Wetting of a solid surface by active matter.

A lattice model is used to study repulsive active particles at a planar surface. A rejection-free Kinetic Monte Carlo method is employed to characterize the wetting behaviour. The model predicts a motility-induced phase separation of active particles, and the bulk coexistence of dense liquid-like and dilute vapour-like steady states is determined. An "ensemble", with a varying number of particles, analogous to a grand canonical ensemble in equilibrium, is introduced. The formation and growth of the liquid film between the solid surface and the vapour phase is investigated. At constant activity, as the system is brought towards coexistence from the vapour side, the thickness of the adsorbed film exhibits a divergent behaviour regardless of the activity. This suggests a complete wetting scenario along the full coexistence curve.

Modeling of Cell-Mediated Self-Assembled Colloidal Scaffolds.

A critical step in tissue engineering is the design and synthesis of 3D biocompatible matrices (scaffolds) to support and guide the proliferation of cells and tissue growth. The most existing techniques rely on the processing of scaffolds under controlled conditions and then implanting them in vivo, with questions related to biocompatibility and implantation that are still challenging. As an alternative, it was proposed to assemble the scaffolds in loco through the self-organization of colloidal particles mediated by cells. To overcome the difficulty to test experimentally all the relevant parameters, we propose the use of large-scale numerical simulation as a tool to reach useful predictive information and to interpret experimental results. Thus, in this study, we combine experiments, particle-based simulations, and mean-field calculations to show that, in general, the size of the self-assembled scaffold scales with the cell-to-particle ratio. However, we have found an optimal value of this ratio, for which the size of the scaffold is maximal when the cell-cell adhesion is suppressed. These results suggest that the size and structure of the self-assembled scaffolds may be designed by tuning the adhesion between cells in the colloidal suspension.

Smoluchowski equations for linker-mediated irreversible aggregation.

We developed a generalized Smoluchowski framework to study linker-mediated aggregation, where linkers and particles are explicitly taken into account. We assume that the bonds between linkers and particles are irreversible, and that clustering occurs through limited diffusion aggregation. The kernel is chosen by analogy with single-component diffusive aggregation but the clusters are distinguished by their number of particles and linkers. We found that the dynamics depends on three relevant factors, all tunable experimentally: (i) the ratio of the diffusion coefficients of particles and linkers; (ii) the relative number of particles and linkers; and (iii) the maximum number of linkers that may bond to a single particle. To solve the Smoluchoski equations analytically we employ a scaling hypothesis that renders the fraction of bondable sites of a cluster independent of the size of the cluster, at each instant. We perform numerical simulations of the corresponding lattice model to test this hypothesis. We obtain results for the asymptotic limit, and the time evolution of the bonding probabilities and the size distribution of the clusters. These findings are in agreement with experimental results reported in the literature and shed light on unexplained experimental observations.

Optimal number of linkers per monomer in linker-mediated aggregation.

We study the dynamics of diffusion-limited irreversible aggregation of monomers, where bonds are mediated by linkers. We combine kinetic Monte Carlo simulations of a lattice model with a mean-field theory to study the dynamics when the diffusion of aggregates is negligible and only monomers diffuse. We find two values of the number of linkers per monomer which maximize the size of the largest aggregate. We explain the existence of the two maxima based on the distribution of linkers per monomer. This observation is well described by a simple mean-field model. We also show that a relevant parameter is the ratio of the diffusion coefficients of monomers and linkers. In particular, when this ratio is close to ten, the two maxima merge at a single maximum.

Crossover from three- to six-fold symmetry of colloidal aggregates in circular traps.

At sufficiently low temperatures and high densities, repulsive spherical particles in two-dimensions (2d) form close-packed structures with six-fold symmetry. By contrast, when the interparticle interaction has an attractive anisotropic component, the structure may exhibit the symmetry of the interaction. We consider a suspension of spherical particles interacting through an isotropic repulsive potential and a three-fold symmetric attractive interaction, confined in circular potential traps in 2d. We find that, due to the competition between the interparticle and the external potentials, the particles self-organize into structures with three- or six-fold symmetry, depending on the width of the traps. For intermediate trap widths, a core-shell structure is formed, where the core has six-fold symmetry and the shell is three-fold symmetric. When the width of the trap changes periodically in time, the symmetry of the colloidal structure also changes, but it does not necessarily follow that of the corresponding static trap.

