements and

titration with indicator dyes.

The mechanical properties of silica filled composites

are examined by an Instron tensile tester at room

temperature. The theological properties of silica filled

polymer melts are measured by a Rheometrics Dynamic

Spectrometer.

When the values of the work of adhesion, and the

mechanical and theological properties of silica filled

polymer composites are available, the quantitative studies

of the relationship between the mechanical and theological

properties of polymer composites and the strength of the

interfacial bonding is then possible.

Since the hydrogen and/or polar contribution of the work

of adhesion is the dominant variation in this study, it

mainly determines the mechanical and physical properties of

the investigated polymer composites.

The study shows that an exponential relationship exists

between the work of adhesion and the mechanical and

theological properties of the composites (30,31). A

mathematical model is proposed to account for the effects of





5
interfacial interactions on the observed properties of

composites.

The effects of the interfacial bonding on the mechanical

and theological properties of composites are dependent on

the materials characteristics and environmental test

conditions (16,31). For example, the work of adhesion has a

greater effect on theological properties at lower testing

rates (31). Volume fraction of filler and filler surface

area (m /g) are examples of materials characteristics of the

polymer composites. Temperature and testing rate such as

strain rate or frequency used to test the mechanical and

theological properties of materials are examples of

environmental test conditions.

The molecular model of the microstructure around the

filler particle gives insight into the nature of the

interfacial bonding, and explains the effect of the bonding

on the mechanical and theological properties. The polymer

around a particle is hydrogen bonds or physical entanglement

by other polymers. These polymer molecules establish an

interphase layer. The extent of polymer interaction with

the silica surface is evaluated by FTIR spectroscopy. The

thickness of the interphase layer is dependent on the work

of adhesion. The effective particle size is thus increased

with an increase in work of adhesion. The friction factor

(32,33) in the flow process is higher when the interphase

layer is thicker.






6

In summary, a model is proposed to evaluate the

interfacial bonding strength between filler particles and

the polymer matrix in terms of the work of adhesion.

Quantitative studies of the effect of interfacial bonding

strength on the mechanical and theological properties of

polymer composites are obtained. The observed mechanical

and theological phenomena are interpreted from the molecular

level in terms of the effective particle size.











CHAPTER 2
BACKGROUND

2.1 Effect of Filler Particles in a Polymer Matrix

The incorporation of filler particles in a polymer

matrix can be used to improve the properties of the matrix

(34). These improvements include (a) increased modulus of

elasticity, (b) reduced coefficient of thermal expansion,

(c) improved heat resistance, (d) higher creep resistance,

(e) lower permeability behavior of gases and liquids, (f)

increased mechanical strength, (g) improved theological

properties, (h) improved electrical properties, (i)

increased flame retardancy, (j) improved wear resistance,

(k) modified damping properties, (1) lower curing

shrinkage, and (m) lower material cost.

Most of the properties discussed above are strongly

dependent upon the interfacial bonding strength. It is

therefore important to study the interface of the filler-

matrix system (35-49) and its effect on the properties of

filled polymer materials.

2.2 Interfacial Bonding

The interaction between a filler and polymer matrix can

be basically classified into three types: (a) chemical

bonding, (b) intermolecular forces, and (c) mechanical

interlocking on the filler surface (17).

7









The Interfacial interactions may be primary or

secondary forces (17,42). These interactions can be

optimized by the application of a silane coupling agent to

the reinforcing or filler surface. The silane improves

these interactions by forming chemical bonds to both the

filler surface and the matrix, or by forming

interpenetrating network bonded to the filler surface (11-

13,17,35-41). The primary forces, such as chemical bonds,

are usually stronger. The secondary forces, such as

dispersion, polar and hydrogen bonds, are generally weaker

and are often due to interaction between hydroxyl groups on

the filler surface and polar groups of the matrix. For

mechanical interlocking, polymer wets a rough surface and

flows into the interstices of the substrate, solidifies and

forms a mechanical interlock (17,42-44).

2.2.1 Bonding and Force across an Interface

2.2.1.1 Aided bonding by coupling agents

A coupling agent is defined as a chemical compound

which has two differently reactive functional groups and

can be used to form a link between filler surface and

polymer matrix (11). One end of the coupling agent may

react with the filler surface and the other end with the

matrix material. Silane coupling agents are the most

important coupling agents currently used in the composite

industry.







The structure and utility of the silane coupling agent

strongly depend upon the application method, solvent, pH,

organofunctionality, concentration, drying process and

temperature as well as other variables (13,35-41,45-49).

Besides the chemical bonding at the interface, silane

coupling agents can also polymerize and form a polymer

network on a filler surface (11). This modifies the

interphase region by forming an interpenetrating network,

which strengthens the organic and inorganic boundary

layers. In addition to improving the mechanical and

physical properties of polymer composites, silane coupling

agents can also improve wetting, dispersion, rheology, and

other properties (11).

These coupling agent layers are not just homogeneous

thin films, but may consist of chemisorbed and physisorbed

layers with a structural and compositional gradient (13).

Therefore, characterization of these molecular structures

and their corresponding interactions will help explain the

performance of silane treated particulate filler or glass

fiber filled polymer composites (35-41).

2.2.1.2 Direct intermolecular interactions

The characteristics of interfacial interactions can be

simplified when there are no coupling agent layers at the

interface.

Various intermolecular interactions between simple

molecules have been compared with the average kinetic






10

energy of a vibrating pair of molecules (i.e., kT at 25C)

by Hirschfelder et al. (50), where k is the Boltzmann

constant, and T is the absolute temperature (K). The

value for kT at room temperature is equal to 4.1 10-14

ergs (or 0.6 kcal/mole).

The electronic charge is shown as q, dipole moment as

p, and polarizability as a. The attraction energies can be

compared based on the molecular pairs at r12 = 4 A

separation and expressed in terms of kT at 25"C, where 1

and 2 represent molecule 1 (or phase 1) and molecule 2

(or phase 2).

(A) Charged force in ionic molecules

(a) Point charges, Uqq (e.g., Na" Cl )




Uqq = 2( 2.1 )
r12


= -139 kT


where

q = 4.8 1010 esu

= 1.6 10-19 coulomb



and 1 and 2 represent different ionic molecules in this

case.


(b) Charge-Dipole, Uc (e.g., Na H20)








-q192
2
12


= -13.2 kT


where


12 = 1.84 1018 esu-cm

= 6.1 10-30 coulomb-m



(c) Charge-Induced dipole, Uqa (e.g., Na- H2O)





q,2 2
Uqa =
4
rl2


= 3.2 kT


where


2 = 1.48 10-24 cm3


(B) Polar force in neutral molecules

(d) Dipole-Dipole, U'" (e.g., phenol-phenol)


-2 2 22
UUU = --


3kT


6
r12


= -0.42 kT


( 2.2 )


( 2.3 )


( 2.4 )








(e) Dipole-Induced dipole, U'" (e.g., phenol-benzene)


212
U =2 ( 2.5)
6
r12


= -0.13 kT



(f) Acid-Base interactions (26,51), UAB (including

Hydrogen bonds) (e.g., phenol-benzene)




UAB = ( CACB + EAE ) ( 2.6

= -4.04 kT [ includes U"" and U" ]




(C) Non-polar force in neutral molecules

(g) Dispersion forces, Ud (e.g., benzene-benzene)




-3 a2hv0
Ud = ( 2.7
4 r


= -7.8 kT


where


v = 2.54 1015 sec1

h = 6.62 1027 erg-sec


I


)







The interactions between molecules usually include

several of these interactions at once. The hydrogen and/or

polar interactions in a neutral system which are due to

intermolecular forces between a filler surface and a

polymer matrix can be calculated using an acid-base concept

(18,19,20) or adsorption theory (52,53). The extent of

intermolecular interactions can be determined by the

surface properties of each phase.

Polymer molecules may be bonded and/or adsorbed to the

filler surface after the polymer wets its surface. In the

neutral system, primary forces usually do not occur if

there is no chemical bonding at the interface. Thus,

secondary forces, such as the dispersion force, the dipole-

dipole force, the dipole-induced dipole force, and hydrogen

bonding, may be the main components in the neutral system

which contribute to the intermolecular forces at the

interface (41,54,55).

Hydrogen bonds are formed between proton acceptors and

hydrogen atoms where the latter are attached to highly

electronegative atoms or groups. The energy of hydrogen

bonding depends upon the strength of the hydrogen bonds

(56). In the case of shorter bond length (2.5 A or less),

the covalent character may be as much as 25%. However, for

longer bond length (2.8 A or greater), the covalent

character may be negligible.







It is reported that the bond energy of the primary

forces is more than 25 kcal/mole, while the bond energy of

the secondary force is below 12 kcal/mole (42,57), as shown

in Table 2.1.

TABLE 2.1



BOND TYPES AND TYPICAL BOND ENERGY (Kcal/Mole)41

TYPE BOND ENERGY

Chemical bonds (kcal/mole)

ionic 140-250

covalent 15-170

metallic 27-83

Intermolecular force

hydrogen bonds < 12

dipole-dipole < 5.0

dispersion < 10

dipole-induced dipole < 0.5



The range of magnitude of the dispersion force, in

Table 2.1, is for the interaction of small molecules, or in

the case of extended molecular polymers, the interaction of

segments, e.g., of a -CH2- group in one molecule with a

-CH2- group in a neighboring molecule (41).

It has been reported that the attraction force between

two planar bulk phases due solely to dispersion forces at a

separation of 1 A is approximately 100 MPa (58-60).







Although there is evidence (61-63) that adhesion

arising from the secondary forces alone may provide

adequate interfacial interaction for bond strength in

composite systems, many investigators believe that the

primary bonding will increase the bond strength and is a

requirement for obtaining an interface which is

environmentally stable.

