Monte Carlo method GCMC

Monte Carlo Methods Grand Canonical Monte Carlo (GCMC)... 

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). 

In this work, we explore the use of the pair correlation function as the target function in our reconstruction method [4]. This speeds up the simulations, allowing us to construct models in much larger simulation boxes. We build models for two saccharose-based carbons treated at different temperatures. We compare the exact pore size distributions and perform Grand Canonical Monte Carlo (GCMC) simulations of nitrogen at 77 K in the resulting models. 

In this study, N2 adsorption in the internal pore of single SWNH particle and on external pores of bundled SWNH particles is simulated with grand canonical Monte Carlo (GCMC) method and the simulated isotherms are compared with the experimental results. 

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. 

The adsorption equilibria of methane, ethane and their mixture into single-walled carbon nanotuhes (SWNTs) were studied by using a Grand Canonical Monte Carlo (GCMC) method. The equilibrium isotherms of methane and ethane and the selectivity from their equimolar mixture were reported. 

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. 

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. 

In the work of Rowley et al. [1-3], the grand canonical Monte Carlo (gcmc) method was used to simulate Ar interacting with graphite. The surface was approximated as a continuum. In such a case, the sum in Eqn (4.3) is replaced by an integral in the x, y, and z dimensions (the graphite solid) and the potential reduces to a L-J 9-3 form that is a function only of the distance of the atom... 

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. 

Grand Canonieal Monte Carlo (GCMC) methods to aehieve equilibrium eonfigurations. for example in the simulation of adsorption. 

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