A modified form of Pastewka-Robbins criterion for adhesion

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 (Formula presented.), 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.