2.2.2 Ways to Characterize Forces at the Interface

2.2.2.1 Work of adhesion and wetting

The process of interfacial interaction involves (a)

wetting and (b) adsorption of polymer on the surface of

filler particles.

Wetting is necessary before a direct intermolecular

interaction between any two phases can occur. A polymer

able to wet the filler surface can increase the

intermolecular contact and therefore improve the polymer

adsorption and bonding. Incomplete wetting will produce

interfacial defects and thereby lower the adhesive bond

strength. The work of adhesion (Wa) was stated by Dupre

(64) as


Wa = L + Ts T7s ( 2.8 )



where Wa is the thermodynamic work of adhesion of a liquid

to a solid, and is expressed as the sum of the surface free

energies of the liquid (r7) and solid (rs) minus that of

the interface (7Ts).






16

Equation ( 2.8 ) has been applied to the spreading of a

liquid on a solid surface. When a drop of liquid is placed

on the surface of a solid, the liquid may spread. If it

does, the surface of the solid disappears, and is replaced

by an equal area of interface and the liquid, provided that

liquid spreads to a film. The change of surface free

energy is defined as the spreading coefficient (65-67),

which is expressed by S,



S = T, ( 7t + 's ) ( 2.9 )



Since a liquid will not spread on a solid surface unless

Ts is greater than 7T + Tst, a positive spreading

coefficient is required for spreading to occur.

As shown in Figure 2.1, when a drop does not spread on

a solid surface, the contact angle of a liquid drop on a

solid surface follows Young's equation, expressed as

follows


Tsv = TsL + Lv cos E ( 2.10 )


sv = s e ( 2.11 )



where ve in equation ( 2.11 ) is the equilibrium film

pressure and reflects the reduction in surface energy of

the solid due to adsorbed vapor. Note that Te is very

small on polymer surfaces and can be normally neglected.




















SATURATED VAPOR


"LV


SOLID rY


rSV


N S 7-e


Figure 2.1


Relationship between Contact Angle and
Silica Surface


re


11









Combining equations ( 2.8 ), ( 2.10 ) and ( 2.11 )

gives the well-known Young-Dupre' equation



Wa = T + Ts Ts

= Tr (1 + COS e ) + Ve ( 2.12 )



This is the equation to express the work of adhesion for a

liquid on a solid surface.

2.2.2.2 Relationship between work of adhesion and force
attraction constant

Summation of various energies across an interface in a

neutral force system gives the total attraction energy,

(U12), expressed as


U +d h -A12
U12 = U12d + U + U12 12 ( 2.13
r



where 1 and 2 represent phase 1 and phase 2. The A12 is

the total attraction constant, and relates to the summation

of forces across an interface discussed in section 2.2.1.2,

and given by



d p* i h
A12 = A12d + 12 + 12 + A12 ( 2.14 )



In equation ( 2.14 ), A12d is the attraction constant

for dispersion interaction (68-70), A12* the attraction





19

constant for dipole interaction (71,72), A121 the attraction

constant for induction (also called dipole-induced dipole)

interaction (73,74), and A12h the attraction constant for

hydrogen bonding (75).

The polar component (p) consists of dipole(p*),

induction (i), and hydrogen bonding (h) interaction.

Since


A12P = A12 + A12i + A12h




equation ( 2.14 ) can be simplified to


A12 = A12d + A12P


( 2.15 )


( 2.16 )


Analogously, the surface free energy and work of

adhesion can be separated into two components, a dispersion

component and a polar component (28,29), where


7- = d + Tp

Wa = Wad + Wap


( 2.17 )

( 2.18 )


2.2.2.3 Work of adhesion and surface energy

Several means of relating the work of adhesion and

surface energy are discussed below.








2.2.2.3.1 Harmonic-mean approach

The Wad can be related to surface energy by



Wad 47 d d 219
Wad = ( 2.19 )
T d + T d




which is called the harmonic-mean approximation, and is

preferred between low-energy materials (76,77).

Similarly, the Wap can also be approached by the

following harmonic-mean approximation (76,77).



47T PT P
WaP = 2 ( 2.20 )
T7 P + T 2P
1 2



which adequately represents the combined polar interactions

(p*, i and h) in most cases and is valid for low-energy

materials.

2.2.2.3.2 Geometric-mean approach

On the other hand, the geometric-mean relation, valid

when the interaction is between a low-energy and a high-

energy material, may be used as follows (76-78),



Wad = 2 ( Td2d )1/2 ( 2.21 )


Using the appropriate approximations for the various

polar attraction constants between a low-energy and a high-

energy material gives









Wap = WaP* + Wa' + Wah

=2 ( 7 P2 )1/2 + ( 71 + ) +
( 7 ha hd + hd 2ha
( T1 '2 + T1 2


( 2.22 )


which is the complete polar component of work of adhesion.

The Tha is the hydrogen-bond acceptor component, and Thd is

the hydrogen-bond donor component.

Several special cases deserve attention here (79):

(a) If the dipole-dipole interaction is predominant, then


Wap = 2 ( 1 *72p )1/2



(b) If the dipole-induced dipole interaction is

predominant, then


Wap = T11+T21


( 2.23 )


( 2.24)


(c) If the hydrogen-bond interaction is predominant, then


WaP = ha hd hd 2ha


( 2.25 )


2.2.2.4 Surface energy

2.2.2.4.1 Surface energy and contact angle

A contact angle can be obtained when a drop of liquid

is on a solid surface. The rd and TP could be calculated








from contact angles according to Owens and Wendt (80).

They proposed a set of simultaneous equations to calculate

Td and r" by measuring the contact angles of two various

liquids against a solid as follows





1+cos e = 2/s d ( ) + 2J/s ( ) ( 2.26 )
rL TL



where 0 is the contact angle, 1 refers to the liquid and s

refers to the solid. The Tsd is the dispersion component

of the surface energy of the solid, and TsP is the polar

component of the surface energy of the solid. The surface

energy of a solid is given by the summation of each

component: Ts = T + P. The 7T and its components refer

to the surface energy of the liquid used to measure the

contact angle on the surface of a solid plate. The surface

free energy of the polymer is dependent on the surface

properties of the polymer. Using X-ray photoelectron

spectroscopy (ESCA), Batich and Wendt (81) studied chemical

labels to distinguish surface functional groups. The

surface chemistry is usually dominated by the number and

types of functional groups present on the surface. When

the surface properties of a polymer are determined, the

surface energy can then be evaluated.







2.2.2.4.2 Surface energy and cohesive energy density

The cohesive energy density (62) has been defined (82)

as

62 = ( AUv a/VL ) ( 2.27 )



where AUvap is the molar internal energy of vaporization,

which means the energy change upon isothermal vaporization

of the saturated liquid to the ideal gas state, and VL is

the molar volume of liquid.

A more useful definition is



62 = ( Hvap RT )/vL ( 2.28 )



where AHVap is the heat of vaporization, R is the gas

constant and T is the absolute temperature.

An equation connecting surface free energy with molar

volume and cohesive energy density was proposed by

Hildebrand and Scott (82,83) as



62 = 2 ( 7/V0.33 )0.86 ( 2.29 )



where F is a temperature dependent constant. This constant

is fairly accurate for non-polar liquids, but when applied

to polar liquids and polymers the limitations of equation

( 2.29 ) are revealed. An extended equation can be used

for polymers, as demonstrated by Wu (84). However, it is








only applied to non-polar polymers since Wu's equation

considers only the dispersion contribution of surface

energy. Wu's equation is stated as



7= 0.327[ ( EF ),/ns 1.85[ n,/V ]1.52 ( 2.30 )



where (EF)s is the summation of the Small force constants

(85) for the segments, ns is the number of atoms and Vs is

the molar volume of the repeat unit.

2.2.2.4.3 Hamilton methods

Hamilton has developed a technique to characterize a

hydrated solid surface (86,87). By measuring the contact

angle of a small n-octane droplet on a solid surface under

water, as shown in Figure 2.2, and assuming that the effect

of gravity is negligible for such a small droplet, the

polar component of the surface free energy can be

determined.

An equation for the work of adhesion at a solid liquid

interface has been developed by Fowkes (88) which assumes

that there is no polar interaction across the interface.

This equation is expressed as



Tst = T + 7Tv 2( T VdTsd )0.5 ( 2.31 )


Although this equation contains a term [ 2( T dTs d )0.5 ],

which accounts for the dispersion forces, there is no term








Sol id


'sw


o
ow


ysw = solid water interfacial free energy

Yso = solid octane interfacial free energy

Yow= octane water interfacial free energy

Figure 2.2 Components of Surface Free Energy for the
Hamilton Technique


Ysw


Ywv


Water


ysw = solid water interfacial free energy

Ywv= water vapour interfacial free energy (ie surface tension of water)

ysy = solid vapour interfacial free energy = ys = solid surface free energy

Figure 2.3 Components of Surface Free Energy for the
Air Bubble Technique





26

to account for the dipole interaction and hydrogen bonding.

A modified form of this expression was developed by Tamai

et al. (89) which accounted for polar forces. This

equation is written as



Tst = s + Tv 2( Tvd d )0.5 ist ( 2.32 )


where

Is = 2( vPTs )0.5 ( 2.33 )



As n-octane has no polar components, and the dispersion

components of n-octane and water (TL7 = 21.8 dyne/cm) are

identical, the combination of Young's equation (Eq. 2.10)

and Tamai's equations (Eq. 2.32 and 2.33) leads to the

determination of the polar component of the surface free

energy of a solid surface.

The relationship between Hamilton's contact angle and

the polar component of surface free energy has been shown

(90-92); it is known that as the contact angle becomes

larger, T s also increases.

