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.

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.

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.

Drag force on a particle straddling a fluid interface: Influence of interfacial deformations.

We numerically investigate the influence of interfacial deformations on the drag force exerted on a particle straddling a fluid interface. We perform finite element simulations of the two-phase flow system in a bounded two-dimensional geometry. The fluid interface is modeled with a phase-field method which is coupled to the Navier-Stokes equations to solve for the flow dynamics. The interfacial deformations are caused by the buoyant weight of the particle, which results in curved menisci. We compute drag coefficients as a function of the three-phase contact angle, the viscosity ratio of the two fluids, and the particle density. Our results show that, for some parameter values, large drag forces are not necessarily correlated with large interfacial distortions and that a lower drag may actually be achieved with non-flat interfaces rather than with unperturbed ones.

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.

Motion of Optically Heated Spheres at the Water-Air Interface.

A micrometer-sized spherical particle classically equilibrates at the water-air interface in partial wetting configuration, causing about no deformation to the interface. In condition of thermal equilibrium, the particle just undergoes faint Brownian motion, well visible under a microscope. We report experimental observations when the particle is made of a light-absorbing material and is heated up by a vertical laser beam. We show that, at small laser power, the particle is trapped in on-axis configuration, similarly to 2-dimensional trapping of a transparent sphere by optical forces. Conversely, on-axis trapping becomes unstable at higher power. The particle escapes off the laser axis and starts orbiting around the axis. We show that the laser-heated particle behaves as a microswimmer with velocities on the order of several 100 µm/s with just a few milliwatts of laser power.

Optically driven oscillations of ellipsoidal particles. Part I: experimental observations.

We report experimental observations of the mechanical effects of light on ellipsoidal micrometre-sized dielectric particles, in water as the continuous medium. The particles, made of polystyrene, have shapes varying between near disk-like (aspect ratio k = 0.2) to very elongated needle-like (k = 8). Rather than the very tightly focused beam geometry of optical tweezers, we use a moderately focused laser beam to manipulate particles individually by optical levitation. The geometry allows us varying the longitudinal position of the particle, and to capture images perpendicular to the beam axis. Experiments show that moderate-k particles are radially trapped with their long axis lying parallel to the beam. Conversely, elongated (k > 3) or flattened (k < 0.3) ellipsoids never come to rest, and permanently "dance" around the beam, through coupled translation-rotation motions. The oscillations are shown to occur in general, be the particle in bulk water or close to a solid boundary, and may be periodic or irregular. We provide evidence for two bifurcations between static and oscillating states, at k ≈ 0.33 and k ≈ 3 for oblate and prolate ellipsoids, respectively. Based on a recently developed 2-dimensional ray-optics simulation (Mihiretie et al., EPL 100, 48005 (2012)), we propose a simple model that allows understanding the physical origin of the oscillations.

Optically driven oscillations of ellipsoidal particles. Part II: ray-optics calculations.

We report numerical calculations on the mechanical effects of light on micrometer-sized dielectric ellipsoids immersed in water. We used a simple two-dimensional ray-optics model to compute the radiation pressure forces and torques exerted on the object as a function of position and orientation within the laser beam. Integration of the equations of motion, written in the Stokes limit, yields the particle dynamics that we investigated for different aspect ratios k. Whether the beam is collimated or focused, the results show that above a critical aspect ratio k(C), the ellipsoids cannot be stably trapped on the beam axis; the particle never comes to rest and rather oscillates permanently in a back-and-forth motion involving both translation and rotation in the vicinity of the beam. Such oscillations are a direct evidence of the non-conservative character of optical forces. Conversely, stable trapping can be achieved for k < k(C) with the particle standing idle in a vertical position. These predictions are in very good qualitative agreement with experimental observations. The physical origin of the instability may be understood from the force and torque fields whose structures greatly depend on the ellipsoid aspect ratio and beam diameter. The oscillations arise from a non-linear coupling of the forces and torques and the torque amplitude was identified as the bifurcation control parameter. Interestingly, simulations predict that sustained oscillations can be suppressed through the use of two coaxial counterpropagating beams, which may be of interest whenever a static equilibrium is required as in basic force and torque measurements or technological applications.

Photonic control of surface anchoring on solid colloids dispersed in liquid crystals.

The anchoring of liquid-crystal (LC) mesogens to the surfaces of colloids is an important factor in determining intercolloidal interactions and the symmetry of the ensuing colloidal assembly in nematic colloids. The dynamic control of surface anchoring could therefore provide a handle to tune the colloidal organization and resulting properties in these systems. In this article, we report our results on the study of thermotropic nematic LC (E7) dispersions of silica and glass microcolloids bearing photosensitive surface azobenzene groups. By the photoinduced modulation of the colloidal-LC interfacial properties, due to the trans-cis isomerization of azobenzene units, we tune the anchoring on silica colloids from homeotropic (trans-azobenzene) to homogeneous planar (cis-azobenzene) reversibly. In tune with the change in surface anchoring, the interparticle interactions were also dictated by dipolar and quadrupolar symmetries for homeotropic and homogeneous planar anchoring, respectively. In our experiments, we find that, in addition to the isomerization state of the surface-bound azobenzene units, the nature of the colloid plays a crucial role in determining the anchoring state obtained on applying photostimuli. We also study the LC anchoring on colloids as a function of the azobenzene surface density and find that beyond a threshold value the anchoring properties remain invariant.

