Amorphous titanium-oxide supercapacitors

The electric capacitance of an amorphous TiO2-x surface increases proportionally to the negative sixth power of the convex diameter d. This occurs because of the van der Waals attraction on the amorphous surface of up to 7 mF/cm2, accompanied by extreme enhanced electron trapping resulting from both the quantum-size effect and an offset effect from positive charges at oxygen-vacancy sites. Here we show that a supercapacitor, constructed with a distributed constant-equipment circuit of large resistance and small capacitance on the amorphous TiO2-x surface, illuminated a red LED for 37 ms after it was charged with 1 mA at 10 V. The fabricated device showed no dielectric breakdown up to 1,100 V. Based on this approach, further advances in the development of amorphous titanium-dioxide supercapacitors might be attained by integrating oxide ribbons with a micro-electro mechanical system.

The negative-sixth-power diameter dependency is known as the van der Waals force, which is based on induced dipole-dipole interactions 11 . This result resembles the hypothesis that the weak adhesive force exerted by the feet of many types of geckos is the result of van der Waals intermolecular forces 12,13 . Figure 1b,c present scanning electron microscope (SEM) images of the surface structure corresponding to values of d = 35.4 nm and 4.7 nm, respectively. Figure 1d shows a three-dimensional AFM image of the surface structure corresponding to d = 35.4 nm. The surface structure resembles that of APP (see Fig. S2 in Supplementary Information). Thus, the use of the ATO surface with unevenness less than 5 nm in diameter shows promise for the production of large EDCCs.
To analyse non-destructively the electrostatic contribution of the specimen, we measured the AC impedance from 0.1 Hz to 1 MHz at room temperature by using a device (inset of Fig. 2c) fabricated by a micro-electro mechanical system (MEMS) method (see Fig. S3 in Supplementary Information). A complex-plane plot of the impedance data obtained from the specimen for d = 35.4 nm is shown in Fig. 2a. The data fit a near-vertical line in the Nyquist plot, as produced by a series-RC circuit, as well as a graphene EDLC 14 . There were rapid increases in the imaginary impedance, as compared with the real impedance, in the lower-frequency region (Fig. 2b). Moreover, the capacitive behaviour (near the − 90° phase angle) throughout the frequency region ( Fig. 2c) is clear evidence for series-RC circuit. Thus, the ATO offers a nearly ideal electric distributed-constant structure for enhancing electrical power storage. Although the electrical storage is not always the same as the capacitance, the value of the series capacitance was 4.17 μ F (2.085 F/cm 3 , 537.6 μ F/kg) at 0.1 Hz (Fig. 2d).
Since decreases in the convex diameter by solvent F ions in anodic oxidisation accompanies decreases in resistance, that is, leakage of electrical charge between electrodes by the formation of penetrating tunnels in the oxide layer 9 , we oxidised the specimens for 36 ks in air to prevent the leakage of charge due to stopping of the tunnels by using specimens anodically oxidised at 10 V and 278 K for 1.8 ks in (NH 4 ) 2 SO 4 -0.05 wt%NH 4 F solution. Figure 3a shows both the resistance variation for the annealing temperature and the discharging time with a constant current of 1 pA after charging with a DC current of 1 mA for 300 s. The resistance increased to 700 GΩ as the temperature increased to 448 K and then decreased to 330 GΩ at 548 K. The increase suggests the filling up of the nanometre-sized tunnels by the diffusion of oxygen atoms, while the decrease might be due to the formation of cracks. The discharging-time curve resembles the resistance curve, except for the maximum discharging time at 473 K. Thus, we selected an annealing temperature of 473 K for ATO specimens with diameters in the range of 5-10 nm and electric resistance greater than 500 GΩ. Figure 3b shows typical results for DC charging and discharging behaviours of specimens with a surface area of 76 cm 2 under constant currents of 1 pA, 1 nA, 1 μ A, and 1 mA, after charging with a DC current of 1 mA for 300 s. These results indicate the electrical power storage performance of the ATO. To provide visible evidence of the ATO electric storage, we attempted to illuminate a red LED. The device, composed of parallel combinations of RC circuits (see Fig. S4 in Supplementary Information), discharged up to 15 s at constant current of 1 nA and powered the LED for 37 ms (Fig. 3c), after the device was charged with 1 μA for 300 s at 10 V. Figure 3d presents an illumination photograph of the LED. Further gains might be attained by integrating oxide ribbons with the MEMS.
Finally, we consider the origin of the electric storage in ATO. Figure 4a shows a microscopic schematic representation proposing a possible mechanism for large electrical charges, along with the electric-field strength and potential change from positive to negative electrodes. The electrically negative convex portion of ATO and the electrically positive concave one form many electrode double layers perpendicular to the electrode. This is a capacitor with an electric distributed-constant circuit (Fig. 4c) as well as the APP 6 . Here, we note that the atomic structure of nanometre-sized ATO has a highly distorted shell and a small, strained anatase-like core with a coordination number of 5.3 for an average Ti-O 15 . Relative to crystalline TiO 2 with a Ti coordination number of 6, the reduction of the coordination number, which is primarily due to the truncation of the Ti-O octahedral (Fig. 4e), corresponds to an oxygen vacancy of 11.7 at.% (Fig. 4b). The vacancies, therefore, serve as the electrically positive offset effect for trapping electrons at convex surfaces on the amorphous structure (Fig. 4b), resulting in large electron adsorption. Analogous to the APP with superior electric storage resulting from the quantum-size effect, the convex-diameter dependencies of the calculated electrostatic potential and the induced outer-electron pressure of titanium atoms that occupy the centre of the ATO structure are presented in Fig. 4d by means of the electronic screening theory (discussed at length in Supplementary Information). The decrease in diameter increases both the negative potential and positive pressure. The calculated potential was consistent with the experimental data (5.5 eV) 7 with a convexity 35.4 nm in diameter. The QSE in this study resembles space-charge polarization.
In conclusion, anodically oxidised surfaces present two advantages for the direct electron charging of giant capacitors. The first is the introduction of van der Waals attractive forces for electron adsorption by homogeneously distributed nanometre-sized convexities on amorphous TiO 2-x surfaces. The second is the offset effect of electron repulsion caused by the appearance of positive charges at a large number of oxygen vacancies in the amorphous TiO 2-x layer. The integrated ATO device, a supercapacitor, succeeded in illuminating an LED for 37 ms. A supercapacitor with an amorphous TiO 2-x surface, as fabricated and tested, demonstrates a nearly ideal electric distributed-constant structure for enhancing electrical power storage. The results of tests indicated that the use of an ATO surface with unevenness maintained at less than 5 nm in diameter shows promise for the production of large EDCCs. These results indicate the potential for making further advances in the fabrication of amorphous titanium dioxide supercapacitors by integrating oxide ribbons with MEMS.

Methods
The ATO specimens having uneven surfaces with convex diameters in the range of 3 nm to 40 nm were prepared under various anodic oxidization conditions in H 2 SO 4 and (NH 4 )SO 4 -NH 4 F solutions. The integrated ATO device was fabricated using many ATO specimens annealed in air at 473 K for 36 ks. I-V and R-V characteristics were measured at DC voltages ranging from 0 V to 1,100 V at a sweep rate of 1.24 V/s by using a Precision Source Measure Unit (B2911A, Agilent). AC impedance and charging/discharging behaviours of the specimen were measured, using a potentiostat/galvanostat (SP-150, BioLogic Science) at room temperature.