Martin A. Bates

Computer simulation studies of anisotropic systems. XXX. The phase behavior and structure of a Gay–Berne mesogen

The Gay–Berne potential is proving to be a valuable model with which to investigate the behavior of liquid crystals using computer simulation techniques. The potential contains four independent parameters which control the anisotropy in the attractive and repulsive interactions. The choice of these parameters is not straightforward and it would seem that those employed in some simulations are not strictly appropriate for mesogenic rodlike molecules. Here we report a detailed computer simulation study of Gay–Berne particles interacting via a potential parametrized to reflect the anisotropic forces based on a fit to a realistic mesogenic molecule. The behavior of the phases and the transitions between them have been investigated for a system of 2000 particles using isothermal–isobaric Monte Carlo simulations. At low pressures, this Gay–Berne mesogen exhibits isotropic, smectic A and smectic B phases but, as the pressure is increased, so a nematic phase is added to the sequence. The nature of the phase trans...

Phase behavior of two-dimensional hard rod fluids

Monte Carlo simulations are used to study two-dimensional hard rod fluids consisting of spherocylinders confined to lie in a plane. The phase behavior is mapped out as a function of the aspect ratio (L/D) of the particles, from the hard disc limit at one extreme (L/D=0) to the thin hard needle limit at the other (L/D=∞). For long rods, a 2D nematic phase is observed at high density in which the orientational correlation functions decay algebraically, indicating that the phase does not possess true long range orientational order. The simulation data indicate that the transition from this phase to the low density isotropic phase is continuous, via a Kosterlitz–Thouless disclination unbinding type mechanism, rather than first order. For short rods the nematic phase disappears so that, on expansion, the solid phase undergoes a first order transition directly to an isotropic phase. Although the latter phase is globally isotropic, we find evidence for strong local positional and orientational correlations betwe...

Nematic–isotropic transition in polydisperse systems of infinitely thin hard platelets

We study the phase behavior of model colloidal systems composed of infinitely thin hard platelets, with polydispersity in the size of the particles. Semi-grand Gibbs ensemble simulations are used to study the coexisting nematic and isotropic phases for a range of systems with varying polydispersity. Particle size segregation is observed in the two coexisting phases, with the larger particles tending to be found in the nematic phase. This fractionation becomes more evident with increasing polydispersity. We examine the relationship between the size of a particle and its orientation in the nematic phase and find that the larger particles tend to be more orientationally ordered than the smaller ones. The coexistence densities determined from the simulations are compared to those obtained from recent experiments on colloidal platelets.

Computer simulation studies of anisotropic systems. XXVI. Monte Carlo investigations of a Gay–Berne discotic at constant pressure

The majority of molecules which form liquid crystals are elongated in shape. However, disk shaped molecules have also been shown to exhibit liquid crystalline phases. In this paper we report a series of constant pressure Monte Carlo simulations of model discotic molecules. We have used the Gay–Berne potential, which is in essence an anisotropic version of a shifted Lennard‐Jones potential, to model the interactions between the disks. Initially we studied a system of 512 molecules over a range of pressures to determine the mesophases formed and to construct the phase diagram. The system was found to exhibit isotropic, nematic, and columnar phases. We have also studied a larger system of 2000 molecules at a single pressure to calculate more accurately the distribution functions used to describe the translational and orientational order within the various phases.

Influence of polydispersity on the phase behavior of colloidal liquid crystals: A Monte Carlo simulation study

Using isobaric semigrand Monte Carlo simulations, we have investigated the phase behavior of a model for polydisperse rodlike colloids. The system consists of hard spherocylinders in the limit of infinite aspect ratio, with polydispersity in the length of the particles. If the polydispersity is small (standard deviation s<0.08), the phase behavior is essentially unchanged from that observed in monodisperse systems; thus nematic, smectic, and crystal phases are exhibited. For an intermediate range of polydispersities (0.08<s<0.18), the smectic phase is found to become increasingly destabilized with respect to the nematic phase at low densities and a columnar phase at high densities. This eventually leads to a terminal polydispersity (s≈0.18) above which the smectic phase is no longer stable. Beyond this value, only nematic and columnar phases are observed.

