# Boron-Decorated Pillared Graphene as the Basic Element for Supercapacitors: An Ab Initio Study
## 3 Results and Discussion  
Figure 1a shows a supercell of PRG containing 400 carbon atoms. The translation vectors of the supercell after geometric relaxation are 24.61 A in the X direction and 21.44 A in the Y direction. During the PGR supercell building, a SWCNT (9,9) with open edges was attached by chemical bonds to a graphene sheet in the area of the hole that was preliminary cut in the graphene surface. The resulting structure matched the experimental data of pillared graphene [38]. The heat of formation of the supercell is 1.2-142 kcal/mol-atom and does not depend on the CNT length. In the graphene-CNT contact area, six pairs of penta- and heptagons as well as three octagons were formed. The supercell in Figure 1b has five B\({}_{12}\) clusters. B\({}_{12}\) clusters are icosahedral clusters with 12 boron atoms. As can be seen from the figure, the B\({}_{12}\) clusters formed bonds with the carbon near the defects in the area of the junction between the graphene sheets and SWCNTs. The length of the bonds varied in the range of 1.669 to 1.682 A. The mass fraction of the boron ranged from 2.64% for one cluster and up to 11.92% for five clusters. The Mulliken charge distribution pattern between the PGR and B\({}_{12}\) framework (Figure 1b) shows that the carbon framework received additional electrons from the B\({}_{12}\) clusters. For the case of five clusters, the additional charge on the PGR is \(-\)0.287 electrons. To calculate C\({}_{Q}\) and predict changes in the material's conductivity, it was necessary to calculate the DOS curves for all considered cases of B\({}_{12}\) concentration. Figure 2 shows the DOS curves for the pure PGR and for PGR decorated with one to five boron clusters. It can be seen that the growth in the B\({}_{12}\) amount increases the DOS amplitude over the entire energy range by increasing the number of electronic states. Earlier [39], we showed that B\({}_{12}\) clusters in the modified CNT increase the DOS peak amplitude and the CNT conductivity. Here, we observed a similar effect, so we assumed that the resistance of the boron-decorated PGR-based electrode would also decrease. To predict the effectiveness of the model as an electron SC material, we built C\({}_{Q}\) curves in the voltage range from \(-\)3 to 3 V (Figure 3). In comparison with the pure PGR (black curve), the modified model had the characteristic peaks in the positive branch of the plot reaching \(\sim\)1.266 kF/g for five B\({}_{12}\) clusters. In accordance with Formula (2), an increase in DOS in the energy range from \(-\)3 to 3 eV (Figure 2) also leads to an increase in C\({}_{Q}\). Despite the increase in the electrode mass due to the addition of clusters, the C\({}_{Q}\) continued to grow as the clusters introduced new electronic states. The details of all C\({}_{Q}\) values are shown in Table 1.  
Figure 1: The PGR/B\({}_{12}\) composite supercell. (**a**) The supercell of the pure PGR and the charge distribution over atoms in the XY and ZY planes; (**b**) the supercell of PGR with five boron clusters and the charge distribution over atoms in the XY and ZY planes. Red indicates a lack of electrons; blue indicates an excess of electrons. Figure 3: \(C_{Q}\) for the pure PGR and for PGR decorated with 1 to 5 boron clusters. \begin{table}
\begin{tabular}{c c c c} \hline
**No.** & \(\Delta H_{z}\)**eV** & \(Q_{SCD}\)**, **kC/g** & \(C_{Q}\)**, **kF/g** \\ \hline Pure PGR & - & \(-2.384/1.748\) & \(0.749\) \\ PGR/(B\({}_{12}\)) \(\times\) 1 & \(-0.00607\) & \(-2.359/2.036\) & \(0.691\) \\ PGR/(B\({}_{12}\)) \(\times\) 2 & \(-0.00965\) & \(-2.466/2.418\) & \(0.943\) \\ PGR/(B\({}_{12}\)) \(\times\) 3 & \(-0.01271\) & \(-2.532/2.757\) & \(1.105\) \\ PGR/(B\({}_{12}\)) \(\times\) 4 & \(-0.01743\) & \(-2.608/3.030\) & \(1.187\) \\ PGR/(B\({}_{12}\)) \(\times\) 5 & \(-0.02272\) & \(-2.534/3.317\) & \(1.266\) \\ \hline \end{tabular}
\end{table} 
Table 1: Heat of formation, specific charge density, and specific capacitance for the pure PGR and for the PGR decorated with 1 to 5 boron clusters.