Global Convective Diffusion Impedance

The dimensionless impedance of a small electrode can be defined by summing the effects of die local convective-diffusion impedance, i.e.. 

For a rectangular electrode of length L and of width W, the expression of the impedance is given by 

In the low-frequency range, the expression of H(K,) is obtained from the series expansion (13.28) 

The first integral corresponds to the low-frequency regime and the second one to the high-frequency regime where equations (13.28) emd (13.31) must be used, respectively. Equation (13.38) becomes 

The term B cri) has been calculated for cri 13, and B(cr ) was foimd to be constant and equal to 0.25 in the frequency range 6 cri 13. This result means that equation (13.39) is valid for Kj 6 and therefore can be written as 

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Figure 13.4 Normalized global convective-diffusion impedance for a small rectangular electrode, The solid line represents the low-frequency solution (equation (13.37)), and the dashed line represents the high-frequency solution (equation (13.40)). Overlap is obtained for 6 < K < 13, with the dimensionless frequency K, given by equation (13.34). (Taken from Delouis et al. and reproduced with permission of The Electrochemical Society.)...

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