Computer simulation studies of molecular orientation in polyethylene networks: Orientation functions and the Legendre addition theorem

摘要

Correction of an averaging procedure used previously to evaluate, from Monte Carlo calculations, (P-2(xi)), the mean orientation function of segments with respect to the direction of uniaxial macroscopic strain in polyethylene networks, is described. The correction takes into account the interdependence of segment orientation and chain orientation as chains become more extended and aligned under uniaxial stress. Segment orientation soon becomes nonrandom, and the corrected values of (P-2(xi)) show significant nonlinear behavior even near deformation ratio lambda = 1, with respect to normalized stress versus lambda(2) - lambda(-1). It is demonstrated that such behavior leads to stress-orientation coefficients (Z(t)) deduced from experimental stress-optical coefficients (C-expt) being larger than the true, limiting values as lambda --> 1. Correction of the experimentally derived values of Z(t) leads to agreement between theory and experiment being achieved for polyethylene on the basis the value of Delta (n) over tilde(max), the maximum segmental birefringence in polyethylene chains, derived using Denbigh's estimates of bond polarizabilities. [References: 14]