From microscopic theory to macroscopic theory: symmetries and order parameters of rigid molecules

TL;DR

This paper employs density functional theory to analyze phase behaviors of rigid molecules, focusing on symmetries, order parameters, and the impact of molecular parameters, providing insights into phase transitions and molecular symmetries.

Contribution

It introduces a method to derive order parameters for rigid molecules by approximating the kernel function with polynomials based on molecular symmetries.

Findings

Order parameters for bent-core molecules are predicted.

Symmetries of the kernel function influence the form of polynomial approximations.

Molecular parameters and temperature determine polynomial coefficients.

Abstract

We use density functional theory to describe the phase behaviors of rigid molecules. The construction of kernel function G(x, P, x, P) is discussed. Excluded-volume potential is calculated for two types of molecules with C_{2v} symmetry. Molecular symmetries lead to the symmetries of G and density function f(P), enabling a reduction of configuration space. By approximating G with a polynomial, the system can be fully characterized by some moments corresponding to the form of G. The symmetries of G determine the form of the polynomial, while the coefficients are determined by temperature and molecular parameters. The analysis of the impact of coefficients helps us to choose independent variables in the moments as order parameters. Order parameters for bent-core molecules are predicted.