A statistical theory of directional isomerism in polymer chains and its application to polyvinylidene fluoride

Abstract

A formal statistical analysis is presented of structural isomerism in a polymer chain having head-head, head-tail and tail-tail orientations of a directional monomer unit (regioisomerism). We derive general relations between the probabilities of regiosequences with up to seven elements (heptads), and treat explicitly Bernoullian and first-order Markov models for chain growth. We then illustrate our theory by analysing 188 MHz 19F n.m.r. spectra of two samples of polyvinylidene fluoride (PVF 2), Kynar 961 and Kureha KF-1100, and show that these polymers have regiosequence distributions which are described by first-order Markov statistics and not Bernoullian statistics. The implication is that the structural disorder in PVF 2 cannot be characterized accurately by a single parameter such as the ‘percent of head-head, tail-tail defect content’. We find that the defect content in Kynar 961 is 5.0% and in Kureha KF-1100 3.7%, and that the appropriate reactivity ratio pairs for the first-order Markov model are r 0 = 0.003, r 1 = 18 and r 0 = 0.003, r 1 = 24, respectively.