Wind-blown Sand Electrification Inspired Triboelectric Energy Harvesting Based on Homogeneous Inorganic Materials Contact: A Theoretical Study and Prediction

Triboelectric nanogenerator (TENG) based on contact electrification between heterogeneous materials has been widely studied. Inspired from wind-blown sand electrification, we design a novel kind of TENG based on size dependent electrification using homogeneous inorganic materials. Based on the asymmetric contact theory between homogeneous material surfaces, a calculation of surface charge density has been carried out. Furthermore, the theoretical output of homogeneous material based TENG has been simulated. Therefore, this work may pave the way of fabricating TENG without the limitation of static sequence.

PVDF and nylon 23 , etc. With the limitation of static sequence, almost either of these two kinds of materials is polymer. Contact electrification occurs not only between heterogeneous but also homogeneous materials, which has been demonstrated by several experimental works, such as silica-silica [24][25][26][27][28][29] , aluminum oxide-aluminum oxide 25 , polymer-polymer [30][31][32] . Some homogeneous materials based TENGs also have promising performance 33 . Although polymer is always cheap, flexible and light, polymer based TENG is highly unfavorable to work in harsh environment such as desert, outer space and so on for its narrow working temperature area, fast aging and poor antiwear property 34 . Therefore, it is valuable to design and develop a new kind of TENG made with total inorganic materials like silica-silica to work in special environment.
For the electrification between identical materials, high energy trapped surface states theory proposed by Lowell and Truscutt 35 has been widely used to explain charge transfer during asymmetric rubbing 26,36,37 Based on high energy trapped states theory, particle-size-dependent charging, such as larger particles tends to be positively charged and smaller particles tends to be negatively charged, has been well explained 26,28,[36][37][38] . In the wind-blown sand granular system, mechanisms of size-dependent electrification between identical insulator particles have been widely studied 16,26,[36][37][38][39][40] , such as asymmetric contact between two particles with transfer of high-energy trapped electrons 37 or holes 26 (HETH). In our previous work, a contact charge model of high-energy trapped holes has been developed 26 and verified with experiments 24,26 for collision of homogeneous silica particles to predict the size-dependent contact electrification. From the experimental point view, silica film, made with earth abundant element oxygen and silicon, is chemical inertia and compatible with many semiconductor fabrication process like thermal oxidation 41 , magnetron sputtering 42 , sol-gel coating 43 , plasma enhanced chemical vapor deposition 44 , atom layer deposition 45 and so on. Meanwhile, the synthesis of silica nanoparticles is also widely studied for many years 46 . Therefore, inspired by these natural phenomenon and studies, using homogenous silica based materials with different sizes as the contact electrification layer to fabricate TENG for energy harvesting, is highly feasible, which may pave a new way to develop a novel kind of TENG working in harsh environment.
In this manuscript, we propose a new kind of TENG based on contact electrification between homogeneous silica materials with different sizes for harvesting energy. A comprehensive theoretical model is established to understand the effect of size dependent elasticity on the surface charge density of chemically identical silica nanoparticles under normal loads. To our best knowledge, it is the first time of calculating the surface charge density after single time contact electrification for TENG through theoretical simulation. Then, these results are applied to predict the output characteristics of the contact-mode and sliding-mode TENGs. We demonstrate that the maximum output power of TENG using earth abundant and identical silica as contact electrification layer will reach 12.98 μ W and 13.92 nW in contact and sliding model respectively. Indeed, the output will be greatly enhanced after multi-times contact electrification for more accumulated charges and higher surface charge density 30,47 Furthermore, the whole TENG is covered with homogenous materials (silica), which may broaden the application of TENG in harsh environment.

