SEMIEMPIRICAL THEORY OF RELAXATION - CONCENTRATED POLYMER-SOLUTION DYNAMICS

Classical models of viscoelasticity neglect memory effects arising from material inhomogeneity and cooperative molecular motion. These memory effects are modeled by using an integral equation approach in which physical arguments are employed to estimate the memory kernel. Our model memory kernel depends on two parameters: beta, which is interpreted as a measure of material inhomogeneity, and phi, which is interpreted as a measure of cooperativity of molecular motion. Here we apply our relaxation model to polymer melt dynamics. An idealized "cluster" model of stress relaxation in glasses is introduced to estimate beta. This model rationalizes well the observed stress relaxation of polymer glasses. A cluster model is also introduced to estimate the molecular weight dependence of the zero-shear rate viscosity and the diffusion coefficient of entangled polymers. For flexible polymers in three dimensions the viscosity molecular weight exponent ranges in the interval 3.3 to 3.7, depending on the strength of the excluded-volume interaction. The diffusion coefficient molecular weight exponent in three dimensions is predicted to lie in the interval -2.3 to -2.5. Results similar to the reptation model are obtained in four dimensions, and the Rouse theory is recovered in the limit of infinite dimensionality. Estimates of the concentration dependence of entangled polymer solution transport properties are also given.