Weikai Qi

Ordered Two-Dimensional Superstructures of Colloidal Octapod-Shaped Nanocrystals on Flat Substrates

We studied crystal structures in a monolayer consisting of anisotropic branched colloidal (nano)octapods. Experimentally, octapods were observed to form a monolayer on a substrate with a square-lattice crystal structure by drop-casting and fast evaporation of solvent. The experimental results were analyzed by Monte Carlo simulations using a hard octapod model consisting of four interpenetrating spherocylinders. We confirmed by means of free-energy calculations that crystal structures with a (binary-lattice) square morphology are indeed thermodynamically stable at high densities. The effect of the pod length-to-diameter ratio on the crystal structures was also considered and we used this to constructed the phase diagram for these hard octapods. In addition to the (binary-lattice) square crystal phase, a rhombic crystal and a hexagonal plastic-crystal (rotator) phase were obtained. Our phase diagram may prove instrumental in guiding future experimental studies.

Electron Tomography Resolves a Novel Crystal Structure in a Binary Nanocrystal Superlattice

The self-assembly of different nanocrystals into a binary superlattice is of interest for both colloidal science and nanomaterials science. New properties may emerge from the interaction between the nanocrystal building blocks that are ordered in close contact in three dimensions. Identification of the superlattice structure including its defects is of key interest in understanding the electrical and optical properties of these systems. Transmission electron microscopy (TEM) has been very instrumental to reach this goal but fails for complex crystal structures and buried defects. Here, we use electron tomography to resolve the three-dimensional crystal structure of a binary superlattice that could not be resolved by TEM only. The structure with a [PbSe]6[CdSe]19 stoichiometry has no analogue in the atomic world. Moreover we will show how tomography can overcome the clouding effects of planar defects on structure identification by TEM.

Melting in two-dimensional Yukawa systems: a Brownian dynamics simulation.

We studied the melting behavior of two-dimensional colloidal crystals with a Yukawa pair potential by Brownian dynamics simulations. The melting follows the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) scenario with two continuous phase transitions and a middle hexatic phase. The two phase-transition points were accurately identified from the divergence of the translational and orientational susceptibilities. Configurational temperatures were employed to monitor the equilibrium of the overdamped system and the strongest temperature fluctuation was observed in the hexatic phase. The inherent structure obtained by rapid quenching exhibits three different behaviors in the solid, hexatic, and liquid phases. The measured core energy of the free dislocations, E(c) = 7.81 ± 0.91 k(B)T, is larger than the critical value of 2.84 k(B)T, which consistently supports the KTHNY melting scenario.

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.

Nonclassical Nucleation in a Solid-Solid Transition of Confined Hard Spheres

A solid-solid phase transition of colloidal hard spheres confined between two planar hard walls is studied using a combination of molecular dynamics and Monte Carlo simulation. The transition from a solid consisting of five crystalline layers with square symmetry (5□) to a solid consisting of four layers with triangular symmetry (4△) is shown to occur through a nonclassical nucleation mechanism that involves the initial formation of a precritical liquid cluster, within which the cluster of the stable 4△ phase grows. Free-energy calculations show that the transition occurs in one step, crossing a single free-energy barrier, and that the critical nucleus consists of a small 4△ solid cluster wetted by a metastable liquid. In addition, the liquid cluster and the solid cluster are shown to grow at the planar hard walls. We also find that the critical nucleus size increases with supersaturation, which is at odds with classical nucleation theory. The △-solid-like cluster is shown to contain both face-centered-cubic and hexagonal-close-packed ordered particles.

Highly cooperative stress relaxation in two-dimensional soft colloidal crystals

Significance The creation, annihilation, and diffusion of defects in crystal lattices play an important role during crystal melting and deformation. Although it is well understood how defects form and react when crystals are subjected to external stresses, it remains unclear how crystals cope with internal stresses. We report a study in which we create a highly localized internal stress in a crystal formed from micrometer-sized colloidal spheres and directly observe how the solid reacts using microscopy. We find that, even though the excitation is highly localized, a collective dance of colloidal particles results, even when the excitations are thermally driven. These data shed light on the importance of highly collective motions on the stability and instability of crystalline solids. Stress relaxation in crystalline solids is mediated by the formation and diffusion of defects. Although it is well established how externally generated stresses relax, through the proliferation and motion of dislocations in the lattice, it remains relatively unknown how crystals cope with internal stresses. We investigate, both experimentally and in simulations, how highly localized stresses relax in 2D soft colloidal crystals. When a single particle is actively excited, by means of optical tweezing, a rich variety of highly collective stress relaxation mechanisms results. These relaxation processes manifest in the form of open strings of cooperatively moving particles through the motion of dissociated vacancy-interstitial pairs, and closed loops of mobile particles, which either result from cooperative rotations in transiently generated circular grain boundaries or through the closure of an open string by annihilation of a vacancy-interstitial pair. Surprisingly, we find that the same collective events occur in crystals that are excited by thermal fluctuations alone; a large thermal agitation inside the crystal lattice can trigger the irreversible displacements of hundreds of particles. Our results illustrate how local stresses can induce large-scale cooperative dynamics in 2D soft colloidal crystals and shed light on the stabilization mechanisms in ultrasoft crystals.

