Phase diagram of one-patch colloids forming tubes and lamellae

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.

Multiple 2D crystal structures in bilayered lamellae from direct self-assembly of 3D systems of soft Janus particles

Numerous crystals and Frank-Kasper phases in two-dimensional (2D) systems of soft particles have been presented by theoretical investigations. How to realize 2D crystals or Frank-kasper phases by direct self-assembly of...

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.

Location of the gel-like boundary in patchy colloidal dispersions: Rigidity percolation, structure, and particle dynamics

During the past decade, there has been a hot debate about the physical mechanisms that determine when a colloidal dispersion approaches the gel transition. However, there is still no consensus on a possible unique route that leads to the conditions for the formation of a gel-like state. Based on gel states identified in experiments, Valadez-Pérez et al. [Phys. Rev. E 88, 060302(R) (2013)PLEEE81539-375510.1103/PhysRevE.88.060302] proposed rigidity percolation as the precursor of colloidal gelation in adhesive hard-sphere dispersions with coordination number 〈n_{b}〉 equal to 2.4. Although this criterion was originally established to describe mechanical transitions in network-forming molecular materials with highly directional interactions, it worked well to explain gel formation in colloidal suspensions with isotropic short-range attractive forces. Recently, this idea has also been used to account for the dynamical arrest experimentally observed in attractive spherocylinders. Then, by assuming that rigidity percolation also drives gelation in spherical colloids interacting with short-ranged and highly directional potentials, we locate the thermodynamic states where gelation seems to occur in dispersions made up of patchy colloids. To check whether the criterion 〈n_{b}〉=2.4 also holds in patchy colloidal systems, we apply the so-called bond-bending analysis to determine the fraction of floppy modes at some percolating clusters. This analysis confirms that the condition 〈n_{b}〉=2.4 is a good approximation to determine those percolating clusters that are either mechanically stable or rigid. Furthermore, our results point out that not all combinations of patches and coverages lead to a gel-like state. Additionally, we systematically study the structure and the cluster size distribution along those thermodynamic states identified as gels. We show that for high coverage values, the structure is very similar for systems that have the same coverage regardless the number or the position of the patches on the particle surface. Finally, by using dynamic Monte Carlo computer simulations, we calculate both the mean-square displacement and the intermediate scattering function at and in the neighborhood of the gel-like states.

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.

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.

Reconfigurable Transitions between One- and Two-Dimensional Structures with Bifunctional DNA-Coated Janus Colloids

Coating colloidal particles with DNA provides one of the most versatile and powerful methods for controlling colloidal self-assembly. Previous studies have shown how combining DNA coatings with DNA strand displacement allows one to design phase transitions between different three-dimensional crystal structures. Here we show that by using DNA coatings with bifunctional colloidal Janus particles, we can realize reconfigurable thermally reversible transitions between one- and two-dimensional self-assembled colloidal structures. We introduce a colloidal system in which DNA-coated asymmetric Janus particles can reversibly switch their Janus balance in response to temperature, resulting in the reconfiguration of assembling structures between colloidal chains and bilayers. Each face of the Janus particles is coated with different self-complementary DNA strands. Toehold strand displacement is employed to selectively activate or deactivate the sticky ends on the smaller face, which enables Janus particles to selectively assemble through either the smaller or larger face. This strategy could be useful for constructing complex systems that could be reconfigured to assemble into different structures in different environments.

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.

Self-assembly of finite-sized colloidal aggregates

One of the challenges of self-assembling finite-sized colloidal aggregates with a sought morphology is the necessity of precisely sorting the position of the colloids at the microscopic scale to avoid the formation of off-target structures. Microfluidic platforms address this problem by loading into single droplets the exact amount of colloids entering the targeted aggregate. Using theory and simulations, in this paper, we validate a more versatile design allowing us to fabricate different types of finite-sized aggregates, including colloidal molecules or core-shell clusters, starting from finite density suspensions of isotropic colloids in bulk. In our model, interactions between particles are mediated by DNA linkers with mobile tethering points, as found in experiments using DNA oligomers tagged with hydrophobic complexes immersed into supported bilayers. By fine-tuning the strength and number of the different types of linkers, we prove the possibility of controlling the morphology of the aggregates, in particular, the valency of the molecules and the size of the core-shell clusters. In general, our design shows how multivalent interactions can lead to microphase separation under equilibrium conditions.