2.2.2.4.4. Captive air bubble technique

The captive air bubble technique (93,94) uses air

bubbles resting on a plane solid surface, as shown in

Figure 2.3. This is similar to the Hamilton technique

where liquid drops are used. Combining both the Hamilton

and the captive air bubble technique, it is possible to







obtain values for Ts, T d, sP and rst for the solid-liquid

interface.

2.2.2.5 Work of adhesion and acid-base interaction

Drago and co-workers (26,27) have related enthalpy

changes of acid-base interactions (AHab) in neutral

solvents to the acidity and basicity of organic molecules.

Drago (26,27,51) expressed the acid-base interaction AHab

with two constants for each base and acid (EB and C,, and

EA and CA, respectively) as



-AHab = CACB + EAE ( 2.34 )



The two constants, C and E, for both the acid and the

base reflect the idea that the strength of interaction of a

pair of groups depends not only on the donor/acceptor

characteristics, but also on the polarizability, where E is

used to refer to the donor/acceptor characteristics, and C

to the polarizability.

The ratio C/E is a measure of the relative ease of

deforming outer electron orbitals by an electric field.

The greater C/E, the "softer" the acid or base (25). Thus,

the iodine and Bronsted acids behave as soft and hard

acids, respectively, while sulfur and oxygen behave as soft

and hard bases, respectively.

It is believed that maximum interaction occurs between

soft acids and soft bases, or hard acids and hard bases






28

(25). Drago et al. were able to accurately predict values

of AHab for many systems involving hydrogen bonds and

Bronsted and Lewis acids and bases (25). In addition,

Drago et al. found a most interesting result: good

correlations could be made by assuming the existence of

only dispersion and acid-base interactions (the

contribution of dipole-dipole interactions is usually very

small or negligible).

Fowkes (21,22) has suggested that acid-base interaction

across an interface may contribute to intrinsic adhesion

forces. Fowkes (23) further postulated that hydrogen bonds

across an interface can be considered as a subset of acid-

base interactions and that the other polar (dipole-dipole

or dipole-induced dipole) interactions are negligibly small

in liquids and solids and can be ignored.

The dipole-dipole interaction, as measured by dipole

moments, is not a significant factor in intermolecular

interactions in solids and liquids (23). This is due to

the fact that in condensed media, where equal sized

molecules have ten or more nearest neighbors, conflicting

local dipole fields are present which minimize dipole

interactions. Due to the existence of conflicting local

dipole fields, the dipole-induced dipole interaction is

even smaller than dipole-dipole interaction.

Drago has developed a correlation of AHab, the acid-

base interaction energy, with the FTIR spectroscopic shifts





29

of the OH stretching frequency of dilute solution of phenol

when interacting with a variety of bases in carbon

tetrachloride (24,28). This is written as



Hab = [ 3.08 + 0.0103 AVOH ( cm1 ) ] kcal/mole ( 2.35 )



Fowkes studied the carbonyl polar group and found that

the shift in the carbonyl stretching frequency, Ave=o, of

esters correlates very well with the calorimetric acid-base

interaction energy, AHab, of these esters with acids such

as chloroform and iodine (28,95).



Hab = 1.0 Avc= ( cm'1 ) kJ/mole

= 0.236 Avc=o ( cm'1 ) kcal/mole ( 2.36 )



In general, without the involvement of the primary

forces at an interface, the interactions of two phases

involve some combinations of dispersion forces (or London

forces), dipole-dipole forces, and specific interactions

such as proton transfer in acid-base reactions (or hydrogen

bonding). However, hydrogen bonding is the dominant factor

controlling the interfacial adhesion in a condensed system.

2.3 Quantitative Evaluation of Interfacial Bonding Strength
of Polymer Composites

There is no generally accepted method to quantitatively

evaluate each individual type of interfacial bonding

strength.








Chahal and St. Pierre (15,16) have proposed a

technique to evaluate the interfacial bonding strength by

an indirect approach. They described methods of changing

the interfacial interaction energy of silica filler. The

modification of the silica filler surface was accomplished

by treating it with normal alcohols in the vapor phase

(15). They also correlated changes in the interfacial

interaction energy with the extent and nature of the

alcohol coverage. The energy of interfacial interaction

was expressed in terms of heat of adsorption of a model

compound, octamethylcyclotetrasiloxane, on silica surface

(15). The modified silica was then incorporated with

polydimethylsiloxane polymer to study the effect of

interfacial bonding strength on the mechanical properties

of these polymer composites. When studied at a constant

filler concentration, the relaxation modulus of

uncrosslinked composites is an exponential function of the

net heat of adsorption of octamethylcyclotetrasiloxane on

the filler surface.

Schreiber et al. (96,97) first used inverse gas

chromatography (IGC) as a technique for acid-base analysis.

The interactions of a series of acidic, neutral and basic

solvents with polyethylene (PE), polyvinylchloride (PVC)

and plasma treated and untreated calcium carbonate (CaCO3)

were measured.







By measuring the retention volume (V ) between a

particular solvent and polymer or filler, the acid or base

strength of the polymer or the filler can be determined

(96). In order to compare acid and base strengths

directly, Schreiber et al. (96,97) suggested an empirical

comparison of these retention volumes using



S = ( Vg )acid/ ( V )base ( 2.37 )



where n is a normalized acid/base interaction parameter.

(Vg')acid and (V g)base are the retention volumes for the

acidic and basic probes respectively. Higher interaction

gives a higher value of retention volume. The definition

of this dimensionless parameter n is arbitrary and based

solely on experimental convenience. Values of

n < 1 would be acidic and n > 1 would be basic.

Schreiber (96,97) suggested that the difference of

np nf (the subscripts refer to polymer and filler,

respectively) can be used as an index of the interaction

strength between polymer and filler.

Using a thermodynamic approach, Williams and Shang

(30,31) have proposed a set of techniques, based on surface

energy and Fowkes's equation (24,28), to evaluate the

interfacial bonding strength between filler surface and

polymer matrix. The interfacial bonding strength is

characterized in terms of work of adhesion (Wa), which








mainly comes from two components, a dispersion component

(Wad) and a hydrogen bonding and/or polar component (WaP).

The value of work of adhesion can be evaluated by Wa = Wad

+ Wap, as shown in equation ( 2.18 ).

Williams and Shang modified the silica surface by heat

and/or chemical treatments. The surface modified silica

fillers were mixed with a polymer. Two different models

were used to evaluate the work of adhesion for good and

poor interfacial interaction, respectively.

When the quantitative value of interfacial bonding

strength is available, it provide a quantitative tool to

study the effect of adhesion on the mechanical and

theological properties of a filled polymer composite

(15,16,30,31).

2.4 Mechanical Properties of a Particulate Filled
Polymer Composite

The mechanical properties of particulate filled

polymers are dependent on many factors (34,98-102). Some

of the materials characteristics influencing the mechanical

properties are listed as follows: (a) particle size,

(b) particle size distribution, (c) particle shape and its

length-width aspect ratio, (d) volume fraction of filler

particle, (e) elastic moduli of filler particles and

polymer matrix, (f) adhesion bond between the two phases,

(g) dispersion of filler particles in the polymer matrix,

and (h) degree of particle agglomeration.





33
Unfortunately, these factors make the composite system

very complex, and it is difficult to separate and evaluate

individual variables.

However, when uniform spherical silica particles of

narrow size distribution are used as filler particles in

the polymer matrix, the effects of particle shape, size and

size distribution can be excluded in determining the

behavior of particulate filled polymers.

In many practical applications, the individual filler

particles are not separated from one another and wetted

individually by the matrix phase, especially the very fine

filler particles. Instead, the filler particles are often

agglomerates made up of many small particles. Thus, the

individual effect of either interfacial adhesion,

dispersion or particle agglomeration on the performance of

the composite is not clearly known. This is due to the

fact that there is no technology or instrument available

currently which allows proper separation and evaluation of

the individual variables in most experimental works (102-

104). Nevertheless, the dispersion and particle

agglomeration are more or less dependent on the interfacial

bonding (102-104).

For a given polymer matrix, the surface properties of

filler particles are the most important variables to affect

the interfacial bonding, dispersion and particle

agglomeration. Thus, surface modification of filler





34

particles by either heat or chemical treatment becomes very

important in the field of polymer composites.

2.4.1 Effect of Properties of Interface/Interphase on a
Polymer Composite

Coupling agents such as silanes or titanates have long

been used to modify the interfacial bonding and improve the

mechanical properties of composites (11,36). Attention

has also been given to the use of a polymeric interlayer

between a reinforcing fiber or a filler particle and matrix

to improve these properties (105-110).

For example, it has been claimed that a relatively soft

interlayer provides a useful balance between stiffness and

toughness in composite systems (105-108). A controlled

crystalline morphology at the interface may also improve

composite properties (109,110). The degree of dispersion

of filler particles in the polymer matrix can be related to

the acid-base interaction of the polymer-filler pair. This

dispersion may vary widely with the surface treatments

given to the filler (96). The mechanical properties at

large deformations of the filled polymers, and their

durability under different conditions, may also depend on

the acid-base interaction (14,96).

With well bonded high modulus inclusions in the polymer

matrix, the modulus, and sometimes the tensile strength and

fracture energy, are increased (102,111). To obtain a

combination of some specific properties, a proper balance







of the modulus of the interphase can be achieved by a

deliberately developed interphase (105-110). When a

composite with this well-controlled interphase is under

large scale deformation, the interfacial bonding strength

and interphase layer can change the balance between

shearing and crazing (102,112).

It is often implied that "good" adhesion is generally

to be desired. This is usually true for tensile strength

and modulus in the filled polymer systems (1,16,30,31).

However, the role of the adhesion on other properties and

systems is more complex. For example, in many composites,

maximum fracture energy, impact strength and fatigue

resistance may actually require poor or moderate adhesion

(1,113-115).

