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 dynamics computer 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.

Distribution of relaxation times from dielectric spectroscopy using Monte Carlo simulated annealing: Application toα−PVDF

“…Referring to the variation of the ␤ c parameter with temperature, the only determination of the variation with temperature of the parameters that characterize the distribution of relaxation times for a mode originated in the crystalline regions is, to the best of our knowledge, in lightly oxidized high-density polyethylene. 44 The author reports a linear dependence with temperature, with positive slope, for the Cole-Cole parameter. This is attributed to the presence of point defects, whose effect is expected to be significant due to their high population.…”

Quantum and disorder effects in Davydov soliton theory

“…Solitary solutions can only occur for nonlinear wave equations, since linear wave packets disperse rapidly. As some examples for an introduction of soliton concepts in physics and chemistry let us mention the dynamics of magnetic materials [3,4], rotations around carboncarbon bonds in polyethylene [5], phase changes in solids [6,7], dynamics of the sugar-phosphate backbone [8] or the nucleotide bases [9] in DNA, and the spinless charge transport in trans polyacetylene - [10].…”

Influence of heat bath and disorder in the sequence of amino acid masses on Davydov solitons

“…They found that a clearly resolved pulse travels through a chain without mass variation for T = 310 K. In the case of mass variation they found that with decreasing excitation energy the ability of the pulse to carry energy decreases. It would seem to be interesting to study effects of mass variation in the case of the quantum equations of motion ( 5 ) for Davydov solitons also.…”

“…It has been applied e.g. to the dynamics of ferro-and antiferro-magnetic materials [3,4] and rotations around carbon-carbon bonds in polyethylene [ 5 ] .…”