Dynamics of a network fluid within the liquid-gas coexistence region.

Low-density networks of molecules or colloids are formed at low temperatures when the interparticle interactions are valence limited. Prototypical examples are networks of patchy particles, where the limited valence results from highly directional pairwise interactions. We combine extensive Langevin simulations and Wertheim's theory of association to study these networks. We find a scale-free (relaxation) dynamics within the liquid-gas coexistence region, which differs from that usually observed for isotropic particles. While for isotropic particles the relaxation dynamics is driven by surface tension (coarsening), when the valence is limited, the slow relaxation proceeds through the formation of an intermediate non-equilibrium gel via a geometrical percolation transition in the Random Percolation universality class. We show that the slow dynamics is universal, being also observed outside the coexistence region at low temperatures in the single phase region.

Interaction anisotropy and the KPZ to KPZQ transition in particle deposition at the edges of drying drops.

The deposition process at the edge of evaporating colloidal drops varies with the shape of suspended particles. Experiments with prolate ellipsoidal particles suggest that the spatiotemporal properties of the deposit depend strongly on particle aspect ratio. As the aspect ratio increases, the particles form less densely-packed deposits and the statistical behavior of the deposit interface crosses over from the Kardar-Parisi-Zhang (KPZ) universality class to another universality class which was suggested to be consistent with the KPZ plus quenched disorder. Here, we numerically study the effect of particle interaction anisotropy on deposit growth. In essence, we model the ellipsoids, at the interface, as disk-like particles with two types of interaction patches that correspond to specific features at the poles and equator of the ellipsoid. The numerical results corroborate experimental observations and further suggest that the deposition transition can stem from interparticle interaction anisotropy. Possible extensions of our model to other systems are also discussed.

Dynamics of Patchy Particles in and out of Equilibrium.

We combine particle-based simulations, mean-field rate equations, and Wertheim's theory to study the dynamics of patchy particles in and out of equilibrium, at different temperatures and densities. We consider an initial random distribution of nonoverlapping three-patch particles, with no bonds, and analyze the time evolution of the breaking and bonding rates of a single bond. We find that the asymptotic (equilibrium) dynamics differs from the initial (out of equilibrium) one. These differences are expected to depend on the initial conditions, temperature, and density.

Dynamics of network fluids.

Network fluids are structured fluids consisting of chains and branches. They are characterized by unusual physical properties, such as, exotic bulk phase diagrams, interfacial roughening and wetting transitions, and equilibrium and nonequilibrium gels. Here, we provide an overview of a selection of their equilibrium and dynamical properties. Recent research efforts towards bridging equilibrium and non-equilibrium studies are discussed, as well as several open questions.

Dynamic Design of Spatial Patterns of Colloidal Suspensions.

We study the collective dynamics of colloidal suspensions in the presence of a time-dependent potential by means of dynamic density functional theory. We consider a nonlinear diffusion equation for the density and show that spatial patterns emerge from a sinusoidal external potential with a time-dependent wavelength. These patterns are characterized by a sinusoidal density with the average wavelength and a Bessel-function envelope with an induced wavelength that depends only on the amplitude of the temporal oscillations. As a generalization of this result, we propose a design strategy to obtain a family of spatial patterns using time-dependent potentials of practically arbitrary shape.

Nematic films at chemically structured surfaces.

We investigate theoretically the morphology of a thin nematic film adsorbed at flat substrate patterned by stripes with alternating aligning properties, normal and tangential respectively. We construct a simple 'exactly-solvable' effective interfacial model where the liquid crystal distortions are accounted for via an effective interface potential. We find that chemically patterned substrates can strongly deform the nematic-air interface. The amplitude of this substrate-induced undulations increases with decreasing average film thickness and with increasing surface pattern pitch. We find a regime where the interfacial deformation may be described in terms of a material-independent universal scaling function. Surprisingly, the predictions of the effective interfacial model agree semi-quantitatively with the results of the numerical solution of a full model based on the Landau-de Gennes theory coupled to a square-gradient phase field free energy functional for a two phase system.

Relaxation dynamics of functionalized colloids on attractive substrates.

