Lattice Gas Monte Carlo Simulation Research Articles

Dewetting transition of water confined between atomically rough surfaces: A lattice gas Monte Carlo simulation study

Using lattice gas Monte Carlo simulations, we studied the dewetting transition of water confined between a spherical tip and a plate, which is relevant to atomic force microscopy measurements conducted in water. The dewetting transition was investigated by varying the tip-plate distance, tip size, and the pressure of water. With introduction of an atomic scale roughness (1 < nm) in the tip and the plate, the dewetting transition significantly increased in range and yielded an enhanced hydrophobic force between the tip and the plate. This finding is in agreement with the experimental results previously reported by Singh et al.

Lattice-geometry effects in garnet solid electrolytes: a lattice-gas Monte Carlo simulation study.

Ionic transport in solid electrolytes can often be approximated as ions performing a sequence of hops between distinct lattice sites. If these hops are uncorrelated, quantitative relationships can be derived that connect microscopic hopping rates to macroscopic transport coefficients; i.e. tracer diffusion coefficients and ionic conductivities. In real materials, hops are uncorrelated only in the dilute limit. At non-dilute concentrations, the relationships between hopping frequency, diffusion coefficient and ionic conductivity deviate from the random walk case, with this deviation quantified by single-particle and collective correlation factors, f and fI, respectively. These factors vary between materials, and depend on the concentration of mobile particles, the nature of the interactions, and the host lattice geometry. Here, we study these correlation effects for the garnet lattice using lattice-gas Monte Carlo simulations. We find that, for non-interacting particles (volume exclusion only), single-particle correlation effects are more significant than for any previously studied three-dimensional lattice. This is attributed to the presence of two-coordinate lattice sites, which causes correlation effects intermediate between typical three-dimensional and one-dimensional lattices. Including nearest-neighbour repulsion and on-site energies produces more complex single-particle correlations and introduces collective correlations. We predict particularly strong correlation effects at xLi=3 (from site energies) and xLi=6 (from nearest-neighbour repulsion), where xLi=9 corresponds to a fully occupied lithium sublattice. Both effects are consequences of ordering of the mobile particles. Using these simulation data, we consider tuning the mobile-ion stoichiometry to maximize the ionic conductivity, and show that the ‘optimal’ composition is highly sensitive to the precise nature and strength of the microscopic interactions. Finally, we discuss the practical implications of these results in the context of lithium garnets and other solid electrolytes.

A multi-scale study of the adsorption of lanthanum on the (110) surface of tungsten

In this study, we utilize a multi-scale approach to studying lanthanum adsorption on the (110) plane of tungsten. The energy of the system is described from density functional theory calculations within the framework of the cluster expansion method. It is found that including two-body figures up to the sixth nearest neighbor yielded a reasonable agreement with density functional theory calculations as evidenced by the reported cross validation score. The results indicate that the interaction between the adsorbate atoms in the adlayer is important and cannot be ignored. The parameterized cluster expansion expression is used in a lattice gas Monte Carlo simulation in the grand canonical ensemble at 773 K and the adsorption isotherm is recorded. Implications of the obtained results for the pyroprocessing application are discussed.

Monte Carlo Study on the Wetting Behavior of a Surface Texturized with Domed Pillars

A lattice gas Monte Carlo simulation was performed to examine the wetting properties of a surface texturized with nanometer-sized, dome-shaped pillars. The vapor and liquid phases of the gap between the pillars were related to the Wenzel and Cassie–Baxter states of a macroscopic water droplet resting on top of the pillars. We studied the effects of the pillar size by systematically varying its height from 6 to 53 nm for a fixed ratio of the height to its width. With increasing interpillar spacing or pressure, the liquid on top of the domed pillars penetrated smoothly down into the gap between the pillars. This wetting transition contrasts with that observed for the gap between rectangular or cylindrical pillars, where a liquid abruptly fills in the interpillar gap at a critical interpillar spacing or pressure. The gap between the domed pillars was more susceptible to the intrusion of the bulk liquid on top of the pillars, due to the open geometry of the gap between the domed pillars. Also, the liquid pene...

Drying Transition of Water Confined between Hydrophobic Pillars

The phase behavior of the water confined between hydrophobic pillars was studied by using a simple thermodynamic theory and the lattice gas Monte Carlo simulation. The drying transition of water with decreasing spacing between pillars is related to the Wenzel (WZ) to Cassie–Baxter (CB) transition of droplet. Our theory agrees with simulation for pillars with heights ranging from 11 to 100 nm. The present theory further predicts that sufficiently large circular pillars cannot sustain a CB state even if the pillars are in contact with each other.

