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小木虫论坛-学术科研互动平台 » 化学化工区 » 高分子 » 成型加工 » 分享——填充的高分子：科学与工业应用（英文版）
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Contents
Preface.......................................................................................................................xi
Author Bio...............................................................................................................xv
1. Introduction....................................................................................................1
1.1. Scope of the Book...................................................................................1
1.2. Filled Polymers vs. Polymer Nanocomposites...................................3
References........................................................................................................8

2. Types of Fillers............................................................................................ 11
3. Concept of Reinforcement......................................................................... 15
Reference........................................................................................................ 19

4. Typical Fillers for Polymers...................................................................... 21
4.1 Carbon Black......................................................................................... 21
4.1.1 Usages of Carbon Blacks.......................................................... 21
4.1.2 Carbon Black Fabrication Processes....................................... 21
4.1.3 Structural Aspects and Characterization
of Carbon Blacks....................................................................... 24
4.1.4 Carbon Black Aggregates as Mass Fractal Objects..............30
4.1.5 Surface Energy Aspects of Carbon Black..............................44
4.2 White Fillers..........................................................................................49
4.2.1 A Few Typical White Fillers....................................................49
4.2.1.1 Silicates.........................................................................49
4.2.1.2 Natural Silica............................................................... 52
4.2.1.3 Synthetic Silica............................................................53
4.2.1.4 Carbonates...................................................................54
4.2.1.5 Miscellaneous Mineral Fillers...................................56
4.2.2. Silica Fabrication Processes.....................................................56
4.2.2.1 Fumed Silica................................................................56
4.2.2.2 Precipitated Silica.......................................................58
4.2.3 Characterization and Structural Aspects of
Synthetic Silica.......................................................................... 62
4.2.4 Surface Energy Aspects of Silica............................................68
4.3 Short Synthetic Fibers..........................................................................69
4.4 Short Fibers of Natural Origin...........................................................72
References......................................................................................................79
Appendix 4....................................................................................................82
A4.1 Carbon Black Data............................................................................82
A4.1.1 Source of Data for Table 4.5...............................................82
A4.1.2 Relationships between Carbon Black
Characterization Data........................................................84
A4.2 Medalia’s Floc Simulation for Carbon Black Aggregate.............85
A4.3 Medalia’s Aggregate Morphology Approach...............................86
A4.4 Carbon Black: Number of Particles/Aggregate............................89

