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24 Results load resistance R given by U2/R is independent of the frequency. For low temper- atures Eq. (2.30) becomes P ≈ N2q2f/(2CA) independent of temperature, and for high temperatures T Eq. (2.30) reduces to N2q2f E 2 P ≈ 2CA 2kBT . (2.31) We have fitted our model of the power density or voltage of a triboelectric nano- generator made of Al-PTFE-Cu to data from Wen et al. [35], Su et al. [34] and Lu et al. [36]. For the three curves we obtained three least square fits for a separation energy corresponding to temperatures of 374 K, 451 K and 269 K, respectively. The average temperature is 365 K. All three fitted values above are in the interval 365±96 K. Ar Kr Xe Au(111) substrate Ag(111) substrate Cu(111) substrate 0.38±0.03 eV 0.40±0.03 eV 0.42±0.03 eV 0.42±0.02 eV 0.46±0.02 eV 0.49±0.03 eV 0.53±0.03 eV 0.59±0.03 eV 0.62±0.03 eV Table 2.1: Average of measured work function differences for Ar, Kr and Xe atoms adsorbed to substrates of Au, Ag and Cu from Hu ̈cksta ̈dt et al. [39]. The work function difference is for a mono layer of adsorbate compared to a clean substrate surface. Table 2.1 shows work function differences for three kinds of nobel gases adsorbed to three different nobel metals. We see that for example the difference in work func- tion for an Ar atom when it sits on an Au surface, compared to when it sits on an Ag surface, is 20 meV corresponding to a temperature of 232 K. This energy should correspond to the separation energy E. The energy difference between different sub- strates for an adsorbed atom seems then to be of the right magnitude to support an ion Schottky model, see legends of Figure 2.5. Can the Schottky model be applied to all nanogenerators containing non-metals so that ion transfer may be the dominating source of triboelectric charging? No. For a generator with one sheet covered with TiO2-nanotubes the reverse temperature behavior was found with increasing charging with temperature [34]. What about another new charging model which assumes electron transfer be- tween potential wells of surface atoms proposed by Xu et al. [24]? This paper was published at about the same time as our ion Schottky model was published. This model by Xu et al. should, however, be equivalent to our model because it should not matter energy-wise if a whole ion moves to the other surface or if it is just its charge that moves to an uncharged atom on the other surface. At least not as long as the electron is transfered to an atom of the same kind as the one it comes from. We believe that the temperature dependence should be the same. It is possible that a high frequency experiment could distinguish between the models because electrons move more easily than ions. In this section we have described a two-level ion Schottky model for the triboelec- tric charging of a nanogenerator. The energy difference for ions on the two surfacesPDF Image | Nanomechanics Quantum Size Effects, Contacts, and Triboelectricity
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