Self-dual structures whose dual counterparts are themselves possess unique hidden symmetry, beyond the description of classical spatial symmetry groups. Here we propose a strategy based on { a nematic monolayer of} attractive half-cylindrical colloids to self-assemble these exotic structures. { This system can be seen as a 2D system of semi-disks.} By using Monte Carlo simulations, we discover two isostatic self-dual crystals, i.e., an unreported crystal with pmg {space-group} symmetry and the twisted Kagome crystal. For the pmg crystal approaching the critical point, we find the double degeneracy of the {full} phononic spectrum at the self-dual point, and the merging of two tilted Weyl nodes into one \emph{critically-tilted} Dirac node. The latter is `accidentally' located on the high-symmetry line. The formation of this unconventional Dirac node is due to the emergence of the critical flat bands at the self-dual point, which are linear combinations of \emph{finite-frequency} floppy modes. These modes can be understood as mechanically-coupled self-dual rhomb chains vibrating in some unique uncoupled ways. Our work paves the way for designing and fabricating self-dual materials with exotic mechanical or phononic properties.
Understanding and engineering the self-assembly of soft colloidal particles (microgels) at liquid-liquid interfaces is broadening their use in colloidal lithography. Here, we present a new route to assemble rectangular lattices of microgels at near zero surface pressure relying on the balance between attractive quadrupolar capillary interactions and steric repulsion among the particles at water/oil interfaces. These self-assembled rectangular lattices are obtained for a broad range of particles and, after deposition, can be used as lithography masks to obtain regular arrays of vertically align…
The nucleation and growth kinetics of highly ordered nanocrystal superlattices during the evaporation of nanocrystal colloidal droplets was elucidated by in situ time resolved small-angle x-ray scattering. We demonstrated for the first time that evaporation kinetics can affect the dimensionality of the superlattices. The formation of two-dimensional nanocrystal superlattices at the liquid-air interface of the droplet has an exponential growth kinetics that originates from interface "crushing".
The emergence of structure through aggregation is a fascinating topic and of both fundamental and practical interest. Here we demonstrate that self-generated solvent flow can be used to generate long-range attractions on the colloidal scale, with sub-pico Newton forces extending into the millimeter-range. We observe a rich dynamic behavior with the formation and fusion of small clusters resembling molecules, the dynamics of which is governed by an effective conservative energy that decays as $1/r$. Breaking the flow symmetry, these clusters can be made active.
The generation of nanoscale square and stripe patterns is of major technological importance since they are compatible with industry-standard electronic circuitry. Recently, a blend of diblock copolymer interacting via hydrogen-bonding was shown to self-assemble in square arrays. Motivated by those experiments we study, using Monte Carlo simulations, the pattern formation in a two-dimensional binary mixture of colloidal particles interacting via isotropic core-corona potentials. We find a rich variety of patterns that can be grouped mainly in aggregates that self-assemble in regular square latt…
The aggregation of attractive colloids has been extensively studied from both theoretical and experimental perspectives as the fraction of solid particles is changed, and the range, type and strength of attractive or repulsive forces between particles varies. The resulting gels consisting of disordered assemblies of attractive colloidal particles, have also been investigated with regards to percolation, phase separation, and the mechanical characteristics of the resulting fractal networks. Despite tremendous progress in our understanding of the gelation process, and the exploration of differen…
Electrostatic interactions play an important role in numerous self-assembly phenomena, including colloidal aggregation. Although colloids typically have a dielectric constant that differs from the surrounding solvent, the effective interactions that arise from inhomogeneous polarization charge distributions are generally neglected in theoretical and computational studies. We introduce an efficient technique to resolve polarization charges in dynamical dielectric geometries, and demonstrate that dielectric effects \emph{qualitatively} alter the predicted self-assembled structures, with surprisi…
We study numerically the hydrodynamics of dip coating from a suspension and report a mechanism for colloidal assembly and pattern formation on smooth and uniform substrates. Below a critical withdrawal speed of the substrate, capillary forces required to deform the meniscus prevent colloidal particles from entering the coating film. Capillary forces are overcome by hydrodynamic drag only after a minimum number of particles organize in a close-packed formation within the meniscus. Once within the film, the formed assembly moves at nearly the withdrawal speed and rapidly separates from the next …
Here, we describe a method for the enhanced self-assembly of triblock Janus colloids targeted to form a kagome lattice. Using computer simulations, we demonstrate that the formation of this elusive structure can be significantly improved by self-propelling or activating the colloids along the axis connecting their hydrophobic hemispheres. The process by which metastable aggregates are destabilized and transformed into the favored kagome lattice is quite general, and we argue this active approach provides a systematic pathway to improving the self-assembly of a large number of colloidal structu…
