Lattice Monte Carlo Method Research Articles

Retention Behavior of Star-Shaped Polystyrene near the Chromatographic Critical Condition

The retention behavior of star-shaped polystyrene (PS) at the liquid chromatographic critical condition of linear PS was investigated. The star-shaped PS samples were prepared by anionic polymerization of styrene and subsequent linking of the polystyryl anions with divinylbenzene. The linking reaction yields a series of star-shaped PS with different number of branches of equal length. Three star-shaped PS samples with different arm molecular weight (MW) were prepared. To investigate the MW (hence the branch number) dependence of the LCCC (liquid chromatography at the critical condition) retention, the two-dimensional liquid chromatography method was used—first separating the polymers with respect to the molecular weight and subsequently separating the effluent by LCCC. Two different pore size columns were used for the LCCC separation to investigate the pore size dependence. The LCCC retention shows a very complex behavior. The retention time of the star-shaped PS shows a strong variation with MW (branch number) at the coelution condition of linear PS, and the deviation from the coelution behavior is more serious at a smaller pore sized column. The peculiar LCCC retention behavior was successfully delineated by a lattice Monte Carlo method taking into account the excluded volume and weak attractive interaction of the chain ends.

In-Diffusion and Out-Diffusion of Oxygen from a Composite Containing Random Traps

In this paper, we investigate oxygen in-diffusion and out-diffusion with respect to a cermet composite where oxygen segregates at the interface between the metal matrix phase and the ceramic oxide phase. This phenomenological diffusion problem is treated by overlaying it with a fine-grained lattice that was addressed using a Lattice Monte Carlo method and a little-known exact expression for the lattice-based effective diffusivity in the presence of random traps. It is shown that there is very good agreement for the oxygen concentration depth profiles between the Monte Carlo results and the exact expression.

Recent Advances in the Prediction of the Thermal Properties of Syntactic Metallic Hollow Sphere Structures

Metallic hollow sphere structures (MHSS) constitute a group of innovative materials which are characterised by more constant material properties compared to classical cellular metals. Their big potential lies within multifunctional applications where combinations of their properties yield symbiotic advantages. In this paper, the effective thermal conductivity of MHSS materials is investigated. Three different approaches, namely a Finite Element Method, a Lattice Monte Carlo Method and an analytical Maxwell model, are used. It is shown that all approaches complement each other and that the results are in excellent agreement.

Dimensional reduction and the Yang-Mills vacuum state in2+1dimensions

We propose an approximation to the ground state of Yang-Mills theory, quantized in temporal gauge and $2+1$ dimensions, which satisfies the Yang-Mills Schr\"odinger equation in both the free-field limit, and in a strong-field zero mode limit. Our proposal contains a single parameter with dimensions of mass; confinement via dimensional reduction is obtained if this parameter is nonzero, and a nonzero value appears to be energetically preferred. A method for numerical simulation of this vacuum state is developed. It is shown that if the mass parameter is fixed from the known string tension in $2+1$ dimensions, the resulting mass gap deduced from the vacuum state agrees, to within a few percent, with known results for the mass gap obtained by standard lattice Monte Carlo methods.

Computer Simulation of the Formation of γ-Precipitates in Nickel-Based Superalloys

Recent 3-Dimensional Atom Probe (3DAP) experimental observations showed the formation of spherical γ-precipitates at a central region of γ’ phases in nickel based superalloys. The γ precipitates should give a significant effect to the material strength. Whereat, in this work, we first developed a simulation technique for the investigation of the formation of γ-precipitates in γ’ phases, which is based on a combination of an Embedded Atom Method (EAM) interatomic potential designed for Molecular Dynamics (MD) and the kinetic lattice Monte Carlo (KLMC) method. As a demonstration of the KLMC simulation, the formation of the L12 structure was simulated from an initial state with randomly distributed aluminum atoms (25at.%Al). Finally, the γ’ phase with the L12 structure is formed in the entire simulation volume. To understand the fundamental mechanism of the formation of the L12 structures, the binding energies between a pair of aluminum atoms in a nickel single crystal were calculated using MD method. The result gave a clear picture of the mechanism. The stability of the γ-precipitate was also investigated using the MD method. Finally, the formation of γ-precipitates was simulated using the KLMC method. The dependence of the formation on the temperature condition is discussed.

