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. The fundamental element of BET theory is associated with the adsorption of a gas on the material's surface. This phenomenon is caused by van der Waals forces that are created by a film of the adsorbate, which consists of atoms, ions, or molecules on the surface of a substance that adsorbs these particles.

Stephen Brunauer, Paul Emmet and Edward Teller published this theory in 1938 in the Journal of the American Chemical Society. It is a theory for multi-layer physisorption and is of profound significance in the development of this field.

The two most widely used equations are the BET and SSL (Single‐Site Langmuir Adsorption) models, the latter of which was first used by Langmuir himself in 1918. While neither model is strictly appropriate for the description of gas adsorption within narrow micropores, it has been shown that the BET model is often suitable for the estimation of the true surface area of microporous and mesoporous materials including MOFs and zeolites (despite that the number of multilayers is constrained) when proper consistency criteria are employed in determining the range of partial pressure over which tofitthedata.

The BET formalism prevalent in the literature is written as follows:

equation 1

where P₀ is the saturation pressure of the adsorbate, defined as:

equation 2

and ܿc is the BET constant, defined as:

equation 3

A common linearized rearrangement, where B is simply the “BET variable”, is:

 equation 4

Brunauer, Emmett, and Teller described three regions along the BET isotherm in Equation 4: a concave region at low pressure, a convex region at high pressure, and a linear region at intermediate pressure. They originally specified the relative pressure P/P0 range of 0.05‐0.3 as the linear region from which the number of surface sites, ߁, can be dependably extracted. In the case of high surface area, microporous materials such as zeolites and MOFs, however, this range has proven to be inadequate as a universal standard and a now widely accepted set of self‐consistency criteria have been proposed. Once the linear range is determined and ߁ is extracted, the BET surface area, SA_BET is calculated as:

equation 5

where SA_B is the surface area of a single binding site. The conventional cross‐sectional area of a N₂ molecule for BET surface area calculation is 0.162 nm², which allows researchers across different laboratories to have a standard for materials comparison. For example, in the case of IRMOF‐16, the BET surface area determined herein corresponds to 61.8 mmolg^-1 or 6030 m²g^-1. This is consistent with the geometrical surface area of the crystal (~6000 m²g^-1 as determined by a Monte Carlo integration technique). It should be noted that challenges still persist in using the BET model to accurately estimate the monolayer capacity of porous materials, especially those with a diversity of pore sizes.

The surface area is estimated using the Brunauer, Emmett & Teller (BET) equation, from a specific region of a gas adsorption isotherm. The gas adsorption isotherm is experimentally obtained as follows. Successive doses of an adsorptive gas probe, typically N2 at 77 K, are sent to the testing samples, preliminarily need to pretreat samples which aims to purify materails. The amount of gas molecules that can adsorb onto the surface of the material is derived from the evolution of the pressure in the system. The cumulative amount of adsorbate plotted with respect to the pressure is the adsorption isotherm.

Brunauer, Emmett & Teller developed a model for type II isotherms, which considers that gas molecules are adsorbed in monolayers, i.e. monomolecular layers. In the specific relative pressure range from 0.05 to 0.30 each monolayer evenly covers the previous one. By applying Langmuir theory to those monolayers they obtained the following BET equation。

The surface area is then estimated from the monolayer amount n_m and the cross-sectional area of a molecule of adsorbate.

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:

1.         gas molecules physically adsorb on a solid in layers infinitely;

2.         gas molecules only interact with adjacent layers;

3.         the Langmuir theory can be applied to each layer;

4.         the enthalpy of adsorption for the first layer is constant and greater than the second (and higher);

5.         the enthalpy of adsorption for the second (and higher) layers is the same as the enthalpy of liquefaction.

Despite the extensive use of the BET method, many authors have discussed the limitations that are inherently related when it is applied for the surface area determination of microporous materials. Since the method is based on gas adsorption, limitations are often related to monolayers. For instance,

1) the validity of n_m (the BET monolayer capacity) is problematic;

2) the monolayer structure is not the same on all surfaces, particularly when N2 isotherms are used since the molecule is quadrupolar;

3) at very low pressure ranges (P/P0) strong adsorption can involve localized monolayer coverage and/or primary micropore filling in the pores of molecular dimensions.

When characterizing materials with micropores below 20 Å, the biggest problem is usually related to micropore filling, which takes place rather than mono or multilayer coverage. This can lead to obtaining higher or overestimated surface areas; however, high rates of micropore filling can potentially be recognized.

Reference list:

• Determination of the specific surface area of solids by gas adsorption — BET method, ISO 9277:2010(E)

• Sing K.S.W., Everett D.H., Haul R.A.W., Moscou L., Pierotti R.A., Rouquérol J. and Siemieniewska T., IUPAC Recommendations 1984: Reporting Physisorption Data for Gas Solid Systems with Special Reference to the Determination of Surface Area and Porosity, Pure & Applied Chemistry 57, 1985, pp. 603-319

• P. C. Hiemenz, R. Rajagopalan, Principles of Colloid and Surface Chemistry, 3rd ed., CRC Press, 2016

•  J. Lyklema, Fundamentals of Interface and Colloid Science: Solid-Liquid Interfaces, Elsevier, 1995

• Filip Ambroz, Thomas J. Macdonald, Vladimir Martis, Ivan P. Parkin, Evaluation of the BET Theory for the Characterization of Meso and Microporous MOFs: small method, wiley, 2018

• Langmuir,I.,TheAdsorptionofGasesonPlaneSurfacesofGlass,MicaandPlatinum.J. Am. Chem.Soc.1918, 40,1361‐1403

• Walton,K.S.;Snurr,R.Q.,ApplicabilityoftheBETMethodforDeterminingSurfaceAreas of MicroporousMetal‐OrganicFrameworks.J.Am.Chem.Soc.2007