Elastocapillary interactions on nematic films

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.

Phase-field model for elastocapillary flows of liquid crystals

We propose a phase-field model to study interfacial flows of nematic liquid crystals that couple the capillary forces on the interface with the elastic stresses in the nematic phase. The theoretical model has two key ingredients: A tensor order parameter that provides a consistent description of the molecular and distortional elasticity, and a phase-field formalism that accurately represents the interfacial tension and the nematic anchoring stress by approximating a sharp-interface limit. Using this model, we carry out finite-element simulations of drop retraction in a surrounding fluid, with either component being nematic. The results are summarized by eight representative steady-state solutions in planar and axisymmetric geometries, each featuring a distinct configuration for the drop and the defects. The dynamics is dominated by the competition between the interfacial tension and the distortional elasticity in the nematic phase, mediated by the anchoring condition on the drop surface. As consequences of this competition, the steady-state drop deformation and the clearance between the defects and the drop surface both depend linearly on the elastocapillary number.

Particle rotation speeds up capillary interactions

We use dynamic numerical simulations to investigate the role of particle rotation in pairwise capillary interactions of particles trapped at a fluid interface. The fluid interface is modeled with a phase-field method which is coupled to the Navier-Stokes equations to solve for the flow dynamics. Numerical solutions are found using a finite element scheme in a bounded two-dimensional geometry. The interfacial deformations are caused by the buoyant weight of the particles, which are allowed to both translate and rotate due to the capillary and viscous forces and torques at play. The results show that the capillary attraction is faster between freely rotating particles than if particle rotation is inhibited, and the higher the viscosity mismatch, the greater the effect. To explain this result, we analyze the drag force exerted on the particles and find that the translational drag force on a rotating particle is always less than its non-rotating counterpart due to attenuated velocity gradients in the vicinity of the particle. We also find that the influence of interfacial deformations on particle rotation is minute.

Ordering of adsorbed rigid rods mediated by the Boussinesq interaction on a soft substrate

Orientational ordering driven by mechanical distortion of soft substrates plays a major role in material transformation processes such as elastocapillarity and surface anchoring. We present a theoretical model of the orientational response of anisotropic rods deposited onto a surface of a soft, elastic substrate of finite thickness. We show that anisotropic rods exhibit a continuous isotropic-nematic phase transition, driven by orientational interactions between surface deposited rods. This interaction is mediated by the deformation of the underlying elastic substrate and is quantified by the Boussinesq solution adapted to the case of slender, surface deposited rods. From the microscopic rod-rod interactions, we derive the appropriate Maier-Saupe mean-field description, which includes the Boussinesq elastic free energy contribution due to the substrate elasticity, derive the conditions for the existence of a continuous orientational ordering transition, and discuss the implication of results in the soft (bio)system context.

Swelling Cholesteric Liquid Crystal Shells to Direct the Assembly of Particles at the Interface

Cholesteric liquid crystals can exhibit spatial patterns in molecular alignment at interfaces that can be exploited for particle assembly. These patterns emerge from the competition between bulk and surface energies, tunable with the system geometry. In this work, we use the osmotic swelling of cholesteric double emulsions to assemble colloidal particles through a pathway-dependent process. Particles can be repositioned from a surface-mediated to an elasticity-mediated state through dynamically thinning the cholesteric shell at a rate comparable to that of colloidal adsorption. By tuning the balance between surface and bulk energies with the system geometry, colloidal assemblies on the cholesteric interface can be molded by the underlying elastic field to form linear aggregates. The transition of adsorbed particles from surface regions with homeotropic anchoring to defect regions is accompanied by a reduction in particle mobility. The arrested assemblies subsequently map out and stabilize topological defects. These results demonstrate the kinetic arrest of interfacial particles within definable patterns by regulating the energetic frustration within cholesterics. This work highlights the importance of kinetic pathways for particle assembly in liquid crystals, of relevance to optical and energy applications.

Capillarity-driven migration of small objects: A critical review

The phenomena on the capillarity-driven migration of small objects are full of interest for both scientific and engineering communities, and a critical review is thereby presented. The small objects mentioned here deal with the non-deformable objects, such as particles, rods, disks and metal sheets; and besides them, the soft objects are considered, such as droplets and bubbles. Two types of interfaces are analyzed, i.e., the solid-fluid interface and the fluid-fluid interface. Due to the easily deformable properties of the soft objects and distorted interfacial shapes induced by small objects, a more convenient way to obtain the driving force is through the potential energy of the system. The asymmetric factors causing the object migration include the asymmetric configuration of the interface, and the difference between the interfacial tensions. Finally, a simple outlook on the potential applications of small object migration is made. These behaviors may cast new light on the design of microfluidics and new devices, environment cleaning, oil and gas displacement and mineral industries.

