We propose a hybrid lattice Boltzmann algorithm to simulate the hydrodynamics of colloidal particles inside a liquid crystalline host. To validate our algorithm, we study the static and the microrheology of a colloid in a nematic, with tangential anchoring of the director field at the particle surface, and we confirm theories and experiments showing that the drag force in a nematic is markedly anisotropic. We then apply our method to consider the case of a colloid inside a cholesteric, and with normal anchoring at the surface. We show that by tuning the ratio between particle size and cholesteric pitch it is possible to control the defect configuration around the particle, and to stabilise novel figure-of-eight or highly twisted loops close to the colloid surface.
We introduce the Poisson-Boltzmann cell model for spherical colloidal particles with a heterogeneous surface charge distribution. This model is obtained by generalizing existing cell models for mixtures of homogeneously charged colloidal spheres. Our new model has similar features as Onsager's second-virial theory for liquid crystals, but it predicts no orientational ordering if there is no positional ordering. This implies that all phases of heterogeneously charged colloids that are liquid-like with respect to translational degrees of freedom are also isotropic with respect to particle orient…
We present a progress report on our work on lattice Boltzmann methods for colloidal suspensions. We focus on the treatment of colloidal particles in binary solvents and on the inclusion of thermal noise. For a benchmark problem of colloids sedimenting and becoming trapped by capillary forces at a horizontal interface between two fluids, we discuss the criteria for parameter selection, and address the inevitable compromise between computational resources and simulation accuracy.
We present a Lattice-Boltzmann method for simulating self-propelling (active) colloidal particles in two-dimensions. Active particles with symmetric and asymmetric force distribution on its surface are considered. The velocity field generated by a single active particle, changing its orientation randomly, and the different time scales involved are characterized in detail. The steady state speed distribution in the fluid, resulting from the activity, is shown to deviate considerably from the equilibrium distribution.
We present a second-order accurate method to include arbitrary distributions of force densities in the lattice Boltzmann formulation of hydrodynamics. Our method may be used to represent singular force densities arising either from momentum-conserving internal forces or from external forces which do not conserve momentum. We validate our method with several examples involving point forces and find excellent agreement with analytical results. A minimal model for dilute sedimenting particles is presented using the method which promises a substantial gain in computational efficiency.
We describe a method to simulate the dynamics of charged colloidal particles suspended in a liquid containing dissociated ions and salt ions. Regimes of prime current interest are those of large volume fraction of colloids, highly charged particles and low salt concentrations. A description which is tractable under these conditions is obtained by treating the small dissociated and salt ions as continuous fields, while keeping the colloidal macroions as discrete particles. For each spatial configuration of the macroions, the electrostatic potential arising from all charges in the system is dete…
A new description of the binary fluid problem via the lattice Boltzmann method is presented which highlights the use of the moments in constructing two equilibrium distribution functions. This offers a number of benefits, including better isotropy, and a more natural route to the inclusion of multiple relaxation times for the binary fluid problem. In addition, the implementation of solid colloidal particles suspended in the binary mixture is addressed, which extends the solid-fluid boundary conditions for mass and momentum to include a single conserved compositional order parameter. A number o…
Colloidal particles trapped at an interface between two fluids can form a wide range of different structures. Replacing one of the fluid with a liquid crystal increases the complexity of interactions and results in a greater range of possible structures. New behaviour emerges when colloidal particles interact with defects in the liquid crystal phases. Here we discuss the templating of colloids at a cholesteric isotropic interface.
