Reinforcement of Polymer Nano-Composites

Half-title......Page 3
Title......Page 5
Copyright......Page 6
Contents......Page 7
Preface......Page 11
Acknowledgement......Page 14
1 Introduction......Page 15
2.1 Gaussian chains – heuristic introduction......Page 24
2.2 Gaussian chains – path integrals......Page 26
2.3 Self-interacting chains......Page 29
3.1 Some general remarks......Page 33
3.2 Collective variables......Page 34
3.3 The statistics of tagged chains......Page 40
4.1 Classical theory of gelation......Page 45
4.2 Percolation......Page 48
4.3 Vulcanization......Page 51
5.1 General remarks......Page 54
5.2 The Gaussian network......Page 56
5.3 Entanglements and the tube model: a material law......Page 59
5.3.1 Entanglement sliding......Page 61
5.3.2 Finite extensibility......Page 63
5.3.3 Tube and sliplinks......Page 66
5.4.1 The stress–strain relationship......Page 67
Basic assumptions......Page 69
Applications for non-ideal networks......Page 71
5.4.3 Testing of the model......Page 73
6.2 D-dimensionally connected polymers in a good solvent......Page 78
6.3 D-dimensionally connected polymers between two parallel plates in a good solvent......Page 80
6.4 D-dimensionally connected polymers in a cylindrical pore (good solvent)......Page 82
6.5 Melts of fractals in restricted geometries......Page 85
6.6 Once more the differences......Page 88
7.1 Fillers for the rubber industry......Page 89
7.2.1 Morphology of carbon black aggregates......Page 91
7.2.2 Surface roughness of carbon blacks......Page 98
7.2.3 Energy distribution of carbon black surfaces......Page 106
7.3 Silica......Page 110
8.1 Reminder: Einstein–Smallwood......Page 115
8.2 Rigid filler aggregates with fractal structure......Page 117
8.2.1 Effective medium theory and linear elasticity......Page 120
8.2.2 Screening lengths......Page 123
8.2.3 Reinforcement by fractal aggregates......Page 124
8.3 Core–shell systems......Page 125
8.3.2 Soft core/hard shell......Page 126
8.3.3 Hard core/soft shell......Page 129
9.1 General remarks and scaling......Page 132
9.1.1 Flat surface......Page 133
9.1.2 Generalization for fractal surfaces......Page 134
9.2.1 Variational calculation......Page 135
9.3 Trial Hamiltonian......Page 136
9.3.1 Minimization of the free energy......Page 137
9.3.2 Effective interaction strength......Page 140
9.4 Some further remarks on the interpretation......Page 144
9.4.1 Modeling by random potentials......Page 145
9.4.2 Annealed and quenched disorder......Page 148
9.4.3 Dynamics of localized chains – freezing, glass transition at filler surfaces......Page 149
9.5.1 Langevin dynamics......Page 151
9.5.2 Self-consistent Hartree approximation......Page 153
9.5.3 Equation of motion......Page 156
9.6.1 Anomalous diffusion......Page 158
9.6.2 Center-of-mass freezing......Page 160
9.6.3 Rouse modes freezing and a two mode toy model......Page 161
9.7 Numerical analysis......Page 162
9.7.1 Bifurcation diagram......Page 163
9.8 Contribution to the modulus......Page 165
10.1.1 Flocculation of fillers during heat treatment......Page 167
10.1.2 Kinetics of filler structures under dynamic excitation......Page 170
10.2.1 The Kraus model......Page 175
10.2.2 The viscoelastic model......Page 178
10.2.3 The van der Walle–Tricot–Gerspacher (WTG) model......Page 183
10.2.4 The links–nodes–blobs (LNB) model......Page 185
10.2.5 The model of the variable network density......Page 186
10.2.6 The cluster–cluster aggregation (CCA) model......Page 188
10.3.1 The dynamic flocculation model......Page 196
10.3.2 The Kantor–Webman model of flexible chain aggregates......Page 207
References......Page 210
Index......Page 218