Michael Grünwald

Self-assembly of uniform polyhedral silver nanocrystals into densest packings and exotic superlattices

Understanding how polyhedra pack into extended arrangements is integral to the design and discovery of crystalline materials at all length scales. Much progress has been made in enumerating and characterizing the packing of polyhedral shapes, and the self-assembly of polyhedral nanocrystals into ordered superstructures. However, directing the self-assembly of polyhedral nanocrystals into densest packings requires precise control of particle shape, polydispersity, interactions and driving forces. Here we show with experiment and computer simulation that a range of nanoscale Ag polyhedra can self-assemble into their conjectured densest packings. When passivated with adsorbing polymer, the polyhedra behave as quasi-hard particles and assemble into millimetre-sized three-dimensional supercrystals by sedimentation. We also show, by inducing depletion attraction through excess polymer in solution, that octahedra form an exotic superstructure with complex helical motifs rather than the densest Minkowski lattice. Such large-scale Ag supercrystals may facilitate the design of scalable three-dimensional plasmonic metamaterials for sensing, nanophotonics and photocatalysis.

Nucleation and Growth in Structural Transformations of Nanocrystals

Using transition path sampling computer simulations, we reveal the nucleation mechanism of a pressure-induced structural transformation in CdSe nanocrystals. Consistent with experiments, the thermodynamic transition pressure of the transformation increases with decreasing crystal size. Through transition state analysis, we identify the critical nuclei and characterize them by calculating activation enthalpies and volumes. Our simulations reproduce the trends with crystal size observed in experiments. This result supports the observed transformation mechanism, which consists of nucleation on the crystal surface and growth by sliding of parallel crystal planes.

The Electronic Structure of CdSe/CdS Core/Shell Seeded Nanorods: Type‑I or Quasi-Type-II?

The electronic structure of CdSe/CdS core/shell seeded nanorods of experimentally relevant size is studied using a combination of molecular dynamics and semiempirical pseudopotential techniques with the aim to address the transition from type-I to a quasi-type-II band alignment. The hole is found to be localized in the core region regardless of its size. The overlap of the electron density with the core region depends markedly on the size of the CdSe core. For small cores, we observe little overlap, consistent with type-II behavior. For large cores, significant core-overlap of a number of excitonic states can lead to type-I behavior. When electron–hole interactions are taken into account, the core-overlap is further increased. Our calculations indicate that the observed transition from type-II to type-I is largely due to simple volume effects and not to band alignment.

Metastability in pressure-induced structural transformations of CdSe/ZnS core/shell nanocrystals.

The kinetics and thermodynamics of structural transformations under pressure depend strongly on particle size due to the influence of surface free energy. By suitable design of surface structure, composition, and passivation it is possible, in principle, to prepare nanocrystals in structures inaccessible to bulk materials. However, few realizations of such extreme size-dependent behavior exist. Here, we show with molecular dynamics computer simulation that in a model of CdSe/ZnS core/shell nanocrystals the core high-pressure structure can be made metastable under ambient conditions by tuning the thickness of the shell. In nanocrystals with thick shells, we furthermore observe a wurtzite to NiAs transformation, which does not occur in the pure bulk materials. These phenomena are linked to a fundamental change in the atomistic transformation mechanism from heterogeneous nucleation at the surface to homogeneous nucleation in the crystal core.

Patterns without patches: hierarchical self-assembly of complex structures from simple building blocks.

Nanoparticles with “sticky patches” have long been proposed as building blocks for the self-assembly of complex structures. The synthetic realizability of such patchy particles, however, greatly lags behind predictions of patterns they could form. Using computer simulations, we show that structures of the same genre can be obtained from a solution of simple isotropic spheres, with control only over their sizes and a small number of binding affinities. In a first step, finite clusters of well-defined structure and composition emerge from natural dynamics with high yield. In effect a kind of patchy particle, these clusters can further assemble into a variety of complex superstructures, including filamentous networks, ordered sheets, and highly porous crystals.

