Computer simulation of hard-core models for liquid crystals

The effect of particle geometry and initial configuration on the phase behavior of twisted convex n-prisms

We study the phase behavior of twisted convex n-prisms with n = 3 and 4, via Monte Carlo simulations. Biaxial phases, in untwisted prisms, can be induced by choosing specific geometries of the prisms. However, due to the convexity of the twisted particles, a strong twisting disables the formation of biaxial phases and stabilizes uniaxial nematic and smectic phases. Using the increased volume of the twisted convex particles, we define an effective aspect ratio of the twisted prisms and find a homogeneous phase behavior across the geometry of the prisms' cross-section and even across different shapes of the cross-section. In this representation biaxial phases are found for large aspect ratios, while the low aspect ratio behavior can be compared to the hard cylinder phase diagram. For 3-prisms with a small base angle, we show the influence of the initial configuration; a polar initial configuration results in a (polar) splay nematic phase, whereas a non-polar initial configuration results in a biaxial phase.

Hidden scale invariance in the Gay-Berne model

This paper presents a numerical study of the Gay-Berne liquid crystal model with parameters corresponding to calamitic (rod-shaped) molecules. The focus is on the isotropic and nematic phases at temperatures above unity, where we find strong correlations between the virial and potential-energy thermal fluctuations, reflecting the hidden scale invariance symmetry. This implies the existence of isomorphs, which are curves in the thermodynamic phase diagram of approximately invariant physics. We study numerically one isomorph in the isotropic phase and one in the nematic phase. In both cases, good invariance of the dynamics is demonstrated via data for the mean-square displacement and the reduced-unit time-autocorrelation functions of the velocity, angular velocity, force, torque, and first- and second-order Legendre polynomial orientational order parameters. Deviations from isomorph invariance are observed at short times for the orientational time-autocorrelation functions, which reflects the fact that the moment of inertia is assumed to be constant and thus not isomorph-invariant in reduced units. Structural isomorph invariance is demonstrated from data for the radial distribution functions of the molecules and their orientations. For comparison, all quantities were also simulated along an isochore of similar temperature variation, in which case invariance is not observed. We conclude that the thermodynamic phase diagram of the calamitic Gay-Berne model is essentially one-dimensional in the studied regions as predicted by isomorph theory, a fact that potentially allows for simplifications of future theories and numerical studies.

Two-dimensional system of hard ellipses: a molecular dynamics study

We have simulated the dynamics of a two-dimensional system of hard ellipses by event-oriented molecular dynamics in microcanonical NVE ensemble. Various quantities, namely longitudinal and transverse velocity auto-correlation functions, translational and rotational diffusion mean-squared displacements, pressure, intermediate self-scattering function, radial distribution function, and angular spatial correlation, have been obtained and their dependence on packing fraction is characterized. Despite absence of prominent positional ordering, the orientational degree of freedom behaves nontrivially and exhibits interesting features. Slowing down is observed in the angular part of the motion near isotropic-nematic phase transition. It is shown that above a certain packing fraction the rotational mean-squared displacement exhibits a three-stage temporal regime including a plateau. Comparison to 2D system of hard needles is made and it is shown that from positional viewpoint, the ellipse system is more ordered.

Isotropic and nematic phases of the hard spheroid fluid: a virial approach

We use a high level virial expansion to investigate the properties of the isotropic and nematic phases of the hard spheroid fluid. We use the Monte Carlo techniques described previously to calculate the virial coefficients up to seventh order and we represent the dependence of these coefficients on particle orientations via a spherical harmonic expansion. The expansion coefficients are determined using Lebedev quadrature which carries out the angular integration required exactly. For fairly spherical spheroids (1/3<a/b<3, where a and b are the semiaxes of the spheroid) the virial expansion appears to be convergent in both the isotropic and nematic phases up to high density. For more aspherical particles, the predictions varied in a more erratic fashion upon increasing the number of virials. The use of a finite angular basis set to represent the orientationally dependent virial coefficients could be a contributory cause to this.

