Entanglement effects in model polymer networks

Abstract

The influence of topological constraints on the local dynamics in cross-linked polymer melts and their contribution to the elastic properties of rubber elastic systems are a long standing problem in statistical mechanics. Polymer networks with diamond lattice connectivity (Everaers and Kremer 1995, Everaers and Kremer 1996a) are idealized model systems which isolate the effect of topology conservation from other sources of quenched disorder. We study their behavior in molecular dynamics simulations under elongational strain. In our analysis we compare the measured, purely entropic shear moduli G to the predictions of statistical mechanical models of rubber elasticity, making extensive use of the microscopic structural and topological information available in computer simulations. We find (Everaers and Kremer 1995) that the classical models of rubber elasticity underestimate the true change in entropy in a deformed network significantly, because they neglect the tension along the contour of the strands which cannot relax due to entanglements (Everaers and Kremer (in preparation)). This contribution and the fluctuations in strained systems seem to be well described by the constrained mode model (Everaers 1998) which allows to treat the crossover from classical rubber elasticity to the tube model for polymer networks with increasing strand length within one transparant formalism. While this is important for the description of the effects we try to do a first quantitative step towards their explanation by topological considerations. We show (Everaers and Kremer 1996a) that for the comparatively short strand lengths of our diamond networks the topology contribution to the shear modulus is proportional to the density of entangled mesh pairs with non-zero Gauss linking number. Moreover, the prefactor can be estimated consistently within a rather simple model developed by Vologodskii et al. and by Graessley and Pearson, which is based on the definition of an entropic interaction between the centers of mass of two loops in a conserved topological state.