Page 275 - Gas Adsorption Equilibria

5. Oscillometry 261

Here is the density of the sorptive gas, is the geometric volume of a
ring slit including the sorbent material in the swelling state and is a (still
unknown) volume of the sorbent / sorbate mass in the same state.
The mass belongs to a surface boundary layer of the sorptive gas
outside the volume and also moved along with the pendulum. This
quantity can be determined from either measurements with non-sorbing
(dummy) pellets made of glass, or from combined oscillometric-gravimetric
measurements with a non-swelling, i. e. rigid sorbent material [5.2, 5.7]. Data
of this quantity have been determined at our pendulum for different gases in a
certain range of pressure and temperature and easily can be correlated and / or
interpolated [5.25]. However, these quantities naturally depend on the
geometry of the pendulum used and hence are not physical parameters related
to the sorbent / sorptive system. Hence we do not present them here.

For swelling processes of polymeric spherical or cylindrical pellets the
ratio (b) of the pellet volume to the bulk volume often remains
constant. * ) As this ratio easily can be determined by He-pycnometer
measurements in an unswollen reference state, i. e. at ambient conditions, we
have

Here is the volume of the sorbent pellets of mass in the reference
state and their bulk volume in the same state which by the way in
principle can be chosen arbitrarily. To give an example we mention that for
simple cubic packing of spherical pellets of radius r in a cubic box of side
length (2rN) we have

Note that in this case – as in many others – b does not depend on the radius (r)
of the pellets.

* )
This does not hold in case that pellets due to sorption of gas undergo plastic deformations or
even melt, then forming a homogenous phase with no interstitial volume.