Use of the Grand Canonical Transition-Matrix Monte Carlo Method to Model Gas Adsorption in Porous Materials Daniel W. Siderius* and Vincent K. Shen Chemical Sciences Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, United States ABSTRACT: 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. I. INTRODUCTION As a general rule, the properties of a fluid can be altered significantly from their bulk values when confined in tight spaces, with the magnitude of such alterations dependent on the characteristics of the confining walls, specifically the affinity of the fluid to the surface. 1 Of particular scientific and technical interest is the effect of confinement on a fluid’s phase behavior (or phase boundaries). 1-3 For example, fluid adsorption in porous materials, the focus of this work, serves as the basis for potential viable carbon capture technologies. 4-7 While theory and simulation have played a historically significant role in the characterization of porous materials, 1,8,9 they have more recently been identified as key tools in screening and developing potential carbon capture materials. 10-12 Thus, the advancement of carbon capture technologies and other applications of gas adsorption will depend on the availability and further development of computationally efficient and precise methods to predict the thermodynamic and dynamic properties of fluids in porous materials. At present, the two primary molecular modeling tools used in studies of adsorption are density functional theory 13 (with which we include the closely related lattice mean field theories 14-17 ) and various forms of Monte Carlo (MC) molecular simulation. 18,19 These methods have proven essential to the advancement of the fundamental understanding of adsorption processes 8 by, for example, suggesting the existence of cavitation-induced capillary evaporation in ink-bottle pores prior to its observance experimentally 20 and confirming the relationship between subcritical adsorption hysteresis and fluid metastability. 21,22 One of the main goals in the simulation of adsorption phenomena is the calculation of the adsorption isotherm, which in turn requires identifying and determining metastable and stable fluid phases. For example, in the quintessential adsorption problem at a subcritical temperature, the adsorption isotherm may include two main density branches, one that is vapor-like and the other that is liquid-like. Both branches of the isotherm will exist at some range of pressures below the bulk saturation pressure, forming a so-called hysteresis loop. Figure 1 shows an example of one such isotherm, known as a type IV isotherm, 23 in which the confined fluid exhibits two capillary Received: January 15, 2013 Revised: February 20, 2013 Published: February 21, 2013 Article pubs.acs.org/JPCC This article not subject to U.S. Copyright. Published 2013 by the American Chemical Society 5861 dx.doi.org/10.1021/jp400480q | J. Phys. Chem. C 2013, 117, 5861-5872