Membranes - Introduction to Carbon Capture and Sequestration - page 310

adsorption and diffusion properties. In Chapters 5 and 6 we discussed
the absorption and adsorption of gasses in materials. The same con-
cepts apply for membrane separations. What is new in membrane sepa-
rations is the role of diffusion, and in this section we discuss the
molecular aspects of diffusion. In Chapter 6, the solubility of a gas was
related to the material properties of the adsorbent; in this chapter we aim
to make a similar connection for diffusion. We feel that it is important to
develop some intuition on how diffusion coeffi cients are related to the
structure of a material.
Which diffusion coeffi cient?
Before discussing diffusion in porous media, it is instructive to start with
diffusion in the bulk. Most people who start reading the literature about
diffusion get confused because the concept of a diffusion coeffi cient has
many meanings, and these differences in meaning result in numerical
values for diffusion coeffi cients that can differ by orders of magnitude. So,
the fi rst thing we will do is introduce these diffusion coeffi cients. We have
to warn you that you will read, and hopefully understand, a little more
about diffusion coeffi cients than you strictly need for carbon capture. In
the literature one can fi nd three distinct types of diffusion coeffi cients:
• The Fick diffusion coeffi cient : this is the diffusion coeffi cient that
is associated with transport of mass caused by a difference in con-
centration. This is the diffusion coeffi cient we use in practical
applications.
• The Maxwell-Stefan (or Darken-corrected , or collective ) diffusion
coeffi cient : this is the diffusion coeffi cient that relates transport of
mass to a gradient in the chemical potential. This is a more funda-
mental way of describing the diffusion coeffi cient and typically follows
from a molecular simulation. If we know how the concentration is
related to the chemical potential, we can easily convert this diffusion
coeffi cient into the Fick diffusion coeffi cient.
• The self-diffusion coeffi cient : this coeffi cient characterizes the dif-
fusion of a single molecule in a fl uid of identical molecules. This type
of diffusion at the molecular level can be measured by labeling some
of the molecules (e.g., by using Nuclear Magnetic Resonance spec-
troscopy (NMR)) or by molecular dynamics simulations.