Component predictions and the relaxation spectrum of the double reptation mixing rule for polydisperse linear flexible polymers

Abstract

General, experimentally verifiable predictions of individual component behavior of linear flexible polymers in arbitrary molecular weight distributions are derived from the double reptation mixing rule. The distribution of stress/orientation among the different components of the molecular weight distribution during steady deformation and constrained elastic recovery are developed for the case of a single exponential monodisperse relaxation function. The des Cloizeaux ‘‘double reptation’’ model and the Tsenoglou network model are shown to be equivalent and the precise relationship between the model parameters is determined. Distinct contributions to the relaxation process from the separate mechanisms of reptation and matrix relaxation (constraint release) are identified. Experimental relaxation spectra of bidisperse blends of nearly monodisperse polybutadienes reveal a cascade of discrete peaks in the terminal zone that are in qualitative agreement with theoretical predictions from the double reptation mixing rule with a Doi–Edwards monodisperse relaxation function. The ability to accurately calculate experimental relaxation spectra for complex blends of nearly monodisperse materials is a powerful tool in developing, discriminating, and evaluating new mixing rules.