The nonlinearities in the galvanostatic charging curves of supercapacitors provide insights into charging mechanisms

Abstract

Supercapacitors are often charged using constant currents. The capacitance can be determined from the slope of the voltage-time curve if the measured voltage over the supercapacitor increases linearly with time. However, the resulting voltage-time curve is often nonlinear, which may lead one to interpret the capacitance as being either time or voltage dependent. In the current work, systematic experimental studies of the nonlinearity of galvanostatic charging curves as a function of applied current and temperature are undertaken for commercial supercapacitors in the range 1–1000 F. A consistent theory is developed to explain the available data. It is demonstrated that the nonlinearity in the voltage-time curve can be attributed to a constant capacitance in parallel with a resistance, the latter which is inversely proportional to the applied current. The influence of faradaic charge transfer reactions or surface charge reorganization on this parallel resistance is analyzed. The proposed theory is also used to analyze galvanostatic charging data available in the research literature, and the different types of nonlinearities observed provide new insight into the mechanisms occurring during charging of various types of supercapacitors.