Constant velocity sliding measurements

One commonly measures of the friction force at a constant velocity using the friction loop. The tip is forced to slide in the lateral direction by the cantilever. The friction force makes the cantilever twist by an angle that is proportional to the friction force. When the movement is reversed and the tip slides in the opposite direction, the cantilever bends by the same but opposite angle. This friction loop corresponds to the difference of the lateral force signal between the back and forth scans. Therefore, the friction force equals half the amplitude of the friction loop. 

We chose a suitable frequency range inside which the measurements are not affected by the mechanical coupling of the system. We checked the validity of our modulation approach by comparing two fiiction coefficients obtained by two different sliding drives at constant velocity. 

The often-cited Amontons law [101. 102] describes friction in tenns of a friction coefiBcient, which is, a priori, a material constant, independent of contact area or dynamic parameters, such as sliding velocity, temperature or load. We know today that all of these parameters can have a significant influence on the magnitude of the measured friction force, especially in thin-film and boundary-lubricated systems. 

Here, V is the sliding velocity in cm/s, P is the pressure in MPa, and T is the interface temperature in degrees Celsius. The constants in the equation have units and these units have been omitted for clarity. At temperatures less than about 110 °C, the stress at the interface is due to a frictional force mechanism. At temperatures higher than 110 °C, the forces are from a viscous mechanism. The friction coefficients provided by Eq. 5.31 have the proper trends. Coefficients derived from the equation, however, need to be used with care because of its empirical nature and the difficulties in measuring frictional data. 

An atomic force microscope is used to stuviscoelastic state at the temperature of experiment. It is shown that, during the preliminary phase of friction and before the transition to the sliding regime, the contact area remains nearly constant. This allows for a determination of the relaxation and of the complex modulus of the material. A good agreement is found between moduli measured by this method and macroscopically determined ones. The position of the transition is seen to scale with the characteristic size of the contact area but it does not depend on the displacement velocity. Finally, a transient stick-slip regime is observed before the sliding steady state is reached. 

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