Particle-based simulations are performed to study the post-relaxation dynamics of functionalized (patchy) colloids adsorbed on an attractive substrate. Kinetically arrested structures that depend on the number of adsorbed particles and the strength of the particle-particle and particle-substrate interactions are identified. The radial distribution function is characterized by a sequence of peaks, with relative intensities that depend on the number of adsorbed particles. The first-layer coverage is a non-monotonic function of the number of particles, with an optimal value around one layer of adsorbed particles. The initial relaxation towards these structures is characterized by a fast (exponential) and a slow (power-law) dynamics. The fast relaxation timescale is a linearly increasing function of the number of adsorbed particles in the submonolayer regime, but it saturates for more than one adsorbed layer. The slow dynamics exhibits two characteristic exponents, depending on the surface coverage.

Generalization of Wertheim's theory for the assembly of various types of rings.

We generalize Wertheim's first order perturbation theory to account for the effect in the thermodynamics of the self-assembly of rings characterized by two energy scales. The theory is applied to a lattice model of patchy particles and tested against Monte Carlo simulations on a fcc lattice. These particles have 2 patches of type A and 10 patches of type B, which may form bonds AA or AB that decrease the energy by εAA and by εAB ≡ rεAA, respectively. The angle θ between the 2 A-patches on each particle is fixed at 60°, 90° or 120°. For values of r below 1/2 and above a threshold rth(θ) the models exhibit a phase diagram with two critical points. Both theory and simulation predict that rth increases when θ decreases. We show that the mechanism that prevents phase separation for models with decreasing values of θ is related to the formation of loops containing AB bonds. Moreover, we show that by including the free energy of B-rings (loops containing one AB bond), the theory describes the trends observed in the simulation results, but that for the lowest values of θ, the theoretical description deteriorates due to the increasing number of loops containing more than one AB bond.

Kinetic interfaces of patchy particles.

We study the irreversible adsorption of patchy particles on substrates in the limit of advective mass transport. Recent numerical results show that the interface roughening depends strongly on the particle attributes, such as, patch-patch correlations, bond flexibility and strength of the interactions, uncovering new absorbing phase transitions. Here, we revisit these results and discuss in detail the transitions. In particular, we present new evidence that the tricritical point, observed in systems of particles with flexible patches, is in the tricritical directed percolation universality class. A scaling analysis of the time evolution of the correlation length for the aggregation of patchy particles with distinct bonding energies confirms that the critical regime is in the Kardar-Parisi-Zhang with quenched disorder universality class.

Nematic droplets on fibers.

The emergence of new techniques for the fabrication of nematic droplets with nontrivial topology provides new routes for the assembly of responsive devices. Here we explore some of the properties of nematic droplets on fibers, which constitute the basic units of a type of device that is able to respond to external stimuli, including the detection of gases. We perform a numerical study of spherical nematic droplets on fibers. We analyze the equilibrium textures for homogeneous and hybrid boundary conditions and find that in some cases the nematic avoids the nucleation of topological defects, which would provide a different optical response. We consider in detail a homeotropic nematic droplet wrapped around a fiber with planar anchoring. We investigate the effect of an electric field on the texture of this droplet. In the presence of a dc field, the system undergoes an orientational transition above a given threshold E(c), for which a ring defect is transformed into a figure-eight defect. We also consider ac fields, at high and low frequencies, and find that the textures are similar to those observed for static fields, in contrast with recently reported experiments.

Particle selection through topographic templates in nematic colloids.

Liquid crystal colloids have been proposed as suitable candidates for responsive photonic crystals. Large scale growth of such colloidal systems is, however, a challenge and recently template-assisted assembly has been proposed to guide the growth of colloidal crystals, with controlled symmetries, in nematic liquid crystals. Known for their long-range anisotropic interactions, these colloidal systems are stabilized typically at the center of the cells due to strong particle-wall repulsion from the confining substrates. This behaviour is dramatically changed in the presence of topographic patterning. Here we propose the use of topographic modulation of surfaces to select and localize particles in nematic colloids. By considering convex and concave deformations of one of the confining surfaces we show that the colloid-flat surface repulsion may be enhanced or switched into an attraction. In particular, we find that when the colloidal particles have the same anchoring conditions as the patterned surfaces, they are strongly attracted to concave dimples, while if they exhibit different anchoring conditions they are pinned at the top of convex protrusions. Although dominated by elastic interactions the first mechanism is reminiscent of the depletion induced attraction or of the key-lock mechanism, while the second is specific to liquid crystal colloids. These long-ranged, highly tunable, surface-colloid interactions contribute to the development of template-assisted assembly of large colloidal crystals, with well defined symmetries, as required for applications.

