Canonical Ensemble Monte Carlo Simulations Research Articles

Grand Canonical Ensemble Monte Carlo Simulations of Donnan Potentials, Nonelectroneutrality, Activity Coefficients and Excess Energy in Spherical Charged or Uncharged Pores with Restricted Primitive Model Electrolytes

Abstract A great number of Grand Canonical Ensemble simulations have been performed for restricted primitive model electrolytes in spherical hard-wall pores with the same dielectric permittivity in the pores and in the wall. The pores have a continuously distributed surface charge from 0 to 10 elementary charges and radii from 1 to 35 ionic diameters. When a pore is in equilibrium with an outside bulk solution, it acquires in the average a certain deviation from electroneutrality (spontaneous electrification). For any given pore surface charge this electrification is a given function of the radius of the accessible part of the pore scaled by the Debye length without regard to the Debye length without regard to the Bjerrum parameter or the bulk concentration of the electrolyte and without regard to the pore size relative to the ion diameter. If an additional uniform electric potential is applied in the pore, the electrification changes. At a certain potential the pore is electroneutral. This potential is a...

Theoretical study on the water structure of the aqueous amino acid solutions using Monte Carlo method.

Abstract Series of canonical ensemble Monte Carlo simulations are carried out at 298K to study the role of water-amino acid interactions in determining solvent water structure. Each simulation box is composed of 222 water molecules and one amino acid zwitterion such as Alanine(Ala), Tyrosine(Tyr), Serine(Ser), Asparagine (Asn) and Aspartate(Asp). Thermodynamic properties and some structural properties are obtained by ensemble averaging during the simulations. Special interests are focused on the analysis of radial distribution functions and four, five, six and seven- membered ring structures connected via hydrogen bonds of solvent water molecules surrounding each amino acids. The hydrophilicity of an amino acid is found to be closely related to the characteristic of hydrogen bond distributions. Especially, the number of topological 6 and 7-membered ring structures increases as the hydrophilicity of an amino acid increases.

A Monte Carlo study of aging effects observed in (RE)Ba 2Cu 3O 7−x films

We have investigated the aging of (RE)Ba 2Cu 3O 7−x thin films using a grand canonical ensemble Monte Carlo simulation of the asymmetric next nearest neighbor Ising (ASYNNNI) model. The effect of aging is a reduction in oxygen content and hole concentration. Discrepancies exist in the calculated and experimentally observed hole concentrations, suggesting that the superconductor-insulator (S-I) transition in these films to be a mobility transition rather than being due to a reduction in the number of carriers.

Computer Simulation of Diffusion and Adsorption in Pillared Clays

ABSTRACTWe developed a model to describe the morphology and energetics of pillared clays. Grand- Canonical Ensemble Monte Carlo and Molecular Dynamics simulations are used to study diffusion and adsorption of finite-size molecules in such systems, and the effect of various factors on these processes is investigated.

Direct Calculation of the Electric Potential Distributions around Ions from High Precision Canonical Ensemble Monte Carlo Simulations of Some Primitive Model Electrolyte Systems

Abstract The conditional electric potential around the ions are found by Poisson integration of the conditional charge densities calculated from the radial distribution functions found by the high precision canonical ensemble Monte Carlo simulations of some Z:Z,2:1 and 1:1:1 primitive model electrolyte systems described in earlier studies. In most cases, the correspondance with the solution given by solving the linear Poisson-Boltzmann equation is very nearly perfect – at least not too far from contact. This is so in spite of the fact, that the linearisation condition of Debye and Huckel is violated near to contact in dilute solutions and in spite of the anticipation that the Debye-Huckel approximation should be of little relevance in more concentrated systems, where the Debye length is of the same order of magnitude as the ionic diameters. The linear Poisson-Boltzmann equation even continues to be of relevance in zones around ions of different sizes, where only part of the ions appearing in the solution ...

