Pair Correlation Functions and a Free-Energy Functional for the Nematic Phase

Abstract

In this paper we have presented the calculation of pair correlation functions in a nematic phase for a model of spherical particles with the long-range anisotropic interaction from the mean spherical approximation(MSA) and the Percus-Yevick (PY) integral equation theories. The results found from the MSA theory have been compared with those found analytically by Holovko and Sokolovska (J. Mol. Liq. $82$, 161(1999)). A free energy functional which involves both the symmetry conserving and symmetry broken parts of the direct pair correlation function has been used to study the properties of the nematic phase. We have also examined the possibility of constructing a free energy functional with the direct pair correlation function which includes only the principal order parameter of the ordered phase and found that the resulting functional gives results that are in good agreement with the original functional. The isotropic-nematic transition has been located using the grand thermodynamic potential. The PY theory has been found to give nematic phase with pair correlation function harmonic coefficients having all the desired features. In a nematic phase the harmonic coefficient of the total pair correlation function $h({\mathbf{x}}_1,{\mathbf{x}}_2)$ connected with the correlations of the director transverse fluctuations should develop a long-range tail. This feature has been found in both the MSA and PY theories.

27 pages, 11 figures, Accepted in J. Chem. Phys

References in corpus (7)

• Fluids of hard ellipsoids: Phase diagram including a nematic instability from Percus-Yevick theory
• Elastic constants from direct correlation functions in nematic liquid crystals: a computer simulation study
• Pair correlation functions in nematics, free-energy functional and isotropic-nematic transition
• Structure of molecular liquids: cavity and bridge functions of the hard spheroid fluid
• Local structure in nematic and isotropic liquid crystals
• The Structure and Freezing of fluids interacting via the Gay-Berne (n-6) potentials
• Effect of shape anisotropy on the phase diagram of the Gay-Berne fluid

Cited by in corpus (5)

• Crystallization of Simple Fluids: Relative Stability of f.c.c. and b.c.c Structures
• Fluid - solid transition in simple systems using density functional theory
• Correlation functions in liquids and crystals : Free energy functional and liquid - crystal transition
• Integral Equation Theory for Pair Correlation Functions in a Crystal
• Freezing of a two dimensional fluid in to a crystalline phase : Density functional approach