Analysis of nucleation ability of cluster configurations with Monte Carlo simulations of argon

We determine the nucleation ability of argon clusters from Monte Carlo simulations. The nucleation rate appears to be defined by a sole characteristic of the clusters, namely, the stability. The stability is calculated as the ratio of grand canonical growth and decay rates and can be assigned to individual cluster configurations. We study the connection between the stability of the cluster configurations and their volume and total potential energy. Neither the potential energy nor the volume of a cluster configuration has a clear relation to its stability, and thus to the nucleation ability. On the other hand, we show that it is possible to use a specific volume for each cluster size to calculate the work of the cluster formation. These clusters with a unique volume have the same average stability as the full set of clusters. Our simulation method allows us to study the effect of possible deviations from equilibrium in the cluster configuration distributions. We argue that the nucleation process itself can produce a source for such a deviation. We show that even a small deviation from equilibrium in the cluster configuration distribution can lead to a dramatic deceleration of the nucleation rate. Although our simulations may overestimate the magnitude of the effect, they give qualitative estimates for its importance.     

Kinetic Monte Carlo simulations of nucleation and growth in electrodeposition

Nucleation and growth during bulk electrodeposition is studied using kinetic Monte Carlo (KMC) simulations. Ion transport in solution is modeled using Brownian dynamics, and the kinetics of nucleation and growth are dependent on the probabilities of metal-on-substrate and metal-on-metal deposition. Using this approach, we make no assumptions about the nucleation rate, island density, or island distribution. The influence of the attachment probabilities and concentration on the time-dependent island density and current transients is reported. Various models have been assessed by recovering the nucleation rate and island density from the current-time transients.     

Grand canonical Monte Carlo simulations of water in protein environments

The grand canonical simulation algorithm is considered as a general methodology to sample the configuration of water molecules confined within protein environments. First, the probability distribution of the number of water molecules and their configuration in a region of interest for biochemical simulations, such as the active site of a protein, is derived by considering a finite subvolume in open equilibrium with a large system serving as a bulk reservoir. It is shown that the influence of the bulk reservoir can be represented as a many-body potential of mean force acting on the atoms located inside the subvolume. The grand canonical Monte Carlo (GCMC) algorithm, augmented by a number of technical advances to increase the acceptance of insertion attempts, is implemented, and tested for simple systems. In particular, the method is illustrated in the case of a pure water box with periodic boundary conditions. In addition, finite spherical systems of pure water and containing a dialanine peptide, are simulated with GCMC while the influence of the surrounding infinite bulk is incorporated using the generalized solvent boundary potential [W. Im, S. Berneche, and B. Roux, J. Chem. Phys. 114, 2924 (2001)]. As a last illustration of water confined in the interior of a protein, the hydration of the central cavity of the KcsA potassium channel is simulated.     

Surface tension of water and acid gases from Monte Carlo simulations

We report direct Monte Carlo (MC) simulations on the liquid-vapor interfaces of pure water, carbon dioxide, and hydrogen sulfide. In the case of water, the recent TIP4P/2005 potential model used with the MC method is shown to reproduce the experimental surface tension and to accurately describe the coexistence curves. The agreement with experiments is also excellent for CO(2) and H(2)S with standard nonpolarizable models. The surface tensions are calculated by using the mechanical and the thermodynamic definitions via profiles along the direction normal to the surface. We also discuss the different contributions to the surface tension due to the repulsion-dispersion and electrostatic interactions. The different profiles of these contributions are proposed in the case of water.     

Monte Carlo simulation study of droplet nucleation

A new rigorous Monte Carlo simulation approach is employed to study nucleation barriers for droplets in Lennard-Jones fluid. Using the gauge cell method we generate the excess isotherm of critical clusters in the size range from two to six molecular diameters. The ghost field method is employed to compute the cluster free energy and the nucleation barrier with desired precision of (1-2)kT. Based on quantitative results obtained by Monte Carlo simulations, we access the limits of applicability of the capillarity approximation of the classical nucleation theory and the Tolman equation. We show that the capillarity approximation corrected for vapor nonideality and liquid compressibility provides a reasonable assessment for the size of critical clusters in Lennard-Jones fluid; however, its accuracy is not sufficient to predict the nucleation barriers for making practical estimates of the rate of nucleation. The established dependence of the droplet surface tension on the droplet size cannot be approximated by the Tolman equation for small droplets of radius less than four molecular diameters. We confirm the conclusion of ten Wolde and Frenkel [J. Chem. Phys. 109, 9901 (1998)] that integration of the normal component of the Irving-Kirkwood pressure tensor severely underestimates the nucleation barriers for small clusters.     

