Grand canonical ensemble Monte Carlo simulations

2 Grand canonical ensemble Monte Carlo simulations 

For pedagogic reasons it seems sensible to eon.sider a fluid confined to a slit-pore with chemically heterogeneous substrates to make contact with the parallel mean-field calculations described in Section 4.3. As in that section we employ a simple cubic lattice of M sites. In accord with our previous notation, represents a configuration of fluid molecules where the (doublevalued, discrete) elements of the A/ -dimensional vector are represented by Eq. (4.51). Molecules of the (pure) lattiee fluid intoraet with each other via a square-well potential where the width of the attractive well is equal to the lattice constant 

The fluid substrate interaction is modelled according to Eqs. (4.48). To minimize finite size effects, periodic boundary conditions are applied at the planes x = l,n and y = l,ny such that a molecule located at the plane a = 1 interacts with its nearest neighbors on lattice sites characterized by a = n and vice versa where a = x, y. 

We treat the lattice fluid as an open thermodynamic system represented microscopically by the grand canonical ensemble. In this ensemble the probability density for the occupation of a given site i on the lattice is given by 

The sequence of M attempts to change the occupation numbers constitutes a MC cycle. 

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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. 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]. 

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 of the adsorption properties of several model faujasite zeolites were performed using the statistical bias method. The results enable a better understanding of the effect of cation exchange in the selective adsorption of binary mixtures of para and meta xylene isomers. We predict that adding a small amount of water molecules could enhance the adsorption selectivity in favour ofp-xylene. 

Sorensen, T.S. and Sloth, P., Ion and potential distribution in charged and non-charged primitive spherical pores in equilibrium with primitive electrolyte solution calculated by grand canonical ensemble Monte Carlo simulation, J. Chem. Soc. Faraday Trans., 88 (4), 571-589, 1992. 

Resat H, Mezei M (1996) Grand canonical ensemble Monte Carlo simulation of the dCpG/ proflavine erystal hydrate. Biophysical J 71(3) 1179-1190... 

Grand Canonical Ensemble Monte Carlo simultadons of nitrogen physisorption performed with this model solid reproduced the experimental isotherms. Moreover different silanol numbers were simulated by randomly changing surface oxides anions by less adsorbing atomic groups of the same size. This model neither can predict any mechanical property of the solid nor its chemical reactivity since it does not take into account the chemical structure of the real solid. We shall later discuss the results obtained with this model. 

Theoretical studies, like first-principles calculations, grand canonical ensemble Monte Carlo (GCMC) simulations, second order Moller-Plesset perturbation theory (MP2) calculations and density functional theory (DFT) calculations, have been utilized to investigate optimal structures and their properties. Combined experimental and theoretical data provide a window to the plan of design of these network structures and lead to a new direction to investigate porous networks. 

Escobedo F A and de Pablo J J 1996 Expanded grand canonical and Gibbs ensemble Monte Carlo simulation of polymers J. Chem. Phys. 705 4391-4... 

Lynch GC, Pettitt BM (1997) Grand canonical ensemble molecular dynamics simulations Reformulation of extended system dynamics approaches. J Chem Phys 107 8594-8610 Madura JD, Pettitt BM, Calef DF (1988) Water under high pressure. Mol Phys 64 325 Mahoney MW, Jorgensen WL (2000) A five-site model for liquid water and the reproduction of the density anomaly by rigid, nonpolarizable potential functions. J ChemPhys 112 8910-8922 March RP, Eyring H (1964) Application of significant stmcture theory to water. J Phys Chem 68 221-228 Martin MG, Chen B, Siepman JI (1998) A novel Monte Carlo algorithm for polarizable force fields. 

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... 

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

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). 

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