Dependence of Sand’s Time on Current Density: Importance of Limiting Current

The time required to obtain a sharp increase in cell voltage was first studied by Sand in 1899. He showed that this time (t_Sand) is the time required for depleting ions at one of the electrodes in the cell. He also obtained an expression wherein t_Sand is proportional to i^(-2), where i is the applied current density. This expression, which is widely used today, suggests that t_Sand can be calculated at any given i. However, ion depletion at one of the electrodes only occurs when the applied current exceeds the limiting current, i_L. A new equation that is consistent with this requirement was presented by Hoffman et al. (J. Electrochem. Soc., 170, 120524 (2023)). Experimental data was obtained from dilute and concentrated polymer electrolytes collapse on a universal master-plot of L^2/Dt_Sand, a dimensionless quantity that depends on the cell thickness (L) and diffusion coefficient (D), versus i/i_L.. The experimental measurements are in quantitative agreement with the predictions of Hoffman et al.