DESCRIPTION OF THE KINETICS OF A MODEL TRIBOPOLYMERIZATION PROCESS

A three-dimensional system of ordinary differential equations of first order has been proposed to describe the kinetics of a model tribopoly merization process for which a linear coupling of the material surface dislocation density and polyreaction fields is assumed. Another impor tant physical motivation on which the model is based stresses the pred ominant role of a highly rough surface under friction as a catalyst in the polyreaction process. In consequence, the fractal-like chemical r eaction concept has been applied. It is demonstrated that the system p roposed is suitable for describing a variety of tribopolymerization pr ocesses and possesses non-trivial time-dependent behaviour even in som e limiting analytical cases studied. As a specific result, a nonlinear equation generalizing the Vogel-Fulcher temperature-dependence of the maximum time scale for the polyreaction caused by friction, character istic of the selective transfer during friction process, has been reco vered. Some comparison with an approach made earlier (G.P. Shpenkov, F riction Surface Phenomena (Elsevier, Amsterdam, 1995) pp. 165-172 and Ref. [239] therein) has been presented as well. Certain basic trends o f modelling and experiment are in good agreement.