The formation and dynamics of a wide variety of binary two-dimensional ordered structures and superlattices are investigated through a phase field crystal model with sublattice ordering. Various types of binary ordered phases, the phase diagrams, and the grain growth dynamics and structural transformation processes, including the emergence of topological defects, are examined. The results are compared to the ordering and assembly of two-component colloidal systems. Two factors governing the binary phase ordering are identified, the coupling and competition between the length scales of two sublattices and the selection of average particle densities of two components. The control and variation of these two factors lead to the prediction of various complex binary ordered patterns, with different types of sublattice ordering for integer vs. noninteger ratios of sublattice length scales. These findings will enable further systematic studies of complex ordering and assembly processes of binary systems particularly binary colloidal crystals.
We successfully fabricated large grains of silica colloidal crystals in an inverted-triangle internal-shaped container (inverted-triangle container) by centrifugation. The largest grain in the container was much larger than that in a container which has a flat bottom and constant width (flat-bottomed container). The edged bottom of the inverted-triangle container eliminated the number of the grains, and then the broadened shape of the container effectively widened the grains.
Using computer simulations we explore how grain boundaries can be removed from three-dimensional colloidal crystals by doping with a small fraction of active colloids. We show that for sufficient self-propulsion, the system is driven into a crystal-fluid coexistence. In this phase separated regime, the active dopants become mobile and spontaneously gather at the grain boundaries. The resulting surface melting and recrystallization of domains result in the motion of the grain boundaries over time and lead to the formation of a large single crystal. However, when the self-propulsion is too low t…
Ferrofluids are familiar as colloidal suspensions of ferromagnetic nanoparticles in aqueous or organic solvents. The dispersed particles are randomly oriented but their moments become aligned if a magnetic field is applied, producing a variety of exotic and useful magneto-mechanical effects. A longstanding interest and challenge has been to make such suspensions macroscopically ferromagnetic, that is having uniform magnetic alignment in absence of a field. Here we report a fluid suspension of magnetic nanoplates which spontaneously aligns into an equilibrium nematic liquid crystal phase that i…
We experimentally investigate the structural behavior of an interacting colloidal monolayer being driven across a decagonal quasiperiodic potential landscape created by an optical interference pattern. When the direction of the driving force is varied, we observe the monolayer to be directionally locked on angles corresponding to the symmetry axes of the underlying potential. At such locking steps we observe a dynamically ordered smectic phase in agreement with recent simulations. We demonstrate, that such dynamical ordering is due to the interaction of particle lanes formed by interstitial an…
We find that laser-induced local melting attracts and deforms grain boundaries in 2D colloidal crystals. When a melted region in contact with the edge of a crystal grain recrystallizes, it deforms the grain boundary --- this attraction is driven by the multiplicity of deformed grain boundary configurations. Furthermore, the attraction provides a method to fabricate artificial colloidal crystal grains of arbitrary shape, enabling new experimental studies of grain boundary dynamics and ultimately hinting at a novel approach for fabricating materials with designer microstructures.
We show in simulations that a rich variety of novel orderings such as pinwheel and star states can be realized for colloidal molecular crystal mixtures at rational ratios of the number of colloids to the number of minima from an underlying periodic substrate. These states can have multi-step melting transitions and also show coexistence in which one species disorders while the other species remains orientationally disordered. For other mixtures, only partially ordered or frustrated states form.
