Quantitive theory for dynamics of entangled Polymer melts

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The detailed understanding of the structure and properties of entangled polymer melt is crucial for successful usage of polymer materials in industry. During last 30 years most of the theoretical efforts in polymer dynamics was concentrated on the attempts to improve the tube theory of de Gennes, Doi and Edwards. In the research project I propose to develop a self-consistent tube theory of entangled polymer melts and concentrated solutions. This theory should combine all known processes additional to reptation, e.g. contour length fluctuations, constraint release, longitudinal modes of the stress relaxation and avoid the crude mathematical approximations used until now. I propose to use a method which combines analytical derivations of desired equations with direct stochastic simulations of the same equations. Stochastic solutions will provide the validity regions of the approximations and allow the calculation of unknown prefactors. This method was first applied to the theory of convective constraint release and gave detailed predictions of rheological and scattering properties of the fast flows of polymer melts. In the research proposal I describe the methods of obtaining linear and nonlinear rheological properties of linear and branched polymer melts using this combined approach.