Pair Correlation Functions in Nematics: Free-Energy Functional and Isotropic-Nematic Transition

Abstract

We develop a free energy functional for an inhomogeneous system that contains both symmetry conserved and symmetry broken parts of the direct pair correlation function. These correlation functions are found by solving the Ornstein-Zernike equation with the Percus-Yevick closure relation. The method developed here gives the pair correlation functions in the ordered phase with features that agree well with the results found by computer simulations. The theory predicts accurately the isotropic-nematic transition in a system of anisotropic molecules and can easily be extended to study other ordered phases such as smectics and crystalline solids.

Nematic van der Waals Free-energy

“…This phase has been confirmed by computer simulations for hard ellipsoids [19,20] spherocylinders [21][22][23][24] and for hard spheres [25]. Recently Mishra et al [26,27] have used the mean spherical approximation and the percus-Yevick integral equation theories to calculate the free energy functional for the nematic phase. A first-order isotropic-nematic transition is to be found in the liquid regime, although these authors do not present results for the phase diagram.…”

Free-energy functional for freezing transitions: Hard-sphere systems freezing into crystalline and amorphous structures

“…The parameter λ raises the density from 0 to ρ 0 as it varies from 0 to 1 whereas the parameter ξ raises the order parameters from 0 to ρ q for each value of q. This gives [9,10].…”

“…The integral equation theory has been used quite successfully to describe the structure of isotropic liquids. But its application to frozen phases has so far been very limited [9,10]. In…”

“…When this functional dependence is ignored and the DPCF is replaced by that of the co-existing isotropic liquid [11] or by an "effective fluid" [14] the free-energy functional becomes approximate and fails to provide an accurate description of freezing transitions and stability of frozen phases. An improved free-energy functional which contains both the symmetry conserved and symmetry broken parts of the DPCF has recently been developed [9,10] and applied to study the isotropic-nematic transition [9] and the crystallization of power-law fluids [10].…”

One Subject, Two Lands: My Journey in Condensed Matter Physics

“…There is need for a more realistic functional that pays attention to the fact that the general (nonequilibrium) fluid configuration described by such a functional has inhomogeneous density. This area has seen surprisingly little serious effort, though there is a promising recent attempt (5). Another basic issue is that of the relative stability of different simple crystal structures from the point of view of (classical) density functional theory.…”