Thermodynamic and kinetic aspects must be considered

for the interfacial bonding. Even though thermodynamics

may favor a particular equilibrium state, and hence a

particular set of properties, the nature of the interphase

will depend on the history of the system, that is, on the

conditions of film formation or solidification from melt

(25,36,116-119). For example, the Tg of silica filled

polystyrene composites was lower than the matrix when first

formed, but became higher on annealing (118). Presumably

the original interphase was not at equilibrium, and was

relatively mobile, while subsequent annealing resulted in

equilibrium with a less mobile conformation.








In another example, the blending of a matrix with a

densely grafted filler which was compatible with the matrix

led to poor strength (120). This was evidently because

crowding at the filler surface inhibited interdiffusion

with the matrix by creating an unfavorable entropy of

mixing.

In general, the required strength of interfacial

bonding in a composite system for a particular application

is dependent the mode of applied stress and the failure

mechanism.

2.4.2 Effect of Volume Fraction and Particle Size on the
Modulus of a Composite

Many models and equations have been derived to describe

the Young's modulus of a filled glassy polymer (100-102,

121-130). In the simplest possible case, two bounds have

been predicted for a composite elastic modulus Ec (102).

These are:

(a) Case of equal strains



Upper bound: Ec = VpEp + VfEf ( 2.38 )



(b) Case of equal stresses



EpEf
Lower bound: Ec = ( 2.39 )
EpVf + EfVp







where Ec, Ep and Ef are moduli of composite, polymer and

filler, respectively. Vp and Vf are the volume fraction of

polymer and filler, respectively.

On the other hand, the Kerner equation (131) is

especially useful in predicting the modulus of the

composite of spherical fillers being randomly dispersed in

a glassy (not elastomeric) matrix. This equation assumes

good adhesion between the phases and is expressed as


Ec Gc

Ep Gp


(GfVf/[( 7-56 )Gp + ( 8-10E )Gf]) + (V/[ 15( 1-E )])

(GpVf/[( 7-5E )Gp + ( 8-10E )Gf]} + (Vp/[ 15( 1-E )]}

( 2.40)

where Ec and Ep are the Young's moduli of the composite and

polymeric matrix, respectively; Gp and Gf are the shear

moduli of the polymer and filler; e is Poisson's ratio of

the polymer; and Vf and Vp are the volume fraction of

filler and polymer, respectively.

Halpin and Tsai (132-134) have shown that the Kerner

equation and many other equations for moduli can be put in

a more general form. Lewis and Nielsen (98,99) showed that

the equation can be generalized to



Mc 1 + ABVf
S( 2.41 )
Mp 1 B0Vf








where Mc is any modulus shear, Young's, or bulk. The

constant A takes into account such factors as geometry of

the filler phase and Poisson's ratio of the matrix. The

constant B takes into account the relative moduli of filler

and matrix phases; its value is 1.0 for very large Mf/Mp

ratios. The quantity B is defined as



M,/M 1
B = 2.42)
Mf/Mp + A



The factor p depends upon the maximum packing fraction $m

of the filler. Two empirical functions which fulfill the

necessary boundary conditions are




1 = 1+ [ ( 1 $m )/m,2 ]Vf ( 2.43 )


1 V
0Vf = 1 exp ( 2.44 )
1 ( Vf/m )




The quantity 0Vf can be visualized as a reduced volume

fraction. For ,m = 1, 0 = 1. The reduced concentration

0Vf is a function of the concentration vf.

The constant A is related to the generalized Einstein

coefficient KE by






39

( 2.45 )


A = KE 1


Einstein (125,126) pointed out that KE = 2.5 for a

suspension of rigid spheres in a liquid with a Poisson's

ratio of 0.5 when the type of deformation is shear. In

general, for the case of the shear modulus with spherical

fillers, the value of A for any Poisson's ratio of the

matrix is


7 5 E

8 10 c


( 2.46 )


For composites filled with particles of nearly

spherical shape, the shear modulus, according to the

modified Kerner's equation is given by


Gc 1 + ABVf

Gp 1 BBVf


( 2.47 )


where A can be evaluated by equation ( 2.46 ), and B by the

modification of equation ( 2.42 ). Thus, B becomes


Gf/GP 1

Gf/Gp + A


( 2.48 )


Most of these models or equations consider glassy

continuous thermoplastic materials, and that Young's








modulus of filled polymers should not depend on the

particle size, but only on the volume fraction of filler.

However, as appears from experiments, the Young's modulus

of a filled polymer is dependent on both volume fraction

and filler particle size (121). Vollenberg et al. showed

that the Young's modulus of bead filled polymer composites

tended to be higher when particle size, in the same micro

order, of the filler was increased (121).

Sumita et al. (122) studied spherical fine silica

particles of various diameters (70, 160 and 400 A and 35

gm) mixed with low density polyethylene (LDPE). The

oriented silica filled composites were made by neck

drawing. The Young's moduli of these oriented composites,

filled with relatively small particles (70, 160 and 400 A),

increased when the filler content was increased or when the

particle size was decreased; whereas the modulus of

composites with the 35 pm silica particle decreased with an

increase in filler content. These results showed that

extremely small particles comparable to the spherulite size

of the LDPE in the crystalline region exerted considerable

reinforcing effect on the oriented polymer matrix (122).

However, Kerner's and related equations are not

suitable for quantitative predictions of moduli of

particulate filled rubbery composites. Eiler's equation

has frequently been used to describe the behavior of filled

elastomeric systems (135). This equation is stated as





41

G,/Gp = [ 1 + 1.25Vf/( 1 V,/m )]2 ( 2.49 )



where Gc/Gp is the relative modulus of the composite to

polymer, and Vf and Pm are the volume fraction of filler

and maximum packing fraction, respectively (136).

The increase in modulus of a filled rubbery polymer may

also be expressed in terms of the Mooney (137) or Guth-

Smallwood (123,124) equations. For example, with glass

bead filled epoxy resins, Lewis and Nielsen (99) found

agreement between predicted and observed values of modulus

in the rubbery region by using the Mooney (137) equation,




ln ( Gc/Gp ) = KEVf/[ 1 ( Vf/'m )] ( 2.50 )




where KE is the Einstein coefficient, which is equal to 2.5

for dispersed spheres. Guth (123) and Smallwood (124)

developed a widely employed modulus equation expressing the

shear modulus of the filled rubber directly in terms of

filler concentration. The equation is based on the famous

viscosity equation of Einstein (125,126). The Guth-

Smallwood equation is given as


Gc = Gp ( 1 + 2.5Vf + 14.1 Vf2 )


( 2.51 )








Generally speaking, the Guth-Smallwood equation

correctly predicts the relatively modest increase in

modulus developed by the addition of inactive or

non-reinforcement fillers whose size is in micro or

submicro order, but this equation has been found relatively

unsatisfactory for highly reinforced systems where large

positive deviations occur (102).

2.4.3 Effect of Volume Fraction and Particle Size on the
Tensile Strength of a Composite

Rigid particulate fillers always increase the modulus

of a polymer matrix, but these fillers generally cause a

dramatic decrease in elongation to break. Fillers also

often decrease the tensile strength of a material; however,

there are numerous exceptions to this tendency, especially

with respect to fine filler particles such as carbon black

in rubber (127).

The decrease in elongation to break in a rigid

particulate filled composites comes from the fact that the

actual elongation experienced by the polymer matrix is much

greater than the measured elongation of the composite

specimen. Since the specimen consists partly of filler and

partly of matrix, most of the elongation comes from the

polymer if the filler is much more rigid than the matrix.

When the adhesion at the interface is perfect, and the

fracture path tends to go from particle to particle rather







than giving a perfectly smooth fracture surface, this can

be expressed by Nielsen's equation (99) as follows



Ec ( 1 Vf/3 ) ( 2.52 )



where Ec and Ep are the elongations to break of the

composite and unfilled polymer, respectively.

When the interfacial bonding is poor, the filler does

not adhere to the matrix, and the filler particles cannot

carry any of load. In addition to the effective porosity

thus introduced by poor adhesion under tensile strength,

stress concentrations around the particles will also reduce

the strength. Nielsen (99) proposed that the tensile

strength (a) should be given approximately by an equation

of the following general form



ac/op ( 1 K'Vf2/ ) S' ( 2.53 )



In Nielsen's treatment, the constant K' is equal to

unity, and the value of S', which symbolizes the stress

concentration factor, is assumed to be about 0.5 for

typical cases.

When the primary filler particle sizes are small

enough, in the range of several hundred angstroms, it is

well known that these small filler particles have more

pronounced reinforcing properties (127). A filled polymer






44

has higher tensile strength than an unfilled polymer if the

size of filler is small enough to reinforce the composite

system, while the opposite is true if the filler particle

size is large. The reason for this is not completely

clear. The increase in interfacial area per unit volume of

filler as particle size decreases is an important factor.

A second factor which may also be important is the stress

field near a particle, which by itself is independent of

the size of filler particle (101). However, the volume of

polymer around a filler which is involved in the dewetting

processes increases with increasing particle size, and

therefore, the probability of finding a large flaw within

this volume also increases. The tensile strength will be

reduced if a large flaw exists within an area of stress

concentration (101).

Landon et al. (128) proposed a linear relationship

between the mean particle diameter and the tensile strength

of a composite with a negative slope at a given volume

fraction. The strength of a particulate filled polymeric

composite can be expressed by



oc = ap-( 1 Vf ) k(Vf) d ( 2.54 )



where d is the average particle diameter and k(Vf) is the

slope of the plot of tensile strength against mean particle

diameter at the particular volume fraction in question.







Alter (129) showed a linear relationship between

modulus as well as tensile strength and the reciprocal of

particle diameter. This linear function expressed a

dependence of modulus as well as tensile strength on the

surface-to-volume ratio of the filler.

