Discussion of the BET equation

The BET equation includes isotherms of types 1. 2 and 3 but not types 4 and 5. Brunauer et al. [28] derived a new isothenn equation to cover all five types. The BET equation has also been derived by statistical reasoning by several authors [16]. 

A further criticism is that horizontal interactions are neglected, i.e. only the forces between the adsorbing molecule and the surface ate considered. Thus the first molecule to be adsorbed is considered to generate the same energy as the final molecule to fill a monolayer, although in the former case the molecule has no near neightors whereas in the latter it has six. These two effects must, in part, cancel each other out. 

It is also questionable whether adsorbing molecules in the second and subsequent layers should be treated as being equal. One would not expect a sudden transition in the energy generated between the first and subsequent layers. 

Cassel [29,30] showed, using Gibbs adsorption isotherm, that the surface tension of the adsorbed film atP = Pq is negative, arising from the total disregard of the interaction forces. Since the BET model assumes the existence of localized adsoq tion at all levels, the molecules being located on top of one another, and since the adsorption can take place in the nth layer before the (n-/ th layer is filled, the adsorbed phase is built up not as a series of continuous layers, but as a random system of vertic molecular columns. Halsey [31] pointed out that the combinational entropy term associated with these random molecular piles is responsible for the stability of the BET adsorbed layers at 

Gregg and Jacobs [32] doubted the validity of the assumption that the adsorbed phase is liquid-like, and found that the integration constant in the Clausius-Clapeyron equation, as applied to adsorption and vapor pressure, do not show the inter-relationship demanded by the BET tlreory. They conclude that any constant can be used in the place of Pq and that the correspondence between the adsorbed and liquid phase is a loose one, arising out of the fact that the same type of force is involved. 

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