Search

This article reviews recent progress in the computer simulation of liquid crystals at the molecular level. It covers the use of simple rigid-body models of the constituent molecules, and more detailed modelling via atomistic force fields. Bulk mesophases, inhomogeneous systems, and interfaces are discussed. Recent progress in calculating elastic properties and dynamics is summarised. As well as presenting an overview, some specific topics of recent interest are highlighted: the biaxial nematic phase, chiral phases, ionic liquid crystals, and charge-transfer systems. [ABSTRACT FROM AUTHOR]

In this paper we present a molecular dynamics calculation of the Frank elastic constants of a nematic liquid crystal. We study two well-known variants of the Gay--Berne potential, and determine the elastic constants by measuring orientational fluctuations as a function of wave vector, using reasonably large system sizes in the range 1000-8000 molecules. For some of the simulations, a set of Lagrangian constraints was applied in order to keep the director fixed along one of the box axes, facilitating the measurement of fluctuations in components of the reciprocal-space order tensor &Qcirc;(k) in the director frame. [ABSTRACT FROM AUTHOR]

In this paper, we present molecular dynamics calculations of the Frank elastic constants, and associated time correlation functions, in nematic liquid crystals. We study two variants of the Gay–Berne potential, and use system sizes of half a million molecules, significantly larger than in previous studies of elastic behaviour. Equilibrium orientational fluctuations in reciprocal (k-) space were calculated, to determine the elastic constants by fitting at low |k|; our results indicate that small system size may be a source of inaccuracy in previous work. Furthermore, the dynamics of the Gay–Berne nematic were studied by calculating time correlation functions of components of the order tensor, together with associated components of the velocity field, for a set of wave vectorsk. Confirming our earlier work, we found exponential decay for splay and twist correlations, and oscillatory exponential decay for the bend correlation. In this work, we confirm similar behaviour for the corresponding velocity components. In all cases, the decay rates, and oscillation frequencies, were found to be accurately proportional tok2for smallk, as predicted by the equations of nematodynamics. However, the observation of oscillatory bend fluctuations, and corresponding oscillatory shear flow decay, is in contradiction to the usual assumptions appearing in the literature, and in standard texts. We discuss the advantages and drawbacks of using large systems in these calculations. [ABSTRACT FROM PUBLISHER]

Supercooled colloidal or molecular systems at low densities are known to form liquid, crystalline or glassy drops, which may remain isolated for a long time before they aggregate. This paper analyses the properties of this large time window, and how it can be tackled by computer simulation. We use single-particle and virtual move Monte Carlo simulations of short-range attractive spheres which are undercooled to the temperature region, where the spinodal intersects the attractive glass line. We study two different systems and we report the following kinetic behavior. A low-density system is shown to exhibit universal linear growth regimes under single-particle Monte Carlo correlating the growth rate to the local structure. These regimes are suppressed under collective motion, where droplets aggregate into a single large disordered domain. It is shown that the aggregation can be avoided and linear regimes recovered, if long-range repulsion is added to the short-range attraction. The results provide an insight into the behavior of the virtual move algorithm generating cluster moves according to the local forcefields. We show that different choices of maximum Monte Carlo displacement affect the dynamical trajectories but lead to the same kinetically slowed down or arrested states. Graphical abstract: [ABSTRACT FROM AUTHOR]

We show, by molecular simulation, that for a range of standard, coarse-grained, nematic liquid crystal models, the director bend fluctuation is a propagating mode. This is in contrast to the generally accepted picture of nematic hydrodynamics, in which all the director modes (splay, twist, bend, and combinations thereof) are overdamped. By considering the various physical parameters that enter the equations of nematodynamics, we propose an explanation of this effect and conclude that propagating bend fluctuations may be observable in some experimental systems. [ABSTRACT FROM AUTHOR]

Virtual move Monte Carlo is a cluster algorithm which was originally developed for strongly attractive colloidal, molecular, or atomistic systems in order to both approximate the collective dynamics and avoid sampling of unphysical kinetic traps. In this paper, we present the algorithm in the form, which selects the moving cluster through a wider class of virtual states and which is applicable to general pairwise interactions, including hard-core repulsion. The newly proposed way of selecting the cluster increases the acceptance probability by up to several orders of magnitude, especially for rotational moves. The results have their applications in simulations of systems interacting via anisotropic potentials both to enhance the sampling of the phase space and to approximate the dynamics. [ABSTRACT FROM AUTHOR]

We highlight some links between molecular dynamics and Monte Carlo algorithms used to simulate condensed matter systems. Special attention is paid to the question of sampling the desired statistical ensemble. [ABSTRACT FROM AUTHOR]

A thermostat of the Nosé-Hoover type, based on relative velocities and a local definition of the temperature, is presented. The thermostat is momentum-conserving and Galilean-invariant, which should make it suitable for use in Dissipative Particle Dynamics (DPD) simulations, as well as nonequilibrium molecular dynamics simulations. [ABSTRACT FROM AUTHOR]

Expressions for intermolecular forces and torques, derived from pair potentials between rigid non-spherical units, are presented. The aim is to give compact and clear expressions, which are easily generalized, and which minimize the risk of error in writing molecular dynamics simulation programs. It is anticipated that these expressions will be useful in the simulation of liquid crystalline systems, and in coarse-grained modelling of macromolecules. [ABSTRACT FROM AUTHOR]

