Equilibrium phases of one-patch colloids with short-range attractions

Formation of various structures caused by particle size difference in colloidal heteroepitaxy

By performing isothermal-isochoric Monte Carlo simulations with depletion force, the author investigated the dependence of the epitxial layer structure on the differences in the particle size between the substrate in colloidal heteroepitaxy. By changing the size of epitaxial particles and performing simulations comprehensively, various structures including the structures observed in a experiment, such as a honeycomb, one created by hexagonal heptamers, and one consisting of both pentagonal tiles and triangular tiles, were created. When the ratio of particle sizes between the epitxial layer and substrate takes a specific value, two types of hexagonal structures were created. One is the hexagonal layer parallel to the substrate layer and the other layer is rotated by 60[Formula: see text] from the substrate layer. The former structure was created over a wide range of particle-size ratios, whereas the latter structure was created when the particle-size ratio was only around the specific ratio, and it seemed a metastable structure.

Self-Assembling of Nonadditive Mixtures Containing Patchy Particles with Tunable Interactions

Mixtures of nanoparticles (NPs) with hybridizing grafted DNA or DNA-like strands have been of particular interest because of the tunable selectivity provided for the interactions between the NP components. A richer self-assembly behavior would be accessible if these NP-NP interactions could be designed to give nonadditive mixing (in analogy to the case of molecular components). Nonadditive mixing occurs when the mixed-state volume is smaller (negative) or larger (positive) than the sum of the individual components' volumes. However, instances of nonadditivity in colloidal/NP mixtures are rare, and systematic studies of such mixtures are nonexistent. This work focuses on patchy NPs whose patches (coarsely representing grafted hybridizing DNA strands) not only encode selectivity across components but also impart a tunable nonadditivity by varying their extent of protrusion. To guide the exploration of the relationship between phase behavior and nonadditivity for different patches' designs, the NP-NP potential of mean force (PMF) and a nonadditive parameter were first calculated. For one-patch NPs, different lamellar morphologies were predominantly observed. In contrast, for mixtures of two-patch NPs and (fully grafted) spherical particles, a rich phase behavior was found depending on patch-patch angle and degree of nonadditivity, resulting in phases such as the gyroid, cylinder, honeycomb, and two-layered crystal. Our results also show that both minimum positive nonadditivity and multivalent interactions are necessary for the formation of ordered network mesophases in the class of models studied.

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.

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.

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.

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.

Thermodynamics of structure-forming systems

Structure-forming systems are ubiquitous in nature, ranging from atoms building molecules to self-assembly of colloidal amphibolic particles. The understanding of the underlying thermodynamics of such systems remains an important problem. Here, we derive the entropy for structure-forming systems that differs from Boltzmann-Gibbs entropy by a term that explicitly captures clustered states. For large systems and low concentrations the approach is equivalent to the grand-canonical ensemble; for small systems we find significant deviations. We derive the detailed fluctuation theorem and Crooks' work fluctuation theorem for structure-forming systems. The connection to the theory of particle self-assembly is discussed. We apply the results to several physical systems. We present the phase diagram for patchy particles described by the Kern-Frenkel potential. We show that the Curie-Weiss model with molecule structures exhibits a first-order phase transition.

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.

Multivalent Patchy Colloids for Quantitative 3D Self-Assembly Studies

We report methods to synthesize sub-micron- and micron-sized patchy silica particles with fluorescently labeled hemispherical titania protrusions, as well as routes to efficiently characterize these particles and self-assemble these particles into non-close-packed structures. The synthesis methods expand upon earlier work in the literature, in which silica particles packed in a colloidal crystal were surface-patterned with a silane coupling agent. Here, hemispherical amorphous titania protrusions were successfully labeled with fluorescent dyes, allowing for imaging by confocal microscopy and super-resolution techniques. Confocal microscopy was exploited to experimentally determine the numbers of protrusions per particle over large numbers of particles for good statistical significance, and these distributions were compared to simulations predicting the number of patches as a function of core particle polydispersity and maximum separation between the particle surfaces. We self-assembled these patchy particles into open percolating gel networks by exploiting solvophobic attractions between the protrusions.