Monte Carlo computer simulations and electron microscopy of colloidal cluster formation via emulsion droplet evaporation

We consider a theoretical model for a binary mixture of colloidal particles and spherical emulsion droplets. The hard sphere colloids interact via additional short-ranged attraction and long-ranged repulsion. The droplet-colloid interaction is an attractive well at the droplet surface, which induces the Pickering effect. The droplet-droplet interaction is a hard-core interaction. The droplets shrink in time, which models the evaporation of the dispersed (oil) phase, and we use Monte Carlo simulations for the dynamics. In the experiments, polystyrene particles were assembled using toluene droplets as templates. The arrangement of the particles on the surface of the droplets was analyzed with cryogenic field emission scanning electron microscopy. Before evaporation of the oil, the particle distribution on the droplet surface was found to be disordered in experiments, and the simulations reproduce this effect. After complete evaporation, ordered colloidal clusters are formed that are stable against thermal fluctuations. Both in the simulations and with field emission scanning electron microscopy, we find stable packings that range from doublets, triplets, and tetrahedra to complex polyhedra of colloids. The simulated cluster structures and size distribution agree well with the experimental results. We also simulate hierarchical assembly in a mixture of tetrahedral clusters and droplets, and find supercluster structures with morphologies that are more complex than those of clusters of single particles.     

Parallel Markov chain Monte Carlo simulations

With strict detailed balance, parallel Monte Carlo simulation through domain decomposition cannot be validated with conventional Markov chain theory, which describes an intrinsically serial stochastic process. In this work, the parallel version of Markov chain theory and its role in accelerating Monte Carlo simulations via cluster computing is explored. It is shown that sequential updating is the key to improving efficiency in parallel simulations through domain decomposition. A parallel scheme is proposed to reduce interprocessor communication or synchronization, which slows down parallel simulation with increasing number of processors. Parallel simulation results for the two-dimensional lattice gas model show substantial reduction of simulation time for systems of moderate and large size.     

Reactive Monte Carlo and grand-canonical Monte Carlo simulations of the propene metathesis reaction system

The influence of silicalite-1 pores on the reaction equilibria and the selectivity of the propene metathesis reaction system in the temperature range between 300 and 600 K and the pressure range from 0.5 to 7 bars has been investigated with molecular simulations. The reactive Monte Carlo (RxMC) technique was applied for bulk-phase simulations in the isobaric-isothermal ensemble and for two phase systems in the Gibbs ensemble. Additionally, Monte Carlo simulations in the grand-canonical ensemble (GCMC) have been carried out with and without using the RxMC technique. The various simulation procedures were combined with the configurational-bias Monte Carlo approach. It was found that the GCMC simulations are superior to the Gibbs ensemble simulations for reactions where the bulk-phase equilibrium can be calculated in advance and does not have to be simulated simultaneously with the molecules inside the pore. The confined environment can increase the conversion significantly. A large change in selectivity between the bulk phase and the pore phase is observed. Pressure and temperature have strong influences on both conversion and selectivity. At low pressure and temperature both conversion and selectivity have the highest values. The effect of confinement decreases as the temperature increases.     

Convergence of Monte Carlo simulations of liquid water in the NPT ensemble

Long Monte Carlo simulations of liquid water at 25° and 1 atm have been carried out to study the convergence characteristics of the calculations. The recently reported TIPS2 potential was employed with system sizes of 125 and 216 monomers. The enthalpy, volume and radial distribution functions converge rapidly and show little size dependence. However, the rates of convergence are much slower for the fluctuation properties and are in the order: heat capacity (Cp) ? isothermal compressibility (?) ? coefficient of thermal expansion (α). In fact,the weak coupling of the enthalpy and volume allows only crude estimates for α. In addition, the estimation of statistical error bounds for the thermodynamic properties is analyzed. It is found that very long (2500-3500 k) simulations are needed to yield valid estimates of the errors for the enthalpy, volume and C_p, while the erros for ? and α would still be elusive.     