Phase diagram of two-patch colloids with competing anisotropic and isotropic interactions

Patchy particles are considered to be a good model for protein aggregation. We propose a novel method to generate different structures of glucose isomerase protein such as chains, crystals and bundles by utilising aggregation of two-patch colloidal particles in presence of competing isotropic and anisotropic potential. We calculate the equilibrium phase diagram of two-patch colloidal particles and demonstrates the coexistence of different phases like disordered clusters, chains, crystals and bundles depending on the relative strength of isotropic and anisotropic potential. We also show that the formation of network of bundles is metastable against the formation of thermodynamically favored finite sized bundles along with thermodynamically stable crystals. These bundles appear to be helical in structure similar to that observed in sickle cell hemoglobin. The simulation results show that the method can characterize phase behaviour of glucose isomerase protein, which provides a novel tool to unveil self-assembly mechanism of protein under different conditions.

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.

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.

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.

Co-assembly of Janus nanoparticles in block copolymer systems

Block copolymer are ideal matrices to control the localisation of colloids. Furthermore, anisotropic nanoparticles such as Janus nanoparticles possess an additional orientational degree of freedom that can play a crucial role in the formation of highly ordered materials made of block copolymers. This work presents a mesoscopic simulation method to assert the co-assembly of Janus nanoparticles in a block copolymer mixture, finding numerous instances of aggregation and formation of ordered configurations. Comparison with chemically homogeneous neutral nanoparticles shows that Janus nanoparticles are less prone to induce bridging along lamellar domains, thus being a less destructive way to segregate nanoparticles at interfaces. The combination of asymmetric block copolymer and asymmetric Janus nanoparticles can result in assembly of colloids with an even number of layers within the minority domain.

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.

Two-dimensional mixture of amphiphilic dimers and spheres: Self-assembly behaviour

The emergence of supramolecular aggregates from simple microscopic interaction rules is a fascinating feature of complex fluids which, besides its fundamental interest, has potential applications in many areas, from biological self-assembly to smart material design. We here investigate by Monte Carlo simulation the equilibrium structure of a two-dimensional mixture of asymmetric dimers and spheres (disks). Dimers and disks are hard particles, with an additional short-range attraction between a disk and the smaller monomer of a dimer. The model parameters and thermodynamic conditions probed are typical of colloidal fluid mixtures. In spite of the minimalistic character of the interaction, we observe-upon varying the relative concentration and size of the two colloidal species-a rich inventory of mesoscale structures at low temperature, such as clusters, lamellæ (i.e., polymer-like chains), and gel-like networks. For colloidal species of similar size and near equimolar concentrations, a dilute fluid of clusters gives way to floating lamellæ upon cooling; at higher densities, the lamellæ percolate through the simulation box, giving rise to an extended network. A crystal-vapour phase-separation may occur for a mixture of dimers and much larger disks. Finally, when the fluid is brought in contact with a planar wall, further structures are obtained at the interface, from layers to branched patterns, depending on the nature of wall-particle interactions.

Self-assembly in a model colloidal mixture of dimers and spherical particles

We investigate the structure of a dilute mixture of amphiphilic dimers and spherical particles, a model relevant to the problem of encapsulating globular "guest" molecules in a dispersion. Dimers and spheres are taken to be hard particles, with an additional attraction between spheres and the smaller monomers in a dimer. Using the Monte Carlo simulation, we document the low-temperature formation of aggregates of guests (clusters) held together by dimers, whose typical size and shape depend on the guest concentration χ. For low χ (less than 10%), most guests are isolated and coated with a layer of dimers. As χ progressively increases, clusters grow in size becoming more and more elongated and polydisperse; after reaching a shallow maximum for χ≈50%, the size of clusters again reduces upon increasing χ further. In one case only (χ=50% and moderately low temperature) the mixture relaxed to a fluid of lamellae, suggesting that in this case clusters are metastable with respect to crystal-vapor separation. On heating, clusters shrink until eventually the system becomes homogeneous on all scales. On the other hand, as the mixture is made denser and denser at low temperature, clusters get increasingly larger until a percolating network is formed.

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.

