Corona patterns around inclusions in freely suspended smectic films

Elastocapillary interaction for particles trapped at the isotropic-nematic liquid crystal interface

We present numerical simulations on pairwise interactions between particles trapped at an isotropic-nematic liquid crystal (Iso-N) interface. The particles are subject to elastocapillary interactions arising from interfacial deformations and elastic distortions of the nematic phase. We use a recent model based on a phase-field approach [see Qiu et al., Phys. Rev. E 103, 022706 (2021)2470-004510.1103/PhysRevE.103.022706] to take into account the coupling between elastic and capillary phenomena. The pair potential is computed in a two-dimensional geometry for a range of particle separations and two anchoring configurations. The first configuration leads to the presence of an anchoring conflict at the three-phase contact line, whereas such a conflict does not exist for the second one. In the first case, the results show that significant interfacial deformations and downward particle displacements occur, resulting in sizable attractive capillary interactions able to overcome repulsive elastic forces at intermediate separations. The pair potential exhibits an equilibrium distance since elastic repulsions prevail at short range and prevent the clustering of particles. However, in the absence of any anchoring conflict, the interfacial deformations are very small and the capillary forces have a negligible contribution to the pair potential, which is fully repulsive and overwhelmed by elastic forces. These results suggest that the self-assembly properties of particles floating at Iso-N interfaces might be controlled by tuning anchoring conflicts.

Undulations of Smectic A Layers in Achiral Liquid Crystals Manifested as Stripe Textures

Self-assembly of organic molecules represents a fascinating playground to create various liquid crystalline nanostructures. In this Letter, we study layer undulations on micrometer scale in smectic A phases for achiral compounds, experimentally demonstrated as regular stripe patterns induced by thermal treatment. Undulations, including their anharmonic properties, are evaluated by means of polarimetric imaging and light diffraction experiments in cells with various thicknesses. The key role in stripe formation is played by high negative values of the thermal expansion coefficient.

Complex-tensor theory of simple smectics

Matter self-assembling into layers generates unique properties, including structures of stacked surfaces, directed transport, and compact area maximization that can be highly functionalized in biology and technology. Smectics represent the paradigm of such lamellar materials - they are a state between fluids and solids, characterized by both orientational and partial positional ordering in one layering direction, making them notoriously difficult to model, particularly in confining geometries. We propose a complex tensor order parameter to describe the local degree of lamellar ordering, layer displacement and orientation of the layers for simple, lamellar smectics. The theory accounts for both dislocations and disclinations, by regularizing singularities within defect cores and so remaining continuous everywhere. The ability to describe disclinations and dislocation allows this theory to simulate arrested configurations and inclusion-induced local ordering. This tensorial theory for simple smectics considerably simplifies numerics, facilitating studies on the mesoscopic structure of topologically complex systems.

Curvature elasticity of smectic-C liquid crystals and formation of stripe domains along thickness gradients in menisci of free-standing films

Smectic liquid crystals with a layering order of rodlike molecules can be drawn in the form of free standing films across holes. Extensive experimental studies have shown that smectic-C (SmC) liquid crystals (LCs) with tilted molecules form periodic stripes in the thinner parts of the meniscus, which persist over a range of temperatures above the transition of the bulk medium to the SmA phase in which the tilt angle is zero. The prevailing theoretical models cannot account for all the experimental observations. We propose a model in which we argue that the negative curvature of the surface of the meniscus results in an energy cost when the molecules tilt at the surface. The energy can be reduced by exploiting the allowed (∇·k)(∇·c) deformation which couples the divergence of k, the unit vector along the layer normal, with that of c, the projection of the tilted molecular director on the layer plane. We propose a structure with periodic bending of layers with opposite curvatures, in which the c-vector field itself has a continuous deformation. Calculations based on the theoretical model can qualitatively account for all the experimental observations. It is suggested that detailed measurements on the stripes may be useful for getting good estimates of a few curvature elastic constants of SmC LCs.

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.

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.

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.

Observations of a streak texture in the hybrid-aligned smectic-C phase

A novel structure was observed below the smectic-A-smectic-C phase transition in a very thin open cell having an air interface above and enforced planar anchoring at the substrate below. The structure appears as periodic dark and light streaks running perpendicular to the oily streaks, which are present in the smectic-A phase [D. Coursault et al., Soft Matter, 2016, 12, 678]. These new streaks, which we call "soapy streaks", form by extending from one oily streak to the next in discrete steps, eliminating optical evidence at visible wavelengths of the oily streaks. At lower temperatures the streaks can undulate and exhibit a sawtooth-like structure; such a structure is chiral in two dimensions. A possible scenario for the origin of these streaks is presented.

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.

Defect Interactions in Anisotropic Two-Dimensional Fluids

Disclinations in liquid crystals bear striking analogies to defect structures in a wide variety of physical systems, and their straightforward optical observability makes them excellent models to study fundamental properties of defect interactions. We employ freely suspended smectic-C films, which behave as quasi-two-dimensional polar nematics. A procedure to capture high-strength disclinations in localized spots is introduced. These disclinations are released in a controlled way, and the motion of the mutually repelling topological charges with strength +1 is studied quantitatively. We demonstrate that the classical models, which employ elastic one-constant approximation, fail to describe their dynamics correctly. In realistic liquid crystals, even small differences between splay and bend constants lead to the selection of pure splay or pure bend +1 defects. For those, the models work only in very special configurations. In general, additional director walls are involved which reinforce the repulsive interactions substantially.

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.

Labyrinthine instability in freely suspended films of a polarization-modulated smectic phase

We report on fingering and labyrinthine instabilities of the layer dislocation lines in freely suspended polar liquid-crystalline films. These polar fingerlike and labyrinth structures reversibly form upon a transition into a modulated phase. External electric fields of several kV/m applied in the film plane can reversibly influence the formation of the finger textures. We show that the labyrinthine pattern is intrinsically related to regular splay deformations of the polarization.

Undulation instabilities in the meniscus of smectic membranes

Using optical microscopy, phase shifting interferometry, and atomic force microscopy, we characterize the undulated structures which appear in the meniscus of freestanding ferroelectric smectic-C* films. We demonstrate that these periodic structures correspond to undulations of the smectic-air interface. The resulting striped pattern disappears in the untilted smectic-A phase. The modulation amplitude and wavelength of the instability both depend on meniscus thickness. We study the temperature evolution and propose a model that qualitatively accounts for the observations.