A study of orientational ordering in a fluid of dipolar Gay–Berne molecules using density-functional theory

Abstract

We present a density-functional approach to describe the orientational ordering of nonpolar and dipolar Gay-Berne fluids. The first-order perturbation theory developed by Velasco et al. ͓J. Chem. Phys. 102, 8107 ͑1995͔͒ for a Gay-Berne fluid is simplified and tested for molecules with a length to breath ratio of ϭ3 and energy anisotropies of Јϭ1, 1.25, 2.5, and 5. The theory is found to be in fair agreement with existing simulation data for the location of the isotopic-nematic phase transition, but it overestimates the vapor-liquid critical point of the fluid due to a description of the free energy at the mean-field level. The effect on the phase behavior of including a central longitudinal point dipole within the Gay-Berne molecule is studied using a correct treatment of the long-range dipolar contribution at the level of a second-order virial theory ͓B. Groh and S. Dietrich, Phys. Rev. E 50, 3814 ͑1994͔͒. For a given energy anisotropy of Јϭ5 and reduced dipole moment *ϭ0.5 we search for a stable ferroelectric nematic phase by changing the length to breath ratio . We do not find any evidence of ferroelectric nematic ordering for Ͼ1.5; the system only exhibits vapor-liquid and isotropic-nematic phase transitions for these values of the aspect ratios. For a slightly elongated and oblate shaped potential ͑e.g., ϭ0.5͒, regions of stable isotropicferroelectric nematic and nematic-ferroelectric nematic phase coexistences are observed. The results of the theory indicate that a ferroelectic nematic fluid phase may be stabilized with respect to the positional ordering in the fluid of oblate dipolar particles. Comparison are made, where appropriate, with the existing results of Monte Carlo simulations for dipolar Gay-Berne fluids ͑Rull and co-workers, Molec. Phys. 94, 439 ͑1998͒; J. Chem. Phys. 109, 9529 ͑1998͒͒.

A generalisation of the Onsager trial-function approach: describing nematic liquid crystals with an algebraic equation of state

“…The original second-virial theory of Onsager [37] is applicable only to molecules with large aspect ratios. The suitability of using a scaled Onsager free energy [81][82][83] in representing the isotropic-nematic phase transition in systems of hard ellipsoids [42,83,174,175], hard spherocylinders [11,84], hard cylinders (oblate or prolate) [137][138][139][140], cut spheres [170], and hard-sphere chains [112,176] has already been confirmed. Scaled Onsager theories which go beyond the original two-body theory of Onsager by including the higher-body terms in an approximate fashion provide an impressive description of the pressure and densities of the coexisting isotropic and nematic state (typically to an accuracy of better than 5% for molecules of moderate aspect ratio), and of the equation of state and degree of orientational order of the nematic phase.…”

“…Though the use of Gaussian trial functions (GTFs) leads to a simpler algebraic treatment, the resulting expressions for the free energy generally provide a less adequate description of the free energy and ordering phase transitions than those obtained with the OTF. In some cases qualitative differences in the types of phase behaviour are seen when compared with the full numerical solution particularly for mixtures (see the studies on mixtures of rod and disk-like particles [137][138][139][140]). The simple model of Zwanzig [88] (in which only the three cartesian orientations of the orientational distribution function are considered) have also found popular use owing to the tractable nature of the free energy [141][142][143][144][145][146][147][148][149][150][151][152][153][154].…”

Revisiting the phase diagram of hard ellipsoids

“…Rickayzen introduced a modification of the well established Berne and Pechukas [16] (BP) (also called hard Gaussian overlap [17]) model. Its aim is to give a better analytical approach, by fixing the T-shape BP mismatch, to the exact solution of the distance of closest approach of a pair (i and j) of uniaxial ellipsoids.…”

Understanding and Describing the Liquid-Crystalline States of Polypeptide Solutions: A Coarse-Grained Model of PBLG in DMF

“…A number of studies have been carried out after the early attempts by Kimura 71 to describe the properties of a system which combines Onsager's hard-rod model with anisotropic dispersion forces. [72][73][74][75][76][77][78][79][80][81][82][83] Some progress has also been made in introducing dipolar [84][85][86][87][88][89] or chiral [90][91][92][93] interactions between LC molecules. Of particular relevance to our current work is the closed-form algebraic equation of state developed within a van der Waals-Onsager treatment for systems of attractive hard-core particles, 94 in which the attractive potential is expanded in spherical harmonics 95 representing different multipolar contributions to the anisotropic attractions.…”