Grand Canonical Monte Carlo Calculations Research Articles

A DFT study on clay–cation–water interaction in montmorillonite and beidellite

This study is the first attempt to generate a realistic model for the clay–cation–water system. We use a molecular description of the solvent and clay sheet. We have chosen two clay materials from 2:1 dioctahedral smectites (1) montmorillonite and (2) beidellite to monitor the effect of negative charge on the location of interlayer cation (Na +), as the negative charge gets introduced in the clay system from octahedral Al substitution and tetrahedral Si substitution as the case may be (1) and (2), respectively. We use Grand Canonical Monte Carlo (GCMC) simulation to locate the interlayer cation and to calculate the number of interlayer water molecules surrounding the cation (Na +) for both the clay materials. The results show that each Na + cation is surrounded by five water molecules. The minimum energy conformer obtained from GCMC calculations has been used to generate the cluster model for Local Density Functional (LDF) calculations. The results show the Na + cation moves towards the negative center of the clay cluster. It is also observed that Na + cation gets more stabilized in montmorillonite in comparison to beidellite.

Phase behavior of ionic solutions: Comparison of the primitive and explicit solvent models

Grand canonical Monte Carlo calculations are used to investigate the demixing transition in model ionic solutions where the solvent is explicitly included. Charged hard sphere ions in hard sphere, dipolar hard sphere and quadrupolar hard sphere solvents are considered and the results are compared with the primitive (continuum solvent) model. For all solvents considered, it is found that the demixing transition is in the same general region of the phase diagram and is roughly described by liquid-vapor equilibrium in the primitive model. However, details such as the precise location of the critical point and the width of the unstable region depend upon the exact nature of the solvent.

Adsorption of Nitrogen on Rutile (110): Monte Carlo Computer Simulations

Grand canonical and canonical ensemble Monte Carlo computer simulations of the adsorption of N2 on the (110) face of rutile at 77 K are reported. A novel ab initio adsorbate−adsorbent interaction potential is employed in conjunction with the X1 nitrogen−nitrogen potential to investigate the adsorption mechanism. It is demonstrated that at low pressures (1 Torr and below) the Ti adsorption sites within the depressed rows of oxides on the rutile (110) face (denoted by A) are completely occupied by nitrogen molecules in end-on orientations with slight alternating tilts perpendicular to the row axis that are produced by repulsive lateral interactions. At higher pressures, adsorption on rows of exposed oxides (denoted by B) commences, typically with a side-on orientation of the N2 molecules. The calculated isotherm of adsorption exhibits type II behavior according to the Brunauer−Deming−Deming−Teller classification, in agreement with experimental findings. Although the experimental isotherms are often evaluate...

The structure and adsorption of diatomic fluids in disordered porous media. A Monte Carlo simulation study

The adsorption isotherms for diatomic fluids in disordered porous media have been obtained from grand canonical Monte Carlo computer simulation. A disordered porous medium, or matrix, is prepared by quenching an equilibrium configuration of spherical hard core molecules. In addition, canonical Monte Carlo simulations have been performed for equilibrium binary mixtures that represent counterparts of quenched-annealed systems in question. For the same chemical potential of diatomic molecules at a fixed density of matrix species, the structure and the density of the diatomic fluid in the binary mixture and in the quenched medium are very similar. This behaviour holds also for systems with attractive interactions in the region of high temperatures. Observed similarity of the structural and thermodynamic properties of the mixture and the corresponding annealed fluid-quenched matrix system permits the use of the thermodynamics of the mixture to evaluate some properties of quenched-annealed fluids. Calculations were made of the adsorption isotherm of the diatomic fluid in a disordered hard sphere matrix using a successful theoretical equation of state for mixtures, agreement with computer simulation data was excellent.

Phase Equilibria of Lattice Polymers from Histogram Reweighting Monte Carlo Simulations

