Predicting crystals of Janus colloids

Synthetic T-Cell Receptor-like Protein Behaves as a Janus Particle in Solution

Protein engineering enables the creation of tailor-made proteins for a variety of applications. ImmTACs stand out as promising therapeutics for cancer and other treatments while also presenting unique challenges for stability, formulation, and delivery. We have shown that ImmTACs behave as Janus particles in solution, leading to self-association at low concentrations, even when the average protein-protein interactions suggest that the molecule should be stable. The formation of small but stable oligomers was confirmed by static and dynamic light scattering and analytical ultracentrifugation. Modeling of the structure using AlphaFold leads to a rational explanation for this behavior, consistent with the Janus particle assembly observed for inverse patchy particles.

Self-assembly and phase behavior of Janus rods: Competition between shape and potential anisotropy

We characterize the self-assembly and phase behavior of Janus rods over a broad range of temperatures and volume fractions, using Langevin dynamics simulations and free energy calculations. The Janus rods consist of a line of fused overlapping spheres that interact via a soft-core repulsive potential, with the addition of an attractive pseudo-square-well tail to a fraction of the spheres (the coverage) ranging from 5% to 100% of sites. Competition between the stability of liquid crystal phases originating from shape anisotropy and assembly driven by directional interactions gives rise to a rich polymorphism that depends on the coverage. At low densities near the Boyle temperature, we observe the formation of spherical and tubular micelles at low coverages, while at higher coverages, randomly oriented monolayers form as the attractive parts of the rods overlap. At higher densities, bilayer structures appear and merge to form smectic and crystalline lamellar phases. All these structures gradually become unstable as the temperature is increased until eventually regular nematic and smectic phases appear, consistent with the hard rod limit. Our results indicate that the intermediate regime where shape-entropic effects compete with anisotropic attractions provided by site specificity is rich in structural possibilities and should help guide the design of rod-like colloids for specific applications.

The Ordered Structures Formed by Janus-like Particles on a Triangular Lattice

The formation of ordered structures by Janus-like particles, composed of two parts (A and B), with orientation-dependent interactions on a triangular lattice was studied using Monte Carlo methods. The assumed lattice model allows each particle to take on one of the six orientations. The interaction between the A parts of neighboring particles was assumed to be attractive, while the AB and BB interactions were assumed to be repulsive. Moreover, it was assumed that the interaction between a pair of neighboring particles depended on the degrees to which their AA, AB, and BB parts face each other. It was shown that several ordered phases of different densities and structures may appear, depending on the magnitudes of AB and BB interactions. In particular, we found several structures composed of small clusters consisting of three (OT), four (OR), and seven (S) particles, surrounded by empty sites, the lamellar phases (OL, OL1, and OL3), the structures with hexagonal symmetry (R3×3 and K), as well as the structures with more complex symmetry (R5×5 and LAD). Several phase diagrams were evaluated, which demonstrated that the stability regions of different ordered phases are primarily determined by the strengths of repulsive AB and BB interactions.

Dilute suspensions of Janus rods: the role of bond and shape anisotropy

Nanometer-sized clusters are often targeted due to their potential applications as nanoreactors or storage/delivery devices. One route to assemble and stabilize finite structures consists of imparting directional bonding patterns between the nanoparticles. When only a portion of the particle surface is able to form an inter-particle bond, finite-size aggregates such as micelles and vesicles may form. Building on this approach, we combine particle shape anisotropy with the directionality of the bonding patterns and investigate the combined effect of particle elongation and surface patchiness on the low density assembly scenario. To this aim, we study the assembly of tip-functionalised Janus hard spherocylinders by means of Monte Carlo simulations. By exploring the effects of changing the interaction strength and range at different packing fractions, we highlight the role played by shape and bond anisotropy on the emerging aggregates (micelles, vesicles, elongated micelles, and lamellae). We observe that shape anisotropy plays a crucial role in suppressing phases that are typical to spherical Janus nanoparticles and that a careful tuning of the interaction parameters allows promoting the formation of spherical micelles. These finite-size spherical clusters composed of elongated particles might offer more interstitials and larger surface areas than those offered by micelles of spherical or almost-spherical units, thus enhancing their storage and catalytic properties.