Leidner et al. (130) proposed a relationship from a

mechanics viewpoint which related the ultimate strength of

a composite to the filler size, volume fraction, and

surface adhesion of a dispersed phase, respectively. With

this relationship, it was shown that the ultimate strength

of a composite, filled with spherical particles, was a

linear function of volume fraction of filler. That is,



ac/op = k1Vf + c ( 2.55)



where kI and cI are constants.

In the case of a fixed volume fraction of filler, the

ultimate strength is inversely proportional to the square

root of the sphere diameter, so that



/p = k2d1/2 + c2 ( 2.56 )



where k2 and c2 are constants.

In general, the tensile strength of polymer composites

filled with large filler particles usually decreases with

an increase in volume fraction of filler (130,138-142).








2.4.4 Effect of Temperature and Testing Rate on the
Mechanical Properties of a composite

Nicolais and Narkis (143,144) studied the stress-strain

curves of different concentrations of glass bead filled

polymers measured at a constant strain rate above and below

the glass transition temperature.

The influence of the filler concentrations on the yield

stress is different in the brittle and rubbery states

(143,144). When the polymer is in the rubbery state, the

yield stress increases with an increase in filler

concentration (144). On the other hand, Nicolais and

Narkis have determined that the yield stress is the first

point at which the tangent of the force-deformation curve

becomes zero when the polymer is in the glassy state.

Thus, the yield stress of a composite decreases with an

increase in glass bead concentrations when the filled

polymer is in the glassy state (143). Meanwhile, from the

stress-strain curves of the glassy state, one can expect

that the stresses at the break point of the polymers are

not far from the corresponding yield stress.

When the polymer was in the glassy state, the yield

stress was linearly increased with the logarithm value of

the strain rate at a given temperature and filler

concentration (143). The same linear dependence held even

when studied at a wide range of different temperatures. A

double shifting procedure to account for the temperature






and the filler effect on the yield stress (ayc) as a

function of strain rate was obtained (143). A single

master curve that can be represented by the equation



Cyc
= A + B ln( Ea ) ( 2.57 )
1 1.21 V/3



relates composite yield stress to strain rate (e), filler

volume fraction (Vf), and temperature (T). Nicolais and

Narkis (143) found that the shifting factor, aT, is

practically independent of the filler concentration.

Moehlenpah et al. (145) pointed out that polymer

changed from a brittle-to-ductile-to-rubbery failure mode

with the transition temperature. The glass transition

temperature is a function of strain rate, filler content,

filler type, and filler surface properties.

Their results show that initial tangent moduli and

stress relaxation of epoxy composites can be correlated by

a time-temperature superposition principle. The time-

temperature shift factors for initial tangent moduli and

for stress relaxation are identical and are independent of

mode of loading and type of filler. Thus, for their system

the shift factors are properties of the matrix (145).

The yield stress of their epoxy composites can also be

correlated by the time-temperature superposition principle

to obtain master plots of yield stress versus logarithm of








shifted strain rate. The time-temperature shift factors

are not affected by the mode of loading, the filler

content, or the type of orientation, even though the actual

values of yield stress, yield strain and transition

temperatures for failure modes are affected by these

variables. Thus the composite shift factors are a property

of the matrix and not dependent on the state of stress

(145).

Furthermore, the Young's modulus of a composite

increases with a decrease in temperature and with an

increase in strain rate (144). The tensile strength of an

amorphous rubber was found to increase with both increasing

strain rate and decreasing temperature (146,147).

2.5 Rheological Properties of Particulate Filled
Polymer Melts

The theological properties of a composite can be

studied with the polymer in the melt phase by subjecting

the samples primarily to shear deformation. The mechanical

properties are usually evaluated at room temperature, with

the polymer in the solid phase undergoing extensional

deformations.

The loss modulus describes the viscous component of

viscoelasticity; i.e., how easily the polymeric molecules

can move over each other. The storage modulus shows the

elastic or network entanglement structure of a polymer, and

it is sensitive to the extent of physical and chemical





49

crosslinking. The dynamic viscosity includes the combined

effect of both moduli, which are related to the overall

dynamic response of a polymer.

The theological behaviors of a filled polymer are very

sensitive to environmental conditions. These conditions

include the testing temperature and testing rate such as

shear rate in the steady mode or frequency in the dynamic

mode, and materials characteristics such as solid loading

and particle size of filler as well as adhesion at the

interface (148-150).

2.5.1 Effect of Volume Fraction, Particle Size and
Size Distribution of Filler on Polymer Melts

Generally speaking, the melt viscosity of a filled

polymer is increased with the increasing volume fraction of

filler (148-153). Einstein showed the viscosity of a

suspension of rigid spherical particles as (126)



n = n, ( 1 + kEVf ) ( 2.58 )



The viscosity of a suspension (n) is related to the

viscosity of the suspending liquid (nL), the Einstein

coefficient (kE), and the volume fraction of the filler

(Vf). The kE is 2.5 for rigid spheres if there is no

slippage of the liquid at the surface of the sphere. In

composite materials, the subscripts 1 and f refer to the

matrix or continuous phase and filler or dispersed phase,








respectively. Einstein's equation only holds for rigid

particles in very dilute concentrations.

An equation that describes the viscosity of many kinds

of suspensions over the entire concentration range is the

Mooney equation (137)




kEV,
In ( n/n1 ) = ( 2.59 )
1 Vf/m



where m, is the maximum volume fraction that the filler can

have because of packing difficulties from the particle-

particle contacts. Im is the actual volume of the sphere

divided by the volume that the sphere appears to occupy.

It is the same form as equation ( 2.50 ), which is related

to the modulus of a filled polymer in the rubbery state.

A second equation which fits many experimental data on

viscosity of all kinds of suspensions is (154)



n/n, = ( 1 Vf/m )-2.5 ( 2.60 )



Chong et al. (155) showed that if the relative

viscosity (n/nL) of a monodispersed as well as a

bidispersed system is plotted as a function of the reduced

solid volume (defined as Vf/4m), all the data obtained fall

on a single curve. This curve can be represented as







n E Vf/Qm
S- = [ 1 + 0.75 ( -) ]2 ( 2.61 )
nl EL 1 Vf/Qm



Furthermore, the effect of particle size on the melt

viscosity is studied over a wide range of particle

diameters (153,155). As the particle size is decreased,

both the magnitude of the melt viscosity and the degree of

shear thinning increase. Shear thinning is exhibited by

those materials whose structure breaks down with increasing

shear rate. The shear thinning of particle filled polymer

is due to breaking agglomerates of filler particles, since

these small particles easily agglomerate. The melt

viscosity is then decreased by breaking the agglomeration

with an increase in shear rate.

The rheology of vinyl plastisol is known to be affected

significantly by the particle size and size distribution of

polyvinyl chloride (PVC) resin particles (156). A broad

size distribution leads to elimination of the shear

instability and a decrease in the shear thickening

dilatantt) observed at high shear rates. The shear

thickening in a polymer system is due to the fact that the

melt viscosity increases with increasing shear rate.

Addition of coarse particles to a suspension is also shown

to result in a reduction in the viscosity at low shear

rate. It has been suggested that this is achieved mainly

by the alternation of voids between the particles (156).








2.5.2 Effect of Testing Rate and Temperature

The effect of filler on the resin viscosity has been

studied at different shear rates or frequencies, and has

shown that a decrease in relative viscosity occurs with

increasing testing rate (148,149,157-159).

The Cross equation often holds for a non-Newtonian

suspension if the apparent viscosity, na, decreases as the

rate of shear, (r), increases (160). This equation is



na = n, + ( no n, )/( 1 + BTm ) ( 2.62 )



The constant B and m depend upon the system, where B is

related to the rate constant for the formation and rupture

of linkages between primary particles. The exponent m

shows dependence on polydispersity and has an upper limit

of unity for a monodisperse system. The value of m is

usually located between 1/2 and 2/3. The viscosity at zero

shear rate is no, while n, is the viscosity at very high

shear rate. For non-Newtonian behavior, the viscosity

decreases with shear rate until some lower limit is

reached. It is generally assumed that the shear rate

dependency is due to some structural change in the

suspension, such as the breaking up of agglomerates by the

shear forces.

Fine filler particles usually form a weak structure in

the polymer matrix, and therefore this structure remains








intact at very low frequencies or shear rates (157).

However, at higher shear rates or frequencies, shearing

causes segregation of the fillers and sometimes also

degrades the polymer, which results in a decrease in the

viscosity of the filled melt (159).

The effect of temperature on the melt viscosity has

been studied (148,150,152,161-164). Melt viscosity

decreases with increasing temperature. Generally speaking,

polymer melts at temperatures within 1000C of the glass

transition temperature follow the WLF equation (162).

However, for polymers at temperatures far above the glass

transition temperature or melting temperature, an Arrhenius

type equation, proposed by Eyring (163), is the most

commonly used equation to predict the temperature

dependence of melt viscosity. This equation is written as

(150,164)

E
( )
RT
n = C-exp ( 2.63 )


where

n = viscosity of polymer

C = a constant characteristic of polymer at a
given frequency or shear rate

R = gas constant

T = temperature in degree Kelvin (oK)

E = the slope of log n vs. 1/RT, it is the
activation energy for the flow process







54

Quantitative estimations of matrix-filler interactions

in a filled polymer have been attempted through dynamic

viscoelastic melt studies (165). The existence of a

correlation between the interaction parameter in the melt

state and that in the solid state at the comparable

frequency of deformation has been shown by Shenoy and Saini

(165) so that the matrix-filler affinity at any temperature

of interest can be estimated. A linear reciprocal

temperature dependence of matrix-filler affinity was

observed (165).

