Frequency spectrum and dynamic correlations of concentrated polymer liquids

Elastic interactions between polymer chains in concentrated liquids are incorporated into the equation of motion by adding a memory term whose kernel is related to the relaxation modulus of the system. Below a characteristic chain length mechanical and dynamical properties are predicted to approach Rouse-like behavior. For long chain systems, an approximate self-consistency condition is obtained for the dynamic viscosity in the form of a nonlinear integral equation. In this limit, the mechanical spectrum is shown to split into a molecular weight independent branch separated from terminal relaxations by a wide plateau region whose elastic modulus is calculated as a function of the same parameters commonly used for the Rouse characterization of low molecular weight polymers. Concentration dependences of plateau modulus, entanglement length, and transitional relaxation time are correctly predicted. Zero shear viscosity and terminal relaxation time are shown to scale with the same power of the molecular weight. Heuristic considerations on the viscosity exponent suggest a value of three. The calculated expression of the single chain scattering function in the transition region shows a continuous change from Rouse-like behavior to flat response with decreasing wave vector. Application to multichain scattering by concentrated solutions predicts long-time exponential behavior only above a critical scattering wavelength. © 1983 American Institute of Physics.