The collective diffusion effects in system of a colloidal particles in a liquid crystal has been proposed. In this article described peculiarity of collective diffusion colloidal particles in a liquid crystal, which can be observe experimentally. The diffusion coefficient should be crucial dependence from temperature and concentration of particles. In system colloidal particles arise from the elastic distortion of the elastic director field the inter-particle interaction. These interaction can cause nontrivial collective behavior, as the results the non-monotonic dependence collective diffusio…
We demonstrate the realization of (laterally) optically bounded colloidal structures on a liquid-liquid interface of an emulsion droplet. We use DNA tethers to graft the particles to the droplet surface, effectively confining them to a quasi-2D plane with minimum constraints on the lateral movement even when optically trapped in a common single-beam configuration. We show that relatively weak interactions such as depletion can be measured in the optically bounded crystals by video-microscopy imaging and analysis. This illustrates the possible use of our system as template to study optically co…
In this article is proposed the general approach to determination the character of the interaction between colloidal particles in a different liquid crystals. The main idea of this approach are in the presentation of the colloidal particle as sours of the possible deformation of the ground state of the director field. The ground state of liquid crystal imposes restrictions on the possible deformations and as result determine the character of the interaction between the colloidal particles. Based on this approach the Coulomb like interaction between dipole particles in a cholesteric liquid crys…
The solid-liquid phase-diagram of charge-stabilized colloidal suspensions is calculated using a technique that combines a continuous Poisson-Boltzmann description for the microscopic electrolyte ions with a molecular-dynamics simulation for the macroionic colloidal spheres. While correlations between the microions are neglected in this approach, many-body interactions between the colloids are fully included. The solid-liquid transition is determined at a high colloid volume fraction where many-body interactions are expected to be strong. With a view to the Derjaguin-Landau-Verwey-Overbeek theo…
The non-equilibrium self-consistent generalized Langevin equation theory of colloid dynamics is used to describe the non-stationary aging processes occurring in a suddenly quenched model colloidal liquid with hard-sphere plus short-ranged attractive interactions, whose static structure factor and van Hove function evolve irreversibly from the initial conditions before the quench to a final, dynamically arrested state. The comparison of our numerical results with available simulation data are highly encouraging.
The assembly of colloids in nematic liquid crystals via topological defects has been extensively studied for spherical particles, and investigations of other colloid shapes have revealed a wide array of new assembly behaviors. We show, using Landau-de Gennes numerical modeling, that nematic defect configurations and colloidal assembly can be strongly influenced by fine details of colloid shape, in particular the presence of sharp edges. For cylinder, microbullet, and cube colloid geometries, we obtain the particles' equilibrium alignment directions and effective pair interaction potentials as …
We present simulation results addressing the phenomena of colloidal gelation induced by attractive interactions. The liquid-gas transition is prevented by the glass arrest at high enough attraction strength, resulting in a colloidal gel. The dynamics of the system is controlled by the glass, with little effect of the liquid-gas transition. When the system separates in a liquid and vapor phases, even if the denser phase enters the non-ergodic region, the vapor phase enables the structural relaxation of the system as a whole.
Recent theories predict that when a supercooled liquid approaches the glass transition, particle clusters with a special "amorphous order" nucleate within the liquid, which lead to static correlations dictating the dramatic slowdown of liquid relaxation. The prediction, however, has yet to be verified in 3D experiments. Here, we design a colloidal system, where particles are confined inside spherical cavities with an amorphous layer of particles pinned at the boundary. Using this novel system, we capture the amorphous-order particle clusters and demonstrate the development of a static correlat…
Microcapsules allow for the controlled containment, transport, and release of cargoes ranging from pharmaceuticals to fragrances. Given the interest from a variety of industries in microcapsules and other core-shell structures, a multitude of fabrication strategies exist. Here, we report on a method relying on a mixture of temperature-responsive microgel particles, poly(N-isopropylacrylamide) (pNIPAM), and a polymer which undergo fluid-fluid phase separation. At room temperature this mixture separates into colloid-rich (liquid) and colloid-poor (gas) fluids. By heating the sample above a criti…
This mini-review discusses the recent contribution of theoretical and computational physics as well as experimental efforts to the understanding of the behavior of colloidal particles in confined geometries and at liquid crystalline interfaces. Theoretical approaches used to study trapping, long- and short-range interactions, and assembly of solid particles and liquid inclusions are outlined. As an example, an interaction of a spherical colloidal particle with a nematic-isotropic interface and a pair interaction potential between two colloids at this interface are obtained by minimizing the La…
