Inclusions in free standing smectic liquid crystal films

Coalescence of biphasic droplets embedded in free standing smectic A films

We investigate micrometer-sized flat droplets consisting of an isotropic core surrounded by a nematic rim in freely suspended smectic A liquid-crystal films. In contrast to purely isotropic droplets which are characterized by a sharp edge and no long-range interactions, the nematic fringe introduces a continuous film thickness change resulting in long-range mutual attraction of droplets. The coalescence scenario is divided in two phases. The first one consists in the fusion of the nematic regions. The second phase involves the dissolution of a thin nematic film between the two isotropic cores. The latter has many similarities with the rupture of thin liquid films between droplets coalescing in an immiscible viscous liquid.

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.

Giant director fluctuations in liquid crystal drops

We report the discovery and elucidation of giant spatiotemporal orientational fluctuations in nematic liquid crystal drops with radial orientation of the nematic anisotropy axis producing a central "hedgehog" defect. We study the spatial and temporal properties of the fluctuations experimentally using polarized optical microscopy, and theoretically, by calculating the eigenspectrum of the Frank elastic free energy of a nematic drop of radius R_{2}, containing a spherical central core of radius R_{1} and constrained by perpendicular boundary conditions on all surfaces. We find that the hedgehog defect with radial orientation has a complex excitation spectrum with a single critical mode whose energy vanishes at a critical value μ_{c} of the ratio μ=R_{2}/R_{1}. When μ<μ_{c}, the mode has positive energy, indicating that the radial hedgehog state is stable; when μ>μ_{c}, it has negative energy indicating that the radial state is unstable to the formation of a lower-energy state. This mode gives rise to the large-amplitude director fluctuations we observe near the core, for μ near μ_{c}. A collapse of the experimental data corroborates model predictions for μ<μ_{c} and provides an estimate of the defect core size.

Director Fluctuations in Two-Dimensional Liquid Crystal Disclinations

We present analytical calculations of the energies and eigenfunctions of all normal modes of excitation of charge +1 two-dimensional splay (bend) disclinations confined to an annular region with inner radius R1 and outer radius R2 and with perpendicular (tangential) boundary conditions on the region’s inner and outer perimeters. Defects such as these appear in islands in smectic-C films and can in principle be created in bolaamphiphilic nematic films. Under perpendicular boundary conditions on the two surfaces and when the ratio β=Ks/Kb of the splay to bend 2D Frank constants is less than one, the splay configuration is stable for all values μ=R2/R1. When β>1, the splay configuration is stable only for μ less than a critical value μc(β), becoming unstable to a “spiral” mixed splay-bend configuration for μ>μc. The same behavior occurs in trapped bend defects with tangential boundary conditions but with Ks and Kb interchanged. By calculating free energies, we verify that the transition from a splay or bend configuration to a mixed one is continuous. We discuss the differences between our calculations that yield expressions for experimentally observable excitation energies and other calculations that produce the same critical points and spiral configurations as ours but not the same excitation energies. We also calculate measurable correlation functions and associated decay times of angular fluctuations.

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.

Fabrication and Electric Field-Driven Active Propulsion of Patchy Microellipsoids

Active colloids are a synthetic analogue of biological microorganisms that consume external energy to swim through viscous fluids. Such motion requires breaking the symmetry of the fluid flow in the vicinity of a particle; however, it is challenging to understand how surface and shape anisotropies of the colloid lead to a particular trajectory. Here, we attempt to deconvolute the effects of particle shape and surface anisotropy on the propulsion of model ellipsoids in alternating current (AC) electric fields. We first introduce a simple process for depositing metal patches of various shapes on the surfaces of ellipsoidal particles. We show that the shape of the metal patch is governed by the assembled structure of the ellipsoids on the substrate used for physical vapor deposition. Under high-frequency AC electric field, ellipsoids dispersed in water show linear, circular, and helical trajectories which depend on the shapes of the surface patches. We demonstrate that features of the helical trajectories such as the pitch and diameter can be tuned by varying the degree of patch asymmetry along the two primary axes of the ellipsoids, namely longitudinal and transverse. Our study reveals the role of patch shape on the trajectory of ellipsoidal particles propelled by induced charge electrophoresis. We develop heuristics based on patch asymmetries that can be used to design patchy particles with specified nonlinear trajectories.