Colloidal assembly represents a powerful method for the fabrication of functional materials. In this article, we describe how acoustic radiation forces can guide the assembly of colloidal particles into structures that serve as microscopic elements in novel acoustic metadevices or act as phononic crystals. Using a simple three-dimensional orthogonal system, we show that a diversity of colloidal structures with orthorhombic symmetry can be assembled with megahertz-frequency (MHz) standing pressure waves. These structures allow rapid tuning of acoustic properties and provide a new platform for d…
We demonstrate scaffolding of plasmonic nanoparticles by topological defects induced by colloidal microspheres to match their surface boundary conditions with a uniform far-field alignment in a liquid crystal host. Displacing energetically costly liquid crystal regions of reduced order, anisotropic nanoparticles with concave or convex shapes not only stably localize in defects but also self-orient with respect to the microsphere surface. Using laser tweezers, we manipulate the ensuing nanoparticle-microsphere colloidal dimers, probing the strength of elastic binding and demonstrating self-asse…
Colloidal molecules are designed to mimic their molecular analogues through their anisotropic shape and interactions. However, current experimental realizations are missing the structural flexibility present in real molecules thereby restricting their use as model systems. We overcome this limitation by assembling reconfigurable colloidal molecules from silica particles functionalized with mobile DNA linkers in high yields. We achieve this by steering the self-assembly pathway towards the formation of finite-sized clusters by employing high number ratios of particles functionalized with comple…
We outline a basic strategy of how self-propulsion can be used to improve the yield of a typical colloidal self-assembly process. The success of this approach is predicated on the thoughtful design of the colloidal building block as well as how self-propulsion is endowed to the particle. As long as a set of criteria are satisfied, it is possible to significantly increase the rate of self-assembly, and greatly expand the window in parameter space where self-assembly can occur. In addition, we show that by tuning the relative on/off time of the self-propelling force it is possible to modulate th…
Colloidal particles absorbed at the interface of a liquid droplet arrange into unique packings during slow evaporation (Manoharan et al. Science 301 pp 483-487). We present a numerical and theoretical analysis of the packing selection problem. The selection of a unique packing arises almost entirely from geometrical constraints during the drying.
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…
Micrometre sized colloidal particles can be viewed as large atoms with tailorable size, shape and interactions. These building blocks can assemble into extremely rich structures and phases, in which the thermal motions of particles can be directly imaged and tracked using optical microscopy. Hence, colloidal particles are excellent model systems for studying phase transitions, especially for poorly understood kinetic and nonequilibrium microscale processes. Advances in colloid fabrication, assembly and computer simulations have opened up numerous possibilities for such research. In this Review…
Assembly of colloidal particles on fluid interfaces is a promising technique for synthesizing two-dimensional micro-crystalline materials useful in fields as diverse as biomedicine1, materials science2, mineral flotation3 and food processing4. Current approaches rely on bulk emulsification methods, require further chemical and thermal treatments, and are restrictive with respect to the materials employed5-9. The development of methods that exploit the great potential of interfacial assembly for producing tailored materials have been hampered by the lack of understanding of the assembly process…
DNA plays a special role in polymer science not just because of the highly selective recognition of complementary single DNA strands but also because bacteria can express DNA chains that are very long yet perfectly monodisperse. The latter reason makes long DNA molecules widely used as model systems in polymer science. Here, we report the unusual self-assembly that takes place in systems of colloids coated with very long double-stranded DNA. In particular, we find that colloids coated with such long DNA can assemble into unique floating crystalline monolayers. Floating colloidal structures hav…
We study the formation of bands of colloidal particles driven by periodic external fields. Using Brownian dynamics, we determine the dependence of the band width on the strength of the particle interactions and on the intensity and periodicity of the field. We also investigate the switching (field-on) dynamics and the relaxation times as a function of the system parameters. The observed scaling relations were analyzed using a simple dynamic density-functional theory of fluids.
We explore the self-assembly process of colloidal structures immersed in active baths. By considering low-valence particles we numerically investigate the irreversible aggregation dynamics originated by the presence of run-and-tumble swimmers. We observe the formation of long closed chains -- vesicles -- densely filled by active swimmers. On the one hand the active bath drives the self-assembly of closed colloidal structures, and on the other hand the vesicles formation fosters the self-trapping of swimmers, suggesting new ways both to build structured nanomaterials and to trap microorganisms.
