Dynamic Monte Carlo with a proper energy barrier: Surface diffusion and two‐dimensional domain ordering

Self-diffusion is temperature independent on active membranes

Molecular transport maintains cellular structures and functions. For example, lipid and protein diffusion sculpts the dynamic shapes and structures on the cell membrane that perform essential cellular functions, such as cell signaling. Temperature variations in thermal equilibrium rapidly change molecular transport properties. The coefficient of lipid self-diffusion increases exponentially with temperature in thermal equilibrium, for example. Hence, maintaining cellular homeostasis through molecular transport is hard in thermal equilibrium in the noisy cellular environment, where temperatures can fluctuate widely due to local heat generation. In this paper, using both molecular and lattice-based modeling of membrane transport, we show that the presence of active transport originating from the cell's cytoskeleton can make the self-diffusion of the molecules on the membrane robust to temperature fluctuations. The resultant temperature-independence of self-diffusion keeps the precision of cellular signaling invariant over a broad range of ambient temperatures, allowing cells to make robust decisions. We have also found that the Kawasaki algorithm, the widely used model of lipid transport on lattices, predicts incorrect temperature dependence of lipid self-diffusion in equilibrium. We propose a new algorithm that correctly captures the equilibrium properties of lipid self-diffusion and reproduces experimental observations.

Kinetic Monte Carlo method applied to micrometric particle detachment mechanisms by aerodynamic forces

The formulation of a kinetic Monte Carlo simulation to account for the different possible mechanisms present in the problem of resuspension of aerosol particles is addressed as an extension of a former model Benitoet al(2016J. Aerosol Sci.10026-37). The re-entrainment of micrometer particles to airflow when detached from a surface by aerodynamic forces is modeled using the similitude of the problem with the desorption process from heterogeneous surfaces. Depending on the relative role of the intervening forces, three main mechanisms for movement initiation can be present:rolling,slidingandlifting-off. Three different transition probabilities are defined for each mechanism and the corresponding transition rates calculated for the kinetic process to be simulated. The decisive factor for the development of the model is to set an appropriate dynamical hierarchy to simulate correctly the evolution of the transition rates as the airflow velocity increases, reflecting the stochastic nature of the process, not always fully captured by other Monte Carlo approaches. The model is applied to spherical and elongated particles on a flat surface, reproducing qualitatively well the experimental trends found by other authors for the case of particles with different shapes. It is also demonstrated that, for elongated particles, the main mechanism assisting the detachment is not rolling but sliding, underscoring the need for an adequate choice of the particles shape and detachment mechanism when looking for the critical conditions for particle removal from surfaces.

Investigating the kinetics of the formation of a C Cottrell atmosphere around a screw dislocation in bcc iron: a mixed-lattice atomistic kinetic Monte-Carlo analysis

We present a mixed-lattice atomistic kinetic Monte-Carlo algorithm (MLKMC) that integrates a rigid-lattice AKMC approach with the kinetic activation-relaxation technique (k-ART), an off-lattice/self-learning AKMC. This approach opens the door to study large and complex systems adapting the cost of identification and evaluation of transition states to the local environment. To demonstrate its capacity, MLKMC is applied to the problem of the formation of a C Cottrell atmosphere decorating a screw dislocation in α-Fe. For this system, transitions that occur near the dislocation core are searched by k-ART, while transitions occurring far from the dislocation are computed before the simulation starts using the rigid-lattice AKMC. This combination of the precision of k-ART and the speed of the rigid-lattice makes it possible to follow the onset of the C Cottrell atmosphere and to identify interesting mechanisms associated with its formation.

Fourier-Spectral Method for the Phase-Field Equations

In this paper, we review the Fourier-spectral method for some phase-field models: Allen–Cahn (AC), Cahn–Hilliard (CH), Swift–Hohenberg (SH), phase-field crystal (PFC), and molecular beam epitaxy (MBE) growth. These equations are very important parabolic partial differential equations and are applicable to many interesting scientific problems. The AC equation is a reaction-diffusion equation modeling anti-phase domain coarsening dynamics. The CH equation models phase segregation of binary mixtures. The SH equation is a popular model for generating patterns in spatially extended dissipative systems. A classical PFC model is originally derived to investigate the dynamics of atomic-scale crystal growth. An isotropic symmetry MBE growth model is originally devised as a method for directly growing high purity epitaxial thin film of molecular beams evaporating on a heated substrate. The Fourier-spectral method is highly accurate and simple to implement. We present a detailed description of the method and explain its connection to MATLAB usage so that the interested readers can use the Fourier-spectral method for their research needs without difficulties. Several standard computational tests are done to demonstrate the performance of the method. Furthermore, we provide the MATLAB codes implementation in the Appendix A.

