We perform numerical simulations of a simple model of one-patch colloidal particles to investigate: (i) the behavior of the gas-liquid phase diagram on moving from a spherical attractive potential to a Janus potential and (ii) the collective structure of a system of Janus particles. We show that, for the case where one of the two hemispheres is attractive and one is repulsive, the system organizes into a dispersion of orientational ordered micelles and vesicles and, at low $T$, the system can be approximated as a fluid of such clusters, interacting essentially via excluded volume. The stability of this cluster phase generates a very peculiar shape of the gas and liquid coexisting densities, with a gas coexistence density which increases on cooling, approaching the liquid coexistence density at very low $T$.
We deeply investigate a simple model representative of the recently synthesized Janus particles, i.e. colloidal spherical particles whose surface is divided into two areas of different chemical composition. When the two surfaces are solvophilic and solvophobic, these particles constitute the simplest example of surfactants. The phase diagram includes a colloidal-poor (gas) colloidal-rich (liquid) de-mixing region, which is progressively suppressed by the insurgence of micelles, providing the first model where micellization and phase-separation are simultaneously observed. The coexistence curve…
We report an entropy-driven orientational hopping transition in a magnetically confined colloidal Janus rod. In a magnetic field, the sedimented rod randomly hops between horizontal and vertical states: the latter state comes at a substantial gravitational cost at no reduction of magnetic potential energy. The probability distribution over the angles of the rod shows that the presence of an external magnetic field leads to the emergence of a metastable vertical state separated from the ground state by an effective barrier. This barrier does not come from the potential energy but rather from th…
A mesoscopic hydrodynamic model to simulate synthetic self-propelled Janus particles which is thermophoretically or diffusiophoretically driven is here developed. We first propose a model for a passive colloidal sphere which reproduces the correct rotational dynamics together with strong phoretic effect. This colloid solution model employs a multiparticle collision dynamics description of the solvent, and combines potential interactions with the solvent, with stick boundary conditions. Asymmetric and specific colloidal surface is introduced to produce the properties of self-phoretic Janus part…
Most available theoretical predictions for the self-diffusiophoretic motion of colloidal particles are based on the hydrodynamic thin boundary layer approximation in combination with a solvent body force due to a self-generated local solute gradient. This gradient is enforced through specifying boundary conditions, typically without accounting for the thermodynamic cost to maintain the gradient. Here we present an alternative thermodynamic approach that exploits a direct link between dynamics and entropy production: the local detailed balance condition. We study two cases: First, we revisit se…
We have recently investigated the phase behaviour of model colloidal dumbbells constituted by two identical tangent hard spheres, with the first one being surrounded by an attractive square-well interaction (Janus dumbbells, Munaò G et al 2014 Soft Matter 10 5269). Here we extend our previous analysis by introducing in the model the size asymmetry of the hard-core diameters, and study the enriched phase scenario thereby obtained. By employing standard Monte Carlo simulations we show that in such "heteronuclear Janus dumbbells" a larger hard-sphere site promotes the formation of clusters, where…
We study colloidal particles with chemically inhomogeneous surfaces suspended in a critical binary liquid mixture. The inhomogeneous particle surface is composed of patches with alternating adsorption preferences for the two components of the binary solvent. By describing the binary liquid mixture \emph{at} its consolute point in terms of the critical Ising model we exploit its conformal invariance in two spatial dimension. This allows us to determine exactly the universal profiles of the order parameter, the energy density, and the stress tensor as well as some of their correlation functions …
Micrometer scale colloidal particles that propel in a deterministic fashion in response to local environmental cues are useful analogs to self-propelling entities found in nature. Both natural and synthetic active colloidal systems are often near boundaries or are located in crowded environments. Herein, we describe experiments in which we measured the influence of hydrogen peroxide concentration and dispersed polyethylene glycol (PEG) on the clustering behavior of 5 micrometer catalytic active Janus particles at low concentration. We found the extent to which clustering occurred in ensembles …
We describe colloidal Janus particles with metallic and dielectric faces that swim vigorously when illuminated by defocused optical tweezers without consuming any chemical fuel. Rather than wandering randomly, these optically-activated colloidal swimmers circulate back and forth through the beam of light, tracing out sinuous rosette patterns. We propose a model for this mode of light-activated transport that accounts for the observed behavior through a combination of self-thermophoresis and optically-induced torque. In the deterministic limit, this model yields trajectories that resemble roset…