Breaking the size constraint for nano cages using annular patchy particles

Engineering structures like nanocages, shells, and containers, by self-assembly of colloids is a challenging problem. One of the main challenges is to define the shape of the individual subunits to control the radius of the closed shell structures. In this work, we have proposed a simple model for the subunit, which comprises a spheroidal or spherical hardcore decorated with an annular patch. The self-assembly of these building blocks leads to the formation of monodispersed spherical cages (close shells) or containers (curved clusters). For a spheroid with a given bonding range, the curvature of the shell is analytically related to only the patch angle of the building blocks and independent of the shape of the subunits. This model with only one control parameter can be used to engineer cages with the desired radius, which also have been verified using thermodynamic calculations. In the phase diagram of the system, 4 phases are identified which includes gas, closed shell, partially closed (containers) shell and percolated structures. When the diameters of the spherical cages formed are small, we observe an icosahedral symmetry similar to virus capsids. We also observed that the kinetics of the cage formation is very similar to the nucleation and growth kinetics of viruses and is the key factor in determining the yield of closed shells.

Amphiphilic Janus Particles Confined in Symmetrical and Janus-Like Slits

We use Monte Carlo simulations to investigate the behavior of Janus spheres composed of attractive and repulsive parts confined between two parallel solid surfaces. The slits with identical and competing walls are studied. The adsorption isotherms of Janus particles are determined, and the impact of the density in the pore on the morphology is discussed in detail. So far, this issue has not been systematically investigated. New, unique structures are observed along the isotherms, including the bilayer and three-layer structures located at different distances from the walls. We analyze how selected parameters affect the positional and orientational ordering in these layers. In some cases, the particles form highly ordered hexagonal lattices.

Universal Critical Behavior of Percolation in Orientationally Ordered Janus Particles and Other Anisotropic Systems

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 behavior of percolation in the Janus system is consistent with that of standard isotropic percolation, when an appropriate spatial rescaling is made. The rescaling procedure can be applied to understand other anisotropic systems, such as the percolation of aligned rigid rods and of the q-state Potts model with anisotropic interactions.

Two-Dimensional Structures Formed by Triblock Patchy Particles with Two Different Patches

Two-dimensional structures formed by spherical triblock patchy particles are examined by performing Monte Carlo simulations. In the model, the triblock patchy particles have two different types of patches at the polar positions. The patch sizes are different from each other, and the attractive interaction acts only between the same types of patches. The particles translate on a flat plane and rotate three-dimensionally. When varying the two patch sizes, the pressure, and interaction energy, various structures are observed. When the difference between two patch sizes is small, kagome lattices, hexagonal structures, and two-dimensional dodecagonal quasi-crystal structures are observed. When the difference between two patch sizes is large, chain-like structures are created. With lower temperature, sparse structures such as ring-like structures form.

Self-sustained non-equilibrium co-existence of fluid and solid states in a strongly coupled complex plasma system

A complex (dusty) plasma system is well known as a paradigmatic model for studying the kinetics of solid-liquid phase transitions in inactive condensed matter. At the same time, under certain conditions a complex plasma system can also display characteristics of an active medium with the micron-sized particles converting energy of the ambient environment into motility and thereby becoming active. We present a detailed analysis of the experimental complex plasmas system that shows evidence of a non-equilibrium stationary coexistence between a cold crystalline and a hot fluid state in the structure due to the conversion of plasma energy into the motion energy of microparticles in the central region of the system. The plasma mediated non-reciprocal interaction between the dust particles is the underlying mechanism for the enormous heating of the central subsystem, and it acts as a micro-scale energy source that keeps the central subsystem in the molten state. Accurate multiscale simulations of the system based on combined molecular dynamics and particle-in-cell approaches show that strong structural nonuniformity of the system under the action of electostatic trap makes development of instabilities a local process. We present both experimental tests conducted with a complex plasmas system in a DC glow discharge plasma and a detailed theoretical analysis.

Solvent-Induced Assembly of One-Patch Silica Nanoparticles into Robust Clusters, Wormlike Chains and Bilayers

We report the synthesis and solvent-induced assembly of one-patch silica nanoparticles in the size range of 100–150 nm. They consisted, as a first approximation, of silica half-spheres of which the truncated face was itself concave and carried in its center a polymeric patch made of grafted polystyrene chains. The multistage synthesis led to 98% pure batches and allowed a fine control of the patch-to-particle size ratio from 0.69 to 1.54. The self-assembly was performed in equivolume mixtures of tetrahydrofuran and ethanol, making the polymeric patches sticky and ready to coalesce together. The assembly kinetics was monitored by collecting samples over time and analyzing statistically their TEM images. Small clusters, such as dimers, trimers, and tetramers, were formed initially and then evolved in part into micelles. Accordingly to previous simulation studies, more or less branched wormlike chains and planar bilayers were observed in the long term, when the patch-to-particle size ratio was high enough. We focused also on the experimental conditions that could allow preparing small clusters in a good morphology yield.

