TiO2-B@VS2 heterogeneous nanowire arrays as superior anodes for lithium-ion batteries

TiO2-B@VS2 heterogeneous nanowire arrays as superior anodes for lithium-ion batteries

Journal of Power Sources 350 (2017) 87e93 Contents lists available at ScienceDirect Journal of Power Sources journal homepage: www.elsevier.com/loca...

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Journal of Power Sources 350 (2017) 87e93

Contents lists available at ScienceDirect

Journal of Power Sources journal homepage: www.elsevier.com/locate/jpowsour

TiO2-B@VS2 heterogeneous nanowire arrays as superior anodes for lithium-ion batteries Minglei Cao, Lin Gao, Xiaowei Lv, Yan Shen* Wuhan National Laboratory for Optoelectronics, Huazhong University of Science and Technology, Wuhan 430074, PR China

h i g h l i g h t s  TiO2-B@VS2 heterogeneous nanowire arrays (TVNAs) are prepared.  Layered VS2 nanoparticles are deposited on TiO2-B nanowire arrays surface.  The TVNAs electrode exhibits enhanced capacity and rate capability.  VS2 improves the electrical conductivity and contributes to extra capacity.

a r t i c l e i n f o

a b s t r a c t

Article history: Received 18 October 2016 Received in revised form 1 March 2017 Accepted 16 March 2017

Heterogeneous nanostructured materials are currently studied as promising electrode materials for lithium-ion batteries (LIBs) due to effective synergy. Herein, we report on TiO2-B@VS2 heterogeneous nanowire arrays (TVNAs) as additives-free anodes for LIBs. The VS2 is a two-dimensional (2D) material with intrinsically metallic nature. Importantly, this layered 2D material offers a large interlayer spacing for facile intercalation of lithium-ions and possesses a high theoretical capacity. The TVNAs electrode shows a reversible capacity of 365.4 mA h g1 after 500 cycles at a current density of 1 C (335 mA g1), being significantly superior than the pure TiO2-B nanowire arrays (TNAs) electrode (192.7 mA h g1). Impressively, the TVNAs electrode delivers a high rate capacity of 171.2 mA h g1 at 10 C rate. The merits of the TVNAs electrode could be ascribed to the outstanding structural stability of the TNAs and the high capacity and conductivity of VS2. © 2017 Published by Elsevier B.V.

Keywords: Lithium-ion battery Effective synergy TiO2-B VS2 Nanowire arrays

1. Introduction Lithium ion batteries (LIBs) have become indispensable in portable electronics and been considered as the robust candidates for the upcoming markets of electric transportation and renewable energy, owing to the high energy density, long cycle life and environmental benignity [1e4]. In recent years, the TiO2 has been intensively studied as a potential anode material for LIBs because of its good safety, low cost and environmental friendliness [5e8]. A low volume expansion (3e4%) during lithium-ions insertion/ desertion endows TiO2 outstanding structural stability, which leads to excellent cycling performance [9,10]. Among all the polymorphs, the bronze phase TiO2 (TiO2-B) is the most attractive one, which has favorable open framework structure for lithium-ions mobility and features a pseudocapacitive process for lithium storage [11e13]. As

* Corresponding author. E-mail address: [email protected] (Y. Shen). http://dx.doi.org/10.1016/j.jpowsour.2017.03.070 0378-7753/© 2017 Published by Elsevier B.V.

such, the theoretical capacity of TiO2-B (335 mA h g1) is much higher than that of anatase or rutile phase TiO2 (167 mA h g1). However, the intrinsically slow transport kinetics for both electrons and lithium-ions in TiO2-B has seriously restricted its lithium storage performance [14e16]. Several strategies have been proposed to circumvent the weaknesses of TiO2-B for lithium storage. Among them, fabricating heterogeneous nanostructures by combining TiO2-B with other active materials has been demonstrated to be an effective solution. This is because that those heterogeneous nanostructures can integrate diverse electrochemical functionalities by tailoring the morphology, composition and assembling organization of the individual components [17e20]. Specifically, hybridizing TiO2-B with carbonaceous materials (carbon nanotubes, graphene, etc.) has attracted numerous attentions [17,21,22]. Among those carbonaceous materials, the two-dimensional (2D) graphene is commonly used due to its high conductivity, structural flexibility and high specific surface area [15,16,21,23e25]. The electrochemical

