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4 Friction Table 2 Surface charge density after triboelectric charge transfer. expressed as S ak4π0saa f(F,F 0 Na f atom (5) Material pair Chromium-Chromium Chromium-Steel Chromium-Gold Metal-SiO2 (quartz) Metal-NaCl Metal-Nylon Metal-PTFE Metal-Polyimide Charge density (C/m2) 2.02 × 10–8 3.37 × 10–8 6.73 × 10–8 ~10–5 5.0 × 10–4 ~10–3 ~10–4–10–3 3.0 × 10–3 ,,T) and consume some of the energy [6, 12]. 2.2 Electron When electrons participate as the charging media in the triboelectric process, the work function Wsurface is an important factor because it describes the minimum thermodynamic work (i.e., energy) needed to remove one electron from solid to a point in the vacuum, as shown in Eq. (4) [30, 31]. Wsurface eF (4) where F indicates the Fermi level of electrons in solids and indicates the electrostatic potential in the vacuum close to the surface ( e shows negative charge of the electron). Nowadays, work functions can be measured with photoemission spectroscopy and the Kevin–Zisman method [32, 33]. Because fermi level will be introduced for the work function calculation, metals will be considered as important surface materials if the electron transfer dominates [31, 34]. Note that an (equivalent) work function can be meaningful for insulators including polymers such as polytetrafluoroethylene (PTFE) and polycarbonate when they serve as a tribosurface [31, 35] (though some studies have considered the electron transfer as trivial for the charging process, due to the mismatch of the correlation between the insulator ionization potentials and the charging behavior [36]). During the process, the driving force of the electron transfer in the triboelectric effect is proven to be a tribologically introduced phonon–electron interaction [30]. The primitive relation of coupling energy between the tribological heat and the transferred electron is where S is the entropy change/energy state change introduced by the friction contact and can be a good indicator to correlate with the surface density of states, Ds ; 0 is the lattice natural well-defined frequency, which demonstrates the phonon energy levels; a is the average lattice parameter; and k is change in the reciprocal lattice parameter corre- sponding to the lattice momentum. f(F ,F ,,T) f atom denotes the influence from external factors including strain and temperature T. According to the experiments conducted with metal–insulator tribo-pairs, the surface density charge can be correlated with the work function using Poisson equation, as follows: M I (6) where is the leading factor, whose value in metal– dielectric cases is 1.77 1013 ; is the dielectric constant for insultors; and M and I demonstrate the work function for metal and insulator, respectively. The Poisson equation is dynamically verified from the fact that the triboelectric effect is a process in which charging and discharging are continuously coupled, and this relation is widely used in the particle triboelectric process simulation and analyses [2, 37]. Following the thoughts of energy levels (including work function), for metal–dielectric–metal tribo-pairs (e.g., alkanethiol monolayer-coated Au(111 on Au) [38]), the main role of friction in electron transfer is to generate electron–hole pairs in mid-gap states near the Fermi surface (which explains why the work function is important) in normally insulating materials if they are in monolayer shape [38, 39]. Given the dielectric electronic parameters, the tribo-current (i.e., the conductance of tunneling electrons transferred) can be calculated as follows [38]: G k exp(1.025 Eg z) (7) 2 ft | https://mc03.manuscriptcentral.com/frictionPDF Image | Fundamental theories and basic principles of triboelectric
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