Electrochemical Impedance Imaging via the Distribution of Diffusion Times

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.

A Bayesian view on the Hilbert transform and the Kramers-Kronig transform of electrochemical impedance data: Probabilistic estimates and quality scores

“…More details can be found in Section S.2 of the SI. We first evaluated the synthetic data obtained using the DDT (distribution of diffusion times) model, [52,53] Figure S4 (e) and (f). All residual center near 0 with a seemingly unimodal distribution, suggesting that the EIS data are consistent.…”

Dendrite nucleation in lithium-conductive ceramics

“…A powerful strategy to approach such issues has been put forward by Song and Bazant. 25 8 Space-charge domains might extend as much as 1 mm according to Yamamoto et al, 13 an observation that could be rationalized by a different constitutive law for conformational free energy, a lower c eq + , or by additional, unknown interfacial chemistry. The result in eqn (4) is independent of these alterations.…”

A Bayesian View on the Hilbert Transform and the Kramers-Kronig Transform of Electrochemical Impedance Data: Probabilistic Estimates and Quality Scores

“…More details can be found in Section S.2 of the SI. We first evaluated the synthetic data obtained using the DDT (distribution of diffusion times) model, [52,53] see Section S.3 for details. The admittance of the real part and the imaginary part as obtained by BHT are shown in Figure S4 (c) and (d); both match well the synthetic experiments.…”