Structure and dynamics of amphiphilic Janus spheres and spherocylinders under shear

We study the structure formation and flow properties of colloidal dispersions comprised of Janus spheres, Janus spherocylinders, and their mixtures, using hybrid molecular dynamics simulations that take into account hydrodynamic interactions. We systematically vary the Janus balance and the shape anisotropy of the particles, and explore a range of colloid volume fractions in the liquid regime of the phase diagram. At rest, Janus spheres with small hydrophobic patches form spherical micelles for all investigated colloid concentrations. In contrast, Janus spheres with an entirely hydrophobic hemisphere aggregate to larger worm-like micelles and network-like structures. Janus spherocylinders exhibit a similar self-assembly behavior. At small and intermediate shear, we observe deformation and rearrangement of the micelles, accompanied by a Newtonian-like rheology with slightly higher shear viscosity compared to homoparticle dispersions at the same concentration. As the shear rate is increased further, the micelles eventually break up into small dimers and free particles, causing a distinct shear-thinning of the dispersions. The network-like structures exhibit a similar flow behavior at high shear rates, but for weak shear we find an almost threefold increase of the shear viscosity and a distinct shear-thinning behavior due to the fracturing of the intertwined networks. In general, we identify a strong correlation between the size of the aggregates and the rheology of the dispersions, allowing for the determination of dynamic properties solely based on structural information.

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.

Colloidal fibers and rings by cooperative assembly

Janus colloids with one attractive patch on an otherwise repulsive particle surface serve as model systems to explore structure formation of particles with chemically heterogeneous surfaces such as proteins. While there are numerous computer studies, there are few experimental realizations due to a lack of means to produce such colloids with a well-controlled variable Janus balance. Here, we report a simple scalable method to precisely vary the Janus balance over a wide range and selectively functionalize one patch with DNA. We observe, via experiment and simulation, the dynamic formation of diverse superstructures: colloidal micelles, chains, or bilayers, depending on the Janus balance. Flexible dimer chains form through cooperative polymerization while trimer chains form by a two-stage process, first by cooperative polymerization into disordered aggregates followed by condensation into more ordered stiff trimer chains. Introducing substrate binding through depletion catalyzes dimer chains to form nonequilibrium rings that otherwise do not form.

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.

Simulating Surface Patterning of Nanoparticles by Polymers via Dissipative Particle Dynamics Method

Patchy particles are often referred to colloidal particles with physically or chemically patterned surfaces. We investigated the patterning of nanoparticle grafted by polymers, mainly consisting of patchy structures with different numbers of patches ( N_patch) and core-shell structure using the dissipative particle dynamics (DPD) method in good or poor solvents based on the experiment research. Poor solvent, large nanoparticle, proper grafting density and medium polymer length contribute to the formation of patchy structure. We introduce the effective volume fraction as an indicator to distinguish the patchy structure from core-shell structure. The reversible transition between core-shell (in a good solvent) and patchy structure (in a poor solvent) and the dependency relationship between the nanoparticle diameter and grafting density in experiment are verified. Our results pave the way for preparing the colloids with well-defined patches. The anisotropic patchy particles can self-assemble into elaborate superstructures, which are potential blocking materials for drug delivery, sensors, and electronics.

