Multilayer Adsorption The Brunauer-Emmett-Teller Equation

As noted above, the range of pressures over which gas adsorption studies are conducted extends from zero to the normal vapor pressure of the adsorbed species p0. An adsorbed layer on a small particle may readily be seen as a potential nucleation center for phase separation at p0. Thus at the upper limit of the pressure range, adsorption and liquefaction appear to converge. At very low pressures it is plausible to restrict the adsorbed molecules to a mono-layer. At the upper limit, however, the imminence of liquefaction suggests that the adsorbed molecules may be more than one layer thick. There is a good deal of evidence supporting the idea that multilayer adsorption is a very common form of physical adsorption on nonporous solids. In this section we are primarily concerned with an adsorption isotherm derived by Brunauer, Emmett, and Teller in 1938 the theory and final equation are invariably known by the initials of the authors BET. 

The BET isotherm has subsequently been derived by a variety of methods, but, as mentioned in the previous section, we follow the approach of the original derivation, namely, a 

If we allow the possibility that a surface site may be covered to a depth of more than one molecule, then the following modifications to the derivation presented in Section 9.4b.2 are required. First, we define M, to be the number of sites covered to a depth of i molecules. Second, Equation (45) is modified to 

Now let us consider the composition of the second layer (i = 2). By analogy with Equation (42), the rate at which molecules adsorb to form layer 2 is proportional to p and M,. For simplicity, the proportionality constant is assumed to be the same as that for adsorption on the bare surface. Therefore we write 

In a similar fashion, we assume the rate of desorption from the second layer to be proportional to M2  

---