Friction on layered media: How deep do phonons reach?

Abstract

We theoretically study the frictional damping of a small probe object on a coated planar surface, analyzing the resulting phonon modes via a theory of viscoelasticity. Three different types of excitations are found to contribute to friction in distinct ways: traveling (3D) spherical waves, traveling (2D) surface waves, and evanescent waves. While traveling waves transport energy away from the probe, determined by long range elastic properties (wavelength), evanescent waves transform energy into heat in a near-field range, characterized by the size of the probe. Thus, fundamentally different behaviors are predicted, depending on coating thickness and material properties.

Nanoscale Friction Measurements on Manganite Thin Films: Which Material Properties are Important?

“…The same functional form also gives a good description of the integrated stress fields under a spherical tip [30,40] (see appendix A.4). Moreover, the functional form is in quantitative agreement with a viscoelastic model developed by Lee et al [3] , which attributes top layer thickness dependent friction to viscous dissipation inside the evanescent waves set up in the top layer by a vibrating tip.…”

“…As far as we can tell, this publication and a recent theoretical study [3] are the first to discuss contributions of thermoelastic damping to measured friction, although thermoelastic damping in AFM cantilevers is routinely considered when interpreting dynamic AFM measurements. [17] We have found no literature discussing thermoelastic damping in the stressed volume around the contact area, which yields an estimate for vibrational damping.…”

“…The question of how material properties below the surface affect friction has received considerable attention. [3,[175][176][177][179][180][181][182][183][184][185][186] Friction measurements on layered materials, such as graphene, MoS 2 , NbSe 2 , WS 2 , WSe 2 and h-BN report a decrease in friction with an increase in layer count. [176,177,179] To explain these observations, several mechanisms have been proposed [3,[179][180][181]185] that are related to the so-called puckering effect, which only is expected in materials with weak interlayer forces, and changes in the elastic properties.…”

“…[3,[175][176][177][179][180][181][182][183][184][185][186] Friction measurements on layered materials, such as graphene, MoS 2 , NbSe 2 , WS 2 , WSe 2 and h-BN report a decrease in friction with an increase in layer count. [176,177,179] To explain these observations, several mechanisms have been proposed [3,[179][180][181]185] that are related to the so-called puckering effect, which only is expected in materials with weak interlayer forces, and changes in the elastic properties. At the same time, studies [176,179] shows that the measured frictional forces approach a bulk value for increasing layer numbers, but do not specify the parameters that determine the length scale at which saturation occurs.…”

“…At the same time, studies [176,179] shows that the measured frictional forces approach a bulk value for increasing layer numbers, but do not specify the parameters that determine the length scale at which saturation occurs. In this regard, a viscoelastic model developed by Lee et al, [3] which attributes top layer thickness dependent friction to viscous dissipation inside the evanescent waves excited in the top layer by a vibrating tip provides a possible explanation. In their study, the authors relate the saturation length to the decay length of such evanescent waves.…”