Supercapacitive performance of electrochemically doped TiO₂ nanotube arrays decorated with Cu₂O nanoparticles

Abstract

Highly ordered TiO₂ nanotube arrays (TNAs) with enhanced electronic conductivity treated by introducing oxygen vacancies have been considered to be a promising electrode material for supercapacitors. In this work, we fabricated electrochemically doped TiO₂ nanotube arrays (ED-TNAs) through a facile cyclic voltammetry method, and then deposited the uniformly dispersed Cu₂O nanoparticles onto ED-TNAs to synthesise a high performance electrode for a supercapacitor. The ED-TNAs electrode exhibited a high specific capacitance of 5.42 mF cm⁻² at a scan rate of 10 mV s⁻¹, which was about 59 times higher than for the pristine TNAs electrode. Moreover, the ED-TNAs were demonstrated to be an appropriate support for Cu₂O nanoparticles. The highest specific capacitance of the Cu₂O/ED-TNAs electrode could reach 198.7 F g⁻¹ at the current density of 0.2 A g⁻¹, and approximately 88.7% of the initial capacitance was retained after 5000 cycles of galvanostatic charge–discharge.

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Introduction

Supercapacitors have been attracting great attention for their promising applications in hybrid electric vehicles, portable electronics and renewable energy power plants due to their high power density, fast charge–discharge, safe operation and long service life.^1–4 In recent years, transition metal oxides including MnO₂, Fe₂O₃, Co₃O₄, V₂O₅, Cu₂O, and WO₃, etc.^5–10 have received more attention owing to their low costs and high specific capacitance. Among them, cuprous oxide (Cu₂O) has been studied for use as a supercapacitor electrode material because of its low cost, relatively high conductivity, good thermal properties and facile synthesis, and has been regarded as one of the most promising materials for supercapacitor systems.¹¹ Furthermore, Cu₂O is a p-type semiconductor with a direct band-gap of 2.17 eV and spin-0 excitons in the electronic structure also make it possible for it to become a promising material in energy storage devices such as solar cells, lithium-ion batteries and supercapacitors.^9,12

Generally, the capacitance performance can be improved by advancing the high surface area, high thermal and chemical stability and high electronic conductivity of the material. So far, highly-ordered TiO₂ nanotube arrays (TNAs) have received great attention owing to their high surface area, stability and direct transport pathways.¹³ However, the poor electric conductivity of TNAs leads to a relatively low specific capacitance. To overcome this limitation, many efforts have been made in recent years. For instance, Salari et al.¹⁴ found that the capacitance of TNAs can be enhanced through annealing treatment under a reducing atmosphere and confirmed that the introduction of oxygen vacancies in TNAs further improves the capacitance due to the faradic reaction. Yat Li's group¹⁵ reported a new and general strategy for improving the capacitive properties of TiO₂ in a hydrogen atmosphere at high annealing temperatures, and the H–TiO₂ prepared at 400 °C yielded the largest specific capacitance of 3.24 mF cm⁻² with a remarkable rate capability and outstanding long-term cycling stability. It is worthy of noting that the treatment in an atmosphere at high annealing temperatures is not suitable for practical application. A simple and easy method is highly required for modification of TNAs to reduce the electric resistance and improve the capacitance properties. Recently, Wu et al.,¹⁶ showed that TNAs exhibited a high specific capacitance of 20.08 mF cm⁻² at the current of 0.05 mA cm⁻² through a facile treatment of electrochemical doping approach. More interestingly, the capacitance of TiO₂ can be recovered by the same doping process after several cycles.

On the one hand, the highly ordered electrochemically doped TiO₂ nanotube arrays (ED-TNAs) offer high surface area and greatly improved electronic conductivity, which has attracted much attention in charge storage devices; on the other hand, Cu₂O is a promising material for pseudo-capacitor owing to its large specific capacitance. The ED-TNAs can serve as a good support for Cu₂O electrode materials to form composite structures. Motivated by this, we employed ED-TNAs as a support for Cu₂O nanoparticles to form Cu₂O/ED-TNAs composite electrodes for supercapacitor. Herein, the ED-TNAs were fabricated by electrochemical doping process using a facile cyclic voltammetry method, and then Cu₂O nanoparticles were deposited onto ED-TNAs though square wave voltammetry (SWV) deposition method to synthesis the Cu₂O/ED-TNAs electrodes. By taking the advantages of both ED-TNAs and Cu₂O nanoparticles, the Cu₂O/ED-TNAs electrodes achieved high electrochemical performance and excellent long-term cycling stability.