Computer simulation studies of anisotropic systems. The density and temperature dependence of the second rank orientational order parameter for the nematic phase of a Gay–Berne liquid crystal

Abstract The relative importance of anisotropic repulsive and attractive forces in stabilising a nematic liquid crystal may be assessed from the thermodynamic parameter Γ =−( ∂ ln T / ∂ ln V ) 〈 P 2 〉 , where 〈 P 2 〉 is the second rank orientational order parameter. A previous attempt to determine this quantity for the nematic phase of a Gay–Berne system has given a value about twice as large as that found experimentally. Here we report the determination of Γ from an extensive simulation study for a Gay–Berne system with parameters more appropriate for mesogenic molecules than those selected originally.

Stable nematic droplets with handles

We stabilize nematic droplets with handles against surface tension-driven instabilities, using a yield-stress material as outer fluid, and study the complex nematic textures and defect structures that result from the competition between topological constraints and the elasticity of the nematic liquid crystal. We uncover a surprisingly persistent twisted configuration of the nematic director inside the droplets when tangential anchoring is established at their boundaries, which we explain after considering the influence of saddle splay on the elastic free energy. For toroidal droplets, we find that the saddle-splay energy screens the twisting energy, resulting in a spontaneous breaking of mirror symmetry; the chiral twisted state persists for aspect ratios as large as ∼20. For droplets with additional handles, we observe in experiments and computer simulations that there are two additional −1 surface defects per handle; these are located in regions with local saddle geometry to minimize the nematic distortions and hence the corresponding elastic free energy.

Defects and ordering in nematic coatings on uniaxial and biaxial colloids

We present a systematic lattice Monte Carlo simulation study of nematic ordering in thin nematic shells on uniaxial and biaxial colloidal particles. Typically, four mutually repulsive half-strength defect lines penetrating the shell are observed, as found for spherical particles. For shells of constant thickness, the defect lines tend to accumulate in the high curvature regions. If the thickness of the nematic coating varies across the surface, the defect lines tend to be located in the thinnest regions. On increasing the shell thickness, the defect lines transform into escaped structures with surface point defects.

Studies of translational diffusion in the smectic A phase of a Gay–Berne mesogen using molecular dynamics computer simulation

Molecular dynamics computer simulations are used to determine the self-diffusion coefficients for a Gay-Berne model mesogen GB (4.4,20,1,1) in the isotropic, nematic and smectic A phases along two isobars. The values of the parallel and perpendicular diffusion coefficients, D(parallel) and D(perpendicular), are calculated and compared in the different phases. For the phase sequence isotropic-smectic A, D(perpendicular)*> or =D(parallel)* over the whole smectic A range with the ratio D(parallel)*/D(perpendicular)* decreasing with decreasing temperature. At a higher pressure, a nematic phase is observed between these two phases and we find that D(parallel)*>D(perpendicular)* throughout the nematic region and the inequality D(parallel)*>D(perpendicular)* remains on entering the smectic A phase. However, the ratio D(parallel)*/D(perpendicular)* decreases with decreasing temperature within the smectic A range and eventually this ratio inverts such that D(perpendicular)*>D(parallel)* at low temperatures. The temperature dependence of the parallel diffusion coefficient in the smectic A phase for this model mesogen is compared to that predicted by a theoretical model for diffusion subject to a cosine potential.

Dissipative particle dynamics simulation of T- and X-shaped polyphilic molecules exhibiting honeycomb columnar phases

Dissipative particle dynamics simulations are used to investigate the structure of the columnar phases in T- and X-shaped bolaamphiphiles. These amphiphilic molecules consist of a rod-like aromatic core, with a polar group at each end. A single lateral chain is present in the T-shaped molecules and two lateral chains are present for X-shaped molecules. The simulations indicate that both types of molecules exhibit square and hexagonal columnar phases, in which the walls of the columns are formed by the aromatic core, the polar groups are located at the edges and the lateral chains fill the interiors of the columns. For the T-shaped molecules, the columns are always double walled. In contrast, for the X-shaped molecules, the columnar phases are single walled, in agreement with X-ray diffraction studies.