High Precision Canonical Ensemble Monte Carlo Simulations of Very Dilute, Primitive Z:Z and 2:1 Electrolytes and of Moderately Concentrated 1:1 Electrolyte Mixtures

Abstract Long-run Canonical Ensemble Monte Carlo Simulations of highly dilute, primitive model z:z and 2:1 electrolytes and of moderately concentrated (1 mol/L) mixtures of 1:1 electrolytes have been performed for a wide range of the number of ions (N) in the simulation cell (up to N = 1728). The excess energy, the excess Helmholtz' free energy, the excess heat capacity and the single ion activity coefficients have been simulated directly. The proper way of extrapolating the data to the thermodynamic limit is emphasized. In particular, the importance of the previously found analytical correction of the Widom method for the deviation from electroneutrality is stressed. The methodology presented opens up for the possible use of ≫ fast Monte Carlo ≪ simulations of e.g. single ion activity coefficients using systems with only a small number of ions. The Poirier formula—base on the exponential integral—for the mean ionic activity coefficients for the restricted primitive case (same ionic radii) seems to be confirmed for z:z and 2:1 electrolytes in highly dilute as well as moderately concentrated solutions. The ≫ negative deviations ≪ from the limiting law predicted at high dilution by the Poirier formula are found also by MC simulations. In mixtures of moderately concentrated 1:1 electrolytes, the Harned rule of linearity in the salt fraction was found valid for the mean ionic excess chemical potentials as well as for the single ion excess chemical potentials, the excess energy and the excess heat capacity at constant volume. The MSA theory gives a quite good approximation of the values. The radial distribution functions are also found by direct simulations and closely examined. In all cases investigated—except for high valency z:z electrolytes—the electric contributions to the potentials of mean force between the ions are very closely given by the electric potential of the linear Debye-Hückel theory. This is the content of the DHX model. Small deviations from the DHX potentials of mean force occur mainly between ions of the same sign and at large separations between the ions. At high Bjerrum parameters, formation of linear triplets perturbs the RDF's, however.

Adsorption of vapor at a solid interface: a molecular model of clay wetting

A molecular description of the clay-water interface is used to simulate the adsorption of water on a solid surface. Grand canonical ensemble and isobaric-isothermal ensemble Monte Carlo simulations are used to describe the organization of the film of liquid water molecules adsorbed on a clay surface. This treatment allows predictions of the wettability of the mineral surface as a function of its charge density and the chemical nature of its different atomic components

Simulations on the counterion and solvent distribution functions around two simple models of a polyelectrolyte

We present our results from a series of long canonical ensemble Monte Carlo simulations on the counterion and solvent distribution functions in regions close to a high charge density negatively charged polyelectrolyte. The simulations are all for the «salt free» solution; i.e., a neutralizing number of counterions are present, but there is no additional supporting electrolyte

Ion and potential distributions in charged and non-charged primitive spherical pores in equilibrium with primitive electrolyte solution calculated by grand canonical ensemble Monte Carlo simulation. Comparison with generalized Debye–Hückel and Donnan theory

Grand canonical ensemble Monte Carlo simulations (GCEMC) have been performed for dilute to moderately concentrated restricted primitive model electrolytes (1 : 1) in equilibrium with spherical micropores with radii from 1.5 to 10 times the ionic diameter. The pores are primitive : hard walls, with the same relative permittivity as the pore fluid and a smeared out fixed charge on the walls. The fixed charge is set to zero, one or five elementary charges. The constraining chemical potentials in the bulk solution are found by canonical Monte Carlo simulations by HNC calculations.

Computer Simulation Study of Adsorption, Isosteric Heat and Phase Transitions of Methane on Graphite

AbstractWe report Canonical (NVTMC), Grand Canonical (GOMC) and Gibbs Ensemble Monte Carlo (GEMC) simulations for adsorption of methane on graphite. Lennard-Jones (LJ) potentials are used for the intermolecular interactions, and both structured and structureless (10–4–3) solid-fluid potentials are considered. Several sets of methane-methane L.I parameters have been used in the literature, and we compare results obtained with these sets throughout our simulations. The adsorption isotherm and isosteric heat curve are obtained at 77.5 K and found in good agreement with experiments. The commensurateincommensurate transition (CIT) of methane on a graphite substrate with periodically varying adsorbate-adsorbent potential at 40.0 K is studied and is in qualitative agreement with experiment. The effect of varying the corrugation of the fluid-wall potential on the commensurate and incommensurate phases is explored. The GEMC simulations have been carried out to study the vapor-liquid equilibrium (VLE) of a two-dimensional (2D) LJ fluid with system sizes up to 3000 particles. The effect of system sizes on the critical behavior is investigated. The GEMC method has also been successfully applied to study the VLE in 2D adsorbed films for the first time.