Molecular structure and multi-body potential of mean force in silica-polystyrene nanocomposites

We perform a systematic application of the hybrid particle-field molecular dynamics technique [Milano, et al., J. Chem. Phys., 2009, 130, 214106] to study interfacial properties and potential of mean force (PMF) for separating nanoparticles (NPs) in a melt. Specifically, we consider Silica NPs bare or grafted with Polystyrene chains, aiming to shed light on the interactions among free and grafted chains affecting the dispersion of NPs in the nanocomposite. The proposed hybrid models show good performances in catching the local structure of the chains, and in particular their density profiles, documenting the existence of the "wet-brush-to-dry-brush" transition. By using these models, the PMF between pairs of ungrafted and grafted NPs in Polystyrene matrix are calculated. Moreover, we estimate the three-particle contribution to the total PMF and its role in regulating the phase separation on the nanometer scale. In particular, the multi-particle contribution to the PMF is able to give an explanation of the complex experimental morphologies observed at low grafting densities. More in general, we propose this approach and the models utilized here for a molecular understanding of specific systems and the impact of the chemical nature of the systems on the composite final properties.

Microstructure and dynamics of Janus particles in a phase separating medium

The evolution of interactions and dynamics of Janus colloidal particles suspended in quasi-binary liquid mixtures undergoing phase separation is presented. The experimental system consisted of silica-nickel Janus particles dispersed in mixtures of 3-methylpyridine, water, and heavy water. Colloidal microstructure and dynamics were probed by ultra-small-angle X-ray scattering and ultra-small-angle X-ray photon correlation spectroscopy, respectively. The observed static and dynamic behaviors are significantly different from those found for Stöber silica colloids in this mixture. The Janus particles manifest a slow aggregation below the coexistence temperature and become strongly attractive upon phase separation of the solvent mixture. In the two-phase region, particles tend to display surfactant-like behavior with silica and nickel surfaces likely preferring water and 3-methylpyridine rich phases, respectively. While the onset of diffusiophoretic motion is evident in the dynamics, it is gradually suppressed by particle clustering at the investigated colloid volume fractions.

Aggregation kinetics of irreversible patches coupled with reversible isotropic interaction leading to chains, bundles and globules

In the present study we are performing simulation of simple model of two patch colloidal particles undergoing irreversible diffusion limited cluster aggregation using patchy Brownian cluster dynamics. In addition to the irreversible aggregation of patches, the spheres are coupled with isotropic reversible aggregation through the Kern–Frenkel potential. Due to the presence of anisotropic and isotropic potential we have also defined three different kinds of clusters formed due to anisotropic potential and isotropic potential only as well as both the potentials together. We have investigated the effect of patch size on self-assembly under different solvent qualities for various volume fractions. We will show that at low volume fractions during aggregation process, we end up in a chain conformation for smaller patch size while in a globular conformation for bigger patch size. We also observed a chain to bundle transformation depending on the attractive interaction strength between the chains or in other words depending on the quality of the solvent. We will also show that bundling process is very similar to nucleation and growth phenomena observed in colloidal system with short range attraction. We have also studied the bond angle distribution for this system, where for small patches only two angles are more probable indicating chain formation, while for bundling at very low volume fraction a tail is developed in the distribution. While for the case of higher patch angle this distribution is broad compared to the case of low patch angles showing we have a more globular conformation. We are also proposing a model for the formation of bundles which are similar to amyloid fibers using two patch colloidal particles.

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.

Steering patchy particles using multivalent electrolytes

Proteins and many recently designed colloids can be regarded as patchy particles where directional interactions strongly influence and govern assembly behavior. Using explicit ion implicit solvent Metropolis Monte Carlo simulations, we investigate spherical model particles, carrying both charge and electric patches, in dilute aqueous 1 : 1, 1 : 3, and 3 : 1 electrolyte solutions. Striking differences in pair interaction free energies and orientational correlations are induced by three different salts which are discussed and rationalized in terms of ion-binding to surface groups, ion-ion correlations, and double layer forces. These findings suggest a general strategy where directional, intermolecular interactions can be invoked and tuned via small amounts of a carefully chosen electrolyte.

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.

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.