Temporal and structural characteristics of a two-dimensional gas of hard needles

We have simulated the dynamics of a 2D gas of hard needles by event-oriented molecular dynamics. Various quantities namely translational and rotational diffusion constants and intermediate self-scattering function have been explored and their dependence on density is obtained. Despite absence of positional ordering, the rotational degree of freedom behaves nontrivially. Slowing down is observed in the angular part of the motion. It is shown that above a certain density the rotational mean-square displacement exhibits a three-stage regime including a plateau.

Mesh-free modeling of liquid crystals using modified smoothed particle hydrodynamics

We present a generalization of the modified smooth particle hydrodynamics simulation technique capable of simulating static and dynamic liquid crystalline behavior. This generalization is then implemented in the context of the Qian-Sheng description of nematodynamics. To test the method, we first use it to simulate switching in both a Fréedericksz setup and a chiral hybrid aligned nematic cell. In both cases, the results obtained give excellent agreement with previously published results. We then apply the technique in a three-dimensional simulation of the switching dynamics of the post aligned bistable nematic device.

Nonuniform liquid-crystalline phases of parallel hard rod-shaped particles: From ellipsoids to cylinders

In this article we consider systems of parallel hard superellipsoids, which can be viewed as a possible interpolation between ellipsoids of revolution and cylinders. Superellipsoids are characterized by an aspect ratio and an exponent alpha (shape parameter) which takes care of the geometry, with alpha=1 corresponding to ellipsoids of revolution, while alpha=infinity is the limit of cylinders. It is well known that, while hard parallel cylinders exhibit nematic, smectic, and solid phases, hard parallel ellipsoids do not stabilize the smectic phase, the nematic phase transforming directly into a solid as density is increased. We use computer simulation to find evidence that for alpha>or=alpha(c), where alpha(c) is a critical value which the simulations estimate to be approximately 1.2-1.3, the smectic phase is stabilized. This is surprisingly close to the ellipsoidal case. In addition, we use a density-functional approach, based on the Parsons-Lee approximation, to describe smectic and columnar orderings. In combination with a free-volume theory for the crystalline phase, a theoretical phase diagram is predicted. While some qualitative features, such as the enhancement of smectic stability for increasing alpha and the probable absence of a stable columnar phase, are correct, the precise location of coexistence densities is quantitatively incorrect.

Energy landscape of a model discotic liquid crystal

The potential energy surface of a model discotic liquid crystal is investigated across mesophases as a function of temperature by characterizing the local potential energy minima. The average depth of the minima sampled by the system gradually grows as orientational order increases through the discotic-nematic phase upon cooling, while it remains fairly constant in the isotropic phase for isochoric temperature variation. The high-temperature Arrhenius behavior of the single-particle orientational correlation times is found to break down at a temperature that marks the onset of exploration of deeper potential energy minima. The structural features of the minima reveal an interplay between orientational and translational order, in particular, when the parent phase is discotic-nematic. The local minima then exhibit short-range columns that tend to have local hexagonal packing. The present study and recent work on calamitic liquid crystals [D. Chakrabarti and B. Bagchi, Proc. Natl. Acad. Sci. U.S.A. 103, 7217 (2006)] together reveal a striking similarity between thermotropic liquid crystals and supercooled liquids in the exploration of the energy landscape and the breakdown of Arrhenius behavior for relaxation times.

