Atomic-scale friction of black phosphorus from first-principles calculations: Insensitivity of friction under the high-load

The Amontons-Coulomb law shows that friction is proportional to load, which limits application of materials. Lubricants can, black phosphorus (BP), effectively inhibit the rapid increase of friction under high-load. However, there are fewer researches focusing on the friction mechanism of BP under load. Based on first-principles, bilayer BP as friction interface is approved. The increasing average shear strength is positively correlated and almost negligible for sigma Z < 20.1 and sigma Z & GE; 20.1 GPa, respectively, implying high-load friction insensitivity of BP. Comparing to Gr and MoS2, high-load friction insensitivity of BP is remarkable, although its friction performance under zero load is inferior relatively. High-load friction insensitivity of BP is closely related to its negative Poisson's ratio that is observed first-time in friction calculation. This will reduce potential dissipation and friction of BP during high-load sliding, due to interlayer-intralayer electronic reconstruction. The conclusions are of great significance for the design of lubrication and microscale mechanism analysis in engineering application.