Facile self-assembly of colloidal diamond from tetrahedral patchy particles via ring selection

The self-assembly of colloidal diamond–a classic example of an open crystal with the low coordination number of four and much sought after due to its applications in visible light management–from designer spherical colloidal particles has proved challenging over the years. The formation of the diamond lattice from tetrahedral patchy particles is hampered by the propensity to form competing open periodic structures for narrow patches or dynamically arrested states for wider patches, leaving a narrow window in design space where diamond crystals may be realized. Our two-component system of designer tetrahedral patchy particles supports a significantly wider range for patch sizes for programmed self-assembly, thus facilitating experimental fabrication, and offers fundamental insight into crystallization into open lattices.

Diamond-structured crystals, particularly those with cubic symmetry, have long been attractive targets for the programmed self-assembly of colloidal particles, due to their applications as photonic crystals that can control the flow of visible light. While spherical particles decorated with four patches in a tetrahedral arrangement—tetrahedral patchy particles—should be an ideal building block for this endeavor, their self-assembly into colloidal diamond has proved elusive. The kinetics of self-assembly pose a major challenge, with competition from an amorphous glassy phase, as well as clathrate crystals, leaving a narrow widow of patch widths where tetrahedral patchy particles can self-assemble into diamond crystals. Here we demonstrate that a two-component system of tetrahedral patchy particles, where bonding is allowed only between particles of different types to select even-member rings, undergoes crystallization into diamond crystals over a significantly wider range of patch widths conducive for experimental fabrication. We show that the crystallization in the two-component system is both thermodynamically and kinetically enhanced, as compared to the one-component system. Although our bottom-up route does not lead to the selection of the cubic polytype exclusively, we find that the cubicity of the self-assembled crystals increases with increasing patch width. Our designer system not only promises a scalable bottom-up route for colloidal diamond but also offers fundamental insight into crystallization into open lattices.

Phase Transitions in Two-Dimensional Systems of Janus-like Particles on a Triangular Lattice

We studied the phase behavior of two-dimensional systems of Janus-like particles on a triangular lattice using Monte Carlo methods. The model assumes that each particle can take on one of the six orientations with respect to the lattice, and the interactions between neighboring particles were weighted depending on the degree to which their A and B halves overlap. In this work, we assumed that the AA interaction was fixed and attractive, while the AB and BB interactions varied. We demonstrated that the phase behavior of the systems considered strongly depended on the magnitude of the interaction energies between the AB and BB halves. Here, we considered systems with non-repulsive interactions only and determined phase diagrams for several systems. We demonstrated that the phase diagram topology depends on the temperature at which the close-packed systems undergo the orientational order–disorder transition.

Asymmetric assembly of Lennard-Jones Janus dimers

Self-assembly of Janus (or "patchy") particles is dependent on the precise interaction between neighboring 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 semianalytical energy calculations are used with hard- and soft-sphere Lennard-Jones potentials, and temperature and hydrophobicity are varied. The most probable center-center-pole angles are in the range of 40^{∘}-55^{∘} with pole-to-pole alignment not observed due to orientational entropy. Angles near 90^{∘} are energetically unfavored due to solvent exclusion, and the relative azimuthal angle between the spheres is affected by solvent ordering. Relatively large polar angles become more favored as the hydrophobic surface area (i.e., Janus balance) is increased.

Clusters formed by dumbbell-like one-patch particles confined in thin systems

Performing isothermal-isochoric Monte Carlo simulations, I examine the types of clusters that dumbbell-like one–patch particles form in thin space between two parallel walls, assuming that each particle is synthesized through the merging of two particles, one non-attracting and the other attracting for which, for example, the inter-particle interaction is approximated by the DLVO model . The shape of these dumbbell-like particles is controlled by the ratio of the diameters q of the two spherical particles and by the dimensionless distance l between these centers. Using a modified Kern–Frenkel potential, I examine the dependence of the cluster shape on l and q. Large island-like clusters are created when \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q<1$$\end{document}q<1. With increasing q, the clusters become chain-like . When q increases further, elongated clusters and regular polygonal clusters are created. In the simulations, the cluster shape becomes three-dimensional with increasing l because the thickness of the thin system increases proportionally to l.

