Ordering of Solid Microparticles at Liquid Crystal−Water Interfaces

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.

Dynamic Microparticle Assembly at the Interface of Chemoresponsive Liquid Crystal Droplets

The confinement of liquid crystals (LCs) in spherical microdroplets results in exotic internal configurations and topological defects in response to physical and chemical stimuli. Recent exploration into the placement of colloids on the surface of LC microdroplets has led to the design of a new class of functional materials with patterned surface properties. It is established that the placement of a colloid on a LC droplet surface can pin the topological defect at the interface, thereby restricting changes in the LC configuration. Herein, we build upon the handful of reports published to provide a fundamental understanding of the colloid positioning in response to external stimuli. Using polystyrene (PS) colloids, we explored the dynamics of particle self-assembly in response to an interfacial enzymatic breakdown of poly-l-lysine by trypsin. We found that for a significant population of droplets, the positioning of the colloid is unaffected by the changes in the internal ordering of LC. Inspired by the new observations, we delved deeper to understand the role of interfacial stabilizers in modulating the preferential alignment of LC and the placement of colloidal microparticles. We also demonstrated that for a certain population of droplets, the positioning of the colloids remains unperturbed in response to multistep reversible adsorption of interfacial amphiphiles. Our findings reveal interesting possibilities of correlating the stimuli-responsive switching of internal configurations of LC with colloid placement on the particle-decorated LC droplets.

Understanding directed assembly of concentrated nanoparticles at energetically heterogeneous interfaces of cholesteric liquid crystal droplets

Colloidal self-assembly has gained significant interest in scientific and technological advances. We investigated the self-assembly of the colloids at fluidic interfaces that mediate elastic interactions. Whereas past studies have reported the assembly of micrometer- or molecular-sized species at aqueous interfaces of liquid crystals (LCs), herein we study the assembly of intermediate-sized nanoparticles. Specifically, surface-modified silica nanoparticles (50 to 500 nm) were adsorbed at the liquid crystal-water interfaces and their positioning was investigated using electron microscopy after polymerization. The study revealed that the electric double layer forces and the elastic forces caused by LC strain are dominant in the assembly of nanoparticles and their contributions can be tuned to direct the self-assembly guided by the sub-interface symmetry of confined cholesteric LCs. At high ionic strengths, we observed a strong localization of nanoparticles at the defects, whereas intermediate strengths resulted in their partial enrichment into cholesteric fingerprint patterns with an interaction energy of ≈3 k_BT. This result is comparable with the calculations based on the strength of the binary interactions of the nanoparticles. The findings also support the role of ion partitioning at the LC-aqueous interfaces on the formation of the assemblies. The results can be utilized for applications in sensors, microelectronics, and photonics.

Particle trapped at the isotropic-nematic liquid crystal interface: Elastocapillary phenomena and drag forces

We present numerical simulations of a particle trapped at the isotropic-nematic liquid crystal (Iso-N) interface. We use our recent model, based on a phase-field approach [see Qiu et al., Phys. Rev. E 103, 022706 (2021)10.1103/PhysRevE.103.022706], to couple the capillary forces acting on the interface with the elastic stresses in the nematic phase along with topological defects. A range of floating configurations are first investigated as a function of the contact angle and various anchoring conditions at the fluid interface. The results show that the response of the system is driven by the existence of an anchoring conflict at the contact line. Substantial particle displacements and/or interfacial deformations may occur in this case even for moderate anchoring strengths. These findings highlight the coupling between elastic and capillary forces. In a second part, we compute drag forces exerted on a particle that moves along the Iso-N interface for several contact angles and a moderate Ericksen number. Because of the coupling between the velocity and order parameter fields, topological defects are swept downstream of the particle by the flow and sometimes escape from the particle or merge with the interface. We also find linear force-velocity laws, with drag forces at the Iso-N interface being slightly greater than their isotropic counterparts due to director distortions. We discuss these results in light of past studies on the behavior of particles being dragged in the bulk of a liquid crystal matrix.

