Influence of bond angle restrictions on polymer elasticity

Abstract

Abstract The statistical distribution of end‐to‐end distances in polymer chains is re‐examined with particular attention to deviations from Gaussian behaviour. The nature of the error involved in the conventional inversion of the Langevin function is specified. The theory of the rubber elastic equation of state is generalized for the case where the chains display changes in internal energy with change in conformation. The temperature coefficient of the ratio f / T of the retractive force to the absolute temperature is shown to be directly related to the change with temperature of the mean‐square distance r between the ends of the free polymer chain. thus, where f e = (∂ E /∂ L ) V,T. represents the contribution of the internal energy to the retractive force, and [η] Θ is the intrinsic viscosity at the theta point. Preliminary experiments are reported on stress‐temperature coefficients for (I) crosslinked poly‐(dimethylsiloxane) and (II) polyethylene. For I, it is found that f e = 0, within experimental error, but for II, f e ≅ − f /2. Results for II are explicable on the basis of a potential energy difference of ca. 500 cal./mole between the gauche and trans forms, in agreement with spectropic results for lower hydrocarbons.