Grand Canonical Monte Carlo method

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. 

Cerius2 (MSI Inc.) was used throughout the simulations. Forcefield parameters obtained by Mellot et all. [3] are listed in Table 1. Ilie Grand Canonical Monte Carlo method (under constant chemical potential (p), volume (V), temperature (T)) was used to get the equilibrium amount adsorbed. 

At a fixed T and for a given value of p, the adsorption process has been simulated by using the grand canonical Monte Carlo method [S]. At any elementary step, a site chosen at random is tested to change its occupancy state according to the Metropolis scheme of probabilities where Hf andtf/ are the hamiltonians... 

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. 

In the grand-canonical Monte Carlo method, the system volume, temperature, and chemical potential are kept fixed, while the number of particles is allowed to fluctuate.There exist three types of trial move (1) displacement of a particle, (2) insertion of a particle, and (3) removal of a particle. These trial moves are generated at random with equal probability. The acceptance probability of the Metropolis method can be used for the trial moves of type (1). For the two other types, the acceptance probabilities are different. Regarding zeolites, an adsorption isotherm can be calculated with the grand-canonical Monte Carlo method by running a series of simulations at varying chemical potentials. 

Computer simulations of the isotherm of adsorption are frequently based on the grand canonical Monte Carlo method [40]. If the atomic structure of the solid adsorbent is known and if the adsorbate/solid and adsorbate/adsorbate energies can be computed, this algorithm makes it possible to calculate isotherms of adsorption directly. 

The first method for simulating chemically reactive systems was proposed by Coker and Watts [11,12]. They presented a modified grand canonical Monte Carlo method wherein the total number of molecules is held fixed but the concentrations of the reacting species is allowed to vary. In their method a molecule is allowed to change species with a probability proportional to the exponential of the difference in chemical potentials between the two components. Thus, their method requires that the chemical potential differences be specified. Coker and Watts applied their method to the reaction... 

The key feature about the grand canonical Monte Carlo method is that the number of particles may change during the simulation. There are three basic moves in a grand canonical Monte Carlo simulation ... 

Such methods of analysing and describing adsorption data have considerable merit in describing microporosity in porous carbons, which are not crystalline, or for microporous solids of unknown structure, but for zeolites of known structure they add little to our understanding. In such cases, the form of the adsorption isotherms can be modelled by computer simulation using Grand Canonical Monte Carlo methods. In this approach all the parameters are known or can be measured or calculated (see Section 4.5.1) so that the adsorption isotherm can be simulated using a physically well-characterised model. 

A new molecular simulation technique is developed to solve the perturbation equations for a multicomponent, isothermal stured-tank adsorber under equilibrium controlled conditions. The method is a hybrid between die Gibbs ensemble and Grand Canonical Monte Carlo methods, coupled to macroscopic material balances. The bulk and adsorbed phases are simulated as two separate boxes, but the former is not actually modelled. To the best of our knowledge, this is the first attempt to predict the macroscopic behavior of an adsorption process from knowledge of the intermolecular forces by combining atomistic and continuum modelling into a single computational tool. 

Gibbs Ensemble and Histogram Reweighting Grand Canonical Monte Carlo Methods... 

Molecular parameters used in the above formulation are usually taken fi-om Ref 49. The grand-canonical Monte Carlo method of Adams [50] is commonly used in simulation. 

One of the most appealing characteristics of the grand canonical Monte Carlo method is that, as in many experimental situations, the chemical potential jx is one of the independent variables. This is the case of low-sweep-rate voltammetry, an electrochemical technique where the electrode potential can be used to control the chemical potential of species at the metal-solution interface. This technique offers a straightforward way of obtaining the adsorption... 

---