Pablo F. Damasceno

Crystalline Assemblies and Densest Packings of a Family of Truncated Tetrahedra and the Role of Directional Entropic Forces

Polyhedra and their arrangements have intrigued humankind since the ancient Greeks and are today important motifs in condensed matter, with application to many classes of liquids and solids. Yet, little is known about the thermodynamically stable phases of polyhedrally shaped building blocks, such as faceted nanoparticles and colloids. Although hard particles are known to organize due to entropy alone, and some unusual phases are reported in the literature, the role of entropic forces in connection with polyhedral shape is not well understood. Here, we study thermodynamic self-assembly of a family of truncated tetrahedra and report several atomic crystal isostructures, including diamond, β-tin, and high-pressure lithium, as the polyhedron shape varies from tetrahedral to octahedral. We compare our findings with the densest packings of the truncated tetrahedron family obtained by numerical compression and report a new space-filling polyhedron, which has been overlooked in previous searches. Interestingly, the self-assembled structures differ from the densest packings. We show that the self-assembled crystal structures can be understood as a tendency for polyhedra to maximize face-to-face alignment, which can be generalized as directional entropic forces.

A Directional Entropic Force Approach to Assemble Anisotropic Nanoparticles into Superlattices

Abstract : Not touching but sticking: By using cationic surfactant micelles as depletants, a directional entropic force approach (DEFA) assembles anisotropic nanoparticles into superlattices in solution. The micelles induce the face-to-face stacking of the nanoparticles to maximize the systems entropy. The shape of the nanoparticles determines the symmetry of the superlattice, the interparticle spacing is determined by the charged surfactant.

Computational self-assembly of a one-component icosahedral quasicrystal

Icosahedral quasicrystals (IQCs) are a form of matter that is ordered but not periodic in any direction. All reported IQCs are intermetallic compounds and either of face-centred-icosahedral or primitive-icosahedral type, and the positions of their atoms have been resolved from diffraction data. However, unlike axially symmetric quasicrystals, IQCs have not been observed in non-atomic (that is, micellar or nanoparticle) systems, where real-space information would be directly available. Here, we show that an IQC can be assembled by means of molecular dynamics simulations from a one-component system of particles interacting via a tunable, isotropic pair potential extending only to the third-neighbour shell. The IQC is body-centred, self-assembles from a fluid phase, and in parameter space neighbours clathrates and other tetrahedrally bonded crystals. Our findings elucidate the structure and dynamics of the IQC, and suggest routes to search for it and design it in soft matter and nanoscale systems.

Complexity in surfaces of densest packings for families of polyhedra

Packings of hard polyhedra have been studied for centuries due to their mathematical aesthetic and more recently for their applications in fields such as nanoscience, granular and colloidal matter, and biology. In all these fields, particle shape is important for structure and properties, especially upon crowding. Here, we explore packing as a function of shape. By combining simulations and analytic calculations, we study three 2-parameter families of hard polyhedra and report an extensive and systematic analysis of the densest packings of more than 55,000 convex shapes. The three families have the symmetries of triangle groups (icosahedral, octahedral, tetrahedral) and interpolate between various symmetric solids (Platonic, Archimedean, Catalan). We find that optimal (maximum) packing density surfaces that reveal unexpected richness and complexity, containing as many as 130 different structures within a single family. Our results demonstrate the utility of thinking of shape not as a static property of an object in the context of packings, but rather as but one point in a higher dimensional shape space whose neighbors in that space may have identical or markedly different packings. Finally, we present and interpret our packing results in a consistent and generally applicable way by proposing a method to distinguish regions of packings and classify types of transitions between them.

Role of Short-Range Order and Hyperuniformity in the Formation of Band Gaps in Disordered Photonic Materials.

We study photonic band gap formation in two-dimensional high-refractive-index disordered materials where the dielectric structure is derived from packing disks in real and reciprocal space. Numerical calculations of the photonic density of states demonstrate the presence of a band gap for all polarizations in both cases. We find that the band gap width is controlled by the increase in positional correlation inducing short-range order and hyperuniformity concurrently. Our findings suggest that the optimization of short-range order, in particular the tailoring of Bragg scattering at the isotropic Brillouin zone, are of key importance for designing disordered PBG materials.

