Dynamics of Polydisperse Polymer Mixtures

TL;DR

This paper develops a comprehensive theoretical framework to analyze the diffusive dynamics of polydisperse polymers within the tube model, deriving coupled equations and exploring their solutions for various types of polydispersity and solvent conditions.

Contribution

It introduces a set of explicitly derived coupled dynamical equations for polydisperse polymers, including solutions for chemical and length polydispersity cases within the tube model.

Findings

Solved coupled equations for chemical polydispersity in certain cases

Analyzed linear mode spectrum after a quench through the spinodal

Studied length polydisperse chains in poor solvent conditions

Abstract

We develop a general analysis of the diffusive dynamics of polydisperse polymers in the presence of chemical potential gradients, within the context of the tube model (with all species entangled). We obtain a set of coupled dynamical equations for the time evolution of the polymeric densities with explicitly derived coefficients. For the case of chemical polydispersity (a set of chains that are identical except for having a continuous spectrum of enthalpic interaction strengths) the coupled equations can be fully solved in certain cases. For these we study the linearised mode spectrum following a quench through the spinodal, with and without a passive (polymeric) solvent. We also study the more conventional case of length polydisperse chains in a poor solvent.