Long term phase separation dynamics in liquid crystal-enriched microdroplets obtained from binary fluid mixtures.

The dynamics of long term phase separation in binary liquid mixtures remains a subject of fundamental interest. Here, we study a binary liquid mixture, where the minority phase is confined to a liquid crystal (LC)-rich droplet, by investigating the evolution of size, defect and mesogen alignment over time. We track the binary liquid mixture evolving towards equilibrium by visualising the configuration of the liquid crystal droplet through polarisation microscopy. We compare our experimental findings with computational simulations and elucidate differences between bulk phases and confined droplets based on the respective thermodynamics of phase separation. Our work provides insights on how phase transitions on the microscale can deviate from bulk phase diagrams with relevance to other material systems, such as the liquid-liquid phase separation of polymer and protein solutions.

Chiral nematic liquid crystals in torus-shaped and cylindrical cavities.

We present a Monte Carlo simulation study of chiral nematic liquid crystals confined in torus-shaped and cylindrical cavities. For an achiral nematic with planar degenerate anchoring confined to a toroidal or cylindrical cavity, the ground state is defect free, with an untwisted director field. As chirality is introduced, the ground state remains defect free but the director field becomes twisted within the cavity. For homeotropic anchoring, the ground state for an achiral nematic within a toroidal cavity consists of two disclination rings, one large and one small, that follow the major circumference of the torus. As chirality is introduced and increased, this ground state becomes unstable with respect to twisted configurations. The closed nature of the toroidal cavity requires that only a half integer number of twists can be formed and this leads to the ground state being either a single disclination line that encircles the torus twice or a pair of intertwined disclination rings forming stable, knotted defect structures.

Ionic N-phenylpyridinium tetracatenar mesogens: competing driving forces in mesophase formation and unprecedented difference in phase stabilisation within a homologous series.

Ionic, tetracatenar liquid crystals containing an N-phenylpyridinum core are described; many of these compounds display a SmA phase, something extremely rare in tetracatenar materials. The competing forces driving mesophase formation lead to an unprecedented difference in phase stabilities for SmA and Colh phases.

Monte Carlo simulations of nematic and chiral nematic shells.

We present a systematic Monte Carlo simulation study of thin nematic and cholesteric shells with planar anchoring using an off-lattice model. The results obtained using the simple model correspond with previously published results for lattice-based systems, with the number, type, and position of defects observed dependent on the shell thickness with four half-strength defects in a tetrahedral arrangement found in very thin shells and a pair of defects in a bipolar (boojum) configuration observed in thicker shells. A third intermediate defect configuration is occasionally observed for intermediate thickness shells, which is stabilized in noncentrosymmetric shells of nonuniform thickness. Chiral nematic (cholesteric) shells are investigated by including a chiral term in the potential. Decreasing the pitch of the chiral nematic leads to a twisted bipolar (chiral boojum) configuration with the director twist increasing from the inner to the outer surface.

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.

Defect coalescence in spherical nematic shells.

We study coalescence of topological defects in nematic liquid crystals confined to spherical shells using both experiments and computer simulations. We observe that the four s=+1/2 defects that are present due to topological constraints imposed by the spherical geometry coalesce by pairs after changing the molecular orientation at the outer surface from tangential to perpendicular; the result is the formation of two single s=+1 defects. It is noteworthy that the speed of the coalescence process is peaked when the defects are at opposite points on the equator of the shell; this maximum results from the thickness inhomogeneity of the shells.

Dissipative particle dynamics simulation of quaternary bolaamphiphiles: multi-colour tiling in hexagonal columnar phases.

We use dissipative particle dynamics simulations to examine the phase behaviour of X-shaped quaternary bolaamphiphiles. These molecules are composed of a rod-shaped core, with polar groups at each end and two different lateral chains. We show that, as for ternary bolaamphiphiles, square and hexagonal columnar phases are observed. The micro-phase segregation in the four-block systems leads to neighbouring columns containing different types of chain. For a square columnar phase, this does not present a problem. For hexagonal systems, however, this necessarily leads to frustration, and we discuss how the molecular structure can influence the way this frustration is relieved.

Computer simulation and high level virial theory of Saturn-ring or UFO colloids.

Monte Carlo simulations are used to map out the complete phase diagram of hard body UFO systems, in which the particles are composed of a concentric sphere and thin disk. The equation of state and phase behavior are determined for a range of relative sizes of the sphere and disk. We show that for relatively large disks, nematic and solid phases are observed in addition to the isotropic fluid. For small disks, two different solid phases exist. For intermediate sizes, only a disordered fluid phase is observed. The positional and orientational structure of the various phases are examined. We also compare the equations of state and the nematic-isotropic coexistence densities with those predicted by an extended Onsager theory using virial coefficients up to B(8).

Nematic ordering and defects on the surface of a sphere: a Monte Carlo simulation study.

