## 3 Results and Discussion  
### Friction  
The effect of graphene on friction is clearly observed in Figure 7. The friction curve related to the bare copper sample (the blue curve) is the reference trend to understand the impact of the carbon coatings. This curve has an initial friction ramp representing the running-in of the sliding contact that brings the CoF to stabilise at about 0.8 after a few metres. Looking at the other curves in the same diagram, it appears evident that the presence of a graphene layer makes the CoF curve deviate from that of the bare copper sample, especially in the first few meters of sliding. All the graphene nano-coatings could reduce the CoF from about 0.7-0.8 to 0.15-0.25. However, this beneficial effect endured relatively shortly. Figure 7b is the zoomed view of the first 7 metres of the tests in Figure 7a, where the difference among the curves is most evident, while Figure 8 displays the whole set of the friction curves for every sample (except those of the direct growth CVD specimen, as anticipated in Section 2.1.2). The friction curves of coated samples can be divided into two parts: Part 1, extending from the beginning of the test to the onset of the friction transition, and Part 2, from transition up to the end of the test. In Part 1, friction is stable; the friction curves of the graphene-coated samples were flat, featuring a CoF value below 0.2 and low scattering. After this initial phase, a transition occurred that closely resembles the running-in phase observed with bare copper, but delayed by a few metres. The related friction ramp was likely associated with the failure and removal of the graphene coating from the contact region, similar to what was observed in a previous work by the authors [37]. It is accepted among researchers that graphene improves the tribological performance as long as it survives at the interface, because it separates the metal surfaces and reduces the shear stresses at the contact spots of asperities [13; 25; 53]. Figure 7: Friction curves measured on the graphene-coated samples at the median radius of 3 mm, (**a**) whole test, (**b**) magnification of forest 7 m.  
The duration of Part 1 was strongly correlated to the structure of the coating itself, and, therefore, to shear strength and adhesion. The analysis of the curves in Figure 8 suggests that the transition was completed within just 15 \(\div\) 20 cycles for transferred graphene. The thickness of the transferred CVD graphene film was so tiny that Part 1 could be hardly distinguished from an ordinary running-in of the steel-copper friction pair. The self-assembled graphene nano-coatings could withstand the tearing-off action of the counter body longer, and the duration was even extended to about 250 cycles on average for the one sonicated 6 h.  
Interestingly, irrespective of the initial frictional behaviour, the curves remained always relatively smooth in Part 2 and levelled off in the second half of the test. Both the uncoated and graphene-coated samples had a similar friction value in the last metres of sliding, equal to about 0.8. Only the friction curves of transferred graphene showed some scattering of the friction signal, mainly between 200 and 500 rotating cycles, which may indicate the activation of abrasion and ploughing. Abrasion grooves are evidenced in on this sample, which are indeed not visible inside the wear tracks of the other samples. The other friction curves acquired with bare copper and with the samples coated by self-assembled graphene are much smoother because a transfer layer due to a dominant tribo-oxidative mechanism was established at the interface. Further details are provided in Section 3.2. The average CoF values measured in Part 1, Part 2, and throughout the whole test are compared in Figure 9. The wearing-out of the self-assembled nano-coatings in Part 1 comes with a stable average friction value equal to 0.17.