We study the phenomenon of self-assembly of silica micro-spheres on a glass plate during evaporation of the solvent from a colloidal suspension. Our experiments unveil an interesting competition between ordering and compaction in a strongly driven, out of equilibrium system arising from a slowing down of dynamics due to an impending glass transition. A suitable choice of experimental conditions minimizing the influence of many other competing phenomena that usually complicate probing of this underlying physics is crucial for our study. A re-entrant behavior in the order-disorder phase diagram …
We study the crystallization of a colloidal model system in presence of secondary nanoparticles acting as impurities. Using confocal microscopy, we show that the nanoparticles segregate in the grain boundaries of the colloidal polycrystal. We demonstrate that the texture of the polycrystal can be tuned by varying independently the nanoparticle volume fraction and the crystallization rate, and quantify our findings using standard models for the nucleation and growth of crystalline materials. Remarkably, we find that the efficiency of the segregation of the nanoparticles in the grain-boundaries …
We describe in detail how to implement a coarse-grained hybrid Molecular Dynamics and Stochastic Rotation Dynamics simulation technique that captures the combined effects of Brownian and hydrodynamic forces in colloidal suspensions. The importance of carefully tuning the simulation parameters to correctly resolve the multiple time and length-scales of this problem is emphasized. We systematically analyze how our coarse-graining scheme resolves dimensionless hydrodynamic numbers such as the Reynolds number, the Schmidt number, the Mach number, the Knudsen number, and the Peclet number. The many…
Using simulations we explore the behaviour of two-dimensional colloidal (poly)crystals doped with active particles. We show that these active dopants can provide an elegant new route to removing grain boundaries in polycrystals. Specifically, we show that active dopants both generate and are attracted to defects, such as vacancies and interstitials, which leads to clustering of dopants at grain boundaries. The active particles both broaden and enhance the mobility of the grain boundaries, causing rapid coarsening of the crystal domains. The remaining defects recrystallize upon turning off the …
Using large scale numerical simulations, we examine the ordering of colloidal particles on square periodic two-dimensional muffin-tin substrates consisting of a flat surface with localized pinning sites. We show that when there are four particles per pinning site, the particles adopt a hexagonal ordering, while for five particles per pinning site, a square ordering appears. For fillings between four and five particles per pinning site, we identify a rich variety of distinct ordering regimes, including disordered grain boundaries, crystalline stripe structures, superlattice orderings, and disor…
From Landau-Alexander-McTague theory and Monte-Carlo simulation results we show that the modulated liquid obtained by subjecting a colloidal system to a periodic laser modulation has long range bond-orientational order and non-zero shear rigidity. From infinite field simulation results we show that in the modulated liquid phase, the translational order parameter correlation function decays to zero exponentially while the correlation function for the bond-orientational order saturates to a finite value at large distances.
Structural defects are ubiquitous in condensed matter, and not always a nuisance. For example, they underlie phenomena such as Anderson localization and hyperuniformity, and they are now being exploited to engineer novel materials. Here, we show experimentally that the density of structural defects in a 2D binary colloidal crystal can be engineered with a random potential. We generate the random potential using an optical speckle pattern, whose induced forces act strongly on one species of particles (strong particles) and weakly on the other (weak particles). Thus, the strong particles are mor…
We study here how phase transitions are induced in colloidal suspensions by a point-like heat source, an optically trapped metal oxide particle absorbing light. We find that thermophoresis increases the number density of colloids around the oxide particle, leading to the appearance of solid clusters. Our analysis based on thermophoresis reveals that the solid-fluid interface position is purely determined by the relationship of the particle concentration profile in the fluid state with the volume fraction of the phase transition, and no other effect of thermodynamics is seen in the cluster size…
Two-dimensional colloidal suspensions exposed to periodic external fields exhibit a variety of molecular crystalline phases. There two or more colloids assemble at lattice sites of potential minima to build new structural entities, referred to as molecules. Using the strength of the potential and the filling fraction as control parameter, phase transition to unconventional orientationally ordered states can be induced. We introduce an approach that focuses at the discrete set of orientational states relevant for the phase ordering. The orientationally ordered states are mapped to classical spi…
