Thermodynamics and statistical mechanics of multilayer adsorption

The multilayer adsorption models of Brunauer-Emmett-Teller and Guggenheim-Anderson-de Boer are reconsidered. The relationship between the fitting parameters and the physical parameters of the equation is discussed. The preexponential factors of the parameters are shown to be in general far different from unity, contrary to a widespread use. A thermodynamical derivation illuminates the hypothesis on which the multilayer sorption equation is dependent and frees it from too restrictive hypothesis usually taken as necessary for its validity. Equations are derived for the number fraction of sorption sites occupied by different numbers of molecules. The Guggenheim-Anderson-de Boer equation is shown to imply incomplete occupation (jamming) of the first sorption layer at saturation.