Establishing the Relationship between Quantum Capacitance and Softness of N-Doped Graphene/Electrolyte Interfaces within the Density Functional Theory Grand Canonical Kohn–Sham Formalism

Abstract

The joint density functional theory (JDFT) is applied in the context of the grand canonical Kohn–Sham theory to calculate the global and local softness of pristine and N-substituted graphene structures. A comparison is established between the different theoretical approaches to evaluate total capacitance, revealing that the JDFT approach presents the closest result of this property with experimental data. A model of series capacitors is used to determine the quantum and nonquantum contributions of total capacitance, which enables us to determine the limitations of the rigid band approximation for the studied systems. It is found that global chemical softness is proportional to the total capacitance measured in the experiments, when the geometry relaxation is neglected. In this context, it is possible to obtain quantum and total capacitance (and consequently softness) from an average number of electrons vs applied potential plots and the model of series capacitors. Likewise, the relation of capacitance and softness gives rise to a new definition of local capacitance within the JDFT formalism. The evaluation of global and local softness paves the way to analyze electrochemical surface reactivity as a function of applied potential for a solid-electrolyte interface.

Surface Charge and Electrostatic Spin Crossover Effects in CoN4 Electrocatalysts

“…The quantum capacitance was first introduced in 1988 in a pioneering work for designing novel transistors . The relevance between quantum capacitance and electrocatalysis of carbon materials has, however, seldomly been studied . It is well-known that, in a metal/electrolyte electrochemical interface, there is an electric potential drop ϕ dl across the interface caused by the surface charge and neutralizing ions in the electrolyte.…”

“…43 The relevance between quantum capacitance and electrocatalysis of carbon materials has, however, seldomly been studied. 44 It is well-known that, in a metal/electrolyte electrochemical interface, there is an electric potential drop ϕ dl across the interface caused by the surface charge and neutralizing ions in the electrolyte. Therefore, the electric double layer acts as a capacitor of capacitance C dl .…”

Theoretical insights into the role of defects in the optimization of the electrochemical capacitance of graphene

“…This approach has been implemented in several studies using the Joint density functional theory (JDFT) [22] to determine Ctot and highlight the limited CQ around the Fermi-level in graphenebased materials. [14][15][16]23] Other experimental and theoretical studies have focused on increasing the number of electronic states around the Fermi-level, with the inclusion of structural vacancy defects, [9,24] doping with nitrogen, [25] or boron [26,27] or the addition of adatoms on the graphene surface. [28] This is of particular importance to the recently fabricated edge-free carbon frameworks, which have shown higher stability, thereby allowing for high operating voltages.…”

“…[32,33] This work provides additional insights compared to previous computational studies. [15,25] Firstly, we do not report our results vs. the PZC, but vs. the standard hydrogen electrode (SHE) electrode, which allows a direct comparison between the different chemical systems. Secondly, we discuss the validity of the FBA performed in vacuum vs. different electroyltes using an implicit solvent model.…”

Achieving high quantum capacitance graphdiyne through doping and adsorption

“…GDY is considered to be the most stable carbon network structure containing diacetylenic bonds, [20][21][22] and has been successfully synthesized on copper sheets in 2010. [23][24][25] The planar sp 2 and sp hybrid carbon structure endows the material with a highly uniformly dispersed pore structure, with abundant carbon chemical bonds, a large conjugated system, a wide interlayer spacing, and a tunable electronic structure. 26,27 Krishnamoorthy et al have constructed an EDLC using GDY-modified stainless steel as the electrode, with a specific capacitance of 71.4 F g À1 at a constant discharge current density of 3.5 A g À1 , 28 which is much higher than those of the commonly used graphene electrodes (47.5 F g À1 ).…”