(155c) Understanding the Vacancy Solution Theory

There are two main approaches to describe adsorption non-ideality using activity coefficient models [1]. The first is based on the Real Adsorbed Solution Theory (RAST) which uses the reference state of the pure adsorbate at the same reduced grand potential of the mixture [2]. In this formulation an ideal mixture reduces to the Ideal Adsorbed Solution Theory (IAST) [3]. The second general method, the Vacancy Solution Theory (VST), was introduced by Danner and coworkers in the early 1980s [4-5] based on the equilibrium between two phases that contain vacancies as a component.

In this contribution we present an alternative formulation of the VST starting from identifying the true reference state at the basis of the method. The basic argument is that a thermodynamically correct reference state for adsorption mixtures (including the hypothetical mixture of a single adsorbate and the vacancies) must be at the same reduced grand potential of the mixture, which means that in this case the thermodynamic framework is based on the use of the zero pressure limit, which corresponds to all adsorbates being at infinite dilution (equivalent to solutes), while the reference state for the vacancies is the normal one of a pure component (equivalent to the solvent). While RAST is the equivalent of a generalization of Raoult’s law, the VST is a generalization to nonideal mixtures of Henry’s law, i.e. asymmetric activity coefficients should be used for the adsorbates.

One hindrance to the application of the VST is the fact that a derivation is needed for different activity coefficient models. This is in fact not true, as we demonstrate that a general expression can be derived valid for any thermodynamically consistent activity coefficient model, i.e. a functional form that obeys the Gibbs-Duhem equation, resulting in a simple general expression of the VST. This new derivation identifies also the need to ensure that for thermodynamic consistency the saturation capacities of all adsorbates are the same. While this is a severe limitation, the VST single component isotherm is thermodynamically consistent and has an explicit relationship for the reduced grand potential, making it a suitable pure component isotherm for the IAST or RAST approaches.

[1] Ruthven D.M. Principles of Adsorption and Adsorption Processes. pp. 70-74, Wiley, New York (1984)

[2] Myers A.L. and Monson P.A. Physical Adsorption of Gases: the Case for Absolute Adsorption as the Basis for Thermodynamic Analysis. Adsorption 20, 591-622 (2014).

[3] Myers A.L. and Prausnitz J.M. Thermodynamics of Mixed-Gas Adsorption. AIChE J. 11, 121-127 (1965)

[4] Suwanayuen S. and Danner R.P. A Gas Adsorption Isotherm Equation Based on Vacancy Solution Theory AIChE J. 26, 68-76 (1980)

[5] Suwanayuen S. and Danner R.P. Vacancy Solution Theory of Adsorption from Gas Mixtures AIChE J. 26, 76-83 (1980)