Wetting of Nematic Liquid Crystals on Crenellated Substrates: A Frank–Oseen Approach

We revisit the wetting of nematic liquid crystals in contact with crenellated substrates, studied previously using the Landau–de Gennes formalism. However, due to computational limitations, the characteristic length scales of the substrate relief considered in that study limited to less than 100 nematic correlation lengths. The current work uses an extended Frank–Oseen formalism, which includes not only the free-energy contribution due to the elastic deformations but also the surface tension contributions and, if disclinations or other orientational field singularities are present, their core contributions. Within this framework, which was successfully applied to the anchoring transitions of a nematic liquid crystal in contact with structured substrates, we extended the study to much larger length scales including the macroscopic scale. In particular, we analyzed the interfacial states and the transitions between them at the nematic–isotropic coexistence

Wetting of cholesteric liquid crystals

We investigate theoretically the wetting properties of cholesteric liquid crystals at a planar substrate. If the properties of substrate and of the interface are such that the cholesteric layers are not distorted the wetting properties are similar to those of a nematic liquid crystal. If, on the other hand, the anchoring conditions force the distortion of the liquid crystal layers the wetting properties are altered, the free cholesteric-isotropic interface is non-planar and there is a layer of topological defects close to the substrate. These deformations can either promote or hinder the wetting of the substrate by a cholesteric, depending on the properties of the cholesteric liquid crystal

Nematic liquid crystals on sinusoidal channels: the zigzag instability

Substrates which are chemically or topographically patterned induce a variety of liquid crystal textures. The response of the liquid crystal to competing surface orientations, typical of patterned substrates, is determined by the anisotropy of the elastic constants and the interplay of the relevant lengths scales, such as the correlation length and the surface geometrical parameters. Transitions between different textures, usually with different symmetries, may occur under a wide range of conditions. We use the Landau–de Gennes free energy to investigate the texture of nematics in sinusoidal channels with parallel anchoring bounded by nematic-air interfaces that favour perpendicular (hometropic) anchoring. In micron size channels 5CB was observed to exhibit a non-trivial texture characterized by a disclination line, within the channel, which is broken into a zigzag pattern. Our calculations reveal that when the elastic anisotropy of the nematic does not favour twist distortions the defect is a straight disclination line that runs along the channel, which breaks into a zigzag pattern with a characteristic period, when the twist elastic constant becomes sufficiently small when compared to the splay and bend constants. The transition occurs through a twist instability that drives the defect line to rotate from its original position. The interplay between the energetically favourable twist distortions that induce the defect rotation and the liquid crystal anchoring at the surfaces leads to the zigzag pattern. We investigate in detail the dependence of the periodicity of the zigzag pattern on the geometrical parameters of the sinusoidal channels, which in line with the experimental results is found to be non-linear.Portugal, Fundación para la Ciencia y la Tecnología UID / FIS / 00618/2013Portugal, Fundación para la Ciencia y la Tecnología EXCEL / FIS-NAN / 0083/2012España, Ministerio de Economía y Competitividad FIS2012-32455Junta de Andalucía P09-FQM-493

Computing the phase diagram of binary mixtures: a patchy particle case study

We investigate the phase behaviour of 2D mixtures of bi-functional and three-functional patchy particles and 3D mixtures of bi-functional and tetra-functional patchy particles by means of Monte Carlo simulations and Wertheim theory. We start by computing the critical points of the pure systems and then we investigate how the critical parameters change upon lowering the temperature. We extend the Successive Umbrella Sampling method to mixtures to make it possible to extract information about the phase behaviour of the system at a fixed temperature for the whole range of densities and compositions of interest.Comment: 13 pages, 13 figure

Nematic wetting and filling of crenellated surfaces

We investigate nematic wetting and filling transitions of crenellated surfaces (rectangular gratings) by numerical minimization of the Landau–de Gennes free energy as a function of the anchoring strength, for a wide range of the surface geometrical parameters: depth, width, and separation of the crenels. We have found a rich phase behavior that depends in detail on the combination of the surface parameters. By comparison to simple fluids, which undergo a continuous filling or unbending transition, where the surface changes from a dry to a filled state, followed by a wetting or unbinding transition, where the thickness of the adsorbed fluid becomes macroscopic and the interface unbinds from the surface, nematics at crenellated surfaces reveal an intriguingly rich behavior: in shallow crenels only wetting is observed, while in deep crenels, only filling transitions occur; for intermediate surface geometrical parameters, a new class of filled states is found, characterized by bent isotropic-nematic interfaces, which persist for surfaces structured on large scales, compared to the nematic correlation length. The global phase diagram displays two wet and four filled states, all separated by first-order transitions. For crenels in the intermediate regime re-entrant filling transitions driven by the anchoring strength are observe

