Linear Semi-Infinite Diffusion - The Warburg Impedance (part 2) | Mass Transport in EIS (E02)

We explain the mathematical derivation of the so-called Warburg impedance to describe the linear semi-infinite diffusion of a redox couple to and from an electrode/electrolyte interface. Traditional electrical circuit elements cannot adequately represent the impedance response of this electrochemical process, so we base the mathematical description of the impedance on equations from physical chemistry. To gain an intuitive understanding of the Warburg impedance, it is essential to visualize the dampened oscillating concentration waves propagating into the electrolyte solution under sinusoidal potential perturbation and to understand their mathematical formulation. We facilitate this understanding for our viewers by showing simulation results of concentration oscillations under conditions of semi-infinite linear diffusion.

Timestamps
00:00 Intro
00:39 Recap: Characteristics of linear semi-infinite diffusion in cyclic voltammetry and impedance spectroscopy
06:51 Getting started with the mathematical description of linear semi-infinite diffusion for an alternating potential perturbation
20:09 Simulations of time-dependent concentration profiles
23:54 Mathematical derivation of the Warburg impedance
50:51 Outro
51:01 Summary panel (Endcard)

This is the second video in our series 'Mass Transport in EIS', which we created to support the Electrochemical Impedance Spectroscopy lectures of the Master's program in Chemistry and our research student interns at the Ruhr-University Bochum (RUB) in Germany.
Since getting started with EIS can be challenging, our goal is to make it accessible regardless of prior knowledge. We provide detailed explanations of the key terms and experimental examples to help viewers understand the concepts, fill in gaps, and promote connections within their knowledge maps. In this way, we hope to prepare our students and interested electrochemistry enthusiasts for more advanced topics in EIS, such as those covered in the Electrochemistry I and II courses at RUB.

#EIS #impedance #electrochemistry #education

written and presented by Sebastian Reinke and Julia Linnemann
filmed and edited by Christian Wunderle and Kathleen Schnaars

Website: https://shape-ec.ruhr-uni-bochum.de/



Acknowledgements:
We thank Niclas Blanc and Sumukh Shankar Sharadaprasad for their support with the simulations of concentration oscillations. We are grateful for financial support from the Stiftung Mercator (project [e-Speicher]3, project ID 18023) and the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under CRC 247 project-ID 388390466 (project A09). Sebastian Reinke thanks the Deutsche Bundesstiftung Umwelt (DBU) for a doctoral scholarship. The videos were recorded at the “Center for Solvation Science ZEMOS” funded by the German Federal Ministry of Education and Research BMBF and by the Ministry of Culture and Research of North Rhine-Westphalia.
Many thanks to Kathleen Schnaars for designing our Impe-DANCE T-shirts.