# Electrochemical Deposition of Copper on Epitaxial Graphene
## 3 Results and Discussion
All calculations were performed using the aquo complexes of copper species, because the intrinsic or extrinsic solvent models did not give satisfactory results. The sequential additions of water molecules yielded the stabilization of all considered particles, computed as a decrease in the electron acceptor reactivity (Figure S1, Supporting Information) and the Hirshfeld charge on the Cu species (Figure S2, Supporting Information). The aquo complex has disordered octahedral geometry (Jahn-Teller distortion) with four short (2.02 A) and two elongated Cu-O bonds (2.26 A). According to the Hirshfeld charge population analysis, the charge located on the copper atom is equal to +0.601\(e^{-}\). The addition of a first electron yielded the aquo Cu\({}^{+}\) complex with a smaller Hirshfeld charge on the copper atom (+0.216) and all elongated Cu-O bonds. The addition of the second electron led to the formation of metallic copper, confirmed by the negligibly small Hirshfeld charge on the copper atom (+0.005\(e^{-}\)) and the destruction of the octahedral geometry. Figure 2: (**a**) Structures of the copper (Cu) complexes: [Cu(H\({}_{2}\)O)\({}_{6}\)]\({}^{2+}\), [Cu(H\({}_{2}\)O)\({}_{6}\)]\({}^{1+}\), [Cu(H\({}_{2}\)O)\({}_{6}\)]\({}^{0}\). The numbers are bond lengths in Å. Light pink, blue and red spheres represent H, Cu and O atoms, respectively. (**b**) The Born–Haber cycle for the calculation of the potential reductions in [Cu(H\({}_{2}\)O)\({}_{6}\)]\({}^{1+}\) to [Cu(H\({}_{2}\)O)\({}_{6}\)]\({}^{0}\). The equilibrium potential of the mono-electronic redox couple [Cu(H\({}_{2}\)O)\({}_{6}\)]\({}^{1+}\)/[Cu(H\({}_{2}\)O)\({}_{6}\)]\({}^{0}\), estimated by applying the Born-Haber methodology (Figure 2b) [99], was \(-0.59\) V, which agrees well with the experimental position of the metallic copper deposition. On the contrary, the computed value of the equilibrium potential of the bi-electronic redox couple [Cu(H\({}_{2}\)O)\({}_{6}\)]\({}^{2+}\)/[Cu(H\({}_{2}\)O)\({}_{6}\)]\({}^{0}\) was \(-0.93\) V, which is too low in comparison with the observed potential. This might imply that the copper deposition proceeds via mono-electronic reduction, followed by the fast exergonic disproportionation of unstable Cu\({}^{1+}\) intermediates. The irreversible process of copper deposition was quantified by the dynamic electrochemical measurements employing Scharifker-Hills formalism [87]. Current transients recorded at different deposition potentials (Figure 3a) are contingent on the applied potential pulse. The short-elapsed times (ca. 0.2 s) are characterized with the equilibration of the electrical double layer at the epitaxial graphene-electrolyte interface. The longer times are characterized with a faradaic process of copper electrodeposition (Inset in Figure 3a). Specifically, the potential pulses of \(-0.39\) and \(-0.4\) V are featured with non-monotonous current transients indicative of the three-dimensional (3D) nucleation process with diffusion-controlled growth [100] which enable analysis of the nucleation mechanism at the early stages of the electrodeposition [87]. The behavior of the active sites available for the formation and growth of the metal nuclei differentiates the two distinctive cases of the nucleation process. Accordingly, the instantaneous nucleation implies the maintenance of the convergent diffusion of the reactant on the limited number of nuclei. On the contrary, progressive nucleation relies on the increase in the number of nuclei yielding the quick establishment of overlapped planar reactant diffusion. The theoretical current transients obey the following equations:  
\[\left\{ \begin{array}{l}\left(\frac{i_{max}}{f_{max}}\right)^{2}=1.9542\big{(} \frac{t}{t_{max}}\big{)}^{-1}\big{[}1-\exp\big{[}-1.2564\big{(}\frac{t}{t_{max }}\big{)}\big{]}\big{)}^{2}\\ \left(\frac{t_{max}}{f_{max}}\right)^{2}=1.2254\big{(}\frac{t}{t_{max}}\big{)}^ {-1}\big{[}1-\exp\big{[}-2.3367\big{(}\frac{t}{t_{max}}\big{)}^{2}\big{]}\big{]} ^{2}\end{array} \right.