Experimental section

Electrochemical doping of TNAs

The highly ordered TNAs films were synthesized as previously described.¹⁷ In brief, the anodization was performed on DH1722A-3 at 60 V for 6 h in ethylene glycol with 0.15 M NH₄F and 5 vol% H₂O. After anodization, the prepared TNAs were annealed at 500 °C in air for 2 h with a heating and cooling rate of 2 °C min⁻¹ to acquire well-crystallized TNAs. The electrochemical doping process was performed on AUTOLAB electrochemical station (PGSTAT302N, Netherland) through the CV test process. The CV measurements were carried out in 0.5 M Na₂SO₄ solution over a potential range from −2.0 to 1.0 V at scanning rate of 100 mV s⁻¹, where TNAs, Ag/AgCl electrode and platinum wire act as working electrode, reference electrode and counter electrode respectively. The doped sample was labelled as ED-TNAs.

Synthesis of Cu₂O/ED-TNAs

The composite Cu₂O/ED-TNAs electrodes were synthesized through square wave voltammetry (SWV) deposition method performed on AUTOLAB electrochemical station. The electrolyte was CuSO₄ solution and lactic acid solution with pH of 9.0 adjusted by 5.0 M NaOH solution. Different concentrations of CuSO₄ (0.005, 0.01, 0.05, and 0.1 M) in the electrolyte, were investigated to understand the influence on morphology and performance of Cu₂O/ED-TNAs. The SWV process was carried out at the initial potential of −1.0 V vs. Ag/AgCl, and the end potential of 0 V vs. Ag/AgCl. During the deposition, the amplitude potential was employed at 0.005 V and the frequency was set at 2 Hz. The obtained samples, consisting of different content of Cu₂O nanoparticles on ED-TNAs, were denoted as 0.005-Cu₂O/ED-TNAs, 0.01-Cu₂O/ED-TNAs, 0.05-Cu₂O/ED-TNAs, and 0.1-Cu₂O/ED-TNAs, respectively.

Characterizations

The morphologies of the samples were analysed with a FE-SEM (SU8020, Hitachi, Japan) and high-resolution transmission electron microscopy (HRTEM, JEM-2100F, JEOL, Japan). The XRD patterns of the samples were performed on D/MAX2500V with Cu-K_α radiation (λ = 1.54056 Å, Regaku, Japan). The chemical valences of the sample elements were measured by XPS using a monochromatic Al Kα X-ray beam (1486.60 eV, ESCALAB250, Thermo, American). All the binding energies of the elements were calibrated to the carbon binding energy of 284.80 eV.

Electrochemical tests

The electrochemical performance of the samples were evaluated using AUTOLAB in a conventional cell with a three-electrode configuration using Ag/AgCl electrode as reference electrode and Pt sheet as the counter electrode. 0.5 M Na₂SO₄ aqueous solution was employed as the electrolyte for all electrochemical tests. The CV was carried out over a potential range from −0.6 to 0.3 V (vs. Ag/AgCL) at different scanning rates ranging from 5 to 100 mV s⁻¹ with active electrodes area of 1.0 cm². Galvanostatic charge–discharge (GCD) measurements were recorded at various current densities ranging from 0.2 to 10 A g⁻¹. The voltage windows of GCD tests were the same as that for CV tests. EIS tests were conducted in the frequency range of 100 KHz to 0.01 Hz at open circuit potential with an AC-voltage amplitude of 5 mV.

