## 5 Conclusions  
In this study, TiO\({}_{2}\) nanoparticles of various crystal forms were doped into a polyester film and frictional charging experiments between the films and iron particle powder were subsequently conducted--measurements of the film surface potential versus time and the saturated surface potential versus relative humidity. The results revealed that TiO\({}_{2}\)-nanoparticle doping (1) changes the film sensitivity to ambient humidity (i.e., changes the humidity dependence) and (2) stabilizes the film charge (i.e., reduces the variation in the charge amount). With regard to Finding (1), the humidity dependence was reduced with rutile, rutile-anatase mixed crystal (P25), and amorphous-dominated TiO\({}_{2}\) doping and increased with anatase TiO\({}_{2}\). Finding (1) was successfully explained by combining our previously proposed CWP model with previous reports showing the dissociative adsorption and associative/molecular adsorption of water on TiO\({}_{2}\). Finding (2) may be explained by assuming that the electrons transferred from the iron powder to the film are trapped on the TiO\({}_{2}\) nanoparticles during contact, whereby the trapping reduces the charge back flow from the film to the iron powder during separation. The variation was significantly reduced, especially when rutile and P25 TiO\({}_{2}\) nanoparticles were used. This was interpreted, with reference to the previous reports, as the electron traps in the rutile and P25 TiO\({}_{2}\) nanoparticles being deeper than those in anatase and amorphous TiO\({}_{2}\), resulting in a more stabilized charge in the former case and more reduced charge back flow during separation. The importance and novelty of this study lies in the fact that we were able to propose the first mechanism for the stabilization of tribocharges on polymer films based on Findings (1) and (2) above. TiO\({}_{2}\) nanoparticles are used as an external additive for electrophographic toners and are known to empirically reduce the variation in the amount of toner charge. The results of this study provide the academic background to the above rule of thumb and should provide useful guidelines for the doping amount and crystal form for future toner design. Moreover, this study significantly contributes to the industrial electrostatic field (electrophotographic toners [65], electrostatic hazard assessment [66], electret air filters [67], etc. ), as it demonstrates that TiO\({}_{2}\) doping influences the humidity dependence of the host polymers and that the selection of the doping amount and the crystal form of TiO\({}_{2}\) is important for reducing this humidity dependence. Figure 11: Water content in the reference (gray bars) and charged (light-blue bars) samples for the PES single film and PES films doped with 10 wt% TiO\({}_{2}\) nanoparticles at 40–50%RH. **Supplementary Materials:** The following are available online at [[https://www.mdpi.com/article/10.3390/app13031468/s1](https://www.mdpi.com/article/10.3390/app13031468/s1)]([https://www.mdpi.com/article/10.3390/app13031468/s1](https://www.mdpi.com/article/10.3390/app13031468/s1)), Figure S1: TEM images of the TiO\({}_{2}\) nanoparticles; Figure S2: X-ray diffraction patterns of the TiO\({}_{2}\) nanoparticles; Figure S3: SEM image of an iron particle; Table S1: Relative permittivity of the TiO\({}_{2}\)-doped PES films; Table S2: Electrical resistivity of the TiO\({}_{2}\)-doped PES films. **Author Contributions:** Y.T. : investigation and writing; K.A. : investigation and data curation; S.T. : validation and writing--review and editing; K.H. : supervision, conceptualization, writing, reviewing, editing, funding acquisition, and project administration. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable. The authors confirm that the data supporting the findings of this study are available within the article [and/or] its Supplementary Materials.