Phase behaviour of the confined lattice gas Lebwohl-Lasher model

Almarza Almarza

doi:10.5488/cmp.16.43602

Abstract

The phase behaviour of the Lebwohl-Lasher lattice gas model (one of the simplest representations of a nematogenic fluid) confined in a slab is investigated by means of extensive Monte Carlo simulations. The model is known to yield a first order gas-liquid transition in both the 2D and 3D limits, that is coupled with an orientational order-disorder transition. This latter transition happens to be first order in the 3D limit and it shares some characteristic features with the continuous defect mediated Berezinskii-Kosterlitz-Thouless transition in 2D. In this work we will analyze in detail the behaviour of this system taking full advantage of the lattice nature of the model and the particular symmetry of the interaction potential, which allows for the use of efficient cluster algorithms.

Highlights

The Lebwohl-Lasher (LL) model [1] is known to be one of the simplest systems that can reproduce the isotropic-nematic transition, which is a key feature in the physics of liquid crystals, ubiquitous materials in today’s technology
Myroslav Holovko, whose 70th birthday we are celebrating with this Festschrift, was one of the first to study the solution of anisotropic integral equation approaches to study the MaierSaupe fluid and its order-disorder transitions [3], and he has recently published a study in which the system is considered in terms of a field theoretical approach [4]
As a tribute to his numerous contributions to the field of statistical mechanics of fluids and phase transitions, we will present a computer simulation study of the phase behaviour of a Lebwohl-Lasher lattice (LLL) gas under confinement. This model is an extension of the previous work by us [5] in which the nature of the orientational transitions of the LL model was analyzed in depth, and its close connection with the defect mediated Berenzinskii-Kosterlitz-Thouless (BKT) transition [6, 7] was investigated

Summary

Introduction

The Lebwohl-Lasher (LL) model [1] is known to be one of the simplest systems that can reproduce the isotropic-nematic transition, which is a key feature in the physics of liquid crystals, ubiquitous materials in today’s technology. According to the previous results [11], we expect to find a first-order (liquid-vapor-like) transition at low temperatures, and a continuous transition between an isotropic and a quasi-nematic phase at higher temperature. In the range of temperatures where the transition is continuous we have performed, for each size À , simulations for a series of Ä values in order perform a finite size scaling Ä analysis, namely 1⁄21⁄4 ̧ 3⁄41⁄4 ̧ ¿1⁄4 ̧ 1⁄4 ̧ 1⁄4 ̧ 1⁄4 ̧ 1⁄4 ̧ 1⁄21⁄41⁄4.

Results

Conclusion