Growth of the Conducting Zones

After a critically sized nucleus is formed, it starts to grow. Under the same hypothesis stated above for chronoamperometric growth, and taking into account that the radial growth of each cylinder occurs at the same time that the overpotential (tj) rises owing to the potential sweep (o)  

By integration of this equation we obtain the evolution of the radius of a cylinder as a function of the overpotential 

Assuming the formation of N0 nuclei at the first stages of oxidation, the effective relaxed area (taking into account the overlap between neighboring expanding conductive regions) at every overpotential tj can be estimated by means of the Avrami equation.177 We arrive at 

Taking into account that the amount of charge consumed during relaxation at a given overpotential under pure conformational relaxation processes is proportional to the relaxation area of the oxidized regions  

By differentiation of Eq. (57), an expression of the current flowing across the film during the relaxation-controlled oxidation process is obtained  

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Figure 37. Lateral section of a polymeric film during the nucleation and growth of the conducting zones after a potential step. (Reprinted from T. F. Otero, H.-J. Grande, and J. Rodriguez, A new model for electrochemical oxidation of polypyrrole under conformational relaxation control. /. Electroanal. Chem. 394, 211, 1995, Figs. 2-5. Copyright 1995. Reprinted with permission from Elsevier Science.)...

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