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performance (especially the rate capability) of TiO2-B could be largely improved after hybridization with graphene owing to the enhanced electronic conduction. Nevertheless, we note most of those heterogeneous nanostructures of TiO2-B and graphene reveal relatively low capacities (less than 300 mA h g1 at 1 C), in which graphene contributes to a low reversible lithium storage [26,27]. Therefore, it could be academically interesting to hybridize TiO2-B with alternative materials that not only possess high conductivity but also show highly reversible lithium storage. In addition to graphene, 2D materials of the transition-metal dichalcogenides (TMDs) can be good candidates to hybridize TiO2-B due to their prominent conductivity as well as highly reversible lithium storage [28e30]. The 2D TMDs with a generalized formula of MX2 are a family of layered materials, where one layer TMD is composed of one layer transition metal M (Mo, W, etc) sandwiched by two atomic layers of chalcogens X (S, Se, or Te) [30]. In the family of TMDs, the VS2 is of special interest for extensive scientific attention due to its intrinsically metallic nature, unique electrical structure and high specific surface area [31e33]. Monolayer VS2 consists of a metal V layer sandwiched between two S layers, with these triple layers stacking together to form a layered structure with an interlayer spacing of 5.76 Å [34]. This large interlayer spacing offers a wide range of electron affinity and sufficient space for the intercalation of lithium-ions. Theoretical study revealed that the monolayer VS2 has a high theoretical capacity of 466 mA h g1 for lithium storage and a similar or lower lithiumions diffusion barrier compared to the widely-investigated MoS2 and graphite [35]. In this report, TiO2-B@VS2 heterogeneous nanowire arrays (TVNAs) on Ti foil were prepared through a facile two-step hydrothermal process and applied as additives-free anodes for LIBs. The layered VS2 nanoparticles are uniformly distributed on the surface of TiO2-B nanowire arrays (TNAs), forming a novel heterogeneous nanostructure. This self-supported one-dimensional heterogeneous nanostructure on a conductive substrate is particularly interesting due to the vertical ion- and electron-transport properties. Importantly, this heterogeneous nanostructure could effectively integrate the well electrochemical functionalities of

individual components, including good cycling stability of the TNAs and high capacity and conductivity of VS2.

2. Experimental section 2.1. Synthesis of TNAs on Ti foil The synthesis method of TNAs on Ti foil refers to the previous reports [36e38]. In brief, a piece of Ti foil (2  3 cm2) was firstly ultrasonically cleaned in water, acetone and ethanol for 15 min respectively. Then, the Ti foil was dried with a nitrogen gas flow and placed against the wall of a 50 mL Teflon-lined stainless steel autoclave filled with 30 mL of 1.0 M NaOH aqueous solution. The autoclave was sealed and put into an electronic oven at 220  C for 16 h. After cooled down to room temperature naturally, the sample was washed by water several times and immersed into a 1.0 M HCl aqueous solution for 30 min to replace Naþ with Hþ. The Ti foil was rinsed with water adequately and dried at 80  C in an oven after the ion exchange process. Finally, TNAs were obtained by annealing the Ti foil at 450  C for 3 h in a quartz tube furnace.

2.2. Preparation of TVNAs on Ti foil The as-prepared TNAs on Ti foil were put into a 50 mL Teflonlined stainless steel autoclave filled with 30 mL of an aqueous solution containing 50 mg NH4VO3, 100 mg thioacetamide (TAA) and 25 mg NaOH. The autoclave was then sealed and heated to 160  C for 20 h in an electronic oven. Afterwards, the obtained sample was rinsed with water and ethanol, and fully dried in a vacuum oven at 60  C for 12 h. To investigate the effects of VS2 content on the electrochemical performance, we prepared the samples with different VS2 contents by facilely tuning the dosages of NH4VO3 and maintaining the mass ratios of NH4VO3 to the other reactants. The samples obtained by using 25, 100 and 200 mg NH4VO3 were marked as TVNAs-S1, TVNAs-S2 and TVNAs-S3, respectively.

Scheme 1. Schematic illustration of fabrication of TiO2@VS2 heterogeneous nanowire arrays (TVNAs).

