Differential Heat of Adsorption and Isosteres

Heat of adsorption is a basic thermodynamic property extensively used not only for understanding thermal effects and heat management in industrial gas storage and separation processes but also for development and validation of adsorption models and materials force fields. Despite a long history of theoretical studies and a vast experimental literature, controversies often arise in the thermodynamic analysis of heat effects due to various assumptions used to describe gas adsorption and inconsistencies between direct calorimetric measurements and isosteric heat obtained from various adsorption isotherms. Here we present a rigorous theoretical procedure for predicting isosteric heat without any assumption about the geometry of porous adsorbents or operating conditions. Quantitative relations between the differential heat and various isosteres have been established with the grand-canonical Monte Carlo simulation for gas adsorption in amorphous as well as crystalline porous materials. The inconsistencies and practical issues with conventional methods for the analysis of the heat effect have been clarified in the context of the exact results for model systems. Via the resolution of a number of controversies about heat analysis, we hope that the new theoretical procedure will be adopted for both fundamental research and industrial applications of gas adsorption processes.