Surface tension of an electrolyte-air interface: a Monte Carlo study

We present a new method for calculating the surface tension of an electrolyte-air interface using Monte Carlo (MC) simulations with an implicit solvent in a spherical drop geometry. The boundary conditions for the electric field at the interface are accounted for using image and counter-image charges. The density profiles obtained from the simulations are used to calculate the excess surface tension of the electrolyte-air interface using the Gibbs adsorption isotherm equation. The results are found to be in good agreement with experiments and the earlier theoretical calculations.     

Thermodynamic and transport properties of simple fluids using lattice sums: bulk phases and liquid-vapour interface

Molecular dynamics simulations in the canonical ensemble have been performed to obtain the thermodynamic and transport properties of the Lennard-Jones fluid. The dispersion interactions were calculated using lattice sums. This method makes it possible to simulate the full potential avoiding the inclusion of the long range corrections (LRC) during or at the end of simulations. In the calculation of dynamic properties in bulk phases and thermodynamic quantities of inhomogeneous systems where the interface is physically present, in general the LRC cannot easily be included. By using the lattice sums method, the results are independent of the truncation of the potential. In the liquid-vapour interface simulations it is not necessary to make any pre-judgments about the form of the LRC formula to calculate coexisting properties such as the surface tension. The lattice sums method has been applied to evaluate how well the full interaction can be calculated in the liquid phase and in the liquid-vapour interface. In the liquid phase the pressure, configurational energy, diffusion coefficient and shear viscosity were obtained. The results of the thermodynamic properties are compared with those obtained using the spherically truncated and shifted (STS) potential with the LRC added at the end of simulations, and excellent agreement is found. The transport properties are calculated on different system sizes for a state near the triple point. The diffusion coefficient using the lattice sums method increases with the number of molecules, and the results are higher than those of the STS model truncated at 2.5σ (STS2.5). The shear viscosity does not show any system size dependence for systems with more than 256 molecules, and the lattice sums results are essentially the same as those for the STS2.5. In the liquid-vapour equilibria the coexisting densities and vapour pressures for the full potential agree well with those obtained using the Gibbs ensemble and the NPT + test particle methods. The surface tension using lattice sums and truncation of forces at 2.5σ agrees well with STS results using large system sizes and cutoff distances.     

Positive Tolman length in a lattice gas with three-body interactions

We present a new method to determine the curvature dependence of the interface tension between coexisting phases in a finite volume from free energies obtained by Monte Carlo simulations. For the example of a lattice gas on a 3D fcc lattice with nearest neighbor three-body interactions, we demonstrate how to calculate the equimolar radius R(e) as well as the radius R(s) of the surface of tension and thus the Tolman length δ(R(s))=R(e)-R(s). Within the physically relevant range of radii, δ(R(s)) shows a pronounced R(s) dependence, such that the simple Tolman parametrization for the interface tension is refutable. For the present model, extrapolation of δ(R(s)) to R(s)→∞ by various methods clearly indicates a positive limiting value.     

Molecular mean field theory for liquid water

Attractive bonding interactions between molecules typically have inherent conservation laws which influence the statistical properties of such systems in terms of corresponding sum rules. We have considered lattice water as an example, and we have enunciated the consequences of the sum rule through a general computational procedure called molecular mean field theory. Fluctuations about the mean field are computed and many of the liquid properties have been deduced and compared with Monte Carlo simulation, molecular dynamics, and experimental results. Large correlation lengths are seen to be a consequence of the sum rule in the liquid phase. Long-range Coulomb interactions are shown to have minor effects on our results.     

Adsorption and interfacial phenomena of a Lennard-Jones fluid adsorbed in slit pores: DFT and GCMC simulations

ABSTRACT

Confinement of fluids in porous media leads to the presence of solid–fluid (SF) interfaces that play a key role in many different fields. The experimental characterisation of SF interfacial properties, in particular the surface tension, is challenging or not accessible. In this work, we apply mean-field density functional theory (DFT) to determine the surface tension and also density profile of a Lennard-Jones fluid in slit-shaped pores for realistic amounts of adsorbed molecules. We consider the pore walls to interact with fluid molecules through the well-known 10-4-3 Steele potential. The results are compared with those obtained from Monte Carlo simulations in the Grand Canonical Ensemble (GCMC) using the test-area method. We analyse the effect on the adsorption and interfacial phenomena of volume and energy factors, in particular, the pore diameter and the ratio between SF and fluid–fluid dispersive energy parameters, respectively. Results from DFT and GCMC simulations were found to be comparable, which points to their reliability.     

