Slow Current or Potential Scanning of Battery Porous Electrodes: Generalized Perturbation Solution and the Merits of Sinusoidal Current Cycling

Abstract

The determination of Open Circuit Voltage (OCV) is required in order to successfully model electrode behavior, and a standard method for doing this is to charge and discharge a cell at very slow current rates while measuring both voltage and State of Charge (SOC). For example, scans at a rate of C/100 (needing 100 h to charge from empty to full) are often used, but faster scans lose accuracy because irreversible losses, including those due to transport phenomena and reaction kinetics, impact the voltage in rough proportion to scan rate. We develop perturbation methods to correct measurements at higher scan rates to make their accuracy comparable to results at slower scan rates. Perturbation corrections are given for cases in which current is scanned (e.g., at different constant C-rates) as well as when voltage is scanned (e.g., linear-sweep voltammetry). Sinusoidal scanning of either voltage or current is proposed to eliminate the discontinuities at scan reversal, increasing the accuracy of these methods. The analytic formulas given here can be combined with a regression analysis of data at multiple scan rates to determine not only the OCV but also other resistances in the electrode, and this is a goal of future work.