Observation of Backflow during the Anihilation of Topologocal Defects in Freely Suspended Smectic Films

Freely suspended films in the smectic C phase are excellent templates for the study of topological defect dynamics. It is well known that, during the annihilation of a pair of disclinations with strengths +/−1, the +1 defect moves faster because it is carried towards its opponent by backflow, whereas the flow in the vicinity of the −1 defect is negligibly small. This backflow pattern is created by the defect motion itself. An experimental confirmation of this theoretical prediction and its quantitative characterization is achieved here by fluorescence labeling. Film regions near the defect positions are labeled and their displacements are tracked optically.

Topological defects due to twist-bend nematic drops mimicking colloidal particles in a nematic medium

Colloids formed of solid/fluid particle dispersions in oriented nematic liquid crystals are known to be an ideal means of realizing fundamentally significant topological defect geometries. We find, experimentally, that twist-bend nematic (NTB) droplets formed in the N-NTB biphasic regime, either of pure compounds or mesogenic mixtures, completely mimic colloidal particles in their ability to generate a rich variety of defects. In the biphasic regime, the topological features of both liquid crystal colloids and chiral nematic droplets are revealed by (i) topological dipoles, quadrupoles and their patterned clusters formed in planar nematic liquid crystals orientationally perturbed by coexisting NTB drops, (ii) the transformation of hyperbolic hedgehogs into knotted Saturn rings encircling the NTB drops dispersed in a 90°-twisted nematic matrix and (iii) the Frank-Pryce defect texture evident in smaller (relative to sample thickness) NTB drops. In larger drops with fingerlike outgrowths, additional line defects appear; most of these are deemed to be pairs of disclinations to which are attached pairs of screw dislocations intervening in the growth process of the NTB droplets.

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.

Self similarity of liquid droplet coalescence in a quasi-2D free-standing liquid-crystal film

Coalescence of droplets is an ubiquitous phenomenon in chemical, physical and biological systems. The process of merging of liquid objects has been studied during the past years experimentally and theoretically in different geometries. We introduce a unique system that allows a quasi two-dimensional description of the coalescence process: Micrometer-sized flat droplets in freely suspended smectic liquid-crystal films. We find that the bridge connecting the droplets grows linearly in time during the initial stage of coalescence, both with respect to its height and lateral width. We also verify self-similar dynamics of the bridge during the first stage of coalescence. We compare our results with a model based on the thin sheet equations. Our experiments confirm that the most important geometrical parameter influencing the coalescence rate is the contact angle of the droplets.

Structure and dynamics of a two-dimensional colloid of liquid droplets

Droplet arrays in thin, freely suspended liquid-crystalline smectic A films can form two-dimensional (2D) colloids. The droplets interact repulsively, arranging locally in a more or less hexagonal arrangement with only short-range spatial and orientational correlations and local lattice cell parameters that depend on droplet size. In contrast to quasi-2D colloids described earlier, there is no 3D bulk liquid subphase that affects the hydrodynamics. Although the films are surrounded by air, the droplet dynamics are genuinely 2D, the mobility of each droplet in its six-neighbor cage being determined by the ratio of cage and droplet sizes, rather than by the droplet size as in quasi-2D colloids. These experimental observations are described well by Saffman's model of a diffusing particle in a finite 2D membrane. The experiments were performed in microgravity, on the International Space Station.

Landau theory for smectic-A-hexatic-B coexistence in smectic films

We explain theoretical peculiarities of the smectic-A-hexatic-B equilibrium phase coexistence in a finite-temperature range recently observed experimentally in free-standing smectic films [I. A. Zaluzhnyy et al., Phys. Rev. E 98, 052703 (2018)2470-004510.1103/PhysRevE.98.052703]. We quantitatively describe this unexpected phenomenon within Landau phase transitions theory assuming that the film state is close to a tricritical point. We found that the surface hexatic order diminishes the phase coexistence range as the film thickness decreases, shrinking it to zero at some minimal film thickness L_{c}, of the order of a few hexatic correlation length. We established universal laws for the temperature width of the phase coexistence range in terms of the reduced variables. Our theory is in agreement with the existing experimental data.