Shear-Induced Alignment of Janus Particle Lamellar Structures

Control over the alignment of colloidal structures plays a crucial role in advanced reconfigurable materials. In this work, we study the alignment of Janus particle lamellar structures under shear flow via Brownian dynamics simulations. Lamellar alignment (orientation relative to flow direction) is measured as a function of the Péclet number (Pe)-the ratio of the viscous shear to the Brownian forces-the particle volume fraction, and the strength of the anisotropic interaction potential made dimensionless with thermal energy. Under conditions where lamellar structures are formed, three orientation regimes are observed: (1) random orientation for very small Pe, (2) parallel orientation-lamellae with their normals parallel to the direction of the velocity gradient-for intermediate values of Pe, and (3) perpendicular orientation-lamellae with their normals parallel to the vorticity direction-for large Pe. To understand the alignment mechanism, we carry out a scaling analysis of competing torques between a pair of particles in the lamellar structure. Our results suggest that the change of parallel to perpendicular orientation is independent of the particle volume fraction and is caused by the hydrodynamic and Brownian torques on the particles overcoming the torques resulting from the interparticle interactions. This initial study of shear-induced alignment on lamellar structures formed by Janus colloidal particles also opens the door for future applications where a reversible actuator for structure orientation is required.

A theory for the effect of patch/non-patch attractions on the self-assembly of patchy colloids

In this paper, we develop a thermodynamic perturbation theory to describe the self-assembly of patchy colloids which exhibit both patch-patch attractions as well as patch/non-patch attractions. That is, patches attract other patches as well as the no patch region (we call this region Ψ). In general, the patch-patch and patch-Ψ attractions operate on different energy scales allowing for a competition between different modes of attraction. This competition may result in anomalous thermodynamic properties. As an application, we tune the patch parameters to reproduce the liquid density (suitably scaled) maximum of water. It is then shown that the liquid branch of the colloids phase diagram has liquid densities consistent with both saturated and super-cooled liquid water. Finally, it is shown that the colloids reproduce water's anomalous minimum in isothermal compressibility and negative volume expansivity.

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.

Interactions and design rules for assembly of porous colloidal mesophases

Porous mesophases, where well-defined particle-depleted 'void' spaces are present within a particle-rich background fluid, can be self-assembled from colloidal particles interacting via isotropic pair interactions with competing attractions and repulsions. While such structures could be of wide interest for technological applications (e.g., filtration, catalysis, absorption, etc.), relatively few studies have investigated the interactions that lead to these morphologies and how they compare to those that produce other micro-phase-separated structures, such as clusters. In this work, we use inverse methods of statistical mechanics to design model isotropic pair potentials that form porous mesophases. We characterize the resulting porous structures, correlating features of the pair potential with the targeted pore size and the particle packing fraction. The former is primarily encoded by the amplitude and range of the repulsive barrier of the designed pair potential and the latter by the attractive well depth. We observe a trade-off with respect to the packing fraction of the targeted morphology: greater values support more spherical and monodisperse pores that themselves organize into periodic structures, while lower values yield more mobile pores that do not assemble into ordered structures but remain stable over a larger range of packing fraction. We conclude by commenting on the limitations of targeting a specific pore diameter within the present inverse design approach as well as by describing future directions to overcome these limitations.

Self-assembly of colloidal micelles in microfluidic channels

The self-assembly of amphiphilic Janus colloids in microfluidic channels is studied using hybrid molecular dynamics simulations with fully resolved hydrodynamic interactions incorporated through the multi-particle collision dynamics algorithm. The simulations are conducted at a density and temperature where the Janus particles spontaneously self-assemble into spherical micelles to minimize the interface between the solvophobic caps and the surrounding solvent. In confined systems, this contact area can also be reduced by aggregation at the channel walls. Indeed, a sizable fraction of free particles and small clusters with three and four members are found at the walls when the microfluidic channel is made up of a comparably solvophobic material as the Janus colloids. When the applied Poiseuille flow is sufficiently strong, the colloidal micelles break up into smaller fragments and isolated particles. However, at intermediate flow rates the shear-induced dissociation and reorganization of aggregates lead to a net growth of the micelles with a sizable amount of particles in icosahedral clusters with 13 particles. Furthermore, the parabolic velocity profile of the flow causes a highly non-uniform cluster size distribution between the channel walls, where the aggregation number decreases close to the walls.

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.

Effect of the surface charge distribution on the fluid phase behavior of charged colloids and proteins

A generic but simple model is presented to evaluate the effect of the heterogeneous surface charge distribution of proteins and zwitterionic nanoparticles on their thermodynamic phase behavior. By considering surface charges as continuous "patches," the rich set of surface patterns that is embedded in proteins and charged patchy particles can readily be described. This model is used to study the fluid phase separation of charged particles where the screening length is of the same order of magnitude as the particle size. In particular, two types of charged particles are studied: dipolar fluids and protein-like fluids. The former represents the simplest case of zwitterionic particles, whose charge distribution can be described by their dipole moment. The latter system corresponds to molecules/particles with complex surface charge arrangements such as those found in biomolecules. The results for both systems suggest a relation between the critical region, the strength of the interparticle interactions, and the arrangement of charged patches, where the critical temperature is strongly correlated to the magnitude of the dipole moment. Additionally, competition between attractive and repulsive charge-charge interactions seems to be related to the formation of fluctuating clusters in the dilute phase of dipolar fluids, as well as to the broadening of the binodal curve in protein-like fluids. Finally, a variety of self-assembled architectures are detected for dipolar fluids upon small changes to the charge distribution, providing the groundwork for studying the self-assembly of charged patchy particles.

