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

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.

Focal conic flowers, dislocation rings, and undulation textures in smectic liquid crystal Janus droplets

Liquid crystalline phases of matter often exhibit visually stunning patterns or textures. Mostly, these liquid crystal (LC) configurations are uniquely determined by bulk LC elasticity, surface anchoring conditions, and confinement geometry. Here, we experimentally explore defect textures of the smectic LC phase in unique confining geometries with variable curvature. We show that a complex range of director configurations can arise from a single system, depending on sample processing procedures. Specifically, we report on LC textures in Janus drops comprised of silicone oil and 8CB in its smectic-A LC phase. The Janus droplets were made in aqueous suspension using solvent-induced phase separation. After drop creation, smectic layers form in the LC compartment, but their self-assembly is frustrated by the need to accommodate both the bowl-shaped cavity geometry and homeotropic (perpendicular) anchoring conditions at boundaries. A variety of stable and metastable smectic textures arise, including focal conic domains, dislocation rings, and undulations. We experimentally characterize their stabilities and follow their spatiotemporal evolution. Overall, a range of fabrication kinetics produce very different intermediate and final states. The observations elucidate assembly mechanisms and suggest new routes for fabrication of complex soft material structures in Janus drops and other confinement geometries.

Hierarchical self-assembling and helical structure in focal conic domains in meniscus of ferroelectric liquid crystal

We investigate experimentally the formation of focal conic domains of the ferroelectric phase of a liquid crystal, chiral smectic C (SmC^{*}), in the meniscus geometry. The meniscus geometry is formed in the gap between two glass plates which are placed on a common substrate. This gap is called here a physical cavity. Focal conic domains (FCDs) in the physical cavity with dimensions of micrometer scale are investigated under an optical polarizing microscope which enables us to extract the information on the helical structure formation in the constraint and gradient topological meniscus interface. The helical pitch in the FCD is observed to be shorter than in planar confined geometry. A crucial phenomenon of unwrapping and wrapping of helical structure from one FCD to another is also observed. In-plane application of an electric field on a FCD revealed the asymmetric helical unwinding process whereas an increase in temperature has shown symmetrical unwinding. The helical structure based observation is significant for understanding the ferroelectric phase in focal conic domains and their application in microlenses and optical components.

Phase-field model for a weakly compressible soft layered material: morphological transitions on smectic-isotropic interfaces

A coupled phase-field and hydrodynamic model is introduced to describe a two-phase, weakly compressible smectic (layered phase) in contact with an isotropic fluid of different density. A non-conserved smectic order parameter is coupled to a conserved mass density in order to accommodate non-solenoidal flows near the smectic-isotropic boundary arising from density contrast between the two phases. The model aims to describe morphological transitions in smectic thin films under heat treatment, in which arrays of focal conic defects evolve into conical pyramids and concentric rings through curvature dependent evaporation of smectic layers. The model leads to an extended thermodynamic relation at a curved surface that includes its Gaussian curvature, non-classical stresses at the boundary and flows arising from density gradients. The temporal evolution given by the model conserves the overall mass of the liquid crystal while still allowing for the modulated smectic structure to grow or shrink. A numerical solution of the governing equations reveals that pyramidal domains are sculpted at the center of focal conics upon a temperature increase, which display tangential flows at their surface. Other cases investigated include the possible coalescence of two cylindrical stacks of smectic layers, formation of droplets, and the interactions between focal conic domains through flow.

Structural Landscapes in Geometrically Frustrated Smectics

A phenomenological free energy model is proposed to describe the behavior of smectic liquid crystals, an intermediate phase that exhibits orientational order and layering at the molecular scale. Advantageous properties render the functional amenable to numerical simulation. The model is applied to a number of scenarios involving geometric frustration, leading to emergent structures such as focal conic domains and oily streaks and enabling detailed elucidation of the very rich energy landscapes that arise in these problems.

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.

Saddle-splay-induced periodic edge undulations in smectic-A disks immersed in a nematic medium

We report experimental studies on the phase behavior of binary mixtures of 1″,7″-bis(4-cyanobiphenyl-4'-yl)heptane (CB7CB) and 4,4-diheptyloxyazoxybenzene, which exhibit, apart from the nematic (N) and twist-bend nematic (N_{TB}) phases, the induced smectic-A (Sm-A) phase for weight fraction of CB7CB between 0.05 and 0.70. In planar nematic layers, the N_{TB} phase separates as droplets of tactoidlike planform; the chirality of droplets manifests in the optical dissimilarity between their opposite angular ends. Our main result is that, in the appropriate two phase region, Sm-A nuclei with positive dielectric anisotropy change over to disks immersed in the nematic above some electric field, their edges decorated by periodic bright spots, a result which was earlier reported in another binary system exhibiting the induced Sm-A phase [R. Pratibha and N. V. Madhusudana, Physica A 224, 9 (1996)10.1016/0378-4371(95)00311-8]. We develop a simple theory for the threshold of this distortion, which is a periodic undulation of the edge of the disk, demonstrating that it arises from saddle-splay elasticity of Sm-A, the low Sm-A-N interfacial tension unable to suppress the distortion. The observed increases in the number of bright spots with field, and with the radius of the disk at a given field, in both the experimental systems are also accounted for by the model. The distortion, which results in the most direct visualization of saddle splay in Sm-A, is also exhibited by disks nucleating on surfaces treated for homeotropic anchoring.

Dynamic wrinkling of freely floating smectic films

We demonstrate spontaneous wrinkling as a transient dynamical pattern in thin freely floating smectic liquid-crystalline films. The peculiarity of such films is that, while behaving liquid-like with respect to flow in the film plane, they cannot quickly expand their thickness because that requires stacking of additional smectic layers. At short time scales, they therefore behave like quasi-incompressible membranes, very different from soap films. Smectic films can develop a transient undulation instability or form bulges in response to lateral compression. Optical experiments with freely floating bubbles on parabolic flights and in ground lab experiments are reported. The characteristic wavelengths of the wrinkles are in the submillimeter range. We demonstrate the dynamic nature of the pattern formation mechanism and develop a basic model that explains the physical mechanism for the wavelength selection and wrinkle orientation.

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.

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.