Results and discussion

The preparation procedure of Cu₂O/ED-TNAs electrodes is illustrated in Fig. 1, and they are described in details in the Experimental section. Highly ordered TNAs were synthesized by electrochemical anodization process on Ti foil, and then annealed in air at 500 °C. The Cu₂O/ED-TNAs electrodes were fabricated by SWV deposition method after electrochemical doping of TNAs process. Distinctly, different colors were observed for the as-anodized (faint yellow), as-annealed (grey), as-doped (dark black), and Cu₂O/ED-TNAs (Reseda), respectively. Fig. 2a shows a typical bottom surface of FE-SEM image of the ED-TNAs and top view of FE-SEM image of the ED-TNAs is shown in the inset of Fig. 2a while the cross-section image is shown in Fig. 2b. As shown in Fig. 2a, it can be seen that the opening of the vertically oriented TNAs are almost circular in shape, and the bottom of the ED-TNAs are regular hexahedron. The average inner diameter of the ED-TNAs is found to be 145 nm, and the wall thickness is about 15 nm. The nanotube length is found to be about 15 μm. The vertically oriented nanotube arrays are revealed from self-organized nanotubes that is orderly arrange on the Ti substrate. The electrochemical doping process did not destroy the vertically oriented nanotubes structure and the parameters of samples. The Cu₂O nanoparticles deposited onto the inner surface and interface of ED-TNAs is shown in Fig. 3. The top views of the composites Cu₂O/ED-TNAs heterojunction prepared by the different concentrations of CuSO₄ solutions are also shown in Fig. 3a–d. The uniformly dispersed Cu₂O nanoparticles can be observed in all samples as shown in Fig. 3a–d and the particle loading contents are increasing with the increasing concentration of CuSO₄ solution in composites of Cu₂O/ED-TNAs heterojunction. Further observation of Cu₂O nanoparticles deposited onto the inner surface of ED-TNAs can be seen from the corresponding cross-section of FE-SEM images in the inset of Fig. 3.

Fig. 1 Schematic diagram illustrating the synthesis procedures of Cu₂O/ED-TNAs electrodes on Ti foil.

Fig. 2 FE-SEM images of the ED-TNAs: (a) bottom surface image of ED-TNAs, the inset showing the typical top SEM image view of ED-TNAs; (b) cross-section SEM image of the ED-TNAs, the inset showing the magnified cross-section of the ED-TNAs.

Fig. 3 FE-SEM images of Cu₂O/ED-TNAs on the top surface prepared by the different concentration of CuSO₄ solution: (a) 0.005; (b) 0.01; (c) 0.05; (d) 0.1 M.

Fig. 4a shows the typical TEM images of Cu₂O/ED-TNAs composites prepared from 0.05 M CuSO₄ solution (0.05-Cu₂O/ED-TNAs). The uniformly distributed Cu₂O nanoparticles with a small average diameter of 5 nm can be clearly observed on the inner surface of ED-TNAs. As shown in Fig. 4b, the selected area of the HRTEM image depicts the Cu₂O nanoparticles embedded inside the TiO₂ nanotubes, where the lattice planes with a spacing of 0.246 nm and 0.351 nm corresponds to the (111) plane of Cu₂O and the (101) plane of anatase TiO₂, respectively, further confirming the crystalline phase of the Cu₂O/ED-TNAs heterojunction composites.

Fig. 4 (a) Typical TEM images of the 0.05-Cu₂O/ED-TNAs; (b) HRTEM image of the corresponding area of the 0.05-Cu₂O/ED-TNAs.

Fig. 5 shows the X-ray diffraction (XRD) patterns of the different crystalline structures of the samples. The samples show the diffraction peaks at 2θ = 25.2, 37.8 and 48.0°, which correspond to the (101), (004), and (200) planes of the TiO₂ anatase phase (JCPDS card no. 21-1272), respectively. The Cu₂O/ED-TNAs fabricated by depositing Cu₂O in the CuSO₄ solution of 0.01, 0.05, and 0.1 M display clear peak at 2θ = 36.42°, which is ascribed to the (111) reflection of Cu₂O (JCPDS card no. 05-0667). Moreover, a distinguishing peak at 2θ = 42.29° can be observed both in 0.05-Cu₂O/ED-TNAs and 0.1-Cu₂O/ED-TNAs samples, which correspond to the (200) reflection of Cu₂O, and the peak of Cu₂O (220) plane at 2θ = 61.34° appear in the sample of 0.1-Cu₂O/ED-TNAs. However, no Cu₂O phase was observed in 0.005-Cu₂O/ED-TNAs, which is attributed to the low content of the Cu₂O phase that cannot be detected through XRD technique. In addition, it can be seen clearly, that when the concentration of Cu₂O increased, the peaks of Cu₂O also increased, indicating that the amount of Cu₂O is related to the deposition voltage. Furthermore, the characteristic peaks of Cu and CuO were not found, which indicated that the deposited nanoparticles were Cu₂O rather than Cu or CuO.

Fig. 5 XRD patterns of the ED-TNAs and Cu₂O/ED-TNAs prepared by the different concentration of CuSO₄ solution.

