Canonical Monte Carlo

Valleau J P and Cohen L K 1980 Primitive model electrolytes. I. Grand canonical Monte Carlo computations J. Chem. Phys. 72 5932... 

Grand Canonical Monte Carlo Simulations of Adsorption Processe ... 

One application of the grand canonical Monte Carlo simulation method is in the study ol adsorption and transport of fluids through porous solids. Mixtures of gases or liquids ca separated by the selective adsorption of one component in an appropriate porous mate The efficacy of the separation depends to a large extent upon the ability of the materit adsorb one component in the mixture much more strongly than the other component, separation may be performed over a range of temperatures and so it is useful to be to predict the adsorption isotherms of the mixtures. 

A7 Ethane/methane selectivity calculated from grand canonical Monte Carlo simulations of mixtures in slit IS at a temperature of 296 K. The selectivity is defined as the ratio of the mole fractions in the pore to the ratio of mole fractions in the bulk. H is the slit width defined in terms of the methane collision diameter (Tch,- (Figure awn from Crackncll R F, D Nicholson and N Quirke 1994. A Grand Canonical Monte Carlo Study ofLennard-s Mixtures in Slit Pores 2 Mixtures of Two-Centre Ethane with Methane. Molecular Simulation 13 161-175.)... 

FIG. 21 Dependence of the average density on the configurational chemical potential. The solid line denotes the grand canonical Monte Carlo data, the long dashed fine corresponds to the osmotic Monte Carlo results for ZL = 40, and the dotted line for ZL = 80. (From Ref. 172.)... 

To conclude, the introduction of species-selective membranes into the simulation box results in the osmotic equilibrium between a part of the system containing the products of association and a part in which only a one-component Lennard-Jones fluid is present. The density of the fluid in the nonreactive part of the system is lower than in the reactive part, at osmotic equilibrium. This makes the calculations of the chemical potential efficient. The quahty of the results is similar to those from the grand canonical Monte Carlo simulation. The method is neither restricted to dimerization nor to spherically symmetric associative interactions. Even in the presence of higher-order complexes in large amounts, the proposed approach remains successful. 

The arrows indicate a semi-permeable membrane and the species allowed to permeate is shown within the arrows. The parentheses show a GEMC phase (or region) and the species it contains. The first and the last region are also connected to each other. Using such a scheme, Bryk et al. showed that osmotic Monte Carlo can be successfully used to study the association of two different molecular species when an associating intermolecular potential is included in the simulation. The results agreed well with the more traditional grand-canonical Monte Carlo methods. 

Berardi et al. [66] have also investigated the influence of central dipoles in discotic molecules. This system was studied using canonical Monte Carlo simulations at constant density over a range of temperatures for a system of 1000 molecules. Just as in discotic systems with no dipolar interaction, isotropic, nematic and columnar phases are observed, although at the low density studied the columnar phase has cavities within the structure. This effect was discovered in an earlier constant density investigation of the phase behaviour of discotic Gay-Berne molecules and is due to the signiflcant difference between the natural densities of the columnar and nematic phases... 

The essential influence of surface roughening is also present in this model. Grand canonical Monte Carlo calculations were used to generate adatom populations at various temperatures up to Chemical potentials corresponding to those in the bulk LJ crystal were used, and these produced adatom densities that increased with temperature and roughly approximated the values observed in Ising model simulations below T. ... 

The discussion in Refs. 17 and 18 is illustrative. Torrie [17] presented very important results for grand canonical Monte Carlo simulations of an electrical double layer in 2 1 electrolytes. Those results provide very convincing evidence that C < 0 can occur under cr-control. However, instead of analyzing the consequences of this fact for real systems, the author simply quotes the statement [21] that sign of C is not restricted, even for -control. Reliance on this result (see a critique in Ref. 22) simply ignored the problem and discouraged closer study of this system. 

Wang, Q. Johnson, J. K. Broughton, J. Q., Path integral grand canonical Monte Carlo, J. Chem. Phys. 1997,107, 5108-5117... 

A grand-canonical Monte Carlo (GCMC) simulation for a one-component system is performed as follows. The simulation cell has a fixed volume V, and periodic... 

Kofke, D. A., Semigrand canonical Monte Carlo simulation integration along coexistence lines, Adv. Chem. Phys. 1999,105, 405 142... 

Woo, H. J. Dinner, A. R. Roux, B., Grand canonical Monte Carlo simulations of water in protein environments, J. Chem. Phys. 2004,121, 6392-6400. 

P. Kowalczyk, H. Tanaka, R. Holyst, K. Kaneko, T. Ohmori, and J. Miyamoto, Storage of hydrogen at 303 K in graphite slitlike pores from grand canonical Monte Carlo simulation, J. Phys. Chem. B, 109, 17174-17183 (2005). 

Abbreviations MD, molecular dynamics TST, transition state theory EM, energy minimization MSD, mean square displacement PFG-NMR, pulsed field gradient nuclear magnetic resonance VAF, velocity autocorrelation function RDF, radial distribution function MEP, minimum energy path MC, Monte Carlo GC-MC, grand canonical Monte Carlo CB-MC, configurational-bias Monte Carlo MM, molecular mechanics QM, quantum mechanics FLF, Hartree-Fock DFT, density functional theory BSSE, basis set superposition error DME, dimethyl ether MTG, methanol to gasoline. 

The grand canonical ensemble is appropriate for adsorption systems, in which the adsorbed phase is in equilibrium with the gas at some specified temperature. The use of a computer simulation allows us to calculate average macroscopic properties directly without having to explicitly calculate the partition function. The grand canonical Monte Carlo (GCMC) method as applied in this work has been described in detail earlier (55). The aspects involving binary fluid mixtures have been described previously in our Xe-Ar work (30). 

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