2.6 Dispersion of Filler Particles in Polymer Matrices

The mechanical and theological properties of polymer

composites depend not only on the interfacial bonding, but

also on the dispersion of filler particles in the polymer

matrix. However, as discussed in section 2.4, the ability

to disperse the silica filler particles in the polymer

matrix is also affected by the interfacial characteristics

of polymer and filler particles (34).

Dispersion is usually achieved through a combination of

three mechanisms: (a) initial wetting, (b) size reduction

and (c) intimate wetting. Without correctly controlling

the interfacial bonding and the mixing process of polymer

and filler particles, an optimum dispersion of filler

particles in the polymer matrix cannot be achieved

(8,103,139,140,148-151).








Dispersion of particulate filler particles in polymer

matrices is dependent on several factors: (a) filler

particle size, (b) interfacial bonding, and (c) mixing

processing, including mixing temperature and mixing torque

force.

Particle sizes less than 1 Am in diameter exhibit a

very strong tendency toward agglomeration and network

formation (12,103,166). Nielsen and Lewis (151) pointed

out that agglomerates reduced the maximum packing fraction,

thereby increasing the viscosity of the composite. Good

dispersion allows higher solid loading to be achieved,

while the mix still maintains reasonably low viscosity.

Bigg showed that the status of the polymer-particle

interface affects the interparticle morphology and state of

dispersion in the high solid loading system (148,149). He

proposed several mechanisms: (a) The polymer may have a

tendency to wet the filler, in which case it merely

surrounds the particle but does not adhere to it. (b) The

polymer may fully wet the filler. Certain polymers form

weak bonds with selected filler. These bonds may be due to

van der Waals, polar or hydrogen bond forces. (c) The

polymer may partially wet the filler particles (or fully

wet a fraction of the particles). This situation occurs

when there is some degree of particle agglomerate and the

polymer cannot penetrate among the adherent particles.

(d) With the use of a coupling agent, the polymer may be









chemically bonded to the filler particles through

bifunctional coupling molecules. Each of these situations

influences the interparticle network and theological

behavior of the system.

Sacks et al. (167,168) studied the effect of mixing

temperature on particulate dispersion in a polymer matrix.

They investigated the steady shear flow curves (ie., shear

stress versus shear rate) of high solid loading polymers

mixed at two different temperatures. Samples prepared at

higher temperatures showed a high yield stress and

extensive hysteresis in the flow curve, which was

indicative of relatively poor dispersion of particles in

the polymer, which in turn resulted in a higher viscosity.

In contrast, the flow curve for samples mixed at lower

temperature showed a low yield stress and very little

hysteresis, indicating that the particulate dispersion was

much improved, which resulted in a lower viscosity (167).

2.7 Friction in a Filled Polymer System

2.7.1 Coefficient of Friction

The frictional behavior of polymers is important in

many practical situations involving abrasion, wear, and

scratching. For example, it is desirable to have high

friction of a tire against a road surface, while low

friction is expected in plastic bearings or for plastic

coated skis against snow. Friction also plays a role in

the first section of extruders where the granulated polymer







must be moved into the section where the polymer becomes

molten.

Friction is a measure of the force resisting the motion

of one surface of a solid against another surface of a

solid. The coefficient of friction, p, between two solid

surfaces is defined by



g = F/W ( 2.64 )



where F denotes the frictional force and W is the load or

force normal to the surface (169,170). In other words, F

is the tangential force required to produce motion at the

interface between two surfaces when they are pressed

together by a normal load W.

Friction (169,170) can be divided into three classes:

(a) static, (b) dynamic, and (c) rolling. These different

classes of friction generally have different values of

coefficient for the friction. The coefficient of friction

depends on many factors such as temperature, velocity of

sliding, load, nature of the surface roughness, surface

adhesion, and presence or absence of lubricants.

Furthermore, when particles are manipulated by

mechanical means, and adhesive and frictional forces act

between the solid particles, it has been observed that

friction appears to increase for small particles. This

apparent increase in friction is explained by considering






58

the results of the contact of loaded, adhesive, and elastic

spheres (171-174).

2.7.1.1 Effect of polar functional groups on the
coefficient of friction

Molecular adhesion is an important factor in

determining the friction between two phases. Studies of

polymer friction and adhesion has been carried out between

bulk or thin films of polymers and the contact of rigid

materials. The effect of chemical structures, such as

polar groups in polymer molecular chains, on the friction

and wear of polymers has been shown to be important (175-

177). Nonpolar polymers tend to have lower coefficients of

friction against metal than polar polymers. It has been

shown, from friction results of various polyimides, that

the higher the coefficient of friction of the polymer, the

higher the density of the polar functional groups in the

polymer molecular chains will be (175-177).

2.7.1.2 Effect of temperature on the coefficient of
friction

The effect of temperature on the friction and wear of

heat-resistant polymers has been studied (178-181). It has

been shown that polyimide carried out a transition from

high friction, high wear to low friction, low wear as the

temperature is increased. Friction of heat resistant

polymers generally varies markedly with the temperature. A

thick transferred polymer layer on a steel sphere is







generally produced at high temperature, decreasing the

friction and wear of the polymer (178).

2.7.2 Friction Factor

The friction factor is the coefficient of friction

between a solid surface and a fluid.

Considering the steady flow of a small molecular fluid

(33,182) with constant density in one of two systems:

(a) the fluid flows in a straight conduit of uniform cross

section; and (b) the fluid flows around a submerged object

which has either an axis or a plane of symmetry parallel to

the direction of the velocity of the approaching fluid.

The fluid will exert a force (F) on the solid surfaces.

This force may be conveniently split into two parts: Fs,

the force which would be exerted by the fluid even if it

was stationary, and Fk, which is the additional force

associated with the kinetic behavior of the fluid. In

systems of type (a), Fk points in the same direction as the

average velocity in the conduit, and in systems of type

(b), Fk points in the same direction as the approach

velocity.

For both systems, the magnitude of the force Fk may be

arbitrarily expressed as the product of a characteristic

area A, a characteristic kinetic energy per unit volume K,

and the dimensionless quantity (f), known as the friction

factor (32,33)






60

Fk = AKf ( 2.65 )



This is not a law of fluid mechanics but just a

definition for f; clearly, for any given flow system f is

not defined until A and K are specified. This is a useful

definition because the dimensionless quantity f can be

given as a relatively simple function of the Reynolds

number (NRe) (183).

For example, considering the laminar flow process of

fluid with low molecular weight in a circular duct, Bird et

al. (33) have shown that the surface friction factor can be

related by



64
f = -( 2.66 )
NRe



where Reynolds number (NRe), can be described as the ratio

of momentum transfer by the turbulence mechanism to

momentum transfer by molecular transport (183). The

Reynolds number can be expressed as



6VD
NRe = ( 2.67 )
n

where

6 = the density of fluid

V = the velocity of fluid far away from the
filler surface







D = the diameter of circular duct

n = the viscosity of fluid


From equations ( 2.66 ) and ( 2.67 ), it is seen that

the friction factor will be in reciprocal proportion to the

velocity of fluid.

2.7.2.1 Types of friction factor in a polymer system

The friction factor in a polymer system is complex.

The entanglements of a polymer melt cause the internal

friction between macromolecular chains (184,185). A filled

polymer melt, in addition to the internal friction, also

involves the friction factor at the contact surface of

filler and polymer melt (32,33).

2.7.2.2 Segmental friction of an unfilled polymer matrix

The viscosity of a fluid represents an internal

friction which resists flow. This internal friction

becomes important in polymers since macromolecules can form

entanglements. It is known from Bueche's theory that the

internal friction of an unfilled polymer melt comes from

segmental friction (fse) (184,185). The interactions of

entanglements of polymer molecules are the source of

internal friction when the polymer melt is under a shear

force. The friction factor (f) of a polymer melt, which is

greatly increased by increasing entanglements, is a measure

of the force required to pull a polymer chain through its

surroundings at unit speed.








2.7.2.3 Surface skin and form friction on particulate
filled polymer melts

Filler particles incorporated with polymer melts make

the system complex. It is known that the links of polymer

molecular chains in a filled polymer consist of three

catalogs: (a) direct linkage with the interparticle

adsorbed polymer chains between different silica particles,

(b) entanglement with the molecular chains adsorbed on the

adjacent filler particles, and (c) the conventional chain

entanglements in the polymer which are not bonded and/or

adsorbed on the silica filler (16).

In addition to segmental friction, the frictions

between the contact surfaces of filler particles and the

polymer melt are involved and must be considered. There

are two kinds of surface friction (32), that is, the skin

friction (fsk) and the form fraction (ffr)

When any surface is in contact with a fluid, and when a

relative motion exists between the fluid and the surface, a

skin friction (fgk) will exist between the surface and the

fluid. Skin friction is thus dependent on the size or

contact surface area of the solid. Skin friction is

associated with a tangential force on a smooth surface that

is oriented parallel to the flow direction (32).

The acceleration or deceleration effects occur when the

fluid changes paths to pass around a solid body in the flow

path. This phenomenon is called form drag, and the





63

coefficient is form friction (ffr). Form friction is

dependent on shape of the solid material. Form friction is

a non-tangential force and depends on the shape of the

immersed material (32). One example of form friction is

evidenced in the existence of a finite velocity at which a

particle settles in a fluid.












CHAPTER 3
MATERIALS AND METHODS

3.1 Materials

3.1.1 Filler

The filler particles used in the experimental composite

materials were either Stober silica (186) or Cab-O-Sil

silica (187).

3.1.1.1 Stober silica

St6ber silica were spherical particles with a narrow

size distribution being prepared from a precipitation method

developed by Stober (186). By standardizing processing

constants such as temperature and reactant ratio, the

particle diameter could be kept below 1 pm with a narrow

particle size distribution (188).

