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 (C_m) at this interface with the gate voltage V_gate ≈ 0.1 V follows approximate laws C_m~T^1.2 and C_m~T^0.11 (T is V_gate 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 (C_int) is only partially charged during the charging period. The observed weaker frequency dependence of the measured capacitance (C_m) at frequencies below 300 Hz is primarily determined by the molecular relaxation of the double-layer capacitance (C_dl) and by the graphene quantum capacitance (C_q), and it also implies that C_int is mostly charged. We have also found a voltage dependence of C_m below 10 Hz, which is likely related to the voltage dependence of C_q. The observation of this effect only at low frequencies indicates that C_q 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.