BET theory

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BET theory is a well-known rule for the physical adsorption of gas molecules on a solid surface. In 1938, Stephen Brunauer, Paul Hugh Emmett, and Edward Teller published an article about the BET theory in a journal^[1] for the first time; “BET” consists of the first initials of their family names.

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: (a) gas molecules physically adsorb on a solid in layers infinitely; (b) there is no interaction between each adsorption layer; and (c) the Langmuir theory can be applied to each layer. The resulting BET equation is expressed by (1):

$\frac{1}{v \left [ \left ( {P_0}/{P} \right ) -1 \right ]} = \frac{c-1}{v_m c} \left ( \frac{P}{P_0} \right ) + \frac{1}{v_m c} \ \ \ \ \ \ \ (1)$

$P$ and $P 0$ are the equilibrium and the saturation pressure of adsorbates at the temperature of adsorption, $v$ is the adsorbed gas quantity (for example, in volume units), and $v m$ is the monolayer adsorbed gas quantity. $c$ is the BET constant, which is expressed by (2):

$c = \exp\left(\frac{E_1 - E_L}{RT}\right) \ \ \ \ \ \ \ (2)$

$E 1$ is the heat of adsorption for the first layer, and $E L$ is that for the second and higher layers and is equal to the heat of liquefaction.

Equation (1) is an adsorption isotherm and can be plotted as a straight line with $1 / v [(P 0 / P) - 1]$ on the y-axis and $P / P 0$ on the x-axis according to experimental results. This plot is called a BET plot. The linear relationship of this equation is maintained only in the range of $0.05 < P / P 0 < 0.35$ . The value of the slope and the y-intercept of the line are used to calculate the monolayer adsorbed gas quantity $v m$ and the BET constant $c$ .

The BET method is widely used in surface science for the calculation of surface areas of solids by physical adsorption of gas molecules. A total surface area $S t o t a l$ and a specific surface area $S$ are evaluated by the following equations:

$S_{total} = \frac{\left ( v_m N s \right )}{V}$ $S = \frac{S_{total}}{a}$

N

: Avogadro's number,

s

: adsorption cross section,

V

: molar volume of adsorbent gas

a

: weight of sample solid

For example, activated carbon, which is a strong adsorbate and usually has an adsorption cross section $s$ of 0.16 nm² for nitrogen adsorption at liquid nitrogen temperature, is revealed from experimental data to have a large surface area around 3000 m² g^-1. Moreover, in the field of solid catalysis, the surface area of catalysts is an important factor in catalytic activity. Porous inorganic materials such as mesoporous silica and layer clay minerals have high surface areas of several hundred m² g^-1 calculated by the BET method, indicating the possibility of application for efficient catalytic materials.

[edit] References

^ S. Brunauer, P. H. Emmett and E. Teller, J. Am. Chem. Soc., 1938, 60, 309. doi:10.1021/ja01269a023

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Category: Physical chemistry

BET theory

From Wikipedia, the free encyclopedia

[edit] References

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