Patchy particles have received great attention due to their ability to develop directional and selective interactions and serve as building units for the self-assembly of innovative colloidal molecules and crystalline structures. Although synthesizing particles with multiple dissimilar patches is still highly challenging and lacks efficient methods, these building blocks would open paths towards a broader range of ordered materials with inherent properties. Herein, we describe a new approach to pattern functional DNA patches at the surface of particles, by the use of colloidal stamps. DNA inks…
Colloidal Janus spheres in water (one hemisphere attractive and the other repulsive) assemble into two-dimensional hexagonal crystals with orientational order controlled by anisotropic interactions. We exploit the decoupled translational and rotational order to quantify the orientational dynamics. Via imaging experiments and Monte Carlo simulations we demonstrate that the correlations in the orientation of individual Janus spheres exhibit glasslike dynamics that can be controlled via the ionic strength. Thus, these colloidal building blocks provide a particularly suitable model glass system fo…
Open structures can display a number of unusual properties, including a negative Poisson's ratio, negative thermal expansion, and holographic elasticity, and have many interesting applications in engineering. However, it is a grand challenge to self-assemble open structures at the colloidal scale, where short-range interactions and low coordination number can leave them mechanically unstable. In this paper we discuss the self-assembly of open structures using triblock Janus particles, which have two large attractive patches that can form multiple bonds, separated by a band with purely hard-sph…
We present a new model of patchy particles in which the interaction sites can be activated or deactivated by varying the temperature of the system. We study the thermodynamics of the system by means of Wertheim's first order perturbation theory, and use Flory-Stockmayer theory of polymerization to analyse the percolation threshold. We find a very rich phase behaviour including lower critical points and reentrant percolation.
Recently there is strong experimental and theoretical interest in studying the self-assembly and the phase behavior of patchy and of Janus particles, which form colloidal suspensions. Although in this quest a variety of effective interactions have been proposed and used in order to achieve directed assembly, the critical Casimir effect stands out as being particularly suitable in this respect because it provides both attractive and repulsive interactions as well as the potential of a sensitive temperature control of their strength. Specifically, we have calculated the critical Casimir force be…
We experimentally investigate active motion of spherical Janus colloidal particles in a viscoelastic fluid. Self-propulsion is achieved by a local concentration gradient of a critical polymer mixture which is imposed by laser illumination. Even in the regime where the fluid's viscosity is independent from the deformation rate induced by the particle, we find a remarkable increase of up to two orders of magnitude of the rotational diffusion with increasing particle velocity, which can be phenomenologically described by an effective rotational diffusion coefficient dependent on the Weissenberg n…
Recent experimental work on spherical colloidal particles decorated with two hydrophobic poles separated by an electrically-charged middle band (triblock Janus particles) has documented self-assembly into a Kagome two-dimensional lattice, when particles are confined by gravity at the bottom of the sample holder [Q. Chen {\em et. al.}, Nature, in press]. Here we assess the ability of a previously proposed simple two-patch effective potential to reproduce the experimental findings. We show that the effective potential is able to reproduce the observed crystallization pathway in the Kagome struct…
The rapid progress in precisely designing the surface decoration of patchy colloidal particles offers a new, yet unexperienced freedom to create building entities for larger, more complex structures in soft matter systems. However, it is extremely difficult to predict the large variety of ordered equilibrium structures that these particles are able to undergo under the variation of external parameters, such as temperature or pressure. Here we show that, by a novel combination of two theoretical tools, it is indeed possible to predict the self-assembly scenario of patchy colloidal particles: on…
Simple models based on isotropic interparticle attractions often fail to capture experimentally observed structures of colloidal gels formed through spinodal decomposition and subsequent arrest: the resulting gels are typically denser and less branched than their experimental counterparts. Here we simulate gels formed from soft particles with directional attractions ("patchy particles"), designed to inhibit lateral particle rearrangement after aggregation. We directly compare simulated structures with experimental colloidal gels made using soft attractive microgel particles, by employing a "sk…
We study orientational ordering of $2$-dimensional closely packed Janus particles by extensive Monte Carlo simulations. For smaller patch sizes the system remains in the plastic crystal phase where the rotational degrees of freedom are disordered down to the lowest temperatures. There the liquid consist of dimers and trimers of the attractive patches. For large enough patch sizes, the system exhibits a thermodynamic transition into a phase with stripe patterns of the patches breaking the three-fold rotational symmetry. Our results strongly suggests that the latter is a 2nd order phase transiti…