Marangoni Flow in Freely Suspended Liquid Films

We demonstrate controlled material transport driven by temperature differences in thin freely suspended smectic films. Films with submicrometer thicknesses and lateral extensions of several millimeters were studied in microgravity during suborbital rocket flights. In-plane temperature differences cause two specific Marangoni effects, directed flow and convection patterns. At low gradients, practically thresholdless, flow transports material with a normal (negative) temperature coefficient of the surface tension dσ/dT<0 from the hot to the cold film edge, it accumulates at the cold film edge. In materials with dσ/dT>0, the reverse transport from the cold to the hot edge is observed. We present a model that describes the effect quantitatively. It predicts that not the temperature gradient in the film plane but the temperature difference between the thermopads is relevant for the effect.

Interfacial behavior of confined mesogens at smectic-C*-water boundary

In this paper, we have investigated the behavior of mesogens at smectic-C*-water interface confined in a liquid crystal (LC) cell with interfacial geometry. Polarized optical microscopy was used to probe the appearance of various smectic-C* domain patterns at water interface owing to the reorientation of mesogens. The undulated stripe domains observed at the air interface of smectic-C* meniscus vanished as the water entered into the smectic layers and focal conical domain patterns appeared at smectic-C*-water boundary. A spatially variable electro-optical switching of LC molecules was also observed outside the electrode area of the interfacial cell. The electrode region at the interface, as well as on the water side, was damaged upon application of an electric field of magnitude more than 150 kV/m. The change in dielectric parameters of mesogens was extensively studied at interface after evaporating the water. These studies give fundamental insights into smectic-C*-water interface and also will be helpful in fabricating better LC devices for electro-optical and sensing applications.

N-SmA-SmC phase transitions probed by a pair of elastically bound colloids

The competing effect of surface anchoring of dispersed microparticles and elasticity of nematic and cholesteric liquid crystals has been shown to stabilize a variety of topological defects. Here we study a pair of colloidal microparticles with homeotropic and planar surface anchoring across N-SmA-SmC phase transitions. We show that below the SmA-SmC phase transition the temperature dependence of interparticle separation (D) of colloids with homeotropic anchoring shows a power-law behavior; D∼(1-T/T_{AC})^{α}, with an exponent α≈0.5. For colloids with planar surface anchoring the angle between the joining line of the centers of the two colloids and the far field director shows characteristic variation elucidating the phase transitions.

Elastocapillary Driven Assembly of Particles at Free-Standing Smectic-A Films

Colloidal particles at complex fluid interfaces and within films assemble to form ordered structures with high degrees of symmetry via interactions that include capillarity, elasticity, and other fields like electrostatic charge. Here we study microparticle interactions within free-standing smectic-A films, in which the elasticity arising from the director field distortion and capillary interactions arising from interface deformation compete to direct the assembly of motile particles. New colloidal assemblies and patterns, ranging from 1D chains to 2D aggregates, sensitive to the initial wetting conditions of particles at the smectic film, are reported. This work paves the way to exploiting LC interfaces as a means to direct spontaneously formed, reconfigurable, and optically active materials.

Topological defects in an unconfined nematic fluid induced by single and double spherical colloidal particles

We present numerical solutions to the Landau-de Gennes free-energy model under the one-constant approximation for systems of single and double spherical colloidal particles immersed in an otherwise uniformly aligned nematic liquid crystal. A perfect homeotropic surface anchoring of liquid-crystal molecules on the spherical surface is considered. A large parameter space is carefully examined, including those in the free-energy model and those describing the dimer configurations and the background liquid-crystal orientation. The stability of the resulting liquid-crystal defects appearing in the neighborhood of the colloidal dimer pair is analyzed in light of the numerical results for their free energies. A number of scenarios are considered: a free dimer pair in a nematic fluid where the free-energy ground states are described in terms of a phase diagram, and a constrained dimer pair where the interparticle distance and the relative orientation of the distance vector to the nematic director can be manipulated. We pay particular attention to the nonsymmetric solutions, which yield several metastable defect states that can be observed in real systems. The high-precision numerical calculations are based on a spectral method, which is an enabling factor that allows us to compare the subtle difference in the free energies of different defect structures.

Two-dimensional island emulsions in ultrathin, freely-suspended smectic liquid crystal films

We report a novel type of two-dimensional colloidal emulsion, in which arrays of disc-shaped liquid crystal domains are created in ultrathin, freely-suspended, fluid smectic C liquid crystal films. After a film has been drawn across an aperture, an island emulsion is produced by repeatedly compressing and expanding the film while maintaining vigorous shear and extensional air flow across its area. Once formed, these emulsions restructure over a period of a few minutes to a stable state that then changes only slowly, over the course of several days. This stability enables study of the sedimentation of the emulsion under in-plane gravitation produced by tilting the film, during which the original island emulsion segregates into regions with different kinds of emulsions distinguished by the size, density, and degree of order of the islands. We observe a rich array of phenomena that includes the formation of chains of islands organized into two-dimensional smectics in the dilute phase, and island deformation and coalescence in the condensed phase.

