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 presented their theory in the Journal of the American Chemical Society.
[1] BET theory applies to systems of multilayer adsorption that usually utilizes a probing gas (called the adsorbate) that does not react chemically with the adsorptive (the material upon which the gas attaches to) to quantify specific surface area.
is the vapor pressure of the adsorptive bulk liquid phase which would be at the temperature of the adsorbate and θ is the surface coverage, defined as:
is the entire amount that would be present as a monolayer (which is theoretically impossible for physical adsorption[citation needed]) that would cover the surface with exactly one layer of adsorbate.
The following equations can be used: The BET method is widely used in materials science for the calculation of surface areas of solids by physical adsorption of gas molecules.
The BET theory can be derived similarly to the Langmuir theory, but by considering multilayered gas molecule adsorption, where it is not required for a layer to be completed before an upper layer formation starts.
Furthermore, the authors made five assumptions:[4] Consider a given amount of solid sample in a controlled atmosphere.
Let θi be the fractional coverage of the sample surface covered by a number i of successive molecule layers.
Assuming an Arrhenius law for desorption, the related constants can be expressed as where Ei is the heat of adsorption, equal to E1 at the sample surface and to EL otherwise.
In summary, Extending this to higher order layers one obtains and similarly Denoting the activity of the number of available sites of the
Employing the fact that this sum is the first derivative of a geometric sum, the volume becomes Since the total coverage of a mono-layer must be unity, the full mono-layer coverage must be In order to properly make the substitution for
forces us to take the zeroth contribution outside the summation, resulting in Lastly, defining the excess coverage as
It is still not clear on how to find the linear range of the BET plot for microporous materials in a way that reduces any subjectivity in the assessment of the monolayer capacity.
A crowd-sourced study involving 61 research groups has shown that reproducibility of BET area determination from identical isotherms is, in some cases, problematic.
[5] Rouquerol et al.[6] suggested a procedure that is based on two criteria: These corrections are an attempt to salvage the BET theory, which is restricted to type II isotherms.
Terrell L. Hill described BET as a theory that is "... extremely useful as a qualitative guide; but it is not quantitatively correct".
[10] Hackerman et al. noted the potential for 10% uncertainty in the method's values,[8] with Sing's group attributed the significant variation in reported values of molecular area to the BET method's possible inaccurate assessment of monolayer capacity.
[10] In subsequent studies using the BET interpretation of nitrogen and water vapor adsorption isotherms, the reported area occupied by an adsorbed water molecule on fully hydroxylated silica ranged from 0.25 to 0.44 nm².
reaching unity,[11] and in some cases, the constant C (surface binding energy) can be determined to be negative.
[12] The rate of curing of concrete depends on the fineness of the cement and of the components used in its manufacture, which may include fly ash, silica fume and other materials, in addition to the calcinated limestone which causes it to harden.
Measurement of the specific surface area using the BET method is useful for comparing different cements.
Activated carbon has strong affinity for many gases and has an adsorption cross section
[14] In the field of solid catalysis, the surface area of catalysts is an important factor in catalytic activity.
Inorganic materials such as mesoporous silica and layered clay minerals have high surface areas of several hundred m2/g calculated by the BET method, indicating the possibility of application for efficient catalytic materials.
The ISO 9277 standard for calculating the specific surface area of solids is based on the BET method.
[15] The method has also been adapted for determination of specific area of ceramics [16] [17] and non-ferrous metal powders.
[18] In 2023, researchers in the United States developed a method to determine BET surface areas using a thermogravimetric analyzer (TGA).
[19] This method uses a TGA to heat a porous sample loaded with an adsorbate, the produced plot of sample mass vs. temperature is then mapped into a standard isotherm to which BET theory is applied as normal.
Common fluids, e.g. water or toluene, can be used as adsorbates for the TGA method allowing the specific interactions of different adsorbates to be determined, as these frequently differ from the commonly used nitrogen.
