Microscopic Model for Cyclic Voltammetry of Porous Electrodes

Abstract

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 ωτ n , with ω the scan frequency of the time-dependent potential and τ n the relaxation timescale of the stack-electrode model, governs the CV curves and capacitance: the capacitance is scan-rate independent for ωτ n ≪ 1 and scan-rate dependent for ωτ n ≫ 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 ω. Meanwhile, the influence of the pore size distribution on the charging dynamics is investigated to explain the experimental data.

Asymptotic analysis on charging dynamics for stack-electrode model of supercapacitors

“…Such a multiscale model that bridges the timescale gap between theories and experiments has been employed to study heat generation of porous electrodes, etc. [15,31,32]. Aslyamov and Janssen have analytically derived the biexponential charging dynamics of a long electrolyte-filled slit pore in [33] and these analytical results are consistent with the experiment data in [16].…”

Four stages of thermal effect coupled with ion‐charge transports during the charging process of porous electrodes

“…Besides, they derived the formulas of relaxation times of surface charge and found the charging process can be divided into three stages by two relaxation times, which has been observed in the experimental data. 13 Whereafter, Lin et al 42 applied the stack-electrode model to the cyclic voltammetry in porous electrodes.…”

Iontronic microscopy of a tungsten microelectrode: “seeing” ionic currents under an optical microscope

“…At this point, the dynamics of our system seem to be too complex to model with a quasi-stationary or one-dimensional approximation [46][47][48] and one has to solve the complete time-dependent equations to resolve the dynamics of ion transport temporally and spatially 25,[49][50][51][52][53] . However, the possibility of simultaneous measurements of the dynamic ion-density response around a micro-or nano-sctructure, as we have demonstrated in this paper, can be hugely beneficial for testing the validity of models proposed for the numerical simulation of such complex processes.…”