Monte Carlo simulations of equilibrium solubilities and structure of water in n-alkanes and polyethylene

Gibbs ensemble Monte Carlo methods based on a force field that combines the simple point charge [Berendsen et al., in Intermolecular Forces, edited by Pullman (Reidel, Dordrecht, 1981), p. 331] and transferable potentials for phase equilibria [Martin and Siepmann, J. Phys. Chem. B 102, 2659 (1998)] models were used to study the equilibrium properties of binary systems consisting of water and n-alkanes with chain lengths from hexane to hexadecane. In addition, systems where extended linear alkane chains (up to 300 carbon units long) were used to represent amorphous polyethylene were simulated in the presence of water using a connectivity altering osmotic Gibbs ensemble. In these simulations the equilibrium between a liquid water phase and a polymer phase into which water was inserted was studied. The predicted solubilities, which were determined between 350 and 550 K, are in good agreement with experiment, where experimental results are available, and the density of water molecules in the hydrocarbons is approximately 63% as high as in saturated water vapor under the same conditions. At the lower temperatures most of the water exists as monomers; increasing the temperature leads to an increase in the density of water in the alkane phase and hence in the fraction of molecules that participate in clusters. Dimers are the most prevalent clusters in all hydrocarbons and at all temperatures studied, and the fraction of clusters of given size decrease with increasing cluster size. A large fraction of trimers, tetramers, and pentamers, which are the cluster sizes for which topologies have been studied, are cyclic at low temperatures, but at higher temperatures linear structures predominate. The same properties are observed for pure water vapor clusters in equilibrium with the liquid phase, showing that the cluster topologies are not significantly affected by the surrounding hydrocarbon.     

Monte Carlo simulations of low background detectors

An implementation of the Electron Gamma Shower 4 code (EGS4) has been developed to allow convenient simulation of typical gamma ray measurement systems. Coincidence gamma rays, beta spectra, and angular correlations have been added to adequately simulate a complete nuclear decay and provide corrections to experimentally determined detector efficiencies. This code has been used to strip certain low-background spectra for the purpose of extremely low-level assay. Monte Carlo calculations of this sort can be extremely successful since low background detectors are usually free of significant contributions from poorly localized radiation sources, such as cosmic muons, secondary cosmic neutrons, and radioactive construction or shielding materials. Previously, validation of this code has been obtained from a series of comparisons between measurements and blind calculations. An example of the application of this code to an exceedingly low background spectrum stripping will be presented.Pacific Northwest Laboratory is operated by Battelle Memorial Institute for the US Department of Energy under Contract DE-AC06-76RLO 1830.     

Dynamic Monte Carlo simulations of anisotropic colloids

We put forward a simple procedure for extracting dynamical information from Monte Carlo simulations, by appropriate matching of the short-time diffusion tensor with its infinite-dilution limit counterpart, which is supposed to be known. This approach - discarding hydrodynamics interactions - first allows us to improve the efficiency of previous dynamic Monte Carlo algorithms for spherical Brownian particles. In the second step, we address the case of anisotropic colloids with orientational degrees of freedom. As an illustration, we present a detailed study of the dynamics of thin platelets, with emphasis on long-time diffusion and orientational correlations.     

Thermodynamic properties of van der Waals fluids from Monte Carlo simulations and perturbative Monte Carlo theory

Computer simulations have been performed for fluids with van der Waals potential, that is, hard spheres with attractive inverse power tails, to determine the equation of state and the excess energy. On the other hand, the first- and second-order perturbative contributions to the energy and the zero- and first-order perturbative contributions to the compressibility factor have been determined too from Monte Carlo simulations performed on the reference hard-sphere system. The aim was to test the reliability of this "exact" perturbation theory. It has been found that the results obtained from the Monte Carlo perturbation theory for these two thermodynamic properties agree well with the direct Monte Carlo simulations. Moreover, it has been found that results from the Barker-Henderson [J. Chem. Phys. 47, 2856 (1967)] perturbation theory are in good agreement with those from the exact perturbation theory.     

