Membranes - Introduction to Carbon Capture and Sequestration - page 332

Section 6
Materials: nanoporous
materials
We have seen that polymer membrane research is focused on develop-
ing strategies to beat the Robeson upper limit. In this section, we will see
that for nanoporous materials the chemistry is fundamentally different.
Nanoporous membranes
Instead of starting with an overview of experimental data, we will look at
a model membrane in order to develop some intuition about how to
design a nanoporous membrane material. Figure 7.6.1 shows a small
part of a model membrane consisting of nanoporous cavities that are
connected by narrow windows. The fi gure shows three cavities. The
dimensions of these cavities and windows are of the same order as the
sizes of the adsorbed molecules (0.5-2 nm). An ideal membrane will be
a perfect unit crystal with a large surface area (parallel to the x,y plane)
and thickness (in the z direction) of a few micrometers. In this crystal, the
cavities form channels that run parallel to the surface ( z -direction).
We assume that we can change the size of the cavities, the size of
the window region, and the corresponding energies of interaction
between the adsorbate and the walls. In this section, we show how we
can tune the permeation of our model membrane. For example, if we
change the diameter of the windows ( L wy ) how will this change the
adsorption and diffusion properties? Or, to change the interaction ener-
gies of our gas molecules with the walls of the material, do we need to
change the interactions in the cavities ( U c ) or in the windows ( U w )?
In previous sections, we have shown that the permeability of our
material is the product of adsorption and diffusion. At low loadings the
adsorption can be computed from the Henry coeffi cient. We have also
shown that at these low loadings the self-, Maxwell-Stefan, and Fick dif-
fusion coeffi cients are the same. We will assume that at fl ue gas condi-
tions the loading is suffi ciently low that we can obtain the number of
adsorbed gas molecules from the Henry coeffi cient and that the