Strings and stripes formed by a protein system interacting via a single-patch attraction

The phase behavior of lactoferrin has been studied as a function of concentration at a pH and ionic strength where lactoferrin is known to interact effectively via a patch-patch attraction. In contrast to isotropic attractive potentials, the directional attraction gives rise to a different phase or solution behavior. At low concentrations, the protein dimerizes. As the concentration is increased, the protein self-assembles into elongated, stripe-like structures at intermediate protein concentrations, a behavior which has been predicted for the case of attractive one-patch colloids. The stripe phase is surprisingly difficult to detect using conventional techniques, i.e. small-angle X-ray scattering, since only a small fraction of the proteins participate in the stripes combined with sedimentation due to micron-sized entities. This is circumvented by monitoring the change in the overall protein concentration by static light scattering and the stripe formation can be followed. For visualization of the structures cryo-TEM is used.

Surface patterning of nanoparticles with polymer patches

Patterning of colloidal particles with chemically or topographically distinct surface domains (patches) has attracted intense research interest. Surface-patterned particles act as colloidal analogues of atoms and molecules, serve as model systems in studies of phase transitions in liquid systems, behave as 'colloidal surfactants' and function as templates for the synthesis of hybrid particles. The generation of micrometre- and submicrometre-sized patchy colloids is now efficient, but surface patterning of inorganic colloidal nanoparticles with dimensions of the order of tens of nanometres is uncommon. Such nanoparticles exhibit size- and shape-dependent optical, electronic and magnetic properties, and their assemblies show new collective properties. At present, nanoparticle patterning is limited to the generation of two-patch nanoparticles, and nanoparticles with surface ripples or a 'raspberry' surface morphology. Here we demonstrate nanoparticle surface patterning, which utilizes thermodynamically driven segregation of polymer ligands from a uniform polymer brush into surface-pinned micelles following a change in solvent quality. Patch formation is reversible but can be permanently preserved using a photocrosslinking step. The methodology offers the ability to control the dimensions of patches, their spatial distribution and the number of patches per nanoparticle, in agreement with a theoretical model. The versatility of the strategy is demonstrated by patterning nanoparticles with different dimensions, shapes and compositions, tethered with various types of polymers and subjected to different external stimuli. These patchy nanocolloids have potential applications in fundamental research, the self-assembly of nanomaterials, diagnostics, sensing and colloidal stabilization.

Phase diagram of a model of the protein amelogenin

There has been considerable recent interest in the self-assembly and phase behavior of models of colloidal and protein particles with anisotropic interactions. One example of particular interest is amelogenin, an important protein involved in the formation of dental enamel. Amelogenin is primarily hydrophobic with a 25-residue charged C-terminus tail. This protein undergoes a hierarchical assembly process that is crucial to mineral deposition, and experimental work has demonstrated that the deletion of the C-terminus tail prevents this self-assembly. A simplified model of amelogenin has been proposed in which the protein is treated as a hydrophobic sphere, interacting via the Asakura-Oosawa (AO) potential, with a tethered point charge on its surface. In this paper, we examine the effect of the Coulomb interaction between the point charges in altering the phase diagram of the AO model. For the parameter case specific to amelogenin, we find that the previous in vitro experimental and model conditions correspond to the system being near the low-density edge of the metastable region of the phase diagram. Our study illustrates more generally the importance of understanding the phase diagram for proteins, in that the kinetic pathway for self-assembly and the resulting aggregate morphology depends on the location of the initial state in the phase diagram.

Self-Assembly of Colloidal Nanocrystals: From Intricate Structures to Functional Materials

