Interaction of surfaces in smectic membranes and their instability near thinning transitions

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.

Dynamics of Dislocations in Smectic A Liquid Crystals Doped with Nanoparticles

Edge dislocations are linear defects that locally break the positional order of the layers in smectic A liquid crystals. As in usual solids, these defects play a central role for explaining the plastic properties of the smectic A phase. This work focuses on the dynamical properties of dislocations in bulk samples prepared between two glass plates and in free-standing films. The emphasis will be put on the measurement of the mobility of edge dislocations in liquid crystals either pure or doped with nanoparticles. The experimental results will be compared to the existing models.

Linear defects forming the ground state of polar free standing smectic-C* films

In this paper we report on observations of unusual linear defects forming spontaneously in polar free-standing smectic-C* films near the temperatures of thinning transitions. At high temperature a periodic structure of defects becomes the ground state of the system. We found that the defects are characterized by continuous rotation of the molecular orientation with a change of the sense of the rotation across the defects. We develop a simple theoretical model that describes the observed behavior. The structure of the defects is governed by the competition between two-dimensional quadratic and linear orientational elasticity. The proposed model explains the origin of the linear defects, the periodic structure and their transformation with temperature and chirality of the liquid crystal.

Nucleation and growth of droplets in the overheated free-standing smectic films

We present a theoretical explanation for the formation of nematic droplets in free-standing smectic films (FSSF) overheated above the temperature of the bulk smectic - nematic transition. The conditions for the formation of the nematic droplets in smectic films are studied on the basis of the general thermodynamic approach to the stability of FSSF. It is shown that the formation of droplets in overheated FSSF is only possible in the presence of a certain amount of thermally generated dislocation loops. We determined the gain in the free energy related with the formation of the nematic droplets, the value of the critical work and the critical size of the drops. The initial increase of the drops size is due to release of material from the growing dislocation loops. At the second stage the drops growth occurs through coalescence of the smaller drops with the larger ones. The droplets attract each other by means of capillary forces arising due to gradients of the surface energy in the area between them. Drops size evolution, the dynamics of their growth and merging are in good agreement with experiments.

Surface-surface interaction in smectic liquid crystal films

Null transmission ellipsometry was employed to study the field induced transition of the surface arrangements in freestanding films of smectic liquid crystals. The interlayer interaction between the two surfaces obtained from the threshold voltage for the transition is found to be antiferroelectric and is quasilong ranged. The possible microscopic origins of the measured interaction and its relevance to the interlayer interaction in antiferroelectric liquid crystal materials are discussed.

Surface-aligning field in smectic liquid-crystal films

Two modified mean-field J(1)-J(2) models are studied to explain the surface reduction of twisting power in the helical smectic-C*(α) phase in free-standing liquid crystal films. Profiles of the surface interlayer interaction are calculated from the experimental results. The calculations reveal the existence of a strong surface field and indicate that the surface field is the reason for the observed reduced twisting power near the surface region. Our results provide a quantitative study of the interlayer interactions through surface effects in smectic liquid crystals.

Long-range elastic-mediated interaction between nanoparticles adsorbed on free-standing smectic films

We determine the elastic-mediated interaction between colloidal nanoparticles adsorbed on the surface of free-standing smectic films. In contrast with the short-range character of the elastic-mediated force between particles adsorbed on smectic films supported by a solid substrate, the effective force acquires a long-range character in free-standing films, decaying with the particles distance R as slow as 1/R . We also discuss the dependence of the effective interaction potential on the surface tension gamma and film thickness. We show that it decays as 1/gamma in the regime of large surface tensions and becomes independent of the film thickness at a characteristic surface tension.

Influence of chirality on director configuration and droplet interaction in ferroelectric free-standing films

Droplets in smectic free-standing films interact due to elastic distortion of the c-director field and formation of topological defects. Our experiments show that chirality of the liquid-crystal medium plays a key role in the interaction between droplets. We find that the configuration of the c-director field near the droplets and the position of the topological defects on the droplet boundary depend on droplet size and film polarity. An intermediate c-director configuration between dipolar and quadrupolar is formed near droplets in smectic films due to the competition between elasticity and chirality. We observed that the distance between droplets in self-organized structures depends on the position of defects on the droplet boundary and significantly changes with respect to that for dipolar droplets. Our results open the way to modify the droplet interaction and the structures formed by droplets.

Inclusions in free standing smectic liquid crystal films

Colloidal inclusions in thin free standing liquid crystal films are ideal model systems for 2D anisotropic dispersions. Different types of self-organization in chain and lattice structures have been observed. The orientational elasticity of the anisotropic matrix and capillary forces are the dominating interaction mechanisms between solid or liquid inclusions, the director field, and dislocations of the films. We give an overview of the progress in this field, focussing on different inclusion types and their interactions in thermotropic smectic films.

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.

Temperature dependence of the Casimir-like force in free-standing smectic films

The thermal Casimir-like force in free-standing liquid crystal films close to the smectic-A-nematic transition temperature is computed using a quadratic functional approach. In the framework of a microscopic mean-field model of free-standing smectic-A films, the temperature dependence of the order parameter profiles is computed and later used to estimate the elastic coupling variability in the vicinity of first- and second-order bulk smectic-A-nematic phase transitions. The strong nonuniformity of the coupling constant profiles promotes a significant increase of the fluctuation-induced force over three orders of magnitude, especially in thin films. This result reinforces the possible predominance of the thermal Casimir force as compared to the standard van der Waals interaction in thin smectic-A liquid crystal films.

Director configuration and self-organization of inclusions in two-dimensional smectic membranes

The behavior of isolated inclusions (nematic droplets, smectic islands) and formation of chains and clusters from inclusions in oriented smectic membranes have been studied. Investigations of inclusions were performed in membranes in which the molecular ordering was oriented by an external magnetic field. At planar boundary conditions on the interface between the membrane and inclusions different configurations of the c-director field were observed: Coulombic, dipolar, quadrupolar, and mixed. The observed orientation of inclusions and their interactions and self-organization correlate with the predictions of the theory based on the electromagnetic analogy. Chaining and formation of superstructures differ in oriented and nonoriented membranes.