Reinforcement of Polymer Nano-Composites:

Reinforced rubber allows the production of passenger car tires with improved rolling resistance and wet grip. This book provides in-depth coverage of the physics behind elastomer reinforcement, with a particular focus on the modification of polymer properties using active fillers such as carbon black and silica. The authors build a firm theoretical base through a detailed discussion of the physics of polymer chains and matrices before moving on to describe reinforcing fillers and their applications in the improvement of the mechanical properties of high-performance rubber materials. Reinforcement is explored on all relevant length scales, from molecular to macroscopic, using a variety of methods ranging from statistical physics and computer simulations to experimental techniques. Presenting numerous technological applications of reinforcement in rubber such as tire tread compounds, this book is ideal for academic researchers and professionals working in polymer science.

T.A.Vilgis is Professor of Theoretical Physics at the University of Mainz and a researcher at the Max Planck institute for Polymer Research, lie is a member of several scientific societies including the German Physical Society, EPS, and APS. He has written more than 250 scientific papers, 3 popular science books, and 2 scientific cookbooks. G.Heinrich is Professor of Polymer Materials at Technische Universitt Dresden and is also Director of the institute of Polymer Materials within the Leibniz Institute of Polymer Research. He has written or contributed to over 250 scientific papers and book chapters on polymer science. M.Klppel is a lecturer in Polymer-Materials at Leibniz University, Hannover and Head of the Department of Material concepts and Modelling at the German Institute of Rubber Technology (DIK). He has published more than 150 scientific papers and is a member of the German Physical Society, the German Rubber Society, and the Rubber Division of ACS

Preface	p. ix
Acknowledgement	p. xii
Introduction	p. 1
Basics about polymers	p. 10
Gaussian chains - heuristic introduction	p. 10
Gaussian chains - path integrals	p. 12
Self-interacting chains	p. 15
Many-chain systems: melts and screening	p. 19
Some general remarks	p. 19
Collective vaniables	p. 20
The statistics of tagged chains	p. 26
Rubber formation	p. 31
Classical theory of gelation	p. 31
Percolation	p. 34
Vulcanization	p. 37
The elastomer matrix	p. 40
General remarks	p. 40
The Gaussian network	p. 42
Entanglements and the tube model: a material law	p. 45
Entanglement sliding	p. 47
Finite extensibility	p. 49
Tube and sliplinks	p. 52
Experiments	p. 53
The stress-strain relationship	p. 53
The extended tube model of rubber elasticity	p. 55
Testing of the model	p. 59
Polymers of larger connectivity: branched polymers and polymeric fractals	p. 64
Preliminary remarks	p. 64
D-dimensionally connected polymers in a good solvent	p. 64
D-dimensionally connected polymers between two parallel plates in a good solvent	p. 66
D-dimensionaIly connected polymers in a cylindrical pore (good solvent)	p. 68
Melts of fractals in restricted geometries	p. 71
Once more the differences	p. 74
Reinforcing fillers	p. 75
Fillers for the rubber industry	p. 75
Carbon black	p. 77
Morphology of carbon black aggregates	p. 77
Surface roughness of carbon blacks	p. 84
Energy distribution of carbon black surfaces	p. 92
Silica	p. 96
Hydrodynamic reinforcement of elastomers	p. 101
Reminder. Einstein-Smallwood	p. 101
	p. 103
Effective medium theory and linear elasticity	p. 106
Screening lengths	p. 109
Reinforcement by fractal aggregates	p. 110
Core-shell systems	p. 111
Uniform soft sphere	p. 112
Softcore/hardshell	p. 112
Hard core/soft shell	p. 115
Polymer-filler interactions	p. 118
General remarks and scaling	p. 118
Flat surface	p. 119
Generalization for fractal surfaces	p. 120
Variational calculation statics	p. 121
Variational calculation	p. 121
Trial Hamiltonian	p. 122
Minimization of the free energy	p. 123
Effective interaction strength	p. 126
Some further remarks on the interpretation	p. 130
Modeling by random potentials	p. 131
Annealed and quenched disorder	p. 134
Dynamics of localized chains - freezing, glass transition at filler surfaces	p. 135
Equation of motion for the time correlation function	p. 137
Langevin dynamics	p. 137
Self-consistent Hartree approximation	p. 139
Equation of motion	p. 142
Dynamic behavior of the chain	p. 144
Anomalous diffusion	p. 144
Center-of-mass freezing	p. 146
Rouse modes freezing and a two mode toy model	p. 147
Numerical analysis	p. 148
Bifurcation diagram	p. 149
Contribution to the modulus	p. 151
Filler-filler interaction	p. 153
Filler networking in elastomers	p. 153
Flocculation of fillers during heat treatment	p. 153
Kinetics of filler structures under dynamic excitation	p. 156
Dynamic small- and medium-strain modeling - the Payne effect	p. 161
The Kraus model	p. 161
The viscoelastic model	p. 164
The van der Walle-Tricot-Gerspacher (WTG) model	p. 169
The links-nodes-blobs (LNB) model	p. 171
The model of the variable network density	p. 172
The cluster-cluster aggregation (CCA) model	p. 174
Stress-softening and quasistatic stress-strain modeling - the Mullins effect	p. 182
The dynamic flocculation model	p. 182
The Kantor-Webman model of flexible chain aggregates	p. 193
References	p. 196
Index	p. 20
Table of Contents provided by Ingram. All Rights Reserved.

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Reinforcement of Polymer Nano-Composites: Theory, Experiments and Applications

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