In order to detect the elemental composition and chemical states of 0.05-Cu₂O/ED-TNAs samples, X-ray photoelectron spectroscopy (XPS) test was carried out and the results are shown in Fig. 6. The typical peaks of Ti 2p, O 1s, Cu 2p, and C 1s in the survey spectrum can be seen clearly in Fig. 6a. Fig. 6b presents a typical high-resolution XPS spectrum of O 1s. The peak at 529.9 eV can be assigned to the oxygen atoms of Ti–O–Ti, and the shoulder peak at higher binding energy of 531.8 eV can be attributed to the hydroxyl group of Ti–OH, which was reported to be located at ∼1.5–1.8 eV higher than the oxygen atoms of Ti–O–Ti.^15,18 This result demonstrates that the hydroxyl group was formed on the sample surface and the TiO₂ surface was activated by electrochemical doping process. The high resolution XPS spectrum of Cu 2p is displayed in Fig. 6c, and it can be observed that the Cu 2p_3/2 and Cu 2p_1/2 were located at binding energies of 932.5 eV and 952.5 eV, respectively, which are in good agreement with the reported values of Cu₂O.^19–21 In order to further distinguish between Cu₂O and Cu or CuO, the Cu LMM Auger transitions was employed, as displayed in Fig. 6d. We can notice clearly that there is only one peak at 570 eV corresponding to the binding energy of Cu₂O.

Fig. 6 XPS spectra of the 0.05-Cu₂O/ED-TNAs sample: (a) XPS survey spectrum; (b) high-resolution XPS spectrum of O 1s region; (c) high-resolution XPS spectrum of Cu 2p region; and (d) Auger electrode spectrum of Cu LMM.

Fig. 7a shows the dynamic CV performance for electrochemical doping process of TNAs electrode. During the first anodic scan, the oxidation current density is very low starting at −1 V, which means the capacitance is small. When in the return at cathodic scan, the reduction current density increases tremendously with bubbles evenly generated around the counter electrode. To a great extent, both the oxidation current density and reduction current density are much larger in the second scan than in the first scan, indicating that the oxygen vacancies were introduced into TNAs to enhance the capacitance. Furthermore, the CV curves of ED-TNAs electrode obtained at various scan rates in the wide range from 10 to 500 mV s⁻¹ display the unchanged quasi-rectangular shapes, shown in Fig. 7b, indicating the good capacitive behavior and higher-rate capability of ED-TNAs.²² Fig. 7c displays the galvanostatic charge–discharge curves at different current densities. The discharge curves are almost symmetrical to the corresponding charge curves even at a high current density of 4.0 mA cm⁻², indicating a good capacitive behavior of the ED-TNAs electrode. Fig. 7d shows the calculated specific capacitance of the ED-TNAs based on the CV curves. The specific capacitance of the ED-TNAs electrode are calculated to be 5.42 mF cm⁻² at a scan rate of 10 mV s⁻¹, which is about 59 times more than pristine TNAs electrode (0.092 mF cm⁻²). Additionally, the specific capacitance of ED-TNAs can be kept at 4.35 mF cm⁻² even at high scan rate of 500 mV s⁻¹, indicating a good rate capability and a good capacitance retention capability.

Fig. 7 (a) Dynamic cyclic voltammetry (CV) performance for electrochemical doping process; (b) CV curves of the ED-TNAs electrode with different scan rates from 10 to 500 mV s⁻¹; (c) galvanostatic charge–discharge curves of ED-TNAs electrode collected from 1.0 to 4.0 mA cm⁻²; (d) calculated specific capacitance of the ED-TNAs electrode at various scan rates.

To further analyze the mechanism of electrochemical doping process, EIS was carried out at open circuit potential with an amplitude of 5 mV. Comparing the Nyquist plots of pristine TNAs and ED-TNAs electrode, the ED-TNAs electrode has a smaller semicircle in the high-frequency region as shown in Fig. 8. It is generally accepted that a semicircle reflects the electrochemical reaction impedance of the electrode, and a smaller semicircle means smaller charge transfer resistance.²³ As shown in the inset image of Fig. 8, the EIS data of ED-TNAs was simulated by an equivalent circuit. The equivalent circuit consists of the bulk solution resistance (R_s), the charge transfer resistance (R_ct), the double-layer capacitance (CPE₁), the interface resistance (R_c) and capacitance (CPE₂) of the space charge layer within the bulk TNAs and a Warburg diffusion element (W). From the result of equivalent circuit, we note that the bulk solution resistance (R_s) of ED-TNAs is about 32.7 Ω, which is much closer to that of pristine TNAs (45.4 Ω); however, the charge transfer resistance (R_ct) between the ED-TNAs and electrolyte interface is only 169 Ω, much lower than that of original TNAs (2.13 KΩ), indicating that the electronic conductivity of TNAs can be increased by electrochemical doping process to facilitate the charge transfer.

