## 1 Introduction  
Titanium dioxide (TiO\({}_{2}\)) nanoparticles are multifunctional materials used in a wide range of applications, including white pigments [1], UV-shielding materials [2], photo-catalysts [3, 4, 5], self-cleaning materials [6], dye-sensitized solar cells [7], electrochromic displays [8, 9], electronic papers [10], and charge control agents for electrophotographic toners [11, 12]. Thus, TiO\({}_{2}\), along with SiO\({}_{2}\), nanoparticles are among the most globally mass-produced nanomaterials [13]. TiO\({}_{2}\) nanoparticles are mostly used under a moisture atmosphere, and, thus, the interactions between TiO\({}_{2}\) and water play a crucial role in the above-mentioned applications. Consequently, these interactions have been studied extensively, mainly through theoretical/computational methods [14, 15]. In such studies, anatase- and rutile-type crystals have been the primary research focus and it has been shown that the interactions depend on the crystal form and face of TiO\({}_{2}\).  
On the other hand, titanium dioxide nanoparticles that are unmodified or surface-modified with organic substances have been externally added to toners used in electrophotography as charge control agents [11, 12], which contribute toward reducing toner aggregation, flowability fluctuations, and charge fluctuations [16, 17]. The reduction effects of the first two phenomena have been clearly attributed to surface modifiers. In contrast, few studies have reported on how TiO\({}_{2}\) contributes to charge stabilization, despite this being a crucial research issue. Hence, if the mechanism of this TiO\({}_{2}\)-induced charge stabilization can be clarified, it will contribute not only to toner design in the huge market for electrophotographic toner but also to our understanding of frictional charging phenomena for insulating and semiconducting materials [18; 19; 20], for which no consensus has been reached.  
We have been conducting frictional charging experiments between insulating polymer films and iron powder beads (spherical iron particles with an average diameter of 80 \(\upmu\)m) to investigate the effect of moisture (humidity) in the ambient atmosphere on the charging of polymer films [21; 22; 23; 24; 25; 26; 27]. These studies have shown that ambient moisture is actively involved in the charging behavior of the films and that moisture-induced charging has an equal or greater effect than the inherent charging of the film (proposal of the charged-water penetration (CWP) model; see Section 2 for more detail).  
In this study, we hypothesized that the CWP model can be used to quantify the above-mentioned effect of TiO\({}_{2}\) on toner charging and to better understand the relationship between the physical properties of TiO\({}_{2}\) and the charging amount. Specifically, anatase, rutile, anatase-rutile mixed crystal, and amorphous TiO\({}_{2}\) nanoparticles were dispersed in polyester films and their frictional electrification experiments were conducted in contact with iron particle powder. The results showed that the effects of humidity on the charging behavior of each film are markedly different from each other, and this can be explained by the difference in the water adsorption forms on the major crystal faces of TiO\({}_{2}\). In addition, an unexpected synergistic charging effect was found when anatase-rutile mixed TiO\({}_{2}\) was used, which is also reported herein along with the above results. The results of this study have led to the proposal of the first mechanism for the stabilization of tribocharges by titanium dioxide nanoparticles, which will contribute to the engineering and science of triboelectrification.