Adsorption Potentials, Adsorbent Self-Potentials, and Thermodynamic Equilibria E. A. FLOOD Division of Pure Chemistry, National Research Council, Sussex Drive, Ottawa, Canada
The Gibbs potential, F , of an adsorbate-adsorbαc
Downloaded by PENNSYLVANIA STATE UNIV on September 16, 2013 | http://pubs.acs.org Publication Date: June 1, 1961 | doi: 10.1021/ba-1961-0033.ch026
ent system may be considered as the sum of the intrinsic potentials of adsorbate, F , and adsorb α
ent, F , together with a mutual interaction poten c
tial,
ω , αc
When adsorbent-adsorbate potentials
are small compared with adsorbent self-potentials, the interaction is largely confined to fields lying outside the adsorbent system and the energies, Gibbs potentials, stresses, etc., are additive, ω , αc
approaching zero.
In this case the free energy
change of the adsorbent is measured by its change in state of stress.
When adsorption potentials are
comparable with adsorbent self-potentials, the Gibbs potentials and stresses are not additive and the free energy change of the adsorbent is not measured by its change in state of stress alone.
y he change in Gibbs potential (δ F) due to immersion of active carbon (F ) in a relatively large mass of gas (F ) at constant pressure (P ) and temperature may be expressed by c
g
g
FQ(PQ, ™g) + Fcipc = 0, m ) = Fadpg, ™o, ™c) + 5F c
or and
μ τη + μ πι 0
0
00
0
8F = (u
co
= μ πι + μ πι + 5F 0
0
0
— μ )ηι €
0
0
= —5F
C
This equation will hold regardless of the kind of reaction involved, provided that no volatile or gas-soluble substance containing carbon is evolved. The equation is therefore applicable to a great variety of possible reactions and pro vides little or no information concerning the state of either adsorbate or adsorbent in the combined system. If, however, a dividing surface exists which separates the adsorbent com pletely from the adsorbate, so that throughout the adsorption reaction no material, electrons, etc., can cross this dividing surface, we can considerably restrict the number of possible types of interaction. When such a surface exists, we can apply equations of the Polanyi (18) or Guggenheim (JO) type [essentially variants of 248
In SOLID SURFACES; Copeland, L., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1961.
(1)
FLOOD
249
Adsorption Potentials
Gibbs' 508, 514 (9)] and obtain expressions for the adsorbate "spreading pres sure." Assuming such spreading pressures to consist literally of purely hydrostatic stresses and these stresses to be in equilibrium with the accompanying purely mechanical stresses of the solid, we can write the approximate equation, (2)
F = Kcby c
where Κ is a proportionality constant, σ the surface area, and y the mean surface mechanical stresses of the solid, or we may write the more general equation, (3)
F = K'vJ&pi Downloaded by PENNSYLVANIA STATE UNIV on September 16, 2013 | http://pubs.acs.org Publication Date: June 1, 1961 | doi: 10.1021/ba-1961-0033.ch026
c
where v is the volume of the solid adsorbent and p\ is the mean principal stress intensity. Equation 2 has been used with some success by Bangham (I), Mcintosh (5), Yates (20), and others to correlate adsorption extension data. Equation 3 has also been used with considerable success by Mcintosh (15) and Dacey (6), and in some of my own work (8, 15). If the adsorption reaction can indeed be represented as a purely mechanical interaction, then from the thermodynamic conditions for equilibrium of systems in purely hydrostatic states of stress, we can deduce c
Vapl
+
OePl
=
+
(V
a
(4)
V )P C
where v is a volume which includes the effective field of the solid (for porous bodies v can be taken as either the whole of the void volume or as the micropore volume, and the value of p i changes accordingly) ; v is the solid volume; p is the volumetric mean of the principal stress intensities acting on the external surfaces of the adsorbate volumes which contribute to v ; p is the similar volu metric mean stress intensity of the solid; and Ρ is the hydrostatic pressure of the fluid in which the system is immersed and with which it is in equilibrium. When the volume v is very small compared with v , so that v is virtually the "surface" of v , Equation 4 reduces to a
a
v
c
a
a
a
c
v
c
a
c
Vc(p*
-
Ρ) = / σ
