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Updated: Feb 12, 2026

Electrochemical Impedance Spectroscopy as a Tool for Electrochemical Rate Constant Estimation
Published on: October 10, 2018
Electrochemical Impedance Imaging via the Distribution of Diffusion Times
1Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
Abstract:
We develop a mathematical framework to analyze electrochemical impedance spectra in terms of a distribution of diffusion times (DDT) for a parallel array of random finite-length Warburg (diffusion) or Gerischer (reaction-diffusion) circuit elements. A robust DDT inversion method is presented based on complex nonlinear least squares regression with Tikhonov regularization and illustrated for three cases of nanostructured electrodes for energy conversion: (i) a carbon nanotube supercapacitor, (ii) a silicon nanowire Li-ion battery, and (iii) a porous-carbon vanadium flow battery. The results demonstrate the feasibility of nondestructive "impedance imaging" to infer microstructural statistics of random, heterogeneous materials.
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