## 2 Simulation Details
### Initial Structure  
Three different structures were investigated to confirm the application of each potential: (i) graphene with one Cu atom, (ii) curved graphene flake with Cu nanoparticle inside, and (iii) a composite precursor obtained from graphene flakes filled with nanoparticles. Initial structures for MD simulation were prepared using visual molecular dynamics (VMD) simulation and visualization software with custom Python code. The melting temperature for Cu can be checked to verify the potential function. To find the melting temperature, Cu nanoparticles with diameter 7 A were heated at a temperature from 0 K to 2000 K, with a heating rate of 50 K/ps. In Table 1, the melting temperature of Cu nanoparticles obtained with different potentials is presented. Consistent with the observations reported in [75], the average melting temperature was 723 K. It should be noted that, for such small nanoparticles, the melting temperature depends substantially on the particle size. It was also found that the presence of a graphene flake near a nanoparticle can slow down the melting of the Cu nanoparticle. It was found that, if a graphene flake with the nanoparticle on its surface is examined in a quite large simulation cell, the Cu nanoparticle in the course of heating will move far from the graphene plane and melt at the same temperature as a single nanoparticle. However, when the nanoparticle was already covered with graphene (as it would be in a 3D structure composed of a number of flakes and nanoparticles), the melting temperature of the Cu nanoparticle increased to 1000 to 1300 K. Similar results were previously obtained in [23]. However, for comparison with the literature, only the melting temperature of pure Cu nanoparticles is presented. For the system composed of a graphene flake and a Cu atom, the equilibrium distance between the graphene and the Cu atom is defined as \(h\) and was found to be 3.2 A for the BOP potential and 6.4 A for the EAM-Morse and Morse potentials. For comparison, results from the literature are presented in Table 1. To understand this very significant difference, the potential energy of the system as a function of the distance between a Cu atom and graphene was investigated. Since the BOP potential was designed specifically for growing graphene on a Cu substrate [75], it reproduces strong bonding between graphene and copper. Therefore, when simulating the interaction of one copper atom on the surface of graphene (the initial distance between a Cu atom and graphene is 3 A), the equilibrium state in the system is already reached at a distance of 3.2 A and the potential energy ceases to change right at the beginning since, in the initial state, the Cu atom is already close to the graphene surface. However, the Morse potential reproduces a very neutral interaction between Cu and graphene. As reported in the literature [47; 59], the binding energy for Cu and graphene is not high in comparison with metals such as Al, Ni, etc. This is why, when the potential energy as a function of distance is calculated using the Morse and EAM-Morse potentials, in both cases the Cu atom moves away from graphene to a distance of up to 6.4A during the first simulation steps. The potential energy in the system with BOP potential is higher than for the Morse and Morse-EAM potentials, which is also understandable from the point of view of reproducing the strong bonding. It should also be noted that the results of an interaction between one Cu atom and graphene are very different from the results for an interaction of a Cu nanoparticle and one graphene flake, and for interaction in 3D graphene filled with Cu nanoparticles, which is discussed further below. In Figure 1a, one graphene flake is shown at the initial state and after exposure at 300 K, simulated with the help of different potential functions. The behavior under exposure is discussed further below. To obtain a composite, one GF filled with nanoparticles was rotated and repeated along the \(x\)-, \(y\)-, and \(z\)-axes to obtain a 3D structure.