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BET model of multilayer adsorption, that is, a random distribution of sites covered by one, two, three, etc., adsorbate molecules. The concept of the theory is an extension of the Langmuir theory, which is a theory for monolayer molecular adsorption, to multilayer adsorption with the following hypotheses:
Brunauer, Emmett and Teller's model of multilayer adsorption is a random distribution of molecules on the material surface. Adsorption is the adhesion [1] of atoms, ions or molecules from a gas, liquid or dissolved solid to a surface. [2] This process creates a film of the adsorbate on the surface of the adsorbent.
The adsorption sites (heavy dots) are equivalent and can have unit occupancy. Also, the adsorbates are immobile on the surface. The Langmuir adsorption model explains adsorption by assuming an adsorbate behaves as an ideal gas at isothermal conditions. According to the model, adsorption and desorption are reversible processes.
The Gibbs adsorption isotherm for multicomponent systems is an equation used to relate the changes in concentration of a component in contact with a surface with changes in the surface tension, which results in a corresponding change in surface energy. For a binary system, the Gibbs adsorption equation in terms of surface excess is
The Hertz–Knudsen equation describes the non-dissociative adsorption of a gas molecule on a surface by expressing the variation of the number of molecules impacting on the surfaces per unit of time as a function of the pressure of the gas and other parameters which characterise both the gas phase molecule and the surface: [1] [2]
where A is the reactant and S is an adsorption site on the surface and the respective rate constants for the adsorption, desorption and reaction are k 1, k −1 and k 2, then the global reaction rate is: = = where: r is the rate, mol·m −2 ·s −1
The potential theory of Polanyi, also called Polanyi adsorption potential theory, is a model of adsorption proposed by Michael Polanyi where adsorption can be measured through the equilibrium between the chemical potential of a gas near the surface and the chemical potential of the gas from a large distance away.
Source: [2] If a solid body is modeled by a constant field and the structure of the field is such that it has a penetrable core, then = ′ [ ()] ′ [ ()]. Here ′ is the position of the dividing surface, = is the external force field, simulating a solid, is the field value deep in the solid, = /, is the Boltzmann constant, and is the temperature.