Membranes - Introduction to Carbon Capture and Sequestration - page 321

coeffi cient, we obtain the Maxwell-Stefan diffusion coeffi cient, which gives
a more true representation of the mobility of the molecules. In many practi-
cal systems the Maxwell-Stefan diffusion coeffi cient is far less dependent
on the concentration. Therefore, many engineering applications simply
assume that this diffusion coeffi cient is independent of the concentration.
The above illustrates what is known as the “Darken” assumption,
namely, that the corrected diffusion coeffi cient is assumed to be independ-
ent of the loading. It is important to mention that it was not Darken who
made this assumption. Darken realized that in many cases the corrected
diffusion coeffi cient does depend on loading. For a historical note on these
aspects, see the article by Reyes et al . [7.7]. Nevertheless, in many engi-
neering applications this assumption has been widely used. Indeed, from
a practical point it is very convenient as it implies that it is suffi cient to have
knowledge of either the self-diffusion coeffi cient at low loading or a single
transport diffusion coeffi cient plus the complete adsorption isotherm to
estimate the transport diffusion coeffi cient for all loadings.
Section 5
Materials: polymers
In the previous sections, we have seen that the engineering design plays
an essential role in defi ning whether or not a membrane separation for CO 2
is feasible. Given the right design, we again have a target for materials
research: to make a material with a high permeability and a suffi cient selec-
tivity. In this section, we will look in more detail at the molecular aspects of
the design of that material. We start our discussion with polymer mem-
branes. In the next section, we will discuss nanoporous materials.
Polymer membranes
Polymer membranes are typical examples of systems in which permea-
tion is ruled by the solution-diffusion mechanism. Figure 7.5.1 shows a
caricature of a disordered polymer fi lm. The fi lm has a typical distribution