Calculations of the Effective Thermal Conductivity in a Model of Syntactic Metallic Hollow Sphere Structures Using a Lattice Monte Carlo Method

In this paper, a Lattice Monte Carlo method is used to determine the effective thermal conductivity in two dimensional models of adhesively bonded metallic hollow sphere structures (MHSS). In contrast to earlier approaches, more realistic distributions of spheres without the simplification of cubic symmetric arrangements are considered in this study. For the Monte Carlo analyses, two-dimensional periodic lattices representing different cutting planes through MHSS are generated. Therefore, an algorithm is used which sequentially fills the lattice by adding cut spherical shells and inclusions in the matrix. Another focus of this work is the analysis of the influence of different geometric circle distributions on the effective thermal conductivity. The findings of the random arrangements are also compared to a regular primitive cubic arrangement and with a Maxwell-type approach.

Formation of New Morphologies of Surfactant−Inorganic−Water Systems under Spherical Confinements

Application of lattice Monte Carlo method to the surfactant−inorganic−solvent system under a spherical confinement reveals that the confined self-assembly leads to a rich variety of morphologies. Many of the ordered structures are observed in our simulations, such as the core−shell spherical network structure and spiral structure with a core network, which have not been found for the bulk surfactant or copolymer systems and in experiments. The simulated results suggest that the occurrence of these novel structures depends on the pore diameter of the spherical cavity and the surfactant architecture.

Analysis of Oxygen Segregation at Metal-Oxide Interfaces Using a New Lattice Monte Carlo Method

The presence of atomic oxygen at internal metal-ceramic oxide interfaces significantly affects the physical properties of the interfaces which in turn affects the bulk properties of the material. We address this problem for the case of a constant source of oxygen at the surface and periodic arrangements of ceramic oxide (MgO) inclusions embedded in a metal (Ag) matrix. We simulate the time-dependence of the oxygen concentration into the material using a newly developed lattice Monte Carlo method that takes into account a constant source of diffusant.

Calculation of the Effective Thermal Conductivity in Composites Using Finite Element and Monte Carlo Methods

In this paper, the Finite Element and lattice Monte Carlo methods are used to calculate the effective thermal conductivity of two models of a composite: circular and square inclusions arranged in a square planar arrangement. A new lattice Monte Carlo method based around Fick’s First Law is also presented. Excellent agreement is found between these quite different methods. It is also shown that the results are in excellent agreement with the century-old Maxwell Equation.

Roughness simulation for thin films prepared by atomic layer deposition

The kinetic lattice Monte Carlo method for film growth simulation without taking crystallization into account was applied to study the roughness of the HfO2 film grown by atomic layer deposition at 100–500°C from HfCl4 and H2O. The calculations were performed using a simplified kinetic mechanism of the growth of HfO2 films obtained by reducing the detailed kinetic mechanism developed earlier. Ab initio quantum-chemical calculations were performed to determine the kinetic parameters of diffusion processes on the surface of hafnium oxide that could influence film roughness. Because of the special features of atomic layer deposition, the rate of film growth and film roughness were finite even if surface relaxation was ignored. It was found that, irrespective of the temperature, the diffusion of hydrogen and adsorbed HfCl4 complexes did not change the profile of the growing film and only insignificantly increased the mean rate of growth. The results obtained were also qualitatively applicable to zirconium dioxide at fairly low (≤100°C) temperatures in the absence of crystallization.

