Page 49 - Adsorption Technology & Design, Elsevier (1998)

46 Fundamentals of adsorption equilibria

Radushkevich (1947) found that there is a direct correlation between the
molar volume in the liquid state and the affinity coefficient fl characterizing
the polarizibility of the adsorbate and assumed that ec'ej - fli/flj = V,,,i/Vmj.
For non-polar and weakly polar adsorbates such a correlation is not always
obeyed but, despite this shortcoming, the relationship is utilized in order to
force the characteristic curves of all gases on the same adsorbent to be
coincident so that now e - fir(O) - a unique method of obtain-
ing a universal isotherm for a given adsorbent.
The semi-empirical equation which Dubinin obtained relating adsorbed
volume v to the adsorption potential e is

v/vo = exp (- K'62/fl 2) (3.20)
where v0 is the total capacity of the adsorbent to adsorb the gas or vapour.
Substitution of equation (3.18) into equation (3.20) gives, in logarithmic
form,
ln(v/vo) = --tc(ggT/fl) 2 {ln(p/ps)} 2 (3.21)

Figure 3.7(a) illustrates a characteristic curve for the adsorption of
tetrafluoroethene on charcoal for four different temperatures while Figure
3.7(b) is the corresponding plot of equation (3.21). Dubinin claimed that the
volume v0 represents the micropore volume which can be extracted from
equation (3.21) by plotting In (v/vo) against (In pips) 2.
For pores of larger diameter in which capillary condensation is not
important, the term (e/fl) was employed by Dubinin and Radush-
kevich (1947) in equation (3.18) rather than (e/fl) 2 used subsequently by
Dubinin (1960). Extensive work by Marsh and Wynne- Jones (1964) and
by Lamond and Marsh (1964) on the adsorption of N2 and CO2 on porous
carbons has enabled the application of equation (3.20), for the determin-
ation of monolayer volumes, to be tested. It was shown that a reliable
monolayer volume could only be extracted if there is no capillary
condensation at low relative pressures. The success which these latter
authors achieved in extending the theory of Dubinin and Radushkevich for
the determination of monolayer volumes (as opposed to micropore
capacities Vo) is attributable to the interpretation by Marsh et al. of Foster's
(1952) descriptions of the differences between the adsorption potential
when micropores and macropores become progressively filled with ad-
sorbate. It emerges that the spontaneous filling of large diameter pores,
resulting in capillary condensation, occurs if the adsorption potential is high
and the repulsive forces are low. This corresponds to strong adsorbate-
adsorbent affinity and weak interaction between successive adsorbate
layers.