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Transport through Carbon Membranes

The ability of ultramicroporous carbon membranes to separate a gas mixture depends on membrane pore size, the physiochemical properties of the gases and the surface properties of the membrane pores. The pore size of a carbon fiber for gas separation is usually within the range of 3.5 to 10 A, depending on the membrane preparation conditions during carbonization or post treatment (post oxidation or chemical vapor deposition). There are basically three transport mechanisms for carbon membranes, as listed below [2]; see also the illustration in Figure 4.2:

  • 1. Knudsen diffusion; the square root of the ratio of gas molecular weights will give the separation factor.
  • 2. Selective surface diffusion, governed by selective adsorption of the larger non-ideal components on the pore surface, hence the smaller components are retained.
  • 3. Molecular sieving; smaller molecules will permeate through carbon membranes, with larger molecules being retained or permeating at a much lower rate.


Illustration of different transport mechanisms through carbon membranes.

Knudsen Diffusion

For Knudsen diffusion, the lower limit for pore diameter has usually been set to df, > 20 A [3]. However, Gilron and Soffer [4] have discussed thoroughly how Knudsen diffusion may contribute to transport in even smaller pores and, from a model considering pore structure, shown that contributions to transport through one specific fiber may come from both activated transport and Knudsen diffusion. It may therefore be difficult to know exactly when transport due to Knudsen diffusion is taking place. One way to approach this problem is to calculate the Knudsen number, NKn, for a system, which is X/df where X is the mean free path. If NK >10, then the separation can be assumed to take place according to Knudsen diffusion [5]. If the preparation of carbon membranes has been unsuccessful, one may get Knudsen diffusion. Gas flux based on Knudsen diffusion is similar to Fick's law, and can be described as follows,

where rp is pore radius, v is the average velocity of gas molecules, M is gas molecular weight and T is the operating temperature. Gas selectivity is then dependent on the ratio of molecular weight of gas molecules:

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