Rotator-to-Lamellar Phase Transition in Janus Colloids Driven by Pressure Anisotropy

We demonstrate through Brownian dynamics simulations a phase transition in plastic crystalline assemblies of Janus spheres through controlled pressure anisotropy. When the pressure in plane with hexagonally ordered layers is increased relative to that normal to the layers, a rapid first-order rotator-to-lamellar transition of Janus sphere orientation occurs at constant temperature. We show that the underlying mechanism closely follows the Maier-Saupe theory, originally developed for isotropic-to-nematic transition in positionally disordered materials but here applied to positionally ordered ones. Since the transition involves almost no translational diffusion or volume change, and occurs rapidly by particle rotation, the results should help guide the design of rapidly switchable colloidal crystals.

Aggregation of Heterogeneously Charged Colloids

Patchy colloids are attractive as programmable building blocks for metamaterials. Inverse patchy colloids, in which a charged surface is decorated with patches of the opposite charge, are additionally noteworthy as models for heterogeneously charged biological materials such as proteins. We study the phases and aggregation behavior of a single charged patch in an oppositely charged colloid with a single-site model. This single-patch inverse patchy colloid model shows a large number of phases when varying patch size. For large patch sizes we find ferroelectric crystals, while small patch sizes produce cross-linked gels. Intermediate values produce monodisperse clusters and unusual worm structures that preserve finite ratios of area to volume. The polarization observed at large patch sizes is robust under extreme disorder in patch size and shape. We examine phase-temperature dependence and coexistence curves and find that large patch sizes produce polarized liquids, in contrast to mean-field predictions. Finally, we introduce small numbers of unpatched charged colloids. These can either suppress or encourage aggregation depending on their concentration and the size of the patches on the patched colloids. These effects can be exploited to control aggregation and to measure effective patch size.

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.

Equilibrium cluster fluids: pair interactions via inverse design

Inverse methods of statistical mechanics are becoming productive tools in the design of materials with specific microstructures or properties. While initial studies have focused on solid-state design targets (e.g., assembly of colloidal superlattices), one can alternatively design fluid states with desired morphologies. This work addresses the latter and demonstrates how a simple iterative Boltzmann inversion strategy can be used to determine the isotropic pair potential that reproduces the radial distribution function of a fluid of amorphous clusters with prescribed size. The inverse designed pair potential of this "ideal" cluster fluid, with its broad attractive well and narrow repulsive barrier at larger separations, is qualitatively different from the so-called SALR form most commonly associated with equilibrium cluster formation in colloids, which features short-range attractive (SA) and long-range repulsive (LR) contributions. These differences reflect alternative mechanisms for promoting cluster formation with an isotropic pair potential, and they in turn produce structured fluids with qualitatively different static and dynamic properties. Specifically, equilibrium simulations show that the amorphous clusters resulting from the inverse designed potentials display more uniformity in size and shape, and they also show greater spatial and temporal resolution than those resulting from SALR interactions.

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.

Anomalous approach to thermodynamic equilibrium: Structure formation of molecules after vapor deposition

We describe experiments and computer simulations of molecular deposition on a substrate in which the molecules (substituted adenine derivatives) self-assemble into ordered structures. The resulting structures depend strongly on the deposition rate (flux). In particular, there are two competing surface morphologies (α and β), which differ by their topology (interdigitated vs lamellar structure). Experimentally, the α phase dominates at both low and high flux, with the β phase being most important in the intermediate regime. A similar nonmonotonic behavior is observed on varying the substrate temperature. To understand these effects from a theoretical perspective, a lattice model is devised which reproduces qualitatively the topological features of both phases. Via extensive Monte Carlo studies we can, on the one hand, reproduce the experimental results and, on the other hand, obtain a microscopic understanding of the mechanisms behind this anomalous behavior. The results are discussed in terms of an interplay between kinetic trapping and temporal exploration of configuration space.