Histogram-reweighting Monte Carlo simulations were used to obtain polymer / solvent phase diagrams for lattice homopolymers of chain lengths up to r=1000 monomers. The simulation technique was based on performing a series of grand canonical Monte Carlo calculations for a small number of state points and combining the results to obtain the phase behavior of a system over a range of temperatures and densities. Critical parameters were determined from mixed-field finite-size scaling concepts by matching the order parameter distribution near the critical point to the distribution for the three-dimensional Ising universality class. Calculations for the simple cubic lattice (coordination number z=6) and for a high coordination number version of the same lattice (z=26) were performed for chain lengths significantly longer than in previous simulation studies. The critical temperature was found to scale with chain length following the Flory-Huggins functional form. For the z=6 lattice, the extrapolated infinite chain length critical temperature is 3.70+-0.01, in excellent agreement with previous calculations of the temperature at which the osmotic second virial coefficient is zero and the mean end-to-end distance proportional to the number of bonds. This confirms that the three alternative definitions of the Theta-temperature are equivalent in the limit of long chains. The critical volume fraction scales with chain length with an exponent equal to 0.38+-0.01, in agreement with experimental data but in disagreement with polymer solution theories. The width of the coexistence curve prefactor was tentatively found to scale with chain length with an exponent of 0.20+-0.03 for z = 6 and 0.22+-0.03 for z = 26. These values are near the lower range of values obtained from experimental data.

Structure in confined fluids: phase separation of binary simple liquid mixtures

One- to five-layer cyclohexane and octamethyltetracyclosiloxane(OMCTS) films confined between mica-like surfaces are studied to elucidate changes in the lattice type and composition of the films. Grand canonical ensemble Monte Carlo computer simulations are used to study the laterally confined film. In contrast to previous studies, solid-like order is induced primarily by the strong fluid-solid interaction and is largely a function of pore width. Solid-like order within the layers causes the composition of the pore fluid to shift from the bulk composition, favoring either cyclohexane or OMCTS, depending on the pore width. A shift in the relative alignment of the surfaces perturbs the solid-like fluid structure but does not cause the sudden shear melting transition associated with epitaxial alignment of the fluid atoms with the surface.

Adsorption energy distribution functions

The adsorption energy distribution functions for nitrogen and argon adsorbed on heterogeneous surfaces are calculated. These distributions are obtained by the least-squares method. The calculated monolayer capacity is proposed as a test of the goodness of the adsorption energy distribution function. Model surfaces are constructed using Bernal's model, and the corresponding adsorption isotherms are generated through grand canonical Monte Carlo computer simulations. The distributions obtained from adsorption isotherms are compared with those obtained from energy maps.

Effect of Loading and Nanopore Shape on Binary Adsorption Selectivity

Grand canonical Monte Carlo (GCMC) computer simulations are employed to predict selective adsorption from binary mixtures into slit, cylindrical, and spherical nanopores. The mixtures are Lennard-Jones fluids representative of Ar, Xe, and tetramethylsilane (TMS), allowing us to gauge the effects of adsorbate size, energy well depth, and mass. The adsorption selectivity can oscillate from favoring one component to the other as nanopore size increases. Beyond simple molecular sieving, two distinct mechanisms can be responsible for size selectivity. At low pore densities, selectivity depends mainly on which species is more energetically favorable in the nanopore. At high pore densities, though, the ability to pack well within the pore is most important so the component size becomes the main criterion for selectivity. In high-pore density processes (many separations, catalytic processes, and templating during zeolite synthesis), the last mechanism can be active and requires consideration.

Integral equation and computer simulation studies of hard spheres in a slit pore

The structure of a hard sphere fluid inside a planar slit pore is studied using integral equation and computer simulation approaches. A robust and efficient method of numerically solving the one-particle Ornstein-Zernike (OZ) equation for the density profile in conjunction with an arbitrary closure is described, which is an approximate Newton-Raphson iteration in Fourier space. A new form of reference hypernetted chain theory is proposed that uses the bridge function of a fluid of hard spheres near a hard wall as a reference system. This is tested against new grand canonical ensemble Monte Carlo computer simulation data obtained herein and the results of other OZ equation based theories, including the Percus-Yevick hypernetted chain, Martynov-Sarkisov and modified Verlet theory, at reduced bulk fluid number densities up to 0·7 and for pore sizes varying from 1·25 to 4·0. The proposed theory gives accurate density profiles and pressures for the entire range of slit sizes, and is superior to the other theories considered.

Electrochemical potentials in the grand canonical ensemble

The grand canonical ensemble has been used to study electrochemical potentials in confined ionic systems. Grand canonical ensemble Monte Carlo calculations for the primitive model of electrolyte solutions are presented for spherical systems, and the evaluation of single ion activity coefficients by such calculations is discussed. It is also shown that the introduction of finite, confined systems resolves a well-known problem associated with the application of the Kirkwood-Buff theory to ionic systems.

