Frequency Response of the Diffuse-Charge Dynamics in Electrochemical Systems with a Graphene Electrode

Abstract

We investigate the frequency response of diffuse-charge dynamics related to a 1:1 symmetric electrolyte containing a graphene electrode by solving the governing Poisson-Nernst-Planck equations subjected to appropriate boundary conditions in the asymptotic limit ε = λ D /H → 0, where λ D is the Debye screening length and H is the half-thickness of the electrolyte. Using the method of matched asymptotic expansion, we first solve the leading order non-linear problem for equilibrium state at a nonzero applied DC voltage in the presence of Stern layer(s). Then, we extend the leading order asymptotic analysis to derive an analytic expression for the impedance of the graphene-based electrochemical cell when a small AC voltage perturbation is added to the applied DC voltage. Finally, we use a suitable scaling of the impedance parameters to expose the impacts of the ion concentration and the DC bias voltage on the frequency response for possible applications involving the graphene-electrolyte interface.