Nematic colloids at liquid crystal-air interfaces via photopolymerization

We demonstrate the preparation of colloidal crystals at nematic liquid crystal-air interfaces by simultaneous photopolymerization and assembly. Polymer colloids are produced by polymerization-induced phase separation of 2-hydroxyethyl methacrylate in the non-reactive liquid crystal (LC) 4-cyano-4'-pentylbiphenyl (5CB) using an open-cell setup. Colloids adsorbed to the nematic 5CB-air interface form non-close-packed hexagonal crystals that cover the entire interface area. We examine the mechanism of growth and assembly for the preparation of LC-templated interfacial colloidal superstructures.

Nematohydrodynamics for colloidal self-assembly and transport phenomena

HYPOTHESIS

Colloidal particles in a nematic liquid crystal (NLC) exhibit very different behaviour to that observed in an isotropic medium. Such differences arise principally due to the nematic-induced elastic stresses exerted due to the interaction of NLC molecules with interfaces, which compete with traditional fluid viscous stresses on the particle.

THEORY

A systematic mathematical analysis of particles in an NLC microfluidic channel is performed using the continuum Beris-Edwards framework coupled to the Navier-Stokes equations. We impose strong homeotropic anchoring on the channel walls and weak homeotropic anchoring on the particle surfaces.

FINDINGS

The viscous and NLC forces act on an individual particle in opposing directions, resulting in a critical location in the channel where the particle experiences zero net force in the direction perpendicular to the flow. For multi-particle aggregation we show that the final arrangement is independent of the initial configuration, but the path towards achieving equilibrium is very different. These results uncover new mechanisms for particle separation and routes towards self-assembly.

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.

Modeling deformation and chaining of flexible shells in a nematic solvent with finite elements on an adaptive moving mesh

A micrometer-scale elastic shell immersed in a nematic liquid crystal may be deformed by the host if the cost of deformation is comparable to the cost of elastic deformation of the nematic. Moreover, such inclusions interact and form chains due to quadrupolar distortions induced in the host. A continuum theory model using finite elements is developed for this system, using mesh regularization and dynamic refinement to ensure quality of the numerical representation even for large deformations. From this model, we determine the influence of the shell elasticity, nematic elasticity, and anchoring condition on the shape of the shell and hence extract parameter values from an experimental realization. Extending the model to multibody interactions, we predict the alignment angle of the chain with respect to the host nematic as a function of aspect ratio, which is found to be in excellent agreement with experiments.

Using liquid crystals to reveal how mechanical anisotropy changes interfacial behaviors of motile bacteria

Bacteria often inhabit and exhibit distinct dynamical behaviors at interfaces, but the physical mechanisms by which interfaces cue bacteria are still poorly understood. In this work, we use interfaces formed between coexisting isotropic and liquid crystal (LC) phases to provide insight into how mechanical anisotropy and defects in LC ordering influence fundamental bacterial behaviors. Specifically, we measure the anisotropic elasticity of the LC to change fundamental behaviors of motile, rod-shaped Proteus mirabilis cells (3 μm in length) adsorbed to the LC interface, including the orientation, speed, and direction of motion of the cells (the cells follow the director of the LC at the interface), transient multicellular self-association, and dynamical escape from the interface. In this latter context, we measure motile bacteria to escape from the interfaces preferentially into the isotropic phase, consistent with the predicted effects of an elastic penalty associated with strain of the LC about the bacteria when escape occurs into the nematic phase. We also observe boojums (surface topological defects) present at the interfaces of droplets of nematic LC (tactoids) to play a central role in mediating the escape of motile bacteria from the LC interface. Whereas the bacteria escape the interface of nematic droplets via a mechanism that involved nematic director-guided motion through one of the two boojums, for isotropic droplets in a continuous nematic phase, the elasticity of the LC generally prevented single bacteria from escaping. Instead, assemblies of bacteria piled up at boojums and escape occurred through a cooperative, multicellular phenomenon. Overall, our studies show that the dynamical behaviors of motile bacteria at anisotropic LC interfaces can be understood within a conceptual framework that reflects the interplay of LC elasticity, surface-induced order, and topological defects.

