Kristen A. Fichthorn

Theoretical foundations of dynamical Monte Carlo simulations

Monte Carlo methods are utilized as computational tools in many areas of chemical physics. In this paper, we present the theoretical basis for a dynamical Monte Carlo method in terms of the theory of Poisson processes. We show that if: (1) a ‘‘dynamical hierarchy’’ of transition probabilities is created which also satisfy the detailed‐balance criterion; (2) time increments upon successful events are calculated appropriately; and (3) the effective independence of various events comprising the system can be achieved, then Monte Carlo methods may be utilized to simulate the Poisson process and both static and dynamic properties of model Hamiltonian systems may be obtained and interpreted consistently.

Island nucleation in thin-film epitaxy: A first-principles investigation

We describe a theoretical study of the role of adsorbate interactions in island nucleation and growth, using Ag/Pt(111) heteroepitaxy as an example. From density-functional theory, we obtain the substrate-mediated Ag adatom pair interaction and we find that, past the short range, a repulsive ring is formed about the adatoms. The magnitude of the repulsion is comparable to the diffusion barrier. In kinetic Monte Carlo simulations, we find that the repulsive interactions lead to island densities over an order of magnitude larger than those predicted by nucleation theory and thus identify a severe limitation of its applicability.

Accelerated molecular dynamics with the bond-boost method

We present a new method for accelerating molecular-dynamics simulations of infrequent events. The method targets simulation of systems that spend most of the time in local energy minima, with slow transitions in between, as is the case with low-temperature surface diffusion. The potential-energy surface is modified by adding a boost potential in regions close to the local minima, such that all transition rates are increased while relative rates are preserved. The boost potential is an empirical function determined by the deviation of the bond lengths of a specified set of atoms from equilibrium. The method requires no previous knowledge of the processes involved and it can be applied to a wide variety of interaction potentials. Application to the diffusion of Cu atoms on the Cu(100) surface using an embedded-atom potential yields correct rates for adatom hopping, exchange, as well as vacancy and dimer diffusion with speed-ups up to several orders of magnitude.

Adsorption of polyvinylpyrrolidone on Ag surfaces: insight into a structure-directing agent.

We use density functional theory to resolve the role of polyvinylpyrrolidone (PVP) in the shape-selective synthesis of Ag nanostructures. At the segment level, PVP binds more strongly to Ag(100) than Ag(111) because of a surface-sensitive balance between direct binding and van der Waals attraction. At the chain level, correlated segment binding leads to a strong preference for PVP bind to Ag(100). Our study underscores differences between small-molecule and polymeric structure-directing agents.

Normal, single-file, and dual-mode diffusion of binary adsorbate mixtures in AlPO4-5

We have used molecular simulations to examine the diffusion of Ne, Ar, Kr, Xe, CH4, CF4, CCl4, SF6, SnCl4, and SnBr4 in the molecular sieve AlPO4-5, both as single species and as coadsorbed mixtures. Single adsorbed species exhibit a transition from normal to single-file diffusion as a function of increasing adsorbate size. In addition to normal and single-file diffusion, coadsorbed mixtures exhibit a qualitatively new diffusion mode in which one species performs normal diffusion while the other undergoes single-file diffusion. We discuss the prospects for experimental verification of this phenomenon, and present measurements of the loading dependence of diffusion rates during the dual-mode diffusion of Ne/CF4 mixtures.

Mechanisms of oriented attachment of TiO2 nanocrystals in vacuum and humid environments: reactive molecular dynamics.

Oriented attachment (OA) of nanocrystals is now widely recognized as a key process in the solution-phase growth of hierarchical nanostructures. However, the microscopic origins of OA remain unclear. We perform molecular dynamics simulations using a recently developed ReaxFF reactive force field to study the aggregation of various titanium dioxide (anatase) nanocrystals in vacuum and humid environments. In vacuum, the nanocrystals merge along their direction of approach, resulting in a polycrystalline material. By contrast, in the presence of water vapor the nanocrystals reorient themselves and aggregate via the OA mechanism to form a single or twinned crystal. They accomplish this by creating a dynamic network of hydrogen bonds between surface hydroxyls and surface oxygens of aggregating nanocrystals. We determine that OA is dominant on surfaces that have the greatest propensity to dissociate water. Our results are consistent with experiment, are likely to be general for aqueous oxide systems, and demonstrate the critical role of solvent in nanocrystal aggregation. This work opens up new possibilities for directing nanocrystal growth to fabricate nanomaterials with desired shapes and sizes.

