Layering Transitions at the Free Surface of a Smectic Liquid Crystal

Circulating Marangoni flows within droplets in smectic films

We present a theoretical study and numerical simulation of Marangoni convection within ellipsoidal isotropic droplets embedded in free-standing smectic films (FSSFs). The thermocapillary flows are analyzed for both isotropic droplets spontaneously formed in FSSF overheated above the bulk smectic-isotropic transition and oil lenses deposited on the surface of the smectic film. The realistic model for which the upper drop interface is free from the smectic layers, while at the lower drop surface the smectic layering persists is considered in detail. For isotropic droplets and oil lenses this leads effectively to a sticking of fluid motion at the border with a smectic shell. The above mentioned asymmetric configuration is realized experimentally when the temperature of the upper side of the film is higher than at the lower one. The full set of stationary solutions for Stokes stream functions describing the Marangoni convection flows within the ellipsoidal drops are derived analytically. The temperature distribution in the ellipsoidal drop and the surrounding air is determined in the frame of the perturbation theory. As a result, the analytical solutions for the stationary thermocapillary convection are obtained for different droplet ellipticity ratios and the heat conductivity of the liquid crystal and air. In parallel, the numerical hydrodynamic calculations of the thermocapillary motion in drops are made. Both analytical and numerical simulations predict the axially symmetric circulatory convection motion determined by the Marangoni effect at the droplet-free surface. Due to a curvature of the drop interface a temperature gradient along its free surface always exists. Thus, the thermocapillary convection within the ellipsoidal droplets in overheated FSSF is possible for the arbitrarily small Marangoni numbers. Possible experimental observations enabling the checking of our predictions are proposed.

Benard-Marangoni convection within isotropic droplets in overheated free standing smectic films

We study theoretically internal flows in isotropic droplets formed in horizontal free-standing smectic films (FSSF) overheated above the bulk smectic-isotropic transition. The convection is due to vertical temperature gradient in the film and is driven by the surface tension variations at the drop interfaces. Using a conventional linear instability theory, we have found analytically the conditions under which the mechanical equilibrium within isotropic droplets in FSSFs becomes unstable relative to the thermocapillary convection. An explicit expression for the Marangoni number characterizing the onset of the convection as a function of the wave vector of in-plane instability and parameters of heat transfer is obtained. The cellular instability in FSSF with isotropic droplets behaving as a normal fluid (surface tension is a decreasing function of temperature) is possible for both directions of thermal gradient across the film: from bottom to top and conversely. We propose possible experimental observations enabling to check our predictions.

Coalescence of isotropic droplets in overheated free standing smectic films

A theoretical study of the interaction and coalescence of isotropic droplets in overheated free-standing smectic films (FSSF) is presented. Experimentally it is clear that merging of such droplets is extremely rare. On the basis of the general thermodynamic approach to the stability of FSSF, we determined the energy gains and losses involved in the coalescence process. The main contributions to the critical work of drop coalescence are due to the gain related to the decrease of the surface energy of the merging drops, which is opposed by the entropic repulsions of elementary steps at the smectic interface between them. To quantify the evolution of the merging drops, we use a simple geometrical model in which the volume of the smectic material, rearranged in the process of coalescence, is described by an asymmetrical pyramid at the intersection of two drops. In this way, the critical work for drop coalescence and the corresponding energy barrier have been calculated. The probability of the thermal activation of the coalescence process was found to be negligibly small, indicating that droplet merging can be initiated by only an external stimulus. The dynamics of drop merging was calculated by equating the capillary force driving the coalescence, and the Stokes viscous force slowing it down. For the latter, an approximation of moving oblate spheroids permitting exact calculations was used. The time evolution of the height of the neck between the coalescing drops and that of their lateral size are in good agreement with experiments.