The ability to assemble mesoscopic colloidal lattices above a surface is important for fundamental studies related with nucleation and crystallization, but also for a variety of technological applications in photonics and micro-engineering. Current techniques based on particle sedimentation above a lithographic template are limited by a slow deposition process and by the use of static templates, which make difficult to implement fast annealing procedures. Here it is demonstrated a method to realize and anneal a series of colloidal lattices displaying triangular, honeycomb or kagome-like symmet…
From dumbbells to FCC crystals, we study the self-assembly pathway of amphiphatic, spherical colloidal particles as a function of the size of the hydrophobic region using molecular dynamics simulations. Specifically, we analyze how local inter-particle interactions correlate to the final self-assembled aggregate and how they affect the dynamical pathway of structure formation. We present a detailed diagram separating the many phases that we find for different sizes of the hydrophobic area, and uncover a narrow region where particles self-assemble into hollow, faceted cages that could potential…
Anisotropy at the level of the inter-particle interaction provides the particles with specific instructions for the self-assembly of target structures. The ability to synthesize non-spherical colloids, together with the possibility of controlling the particle bonding pattern via suitably placed interaction sites, is nowadays enlarging the playfield for materials design. We consider a model of anisotropic colloidal platelets with regular rhombic shape and two attractive sites placed along adjacent edges and we run Monte Carlo simulations in two-dimensions to investigate the two-stage assembly o…
Colloidal particles can self-assemble into various ordered structures in fluid flows that have potential applications in biomedicine, materials synthesis and encryption. These dynamic processes are also of fundamental interest for probing the general principles of self-assembly in non-equilibrium conditions. Here, we report a simple microfluidic experiment, where charged colloidal particles self-assemble into flow-aligned 1D strings with regular particle spacing near a solid boundary. Using high-speed confocal microscopy, we systematically investigate the influence of flow rates, electrostatic…
The use of colloidal supported lipid bilayers (CSLBs) has recently been extended to create colloidal joints, that - in analogy to their macroscopic counterparts - can flexibly connect colloidal particles. These novel elements enable the assembly of structures with internal degrees of flexibility, but rely on previously unappreciated properties: the simultaneous fluidity of the bilayer, lateral mobility of inserted (linker) molecules and colloidal stability. Here we characterize every step in the manufacturing of CSLBs in view of these requirements using confocal microscopy and fluorescence rec…
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…
We report a technique to realize reconfigurable colloidal crystals by using the controlled motion of particle defects above an externally modulated magnetic substrate. The transport of particles is induced by applying a uniform rotating magnetic field to a ferrite garnet film characterized by a periodic lattice of magnetic bubbles. For filling factor larger than one colloid per bubble domain, the particle current arises from propagating defects where particles synchronously exchange their position when passing from one occupied domain to the next. The amplitude of an applied alternating magnet…
We investigate the behavior of a mixture of asymmetric colloidal dumbbells and emulsion droplets by means of kinetic Monte Carlo simulations. The evaporation of the droplets and the competition between droplet-colloid attraction and colloid-colloid interactions leads to the formation of clusters built up of colloid aggregates with both closed and open structures. We find that stable packings and hence complex colloidal structures can be obtained by changing the relative size of the colloidal spheres and/or their interfacial tension with the droplets.
The spontaneous assembly of particles in suspension provides a strategy for inexpensive fabrication of devices with nanometer-scale control, such as single-electron transistors for memory or logic applications. A scaleable and robust method to form electrodes with the required nanometer-scale spacing, however, remains a major challenge. Here, we demonstrate a straightforward assembly approach in which metallic colloidal spheres serve as the electrodes. The devices are formed by assembly in suspension followed by deposition onto a patterned substrate. The key to this approach is that the inter-…
We demonstrate a novel route of spatially organizing the colloid arrangements on the polymer-grafted substrate by use of self-consistent field and density functional theories. We find that grafting of polymers onto a substrate can effectively control spatial dispersions of deposited colloids as a result of the balance between colloidal settling force and entropically elastic force of brushes, and colloids can form unexpected ordered structures on a grafting substrate. The depositing process of colloidal particles onto the elastic "soft" substrate includes two steps: brush-mediated one-dimensio…
We study theoretically a binary system in which an attraction of unlike particles is combined with a type-independent soft core repulsion. The possible experimental implementation of the system is a mixture of DNA-covered colloids, in which both the repulsion and the attraction may be induced by DNA solution. The system is shown to exhibit surprisingly diverse and unusual morphologies. Among them are the diamond lattice and the membrane phase with in-plane square order, a striking example of spontaneous compactification.