Kirkendall effect in the two-dimensional lattice-gas model

Customarily, the Kirkendall effect is associated with the vacancy-mediated balance of diffusion fluxes of atoms at the interface between two metals. Nowadays, this effect attracts appreciable attention due to its crucial role in the formation of various hollow nanoparticles via oxidation of metal nanocrystallites. The understanding of the physics behind this effect in general and especially in the case of nanoparticles is still incomplete due to abundant complicating factors. Herein, the Kirkendall effect is illustrated in detail at the generic level by performing two-dimensional (2D) lattice Monte Carlo simulations of diffusion of A and B monomers with attractive nearest-neighbor interaction for times up to 10^{7} Monte Carlo steps. Initially, A monomers are considered to form a close-packed array, while B monomers are in the 2D-gas state. The A-B interaction is assumed to be stronger compared to the other interactions, so that thermodynamically the c(2×2) A-B phase is preferable compared to the close-packed A phase (as in the case of metal oxidation). Depending on the relative rate of the diffusion jumps of A and B monomers, the patterns observed at the late stage of the formation of the mixed phase are shown to range from a single array without voids to those with appreciable disintegration of the initial array. In this way, the model predicts a single array with numerous small voids, a few moderate voids, or a single large void inside.

An empirical potential for simulating vacancy clusters in tungsten

We present an empirical interatomic potential for tungsten, particularly well suited for simulations of vacancy-type defects. We compare energies and structures of vacancy clusters generated with the empirical potential with an extensive new database of values computed using density functional theory, and show that the new potential predicts low-energy defect structures and formation energies with high accuracy. A significant difference to other popular embedded-atom empirical potentials for tungsten is the correct prediction of surface energies. Interstitial properties and short-range pairwise behaviour remain similar to the Ackford-Thetford potential on which it is based, making this potential well-suited to simulations of microstructural evolution following irradiation damage cascades. Using atomistic kinetic Monte Carlo simulations, we predict vacancy cluster dissociation in the range 1100-1300 K, the temperature range generally associated with stage IV recovery.

Thermodynamics of the one-dimensional parallel Kawasaki model: exact solution and mean-field approximations

The adsorption isotherm for the recently proposed parallel Kawasaki (PK) lattice-gas model [Phys. Rev. E 88, 062144 (2013)] is calculated exactly in one dimension. To do so, a third-order difference equation for the grand-canonical partition function is derived and solved analytically. In the present version of the PK model, the attraction and repulsion effects between two neighboring particles and between a particle and a neighboring empty site are ruled, respectively, by the dimensionless parameters ϕ and θ. We discuss the inflections induced in the isotherms by situations of high repulsion, the role played by finite lattice sizes in the emergence of substeps, and the adequacy of the two most widely used mean-field approximations in lattice gases, namely, the Bragg-Williams and the Bethe-Peierls approximations.

Conciliating synchronicity with spatial discretization, exclusion, interactions, and detailed balance

The construction of a discrete stochastic system of interacting particles that evolves through a fully synchronous evolution rule while satisfying detailed balance is a highly demanding task. As a consequence, the presence of nontrivial interaction fields can make synchronicity and thermodynamic equilibrium look as two conflicting counterparts. We show that, with the proper prescriptions, the process of migration of particles in a lattice of mutually exclusive nodes can be simulated with a fully synchronous algorithm, which we call parallel Kawasaki dynamics (PKD), that incorporates site exclusion, local interactions, and detailed balance without the need of system partitioning schemes. We show that the underlying pseudo-Hamiltonian (which is derived from the PKD dynamics instead of being assumed a priori as usual in a sequential Monte Carlo scheme) is temperature dependent and causes the resulting equilibrium properties to differ substantially from the conventional hopping model when the system is near critical conditions.