Surface crystallization of ionic liquid crystals

The evidence for surface crystallization in ionic liquids is scarce. The existing reports seem to be contradictory as for its driving forces, since in the two compounds investigated in the literature, the contribution of coloumbic and van der Waals forces is very different. In this work 1-dodecyl-3-methylimidazolium tetrafluoroborate was studied and its surface crystallization characterized by surface tension, ellipsometry and optical microscopy. The results obtained seem to reconcile previous observations, and it was further shown, using the same techniques, that this phenomenon is prevalent in other ionic liquids. MD simulation results illustrate the different possibilities of organization, providing reasonable models to rationalize the experimental observations.

Interface induced crystal structures of dioctyl-terthiophene thin films

Temperature dependent structural and morphological investigations on semiconducting dioctyl-terthiophene (DOTT) thin films prepared on silica surfaces reveals the coexistence of surface induce order and distinct crystalline/liquid crystalline bulk polymorphs. X-ray diffraction and scanning force microscopy measurements indicate that at room temperature two polymorphs are present: the surface induced phase grows directly on the silica interface and the bulk phase on top. At elevated temperatures the long-range order gradually decreases, and the crystal G (340 K), smectic F (348 K), and smectic C (360 K) phases are observed. Indexation of diffraction peaks reveals that an up-right standing conformation of DOTT molecules is present within all phases. A temperature stable interfacial layer close to the silica-DOTT interface acts as template for the formation of the different phases. Rapid cooling of the DOTT sample from the smectic C phase to room temperature results in freezing into a metastable crystalline state with an intermediated unit cell between the room temperature crystalline phase and the smectic C phase. The understanding of such interfacial induced phases in thin semiconducting liquid crystal films allows tuning of crystallographic and therefore physical properties within organic thin films.

Surface and smectic layering transitions in binary mixtures of parallel hard rods

The surface phase behavior of binary mixtures of colloidal hard rods in contact with a solid substrate (hard wall) is studied, with special emphasis on the region of the phase diagram that includes the smectic A phase. The colloidal rods are modeled as hard cylinders of the same diameter and different lengths, in the approximation of perfect alignment. A fundamental-measure density functional is used to obtain equilibrium density profiles and thermodynamic properties such as surface tensions and adsorption coefficients. The bulk phase diagram exhibits nematic-smectic and smectic-smectic demixing, with smectic phases having different compositions; in some cases they are microfractionated. The calculated surface phase diagram of the wall-nematic interface shows a very rich phase behavior, including layering transitions and complete wetting at high pressures, whereby an infinitely thick smectic film grows at the wall via an infinite sequence of stepwise first-order layering transitions. For lower pressures complete wetting also obtains, but here the smectic film grows in a continuous fashion. Finally, at very low pressures, the wall-nematic interface exhibits critical adsorption by the smectic phase, due to the second-order character of the bulk nematic-smectic transition.

Homeotropic surface anchoring and the layer-thinning transition in free-standing films

In this work, we investigate the interplay between surface anchoring and finite-size effects on the smectic-isotropic transition in free-standing smectic films. Using an extended McMillan model, we study how a homeotropic anchoring stabilizes the smectic order above the bulk transition temperature. In particular, we determine how the transition temperature depends on the surface ordering and film thickness. We identify a characteristic anchoring for which the transition temperature does not depend on the film thickness. For strong surface ordering, we found that the thickness dependence of the transition temperature can be well represented by a power-law relation. The power-law exponent exhibits a weak dependence on the range of film thicknesses, as well as on the molecular alkyl tail length. Our results reproduce the main experimental findings concerning the layer-thinning transitions in free-standing smectic films.

Surface triple points and multiple-layer transitions observed by tuning the surface field at smectic liquid-crystal-water interfaces

We present an ellipsometric study of the interface between a smectic liquid crystal and water in the presence of a nonionic surfactant. The surfactant concentration serves as a handle to tune the surface field. For sufficiently large surfactant concentrations, a smectic phase is present at the interface in the temperature range above the smectic-A-isotropic bulk transition; when the bulk transition is approached, the thickness of this surface phase grows via a series of layer-by-layer transitions at which single smectic layers are formed. At lower surfactant concentrations, transitions appear at which the thickness of the surface phase jumps by multiple smectic layers, thereby implying the existence of triple points at which surface phases with different smectic layer numbers coexist. This is the first experimental demonstration of such surface triple points which are predicted by theoretical models.

