7.2.2 Other useful adsorption isotherms
The Langmuir isotherm makes a number of assumptions that may not
apply to all adsorbates and adsorbents. For instance, strong intermolecular interactions may cause deviations from Langmuir adsorption
behavior. Many systems display multilayer adsorption. The Brunauer
Emmett Teller, or BET, isotherm is useful for modeling such behavior.
The key assumptions made in the BET isotherms are that physisorption
on a solid is infinite, that there are no interlayer interactions in the
multilayer film, and that each layer can be described by the Langmuir
model. The BET isotherm takes the form shown in Equation 7.16
q =
V
V m
=
cz
1 − z
ð
Þ1 − 1 − c
ð
Þz
½
Š
(7.16)
The term z = P/P*, where P* is the vapor pressure above the adsorbate
before any adsorption occurs. The constant c is related to the enthalpy of
adsorption of the first layer (ΔH 1 ) and the enthalpy of vaporization of the
subsequent layers (ΔH vap )(Equation 7.17)
c = exp
ΔH 1 − ΔH vap
RT
(7.17)
Figure 7.12 shows how the form of the isotherm changes for different
values of c. When c ≫ 1, the isotherm simplifies to Equation 7.16 and is
C 1 > C 2 > C 3
c 2
c 1
c 3
V/V
m
z = P/P *
Figure 7.12 The effect of
changing the parameter c on
the BET isotherm.
CHAPTER 7: Fundamentals of Surface Nanoscience
240