Phase behavior and fluid-solid surface tension of argon in slit pores and carbon nanotubes

Phase behaviors of argon in several types of cylindrical and slit pores are examined by grand-canonical Monte Carlo simulations. Condensation processes in single- and multi-walled carbon nanotubes along with those in hard-wall tubes are compared. Effects of the pore size on pressure-tensor components, the fluid-wall surface tension, and the adsorption are also compared for the different fluid-pore interactions. The chemical potential at which the fluid begins to condense in the single-walled nanotube is greater than that in the multi-walled nanotube by an amount nearly equal to the difference in the potential-well depth of the fluid-pore interaction, and the adsorption isotherms overlap each other almost completely for narrow pores and partially for wider pores. Similar analyses are performed for slit pores of two different hydrocarbon models.     

Kinetic Monte Carlo simulations of electrodeposition: Crossover from continuous to instantaneous homogeneous nucleation within Avrami’s law

The influence of lateral adsorbate diffusion on the dynamics of the first-order phase transition in a two-dimensional Ising lattice gas with attractive nearest-neighbor interactions is investigated by means of kinetic Monte Carlo simulations. For example, electrochemical underpotential deposition proceeds by this mechanism. One major difference from adsorption in vacuum surface science is that under control of the electrode potential and in the absence of mass-transport limitations, local adsorption equilibrium is approximately established. We analyze our results using the theory of Kolmogorov, Johnson and Mehl, and Avrami (KJMA), which we extend to an exponentially decaying nucleation rate. Such a decay may occur due to a suppression of nucleation around existing clusters in the presence of lateral adsorbate diffusion. Correlation functions prove the existence of such exclusion zones. By comparison with microscopic results for the nucleation rate I and the interface velocity of the growing clusters v, we can show that the KJMA theory yields the correct order of magnitude for Iv². This is true even though the spatial correlations mediated by diffusion are neglected. The decaying nucleation rate causes a gradual crossover from continuous to instantaneous nucleation, which is complete when the decay of the nucleation rate is very fast on the time scale of the phase transformation. Hence, instantaneous nucleation can be homogeneous, producing negative minima in the two-point correlation functions. We also present in this paper an n-fold way Monte Carlo algorithm for a square lattice gas with adsorption/desorption and lateral diffusion.     

Studies of adsorption kinetics by means of the stochastic numerical simulation

This paper surveys the methods used in the theoretical studies of kinetics with a special emphasis on the works dealing with the stochastic methods and their application in studies of adsorption kinetics. One of the stochastic methods — Monte Carlo numerical simulation of the stochastic time evolution — is mainly discussed. Numerous studies show that this method, introduced by Gillespie [J. Comput. Phys. 22 (1976) 403], is very useful to investigate the adsorption kinetics. The systematic studies of adsorption kinetics of single gases and gas mixtures on solid surfaces are presented. The kinetic adsorption isotherms, involving the lateral interactions between molecules in the surface phase, energetic heterogeneity of the adsorbent surface and surface diffusion, are numerically simulated by means of the numerical program, which is presented in the appendix. These simulations show influence of the adsorbent heterogeneity, lateral interactions and surface diffusion on the adsorption kinetics.     

Quantum Monte Carlo investigations of adsorption energetics on graphene

We have performed calculations of adsorption energetics on the graphene surface using the state-of-the-art diffusion quantum Monte Carlo method. Two types of configurations are considered in this work: the adsorption of a single O, F, or H atom on the graphene surface and the H-saturated graphene system (graphane). The adsorption energies are compared with those obtained from density functional theory with various exchange-correlation functionals. The results indicate that the approximate exchange-correlation functionals significantly overestimate the binding of O and F atoms on graphene, although the preferred adsorption sites are consistent. The energy errors are much less for atomic hydrogen adsorbed on the surface. We also find that a single O or H atom on graphene has a higher energy than in the molecular state, while the adsorption of a single F atom is preferred over the gas phase. In addition, the energetics of graphane is reported. The calculated equilibrium lattice constant turns out to be larger than that of graphene, at variance with a recent experimental suggestion.     