Spherical microparticles dispersed in nematic liquid crystals have been extensively investigated in the past years. Here, we report experimental studies on the elastic deformation, colloidal interaction and self-assembly of hematite microcubes with homeotropic surface anchoring in a nematic liquid crystal. We demonstrate that the colloidal interaction and self-assembly of cubic colloids are orientation dependent. In a notable departure from the conventional microspheres, the microcubes stabilise diverse structures, such as bent chains, branches, kinks and closed-loops. The microcubes reorient …
We apply the recently developed triangular tessellation technique as presented in [J. de Graaf et al., Phys. Rev. E 80, 051405 (2009)] to calculate the free energy associated with the adsorption of anisotropic colloidal particles at a flat interface. From the free-energy landscape, we analyze the adsorption process, using a simplified version of Langevin dynamics. The present result is a first step to understand the time-dependent behavior of colloids near interfaces. This study shows a wide range of adsorption trajectories, where the emphasis lies on a strong dependence of the dynamics on the…
The physical mechanism of elasticity of liquid surfaces coated with colloidal particles is proposed. It is suggested that particles are separated by water clearings and the capillary interaction between them is negligible. The case is treated when the colloidal layer is deformed normally to its surface. The elasticity arises as an interfacial effect. The effective Young modulus of a surface depends on the interfacial tension, equilibrium contact angle, radius of colloidal particles and their surface density. For the nanometrically scaled particles the line tension becomes essential and has an …
We propose a simple theoretical model which explains a formation of dipolar 2D and 3D colloidal structures in nematic liquid crystal. Colloidal particles are treated as effective hard spheres interacting via their elastic dipole, quadrupole and octopole moments. It is shown that octopole moment plays an important role in the formation of 2D and 3D nematic colloidal crystals. We generalize this assumption on the case of the external electric field and theoretically explain a giant electrostriction effect in 3D crystals observed recently [A. Nych et al., Nature Communications \textbf{4}, 1489 (2…
A new method is presented for mesoscopic simulations of particle dispersions in liquid crystal solvents. It allows efficient first-principle simulations of the dispersions involving many particles with many-body interactions mediated by the solvents. Demonstrations have been performed for the aggregation of colloid dispersions in two-dimensional nematic and smectic-C* solvents neglecting hydrodynamic effects, which will be taken into account in the near future.
The new free energy functional that describes general elastic interaction between colloidal particles and nematic liquid crystal has been proposed. It generalizes results of the paper \cite{lupe} on the case of arbitrary orientation of colloidal particles and is valid for arbitrary surface anchoring strength. Formal analogies and differences between electric particles and colloidal particles in LC are found. It is first time shown that spur of the quadrupole moment tensor is different from zero $Sp\hat{Q}_μ\neq 0$ in the case of axial symmetry breaking of the director field around colloidal pa…
Within mean field theory, we investigate the bridging transition between a pair of parallel cylindrical colloids immersed in a binary liquid mixture as a solvent which is close to its critical consolute point $T_c$. We determine the universal scaling functions of the effective potential and of the force between the colloids. For a solvent which is at the critical concentration and close to $T_c$, we find that the critical Casimir force is the dominant interaction at close separations. This agrees very well with the corresponding Derjaguin approximation for the effective interaction between the…
We study colloidal particle dynamics of a model glass system using confocal and fluorescence microscopy as the sample evolves from a hard-sphere glass to a liquid with attractive interparticle interactions. The transition from hard-sphere glass to attractive liquid is induced by short-range depletion forces. The development of liquid-like structure is indicated by particle dynamics. We identify particles which exhibit substantial motional events and characterize the transition using the properties of these motional events. As samples enter the attractive liquid region, particle speed during th…
The progress of realizing colloidal structures mimicking natural forms of organization in condensed matter is inherently limited by the availability of suitable colloidal building blocks. To enable new forms of crystalline and quasicrystalline self-organization of colloids, we develop truncated pyramidal particles that form nematic elastic dipoles with long-range electrostaticlike and geometry-guided low-symmetry short-range interactions. Using a combination of nonlinear optical imaging, laser tweezers, and video microscopy, we characterize colloidal pair interactions and demonstrate unusual f…
A simple theory of the fluid state of a charged colloidal suspension is proposed. The full free energy of a polyelectrolyte solution is calculated. It is found that the counterions condense onto the polyions forming clusters composed of one polyion and n counterions. The distribution of cluster sizes is determined explicitly. In agreement with the current experimental and Monte Carlo results, no liquid-gas phase separation was encountered.
