# Electrochemical Deposition of Copper on Epitaxial Graphene
## 3 Results and Discussion
Insert: zoomed current transients; (**b**) comparison of the dimensionless experimental (open symbols) and theoretical transients for instantaneous (bold solid black curve) and progressive (bold dashed–dotted curve black curve) nucleation; (**c**) experimental current transient recorded at \(-0.45\) V (red circles) and Elovich fitting curve (blue solid curve), respectively. based on forcefield (EDA-FF), presented in Table 1 showed that the interaction between copper and graphene was very weak and was dominated by dispersion forces, while a strong repulsion is expected between the water molecules and the Cu atom because these two fragments both have a positive charge. Noncovalent interaction (NCI) analysis enabled us to visualize the weak interaction between [Cu(H\({}_{2}\)O)\({}_{6}\)]\({}^{0}\) and graphene, which manifests itself as the green and light brown-colored nonbonding interaction areas located between copper and graphene in the vicinity of the top site (Figure 4a) and in the presence of two spikes within the sign(\(\uplambda_{2}\))\(\rho\) region ranging from \(-0.01\) to \(0.01\) a.u. (Figure 4b). As was estimated by our DFT calculations, whenever the electro-reduced Cu species reach the graphene surface, they can freely diffuse along both considered diffusion paths with a small energy barrier of 35 meV (Figure 5a,b). Copper atoms tend to avoid occupation of the unfavorable hollow sites. It is interesting to note that the presence of the second copper atom (the already reduced and adsorbed Cu species) at the graphene surface significantly modifies the diffusion path due to the attractive interatomic interaction between neutral Cu species, making the Cu migration energetically favorable and promoting Cu clusterization. From a practical point of view, this means that, due to the favorable mass transfer and nucleation rate, the discrete diffusion zones of individual Cu nuclei will overlap very fast with time. For this reason, the cathodic current reaches a peak current maximum during the first two seconds and then decays slowly (as was demonstrated in Figure 3a). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Interaction between** & **Electrostatic,** & **Repulsion,** & **Dispersion,** & **Total Energy,** \\
**Fragments** & **kJ/mol** & **kJ/mol** & **kJ/mol** & **kJ/mol** \\ \hline Graphene–Cu & 0.00 & 1.33 & \(-\)2.59 & \(-\)1.26 \\ Graphene–water & \(-\)3.58 & 42.38 & \(-\)86.01 & \(-\)47.21 \\ Cu–water & 0.00 & 420.21 & \(-\)20.10 & 400.11 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Results of energy decomposition analysis. Figure 4: (**a**) Top and side view plots of the noncovalent interaction (NCI) iso-surface (reduced density gradient, RDG = 0.5) for reduced [Cu(H\({}_{2}\)O)\({}_{6}\)]\({}^{0}\) complex on graphene and (**b**) corresponding NCI diagram (RDG vs. sign(\(\uplambda_{2}\))\(\rho\)). The iso-surfaces are colored according to sign(\(\uplambda_{2}\))\(\rho\) in the range \(-\)0.035\(-\)0.02 a.u. Red indicates the steric repulsion region; green (light brown) indicates the van der Waals interaction region, and blue implies the strong attractive interaction. Note: the optimization of the [Cu(H\({}_{2}\)O)\({}_{6}\)]\({}^{0}\) complex on graphene has been performed with consideration of solvent effect (water in our case) by using polarizable continuum model.