Designer Nanomaterials through Programmable Assembly

Nanoparticles have long been recognized for their unique properties, leading to exciting potential applications across optics, electronics, magnetism, and catalysis. These specific functions often require a designed organization of particles, which includes the type of order as well as placement and relative orientation of particles of the same or different kinds. DNA nanotechnology offers the ability to introduce highly addressable bonds, tailor particle interactions, and control the geometry of bindings motifs. Here, we discuss how developments in structural DNA nanotechnology have enabled greater control over 1D, 2D, and 3D particle organizations through programmable assembly. This Review focuses on how the use of DNA binding between nanocomponents and DNA structural motifs has progressively allowed the rational formation of prescribed particle organizations. We offer insight into how DNA-based motifs and elements can be further developed to control particle organizations and how particles and DNA can be integrated into nanoscale building blocks, so-called "material voxels", to realize designer nanomaterials with desired functions.

Monodisperse patchy particle glass former

Glass formers are characterized by their ability to avoid crystallization. As monodisperse systems tend to rapidly crystallize, the most common glass formers in simulations are systems composed of mixtures of particles with different sizes. Here, we make use of the ability of patchy particles to change their local structure to propose them as monodisperse glass formers. We explore monodisperse systems with two patch geometries: a 12-patch geometry that enhances the formation of icosahedral clusters and an 8-patch geometry that does not appear to strongly favor any particular local structure. We show that both geometries avoid crystallization and present glassy features at low temperatures. However, the 8-patch geometry better preserves the structure of a simple liquid at a wide range of temperatures and packing fractions, making it a good candidate for a monodisperse glass former.

Stabilizing ordered structures with single patch inverse patchy colloids in two dimensions

Oppositely charged bipolar colloids or colloids decorated with complementary deoxyribonucleic acid (DNA) on their surfaces are special kinds of patchy particles where only patch and non-patch parts are attractive. These are classified as inverse patchy colloids (IPCs). In this work, equilibrium self-assembly of IPC in two-dimensions is reported using Monte Carlo simulations. Square (SCs) and triangular crystals (TCs) are found to be stable at 0.5 patch coverage. Upon decreasing the patch coverage to 0.33, the regular SC is destabilized; instead rhombic and TCs are found to be stable. At low patch coverages such as 0.22 and 0.12, only TC is stabilized at high density. Particles of all the patch coverages show kinetically stable cluster phases of different shapes and sizes at low densities, and the average cluster size depends on the patch coverage and particle density. State-diagrams showing all the stable phases for each patch coverage are presented. Ordered phases are characterized by bond order parametersψ₄,ψ₆and radial distribution function. The effect of polydispersity in patch coverage on the polarization of the stable structures are also studied. The study demonstrates that IPCs can stabilize various ordered two-dimensional structures by tuning the size of the patch, density and interaction strengths.

Effect of the Interaction Length on Clusters Formed by Spherical One-Patch Particles on Flat Planes

Considering that one-patch particles rotate three-dimensionally and translate on a two-dimensional flat plane, I performed isothermal-isochoric Monte Carlo simulations to study how two-dimensional self-assemblies formed by spherical patchy particles depending on the interaction length and patch area. As the interaction potential between one-patch particles, the Kern-Frenkel (KF) potential is used in the simulations. With increasing patch area, the shape of the most numerous clusters changes from dimers to island-like clusters with a square lattice via triangular trimers, square tetramers, and chain-like clusters when the interaction length is as long as the particle radius. With a longer interaction length, other shapes of polygonal clusters such as another type of square tetramers, two types of pentagonal pentamers, hexagonal hexamers, and hexagonal heptamers also form.