We present a confocal-microscopy study of demixing and remixing in binary liquids containing colloidal particles. First, particle-stabilized emulsions have been fabricated by nucleation and growth of droplets upon cooling from the single-fluid phase. We show that their stability mainly derives from interfacial particles; the surplus of colloids in the continuous phase possibly provides additional stability. Upon heating these emulsions, we have observed the formation of polyhedral cellular networks of colloids, just before the system remixes. Given a suitable liquid-liquid composition, the ini…
We study elastic interactions between colloidal particles and deformation landscapes of undulations in a cholesteric liquid crystal under an electric field applied normal to cholesteric layers. The onset of undulation instability is influenced by the presence of colloidal inclusions and, in turn, layers' undulations mediate the spatial patterning of particle locations. We find that the bending of cholesteric layers around a colloidal particle surface prompts the local nucleation of an undulations lattice at electric fields below the well-defined threshold known for liquid crystals without incl…
We introduce a new numerical technique, namely triangular tessellation, to calculate the free energy associated with the adsorption of a colloidal particle at a flat interface. The theory and numerical scheme presented here are sufficiently general to handle non-convex patchy colloids with arbitrary surface patterns characterized by a wetting angle, e.g., amphiphilicity. We ignore interfacial deformation due to capillary, electrostatic, or gravitational forces, but the method can be extended to take such effects into account. It is verified that the numerical method presented is accurate and s…
Using laser tweezers and fluorescence confocal polarizing microscopy, we study colloidal interactions of solid microspheres in the nematic bulk caused by elastic distortions around the particles with strong tangential surface anchoring. The particles aggregate into chains directed at about 30 degrees to the far field director and, at higher concentrations, form complex kinetically trapped structures. We characterize the distance and angular dependencies of the colloidal interaction forces.
A promising approach in designing composite materials with unusual physical behavior combines solid nanostructures and orientationally ordered soft matter at the mesoscale. Such composites not only inherit properties of their constituents but also can exhibit emergent behavior, such as ferromagnetic ordering of colloidal metal nanoparticles forming mesoscopic magnetization domains when dispersed in a nematic liquid crystal. Here we demonstrate the optical patterning of domain structures and topological defects in such ferromagnetic liquid crystal colloids, which allows for altering their respo…
Sedimentation-diffusion equilibrium density profiles of suspensions of charge-stabilized colloids are calculated theoretically and by Monte Carlo simulation, both for a one-component model of colloidal particles interacting through pairwise screened-Coulomb repulsions and for a three-component model of colloids, cations, and anions with unscreened-Coulomb interactions. We focus on a state point for which experimental measurements are available [C.P. Royall et al., J. Phys.: Cond. Matt. {\bf 17}, 2315 (2005)]. Despite the apparently different picture that emerges from the one- and three-compone…
The ability to dictate colloid motion is an important challenge in fields ranging from materials science to living systems. Here, by embedding energy landscapes in confined nematic liquid crystals, we design a versatile platform to define colloidal migration. This is achieved by placing a wavy wall, with alternating hills and wells, in nematic liquid crystals, to impose a smooth elastic energy field with alternating splay and bend distortions. This domain generates (meta) stable loci that act as attractors and unstable loci that repel colloids over distances large compared to the colloid radiu…
A theory is presented which allows us to accurately calculate the density profile of monovalent and multivalent counterions in suspensions of polarizable colloids or nano-particles. In the case of monovalent ions, we derive a weak-coupling theory that explicitly accounts for the ion-image interaction, leading to a modified Poisson-Boltzmann equation. For suspensions with multivalent counterions, a strong-coupling theory is used to calculate the density profile near the colloidal surface and a Poisson-Boltzmann equation with a renormalized boundary condition to account for the counterion distri…
