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12 Friction 7(1): 2–17 (2019) where xiδ depicts the number fraction of particles in size i (iL,S ) to be charged in state ( positively, negatively). Using this model from binary viewpoint, 1 is proved to be valid, and the trend that large particles tend to charge positively (e.g., x is large and dominates) and small particles L tend to charge negatively can then be physically understood and statistically solved. Meanwhile, the size effect can also show up in how the particle triboelectrification can respond to the environment they are in. For example, under an external electric field, for a spherical dust grain of radius r and a homogenous electric field E0 perpendicular to the surface, the induced charge is expressed as Q4π αEr2 (20) 00 where α is the electric field‐related factor showing the geometry effect from the field and r denotes the particle radius. This model is significant because when particles are electrified, any single particle is placed in a series of linearly addable particle‐introduced electric fields [24]. 4.3 Load stress It has long been proved that stress can produce ions [72, 73] and electrons [74] and greatly affect their behavior [14], because the load stress is where friction can be introduced. For instance, different loads can involve different charging mechanisms: when the frictional contact is gentle and brief, (nano‐)material transfer can be precluded [51]. More theoretically, the energy barrier analyses and wear rate correlation from Eqs. (11) and (12) all demonstrate the possibility that the triboelectric effect is highly load‐dependent [34]. Though the exact depiction for the triboelectric effect from load stress behavior is incomplete, many applications have already utilized this important factor to compromise or take advantage of the triboelectric process. TENGs designed with a triple cantilever is used to harvest the vibration energy, which is operating under the variable normal load condition [75]. Especially when the electromechanical phenomena are involved (e.g., the coupling between the piezoelectric effect and charge separation), the understanding of the role of the normal load is essential [76–78]. Since more load stress effects are analyzed for a pure mechanical tribological process for now, more notions into the load dependence in the triboelectric process would be beneficial to understanding the intrinsic roles of normal force as the initializing potential. 4.4 Humidity and acidity Humidity and acidity have obvious significance owing to their strong effects on surface electrical conductivity and capacitance configuration (for example, the charge leakage required to achieve a dynamical balance in the triboelectric effect will be affected [1]; in real applications, salts including quaternary ammonium [29] can then be used as the charge control agent) [79, 80]. The acid‐alkaline theory [18, 27] is both a supple‐ mentary and an extensive theory to understand the triboelectric effect influenced by the environment. Here, the acid and base are in the scope of Lewis classification [2], and works significantly for insulator tribo‐pairs. As stated in Section 1.3, the equilibrium constant for the dissociation of a proton ( pKb ) of insulators (especially polymers) is found to determine the position in the triboelectric series. Humidity and acidity are similar because the ion/polarity generation and chemical reactions play a clear role [2, 15]. For instance, the process linking humidity and acidity can work in the following way: when a hydroscopic surface (or a surface with hydroscopic groups) is placed in the humid environment before/during tribo‐contact, more water or salt will be attracted to form a conducting layer (in reality, it might still not be conductive), which may help charge leakage, and thus, influence the charging process [1]. This is illustratively shown in Fig. 10. However, note The schematic illustration about the influence of humidity onto organic insulator surface during triboelectric process [2, 84]. Fig. 10 | https://mc03.manuscriptcentral.com/frictionPDF Image | Fundamental theories basic principles of triboelectric effect
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