Chemical methods developed over the past two decades enable preparation of colloidal nanocrystals with uniform size and shape. These Brownian objects readily order into superlattices. Recently, the range of accessible inorganic cores and tunable surface chemistries dramatically increased, expanding the set of nanocrystal arrangements experimentally attainable. In this review, we discuss efforts to create next-generation materials via bottom-up organization of nanocrystals with preprogrammed functionality and self-assembly instructions. This process is often driven by both interparticle interactions and the influence of the assembly environment. The introduction provides the reader with a practical overview of nanocrystal synthesis, self-assembly, and superlattice characterization. We then summarize the theory of nanocrystal interactions and examine fundamental principles governing nanocrystal self-assembly from hard and soft particle perspectives borrowed from the comparatively established fields of micrometer colloids and block copolymer assembly. We outline the extensive catalog of superlattices prepared to date using hydrocarbon-capped nanocrystals with spherical, polyhedral, rod, plate, and branched inorganic core shapes, as well as those obtained by mixing combinations thereof. We also provide an overview of structural defects in nanocrystal superlattices. We then explore the unique possibilities offered by leveraging nontraditional surface chemistries and assembly environments to control superlattice structure and produce nonbulk assemblies. We end with a discussion of the unique optical, magnetic, electronic, and catalytic properties of ordered nanocrystal superlattices, and the coming advances required to make use of this new class of solids.

Critical Casimir interactions between Janus particles

Recently there has been strong experimental and theoretical interest in studying the self-assembly and the phase behavior of patchy and Janus particles, which form colloidal suspensions. Although in this quest a variety of effective interactions have been proposed and used in order to achieve a directed assembly, the critical Casimir effect stands out as being particularly suitable in this respect because it provides both attractive and repulsive interactions as well as the potential of a sensitive temperature control of their strength. Specifically, we have calculated the critical Casimir force between a single Janus particle and a laterally homogeneous substrate as well as a substrate with a chemical step. We have used the Derjaguin approximation and compared it with results from full mean field theory. A modification of the Derjaguin approximation turns out to be generally reliable. Based on this approach we have derived the effective force and the effective potential between two Janus cylinders as well as between two Janus spheres.

Spatial confinement governs orientational order in patchy particles

Orientational order in condensed matter plays a key role in determining material properties such as ferromagnetism, viscoelasticity or birefringence. We studied purely orientational ordering in closely-packed one-patch colloidal particles confined between flat substrates, where the particles can only rotate and are ordered via the sticky interaction between the patches. For the first time, we experimentally realized a rich variety of mesoscopic patterns through orientational ordering of colloids by controlling patch size and confinement thickness. The combination of experiment and numerical simulation reveals the decisive role of confinement: An ordered state(s) is selected from the (meta)stable options in bulk when it is commensurate with the system geometry and boundary conditions; otherwise, frustration induces a unique order. Our study offers a new means of systematic control over mesoscopic structures via orientational ordering in patchy particles. The system would also possess unique functionalities through the rotational response of the particles to external stimuli.

Rich Janus colloid phase behavior under steady shear

We study the assembly of single-patch colloidal Janus particles under steady shear flow via Brownian dynamics simulations. In the absence of flow, by varying the Janus patch size and the range and strength of the anisotropic interaction potential, Janus colloids form different aggregates such as micelles, wormlike clusters, vesicles and lamellae. Under shear flow we observe rearrangement, deformation, and break-up of aggregates. At small and intermediate Péclet (Pe) numbers-the ratio between shear and Brownian forces-the competition between rearrangement, deformation, and break-up favors the growth of micelles and vesicles increasing mean cluster size, which is consistent with a previous numerical study of Janus particles under shear. This initial shear-induced growth causes micelles and vesicles to reach a maximum cluster size at Pe ≈ 1 and Pe ≈ 10, respectively. After this growth micelles dissociate continuously to reach a dilute colloidal "gas phase" at Pe ≈ 10 while vesicles dissociate into micelles with high aspect ratio at Pe ≈ 10 and finally break-up into a gas phase at Pe ≈ 30. Wormlike clusters initially break-up into micelles with high aspect ratio at Pe ≈ 0.1, and proceed to finally reach a gas phase at Pe ≈ 10. Lamellae initially break into smaller lamellae that align with the flow in the velocity-velocity-gradient plane and finally break-up into a gas phase at Pe ≈ 100. The different cluster sizes and morphologies observed as functions of interaction range, Janus patch size, interaction strength, and shear rate, open new actuation routes for reconfigurable materials and applications.

