Friction and adhesion of graphene nanoribbons on gold: an MD investigation

The frictional motion of contacting bodies is an ubiquitous phenomenon in physics. It encompasses a vast range of time, energy, and length scales, ranging from the macroscale of earthquakes, down to the nanometer scale of atomically flat surfaces and Atomic Force Microscopy (AFM) experiments [1, 2]. Despite the impressive amount of data that has been obtained through the centuries concerning frictional phenomena, a complete theory of friction is still lacking. The main reason is the fact that the frictional response of an interface is determined by a large number of factors, such as the specific nature and chemistry of the surfaces in contact, the operational conditions, the ageing and the sliding history of the contact [3, 4], just to mention a few of them. Moreover, the presence of out-of-equilibrium and highly non-linear processes often occurring at ill-characterized frictional contacts makes a complete understanding of friction even more challenging [5, 6].In this context, new opportunities have been brought about by advances in nanotechnology, where the invention of scanning tip instruments of the AFM family [7] enabled a systematic study of friction for well-characterized materials and surfaces at the nanoscale [8, 9, 10, 11]. Progresses in both the computer modeling of interatomic interactions, that made atomistic sim-ulations of nanostructured materials more powerful and reliable [12, 13], and the development in the theory of non-linear processes [5, 14] o˙ered new theoretical tools to understand frictional phe-nomena. In particular, the diÿculty of dealing with extremely complex systems where friction is determined by collective phenomena involving many degrees of freedom, gave a strong impulse to the search of simplified 1D- and 2D-models, such as the Prandtl-Tomlinson (PT) [15, 16, 17] and generalized Frenkel-Kontorova (FK) models [14, 18, 19, 20] to capture the essential ingredients of friction. To summarize, understanding frictional phenomena at the nanoscale seems of great importance now, since dealing with experimentally well-defined interfaces makes the fundamental mechanisms of friction easier to identify, possibly with the aim of merging the existing gap between nano-and macroscale friction, where many di˙erent physical actors are at play. Technological advances in this endeavor are to be considered, since controlling friction could limit wear and dissipation, with possible impacts in improving the performances of nano- and micromachines [21], as well as biological motors [22]. In this general framework, the ongoing experimental and theoretical research on nanoscale fric-tion is covering three central topics. First of all, the study of electronic and quantum effects in friction, which happen whenever a tip or a moving agent dissipates energy by exciting local currents in the sample [2, 3]. Secondly, the study of trapped optical systems, such as driven ion chains and colloids in confined configurations [26, 27], that turned out as elegant experimental realizations of the Prandtl-Tomlinson and the Frenkel-Kontorova model. These systems are now attracting a lot of interest because of the possibility of tuning the various parameters of the experimental setup, such as temperature, substrate corrugation and degree of commensurability between the sample and the substrate, almost freely. At last, a very important field of research is represented by the frictional properties of layered and 2D materials, where evidence of a large reduction of friction (up to a factor 10) has been obtained in many graphene-based systems, grown on both amorphous [23, 24, 25] and metallic substrates [28, 29, 30]. The interest for graphene in this field is stimulated by its peculiar tribological features: the decrease of friction by increasing the number of graphene layers [23, 28, 31, 32], the increase of friction upon decreasing the normal load when graphene is chemically modified [33] and the use of graphene as solid lubricant [25]. In this Thesis, we are interested in gaining a deeper insight in the molecular mechanisms of dissipation in a specific type of graphene/metal interface, the graphene nanoribbons (or GNRs) on gold, inspired by the works of Kawai et al. [34, 35] regarding their structural and dynamical properties under the action of an external driving. The papers that represent the basis and core of the Thesis are: L. Gigli, N. Manini, A. Benassi, E. Tosatti, A. Vanossi and R. Guerra, Graphene nanoribbons on gold: understanding superlubricity and edge e˙ects, 2D Materials, 4, 4 (2017); • L. Gigli, N. Manini, E. Tosatti, R. Guerra and A. Vanossi, Lifted graphene nanoribbons: from smooth sliding to multiple stick-slip regimes, Nanoscale, 10, 2073-2080 (2018); L. Gigli, S. Kawai, R. Guerra, N. Manini, R. Pawlak, X. Feng, K. Müllen, P. Ruÿeux, R. Fasel, E. Tosatti, E. Meyer, A. Vanossi, Detachment dynamics of graphene nanoribbons on gold, in press in ACSNano (2018). The Molecular Simulations that have been used for the papers [36, 37] show that the GNR/gold interface has a very low friction, with basically zero average increase upon increasing the GNR length. This property, called superlubricity (see chapter 3), is experimentally very rare and due to the interplay between the large in-plane sti˙ness of graphene and the incommensurability between the GNR and the gold substrate structure (see chapter 4). We will show that this system is suitable to obtain a dynamical transition between low-friction smooth sliding states and violent stick-slip regimes by lifting one edge of the GNR at increasing heights, thus changing the e˙ective GNR out-of-plane softness. Furthermore, an external driving of the GNRs along their longitudinal axis directly provides an asymmetric response of the system against pulling/pushing of the edge (see chapter 5). In the last part of the Thesis, we will analyze the dynamical behavior of the GNRs against vertical pulling and show that an Atomic Force Microscope is able to unveil the detailed structure of the system by producing unilateral detachment of its individual unit cells. A good agreement between the experimentally recorded vertical force traces and the results of the molecular simulations shows that the GNR vertical dynamics is characterized by discrete detachments, accompanied by slips of the tail, which are responsible for the complex double-periodicity observed in the vertical force profile (see chapter 6).