Page 135 - Adsorption by Powders and Porous Solids

CHAPTER 5. ADSORPTION AT THE LJQUID-SOLID INTERFACE 121
at the solid-liquid film interface and
UU(LG) = Au '(LG)

the liquid film-vapour interface.
The maximum energy of immersion, which we designate A,,U", is liberated
when the vacuum-solid interface is replaced by the liquid-solid interface. Thus, for
fie immersion of an outgassed adsorbent of surface area A, we obtain:

A,, vo = A[U'(SL) - u'(so)] (5.12)
where ui(sL) and ui(SO) are the areal surface excess energies corresponding to
uU(SL) and Vu(SO) in Figure 5.1. (Note that since the process is exothermic, the
A U values are all negative.)
When area A is already covered with a physisorbed layer at surface excess con-
centration r (i.e. nU/A), the energy of immersion becomes

Finally, when the adsorbed layer is thick enough to behave as a liquid film, the
energy of immersion, A ,,U1, which corresponds to the disappearance of the liquid-
gas interface, is simply:

A,,, u1 = -AU'(LG) (5.14)
The above equations are all based on the internal energy. Similar equations can be
witten with the enthalpy since the surface excess enthalpy and energy are identical
in the Gibbs representation when V" = 0 (Harkins and Boyd, 1942). Therefore the
various energies of immersion defined by Equations (5.6)-(5.8) are all virtually
equal to the corresponding enthalpies of immersion, i.e. (A-HO, Aim,~r and
A-HI), thus:

The latter definition of the enthalpy of immersion is that given by Everett (1972,
1986).
Nevertheless, in this chapter we shall refer to the energy of immersion which is
unambiguous and consistent with our thermodynamic treatment.
In fact, 'energy of immersion' was the term originally used by Harkins in his early
papers (Harkins and Dahlstrom, 1930), before resorting to the usual laboratory term
of 'heat of immersion'. Although the Latter term is still used by a few authors, it is to
be discouraged since 'heat' is not a precise term and is not directly related to any
thermodynamic state of the system: as will be stressed in Section 5.2.2 describing
experimental techniques, in practice, the microcalorimetric measurement of the heat
exchanged is never equal to the required energy of immersion.

Relation between the energies of immersion and gas adsorption
The process of the immersion of a clean solid surface (which gives rise to A i,, Uo)