Structures in the meniscus of smectic membranes: the role of dislocations?

We report an experimental investigation of the structure of periodic patterns observed in the meniscus of free-standing smectic films. Combination of polarizing optical microscopy and phase shifting interferometry enabled us to obtain new information on the structure of the meniscus, and in particular, on the topography of the smectic-air interface. We investigate the profile of the undulations in the striped structure in the thin part of the meniscus, change of the stripe period with the meniscus thickness and subsequent transition into a two-dimensional structure. It is shown that the two-dimensional structure has an unusual complex profile of "egg-box" type. The striped texture occurs upon cooling from the nontilted smectic-A to the smectic-C* phase, whereas the two-dimensional pattern is present in both phases. We discuss the possible origin of the modulated structures, the role of the dislocations in the meniscus, the elasticity of smectic layers, and the mechanical stress induced by dislocations.

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.

Chiral twist drives raft formation and organization in membranes composed of rod-like particles

Lipid rafts are hypothesized to facilitate protein interaction, tension regulation, and trafficking in biological membranes, but the mechanisms responsible for their formation and maintenance are not clear. Insights into many other condensed matter phenomena have come from colloidal systems, whose micron-scale particles mimic basic properties of atoms and molecules but permit dynamic visualization with single-particle resolution. Recently, experiments showed that bidisperse mixtures of filamentous viruses can self-assemble into colloidal monolayers with thermodynamically stable rafts exhibiting chiral structure and repulsive interactions. We quantitatively explain these observations by modeling the membrane particles as chiral liquid crystals. Chiral twist promotes the formation of finite-sized rafts and mediates a repulsion that distributes them evenly throughout the membrane. Although this system is composed of filamentous viruses whose aggregation is entropically driven by dextran depletants instead of phospholipids and cholesterol with prominent electrostatic interactions, colloidal and biological membranes share many of the same physical symmetries. Chiral twist can contribute to the behavior of both systems and may account for certain stereospecific effects observed in molecular membranes.

Orientational relaxation in free-standing smectic C film driven by rotating circular frame

The pecularities in the cˆ-director reorientation in free-standing smectic C film without of defects and stretched between two circular frames, the rest outer and rotating inner, have been investigated theoretically based on the hydrodynamic theory including the cˆ-director motion and with accounting for backflow. Since the orientation of the cˆ-director is fixed at the rims of the smectic film, the shear flow induced by rotating frame winds up of the cˆ-director field. It is found that the higher shearing flow produces the greater twisting rotation of the cˆ-director around the normal to the smectic film directed in the opposite sense with respect to the direction of the angular velocity. Calculations also show that the relaxation dynamics of the cˆ-director field depends crucially on the curvature of the inner rotating frame.

Microdroplets Impinging on Freely Suspended Smectic Films: Three Impact Regimes

We employ high-speed video imaging to study microdroplets of a few picoliters volume impacting freely suspended smectic liquid-crystal films. Depending on the impact parameters, in particular, droplet velocity and mass, three different regimes are observed such as trapping, rebounding, and tunneling. Fast droplets penetrate the films completely. After they have passed the film, they are coated with a layer of film material while the original smectic film remains intact. Droplets in a certain intermediate velocity range bounce back from the film. After impact, the film deforms and hurls the droplet back, depleting a substantial share of the initial kinetic energy. Slow droplets are caught and embedded in the film. During impact and tunneling, an appreciable amount of kinetic energy is lost. The energy is partially dissipated during droplet impact and during subsequent mechanical vibrations and oscillations of the film and the droplet. The tunneling process of high-speed droplets can be exploited to prepare smectic shells of well-defined sizes that enclose picoliters of an immiscible liquid.

