Uniaxial and biaxial structures in the elastic Maier-Saupe model

TL;DR

This paper analyzes the phase diagram of a Maier-Saupe elastic model, revealing how uniaxial and biaxial nematic phases depend on temperature and stress, with detailed phase transition insights.

Contribution

It introduces a fully-connected elastic Maier-Saupe model with analytical results on phase boundaries, critical points, and the influence of stress on nematic structures.

Findings

Uniaxial stress favors uniaxial orientation with a first-order transition.

Compressive stress promotes biaxial orientation with a tricritical point.

Analytic determination of critical, tricritical points, and phase stability lines.

Abstract

We perform statistical mechanics calculations to analyze the global phase diagram of a fully-connected version of a Maier-Saupe-Zwanzig lattice model with the inclusion of couplings to an elastic strain field. We point out the presence of uniaxial and biaxial nematic structures, depending on temperature $T$ and on the applied stress $\sigma$. Under uniaxial extensive tension, applied stress favors uniaxial orientation, and we obtain a first-order boundary, along which there is a coexistence of two uniaxial paranematic phases, and which ends at a simple critical point. Under uniaxial compressive tension, stress favors biaxial orientation; for small values of the coupling parameters, the first-order boundary ends at a tricritical point, beyond which there is a continuous transition between a paranematic and a biaxially ordered structure. For some representative choices of the model parameters, we obtain a number of analytic results, including the location of critical and tricritical points and the line of stability of the biaxial phase.