Hysteresis, and Energy Dissipation

Earlier we used a relatively simple model composed of a slider and substrate to demonstrate how mechanical instabilities lead to energy dissipation and friction. However, realistic contacts are much more complex. For instance, real contacts can rarely be described as one-dimensional and almost always contain some molecules that act as impurities. Understanding the frictional aspects of these systems will require a consideration of the role instabilities play in systems that are more complex than the PT model. In this section, we discuss studies that investigate instabilities in more realistic systems. 

The role of instabilities involving confined impurity atoms has been investigated by Mtiser using a model in which two one-dimensional (1-D) or 2-D surfaces were separated by a very low concentration of confined atoms and slid past one another.25 The motion of the confined atoms was simulated with Langevin dynamics where the interactions between these atoms were neglected and the atom-wall interactions were described by 

Simulations of incommensurate surfaces showed a similar dependence on Vi, with first-order instabilities occurring if Vi Vj, where Vj is some positive, critical value that depends on the degree of mismatch between the lattice constants of the top and bottom surfaces. This process leads to nonvanishing Fk as l o goes to zero. In the case where Vi V, the atoms are dragged with the wall that exerts the maximum lateral force. It, in turn, leads to friction that scales linearly with the sliding velocity. As a result, the friction force will go to zero with vq. 

The effect of dimensionality was also considered in that study. It was found that systems with commensurate 2-D walls yield results that are similar to the 1-D case because the interference between Vt and V[, persists. This situation is no longer true for the incommensurate case, where the adsorbed atoms can circumnavigate the points of maximum lateral force, which permits first-order instabilities regardless of the nature of the higher order harmonics in the wall-atom potential. Thus, one would expect friction to remain finite as Vq 

First-order instabilities may not only involve the translational motion of atoms confined within contacts, but they may also involve chemical reactions within the confined fluid itself. This has been demonstrated recently in first-principles studies of zinc phosphates, which are found in protective films formed in automobile engines.19,83 Here, we focus on simulations of systems containing phosphate molecules in which pressure-induced chemical reactions lead to hysteresis and energy dissipation. The reactions involving zinc phosphates are discussed below along with other tribochemical reactions. 

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