Simulation of Confined Primitive Electrolytes: Application of a New Method of Summing the Coulomb Field

Abstract Recently, Lekner has presented a new method to sum the Coulomb forces between charged particles of a central system and its images extended periodically in 2- and 3- dimensions. In this paper we apply the new method in canonical ensemble Monte Carlo (CMC) simulations of the primitive electrolyte confined between two planar surfaces: one is charged and the other is neutral. The anions and cations have identical size with diameter d = 4.25 A and interact with a hard sphere repulsion and Coulomb interaction. In Lekner's method the long range Coulomb potential is computed from a series of Bessel functions. We have demonstrated that the series converges after about 10 terms and so is computationally quite simpler than the Ewald sum methods. The method is also faster for confined electrolytes than are those Ewald-like sum methods with which we compared it. In our simulations, we obtained the density distributions and mean electrostatic potentials of the confined system for the 1:1 electrolyte having co...

Charge fluctuation in reverse micelles

Electrostatic interactions in and among reverse micelles in the microemulsion are studied by the grand canonical ensemble Monte Carlo simulation (GCEMC) and by the linear response/Poisson–Boltzmann approximation (LPB). The latter theory is found to reproduce the ion-correlation effects among the micelles seen in the earlier canonical Monte Carlo approach. The open ensemble simulation and the Poisson–Boltzmann (PB) equation are used to study solubilization of simple electrolyte in the microemulsion. In systems with monovalent ions, the PB approximation agrees well with the simulation. Since individual ions are allowed to enter or leave the micelle in our GCEMC simulation, the deviations from the electroneutrality of the droplets are also studied. A good agreement with the LPB theory and with the simple charge fluctuation models considering only the Born solvation energy of charged droplets is observed. For large reverse micelles, the LPB theory and the continuum approach of Eicke and co-workers [J. Phys. Chem. 93, 314 (1989)] proved satisfactory while only the discrete model of Hall [J. Phys. Chem. 94, 429 (1990)] agrees with the simulation for small droplets. The GCEMC results lend support to recent interpretations of electric conductivity of microemulsions. The intermicellar forces due to the correlated charge fluctuation on adjacent droplets are discussed. An approximate expression for the charge fluctuation contribution to the long-ranged pair potential among large droplets with the radius Rm of the form w(r)/kT≂−(1/2)(Rm/r)2 is derived.

Rotational insertion bias: a novel method for simulating dense phases of structured particles, with particular application to water

A novel method has been developed to bias the insertion of structured particles into dense phases during grand canonical and Gibbs ensemble Monte Carlo simulations. The method biases the orientation rather than the position of a trial insertion. The method has been shown to increase the acceptance rate by a factor of two. It has been used in Gibbs ensemble simulations of TIPS2 and TIP4P water at and above ambient temperature, and points on a coexistence curve have been simulated. The TIP4P model has been shown to reproduce experimental data much more closely than the TIPS2 model.

Grand Canonical Ensemble Monte Carlo Simulation on a Transputer Array

Abstract Five methods are described for the distribution over a 3D Transputer array of the calculation of the pair interaction component of particle energy. The most efficient method, expressed in terms of the time to complete a simulation, depends on the size of the simulation and the Transputer array. This dependence is quantified, with emphasis on Grand Canonical Ensemble Monte Carlo simulation, and yields criteria for the optimum strategy for parallel implementation of GCEMC algorithms. The equations derived are generally applicable, and have implications for the programming of Molecular Dynamics simulations.

