The quantum mechanical origin of the supercapacitance phenomenon in reduced graphene oxide structures

We investigated supercapacitance phenomena observed in reduced graphene oxide structures from a quantum mechanical rate viewpoint. The supercapacitance phenomenon in carbonaceous materials has been majorly attributed to electrostatic capacitance contributions, in which the magnitude of this capacitance is correlated with the amount of surface area available to be charged under the presence of electric potential perturbations. Nonetheless, the quantum rate theory predicts a superposition between electrostatic $C_e$ and chemical $C_q$ (also called quantum) capacitance energetic levels. The superposition of these capacitive states implies that the electric potential perturbation not only drives the separation of charges in space (thus correlating with the geometry of the capacitor and consequently with the surface area) but also governs the occupancy of the electric-field screened electronic structure of reduced graphene oxide embedded in the electrolyte environment. This leads to an energy degeneracy between electrostatic $e^2/C_q$ and quantum $e^2/C_q$ capacitive energy states, as confirmed in this work for reduced graphene oxide carbonaceous structures. Accordingly, the analysis proves that the charge dynamics associated with the resistance for charging the pseudo-capacitive $E=e^2/C_q$ states of reduced graphene oxide structure follows a quantum resistance limit $R_K=h/e^2\sim 25.8$ k$\Omega$ within a charging frequency of $\nu =1/R_K{C}_q=E/h=e^2/h{C}_q$ that obeys quantum electrodynamics principles, in agreement with the premises of the quantum rate theory. Two energy levels associated with the occupancy of the electronic states upon the reduction of graphene oxide were identified.