Electrochemical impedance spectroscopy of thin films with two mobile charge carriers: effects of the interfacial charging

In the electrochemical systems containing an excess of the background electrolyte, the faradaic process and the interfacial ('double-layer') charging are coupled to the fluxes of different charge carriers, the former being related to the diffusional transport of electroactive entities while the latter being realized mostly by ions of the supporting electrolyte. As a result, the interfacial capacitance C-dl may simply be added in parallel to the faradaic impedance specific for each particular system (Randles & Ershler). This simple treatment is not justified in the absence of an indifferent electrolyte, if the same charged species take part in both the electrode reaction and the double layer charging. This is the case where at least one of the ions of a binary electrolyte participates in the electron transfer process or cross the interface. A similar situation arises in the case of an electrochemically active polymer film in that mixed electronic-ionic conductivity prevails, i.e. the charging of the polymer (electron transport) is accompanied by the motion of the charge-compensating counterions (:or co-ions). In such systems both interfacial processes are coupled with the same flux of the 'electroactive' component. Moreover, the distributions of both charged species inside the film are interrelated due to the electroneutrality condition and the self-consistent electric field so that their transport cannot be: considered as pure diffusion. This paper presents an analysis of the alternating current passage across a thin film containing mobile charge carriers of two types, which for the sake of specificity are referred to as 'electrons' and 'counterions' (although the results are also valid for other systems with two charge carriers). The contributions at the interfaces related to the faradaic processes (or the ion exchange) and to the double-layer charging have been taken into consideration 'ab initio'. Analytical expressions for the complex impedance have been obtained for three principal arrangements of the system, m \ f \ m' (film between two electronic conductors), s' \ f \ s ('membrane', film between two solutions) and m \ f \ s (modified electrode). Besides the parameters characterizing the transport processes of the charged species in the bulk film, these formulae contain four characteristics of each interface alpha (alpha = m \ f or f \ s), R-alpha (charge transfer resistance), C-alpha (interfacial capacitance), t(e)(alpha) = 1 - t(i)(alpha) ('double-layer numbers') and C(mu)alpha ('asymmetry factor'). The predicted complex-impedance plots demonstrate a greater variety of shapes compared to those predicted by traditional approaches. (C) 1999 Elsevier Science S.A. All rights reserved.