Fig. 8 Nyquist plots of pristine TNAs and ED-TNAs electrodes and corresponding equivalent circuit, the inset showing the Nyquist plot of the experiment and fitting result of the ED-TNAs.

Fig. 9a–d shows the CV curves of 0.005-Cu₂O/ED-TNAs, 0.01-Cu₂O/ED-TNAs, 0.05-Cu₂O/ED-TNAs and 0.1-Cu₂O/ED-TNAs electrodes, respectively. It can be examined that the CV curves of those film electrodes display the same shapes; however, the intensity of the redox peaks of those film electrodes firstly increase and then decreased with the loading contents of Cu₂O nanoparticles. The evenly distributed Cu₂O nanoparticles can reduce the internal resistance of the electrode but excess Cu₂O nanoparticles prevented the diffusion of electrons and ions in the ED-TNAs. This further verifies the loading content dependence of the enhancement of the capacitive performance of Cu₂O/ED-TNAs electrodes. All the CV curves show similar shapes even at a high scan rate of 100 mV s⁻¹, which indicates the excellent capacitive behavior and high rate capability. Fig. 9e displays the CV curves of Cu₂O/ED-TNAs electrodes obtained from different concentrations of CuSO₄ solution at a scan rate of 100 mV s⁻¹. It can be observed that there are remarkable redox peaks in all electrodes at the same scan rate. A pair of redox peaks in the CV curves owing to the combination effects of Cu₂O nanoparticles, indicating that faradic reactions were generated during the electrode charging and discharging process and the capacitance of Cu₂O/ED-TNAs electrodes were attributed to the redox pairs of Cu⁺/Cu²⁺. Moreover, the 0.05-Cu₂O/ED-TNAs electrode displayed the largest anodic and reduction current densities than that of other electrodes in the CV curves, indicating that it possess the largest specific capacitance. Besides, it can be observed from Fig. 9f that both the oxidation peak current density and reduction peak current density of those electrodes increased almost linearly with the scan rate as high as 100 mV s⁻¹, which reveals the excellent kinetic performance and further proves that these electrodes have ideal capacitive behaviors.²⁴

Fig. 9 CV curves of (a) 0.005-Cu₂O/ED-TNAs, (b) 0.01-Cu₂O/ED-TNAs, (c) 0.05-Cu₂O/ED-TNAs, (d) 0.1-Cu₂O/ED-TNAs electrode at various scan rates. (e) CV curves of Cu₂O/ED-TNAs electrodes obtained at 10 mV s⁻¹; (f) the peak current densities of Cu₂O/ED-TNAs electrodes collected as a function of the scan rate ranging from 10 to 200 mV s⁻¹.

The GCD test provides a reliable method for evaluating the specific capacitance of materials. Typical discharge curves of all Cu₂O/ED-TNAs electrodes were investigated at various current densities in the range of 0.2 to 5 A g⁻¹, as shown from Fig. 10a–d. It can be seen that all the discharge curves are not ideal straight line, indicating that these electrodes have faradic capacitive performance.²⁵ The shapes of discharge curves for each Cu₂O/ED-TNAs electrode have no changes even at a high current density of 5 A g⁻¹, which reveals these Cu₂O/ED-TNAs electrodes have high rate capability. As shown in Fig. 10e, the charge–discharge time of the 0.05-Cu₂O/ED-TNAs electrodes was significantly enhanced than that of other electrodes at the current density of 1 A g⁻¹, implying that the 0.05-Cu₂O/ED-TNAs electrodes possessed the highest specific capacitance. This result is good in accordance with the above results of CV tests. The specific capacitance of these film electrodes can be calculated by the following equation:

where C_s is the specific capacitance (F g⁻¹), I is the discharge current (A), Δt is the discharge time (s), ΔV is the potential window (V), and m is the amount of active material on the working electrode (g). The specific capacitance of Cu₂O/ED-TNAs obtained by different concentration of 0.005, 0.01, 0.05, and 0.1 M was calculated to be 96.7, 125.5, 198.7, and 170.4 F g⁻¹ at the current density of 0.2 A g⁻¹, respectively, as shown in Fig. 10f. Moreover, for each Cu₂O/ED-TNAs electrode, over 60.8%, 62.2%, 78.5% and 78% of initial capacitance were still retained even at current density of 5 A g⁻¹ respectively. The results of the calculated specific capacitance further proved that 0.05-Cu₂O/ED-TNAs film electrodes acquired the largest specific capacitance and the best rate capability.

