(208d) Calculation of the Isosteric Enthalpy of Adsorption in Monte Carlo Molecular Simulation: New Equations Addressing Bulk Phase Nonideality and Isosteres of Total Adsorption

In engineering applications of adsorption, it is important to consider the heat released by the adsorption process, as the various choices made in managing that heat will have different effects on the overall process. It may represent any or all of 1) the energy cost of controlling column temperature, 2) a change in adsorption equilibrium to lower loading capacity, or 3) the energy cost of desorption during adsorbent regeneration. A differential heat of adsorption, that is the change in molar enthalpy of during transfer of gas to the adsorbed phase, is the usual thermodynamic metric for describing the heat evolved by adsorption. The preferred version of the differential heat is now usually called the isosteric enthalpy of adsorption (IEA), i.e., the heat released by the transfer of gas at fixed adsorbate loading [1]. Whether from experiment or simulation, this quantity may be obtained by isostere analysis of a sequence of isotherms at closely spaced temperatures, via the Clausius-Clapeyron equation. For molecular simulations, this IEA may alternatively be computed from fluctuations of the internal energy and molecule count. Yet, there are competing fluctuation definitions of the IEA, which yield markedly different results [2-4], and controversies regarding which measure of adsorbate loading (absolute, total, or excess) should be held fixed [5-8]. Furthermore, equations for the IEA for multi-component adsorption are underdeveloped compared to their single-component counterparts.

In the present work, we reexamine equations for the IEA in light of recent work [5-8] that stresses the importance of analyzing absolute adsorption isotherms during isostere analysis, and accordingly present new fluctuation-based expressions for the IEA for both single- and multi-component adsorption. These expressions account for non-ideality of both the adsorbed and bulk gas phases, regardless of the gas composition. Using flat-histogram sampling in Monte Carlo molecular simulation [9], we apply these equations to both single- and multi-component gas adsorption to show how TMMC can yield the IEA for an entire isotherm from statistics collected in a single simulation. We also demonstrate that these calculations compare favorably with isostere-based calculations from either the simple Clapeyron equation or the Clausius-Clapeyron, depending departure from ideality in the bulk gas phase. Additionally, we present sample calculations that highlight the differences between the various definitions of the IEA and discuss when these differences may prove critically important. Overall, we aim to place simulation-based IEA calculations on a firmer foundation so that this important thermodynamic quantity may be used more confidently for the design and analysis of adsorption processes.

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