## 3 Results and Discussion
### Application as Anode Materials for Li, Na, K, Mg and Ca-Ions Batteries
The average adsorption energy (\(\overline{E}_{\text{Ad}}\) ) is calculated by:  
\[\overline{E}_{\text{Ad}}\ =\ \frac{(E_{\text{SM}}-E_{P}-n\times E_{At})}{n} \tag{3}\]  
where \(E_{\text{SM}}\), \(E_{P}\), \(E_{At}\), and \(n\) are the system's energy, pristine-substrate, single adatom, and the number of adsorbed-ions on the surface, respectively. Metal ions intercalation are simulated over P-TpG by gradually and consistently increase in ions coverage. Therefore, ions are positioned uniformly on both surfaces with a priority of predicted stable binding sites. Due to the surface energy-dependent and stochastic nature of the ions positioning, we constructed three different ion distributions over the considered substrate, where the lowest energy structure was selected to calculate the average adsorption energy. Electronic self-consistent iterations find out the ground state of the electrons at each fixed atom position. Then, geometry optimization is accomplished using the conjugate gradient approach, in order to reach the minimum energy configuration in which the forces on ever atoms  
Figure 4: Charge exchange between P-TpG and single Li, Na, K, and Ca-ions for S1 and S2 adsorption sites. Color coding represents the binding charge transfer, such that green and red show the charge losses and charge gains, respectively. fall below a predefined threshold of 10\({}^{-4}\) eV eV/A. Figure 5 demonstrates the average adsorption energy versus storage capacity over P-TpG. The adsorption of adatoms does not lead to new chemical bonds formation or substrate defects. According to Figure 5, at the initial storage levels, the adsorption energy decreases suddenly and then smoothly by increasing the adatoms' coverage. Increasing the ion coverages leads to weaker interactions between adsorbed adatoms and the substrate. No ion agglomerations are observed due to the weak bonding or physisorption [64]. The Faraday equation calculates the storage capacity (\(S_{c}\)) for different ion coverage (\(n\)) and given by:  
\[S_{c}=\ \frac{n\cdot V_{e}\cdot F}{m_{a}} \tag{4}\]  
where \(n\), \(F\), \(V_{e}\), and \(m_{a}\) are the number of adatoms, Faraday constant, number of valance electrons of ion, and the unit-cell atomic mass, respectively. In this study, the ion coverage is calculated as 4, 7, 10,18, 22, 26, 30, and 38 adatoms for different ions. For all configurations, the absolute values of the adsorption energies decrease with increasing ion coverage. Subsequently, the repulsive forces increase hampering the adsorption for newly coming atoms. As shown in Figure 5, despite the low-coverage of Mg atoms, the adsorption energy quantity approaches zero or takes undesirable positive values, making Mg not suitable for adsorbing over P-TpG. For the remaining ions, the adsorption energies remain negative and far enough from zero. Interestingly, for ultra-high capacities of the Ca ion, the adsorption energy remains in the optimal range. However, the considered substrate's structural stability should be demonstrated for a high amount of ion adsorption. The K adatom has shown maximum changes in the average adsorption energy. The N-TpG monolayers followed almost the same adsorption energy trends as the P-TpG nanosheets with different values [53]. Figure 5: The average adsorption energy versus storage capacity for Li, Na, Mg, K, and Ca-ions over P-TpG. The open-circuit voltage is another significant parameter for anode substrates. Substrates with lower positive voltage (around 0.3 volts and far away from zero) could deliver higher output voltage in a battery cell. The voltage values should not be close to zero or take negative values; otherwise, resulting in ions clusterization and dendrites formation. The metallic-ion-clusters reduce the electrode adsorption capacity, and dendrites lead to thermal explosion and performance failure of batteries.