Calculation of the impedance of noncylindrical pores Part I: Introduction of a matrix calculation method

Abstract

In this paper a new method is proposed for the calculation of the impedance of arbitrary electrodes containing noncylindrical pores and/or having place-dependent impedances. The method is based on splitting up the pore and the surrounding material into N discs. For the equivalent circuit of each disc a transmission line with constant impedances is adopted. By matrix calculations the impedance of the porous electrode can be obtained. A comparison is made between this, very general, matrix method and a recursion method developed by Keiser et al. for purely capacitive interface behaviour of pores in an electrode material with negligible impedance. It is shown that the matrix method requires much smaller N-values owing to the use of transmission lines for each disc. This makes it more appropriate to be used in curve fitting procedures. Moreover, it is shown that the typical behaviour of the pore impedance at low penetration depths is much better simulated with the matrix method. Furthermore, an attempt is made to provide more general knowledge about the impedance behaviour of noncylindrical pores as a function of the penetration depth of the a.c. signal. Finally, the theory is enlarged using constant phase elements instead of capacities to describe the behaviour of the electrode/electrolyte interfaces.