We investigate the thermodynamics and percolation regimes of model binary mixtures of patchy colloidal particles. The particles of each species have three sites of two types, one of which promotes bonding of particles of the same species while the other promotes bonding of different species. We find up to four percolated structures at low temperatures and densities: two gels where only one species percolates, a mixed gel where particles of both species percolate but neither species percolates separately, and a bicontinuous gel where particles of both species percolate separately forming two in…
Review paper. Chapter 6 in Janus Particles Synthesis, Self-Assembly, and Applications pages 108-137, Edited by Steve Granick and Shan Jiang (RCS Publishing 2012) http://www.rsc.org/Shop/books/2012/9781849734233.asp
We study thermophysical properties of a Janus fluid with constrained orientations, using analytical techniques and numerical simulations. The Janus character is modeled by means of a Kern-Frenkel potential where each sphere has one hemisphere of square-well and the other of hard-sphere character. The orientational constraint is enforced by assuming that each hemisphere can only point either North or South with equal probability. The analytical approach hinges on a mapping of the above Janus fluid onto a binary mixture interacting via a "quasi" isotropic potential. The anisotropic nature of the…
A class of binary mixtures of Janus fluids formed by colloidal spheres with the hydrophobic hemispheres constrained to point either up or down are studied by means of Gibbs ensemble Monte Carlo simulations and simple analytical approximations. These fluids can be experimentally realized by the application of an external static electrical field. The gas-liquid and demixing phase transitions in five specific models with different patch-patch affinities are analyzed. It is found that a gas-liquid transition is present in all the models, even if only one of the four possible patch-patch interactio…
Self-assembly of Janus (or `patchy') particles is dependent on the precise interaction between neighbouring particles. Here, the orientations of two amphiphilic Janus spheres within a dimer in an explicit fluid are studied with high geometric resolution. Molecular dynamics simulations and first-principles energy calculations are used with hard- and soft-sphere Lennard-Jones potentials, and temperature and hydrophobicity are varied. The most probable centre-centre-pole angles are in the range 40° to 55°, with pole-to-pole alignment not observed due to orientational entropy. Angles near 90° are …
In this article, we study the phenomenology of a two dimensional dilute suspension of active amphiphilic Janus particles. We analyze how the morphology of the aggregates emerging from their self-assembly depends on the strength and the direction of the active forces. We systematically explore and contrast the phenomenologies resulting from particles with a range of attractive patch coverages. Finally, we illustrate how the geometry of the colloids and the directionality of their interactions can be used to control the physical properties of the assembled active aggregates and suggest possible …
Colloidal particles partially coated with platinum and dispersed in H2O2 solution are often used as model self-propelled colloids. Most current data suggest that neutral self-diffusiophoresis propels these particles. However, several studies have shown strong ionic effects in this and related systems, such as a reduction of propulsion speed by salt. We investigate these ionic effects in Pt-coated polystyrene colloids, and find here that the direction of propulsion can be reversed by addition of an ionic surfactant, and that although adding pH neutral salts reduces the propulsion speed, adding …
We study experimentally and numerically a (quasi) two dimensional colloidal suspension of self-propelled spherical particles. The particles are carbon-coated Janus particles, which are propelled due to diffusiophoresis in a near-critical water-lutidine mixture. At low densities, we find that the driving stabilizes small clusters. At higher densities, the suspension undergoes a phase separation into large clusters and a dilute gas phase. The same qualitative behavior is observed in simulations of a minimal model for repulsive self-propelled particles lacking any alignment interactions. The obse…
The addition of co-solutes to colloidal suspensions is often employed to induce tunable depletion interactions. In this work we investigate effective colloidal interactions arising from binary co-solute mixtures of hard spheres and patchy particles. By changing the relative concentration of the two species, we show that the resulting effective potential $V_\text{eff}$ continuously changes from the one obtained for a single-component hard sphere co-solute to that mediated by the single-component patchy particle co-solute. Interestingly, we find that, independently of the relative concentration …
In this review we discuss recent advances in the self-assembly of self-propelled colloidal particles and highlight some of the most exciting results in this field with a specific focus on dry active matter. We explore this phenomenology through the lens of the complexity of the colloidal building blocks. We begin by considering the behavior of isotropic spherical particles. We then discuss the case of amphiphilic and dipolar Janus particles. Finally, we show how the geometry of the colloids and/or the directionality of their interactions can be used to control the physical properties of the as…
The dynamics of anisotropic nano- to microscale colloidal particles in confined environments, either near neighboring particles or boundaries, is relevant to a wide range of applications. We utilized Brownian dynamics simulations to predict the translational and rotational fluctuations of a Janus sphere with a cap of non-matching density. The presence of the cap significantly impacted the rotational dynamics of the particle as a consequence of gravitational torque at experimentally relevant conditions. Gravitational torque dominated stochastic torque for a particle > 1 micrometer in diameter a…
