Solitons, defect diffusion, and dielectric relaxation of polymers

Abstract

We propose that the sine-Gordon model provides a reasonable Hamiltonian for a single polymer chain in crystalline polyethylene. We show that the soliton solutions of this model are very similar to the twist defects proposed, on the basis of detailed conformational energy studies, by Mansfield and Boyd as a mechanism for the α-relaxation process in crystalline polyethylene. Allowing for the possibility that the soliton solutions describe Brownian motion, we make the connection to the theory of dielectric relaxation, showing that the macroscopic decay function is given approximately by the hopping correlation function previously derived by us. More generally, we argue that this decay function arises from the one-dimensional Brownian motion of unspecified defects. When the phenomenological friction constant is very large, we find agreement between our result and the theory of defect diffusion. We then briefly discuss dielectric relaxation in amorphous polymers, noting that our decay function is similar in several respects to the successful empirical decay function proposed by Williams and Watts.