Dirac Electrons with Molecular Relaxation Time at Electrochemical Interface between Graphene and Water.

The time dynamics of charge accumulation at the electrochemical interface between graphene and water is important for supercapacitors, batteries, and chemical and biological sensors. By using impedance spectroscopy, we have found that measured capacitance (Cm) at this interface with the gate voltage Vgate ≈ 0.1 V follows approximate laws Cm~T1.2 and Cm~T0.11 (T is Vgate period) in frequency ranges (1000-50,000) Hz and (0.02-300) Hz, respectively. In the first range, this dependence demonstrates that the interfacial capacitance (Cint) is only partially charged during the charging period. The observed weaker frequency dependence of the measured capacitance (Cm) at frequencies below 300 Hz is primarily determined by the molecular relaxation of the double-layer capacitance (Cdl) and by the graphene quantum capacitance (Cq), and it also implies that Cint is mostly charged. We have also found a voltage dependence of Cm below 10 Hz, which is likely related to the voltage dependence of Cq. The observation of this effect only at low frequencies indicates that Cq relaxation time is much longer than is typical for electron processes, probably due to Dirac cone reconstruction from graphene electrons with increased effective mass as a result of their quasichemical bonding with interfacial molecular charges.

General Capacitance Upper Limit and Its Manifestation for Aqueous Graphene Interfaces.

Double-layer capacitance (Cdl) is essential for chemical and biological sensors and capacitor applications. The correct formula for Cdl is a controversial subject for practically useful graphene interfaces with water, aqueous solutions, and other liquids. We have developed a model of Cdl, considering the capacitance of a charge accumulation layer (Cca) and capacitance (Ce) 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 Cdl can be obtained from 1/Cdl = 1/Cca + 1/Ce. In the case of aqueous graphene interfaces, this model predicts that Cdl is significantly affected by Ce. 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/cm2.