Recent experiments have shown that colloidal suspensions can spontaneously self-assemble into dense clusters of various internal structures, sizes and dynamical properties when doped with active Janus particles. Characteristically, these clusters move ballistically during their formation, but dynamically revert their velocity and temporarily move opposite to the self-propulsion direction of the Janus particles they contain. Here we explore a simple effective model of colloidal mixtures which allows reproducing most aspects seen in experiments, including the morphology and the velocity-reversal…
Recent experiments have demonstrated a fluctuation-induced lateral trapping of spherical colloidal particles immersed in a binary liquid mixture near its critical demixing point and exposed to chemically patterned substrates. Inspired by these experiments, we study this kind of effective interaction, known as the critical Casimir effect, for elongated colloids of cylindrical shape. This adds orientational degrees of freedom. When the colloidal particles are close to a chemically structured substrate, a critical Casimir torque acting on the colloids emerges. We calculate this torque on the basi…
In this work we characterize the configurational space of a short chain of colloidal particles as function of the range of directional and heterogeneous isotropic interactions. The individual particles forming the chain are colloids decorated with patches that act as interaction sites between them. We show, using computer simulations, that it is possible to sample the relative probability of occurrence of a structure with a sequence in the space of all possible realizations of the chain. The results presented here represent a first attempt to map the space of possible configurations that a cha…
Crystals melt when thermal excitations or the concentration of defects in the lattice is sufficiently high. Upon melting, the crystalline long-range order vanishes, turning the solid to a fluid. In contrast to this classical scenario of solid melting, here we demonstrate a counter-intuitive behavior of the occurrence of crystalline long-range order in an initially disordered matrix. This unusual solidification is demonstrated in a system of passive colloidal particles accommodating chemically active defects -- photocatalytic Janus particles. The observed crystallization occurs when the amount …
We study self-propulsion of a half-metal coated colloidal particle under laser irradiation. The motion is caused by self-thermophoresis: i.e. absorption of laser at the metal-coated side of the particle creates local temperature gradient which in turn drives the particle by thermophoresis. To clarify the mechanism, temperature distribution and a thermal slip flow field around a micro-scale Janus particle are measured for the first time. With measured temperature drop across the particle, the speed of self-propulsion is corroborated with the prediction based on accessible parameters. As an appl…
We study catalytic Janus swimmers and Escherichia coli bacteria swimming in a two-dimensional colloidal crystal. The Janus swimmers orbit individual colloids and hop between colloids stochastically, with a hopping rate that varies inversely with fuel (hydrogen peroxide) concentration. At high fuel concentration, these orbits are stable for 100s of revolutions, and the orbital speed oscillates periodically as a result of hydrodynamic, and possibly also phoretic, interactions between the swimmer and the six neighbouring colloids. Motile E.~coli bacteria behave very differently in the same colloi…
Based on Brownian Dynamics computer simulations in two dimensions we investigate aggregation scenarios of colloidal particles with directional interactions induced by multiple external fields. To this end we propose a model which allows continuous change in the particle interactions from point-dipole-like to patchy-like (with four patches). We show that, as a result of this change, the non-equilibrium aggregation occurring at low densities and temperatures transforms from conventional diffusion-limited cluster aggregation (DLCA) to slippery DLCA involving rotating bonds; this is accompanied by…
In the present study we are performing simulation of simple model of two patch colloidal particles undergoing irreversible diffusion limited cluster aggregation using patchy Brownian cluster dynamics. In addition to the irreversible aggregation of patches, the spheres are coupled with isotropic reversible aggregation through the Kern-Frenkel potential. Due to the presence of anisotropic and isotropic potential we have also defined 3 different kinds of clusters formed due to anisotropic potential and isotropic potential only as well as both the potentials together. We have investigated the effe…
Self-assembly and dynamical properties of Janus nanoparticles have been studied by molecular dynamic simulations. The nanoparticles are modeled as dimers and they are confined between two flat parallel plates to simulate a thin film. One monomer from the dumbbells interacts by a standard Lennard Jones potential and the other by a two-length scales shoulder potential, typically used for anomalous fluids. Here, we study the effects of remove the Brownian effects, typical from colloidal systems immersed in aqueous solution, and consider a molecular system, without the drag force and the random co…
