Molecular Model for Linear Viscoelastic Properties of Entangled Polymer Networks

A molecular Kuhn-scale model is presented for the stress relaxation dynamics of entangled polymer networks. The governing equation of the model is given by the general form of the linearized Langevin equation. Based on the fluctuation-dissipation theorem, the stress relaxation modulus is derived using the normal mode representation. The entanglements are introduced as additional entropic springs connecting internal beads of the network strands. The validity of the model is assessed by comparing predicted stress relaxation modulus and viscoelastic storage and loss moduli with the estimates from molecular dynamics (MD) simulations, using the same computer models. A finite element procedure is proposed and used to assemble the network connectivity matrix, and its numerically solved eigenvalues are used to predict the linear stress relaxation dynamics. Both perfect (fully polymerized stoichiometric) and imperfect networks with different soluble and dangling structures and loops are studied using mapped Kuhn-scale network models with up to several dozen thousand Kuhn segments. It is shown that for the overlapping ranges of times and frequencies, the model predictions and MD estimates agree well.