Multicomponent potential theory of adsorption MPTA

An alternative approach to lAST/RAST which combines a thermodynamic treatment with a specific consideration of fluid-solid interactions is the potential theory of adsorption (Polanyi (1914)-Dubinin (1950)), especially in the form designed for multi-component mixtures pioneered by Shapiro and Stenby (1998). 

The distribution of the fluid (gas, liquid) near the solid surface is given by the equilibrium conditions for segregation in the external potential field, with fluid parameters which may vary with the distance. 

We assume we have isothermal adsorption on a surface from a gas phase wifli pressure P and mole fraction compositions in the gas phase y. Close to the surface, each component i of the gas mixture is affected by its own adsorption potential e(z), where z is the distance to the surface of the adsorbent. These potentials are not necessarily the same for all components they may differ from one component to another due to different interaction forces with the surface. 

At equilibrium, we obtain what is called the basic equation of MPTA by equating the chemical potentials in the external field as  

Equation 14.16 will be written for all components adsorbing. In the specific case of a binary adsorbing mixture, at a given temperature the systems of chemical potentials are given as  

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