Environmental Engineering Reference
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Figure 7.5.1 Diffusion in a polymer membrane
Example of a polymer (blue) with a gas molecule (red) hopping from one cavity to
another. The black arrows indicate different paths.
of holes in which the gas can dissolve (solubility) and the gas molecules
can hop between one cavity and another (diffusion). Depending on the
chemical make-up of the polymer fi lms, these cavities can be dynamic;
they form or disappear depending on the movement of polymer seg-
ments. Most materials will have a distribution of different cavities and
hence of hopping rates.
We have seen that the ideal membrane for separation has a high selec-
tivity and a high permeability. Robeson [7.8,7.9] discovered that polymeric
materials with a high selectivity have a low permeability, while materials
with a high permeability have a low selectivity. This behavior is illustrated
in Figure 7.5.2 . In this “ Robeson plot ”, the selectivity for CO 2 /N 2 mixtures
is plotted as a function of the CO 2 permeation. This plot shows that for a
wide range of materials, the upper bound in selectivity is an approxi-
mately linear function of the permeation, as shown by the black line.
In the simple model we described previously, we saw that we can
increase the permeability in two ways: change the diffusion coeffi cients
or change the solubility. It turns out that the solubility of gasses in most
of the available polymeric materials does not vary signifi cantly. The diffu-
sion coeffi cients, on the other hand, do change if we change the material.
However, the materials with the highest diffusion coeffi cients tend to
have more open structures; as a consequence all adsorbed molecules
move faster and one loses selectivity. Because of this effect, we see that
materials with a high permeability also have a low selectivity. This is the
explanation for the upper bound shown in Figure 7.5.2 .
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