Understanding the phase behaviour of mixtures continues to pose challenges, even for systems that might be considered "simple". Here we consider a very simple mixture of two colloidal and one non-adsorbing polymer species which can be simplified even further to a size-asymmetrical binary mixture, in which the effective colloid-colloid interactions depend on the polymer concentration. We show that this basic system exhibits surprisingly rich phase behaviour. In particular, we enquire whether such a system features only a liquid-vapor phase separation (as in one-component colloid-polymer mixture…
We predict theoretically the existence of a class of colloidal structures in nematic liquid crystal (NLC) cells, which are induced by surface patterns on the plates of the cell (like cells with UV-irradiated polyimide surfaces using micron size masks). These bulk structures arise from non-zero boundary conditions for the director distortions at the confining surfaces. In particular, we demonstrate that quadrupole spherical particles (like spheres with boojums or Saturn-ring director configurations) form a square lattice inside a planar NLC cell, which has checkerboard patterns on both its plat…
We demonstrate several examples of driving and steering of colloids when dispersed in nematic liquid crystals. The driving mechanism is based on the principle of nonlinear electrophoresis which is mediated by the asymmetry in the structure of the defects that the inclusions generate in the host elastic matrix. The steering mechanism originates in the photoactivation of the anchoring conditions of the nematic liquid crystal on one of the enclosing plates. As experimental realizations we first review a scenario of water microdroplets being phoretically transported for cargo release and chemical …
Combining molecular dynamics and Monte Carlo simulation we study defect structures around an elongated colloidal particle embedded in a nematic liquid crystal host. By studying nematic ordering near the particle and the disclination core region we are able to examine the defect core structure and the difference between two simulation techniques. In addition, we also study the torque on a particle tilted with respect to the director, and modification of this torque when the particle is close to the cell wall.
We present experiments where anisometric colloidal microparticles dispersed in a nematic liquid crystal cell with homeotropic anchoring conditions are dynamically assembled by means of liquid-crystal-enabled electrophoresis (LCEEP) using an AC electric field perpendicular to the confining plates. A nematic host with negative dielectric anisotropy leads to a driving force parallel to the cell plates. We take advantage of the resulting gliding anchoring conditions and the degeneracy in the direction of particle motion to design reconfigurable trajectories using a photosensitive anchoring layer (…
We use confocal microscopy to study an equilibrated crystal-liquid interface in a colloidal suspension. Capillary waves roughen the surface, but locally the intrinsic interface is sharply defined. We use local measurements of the structure and dynamics to characterize the intrinsic interface, and different measurements find slightly different widths of this interface. In terms of the particle diameter $d$, this width is either $1.5d$ (based on structural information) or $2.4d$ (based on dynamics), both not much larger than the particle size. This work is the first direct experimental visualiza…
We propose a simple approximation scheme to compute the effective charge of highly charged colloids (spherical or cylindrical with infinite length). Within non-linear Poisson-Boltzmann theory, we start from an expression of the effective charge in the infinite dilution limit which is asymptotically valid for large salt concentrations; this result is then extended to finite colloidal concentration, approximating the salt partitioning effect which relates the salt content in the suspension to that of a dializing reservoir. This leads to an analytical expression of the effective charge as a funct…
The transport properties of colloidal particles in active liquids have been studied extensively. It has led to a deeper understanding of the interactions between passive and active particles. However, the phase behavior of colloidal particles in active media has received little attention. Here, we present a combined experimental and numerical investigation of passive colloids dispersed in suspensions of active particles. Our study reveals dynamic clustering of colloids in active media due to an interplay of active noise and an attractive effective potential between the colloids. The size-ratio…
We report theoretical and numerical evaluations of the phase diagram for patchy colloidal particles of new generation. We show that the reduction of the number of bonded nearest neighbours offers the possibility of generating liquid states (i.e. states with temperature $T$ lower than the liquid-gas critical temperature) with a vanishing occupied packing fraction ($ϕ$), a case which can not be realized with spherically interacting particles. Theoretical results suggest that such reduction is accompanied by an increase of the region of stability of the liquid phase in the ($T$-$ϕ$) plane, possib…
