Debye Length vs Diffusion Layer Thickness

1 Debye Length vs Diffusion Layer Thickness Problem 

As was discussed in Chapter 5, diffusion towards a spherical electrode will attain a steady state at long times after a potential step. The expression for the concentration profile, following a potential step to a potential where electron transfer is rapid, is 

Therefore, when c/c attains some critical fraction a, implying a certain degree of transition from the diffusion layer to bulk solution, 1 — (r /r) = a. Hence 

From the special case a = 0.5, we note that where c = (c /2), r = 2rg. Hence, over the distance of one electrode radius away from the electrode surface, the concentration rises from total depletion to one half of the bulk value. 

If the electrode has a radius of the order 10 run, the diffusion layer is concentrated within a few tens of nanometres away from the electrode surface. This is in contrast to a microelectrode where the diffusion layer will be microns thick, or a macroelectrode where the steady-state diffusion layer is so large that the steady-state limit is not achieved on an experimental timescale. Instead, the diffusion layer continues to grow at a rate proportional to s/, throughout the course of an experiment. 

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