Due to the outstanding tribological and wear properties at cryogenic temperatures, Diamond-Like Carbon (DLC) materials are widely used in fields such as deep space exploration and superconducting magnets. Wherein, the temperature dependent frictional behavior of DLC is expected to follow the conventional thermally activated process. In this article, the frictional properties of DLC are scrutinized in the temperature range of 300 to 100 K by reciprocally scanning a DLC coated atomic force microscopy (AFM) tip against a DLC substrate in ultra-high vacuum (UHV) conditions. The results reveal a remarkable monotonical temperature dependence of frictional behavior, which remains robust under varying normal loads and sliding velocities. Specially, the overall friction force raises as temperature decreases, with a distinct friction peak at T_max = 215 ± 10 K. While a logarithmic dependence of friction on velocity is observed at temperatures far from T_max, friction becomes nearly velocity-independent in the vicinity of T_max. This non-monotonically temperature dependence of friction beyond conventional thermally activated framework is well interpreted involving the formation/rupture of interfacial bonds. This work provides new insights into the interfacial bonding mechanisms affecting the tribological properties of DLC materials at cryogenic temperatures.

The widely used Amonton’s law, which describes the common observation that dry friction between two surfaces is proportional to the normal load, has yet to be explicitly derived since its discovery from Leonardo da Vinci era. Here, Amonton’s law is explicitly extrapolated as the friction coefficient $\mu =\mathrm{\Delta }{F}_{\mathrm{N}}/\left(k\mathrm{\Delta }x\right)$ via concise perturbation theory analysis of the frictional energy landscape parametrized by the load. This reveals that Amonton’s law may arise from the competition between the normal stiffness (k) and the interfacial normal force fluctuation during sliding (ΔF_N/Δx). The predicted friction coefficient is quantitatively validated through both atomic force microscopy (AFM) experiments and atomistic simulations of frictional systems ranging from bulk to layered materials. Unlike the traditional framework of recondite rough contact theory, this study concisely extrapolates Amonton’s law and friction coefficient and traces their microscopic origins to the inherent mechanical properties, thereby enabling their rational design.

Non-empirical law depicting how atomic-scale friction behaves is crucial for facilitating the practical design of tribosystems. However, progress in developing a practically usable friction law has stagnated because atomic-scale friction arises from the continuous formation and rupture of interfacial chemical bonds, and such interfacial chemical reactions are difficult to measure precisely. Here, we propose a usable friction law for atomic-scale contact by using large-scale atomistic simulations to correctly measure the interfacial chemical reactions of a realistic rough surface. This friction model is effective to predict how atomic-scale friction force varies with temperature, sliding velocity, and load. As a special example, our model predicts velocity-related mountain-like temperature dependence of friction, and this prediction result is then carefully validated by comparison with ultra-high-vacuum atomic force microscopy (AFM) experiments.