Self-Assembly of Patchy Colloidal Rods into Photonic Crystals Robust to Stacking Faults

Diamond-structured colloidal photonic crystals are much sought-after for their applications in visible light management because of their ability to support a complete photonic band gap (PBG). However, their realization via self-assembly pathways is a long-standing challenge. This challenge is rooted in three fundamental problems: the design of building blocks that assemble into diamond-like structures, the sensitivity of the PBG to stacking faults, and ensuring that the PBG opens at an experimentally attainable refractive index. Here we address these problems simultaneously using a multipronged computational approach. We use reverse engineering to establish the design principles for the rod-connected diamond structure (RCD), the so-called "champion" photonic crystal. We devise two distinct self-assembly routes for designer triblock patchy colloidal rods, both proceeding via tetrahedral clusters to yield a mixed phase of cubic and hexagonal polymorphs closely related to RCD. We use Monte Carlo simulations to show how these routes avoid a metastable amorphous phase. Finally, we show that both the polymorphs support spectrally overlapping PBGs. Importantly, randomly stacked hybrids of these polymorphs also display PBGs, thus circumventing the requirement of polymorph selection in a scalable fabrication method.

Effect of Patch Area and Interaction Length on Clusters and Structures Formed by One-Patch Particles in Thin Systems

Assuming that the interaction between particles is given by the Kern-Frenkel potential, Monte Carlo simulations are performed to study the clusters and structures formed by one-patch particles in a thin space between two parallel walls. In isothermal-isochoric systems with a short interaction length, tetrahedral tetramers, octahedral hexamers, and pentagonal dipyramidal heptamers are created with increasing patch area. In isothermal-isobaric systems, the double layers of a triangular lattice, which is the (111) face of the face-centered cubic (fcc) lattice, form when the pressure is high. For a long interaction length, a different type of cluster, trigonal prismatic hexamers, is created. The structures in the double layers also changed as follows: a simple hexagonal lattice or square lattice, which is the (100) face of the fcc structure, is created in isothermal-isobaric systems.

Dynamic Interfacial Trapping of Janus Nanorod Aggregates

Taking advantage of both shape and chemical anisotropy on the same nanoparticle offers rich self-assembly possibilities for nanotechnology. Through dissipative particle dynamics calculations, in the present work, the directed assembly of Janus nanorod aggregates and their capability to assemble into metastable novel structures at an interfacial level have been assessed. Symmetric Janus rods become kinetically trapped and exhibit either parallel or antiparallel alignment with respect to their long axis (different compositions). This depends on several factors that have been mapped herein and that can be precisely tuned: Flory-Huggins interaction parameter χ between polymer phases; concentration; shear rate; and even aggregate shape. Ultimately, two different aggregate structures result from rod tumbling that are not observed under quiescent conditions: monolayer-like aggregates exhibiting trapped rods with antiparallel configuration; and stacked nanorod arrays similar to superlattice sheets. These different structures can be controlled by the likelihood with which tumbling Janus rods encounter other aggregate portions showing parallel alignment. Hence, the present study offers fundamental insight into relevant parameters that govern the directed assembly of Janus nanoparticles at an interfacial level. Novel applications may potentially derive from the resulting aggregate structures, such as peculiar displays and sensors.

Engineering Surface Patterning of Colloidal Rings through Plateau-Rayleigh Instability

Plateau-Rayleigh (P-R) instability occurring on Brownian colloidal particles is presented. This instability can be used for the surface patterning of Brownian colloidal rings. This idea was realized by employing polystyrene(PS)/SiO₂ core/shell rings, for which PS layer was selectively grown onto the interior surface of SiO₂ rings. The P-R instability was initiated in the ring's dispersion by adding a good solvent of PS. By using both experiments and theory, it is shown that the number of patches is tunable and that it is linearly related to a function of two variables, namely, solvent quantity and contact angle. In particular, one-patch Janus rings and patchy disks were also synthesized at high yields. The patch size of all particles is tunable by step-by-step polymerization and the patches can be functionalized, for example by ATRP grafting with pH-sensitive polymers. This approach can be adapted for the synthesis of other patchy colloids with designated complexity.

Brownian dynamics simulations of one-patch inverse patchy particles

Inverse patchy particles are promising colloids to develop new architectures in ceramic materials based on their self-assembly. Nonetheless, a good understanding of their aggregation is required. Several previous studies have shown that the behavior of ceramic colloids can be well described by the DLVO interaction potential. In the present paper, we develop new coarse-grained Brownian dynamics simulations, where particles are represented by an assembly of beads interacting via DLVO interactions, whose parameters can be directly linked to experimental characterization. First, the validity of the simulations is proved by studying the heteroaggregation of homogeneously charged particles. Then, simulations are applied to one-patch inverse patchy particles to study the effect of the patch size. They show that the smaller the patch, the more elongated the aggregates. Simulations are also performed to understand the role of the Debye screening length in the particular case of large patches and they show that aggregation leads always to compact aggregates.