How do mosquito eggs self-assemble on the water surface?

This work reports a detailed numerical study of the behavior of ellipsoid-shaped particles adsorbed at fluid interfaces. Former experiments have shown that micrometer-sized prolate ellipsoids aggregate under the action of strong and long-ranged capillary interactions. The latter are due to nonplanar contact lines and to the resulting deformations of the interface in the vicinity of the trapped objects. We first consider the case of a single ellipsoid and examine in detail the influence of contact angle and ellipsoid aspect ratio on interfacial distortions. We then focus on two contacting ellipsoids and study the optimum packing configuration depending on their size and/or aspect ratio mismatch. We thoroughly explore the variety of contact configurations between both ellipsoids and provide corresponding energy maps. Whereas the side-by-side configuration is the most stable state for identical ellipsoids, we find that the mismatched pair adopts an "arrow" configuration in which a finite angle exists between the particles long axes. Such arrows are actually seen in experiments with micron-sized ellipsoids and similarly with millimeter-sized mosquito eggs. These results complement our previous work (J.C. Loudet, B. Pouligny, EPL 85, 28003 (2009)) and highlight the importance of geometrical factors to explain the morphology of aggregated structures at fluid interfaces.

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.

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.

Wetting and contact lines of micrometer-sized ellipsoids.

We experimentally and theoretically investigate the shapes of contact lines on the surfaces of micrometer-sized polystyrene ellipsoids at the water-air interface. By combining interferometry and optical trapping, we directly observe quadrupolar symmetry of the interface deformations around such particles. We then develop numerical solutions of the partial wetting problem for ellipsoids, and use these solutions to deduce the shapes of the corresponding contact lines and the values of the contact angles, theta(c)(k), as a function of the ellipsoid aspect ratio k. Surprisingly, theta(c) is found to decrease for increasing k suggesting that ellipsoid microscopic surface properties depend on ellipsoid aspect ratio.

Capillary interactions between anisotropic colloidal particles.

We report on the behavior of micron-sized prolate ellipsoids trapped at an oil-water interface. The particles experience strong, anisotropic, and long-ranged attractive capillary interactions which greatly exceed the thermal energy k(B)T. Depending on surface chemistry, the particles aggregate into open structures or chains. Using video microscopy, we extract the pair interaction potential between ellipsoids and show it exhibits a power law behavior over the length scales probed. Our observations can be explained using recent calculations, if we describe the interfacial ellipsoids as capillary quadrupoles.

Colloidal structures from bulk demixing in liquid crystals.

This experimental paper deals with phase separations of binary mixtures composed of a continuous liquid crystal phase and an isotropic dispersed phase. In contrast to isotropic binary mixtures, the investigated mixtures do not lead to a full phase separation but to a self-ordering of colloidal particles, as reported earlier (Loudet, J. C. et al. Nature 2000, 407, 611). We present here further aspects of such phase separations which include the kinetics of the phase separation, the origin of the formation of dislocation-like patterns, the influence of surfactants, chiral additives, and temperature on the formed colloidal structures. The present results show that (i) the dislocations in chain arrays can be seen as kinetically frozen defects, (ii) temperature can be used to control the size of the domains formed upon demixing, (iii) a slight change in surface chemistry, via the addition of surfactants, profoundly alters the formed colloidal structures, and (iv) chiral additives allow the formation of unique helical pearl chains which reflect the symmetry of the liquid crystal phase they are embedded in.

Stokes drag on a sphere in a nematic liquid crystal.

The Stokes-Einstein relation relates the diffusion coefficient of a spherical Brownian particle in a viscous fluid to its friction coefficient. For a particle suspended in anisotropic liquid, theory predicts that the drag coefficient should also be anisotropic. Using video microscopy coupled with particle tracking routines, the Brownian fluctuations of micrometer-sized particles were analyzed to yield a quantitative measurement of the diffusion coefficients parallel and perpendicular to the nematic director. The experimental values agree quite well with recent numerical calculations that take into account the distortions of the director field in the vicinity of the particles.

Application of an electric field to colloidal particles suspended in a liquid-crystal solvent.

We study the behavior of colloidal particles suspended in a thermotropic nematic solvent in the presence of an electric field. For normal boundary conditions of the nematic director at the particles' surface, we show experimentally that an electric field applied along the dipolar axis of an elastic dipole induces a transition to an elastic quadrupolar configuration. Turning the field off makes the system go back to the initial state. We also show that it is possible to directly evidence an elastic quadrupolar repulsion between droplets.

From macroscopic adhesion energy to molecular bonds: a test of the theory.

We present a statistical mechanical treatment relating the macroscopic adhesion energy of two surfaces, which can be obtained by micropipette aspiration studies, to the microscopic adhesion energy between individual bonds. The treatment deals with the case of weak reversible bonds, so that the equilibrium partition function has significance. This description is coherent with previous theories. Experiment and theory are compared to probe the nature of weak bonds in membranes, where local equilibria can be obtained. The case of a bead and a vesicle decorated by nucleosides was considered.