Marjolein Dijkstra

Ionic colloidal crystals of oppositely charged particles.

Colloidal suspensions are widely used to study processes such as melting, freezing and glass transitions. This is because they display the same phase behaviour as atoms or molecules, with the nano- to micrometre size of the colloidal particles making it possible to observe them directly in real space. Another attractive feature is that different types of colloidal interactions, such as long-range repulsive, short-range attractive, hard-sphere-like and dipolar, can be realized and give rise to equilibrium phases. However, spherically symmetric, long-range attractions (that is, ionic interactions) have so far always resulted in irreversible colloidal aggregation. Here we show that the electrostatic interaction between oppositely charged particles can be tuned such that large ionic colloidal crystals form readily, with our theory and simulations confirming the stability of these structures. We find that in contrast to atomic systems, the stoichiometry of our colloidal crystals is not dictated by charge neutrality; this allows us to obtain a remarkable diversity of new binary structures. An external electric field melts the crystals, confirming that the constituent particles are indeed oppositely charged. Colloidal model systems can thus be used to study the phase behaviour of ionic species. We also expect that our approach to controlling opposite-charge interactions will facilitate the production of binary crystals of micrometre-sized particles, which could find use as advanced materials for photonic applications.

Hierarchical self-assembly of suspended branched colloidal nanocrystals into superlattice structures

Self-assembly of molecular units into complex and functional superstructures is ubiquitous in biology. The number of superstructures realized by self-assembly of man-made nanoscale units is also growing. However, assemblies of colloidal inorganic nanocrystals are still at an elementary level, not only because of the simplicity of the shape of the nanocrystal building blocks and their interactions, but also because of the poor control over these parameters in the fabrication of more elaborate nanocrystals. Here, we show how monodisperse colloidal octapod-shaped nanocrystals self-assemble, in a suitable solution environment, on two sequential levels. First, linear chains of interlocked octapods are formed, and subsequently the chains spontaneously self-assemble into three-dimensional superstructures. Remarkably, all the instructions for the hierarchical self-assembly are encoded in the octapod shape. The mechanical strength of these superstructures is improved by welding the constituent nanocrystals together.

Surface roughness directed self-assembly of patchy particles into colloidal micelles

Colloidal particles with site-specific directional interactions, so called “patchy particles”, are promising candidates for bottom-up assembly routes towards complex structures with rationally designed properties. Here we present an experimental realization of patchy colloidal particles based on material independent depletion interaction and surface roughness. Curved, smooth patches on rough colloids are shown to be exclusively attractive due to their different overlap volumes. We discuss in detail the case of colloids with one patch that serves as a model for molecular surfactants both with respect to their geometry and their interactions. These one-patch particles assemble into clusters that resemble surfactant micelles with the smooth and attractive sides of the colloids located at the interior. We term these clusters “colloidal micelles”. Direct Monte Carlo simulations starting from a homogeneous state give rise to cluster size distributions that are in good agreement with those found in experiments. Important differences with surfactant micelles originate from the colloidal character of our model system and are investigated by simulations and addressed theoretically. Our new “patchy” model system opens up the possibility for self-assembly studies into finite-sized superstructures as well as crystals with as of yet inaccessible structures.

Phase behaviour and structure of model colloid-polymer mixtures

We study the phase behaviour and structure of model colloid-polymer mixtures. By integrating out the degrees of freedom of the non-adsorbing ideal polymer coils, we derive a formal expression for the effective one-component Hamiltonian of the colloids. Using the two-body (Asakura-Oosawa pair potential) approximation to this effective Hamiltonian in computer simulations, we determine the phase behaviour for size ratios q = p/c = 0.1, 0.4, 0.6, and 0.8, where c and p denote the diameters of the colloids and the polymer coils, respectively. For large q, we find both a fluid-solid and a stable fluid-fluid transition. However, the latter becomes metastable with respect to a broad fluid-solid transition for q0.4. For q = 0.1 there is a metastable isostructural solid-solid transition which is likely to become stable for smaller values of q. We compare the phase diagrams obtained from simulation with those of perturbation theory using the same effective one-component Hamiltonian and with the results of the free-volume approach. Although both theories capture the main features of the topologies of the phase diagrams, neither provides an accurate description of the simulation results. Using simulation and the Percus-Yevick approximation we determine the radial distribution function g(r) and the structure factor S(k) of the effective one-component system along the fluid-solid and fluid-fluid phase boundaries. At state-points on the fluid-solid boundary corresponding to high colloid packing fractions (packing fractions equal to or larger than that at the triple point), the value of S(k) at its first maximum is close to the value 2.85 given by the Hansen-Verlet freezing criterion. However, at lower colloid packing fractions freezing occurs when the maximum value is much lower than 2.85. Close to the critical point of the fluid-fluid transition we find Ornstein-Zernike behaviour and at very dilute colloid concentrations S(k) exhibits pronounced small-angle scattering which reflects the growth of clusters of the colloids. We compare the phase behaviour of this model with that found in studies of additive binary hard-sphere mixtures.

Low-dimensional semiconductor superlattices formed by geometric control over nanocrystal attachment.

