Page 54 - Partition & Adsorption of Organic Contaminants in Environmental Systems

POLANYI ADSORPTION POTENTIAL THEORY 45

the surface area is then calculated along with the assumed N 2 molecular area
2
of 16.2 ¥ 10 -20 m .

4.5 POLANYI ADSORPTION POTENTIAL THEORY

If adsorption is highly energetically heterogeneous, as with high-surface-area
microporous solids such as activated carbon and silica gel, the adsorption data
exhibit serious deviations from the Langmuir model or the BET model. This
is because the force field within a pore space (adsorption space) of a micro-
porous material that attracts a molecule varies considerably with the location.
The Polanyi adsorption potential theory (Polanyi, 1916) has long been recog-
nized as the most powerful model for dealing with vapor adsorption on ener-
getically heterogeneous solids (Brunauer, 1945). The basic Polanyi model
has been extended to a wide range of vapor- and liquid-phase systems by
Manes and co-workers (Manes, 1998), and will therefore be referred to as
Polanyi–Manes model. The model relates a wide variety of both vapor- and
liquid-phase data to each other, and in particular, it correlates liquid-phase
with vapor-phase adsorption. For a detailed account of the extended model,
see Manes (1998).
The Polanyi theory considers that for a molecule located within the attrac-
tive force field of a microporous solid, there exists an (attractive) adsorption
potential (e) between the molecule and the solid surface. This attraction
derives from the induced dipole–induced dipole force (i.e., the London force)
of the molecule and surface atoms, which is short range in nature. The poten-
tial e at a particular location within the adsorption space may be viewed as the
energy required to remove the molecule from that location to a point outside
the attractive force field of the solid. Thus, the magnitude of e for an adsor-
bate depends on its proximity to the solid surface. It is highest in the narrow-
est pore (or in the narrowest portion of a pore) because the adsorbate is close
to more solid material. A series of equipotential surfaces are formed by con-
necting the points in adsorption space with the same e, as shown schematically
in Figure 4.2.
When a vapor is placed within an attractive force field of a solid, two oppos-
ing thermodynamic effects occur. The system energy is minimized by vapor
concentration into the region of the lowest potential energy, but the system
entropy is reduced by this concentration. The impact of these two effects at a
constant temperature on the molar free energy is given by

d G =-de+ V dP (4.8)

where -de is the differential potential energy change per mole of the vapor,
V the molar volume of the vapor, and dP the differential change in vapor
partial pressure. At adsorption equilibrium, dG = 0, and the reduction in
potential energy offsets the loss in entropy: