Superior electric storage on an amorphous perfluorinated polymer surface

Amorphous perfluoroalkenyl vinyl ether polymer devices can store a remarkably powerful electric charge because their surface contains nanometre-sized cavities that are sensitive to the so-called quantum-size effect. With a work function of approximately 10 eV, the devices show a near-vertical line in the Nyquist diagram and a horizontal line near the −90° phase angle in the Bode diagram. Moreover, they have an integrated effect on the surface area for constant current discharging. This effect can be explained by the distributed constant electric circuit with a parallel assembly of nanometre-sized capacitors on a highly insulating polymer. The device can illuminate a red LED light for 3 ms after charging it with 1 mA at 10 V. Further gains might be attained by integrating polymer sheets with a micro-electro mechanical system.

constant capacitor with low capacitance and high resistance (~48 TΩ cm) (inset of Fig. 1a). Nevertheless, each capacitor on the PVDF film is connected by a series circuit, indicating the absence of an integration effect for electric storage. To provide visible evidence of the APP's electric storage, we illuminated a red LED light. The device, which has a surface area of 600 mm 2 , lit the LED for 3 ms (inset of Fig. 1b) after the device was charged with 1 mA at 10 V. The fact that we were able to light the LED confirms the potential for electric storage.
A complex plane plot of the impedance data obtained from the APP film is shown in Fig. 2a. The polymer's variation in impedance with frequency did not show the combined pattern of a line with a slope of 45°, which would associate it with the distributed resistance/capacitance in a porous electrode 11 and a high-frequency semicircle (i.e., a series-passive layer). A near-vertical line in the Nyquist plot suggests evidence of a series-RC circuit as well as a graphene double-layer capacitor 12 . There were rapid increases in the imaginary impedance compared with the real impedance in the lower-frequency region (Fig. 2b). Moreover, the capacitive behaviour (near the − 90° phase angle) all over the frequency region (Fig. 2c) is clear evidence of a series-RC circuit. Thus, APP films offer a near-ideal electric distributed constant structure (inset of Fig. 2c) for enhancing electric storage. However, the value of the series capacitance was 0.4 nF (178.8 nF/ cm 3 , 88.9 μ F/kg) at 1 mHz (Fig. 2d).
We investigated the surface characteristics to understand the microscopic origin of the APP's higher electric storage. Figure 3a shows an atomic force microscope (AFM) image, and Fig. 3b shows the corresponding scanning Kelvin probe-force microscope (SKPM) image. These figures depict an uneven surface with a convexity of 28 nm in diameter and a concavity of 31 nm in length. The outside appearance of the surface bears a close resemblance to that of anodic oxidized amorphous TiO 2-x surfaces in previous papers 8,9 . The line profiles of the noncontact AFM reveal spots that are distributed on the uneven surface. These spots have a high work function Ф, averaging 10.13 eV (= 5.65 (Ф Pt ) + 4.48(Ф CPD ). This means that they can store electric charges; the same is true for the TiO 2-x layer 8 . The value of the work function is higher than 9.1 eV and was obtained from an ultraviolet photoelectron spectroscopy measurement 13 . After an additional positive 20 V was applied for 60 s at the centre of the Si back surface (see Fig. S5 in Supplementary Information), we observed an electrostatic potential distribution (Fig. 3c) and the corresponding electrostatic potential profiles in four directions (L1, L2, L3 and L4) every 90° (Fig. 3d). The potential negatively increased to − 76.93 eV (= 5.65 + 71.28 eV) at the centre. This value demonstrates the remarkable electric-absorption effect of the APP under applied voltage. We now turn to an explanation of the superior electric storage on the APP. The APP structure consists of PVDF main chains containing C = O and N-H radicles 14 (Fig. 4a). The APP has rugged half-sphere surface (convex diameter of 2R, Fig. 4b) with nanometre-sized cavities. Notably, lattice contractions have been observed in nanometre-sized metallic particles, such as silver 15 , copper and platinum 16 , and gold 17 . Such contractions are due to the extreme confinement of the inner electrons-the so-called quantum-size effect 18,19 . This effect is interpreted by screening multiple inner-combined electrons for a strong positive-charge nucleus 20 . Analogously, we inferred that the superior electric storage on the uneven APP surface is due to the same quantum-size effect, which induces a relative increase in the combined electrons, resulting in fewer free outer electrons from the screening effect. The convex-diameter dependencies of the calculated electrostatic potential and the induced outer electron pressure of fluorine atoms surrounding the APP structure are presented in Fig. 4c by means of the Thomas-Fermi (TF)'s electronic screening theory (discussed at length in the Supplementary Information). The decrease in diameter increases the negative potential and the positive pressure. The calculated potential was consistent with the experimental data at a convexity of 14 nm in diameter. A microscopic schematic is provided in Fig. 4d. In sharp contrast to conventional EDLC, in which its electrode is parallel to the circuit, the electrically-negative convex portion of APVEP main chains and the electrically-positive concave one dominated by C=O and N-H radicles with permanent dipoles 21 form many electric double layers (EDLs) perpendicular to the electrode (see Fig. S4 in Supplementary Information). This model shows that the more an EDL's density increases (namely, the more convex-diameter decreases due to quantum-size effect), the more the electric storage increases. The uneven surface serves as a series of resistors for an insulation layer with tiny capacitors through the bulk, as shown in inset of Fig. 2c. Thus, in comparison with EDLCs, the APP device has some advantages, such as a wide operation temperature, higher charging/discharging voltage, larger integration, lighter weight, and prevention of IV drop at long distance from electrodes.
We demonstrated the storage potential for the APP given its nanometre-sized cavities on an uneven surface. The APP has a high work function, measured at 10.13 eV, and it succeeded in illuminating an LED. We inferred that the potential for electric storage is related to the quantum-size effect derived from the TF theory. The integration of the film with a micro-electro mechanical system is likely to provide even higher levels of charge storage for portable electric application.

Methods
The APVEP film with nanometre-cluster was prepared by doping a 3-aminopropyl (triethoxy) silane-coupling reagent into the APP. Sheet specimens with a thickness of 15 μ m were fabricated on the Si substrate by spin-coating. The specific density, glass-transition temperature, and water-adsorption rate was 2.03, 471 K, and 0.01%, respectively 22 . The devices were fabricated mechanically 8 .
Scanning Kelvin probe-force microscopy (NC-AFM, JSPM-5200, JEOL) based on the measurement of electrostatic force gradient was applied to measure the absolute electrical potential between the Pt-coated cantilever tip at 0 and 20 V and the APP surface as the work-function difference. The DC charging/discharging behaviour was analysed at 10 V, 1 pA~1 mA for ~300 s at room temperature, with a complex impedance between 1 mHz and 1 M Hz and 10 mV, using the galvanostatic charge/discharge on a potentiostat/galvanostat (SP-150, BioLogic Science). A red LED lump with standard power of 2 × 10 −4 W was used to verify the electric storage.