Diffusion coefficient effective transition region

In the specific instance of A diffusing through a catalytic pore and reacting at the end of the pore to form gaseous component B, equimolar counterdiffusion can be assumed, and an effective transition region diffusivity, D a is independent of concentration and can be calculated from the Knudsen and binary diffusion coefficients ... 

If equimolecular counterdiffusion takes place N = -N B (see Volume 1, Chapter 10) and the total pressure is constant, we obtain from equation 3.5 an expression for the effective self-diffusion coefficient in the transition region ... 

We would be remiss if we did not comment on isomerization dynamics in liquids, since they form a very important and widely studied class of reactions. There have been many theoretical models for isomerization reactions in liquids. In Section III.C we briefly outlined Kramers approach to this problem. Since that time much more extensive studies of such barrier-crossing problems have been carried out. These studies have been concerned mainly with obtaining expressions for the rates in the transition region between the low- and high-friction cases, or with effects arising from the nonlocality of the diffusion coefficient in the context of Smoluchowski equation descriptions, applications to polymeric systems, and so on." ... 

Figure 5.33 presents the effect of particle size on the Nyquist impedance behavior of the electrode [75]. The plot shows that the effect of particle size is opposite to that of the diffusion coefficient, that is, a decrease in the particle radius shifts the appearance of the transition region to higher frequencies. In smaller particles, hydrogen needs to travel only... 

In addition to molecular difiusion, Knudsen diffusion can also be a significant transport mechanism in the p)ore space of SOFC electrodes. In Knudsen diffusion, the interactions of gas molecules with the pore walls are of the same frequency as the interactions between gas molecules. Knudsen diffusion is typically formulated as Fickian diffusion [Eq. (26.2)], with the Knudsen diffusion coefficient being used in place of the binary diffusion coefiicient. The Knudsen diffusion coefficient of a species is independent of the other species in the system and is derived from the molecular motion of the gas molecules and the geometry of the pores [8, 11, 12). Owing to the small average pore radii of SOFCs ( 10 m [13-15]), diffusion in the pore space of the electrodes usually falls within a transition region where both molecular and Knudsen diffusion are important [16]. To model the transition region. Pick s law can be used with an effective diffusion coefficient to account for... 

In aU calculations the presence of a crystalline phase was assumed to affect neither the solubility of the probe in the amorphous regions nor the diffusion coefficients. Examination of Figure 5.17 shows that the higher the crystallinity of the stationary phase, the less pronounced is the deviation from linearity and consequently the less pronounced is the glass transition (decrease of film thickness has the same effect). The impossibility of detecting a glass transition in polymers of high crystallinity, such as isotactic polypropylene [170], is believed to be due to this phenomenon. 

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