We report an extensive molecular dynamics study on the translational dynamics of a hybrid system composed of dipolar soft spheres (DSS), representing ferromagnetic particles, suspended in a liquid crystal (LC) matrix. We observe that the LC matrix strongly modifies the dynamics of the DSS. In the isotropic regime, the DSS show a crossover from subdiffusive to normal diffusive behavior at long times, with an increase of the subdiffusive regime as the dipolar coupling strength is increased. In the nematic regime, the LC matrix, due to collective reorientation of LC particles, imposes a cylindric…
The assembly of colloidal particles at liquid/liquid or air/liquid interfaces is a versatile procedure to create microstructured monolayers and study their behavior under compression. When combined with soft and deformable particles such as microgels, compression is used to tune not only the interparticle distance but also the underlying microstructure of the monolayer. So far, the great majority of studies on microgel-laden interfaces is conducted ex situ after transfer to solid substrates, for example, via Langmuir-Blodgett deposition. This type of analysis relies on the stringent assumption…
A model is presented for the solution of electrokinetic phenomena of colloidal suspensions in fluid mixtures. We solve the discrete Boltzmann equation with a BGK collision operator using the lattice Boltzmann method to simulate binary fluid flows. Solvent-solvent and solvent-solute interactions are implemented using a pseudopotential model. The Nernst-Planck equation, describing the kinetics of dissolved ion species, is solved using a finite difference discretization based on the link-flux method. The colloids are resolved on the lattice and coupled to the hydrodynamics and electrokinetics thr…
Up to now it is commonly believed that a colloidal particle suspended in a nematic liquid crystal never produces elastic monopoles because this violates the mechanical equilibrium condition. And the only way to obtain deformations of director field falling off with distance as r^{-1} is to exert an external torque Γ_{ext} on the colloid \cite{de_Gennes}. In this paper we demonstrate that this statement is not quite correct and elastic monopoles, as well as dipoles and quadrupoles, can be induced without any external influence just by the particle itself. A behavior of a spherical colloidal par…
Optical microscopy and multi-particle tracking are used to investigate the cross-correlated diffusion of quasi two-dimensional (2D) colloidal particles near an oil-water interface. It is shown that the effect of the interface on correlated diffusion is asymmetric. Along the line joining the centers of particles, the amplitude of correlated diffusion coefficient ${D}_{\|}(r)$ is enhanced by the interface, while the decay rate of ${D}_{\|}(r)$ is hardly affected. At the direction perpendicular to the line, the decay rate of ${D}_{\bot}(r)$ is enhanced at short inter-particle separation $r$. This…
Machine-Learned Many-Body Potentials for Charged Colloids reveal Gas-Liquid Spinodal Instabilities only in the strong-coupling regime of Primitive Models
We determine the capillary attraction and equilibrium configurations of particles trapped at a liquid-fluid interface due to the pinning of their contact-line. We calculate analytically the asymptotic interaction energy between two particles and, numerically, the multi-body energy landscape for up to four contacting particles. Our results are consistent with recent experiments. We show that a system composed of a large number of such particles behaves as a jammed system.
The liquid-gas transition of an electroneutral mixture of oppositely charged colloids, studied by Monte Carlo simulations, is found in the low temperature -- low density region. The critical temperature shows a non-monotonous behavior as a function of the interaction range, $κ^{-1}$, with a maximum at $κσ\approx 10$, implying an island of coexistence in the $κ$-$ρ$ plane. The system is arranged in such a way that each particle is surrounded by shells of particles with alternating charge. In contrast with the electrolyte primitive model, both neutral and charged clusters are obtained in the vap…
Phase equilibria between regions of different thickness in thin liquid films stabilized by colloidal particles are investigated using a quasi-two-dimensional thermodynamic formalism. Appropriate equilibrium conditions for the film tension, normal pressure, and chemical potential of the particles in the film are formulated, and it is shown that the relaxation of these parameters occurs consecutively on three distinct time scales. Film stratification is described quantitatively for a hard-sphere suspension using a Monte-Carlo method to evaluate thermodynamic equations of state. Coexisting phases…