Water formation at low temperatures by surface O2 hydrogenation III: Monte Carlo simulation

Water is the most abundant molecule found in interstellar icy mantles. In space it is thought to be efficiently formed on the surfaces of dust grains through successive hydrogenation of O, O2 and O3. The underlying physico-chemical mechanisms have been studied experimentally in the past decade and in this paper we extend this work theoretically, using Continuous-Time Random-Walk Monte Carlo simulations to disentangle the different processes at play during hydrogenation of molecular oxygen. CTRW-MC offers a kinetic approach to compare simulated surface abundances of different species to the experimental values. For this purpose, the results of four key experiments-sequential hydrogenation as well as co-deposition experiments at 15 and 25 K-are selected that serve as a reference throughout the modeling stage. The aim is to reproduce all four experiments with a single set of parameters. Input for the simulations consists of binding energies as well as reaction barriers (activation energies). In order to understand the influence of the parameters separately, we vary a single process rate at a time. Our main findings are: (i) The key reactions for the hydrogenation route starting from O2 are H + O2, H + HO2, OH + OH, H + H2O2, H + OH. (ii) The relatively high experimental abundance of H2O2 is due to its slow destruction. (iii) The large consumption of O2 at a temperature of 25 K is due to a high hydrogen diffusion rate. (iv) The diffusion of radicals plays an important role in the full reaction network. The resulting set of 'best fit' parameters is presented and discussed for use in future astrochemical modeling.

A kinetic Monte Carlo study of Pt on Au(111) with applications to bimetallic catalysis

Pt-decorated Au nanostructures and bimetallic PtAu nanoparticles have been shown to act as catalysts. Consequently we investigate the formation of extended Pt decorations of an Au island edge on Au(111) as possible catalysts. The investigation is by simulation using the kinetic Monte Carlo method. The effects of varying the rate of deposition of Pt atoms and the simulation temperature on the morphology of the resulting Pt nanostructures were investigated. The thickness and roughness of the nanostructures are readily influenced, with temperature being the more important factor. A combination of both high temperature and low deposition rate was the most effective at reducing the roughness. PtAu alloying in the Au island edge was identified. This work is (to the best of our knowledge) the first kinetic Monte Carlo simulation study of the formation of Pt nanostructures on Au. We demonstrate how the morphology of the Pt nanostructures can be controlled. The nanostructures studied here, comprising an adjustable mix of Pt overlayers and novel 1D PtAu surface alloys, are expected to be of considerable interest as potential bimetallic nano-catalysts.

Epitaxial growth and the art of computer simulations

The results of kinetic simulations of the aggregates formed during the deposition of atoms on a semiconductor surface are reviewed. Because the kinetic parameters are poorly known and the accuracy of the existing interatomic potentials has not been sufficiently tested, the goal has been to reach a qualitative understanding of the formation of unusual patterns during growth, such as the segregation of aluminum during the growth of aluminum-gallium-arsenide (AlGaAs) coherent tilted superlattices and the formation of thin, long, and parallel islands during the deposition of Si on an Si(100) surface. Kinetic mechanisms for these phenomena are proposed.

Hard versus soft dynamics for adsorption-desorption kinetics: Exact results in one-dimension

The adsorption-desorption kinetics is discussed in the framework of the kinetic lattice-gas model. The master equation formalism has been introduced to describe the evolution of the system, where the transition probabilities are written as an expansion of the occupation configurations of all neighboring sites. Since the detailed balance principle determines half of the coefficients that arise from the expansion, it is necessary to introduce ad hoc, a dynamic scheme to get the rest of them. Three schemes of the so-called hard dynamics, in which the probability of transition from single site cannot be factored into a part which depends only on the interaction energy and one that only depends on the field energy, and five schemes of the so-called soft dynamics, in which this factorization is possible, were introduced for this purpose. It is observed that for the hard dynamic schemes, the equilibrium and nonequilibrium observables, such as adsorption isotherms, sticking coefficients, and thermal desorption spectra, have a normal or physical sustainable behavior. While for the soft dynamics schemes, with the exception of the transition state theory, the equilibrium and nonequilibrium observables have several problems. Some of them can be regarded as abnormal behavior.