Self-assembly of Janus disks confined in a slit

Using Monte Carlo simulations, we investigate the self-organization of Janus disks confined in two-dimensional slits. Janus particles are modeled as circles composed of attractive and repulsive parts. We consider the slits with identical walls and slits with competing walls (the so-called Janus-like pores). We investigate how the system morphology depends on the slit width, density, and temperature. Different unique orientationally ordered structures are found. The mechanism of formation of these structures is discussed in detail. We show that the anisotropic interactions between the confined molecules, the nature of the "walls," and the slit size strongly affect the self-organization.

Mobile obstacles accelerate and inhibit the bundle formation in two-patch colloidal particle

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 networklike structures using patchy Brownian cluster dynamics. We also analyze the ways to inhibit and accelerate the formation of these bundles. We show that in the presence of inert immobile obstacles, the kinetics of formation of bundles slows down. However, in the presence of mobile aggregating particles, which exhibit interspecies hard sphere repulsion and intraspecies attraction, the kinetics of bundle formation accelerates slightly. We also show that if we introduce mobile obstacles, which exhibit interspecies attraction and intraspecies hard sphere repulsion, the kinetics of formation of bundles is inhibited. This is similar to the inhibitory effect of peptide P4 on the formation of insulin fibers. We are providing a model of mobile obstacles undergoing directional interactions to inhibit the formation of bundles.

Designing active particles for colloidal microstructure manipulation via strain field alchemy

Defects in a crystal can exert forces on each other via strain field interactions. Here we explore the strain-field-mediated interaction between an anisotropic interstitial probe particle and dislocation microstructures in a colloidal crystal composed of particles interacting via steep repulsive isotropic potentials. We optimize the interaction between probe particle and dislocation with the anisotropic shape of the probe as a free parameter. Such alchemical optimization is typically carried out upon the explicitly defined interaction potential parameters; instead, we optimize the strain field of the probe and then map back to particle shape. We distinguish this tactic from other alchemical methods as 'strain alchemy'. We report several findings: (1) a robust mapping exists between strain field calculation methods (the method of eigenstrains) and strains produced by an anisotropic interstitial, (2) optimization of strain field interactions in the strain domain permits rapid evaluation of candidate shapes for interstitials, (3) interstitial mobility barriers can be estimated from the strain field, and (4) strongly interacting and highly mobile interstitial particles can be found that are capable of driving dislocation glide with applied force. Active particle-induced dislocation glide is examined for the cases of edge dislocation arrays and extrinsic dislocation loops. For edge dislocations, particle geometries of alternating large and small diameter segments were found to interact most strongly. For dislocation loops, interstitials with a single small radius segment surrounded by large radius segments are best.

Plastic Crystal-to-Crystal Transition of Janus Particles under Shear

Colloidal Janus spheres in the bulk typically spontaneously assemble into plastic crystalline phases, while particle orientations exhibit glasslike dynamics without long-range order. Through Brownian dynamics simulations, we demonstrate that shear can trigger a phase transition from an isotropic crystal with orientational disorder to an orientationally ordered crystal with lamellae along the shear direction. This nonequilibrium transition is accompanied with the orientational ordering following a nucleation and growth mechanism. By performing a phenomenological extension of free energy analysis, we reveal that the nucleation originates from the orientation fluctuations induced by shear. The growth of the orientationally crystalline cluster is examined to be disklike, captured by developing a lattice model with memoryless state functions. These findings bring new insights into the mechanisms for the ordering transition of anisotropic particles at nonequilibrium states.

Controlled armoring of metal surfaces with metallodielectric patchy particles

A patchy colloidal particle possesses distinctive regions with different physical or chemical properties on its surface and thus exhibits anisotropic interactions with another particle or object. By utilizing the large van der Waals attraction between metal surfaces and the electric double layer repulsion originating from surface charge, we succeeded in controlling the adsorption behavior of metallodielectric particles (MDPs), which were composed of dielectric spheres each with a thin gold patch modified with dissociable groups, to gold surfaces. When MDPs were dispersed on a dielectric substrate with a thick gold pattern in aqueous solution, the particles selectively adsorbed onto the gold surface of the substrate at a moderate salt concentration. Furthermore, when MDPs were mixed with large particles coated with a thick gold film, MDPs adsorbed on the gold surface at a moderate salt concentration and formed a monolayer. In the monolayer, gold patches of MDPs bonded to the gold surface and the dielectric surface of MDPs faced outward. In other words, this monolayer was a solid dielectric layer formed on the metal surface of a large particle. Such selectivity, i.e., that a gold patch of an MDP bonded to a gold surface but the patches did not bond to each other, was realized by controlling the thickness and surface charge of gold patches.

