According to the molecular dynamics simulations and the mechanism of energy dissipation of nanofriction, we construct a model system with a flake sliding in commensurate configuration on a monolayer suspended graphene anchored on a bed of springs. The system is to analyze the contributions of different regions (T1-T7) of the graphene flake to friction force, with the substrate characterized by different stiffness gradients and midpoint stiffness.
The results indicate that the soft region of contact (T1) always contributes to the driving force, whereas the hard region (T7) leads to the biggest friction force on all column atoms of the flake. Moreover, as the support stiffness increases, when the stiffness gradient and the midpoint stiffness are equal to 1.34 nN/nm ²and 12 nN/nm, respectively, the contribution ratio of T7 to the total friction increases from 33% to 47%, which is approximately 4-15 times greater than those of each column atoms in T3-T6. The results also indicate that the energy barrier decreases with the increase of support stiffness along the stiffness gradient direction of the substrate, which induces the resistance forces on the relative motion to decrease. Meanwhile, the amplitude of the thermal atomic fluctuation is higher in the softer region while lower in the harder one. This difference in amplitude leads to the considerable potential gradient that ultimately causes the driving force. Finally, for a given point at the end of the flake (T1 or T7), the intensity of the van der Waals potential field is mainly determined by the nearest substrate atoms at that point. Part of these nearest atoms lie inside the contact region while the others do not. Consequently, the thermal vibration of the atoms inside the contact region is different from that of the atoms outside the confinement. The different thermal vibrations induce the greater edge barriers. In addition, T1 lies in the soft edge region and T7 in the hard one. As a result, the normal deformations of these two regions are always different, and therefore they also generate the driving force.
At these points, the results reported here suggest that the friction force in each contact region is caused by the coupling of the energy barrier and the elastic deformation between the graphene surfaces. The former contribution, i.e.the energy barrier, includes the interfacial potential barrier in commensurate state which is against the sliding of the surfaces with respect to each other, and the potential gradient caused by the different vibration magnitudes of the substrate atoms against the different spring stiffness in the direction of stiffness gradient. The latter contribution, i.e. the elastic deformation, is the unbalanced edge energy barrier resulting from the asymmetrical deformation and the different degrees of freedom between the edge atoms of the slider and atoms inside and outside the contact area of the substrate. Results of this paper are expected to be able to provide theoretical guidance in considering the influence of stiffness gradient on friction between commensurate surfaces and in designing the nanodevices.