Anjan P. Gantapara

Phase diagram of colloidal hard superballs: from cubes via spheres to octahedra

For hard anisotropic particles the formation of a wide variety of fascinating crystal and liquid-crystal phases is accomplished by entropy alone. A better understanding of these entropy-driven phase transitions will shed light on the self-assembly of nanoparticles, however, there are still many open questions in this regard. In this work, we use Monte Carlo simulations and free-energy calculations to determine the phase diagram of colloidal hard superballs, of which the shape interpolates between cubes and octahedra via spheres. We discover not only a stable face-centered cubic (fcc) plastic crystal phase for near-spherical particles, but also a stable body-centered cubic (bcc) plastic crystal close to the octahedron shape. Moreover, coexistence of these two plastic crystals is observed with a substantial density gap. The plastic fcc and bcc crystals are, however, both unstable in the cube and octahedron limit, suggesting that the local curvature, i.e. rounded corners and curved faces, of superballs plays an important role in stabilizing the rotator phases. In addition, we observe a two-step melting phenomenon for hard octahedra, in which the Minkowski crystal melts into a metastable bcc plastic crystal before melting into the fluid phase.

In situ study of the formation mechanism of two-dimensional superlattices from PbSe nanocrystals

Oriented attachment of PbSe nanocubes can result in the formation of two-dimensional (2D) superstructures with long-range nanoscale and atomic order. This questions the applicability of classic models in which the superlattice grows by first forming a nucleus, followed by sequential irreversible attachment of nanocrystals, as one misaligned attachment would disrupt the 2D order beyond repair. Here, we demonstrate the formation mechanism of 2D PbSe superstructures with square geometry by using in situ grazing-incidence X-ray scattering (small angle and wide angle), ex situ electron microscopy, and Monte Carlo simulations. We observed nanocrystal adsorption at the liquid/gas interface, followed by the formation of a hexagonal nanocrystal monolayer. The hexagonal geometry transforms gradually through a pseudo-hexagonal phase into a phase with square order, driven by attractive interactions between the {100} planes perpendicular to the liquid substrate, which maximize facet-to-facet overlap. The nanocrystals then attach atomically via a necking process, resulting in 2D square superlattices.

Self-Assembly of Colloidal Hexagonal Bipyramid- and Bifrustum-Shaped ZnS Nanocrystals into Two-Dimensional Superstructures

We present a combined experimental, theoretical, and simulation study on the self-assembly of colloidal hexagonal bipyramid- and hexagonal bifrustum-shaped ZnS nanocrystals (NCs) into two-dimensional superlattices. The simulated NC superstructures are in good agreement with the experimental ones. This shows that the self-assembly process is primarily driven by minimization of the interfacial free-energies and maximization of the packing density. Our study shows that a small truncation of the hexagonal bipyramids is sufficient to change the symmetry of the resulting superlattice from hexagonal to tetragonal, highlighting the crucial importance of precise shape control in the fabrication of functional metamaterials by self-assembly of colloidal NCs.

Two-stage melting induced by dislocations and grain boundaries in monolayers of hard spheres†

Melting in two-dimensional systems has remained controversial as theory, simulations, and experiments show contrasting results. One issue that obscures this discussion is whether or not theoretical predictions on strictly 2D systems describe those on quasi-2D experimental systems, where out-of-plane fluctuations may alter the melting mechanism. Using event-driven molecular dynamics simulations, we find that the peculiar two-stage melting scenario of a continuous solid-hexatic and a first-order hexatic-liquid transition as observed for a truly 2D system of hard disks [Bernard and Krauth, Phys. Rev. Lett., 2011, 107, 155704] persists for a quasi-2D system of hard spheres with out-of-plane particle motions as high as half the particle diameter. By calculating the renormalized Youngs modulus, we show that the solid-hexatic transition is of the Kosterlitz-Thouless type and occurs via dissociation of bound dislocation pairs. In addition, we find a first-order hexatic-liquid transition that seems to be driven by spontaneous proliferation of grain boundaries.

On the stability of a quasicrystal and its crystalline approximant in a system of hard disks with a soft corona

Using computer simulations, we study the phase behavior of a model system of colloidal hard disks with a diameter σ and a soft corona of width 1.4σ. The particles interact with a hard core and a repulsive square-shoulder potential. We calculate the free energy of the random-tiling quasicrystal and its crystalline approximants using the Frenkel-Ladd method. We explicitly account for the configurational entropy associated with the number of distinct configurations of the random-tiling quasicrystal. We map out the phase diagram and find that the random tiling dodecagonal quasicrystal is stabilised by entropy at finite temperatures with respect to the crystalline approximants that we considered, and its stability region seems to extend to zero temperature as the energies of the defect-free quasicrystal and the crystalline approximants are equal within our statistical accuracy.

Phase behavior of a family of truncated hard cubes

In continuation of our work in Gantapara et al., [Phys. Rev. Lett. 111, 015501 (2013)], we investigate here the thermodynamic phase behavior of a family of truncated hard cubes, for which the shape evolves smoothly from a cube via a cuboctahedron to an octahedron. We used Monte Carlo simulations and free-energy calculations to establish the full phase diagram. This phase diagram exhibits a remarkable richness in crystal and mesophase structures, depending sensitively on the precise particle shape. In addition, we examined in detail the nature of the plastic crystal (rotator) phases that appear for intermediate densities and levels of truncation. Our results allow us to probe the relation between phase behavior and building-block shape and to further the understanding of rotator phases. Furthermore, the phase diagram presented here should prove instrumental for guiding future experimental studies on similarly shaped nanoparticles and the creation of new materials.

Glassy dynamics of convex polyhedra

Self-assembly of polyhedral-shaped particles has attracted huge interest with the advent of new synthesis methods that realize these faceted particles in the lab. Recent studies have shown that polyhedral-shaped particles exhibit a rich phase behavior by excluded volume interactions alone; some of these particles are even alleged to show a transition to a glass phase by quenching the liquid sufficiently fast beyond the glass transition (supercooling), such that the formation of structures with long-range order is suppressed. Despite the recent progress, no study has been made on the glass formation of polyhedral-shaped particles. Here, we study the glass behavior of polyhedral particles using advanced Monte Carlo methods. We investigate the formation of a glass of monodisperse hard polyhedral-shaped particles, namely, octahedra, tetrahedra, and triangular cupola, using simulations. Finally, the fragility of these particles is determined and compared to that of a polydisperse hard-sphere system.