Rotational Isomerization of Polymer Chains by Stretching

Abstract

A general theory is presented on the effect of elongation of a polymer chain on the apportionment of its bonds and bond sequences among various rotational isomeric states. The perturbation of the population of a state η is found to be proportional to 3 2 [(r 2 / 〈r 2 〉 0 ) − 1][(〈r η;i 2 〉 0 / 〈r 2 〉 0 ) − 1] , where r is the length of the chain vector, 〈r 2 〉 0 is the mean square of r for the unperturbed chain, and 〈r η;i 2 〉 0 is the same quantity subject to the condition that the bond i or bond sequence i is in the conformational state specified by η . The theory is limited to the range of moderate deformations; it is inapplicable for lengths r approaching full extension of the chain. Numerical calculations are presented for polymethylene chains and for syndiotactic vinyl polymers. The calculated effects are very small; unit increase in r 2 / 〈r 2 〉 0 generally alters the conformation population of a given state by no more than about one bond (or sequence) per chain. The length of the given conformation and its susceptibility to orientation by stretching are the main factors governing the effect. The connection with strain dichroism is discussed.