BETisotherm

The BET isotherm is an adsorption model used to analyze physical adsorption of gas molecules on solid surfaces in order to determine the surface area of a material. It extends the Langmuir theory to multilayer adsorption and is widely applied in surface science and materials characterization. The fundamental equation, known as the BET equation, is [P/(N(P0 − P))] = 1/(N_m C) + (C − 1)/(N_m C) · (P/P0), where N is the amount adsorbed, P is the equilibrium pressure, P0 is the saturated vapor pressure of the adsorbate, N_m is the monolayer capacity, and C is a constant related to the heat of adsorption. A plot of P/[N(P0 − P)] against P/P0 yields a straight line with slope (C − 1)/(N_m C) and intercept 1/(N_m C). From these, N_m and C can be determined and used to characterize the surface.

Typically, nitrogen adsorption at 77 K is used, and N_m is converted to a specific surface area S (in m^2/g) using the adsorbate’s molecular cross-sectional area and Avogadro’s number. The BET method provides a practical measure of accessible surface area for a wide range of porous and nonporous materials, including activated carbons, silica, zeolites, and metal–organic frameworks.

Limitations include the choice of appropriate relative pressure range for the linear BET plot, assumptions of multilayer adsorption and uniform surface energy, and the method’s reduced reliability for highly microporous materials where capillary condensation or chemisorption may occur. In such cases, supplementary analyses may be employed. The BET theory was introduced in 1938 by Brunauer, Emmett, and Teller.