## The Theory of Polymer DynamicsOver the past twenty years our understanding of polymer solutions has undergone a dramatic evolution. New methods and concepts have extended the frontier of the theory from dilute solutions in which polymers move independently of each other, to concentrated solutions where many polymers entangle with each other. This book provides a comprehensive account of the modern theory for the dynamical properties of polymer solutions. This includes viscoelasticity, diffusion, dynamic light scattering and flow and electric birefringence. Nonlinear viscoelasticity is discussed in detail on the basis of molecular dynamical models. The book fills a gap between classical theory and modern developments and constructs a consistent picture for the dynamics of polymer solutions over the entire concentration range. |

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### Contents

INTRODUCTION | 1 |

STATIC PROPERTIES OF POLYMERS | 8 |

References | 43 |

1 Eigenfunctions of the Smoluchowski equation | 83 |

References | 89 |

1 The VerdierStockmayer model | 129 |

IV Polarizability tensor of a Gaussian chain | 135 |

1 Transformation to collective coordinates | 180 |

1 Entropy of a polymer in a tube | 215 |

References | 283 |

DILUTE SOLUTIONS OF RIGID RODLIKE | 289 |

1 Derivation of the Smoluchowski equation by | 318 |

1 Tube dilation by orientational ordering | 345 |

379 | |

AUTHOR INDEX | 386 |

DYNAMICS OF A POLYMER IN A FIXED NETWORK | 188 |

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### Common terms and phrases

approximation average beads becomes behaviour Brownian motion Chem coefficient concentrated solutions condition consider constitutive equation contour length fluctuation correlation function defined deformation denotes depends diffusion constant dilute solution discussed distribution function dynamic light scattering effect end-to-end vector flexible polymers fluid form birefringence free energy Gaussian chain Gennes given by eqn gives Green function Hence hydrodynamic hydrodynamic interaction integral intrinsic viscosity isotropic Langevin equation linear Macromolecules Macromolecules 17 macroscopic molecular weight nematic nonlinear obtained orientation Osaki parameter particles Phys polarizability polymer solutions polymeric liquids potential primitive chain problem properties region relaxation modulus Reproduced from ref reptation rewritten Rheol rodlike polymers rotational diffusion Rouse model Section shear flow shear rate shear stress shown in Fig Smoluchowski equation solvent stress tensor structure factor term test polymer theory time-scale topological constraints velocity gradient viscoelasticity viscosity written Zimm model