Theory of Viscoelasticity of Amorphous Polymers

Abstract

A statistical mechanical theory of the intra-chain relaxation (or relaxation of the micro-Brownian motion) in amorphous polymers is presented. The generalized diffusion equation of configurational changes of a chain imbedded in polymer environment is solved for a dynamical case under suitable potentials assumed. In order to avoid the complication of the chain space geometry, an artifice is adopted such that we replace each chain bond with a fictitious spring. The derived spectrum of relaxation times just coincides with the experimental formula of the wedge type spectrum found by Tobolsky for polyisobutylene, manifesting a characteristic slope of −1⁄2 in the log-log plot of the relaxation spectrum. The theoretical expression also satisfies the condition of the thermorheological simplicity.