Scaling feature of nano-scale friction based on the inverse statistical approach

Friction is known as a scaling phenomenon between rough surfaces. However, at the atomic scales, thermal fluctuations could be appreciated to scaling features. Previous studies revealed global information about the nano-friction fluctuations and showed that the fluctuations are multi-affine and correlated, and cannot be described by a white noise. In the present study, we are looking for local criteria which reveal the different features of nano-friction fluctuations and investigate whether the inverse Kolmogorov scaling is applied for the nano-friction fluctuations. If the inverse scaling is verified, we can say that kinetic energy which is converted into thermal energy, is dissipated from larger scales to smaller ones and is released at the atomic scales due to interatomic electrostatic forces. To this end, the friction force is determined using the atomic force microscope and tip dragging over the NaCl(001) surface. The minimal distance distributions for which the friction variation exceeds predefined values are studied. The results demonstrate that the dissipation distance distribution has a power-law behavior for large atomic distances as turbulence and the related exponent is determined. Furthermore, indicating the shuffled and surrogated probability distributions demonstrates that the rare friction differences are caused by the effect of both correlation and the probability distribution function. Although, it had been demonstrated that the atomic-scale friction of NaCl has a multi-scaling behavior, the current results indicate that inverse scaling is mono-fractal. It confirms that the energy loss dissipation is scaled from larger scales to the smallest atomic ones.