Symmetry Considerations for the Targeted Assembly of Entropically Stabilized Colloidal Crystals via Voronoi Particles

The relationship between colloidal building blocks and their assemblies is an active field of research. As a strategy for targeting novel crystal structures, we examine the use of Voronoi particles, which are hard, space-filling particles in the shape of Voronoi cells of a target structure. Although Voronoi particles stabilize their target structure in the limit of high pressure by construction, the thermodynamic assembly of the same structure at moderate pressure, close to the onset of crystallization, is not guaranteed. Indeed, we find that a more symmetric crystal is often preferred due to additional entropic contributions arising from configurational or occupational degeneracy. We characterize the assembly behavior of the Voronoi particles in terms of the symmetries of the building blocks as well as the symmetries of crystal structures and demonstrate how controlling the degeneracies through a modification of particle shape and field-directed assembly can significantly improve the assembly propensity.

Non-close-packed three-dimensional quasicrystals

Quasicrystals are frequently encountered in condensed matter. They are important candidates for equilibrium phases from the atomic scale to the nanoscale. Here, we investigate the computational self-assembly of four quasicrystals in a single model system of identical particles interacting with a tunable isotropic pair potential. We reproduce a known icosahedral quasicrystal and report a decagonal quasicrystal, a dodecagonal quasicrystal, and an octagonal quasicrystal. The quasicrystals have low coordination number or occur in systems with mesoscale density variations. We also report a network gel phase.

Self-assembly of a space-tessellating structure in the binary system of hard tetrahedra and octahedra

We report the formation of a binary crystal of hard polyhedra due solely to entropic forces. Although the alternating arrangement of octahedra and tetrahedra is a known space-tessellation, it had not previously been observed in self-assembly simulations. Both known one-component phases - the dodecagonal quasicrystal of tetrahedra and the densest-packing of octahedra in the Minkowski lattice - are found to coexist with the binary phase. Apart from an alternative, monoclinic packing of octahedra, no additional crystalline phases were observed.

Universal folding pathways of polyhedron nets

Significance What makes an object successful at thermal folding? Protein scientists study how sequence affects the pathways by which chained amino acids fold and the structures into which they fold. Here we investigate the inverse problem: Starting with a 3D object as a polyhedron we ask, which ones, among the many choices of 2D unfoldings, are able to fold most consistently? We find that these “nets” follow a universal balance between entropy loss and potential energy gain, allowing us to explain why some of their geometrical attributes (such as compactness) represent a good predictor for the folding propensity of a given shape. Our results can be used to guide the stochastic folding of nanoscale objects into drug-delivery devices and thermally folded robots. Low-dimensional objects such as molecular strands, ladders, and sheets have intrinsic features that affect their propensity to fold into 3D objects. Understanding this relationship remains a challenge for de novo design of functional structures. Using molecular dynamics simulations, we investigate the refolding of the 24 possible 2D unfoldings (“nets”) of the three simplest Platonic shapes and demonstrate that attributes of a net’s topology—net compactness and leaves on the cutting graph—correlate with thermodynamic folding propensity. To explain these correlations we exhaustively enumerate the pathways followed by nets during folding and identify a crossover temperature Tx below which nets fold via nonnative contacts (bonds must break before the net can fold completely) and above which nets fold via native contacts (newly formed bonds are also present in the folded structure). Folding above Tx shows a universal balance between reduction of entropy via the elimination of internal degrees of freedom when bonds are formed and gain in potential energy via local, cooperative edge binding. Exploiting this universality, we devised a numerical method to efficiently compute all high-temperature folding pathways for any net, allowing us to predict, among the combined 86,760 nets for the remaining Platonic solids, those with highest folding propensity. Our results provide a general heuristic for the design of 2D objects to stochastically fold into target 3D geometries and suggest a mechanism by which geometry and folding propensity are related above Tx, where native bonds dominate folding.