Continuous and discrete modeling of the decay of two-dimensional nanostructures

In this work we review some recent research on the surface diffusion-mediated decay of two-dimensional nanostructures. These results include both a continuous, vectorial model and a discrete kinetic Monte Carlo approach. Predictions from the standard linear continuous theory of surface-diffusion-driven interface decay are contrasted with simulational results both from kinetic and morphological points of view. In particular, we focused our attention on high-aspect-ratio nanostructures, where strong deviations from linear theory take place, including nonexponential amplitude decay and the emergence of several interesting nanostructures such as overhangs developing, nanoislands and nanovoids formation, loss of convexity, nanostructures-pinch off and nanostructures-break off, etc.

Additional constraints in adsorption-desorption kinetics

In this work, the adsorption-desorption kinetic in the framework of the lattice gas model is analyzed. The transition probabilities are written as an expansion of the occupation configurations. Due to that, the detail balance principle determine half of the adsorption A{i} and desorption D{i} coefficients, consequently, different functional relations between them are proposed. Introducing additional constrains, it is demonstrated that when those coefficients are linearly related through a parameter gamma , there are values of lateral interaction V , that lead to anomalous behavior in the adsorption isotherms, the sticking coefficient and the thermal programmed desorption spectra. Diagrams for the allowed values of V and gamma are also shown. Alternatively, a more reliable formulation for the adsorption desorption kinetic based on the transition state theory is introduced. In such way the equilibrium and non equilibrium observables do not present anomalous or inconsistent behavior.

Spontaneous nanoripple formation on metallic templates

Nanoripple structures spontaneously formed at room temperature during chemical and electrochemical deposition of metals, semiconductors, and alloys on gold and copper templates, patterned with nanocavities, have been studied by atomic force microscopy (AFM) and scanning tunneling microscopy (STM). Annealing the templates at approximately equal to 373 K also results in ripple formation. Both experimental results and modeling, including anisotropic surface diffusion, demonstrate that nanocavity size in the template determines the ripple wavelength and amplitude, prior to a final stage of coarsening. Therefore, an ordered array of "nanodefects" introduced in the substrate is able to guide the self-organization of these nanofeatures during their growth, creating the possibility for nanofabrication of parallel interconnections with adjustable periodicity. Ripples are robust nanostructures that can in turn be used as templates for the preparation of hybrid nanostructured surfaces with specific physical properties.

Front instabilities in evaporatively dewetting nanofluids

Various experimental settings that involve drying solutions or suspensions of nanoparticles-often called nanofluids-have recently been used to produce structured nanoparticle layers. In addition to the formation of polygonal networks and spinodal-like patterns, the occurrence of branched structures has been reported. After reviewing the experimental results we use a modified version of the Monte Carlo model first introduced by Rabani [Nature 426, 271 (2003)] to study structure formation in evaporating films of nanoparticle solutions for the case that all structuring is driven by the interplay of evaporating solvent and diffusing nanoparticles. After introducing the model and its general behavior we focus on receding dewetting fronts which are initially straight but develop a transverse fingering instability. We analyze the dependence of the characteristics of the resulting branching patterns on the driving effective chemical potential, the mobility and concentration of the nanoparticles, and the interaction strength between liquid and nanoparticles. This allows us to understand the underlying instability mechanism.

Kinetic Monte Carlo study on the decay of two-dimensional nanostructures: influence of the activation energy of diffusion on kinetic and morphological properties

Surface diffusion-mediated decay of two-dimensional nanostructures is studied by means of a kinetic Monte Carlo model. We consider several possible choices for the activation energies associated with possible diffusion paths, including simple phenomenological models, as well as results provided by the embedded atom model. Numerical results show that kinetic aspects of the evolution are quite sensitive to the activation energy model chosen. In contrast, morphological aspects of the evolution exhibit a similar qualitative behavior, irrespective of the activation energy model considered. It is shown that this common behavior closely agrees with predictions from the continuous theory of surface diffusion-driven interface decay.

