This study is to examine the effectiveness of the two ways forming the incommensurate contacts on reducing friction. Two dimensional (2D) penta-graphene (PG) and B₂N₄ possessing the same lattice structure and excellent lubricating property were chosen to construct the homogenous and heterogenous interfaces. We studied the frictional properties at the homogenous interfaces of PG/PG and B₂N₄/B₂N₄, and the heterogenous interface of B₂N₄/PG. Our calculations show that the friction coefficients at the homogenous interface of B₂N₄/B₂N₄ are smaller than those at the heterogenous interface of B₂N₄/PG. The different compositional elements at the commensurate contacting surfaces hardly reduce the interlayer friction. It indicates the ineffectiveness of heterogenous interface on reducing friction when it is commensurate contacting. Additionally, the incommensurate contact formed via biaxial stretching one layer can significantly reduce the interlayer friction, which is the superposition of uniaxial stretching. In addition, the interlayer friction was elucidated from the point views of potential energy, charge density difference and registry index (RI). This study highlights the importance and effectiveness of twisting in reducing the interlayer friction compared to stretching.

Two-dimensional (2D) van der Waals layered materials have been widely used as lubricant. Penta-graphene (PG), a 2D carbon allotrope exclusively composed of irregular carbon pentagons has recently been predicted to have superlubricating property. In the present study, by combining the molecular dynamics simulation and first-principles calculations, we investigated the frictional property of PG in both commensurate and incommensurate contacts. Our calculations show the ultra-low friction at the interface of relatively rotated bilayer PG with twist angles of more than 10° away from the commensurate configuration. Meanwhile, our calculations demonstrate the isotropy of the ultra-low friction at the interface of incommensurate contact, in contrast to the anisotropic of the commensurate contacting interface. Additionally, the evolution of friction force and the fluctuation of potential energy along sliding path correlate closely with the interface’s structure. The energetics and charge density explain the difference between the friction at the interfaces of the commensurate and incommensurate contacts. Not only that, we found the correlation between the intrinsic structural feature and interlayer binding energy. Importantly, our findings on the retainment of the ultra-low friction under work conditions indicates that the superlubricating state of PG has good practical adaptability.