Shaping nanoparticle fingerprints at the interface of cholesteric droplets

The ordering of nanoparticles into predetermined configurations is of importance to the design of advanced technologies. Here, we balance the interfacial energy of nanoparticles against the elastic energy of cholesteric liquid crystals to dynamically shape nanoparticle assemblies at a fluid interface. By adjusting the concentration of surfactant that plays the dual role of tuning the degree of nanoparticle hydrophobicity and altering the molecular anchoring of liquid crystals, we pattern nanoparticles at the interface of cholesteric liquid crystal emulsions. In this system, interfacial assembly is tempered by elastic patterns that arise from the geometric frustration of confined cholesterics. Patterns are tunable by varying both surfactant and chiral dopant concentrations. Adjusting the particle hydrophobicity more finely by regulating the surfactant concentration and solution pH further modifies the rigidity of assemblies, giving rise to surprising assembly dynamics dictated by the underlying elasticity of the cholesteric. Because particle assembly occurs at the interface with the desired structures exposed to the surrounding water solution, we demonstrate that particles can be readily cross-linked and manipulated, forming structures that retain their shape under external perturbations. This study serves as a foundation for better understanding inter-nanoparticle interactions at interfaces by tempering their assembly with elasticity and for creating materials with chemical heterogeneity and linear, periodic structures, essential for optical and energy applications.

Electrically modulated capillary filling imbibition of nematic liquid crystals

The flow of nematic liquid crystals (NLCs) in the presence of an electric field is typically characterized by the variation in its rheological properties due to transition in its molecular arrangements. Here, we bring out a nontrivial interplay of a consequent alteration in the resistive viscous effects and driving electrocapillary interactions, toward maneuvering the capillary filling dynamics over miniaturized scales. Considering a dynamic interplay of the relevant bulk and interfacial forces acting in tandem, our results converge nicely to previously reported experimental data. Finally, we attempt a scaling analysis to bring forth further insight to the reported observations. Our analysis paves the way for the development of microfluidic strategies with previously unexplored paradigms of interaction between electrical and fluidic phenomenon, providing with an augmented controllability on capillary filling as compared to tthose reported to be achievable by the existing strategies. This, in turn, holds utilitarian scopes in improved designs of functional capillarities in electro-optical systems, electrorheological utilities, electrokinetic flow control, as well as in interfacing and imaging systems for biomedical microdevices.

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.

Conformations and membrane-driven self-organization of rodlike fd virus particles on freestanding lipid membranes

Membrane-mediated interactions and aggregation of colloidal particles adsorbed to responsive elastic membranes are challenging problems relevant for understanding the microscopic organization and dynamics of biological membranes. We experimentally study the behavior of rodlike semiflexible fd virus particles electrostatically adsorbed to freestanding cationic lipid membranes and find that their behavior can be controlled by tuning the membrane charge and ionic strength of the surrounding medium. Three distinct interaction regimes of rodlike virus particles with responsive elastic membranes can be observed. (i) A weakly charged freestanding cationic lipid bilayer in a low ionic strength medium represents a gentle quasi-2D substrate preserving the integrity, structure, and mechanical properties of the membrane-bound semiflexible fd virus, which under these conditions is characterized by a monomer length of 884 ± 4 nm and a persistence length of 2.5 ± 0.2 μm, in perfect agreement with its properties in bulk media. (ii) An increase in the membrane charge leads to the membrane-driven collapse of fd virus particles on freestanding lipid bilayers and lipid nanotubes into compact globules. (iii) When the membrane charge is low, and the mutual electrostatic repulsion of membrane-bound virus particles is screened to a considerable degree, membrane-driven self-organization of membrane-bound fd virus particles into long linear tip-to-tip aggregates showing dynamic self-assembly/disassembly and quasi-semiflexible behavior takes place. These observations are in perfect agreement with the results of recent theoretical and simulation studies predicting that membrane-mediated interactions can control the behavior of colloidal particles adsorbed on responsive elastic membranes.

Nano- and microparticles at fluid and biological interfaces

Systems with interfaces are abundant in both technological applications and biology. While a fluid interface separates two fluids, membranes separate the inside of vesicles from the outside, the interior of biological cells from the environment, and compartmentalize cells into organelles. The physical properties of interfaces are characterized by interface tension, those of membranes are characterized by bending and stretching elasticity. Amphiphilic molecules like surfactants that are added to a system with two immiscible fluids decrease the interface tension and induce a bending rigidity. Lipid bilayer membranes of vesicles can be stretched or compressed by osmotic pressure; in biological cells, also the presence of a cytoskeleton can induce membrane tension. If the thickness of the interface or the membrane is small compared with its lateral extension, both can be described using two-dimensional mathematical surfaces embedded in three-dimensional space. We review recent work on the interaction of particles with interfaces and membranes. This can be micrometer-sized particles at interfaces that stabilise emulsions or form colloidosomes, as well as typically nanometer-sized particles at membranes, such as viruses, parasites, and engineered drug delivery systems. In both cases, we first discuss the interaction of single particles with interfaces and membranes, e.g. particles in external fields, non-spherical particles, and particles at curved interfaces, followed by interface-mediated interaction between two particles, many-particle interactions, interface and membrane curvature-induced phenomena, and applications.

