Anisotropic translational diffusion in the nematic phase: Dynamical signature of the coupling between orientational and translational order in the energy landscape

We propose an approach to a multiscale problem in the theory of thermotropic uniaxial nematics based on the method of statistical field theory. This approach enables us to relate the coefficients $A$, $B$, $C$, $L_1$ and $L_2$ of the Landau-de Gennes free energy for the isotropic-nematic phase transition to the parameters of a molecular model of uniaxial nematics, which we take to be a lattice gas model of nematogenic molecules interacting via a short-ranged potential. We obt...

We study the gradient flow model for the Landau-de Gennes energy functional for nematic liquid crystals at the nematic-isotropic transition temperature on prototype geometries. We study the dynamic model on a three-dimensional droplet and on a disc with Dirichlet boundary conditions and different types of initial conditions. In the case of a droplet with radial boundary conditions, a large class of physically relevant initial conditions generate dynamic solutions with a well-...

In the last decade Diffusing Wave Spectroscopy (DWS) has emerged as a powerful tool to study turbid media. In this article we develop the formalism to describe light diffusion in general anisotropic turbid media. We give explicit formulas to calculate the diffusion tensor and the dynamic absorption coefficient, measured in DWS experiments. We apply our theory to uniaxial systems, namely nematic liquid crystals, where light is scattered from thermal fluctuations of the local o...

The phase-field-crystal model for liquid crystals is solved numerically in two spatial dimensions. This model is formulated with three position-dependent order parameters, namely the reduced translational density, the local nematic order parameter, and the mean local direction of the orientations. The equilibrium free-energy functional involves local powers of the order parameters up to fourth order, gradients of the order parameters up to fourth order, and different coupling...

Liquid crystals (LCs) composed of mesogens play important roles in various scientific and engineering problems. How a system with many mesogens can enter a LC state is an interesting and important problem. Using stiff and free-joint Lennard-Jones chain molecules as mesogens, we study the conditions under which the mesogens can enter various LC phases. The guideline is to eliminate the unwanted translational orders under a controlled fine-tuning procedure across a sequence of ...

In this work, we study the nematic-isotropic phase transition based on the dynamics of the Landau--De Gennes theory of liquid crystals. At the critical temperature, the Landau--De Gennes bulk potential favors the isotropic phase and nematic phase equally. When the elastic coefficient is much smaller than that of the bulk potential, a scaling limit can be derived by formal asymptotic expansions: the solution gradient concentrates on a closed surface evolving by mean curvature ...

We investigate orientational relaxation of a model discotic liquid crystal, consists of disc-like molecules, by molecular dynamics simulations along two isobars starting from the high temperature isotropic phase. The two isobars have been so chosen that (A) the phase sequence isotropic (I)-nematic (N)-columnar (C) appears upon cooling along one of them and (B) the sequence isotropic (I)-columnar (C) along the other. While the orientational relaxation in the isotropic phase ne...

The ferroelectric nematic phase (N$_{\text{F}}$) has quickly become the most studied system in liquid crystal research. In this work, we investigate the origin of such polar structure by studying a compound for which the N$_{\text{F}}$ phase directly follows the isotropic liquid phase on cooling, making it a particularly interesting system. Our experimental results evidence the presence of polar correlations already in the high-temperature phase, in which ferroelectric order ...

For isotropic fluids, classical nucleation theory predicts the nucleation rate, barrier height and critical droplet size by accounting for the competition between bulk energy and interfacial tension. The nucleation process in liquid crystals is less understood. We numerically investigate nucleation in monolayered nematogenic films using a mesoscopic framework, in particular, we study the mor- phology and kinetic pathway in spontaneous formation and growth of droplets of the s...

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 cocontinuous energy spectrum. We propose in this paper modifications nsidering 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 i...