Fig. 10 Discharge curves of (a) 0.005-Cu₂O/ED-TNAs, (b) 0.01-Cu₂O/ED-TNAs, (c) 0.05-Cu₂O/ED-TNAs, (d) 0.1-Cu₂O/ED-TNAs; (e) galvanostatic charge–discharge curves of Cu₂O/ED-TNAs electrodes collected at a current density of 5 A g⁻¹; (f) the specific capacitance of Cu₂O/ED-TNAs electrodes measured as a function of current density.

Fig. 11 gives the Nyquist impedance spectra of ED-TNAs and Cu₂O/ED-TNAs electrodes at open circuit potential. The Cu₂O/ED-TNAs electrodes have much smaller semicircles in the high-frequency region than the ED-TNAs film electrode, indicating that the resistance of the Cu₂O/ED-TNAs electrodes are much lower than that of the ED-TNAs electrode. For example, the bulk solution resistance (R_s) estimated from the equivalent circuit is about 10.5 Ω, and the charge transfer resistance (R_ct) is about 32.4 Ω for the 0.05-Cu₂O/ED-TNAs electrode film, which is much lower than that of the ED-TNAs (32.7 Ω for the R_s and 169 Ω for the R_ct). These remarkable results further demonstrate that the ED-TNAs film electrode deposited with Cu₂O nanoparticles can substantially reduce the charge transfer resistance and accelerate electronic transmission between the electrode and electrolyte.

Fig. 11 Nyquist plots of ED-TNAs electrode and Cu₂O/ED-TNAs electrodes obtained from different concentration of CuSO₄ solution.

The cycling life test for 0.05-Cu₂O/ED-TNAs film electrodes were carried out through a cyclic galvanostatic charge–discharge process over 5000 cycles at current density of 1 A g⁻¹. The specific capacitance of 0.05-Cu₂O/ED-TNAs electrode as the function of the cycle number is shown in Fig. 12. The specific capacitance maintained 152.8 F g⁻¹ after 5000 cycles, which is about 88.7% of the initial capacitance. Additionally, the charge–discharge curves are more or less the same as that of the first cycle after 5000 cycles of measurement. This result illustrates the 0.05-Cu₂O/ED-TNAs electrode has a good capacitance recovery and excellent long-term stability.

Fig. 12 Long-term cycling stability of 0.05-Cu₂O/ED-TNAs electrode at a charge–discharge current density of 5 A g⁻¹. The inset shows the first 10 and last 10 cycles charge–discharge curves for 0.05-Cu₂O/ED-TNAs electrode at current density of 5 A g⁻¹.

Conclusions

In conclusion, the Cu₂O/ED-TNAs composite have been successfully fabricated for the supercapacitor electrode by SWV deposition method with electrochemical doping modification process. It has been demonstrated that the coupling of ED-TNAs film with Cu₂O nanoparticles is an effective way to improve the performance of the supercapacitor. The synergistic effect between the high pseudo-capacitance of Cu₂O and higher surface area of ED-TNAs contributes to the better performance of the Cu₂O/ED-TNAs film electrodes. The 0.05-Cu₂O/ED-TNAs electrode exhibits a high specific capacitance of 198.7 F g⁻¹ at the current density of 0.2 A g⁻¹ in 0.5 M Na₂SO₄ aqueous solution with excellent long-term cyclic stability.

Acknowledgements

This work was financially supported by the National Natural Science Foundation of China (51302060, 51272062, 51402081, 51502071, 51372063) and National Basic Research Program of China (973 Program, 2014CB660815). The Specialized Research Fund for the Doctoral Program of Higher Education (20130111120019) and Natural Science Foundation of Anhui Province (1608085QE105, 1508085ME97) are also gratefully appreciated. Dr Y. Wang also would like to thank the financial support from the China Scholarship Council during his visit to Rice University.

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