Lattice gas models with competing interactions

The phase diagrams of lattice gas models on square and centred rectangular lattices with short range competing pair interactions and three-body forces are studied using Monte Carlo techniques and the transfer matrix method. A variety of commensurate (C) phases can be described as observed experimentally for adsorbed monolayers like H on Pd(100), O on W (110) and especially H on Fe(110). In addition, due to the competition between different C phases incommensurate (IC) structures may occur. Their properties and related aspects (C-IC transitions, disorder lines) are discussed in connection with the widely studied ANNNI model, and general concepts on two-dimensional C and IC phases and experiments. Also dynamic properties — such as the self-diffusion of the adsorbate at the surface — are briefly mentioned.     

Adsorption thermodynamics of monomers on diluted-bonds triangular lattices

The surface of amorphous solids cannot be usually represented by a regular lattice of adsorbing sites. One of the main characteristics of such surfaces is a variable connectivity for each site. A simple model consisting of a triangular lattice where a fraction of bonds (interactions) is suppressed at random is used here to find out, by using Monte Carlo simulations, how the adsorption thermodynamics of repulsively interacting monomers is modified with respect to the same process in the regular lattice. Adsorption isotherm, differential heat of adsorption and adsorbed phase entropy calculations are carried out showing and interpreting the effects of the variable connectivity. In particular, it is found that the order-disorder phase transition observed for the regular lattice survives, though with modifications, above a critical mean connectivity.     

Stimulation of vapor nucleation on perfect and imperfect hexagonal lattice surfaces

Monte Carlo simulations of water vapor nucleation on a perfect crystal surface and on a surface with defects are performed. Mass exchange with the vapor phase is modeled by using an open ensemble. Cluster-substrate interaction is described in terms of conventional atom-atom potentials. The Hamiltonian of the system includes expressions for electrostatic, polarization, exchange, and dispersion interactions. The Gibbs free energy and work of adsorption are calculated by Monte Carlo simulation in the bicano?nical ensemble. The microscopic structure of nuclei is analyzed in terms of pair correlation functions. Periodic boundary conditions are used to simulate an infinite substrate surface. Molecule-substrate and molecule-molecule long-range electrostatic interactions are calculated by summing the Fourier harmonics of the electrostatic potential. Dispersion interactions are calculated by direct summation over layers of unit cells. Nucleation on a surface with matching structure follows a layer-by-layer mechanism. The work of adsorption per molecule of a monolayer on the substrate surface has a maximum as a function of nucleus size. The steady rate of nucleation of islands of supercritical size is evaluated. The work of adsorption per molecule for layer-by-layer film growth is an oscillating function of cluster size. As a function of layer number, it has a minimum depending on the vapor pressure. The electric field generated by a microscopic surface protrusion destroys the layered structure of the condensate and eliminates free-energy nucleation barriers. However, point lattice defects do not stimulate explosive nucleation.     

BC3复合纳米管的储氢性能研究

采用巨正则蒙特卡罗方法（GCMC）研究了BC3复合纳米管的物理吸附储氢性能,获得了该纳米管在不同温度和压强下的吸附等温线,及其在不同条件下的物理储氢吸附量,并和相应的碳纳米管进行了对比研究。结果表明,BC3纳米管在所有条件下的储氢性能均优于相应的碳纳米管,因而它是一种比碳纳米管更强的氢存储介质,并从纳米管和H2分子以及H2分子和H2分子之间的平均总相互作用能的分布情况等因素出发解释了这两种纳米管有不同储氢行为的原因。     

Multilevel coarse graining and nano-pattern discovery in many particle stochastic systems

In this work we propose a hierarchy of Markov chain Monte Carlo methods for sampling equilibrium properties of stochastic lattice systems with competing short and long range interactions. Each Monte Carlo step is composed by two or more sub-steps efficiently coupling coarse and finer state spaces. The method can be designed to sample the exact or controlled-error approximations of the target distribution, providing information on levels of different resolutions, as well as at the microscopic level. In both strategies the method achieves significant reduction of the computational cost compared to conventional Markov chain Monte Carlo methods. Applications in phase transition and pattern formation problems confirm the efficiency of the proposed methods.     