We present a method of organizing incoherent motion of a colloidal suspension to produce synchronized, coherent motion. This method exploits general features of rotational response to time-dependent forcing, and it does not require interaction between the particles. We report two methods of achieving orientational alignment of an ensemble of identical colloids by means of a time-dependent, but spatially uniform forcing: a) a piecewise constant force alternating between two directions and b) a force uniformly rotating about an axis. The physical origin of the forcing may be e.g., sedimentation …
In established theories of grain coarsening, grains disappear either by shrinking or by rotating as a rigid object to coalesce with an adjacent grain. Here we report a third mechanism for grain coarsening, in which a grain splits apart into two regions that rotate in opposite directions to match two adjacent grains' orientations. We experimentally observe both conventional grain rotation and grain splitting in 2D colloidal polycrystals. We find that grain splitting occurs via independently rotating "granules" whose shapes are determined by the underlying triangular lattices of the two merging …
We propose that a system of colloidal particles interacting with a honeycomb array of optical traps that each contain three wells can be used to realize a fully packed loop model. One of the phases in this system can be mapped to Baxter's three-coloring problem, offering an easily accessible physical realization of this problem. As a function of temperature and interaction strength, we find a series of phases, including long range ordered loop or stripe states, stripes with sliding symmetries, random packed loop states, and disordered states in which the loops break apart. Our geometry could b…
Freezing of charged colloids on square or triangular two-dimensional periodic substrates has been recently shown to realize a rich variety of orientational orders. We propose a theoretical framework to analyze the corresponding structures. A fundamental ingredient is that a non spherical charged object in an electrolyte creates a screened electrostatic potential that is anisotropic at any distance. Our approach is in excellent agreement with the known experimental and numerical results, and explains in simple terms the reentrant orientational melting observed in these so called colloidal molec…
The response of a suspension under a variety of static or alternating external fields strongly depends on the equilibrium electric double layer that surrounds the colloidal particles in the suspension. The theoretical models for salt-free suspensions can be improved by incorporating non-uniform size effects and orientational ordering of water dipoles neglected in previous mean-field approaches, which are based on the Poisson-Boltzmann approach. Our model including non-uniform size effects and orientational ordering of water dipoles seems to have quite a promising effect because the model can p…
We study colloidal ordering and disordering on two-dimensional periodic substrates where the number of colloids per substrate minima is two or three. The colloids form dimer or trimer states with orientational ordering, referred to as colloidal molecular crystals. At a fixed temperature such that, in the absence of a substrate, the colloids are in a triangular floating solid state, upon increasing the substrate strength we find a transition to an ordered colloidal molecular crystal state, followed by a transition to a disordered state where the colloids still form dimers or trimers but the ori…
By applying a hybrid Molecular dynamics and mesoscopic simulation technique, we study the classic convection-diffusion problem of Taylor dispersion for colloidal discs in confined flow. We carefully consider the time and length-scales of the underlying colloidal system. These are, by computational necessity, altered in the coarse-grained simulation method, but as long as this is carefully managed, the underlying physics can be correctly interpreted. We find that when the disc diameter becomes non-negligible compared to the diameter of the pipe, there are important corrections to the original T…
We poorly understand the macroscopic properties of complex fluids and of amorphous bodies in general. This is mainly due to the interplay between phenomena at different levels and length-scales. In particular, it is not necessarily true that the microscopic level (dominated by direct interactions) coincides with the level where the continuum description comes into play. This is typically the case in the presence of structural inhomogeneities which are inherent to all structurally disordered states of matter below close packing. As a consequence, the macroscopic response to external fields of e…