Kinetic Monte Carlo modeling of chemical reactions coupled with heat transfer

In this paper, we describe two types of effective events for describing heat transfer in a kinetic Monte Carlo (KMC) simulation that may involve stochastic chemical reactions. Simulations employing these events are referred to as KMC-TBT and KMC-PHE. In KMC-TBT, heat transfer is modeled as the stochastic transfer of "thermal bits" between adjacent grid points. In KMC-PHE, heat transfer is modeled by integrating the Poisson heat equation for a short time. Either approach is capable of capturing the time dependent system behavior exactly. Both KMC-PHE and KMC-TBT are validated by simulating pure heat transfer in a rod and a square and modeling a heated desorption problem where exact numerical results are available. KMC-PHE is much faster than KMC-TBT and is used to study the endothermic desorption of a lattice gas. Interesting findings from this study are reported.

Lattice gas modeling of nanowhisker growth

Building upon the ideas of Gerischer et al., we have developed a cellular automaton for the growth dynamics of nanowhiskers. We present two models for the whisker growth. The first is a simple extension of the surface model, whereas the second includes diffusion on the rim of the whiskers. Results for one-dimensional calculations are presented and discussed, together with a comparison between the two models and with experimental results as well.

Computer simulation of adsorption kinetics of surfactants on solid surfaces

Adsorption kinetics of surfactants on solid surfaces has been studied by using computer simulation. Both bulk surfactant concentration and diffusion region are explicitly integrated in our model. Depending on the head-surface interaction, our simulation results indicate that there exist two different kinetic modes in adsorption process of surfactants on solid surfaces. One is the four-regime mode and the other is step-wise mode. For the strongly attractive head-surface interaction, four distinct regimes of surfactant adsorption are found: a diffusion-controlled regime, a self-assembly controlled regime, an intermediate coverage regime and a saturated regime. In particular, the adsorption in second regime displays a power-law time dependence with an exponent unrelated to bulk concentrations and diffusion coefficients. While for the weaker adsorption surfaces, the step-wise mode is found. The mode includes a low-coverage nucleation regime and the saturated regime after a sudden aggregation of surfactants on the substrates which occurs stochastically. Besides the head-surface interaction, in this work, the effects of surfactant diffusivity, bulk concentration, the length of diffusion zone and surfactant architecture on the adsorption kinetics are also considered. The simulated adsorption kinetics is compared qualitatively with experimental results.

Continuum mesoscopic framework for multiple interacting species and processes on multiple site types and/or crystallographic planes

While recently derived continuum mesoscopic equations successfully bridge the gap between microscopic and macroscopic physics, so far they have been derived only for simple lattice models. In this paper, general deterministic continuum mesoscopic equations are derived rigorously via nonequilibrium statistical mechanics to account for multiple interacting surface species and multiple processes on multiple site types and/or different crystallographic planes. Adsorption, desorption, reaction, and surface diffusion are modeled. It is demonstrated that contrary to conventional phenomenological continuum models, microscopic physics, such as the interaction potential, determines the final form of the mesoscopic equation. Models of single component diffusion and binary diffusion of interacting particles on single-type site lattice and of single component diffusion on complex microporous materials' lattices consisting of two types of sites are derived, as illustrations of the mesoscopic framework. Simplification of the diffusion mesoscopic model illustrates the relation to phenomenological models, such as the Fickian and Maxwell-Stefan transport models. It is demonstrated that the mesoscopic equations are in good agreement with lattice kinetic Monte Carlo simulations for several prototype examples studied.

CO oxidation reaction on Pt(111) studied by the dynamic Monte Carlo method including lateral interactions of adsorbates

The dynamics of adsorbate structures during CO oxidation on Pt(111) surfaces and its effects on the reaction were studied by the dynamic Monte Carlo method including lateral interactions of adsorbates. The lateral interaction energies between adsorbed species were calculated by the density functional theory method. Dynamic Monte Carlo simulations were performed for the oxidation reaction over a mesoscopic scale, where the experimentally determined activation energies of elementary paths were altered by the calculated lateral interaction energies. The simulated results reproduced the characteristics of the microscopic and mesoscopic scale adsorbate structures formed during the reaction, and revealed that the complicated reaction kinetics is comprehensively explained by a single reaction path affected by the surrounding adsorbates. We also propose from the simulations that weakly adsorbed CO molecules at domain boundaries promote the island-periphery specific reaction.

