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Friction 7(1): 2–17 (2019) also be considered from the metal (mainly as donors) side. The donor number (DN) values reflect the enthalpy associated with the coordination reaction between the metal cations and repeat unit of polymers [50]. Then, the fitting relation between the charge density q and DN values is [36] log(q)0.09DN0.36 (with R2 0.80) (10) Equations (9) and (10) follow a similar trend for describing the ion transfer in metal–polymer cases, and it is a natural analogy, because pKb and DN parameters are related to the ability of the chemical site to donate a pair of electrons to either a proton center or a metal cation center, respectively, as illustrated in Fig. 4. 2.4 (Nano‐) material Material transfer to cause charging is believed to occur when vigorous rubbing or pressing is introduced [29, 51]. For example, when some polymers are rubbed with friction, an exchange of deeper layer materials occurs [52]. (This helps explain why even the same polymers can be charged by tribo‐contacts; it is because even identical polymers will have different material compositions at each depth, which account for the same material charge transfer [29].) Moreover, material transfer is possible if dynamical changes in the surfaces and tribological environments exist, because materials will tend toward a lower potential energy state and these dynamical changes can lead to the potential energy minimum shifts [53, 54]. For example, one dynamical change (in quasi‐ static form) can be strain and its corresponding potential energy form (near the potential energy local maximum, i.e., the local energy barrier at interface) is E f()213 (11) 7 to be below 0, the local potential energy barrier will be demolished and the materials (originally in the nearest locations of minimum potential energy and hindered by this energy barrier) will begin to migrate to the new energy‐stable developed by this dynamical tribological environment change, as shown in Fig. 5 [53]. This understanding from catastrophe theories can be extended to many other factors, including tem‐ perature, density, and normal loads, for a more complete discussion of (nano‐)materials’ transfer in the triboelectric process. This is because the charging process initiated by material transfer can be viewed as a balance or nonequilibrium between the driving force of friction and the energy barrier erected in accordance with various physical properties. After the material transfer prerequisite from energy consideration is fulfilled, more recently, studies have been conducted to investigate the material removal rate both physically and chemically [55,56]. The material wear rate is physically deduced and the load stress is calculated to dominate in the wear process, as follows [55, 57]: where is the actual strain and is the strain‐ related parameter (which has a relation f1()). When evolves with the increased strain and changes Fig. 4 pKb and DN parameters in ion transfer relationships. http://friction.tsinghuajournals.com∣www.Springer.com/journal/40544 | Friction expG expU the term and physical σ V 0 act act K B T 0 V K B T (12) exp N act KBT where (in the unit of a.u./s) is the actual wear rate considering both chemical wear nature (shown by act exp U ) load stress (shown by the term exp N act ), and is the 0 KBT KBT p 3 Fig. 5 Schematic of changes in the potential energy landscape with strain.PDF Image | Fundamental theories basic principles of triboelectric effect
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