Adsorption isotherms that do not follow the Langmuir model

Adsorption isotherms that do not follow the Langmuir model 

The Langmuir expression (and its derivative) could be regarded as verified by the experiment as long as the precision of measurements are weak. Currently, it is known that this expression represents a more or less accurate approximation. It generates great interest, however, because all the expressions established more recently could be derived from it. Moreover, this is a simple analytical expression that is most of the time sufficient when adsorption is one of the associated phenomena occmring in a heterogenous reaction 

Two methods have been used to obtain other expressions of the adsorption isotherm. The first considers that all the sites of adsorption are not equivalent The distribution of sites, which can be continuous or discontinuous, is ch cterized by their heats of adsorption. It is not possible to detect whether this heterogeneity of the sites pre-exists to adsorption on the surface of the solid or whether it is progressively created while filling the surface, due to the interaction between the adsorbed molecules, or both the reasons). These two methods obviously lead to the same result. 

In this method, we apply an enthalpy to the sites of category i. 

Several energy distribution sites were proposed  

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