Types of Solid Diffusion

The structure of the solid and its interaction with the diffusing substance have a profound influence on how diffusion occurs and on the rate of transport. 

In many respects, diffusion of solutes through certain types of polymeric solids is more like diffusion through liquid solutions than any of the other solid-diffusion phenomena, at least for the permanent gases as solutes. Ima ne two bodies of a gas (e.g., Hj) at different pressures separated by a polymeric membrane (e.g., polyethylene). The gas dissolves in the solid at the faces exposed to the gas to an extent usually describable by Henry s law, concentration directly proportional to pressure. The gas then diffuses from the high- to the low-pressure side in a manner usually described as activated the polymeric chains are in a state of constant thermal motion, and the diffusing molecules jump from one position to another over a potential barrier [4, 11]. A successful jump requires that a hole or passage of sufficient size be available, and this in turn depends on the thermal motion of the polymer chains. The term activated refers to the temperature dependence of the diffusivity, which follows an Arrhenius-type expression, 

Particularly for large molecules, the size and shape of the diffusing molecules (as measured by molecular volume, branched as opposed to straight-chain structure, etc.) determine the hole size required. Solvents sometimes diffuse by plasticizing the polymersf, and consequently the rate may be very much higher 

Unfortunately (because it necessarily adds complicated dimensions and awkward units) it has become the practice to describe the diffusional characteristics in terms of a quantity P, the permeability. Since at the two faces of a membrane the equilibrium solubility of the gas in the polymer is directly proportional to the pressure, Eq. (4.2) can be converted intof 

Commercial application of these principles has been made for separating hydrogen from waste refinery gases in shell-and-tube devices which resemble in part the common heat exchanger. However, in this use the polymeric-fiber tubes are only 30 jum OD, and there are 50 million of them in a shell roughly 0.4 m in diameter [6]. 

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