Page 117 - Adsorption by Powders and Porous Solids

102 ADSORPTION BY POWDERS AND POROUS SOLIoS

changed and the point of inflection is lost. The BET equation then gives a Type Q
isotherm. In practice, the range of validity of Equation (4.32) is always confined toa
limited part of the isotherm.
If the adsorption at saturation is restricted to a finite number of layers, N, the BET
treatment leads to a modified equation which includes this additional parameter (c.
Chapter 6). Naturally, in the special case when N = 1, the extended BET equation
corresponds to the Langrnuir equation.
The BET model appears to be unrealistic in a number of respects. For example, i,
addition to the Langmuir concept of an ideal localized monolayer adsorption, it is
assumed that all the adsorption sites for multilayer adsorption are energetically iden.
tical and that all layers after the first have liquid-like properties. It is now generally
recognized that the significance of the parameter C is oversimplified and that
Equation (4.33) cannot provide a reliable evaluation of E,.
A recent molecular simulation study (Seri-Levy and Avnir, 1993) has also
revealed the artificial nature of the BET model and has illustrated the effect of &g
adsorbate-adsorbate interactions into account. Thus, the addition of lateral interac-
tions appears to flatten the BET stacks into more realistically shaped islands.
In spite of the inadequacy of the underlying theory, the BET equation remains the
most used of all adsorption isotherm equations. The reasons for this situation and the
advantages and limitations of the BET method are discussed in Chapter 6.

4.2.5. Multilayer equations
An extension to the BET model was put forward by Brunauer, Deming, Deming and
Teller (BDDT) in 1940. The BDDT equation contains four adjustable parameters and
was designed to fit the isotherm Types I-V. From a theoretical standpoint, the BDDT
treatment appears to offer very little more than the original BET theory and the cum-
bersome equation has very rarely been applied to experimental data.
Several other attempts have been made to modify the BET equation in order to
improve the agreement with isotherm data in the multilayer region. Brunauer et al.
(1969) pointed out that the BET assumption of an infiite number of molecular layers
at saturation pressure is not always justified. By replacingp by kp, where k is an addi-
tional parameter with a value less than unity, they arrived at the following equation,
which has the same form as that originally proposed by Anderson (1946):
@ =-+- 1 (C- 1) kp
X-
n(pO -kp) n,C n,C PO
On an empirical basis, this Anderson-Brunauer equation can be applied to some
isotherms (e.g. nitrogen and argon at 77 K on various non-porous oxides) over a
much wider range of p/pO than the original BET equation.
When the adsorbate reaches a thickness of several molecular layers, the effects of
surface heterogeneity are considerably reduced. If the temperature is not too low,
some - but not all - multilayers appear to undergo a continuous increase in thickness
as the pressure approaches saturation and bulk behaviour is gradually developed
(Venables et al., 1984). With such systems, it seems reasonable to assume that the