Temperature Dependences in the Tomlinson/Prandtl Model for Atomic Sliding Friction

The temperature dependence of the Tomlinson/Prandtl model for nanoscale sliding friction is analyzed by considering the properties of the initial and final states between which the tip can move, as well as the energy barrier between them, for various sliding regimes defined by the value of the corrugation factor γ. When γ < 1, the friction force tends to zero, defining a so-called superlubricious regime. The most commonly observed behavior is found for γ > 4.603, where the friction force increases monotonically with increasing sliding velocity up to a critical value equal to the value of F ^* (lateral force at T = 0) and monotonically decreases with temperature from F ^* at T = 0. However, completely different behavior is found when 1 < γ < 4.603. The temperature dependence of the lateral force in this regime is investigated using Monte Carlo simulations. The friction force still tends to F ^* as T approaches 0 K, but in contrast to the behavior found when γ > 4.603, the friction force increases with increasing temperature from F ^* , reaches a maximum value, and then decreases monotonically as the temperature rises further. Such behavior has been observed in atomic force microscopy friction measurements.