Results
Denote two neutrally-charged sphere particles, A and B with radii R A and R B respectively, in a normally elastic colliding process, as shown in Fig. 1(a). Based on high-energy trapped hole contact charging model 26 , the net Scientific RepoRts | 6:19912 | DOI: 10.1038/srep19912 charge transfer of particle Aequals to the number of high-energy trapped holes gained from particle B to particle A subtracting that lost from particle A to particle B, that is, where S i is the surface area of the contact part of sphere is the surface density of the high-energy trapped holes which is assumed to be identical for all particles initially 26,37 The net charge transfer , Hertzian normal contact of two spheres will become the contact between a sphere and a rigid flat, as shown in Fig. 1(b). If the contact surface radius R c is given, the surface area of the contact part S i of sphere i can be predicted, The net charge transfer of normal contact spheres is determined by the difference of surface areas of contact part , the contacted surface area S A will be greater than the contacted surface area S B , and then the net charge transfer ∆ > q 0 B and ∆ < q 0 A . If pre-collisional particles are both neutrally charged, the larger particle tends to be positively charged and the smaller particle tends to be negatively charged.
In order to achieve an optimal design of TENGs, the surface charge density is a vital parameter determining the output characteristics. When R A is fixed, Fig. 2 shows that the surface charge density σ A of the post-collisional particle A decreases with radius R B (or increases with /R 1 B ) and finally reaches its minimum value while ). When the radius R B tends to infinite, the particle-particle Hertzian contact can be treated as the particle-plane contact, and in such case the surface charge density tends to its extreme value.  Therefore the particle-plane Hertzian contact case will be an optimal design to obtain the maximum charge & power outputs for TENGs.
In the case of elastic particle-plane Hertzian contact, we predict the surface charge density σ A varying with the normal load P and the radius R A , as shown in Fig. 3. The absolute value of the surface charge density, σ A , increases with the normal load P increasing, but decreases with the increase of the radius R A . Materials reduced to submicron or/and nanoscale show different mechanical properties compared to what they show on macroscale. Wang et al. 48 pointed out that the Young's module of silica nanowires of 100 nm diameter SiO 2 nanowires is much lower than that of bulk SiO 2 materials. Since the Young's module reveals the strain-stress relationship, it will have an impact on the contact area of Hertzian contact and also on the contact charge. Figures 2 and 3 demonstrate that the Young's module have significant effects on the surface charge density. For instance, as shown in Fig. 2, when E A = 25 GPa, the absolute value of the extreme surface charge density, will be 53.5% greater than the case E A = 70 GPa, respectively. Therefore, in this study we consider the nanoscale effect and take the Young's module as 25 GPa.
Instead of taking advantage of contact electrification between different insulators 6,17-23 , we choose the identical silica insulators with the property of size-dependent polarity during contact electrification. Figure 4 shows the schemes of contact-mode and sliding-mode TENGs. The top surface is decorated with a layer of SiO 2 nanoparticles, and the bottom surface is flat SiO 2 plate. Thin layers of metal film are deposited on two SiO 2 material plates as the metal electrodes. The metal electrodes in the upper and lower plates are called the top and down electrodes, respectively. Figure 4(a) is the schematic diagram of the structure of our TENG containing two metal electrodes, silica nanoparticle and silica plate. Initially, the two surfaces are neutrally charged. As observed in wind-blown sand granular systems and our previous work, the surface coated with SiO 2 nanoparticles will be negatively charged and the SiO 2 plane surface will be positively charged after single time contacting 26 , and the bottom surface has the surface charge density σ 0 and the top surface the surface charge density σ − 0 as shown in Fig. 4(b-d) are the schematic diagrams of sliding and contact mode separately. After separation, the electric charge of a single SiO 2 nanoparticle will be If there are N particles decorated on a plane with the surface area S(S = wl, l: length; w: width), the number density will be = / n N S. After separation of two planes, the total electric charge of nanoparticle-decorated top plane will be, And the averaged surface charge density of the down plane σ 0 will be Then, the averaged surface charge density of the top plane will be σ − 0 . For a rectangle plane with length l and width w, the maximum number of particles coated on such surface will be N N 1 2 , where N 1 and N 2 can be solved by , respectively. Noticeably, the surface charge densit y σ 0 incre as es w it h n, and t he maximum sur face charge densit yσ , 0 max w i l l b e π ρ − + − / For instance, when R A = 10 nm,the maximum surface charge density. Figure 5 shows thatσ , 0 max slightly increase linearly with R A and is nearly a constant value − 0.953 μ C m −2 with R A in the range 10 ~ 100 nm, and the relative error σ σ σ ( − )/ , , , , , nm nm 0 max 0 max 10 0 max 10 is very small. The above maximum surface charge density means that particles are densely distributed, and this is an ideal state. While in this ideal state, the squeezing action between a particle and its adjacent particles under external forces also affects the Hertzian deformation of particle-plane contact. In order to avoid such inter-particle effects, sparse distribution of nanoparticles is more reasonable. For example, when a quarter of the maximum number of particles such as / N N 4 1 2 are decorated on the top surface, the surface charge density will be σ σ = / = . µ ⋅ , − 4 0 238 C m 0 0 max 2 . For normal contact-mode and sliding-mode TENGs connected to an arbitrary resistorR, the output properties have been respectively discussed 14,49 . Figures 6 and 7 respectively depicts the theoretical output properties of normal contact-model and sliding-mode of TENGs. The parameters of our TENGs are given in Table 1. For instance, the width = w 50 mm, the length l = 100 mm, the thicknesses = = d R 2 100 nm A 1 , and = µ d 100 m 2 for both contact-mode and sliding-mode TENGs. The maximum departing distance of contact-mode TENGs is 80mm, and the maximum sliding distance d max of sliding-mode TENGs is also 80mm. When the velocities are respectively 0.1 m/s, 0.5 m/s, 1 m/s, theoretical calculations of maximum power outputs are carried out with different resistances, as shown in Figs 6(a) and 7(a). Obviously, there will be optimum values of resistance R for contact model and sliding-mode 14,49 . For instance, as shown in Fig. 6(a), when the power outputs reach their

Discussion
Inspired from wind-blown sand electrification, we design a novel kind of TENG based on size dependent electrification using identical silica materials for harvesting energy. A theoretical mode is established to elucidate the mechanism of the contact electrification process and a calculation of surface charge density has been carried out. Furthermore, the output of homogeneous material based TENG has been simulated. We demonstrate that the maximum power outputs of TENG using earth abundant and homogenous silica as contact electrification layer will reach 12.98 μ W and 13.92 nW in contact and sliding model after single time contact electrification, respectively. Indeed, the output will be greatly enhanced after multi-times contact electrification for more accumulated charges and higher surface charge density. The design of our TENG is polymer free and breaks the limitation of static sequence, which may broaden the application of TENG in harsh environment.

Method
The high-energy trapped hole contact charging model 26 is used to predict the net charge transfer and the surface charge density when identical SiO 2 particle-particle or particle-plane contact. The net charge transfer is related to the Hertzian contact area. According to Hertzian normal contact theory, each sphere will undergo a normal deflection and a contact surface when the two spheres are subjected to a normal loadP, as shown in Fig. 1(a). And the normal deflection δ is given by,  where K is a material constant and commonly referred to as the effective stiffness, where E A , E A are the Young's modules and ν A , ν B are the Poisson's ratios, respectively. The effective radius of curvature R of the two spheres is defined as, where R i is the radius of sphere i ( = , i A B).When → ∞ R B , Hertzian normal contact of two spheres will become the contact of a sphere and a rigid flat, as shown in Fig. 1(b). The contact surface radius R c and the normal deflection δ satisfy δ = R R c 2 , and thus the contact surface radius R c will be, Here, we only consider the elastic Hertzian contact; therefore we need to calculate the critical normal load