Filled Polymers: Science and Industrial Applications Book

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 Floe 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 andCarbon 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

A.6 Models for the Rheology of Suspensions of Rigid Particles, Involving the Maximum Packing Fraction Φ_m 315

A.6 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 σ_c 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

A.7 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

A.7 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

A.7 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 E_y 398

A7.3.4 Shear Modulus G 398

A.7 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

A.7 Shear Lag Model: Numerical illustration 409

Index 411