Thermodynamic aspects of nanoscale friction

Abstract

Developing the non-equilibrium thermodynamics of friction is required for systematic design of low friction surfaces for a broad range of technological applications. Intuitively, the thermodynamic work done by a material sliding along a surface is expected to be partially dissipated as heat and partially transformed into the change of the internal energy of the system. However, general nonequilibrium thermodynamic principles governing this separation are presently unknown. We develop a theoretical framework based on the transition state theory combined with the conventional Prandtl-Tomlinson model, allowing to set explicit expressions for evaluating the heat dissipation and internal energy change produced during the frictional stick-slip motion of a tip of a typical friction force microscope (FFM). We use the formalism to quantify the heat dissipation for a range of parameters relevant to materials in practical applications of nanoscale friction.

Stochastic thermodynamics of nanoscale friction

“…( 9) and ( 10) are satisfied. These definitions are consistent with their ensemble-averaged equivalents [4,23]. Given the definitions above we observe that Eq.…”

“…(3). This assumption is justifiable for over-damped systems when the thermally activated transitions between distant states are expected to be statistically rare [23]. Finally, note that in the limit of high energy barriers and large damping, the present master equation approach becomes equivalent to the frequently used stochastic Langevin dynamics, and is often adopted for studying the thermally activated processes in a typical FFM experiment for the sake of computational convenience [42].…”

“…However, the atomistic modelling techniques are often practically limited by their computational scalability to mesoscopic length and time-scales of a typical FFM experiment, and instead adopted are often non-linear coarse-grained approaches based on the Prandtl-Tomlinson [18,19] or Frenkel-Kontrova [20] models. This 'mesoscopic' level of modelling is therefore typically adopted for studying the thermodynamics aspects of nanoscale friction [21][22][23].…”

“…In this work, we considered the classical Prandtl-Tomlinson model combined with Kramers transition state theory of thermal fluctuations [24] as a model of single asperity friction. We quantified the energy barrier distributions, and assembled the master-equation governing the thermally activated dynamics using the standard approach [21][22][23][25][26][27]. Solving the thermally activated dynamics allowed evaluating the time-dependent probability distributions and formulating the expressions for fluctuating entropy based on ST [4], and express the first thermodynamic law in terms of the fluctuating work and heat produced during the frictional sliding [28].…”

Thermodynamics of interacting magnetic nanoparticles

“…The developed formalism can be applied in other application settings such as, for example, in magnetic recording, which often relies on similar modelling techniques [38,39], or for evaluating the entropy changes in MP systems for magnetic refrigeration [2]. It can also be applied naturally to study problems outside of particulate magnetism such as, for example, to model nanoscale friction [40] or biological systems [20].…”