Prediction of adhesion between randomly rough surfaces by order statistics

Understanding the adhesion between rough surfaces has practical significance. We derive a simple analytical formula on the basis of the classic order statistics to predict the interfacial binding energy between rough surfaces. It is found that the strong length scale dependence of adhesion ranging from the nominal size scale down to any artificially defined cutoff length scale in constructing a rough profile can be considered as a purely statistic performance resulted from different samplings and can be further described by a single parameter called sampling number. We compare the formula predictions with the experimental results and demonstrate that our simple formula holds its accuracy especially for the Derjaguin-Muller-Toporov adhesion case.