### Dynamic EIS

In 1997 we first used dynamic impedance (dEIS) to study Pt oxide growth . Impedance spectra are acquired while the system is slowly changing, usually in a slow sweep voltammogram, which allows the study of surface electrochemistry under conditions that may not be accessible by conventional steady-state impedance. Our early work used lock-in amplifier methods. More recently, we have developed hardware and software to acquire and analyse impedance spectra through the muiltisine method. Ref 1 describes the hardware, and Ref 2 describes the software, algorithms, and capabilities and limitations of the method. See the main publications list for application papers.

- R.L. Sacci and D.A. Harrington, Dynamic Electrochemical Impedance Spectroscopy,
*ECS Transactions*, 19 (2009) 31-42. - R.L. Sacci, F. Seland and D.A. Harrington, Dynamic Electrochemical Impedance Spectroscopy for Electrocatalytic Reactions,
*Electrochim. Acta.*, 131 (2014) 13-19.

### EIS fitting

While fitting to equivalent circuits is possible in many commercial programs, it is harder to fit arbitrary impedance expressions, e.g., those arising from a kinetic model. I have made a Maple program available free to Maple users, which fits any impedance expression, and generates the usual statistical outputs.

When fitting impedance data to equivalent circuits, adding a circuit element generally improves the fit, though the addition may not be statistically significant. We recently discussed how to use the Akaike Information Criterion (AIC) to determine whether to add elements. This is a single number figure of merit that can be used to compare models and also the common weighting schemes.

- M. Ingdal, R, Johnsen, D.A. Harrington, The Akaike Information Criterion in Weighted Regression of Immittance Data,
*Electrochim. Acta*, 317 (2019) 648-653.

### EIS of multistep mechanisms

I have developed a general theory for the electrochemical impedance of multistep mechanisms. This theory enables prediction of the number of bends in a Bode plot for an arbitrary mechanistic scheme, without a detailed mathematical analysis, and predicts types of equivalent circuits for some classes of mechanisms.

A tutorial introduction to some aspects of the theory is given in this powerpoint presentation, which is an annotated and slightly expanded version of a talk given at the 6th International Symposium on Electrochemical Impedance Spectroscopy, Cocoa Beach, Florida, 2004. Ref 3 is more recent, covers some more general issues and is probably the best starting point.

More recently, I have shown (ref 2) that the Nyquist plot reduces to a single semicircle when one step is rate determining. This is the simplest case in understanding how impedances simplify when some sets are much faster than others. I explore some slightly more complicated cases in ref 1, which shows that evidence for adsorption may be masked, and some steps that do not have electron transfer acquire potential-dependent pseudo rate constants.

- D.A. Harrington, Simplifying Mechanistic Impedances,
*Electrochim. Acta*, 338 (2020) 135895. - D.A. Harrington, The Rate-Determining Step in EIS,
*J. Electroanal. Chem.,*737 (2015) 30-36. - D.A. Harrington and P. van den Driessche, Mechanism and Equivalent Circuits in EIS,
*Electrochim. Acta*, 56 (2011) 8005-8013. - D.A. Harrington and P. van den Driessche, Equivalent Circuits for Some
Surface Electrochemical Mechanisms,
*J. Electroanal. Chem*., 567 (2004) 153-166. - J. D. Campbell, D. A. Harrington, P. van den Driessche and J. Watmough,
Stability of Surface Mechanisms with Three Species and Mass-Action Kinetics,
*J. Math. Chem.*, 32 (2002) 281-301. - D.A. Harrington and P. van den Driessche, Stability and Electrochemical
Impedance of Mechanisms with a Single Adsorbed Species,
*J. Electroanal. Chem.*, 501 (2001) 222-234. - D.A. Harrington, Stability and Inductive Behaviour in Electrochemical
Impedance,
*Proc. of Corrosion and Prevention 2000, November 19-22, Auckland*, Proceedings Volume 2000, paper 112 pp. 1-7, Australasian Corrosion Association, Brentford Square, Victoria, Australia. - D.A. Harrington and P. van den Driessche, Impedance of Multistep
Mechanisms: Equivalent Circuits at Equilibrium,
*Electrochim. Acta*, 44 (1999) 4321-4329. - D.A. Harrington, Electrochemical Impedance of Multistep Mechanisms:
Mechanisms with Static Species,
*J. Electroanal. Chem.*, 449 (1998) 29-37. - D.A. Harrington, Electrochemical Impedance of Multistep Mechanisms: A
General Theory,
*J. Electroanal. Chem.*, 449 (1998) 9-28. - D.A. Harrington, Electrochemical Impedance of Multistep Mechanisms:
Mechanisms with Diffusing Species,
*J. Electroanal. Chem*., 403 (1996) 11-24. - D.A. Harrington and B.E. Conway. A.C. Impedance of Faradaic Reactions
Involving Electrosorbed Intermediates; Part I: Kinetic Theory,
*Electrochim. Acta*, 32 (1987) 1703-1712.

### EIS for large amplitude signals

A theory for large-amplitude and second-harmonic impedances for mechanisms with a single adsorbed species was presented in *Can. J. Chem.*, 75 (1997) 1508 , and the MAPLE worksheet is available for download.

### EIS for fuel cells

We used EIS to diagnose faults in PEM fuel cell stacks running under load.

- J.-M. Le Canut, R. Latham, W. Mérida and D.A. Harrington, Impedance Study of Membrane Dehydration and Compression in PEM Fuel Cells,
*J. Power Sources*, 192 (2009) 457-466. - W. Mérida, D. Harrington, J.M. Le Canut, and G. McLean, Characterisation of Proton Exchange Membrane Fuel Cell (PEMFC) Failures via Electrochemical Impedance Spectroscopy,
*J. Power Sources*, 161 (2006) 264–274. - J.-M. Le Canut, R.M. Abouatallah and D.A. Harrington,
Detection of Membrane Drying, Fuel Cell Flooding and Anode Catalyst Poisoning on
PEMFC Stacks by Electrochemical Impedance Spectroscopy,
*J. Electrochem. Soc.*, 153 (2006) A857-A864.