Simulating the friction between atomic layers by using a two-q model: Analysis of the relative motion and coherence

Studying friction between atomic layers is not only of great interest for the fundamental aspect of the tribology but also important for many applications such as the layer adhesion in wearable technologies and energy saving. The previous theoretical study has used the modified Prandtl-Tomlinson model to describe the motion of the tip above a two-dimensional atomic layer in an atomic force microscopy experiment. Here the degree of freedom for the substrate has been further explicitly included in the simulation, which is significant because the coherence between the sensing and the substrate layers can be explicitly addressed by computing their relative motion. For both layers, graphene has been chosen as an example for the simulations. Based on the simulations reported here, which agree with the previous relevant theoretical and atomic-force-microscopy experimental results, the motions between the sensing sheet and the substrate can be clearly distinguished. The dependence of motion and force on the parameters for the mechanical properties of the individual layers and the interaction potential between the layers has been carefully studied. For the relatively large values of the parameters for the mechanical properties, the relative motions between the sensing sheet and the substrate show that there would be coherence between the layers, which is beneficial for the adhesion between them. However, many other parameter spaces can be studied further in the future. Similar to the simulations of the motions of the atomic layers, the computed force of the atomic-force-microscopy tip can also indicate the stability of the layers. The theoretical work reported can be used to identify explicitly the relative motions between the sensing sheet and the substrate, providing a substantial improvement for the understanding of the friction between atomic layers. Moreover, in principles, the modeling methodology proposed can be generalized to describe any number of layers in the thin-film devices, by adding a q-parameter for each layer.