3.1.1.2 Cab-O-Sil silica

In addition to Stober silica, Cab-O-Sil silica

(Cab-O-Sil Division, Cabot Corporation, Tuscola, IL) was

also used (187). Particles of this type were prepared from

a combustion process, by burning silicon tetrachloride vapor

in a flame of hydrogen and oxygen gas to produce the

spherical particles. While still semi-molten, the primary

particles fused irreversibly into aggregates. During

further cooling, these aggregates became physically







entangled to form agglomerates, a process which can be

reversed by proper dispersion in a suitable medium.

Cab-O-Sil fumed silica is available in several grades. The

MS-7 grade of Cab-O-Sil silica with a mean particle size of

140 A and with a surface area of 200+25 m2/g was used in

this study.

3.1.1.3 Quartz plates

Amorphous fumed quartz plates (Quartz Scientific, Inc.,

Fairport Harbor, OH) were used as a model material to

characterize the surface properties of silica. It was

assumed that the surface properties of the plates would be

similar to the surface properties of silica fillers. After

modifying the surface of the quartz plates, the contact

angles of liquid drops on the quartz plates could be

obtained and used to evaluate the surface properties of the

silica powders.

3.1.2 Polymer

Ethylene-vinyl acetate (E-Va, 72% wt.-28% wt.,

Scientific Polymer Products, Inc., Ontario, NY) is a random

copolymer which is in a rubber state at 250C. The structure

of the ethylene-vinyl acetate copolymer is



H H H H

--(--C-C--,--(-----C- ,--
I I I
H H H O-- C CH3

0








where the polar carbonyl group of E-Va copolymer can form

hydrogen bonds with hydroxyl groups on the silica surfaces.

Salyer and Kenyon (189) showed that the crystallinity of

the ethylene-vinyl acetate copolymer gradually decreases

with an increase in vinyl acetate content. The E-Va

copolymer is amorphous due to high weight percentage of

vinyl acetate (189).

According to the information provided by Scientific

Polymer Products, Inc., the E-Va (72% wt.-28% wt.) copolymer

pellets are soluble in benzene, toluene and tetrahydrofuran

(THF). The weight average molecular weight (M.W.) is

approximately 285,000 when determined by gel permeation

chromatography (GPC), using a polystyrene standard for

calibration. Inherent viscosity is 0.82, density is 0.950

g/cm3 and melt index is 20. The melt index is defined as

the mass rate of flow of polymer through a specified

capillary under controlled conditions of temperature and

pressure.

3.1.3 Chemical for Surface Modification

Trimethylchlorosilane (TMCS, Fisher Scientific Co.) was

used to modify the surface of silica. The methyl groups of

TMCS made the surface more hydrophobic. The structure of

TMCS is
( CH3 )3-Si-Cl


Thus, the surface of silica should become hydrophobic when

TMCS was bonded on its surface.








3.2 Techniques

3.2.1 Preparation of Stober Silica

The silica particles were prepared by controlled

hydrolysis and condensation reaction of

tetraethylorthosilicate (TEOS, Fisher Scientific Co.) in a

solution of ethanol and ammonium hydroxide (186,188).

The preparation of a batch (about 40 grams) of Stober

silica, was initiated by stirring 850 ml ammonium hydroxide

with 4500 ml ethanol for 15 minutes at room temperature to

avoid concentration gradients and to promote homogeneous

nucleation. Following this initial step, 250 ml TEOS were

then added to the mixture, yielding the final solution.

Within 2 minutes after the addition of TEOS, amorphous

hydrated silica particles began to precipitate. After the

initial precipitation, stirring was continued for 20 minutes

in order to achieve equilibrium. The silica particles were

then filtered, using a Millipore filtration unit (Millipore,

Inc., Bedfold, MA), washed by deionized water and dried at

700C for 24 hours to remove adsorbed ammonium hydroxide.

The obtained particles were purified by washing in the

deionized water for 10 minutes to remove any supernatant and

then dried again at 700C for 12 hours. The particles were

subsequently cooled to room temperature and transferred into

an air-tight polyethylene bottle which was kept in a vacuum

desiccator.






68

Nearly monodisperse, 0.6 um, spherical silica particles

were obtained according to the procedure described above.

Different particle sizes of St6ber silica have been reported

in the literature. Thus, by controlling the reactant

concentrations, averaging in diameter from 0.02 gm to 2.0 gm

can be produced (186). By using TEOS along with a short

chain alcoholic solvent (ethanol or n-propanol), and by

simply varying the reaction temperature, it is possible to

produce uniform silica spheres of the same size range (188).

3.2.2 Surface Modification on Silica Particle

The surface concentrations of hydroxyl groups on the

fresh silica powders are high but can be modified. Two

kinds of surface treatments of the silica particles were

used: heat and chemical treatments. Both heat and/or

chemical treatments will reduce the surface concentrations

of hydroxyl groups on silica powders.

3.2.2.1 Heat treatment

The surface concentrations of hydroxyl groups can

gradually be reduced when silica particles are treated at

higher temperature. In this study the silica particles were

heat treated at either 1100C, 5000C, or 7500C for 24 hours at

atmospheric pressure. The temperature was kept below 8000C

to prevent sintering. Following this heat treatment the

particles were cooled to room temperature inside the

furnace. The silica particles were reheated at 1100C under

vacuum for 12 hours and then kept at 250C for another 12







hours before being stored in the vacuum desiccator for

further use.

3.2.2.2 Chemical treatment by trimethylchlorosilane (TMCS)

Surface concentrations of hydroxyl groups can also be

reduced when silica surfaces react with TMCS. Silica

particles were completely immersed in a 10% by volume

solution of TMCS in hexane to give a ratio between TMCS and

silica equal to 0.4% mole TMCS per gram of silica (190,191).

This silica suspension was stirred by a magnetic stirrer for

1 hour. The silica particles were then collected and dried

at 250C after the solvent containing TMCS had been removed.

The TMCS-treated silica was then heated at 1100C under

vacuum for 12 hours and kept at 250C for another 12 hours

before being stored in a vacuum desiccator for further use.

3.2.3 Contact Angle Measurement

The surface properties of amorphous fumed quartz plates

are similar to those of silica powders. Amorphous fumed

quartz plates were used as model surfaces to evaluate the

surface characteristics of silica after heat and/or chemical

treatments.

Cerium oxide (CeO2, Fisher Scientific Co.) powders mixed

with water were used to polish the surfaces of the amorphous

quartz plates to get fresh surfaces before any treatment.

Similar processes of surface modification on the silica

particles were also applied to the amorphous fumed quartz

plates. Heat and/or chemical treatments were used. The









chemically hydrophobic treatment was conducted by placing

the plate in a 10% by volume solution of TMCS in hexane for

15 minutes, followed by drying in nitrogen gas after removal

from solution.

The contact angles of distilled water and methylene

iodine (MI, Fisher Scientific Co.) were measured

immediately, after the surface of plate was treated, by

using a goniometer (NRL Model 100, Rame-Hart, Inc., Mountain

Lakes, NJ). Water and MI were chosen because the former is

a polar liquid, while the latter is a non-polar liquid.

The method used for measuring the contact angle in this

study was by a direct observation of the profile of a liquid

drop resting on a plane solid surface in an ambient

environment. The contact angle was obtained by measuring

the angle made between the tangent to the profile at the

point of contact with the solid surface. This was measured

by using a telescope fitted with a goniometer eyepiece. For

each contact angle measurement, a drop of approximately 5 il

was placed on a solid surface by means of a microsyringe.

For such a small drop, the distorting effect of gravity is

negligible (192,193), and the drop takes the shape of a

spherical segment. Contact angles accurate to +1 or 20 were

readily obtained. The uncertainties are higher for small

angles (less than 100) and large angles (large than 1600),

because of the difficulties in locating the point of contact

for constructing a tangent.







3.2.4 Titration by Indicator Dye

The surface concentrations of hydroxyl groups on silica

particles can be evaluated by a titration technique using an

indicator dye. The surface concentrations of hydroxyl

groups are determined from color changes of indicator dye.

For titration measurement, 1.5 gram neutral red (Pfaltz

& Bauer, Inc., Stamford, CT) dissolved in 40 ml benzene

(Fisher Scientific Co.) was used as indicator dye. The 0.1

M n-butylamine (Fisher Scientific Co.) in benzene was used

to titrate the hydroxyl groups on the silica surface.

A technique, originally developed by Johnson (194) and

modified by Benesi (195,196), was used to determine the

surface concentration of hydroxyl groups. The indicator dye

was added to the silica solution after the hydroxyl groups

on the silica surface had been equilibrated with

n-butylamine. The end-point was determined by a series of

successive approximations.

Since the surface area per gram of silica differs

between Stober and Cab-O-Sil silica, amount of these two

types of silica used for titration study is then different.

Approximately 10 grams of the desired heat and/or

chemically-treated Stober silica (or 1 gram of Cab-O-Sil

silica) were prepared. About 0.1 gram of St6ber silica

(or 0.01 gram of Cab-O-Sil silica) was transferred to a

series of bottles and each bottle was heated at 1100C for 12

hours under vacuum and then kept at 250C for another 12








hours. The silica was reweighed to get the exact weight.

The 4 ml (or 6 ml) dry benzene was added to each of the

silica samples immediately after weighing.

The 0.1 M n-butylamine in benzene was then added from a

buret to each weighed silica sample so as to bracket the

expected titer by the approximate number of millimoles of

n-butylamine per gram of silica (195,196). The tightly

capped silica was then equilibrated and rotated overnight at

room temperature. The 0.01 ml prepared neutral red was then

added to each silica sample.

After arranging the test tubes in order of increasing

n-butylamine content, it was easy to determine at which

stage enough n-butylamine had been added to neutralize the

hydroxyl groups on the silica surface. This was easy since

the neutral red was red in the acidic environments and

became yellow in the basic environments.