Lattice Gas Monte Carlo Simulation of Capillary Forces in Atomic Force Microscopy

We review recent work concerned with lattice gas (LG) Monte Carlo (MC) simulations of the water meniscus formed between an atomic force microscope (AFM) tip and the surface in contact with the tip. Grand canonical MC simulations were performed to study the meniscus structure and capillary force, and this work allowed us to examine the mechanism of meniscus formation as a function of the tip–surface distance and humidity. It is found that the meniscus becomes unstable when it is narrower than the diameter of the tip–surface contact area. The calculations suggest that the ultimate size limit for a stable meniscus is five molecular diameters. We developed thermodynamic integration and perturbation methods to calculate the capillary force. The magnitude and humidity dependence of capillary force are significantly affected by the hydrophilicity of both the tip and surface. A mean field density functional theory (DFT) closely approximates the capillary forces calculated from the MC simulation. Changing the atomic scale roughness of the tip and surface drastically changes the capillary force. In particular, at low humidity, a slight roughening of the tip or surface leads to a drastic change in the force. The roughness effect persists even at 80% relative humidity. The capillary force is governed by the degree of confinement of the water and, therefore, increases as the free volume between the tip and surface decreases. The humidity dependence of the capillary force depends on the susceptibility of the meniscus width to tip retraction. For strongly hydrophilic tips at high humidity, the susceptibility is small so that the capillary force decreases as the humidity rises.

First-Principles Thermodynamics of Coherent Interfaces in Samarium-Doped Ceria Nanoscale Superlattices

Nanoscale superlattices of samarium-doped ceria layers with varying doping levels have been recently proposed as a novel fuel cell electrolyte. We calculate the equilibrium composition profile across the coherent {100} interfaces present in this system using lattice-gas Monte Carlo simulations with long-range interactions determined from electrostatics and short-range interactions obtained from ab initio calculations. These simulations reveal the formation of a diffuse, nonmonotonic, and surprisingly wide (11 nm at 400 K) interface composition profile, despite the absence of space charge regions.

Flow response of a segregating mixture by interacting lattice gas simulation

Steady-state flow and structural profiles of immiscible components A and B (molecular weights M A and M B , M A < M B ) in a non-conservative open system are studied by an interacting lattice gas Monte Carlo simulation. Concentration gradient and hydrostatic bias H drive the constituents ( A , B ) which are continuously released from the bottom with equal probability against gravity. At low bias, the segregation of A and B leading to a partial layering is enhanced toward the bottom. The longitudinal density profile with a high density in the bottom region and low toward the top shows linear, exponential, and power-law decays in different regions of depth or altitude which varies systematically with the pressure bias. The transverse density profiles show segregation with different domain sizes and layering depending on the bias. Response of their steady-state flux density j to the hydrostatic bias H is found to be linear at higher bias. The difference in response of the flux density of the two components becomes more pronounced at low bias and higher miscibility gap.

Atomic surface occupancy of decagonal AlNiCo

We investigate the atomic surface structure of the high temperature decagonal quasicrystalline phase of ${\mathrm{Al}}_{72}{\mathrm{Ni}}_{20}{\mathrm{Co}}_{8}$ using a lattice gas Monte Carlo simulation. To avoid biasing towards a specific model we use an overdense site list with a large fraction of free sites, permitting the simulation to explore an extended region of perpendicular space. Representing the atomic surface occupancy in a basis of harmonic functions aids our analysis by directly revealing the fivefold symmetric component of our data. Patterns of occupancy are examined in both physical (``parallel'') and perpendicular space, and compared with experiment in both cases. Additionally we compute the Patterson function representing correlations among atomic positions. Our results yield atomic surface structure with smooth variation of occupation and chemistry. Short distances in this model are avoided through correlations among partially occupied sites. The model naturally incorporates both an idealized average structure and intrinsic structural disorder, providing a more realistic description of the quasicrystal than is possible from an atomic surface model alone.

