Theoretical insight of physical adsorption for a single component adsorbent-adsorbate system

The article describes the thermodynamic analysis of physical adsorption and consists of two parts. The first part relates to the development of the thermodynamic property surfaces for a single-component adsorbent + adsorbate system, which are derived and developed from the view point of classical thermodynamics, thermodynamic requirements of chemical equilibrium, Gibbs law and Maxwell relations. They enable us to compute the entropy and enthalpy of the adsorbed phase, the isosteric heat of adsorption, specific heat capacity and the adsorbed phase volume thoroughly. We have shown here that the derived thermodynamic formulations fill up the information gap with respect to the state of adsorbed phase to dispel the confusion as to what is the actual state of the adsorbed phase. The second part derives the Henry coefficients of a single component adsorbent + adsorbate system as a function the heat of adsorption at zero coverage. A thermodynamic framework is presented to capture the relationship between the specific surface area (A_i) and the energy factor, and the surface-structural and the surface-energy heterogeneity distribution factors are analyzed. Using the outlined approach, the maximum possible amount of adsorbate uptake has been evaluated and compared with experimental data. It is found that the adsorbents with higher specific surface areas tend to possess lower heat of adsorption (formula presented) at Henry regime. In this paper, we have established the definitive relation between A_i and (formula presented) for (i) carbonaceous materials, metal organic frameworks (MOFs), carbon nanotubes, zeolites + hydrogen, and (ii) activated carbons + methane systems. The proposed theoretical framework of A_i and (formula presented) provides valuable guides for researchers in developing advanced porous adsorbents for methane and hydrogen uptakes. In this article, we have also discussed and established the temperature-entropy diagrams of silica gel + water system for adsorption cooling and desalination applications.