Diffusion through crystalline solids

There are two overriding considerations to keep in mind when discussing diffusion in solids the structure of the matrix across which diffusion occurs and the defects present. In a normal crystalline solid, diffusion is mediated by the defects present, and the speed of diffusion will vary significantly if the predominant defect type changes. This is because diffusion involves the movement of a species from a stable position, through some sort of less stable position or bottleneck, to another stable position. Any disorder in the solid due to defects will make this process easier. 

In industrial PET synthesis, two or three phases are involved in every reaction step and mass transport within and between the phases plays a dominant role. The solubility of TPA in the complex mixture within the esterification reactor is critical. Esterification and melt-phase polycondensation take place in the liquid phase and volatile by-products have to be transferred to the gas phase. The effective removal of the volatile by-products from the reaction zone is essential to ensure high reaction rates and low concentrations of undesirable side products. This process includes diffusion of molecules through the bulk phase, as well as mass transfer through the liquid/gas interface. In solid-state polycondensation (SSP), the volatile by-products diffuse through the solid and traverse the solid/gas interface. The situation is further complicated by the co-existence of amorphous and crystalline phases within the solid particles. 

As explained in Chapter 5, the transport mechanism in dense crystalline materials is generally made up of incessant displacements of mobile atoms because of the so-called vacancy or interstitial mechanisms. In this sense, the solution-diffusion mechanism is the most commonly used physical model to describe gas transport through dense membranes. The solution-diffusion separation mechanism is based on both solubility and mobility of one species in an effective solid barrier [23-25], This mechanism can be described as follows first, a gas molecule is adsorbed, and in some cases dissociated, on the surface of one side of the membrane, it then dissolves in the membrane material, and thereafter diffuses through the membrane. Finally, in some cases it is associated and desorbs, and in other cases, it only desorbs on the other side of the membrane. For example, for hydrogen transport through a dense metal such as Pd, the H2 molecule has to split up after adsorption, and, thereafter, recombine after diffusing through the membrane on the other side (see Section 5.6.1). 

Charge transport through organic polymeric systems shows some unusual features. When the time of flight experiments are performed in inorganic crystalline solids the charge carriers drift in a sheet without any dispersion (except for the normal diffusion effects). All the carriers exit the sample at a specific time Tt. However a similar experiment with polymer films shows a very dispersive transit (Fig. 5 a) which indicates that only a small fraction of the carriers exit the sample at t = Tt. 

When the active centre is surrounded by a layer of solid polymer, further propagation will be controlled by the rate of monomer diffusion through the polymer layer. Usually it will be retarded. With a porous polymer layer surrounding the active centres, monomer transport will be easier. These effects must be considered when highly crystalline polymers are formed, especially when the chains grow from a non-transferring monomer as, for example, with coordination polymerizations [56],... 

Diffusion of molecules or ions through crystalline solids is extremely slow at 25 C, so that the term solid diffusion should generally be interpreted to mean transfer through micropores, faults, or interfaces of the solid rather than through the lattice itself. Only at very high temperatures does true diflfiision of ions and molecules into a crystal lattice become significant. 

Describe the mechanisms of diffusion through polymeric, crystalline, and porous solids. 

Diffusion through nonporous crystalline solids depends markedly on the crystal lattice structure and the diffusing entity. The mechanisms of diffusion in crystalline solids include (Seader and Henley, 2006) ... 

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