Mesoscopic theory of the viscoelasticity of polymers

TL;DR

This paper develops a dynamic mesoscopic theory for polymer viscoelasticity, extending previous static models to include frequency-dependent behavior and fitting parameters to experimental data.

Contribution

It introduces a time-dependent extension of the static entanglement theory using an extended Cahn-Hilliard functional beyond Gaussian approximation.

Findings

The model accurately predicts frequency-dependent storage and loss moduli.

Parameters are physically related to polymer chain length.

The theory highlights the significance of various energy functional terms.

Abstract

We have advanced our previous static theory of polymer entanglement involving an extended Cahn-Hilliard functional, to include time-dependent dynamics. We go beyond the Gaussian approximation, to the one-loop level, to compute the frequency dependent storage and loss moduli of the system. The three parameters in our theory are obtained by fitting to available experimental data on polystyrene melts of various chain lengths. This provides a physical representation of the parameters in terms of the chain length of the system. We discuss the importance of the various terms in our energy functional with respect to their contribution to the viscoelastic response of the polymeric system.