BETModell

The BET model is a theory used to analyze physical adsorption of gas molecules on solid surfaces and to determine the specific surface area of porous and powdered materials. It extends the Langmuir approach to multilayer adsorption and is widely applied in catalysis, material science, and surface chemistry.

The model was proposed in 1938 by Brunauer, Emmett and Teller. It assumes that adsorption occurs in a monolayer first, followed by additional layers in equilibrium with the vapor phase. The heat of adsorption for the first layer is higher than for subsequent layers, while the condensed layers have an average adsorption heat similar to the latent heat of condensation.

The BET equation relates the amount adsorbed n (per unit mass) to relative pressure P/P0 by 1/[n((P0/P) - 1)] = (c - 1)/(n_m c) · (P/P0) + 1/(n_m c), where n_m is the monolayer capacity and c is a constant related to the heat of adsorption. By plotting the left-hand side against P/P0 in an appropriate relative-pressure range (typically 0.05–0.35), a straight line is obtained from which n_m and c can be extracted.

Specific surface area, S_BET, is derived from the monolayer capacity: S_BET = (n_m × N_A × σ) / m, where N_A is Avogadro’s number, σ is the cross-sectional area of the adsorbate molecule, and m is the sample mass. The BET method is standard for nitrogen adsorption at liquid nitrogen temperature, but it can overestimate areas for microporous materials, necessitating complementary models.

Limitations include assumptions of a uniform surface and applicability primarily to physisorption in the relative-pressure range mentioned. Despite these, the BET model remains a foundational tool for characterizing surface areas of solids.