Impact of electrostatic correlations on the frequency response of a graphene electrode in ionic liquid

We investigate the frequency response of the graphene-based electrochemical systems containing room-temperature ionic liquids using the method of matched asymptotic expansion in the limit of thin double-layers to study the diffuse-charge dynamics of graphene electrodes interfaced with the ionic liquids. The theory in the framework of the asymptotic matching is mainly supported by (1) the length scale sqrt[λ_{D}L_{c}] that suitably characterizes the structure of the double layer in ionic liquids, with λ_{D} referring to the Debye length and L_{c} referring to the electrostatic correlation length, and (2) the charging time, τ_{c}=λ_{D}^{3/2}L/(DL_{c}^{1/2}), where D is the diffusion coefficient and L is the thickness of the electrolyte. With this response time, the diffuse-charge dynamics is deduced at the leading order to obtain an analytic expression for low-frequency impedance. As a result of the new length scaling sqrt[λ_{D}L_{c}], we additionally study the behavior of double-layer in graphene-metal electrochemical systems involving ionic liquids, where electrostatic correlation length L_{c} is found to play a prominent role in the linear regime. The results are then compared with the conventional electrochemical cells containing a metal-metal electrode pair.