Abstract
Friction is a complicated phenomenon involving nonlinear dynamics at different length and time scales. Understanding its microscopic origin requires methods for measuring force on nanometer-scale asperities sliding at velocities reaching centimetres per second. Despite enormous advances in experimental technique, this combination of small length scale and high velocity remain elusive. We present a technique for rapidly measuring the frictional forces on a single asperity over a velocity range from zero to several centimetres per second. At each image pixel we obtain the velocity dependence of both conservative and dissipative forces, revealing the transition from stick-slip to smooth sliding friction. We explain measurements on graphite using a modified Prandtl–Tomlinson model, including the damped elastic deformation of the asperity. With its improved force sensitivity and small sliding amplitude, our method enables rapid and detailed surface mapping of the velocity dependence of frictional forces with less than 10 nm spatial resolution.
Highlights
Friction is a complicated phenomenon involving nonlinear dynamics at different length and time scales
Traditional nanoscale friction experiments use an atomic force microscope (AFM), where the frictional force on the tip or colloidal probe is measured while sliding on a surface at constant velocity[3,4,5,6,7]
Friction induces a lateral force on the tip, resulting in a twist f around the major axis of the AFM cantilever, which is detected by optical beam deflection
Summary
Friction is a complicated phenomenon involving nonlinear dynamics at different length and time scales. Understanding its microscopic origin requires methods for measuring force on nanometer-scale asperities sliding at velocities reaching centimetres per second. Owing to the enhanced force sensitivity of the high Q resonance, a good AFM can see the thermal random torque acting on the cantilever, which is resolved near resonance as twisting Brownian motion noise, above the voltage noise floor of the detector. In this case, force measurement is at the thermal limit of sensitivity, which for the stiff 2 MHz cantilever gives Fmin 1⁄4 0.88 pN in the same 1 ms measurement time (see Methods). In contrast to the quasi-static method, dynamic force quadratures do not give the instantaneous lateral force on the tip, but rather the conservative force FI and dissipative force FQ, integrated over one single oscillation cycle of the tip with amplitude A (see Methods)
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