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.

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.

A novel chiral phase of achiral hard triangles and an entropy-driven demixing of enantiomers.

We investigate the phase behavior of a system of hard equilateral and right-angled triangles in two dimensions using Monte Carlo simulations. Hard equilateral triangles undergo a continuous isotropic-triatic liquid crystal phase transition at packing fraction ϕ = 0.7. Similarly, hard right-angled isosceles triangles exhibit a first-order phase transition from an isotropic fluid phase to a rhombic liquid crystal phase with a coexistence region ϕ ∈ [0.733, 0.782]. Both these liquid crystals undergo a continuous phase transition to their respective close-packed crystal structures at high pressures. Although the particles and their close-packed crystals are both achiral, the solid phases of equilateral and right-angled triangles exhibit spontaneous chiral symmetry breaking at sufficiently high packing fractions. The colloidal triangles rotate either in the clockwise or anti-clockwise direction with respect to one of the lattice vectors for packing fractions higher than ϕχ. As a consequence, these triangles spontaneously form a regular lattice of left- or right-handed chiral holes which are surrounded by six triangles in the case of equilateral triangles and four or eight triangles for right-angled triangles. Moreover, our simulations show a spontaneous entropy-driven demixing transition of the right- and left-handed "enantiomers".

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.

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 Young's 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.

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.

Phase diagram and structural diversity of a family of truncated cubes: degenerate close-packed structures and vacancy-rich states.

Using Monte Carlo simulations and free-energy calculations, we determine the phase diagram of a family of truncated hard cubes, where the shape evolves smoothly from a cube via a cuboctahedron to an octahedron. A remarkable diversity in crystal phases and close-packed structures is found, including a fully degenerate crystal structure, several plastic crystals, as well as vacancy-stabilized crystal phases, all depending sensitively on the precise particle shape. Our results illustrate the intricate relation between phase behavior and building-block shape, and can guide future experimental studies on polyhedral-shaped nanoparticles.