Recent advances in colloidal and interfacial phenomena involving liquid crystals

This feature article describes recent advances in several areas of research involving the interfacial ordering of liquid crystals (LCs). The first advance revolves around the ordering of LCs at bio/chemically functionalized surfaces. Whereas the majority of past studies of surface-induced ordering of LCs have involved surfaces of solids that present a limited diversity of chemical functional groups (surfaces at which van der Waals forces dominate surface-induced ordering), recent studies have moved to investigate the ordering of LCs on chemically complex surfaces. For example, surfaces decorated with biomolecules (e.g., oligopeptides and proteins) and transition-metal ions have been investigated, leading to an understanding of the roles that metal-ligand coordination interactions, electrical double layers, acid-base interactions, and hydrogen bonding can play in the interfacial ordering of LCs. The opportunity to create chemically responsive LCs capable of undergoing ordering transitions in the presence of targeted molecular events (e.g., ligand exchange around a metal center) has emerged from these fundamental studies. A second advance has focused on investigations of the ordering of LCs at interfaces with immiscible isotropic fluids, particularly water. In contrast to prior studies of surface-induced ordering of LCs on solid surfaces, LC-aqueous interfaces are deformable and molecules at these interfaces exhibit high levels of mobility and thus can reorganize in response to changes in the interfacial environment. A range of fundamental investigations involving these LC-aqueous interfaces have revealed that (i) the spatial and temporal characteristics of assemblies formed from biomolecular interactions can be reported by surface-driven ordering transitions in the LCs, (ii) the interfacial phase behavior of molecules and colloids can be coupled to (and manipulated via) the ordering (and nematic elasticity) of LCs, and (iii) the confinement of LCs leads to unanticipated size-dependent ordering (particularly in the context of LC emulsion droplets). The third and final advance addressed in this article involves interactions between colloids mediated by LCs. Recent experiments involving microparticles deposited at the LC-aqueous interface have revealed that LC-mediated interactions can drive interfacial assemblies of particles through reversible ordering transitions (e.g., from 1D chains to 2D arrays with local hexagonal symmetry). In addition, recent single-nanoparticle measurements suggest that the ordering of LCs about nanoparticles differs substantially from micrometer-sized particles and that the interactions between nanoparticles mediated by the LCs are far weaker than predicted by theory (sufficiently weak that the interactions are reversible and thus enable self-assembly). Finally, LC-mediated interactions between colloidal particles have also been shown to lead to the formation of colloid-in-LC gels that possess mechanical properties relevant to the design of materials that interface with living biological systems. Overall, these three topics serve to illustrate the broad opportunities that exist to do fundamental interfacial science and discovery-oriented research involving LCs.

Chemoresponsive assemblies of microparticles at liquid crystalline interfaces

Assemblies formed by solid particles at interfaces have been widely studied because they serve as models of molecular phenomena, including molecular self-assembly. Solid particles adsorbed at interfaces also provide a means of stabilizing liquid-liquid emulsions and synthesizing materials with tunable mechanical, optical, or electronic properties. Whereas many past studies have investigated colloids at interfaces of isotropic liquids, recently, new types of intercolloidal interactions have been unmasked at interfaces of liquid crystals (LCs): The long-range ordering of the LCs, as well as defects within the LCs, mediates intercolloidal interactions with symmetries that differ from those observed with isotropic liquids. Herein, we report the decoration of interfaces formed between aqueous phases and nematic LCs with prescribed densities of solid, micrometer-sized particles. The microparticles assemble into chains with controlled interparticle spacing, consistent with the dipolar symmetry of the defects observed to form about each microparticle. Addition of a molecular surfactant to the aqueous phase results in a continuous ordering transition in the LC, which triggers reorganization of the microparticles, first by increasing the spacing between microparticles within chains and ultimately by forming two-dimensional arrays with local hexagonal symmetry. The ordering transition of the microparticles is reversible and is driven by surfactant-induced changes in the symmetry of the topological defects induced by the microparticles. These results demonstrate that the orderings of solid microparticles and molecular adsorbates are strongly coupled at the interfaces of LCs and that LCs offer the basis of methods for reversible, chemosensitive control of the interfacial organization of solid microparticles.