CALCULATION OF THE IMPEDANCE OF NONCYLINDRICAL PORES .1. INTRODUCTIONOF A MATRIX CALCULATION METHOD

In this paper a new method is proposed for the calculation of the impe dance of arbitrary electrodes containing noncylindrical pores and/or h aving 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, matr ix 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 muc h smaller N-values owing to the use of transmission lines for each dis c. This makes it more appropriate to be used in curve fitting procedur es. Moreover, it is shown that the typical behaviour of the pore imped ance at low penetration depths is much better simulated with the matri x method. Furthermore, an attempt is made to provide more general know ledge about the impedance behaviour of noncylindrical pores as a funct ion of the penetration depth of the a.c. signal. Finally, the theory i s enlarged using constant phase elements instead of capacities to desc ribe the behaviour of the electrode/electrolyte interfaces.