CAMELOT: A machine learning approach for coarse-grained simulations of aggregation of block-copolymeric protein sequences

We report the development and deployment of a coarse-graining method that is well suited for computer simulations of aggregation and phase separation of protein sequences with block-copolymeric architectures. Our algorithm, named CAMELOT for Coarse-grained simulations Aided by MachinE Learning Optimization and Training, leverages information from converged all atom simulations that is used to determine a suitable resolution and parameterize the coarse-grained model. To parameterize a system-specific coarse-grained model, we use a combination of Boltzmann inversion, non-linear regression, and a Gaussian process Bayesian optimization approach. The accuracy of the coarse-grained model is demonstrated through direct comparisons to results from all atom simulations. We demonstrate the utility of our coarse-graining approach using the block-copolymeric sequence from the exon 1 encoded sequence of the huntingtin protein. This sequence comprises of 17 residues from the N-terminal end of huntingtin (N17) followed by a polyglutamine (polyQ) tract. Simulations based on the CAMELOT approach are used to show that the adsorption and unfolding of the wild type N17 and its sequence variants on the surface of polyQ tracts engender a patchy colloid like architecture that promotes the formation of linear aggregates. These results provide a plausible explanation for experimental observations, which show that N17 accelerates the formation of linear aggregates in block-copolymeric N17-polyQ sequences. The CAMELOT approach is versatile and is generalizable for simulating the aggregation and phase behavior of a range of block-copolymeric protein sequences.

Rotational diffusion affects the dynamical self-assembly pathways of patchy particles

Predicting the self-assembly kinetics of particles with anisotropic interactions, such as colloidal patchy particles or proteins with multiple binding sites, is important for the design of novel high-tech materials, as well as for understanding biological systems, e.g., viruses or regulatory networks. Often stochastic in nature, such self-assembly processes are fundamentally governed by rotational and translational diffusion. Whereas the rotational diffusion constant of particles is usually considered to be coupled to the translational diffusion via the Stokes-Einstein relation, in the past decade it has become clear that they can be independently altered by molecular crowding agents or via external fields. Because virus capsids naturally assemble in crowded environments such as the cell cytoplasm but also in aqueous solution in vitro, it is important to investigate how varying the rotational diffusion with respect to transitional diffusion alters the kinetic pathways of self-assembly. Kinetic trapping in malformed or intermediate structures often impedes a direct simulation approach of a kinetic network by dramatically slowing down the relaxation to the designed ground state. However, using recently developed path-sampling techniques, we can sample and analyze the entire self-assembly kinetic network of simple patchy particle systems. For assembly of a designed cluster of patchy particles we find that changing the rotational diffusion does not change the equilibrium constants, but significantly affects the dynamical pathways, and enhances (suppresses) the overall relaxation process and the yield of the target structure, by avoiding (encountering) frustrated states. Besides insight, this finding provides a design principle for improved control of nanoparticle self-assembly.

Self-assembly of Janus ellipsoids: a Brownian dynamics simulation with a quantitative nonspherical-particle model

Janus ellipsoids as mesoscale building blocks can aggregate into various micelle-like structures in solution that have potential applications in many fields such as novel surfactants, photonic crystals, drug delivery and biochemical sensors. In this work, we present a novel nonspherical-particle model to investigate the self-assembly of Janus ellipsoids, which quantitatively reflects interaction dependence on the particle shape. The phase diagrams of Janus ellipsoids depending on the aspect ratio and the component ratio are achieved and various aggregates are observed such as a sandwich-type structure, columnar aggregates, vesicles, liquid crystals, random aggregation structures, spherical micelles and wormlike micelles. The specific heat capacity curves and temperature evolutions illustrate the formation processes of assembled superstructures detailedly. We analyze the potential energy surfaces (PESs) of interaction between two Janus ellipsoids and the minimum energy paths (MEPs) between saddle points on the PESs. It is found that the number of metastable conformation and the activation energy along MEPs rely not only on the ellipsoidal shape but also on the component ratio. This work provides rich and valuable information for a deep understanding of the self-assembly mechanism of Janus ellipsoids and design of new mesoscale building blocks.

