Theory in Practice: Testing the Limits of the Randles–Ševčík Equation

The Randles–Ševčík equation remains one of the most used equations in electrochemistry, and when used within its boundary conditions, it is an analytical solution for a 1-dimension diffusion problem. Despite being derived under strict and very clear boundary conditions, experiments rarely observe them or work within these limits. One of the more elusive boundary conditions is that diffusion must be one-dimensional, which in theory would require an infinitely large, “edgeless”, electrode. Here, we systematically test the limits of the Randles–Ševčík equation across a wide experimental parameter space by combining cyclic voltammetry and numerical simulations. We use an electrically conductive thermoplastic filament to 3D print disk electrodes with radii ranging from 1 to 5 mm and use them to record cyclic voltammograms of [Ru(NH3)6]3+ in aqueous solution at a wide range of scan rates. Experimental results reveal large positive deviations, exceeding 100%, from the Randles–Ševčík prediction for small radius electrodes and small scan rates, arising from contributions of radial diffusion and natural convection. Small negative deviations are seen for larger electrodes, and large scan rates are attributed to uncompensated Ohmic resistances. We propose the use of the integration of normalized voltammograms in the time domain (normalized charge) as a tool to quantify the experimental deviations from theory, establishing a practical framework for researchers to critically evaluate and quantify the applicability of the Randles–Ševčík equation in real electrochemical systems.