Computer Simulations of Cylindrically Confined Nematics

Elastic response and phase behavior in binary liquid crystal mixtures

Utilizing density-of-states simulations, we perform a full mapping of the phase behavior and elastic responses of binary liquid crystalline mixtures represented by the multicomponent Lebwohl-Lasher model. Our techniques are able to characterize the complete phase diagram, including nematic-nematic phase separation predicted by mean-field theories, but previously not observed in simulations. Mapping this phase diagram permits detailed study of elastic properties across the miscible nematic region. Importantly, we observe for the first time local phase separation and disordering driven by the application of small linear perturbations near the transition temperature and more significantly through nonlinear stresses. These findings are of key importance in systems of blended nematics which contain particulate inclusions, or are otherwise confined.

Field-driven dynamics of nematic microcapillaries

Polymer-dispersed liquid-crystal (PDLC) composites long have been a focus of study for their unique electro-optical properties which have resulted in various applications such as switchable (transparent or translucent) windows. These composites are manufactured using desirable "bottom-up" techniques, such as phase separation of a liquid-crystal-polymer mixture, which enable production of PDLC films at very large scales. LC domains within PDLCs are typically spheroidal, as opposed to rectangular for an LCD panel, and thus exhibit substantially different behavior in the presence of an external field. The fundamental difference between spheroidal and rectangular nematic domains is that the former results in the presence of nanoscale orientational defects in LC order while the latter does not. Progress in the development and optimization of PDLC electro-optical properties has progressed at a relatively slow pace due to this increased complexity. In this work, continuum simulations are performed in order to capture the complex formation and electric field-driven switching dynamics of approximations of PDLC domains. Using a simplified elliptic cylinder (microcapillary) geometry as an approximation of spheroidal PDLC domains, the effects of geometry (aspect ratio), surface anchoring, and external field strength are studied through the use of the Landau-de Gennes model of the nematic LC phase.

Computer simulations of the ordering in a hybrid cylindrical film of nematic liquid crystals

We present an investigation of the ordering in a nematic liquid-crystal film confined between two cylindrical surfaces with antagonistic (radial and planar) anchoring alignments. A Monte Carlo study of a Lebwohl-Lasher model with suitable boundary conditions has been performed to calculate the ordering and the molecular organization for different film thicknesses. The simulation results are compared with some theoretical predictions obtained with the elastic continuum approach. The agreement between theory and simulation is improved as the thickness decreases.

Competition between capillarity, layering and biaxiality in a confined liquid crystal

The effect of confinement on the phase behaviour and structure of fluids made of biaxial hard particles (cuboids) is examined theoretically by means of Onsager second-order virial theory in the limit where the long particle axes are frozen in a mutually parallel configuration. Confinement is induced by two parallel planar hard walls (slit-pore geometry), with particle long axes perpendicular to the walls (perfect homeotropic anchoring). In bulk, a continuous nematic-to-smectic transition takes place, while shape anisotropy in the (rectangular) particle cross-section induces biaxial ordering. As a consequence, four bulk phases, uniaxial and biaxial nematic and smectic phases, can be stabilised as the cross-sectional aspect ratio is varied. On confining the fluid, the nematic-to-smectic transition is suppressed, and either uniaxial or biaxial phases, separated by a continuous transition, can be present. Smectic ordering develops continuously from the walls for increasing particle concentration (in agreement with the supression of nematic-smectic second-order transition at confinement), but first-order layering transitions, involving structures with n and n + 1 layers, arise in the confined fluid at high concentration. Competition between layering and uniaxial-biaxial ordering leads to three different types of layering transitions, at which the two coexisting structures can be both uniaxial, one uniaxial and another biaxial, or both biaxial. Also, the interplay between molecular biaxiality and wall interactions is very subtle: while the hard wall disfavours the formation of the biaxial phase, biaxiality is against the layering transitions, as we have shown by comparing the confined phase behaviour of cylinders and cuboids. The predictive power of Onsager theory is checked and confirmed by performing some calculations based on fundamental-measure theory.

Discotic molecules in cylindrical nanopores: a Monte Carlo study

We report Monte Carlo simulations of a model discotic molecule embedded in cylindrical pores. We consider a planar anchoring of the molecules on the surface for two different cylinder radii: R(*) = 5 and R(*) = 10 , in units of the molecular diameter. For both radii, we note that the system is progressively structured in concentric shells when decreasing the temperature. With the small radius, we observe continuous transitions from an isotropic to a nematic phase and then to a crystal one. The radius of the pores is sufficiently small to force the crystal to grow along their main axis. However some orientational discrepancies are observed: some samples present a zigzag configuration. With the big radius, the situation is more complex and it is likely that different scenarios are available. The crystals can be built along the main axis of the cylinders, as for the small radius, but also in any other direction. Thus we observe samples with different orientational domains. In the case of crystals oriented along the nanopore axis, we note that only the first 5 shells close to the wall are sensitive to it.

Surface-induced morphology and free-energy pathways in breakup of a nematic liquid crystalline cylinder

We compute the surface-induced morphology and the free-energy pathways as a cylindrical liquid crystalline filament with preferred homeotropic (orthogonal) interface orientation passes through a sequence of growing sinusoidal perturbations and breaks up into droplets. Liquid crystalline morphology is determined using a simulated annealing algorithm [R. K. Goyal and M. M. Denn, Phys. Rev. E, 75, 021704 (2007)] to minimize the Oseen-Frank free energy. A first-order morphological transition with a finite energy barrier is required when the perturbation amplitude exceeds a critical value, and it is possible that progress towards breakup will be kinetically trapped in a varicose cylindrical shape. This result may be related to the apparent kinetic trapping of dispersed nematic 4'-octyl-4-biphenylcarbonitrile in a gel state reported by Inn and Denn [J. Rheol., 49, 887 (2005)].

Annihilation of nematic point defects: postcollision scenarios

We perform a study of the annihilation of a nematic radial and hyperbolic point defects with the main focus on the confinement induced collision and postcollision scenarios. Brownian molecular dynamics on a semimicroscopic lattice is used. Initially a pair of defects, separated for 1.4-1.7 radii, is induced at the axis of the cylindrical capillary. In such a configuration defects start to approach slowly. In the early stage, their cores are negligibly influenced by the mutual interaction. When the distance becomes comparable to the nematic correlation length, the cores significantly deform. In the collision regime, defects gradually merge. We observe two qualitatively different scenarios in the postcollision regime, depending on the degree of (meta) stability of the initially imposed escaped structure with point defects.

Surface extrapolation length and director structures in confined nematics

We report the results of Monte Carlo simulations of the Lebwohl-Lasher model of nematic liquid crystals confined to cylindrical cavities with homeotropic anchoring. We show that the ratio of the bulk to surface couplings is not in general equal to the corresponding parameter K/W used in elastic theory (where K is the Frank elastic constant in the one-constant approximation and W is the surface anchoring strength). By measuring the temperature dependence of K/W (which is equivalent to the surface extrapolation length) we are able to reconcile the results of our simulations as well as others with the predictions of elastic theory. We find that the rate at which we cool the system from the isotropic to nematic phase plays a crucial role in the development of the final director structure, because of a large free energy barrier separating different director structures as well as the temperature dependence of K/W. With a suitably fast cooling rate we are able to keep the system out of a metastable planar state and form an escaped radial structure for large enough systems. Copyright 2000 The American Physical Society.