Oriented attachment, the process in which nanometer-sized crystals fuse by atomic bonding of specific crystal facets, is expected to be more difficult to control than nanocrystal self-assembly that is driven by entropic factors or weak van der Waals attractions. Here, we present a study of oriented attachment of PbSe nanocrystals that counteract this tuition. The reaction was studied in a thin film of the suspension casted on an immiscible liquid at a given temperature. We report that attachment can be controlled such that it occurs with one type of facets exclusively. By control of the temperature and particle concentration we obtain one- or two-dimensional PbSe single crystals, the latter with a honeycomb or square superimposed periodicity in the nanometer range. We demonstrate the ability to convert these PbSe superstructures into other semiconductor compounds with the preservation of crystallinity and geometry.

Entropy-Driven Formation of Binary Semiconductor-Nanocrystal Superlattices

One of the main reasons for the current interest in colloidal nanocrystals is their propensity to form superlattices, systems in which (different) nanocrystals are in close contact in a well-ordered three-dimensional (3D) geometry resulting in novel material properties. However, the principles underlying the formation of binary nanocrystal superlattices are not well understood. Here, we present a study of the driving forces for the formation of binary nanocrystal superlattices by comparing the formed structures with full free energy calculations. The nature (metallic or semiconducting) and the size-ratio of the two nanocrystals are varied systematically. With semiconductor nanocrystals, self-organization at high temperature leads to superlattices (AlB(2), NaZn(13), MgZn(2)) in accordance with the phase diagrams for binary hard-sphere mixtures; hence entropy increase is the dominant driving force. A slight change of the conditions results in structures that are energetically stabilized. This study provides rules for the rational design of 3D nanostructured binary semiconductors, materials with promises in thermoelectrics and photovoltaics and which cannot be reached by any other technology.

Crystal nucleation of hard spheres using molecular dynamics, umbrella sampling, and forward flux sampling: a comparison of simulation techniques.

Over the last number of years several simulation methods have been introduced to study rare events such as nucleation. In this paper we examine the crystal nucleation rate of hard spheres using three such numerical techniques: molecular dynamics, forward flux sampling, and a Bennett-Chandler-type theory where the nucleation barrier is determined using umbrella sampling simulations. The resulting nucleation rates are compared with the experimental rates of Harland and van Megen [Phys. Rev. E 55, 3054 (1997)], Sinn et al. [Prog. Colloid Polym. Sci. 118, 266 (2001)], Schätzel and Ackerson [Phys. Rev. E 48, 3766 (1993)], and the predicted rates for monodisperse and 5% polydisperse hard spheres of Auer and Frenkel [Nature 409, 1020 (2001)]. When the rates are examined in units of the long-time diffusion coefficient, we find agreement between all the theoretically predicted nucleation rates, however, the experimental results display a markedly different behavior for low supersaturation. Additionally, we examined the precritical nuclei arising in the molecular dynamics, forward flux sampling, and umbrella sampling simulations. The structure of the nuclei appears independent of the simulation method, and in all cases, the nuclei contains on average significantly more face-centered-cubic ordered particles than hexagonal-close-packed ordered particles.

Phase separation in binary hard‐core mixtures

We report the observation of a purely entropic demixing transition in a three-dimensional binary hard-core mixture by computer simulations. This transition is observed in a lattice model of a binary hard-core mixture of parallel cubes provided that the size asymmetry of the large and small particles is sufficiently large (≥3, in the present case). In addition, we have performed simulations of a single athermal polymer in a hard-core solvent. As we increase the chemical potential of the solvent, we observe a purely entropy-driven collapse of the polymer: the scaling of the radius of gyration Rg of the polymer with the number of segments N changes from that of a polymer in a good solvent to that of a collapsed polymer. Both for the study of the hard-core demixing and of the polymer collapse, it was essential to use novel collective Monte Carlo moves to speed up equilibration. We show that in the limit σ1/σ2→0, the pair distribution function for an off-lattice binary hard-core mixture of parallel cubes with side lengths σ1 and σ2 diverges at contact for the large particles. For the lattice system, we calculated the pair distribution functions g(r) up to the fourth virial coefficient. The difference in g(r) at contact for a binary system and a pure system at the same packing fraction gives a rough criterion, whether the mixture phase separates

Dense Regular Packings of Irregular Nonconvex Particles

We present a new numerical scheme to study systems of nonconvex, irregular, and punctured particles in an efficient manner. We employ this method to analyze regular packings of odd-shaped bodies, both from a nanoparticle and from a computational geometry perspective. Besides determining close-packed structures for 17 irregular shapes, we confirm several conjectures for the packings of a large set of 142 convex polyhedra and extend upon these. We also prove that we have obtained the densest packing for both rhombicuboctahedra and rhombic enneacontrahedra and we have improved upon the packing of enneagons and truncated tetrahedra.

Phase behaviour of hard spheres confined between parallel hard plates: manipulation of colloidal crystal structures by confinement

We study the phase behaviour of hard spheres confined between two parallel hard plates using extensive computer simulations. We determine the full equilibrium phase diagram for arbitrary densities and plate separations from one to five hard-sphere diameters using free energy calculations. We find a first-order fluid-solid transition, which corresponds to either capillary freezing or melting depending on the plate separation. The coexisting solid phase consists of crystalline layers with either triangular ([Formula: see text]) or square ([Formula: see text]) symmetry. Increasing the plate separation, we find a sequence of crystal structures from [Formula: see text], where n is the number of crystal layers, in agreement with experiments on colloids. At high densities, the transition between square to triangular phases is interrupted by intermediate structures, e.g., prism, buckled, and rhombic phases.