Mean-Field Nematic--Smectic-{\sl A} Transition in a Random Polymer Network

TL;DR

This paper investigates how the network in liquid crystal elastomers influences the nematic--smectic-A transition, predicting modifications such as transition temperature shifts, suppression of fluctuation effects, and the emergence of a tri-critical point.

Contribution

It introduces a mean-field theoretical framework incorporating network effects as a random field, revealing new transition behaviors and critical points in liquid crystal elastomers.

Findings

Transition temperature $T_{NA}$ is shifted by network effects.

Suppression of the HLM fluctuation effect leads to a mean-field continuous transition.

A tri-critical point emerges depending on network formation conditions.

Abstract

Liquid crystal elastomers present a rich combination of effects associated with orientational symmetry breaking and the underlying rubber elasticity. In this work we focus on the effect of the network on the nematic--smectic-{\sl A} transition, exploring the additional translational symmetry breaking in these elastomers. We incorporate the crosslinks as a random field in a microscopic picture, thus expressing the degree to which the smectic order is locally frozen with respect to the network. We predict a modification of the NA transition, notably that it can be treated at the mean-field level (type-I system), due to the coupling with elastic degrees of freedom. There is a shift in the transition temperature $T_{\scriptscriptstyle NA}$, a suppression of the Halperin-Lubensky-Ma (HLM) effect (thus recovering the mean-field continuous transition to the smectic state), and a new tri-critical point, depending on the conditions of network formation. When the nematic phase possesses `soft elasticity', the NA transition becomes of first order due to the coupling with soft phonons in the network. We also discuss the microscopic origin of phenomenological long-wavelength coupling between smectic phase and elastic strain.