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The liquid lubrication, thermolubricity and dynamic lubricity due to mechanical oscillations are investigated with an atomic force microscope in ambient environmental conditions with different relative humidity (RH) levels. Experimental results demonstrate that high humidity at low-temperature regime enhances the liquid lubricity while at high-temperature regime it hinders the effect of the thermolubricity due to the formation of liquid bridges. Friction response to the dynamic lubricity in both high- and low-temperature regimes keeps the same trends, namely the friction force decreases with increasing the amplitude of the applied vibration on the tip regardless of the RH levels. An interesting finding is that for the dynamic lubricity at high temperature, high-humidity condition leads to the friction forces higher than that at low-humidity condition while at low temperature the opposite trend is observed. An extended two-dimensional dynamic model accounting for the RH is proposed to interpret the frictional mechanism in ambient conditions.

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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.</br>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/nm² and 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.</br>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.

A more adequate extended Prandtl-Tomlinson model in two dimensions (2D) analysis is proposed in the aim to thoroughly investigate the interplay between kinetic friction, relative humidity (RH), normal load, and temperature in both contact and tapping mode atomic force microscopic (AFM). In contact mode operation, results firstly show that for various applied normal loads highly wetted surface in contrast to partially wetted surface exhibits lower friction at finite temperature range. This phenomenon is attributed to the film layer acting as a lubricant. Secondly, two different regimes when varying the relative humidity were further observed with increasing temperature. The first one shows the thermolubricity’s effect at low RH (RH 20%) while the second regime remarkably confirms an increase of friction with temperature at higher RH (RH60%) which is inconsistent with common observation. The latter regime is characterized by the thermally activated capillary bridge formation leading to an increase of the total adhesion force. Thirdly we demonstrated that both regimes also hold in ac mode operation and regardless to the humidity level, either low or high RH, friction force decreases with increasing amplitude modulation. Good agreement was found with measurement and analytical data reported previously. In the model treatment, however, only effects of capillary force which dominate in AFM measurement were considered.

In this paper, based on molecular dynamics simulation method, the authors construct a graphene flake sliding on a suspended graphene layer which is anchored on a bed of springs. This graphene-spring system provides an ideal model to replace the multilayer graphene under the top layer. We firstly mimic different layers of suspended graphene through changing the stiffness of spring bed; then the contributions of Van der Waals force of the tip and elastic deformation of the top layer supported by spring bed to friction force are analyzed; finally, an energy dissipation mechanism based on the amount of corrugation potential energy and sample deformation elastic energy is proposed. It is demonstrated that the effects of energy barrier and surface compliance are directly related to the observed friction force. It is helpful to achieve a theoretical basis for the design of graphene-based nano electromechanical systems (NEMS) devices.