Page 93 - Adsorption by Powders and Porous Solids

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ADSORPTION BY POWDERS AND POROUS SOAJD~

bulb when immersed in liquid nitrogen during Step 2 (with reproducible but
unknown temperature gradients). V,, does not depend on the presence or absence of
the sample. From V, and V,, we therefore obtain the modified V,,, which takes
account of the presence of the adsorbent. Since Vup remains constant, only Step 3 is
required for a new sample.
The gas to be used in the dead space determination must be carefully selected. I,
the procedure described, Step 1 can be carried out with any permanent gas (eag,
helium or nitrogen), whereas for Step 2 it is advisable to use a gas with the same virial
coefficient B, as the adsorptive, since B, and the subsequent correction can vary
considerably from one gas to another (see Section 3.4.8). Since the measured value
of V, depends on the virial coefficient B, of the gas used, the simplest procedure is
to use the adsorptive itself. Step 3 is also preferably carried out with a gas whose
accessibility to the sample is comparable to that of the adsorptive: here again the
adsorptive itself, at a temperature at which it is known not to adsorb, is the best.
As can be seen, helium, in contrast to what was once assumed, is not necessarily
the best gas to select for the determination of dead space. It is sometimes thought that
helium allows dead space to be determined directly at 77 K in the presence of the
sample, since it will not adsorb. However, since its virial coefficient is much smaller
than that of most adsorptives (see Table 3.2), and because of the possibility of
adsorption in micropores (see Chapter 9), its use cannot be recommended. This
problem has been discussed recently by Neimark and Ravikovitch (1997).

The indirect route for determining the dead space volume makes use of an estimated
volume of the adsorbent sample. This volume can be obtained in two ways:
(a) From the theoretical density. This leads to a dead space which, by definition,
contains all pores of any size (including closed pores and also any micropores
inaccessible to the adsorptive).
(b) From pycnometric measurements (in a liquid or in a gas) carried out separately.
In this case the nature and temperature of the fluid must always be stated.
Both have the advantage of giving a sample volume (and therefore a location of the
dividing surface) which is, by definition, perfectly reproducible from one adsorption
bulb to another and from one laboratory to another. Even if not always realistic, it is
a sound convention, if the aim is to obtain reproducible measurements and calcula-
tions and is consistent with the spirit of the Gibbs representation. It is, for these
reasons, certainly well suited for the study of reference materials. Of course, this
approach would replace Step 3 in the procedure described above, whereas Steps 1
and 2 would remain necessary.
In the case of differential or twin arrangements of adsorption manometry (cf.
Figures 3.4-3.6), the dead volume determination is not required, but the volume
equalization and the symmetry of the set-up are essential. The volume equalization is
usually obtained with glass beads on the reference side and sometimes also with
adjustable bellows or a piston. The check or adjustment is normally carried out at
ambient temperature: the introduction of an identical amount of gas on both sides
must result in a zero pressure difference between them.