Maier-Saupe nematogenic fluid: field theoretical approach

TL;DR

This paper develops a field theoretical framework to analyze the structure and thermodynamics of Maier-Saupe nematogenic fluids, deriving analytical expressions and fluctuation corrections to classical liquid crystal theory.

Contribution

It introduces a field theoretical approach to the Maier-Saupe model, providing analytical formulas for correlation functions and fluctuation effects beyond mean field theory.

Findings

Recovered standard Maier-Saupe theory in mean field approximation

Derived analytical expressions for correlation functions and thermodynamic quantities

Identified fluctuation corrections leading to higher-order Legendre polynomial contributions

Abstract

We adopt a field theoretical approach to study the structure and thermodynamics of a homogeneous Maier-Saupe nematogenic fluid interacting with anisotropic Yukawa potential. In the mean field approximation we retrieve the standard Maier-Saupe theory for liquid crystals. In this theory the density is expressed via the second order Legendre polynomial of molecule orientations. In the Gaussian approximation we obtain analytical expressions for the correlation functions, the elasticity constant, the free energy, the pressure, and the chemical potential. We also use Ward symmetry identities to set a simple condition for the correlation functions. Subsequently we find corrections due to fluctuations and show that density now contains Legendre polynomials of higher orders.