Electrochemical Impedance Imaging via the Distribution of Diffusion Times

TL;DR

This paper introduces a mathematical framework and inversion method for electrochemical impedance spectra analysis using a distribution of diffusion times, enabling non-destructive microstructural imaging of nanostructured electrodes.

Contribution

It presents a novel DDT inversion technique based on CNLS regression with Tikhonov regularization for impedance imaging of heterogeneous materials.

Findings

Successfully applied to nanostructured electrodes in energy devices

Demonstrated non-destructive microstructural inference

Validated feasibility of impedance imaging for heterogeneous systems

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 (CNLS) 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 non-destructive "impedance imaging" to infer microstructural statistics of random, heterogeneous materials.