Coarse-grained computations for a micellar system

We establish, through coarse-grained computation, a connection between traditional, continuum numerical algorithms (initial value problems as well as fixed point algorithms), and atomistic simulations of the Larson model of micelle formation. The procedure hinges on the (expected) evolution of a few slow, coarse-grained mesoscopic observables of the Monte Carlo simulation, and on (computational) time scale separation between these and the remaining "slaved," fast variables. Short bursts of appropriately initialized atomistic simulation are used to estimate the (coarse grained, deterministic) local dynamics of the evolution of the observables. These estimates are then in turn used to accelerate the evolution to computational stationarity through traditional continuum algorithms (forward Euler integration, Newton-Raphson fixed point computation). This "equation-free" framework, bypassing the derivation of explicit, closed equations for the observables (e.g., equations of state), may provide a computational bridge between direct atomistic/stochastic simulation and the analysis of its macroscopic, system-level consequences.

Irreversible adsorption of tethered chains at substrates: Monte Carlo study

The irreversible adsorption of single chains grafted with one end to the surface is studied using scaling arguments and computer simulations. We introduce a two-phase model, in which the chain is described by an adsorbate portion and a corona portion formed by nonadsorbed monomers. The adsorption process can be viewed as consisting of a main stage, during which monomers join by "zipping" (along their order in the chain) the surface, and a late stage, in which the remaining corona collapses on the surface. Based on our model we derive a scaling relation for the time of adsorption t(M) as a function of the number M of adsorbed monomers; t(M) follows a power law, M(alpha), with alpha > 1. We find that alpha is related to the Flory exponent nu by alpha = 1 + nu. Using further scaling arguments we derive relations between the overall time of adsorption, the characteristic time of adsorption (given by the crossover time between the main and the last stage of adsorption), and the chain length. To support our analysis we perform Monte Carlo simulations using the bond fluctuation model. In particular, the sequence of adsorption events is very well reproduced by the simulations, and an analysis of the various density profiles supports our theoretical model. Especially the loop formation during adsorption clearly shows that the growth of the adsorbate is dominated by zipping. The simulations are also in almost quantitative agreement with our theoretical scaling analysis, showing that here the assumption of a linear relation between Monte Carlo steps and time is well obeyed. We conclude by also discussing the geometrical shape of the adsorbate.

Water formation reaction on Pt(111): Role of the proton transfer

The catalytic water formation reaction on Pt(111) was investigated by kinetic Monte Carlo simulations, where the interaction energy between reaction species and the high mobility of H(2)O molecule was considered. Results obtained clearly reproduce the scanning tunneling microscopy images which show that the reaction proceeds via traveling the reaction fronts on the O-covered Pt(111) surface by creating H(2)O islands backwards. The reaction front is a mixed layer of OH and H(2)O with a (square root 3 x square root 3)R30(o) structure. Coverage change during the reaction is also reproduced in which the reaction consists of three characteristic processes, as observed by the previous experiments. The simulation also revealed that the proton transfer from H(2)O to OH plays an important role to propagate the water formation.

Mechanism of the CO oxidation reaction on O-precovered Pt(111) surfaces studied with near-edge x-ray absorption fine structure spectroscopy

The mechanism of CO oxidation reaction on oxygen-precovered Pt(111) surfaces has been studied by using time-resolved near-edge x-ray absorption fine structure spectroscopy. The whole reaction process is composed of two distinct paths: (1) a reaction of isolated oxygen atoms with adsorbed CO, and (2) a reaction of island-periphery oxygen atoms after the CO saturation. CO coadsorption plays a role to induce the dynamic change in spatial distribution of O atoms, which switches over the two reaction paths. These mechanisms were confirmed by kinetic Monte Carlo simulations. The effect of coadsorbed water in the reaction mechanism was also examined.

