Page 58 - Gas Adsorption Equilibria

44 Chapter 1

installation and insufficient approach to true equilibrium may considerably
influence measurement results.

Second, as already mentioned, volumetric as well as gravimetric
measurements in principle do not allow one to determine the mass of gas
adsorbed on the surface of a porous solid (mass but only the so-called
reduced mass defined by Eq. (1.5). Hence, in order to calculate from
a model assumption for the volume of the sorbent impenetrable
to sorptive gas molecules and that for the sorbed phase or
equivalently for their sum

has to be introduced. Obviously, resulting will depend on this
assumption. Unfortunately, this basic problem is not often addressed in
today’s literature, (for exceptions see [1.49, 1.52-1.53]), but most authors
choose to use for the helium volume approximation, i. e. assume
Here is gained from Eq. (1.5) applied to helium experiments
and assuming helium not to be adsorbed or absorbed in the sorbent material
during time of observation, i. e. by assuming Additionally it often is
assumed that which leads to the concept of the Gibbs excess mass
adsorbed cp. Chaps. 2, 3 [1.1-1.3, 1.18, 1.19, 1.42]. This will be
discussed in the next Sect. 5 of this chapter. As for low gas pressures
the above mentioned model assumptions seem to be reasonable
from a pragmatic point of view. However, as for high pressures considerable
differences between and normally occur, cp. examples given in
Chap. 3, these assumptions should be abandoned and measurement methods
should be used – at least for calibration data – allowing one to determine the
absolute mass adsorbed without introducing additional assumptions for
the volume Indeed, a method which in principle would allow to do this
has been developed and preliminary measurements have been performed. The
method consists on the combined measurements of two extensive quantities of
the adsorbed phase, namely its (integral) enthalpy and its dielectric
polarization. By combining the respective caloric and dielectric equations of
state of the sorbate phase, an algebraic equation can be derived including the
mass as single unknown quantity. Hence, up to now can be
calculated by standard algebraic procedures. Unfortunately, measurements are
laborious and even cumbersome. Hence, there are only a few data of
measured absolute masses of adsorbates available in literature [1.54].

A third obstacle for determining pore spectra of a sorbent material from
gas adsorption data is the fact that today there are several different methods in