Microscopic Model for Cyclic Voltammetry of Porous Electrodes

Cyclic voltammetry (CV) is a widespread experimental technique for characterizing electrochemical devices such as supercapacitors. Despite its wide use, a quantitative relation between CV and microscopic properties of supercapacitors is still lacking. In this Letter, we use both the microscopic ``stack-electrode'' model and its equivalent circuit for predicting the cyclic voltammetry of electric double-layer formation in porous electrodes. We find that the dimensionless combination $\ensuremath{\omega}{\ensuremath{\tau}}_{n}$, with $\ensuremath{\omega}$ the scan frequency of the time-dependent potential and ${\ensuremath{\tau}}_{n}$ the relaxation timescale of the stack-electrode model, governs the CV curves and capacitance: the capacitance is scan-rate independent for $\ensuremath{\omega}{\ensuremath{\tau}}_{n}\ensuremath{\ll}1$ and scan-rate dependent for $\ensuremath{\omega}{\ensuremath{\tau}}_{n}\ensuremath{\gg}1$. With a single fit parameter and all other model parameters dictated by experiments, our model reproduces experimental CV curves over a wide range of $\ensuremath{\omega}$. Meanwhile, the influence of the pore size distribution on the charging dynamics is investigated to explain the experimental data.