Derivation of Azizian–Volkov (AV)-isotherm based on statistical thermodynamics

The Azizian–Volkov (AV)-isotherm is a general isotherm for gas adsorption with two different states of an adsorbate. It has been derived previously by a classical thermodynamic approach. The new AV-isotherm gives the possibility to analyze multi and single centered adsorption and the interfacial structure in a general case. The AV-isotherm takes into account the interaction between adsorbed molecules and adsorbent and provides information about the orientation of adsorbates. Traditional isotherms (Henry, Langmuir, and Frumkin) for homogeneous adsorption can be derived from the AV-isotherm. In the present work the AV-isotherm is derived using statistical thermodynamics. This derivation provides a stronger basis for this isotherm. A new concept of the important parameter (η) of AV-isotherm is obtained. Finally, the AV-isotherm was simplified and its application was justified by analysis of the equilibrium data of a numerically generated and experimental systems.