General Capacitance Upper Limit and Its Manifestation for Aqueous Graphene Interfaces

Double-layer capacitance (C(dl)) is essential for chemical and biological sensors and capacitor applications. The correct formula for C(dl) is a controversial subject for practically useful graphene interfaces with water, aqueous solutions, and other liquids. We have developed a model of C(dl), considering the capacitance of a charge accumulation layer (C(ca)) and capacitance (C(e)) of a capacitance-limiting edge region with negligible electric susceptibility and conductivity between this layer and the capacitor electrode. These capacitances are connected in series, and C(dl) can be obtained from 1/C(dl) = 1/C(ca) + 1/C(e). In the case of aqueous graphene interfaces, this model predicts that C(dl) is significantly affected by C(e). We have studied the graphene/water interface capacitance by low-frequency impedance spectroscopy. Comparison of the model predictions with the experimental results implies that the distance from charge carriers in graphene to the nearest molecular charges at the interface can be ~(0.05–0.1)nm and is about a typical length of the carbon-hydrogen bond. Generalization of this model, assuming that such an edge region between a conducting electrode and a charge accumulating region is intrinsic for a broad range of non-faradaic capacitors and cannot be thinner than an atomic size of ~0.05 nm, predicts a general capacitance upper limit of ~18 μF/cm(2).