Phononic perspective of anisotropic friction: Universal laws from the frictional phonon spectrum

Friction, defined as the resistance to relative motion between two contacting objects, has historically been regarded as a consequence of mechanical energy dissipation. However, the precise mechanism by which it operates in the context of phonon excitation has not been fully elucidated. In this study, we present a theoretical framework based on the atomistic Green's function method that connects friction-excited phonons to the resulting friction force. Our analysis reveals that phonons are primarily excited at bi-washboard frequencies and their harmonics when relative motion occurs in arbitrary directions. The theoretical predictions are validated through detailed molecular dynamics simulations and further supported by experimental evidence. A key finding of our work is the identification of a spectral function that links the normalized number densities of friction-excited phonons to their frequencies. This relationship is intrinsic to the friction system and remains independent of specific factors such as sliding velocity or direction. Our discovery enables a quantitative explanation of anisotropic friction, nonmonotonic velocity dependence of friction, and fluctuations in friction, all without relying on additional assumptions. By resolving the spectral characteristics of phonon excitations, this study provides systematic insights into the fundamental nature of friction.