5. Polymers and Carbon Black...................................................................... 91
5.1 Elastomers and Carbon Black (CB).................................................... 91
5.1.1 Generalities................................................................................ 91
5.1.2 Effects of Carbon Black on Rheological Properties.............95
5.1.3 Concept of Bound Rubber (BdR).......................................... 108
5.1.4 Bound Rubber at the Origin of Singular Flow
Properties of Rubber Compounds.......................... ............... 112
5.1.5 Factors Affecting Bound Rubber.......................................... 114
5.1.6 Viscosity and Carbon Black Level........................................ 121
5.1.7 Effect of Carbon Black on Mechanical Properties.............. 125
5.1.8 Effect of Carbon Black on Dynamic Properties.................. 140
5.1.8.1 Variation of Dynamic Moduli with Strain
Amplitude (at Constant Frequency and
Temperature)............................................................. 141
5.1.8.2 Variation of tan δ with Strain Amplitude and
Temperature (at Constant Frequency)...................142
5.1.8.3 Variation of Dynamic Moduli with
Temperature (at Constant Frequency and
Strain Amplitude)..................................................... 142
5.1.8.4 Effect of Carbon Black Type on G′
and tan δ.................................................................... 144
5.1.8.5 Effect of Carbon Black Dispersion on
Dynamic Properties................................................. 146
5.1.9 Origin of Rubber Reinforcement by
Carbon Black............................................................................ 148
5.1.10 Dynamic Stress Softening Effect.......................................... 151
5.1.10.1 Physical Considerations........................................... 151
5.1.10.2 Modeling Dynamic Stress Softening as a
“Filler Network” Effect............................................ 152
5.1.10.3 Modeling Dynamic Stress Softening as a
“Filler–Polymer Network” Effect........................... 168
5.2 Thermoplastics and Carbon Black................................................... 172
5.2.1 Generalities.............................................................................. 172
5.2.2 Effect of Carbon Black on Rheological Properties of
Thermoplastics........................................................................ 173
5.2.3 Effect of Carbon Black on Electrical Conductivity of
Thermoplastics........................................................................ 175
References.................................................................................................... 179
Appendix 5.................................................................................................. 185
A5.1 Network Junction Theory.............................................................. 185
A5.1.1 Developing the Model...................................................... 185
A5.1.2 Typical Calculations with the Network
Junction Model.................................................................. 188
A5.1.3 Strain Amplification Factor from the Network
Junction Theory................................................................. 190
A5.1.3.1 Modeling the Elastic Behavior
of a Rubber Layer between Two
Rigid Spheres................................................... 190
A5.1.3.2 Experimental Results vs.
Calculated Data................................................ 191
A5.1.3.3 Comparing the Theoretical Model with
the Approximate Fitted Equation.... ............ 192
A5.1.3.4 Strain Amplification Factor............................ 193
A5.1.4 Comparing the Network Junction Strain
Amplification Factor with Experimental Data............. 194
A5.2 Kraus Deagglomeration–Reagglomeration Model for
Dynamic Strain Softening............................................................. 196
A5.2.1 Soft Spheres Interactions................................................. 196
A5.2.2 Modeling G′ vs. γ0............................................................. 197
A5.2.3 Modeling G″ vs. γ0............................................................. 198
A5.2.4 Modeling tan δ vs. γ0.........................................................200
A5.2.5 Complex Modulus G* vs. γ0............................................. 202
A5.2.6 A Few Mathematical Aspects of the
Kraus Model......................................................................204
A5.2.7 Fitting Model to Experimental Data..............................206
A5.2.7.1 Modeling G′ vs. Strain.................................... 207
A5.2.7.2 Modeling G″ vs. Strain....................................209
A5.3 Ulmer Modification of the Kraus Model for Dynamic
Strain Softening: Fitting the Model.............................................. 212
A5.3.1 Modeling G′ vs. Strain (same as Kraus)......................... 213
A5.3.2 Modeling G′′ vs. Strain..................................................... 215
A5.4 Aggregates Flocculation/Entanglement Model
(Cluster–Cluster Aggregation Model, Klüppel et al.)............... 218
A5.4.1 Mechanically Effective Solid Fraction
of Aggregate...................................................................... 219
A5.4.2 Modulus as Function of Filler Volume Fraction...........220
A5.4.3 Strain Dependence of Storage Modulus........................ 221
A5.5 Lion et al. Model for Dynamic Strain Softening........................222
A5.5.1 Fractional Linear Solid Model.........................................222
A5.5.2 Modeling the Dynamic Strain Softening Effect...........223
A5.5.3 A Few Mathematical Aspects of the Model..................226
A5.6 Maier and Göritz Model for Dynamic Strain Softening...........227
A5.6.1 Developing the Model......................................................227
A5.6.2 A Few Mathematical Aspects of the Model..................229
A5.6.3 Fitting the Model to Experimental Data........................230
A5.6.3.1 Modeling G′ vs. Strain.................................... 231
A5.6.3.2 Modeling G″ vs. Strain.................................... 232

6. Polymers and White Fillers.....................................................................235
6.1 Elastomers and White Fillers...........................................................235
6.1.1 Elastomers and Silica..............................................................235
6.1.1.1 Generalities................................................................235
6.1.1.2 Surface Chemistry of Silica.....................................236
6.1.1.3 Comparing Carbon Black and (Untreated)
Silica in Diene Elastomers....................................... 237
6.1.1.4 Silanisation of Silica and Reinforcement of
Diene Elastomers...................................................... 239
6.1.1.5 Silica and Polydimethylsiloxane............................. 246
6.1.2 Elastomers and Clays (Kaolins)............................................ 257
6.1.3 Elastomers and Talc................................................................ 260
6.2 Thermoplastics and White Fillers.................................................... 262
6.2.1 Generalities.............................................................................. 262
6.2.2 Typical White Filler Effects and the Concept of
Maximum Volume Fraction.................................................. 266
6.2.3 Thermoplastics and Calcium Carbonates...........................280
6.2.4 Thermoplastics and Talc........................................................ 291
6.2.5 Thermoplastics and Mica...................................................... 297
6.2.6 Thermoplastics and Clay(s)...................................................300
References....................................................................................................302
Appendix 6..................................................................................................308
A6.1 Adsorption Kinetics of Silica on Silicone Polymers...................308
A6.1.1 Effect of Polymer Molecular Weight..............................308
A6.1.2 Effect of Silica Weight Fraction....................................... 310
A6.2 Modeling the Shear Viscosity Function of Filled
Polymer Systems............................................................................. 312
A6.3 Models for the Rheology of Suspensions of Rigid Particles,
Involving the Maximum Packing Fraction Φm........................... 315
A6.4 Assessing the Capabilities of Model for the Shear
Viscosity Function of Filled Polymers......................................... 319
A6.4.1 Effect of Filler Fraction..................................................... 320
A6.4.2 Effect of Characteristic Time λ0...................................... 320
A6.4.3 Effect of Yasuda Exponent a............................................ 321
A6.4.4 Effect of Yield Stress σc................................................... 321
A6.4.5 Fitting Experimental Data for Filled
Polymer Systems.............................................................. 322
A6.4.6 Observations on Experimental Data............................ 323
A6.4.7 Extracting and Arranging Shear
Viscosity Data.................................................................. 324
A6.4.8 Fitting the Virgin Polystyrene Data with the
Carreau–Yasuda Model.................................................. 324
A6.4.9 Fitting the Filled Polystyrene Shear Viscosity
Data................................................................................... 326
A6.4.10 Assembling and Analyzing all Results........................ 332
A6.5 Expanding the Krieger–Dougherty Relationship......................335