Preparation of Highly Monodisperse Monopatch Particles with Orthogonal Click-Type Functionalization and Biorecognition

Patchy particles are next generation colloidal building blocks for self-assembly and find further use as (bio) sensors. Progress in this direction crucially depends on developing straightforward preparation pathways able to provide patchy particles with highest uniformity and integrating precise, orthogonal, and spatially localized functionalizations to mediate interaction patterns. This continues to be one of the great challenges in colloid science. Herein, a method is shown utilizing functionalized random and block copolymers as microcontact printing inks to prepare patchy particles with outstanding control over patch size and quality. The polymeric nature and tight covalent attachment of the ink prevents flow of the ink over the particle during printing. This minimizes patch broadening and yields very small and extremely uniform patches, which is especially challenging for particle sizes below 10 μm. Click-type (amine/active ester, alkyne/azide, biotin/avidin) reactions can be performed selectively on the patch or on the particle body, rendering the particles interesting for application in imaging, biomolecular detection, and as advanced precision colloid-based building blocks.

Mechanisms Involved in the Formation of Biocompatible Lipid Polymeric Hollow Patchy Particles

Patchy polymeric particles have anisotropic surface domains that can be remarkably useful in diverse medical and industrial fields because of their ability to simultaneously present two different surface chemistries on the same construct. In this article, we report the mechanisms involved in the formation of novel lipid-polymeric hollow patchy particles during their synthesis. By cross-sectioning the patchy particles, we found that a phase segregation phenomenon occurs between the core, shell, and patch. Importantly, we found that the shear stress that the polymer blend undergoes during the particle synthesis is the most important parameter for the formation of these patchy particles. In addition, we found that the interplay of solvent-solvent, polymer-solvent, and polymer-polymer-solvent interactions generates particles with different surface morphologies. Understanding the mechanisms involved in the formation of patchy particles allows us to have a better control on their physicochemical properties. Therefore, these fundamental studies are critical to achieve batch control and scalability, which are essential aspects that must be addressed in any type of particle synthesis to be safely used in medicine.

The effect of links on the interparticle dipolar correlations in supramolecular magnetic filaments

We present a combined computational and analytical study of supramolecular magnetic filaments, i.e., permanently linked chains of ferromagnetic nanocolloids. We put forward two different models for the interparticle connectivity within the chain. In the first model, the magnetic dipoles of the particles are free to rotate independently from the permanent links. The second model penalises the misalignment of the dipoles by coupling their orientations to the chain backbone. We show that the effect of the long-range magnetic dipolar interactions on the zero field net magnetic moment of the chain becomes less significant in the second case. However, the overall magnetic response in the model of freely rotating dipoles is much weaker.

Self-assembly of "Mickey Mouse" shaped colloids into tube-like structures: experiments and simulations

The self-assembly of anisotropic patchy particles with a triangular shape was studied by experiments and computer simulations. The colloidal particles were synthesized in a two-step seeded emulsion polymerization process, and consist of a central smooth lobe connected to two rough lobes at an angle of ∼90°, resembling the shape of a "Mickey Mouse" head. Due to the difference in overlap volume, adding an appropriate depletant induces an attractive interaction between the smooth lobes of the colloids only, while the two rough lobes act as steric constraints. The essentially planar geometry of the Mickey Mouse particles is a first geometric deviation of dumbbell shaped patchy particles. This new geometry enables the formation of one-dimensional tube-like structures rather than spherical, essentially zero-dimensional micelles. At sufficiently strong attractions, we indeed find tube-like structures with the sticky lobes at the core and the non-sticky lobes pointing out as steric constraints that limit the growth to one direction, providing the tubes with a well-defined diameter but variable length both in experiments and simulations. In the simulations, we found that the internal structure of the tubular fragments could either be straight or twisted into so-called Bernal spirals.