Computer simulation studies of soliton models for dielectric relaxation in crystalline polyethylene and related polymers. I. Continuum and pinned limits

Abstract

We study the sine‐Gordon soliton model of the dielectric α relaxation in crystalline polyethylene and similar polymers. These systems are characterized by a coupling constant which is essentially the ratio of intramolecular to intermolecular interaction strengths. We perform a stochastic molecular dynamicscomputer simulation for a wide range of coupling constants. We investigate analytically the high coupling (continuum) limit, modeled as free particle Brownian motion of the soliton, and the low coupling (pinned) limit, treated as hopping diffusion of the soliton over barriers at the sites on the polymer chain. We compare the simulation with these analytical theories and with experimental results for polyethylene. Agreement between simulation and theory for nonpolar polymers is excellent in the continuum limit down to relatively small coupling constants, and we also find quite reasonable agreement with experiments in that limit, considering the neglect of defects on the chains. The best fits of the pinned limit theory with the simulation are identical to those of the continuum limit in the lower coupling regime, and are not very successful. The continuum limit analytical theory is extended to polar polymers and qualitative agreement with other theories is shown, in the absence of experimental data for comparison. It is suggested that a more specific theoretical treatment in the intermediate to low coupling regime might improve agreement with the simulation and that the inclusion of defect effects is necessary for more successful agreement with experimental results.