A molecular field theory for uniaxial nematic liquid crystals formed by non-cylindrically symmetric molecules

Abstract

Most molecular theories of nematic liquid crystals assume that the constituent molecules are cylindrically symmetric. However, although this may be a useful approximation the molecules of real nematogens are of lower symmetry ; here we develop a theory for an ensemble of such particles based on a general expansion of the pairwise intermolecular potential together with the molecular field approximation. The dependence of the orientational properties of the uniaxial mesophase on the deviation from molecular cylindrical symmetry is calculated from the series expansio n of the pseudopotential. In these calculations the number of arbitrary parameters in the orientational pseudo-potential is reduced by assuming that the anisotropic intermolecular potential originates solely from dispersion forces. The theoretical predictions for the values of the ordering matrix and the entropy change at the nematic-isotropic transition are found to be in good agreement with those observed for 4,4'-dimethoxyazoxybenzene. In addition, the theory provides a reasonable account of the temperature dependence of the order parameter at constant volume for this nematogen. The allowance for deviations from molecular cylindrical symmetry appears to remove many of the discrepancies between the Maier-Saupe theory and experiment.

Biaxiality-induced magnetic field effects in bent-core nematics: Molecular-field and Landau theory

“…Background to theory. The theory combines elements of the molecular field theory of biaxial liquid crystals developed elsewhere [15,[18][19][20][21], with the molecular field theory of uniaxial liquid crystals in an external field [9]. Molecular orientation ω is parameterized in terms of two Euler angles β, γ taking their conventional meanings (polar angle β and azimuthal angle γ).…”

“…We develop a molecular field theory as an extension of the theory by Wojtowicz and Sheng [9] since it is a straightforward theory which allows us to include molecular biaxiality. We note that a simple molecular field theory for uniaxial nematic formed from biaxial molecules in the absence of any external field was developed some time ago by Luckhurst et al [15]. This theory has been used to improve the numerical agreement between theory and experiment of the major order parameter S at the transition, the transitional entropy, the dependence of S on the temperature and the non-zero value of the molecular biaxial order parameter D [15].…”

“…We note that a simple molecular field theory for uniaxial nematic formed from biaxial molecules in the absence of any external field was developed some time ago by Luckhurst et al [15]. This theory has been used to improve the numerical agreement between theory and experiment of the major order parameter S at the transition, the transitional entropy, the dependence of S on the temperature and the non-zero value of the molecular biaxial order parameter D [15]. In this context, the present theory may also be viewed as an extension of that theory for a uniaxial nematic formed from biaxial molecules, now also specifically including the interaction of the constituent molecules with the magnetic field.…”

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

“…However, these theories involve a complicated mathematical treatment which make them difficult to apply to realistic LC models. The more commonly employed mean-field approaches for anisotropic phases such as the MaierSaupe 61,62 and the related molecular-field theories [63][64][65][66][67] (which are based the assumption that orientationally dependent attractive interactions are the molecular feature that give rise to liquid-crystalline order) are not appropriate for the description of lyotropic systems such as solutions of PBLG. This is because the LC phases exhibited by these polypeptides are governed principally by the repulsive interactions between the highly anisometric rod-like macromolecules.…”

Biaxial Nematic Droplets and their Optical Textures: A Lattice Model Computer Simulation Study

“…Our model biaxial and uniaxial nematics are obtained from a discretized version of the orientational biaxial potential put forward many years ago by Luckhurst et al [12,13] and whose phase diagram has already been studied in detail by us through extensive computer simulations of bulk systems [14]. This lattice model reproduces the rich phase diagram of a biaxial nematic system with isotropic, uniaxial and biaxial phases and it reduces to the well known Lebwohl-Lasher (LL) uniaxial one [1] for nematics when the molecular biaxiality vanishes.…”