Self-assembly of nanoparticles can enable composites with pre-designed properties but remains challenged by reproducing structural diversity of atomic and molecular crystals. We combine anisotropic elastic and weakly screened electrostatic interactions to guide both orientational and triclinic positional self-ordering of inorganic nanocrystals in a nematic fluid host. The lattice periodicity of these low-symmetry colloidal crystals is more than an order of magnitude larger than the nanoparticle size. Orientations of nanocrystals, as well as crystallographic axes of ensuing triclinic colloidal …
Macromolecular diffusion in dense colloidal suspensions is an intriguing topic of interdisciplinary relevance in Science and Engineering. While significant efforts have been undertaken to establish the impact of crowding on the dynamics of macromolecules, less clear is the role played by long-range ordering. In this work, we perform Dynamic Monte Carlo simulations to assess the importance of ordered crowding on the diffusion of globular macromolecules, here modelled as spherical tracers, in suspensions of colloidal cuboids. We first investigate the diffusion of such guest tracers in very weakl…
Using numerical simulations we examine colloids with a long-range Coulomb interaction confined in a two-dimensional trough potential undergoing dynamical compression. As the depth of the confining well is increased, the colloids move via elastic distortions interspersed with intermittent bursts or avalanches of plastic motion. In these avalanches, the colloids rearrange to minimize their colloid-colloid repulsive interaction energy by adopting an average lattice constant that is isotropic despite the anisotropic nature of the compression. The avalanches take the form of shear banding events th…
Using self-consistent field and density-functional theories, we first investigate colloidal self-assembling of colloid/polymer films confined between two soft surfaces grafted by polymers. With the increase of colloidal concentrations, the film undergoes a series of transitions from disordered liquid $\to$ sparse square $\to$ hexagonal (or mixed square-hexagonal) $\to$ dense square $\to$ cylindric structures in plane, which results from the competition between the entropic elasticity of polymer brushes and the steric packing effect of colloidal particles. A phase diagram displays the stable re…
We use confocal microscopy and time-resolved light scattering to investigate plasticity in a col- loidal polycrystal, following the evolution of the network of grain boundaries as the sample is submitted to thousands of shear deformation cycles. The grain boundary motion is found to be ballistic, with a velocity distribution function exhibiting non-trivial power law tails. The shear- induced dynamics initially slow down, similarly to the aging of the spontaneous dynamics in glassy materials, but eventually reach a steady state. Surprisingly, the cross-over time between the ini- tial aging regi…
Electrostatic interactions between macroions largely govern the equilibrium thermodynamic and dynamical properties of charge-stabilized colloidal suspensions and polyelectrolyte solutions. Predicting the properties of such complex, multicomponent systems with accuracy sufficient to guide and interpret experiments requires realistic modeling of the interparticle interactions and collective behavior of many-particle systems. While the fundamental interactions may be simple, the sheer number of particles and the broad ranges of length and time scales confront the modeler with significant computat…
Since the 1920s, packing arguments have been used to rationalize crystal structures in systems ranging from atomic mixtures to colloidal crystals. Packing arguments have recently been applied to complex nanoparticle structures, where they often, but not always, work. We examine when, if ever, packing is a causal mechanism in hard particle approximations of colloidal crystals. We investigate three crystal structures comprised of their ideal packing shapes. We show that, contrary to expectations, the ordering mechanism cannot be packing, even when the thermodynamically self-assembled structure i…
Coarse-graining atomic displacements in a solid produces both local affine strains and "non-affine" fluctuations. Here we study the equilibrium dynamics of these coarse grained quantities to obtain space-time dependent correlation functions. We show how a subset of these thermally excited, non-affine fluctuations act as precursors for the nucleation of lattice defects and suggest how defect probabilities may be altered by an {\it experimentally realisable} "external" field conjugate to the global non-affinity parameter. Our results are amenable to verification in experiments on colloidal cryst…
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 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 demonstrate facile optical manipulation of shape of birefringent colloidal microparticles made from liquid crystal elastomers. Using soft lithography and polymerization, we fabricate elastomeric microcylinders with weakly undulating director oriented on average along their long axes. These particles are infiltrated with gold nanospheres acting as heat transducers that allow for an efficient localized transfer of heat from a focused infrared laser beam to a submicrometer region within a microparticle. Photothermal control of ordering in the liquid crystal elastomer using scanned beams allows…
