The Modeling of Electrochemical Systems

2 PHYSICAL AND ELECTROCHEMICAL MODELS 2.2.1 The Modeling of Electrochemical Systems 

For solid electrolytes one usually is concerned with intrinsically condncting systems rather than with intrinsically nonconducting (dielectric) ones. It is then appropriate and usual to consider basic systan response at the impedance rather than the complex dielectric constant level. Then if one assumes that the overall impedance of the system, Z, approaches Ro at sufficiently low frequencies and at sufficiently high ones, one can form the normalized dimensionless quantity 

Since Eqs (1) and (2) are similar in form, we can combine them in the single expression 

as already mentioned in Section 1.3, the h of that section s Eq. (6) is of just the same form as the well-known Cole-Cole dielectric dispersion response function (Cole and Cole [1941]). In its normalized form, the same / function can thus apply at either the impedance or the complex dielectric constant level. We may generalize this result (J. R Macdonald [1985a,c,d]) by asserting that any IS response 

Conductive System (k = Z) General System Normalized Dielectric System (k = ) 

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Van Parys, H., Telias, G., Nedashkivskyi, V, Mollay, B., Vandendael, I., Van Damme, S., Deconinck, J. Hubin, A. (2010). On the modeling of electrochemical systems with simultaneous gas evolution. Case study The zinc deposition mechanism, Electrochimica Acta 55(20) 5709-5718. 

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