Correlation functions of main-chain polymer nematics constrained by tensorial and vectorial conservation laws

TL;DR

This paper analyzes correlation functions in main-chain polymer nematics under tensorial and vectorial constraints, revealing how these constraints influence density and director correlations, especially in long chains with specific persistence lengths.

Contribution

It provides a detailed comparison of correlation functions under two different microscopic constraints, highlighting their distinct signatures and dependence on chain properties.

Findings

Correlation functions differ significantly under strong constraints.

Density-director correlations serve as signatures of specific constraints.

Chain length and persistence length influence the distinguishability of constraints.

Abstract

We present and analyze correlation functions of a main-chain polymer nematic in a continuum worm-like chain description for two types of constraints formalized by the tensorial and vectorial conservation laws, both originating in the microscopic chain integrity, i.e., the conectivity of the polymer chains. In particular, our aim is to identify the features of the correlation functions that are most susceptible to the differences between the two constraints. Besides the density and director autocorrelations in both the tensorial and vectorial cases, we calculate also the density -- director correlation functions, the latter being a direct signature of the presence of a specific constraint. Its amplitude is connected to the strength of the constraint and is zero if none of the constraints is present, i.e., for a standard non-polymeric nematic. Generally, the correlation functions with the constraints differ substantially from the correlation functions in the non-polymeric case, if the constraints are strong which in practice requires long chains. Moreover, for the tensorial conservation law to be well distinguishable from the vectorial one, the chain persistence length should be much smaller than the total length of the chain, so that hairpins (chain backfolding) are numerous and the polar order is small.