We induce and investigate the coarsening and melting dynamics of an initially static nanoparticle colloidal monolayer at an ionic liquid-vacuum interface, driven by a focused, scanning electron beam. Coarsening occurs through grain interface migration and larger-scale motions such as grain rotations, often facilitated by sliding dislocations. The progressive decrease in area fraction that drives melting of the monolayer is explained using an electrowetting model whereby particles at the interface are solvated once their accumulating charge recruits sufficient counterions to subsume the particl…
We study the phase ordering dynamics of a two dimensional model colloidal solid using molecular dynamics simulations. The colloid particles interact with each other with a Hamaker potential modified by the presence of equatorial "patches" of attractive and negative regions. The total interaction potential between two such colloids is, therefore, strongly directional and has three-fold symmetry. Working in the canonical ensemble, we determine the tentative phase diagram in the density-temperature plane which features three distinct crystalline ground states viz, a low density honeycomb solid fo…
Impurities in crystalline materials introduce disorder into an otherwise ordered structure due to the formation of lattice defects and grain boundaries. The properties of the resulting polycrystal can differ remarkably from those of the ideal single crystal. Here we investigate a quasi-two-dimensional system of colloidal spheres containing a small fraction of aspherical impurities and characterise the resulting polycrystalline monolayer. We find that, in the vicinity of an impurity, the underlying hexagonal lattice is deformed due to a preference for 5-fold co-ordinated particles adjacent to i…
Control of physical behaviors of nematic colloids and colloidal crystals has been demonstrated by tuning particle shape, topology, chirality and surface charging. However, the capability of altering physical behaviors of such soft matter systems by changing particle shape and the ensuing responses to external stimuli has remained elusive. We fabricated genus-one nematic elastomeric colloidal ring-shaped particles and various microstructures using two-photon photopolymerization. Nematic ordering within both the nano-printed particle and the surrounding medium leads to anisotropic responses and …
Crystalline bilayers of charged colloidal suspensions which are confined between two parallel plates and sheared via a relative motion of the two plates are studied by extensive Brownian dynamics computer simulations. The charge-stabilized suspension is modeled by a Yukawa pair potential. The unsheared equilibrium configuration are two crystalline layers with a nested quadratic in-plane structure. For increasing shear rates $\dot γ$, we find the following steady states: first, there is a static solid which is elastically sheared until a yield-stress limit is reached. Then there are two crystal…
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…
We show that amphiphilic and colloidal systems with competing interactions can be described by the same Landau-Brazovskii functional. The functional is obtained by a systematic coarse-graining procedure applied tosystems with isotropic interaction potentials. Microscopic expressions for the coefficients in the functional are derived. We propose simple criteria to distinguish the effective interparticle potentials that can lead to macro- or microsegregation. Our considerations concern also charged globular proteins in aqueous solutions and other system with effective short-range attraction long…
We report on the identification and quantitative characterization of elementary edge and screw dislocations in a colloidal smectic phase of tip-labeled rods. Thanks to the micrometer layer spacing, direct visualization of dislocations has been performed at the \textit{smectic periodicity scale} by optical fluorescence microscopy. As a result, the displacement field around an edge dislocation has been experimentally established and compared with the profile predicted by elastic theory. Elementary screw dislocations have been also evidenced, for which the core size as well as the \textit{in situ…
We use X-ray Photon Correlation Spectroscopy (XPCS) to probe the dynamics of colloidal particles in polycrystalline ice. During freezing, the dendritic ice morphology and rejection of particles from the ice created regions of high-particle-density, where some of the colloids were forced into contact and formed disordered aggregates. We find that the particles in these high density regions underwent ballistic motion coupled with both stretched and compressed exponential decays of the intensity autocorrelation function, and that the particles' characteristic velocity increased with temperature. …
