Lock-and-key dimerization in dense Brownian systems of hard annular sector particles

Properties of packings and dispersions of superellipse sector particles

Superellipse sector particles (SeSPs) are segments of superelliptical curves that form a tunable set of hard-particle shapes for granular and colloidal systems. SeSPs allow for continuous parametrization of corner sharpness, aspect ratio, and particle curvature; rods, circles, rectangles, and staples are examples of shapes SeSPs can model. We compare three computational processes: pair-wise Monte Carlo simulations that explore particle-particle geometric constraints, Monte Carlo simulations that reveal how these geometric constraints play out over dispersions of many particles, and Molecular Dynamics simulations that form random loose and close packings. We investigate the dependence of critical random loose and close packing fractions on particle parameters, finding that both values increase with opening aperture and decrease with increasing corner sharpness. The identified packing fractions are compared with the mean-field prediction of the random contact model; we find deviations from the model's prediction due to correlations between particle orientations. The complex interaction of spatial proximity and orientational alignment is also explored with a generalized spatioorientational distribution area (SODA) plot, which shows how higher density packings are achieved through particles assuming a small number of preferred configurations that depend sensitively on particle shape and system preparation.

Excluded area of superellipse sector particles

Superellipse sector particles (SeSPs) are segments of superelliptical curves that form a tunable set of hard-particle shapes for granular and colloidal systems. SeSPs allow for continuous parametrization of corner sharpness, aspect ratio, and particle curvature; rods, circles, rectangles, and staples are examples of shapes SeSPs can model. We investigate the space of allowable (nonoverlapping) configurations of two SeSPs, which depends on both the center-of-mass separation and relative orientation. Radial correlation plots of the allowed configurations reveal circular regions centered at each of the particle's two end points that indicate configurations of mutually entangled particle interactions. Simultaneous entanglement with both end points is geometrically impossible; the overlap of these two regions therefore represents an excluded area in which no particles can be placed regardless of orientation. The regions' distinct boundaries indicate a translational frustration with implications for the dynamics of particle rearrangements (e.g., under shear). Representing translational and rotational degrees of freedom as a hypervolume, we find a topological change that suggests geometric frustration arises from a phase transition in this space. The excluded area is a straightforward integration over excluded states; for arbitrary relative orientation this decreases sigmoidally with increasing opening aperture, with sharper SeSP corners resulting in a sharper decrease. Together, this work offers a path towards a unified theory for particle shape control of bulk material properties.

Dynamic heterogeneity flow promotes binding reactions in a dense system of hard annular sector particles

We perform molecular dynamics simulations on a system of hard annular sector particles (ASPs) to investigate the reaction-dynamics relationship. The dimerization reaction zone, mixing reaction zone including dimerization and n-merization (n > 2), and arrested region are observed successively as area fraction φ_A increases from low to high. In this work, we focus on the properties of the concentrated arrested region (φ_A≥ 0.400). The results show that for systems at φ_A≥ 0.400, the ratio of n-merization increases with φ_A and n-merization finally becomes the dominant reaction in the system; dynamic heterogeneity (DH) is observed and is demonstrated to originate from the divergent size of clusters consisting of high-mobility particles; the particles with a high translational or rotational mobility are found to have a high ability to react with other particles at φ_A > 0.400; more interestingly, binding reactions are found to correlate spatially with DH at φ_A > 0.400. Our work sheds new light on understanding the role of DH in binding reactions or specific-site recognition assembly in a crowded environment.

Dense packings of hard circular arcs

This work investigates dense packings of congruent hard infinitesimally thin circular arcs in the two-dimensional Euclidean space. It focuses on those denotable as major whose subtended angle θ∈(π,2π]. Differently than those denotable as minor whose subtended angle θ∈[0,π], it is impossible for two hard infinitesimally thin circular arcs with θ∈(π,2π] to arbitrarily closely approach once they are arranged in a configuration, e.g., on top of one another, replicable ad infinitum without introducing any overlap. This makes these hard concave particles, in spite of being infinitesimally thin, most densely pack with a finite number density. This raises the question as to what are these densest packings and what is the number density that they achieve. Supported by Monte Carlo numerical simulations, this work shows that one can analytically construct compact closed circular groups of hard major circular arcs in which a specific, θ-dependent, number of them (counter) clockwise intertwine. These compact closed circular groups then arrange on a triangular lattice. These analytically constructed densest-known packings are compared to corresponding results of Monte Carlo numerical simulations to assess whether they can spontaneously turn up.

Assembly of colloidal particles in solution

Advances in both top-down and bottom-up syntheses of a wide variety of complex colloidal building blocks and also in methods of controlling their assembly in solution have led to new and interesting forms of highly controlled soft matter. In particular, top-down lithographic methods of producing monodisperse colloids now provide precise human-designed control over their sub-particle features, opening up a wide range of new possibilities for assembly structures that had been previously limited by the range of shapes available through bottom-up methods. Moreover, an increasing level of control over anisotropic interactions between these colloidal building blocks, which can be tailored through local geometries of sub-particle features as well as site-specific surface modifications, is giving rise to new demonstrations of massively parallel off-chip self-assembly of specific target structures with low defect rates. In particular, new experimental realizations of hierarchical self-assembly and control over the chiral purity of resulting assembly structures have been achieved. Increasingly, shape-dependent, shape-complementary, and roughness-controlled depletion attractions between non-spherical colloids are being used in novel ways to create assemblies that go far beyond early examples, such as fractal clusters formed by diffusion-limited and reaction-limited aggregation of spheres. As self-assembly methods have progressed, a wide variety of advanced directed assembly methods have also been developed; approaches based on microfluidic control and applying structured electromagnetic fields are particularly promising.

Dimer crystallization of chiral proteoids

When slowly crowded while undergoing Brownian motion, hard proteomimetic colloids (“proteoids”) hierarchically self-assemble into microcrystals of enantiopure lock-and-key dimers.