Influence of Contact Aging on Nanoparticle Friction Kinetics

One of the oldest concepts in tribology is stick-slip dynamics, where a disruptive sequence of stick and slip phases determine the overall resistance in sliding friction. While the mechanical energy dissipates in the sudden slip phase, the stick phase has been shown to be characterized by contact strengthening mechanisms, also termed contact aging. We present experiments of sliding nanoparticles, where friction is measured as a function of sliding velocity and interface temperature. The resulting complex interdependence is in good agreement with Monte Carlo simulations, in which the energy barrier for contact breaking increases logarithmically with time, at a rate governed by thermal activation.

Figure 1

Illustration of nanoparticle manipulation with an AFM in tip-on-top mode. (a) Placement of AFM tip on top of particle. (b) Translation of particle by pulling with the AFM tip. (c) 20 typical raw friction loops for a range of velocities at $T=200\mathrm{K}$. (d) Topography scan showing a particle before and (e) after a translation.

Figure 2

Experimental results of particle friction measurements for a single particle. (a) Temperature dependence of $F_F$ for different velocities. The markers represent averaged measurement data, the lines represent spline interpolations. $F_F$ shows strongly nonmonotonic behavior. (b) Velocity dependence of $F_F$ for different temperatures, displaying rising and falling slopes.

Figure 3

Simulation details. (a) Time dependence of $\mathrm{\Delta }{E}_{\mathrm{off}}$ for different temperatures. (b) Typical friction loops for different velocities at $\mathrm{T}=200\mathrm{K}$. Parameters used: ${\mathrm{\Omega }}_{\text{Relax}}={10}^{10}\mathrm{Hz}$, $K=15\mathrm{N}/\mathrm{m}$, $\kappa =2\times {10}^5\mathrm{N}/\mathrm{m}$, $\eta =5\times {10}^{-5}\mathrm{kg}/\mathrm{s}$, $\mathrm{\Delta }{E}_{\text{Relax}}=0.14\hspace{0.17em}\hspace{0.17em}\mathrm{eV}$, $\mathrm{\Delta }{E}_{\mathrm{off}}^0=0.11\hspace{0.17em}\hspace{0.17em}\mathrm{eV}$, $\mathrm{\Delta }{E}_{\mathrm{off}}^1=0.27\hspace{0.17em}\hspace{0.17em}\mathrm{eV}$, $\alpha =0.2$.

Figure 4

Simulation results regarding the temperature- and velocity-dependence of friction with simulation parameters as given in Fig. 3. (a) Temperature dependence of friction. At low temperatures the friction approaches a curve, as it would result from a fixed energy barrier $\mathrm{\Delta }{E}_{\mathrm{off}}=\mathrm{\Delta }{E}_{\mathrm{off}}^0=0.11\mathrm{eV}$, while at high temperatures the friction values approach a curve, which would result for constant $\mathrm{\Delta }{E}_{\mathrm{off}}=\mathrm{\Delta }{E}_{\mathrm{off}}^0+\mathrm{\Delta }{E}_{\mathrm{off}}^1=0.38\mathrm{eV}$ (gray curves, $v=3\times {10}^{-6}\mathrm{m}/\mathrm{s}$). (b) Velocity dependence of friction. Friction increases with $\ln (v)$, except for $T=100\mathrm{K}$, where a decrease with $\ln (v)$ is observed, consistent with the measurement results in Fig. 2.