Shape-directional growth of Pt and Pd nanoparticles.

The design and synthesis of shape-directed nanoscale noble metal particles have attracted much attention due to their enhanced catalytic properties and the opportunities to study fundamental aspects of nanoscale systems. As such, numerous methods have been developed to synthesize crystals with tunable shapes, sizes, and facets by adding foreign species that promote or restrict growth on specific sites. Many hypotheses regarding how and why certain species direct growth have been put forward, however there has been no consensus on a unifying mechanism of nanocrystal growth. Herein, we develop and demonstrate the capabilities of a mathematical growth model for predicting metal nanoparticle shapes by studying a well known procedure that employs AgNO3 to produce {111} faceted Pt nanocrystals. The insight gained about the role of auxiliary species is then utilized to predict the shape of Pd nanocrystals and to corroborate other shape-directing syntheses reported in literature. The fundamental understanding obtained herein by combining modeling with experimentation is a step toward computationally guided syntheses and, in principle, applicable to predictive design of the growth of crystalline solids at all length scales (nano to bulk).

Self-assembly of collagen on flat surfaces: the interplay of collagen-collagen and collagen-substrate interactions.

Fibrillar collagens, common tissue scaffolds in live organisms, can also self-assemble in vitro from solution. While previous in vitro studies showed that the pH and the electrolyte concentration in solution largely control the collagen assembly, the physical reasons why such control could be exerted are still elusive. To address this issue and to be able to simulate self-assembly over large spatial and temporal scales, we have developed a microscopic model of collagen with explicit interactions between the units that make up the collagen molecules, as well as between these units and the substrate. We have used this model to investigate assemblies obtained via molecular dynamics deposition of collagen on a substrate at room temperature using an implicit solvent. By comparing the morphologies from our molecular dynamics simulations with those from our atomic-force microscopy experiments, we have found that the assembly is governed by the competition between the collagen-collagen interactions and those between collagen and the substrate. The microscopic model developed here can serve for guiding future experiments that would explore new regions of the parameter space.

Atomistics of vapour-liquid-solid nanowire growth.

Vapour-liquid-solid route and its variants are routinely used for scalable synthesis of semiconducting nanowires, yet the fundamental growth processes remain unknown. Here we employ atomic-scale computations based on model potentials to study the stability and growth of gold-catalysed silicon nanowires. Equilibrium studies uncover segregation at the solid-like surface of the catalyst particle, a liquid AuSi droplet, and a silicon-rich droplet-nanowire interface enveloped by heterogeneous truncating facets. Supersaturation of the droplets leads to rapid one-dimensional growth on the truncating facets and much slower nucleation-controlled two-dimensional growth on the main facet. Surface diffusion is suppressed and the excess Si flux occurs through the droplet bulk which, together with the Si-rich interface and contact line, lowers the nucleation barrier on the main facet. The ensuing step flow is modified by Au diffusion away from the step edges. Our study highlights key interfacial characteristics for morphological and compositional control of semiconducting nanowire arrays.

First-passage kinetic Monte Carlo method.

We present an efficient method for Monte Carlo simulations of diffusion-reaction processes. Introduced by us in a previous paper [Phys. Rev. Lett. 97, 230602 (2006)], our algorithm skips the traditional small diffusion hops and propagates the diffusing particles over long distances through a sequence of superhops, one particle at a time. By partitioning the simulation space into nonoverlapping protecting domains each containing only one or two particles, the algorithm factorizes the N -body problem of collisions among multiple Brownian particles into a set of much simpler single-body and two-body problems. Efficient propagation of particles inside their protective domains is enabled through the use of time-dependent Green's functions (propagators) obtained as solutions for the first-passage statistics of random walks. The resulting Monte Carlo algorithm is event-driven and asynchronous; each Brownian particle propagates inside its own protective domain and on its own time clock. The algorithm reproduces the statistics of the underlying Monte Carlo model exactly. Extensive numerical examples demonstrate that for an important class of diffusion-reaction models the algorithm is efficient at low particle densities, where other existing algorithms slow down severely.

First-passage Monte Carlo algorithm: diffusion without all the hops.

We present a novel Monte Carlo algorithm for N diffusing finite particles that react on collisions. Using the theory of first-passage processes and time dependent Green's functions, we break the difficult N-body problem into independent single- and two-body propagations circumventing numerous diffusion hops used in standard Monte Carlo simulations. The new algorithm is exact, extremely efficient, and applicable to many important physical situations in arbitrary integer dimensions.