BETmodel

The BET model, named after Stephen Brunauer, Paul Emmett, and Edward Teller, is a theory of physical adsorption that describes how gas molecules accumulate on solid surfaces in multiple layers. Developed in 1938, it extends the Langmuir model to account for multilayer adsorption and is widely used to estimate the specific surface area of solids.

The core idea is that the first layer binds more strongly than subsequent layers, while the upper layers behave like a gas relative to the layer beneath. The standard linear form of the BET equation is: P/[v (P0 − P)] = 1/(v_m C) + (C − 1)/(v_m C) · (P/P0), where P is the equilibrium pressure, P0 is the saturation pressure, v is the volume of gas adsorbed, v_m is the monolayer adsorbed volume, and C is a constant related to the adsorption energy of the first layer. A plot of P/[v (P0 − P)] versus P/P0 should be linear in an appropriate relative-pressure range, from which v_m and C are obtained. The monolayer volume v_m corresponds to the amount of gas needed to cover the surface with a single molecular layer, and C reflects the energy difference between the first layer and the subsequent layers.

Applications and limitations: The BET model is commonly applied using nitrogen adsorption at 77 K to determine specific surface area, calculated from v_m and the cross-sectional area of the adsorbate molecule. It is best suited for physical adsorption on non-microporous or mesoporous materials; microporous systems may require alternative analyses. The method remains a standard tool in catalysis, materials science, and surface characterization.