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

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.