Structural Transitions in Fibers of Bent-Core Liquid Crystals from Field-Theory Monte Carlo Simulations

TL;DR

This study employs field-theoretical Monte Carlo simulations to analyze the complex internal structures and phase transitions of bent-core liquid crystal fibers, revealing both differentiable and non-differentiable equilibrium states with boundary layers.

Contribution

It introduces a Monte Carlo approach to identify all equilibrium states in a nonlinear, non-differentiable liquid crystal model, surpassing traditional Euler-Lagrange methods.

Findings

Identified both differentiable and non-differentiable equilibrium states.

Discovered first-order transitions between different equilibrium configurations.

Observed inhomogeneous structures with boundary layers in the fibers.

Abstract

Fibers of bent-core liquid crystals present an internal structure of a rolled smectic layer and can be used as optical waveguides. We used a field-theoretical Monte Carlo simulation to analyze the internal configuration of such fibers as a function of the radial coordinate and to study their equilibrium sates. In contrast to previous studies, we analyzed the fully nonlinear model proposed in [Bailey et al., Phys. Rev. E, 2007, 75, 031701] and revised in [P\'erez-Ortiz et al., Phys. Rev. E, 2011, 84, 011701]. We found that, due to the non-differentiable character of such model, the Euler-Lagrange equations are not able to find all equilibrium states. Our Monte Carlo procedure identified both differentiable and non-differentiable equilibria and first order transitions between them. In all cases, the equilibrium states show inhomogenous configurations that display a boundary layer. This methodology can by applied to other models of liquid crystals that have more degrees of freedom, including those with non-differentiable minima. The equilibrium structures found can be used as inputs to model the transmission of light along the liquid crystal fibers.