Impedance of blocking electrodes having parallel cylindrical pores with distributed radii

The impedance of blocking porous electrodes having parallel cylindrical pores with a lognormal distribution of their radii, identical pore depth and identical pore volume is calculated. Electrodes with size distribution of variable width, defined by different standard deviation (σ) values, are compared. The effect of varying σ is illustrated for the following cases: (i) the number of pores per unit surface (n) varies with σ while the median of the pore radius distribution (rμ) remains constant; (ii) rμ varies with σ while n remains constant; (iii) both n and rμ vary with σ. It is shown that, although the general shape of the impedance plots is similar in all cases, the assumptions concerning n and rμ have a major effect on the calculated frequency dependence. All impedance plots exhibit porous behaviour at high frequency and capacitive behaviour at low frequency, the transition being smoother for larger σ values. However, the frequency around which the porous-to-capacitive transition occurs depends on the additional assumptions: it increases as σ increases in cases (i) and (ii) but, in accordance with other authors’ calculations, decreases as σ increases for case (iii).