Theoretical Prediction of Capacitance of Bilayer Graphene Flakes

Abstract

Electric double layer capacitors (EDLCs) have been known as energy storage device and different materials have been used as EDLC electrode materials. Recently, graphene has been considered as one of the most promising materials for use in EDLC structure. In this research, a theoretical study on bilayer graphene (as an EDLC with vacuum dielectric) in two symmetries (D2h and D6h) with different distances and applied voltages is done, where the charge separation among a bilayer graphene structure is calculated by electron deformation orbital theory. Although it was found that capacitance is almost independent of applied voltage in constant distances, the relationship between capacitance and inverse of distance was nonlinear in the cases of constant voltages. The structure change from D2h to D6h did not affect the specific capacitances, significantly, although the areal capacitance of D2h structure was greater than that of D6h structure.

Evaluation of Charge and Energy Storage in Molecular Nanocapacitors

“…On the other hand, as it has been shown in ref , there exist two types of charge transfers: the first one is net charge transfer from one electrode to the other, and the second is charge transfer from one side of an electrode to the other side of the same electrode as self-polarization, which is shown in Figure b. Hence, the net charge transfer can be estimated as eq Q ( n e t ) = Q ( b i l a y e r ) .25em − .25em 2 Q ( m o n o l a y e r ) where Q (net), Q (bilayer), and Q (monolayer) stand for net, bilayer, and monolayer charge displacements, respectively.…”

“…On the other hand, as it has been shown in ref , there exist two types of charge transfers: the first one is net charge transfer from one electrode to the other, and the second is charge transfer from one side of an electrode to the other side of the same electrode as self-polarization, which is shown in Figure b. Hence, the net charge transfer can be estimated as eq Q ( n e t ) = Q ( b i l a y e r ) .25em − .25em 2 Q ( m o n o l a y e r ) where Q (net), Q (bilayer), and Q (monolayer) stand for net, bilayer, and monolayer charge displacements, respectively. Since the polarization of electrodes is removed once the electric field is turned off, not all the energy of stage (III) can be retrieved as stored energy in eq .…”

“…The reason is that the stored energy is not the simple difference between the quantum mechanical energy of charged and discharged states, as not all of this energy difference can be retrieved from the molecular capacitor due to the polarization energy of electrodes. Figure shows the schematic polarization of a molecular capacitor’s electrodes exposed to an external electric field as a bias voltage and the corresponding electron deformation density …”

“…Analogues to stored charge, total energy difference also originates from both charge transfer and polarization of electrodes, while stored energy originates from charge transfer between the two electrodes, regardless of the extent of the electrodes’ polarization. Therefore, to estimate the stored energy, one should exclude polarization energy induced by the external electric field.…”

“…On the other hand, electronic deformation density analysis has been applied to many molecular systems, including electronic structure analysis, , electronic excitation, topological analysis of kinetic energy pressure, , response of molecules to an external electric field, − and the detection of molecular plasmons . Mandado and Ramos-Berdullas have shown that molecular-level electronic conduction can be simulated via an electric field for finite-length molecules, where they have employed deformation density analysis to identify transmission eigenchannels and the corresponding eigenvalues. − This analysis has also been applied to EDLC to predict their capacitances and the asymmetric distribution of charge carriers in carbon nanotubes exposed to the external electric field …”