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468883 Calculation of the Isosteric Heat of Adsorption Using Quenched Solid Density Functional Theory

**Calculation of the Isosteric Heat of Adsorption using Quenched Solid Density Functional Theory**

Richard T. Cimino^{1}, Piotr Kowalczyk^{2}, Alexander V. Neimark^{1}^{1}Department of Chemical and Biochemical Engineering, Rutgers University, Piscataway, NJ 08854

^{2}School of Engineering and Information Technology, Murdoch University, Perth, WA, 6150

When a fluid adsorbs on a surface, it releases energy in the form of heat. At equilibrium, the change in energy (enthalpy) of the adsorbate upon adsorption is characterized by the isosteric heat, which obeys the Clausius-Clapeyron (C-C) Equation: *q _{iso}* =

*RT1T2/(T2-T1)(lnp2-lnp1)*

*. There are several methods for measuring the heat of adsorption, which along with the adsorption isotherm provide valuable information about the state of the adsorbed fluid in a material and the materialâ€™s pore structure. One of the direct methods is to calculate the isosteric heat from the adsorption isotherms measured at different temperatures using the C-C equation. Theoretically, the heat of adsorption can be estimated in the course of Monte Carlo simulation by calculating respective fluctuations of potential energy and number of particles in the Grand Canonical ensemble. Alternatively, the classical density functional theory can be applied either to directly calculate the adsorption heat from the free energy functional or by calculating the adsorption isotherms at different temperatures (at least two) and applying the C-C equation in the same way as it is done experimentally. Here, we employ the latter approach based on the quenched solid density functional theory (QSDFT). We explore the isosteric heat of adsorption of several probe molecules (N*

_{N}_{2}, Ar, and CO

_{2}) on reference mesoporous silica materials and several classes of microporous carbons with hierarchical pore structures. The calculated values of the isosteric heat are compared with experimental measurements and the results of direct MC simulations.

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