BET theory

Brunauer–Emmett–Teller (BET) theory aims to explain the physical adsorption of gas molecules on a solid surface and serves as the basis for an important analysis technique for the measurement of the specific surface area of materials. In 1938, Stephen Brunauer, Paul Hugh Emmett, and Edward Teller published the first article about the BET theory in the Journal of the American Chemical Society. The BET theory applies to systems of multi layer adsorption, and usually utilizes probing gases that do not chemically react with material surfaces as adsorbates to quantify specific surface area. Nitrogen is the most commonly employed gaseous adsorbate used for surface probing by BET methods. For this reason, standard BET analysis is most often conducted at the boiling temperature of N₂ (77 K). Further probing adsorbates are also utilized, albeit with lower frequency, allowing the measurement of surface area at different temperatures and measurement scales. These have included argon, carbon dioxide, and water. Specific surface area is a scale-dependent property, with no single true value of specific surface area definable, and thus quantities of specific surface area determined through BET theory may depend on the adsorbate molecule utilized and its adsorption cross section.

The concept of the theory is an extension of the Langmuir theory, which is a theory for monolayer molecular adsorption, to multilayer adsorption with the following hypotheses:

The resulting BET equation is

where ${\displaystyle p}$ and ${\displaystyle p_{0}}$ are the equilibrium and the saturation pressure of adsorbates at the temperature of adsorption, ${\displaystyle v}$ is the adsorbed gas quantity (for example, in volume units), and ${\displaystyle v_{\mathrm {m} }}$ is the monolayer adsorbed gas quantity. ${\displaystyle c}$ is the BET constant,

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