Complex free-energy landscapes in biaxial nematic liquid crystals and the role of repulsive interactions: A Wang-Landau study

Abstract

General quadratic Hamiltonian models, describing interaction between crystal molecules (typically with D 2h symmetry) take into account couplings between their uniaxial and biaxial tensors.While the attractive contributions arising from interactions between similar tensors of the participating molecules provide for eventual condensation of the respective orders at suitably low temperatures, the role of cross-coupling between unlike tensors is not fully appreciated. Our recent study with an advanced Monte Carlo technique (entropic sampling) showed clearly the increasing relevance of this cross term in determining the phase diagram, contravening in some regions of model parameter space, the predictions of mean field theory and standard Monte Carlo simulation results. In this context, we investigated the phase diagrams and the nature of the phases therein, on two trajectories in the parameter space: one is a line in the interior region of biaxial stability believed to be representative of the real systems, and the second is the extensively investigated parabolic path resulting from the London dispersion approximation. In both the cases, we find the destabilizing effect of increased cross-coupling interactions, which invariably result in the formation of local biaxial organizations inhomogeneously distributed. This manifests as a small, but unmistakable, contribution of biaxial order in the uniaxial phase.The free energy profiles computed in the present study as a function of the two dominant order parameters indicate complex landscapes. On the one hand these profiles account for the unusual thermal behaviour of the biaxial order parameter under significant destabilizing influence from the cross terms. On the other, they also allude to the possibility that in real systems these complexities might be indeed inhibiting the formation of a low temperature biaxial order itself -perhaps reflecting the difficulties in their ready realization in the laboratory. 64.70.mf

Theoretical Model of a Nematogen: Estimation of Phase Stability, Absorption, Electrochemical, and Nonlinear Optical Properties

“…The phase structure arises from a delicate interplay between the internal molecular structure and the moleculemolecule interaction energy, which has a close relation with anisotropy of physical properties [7]. These mesophases are controlled by the interplay between probability and entropy.…”