Role of stacking disorder in ice nucleation

The freezing of water affects the processes that determine Earth’s climate. Therefore, accurate weather and climate forecasts hinge on good predictions of ice nucleation rates. Such rate predictions are based on extrapolations using classical nucleation theory, which assumes that the structure of nanometre-sized ice crystallites corresponds to that of hexagonal ice, the thermodynamically stable form of bulk ice. However, simulations with various water models find that ice nucleated and grown under atmospheric temperatures is at all sizes stacking-disordered, consisting of random sequences of cubic and hexagonal ice layers. This implies that stacking-disordered ice crystallites either are more stable than hexagonal ice crystallites or form because of non-equilibrium dynamical effects. Both scenarios challenge central tenets of classical nucleation theory. Here we use rare-event sampling and free energy calculations with the mW water model to show that the entropy of mixing cubic and hexagonal layers makes stacking-disordered ice the stable phase for crystallites up to a size of at least 100,000 molecules. We find that stacking-disordered critical crystallites at 230 kelvin are about 14 kilojoules per mole of crystallite more stable than hexagonal crystallites, making their ice nucleation rates more than three orders of magnitude higher than predicted by classical nucleation theory. This effect on nucleation rates is temperature dependent, being the most pronounced at the warmest conditions, and should affect the modelling of cloud formation and ice particle numbers, which are very sensitive to the temperature dependence of ice nucleation rates. We conclude that classical nucleation theory needs to be corrected to include the dependence of the crystallization driving force on the size of the ice crystallite when interpreting and extrapolating ice nucleation rates from experimental laboratory conditions to the temperatures that occur in clouds.

Transferable pair potentials for CdS and ZnS crystals.

A set of interatomic pair potentials is developed for CdS and ZnS crystals. We show that a simple energy function, which has been used to describe the properties of CdSe [E. Rabani, J. Chem. Phys. 116, 258 (2002)], can be parametrized to accurately describe the lattice and elastic constants, and phonon dispersion relations of bulk CdS and ZnS in the wurtzite and rocksalt crystal structures. The predicted coexistence pressure of the wurtzite and rocksalt structures as well as the equation of state are in good agreement with experimental observations. These new pair potentials enable the study of a wide range of processes in bulk and nanocrystalline II-VI semiconductor materials.

An efficient transition path sampling algorithm for nanoparticles under pressure.

We apply transition path sampling to the simulation of nanoparticles under pressure. As a barostat we use a bath of ideal gas particles that form a stochastically updated atmosphere around the nanoparticle. We justify this algorithm by showing that it preserves the distribution of an ideal gas at constant temperature and pressure by satisfying detailed balance. Based on this result, we present a simple and efficient transition path sampling scheme for the study of activated processes in nanoparticles under pressure. As a first application, we investigate the h-MgO to rocksalt transformation in faceted CdSe nanocrystals. Starting from an artificial mechanism involving a uniform motion of all atoms, trajectories quickly converge towards the dominant mechanism of nucleation and growth along parallel (100) planes.

Transition state analysis of solid-solid transformations in nanocrystals

A systematic simulation methodology is introduced for the accurate determination of experimentally measurable quantities characterizing solid-solid phase transformations under pressure. The atomistic mechanisms of nucleation and growth in a structural transformation of pressurized CdSe nanocrystals are identified using transition path sampling computer simulation. A committor-based transition state analysis is applied to extract activation enthalpies and activation volumes from transformation pathways at experimental conditions. The qualitative dependence of activation enthalpies on nanocrystal size is in good agreement with experimental data and supports the observed nucleation mechanism, which is characterized by a critical nucleus of elongated shape located on the crystal surface. Based on committor distributions along typical transformation pathways, the coordination number is identified as a suitable reaction coordinate for the process.

Ideal gas pressure bath: a method for applying hydrostatic pressure in the computer simulation of nanoparticles

We present a method for applying hydrostatic pressure in the computer simulation of nanoparticles, using an ideal gas as the pressure medium and thermostat. As the equation of state is known for the ideal gas, the exerted pressure can easily be tuned by adjusting the number of gas particles, while the temperature is controlled by their kinetic energy. Applying this method, we study the pressure-induced transformation from the four-coordinate wurtzite to the six-coordinate rocksalt structure in faceted CdSe nanocrystals. The transformation involves the consecutive sliding of parallel (100) planes and proceeds through a five-coordinate intermediate structure.