Use of the Grand Canonical Transition-Matrix Monte Carlo Method to Model Gas Adsorption in Porous Materials

We present grand canonical transition-matrix Monte Carlo (GC-TMMC) as an efficient method for simulating gas adsorption processes, with particular emphasis on subcritical gas adsorption in which capillary phase transitions are present. As in other applications of TMMC, the goal of the simulation is to compute a particle number probability distribution (PNPD), from which thermophysical properties of the system can be computed. The key advantage of GC-TMMC is that, by appropriate use of histogram reweighting, one can generate an entire adsorption isotherm, including those with hysteresis loops, from the PNPD generated by a single GC-TMMC simulation. We discuss how to determine various thermophysical properties of an adsorptive system from the PNPD, including the identification of capillary phases and capillary phase transitions, the equilibrium phase transition, other free energies, and the heat of adsorption. To demonstrate the utility of GC-Tmmc for studies of adsorption, we apply the method to various systems including cylindrical pores and a crystalline adsorbent to compute various properties and compare results to previously published data. Our results demonstrate that the GC-TMMC method efficiently yields adsorption isotherms and high-quality properties of adsorptive systems and can be straightforwardly applied to more complex fluids and adsorbent materials.