Modeling the Frequency Response of the Graphene/Electrolyte Interface in Electrochemical Systems

Abstract

The graphene/electrolyte interface plays a central role in applications such as supercapacitors and biosensors. Traditionally modeled as two capacitors in series—the Debye capacitance of the electrolyte and the quantum capacitance of graphene—the interface is predominantly governed by the latter. While prior studies have focused on graphene’s voltage-dependent capacitance, its frequency response remains underexplored theoretically. This thesis develops a rigorous mathematical framework to model and analyze the frequency response of the graphene/electrolyte interface under diverse conditions, including finite-conductivity neutral graphene, charged graphene with infinite conductivity, and systems with room-temperature ionic liquids (RTILs).

We first examine a graphene electrode in a dilute electrolyte under small AC voltages. By linearizing and normalizing the Poisson–Nernst–Planck (PNP) equations, we derive analytical impedance expressions for graphene-metal and metal-metal systems, elucidating the role of quantum capacitance across electrolyte concentrations. For finite-sized graphene disk electrodes, we incorporate graphene’s intrinsic conductivity to obtain explicit quantum impedance expressions. The results reveal a transition from Warburg-type behavior at high frequencies to RC-circuit behavior at low frequencies, governed by quantum capacitance and conductivity.

The analysis extends to charged graphene electrodes under DC bias, using matched asymptotic expansions in the thin double-layer limit. We derive an analytical impedance expression that highlights the dependence of frequency response on ion concentration and bias voltage. Finally, we explore concentrated electrolytes with RTILs, introducing a new length scale to capture electrostatic correlations and characterizing their impact on low-frequency impedance.