Modeling of kinetic and static friction between an elastically bent nanowire and a flat surface
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Boris Polyakov Institute of Physics, University of Tartu, Tartu 51014, Estonia; and Institute of Solid State Physics, University of Latvia, LV-1063, Riga, Latvia
Andrejs Petruhins Institute of Solid State Physics, University of Latvia, LV-1063, Riga, Latvia
Sergei Vlassov, Rünno Lõhmus, and Ilmar Kink Institute of Physics, University of Tartu, Tartu 51014, Estonia
Alexey E. Romanov Institute of Physics, University of Tartu, Tartu 51014, Estonia; and Ioffe Physical Technical Institute, Russian Academy of Sciences, 194021 St. Petersburg, Russia (Received 27 June 2011; accepted 19 September 2011)
Friction forces for a nanowire (NW) elastically bent on flat substrate were investigated both theoretically and experimentally. Models based on elastic beam theory were proposed considering balance of external, frictional, and elastic forces along the NW. The distributed friction force was determined for two cases: (i) the NW was uniformly dragged at its midpoint and bent by kinetic friction forces and (ii) the NW was held in a bent state by static friction forces. The first case considers a uniform distribution of kinetic friction along the NW and enables the measurement of the friction force from the elastically deformed NW profile. The second case exploits the interplay between static friction and elastic forces inside the NW to find the distributed friction force. An original method for the measurement of frictional forces in both cases while maintaining total force and momentum equilibrium was introduced and demonstrated for ZnO NWs on a Si wafer. Averaged kinetic and static friction forces were compared for the same individual NW.
I. INTRODUCTION
Semiconducting crystalline nanowires (NWs) comprise a prospective class of materials for future electronic and nanoelectromechanical applications due to their superior electronic, mechanical, and piezoresistive properties.1–8 Considering that fabrication of NW-based devices requires precise control over positioning and subsequent behavior of the NWs, it is evident that deeper understanding of NW– surface bilateral tribology mechanisms is crucial from both fundamental and practical points of view. Several methods were used to investigate NW–substrate interaction.9–11 The most popular method consists in manipulation of NWs or nanotubes by atomic force microscope (AFM) tip, e.g., Falvo et al.12 manipulated multiwall carbon nanotubes (CNTs) with AFM on a graphite substrate with simultaneous lateral force measurement. AFM provides a high precision of force control; however, AFM measurements are time-consuming due to the need of imaging after each manipulation step. a)
Address all correspondence to this author. e-mail [email protected] DOI: 10.1557/jmr.2011.339 580
J. Mater. Res., Vol. 27, No. 3, Feb 14, 2012
A simple approach, which utilizes the bent shape of a NW on a substrate to estimate the NW–substrate friction, was proposed by Bordag et al.13 The profile of bent NW comes as a result of the interplay between elastic and friction forces. The modeled NW was assumed to form a circle
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