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Rotating Disk Electrodes beyond the Levich Approximation: Physics-Informed Neural Networks Reveal and Quantify Edge

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Physics-informed neural networks (PINNs) accurately model mass transport in rotating disk electrodes (RDEs), surpassing Levich equation limitations for various Schmidt numbers. PINNs reveal RDE edge effects, offering a powerful alternative to conventional electroanalysis methods.

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Area of Science:

  • Electrochemistry
  • Computational Science
  • Machine Learning

Background:

  • The rotating disk electrode (RDE) is a fundamental tool in electroanalysis, but its theoretical models, like the Levich approximation, have limitations.
  • The Levich approximation is accurate only for high Schmidt numbers (Sc > 1000), potentially leading to significant errors for rapidly diffusing species.
  • Conventional methods for RDE analysis include analytical equations and numerical simulations, which can be complex or limited in scope.

Purpose of the Study:

  • To apply physics-informed neural networks (PINNs) for characterizing mass transport to the RDE.
  • To verify the PINN approach against established methods and explore its accuracy beyond the Levich approximation's limitations.
  • To investigate novel aspects of RDE behavior, such as the edge effect, using the developed PINN model.

Main Methods:

  • Physics-informed neural networks (PINNs) were employed to solve the diffusion equation under RDE conditions.
  • The PINN model was quantitatively validated using 1D simulations, comparing results with analytical equations and finite difference methods.
  • The study extended the PINN approach to a 2D cylindrical geometry, incorporating radial diffusion effects.

Main Results:

  • PINNs achieved analytical-level accuracy (<0.1% error) for mass transport characterization, even at lower Schmidt numbers where the Levich approximation fails.
  • The study confirmed that the Levich equation can introduce errors up to 3% at Sc = 1000 for specific conditions.
  • Novelly, PINNs revealed and quantified the RDE edge effect, demonstrating increased current near the disk's extremities due to radial diffusion.

Conclusions:

  • Physics-informed neural networks provide a more accurate and versatile tool for RDE mass transport analysis than conventional methods.
  • PINNs successfully extend RDE theory beyond the Levich approximation, enabling the study of complex phenomena like the edge effect.
  • The findings suggest PINNs are a powerful and potentially simpler substitute for traditional analytical and simulation-based approaches in electroanalysis.