Structural response in steady-state flow of a multi-component driven system: interacting lattice gas simulation

The effects of molecular weights (MA,MB) on the self-organized segregation of immiscible constituents (A,B) driven by pressure bias (H=0.0–1.0) generated by geologic processes are examined by an interacting lattice gas Monte Carlo simulation. Constituents (A,B), released from a source at the bottom according to their lattice concentrations, can escape the lattice from top or bottom. The longitudinal steady-state density profiles (A,B) depend on their molecular weight and bias with linear, exponential, and non-monotonic decays with the height. The transverse density profiles show signatures of partial layering. The total number (N) of constituents remains nearly constant in steady state and seems to decay with the bias, N∝H-0.14 for all but extreme range of H. At MA=0.1, MB⩾0.8, number of constituents (NA,NB) show non-monotonic dependence on H with NB⪢NA but a maximum in NA and minimum in NB.

Structural response in steady-state flow of a multi-component driven system: interacting lattice gas simulation

The effects of molecular weights ( M A , M B ) on the self-organized segregation of immiscible constituents ( A , B ) driven by pressure bias ( H = 0.0 –1.0) generated by geologic processes are examined by an interacting lattice gas Monte Carlo simulation. Constituents ( A , B ) , released from a source at the bottom according to their lattice concentrations, can escape the lattice from top or bottom. The longitudinal steady-state density profiles ( A , B ) depend on their molecular weight and bias with linear, exponential, and non-monotonic decays with the height. The transverse density profiles show signatures of partial layering. The total number ( N ) of constituents remains nearly constant in steady state and seems to decay with the bias, N ∝ H - 0.14 for all but extreme range of H . At M A = 0.1 , M B ⩾ 0.8 , number of constituents ( N A , N B ) show non-monotonic dependence on H with N B ⪢ N A but a maximum in N A and minimum in N B .

How narrow can a meniscus be?

A water meniscus naturally forms in air between an atomic force microscope (AFM) tip and a substrate. This nanoscale meniscus produces a capillary force on the AFM, and also serves as a molecular transport channel in dip-pen nanolithography (DPN). A stable meniscus is a necessary condition for DPN and for the validity of the Kelvin equation commonly applied to AFM experiments. Lattice gas Monte Carlo simulations show that, due to thermal fluctuation, a stable meniscus has a lower limit in width. We find a minimum width of 5 molecular diameters (1.9 nm) when the tip becomes atomically sharp (terminated by a single atom).

Molecular dynamics calculations and Monte Carlo simulation of diffusivities in aqueous systems application to nitrate reduction on bimetal catalyst immobilized in poly (vinyl alcohol)-hydrogel

Denitrification of drinking water in poly (vinyl alcohol) pellets by reduction with the aid of hydrogen and Pd Cu catalyst particles, which were immobilized inside the pellet, was modeled by the Stefan-Maxwell approach. Pure diffusivities of potassium nitrate were calculated using Molecular Dynamics. To obtain effective diffusion coefficients, the structure of a cryogel was first simulated by the ISING-model on a cubic lattice. The diffusion coefficients then result from the following lattice gas Monte Carlo simulation.

Roughening of the Pb (110) surface: combined Monte Carlo and molecular-dynamics study

The roughening transition on the Pb (110) surface has been studied using a combination of lattice-gas Monte Carlo and molecular-dynamics methods in conjunction with a many-body glue potential. Lattice-gas Monte Carlo simulations yield a roughening transition temperature of approximately T R LGMC ≈ 1100 K. Molecular-dynamics simulations, which account for surface relaxation and lattice vibrations, detect the roughening transition at T R MD ≈ 545 K, above the high-resolution low-energy diffraction measurements of T R EXP ≈ 415 K. The anisotropic body-centered solid-on-solid model is used in the interpretation of these results. The time scale of local roughening at 545 K is about 0.6 ns. The time evolution of the Pb (110) surface from an initially smooth to a rough configuration is illustrated by the use of modem visualization techniques. Means for improving the theoretical results are discussed.

Effects of strain on island scaling studied by Monte Carlo simulations

Strained heteroepitaxial growth is a possible means of obtaining carrier confinement in reduced-dimensional systems for applications in optoelectronic devices. The epitaxial growth of InAs on GaAs provides an excellent prototypical system due to the significant lattice mismatch of approximately 7% between the two constituents. At submonolayer coverages, highly elongated two-dimensional InAs islands were observed experimentally with a preferred width of approximately 4 nm. When the island size distributions were separated into [110] and [1̄10] components, scaling was only observed in the [1̄10] direction, and clustering was observed in the radial separation distribution. We have used lattice gas Monte Carlo simulations to explore the effects of intrinsic system anisotropies and strain on island scaling. We found that the experimentally observed scaling behavior can only be explained by taking into consideration both the system anisotropies and strain.