A practical guide to calculate the isosteric heat/enthalpy of adsorption via adsorption isotherms in metal–organic frameworks, MOFs

Abstract

Porous materials such as MOFs are interesting candidates for gas separation and storage. An important parameter to gain deeper insights to the adsorption process of an adsorptive on an adsorbent is the isosteric enthalpy of adsorption, ΔH_ads which is defined as the heat to be released/required when an adsorptive binds to/detaches from the solid surface of an adsorbent. Two or three adsorption isotherms at different but close temperatures with ΔT ≤ 20 K for two and ΔT ≈ 10 K for three isotherms are the basis to derive the isosteric enthalpy of adsorption through the Clausius–Clapeyron approach or the virial analysis. This Perspective presents the procedure of the common (dual-site) Freundlich–Langmuir fit/Clausius–Clapeyron approach and the virial fit of the isotherms with usable Excel sheets and Origin files for the subsequent derivation of ΔH_ads. Exemplary adsorption isotherms of CO₂, SO₂ and H₂ at two temperatures on MOFs are analyzed. The detailed computational description and comparison of the Clausius–Clapeyron approach and the virial analysis to determine ΔH_ads outlines the limitations of the two methods with respect to the available experimental data, especially at low pressure/low uptake values. It is emphasized that no extrapolation beyond the experimental data range should be done. The quality of the important and underlying isotherm fits must be checked and ensured with logarithmic-scale n/p isotherm plots for the (dual-site) Freundlich–Langmuir fit in the low-pressure region and through low standard deviations for the coefficients in the virial analysis.