Phononic Doppler effect in sliding friction

The Doppler effect plays a fundamental role in a vast array of applications, spanning from the quantum domain to cosmic scales. Nevertheless, its manifestation in the context of phonon excitation during the friction between two objects with relative motion remains unexplored. In this study, we predict and investigate the occurrence of the phononic Doppler effect within sliding friction, employing a phononic dynamics model derived through the atomistic Green's function method. As the friction-excited phonons propagate both forward and backward relative to the moving object, we predict frequency high-shift and low-shift phenomena, respectively. We propose a phonon excitation rule, grounded in the phonon dispersion relation, to elucidate the frequency-shift behavior, essentially capturing the Doppler effect on friction-excited phonons. The predicted frequency shift, as determined by the phonon excitation rule, finds validation through molecular dynamics simulations. The observation of the phononic Doppler effect in sliding friction opens a range of potential applications, providing innovative tools for detecting energy-dissipation mechanisms at interfaces caused by friction.

Figure 1

(a) Schematic illustration of the friction system contains a graphene flake sliding over another graphene substrate. The variable $d$ represents the interfacial distance between the slider and the substrate. (b) Predicted friction forces per unit area by the PD model under three different interfacial distances.

Figure 2

The number density of excited phonons at different sliding velocities for $d=3.20\AA$. The labels from $P_1$ to $P_3$ in the legends correspond to the marked points in Fig. 1, while the dashed magenta lines denote the washboard frequency ($f_0$) and its harmonics.

Figure 3

(a) Schematic diagram of the phononic Doppler effect in sliding friction. (b) Phonon dispersion relation of the graphene substrate. (c) The vibrational amplitudes of the $n\mathrm{th}$ harmonic for atoms positioned at the center unit cell of the CR, along the $x$- and $z$ axes. The right vertical axis represents the ratio of the vibrational amplitude along the $z$ axis to that along the $x$ axis. (d) The vibrational amplitudes of the $n\mathrm{th}$ harmonic along the $x$- and $z$-axis directions for atoms located within various unit cells in the CR, with the inset denoting the position of each unit cell. The sliding velocity is $v_0=100\mathrm{m}/\mathrm{s}$ for (b), (c), and (d), and $d=3.20\AA$ for (d).

Figure 4

(a) Schematic illustration of a MD model to simulate a slider moving across a substrate with a constant velocity. (b) The calculated vibrational velocity spectrum vs wave vector, which is the SFFT of the instantaneous atomic velocity vs the atomic positions as shown in the inset. The magenta dashed line in the inset denotes the central position of the slider.

Figure 5

(a) Schematic diagram of a graphene flake sliding over another graphene substrate. (b) The side view of the friction system with meshed unit cells in FLR and BLR, respectively. (c) The side view of the friction system at the time moments $t=0$ and $t=2T$ for examples.