We examine the ordering of hard rods on the surface of a sphere using computer simulations. As predicted by previous theories of thin nematic shells we observe four s = + 1/2 defects. However, the predicted tetrahedral symmetry for the defects and the "baseball" director configuration is not observed. Instead the four defects are located, on average, on a great circle which splits the sphere into two hemispheres, each of which has a splay dominated director configuration. We argue that this result occurs as the bend elastic constant for hard rods is much larger than the splay elastic constant.

Influence of flexibility on the biaxial nematic phase of bent core liquid crystals: a Monte Carlo simulation study.

The influence of flexibility on the phase behavior of bent core biaxial nematic liquid crystals is investigated using Monte Carlo simulation. A generic model for rigid V-shaped molecules is extended to include a bending potential, which allows us to investigate the relationship between the flexibility of a bent core molecule and its ability to form a biaxial nematic phase. The simulation results indicate that, as the flexibility is increased, the biaxial nematic phase is typically forced to lower temperatures. In contrast, the stability of the uniaxial nematic phase with respect to the isotropic phase is not significantly affected. The Landau point is split into a line of first order phase transitions between two different uniaxial phases. In some cases, the uniaxial nematic to biaxial nematic transition becomes first order, and a shape change is observed at this transition.

Biaxial nematic phases and V-shaped molecules: a Monte Carlo simulation study.

Inspired by recent claims that compounds composed of V-shaped molecules can exhibit the elusive biaxial nematic phase, we have developed a generic simulation model for such systems. This contains the features of the molecule that are essential to its liquid crystal behavior, namely the anisotropies of the two arms and the angle between them. The behavior of the model has been investigated using Monte Carlo simulations for a wide range of these structural parameters. This allows us to establish the relationship between the V-shaped molecule and its ability to form a biaxial nematic phase. Of particular importance are the criteria of geometry and the relative anisotropy necessary for the system to exhibit a Landau point, at which the biaxial nematic is formed directly from the isotropic phase. The simulations have also been used to determine the orientational order parameters for a selection of molecular axes. These are especially important because they reveal the phase symmetry and are connected to the experimental determination of this. The simulation results show that, whereas some positions are extremely sensitive to the phase biaxiality, others are totally blind to this.

Biaxial nematics: computer simulation studies of a generic rod-disc dimer model.

One possible route to the elusive biaxial nematic phase is through rod-disc dimers in which the rod and disc mesogenic units are linked via a flexible spacer. We have developed a continuous generic model of such rod-disc dimers in which neighbouring like groups tend to align parallel to each other while unlike groups tend to be orthogonal. A torsional potential controls the relative orientations of the groups within a single dimer; depending on the strength of the torsional potential, the groups may be orthogonal or parallel in the conformational ground state. Monte Carlo simulations show that a rigid rod-disc dimer is most likely to form a biaxial nematic phase if the anisotropies of the two groups are the same. Introduction of flexibility is found to have little effect on the qualitative behaviour of the dimer as the relative anisotropy of the two mesogenic groups is changed. However, when the torsional potential strongly favours the alignment of the rod and disc within a single molecule with their symmetry axes parallel there is a dramatic change. The system then exhibits a strong hysteresis in the molecular shape and biaxiality and the biaxial nematic-isotropic transition becomes strongly first order, in marked contrast to the second-order character usually found for this transition. This first-order transition is observed to occur for a range of relative anisotropies of the two groups rather than at a single point.

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.

Coarse grained models for flexible liquid crystals: parameterization of the bond fluctuation model.

We extend the bond fluctuation model, originally devised to investigate polymer systems, to contain anisotropic interactions suitable for the simulation of large flexible molecules such as liquid crystalline polymers and dendrimers. This extended model coarse grains the interaction between the flexible chains at a similar level of detail to the mesogenic units. Suitable interaction parameters are obtained by performing trial simulations on a low molar mass liquid crystalline system. The phase diagram of this system is determined as a function of the molecular stiffness. The nematic to isotropic transition temperature is found to increase with increasing stiffness.

Phase behavior and free interfaces of a lattice-gas nematic-liquid-crystal model.

The phase behavior of a mesogenic lattice-gas model consisting of molecules located at the sites of a three-dimensional cubic lattice has been studied using grand canonical Monte Carlo simulations. When two neighboring sites are occupied, the molecules interact via a potential composed of an isotropic lattice-gas (LG) term and an anisotropic Humphries-Luckhurst-Romano (HLR) term [Mol. Phys. 42, 1205 (1981)]. The LGHLR model is shown to exhibit either nematic-isotropic, nematic-vapor (NV), and isotropic-vapor (IV) coexistence or just nematic-isotropic fluid coexistence, depending on the strength of the isotropic term. The liquid-vapor (i.e., NV and IV) interfaces were studied using canonical Monte Carlo simulations. By controlling the strength of the term that governs the anisotropy in the attractive forces, either planar or homeotropic anchoring is observed at the NV interface. The temperature dependencies of the density and order parameter profiles across the interfaces are determined for these two anchoring geometries.