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We review and compare recent work on the properties of fluctuating interfaces between nematic and isotropic liquid-crystalline phases. Molecular dynamics and Monte Carlo simulations have been carried out for systems of ellipsoids and hard rods with aspect ratio 15:1, and the fluctuation spectrum of interface positions (the capillary wave spectrum) has been analyzed. In addition, the capillary wave spectrum has been calculated analytically within the Landau-de Gennes theory. The theory predicts that the interfacial fluctuations can be described in terms of a wave vector dependent interfacial tension, which is anisotropic at small wavelengths (stiff director regime) and becomes isotropic at large wavelengths (flexible director regime). After determining the elastic constants in the nematic phase, theory and simulation can be compared quantitatively. We obtain good agreement for the stiff director regime. The crossover to the flexible director regime is expected at wavelengths of the order of several thousand particle diameters, which was not accessible to our simulations.
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Using nCB films adsorbed on MoS 2 substrates studied by x-ray diffraction, optical microscopy and Scanning Tunneling Microscopy, we demonstrate that ordered interfaces with well-defined orientations of adsorbed dipoles induce planar anchoring locked along the adsorbed dipoles or the alkyl chains, which play the role of easy axes. For two alternating orientations of the adsorbed dipoles or dipoles and alkyl chains, bi-stability of anchoring can be obtained. The results are explained using the introduction of fourth order terms in the phenomenological anchoring potential, leading to the demonstration of first order anchoring transition in these systems. Using this phenomenological anchoring potential, we finally show how the nature of anchoring in presence of dual easy axes (inducing bi-stability or average orientation between the two easy axes) can be related to the microscopical nature of the interface. Introduction Understanding the interactions between liquid crystal (LC) and a solid substrate is of clear applied interest, the vast majority of LC displays relying on control of interfaces. However this concerns also fundamental problems like wetting phenomena and all phenomena of orientation of soft matter bulk induced by the presence of an interface. In LCs at interfaces, the so-called easy axes correspond to the favoured orientations of the LC director close to the interface. If one easy axis only is defined for one given interface, the bulk director orients along or close to this axis [1]. It is well known that, in anchoring phenomena, two major effects compete to impose the anchoring directions of a liquid crystal, first, the interactions between molecules and the interface, second, the substrate roughness whose role has been analyzed by Berreman [2]. The influence of adsorbed molecular functional groups at the interface is most often dominant with, for example in carbon substrates, a main influence of unsaturated carbon bonds orientation at the interface [3]. In common LC displays, there is one unique easy axis, but modifications of surfaces have allowed for the discovery of promising new anchoring-related properties. For instance, the first anchoring bi-stability has been established on rough surfaces, associated with electric ordo-polarization [4] and the competition between a stabilizing short-range term and a destabilizing long-range term induced by an external field, can induce a continuous variation of anchoring orientation [5]. More recently, surfaces with several easy axes have been studied extensively. It has been shown that control of a continuous variation of director pretilt, obtained in several systems [6, 7], is associated with the presence of two different easy axes, one perpendicular to the substrate (homeotropic) and one planar [7, 8]. Similar models can explain the continuous evolution of anchoring between two planar orientations observed on some crystalline substrates [9]. However, in the same time, two easy axes can also lead to anchoring bi-stability [10, 11] or discontinuous transitions of anchoring [9], which is not compatible with the model established to interpret observed control of pretilt. In order to be able to predict if bi-stability or continuous combination of the two easy axes occurs for one given system, it becomes necessary to understand the microscopic origin of the easy axes.
Previous theoretical studies of calamitic (i.e., rod-like) ionic liquid crystals (ILCs) based on an effective one-species model led to indications of a novel smectic-A phase with a layer spacing being much larger than the length of the mesogenic (i.e., liquid-crystal forming) ions. In order to rule out the possibility that this wide smectic-A phase is merely an artifact caused by the one-species approximation, we investigate an extension which accounts explicitly for cations and anions in ILCs. Our present findings, obtained by grand canonical Monte Carlo simulations, show that the phase transitions between the isotropic and the smectic-A phases of the cation-anion system are in qualitative agreement with the effective one-species model used in the preceding studies. In particular, for ILCs with mesogenes (i.e., liquid-crystal forming species) carrying charged sites at their tips, the wide smectic-A phase forms, at low temperatures and within an intermediate density range, in between the isotropic and a hexagonal crystal phase. We find that in the ordinary smectic-A phase the spatial distribution of the counterions of the mesogens is approximately uniform, whereas in the wide smectic-A phase the small counterions accumulate in between the smectic layers. Due to this phenomenology the wide smectic-A phase could be interesting for applications which hinge on the presence of conductivity channels for mobile ions.
We construct a mean-field formulation of the thermodynamics of ion solvation in immiscible polar binary mixtures. Assuming an equilibrium planar interface separating two semi-infinite regions of different constant dielectric medium, we study the electrostatic phenomenon of differential adsorption of ions at the interface. Using general thermodynamic considerations, we construct the mean-field $Omega$-potential and demonstrate the spontaneous formation of an electric double-layer around the interface necessarily follow. In our framework, we can also relate both the bulk ion densities in the two phases and the distribution potential across the interface to the fundamental Born free energy of ion polarization. We further illustrate this selective ion adsorption phenomenon in respective examples of fully permeable membranes that are neutral, negative, or positive in charge polarity.
Fluctuations of the interface between coexisting colloidal fluid phases have been measured with confocal microscopy. Due to a very low surface tension, the thermal motions of the interface are so slow, that a record can be made of the positions of the interface. The theory of the interfacial height fluctuations is developed. For a host of correlation functions, the experimental data are compared with the theoretical expressions. The agreement between theory and experiment is remarkably good.
General microscopic mechanism of ferroelectric ordering in chiral smectic C* liquid crystals is considered. It is shown that if the mesogenic molecules have a sufficiently low symmetry, the spontaneous polarization is proportional to one of the biaxial vector order parameters of the smectic C phase. This order parameter may be determined by intermolecular interactions which are not sensitive to molecular chirality. At the same time, the polarization is also proportional to a pseudoscalar parameter which vanishes if the molecules are nonchiral. The general statistical theory of ferroelectric ordering is illustrated by two particular models. The first model is based on electrostatic quadrupole-quadrupole interactions, and it enables one to obtain explicit analytical expressions for the spontaneous polarization. In the second model, the molecular chirality and polarity are determined by a pair of off-center nonparallel dipoles. For this case, the spontaneous polarization is calculated numerically as a function of temperature. The theory provides a more general interpretation of the previous approaches including the classical Boulder model.
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