The organization of nano-particles inside grafted polymer layers is governed by the interplay of polymer-induced entropic interactions and the action of externally applied fields. Earlier work had shown that strong external forces can drive the formation of colloidal structures in polymer brushes. Here we show that external fields are not essential to obtain such colloidal patterns: we report Monte Carlo and Molecular dynamics simulations that demonstrate that ordered structures can be achieved by compressing a `sandwich' of two grafted polymer layers, or by squeezing a coated nanotube, with n…
Two dimensional suspensions of spherical colloids subject to periodic external fields exhibit a rich variety of molecular crystalline phases. We study in simulations the ground state configurations of dimeric and trimeric systems, that are realized on square and triangular lattices, when either two or three macroions are trapped in each external potential minimum. Bipartite orders of the checkerboard or stripe types are reported together with more complex quadripartite orderings, and the shortcomings of envisioning the colloids gathered in a single potential minimum as a composite rigid object…
Stress relaxation in crystalline solids is mediated by the formation and diffusion of defects. While it is well established how externally-generated stresses relax, through the proliferation and motion of dislocations in the lattice, it remains relatively unknown how crystals cope with internal stresses. We investigate, both experimentally and in simulations, how highly localized stresses relax in two-dimensional soft colloidal crystals. When a single particle is actively excited, by means of optical tweezing, a rich variety of highly collective stress relaxation mechanisms results. These mani…
We discuss the stochastic thermodynamics of systems that are described by a time-dependent density field, for example simple liquids and colloidal suspensions. For a time-dependent change of external parameters, we show that the Jarzynski relation connecting work with the change of free energy holds if the time evolution of the density follows the Kawasaki-Dean equation. Specifically, we study the work distributions for the compression and expansion of a two-dimensional colloidal model suspension implementing a practical coarse-graining scheme of the microscopic particle positions. We demonstr…
Depletion interactions arise from entropic forces, and their ability to induce aggregation and even ordering of colloidal particles through self-assembly is well established, especially for spherical colloids. We vary the size and concentration of penetrable hard sphere depletants in a system of cuboctahedra, and we show how depletion changes the preferential facet alignment of the colloids and thereby selects different crystal structures. Moreover, we explain the cuboctahedra phase behavior using perturbative free energy calculations. We find that cuboctahedra can form a stable simple cubic p…
Graphene materials and structures have become an essential part of modern electronics and photovoltaics. However, despite many production methods, applications of graphene-based structures are hindered by high costs, lack of scalability and limitations in spatial patterning. Here we fabricate three-dimensional functional solid microstructures of reduced graphene oxide in a lyotropic nematic liquid crystal of graphene oxide flakes using a pulsed near-infrared laser. This reliable, scalable approach is mask-free, does not require special chemical reduction agents, and can be implemented at ambie…
Particle tracking is a key to single-particle-level confocal microscopy observation of colloidal suspensions, emulsions, and granular matter. The conventional tracking method has not been able to provide accurate information on the size of individual particle. Here we propose a novel method to localise spherical particles of arbitrary relative sizes from either 2D or 3D (confocal) images either in dilute or crowded environment. Moreover this method allows us to estimate the size of each particle reliably. We use this method to analyse local bond orientational ordering in a supercooled polydisp…
Confining a colloidal crystal within a long narrow channel produced by two parallel walls can be used to impose a meso-scale superstructure of a predominantly mechanical elastic character [Chui et al., EPL 2008, 83, 58004]. When the crystal is compressed in the direction perpendicular to the walls, we obtain a structural transition when the number of rows of particles parallel to the walls decreases by one. All the particles of this vanishing row are distributed throughout the crystal. If the confining walls are structured (say with a corrugation along the length of the walls), then these extr…
We report the nematic and smectic ordering in a new aqueous suspension of monolayer $α$-Zirconium phosphate platelets possessing a high polydispersity in diameter but uniform thickness. We observe an isotropic--nematic transition as the platelet volume fraction increases, followed by the formation of a smectic, an elusive phase that has been rarely seen in discotic liquid crystals. The smectic phase is characterized by X-ray diffraction, high-resolution transmission electron microscopy, and optical microscopy. The phase equilibria in this highly polydisperse suspension is rationalized in terms…
