Simulation of a relativistic soliton model of crystalline polymer dynamics

Abstract

The study of the sine-Gordon soliton model of the dielectric α relaxation in crystalline polymers is continued. We examine the intermediate range of the coupling constant, which is essentially the ratio of intramolecular to intermolecular interaction strengths, via another stochastic molecular dynamics computer simulation. The model is that of Currie et al. of the soliton as a pseudo-relativistic particle moving in an effective periodic potential. Comparison with the previous sine-Gordon chain simulation results in increasingly poor agreement with decreasing coupling constant, probably because of the neglect of multiple soliton effects. However, we find in the process the interesting result that relativity lowers the effective rate constant in such barrier-crossing problems. Finally, we also note that the continuum limit theory which is successful for nonpolar polymers may apply to other soliton-related physical systems as well.

Nonlinear dynamics of oriented elastic solids

“…Here, however, we consider the solution of Eq. (15) such that ~b ~ kn at infinity, and then Eo=)'/2+(-1) k. In this case the first integral of Eq. (15a) can be written as…”

“…The underlying physics of the micro-motion corresponds to various media, and the micro-system possesses both nonlinearities related to the internal degrees of freedom (large amplitude rotational motions of the directors) and dispersion (long-range interactions between neighboring directors accounting for the spatial nonuniformity in the director field). Thus the above-developed model can be applied to the study of nonlinear excitations in nematic liquid crystals [13] where a bunch of rigid nematic molecules is well enough modelled by a director, in polymer media (poly-vinylidenefluoride) [14,15,[43][44][45], or in long elastic chains of macromolecules (biological materials, e.g. DNA); in the latter case more complicated interactions between macromolecules may be involved [ 17,[46][47][48].…”

“…The interactions of special interest are those which permit nonlinear excitations of the soliton type (especially competitive interactions). The latter are found in media such as nematic liquid crystals [13], long chains of polymers [14,15], molecular ferroelectric crystals of which we have already a microscopic model [ 16], and elastic chains of molecules (e.g. DNA) [17].…”

Exact topological twistons in crystalline polyethylene

“…The existence of twistons in crystalline polyethylene (PE) was postulated [1] two decades ago, and refers to a twist of 180 0 that extends smoothly over several CH 2 groups in crystalline PE, in the plane orthogonal to the chain direction, with the corresponding CH 2 unit length contraction along the polymeric chain. These twiston configurations appear in crystalline PE as a result of its large torsional flexibility, and may contribute to elucidate some of its properties, in particular the dielectric α relaxation [2,3,4,5,6,7].…”

“…These twiston configurations appear in crystalline PE as a result of its large torsional flexibility, and may contribute to elucidate some of its properties, in particular the dielectric α relaxation [2,3,4,5,6,7].…”