Capacitance of graphene in aqueous electrolytes: The effects of dielectric saturation of water and finite size of ions

We present a theoretical model for electrolytically top-gated graphene, in which we analyze the effects of dielectric saturation of water due to possibly strong electric fields near the surface of a highly charged graphene, as well as the steric effects due to the finite size of salt ions in an aqueous electrolyte. By combining two well-established analytical models for those two effects, we show that the total capacitance of the solution-gated graphene is dominated by its quantum capacitance for gating potentials less than or similar to 1 V, which is the range of primary interest for most sensor applications of graphene. On the other hand, at the potentials greater than or similar to 1 V the total capacitance is dominated by a universal capacitance of the electric double layer in the electrolyte, which exhibits a dramatic decrease of capacitance with increasing gating potential due to the interplay of a fully saturated dielectric constant of water and ion crowding near graphene.