Removing 65 Years of Approximation in Rotating Ring Disk Electrode Theory with Physics-Informed Neural Networks

The rotating Ring Disk Electrode (RRDE), since its introduction in 1959 by Frumkin and Nekrasov, has become indispensable with diverse applications in electrochemistry, catalysis, and material science. The collection efficiency ($$) is an important parameter extracted from the ring and disk currents of the RRDE, providing valuable information about reaction mechanism, kinetics, and pathways. The theoretical prediction of $$ is a challenging task: requiring solution of the complete convective diffusion mass transport equation with complex velocity profiles. Previous efforts, including by Albery and Bruckenstein who developed the most widely used analytical equations, heavily relied on approximations by removing radial diffusion and using approximate velocity profiles. 65 years after the introduction of RRDE, we employ a physics-informed neural network to solve the complete convective diffusion mass transport equation, to reveal the formerly neglected edge effects and velocity corrections on $$, and to provide a guideline where conventional approximation is applicable.