Transport properties of isotropic fluids composed of hard ellipsoids of revolution are studied using molecular dynamics simulation. The self-diffusion coefficient, the shear viscosity, and the thermal conductivity are evaluated for a range of densities and elongations and are compared with the results from an Enskog kinetic theory for nonspherical bodies. The full anisotropic pair correlation function, which is required input in an Enskog kinetic theory, can be obtained from simulation or can be approximated. If the pair correlation function is taken as isotropic on the contact surface, with a contact value derived from an accurate equation of state, the resulting kinetic theory transport properties agree to within a few percent of those calculated on the basis of the exact pair correlation function. The simulation and the kinetic theory values for the shear viscosity and the thermal conductivity show the same qualitative behavior, i.e., increasing with density and with particle nonsphericity. Quantitatively, there is good agreement at low densities (up to 30% of closest packing); at higher densities (60% of closest packing), deviations from Enskog theory are larger than and in the opposite direction to those seen for hard spheres. The Stokes–Einstein and Debye relations are tested and indicate a transition from a kinetic theory region towards the hydrodynamic limit as density increases. [ABSTRACT FROM AUTHOR]

We investigate the defect structures forming around two nanoparticles in a Gay-Berne nematic liquid crystal using molecular simulations. For small separations, disclinations entangle both particles forming the figure of eight, the figure of omega and the figure of theta. These defect structures are similar in shape and occur with a comparable frequency to micron-sized particles studied in experiments. The simulations reveal fast transitions from one defect structure to another suggesting that particles of nanometre size cannot be bound together effectively. We identify the 'three-ring' structure observed in previous molecular simulations as a superposition of the different entangled and non-entangled states over time and conclude that it is not itself a stable defect structure. [ABSTRACT FROM AUTHOR]

We present in this paper a computer simulation study of the phase behavior of the Gay–Berne liquid crystal model. The effect of the anisotropic attractive interactions on stabilizing orientationally ordered phases is analyzed by varying the anisotropy parameter κ′ at fixed values of the molecular elongation parameter κ. Molecular dynamics simulations have been performed at constant density and temperature along several isotherms and approximate transition densities are reported. It is found that, for a given value of the molecular elongation κ=3, smectic order is favored at lower densities as κ′ increases. When κ′ is lowered, the smectic phase is preempted by the nematic phase. As a result, the nematic phase becomes increasingly stable at lower temperatures as κ′ is decreased. Additionally, we have studied the liquid–vapor coexistence region for different values of κ′ by using Gibbs ensemble and Gibbs–Duhem Monte Carlo techniques. We have found evidence of a vapor–isotropic–nematic triple point for κ′=1 and κ′=1.25. For temperatures below this triple point, we have observed nematic–vapor coexistence as is found for many liquid crystals in experiments. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The frequency-dependent shear viscosity η(ω) and the shear-orientation coupling parameter R are calculated for fluids of hard prolate ellipsoids of revolution, using kinetic theory and molecular dynamics. Two effects which contribute to the shear viscosity are considered. First, the D∞h particle symmetry influences both the spectrum of the collision operator and the multi-Lorentzian decay of η(ω). These multiple decays are most important at low densities for elongated particles. Second, coupling between the stress tensor and the collective molecular orientation leads to a minimum in η(ω) between its zero-frequency limit η and its infinite-frequency plateau value η∞. At densities approaching the transition to a nematic phase, the zero-frequency shear viscosity is predicted to be dominated by its infinite-frequency plateau value, i.e., η/η∞∼1. Molecular dynamics simulations, extended to longer times than those previously reported, confirm the existence of the dip in η(ω) and the importance of stress-orientation coupling in determining the value of η. Discrepancies previously thought to exist between simulation and theory are attributed to this coupling between the stress and slow collective reorientation; we now obtain good agreement between simulation and theory at low and moderate densities. The kinetic theory predicts the position of the dip quite well, but underestimates its magnitude for elongated particles at medium and high densities.The theory also predicts a weak density dependence of the shear-orientation coupling parameter R, and a decrease in this parameter with increasing elongation, whereas the simulations show a steady increase in R with both density and elongation. Moreover, the ratio η/η∞ falls below unity, rather than approaching unity, as the density increases, in several of the cases studied. The Stokes–Einstein relation and... [ABSTRACT FROM AUTHOR]

We have calculated the direct correlation function, c(1, 2), via a high-order virial expansion, for systems of hard spheres and spheroids, in both the isotropic and nematic phases. For hard spheres, we find that truncation at sixth order in density gives good agreement with simulation data. Close to freezing, the virial series still appears to converge to the simulation results, but there are significant discrepancies, particularly at very small separations. In the non-overlap region, the virial theory begins to capture the features found from simulation. We also calculate the pair distribution function, g(1, 2), from our estimates of c(1, 2), and find good agreement with simulation data at all densities up to freezing. For hard, prolate spheroids of aspect ratio 3 : 1, we calculate c(1, 2) and g(1, 2) in the isotropic phase, again finding good agreement with simulation data at moderate densities. Finally, we present the result of our calculations on c(1, 2) for 3 : 1 spheroids in the nematic phase. [ABSTRACT FROM AUTHOR]