Grand canonical Monte Carlo molecular simulation

Essential progress has been made recently in the area of molecular level modeling of capillary condensation. The methods of grand canonical Monte Carlo (GCMC) simulations [4], molecular dynamics (MD) [5], and density functional theory (DFT) [6] are capable of generating hysteresis loops for sorption of simple fluids in model pores. In our previous publications (see [7] and references therein), we have shown that the non-local density functional theory (NLDFT) with properly chosen parameters of fluid-fluid and fluid-solid intermolecular interactions quantitatively predicts desorption branches of hysteretic isotherms of nitrogen and argon on reference MCM-41 samples with pore channels narrower than 5 nm. 

Beside classical methods of pore size analysis, there are many advanced methods. Seaton et al. [161] proposed a method based on the mean field theory. Initially this method was less accurate in the range of small pore sizes, but even so it g ve a more realistic -way for evaluation of the pore size distribution than the classical methods based on the Kelvin equation [162]. More rigorous methods based on molecular approaches such as grand canonical Monte Carlo (GCMC) simulations [147, 163-165] and nonlocal density functional theory (NLDFT) [86, 146, 147, 161, 163-169] have been developed and their use for pore size analysis of active carbons is continuously growing. 

The molecular simulation method employed in this paper is the Grand Canonical Monte Carlo (GCMC) simulation. The parameters associated with the MC simulation used in this paper are (i) the linear dimension of the simulation box in the X- and y-diiections is at least 10 times the collision diameter, (ii) the cut-off radius is taken to be half of the box length, (iii) the number of cycles for equilibration and statistical collection step is 50,000 and (iv) in each cycle, there are N displacement moves and N rotations (in the case of 5-Site model) where N... 

It can be seen from Eq. (14) that the problem basically bods down to the accurate and efficient determination of p(P, w). In the last decade, two main methods based on statistical mechanics have emerged. These are the density functional theory (DFT), and molecular simulation methods such as grand-canonical Monte Carlo (GCMC) simulations. Both of these methods are steadily gaining popularity for PSD estimation and are discussed briefly in the following subsections. 

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.)... 

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. 

Abstract We use Nuclear Magnetic Resonance relaxometry (i.e. the frequency variation of the NMR relaxation rates) of quadrupolar nucleus ( Na) and H Pulsed Gradient Spin Echo NMR to determine the mobility of the counterions and the water molecules within aqueous dispersions of clays. The local ordering of isotropic dilute clay dispersions is investigated by NMR relaxometry. In contrast, the NMR spectra of the quadrupolar nucleus and the anisotropy of the water self-diffusion tensor clearly exhibit the occurrence of nematic ordering in dense aqueous dispersions. Multi-scale numerical models exploiting molecular orbital quantum calculations, Grand Canonical Monte Carlo simulations, Molecular and Brownian Dynamics are used to interpret the measured water mobility and the ionic quadrupolar relaxation measurements. 

The principal tools have been density functional theory and computer simulation, especially grand canonical Monte Carlo and molecular dynamics [17-19]. Typical phase diagrams for a simple Lennard-Jones fluid and for a binary mixture of Lennard-Jones fluids confined within cylindrical pores of various diameters are shown in Figs. 9 and 10, respectively. Also shown in Fig. 10 is the vapor-liquid phase diagram for the bulk fluid (i.e., a pore of infinite radius). In these examples, the walls are inert and exert only weak forces on the molecules, which themselves interact weakly. Nevertheless,... 

The complexity of xylene adsorption over zeolites is too high to predict the selectivity from the chemical properties of the zeolite only (electronegativity of the cations, charge of the framework oxygens). The interactions between xylenes and the zeolite must necessarily be considered, which explains the important development of molecular simulation methods. This is supported by the work of V. Lachet et al. (18) who succeeded in reproducing the inversion of selectivity between KY and NaY with Grand Canonical Monte Carlo Simulations. 

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. 

In the molecular simulation of adsorption in confined space such as pores of adsorbent, the most widely used and success l ensemble is the grand canonical Monte Carlo simulation. In this ensemble, we specify the chemical potential of the fluid,p, that the candidate pore is immersed in, the size of the pore, and the temperature. 

The absolute adsorption isotherm as a function of gas-phase fuga ity is obtained directly from molecular simulations based on the grand canonical Monte Carlo (GCMC) method. Since the difference between absolute and excess adsorption is negligible at sub-atmospheric pressure, the low-pressure portion of the absolute isotherm can adso be determined from experiment. Eq. (2) is suitable for extrapolating the absolute isotherm from low to high pressure and Eq. (3) provides the conversion to excess adsorption. Experiments are needed to test these predictions of adsorption at high pressure. 

Up to now, numerous studies have been conducted on their synthesis [9,10], treatment [5,13] and physical properties [4], However only limited number of studies has been carried out on die adsorption of gas in CNTs, including experimental works [8,11] and molecular simulations [3,7,14-lS]. Adsorption behavior depends strongly on the microporous structure of the particular adsorbent. In this work the effect of pore size on the adsorption behavior is of interest. The adsorption equilibria of methane, ethane and their mixture into SWNTs were studied by using a Grand Canonical Monte Carlo (GCMC) method. We reported equilibrium isotherms of methane and ethane, and the selectivity from their equimolar mixture. 

The shape of a zeolite sorption uptake isotherm, a quantitation of the amount of a given sorbate taken up as a function of its partial pressure in the gas phase in equilibiitun with the zeolite sorbent, depends both on the zeolite sorbate interaction and on the sorbate - sorbate interactions. Simulation of such isotherms for one or more sorbates is accomplished by the Grand Canonical Monte Carlo method. Additional to the molecular reorientation and movement attempts is a particle creation or annihilation, the probability of which scales with the partial pressure [100,101]. This procedure thus simulates the eqmlibrium between the sorbed phase in the zeolite and an infinite gas / vapor bath. Reasonable reproduction of uptake isotherms for simple gases has been achieved for a small number of systems (e.g. [100,101]), and the molecular simulations have, for example, explained at a molecular level the discontinuity observed in the Ar - VPI-5 isotherm. 

---