Effects of lateral diffusion on morphology and dynamics of a microscopic lattice-gas model of pulsed electrodeposition

The influence of nearest-neighbor diffusion on the decay of a metastable low-coverage phase (monolayer adsorption) in a square lattice-gas model of electrochemical metal deposition is investigated by kinetic Monte Carlo simulations. The phase-transformation dynamics are compared to the well-established Kolmogorov-Johnson-Mehl-Avrami theory. The phase transformation is accelerated by diffusion, but remains in accord with the theory for continuous nucleation up to moderate diffusion rates. At very high diffusion rates the phase-transformation kinetic shows a crossover to instantaneous nucleation. Then, the probability of medium-sized clusters is reduced in favor of large clusters. Upon reversal of the supersaturation, the adsorbate desorbs, but large clusters still tend to grow during the initial stages of desorption. Calculation of the free energy of subcritical clusters by enumeration of lattice animals yields a quasiequilibrium distribution which is in reasonable agreement with the simulation results. This is an improvement relative to classical droplet theory, which fails to describe the distributions, since the macroscopic surface tension is a bad approximation for small clusters.

Oxygen island formation on Pt(111) studied by dynamic Monte Carlo simulation

The formation of oxygen islands on the Pt(111) surface has been studied as a function of temperature by low energy electron diffraction (LEED) experiments and dynamic Monte Carlo (DMC) simulations. By raising the temperature, the (2 x 2) LEED spot intensity increases gradually and decays after a peak at around 255 K (T(p)) with full width of half maximum of 160 K. This behavior is interpreted by DMC simulations with the kinematical LEED analysis. In the DMC simulation, an oxygen atom hops to the neighboring site via the activation barrier of the saddle point. The potential energies at initial, saddle, and final points are changed at each hopping event depending on the surrounding oxygen atoms. By comparing the observed T(p) with the simulated one, the interaction energy E of oxygen atoms on Pt(111) was determined to be 25+/-3 meV at 2a(0). The DMC simulations visualize how the oxygen islands are formed and collapse on Pt(111) with increase of the temperature and well reproduce the surface configurations observed by scanning tunneling microscopy.

Low-temperature nucleation in a kinetic Ising model under different stochastic dynamics with local energy barriers

Using both analytical and simulational methods, we study low-temperature nucleation rates in kinetic Ising lattice-gas models that evolve under two different Arrhenius dynamics that interpose between the Ising states a transition state representing a local energy barrier. The two dynamics are the transition-state approximation [T. Ala-Nissila, J. Kjoll, and S. C. Ying, Phys. Rev. B 46, 846 (1992)] and the one-step dynamic [H. C. Kang and W. H. Weinberg, J. Chem. Phys. 90, 2824 (1989)]. Even though they both obey detailed balance and are here applied to a situation that does not conserve the order parameter, we find significant differences between the nucleation rates observed with the two dynamics, and between them and the standard Glauber dynamic [R. J. Glauber, J. Math. Phys. 4, 294 (1963)], which does not contain transition states. Our results show that great care must be exercised when devising kinetic Monte Carlo transition rates for specific physical or chemical systems.

Monte Carlo simulation for the formation of a mixed crystal from two solids in contact

The study focuses on nucleation and growth of a binary mixed crystal phase from two pure crystals in contact. Monte Carlo simulations of this process are conducted, with the dynamics proceeding via activated atom-vacancy exchanges. Intermolecular interactions, ranging up to next-nearest neighbors, are of size typical of hydrogen bonded systems. The process is driven by the formation of strong AB bonds at the expense of weaker AA and BB bonds. In the resulting model, the material is channeled and transported through the mixed phase crust along antiphase boundaries. The flow of molecules through the channels is directed, due to molecular energy lowering via gradual acquisition of an increasing number of nearest neighbors of the second species. On the other hand, defect motion is quasirandom. The model accounts partially for the t(1/alpha) (alpha>3) time dependence observed for conversion of nanoparticles of HBr dihydrate to monohydrate, by exposure to acid adsorbate.

Comparison of kinetic Monte Carlo and molecular dynamics simulations of diffusion in a model glass former

We present results from kinetic Monte Carlo (KMC) simulations of diffusion in a model glass former. We find that the diffusion constants obtained from KMC simulations have Arrhenius temperature dependence, while the correct behavior, obtained from molecular dynamics simulations, can be super-Arrhenius. We conclude that the discrepancy is due to undersampling of higher-lying local minima in the KMC runs. We suggest that the relevant connectivity of minima on the potential energy surface is proportional to the energy density of the local minima, which determines the "inherent structure entropy." The changing connectivity with potential energy may produce a correlation between dynamics and thermodynamics.

