Dynamic density functional theory for the charging of electric double layer capacitors

We consider the charging of a model capacitor comprised of two planar electrodes and an electrolyte. Upon switching on a voltage difference, electric double layers build up in this setup, which we characterize with a classical dynamic density functional theory (DDFT) that accounts for electrostatic correlations and for molecular excluded volume of finite-sized ions and solvent molecules. Our DDFT predicts the electrode charge Q(t) to form exponentially with two timescales: at early times, the system relaxes on the RC time, namely, lambda L-D/[D(2 + sigma/lambda(D))], with lambda(D) being the Debye length, L being the electrode separation, sigma being the ion diameter, and D being the ionic diffusivity. Contrasting an earlier DDFT study, this early-time response does not depend on the applied potential. At late times, the capacitor relaxes with a relaxation time proportional to the diffusion time L-2/D.

Automated summary

In this study, we investigate the charging process of a model capacitor consisting of two planar electrodes and an electrolyte. By employing dynamic density functional theory, we analyze the evolution of the electrode charge with time. Our findings reveal distinct dynamical behaviors of the capacitor during the early and late stages of charging.