Tribology is concerned with the influence of\nmechanically applied forces on interfacial phenomena that\naccompany and control sliding. A wide range of models\nhas been developed to describe these phenomena, which\ninclude frictional dissipation, wear and tribochemical reactions.\nThis paper shows that these apparently disparate\nmodels are based on the same fundamental concept that an\nexternally applied force accelerates the rate of thermal\ntransition of atoms or molecules across energy barriers\npresent in solid and liquid materials, thereby promoting\nflow, slip or bond cleavage. Such ââ?¬Ë?ââ?¬Ë?stress-assistedââ?¬â?¢Ã¢â?¬â?¢ effects\nand the associated thermal activation concepts were developed\nindependently and in different forms by Prandtl (Z\nAngew Math Mech 8:85, 1928) and Eyring (J Chem Phys\n4(4):283ââ?¬â??291, 1936). These two works have underpinned\nsubsequent theories of dry friction, boundary lubrication,\nEHD rheology, tribochemistry and nanoscale wear modelling.\nThis paper first reviews the historical development\nof the concepts, focussing in particular on the models of\nPrandtl and Eyring and how they have subsequently been\nused and adapted by others. The two approaches are then\ncompared and contrasted, noting that although superficially\nsimilar, they contain quite different assumptions and constraints.\nFirst, the Prandtl model assumes that the force is\nexerted through a compliant spring, while constant force\nsliding is assumed by Eyring. Second, different approximations\nare made in the two models to describe the\nchange in energy barrier with external force. Prandtl explores\nthe asymptotic behaviour of the energy barrier as the\napplied force become sufficiently high to reduce it to zero,\nwhile Eyring assumes that the energy barrier is reduced by\nan amount equal to the external work carried out on the\nsystem. The theoretical underpinnings of these differences\nare discussed along with the implications of compliant\ncoupling and constant force sliding on the velocity and\ntemperature dependence of the friction forces for the two\nmodels.
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