Accelerating charging dynamics of electric double-layer capacitors
Electric double-layer capacitors (EDLCs), consisting of an ionic fluid between two metallic electrodes, are electrochemical energy storage devices complementary to batteries, allowing for a faster charge/discharge. The charging dynamics in response to a voltage step features a variety of regimes and relaxation timescales, depending on the applied voltage and the various lengths characterizing the system, most importantly the inter-electrode distance and the Debye length over which electrostatic effects are screened in the electrolyte. Inspired by recent works on "shortcut to adiabaticity" in colloidal systems, here we investigate the possibility to control the charge and discharge of planar EDLCs using time-dependent voltages. Specifically, our aim is to achieve a full charge or discharge within a finite time shorter than their intrinsic relaxation timescales. Within the Poisson-Nernst-Planck model and the small-voltage regime, we derive time-dependent protocols that can eliminate an arbitrary number of relaxation modes. This permits to approach the equilibrium charged state within a finite time, that can be in practice an order of magnitude faster than the natural equilibration time. We illustrate the relevance and efficacy of the method on polynomial drivings and show that the surface charge density, charge-density profiles, and global deviation from equilibrium (quantified by a Kullback-Leibler-like divergence) can all be significantly accelerated, even for driving times comparable to or shorter than the natural RC time of the system.