Molecular-dynamics simulation of forces between nanoparticles in a Lennard-Jones liquid

Molecular-dynamics simulations are utilized to simulate solvation and van der Waals forces between two nanoparticles immersed in a Lennard-Jones liquid. Three different sizes and shapes of nanoparticles with solvophilic and solvophobic properties are investigated. We compare different methods for calculating van der Waals forces. For solvophilic nanoparticles, the solvation forces oscillate between attraction and repulsion as the particle separation is increased. Solvophilic solvation forces are comparable to or stronger than van der Waals forces. In the solvophobic case, solvation forces are attractive. We find that surface roughness can significantly affect the solvation-force profile for solvophilic nanoparticles. Our results indicate that surface roughness can alter the balance between solvation and van der Waals forces in a solvophilic colloidal suspension and that a desirable force balance can be achieved by choosing nanoparticles with certain textures and/or shapes.

A method for molecular dynamics simulation of confined fluids

We report the development of a simulation method, with advantages for simulating fluids confined between solid substrates and in equilibrium with bulk fluids. For molecular-dynamics simulations, the isothermal–isobaric constraint method is modified to implement this method. Long-range corrections to the pressure tensor for simple confined systems are also derived and included. Consistent with previous studies employing the grand-canonical ensemble, confined Lennard-Jones and model n-decane fluids investigated with this method show layering induced by the confining surfaces, oscillatory surface-force profiles, and step-like dependencies of the number of confined molecules on surface separation. For a confined Lennard-Jones fluid, increasing the bulk pressure at a fixed temperature enhances layering, increases the effect of surface structure on the surface-force profile, and causes the surface forces to be more repulsive.

How Structure-Directing Agents Control Nanocrystal Shape: Polyvinylpyrrolidone-Mediated Growth of Ag Nanocubes

The importance of structure-directing agents (SDAs) in the shape-selective synthesis of colloidal nanostructures has been well documented. However, the mechanisms by which SDAs actuate shape control are poorly understood. In the polyvinylpyrrolidone (PVP)-mediated growth of {100}-faceted Ag nanocrystals, this capability has been attributed to preferential binding of PVP to Ag(100). We use molecular dynamics simulations to probe the mechanisms by which Ag atoms add to Ag(100) and Ag(111) in ethylene glycol solution with PVP. We find that PVP induces kinetic Ag nanocrystal shapes by regulating the relative Ag fluxes to these facets. Stronger PVP binding to Ag(100) leads to a larger Ag flux to Ag(111) and cubic nanostructures through two mechanisms: enhanced Ag trapping by more extended PVP films on Ag(111) and a reduced free-energy barrier for Ag to cross lower-density films on Ag(111). These flux-regulating capabilities depend on PVP concentration and chain length, consistent with experiment.

Self-sustained oscillations in a heterrogeneous catalytic reaction: a monte carlo simulation

We have utilized Monte Carlo methods to study the kinetics of a generic heterogeneous catalytic reaction, A + B 4 AR This reaction includes the elementary steps of adsorption and desorption of reactants A and B, surface reaction through the Langmuir-Hinshelwood mechanism, and desorption of product AB. It is shown that this model is capable of producing self-sustained oscillations in the rate of reaction. The oscillations are dependent on the rate of desorption and exhibit a time scale much greater than those of the adsorption and surface reaction steps in the model. We analyze the dvnamic aualitv of the oscillations and discern that they stem from chaos. To our best knowledge, -this is thk first st;dy in which chaos has bein observed and characterized through a Monte Carlo simulation. With the results of this work. we have been able to analyze the fundamental components responsible for producing the chaos in our simulations. We discuss the implications of our results for actual catalytic systems with oscillatory behavior.