Phase diagram of octapod-shaped nanocrystals in a quasi-two-dimensional planar geometry

Recently, we reported the formation of crystalline monolayers consisting of octapod-shaped nanocrystals (so-called octapods) that had arranged in a square-lattice geometry through drop deposition and fast evaporation on a substrate [W. Qi, J. de Graaf, F. Qiao, S. Marras, L. Manna, and M. Dijkstra, Nano Lett. 12, 5299 (2012)]. In this paper we give a more in-depth exposition on the Monte Carlo simulations in a quasi-two-dimensional (quasi-2D) geometry, by which we modelled the experimentally observed crystal structure formation. Using a simulation model for the octapods consisting of four hard interpenetrating spherocylinders, we considered the effect of the pod length-to-diameter ratio on the phase behavior and we constructed the full phase diagram. The methods we applied to establish the nature of the phase transitions between the various phases are discussed in detail. We also considered the possible existence of a Kosterlitz-Thouless-type phase transition between the isotropic liquid and hexagonal rotator phase for certain pod length-to-diameter ratios. Our methods may prove instrumental in guiding future simulation studies of similar anisotropic nanoparticles in confined geometries and monolayers.

Two features at the two-dimensional freezing transitions.

We studied the two-dimensional freezing transitions in monolayers of microgel colloidal spheres with short-ranged repulsions in video-microscopy experiments, and monolayers of hard disks, and Yukawa particles in simulations. These systems share two common features at the freezing points: (1) the bimodal distribution profile of the local orientational order parameter; (2) the two-body excess entropy, s(2), reaches -4.5±0.5 k(B). Both features are robust and sensitive to the freezing points, so that they can potentially serve as empirical freezing criteria in two dimensions. Compared with the conventional freezing criteria, the first feature has no finite-size ambiguities and can be resolved adequately with much less statistics; and the second feature can be directly measured in macroscopic experiments without the need for microscopic information.

Vapor Condensed and Supercooled Glassy Nanoclusters

We use molecular simulation to study the structural and dynamic properties of glassy nanoclusters formed both through the direct condensation of the vapor below the glass transition temperature, without the presence of a substrate, and via the slow supercooling of unsupported liquid nanodroplets. An analysis of local structure using Voronoi polyhedra shows that the energetic stability of the clusters is characterized by a large, increasing fraction of bicapped square antiprism motifs. We also show that nanoclusters with similar inherent structure energies are structurally similar, independent of their history, which suggests the supercooled clusters access the same low energy regions of the potential energy landscape as the vapor condensed clusters despite their different methods of formation. By measuring the intermediate scattering function at different radii from the cluster center, we find that the relaxation dynamics of the clusters are inhomogeneous, with the core becoming glassy above the glass transition temperature while the surface remains mobile at low temperatures. This helps the clusters sample the highly stable, low energy structures on the potential energy surface. Our work suggests the nanocluster systems are structurally more stable than the ultrastable glassy thin films, formed through vapor deposition onto a cold substrate, but the nanoclusters do not exhibit the superheating effects characteristic of the ultrastable glass states.

Dynamical heterogeneities and defects in two-dimensional soft colloidal crystals

In this paper we study a two-dimensional system of charged colloidal particles using Brownian dynamics simulations. We determine the phase diagram and investigate the dynamics of this system in the density regime where hexatic and solid phases are stable. We find that the dynamics in these phases is heterogeneous by means of the spontaneous formation and diffusion of highly mobile defects. We identify two key mechanisms associated with the areas of high mobility. The first mechanism involves the highly cooperative motion of a closed loop of particles which shift coherently along the loop until each particle has replaced the position of its predecessor in the chain. The second mechanism involves the spontaneous creation of vacancy-interstitial pairs which diffuse within the hexatic and solid phases. We further explore quantitatively the properties of the open-ended and closed rearrangement strings and find that in the crystal phase the string-size distribution can be approximately matched with a simple, random walk description of vacancies and interstitials on a lattice.