Using smaller stepwise increases in n-butylamine content

between the established border zone in the previous trial,

the number of hydroxyl groups on the silica surface could be

determined more accurately.

3.2.5 Diffuse Reflectance Infrared Fourier Transform
(DRIFT) Spectrometry

A Nicolet 60SX Fourier Transform Infrared (FTIR)

spectrometer (Nicolet Analytical Instruments, Madison, WI)

purged with dry air and equipped with a wide-band

liquid-nitrogen-cooled mercury-cadmium telluride detector








was used. Diffuse Reflectance Infrared Fourier Transform

(DRIFT) spectra were acquired at a nominal resolution of 4

cm1. A diffuse reflectance accessory (Model DRA-3SO,

Harrick Scientific Corp., Ossining, NY) was used. It

consisted of two 6:1 900 off-axis ellipsoidal mirrors for

focusing the radiation onto the sample and collecting the

diffusely reflected radiation. The four mirrors in the

accessory were aligned for maximum throughout using the

alignment mirror at 30.750 tilt. This mirror was later

replaced by the sample cup containing KBr powder to obtain a

reference spectrum. A hot stage was used and replaced the

sample cup when the sample was studied at different

temperatures in the heating/cooling process.

Blitz et al. (197) have demonstrated that the employing

simple sample preparation step, involving the mixing of

silane-modified Cab-O-Sil silica with KC1 to obtain diffuse

reflectance infrared Fourier transform (DRIFT) spectra, is

superior to using pressed pellets of the sample for

transmission studies. For example, in the case of

transmission FTIR spectrometry, Cab-O-Sil pressed pellets

can react with trimethoxymethylsilane (TMMS) from a toluene

medium. Therefore, such pellets are unsuitable for

quantitative work because the pressure applied to prepare

the pellet could increase the hydrolysis of the methoxy

groups by releasing water from the silica (197).






74

However, silica particle size and size distribution are

also important variables for quantitative study with the

diffuse reflectance technique even after dilution with a

non-absorbing matrix. A detailed study the effect of silica

particle size on the intensity of the strong Si-O stretch

band at 1100 cm1 and other weak bands, such as the Si-O

combination band at 1870 cm-1 or the Si-O stretch band at

810 cm-1, has been published by Benesi and Jones (198). It

has shown that a change in particle size affects the

intensity of some bands differently from other bands (199).

DRIFT spectrometry, therefore, seemed to be the most

suitable technique to quantify the surface properties of

silica (200-205) and its surface modification.

In spite of its popularity, the use of DRIFT to obtain

(a) quantitative data and (b) spectra of a dynamically

changing sample either by heating or by chemical reaction

has not yet received adequate attention (199,204,206).

The investigation of temperature effects on the dynamic

change of interfacial bonding strength from the polymer

adsorption onto the surface of silica particles was also

carried out by DRIFT technique combined with the use of the

hot stage.

3.2.6 Thermogravimetric Analysis (TGA)

Thermogravimetric analysis (207-210) was carried out

with a thermal analyzer (STA409, Netzsch Brothers, Inc.,

Exton, PA) using a PtRh 10% Pt thermocouple. The







measurements were done in air under atmosphere pressure.

The temperature range for studying the weight loss of silica

was from 300C to 10000C, with a heating rate 50 C/min. The

data were collected with a Hewlett-Packard 86B computer

using the standard Netzsch software.

3.2.7 Polymer Adsorption on the Silica Surface

Adsorption of polymer on a solid surface from different

concentrations of polymer solutions was studied (211-215).

Each Cab-O-Sil silica sample of MS-7 grade weighing by

0.30 grams, which was previously heat treated (1100C, 5000C

or 750C) or heat/chemically treated (7500C/TMCS, 5000C/TMCS

or 1100C/TMCS), was used to study polymer adsorption.

Different concentrations of the ethylene-vinyl acetate

copolymer (E-Va) were prepared by dissolving in benzene

solvent for polymer adsorption. Each 0.30 grams Cab-O-Sil

silica adsorbed the E-Va copolymer onto its surface from

0.5%, 2% and 6% volume concentrations (ethylene-vinyl

acetate versus Cab-O-Sil) of 100 ml polymer solution.

After the silica particles in polymer solution were

stirred for one hour, the polymer-absorbed silica particles

were separated from the polymer solution by centrifuge for 5

minutes at 5000 rpm and then dried in air.

The amount of polymer adsorbed from different polymer

solutions was measured by DRIFT technique. The relative

peak intensity carbonyll groups of polymer versus siloxane

groups of silica), measured from the area under the peak of






76

specific groups, was used to evaluate the relative amount of

polymer adsorbed onto the silica surface.

The characteristic properties of the E-Va copolymer were

also studied. The E-Va copolymer was first dissolved in

benzene. One drop of the E-Va polymer solution from pipette

was added on the sample cup of DRIFT filled with non- or

low-infrared-adsorbing powders such as KBr. The carbonyl

groups of the E-Va copolymer were characterized by DRIFT

technique after the solvent had been evaporated.

The effect of heating and/or cooling on a thin layer of

silica-surface-adsorbed polymer was also examined by the

DRIFT techniques. This was done with the hot stage to

investigate the effect of temperature on the interfacial

bonding. The heating rate was 50C/min. The effect of

cooling was studied when the sample was cooled down in the

sample chamber from a high temperature.

3.2.8 Preparation of Polymer Composites

Polymer composites of different volume fractions of

filler (Stober silica and Cab-O-Sil silica, respectively)

with various surface modifications (1100C, 5000C, 7500C,

7500C/TMCS, 5000C/TMCS and 1100C/TMCS, respectively) were

cast from polymer solutions. Forty grams of E-Va copolymer

were completely dissolved in 800 ml benzene at 400C. Silica

filler volume fractions ranging from 5% to 20% (silica vs.

polymer) were then incorporated into the polymer solution.

A magnetic stirrer was applied to disperse the silica filler





77

particles in the polymer solution. In addition, sonication

(Model W-375, Heat Systems-Ultrasonic, Inc., Plainview, NY)

was used for the Cab-O-Sil silica solutions for 15 minutes

at 20KHZ frequency to increase the Cab-O-Sil silica particle

dispersion in the polymer solution. Benzene was chosen as

the solvent because it is non-polar and is a good solvent

for E-Va copolymer. The filler particles were expected to

disperse and stabilize in the polymer solution since the

solvent had induced the polymer chains to expand to their

optimum lengths.

The polymer composite solution was then spread over a

large teflon pan and rapidly evaporated to prevent an

uneven filler precipitation and to avoid the polymer

sticking to the pan when benzene was vaporized. The polymer

composite was then made into a 12cm*12cm composite sheet

with a thickness of 0.65 cm by compression molding,

3.2.9 Mechanical and Rheological Measurements

Tensile specimens were prepared according to ASTM 1822

from the compression-molded sheets. Before the tensile

test, the Stober silica and Cab-O-Sil silica filled E-Va

copolymers were annealed at 1000C and 1300C, respectively,

for Three hours and then conditioned at 250C for 3 days.

The composites were tested at a crosshead speed of 2 in/min

at 250C using an Instron model 1122 (Instron Corporation,

Atlanta, GA). At least six specimens were used for each






78

data point. The Young's modulus and the tensile strength of

silica filled composites were measured.

The theological properties of silica filled E-Va

copolymer were studied by dynamic spectrometer since the

results of the dynamic mode can be directly related to the

structure of the materials. The dynamic viscosity and the

shear modulus (216,217) were measured by a Rheometrics

Dynamic Spectrometer (Model RDS-II, Rheometrics, Inc.,

Piscataway, NJ).

In dynamic measurements of polymer melts, the angular

frequency becomes analogous to the shear rate in the usual

theological measurements (163,164,216,217).

The volume fractions ranged from 5% to 20% for the

Stober silica and 5% volume of Cab-O-Sil silica filled E-Va

were measured by dynamic model with the parallel plates.

Dynamic rate sweeps from frequencies of 0.1 to 100 rad/sec

with 100% strain were used. The theological tests of Stober

filled composites were measured at 1500C with a 0.6 mm gap

between the parallel plates. The Cab-O-Sil silica filled

composites had higher glass transition and softening

temperature than the Stober silica filled composite based on

the same volume fraction of filler particle. This was

related to the high surface area of the Cab-O-Sil silica.

The Cab-O-Sil silica filled composites were therefore

measured at 2100C with a 2.0 mm gap between the parallel

plates.







3.2.10 Scanning Electron Microscopy (SEM) and Scanning
Transmission Electron Microscopy (STEM) Studies

Observation of spherical particles of Stober silica with

a narrow size distribution was accomplished by scanning

electron microscopy (SEM) (Model JSM-35CF, Japan Electron

Optics Co. Ltd., Tokyo, Japan).

The dispersion of filler particles in the polymer matrix

can be studied from the fracture surface of composites. The

fracture surface is prepared at liquid nitrogen temperature

to keep the original positions of silica particles in the

polymer matrix without any disturbance from plastic

deformation in the polymer during sample preparation.

The dispersion of silica particles in the polymer matrix

was studied by SEM and scanning transmission electron

microscopy STEM (Model JSM-200CX, Japan Electron Optics Co.

Ltd., Tokyo, Japan). The samples of silica filled E-Va

copolymer were immersed in liquid nitrogen for 30 minutes,

the silica filled composites were then broken by impact

force with a hammer. The brittle fracture surface of

composite samples was thus obtained. Examination of

dispersion of either Stober or Cab-O-Sil silica particles in

the E-Va matrix was carried out on these brittle fracture

surfaces by SEM. Since the particle size of Cab-O-Sil

silica is very small, the Cab-O-Sil silica filled E-Va

copolymer samples were prepared by a microtome (Model MT-2,

Ultra-Microtome, DuPont Company, Newtown, CT) at liquid




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