Electrochemical porosimetry: Deconvolution of distribution functions

Discrete Fourier transform (DFT) was used to deconvolute the distribution of penetrability coefficient (αo-distribution, equivalent to pore size distribution) from electrochemical impedance data of porous electrodes. The working equation is the Fredholm integral equation of the first kind to correlate macroscopic impedance data to a theoretical model describing microscopic signal with the αo-distribution. Simulated and experimental impedance data were tested. Noise observed at high frequencies in Fourier space was removed before inversely Fourier-transforming the αo-distribution from Fourier space to real space. The accuracy of αo-distributions deconvoluted by DFT depended on the number, frequency range and quality of impedance data. The examples in this work showed that fairly accurate αo-distributions could be obtained by DFT deconvolution. Most promising method was to use the αo-distribution obtained from DFT deconvolution as the first guess to shape the true αo-distribution. Then, accurate αo-distributions could be obtained by estimating parameters of the pre-assumed distributions by using complex nonlinear least square fitting.