BET Model

The BET model, named after Stephen Brunauer, Paul H. Emmett and Edward Teller (father of the H-bomb) is a model describing molecular adsorption, and can be used to measure (BET) surface area's of materials. The model allows for multilayer adsorption where gas atoms or molecules can either land on a lattice (primary adsorbate layer), or on top of each other. The BET model follows from the following assumptions:

1. Adsorption takes place on a lattice
2. The first adsorbate layer is adsorbed on the solid surface, the second adsorbate layer is adsorbed on the first etc. Except, of course, for the first layer, a molecule can only be adsorbed on a given site in layer number n, if the same site is occupied in layer n-1.
3. At the saturation pressure P₀ the number of adsorbed layers is infinite
4. The adsorption enthalpy is H_ads for molecules in the first layer and H_L for molecules in the following layers.

The BET model leads to a two-parameter adsorption equation of the form:

P/(sigma(P₀ - P)) = 1 /(sigma₀ c) + (c-1) / (sigma₀ c) (P/P₀)

where P₀ is the saturation pressure of the vapor at which an infinite number of layers can be built up on the surface, and c is a constant at a given temperature { =exp(-(H_ads-H_L)/RT) }, sigma is the amount of gas adsorbed at pressure P, sigma₀ is the amount of gas correponding to one monolayer.

The story goes that Teller, when confronted with the problem of measuring surface areas (definitely not his area of expertise) during lunch, he scribbled down the derivation to the BET equation on a napkin.

The original publication:

S. Brunauer, P. H. Emmett, E. Teller, "Adsorption of gases in multimolecular layers," J. Amer. Chem. Soc., 60:309-19, 1938