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ABSTRACT
Recent numerical investigation on self-affine Gaussian surfaces by Pastewka and Robbins (PR) has led to a criterion for “stickiness” based on when the slope of the (repulsive) area–load relationship appears to become vertical in numerical simulations at a ratio of contact area to nominal one (rather arbitrarily) fixed to 1%. Since pull-off and slope of the area–load are two faces of the same medal, a simple check of the results in terms of pull-off shows that PR have many more data which fail their criterion than the ones that satisfy it, and this is evident even in their own figures. As a small improvement, a proposal to modify the criterion to better fit their own data is put forward. However, the pull-off decay seems rather exponential so that it is unclear if their slope criterion really corresponds to a “thermodynamic” limit, and consequently their conclusion that stickiness should depend only on slopes and curvature may be an artifact of their assumption of defining a secant at 1% contact area ratio and of using truncated potentials, rather than a true important property of rough contact. Both the PR criterion and the present modified one imply that for fractal dimension , stickiness should increase with resolution, so the problem of truncation of the spectrum seems ill-defined: in fact, PR define rigid self-affine surfaces with rather smooth and well-defined slopes, and not a realistic atomic roughness as first studied by Luan and Robbins.
Funding
A. P. is thankful to the DFG (German Research Foundation) for funding the project HO 3852/11-1.
Notes
1 For an isotropic surface, the sum of two orthogonal components of the gradient should be summed and being uncorrelated, this gives .
2 Although there is clear indication that the symbols have been inverted.