Dynamic modelling on the confined crystallization of mono-sized cubic particles under mechanical vibration

The dynamic crystallization of cubic granular particles under three-dimensional mechanical vibration is numerically investigated by the discrete element method. The effects of operational conditions (vibration, container shape and system size) and particle properties (gravity and friction) on the formation of crystals and defects are discussed. The results show that the formation and growth of clusters with face-to-face aligned cubic particles can be easily realized under vibrations. Especially, a single crystal with both translational and orientational ordering can be reproduced in a rectangular container under appropriate vibrations. It is also found that the gravitational effect is beneficial for the ordering of a packing; the ordering of frictional particles can be improved significantly with an enlarged gravitational acceleration. The flat walls of a rectangular container facilitate the formation of orderly layered structures. The curved walls of a cylindrical container contribute to the formation of ring-like structures, whereas they also cause distortions and defects in the packing centers. Finally, it is shown that the crystallization of inelastic particles is basically accomplished by the pursuit of a better mechanical stability of the system, with decreasing kinetic and potential energies.

Orientational ordering of closely packed Janus particles

We study the 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 consists of dimers and trimers of the attractive patches. For large enough patch sizes, the system exhibits a thermodynamic transition into a phase with the stripe patterns of the patches breaking the three-fold rotational symmetry. Our results strongly suggest that the latter is a 2nd order phase transition whose universality is the same as that of the 3-state Potts model in 2-dimensions. Furthermore we analyzed the relaxation dynamics of the system performing quenching simulations on the stripe phase. We found growth of the domains of the stripes. The relaxation of key dynamical quantities follows universal scaling features in terms of the domain size.

How to simulate patchy particles⋆

Patchy particles is the name given to a large class of systems of mesoscopic particles characterized by a repulsive core and a discrete number of short-range and highly directional interaction sites. Numerical simulations have contributed significantly to our understanding of the behaviour of patchy particles, but, although simple in principle, advanced simulation techniques are often required to sample the low temperatures and long time-scales associated with their self-assembly behaviour. In this work we review the most popular simulation techniques that have been used to study patchy particles, with a special focus on Monte Carlo methods. We cover many of the tools required to simulate patchy systems, from interaction potentials to biased moves, cluster moves, and free-energy methods. The review is complemented by an educationally oriented Monte Carlo computer code that implements all the techniques described in the text to simulate a well-known tetrahedral patchy particle model.

Irregular model DNA particles self-assemble into a regular structure

DNA nanoparticles with three-fold coordination have been observed to self-assemble in experiment into a network equivalent to the hexagonal (6.6.6) tiling, and a network equivalent to the 4.8.8 Archimedean tiling. Both networks are built from a single type of vertex. Here we use analytic theory and equilibrium and dynamic simulation to show that a model particle, whose rotational properties lie between those of the vertices of the 6.6.6 and 4.8.8 networks, can self-assemble into a network built from three types of vertex. Important in forming this network is the ability of the particle to rotate when bound, thereby allowing the formation of more than one type of binding motif. The network in question is equivalent to a false tiling, a periodic structure built from irregular polygons, and possesses 40 particles in its unit cell. The emergence of this complex structure, whose symmetry properties are not obviously related to those of its constituent particles, highlights the potential for creating new structures from simple variants of existing nanoparticles.

Free energy calculations for rings and chains formed by dipolar hard spheres

We employ a method based on Monte Carlo grand-canonical simulations to precisely calculate partition functions of non-interacting chains and rings formed by dipolar hard spheres (DHS) at low temperature. The extended low temperature region offered by such cluster calculations, compared to what had been previously achieved with standard simulations, opens up the possibility of exploring a part of the DHS phase diagram which was inaccessible before. The reported results offer the unique opportunity of verifying well-established theoretical models based on the ideal gas of cluster approximation in order to clarify their range of validity. They also provide the basis for future studies in which cluster-cluster interactions will be included.

