Page 47 - Adsorption Technology & Design, Elsevier (1998)

44 Fundamentals of adsorption equilibria

equals the heat of liquefaction. Neither of these assumptions is strictly valid,
but despite such difficulties, the BET equation has been widely applied as a
semi-empirical tool for the investigation of the characteristics of porous
adsorbents. By appropriate choice of c and qm the equation can be made to
fit any of the isotherm types II to V inclusive. For small values of plp~ the
BET equation reduces to the Langmuir equation. A typical BET plot (with
volume v replacing q as explained in Section 3.3.1) displaying a distinct
intercept and slope from which the surface area of the adsorbent may be
estimated is shown in Figure 3.6.

3.3.5 Polanyi's Potential Theory
The Potential Theory as originally conceived by Polanyi is well documented
in the classic text by Brunauer (1943). Polanyi considered contours of
equipotential energy above solid surfaces and ascribed a volume ~bi to the
space between the ith equipotential surface of energy e and the adsorbent
surface. The potential e was assumed to be independent of temperature so
that e = f(~b) is essentially an isotherm equation. The adsorption potential is
defined as the work of compression of the gas from a pressure p to the
saturation pressure ps. For one mole of a perfect gas of volume v in an open
thermodynamic system the adsorption potential is therefore
P,
e = ~ v dp = RgT ln(ps/p) (3.18)
P

assuming that the work of creating a liquid surface is small in comparison
with the magnitude of e. The volume in the adsorption space is

~=nVm (3.19)
where n is the number of moles adsorbed per unit mass of adsorbent and Vm
is the molar volume. By plotting e as a function of ~b a characteristic curve
~e) is obtained which represents, for a given adsorbate-adsorbent system,
the extent of adsorption at any relative pressure and temperature below the
critical temperature of the gas. The validity of the characteristic curve may
be extended for application to non-ideal gases and vapours by substituting
fugacities, f, for partial pressures.
Two different applications of the potential theory, one for microporous
solids and the other for adsorbents with larger pores, have been formulated
and will now be briefly considered. Dubinin (1960) related the volume v
adsorbed in micropores to the adsorption potential. Earlier, Dubinin and