Mass Transport into a Thin Film

Electrochemical charge storage in a bulk film of material consists of the movement of two types of species, into or out of the film. These may be, for example, a cation and an electron. The requirement of charge neutrality stipulates that the two species move essentially together. We may therefore solve the coupled transport equations to give an equation that describes the flux of the neutral combination of species, in terms of the gradient in concentration (36). This allows us to define the chemical diffusion coefficient, which describes the motion of a neutral species in a non-ideal solid solution. 

response has been calculated for such an electode, subject to a change in the applied potential or current. The complex impedance is of the form (37) 

The same equations are also applicable to the kinetics of charge diffusion in redox systems. For example. Hunter et al. (42) have studied thechargingbehaviorofpolyvinylferrocenefilms using this methodology, 

It is very important to note the identical forms of Eqs. (22) and (16), Electrochemically, they correspond to very different processes, even though the essential physics, that of a distributed storage/dissipatlon process is the same. The mathematical similarity Is a source of ambiguity in the interpretation of a,c, and transient data. The presence of a Warburg Impedance (w dependence of the impedance) is often taken as proof of the existence of a diffusion process, as in Eq, (22), It may often, however, be caused by the presence of porosity or even roughness In the electrode. 

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