7. Polymers and Short Fibers...................................................................... 339
7.1 Generalities......................................................................................... 339
7.2 Micromechanic Models for Short Fibers-Filled Polymer
Composites..........................................................................................344
7.2.1 Minimum Fiber Length.........................................................344
7.2.2 Halpin–Tsai Equations...........................................................345
7.2.3 Mori–Tanaka’s Averaging Hypothesis and Derived
Models...................................................................................... 351
7.2.4 Shear Lag Models....................................................................353
7.3 Thermoplastics and Short Glass Fibers...........................................358
7.4 Typical Rheological Aspect of Short Fiber-Filled
Thermoplastic Melts..........................................................................368
7.5 Thermoplastics and Short Fibers of Natural Origin..................... 370
7.6 Elastomers and Short Fibers............................................................. 375
References....................................................................................................383
Appendix 7.................................................................................................. 389
A7.1 Short Fiber-Reinforced Composites: Minimum Fiber
Aspect Ratio..................................................................................... 389
A7.1.1 Effect of Volume Fraction on Effective
Fiber Length...................................................................... 389
A7.1.2 Effect of Matrix Modulus on Effective
Fiber Length...................................................................... 390
A7.1.3 Effect of Fiber-to-Matrix Modulus Ratio on
Effective Fiber Length/Diameter Ratio......................... 391
A7.2 Halpin–Tsai Equations for Short Fibers Filled Systems:
Numerical Illustration.................................................................... 391
A7.2.1 Longitudinal (Tensile) Modulus E11............................... 392
A7.2.2 Transversal (Tensile) Modulus E22.................................. 393
A7.2.3 Shear Modulus G12............................................................ 393
A7.2.4 Modulus for Random Fiber Orientation........................ 394
A7.2.5 Fiber Orientation as an Adjustable
Parameter. ......................................................................................394
A7.2.6 Average Orientation Parameters from
Halpin–Tsai Equations for Short Fibers
Filled Systems.................................................................... 394
A7.2.6.1 Longitudinal (Tensile) Modulus E11.............. 395
A7.2.6.2 Transversal (Tensile) Modulus E22................. 396
A7.2.6.3 Orientation Parameter X................................. 396
A7.3 Nielsen Modification of Halpin–Tsai Equations with
Respect to the Maximum Packing Fraction: Numerical
Illustration........................................................................................ 396
A7.3.1 Maximum Packing Functions......................................... 397
A7.3.2 Longitudinal (Tensile) Modulus E11............................... 398
A7.3.3 Transverse (Tensile) Modulus Ey.................................... 398
A7.3.4 Shear Modulus G.............................................................. 398
A7.4 Mori–Tanaka’s Average Stress Concept: Tandon–Weng
Expressions for Randomly Distributed Ellipsoidal
(Fiber-Like) Particles: Numerical Illustration............................. 399
A7.4.1 Eshelby’s Tensor (Depending on Matrix Poisson’s
Ratio and Fibers Aspect Ratio Only).............................. 399
A7.4.2 Materials’ Constants (i.e., Not Depending on Fiber
Volume Fraction)...............................................................400
A7.4.3 Materials and Volume Fraction Depending
Constants............................................................................ 401
A7.4.4 Calculating the Longitudinal
(Tensile) Modulus E11........................................................402
A7.4.5 Calculating the Transverse (Tensile) Modulus E22.......402
A7.4.6 Calculating the (In-Plane) Shear Modulus G12.............403
A7.4.7 Calculating the (Out-Plane) Shear Modulus G23...........404
A7.4.8 Comparing with Experimental Data.............................404
A7.4.9 Tandon–Weng Expressions for Randomly
Distributed Spherical Particles:
Numerical illustration...................................................... 406
A7.4.9.1 Eshelby’s Tensor (Depending on Matrix
Poisson’s Ratio Only).......................................406
A7.4.9.2 Materials’ Constants (i.e., Not
Depending on Filler Volume Fraction).........406
A7.4.9.3 Materials and Volume Fraction
Depending Constants.....................................407
A7.4.9.4 Calculating the Tensile Modulus E...............408
A7.4.9.5 Calculating the Shear Modulus G.................408
A7.5 Shear Lag Model: Numerical illustration....................................409
Index........................................................................................................... 411
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