We combine percolation theory and Monte Carlo simulation to study in two dimensions the connectivity of an equilibrium lattice model of interacting Janus disks which self-assemble into an orientationally ordered stripe phase at low temperature. As the patch size is increased or the temperature is lowered, clusters of patch-connected disks grow, and a percolating cluster emerges at a threshold. In the stripe phase, the critical clusters extend longer in the direction parallel to the stripes than in the perpendicular direction, and percolation is thus anisotropic. It is found that the critical b…
Building upon past work on the phase diagram of Janus fluids [Sciortino et al., Phys. Rev. Lett. \textbf{103}, 237801 (2009)], we perform a detailed study of integral equation theory of the Kern-Frenkel potential with coverage that is tuned from the isotropic square-well fluid to the Janus limit. An improved algorithm for the reference hypernetted-chain (RHNC) equation for this problem is implemented that significantly extends the range of applicability of RHNC. Results for both structure and thermodynamics are presented and compared with numerical simulations. Unlike previous attempts, this a…
We study the polar collective dynamics of Janus colloidal particles fueled by an AC electric field. When the density is high enough, the polar interactions between the particles induce a polar orientationally ordered state which exhibits features reminiscent of the Vicsek model such as true long-range order and giant number fluctuations. Independent measurements of the polarity and velocity at the single particle level allowed us to investigate the single particle dynamics within the ordered state. We discovered theoretically-unaddressed statistical properties of the ordered state such as the …
A trapping mechanism for propelled colloidal particles based on an inhomogeneous drive is presented and studied by means of computer simulations. In experiments this method can be realized using photophoretic Janus particles driven by a light source, which shines through a shading mask and leads to an accumulation of the particles in the passive part. An equation for an accumulation parameter is derived using the effective inhomogeneous diffusion constant generated by the inhomogeneous drive. The impact of particle interaction on the trapping mechanism is studied, as well as the interplay betw…
In living cells, molecular motors create activity that enhances the diffusion of particles throughout the cytoplasm, and not just ones attached to the motors. We demonstrate initial steps toward creating artificial cells that mimic this phenomenon. Our system consists of active, Pt-coated Janus particles and passive tracers confined to emulsion droplets. We track the motion of both the active particles and passive tracers in a hydrogen peroxide solution, which serves as the fuel to drive the motion. We first show that correcting for bulk translational and rotational motion of the droplets indu…
Aggregation of protein into bundles is responsible for many neurodegenerative diseases. In this work, we show how two-patch colloidal particles self assemble into chains and a sudden transition to bundles takes place by tuning the patch size and solvent condition. We study the kinetics of formation of chains, bundles and network like structures using Patchy Brownian cluster dynamics. We also analyse the ways to inhibit and accelerate the formation of these bundles. We show that in presence of inert immobile obstacles, the kinetics of formation of bundles slows down. Whereas, in presence of mob…
Colloidal assembly at fluid interfaces has a great potential for the bottom-up fabrication of novel structured materials. However, challenges remain in realizing controllable and tunable assembly of particles into diverse structures. Herein, we report the capillary assembly of magnetic ellipsoidal Janus particles at a fluid-fluid interface. Depending on their tilt angle, i.e. the angle the particle main axis forms with the fluid interface, these particles deform the interface and generate capillary dipoles or hexapoles. Driven by capillary interactions, multiple particles thus assemble into ch…
We present a new, high-speed technique to track the three-dimensional translation and rotation of non-spherical colloidal particles. We capture digital holograms of micrometer-scale silica rods and sub-micrometer-scale Janus particles freely diffusing in water, and then fit numerical scattering models based on the discrete dipole approximation to the measured holograms. This inverse-scattering approach allows us to extract the the position and orientation of the particles as a function of time, along with static parameters including the size, shape, and refractive index. The best-fit sizes and…
To elucidate mechanisms of mesoscopic turbulence exhibited by active particles, we experimentally study turbulent states of non-living self-propelled particles. We realize an experimental system with dense suspensions of asymmetrical colloidal particles (Janus particles) self-propelling on a two-dimensional surface under an AC electric field. Velocity fields of the Janus particles in the crowded situation can be regarded as a sort of turbulence because it contains many vortices and their velocities change abruptly. Correlation functions of their velocity field reveal the coexistence of polar a…
This article discusses recent attempts to provide a deeper understanding of the thermoreversible "gel" state of colloidal matter and to unravel the analogies between gels at the colloidal level and gels at the molecular level, commonly known as network-forming strong liquids. The connection between gel-forming patchy colloids and strong liquids is provided by the limited valence of the inter-particle interactions, i.e. by the presence of a limit in the number of bonded nearest neighbors.
