Monte Carlo Simulations for Tomlinson Sliding Models for Non-Sinusoidal Periodic Potentials

It is shown that the velocity dependence of a tungsten tip sliding against a mica surface cannot be fit to a semi-empirical analytical solution of the Tomlinson/Prandtl model using a simple sinusoidal sliding potential. This could be due to invalid assumptions in the model itself. However, if it is assumed that the periodic sliding potential is much sharper than a simple sinusoid, quantitative agreement between the experimental velocity dependence of the sliding force and theory is obtained using a single variable parameter, the height of the surface potential. Sliding is modeled in this case using Monte Carlo theory, and it is found that the height of the potential varies linearly with the normal load.