Molecular dynamics study of the vulcanization transition

Abstract

We report on extensive computer simulations of randomly cross-linked polymer networks in the vicinity of the liquid-solid transition. We have determined the order parameter and the distribution of localization lengths as a function of cross-link density n near the critical point for up to $M=500$ chains of length $N=10$ and $M=100$ chains of length $n=20.$ We find that the order parameter varies as $q(n)\ensuremath{\sim}n\ensuremath{-}{n}_{c},$ in agreement with the classical and modern theories of rubber elasticity and that the distribution of localization lengths assumes a universal form, in agreement with recent predictions.