Thinning and thickening of free-standing smectic films revisited

We present a theoretical explanation of the remarkable thickness instabilities that occur in free-standing smectic films (FSSF) upon changing the external conditions: i) upon heating the film above the bulk smectic disordering temperature, generally the film does not rupture but instead shows successive layer-by-layer thinning transitions; ii) thickening of FSSF, which occurs within the thermal range of the smectic phase upon local heating. All observations reported so far can be explained on the basis of the Landau-de Gennes theory of the smectic state in combination with nucleation theory. In overheated smectic films (thinning) or locally heated FSSF (thickening) an additional normal tensile force appears due to a change of the mean density of the film. In the case of an overheated FSSF the free energy has oscillatory character, and upon heating the balance of tensile and elastic forces breaks down spontaneously. This leads to thinning of the film, which proceeds via thermal nucleation and growing of dislocation loops in the middle plane of the film. The expression for the envelope of the points of thinning as well as estimates of the dynamics of growth of dislocation loops, are in good agreement with experiments. Local heating of a FSSF within the smectic temperature range induces thermal expansion, which shifts the system to a metastable state. This favors nucleation and growth of dislocation loops of excess smectic layers in the middle plane of the film. The activation energy of such dislocation loops attains values below the threshold energy and decreases upon further heating. This leads to local film thickening by many tens of layers. Realization of this scenario depends crucially on the energy dissipated locally in the film. Estimates of the thickness of the growing "island" in the film and of the velocity of the dislocation loop growth are in reasonable agreement with experiments.

Probing the dynamics of geometrically confined ferroelectric mesogens at the air interface

This article focuses on the alignment and dynamics of mesogens at the ferroelectric liquid crystal (FLC)/air interface in a confined geometry. The interface has been systematically prepared and characterised with provision for applying an electric field separately to the bulk and air interface of the FLC. Polarizing optical microscopy (POM) investigations done at the FLC/air interface have exposed the concave geometry, cell thickness dependent boundary width and phase dependent optical textures of the FLC meniscus at the interface. Dielectric spectroscopy investigations revealed the presence of an additional molecular relaxation mode at the FLC/air interface, which is attributed to the short axis rotation of homeotropically aligned mesogens at the interface. Based on the observations from the POM, dielectric spectroscopy and X-ray diffraction profiles, we schematically envisaged the molecular arrangement and dynamics of the FLC/air boundary. These studies would be helpful for innovations in liquid crystal based devices and also for many other applications, where soft surfaces, interfaces and confinement play a momentous role.

Molecular organization in freely suspended nano-thick 8CB smectic films. An atomistic simulation

Atomistic simulations of nano-thick free 8CB smectic films show the change of order across the film with temperature and thickness.

Impact and embedding of picoliter droplets into freely suspended smectic films

We study the impact of liquid microdroplets on thin freely suspended smectic films. Such films are very thin but robust objects that can serve as model systems for quasi-two-dimensional liquids. Droplet velocities and sizes determine the character of the collisions. The dynamics of the integration of droplets into the film can be divided into three phases, starting with the impact and a dissipation of the kinetic energy, followed by a balancing of capillary forces within fractions of a second. The analysis of the droplet shape evolution with high-speed imaging allows us to study the dynamics of this process. The final phase, formation of a meniscus of smectic material, takes several seconds up to minutes.

Physics of Free-Standing Lyotropic Films

We explore the structures and properties of stable, free-standing films of lyotropic mesophases drawn on apertures of various shapes in an atmosphere of controlled humidity. New phenomena are uncovered and interpreted.

Tuning the defect configurations in nematic and smectic liquid crystalline shells

Thin liquid crystalline shells surrounding and surrounded by aqueous phases can be conveniently produced using a nested capillary microfluidic system, as was first demonstrated by Fernandez-Nieves et al. in 2007. By choosing particular combinations of stabilizers in the internal and external phases, different types of alignment, uniform or hybrid, can be ensured within the shell. Here, we investigate shells in the nematic and smectic phases under varying boundary conditions, focusing in particular on textural transformations during phase transitions, on the interaction between topological defects in the director field and inclusions in the liquid crystal (LC), and on the possibility to relocate defects within the shell by rotating the shell in the gravitational field. We demonstrate that inclusions in a shell can seed defects that cannot form in a pristine shell, adding a further means of tuning the defect configuration, and that shells in which the internal aqueous phase is not density matched with the LC will gently rearrange the internal structure upon a rotation that changes the influence of gravity. Because the defects can act as anchor points for added linker molecules, allowing self-assembly of adjacent shells, the various arrangements of defects developing in these shells and the possibility of tuning the result by modifying boundary conditions, LC phase, thickness and diameter of the shell or applying external forces make this new LC configuration very attractive.

