A parallel algorithm for implicit depletant simulations

Janus particles with tunable patch symmetry and their assembly into chiral colloidal clusters

Janus particles, which have an attractive patch on the otherwise repulsive surface, have been commonly employed for anisotropic colloidal assembly. While current methods of particle synthesis allow for control over the patch size, they are generally limited to producing dome-shaped patches with a high symmetry (C∞). Here, we report on the synthesis of Janus particles with patches of various tunable shapes, having reduced symmetries ranging from C2v to C3v and C4v. The Janus particles are synthesized by partial encapsulation of an octahedral metal-organic framework particle (UiO-66) in a polymer matrix. The extent of encapsulation is precisely regulated by a stepwise, asymmetric dewetting process that exposes selected facets of the UiO-66 particle. With depletion interaction, the Janus particles spontaneously assemble into colloidal clusters reflecting the particles' shapes and patch symmetries. We observe the formation of chiral structures, whereby chirality emerges from achiral building blocks. With the ability to encode symmetry and directional bonding information, our strategy could give access to more complex colloidal superstructures through assembly.

Structure of nematic tactoids of hard rods

We study by means of Monte Carlo simulations the internal structure of nematic droplets or tactoids formed by hard, rod-like particles in a gas of spherical ghost particles that act as depletion agents for the rods. We find that the shape and internal structure of tactoids are strongly affected by the size of the droplets. The monotonically increasing degree of nematic order with increasing particle density that characterizes the bulk nematic phase is locally violated and more so the smaller the tactoid. We also investigate the impact of an external quadrupolar alignment field on tactoids and find that this tends to make the director field more uniform, but not to very significantly increase the tactoid’s aspect ratio. This agrees with recent theoretical predictions yet is at variance with experimental observations and dynamical simulations. We explain this discrepancy in terms of competing relaxation times.

Colloidal membranes of chiral rod-like particles

We study colloidal (or smectic) membranes composed of chiral rod-like particles through Monte Carlo simulations. These objects are formed due to the presence of Asakura-Oosawa spheres acting as depletants and creating an effective attraction between the rods. The membranes' shape and structure can be influenced by several parameters, e.g. the number of spheres and rods, their length and their interaction. In order to compare simulation results to an elastic theory, we follow two ansatzes, approximating the free elastic energy in different ways. Both of them lead to reasonable results and capture the behaviour of the colloidal membrane system. One approximation, however, is not suited for achiral rods, where twisting occurs due to surface energy rather than elastic energy. We extract the inverse cholesteric pitch and twist penetration depth for chiral rods with this approximation. The other one is used to introduce a complementary method to estimate elastic constants from the shape of colloidal membranes. Besides, we describe the transition from homogeneously twisted membranes to membranes composed of substructures that occur when the chiral interaction exceeds a length-dependent threshold. We believe that our detailed study and discussion of different aspects of this model system are valuable from a fundamental research viewpoint and suitable for material design suggestions.

Thin smectic liquid crystalline fibrils of chiral rodlike particles

Inspired by recent experimental work on virus-polymer mixtures, we study the properties of thin smectic fibrils composed of chiral rodlike particles using Monte Carlo simulations. Due to the interplay between surface energy, elastic deformation energy, and entropic effects, the fibril's layers relax into a twisted state. We focus our study on the layers' twist direction and map our results to the antiferromagnetic Ising model. In this view, the chiral interaction mimics an external field that drives the layers to have the same sense of twist. Besides, we determine the free energy difference and barrier height between an alternating and a nonalternating sequence of twisted layers composed of achiral rods and find that an alternating sequence is slightly preferred. We also see that the fibrils contract on increasing the chiral interaction strength and think that further studies on self-assembled functional materials can use our results.

The role of complementary shape in protein dimerization

Shape guides colloidal nanoparticles to form complex assemblies, but its role in defining interfaces in biomolecular complexes is less clear. In this work, we isolate the role of shape in protein complexes by studying the reversible binding processes of 46 protein dimer pairs, and investigate when entropic effects from shape complementarity alone are sufficient to predict the native protein binding interface. We employ depletants using a generic, implicit depletion model to amplify the magnitude of the entropic forces arising from lock-and-key binding and isolate the effect of shape complementarity in protein dimerization. For 13% of the complexes studied here, protein shape is sufficient to predict native complexes as equilibrium assemblies. We elucidate the results by analyzing the importance of competing binding configurations and how it affects the assembly. A machine learning classifier, with a precision of 89.14% and a recall of 77.11%, is able to identify the cases where shape alone predicts the native protein interface.

Particle shape tunes fragility in hard polyhedron glass-formers

We demonstrate that fragility, a technologically relevant characteristic of glass formation, depends on particle shape for glass-formers comprised of hard polyhedral particles. We find that hard polyhedron glass-formers become stronger (less fragile) as particle shape becomes increasingly tetrahedral. We correlate fragility with local structure, and show that stronger systems display a stronger preference for a pairwise face-to-face motif that frustrates global periodic ordering and gives rise in most systems studied to bond angle distributions that are peaked around the ideal tetrahedral bond angle. We demonstrate through mean-field-like simulations of explicit particle pairs and surrounding baths of "ghost" particles that the prevalence of this pairwise configuration can be explained via free volume exchange and emergent entropic force arguments. Our study provides a clear and direct link between the local geometry of fluid structure and the properties of glass formation, independent of interaction potential or other non-geometric tuning parameters. We ultimately demonstrate that the engineering of fragility in colloidal systems via slight changes to particle shape is possible.