Density functional theory and simulation of the columnar phase of a system of parallel hard ellipsoids with attractive interactions

A simple molecular model consisting of parallel hard oblate ellipsoids with superimposed square-well attractive interactions of variable range is considered for the study of the phase behavior of thermotropic discotic molecules. A density functional theory appropriate for nonuniform fluids is formulated in which the hard-core contributions to the free energy are treated within a nonlocal weighted-density approximation (WDA) while the attractive contributions are treated at a mean-field level. It is shown that the columnar phase becomes stable relative to the nematic phase at fluid densities for a range of values of the range of the attractive well. In these cases, the region of stability of the columnar phase is bounded at high temperatures by a nematic-columnar-solid triple point. The calculations show that if the attractions are made too long ranged (lambda/D> or approximately =0.84 for particles of aspect ratio of L/D=0.1, where lambda/D is the range of the attractive interaction in units of the molecular diameter D), columnar ordering becomes unstable and the nematic phase dominates at all fluid densities. It is shown that columnar ordering is also predicted when the density functional theory is supplemented with the smoothed-density approximation (SDA). Computer simulations have also been carried out for a particular choice of model parameters; our simulation data confirm the stabilization of the hexagonal columnar phase between the solid and nematic phases. A comparison with simulation data allows us to conclude that the WDA provides a fairly good description of the columnar phase and very good agreement for the nematic-columnar transition properties. On the other hand, our calculations show that the SDA largely underestimates the transition pressure and predicts a too-strongly first-order nematic-columnar transition

Nematic-smectic-A phase boundary of ideally oriented Gay-Berne system: local density functional versus isothermal-isobaric Monte Carlo simulation

The main focus of the present paper is on studying the nematic-smectic- A phase boundary of an ideally oriented Gay-Berne system. The phase diagram is determined by means of an isothermal-isobaric Monte Carlo simulation. The results are compared with predictions of the local density functional expanded up to second and third order in the one-particle distribution function. It is shown that generally the second-order expansion does not give satisfactory predictions for smectics. Going beyond the leading order yields good quantitative agreement at moderate densities. With increasing density the relative error of the local density functional calculations increases, but usually does not exceed 10% in densities. We conclude that the density functional approach could be competitive to time-consuming simulations in determining phase diagrams of spatially and orientationally ordered liquid crystalline structures.

Phase and orientational ordering of low molecular weight rod molecules in a quenched liquid crystalline polymer matrix with mobile side chains

We study the phase diagram and orientational ordering of guest liquid crystalline (LC) rods immersed in a quenched host made of a liquid crystalline polymer (LCP) matrix with mobile side chains. The LCP matrix lies below the glass transition of the polymer backbone. The side chains are mobile and can align to the guest rod molecules in a plane normal to the local LCP chain contour. A field theoretic formulation for this system is proposed and the effects of the LCP matrix on LC ordering are determined numerically. We obtain simple analytical equations for the nematic/isotropic phase diagram boundaries. Our calculation show a nematic-nematic (N/N) first order transition from a guest stabilized to a guest-host stabilized region and the possibility of a reentrant transition from a guest stabilized nematic region to a host only stabilized regime separated by an isotropic phase. A detailed study of thermodynamic variables and interactions on orientational ordering and phases is carried out and the relevance of our predictions to experiments and computer simulations is presented.

Kinetic theory of dense fluids of rigid biaxial ellipsoids

The transport equation for a one-particle distribution function f of a pure and dense fluid composed of hard biaxial ellipsoids has been derived by the Enskog method through a modification of the Taxman equation which describes the corresponding low-density fluid. The equation for f has been utilized in obtaining approximate equations of continuity, linear momentum, and energy of the dense fluid, and has then been solved through the Enskog infinite series expansion technique, and a second-order approximate formula for f has been achieved. Using this, results are derived for the hydrodynamic pressure, shear and bulk viscosity coefficients, and heat conductivity of the fluid. Fast exchange of energy between the translational and rotational motions is assumed throughout the calculation. The quantities ultimately appearing in the results, which cannot further be reduced analytically and require numerical evaluation, are the four-dimensional quadratures over the orientational coordinates of two interacting rigid ellipsoidal molecules. In the appropriate limit, all results reduce to those obtained by Enskog for a dense fluid of hard spheres, and a first-order modified Eucken-type formula for the dense fluid emerges.