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

The Joint Density Functional Theory (JDFT) is applied in the context of Grand Canonical Kohn-Sham theory to calculate the global and local softness of pristine and N-substituted graphene structures. A comparison is established between different theoretical approaches to evaluate total capacitance, revealing that JDFT approach presents the closest result of this property with experimental data. A model of series capacitors is used to determine the quantum and non-quantum contributions of total capacitance, which enables 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 average number of electrons vs. applied potential plots, and the model of series capacitors. Likewise, the relation of capacitance and softness gives...