Organization of four thermotropic liquid crystals of different polarities on model liquid and solid surfaces

The thermodynamic and surface properties of four structurally related thermotropic liquid crystals (LC) were investigated to understand their organization at gas-liquid and gas-solid interfaces. In this study, LC with a benzoyloxy azobenzene mesogenic core substituted with heptyloxy and/or dioxyethylene ether groups were used. The propensity of the LC to form self-assembled multilayers was demonstrated in the films spread at the air/aqueous interface using the Langmuir technique and Brewster angle microscopy and on the solid surfaces of Chromosorb WHP and silica, using differential scanning calorimetry. On the basis of the results obtained, a molecular recognition mechanism underlying separation processes using LC as selectors in gas chromatography is proposed.

Surface ordering above the isotropic-smectic-A transition at a silane-treated substrate

Surface ordering in a homologous series of alkyl cyanobiphenyl (nCB) liquid crystals having a direct isotropic-smectic-A (I-A) transition was investigated using evanescent-wave ellipsometry. The liquid crystal was bounded by a solid substrate treated with a silane surfactant which induced homeotropic (perpendicular) ordering of the liquid crystal molecules in the smectic-A phase. In the isotropic phase, one of the liquid crystals (10CB) partially wet the interface with an orientationally ordered, homeotropically aligned layer. The ordered interfacial layer grew without layering transitions but remained finite in thickness as the bulk I-A transition was approached. The interfacial layer has significantly lower orientational order than is observed in the smectic phase, indicating the possibility that the surface region of 10CB may be in a surface-induced, nonspontaneous nematic phase. The other liquid crystals (11 and 12CB) showed no surface ordering behavior whatsoever. Models describing the ordered surface layer of 10CB are presented. The results can be interpreted as a sharp transition in the surface ordering behavior as the chain length of the liquid crystal is varied, at the I-A transition of a liquid crystal.

X-ray reflectivity study of smectic wetting and prewetting at the free surface of isotropic liquid crystals

We study the structures of free-surface-wetting layers above the isotropic to smectic-A transition of three liquid-crystal compounds that show different kinds of growth of the wetting film as the bulk transition is approached: layer-by-layer, continuous, and continuous with prewetting. The smectic-A surface phase of the layer-by-layer compound consists of well-defined layers and possesses a sharp boundary to the isotropic bulk phase, whereas in the two continuous compounds sinusoidal density oscillations with a continuously decaying amplitude are found. In the continuous case with prewetting, the wetting film below the prewetting transition does not show an essential difference to the continuous case without prewetting.

Wetting behavior above the liquid-crystal-isotropic transition in a homologous series

An ellipsometric study of the wetting behavior at the free surface above the isotropic to nematic or isotropic to smectic-A transition of nine homologous compounds with even alkyl chain lengths n in the range from four to twenty carbon atoms is presented. All compounds show a pretransitional increase of the nematic or smectic surface coverage as the bulk isotropic to liquid-crystal transition is approached from above. The behavior of the nematic compounds (n=4 to 10) can be interpreted, within the framework of a Landau model, as complete wetting. In short nematic homologs the divergence of the nematic coverage is strongly reduced by a decrease of the nematic susceptibility of the isotropic phase. The elastic coefficient L of the Landau model shows a pronounced increase with increasing n, resulting in the occurrence of a discontinuous prewetting transition in the shortest smectic homolog (n=12) that is still describable by the nematic Landau model. In the longer smectic homologs (n=14 to 20), layering steps appear in the pretransitional increase of the coverage. The results indicate probable partial wetting for the longest homolog, whereas for the other smectic compounds the distinction between complete and partial wetting is difficult on the basis of ellipsometry.