Grand Canonical Ensemble Monte Carlo

Orkoulas G and Panagiotopoulos A Z 1999 Phase behavior of the restricted primitive model and square-well fluids from Monte Carlo simulations in the grand canonical ensemble J. Chem. Phys. 110 1581... 

Chesnut D A and Salsburg Z W 1963 Monte Carlo procedure for statistical mechanical calculation in a grand canonical ensemble of lattice systems J. Chem. Phys. 38 2861-75... 

If a confined fluid is thermodynamically open to a bulk reservoir, its exposure to a shear strain generally gives rise to an apparent multiplicity of microstates all compatible with a unique macrostate of the fluid. To illustrate the associated problem, consider the normal stress which can be computed for various substrate separations in grand canonical ensemble Monte Carlo simulations. A typical curve, plotted in Fig. 16, shows the oscillatory decay discussed in Sec. IV A 2. Suppose that instead... 

M. Schoen. Taylor-expansion Monte Carlo simulations of classical fluids in the canonical and grand canonical ensembles. J Comput Phys 775 159-171, 1995. 

T. Gruhn, M. Schoen. A grand canonical ensemble Monte Carlo study of confined planar and homeotropically anchored Gay-Berne films. Mol Phys 95 681-692, 1998. 

M. Thommes, G. H. Findenegg, M. Schoen. Critical depletion of a pure fluid in controlled-pore glass. Experimental results and grand canonical ensemble Monte Carlo simulation. Langmuir 77 2137-2142, 1995. 

To test the results of the chemical potential evaluation, the grand canonical ensemble Monte Carlo simulation of the bulk associating fluid has also been performed. The algorithm of this simulation was identical to that described in Ref. 172. All the calculations have been performed for states far from the liquid-gas coexistence curve [173]. 

Adams, D.J., Grand canonical ensemble Monte Carlo for a Lennard-Jones fluid, Mol. Phys. 1975, 29, 307-311... 

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). 

There are many excellent reviews on the standard molecular dynamics method dealing with calculations in the microcanonical ensemble as well as on the Monte Carlo method involving calculations in the canonical, isothermal isobaric, and grand canonical ensemble (< ). In the present article, we shall limit ourselves exclusively to those developments that have taken place since the work of Andersen (4). In the molecular dynamics method, the developments are the constant-pressure, constant-temperature, constant-temperature-constant-pressure, variable shape simulation cell MD, and isostress calculations in the Monte Carlo method, it is the variable shape simulation cell calculation. 

In a sequence of three papers, Papadimitriou et al. [47-49] performed Monte Carlo molecular simulations in the Grand Canonical Ensemble to study the multiple occupancy of argon and hydrogen in the various cavities of structures II and H. 

Those different aspects (pore size and pore geometry) have been considered in this paper in which we present a study of gas adsorption (Ar, 77 K) in silica pores of different size and shape by atomistic Monte Carlo simulations in the Grand Canonical ensemble (GCMC). 

Monte Carlo Simulation in Grand Canonical Ensemble... 

The simulation runs were performed in the grand canonical ensemble, fixing the chemical potential ji, the volume V of the pore and the temperature T. The system typically consisted of 600-700 adsorbed molecules. For the case of attractive pore-wall interaction, the adsorbed molecules formed seven layers parallel to the plane of the pore walls. A rectilinear simulation cell of 10a// by 10a// in the plane parallel to the pore walls was used, consistent with a cutoff of 5a// for the fluid-fluid interaction. The simulation was set up such that insertion, deletion and displacement moves were attempted with equal probability, and the displacement step was adjusted to have a 50% probability of acceptance. Thermodynamic properties were averaged over 100-500 million individual Monte Carlo steps. The length of the simulation was adjusted such that a minimum of fifty times the average number of particles in the system would be inserted and deleted during a single simulation run. 

For a given pore of size r/, the adsorption isotherm is obtained by Monte Carlo simulation of the adsorption process in the continuum, following the usual grand canonical ensemble algorithm [15, 17,18],... 

This review discusses a newly proposed class of tempering Monte Carlo methods and their application to the study of complex fluids. The methods are based on a combination of the expanded grand canonical ensemble formalism (or simple tempering) and the multidimensional parallel tempering technique. We first introduce the method in the framework of a general ensemble. We then discuss a few implementations for specific systems, including primitive models of electrolytes, vapor-liquid and liquid-liquid phase behavior for homopolymers, copolymers, and blends of flexible and semiflexible... 

Rowley, L.A., Nicholson, D., and Parsonage, N.G. (1978). Long-range corrections to grand canonical ensemble Monte Carlo calculations for adsorption systems. J. Comput. Phys., 26, 66—79. 

Once the ideal heterogeneous solids are prepared, the adsorption process is simulated through a continuum space Monte Carlo method in the grand canonical ensemble [26, 27]. 

Bottani, E. and Bakaev, V. (1994). The grand canonical ensemble Monte Carlo simulation of nitrogen on graphite. Langmuir, 10, 1550—5. 

Grand canonical ensemble Monte Carlo simulations... 

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