Charging dynamics of electric double layer capacitors including beyond-mean-field electrostatic correlations.

Abstract

Electric double layer (EDL) formation underlies the functioning of supercapacitors and several other electrochemical technologies. Here we study how the EDL formation near two flat blocking electrodes separated by 2L is affected by beyond-mean-field Coulombic interactions, which can be substantial for electrolytes of high salt concentration or with multivalent ions. Our model combines the Nernst-Planck and Bazant-Storey-Kornyshev (BSK) equations; the latter is a modified Poisson equation with a correlation length ℓ_{c}. In response to a voltage step, the system charges exponentially with a characteristic timescale τ that depends nonmonotonically on ℓ_{c}. For small ℓ_{c}, τ is given by the BSK capacitance times a dilute electrolyte's resistance, in line with Zhao [Phys. Rev. E 84, 051504 (2011)1539-375510.1103/PhysRevE.84.051504]; here τ decreases with increasing ℓ_{c}. Increasing the correlation length beyond ℓ_{c}≈L^{2/3}λ_{D}^{1/3}, with λ_{D} the Debye length, τ reaches a minimum, rises as τ∝λ_{D}ℓ_{c}/D, and plateaus at τ=4L^{2}/(π^{2}D). Our results imply that strongly correlated, strongly confined electrolytes-such as ionic liquids in the surface force balance apparatus-move slower than predicted so far.