A model for the viscoelastic behavior of rubberlike polymers including entanglement effects

Abstract

A model r epresen ting t he mechanical response of a rubberlike polym er is derived , using t he same molecular concep ts of ent ropy elasticity and a viscous parameter expressing interactions between polymer molecul es employed by R ouse, Bueche, and Zimm in thei r molec ular theories. Since t he model developed here r epresents the mechanical response of a chain, rather t han representing t he chain itself, it can be modifi ed more easily t han t hese strict molecular t heories to includ e effects due to entanglements between chains which modify the cha racter of the viscosity-molecular weight relat ionship at a crit ical molecu lar weight. This m odifi cation is in trod uced, t he results for both steady-state and transient response funct ions are calcu lated , and t hese result s compared wit h experiment for t he " standard " polyisobutyle ne. The agreement ind icates t hat the same "entanglements," whatever t heir precise natu re, a re responsible for the proportionality of viscosity to M 3 .• for a high molecular weight polymer, the s teady-s tate elastic compli ance, a nd t he pseudo-equ ilibr ium co mplia nce at intermed iate t im es or frequencies.