Phase behaviour of colloidal superballs mixed with non-adsorbing polymers

Inspired by experimental work on colloidal cuboid-polymer dispersions (Rossi et al., Soft Matter, 7, 4139 (2011)) we have theoretically studied the phase behaviour of such mixtures. To that end, free volume theory (FVT) was applied to predict the phase behaviour of mixtures of superballs and non-adsorbing polymer chains in a common solvent. Closed expressions for the thermodynamic properties of a suspension of hard colloidal superballs have been derived, accounting for fluid (F), face-centred cubic (FCC) and simple cubic (SC) phase states. Even though the considered solid phases are approximate, the hard superballs phase diagram semi-quantitatively matches with more evolved methods. The theory developed for the cuboid-polymer mixture reveals a rich phase behaviour, which includes not only isostructural F₁-F₂ coexistence, but also SC₁-SC₂ coexistence, several triple coexistences, and even a quadruple-phase coexistence region (F₁-F₂-SC-FCC). The model proposed offers a tool to asses the stability of cuboid-polymer mixtures in terms of the colloid-to-polymer size ratio.

Monte Carlo simulation of cylinders with short-range attractions

Cylindrical or rod-like particles are promising materials for the applications of fillers in nanocomposite materials and additives to control rheological properties of colloidal suspensions. Recent advances in particle synthesis allows for cylinders to be manufactured with short-ranged attractions to study the gelation as a function of packing fraction, aspect ratio and attraction strength. In order to aid in the analysis of small-angle scattering experiments of rod-like particles, computer simulation methods were used to model these particles with specialized Monte Carlo algorithms and tabular superquadric potentials. The attractive interaction between neighboring rods increases with the amount of locally-accessible surface area, thus leading to patchy-like interactions. We characterize the clustering and percolation of cylinders as the attractive interaction increases from the homogenous fluid at relatively low attraction strength, for a variety of aspect ratios and packing fractions. Comparisons with the experimental scattering results are also presented, which are in agreement.

Phase behaviour and gravity-directed self assembly of hard convex spherical caps

We investigate the phase behaviour and self-assembly of convex spherical caps using Monte Carlo simulations. This model is used to represent the main features observed in experimental colloidal particles with mushroom-cap shape [Riley et al., Langmuir, 2010, 26, 1648]. The geometry of this non-centrosymmetric convex model is fully characterized by the aspect ratio χ* defined as the spherical cap height to diameter ratio. We use NPT Monte Carlo simulations combined with free energy calculations to determine the most stable crystal structures and the phase behaviour of convex spherical caps with different aspect ratios. We find a variety of crystal structures at each aspect ratio, including plastic and dimer-based crystals; small differences in chemical potential between the structures with similar morphology suggest that convex spherical caps have the tendency to form polycrystalline phases rather than crystallising into a single uniform structure. With the exception of plastic crystals observed at large aspect ratios (χ* > 0.75), crystallisation kinetics seem to be too slow, hindering the spontaneous formation of ordered structures. As an alternative, we also present a study of directing the self-assembly of convex spherical caps via sedimentation onto solid substrates. This study contributes to show how small changes to particle shape can significantly alter the self-assembly of crystal structures, and how a simple gravity field and a template can substantially enhance the process.

Depletion-driven crystallization of cubic colloids sedimented on a surface

Cubic colloids, sedimented on a surface and immersed in a solution of depletant molecules, were modeled with a family of shapes which smoothly varies from squares to circles. Using Wang-Landau simulations with expanded ensembles, we observe the formation of rhombic lattices, square lattices, hexagonal lattices, and a fluid phase. This systematic investigation includes locating transitions between all combinations of the three lattice structures upon changing the shape and transitions between the fluid and crystal upon changing the depletant concentration. The rhombic lattice deforms smoothly between square-like and hexagonal-like angles, depending on both the shape and the depletant concentration. Our results on the effect of the depletant concentration, depletant size, and colloid shape to influence the stability of the fluid and the lattice structures may help guide experimental studies with recently synthesized cubic colloids.

Using depletion to control colloidal crystal assemblies of hard cuboctahedra

Depletion interactions arise from entropic forces, and their ability to induce aggregation and even ordering of colloidal particles through self-assembly is well established, especially for spherical colloids. We vary the size and concentration of penetrable hard sphere depletants in a system of cuboctahedra, and we show how depletion changes the preferential facet alignment of the colloids and thereby selects different crystal structures. Moreover, we explain the cuboctahedra phase behavior using perturbative free energy calculations. We find that cuboctahedra can form a stable simple cubic phase, and, remarkably, that the stability of this phase can be rationalized only by considering the effects of both the colloid and depletant entropy. We corroborate our results by analyzing how the depletant concentration and size affect the emergent directional entropic forces and hence the effective particle shape. We propose the use of depletants as a means of easily changing the effective shape of self-assembling anisotropic colloids.

Metastable orientational order of colloidal discoids

The interplay between phase separation and kinetic arrest is important in supramolecular self-assembly, but their effects on emergent orientational order are not well understood when anisotropic building blocks are used. Contrary to the typical progression from disorder to order in isotropic systems, here we report that colloidal oblate discoids initially self-assemble into short, metastable strands with orientational order—regardless of the final structure. The model discoids are suspended in a refractive index and density-matched solvent. Then, we use confocal microscopy experiments and Monte Carlo simulations spanning a broad range of volume fractions and attraction strengths to show that disordered clusters form near coexistence boundaries, whereas oriented strands persist with strong attractions. We rationalize this unusual observation in light of the interaction anisotropy imparted by the discoids. These findings may guide self-assembly for anisotropic systems in which orientational order is desired, such as when tailored mechanical properties are sought.

The pathways available for self-assembly are affected by the shape anisotropy of the building blocks, but the details are still unclear. Here, Hsiao et al. show that colloidal discoids self-assemble into metastable states with orientational order when kinetic trapping is incorporated as a design principle.