Cooperative polymerization of one-patch colloids

We numerically investigate cooperative polymerization in an off-lattice model based on a pairwise additive potential using particles with a single attractive patch that covers 30% of the colloid surface. Upon cooling, these particles self-assemble into small clusters which, below a density-dependent temperature, spontaneously reorganize into long straight tubes. We evaluate the partition functions of clusters of all sizes to provide an accurate description of the chemical reaction constants governing this process. Our calculations show that, for intermediate sizes, the partition functions retain contributions from two different structures, differing in both energy and entropy. We illustrate the microscopic mechanism behind the complex polymerization process in this system and provide a detailed evaluation of its thermodynamics.

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.

Self-assembly of kagome lattices, entangled webs and linear fibers with vibrating patchy particles in two dimensions

A vibrating version of patchy particles in two dimensions is introduced to study self-assembly of kagome lattices, disordered networks of looping structures, and linear arrays. Discontinuous molecular dynamics simulations in the canonical ensemble are used to characterize the molecular architectures and thermodynamic conditions that result in each of those morphologies, as well as the time evolution of lattice formation. Several versions of the new model are tested and analysed in terms of their ability to produce kagome lattices. Due to molecular flexibility, particles with just attractive sites adopt a polarized-like configuration and assemble into linear arrays. Particles with additional repulsive sites are able to form kagome lattices, but at low temperature connect as entangled webs. Abundance of hexagonal motifs, required for the kagome lattice, is promoted even for very small repulsive sites but hindered when the attractive range is large. Differences in behavior between the new flexible model and previous ones based on rigid bodies offer opportunities to test and develop theories about the relative stability, kinetics of formation and mechanical response of the observed morphologies.

Orientational order of one-patch colloidal particles in two dimensions

We studied the orientational order of one-patch colloidal particles (Janus particles) in a close-packed monolayer. In an experiment on hemispherically patched particles, we realized a highly ordered zigzag stripe pattern by inducing directional growth of the pattern via a phase transition of the solvent. Upon spontaneous ordering by strengthening the inter-patch attraction, however, the particles are trapped in a poorly ordered zigzag pattern, illustrating the importance of controlling kinetics to attain a highly ordered state. The patch-size dependence of an equilibrium orientational order is experimentally observed under moderate inter-patch attraction. We also calculated the equilibrium order against the patch size and attraction in a Monte Carlo simulation. In the simulation, the rather discrete transition between a zigzag stripe, tiling of triangular trimers and tiling of dimers under strong attraction becomes continuous with weakening attraction. The experimental result not only coincides with the simulation qualitatively but also suggests that a particular cluster is selectively formed by nonuniform inter-patch attraction in the experiment. The effect of patch-substrate attraction and commonalities of the order with liquid crystals are also discussed.

Design principles for Bernal spirals and helices with tunable pitch

Using the framework of potential energy landscape theory, we describe two in silico designs for self-assembling helical colloidal superstructures based upon dipolar dumbbells and Janus-type building blocks, respectively. Helical superstructures with controllable pitch length are obtained using external magnetic field driven assembly of asymmetric dumbbells involving screened electrostatic as well as magnetic dipolar interactions. The pitch of the helix is tuned by modulating the Debye screening length over an experimentally accessible range. The second design is based on building blocks composed of rigidly linked spheres with short-range anisotropic interactions, which are predicted to self-assemble into Bernal spirals. These spirals are quite flexible, and longer helices undergo rearrangements via cooperative, hinge-like moves, in agreement with experiment.

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

Inspired by experimental studies of short-ranged attractive patchy particles, we study with computer simulations the phase behavior and the crystalline structures of one-patch colloids with an interaction range equal to 5% of the particle diameter. In particular, we study the effects of the patch surface coverage fraction, defined as the ratio between the attractive and the total surface of a particle. Using free-energy calculations and thermodynamic integration schemes, we evaluate the equilibrium phase diagrams for particles with patch coverage fractions of 30%, 50% and 60%. For a 60% surface coverage fraction, we observe stable lamellar crystals consisting of stacked bilayers that directly coexist with a low density fluid. Inside the coexistence region, we observe the formation of lamellar structures also in direct NVT simulations, indicating that the barrier of formation is low and experimental realization is feasible. For sufficiently strong interactions, these structures spontaneously assemble from the fluid in simulations, suggesting that they might also easily form in experimental systems. In the Janus case, i.e. at 50% surface coverage fraction, no lamellar structures are formed, and the stable crystals are similar to those that have been found previously for a longer interaction range (i.e. 20% of the particle diameter). At 30% coverage fraction, we identify novel 'open' crystal structures with large unit cells of up to 14 particles that are stable in the strong interaction limit.