V. S. S. Sastry

Wang-Landau Monte Carlo simulation of isotropic-nematic transition in liquid crystals.

Wang and Landau proposed recently, a simple and flexible non-Boltzmann Monte Carlo method for estimating the density of states, from which the macroscopic properties of a closed system can be calculated. They demonstrated their algorithm by considering systems with discrete energy spectrum. We find that the Wang-Landau algorithm does not perform well when the system has continuous energy spectrum. We propose in this paper modifications to the algorithm and demonstrate their performance on a lattice model of liquid crystalline system (with Lebwohl-Lasher interaction having continuously varying energy), exhibiting transition from high temperature isotropic to low temperature nematic phase.

Birefringence, permittivity, elasticity and rotational viscosity of ambient temperature, high birefringent nematic liquid crystal mixtures

We prepared a few binary nematic liquid crystal mixtures with high birefringence ( at room temperature) and studied the temperature variation of physical properties. All the mixtures show a small, positive dielectric anisotropy and the parallel component of dielectric constant exhibits anomalous temperature dependence. Orientational order parameter, both splay, bend elastic constants and rotational viscosity are comparatively larger than conventional low birefringent liquid crystal mixtures. The figure of merit (FoM) of the mixtures are also calculated as a function of temperature and expected to be useful for various applications.

Anchoring transition and influence of director fluctuations in liquid crystal droplets

Micro-droplets of nematic liquid crystals have been investigated under radial boundary conditions, based on a lattice model which incorporates explicitly the elastic properties of the medium as variable parameters in the Hamiltonian. Equilibrium director configurations have been simulated, employing the Monte Carlo technique, as a function of anchoring strength ϵ S at the spherical boundary surface. A very sharp transition from a uniaxial nematic structure to a radially ordered state results in ϵ S being increased beyond a threshold. The flexibility offered by this Hamiltonian is utilised to investigate this structural transition as a function of the splay elastic coefficient K 1. The results indicate several features: (1) the transition is as expected influenced by K 1; (2) the transition seems to be mediated by a process of complete wetting by the outer spherical surface, except for the small uniaxial core region sustained by the elastic energy penalty otherwise incurred; (3) the degree of splay contribution has multiple effects on the transition including changes in the critical anchoring strength at the transition, and the nature of the transition itself; (4) profiles of the director fluctuations across the (concentric) spherical layers indicate evidence of frustration caused by the competing interactions generated in the system due to the boundary conditions imposed.

Reexamination of the mean-field phase diagram of biaxial nematic liquid crystals: Insights from Monte Carlo studies.

Investigations of the phase diagram of biaxial liquid-crystal systems through analyses of general Hamiltonian models within the simplifications of mean-field theory (MFT), as well as by computer simulations based on microscopic models, are directed toward an appreciation of the role of the underlying molecular-level interactions to facilitate its spontaneous condensation into a nematic phase with biaxial symmetry. Continuing experimental challenges in realizing such a system unambiguously, despite encouraging predictions from MFT, for example, are requiring more versatile simulational methodologies capable of providing insights into possible hindering barriers within the system, typically gleaned through its free-energy dependences on relevant observables as the system is driven through the transitions. The recent paper from this group [Kamala Latha et al., Phys. Rev. E 89, 050501(R) (2014)], summarizing the outcome of detailed Monte Carlo simulations carried out employing an entropic sampling technique, suggested a qualitative modification of the MFT phase diagram as the Hamiltonian is asymptotically driven toward the so-called partly repulsive regions. It was argued that the degree of (cross) coupling between the uniaxial and biaxial tensor components of neighboring molecules plays a crucial role in facilitating a ready condensation of the biaxial phase, suggesting that this could be a plausible factor in explaining the experimental difficulties. In this paper, we elaborate this point further, providing additional evidence from curious variations of free-energy profiles with respect to the relevant orientational order parameters, at different temperatures bracketing the phase transitions.

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

General quadratic Hamiltonian models, describing the interaction between liquid-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 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 behavior 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 indeed be inhibiting the formation of a low-temperature biaxial order itself-perhaps reflecting the difficulties in their ready realization in the laboratory.

Phase diagram of a general biaxial nematic model based on density of states computation

ABSTRACT The phase diagram of a general biquadratic Hamiltonian model of biaxial nematic liquid crystals was investigated both analytically through mean-field approximation and with computer simulations. However, their largely concurrent predictions are not borne out by experimentation, and the issue is still debated. We revisited this problem with Monte Carlo simulations based on the computation of density of states of the system through entropic sampling procedure, traversing through the relevant model parameter space (S) along representative trajectories. Our recent work indicated that the competing roles of different contributions in the Hamiltonian over significant regions of S could be the underlying entropic reason defying the earlier predictions. We find that our data differ from the reported results qualitatively, specifically as the trajectories approach the so-called partly repulsive regions of S. The complex free-energy profiles that we obtain in such cases, as a function of system order parameters, indicate entropic barriers to the development of the biaxial order to the expected degree. Significant increase in the influence of the intermolecular interactions between the uniaxial and biaxial tensors, at the expense of contributions from pure biaxial couplings, is indicated to be the inhibiting factor for the onset of the biaxial phase. Graphical Abstract

Free energy computations employing Jarzynski identity and Wang – Landau algorithm

We introduce a simple method to compute free energy differences employing Jarzynski identity in conjunction with Wang – Landau algorithm. We demonstrate this method on Ising spin system by comparing the results with those obtained from canonical sampling.

Azimuthal Bistability in Patterened Nematic Liquid Crystal Films: A Monte Carlo Study

Monte Carlo simulations are carried out on a thin planar film of nematic liquid crystal, subjected to specific textured anchoring conditions, so as to generate azimuthal (in‐plane) bistability, as was recently reported experimentally. We investigated the switching characteristics of this system between the two director structures under the influence of an external (in‐plane) field, with focus on the role of the relative length scales in the system, viz. the thickness of the film and the dimension of the texturing pattern in the lateral dimension. We find that the observed experimental results require that patterning lengths on the textured substrate are to be restricted, primarily determined by the thickness of the film. For larger dimensions of the patterns (for a given thickness of the film), the simulations indicate qualitatively different director configurations, not related to those encountered in the reported experiments.

Anchoring Transitions in Biaxial Nematic Droplets: A Monte Carlo Study

Equilibrium order parameters of a liquid crystal micro-droplet of biaxial molecules, with radial anchoring conditions at the boundary, are computed based on Monte Carlo simulations. Their spatial variation within the droplet, and their temperature dependence covering uniaxial and biaxial nematic phases, are reported as a function of the biaxiality parameter. Central core, known to form for minimizing the energy cost of the boundary-induced distortion at low curvature regions, is characterized from these studies by estimating its size and spatial variation of relevant order parameters. Anchoring induced configuration transition in biaxial phases, and its dependence on the biaxiality parameter are studied.