Building the bridge from atomistic to stochastic modelling of nanoscale friction phenomena

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Direct molecular dynamic simulation of a nanoscale object involves numerical integration of the equations of motion for all its atoms. This approach is exact, but it has severe size and time-scale limitations. Stochastic modelling overcomes these limitations by focusing on only a small subset of the relevant degrees of freedom, termed "the system". The remaining large number of the irrelevant ones, denoted as "the heat bath", are not simulated explicitly, but taken into account by (i) renormalizing the forces acting on and between the system coordinates, (ii) including dissipative forces describing the energy transfer from the system into the heat bath, and (iii) introducing random forces describing the effect of thermal motion of the heat-bath atoms on the system.  ***Stochastic modelling requires approximative assumptions, and thus it is not always clear how to correctly incorporate the heat-bath effects (i)-(iii) into the system's equations of motion. The goal of this program is to work out the rules allowing one to obtain the ingredients (i)-(iii) from the knowledge of the forces acting between the system and the bath atoms. The second goal is to apply these rules to study the dynamics of nanoscale objects, such as single atoms, atomic clusters, and nanoparticles in contact with a solid surface.***An important nanoscale object is the tip of an atomic force microscope, a standard experimental tool used for surface analysis. Its application particularly pertinent to this program is the study of friction phenomena at the nanoscale. While macroscopic friction results from complex interaction between many asperities on the two surfaces in contact, the newly emerging research field of nanotribology is focused on the interaction of a single such asperity - the atomic force microscope tip - with an atomically flat surface. The common feature of macro- and nanoscale friction is that both exhibit the phenomenon of aging, that is, gradual increase of friction force with contact duration. While aging in the macroscopic friction has been investigated for several decades, its nanoscale counterpart was first established experimentally less than a decade ago. ***Nanoscale friction has been studied theoretically using stochastic modelling, but the majority of such models do not consider the possibility of contact aging. The further goal of the present program is to improve the existing stochastic models of nanoscale friction by including the effect of aging of the tip-substrate contact.***The*anticipated outcome of this program is improvement of our understanding of the laws of nature acting at the nanoscale, and development of efficient numerical*tools to simulate the dynamics of nanoscale objects on solid surfaces. These tools should find a number of scientific and technological applications in such fields as manipulation of nanoparticles, investigation of their interactions, and control of friction.**