Ideal Multilayer BET Isotherm

In the following, we will write 6j) for the fraction of sites that are empty, and 9, 82, and so on for the fraction of sites occupied by 1, 2, and so on molecules, respectively. Recalling Equations 4.35 and 4.36, we can write under the same considerations the adsorption and desorption rates of layer i 

FIGURE 4.23 Schematic drawing of the ideal multilayer adsorption, as assumed in the BET model multilayer adsorption takes place, but in this example, the adsorbate-surface interaction is stronger than adsorbate-adsorbate interaction, thus the first layer forms preferentially to multilayer growth. The adsorbate molecules are assumed to form stacks independent of each other, so that every molecule has only up and down interactions, not lateral ones. 

Note that the number of layers has no upper bound an essentially infinite number of layers means adsorbate condensation. Now, there is an assumption introduced by Brunauer et al. the adsorbing molecules interact only with the nearest ones above and below, so that beyond layer 1, aU interactions, and hence adsorption constants, are equal and also the same as in the adsorbate liquid that is, = With this condi- 

As usual, it has been assumed above that an infinite number of layers can be adsorbed. If this number is finite, N, the isotherm obtained reads (Brunauer, Emmett, and Teller 1938) 

The BET isotherm has little, if any, application in problons of adsorption in the soil but is important, because it constitutes the basis of a commonly applied method to determine surface areas, as we shall see in Chapter 7. There are a number of cases where adsorption beyond a monolayer is observed, especially for transition metal 

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