Hard, charged spheres in spherical pores. Grand canonical ensemble Monte Carlo calculations

A model consisting of hard charged spheres inside hard spherical pores is investigated by grand canonical ensemble Monte Carlo calculations. It is found that the mean ionic density profiles in the pores are almost the same when the wall of the pore is moderately charged as when it is uncharged. Also, a bulklike phase is found to be present at the center of the pores in surprisingly small systems. Finally, the Poisson–Boltzman approximation is discussed in the light of our Monte Carlo results.

Grand canonical Monte Carlo simulations on aqueous solutions of sodium chloride and sodium DNA: excess chemical potentials and sources of nonideality in electrolyte and polyelectrolyte solutions

Grand canonical Monte Carlo computer simulations on [NaCl] aq and [NaDNA] aq in the presence of added salt are reported. The results for the simple electrolyte indicate that a (12,6,1) potential function for the ions in a solvent treated as a dielectric continuum supplemented with a Gurney correction term for desolvation describes the behavior of activity coefficients as a function of concentration quite well over a concentration range of 5-500 mM

Hard-sphere fluids inside spherical, hard pores. Grand canonical ensemble Monte Carlo calculations and integral equation approximations

Density profiles and partition coefficients are obtained for hard-sphere fluids inside hard, spherical pores of different sizes by grand canonical ensemble Monte Carlo calculations. The Monte Carlo results are compared to the results obtained by application of different kinds of integral equation approximations. Also, some exact, analytical results for the partition coefficients are given, which are valid in the case of (very) small pores or at low density, respectively.

Salt exclusion from charged and uncharged micropores

The exclusion of electrolytes from charged and uncharged capillaries is studied using (a) the Poisson-Boltzmann equation and (b) Grand Canonical Monte Carlo computer simulations. The thermodynamics and structure are examined as a function of the charge fixed on the inner capillary surfaces. The results for 2:2 electrolytes indicate that the classical Poisson-Boltzmann equation breaks down under these conditions, and in fact its predictions are in serious disagreement with the simulation results for the same system over the whole range of surface charge densities. An additional interesting result of this study concerns the ability of microporous materials to exclude electrolytes. The salt exclusion first increases by increasing the charge density, passes through a maximum, and then decreases with further increase of the surface charge. This behavior (completely missed by the Poisson-Boltzmann approximation) can be explained by the influence of the interionic correlations on the distribution of electrolyte inside the capillary.

Grand canonical Monte Carlo calculations of thermodynamic coefficients for a primitive model of DNA-salt solutions

Grand canonical Monte Carlo calculations of thermodynamic coefficients for a primitive model of DNA-salt solutions

Microscopic studies of fluids in pores: Computer simulation and mean-field theory

The behavior of a simple model of a fluid confined to a single, infinitely long cylindrical pore is investigated by means of both a grand canonical Monte Carlo computer simulation and a mean-field theory. The theory is used to calculate the density profile of the fluid, as well as the grand potential of the system. The effect of the (size of the) pore radius as well as the temperature and pressure on the phase behavior of the fluid is studied in some detail, and the results are compared to those produced by related work in this field. The preliminary results from the simulation indicate that, in pores whose radii are a few molecular diameters in size, the fluid molecules tend to pack in cylindrically concentric shells about the axis of the pore.

The chloroform/graphite and carbon tetrachloride/graphite interfaces : Monte Carlo calculations of their properties

The Grand Canonical Monte Carlo calculations of the properties of the chloroform/graphite and carbon tetrachloride/graphite interface have been performed at temperatures of 231.2, 268.2 (chloroform only) and 323.2 K. Agreement with experimental results is good for the chloroform/ graphite interface but less satisfactory for the carbon tetrachloride/graphite interface.

Calculating the low temperature vapour line by Monte Carlo

A combination of canonical and grand-canonical ensemble Monte Carlo calculations, together with the virial expansion, have been used to calculate the thermodynamic properties of the liquid/vapour co-existence curve of the (6 : 12) Lennard-Jones fluid for reduced temperatures, [Ttilde] ⩽ 1·1. The results for the liquid density and energy and the latent heat of vaporization are believed to be precise, with the exception of the point at [Ttilde]=1·1 which may lie outside the range of the function fitting the liquid phase Monte Carlo data. The liquid density and the saturated vapour pressure are in very good agreement with the results of perturbation theory. The latent heat of vaporization does not agree well with the experimental data for argon though the fit to liquid density and internal energy is good.