Phase diagrams of Zwanzig models: The effect of polydispersity

TL;DR

This paper investigates the phase behavior of Zwanzig models for liquid crystals, focusing on how polydispersity and binary mixtures of rods and plates influence phase transitions and stability of various phases.

Contribution

It extends the Zwanzig model to binary mixtures and examines the impact of polydispersity on phase diagrams and phase stability, especially the biaxial nematic phase.

Findings

Polydispersity enhances the stability of the biaxial nematic phase.

Phase diagrams for $ =5$ and 15 are determined and compared with Onsager results.

The model predicts transitions to inhomogeneous phases like smectic and columnar.

Abstract

The first goal of this article is to study the validity of the Zwanzig model for liquid crystals to predict transitions to inhomogeneous phases (like smectic and columnar) and the way polydispersity affects these transitions. The second goal is to analyze the extension of the Zwanzig model to a binary mixture of rods and plates. The mixture is symmetric in that all particles have equal volume and length-to-breadth ratio, $\kappa$. The phase diagram containing the homogeneous phases as well as the spinodals of the transitions to inhomogeneous phases is determined for the cases $\kappa=5$ and 15 in order to compare with previous results obtained in the Onsager approximation. We then study the effect of polydispersity on these phase diagrams, emphasizing the enhancement of the stability of the biaxial nematic phase it induces.