Page 56 - Partition & Adsorption of Organic Contaminants in Environmental Systems

POLANYI ADSORPTION POTENTIAL THEORY 47

For a vapor at a given equilibrium P/P° or a given e, which corresponds to
a given equipotential surface inside the adsorption space, the volume enclosed
by the equipotential surface and the solid surface is the adsorbed volume. The
net molar heat of adsorption at the equilibrium potential surface is -e. If the
vapor is condensed as a liquidlike adsorbate, the total molar heat of adsorp-
tion is -(e+DH evap ), where DH evap is the molar heat of evaporation of the
liquid. If the vapor is condensed as a solid adsorbate, the total molar heat of
is the molar heat of sublimation of
adsorption is -(e+DH sub ), where DH sub
the adsorbate.
For vapor adsorption on a relatively inert porous solid (e.g., activated
carbon) that involves primarily London forces (i.e., in the absence of
chemisorption or specific interaction), the adsorption potential (e) is inde-
pendent of temperature. A direct consequence of this temperature independ-
ence and of the vapor condensation is that a plot of the total adsorbed liquid
(or solid) volume (f) against e at that volume (called a characteristic curve) is
temperature invariant and depends only on the vapor and the solid structure.
Thus, once the characteristic curve is obtained for a vapor on a porous solid
from its adsorption data at one temperature, it can be used in a reverse manner
to construct the isotherm at a different temperature. The Polanyi model pos-
tulates no specific mathematical form for the characteristic curve, which is
fixed instead by the structure of the porous solid.
If there is no molecular sieving involved in vapor adsorption, the Polanyi
model expects the characteristic curves for all vapor adsorbates on a chemi-
cally inert porous solid to have a common shape and a common limiting adsor-
bate volume (at e= 0). For any adsorbed volume, the adsorption potentials of
different vapor adsorbates are related to each other by constant characteris-
tic factors. Therefore, all characteristic curves on a given solid can be made to
collapse into a single curve by appropriate divisors of the individual adsorp-
tion potentials for any given adsorbed volumes. The most effective and con-
venient divisors are found to be the liquid molar volumes ( ) of the vapor
V
adsorbates (Dubinin and Timofeyev, 1946). The resulting plot of the adsorbed
volume versus e/V for a vapor adsorbate is called a correlation curve (Lewis
et al., 1950). As shown by Polanyi and Manes, correlation curves provide a
basis to predict the adsorption of a solute from solution on an inert porous
solid from the respective vapor isotherms of the pure solute and solvent.
If a solute in solution is partially miscible with the solvent, the basic Polanyi
model expects that the solute condense into the adsorption space as a liquid
or a solid phase, depending on the state of the pure solute at the system tem-
perature. Therefore, the critical difference between vapor-phase and liquid-
phase adsorption is that the vapor condenses in a hitherto unoccupied space,
whereas the liquid or solid solute condenses to displace an equal volume of
the solvent. According to Polanyi, the adsorption potential of a partially mis-
cible solute can thus be expressed as

e sl = e s - ( s l RT ln C ( s C ) (4.12)
e l VV ) =
e