Elastic mediated force between nanoparticles adsorbed on smectic films under an external field

Within the harmonic approximation, we analytically determine the elastic-mediated interaction between colloidal nanoparticles adsorbed on the surface of smectic films under the influence of an external field. Both cases of free-standing films and films deposited over a solid substrate are considered. We show that the asymptotic decay (1/R in free-standing and exponential in deposited films) is not altered by the external field. However, the external field plays distinct roles according to the film configuration, the interparticle distance, the film thickness, and the surface tension at the film-gas interface. We provide a detailed discussion under the light of the distinct mechanisms controlling the undulations of the surface layer.

Alignment of liquid crystals using a molecular layer with patterned molecular density

The surface of self-constructed molecular density modulation (SDM) exhibits a wide range of liquid crystal alignment capabilities including planar, tilted, and homeotropic alignments, disclination-free uniform and heterogeneous alignments, and even spatially varying alignments through the single non-contact process. Alignment defects are eliminated by temporary lowering the frictional energy barrier via the open-boundary elastic stabilization (OES) treatment.

Dipolar colloids in nematostatics: tensorial structure, symmetry, different types, and their interaction

In spite of the analogy to the electrostatics, the three-dimensional colloidal nematostatics is substantially different in both its mathematical structure and its physical implications. The general tensorial structure of elastic multipoles derived in V. M. Pergamenshchik and V. O. Uzunova [Eur. Phys. J. E 23, 161 (2007); Phys. Rev. E 76, 011707 (2007)] allows for a classification of different types of colloids in the nematostatics. In comparison to their electrostatic counterparts, the elastic multipoles have one extra tensorial index. Based on this structure, we identify possible types of elastic dipoles. An elastic dipole is characterized by three coefficients--isotropic strength, anisotropy, and chirality--and a two-component vector along the unperturbed director. The relationship between the dipole type and symmetry groups is established and sketches of various representative types of dipolar colloids are given. Instead of a single electric dipole, in the nematostatics there are four different pure types (dipolar singlets) and eight mixed types of elastic dipoles (one quintet, one quartet, two triplets, and four doublets). It is shown that the full symmetry of the colloid-induced director field and the colloid's shape (body) symmetry determine different dipole components. For instance, a helicoidal component of the anchoring easy axes can make a chiral elastic dipole of a colloid with the quadrupolar shape symmetry. The interaction potentials for different singlet and doublet dipoles are derived and illustrated in terms of the dipolar dyads and elastic Coulomb law. We argue that multipole parameters must be found by pure numerical means, as from ansatz director distributions one can find only orders of their magnitudes.

Stepwise transition of a topological defect from the smectic film to the boundary of a dipolar inclusion

Cholesteric droplets accompanied by a topological defect are studied in free standing smectic C;{ *} films. We observed a transition between two droplet-defect configurations with the defect in the film and on the droplet boundary. We found that the distance between the droplet surface and the topological defect decreases continuously with increasing temperature and above a certain critical temperature the defect jumps to the droplet boundary. We relate this stepwise change in the defect position to the change in the anchoring on the droplet boundary. This transformation leads to a decrease in the interparticle distances in self-organized chains from droplets. Our simple theory allows us to estimate the value of the anchoring energy.

Shape-induced dispersion of colloids in anisotropic fluids

We experimentally study the behavior of micrometer-sized prolate ellipsoidal particles dispersed in a nematic liquid crystal. The latter is an aqueous solution of rodlike micelles. When embedded into such a solvent, ellipsoids with small enough aspect ratios aggregate to form anisotropic structures oriented at an angle with respect to the local background director (as already observed for spheres). This is, however, no longer the case when the aspect ratio reaches a well-defined value: above that value, the ellipsoids remain well dispersed and apparently do no interact with each other, even over very long periods of time (several months). Therefore, there exists a transition from an aggregated to a nonaggregated state as a function of aspect ratio and for a given particle concentration. This behavior has not been predicted so far and we put forward simple calculations to rationalize our observations.

Frequency-dependent deformation of liquid crystal droplets in an external electric field

Nematic droplets suspended in the isotropic phase of the same substance were subjected to alternating electrical fields of varying frequency. To keep the system at a constant nematic/isotropic volume ratio with constant droplet size, we carefully kept the temperature in the isotropic/nematic coexistence region, which was broadened by adding small amounts of a non-mesogenic liquid. Whereas the nematic droplets remained spherical at low (in the order of 10 Hz) and high frequencies (in the order of 1 kHz), at intermediate frequencies we observed a marked flattening of the droplets in the plane perpendicular to the applied field. Droplet deformation occurred both in liquid crystals (LCs) with positive and negative dielectric anisotropy. The experimental data can be quantitatively modelled with a combination of the leaky dielectric model and screening of the applied electric field due to finite conductivity.

Modeling dipolar and quadrupolar defect structures generated by chiral islands in freely suspended liquid crystal films

We report a detailed theoretical analysis of quadrupolar interactions observed between islands, which are disklike inclusions of extra layers, floating in thin, freely suspended smectic- C liquid crystal films. Strong tangential anchoring at the island boundaries results in a strength +1 chiral defect in each island and a companion -1 defect in the film--these forming a topological dipole. While islands of the same handedness form linear chains with the topological dipoles pointing in the same direction, as reported in the literature, islands with different handedness form compact quadrupolar structures with the associated dipoles pointing in opposite directions. The interaction between such heterochiral-island-defect pairs is complex, with the defects moving to minimize the director field distortion as the distance between the islands changes. The details of the interisland potential and the trajectories of the -1 defects depend strongly on the elastic anisotropy of the liquid crystal, which can be modified in the experiments by varying the material chirality of the liquid crystal. A Landau model that describes the energetics of freely mobile defects is solved numerically to find equilibrium configurations for a wide range of parameters.

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.

Corona patterns around inclusions in freely suspended smectic films

We discuss the structure and physical origin of corona patterns observed around solid or liquid spherical inclusions in freely suspended smectic films. Such patterns are observed when droplets or solid beads of micrometer size are sprayed onto the films. They are found in the smectic C phase and in the smectic A phase above such a smectic C phase, but disappear, for example, at the transition into a lower-temperature smectic B phase. We show that these structures are equivalent to splay domains found in the meniscus of freely suspended films, originating from surface-induced spontaneous splay.

Colloid-wall interaction in a nematic liquid crystal: the mirror-image method of colloidal nematostatics

The new area of nematic colloidal systems (or nematic emulsions) has been greatly guided by the fruitful analogy between the colloidal nematostatics and electrostatics. The elastic charge density representation of the colloidal nematostatics [V. M. Pergamenshchik and V. O. Uzunova, Eur. Phys. J. E 23, 161 (2007); Phys. Rev. E 76, 011707 (2007)] develops this analogy at the level of charge density and Coulomb interaction. It shows, however, that the colloidal nematostatics in three dimensions substantially differs from the electrostatics both in its mathematical structure and physical implications: the elastic charge and multipoles are dyads; similar charges attract while opposite charges repel each other, and so on. In this paper we consider the interaction between an elastic charge and elastic dipole with a nematic surface (wall) at which the director alignment is fixed. Using the mirror image method of electrostatics as a guiding idea, we develop the mirror image method in the nematostatics for arbitrary director tilt at the wall. A wall is shown to induce a repulsive 1R{4} force on the elastic dipole which, in general, is accompanied by its reorientation. External torque on the colloid induces an elastic charge therein and triggers switching to the 1R{2} repulsion. The dyadic nature of an elastic dipole is shown to be essential: a particle-wall interaction potential cannot be obtained in phenomenological theories with a single component dipole. In the introductory sections we discuss connection between the director-mediated interaction in two and three dimensions and the electrostatic interaction and consider different symmetries of elastic dipoles. Conservation of the torque components exerted upon colloids is shown to play the role of Gauss' theorem and determines the elastic charge dyad.

Ambidextrous bend patterns in free-standing polar smectic- CP{F} films

We report an unusual behavior of a ferroelectric smectic-CP{F} film formed by bent-shaped molecules. The ground state of the c -director in such film is not uniform but forms a striped pattern with alternating bend deformation. We found that the sense of the alternating bend is not related to an alternating handedness defined by the mutual orientation of the tilt ( c director) and the bow ( p director) of the molecules. Despite its similarity to a previously described twist-bend instability [J. Pang and N. A. Clark, Phys. Rev. Lett. 73, 2332 (1994)], this pattern cannot be explained in terms of spontaneous chiral symmetry breaking with continuous variation of the chirality order parameter, since the synclinic order of the polar molecules predefines the chirality of the film. We discuss possible models describing the spontaneous formation of an ambidextrous bend pattern of the c director.