Phase diagram of Janus particles: The missing dimension of pressure anisotropy

Brownian dynamics simulations of single-patch Janus particles under sedimentation equilibrium reveal that the phases found at fixed temperature and volume fraction are extremely sensitive to small changes in lateral box dimension. We trace this sensitivity to an uncontrolled parameter, namely, the pressure component parallel to the hexagonally ordered layers formed through sedimentation. We employ a flexible-cell constant-pressure scheme to achieve explicit control over this usually overlooked parameter, enabling the estimation of phase behavior under given pressure anisotropy. Our results show an increase in the stability range of an orientationally ordered lamellar phase with lateral layer compression and suggest a novel mechanism to control solid-solid phase transitions with negligible change in system volume, thus showing prospect for design of novel structures and switchable crystals from anisotropic building blocks.

Assembly of trivalent particles under confinement: from an exotic solid phase to a liquid phase at low temperature

Using computer simulations, we study the phase diagram of a two-dimensional system of disk particles with three patches distributed symmetrically along the particle equator. The geometry of the particles is compatible with a honey-comb lattice at moderately low temperature and pressure, whereas it is expected that the system forms a close-packed triangular lattice at high temperature and pressure. The effect of patch size within the single bond per patch regime was investigated, and it was found that the topology of the phase diagram changes drastically with patch size. Interestingly, in particles with small patches (with a half opening angle of 10°), the fluid transforms upon increasing the pressure into a rather exotic phase that can be understood as a honey-comb lattice whose voids are filled continuously with additional particles that remain, on average, unbound. Eventually, all the voids are occupied so that particles are located at the positions of a triangular lattice, but only two thirds of the particles are orientationally ordered whereas the remaining one third can rotate almost freely as in a plastic crystal. At moderately low temperature, the fluid transforms into a nearly empty honey-comb lattice, whereas at high temperature it transforms directly into the almost filled lattice. Interestingly, for particles with big patches (with a half opening angle of 20°), the honey-comb and triangular lattices are separated by a liquid phase that remains stable down to fairly low temperatures. Less surprisingly, only particles with big patches exhibit an equilibrium gas-liquid separation.

Spontaneous assembly of a hybrid crystal-liquid phase in inverse patchy colloid systems

Materials with well-defined architectures are heavily sought after in view of their diverse technological applications. Among the desired target architectures, lamellar phases stand out for their exceptional mechanical and optical features. Here we show that charged colloids, decorated on their poles with two oppositely charged regions possess the unusual ability to spontaneously assemble in different morphologies of (semi-)ordered, layered particle arrangements which maintain their structural stability over a surprisingly large temperature range. This remarkable capacity is related to a characteristic bonding mechanism: stable intra-layer bonds guarantee the formation of planar aggregates, while strong inter-layer bonds favor the stacking of the emerging planar assemblies. These two types of bonds together are responsible for the self-healing processes occurring during the spontaneous assembly. The resulting phases are characterized by parallel, densely packed, particle layers connected by a relatively small number of intra-layer particles. We investigate the properties of the (semi-)ordered phases in terms of static and dynamic correlation functions, focusing in particular on a novel hybrid crystal-liquid phase that prevails at intermediate temperatures where the inter-layer particles form a mobile, fluid phase.

Out of Equilibrium Self-Assembly of Janus Nanoparticles: Steering It from Disordered Amorphous to 2D Patterned Aggregates

Solvent evaporation driven self-assembly of Janus nanoparticles (J-NPs) has been simulated employing lattice-gas models to investigate the possible emergence of new superlattices. Depending on the chemical nature of NP faces (hence solvophilicity and relative interaction strength), zebra-like or check-like patterns and micellar agglomerates can be obtained. Vesicle-like aggregates can be produced by micelle-based corrals during heterogeneous evaporation. Patterns formed during aggregation appear to be robust against changes in evaporation modality (i.e., spinodal or heterogeneous) or interaction strengths, and they are due to a strictly nanoscopic orientation of single J-NPs in all cases. Due to the latter feature, the aggregate size growth law N(t) ∝ t^a has its exponent a markedly depending on the chemical nature of the J-NPs involved in spite of the unvaried growth mechanism. We interpret such a finding as connected to the increasingly stricter orientation pre-requirements for successful (binding) NP landing upon going from isotropic (a ≃ 0.50), to "zebra" (a ≃ 0.38), to "check" (a ≃ 0.23), and finally to "micelle" (a = 0.15-0.17) pattern forming NPs.