A simple effective pair potential for the molecular simulation of the thermodynamic properties of ammonia

A new optimized effective pair potential model is proposed, which is appropriate for the prediction of thermodynamic properties of fluid ammonia including vapour—liquid coexistence data. The phase behaviour is determined using a recently developed version of the Gibbs ensemble Monte Carlo method. Furthermore, liquid structure characteristics, the dielectric constant and supercritical properties are determined by Monte Carlo simulations in the isothermal—isobaric ensemble. The second virial coefficient of the pair potential model is calculated over a broad range of temperature. All properties are compared with experimental data or results of a multi-parameter equation of state for ammonia. The new model is found to yield coexistence properties and second virial coefficients in good agreement with experimental data and the results of the equation of state, respectively.     

A Monte Carlo simulation of the heterogeneous adsorption of hydrogen ions on metal oxides: Effect of inert electrolyte

Charging of the surface of an oxide caused by the adsorption of hydrogen ions and ions of inert 1:1 electrolyte was investigated by using grand canonical Monte Carlo simulation technique. In particular, adsorption isotherms of protons as well as of ions of the electrolyte together with the resulting charge density of the surface were obtained for different system parameters. Also, the effect of the surface energetic heterogeneity and the concentration of the background electrolyte on the isotherms and the charge density curves was examined. Furthermore, lateral interactions in the mixed adsorbed phase were taken into account in the modeling of the system behavior. The obtained results, in general, suggest that the three factors mentioned above may have substantial influence on the charging mechanism at the liquid/oxide interface.     

Influence of unlike dispersive interactions on methane adsorption in graphite: a grand canonical Monte Carlo simulation and classical density functional theory study

Activated carbons are popular adsorbents due to their large micro- and mesoporous volumes and high specific surface areas. Modeling adsorption behaviour using molecular computations is frequently undertaken, but the influence of the unlike intermolecular interactions on adsorption behaviour is often not well understood. This study employed grand canonical Monte Carlo simulations, and classical density functional theory coupled with a simple lattice gas model to study the influence of unlike intermolecular interactions on adsorption behaviour, with a focus on the dispersive interactions. Both approaches yielded qualitative agreement with experimental data from the literature, although only a fitted classical density functional theory approach agreed quantitatively. Changing the potential energy well depth of the methane-carbon interaction did not change the Langmuir-type adsorption behaviour observed, however, there was some dependence of the adsorption behaviour on the unlike interactions, depending on the thermodynamic conditions.     

Two-scale modeling of adsorption processes at structured surfaces

We present an algorithm for the simulation of vicinal surface growth. It combines a lattice gas anisotropic Ising model with a phase-field model. The molecular behavior of individual adatoms is described by the lattice gas model. The microstructure dynamics on the vicinal surface are calculated using the phase-field method. In this way, adsorption processes on two different length scales can be described: nucleation processes on the terraces (lattice gas model) and step-flow growth (phase field model). The hybrid algorithm that is proposed here, is therefore able to describe an epitaxial layer-by-layer growth controlled by temperature and by deposition rate. This method is faster than kinetic Monte Carlo simulations and can take into account the stochastic processes in a comparable way.     

Interface tension in the Polyakov loop model

The interface tension of the Polyakov loop model is calculated by Monte Carlo simulation. The form of the operator measuring the tension is derived from QCD in the strong coupling limit. The result is αa ³=0.0255±0.0003 in terms of the lattice constanta. The interface profile is also calculated and the spatial extent of the interface is estimated to be 10 lattice spacings. The result implies that the phase transition in the Polyakov loop model is of first order.     

Topological charge of (lattice) gauge fields

Using recently derived explicit formulae for the 2- and 3-cochains in SU(2) gauge theory, we are able to integrate the Chern-Simons density analytically. We arrive — in SU(2) — at a local algebraic expression for the topological charge, which is the sum of local winding numbers associated with the corners (lattice points) of the cells covering the manifold plus contributions from possible isolated gauge singularities which manifest themselves as “vortices” in the 1-, 2- or 3-cochains. Among others we consider hypercubic geometry — i.e. covering the manifold by hypercubes — which is of particular interest to lattice Monte Carlo applications. Finally, we extend our results to SU(3) gauge theory.