Canonical Distribution Functions in Polymer Dynamics: I. Dilute Solutions of Flexible Polymers

TL;DR

This paper applies the maximum entropy approximation to derive and numerically implement constitutive equations for dilute flexible polymer solutions, assessing the approximation's accuracy and its dependence on macroscopic variables.

Contribution

It introduces a systematic method to derive constitutive equations using canonical distribution functions from the maximum entropy principle in polymer dynamics.

Findings

Including more macroscopic variables improves approximation accuracy.

More variables are needed above the coil-stretch transition for steady elongational flow.

The proposed measure evaluates the quasi-equilibrium approximation's accuracy during integration.

Abstract

The quasi--equilibrium or maximum entropy approximation is applied in order to derive constitutive equations from kinetic models of polymer dynamics. It is shown in general and illustrated for an example how canonical distribution functions are obtained from the maximum entropy principle, how macroscopic and constitutive equations are derived therefrom and how these constitutive equations can be implemented numerically. In addition, a measure for the accuracy of the quasi--equilibrium approximation is proposed that can be evaluated while integrating the constitutive equations. In the example considered, it is confirmed that the accuracy of the approximation is increased by including more macroscopic variables. In steady elongational flow, it is found that more macroscopic variables need to be included above the coil--stretch transition to achieve the same accuracy as below.