DNA Damage Response and Autophagy: A Meaningful Partnership

Autophagy and the DNA damage response (DDR) are biological processes essential for cellular and organismal homeostasis. Herein, we summarize and discuss emerging evidence linking DDR to autophagy. We highlight published data suggesting that autophagy is activated by DNA damage and is required for several functional outcomes of DDR signaling, including repair of DNA lesions, senescence, cell death, and cytokine secretion. Uncovering the mechanisms by which autophagy and DDR are intertwined provides novel insight into the pathobiology of conditions associated with accumulation of DNA damage, including cancer and aging, and novel concepts for the development of improved therapeutic strategies against these pathologies.

Colloidal Particles in Thin Nematic Wetting Films

We experimentally and theoretically study the variety of elastic deformations that appear when colloidal inclusions are embedded in thin wetting films of a nematic liquid crystal with hybrid anchoring conditions. In the thickest films, the elastic dipoles formed by particles and their accompanying defects share features with the patterns commonly observed in liquid crystal cells. When the film gets thinner than the particles size, however, the capillary effects strongly modify the appearance of the elastic dipoles and the birefringence patterns. The influence of the film thickness and particles sizes on the patterns has been explored. The main experimental features and the transitions observed at large scale-with respect to the inclusions' size-are explained with a simple two-dimensional Ansatz, combining capillarity and nematic elasticity. In a second step, we discuss the origin of the variety of observed textures. Developing a three-dimensional Landau-de Gennes model at the scale of the particles, we show that the presence of free interfaces and the beads confinement yield metastable configurations that are quenched during the film spreading or the beads trapping at interfaces.

Curvature-driven assembly in soft matter

Control over the spatial arrangement of colloids in soft matter hosts implies control over a wide variety of properties, ranging from the system's rheology, optics, and catalytic activity. In directed assembly, colloids are typically manipulated using external fields to form well-defined structures at given locations. We have been developing alternative strategies based on fields that arise when a colloid is placed within soft matter to form an inclusion that generates a potential field. Such potential fields allow particles to interact with each other. If the soft matter host is deformed in some way, the potential allows the particles to interact with the global system distortion. One important example is capillary assembly of colloids on curved fluid interfaces. Upon attaching, the particle distorts that interface, with an associated energy field, given by the product of its interfacial area and the surface tension. The particle's capillary energy depends on the local interface curvature. We explore this coupling in experiment and theory. There are important analogies in liquid crystals. Colloids in liquid crystals elicit an elastic energy response. When director fields are moulded by confinement, the imposed elastic energy field can couple to that of the colloid to define particle paths and sites for assembly. By improving our understanding of these and related systems, we seek to develop new, parallelizable routes for particle assembly to form reconfigurable systems in soft matter that go far beyond the usual close-packed colloidal structures.This article is part of the themed issue 'Soft interfacial materials: from fundamentals to formulation'.

Wetting behaviour and contact angles anisotropy of nematic nanodroplets on flat surfaces

We have studied the wetting behaviour of liquid crystal nanodroplets deposited on a planar surface, modelling the mesogens with Gay-Berne ellipsoids and the support surface with a slab of Lennard-Jones (LJ) spherical particles whose mesogen-surface affinity can be tuned. A crystalline and an amorphous planar surface, both showing planar anchoring, have been investigated: the first is the (001) facet of a LJ fcc crystal, the second is obtained from a disordered LJ glass. In both cases we find that the deposited nanodroplet is, in general, elongated and that the contact angle changes around its contour. Simulations for the crystalline substrate show that the angle of contact turns reversibly from anisotropic to isotropic when crossing the clearing transition. As far as we know this is a novel, not yet explored effect for thermotropic liquid crystals, that we hope will stimulate experimental investigations.

Capillary-induced giant elastic dipoles in thin nematic films

Directed and true self-assembly mechanisms in nematic liquid crystal colloids rely on specific interactions between microparticles and the topological defects of the matrix. Most ordered structures formed in thin nematic cells are thus based on elastic multipoles consisting of a particle and nearby defects. Here, we report, for the first time to our knowledge, the existence of giant elastic dipoles arising from particles dispersed in free nematic liquid crystal films. We discuss the role of capillarity and film thickness on the dimensions of the dipoles and explain their main features with a simple 2D model. Coupling of capillarity with nematic elasticity could offer ways to tune finely the spatial organization of complex colloidal systems.