$$\rightleftharpoonup{xx}$$
$$\longleftharp{xx}$$,
$$\longrightharp{xx}$$,
Brunauer, Emmett, and Teller (BET) introduced a theory in 1938 that modified Langmuir's assumptions to explain multilayer physical adsorption. This theory is applicable to Type II isotherms and provides a more realistic picture of adsorption processes. The BET theory assumes a uniform solid surface with localized adsorption sites, where adsorption at one site doesn't affect adsorption at neighboring sites. This theory also allows for the possibility of additional molecules being adsorbed on top of one another to form second, third, and nth layers. Each layer is held in place by van der Waals forces (weak attractive forces between molecules) from the one below it. Importantly, the surface area available for the nth layer is equal to the coverage of the (n – 1)th layer. The amount of adsorption increases with increasing pressure due to the formation of these additional layers.
The energy of adsorption in the first layer is assumed to be constant, while the energy of adsorption in succeeding layers is assumed to be the same as the energy of gas liquefaction. This forms the basis for the BET equation, which quantifies the relationship between the volume of gas adsorbed and the pressure. By plotting the relative adsorption pressure against the BET function, a BET plot is generated. The slope and intercepts of the linear regression line give the monolayer adsorption volume and constant c. By knowing the monolayer adsorption volume, the number of molecules needed to form a monolayer, and the surface area per unit mass of the solid sample can be estimated.
The BET isotherm also permits the determination of the isosteric heat of adsorption, which decreases significantly as the surface coverage increases. This occurs because the energetically favorable binding sites are filled first, and repulsions between adsorbed molecules increase as surface coverage increases. Despite providing a more comprehensive view of adsorption than the Langmuir theory, the BET theory does have limitations. It is most accurate for pressures up to one-third of the saturation pressure, with deviations occurring at higher pressures. At higher pressures, deviations arise as the assumptions of uniform adsorption layers and distinct monolayer formation no longer hold true.
Additionally, it assumes equal adsorption energy for all layers beyond the first, equating to the energy of gas liquefaction, which may not always be accurate in practice.
In summary, unlike the Langmuir model, which assumes only monolayer adsorption, the BET theory extends to multilayer physical adsorption (especially for Type II isotherms). The BET equation allows estimation of the monolayer capacity and the specific surface area of a solid from adsorption data.