We propose a simple seedless approach to assemble millimeter sized monolayer single colloidal crystals with desired orientations at predetermined locations on an unstructured charged substrate. This approach utilizes the millimeter-ranged fluid flow on the bottom glass substrate induced by an ion exchange resin (IEX) fixed on top of the closed sample cell. This fluid flow increases with decreasing height of the sample cell and increasing radius R of the IEX. For a single inverted pump, millimeter sized monolayer single crystals of hexagonal close packing can be obtained. For two closely spaced…
We employ Monte Carlo simulations to investigate the self-assembly of patchy colloidal dumbbells interacting via a modified Kern-Frenkel potential by probing the system concentration and dumbbell shape. We consider dumbbells consisting of one attractive sphere with diameter $σ_1$ and one repulsive sphere with diameter $σ_2$ and center-to-center distance $d$ between the spheres. For three different size ratios, we study the self-assembled structures for different separations $l = 2d/(σ_1+σ_2)$ between the two spheres. In particular, we focus on structures that can be assembled from the homogene…
Understanding the relationship between colloidal building block shape and self-assembled material structure is important for the development of novel materials by self-assembly. In this regard, colloidal superballs are unique building blocks because their shape can smoothly transition between spherical and cubic. Assembly of colloidal superballs under spherical confinement results in macroscopic clusters with ordered internal structure. By utilizing Small Angle X-Ray Scattering (SAXS), we probe the internal structure of colloidal superball dispersion droplets during confinement. We observe and…
Self-assembly of colloidal particles is poised to become a powerful composite material fabrication technique, but remains challenged by a limited control over the ensuing structures. We develop a new breed of nematic colloids that are physical analogs of a mathematical surface with boundary, interacting with the molecular alignment field without inducing defects when flat. However, made from a thin nanofoil, they can be shaped to prompt formation of self-compensating defects that drive pre-programmed elastic interactions mediated by the nematic host. To show this, we wrap the nanofoil on all t…
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 study mutual alignment and interactions between colloidal particles of dissimilar shapes and dimensions when dispersed in a nematic host fluid. Convex pentagonal and concave starfruit-shaped nanoprisms and microspheres induce dipolar or quadrupolar director structures. The ensuing elastic pair interactions between microspheres and nanoprisms are highly dependent on the nanoparticle shape being omnidirectionally attractive for convex prisms but strongly anisotropic for concave prisms. Elastic deformations due to spherical particles cause well-defined alignment of complex-shaped nanoparticles…
A heterogeneous and dilute suspension of catalytically active colloids is studied as a non-equilibrium analogue of ionic systems, which has the remarkable feature of action-reaction symmetry breaking. Symmetrically coated colloids are found to join up to form self-assembled molecules that could be inert or have spontaneous activity in the form of net translational velocity and spin depending on their symmetry properties and their constituents. The type of activity can be adjusted by changing the surface chemistry and ambient variables that control the surface reactions and the phoretic drift.