Surface-induced alignment at model nematic interfaces

We have applied the generalized van der Waals theory to a model liquid crystal that includes, explicitly, all of the second-order terms in the spherical harmonic expansion of the anisotropic intermolecular potential. We have investigated the orientational order induced by each one of these terms, as well as the order resulting from the competition of various terms included in the potential. It was shown that, for appropriate choices of the relative strengths of the spherical harmonic coeKcients, the theory is capable of accounting qualitatively for all the orientational e8'ects observed at nematic interfaces, including tilted orientations. In particular, different molecular alignments at the nematic-vapor and nematic-isotropic interfaces of a given nematogen were described as the result of competing terms in the anisotropic interactions. Additionally, we have shown that temperaturedriven orientational transitions may occur in systems characterized by this type of interaction. For a given choice of parameters, we have also found an orientational transition, which is related to a wetting transition at the nematic-vapor interface. Finally, it was shown that complete wetting of the isotropic liquid-vapor interface by the nematic phase may be destroyed as a result of the competition between di8'erent terms in the potential. Similarly, a reentrant wetting transition at the nematic-vapor interface by the isotropic phase was found, as a result of this competition, at the nematic-vapor interface

Wetting and interfacial order at nematic free surfaces

We apply a density-functional theory to the free surface of a model liquid crystal, to investigate the orientational order at the nematic free surface of systems exhibiting orientational wetting at the isotropic liquid-vapour interface. It is shown that the theory accounts for the growth of the surface ordered layer which develops at the nematic-vapour interface, as the temperature increases up to the triple point, as was recently reported for 4-cyano-4′-n-alkyl-biphenyls. We have found a correlation between the growth of this layer and the non-monotonic temperature dependence of the interfacial tension below the triple point. The theoretical results are in excellent agreement with the results for 8CB.Dirección General de Investigación Científica y Técnica (DGICYT) PB91-060

Properties of patchy colloidal particles close to a surface: a Monte Carlo and density functional study

We investigate the behavior of a patchy particle model close to a hard-wall via Monte Carlo simulation and density functional theory (DFT). Two DFT approaches, based on the homogeneous and inhomogeneous versions of Wertheim's first order perturbation theory for the association free energy are used. We evaluate, by simulation and theory, the equilibrium bulk phase diagram of the fluid and analyze the surface properties for two isochores, one of which is close to the liquid side of the gas-liquid coexistence curve. We find that the density profile near the wall crosses over from a typical high-temperature adsorption profile to a low-temperature desorption one, for the isochore close to coexistence. We relate this behavior to the properties of the bulk network liquid and find that the theoretical descriptions are reasonably accurate in this regime. At very low temperatures, however, an almost fully bonded network is formed, and the simulations reveal a second adsorption regime which is not captured by DFT. We trace this failure to the neglect of orientational correlations of the particles, which are found to exhibit surface induced orientational order in this regime

Phase diagrams of binary mixtures of patchy colloids with distinct numbers and types of patches: Theempty fluid regime

We investigate the effect of distinct bonding energies on the onset of criticality of low functionality fluid mixtures. We focus on mixtures ofparticles with two and three patches as this includes the mixture where "empty" fluids were originally reported. In addition to the number of patches, thespecies differ in the type of patches or bonding sites. For simplicity, we consider that the patches on each species are identical: one species has threepatches of type A and the other has two patches of type B. We have found a rich phase behavior with closed miscibility gaps, liquid-liquid demixing, and negative azeotropes. Liquid-liquid demixing was found to pre-empt the "empty" fluid regime, of these mixtures, when the AB bonds are weaker than the AA or BB bonds. By contrast, mixtures in this class exhibit "empty" fluid behavior when the AB bonds are stronger than at least one of the other two. Mixtureswith bonding energies epsilon(BB) = epsilon(AB) and epsilon(AA) < epsilon(BB), were found to exhibit an unusual negative azeotrope. (C) 2011 American Institute of Physics. [doi:10.1063/1.3561396