Grand canonical ensemble, equilibrium phase

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). 

The grand canonical ensemble simulations model systems in which the chemical potential (/x), the volume and temperature are held fixed while the number of particles changes. The approach is very useful for simulating phase behavior which requires a constant chemical potential. Grand Canonical Monte Carlo simulation has been used to calculate sorption isotherms for a number of difierent microporous silicate systems. The simulations are used to model the equilibrium between zeolite and sorbate phases and, as such, it provides a natural way of simulating sorption isothermsl ... 

A member system of the grand-canonical ensemble has constant volume and temperature, and it can exchange particles with the environment. At equilibrium, net diffusion of particles stops when the chemical potential of the particles inside the system is the same as outside. The grand-canonical ensemble is also called the (xUr ensemble (Fig. 6.3). This ensemble is useful for calculating phase equilibria of different systems (see Further reading). 

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. 

Particle exchanges, in order to achieve chemical equilibrium between the phases. We consider two simultaneous grand canonical Monte Carlo moves for the two systems in lV T and ensembles. 

---