Adsorbed films of three-patch colloids: continuous and discontinuous transitions between thick and thin films.

We investigate numerically the role of spatial arrangement of the patches on the irreversible adsorption of patchy colloids on a substrate. We consider spherical three-patch colloids and study the dependence of the kinetics on the opening angle between patches. We show that growth is suppressed below and above minimum and maximum opening angles, revealing two absorbing phase transitions between thick and thin film regimes. While the transition at the minimum angle is continuous, in the directed percolation class, that at the maximum angle is clearly discontinuous. For intermediate values of the opening angle, a rough colloidal network in the Kardar-Parisi-Zhang universality class grows indefinitely. The nature of the transitions was analyzed in detail by considering bond flexibility, defined as the dispersion of the angle between the bond and the center of the patch. For the range of flexibilities considered we always observe two phase transitions. However, the range of opening angles where growth is sustained increases with flexibility. At a tricritical flexibility, the discontinuous transition becomes continuous. The practical implications of our findings and the relation to other nonequilibrium transitions are discussed.

Three-dimensional patchy lattice model: ring formation and phase separation.

We investigate the structural and thermodynamic properties of a model of particles with 2 patches of type A and 10 patches of type B. Particles are placed on the sites of a face centered cubic lattice with the patches oriented along the nearest neighbor directions. The competition between the self-assembly of chains, rings, and networks on the phase diagram is investigated by carrying out a systematic investigation of this class of models, using an extension of Wertheim's theory for associating fluids and Monte Carlo numerical simulations. We varied the ratio r ≡ εAB/εAA of the interaction between patches A and B, εAB, and between A patches, εAA (εBB is set to 0) as well as the relative position of the A patches, i.e., the angle θ between the (lattice) directions of the A patches. We found that both r and θ (60°, 90°, or 120°) have a profound effect on the phase diagram. In the empty fluid regime (r < 1/2) the phase diagram is reentrant with a closed miscibility loop. The region around the lower critical point exhibits unusual structural and thermodynamic behavior determined by the presence of relatively short rings. The agreement between the results of theory and simulation is excellent for θ = 120° but deteriorates as θ decreases, revealing the need for new theoretical approaches to describe the structure and thermodynamics of systems dominated by small rings.

Mixtures of functionalized colloids on substrates.

Patchy particles are a class of colloids with functionalized surfaces. Through surface functionalization, the strength and directionality of the colloidal interactions are tunable allowing control over coordination of the particle. Exquisite equilibrium phase diagrams of mixtures of coordination two and three have been reported. However, the kinetics of self-organization and the feasibility of the predicted structures are still largely unexplored. Here, we study the irreversible aggregation of these mixtures on a substrate, for different fractions of two-patch particles. Two mechanisms of mass transport are compared: diffusion and advection. In the diffusive case, an optimal fraction is found that maximizes the density of the aggregate. By contrast, for advective transport, the density decreases monotonically with the fraction of two-patch colloids, in line with the behavior of the liquid density on the spinodal of the equilibrium phase diagram.

Interfacial motion in flexo- and order-electric switching between nematic filled states.

We consider a nematic liquid crystal, in coexistence with its isotropic phase, in contact with a substrate patterned with rectangular grooves. In such a system the nematic phase may fill the grooves without the occurrence of complete wetting. There may exist multiple (meta)stable filled states, each characterized by the type of distortion (bend or splay) in each corner of the groove and by the shape of the nematic-isotropic interface, and additionally the plateaux that separate the grooves may be either dry or wet with a thin layer of nematic. Using numerical simulations, we analyse the dynamical response of the system to an externally-applied electric field, with the aim of identifying switching transitions between these filled states. We find that order-electric coupling between the fluid and the field provides a means of switching between states where the plateaux between grooves are dry and states where they are wetted by a nematic layer, without affecting the configuration of the nematic within the groove. We find that flexoelectric coupling may change the nematic texture in the groove, provided that the flexoelectric coupling differentiates between the types of distortion at the corners of the substrate. We identify intermediate stages of the transitions, and the role played by the motion of the nematic-isotropic interface. We determine quantitatively the field magnitudes and orientations required to effect each type of transition.