Evaluation of self-affine surfaces and their implication for frictional dynamics as illustrated with a Rouse material

We present a theory of hysteresis friction of sliding bulk rubber networks using the dynamic Rouse model for the rubber-glass transition region. The h ard substrate is described by a self-affine rough surface that is a good re presentative for real surfaces having asperities within different length sc ales of different orders of magnitude. We find a general solution of the fr iction coefficient as a function of sliding velocity and typical surface pa rameters (e.g, surface fractal dimension, correlation lengths of surface pr ofile). Further, we show the correlation with the viscoelastic loss modulus of the bulk rubber and the applicability of the Williams-Landel-Ferry tran sform to the velocity and temperature dependence of the frictional force as found experimentally. We demonstrate how the succesive inclusion of relaxa tion Rouse modes p = 1,2, 3,... into the final expression for the frictiona l force leads to a superposition of the contributions of the different mode s and, as a consequence, to a broad, bell-shaped frictional curve as observ ed in the pioneering experiments of Grosch. We show how the theory simplifi es for the special case of a Rouse slider interacting with a Brownian surfa ce. (C) 2000 Elsevier Science Ltd. All rights reserved.