Understanding Effects of Matrix Protease and Matrix Organization on Directional Persistence and Translational Speed in Three-Dimensional Cell Migration

Recent studies have shown significant differences in migration mechanisms between two- and three-dimensional environments. While experiments have suggested a strong dependence of in vivo migration on both structure and proteolytic activity, the underlying biophysics of such dependence has not been studied adequately. In addition, the existing models of persistent random walk migration are primarily based on two-dimensional movement and do not account for the effect of proteolysis or matrix inhomogeneity. Using lattice Monte Carlo methods, we present a model to study the role of matrix metallo-proteases (MMPs) on directional persistence and speed. The simulations account for a given cell's ability to deform as well as to digest the matrix as the cell moves in three dimensions. Our results show a bimodal dependence of speed and persistence on matrix pore size and suggest high sensitivity on MMP activity, which is in very good agreement with experimental studies carried out in 3D matrices.

Computer Simulation of Microstructure Evolution of Fe-Cu Alloy during Thermal Ageing

This paper describes a computer simulation of thermal ageing process in Fe-Cu alloy. In order to perform accurate numerical simulation, firstly, we make numerical models of the diffusion and dissociation of Cu and Cu-vacancy clusters. This modeling was performed with kinetic lattice Monte Carlo method, which allows us to perform long-time simulation of vacancy diffusion in Fe-Cu dilute alloy. The model is input to the kinetic Monte Carlo method, and then, we performed the kinetic Monte Carlo simulation of the thermal ageing in the Fe-Cu alloy. The results of the KMC simulations tell us that the our new models describes well the rate and kinetics of the diffusion and dissociation of Cu and Cu-vacancy clusters, and works well in the kinetic Monte Carlo simulations. Finally, we discussed the further application of these numerical models.

Modeling the effects of impurities on microstructure formation in nanocrystalline nickel thin films

The Atomic Kinetic Lattice Monte Carlo method was used to model the effects of a clustering impurity species on the deposition of nanocrystalline nickel films onto (001) copper. The deposition model was partly parameterized by physical inputs from atomistic calculations of copper-nickel alloys. The grain size and shape is shown to depend on the concentration of impurities in the deposited film. Low concentrations yield elongated columnar grains, while higher concentrations produce much smaller and more equiaxed grains.

Spatially adaptive lattice coarse-grained Monte Carlo simulations for diffusion of interacting molecules

While lattice kinetic Monte Carlo (KMC) methods provide insight into numerous complex physical systems governed by interatomic interactions, they are limited to relatively short length and time scales. Recently introduced coarse-grained Monte Carlo (CGMC) simulations can reach much larger length and time scales at considerably lower computational cost. In this paper we extend the CGMC methods to spatially adaptive meshes for the case of surface diffusion (canonical ensemble). We introduce a systematic methodology to derive the transition probabilities for the coarse-grained diffusion process that ensure the correct dynamics and noise, give the correct continuum mesoscopic equations, and satisfy detailed balance. Substantial savings in CPU time are demonstrated compared to microscopic KMC while retaining high accuracy.

Polyelectrolyte shells of copolymer micelles in aqueous solutions: a Monte Carlo study.

Multimolecular micelles, formed by polystyrene-block-poly(methacrylic acid) in water, are studied by lattice Monte Carlo method. Electrostatic interactions are calculated in the mean-field approximation by solving the Poisson-Boltzmann equation. The model is parametrized according to available experimental data. The dependence of micellar size on pH and ionic strength is calculated and compared with experimental data. A special attention is devoted to the behavior in solutions with a low ionic strength.

Simulation of mineral solid solutions at zero and high pressure using lattice statics, latticedynamics and Monte Carlo methods

We discuss how two techniques, based on (1) lattice statics/lattice dynamics simulationsand (2) Monte Carlo methods may be used to calculate the thermodynamic properties ofoxide mixtures at zero and high pressure. The lattice statics/lattice dynamics calculationsinvolve a full free energy structural optimization of each of a number of configurations,followed by thermodynamic averaging. Strategies for generating a suitable set ofconfigurations are discussed. We compare results obtained by random generation with thoseobtained using radial distribution functions or explicit symmetry arguments to obtainapproximate or exact weightings respectively for individual configurations. The MonteCarlo simulations include the explicit interchange of cations and use the semigrandcanonical ensemble for chemical potential differences. Both methods are readilyapplied to high pressures and elevated temperatures without the need for anynew parametrization. Agreement between the two techniques is better at highpressures where anharmonic terms are smaller. We compare in detail the useof each technique for properties such as enthalpies, entropies, volume and freeenergies of mixing at zero and high pressure and thus calculation of the phasediagram. We assess the vibrational contributions to these quantities and compareresults with those in the dilute limit. The techniques are illustrated throughoutusing MnO–MgO and should be readily applicable to more complicated systems.