We investigate the self-assembly (crystallisation) of particles with hard cores and isotropic, square-well interactions, using a Monte Carlo scheme to simulate overdamped Langevin dynamics. We measure correlation and response functions during the early stages of assembly, and we analyse the results using fluctuation-dissipation theorems, aiming to predict which systems will self-assemble successfully and which will get stuck in disordered states. The early-time correlation and response measurements are made before significant crystallisation has taken place, indicating that dynamical measureme…
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…
Hierarchical self-assembly consisting of local associations of simple building-blocks for the formation of complex structures widely exists in nature, while the essential role of local assembly remains unknown. In this work, by using computer simulations, we study a simple model system consisting of associating colloidal hemispheres crystallizing into face-centered-cubic crystals comprised of spherical dimers of hemispheres, focusing on the effect of dimer formation on the hierarchical crystallization. We found that besides assisting the crystal nucleation because of increasing the symmetry of…
We study theoretically a new generic scheme of programmable self-assembly of nanoparticles into clusters of desired geometry. The problem is motivated by the feasibility of highly selective DNA-mediated interactions between colloidal particles. By analyzing both a simple generic model and a more realistic description of a DNA-colloidal system, we demonstrate that it is possible to suppress the glassy behavior of the system, and to make the self-assembly nearly error-proof. This regime requires a combination of stretchable interparticle linkers (e.g. sufficiently long DNA), and a soft repulsive…
We study the depletion-induced self-assembly of indented colloids. Using state-of-the-art Monte Carlo simulation techniques that treat the depletant particles explicitly, we demonstrate that colloids assemble by a lock-and-key mechanism, leading to colloidal polymerization. The morphology of the chains that are formed depends sensitively on the size of the colloidal indentation, with smaller values additionally permitting chain branching. In contrast to the case of spheres with attractive patches, Wertheim's thermodynamic perturbation theory fails to provide a fully quantitative description of…
We report small-angle x-ray scattering (SAXS) experiments on aqueous dispersions of colloidal silica with a broad monomodal size distribution (polydispersity 18%, size 8 nm). Over a range of volume fractions the silica particles segregate to build first one, then two distinct sets of colloidal crystals. These dispersions thus demonstrate fractional crystallization and multiple-phase (bcc, Laves AB$_2$, liquid) coexistence. Their remarkable ability to build complex crystal structures from a polydisperse population originates from the intermediate-range nature of interparticle forces, and sugges…
We analyze the geometric structure and mechanical stability of a complete set of isostatic and hyperstatic sphere packings obtained via exact enumeration. The number of nonisomorphic isostatic packings grows exponentially with the number of spheres $N$, and their diversity of structure and symmetry increases with increasing $N$ and decreases with increasing hyperstaticity $H \equiv N_c - N_{ISO}$, where $N_c$ is the number of pair contacts and $N_{ISO} = 3N-6$. Maximally contacting packings are in general neither the densest nor the most symmetric. Analyses of local structure show that the fra…
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 subl…
We study structural phase transition of polymer-grafted colloidal particles by Monte Carlo simulations on hard spherical particles. The interaction potential, which has a weak repulsive step outside the hard core, was validated with use of the self-consistent field calculations. With this potential, canonical Monte Carlo simulations have been carried out in two and three dimensions using the Metropolis algorithm. At low temperature and high density, we find that the particles start to self-assemble and finally align in strings. By analyzing the cluster size distribution and string length distr…
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 simulate colloids (radius $R \sim 1μ$m) trapped at the interface between a cholesteric liquid crystal and an immiscible oil, at which the helical order (pitch p) in the bulk conflicts with the orientation induced at the interface, stabilizing an ordered array of disclinations. For weak anchoring strength W of the director field at the colloidal surface, this creates a template, favoring particle positions eitheron top of or midway between defect lines, depending on $α= R/p$. For small $α$, optical microscopy experiments confirm this picture, but for larger $α$ no templating is seen. This ma…
We study by simulation the physics of two colloidal particles in a cholesteric liquid crystal with tangential order parameter alignment at the particle surface. The effective force between the pair is attractive at short range and favors assembly of colloid dimers at specific orientations relative to the local director field. When pulled through the fluid by a constant force along the helical axis, we find that such a dimer rotates, either continuously or stepwise with phase-slip events. These cases are separated by a sharp dynamical transition and lead, respectively, to a constant or an ever-…
We investigate the elastic and yielding properties of two dimensional defect-free mono-crystals made of highly monodisperse droplets. Crystals are compressed between two parallel boundaries of which one acts as a force sensor. As the available space between boundaries is reduced, the crystal goes through successive row-reduction transitions. For small compression forces, the crystal responds elastically until a critical force is reached and the assembly fractures in a single catastrophic global event. Correspondingly there is a peak in the force measurement associated with each row-reduction. …
We simulate structural phase behavior of polymer-grafted colloidal particles by molecular Monte Carlo technique. Interparticle potential, which has a finite repulsive square-step outside a rigid core of the colloid, was previously confirmed via numerical self-consistent field calculation. This model potential is purely repulsive. We simulate these model colloids in the canonical ensemble in 2 dimensions and find that these particles containing no interparticle attraction self-assemble and align in a string-like assembly, at low temperature and high density. This string-like colloidal assembly …
We assemble charged colloidal spheres at deliberately chosen locations on a charged unstructured glass substrate utilizing ion exchange based electro-osmotic micro-pumps. Using microscopy, a simple scaling theory and Brownian Dynamics simulations, we systematically explore the control parameters of crystal assembly and the mechanisms through which they depend on the experimental boundary conditions. We demonstrate that crystal quality depends crucially on the assembly distance of the colloids. This is understood as resulting from the competition between inward transport by the electro-osmotic …