Deposition and reentrainment of Brownian particles in porous media under unfavorable chemical conditions: some concepts and applications

The deposition and reentrainment of particles in porous media have been examined theoretically and experimentally. A Brownian Dynamics/Monte Carlo (MC/BD) model has been developed that simulates the movement of Brownian particles near a collector under "unfavorable" chemical conditions and allows deposition in primary and secondary minima. A simple Maxwell approach has been used to estimate particle attachment efficiency by assuming deposition in the secondary minimum and calculating the probability of reentrainment. The MC/BD simulations and the Maxwell calculations support an alternative view of the deposition and reentrainment of Brownian particles under unfavorable chemical conditions. These calculations indicate that deposition into and subsequent release from secondary minima can explain reported discrepancies between classic model predictions that assume irreversible deposition in a primary well and experimentally determined deposition efficiencies that are orders of magnitude larger than Interaction Force Boundary Layer (IFBL) predictions. The commonly used IFBL model, for example, is based on the notion of transport over an energy barrier into the primary well and does not address contributions of secondary minimum deposition. A simple Maxwell model based on deposition into and reentrainment from secondary minima is much more accurate in predicting deposition rates for column experiments at low ionic strengths. It also greatly reduces the substantial particle size effects inherent in IFBL models, wherein particle attachment rates are predicted to decrease significantly with increasing particle size. This view is consistent with recent work by others addressing the composition and structure of the first few nanometers at solid-water interfaces including research on modeling water at solid-liquid interfaces, surface speciation, interfacial force measurements, and the rheological properties of concentrated suspensions. It follows that deposition under these conditions will depend on the depth of the secondary minimum and that some transition between secondary and primary depositions should occur when the height of the energy barrier is on the order of several kT. When deposition in secondary minima predominates, observed deposition should increase with increasing ionic strength, particle size, and Hamaker constant. Since an equilibrium can develop between bound and bulk particles, the collision efficiency [alpha] can no longer be considered a constant for a given physical and chemical system. Rather, in many cases it can decrease over time until it eventually reaches zero as equilibrium is established.

Microstructure and velocity of field-driven solid-on-solid interfaces: analytic approximations and numerical results

The local structure of a solid-on-solid interface in a two-dimensional kinetic Ising ferromagnet or attractive lattice-gas model with single-spin-flip Glauber dynamics, which is driven far from equilibrium by an applied field or chemical potential, is studied by an analytic mean-field, nonlinear-response theory [P. A. Rikvold and M. Kolesik, J. Stat. Phys. 100, 377 (2000)], and by dynamic Monte Carlo simulations. The probability density of the height of an individual step in the surface is obtained, both analytically and by simulation. The width of the probability density is found to increase dramatically with the magnitude of the applied field, with close agreement between the theoretical predictions and the simulation results. Excellent agreement between theory and simulations is also found for the field dependence and anisotropy of the interface velocity. The joint distribution of nearest-neighbor step heights is obtained by simulation. It shows increasing correlations with increasing field, similar to the skewness observed in other examples of growing surfaces.

Self-organized nanostructures in surface chemical reactions: Mechanisms and mesoscopic modeling

Nanoscale patterns can form in reactive adsorbates on catalytic surfaces as a result of attractive lateral interactions. These structures can be described within a mesoscopic theory that is derived by coarse graining the microscopic master equation thus providing a link between microscopic lattice models and reaction-diffusion equations. Such mesoscopic models allow to systematically investigate mechanisms responsible for the formation of nanoscale nonequilibrium patterns in reactive condensed matter. We have found that stationary and traveling nanostructures may result from the interplay of the attractive lateral interactions and nonequilibrium reactions. Besides reviewing these results, a detailed investigation of a single reactive adsorbate in the presence of attractive lateral interactions and global coupling through the gas phase is presented. Finally, it is outlined how a mesoscopic theory should be constructed for a particular scanning tunneling microscopy experiment [the oxidation of hydrogen on a Pt(111) surface] in order to overcome the failure of a corresponding reaction-diffusion model to quantitatively reproduce the experiments. (c) 2002 American Institute of Physics.