Canonical and microcanonical Monte Carlo simulations of lattice-gas mixtures

We propose strict canonical and microcanonical Monte Carlo algorithms for an arbitrary lattice-gas binary mixture. We deduce formulas that allow us to obtain field quantities over the ensembles in which their conjugate extensive quantities are conserved. As an example, we have considered a lattice-gas mixture that is equivalent to the spin-1 Blume-Emery-Griffiths model [Phys. Rev. A 4, 1071 (1971)]. For a finite system and near a phase coexistence, the field as a function of its extensive conjugate shows a loop that disappears in the thermodynamic limit giving rise to the usual tie line. The first-order phase transition was determined by the use of three criteria.     

Titration of hydrophobic polyelectrolytes using Monte Carlo simulations

The conformation and titration curves of weak (or annealed) hydrophobic polyelectrolytes have been examined using Monte Carlo simulations with screened Coulomb potentials in the grand canonical ensemble. The influence of the ionic concentration pH and presence of hydrophobic interactions has been systematically investigated. A large number of conformations such as extended, pearl-necklace, cigar-shape, and collapsed structures resulting from the subtle balance of short-range hydrophobic attractive interactions and long-range electrostatic repulsive interactions between the monomers have been observed. Titration curves were calculated by adjusting the pH-pK(0) values (pK(0) represents the intrinsic dissociation constant of an isolated monomer) and then calculating the ionization degree alpha of the polyelectrolyte. Important transitions related to cascades of conformational changes were observed in the titration curves, mainly at low ionic concentration and with the presence of strong hydrophobic interactions. We demonstrated that the presence of hydrophobic interactions plays an important role in the acid-base properties of a polyelectrolyte in promoting the formation of compact conformations and hence decreasing the polyelectrolyte degree of ionization for a given pH-pK(0) value.     

Kinetic Monte Carlo study of nucleation processes on patterned surfaces

The properties of template-directed nucleation are studied in the transition region where full nucleation control is lost and additional nucleation beyond the prepatterned structure is observed. To get deeper insight into the microscopic mechanisms, Monte Carlo simulations were performed. In this context, the previously used continuous algorithm [F. Kalischewski, J. Zhu, and A. Heuer, Phys. Rev. B 77, 155401, (2008)] was replaced by a discrete one to reduce simulation time and to allow more detailed calculations. The applied method is based on the assumption that the molecules on the surface occupy the sites of a simple fcc lattice. It is shown that a careful mapping of the continuous Monte Carlo technique onto the discrete algorithm leads to a good reproduction of the former results by means of the latter method. Furthermore, the new method facilitates the calculation of the spatial distribution of nuclei on the surface. This provides a detailed comparison with experimental data.     

Efficient Monte Carlo trial moves for polypeptide simulations

A new move set for the Monte Carlo simulations of polypeptide chains is introduced. It consists of a rigid rotation along the (C(alpha)) ends of an arbitrary long segment of the backbone in such a way that the atoms outside this segment remain fixed. This fixed end move, or FEM, alters only the backbone dihedral angles phi and psi and the C(alpha) bond angles of the segment ends. Rotations are restricted to those who keep the alpha bond angles within their maximum natural range of approximately +/-10 degrees. The equations for the angular intervals (tau) of the allowed rigid rotations and the equations required for satisfying the detailed balance condition are presented in detail. One appealing property of the FEM is that the required number of calculations is minimal, as it is evident from the simplicity of the equations. In addition, the moving backbone atoms undergo considerable but limited displacements of up to 3 A. These properties, combined with the small number of backbone angles changed, lead to high acceptance rates for the new conformations and make the algorithm very efficient for sampling the conformational space. The FEMs, combined with pivot moves, are used in a test to fold a group of coarse-grained proteins with lengths of up to 200 residues.     

Mercedes-Benz water molecules near hydrophobic wall: integral equation theories vs Monte Carlo simulations

Associative version of Henderson-Abraham-Barker theory is applied for the study of Mercedes-Benz model of water near hydrophobic surface. We calculated density profiles and adsorption coefficients using Percus-Yevick and soft mean spherical associative approximations. The results are compared with Monte Carlo simulation data. It is shown that at higher temperatures both approximations satisfactory reproduce the simulation data. For lower temperatures, soft mean spherical approximation gives good agreement at low and at high densities while in at mid range densities, the prediction is only qualitative. The formation of a depletion layer between water and hydrophobic surface was also demonstrated and studied.