A Monte Carlo study of shells of hydrophobically modified amphiphilic copolymer micelles in polar solvents

Multimolecular micelles in polar solvents formed by polystyrene-block-poly(methacrylic acid) (PS-PMA), hydrophobically modified by a naphthalene tag between blocks and an anthracene tag at the end of PMA block, are studied by a lattice Monte Carlo method. The model is parametrized according to available experimental data and several structural characteristics of the PMA shell together with the fluorometric decay functions are calculated and compared with results obtained for system without anthracene tags. The hydrophobic tags at the ends of shell-forming blocks try to avoid the polar medium and bury in the shell forcing the chains to loop back. The resulting distribution of traps is bimodal with a smaller peak in the vicinity of the core and a larger one farther from the core than the maximum on the distribution of segments.

Adsorption Profiles of Long‐Chain Polymer in Semidilute Solutions Physisorbed to a Wall

AbstractEquilibrium concentration profiles for long macromolecules in solution strongly adsorbed to a flat wall were estimated by a combination of persistent reptation and partial chain regrowth using a configurational bias lattice Monte Carlo method. The profiles were obtained for various concentrations in the semidilute regime and different chain lengths. A master curve exists in a plot of the profile reduced by the bulk concentration as a function of the distance to the wall reduced by the correlation length estimated for the bulk concentration. Near the wall, the master curve follows a power law with an exponent predicted in the scaling theory. Compared to depletion profiles at a repulsive wall that require a small penetration length, no correction of the distance to the wall is needed for the adsorption profiles.Reduced plot of ϕ(x)/ϕbulk vs. x/ξ for chain length N = 1 000 and five bulk concentrations above ϕ* indicated in legend. Slope with the exact exponent from scaling theory is shown for comparison.imageReduced plot of ϕ(x)/ϕbulk vs. x/ξ for chain length N = 1 000 and five bulk concentrations above ϕ* indicated in legend. Slope with the exact exponent from scaling theory is shown for comparison.

Quantitative Evaluation of Copper Clustering Process by Lattice Monte Carlo Simulation.

In this study, we simulate nanoscale copper precipitation process based on the vacancy jump model using Lattice Monte Carlo (LMC) method, where an activation energy is calculated from the first neighboring interaction model. We confirmed that status of copper clustering at temperature of 300 K is different from those of 600 K and 900 K at the same potential energy decrease, and copper clusters are formed more rapidly at higher temperature. We obtained a fact that process of copper clustering consists of the two phases which are formation phase, and coalescence and/or absorption phase.

Copper precipitation in iron: a comparison between metropolis Monte Carlo and lattice kinetic Monte Carlo methods

Several variants are possible in the suite of programs forming multiscale predictive tools to estimate the yield strength increase caused by irradiation in RPV steels. For instance, at the atomic scale, both the Metropolis and the lattice kinetic Monte Carlo methods (MMC and LKMC respectively) allow predicting copper precipitation under irradiation conditions. Since these methods are based on different physical models, the present contribution discusses their consistency on the basis of a realistic case study. A cascade debris in iron containing 0.2% of copper was modelled by molecular dynamics with the DYMOKA code, which is part of the REVE suite. We use this debris as input for both the MMC and the LKMC simulations. Thermal motion and lattice relaxation can be avoided in the MMC, making the model closer to the LKMC (LMMC method). The predictions and the complementarity of the three methods for modelling the same phenomenon are then discussed.