Slit-shaped pores GCMC simulation

In this paper we report, first, grand canonical Monte Carlo (GCMC) simulations of LJ fluid modeled on methane in slit-shaped nanopores that are kept equilibrium with saturated vapor, or pure liquid, in bulk phase. Depending on the strength of the attractive potential energy from pore walls, fluid in a pore shows freezing point elevation as well as depression. 

An iteration scheme is used to numerically solve this minimization condition to obtain Peq(r) at the selected temperature, pore width, and chemical potential. For simple geometric pore shapes such as slits or cylinders, the local density is a function of one spatial coordinate only (the coordinate normal to the adsorbent surface) and an efficient solution of Eq. (29) is possible. The adsorption and desorption branches of the isotherm can be constructed in a manner analogous to that used for GCMC simulation. The chemical potential is increased or decreased sequentially, and the solution for the local density profile at previous value of fx is used as the initial guess for the density profile at the next value of /z. The chemical potential at which the equilibrium phase transition occurs is identified as the value of /z for which the liquid and vapor states have the same grand potential. 

Fig. 2 GCMC simulation of the adsorption of H2/N2 mixtures in slit-shaped carbon pores at 77 K. Top 0.74 nm pore width bottom 2.664 nm pore width.

The DFT method [15, 77-79] is derived from statistical thermodynamics and offers an efficient means of computing model isotherms for simple pore geometries. The accuracy of the DFT model isotherms rivals that of the isotherms obtained from molecular simulation, but the computational time required by DFT is typically about 1% of the CPU time needed to complete GCMC or GEMC isotherm calculations for a comparable system. The DFT method retains its computational advantage over molecular simulation only for pore shapes of low dimensionality, such as slits, spheres, or... 

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