Poisson Bracket Formulation of Nematic Polymer Dynamics

TL;DR

This paper develops a microscopic Poisson bracket framework for nematic polymer dynamics, revealing how the nematic director couples to momentum and strain rates, and analyzing the effects of polymer overlap on local dynamics.

Contribution

It introduces a novel Poisson bracket formulation for nematic polymers, linking microscopic order parameters to macroscopic dynamical couplings and breakdown phenomena.

Findings

Poisson brackets depend on the nematic order parameter.

Reactive couplings between director and strain rates are derived.

Local dynamics break down with polymer overlap.

Abstract

We formulate the dynamical theory of nematic polymers, starting from a microscopic Poisson bracket approach. We find that the Poisson bracket between the nematic director and momentum depends on the (Maier-Saupe) order parameter of the nematic phase. We use this to derive reactive couplings of the nematic director to the strain rates. Additionally, we find that local dynamics breaks down as the polymers begin to overlap. We offer a physical picture for both results.