Monomolecular mobile layer of oxygen adsorbed on graphite: The liquid-vapour coexistence curve

In this work we present van der Waals type theory for describing submonolayer adsorption of oxygen on graphite. The theory includes the tilting of admolecules with respect to the surface. The results of theoretical calculations are compared with those resulting from the Grand canonical Ensemble Monte Carlo simulations.

Mixed valency counterions between charged walls: An investigation using Monte Carlo simulation and comparison with Poisson-Boltzmann theory

Systems consisting of parallel charged surfaces of infinite extent delimiting a dielectric medium, containing both monovalent and divalent counterions, have been investigated using canonical ensemble Monte Carlo simulation and a restricted primitive model. Singlet distributions, potential energies, and pressures have been obtained for counterion mixtures containing 0, 20, 40, 60, 80, and 100% of the charge as the monovalent species, with the surface charge either in the form of a regular lattice of discrete charges (the DSC model) or as a continuous sheet of charge (the CSC model). A solution of the Poisson-Boltzmann (PB) equation, which does not appear to have been obtained previously, has been derived for the CSC model and singlet density predictions are compared with the results of simulation. The PB equation provides a qualitative prediction of the singlet densities of all counterion species for the CSC system. In the DSC system the singlet charge density distributions show significant variations parallel to the surface which can be approximated by a Boltzmann distribution; the PB prediction for the singlet density normal to the surface is poorer than in the CSC system. Energies and pressures differ significantly between the DSC and CSC simulations, with the ion-wall part of the interaction being enhanced in the latter. The differences from PB predictions for all system properties increase with the divalent composition of the counterions.

Structure of hard sphere fluids in narrow cylindrical pores

The structure of hard sphere fluid confined to cylindrical capillaries in equilibrium with the bulk fluid phase is considered. Simple analytical approaches are examined and compared with the results of simultaneous grand canonical ensemble Monte Carlo simulations. The validity of the limiting law according to which the fluid density in the capillary approaches its fugacity in vanishingly narrow pores is confirmed. The truncated graphical expansion around the exact narrow pore limit is found to represent a useful approximation for very narrow capillaries. In systems with the pore diameter exceeding a few diameters of the spheres and at the reduced bulk densities of the fluid ρbσ3≤0.6, the Percus–Yevick approximation provides a satisfactory description of the fluid distribution.

Simulation Studies of a Lennard-Jones Liquid in Micropores

Abstract In this paper grand canonical ensemble Monte Carlo and molecular dynamics simulation techniques are used to establish the degree to which the equilibrium and transport properties of fluids in micropores are influenced both by confinement in the narrow pore space and by the lattice structure of the pore wall. Partition coefficients, solvation forces, and diffusion coefficients for a Lennard-Jones liquid confined within two model cylindrical pores are determined over a range of effective micropore sizes. In one model the cylindrical pore wall is described by a structureless, continuum interaction potential similar to that which is frequently employed in theoretical studies of adsorption. In the second model a single embedded layer of lattice atoms is placed at the solid/fluid interface. The results obtained are compared with the prediction of a bulk fluid approximation and the Fischer-Methfessel approximation to the Yvon-Born-Green equation and the recently developed kinetic theory of Davis for mic...

Computer simulations of fluids in zeolites X and Y

We report grand canonical ensemble Monte Carlo simulations of xenon and methane adsorbed in zeolites X and Y. The thermodynamic quantities sampled include the configurational energy per molecule, average occupancy, one-body density distribution function and the distribution of occupancies in the unit cell. From these quantities and the bulk properties of the fluids, adsorption isotherms and isosteric heats of adsorption can be generated and compared with experimental results. Good agreement has been found where such comparisons can be made.

Freezing of binary hard-disc alloys: I. The equation of state and pair structure of the fluid phase

A simple scaling procedure based on the known low-density results is shown to yield an equation of state and partial pair correlation functions of binary hard-disc alloys which agree closely with the results of canonical and isobaric ensemble Monte Carlo simulations. These results will serve as the basic input in a density functional calculation of the fluid-solid phase diagram of such mixtures regarded as a simple model for monolayers of rare-gas mixtures.