Theoretical models for ac impedance of finite diffusion layers exhibiting low frequency dispersion

This paper is concerned with frequency dispersion in the low frequency rang e of electrochemical impedance measurements in thin layer cells such as ele ctrochromic devices, conducting polymer-coated electrodes, ion exchange mem branes, and in general any type of diffusion layer which exerts some hindra nce to mass transport at the boundaries. New theoretical models are develop ed for diagnostic applications and treatment of cases in which systematic d eviations from the standard models for spatially restricted diffusion imped ances are found. This is done by using a generalized boundary condition in the solution of Fick's law for a small ac perturbation. The resulting model has several satisfactory properties: (a) it generalizes in effect classica l boundary conditions related to absorbing and reflecting boundaries, (b) i t provides exact analytical solutions which can be tested experimentally, a nd (c) it provides a very simple physical picture of the origin of low freq uency dispersion in film electrodes in terms of interfacial transfer functi ons. The properties of the generalized diffusion impedance imply that bound ary effects cannot influence the impedance for frequencies in excess of the characteristic diffusion frequency omega(d) = D/L-2. On the other hand, at low frequencies the i response is a mixture of 'volume' and 'boundary' pro perties of the layer. Several particularized examples of blocking and non-b locking dispersive boundary conditions are studied in detail. An extended d iscussion is focused on a blocking interface that presents a capacitive dis persion describable as a constant phase element (CPE). Approximating expres sions are derived which allow separation of boundary and volume contributio ns in the extreme low frequency range. This is expected to provide a powerf ul analytical tool for analysis in those instances where a sloped line is f ound in the low frequency region of the measured impedance. (C) 1999 Elsevi er Science S.A. All rights reserved.