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2.3. Materials characterization X-ray diffraction (XRD) patterns of the materials were obtained with an X'Pert PRO X-ray diffractometer with Cu Ka radiation in the 2q range of 10 e80 at a scan rate of 3.5 min1. To further understand the phase structure of the as-prepared samples, Raman spectra of the products were collected on a Thermo scientific FTRaman spectrometer using an Nd-line laser source with an excitation wavelength of 532 nm. The morphology and crystalline structure of the samples were investigated by using Field emission scanning electron microscopy (FSEM, Nova NanoSEM 450) and high-resolution transmission electron microscopy (HR-TEM, Tecnai G220). 2.4. Electrochemical measurements The electrochemical measurements were carried out using 2032-type coin cells which were assembled in an Ar-filled dry glove box. The TNAs or TVNAs on Ti foil with cutting size of 1  1 cm2 was directly used as the working electrode and a metallic lithium foil was the counter electrode. 1.0 M LiPF6 dissolved in a mixture of EC (ethylene carbonate) and DEC (diethyl carbonate) with a volume ratio of 1:1 and Celgard 2400 membranes were used as the electrolyte and the cell separators respectively. Galvanostatic chargedischarge tests were carried out with a LAND CT-2001A battery tester at different current densities between the potential region of 0.01 and 3.0 V. Cyclic voltammetry (CV) tests were performed on a CHI660D electrochemical workstation between 0.01 and 3.0 V (vs. Liþ/Li) at a scan rate of 0.2 mV s1. Electrochemical impedance spectroscopy (EIS) measurements were conducted using the CHI660D electrochemical workstation in the frequency range of 100 kHz to 10 mHz with an AC amplitude of 5 mV. The mass loading of TNAs is about 1.2 mg cm2 determined by peeling off the film from Ti foil and measuring the weight difference by a Sartorius analytical balance (CPA225D, with a resolution of 10 mg). The mass percentages of VS2 in TVNAs, TVNAs-S1, TVNAs-S2 and TVNAs-S3 are about 21.5%, 12.0%, 45.0% and 76.5%, respectively, determined by the weight difference of the Ti foils before and after VS2 coating. 3. Results and discussion Scheme 1 presents the fabrication process of TVNAs on Ti foil. Firstly, TNAs grow onto a cleaned Ti foil with alkaline (NaOH) hydrothermal method, followed by ion exchange in HCl aqueous solution and calcination treatment at 450  C. Secondly, the layered VS2 nanoparticles are homogeneously deposited on the surface of TNAs via a second hydrothermal process in a low concentration of NaOH aqueous solution using NH4VO3 and TAA as reactants. The obtained TVNAs on Ti foil are directly used as additives-free anodes for LIBs without additional treatments, which can simplify manufacturing operation of the electrodes. The well-ordered heterogeneous nanowire arrays can be thoroughly exposed to electrolyte, exhibiting high lithium-ions accessibility. Meanwhile, the vertical electron-transport of TNAs could be enhanced after being decorated with the high-conductive VS2. Fig. 1a presents XRD patterns of the TNAs and TVNAs powder samples removed from Ti foils. Most diffraction peaks of the TNAs XRD pattern match well with those of the monoclinic TiO2-B phase (JCPDS no. 46e1237), indicating their primary crystal phase [16,25]. In addition, several weak diffraction peaks at 2-theta of 37.8 , 53.9 , 55.1, 62.3 can be indexed to the anatase (JCPDS no. 21e1272) [7,39], which is ascribed to the partial transformation of metastable TiO2-B under heating treatment [14,20,40]. After the second hydrothermal reaction, a few new diffraction peaks are observed in the XRD profile of the TVNAs sample. The diffraction peaks

Fig. 1. (a) XRD patterns of the TNAs and TVNAs powder samples removed from Ti foils; (b) Raman spectra of the TNAs and TVNAs samples on Ti foils.

appearing at 2-theta of 35.8 , 47.5 and 64.8 correspond, respectively, to the (011), (003) and (004) planes of hexagonal VS2 phase with a ¼ b ¼ 3.22 and c ¼ 5.75 Å (JCPDS no. 89e1640) [41,42]. The diffraction peaks of VS2 are much weaker than that of TiO2-B, which is due to the lower content of VS2. Fig. S1 shows the XRD patterns of the as-prepared samples with different VS2 contents (the mass percentages of VS2 in TVNAs, TVNAs-S1, TVNAs-S2 and TVNAs-S3 are about 21.5%, 12.0%, 45.0% and 76.5%, respectively). It is found that the diffraction peak of VS2 can be clearly observed with increasing the content of VS2. Raman characterization was further performed to understand the phase structures of the TNAs and TVNAs samples. In addition to the TiO2-B and anatase peaks, the observed peaks for the TVNAs sample in Fig. 1b at 286, 406, 693 and 995 cm1 are attributed to VS2 [41,43,44]. Among them, the peaks at 286 and 406 cm1 correspond to the E1g curvature mode and the A1g vibration mode of VS2 respectively. This further confirms the successful formation of VS2 in the TVNAs. Fig. 2 shows the SEM images of TNAs and TVNAs samples. The well-ordered vertical nanowire arrays are clearly observed for both samples. The length of the TNAs determined from Fig. 2a is 12 ± 0.5 mm. Besides, high-magnification SEM image shown in Fig. 2b reveals the TNAs consist of smooth nanowires with a

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diameter of 75e100 nm. The large aspect ratio (~130) of length to diameter for these nanowires ensures their full contact with electrolyte, exhibiting high lithium-ions accessibility. Fig. 2c and d present SEM images of the TVNAs sample with different magnification. Clearly, deposition of VS2 nanoparticles onto the TNAs largely increases their surface roughness. The TVNAs keep a similar length to the TNAs sample, while the diameters of individual nanowires increase to 105e130 nm. Fig. S2 presents the SEM images of TVNAs-S1 and TVNAs-S2 samples. The TVNAs-S1 sample shows a small quantity of VS2 nanoparticles attaching to the TNAs, while a mass of VS2 nanoparticles coat onto the TNAs thoroughly for the TVNAs-S2 sample. Obviously, the deposition amount of VS2 plays an important role on the morphology of the samples. The surface of TNAs varies from partially decoration to fully coverage with increasing the VS2 content. This would largely determine the electrochemical performance of the samples. The morphological and structural characterizations of TNAs and TVNAs samples were further investigated with transmission electron microscopy (TEM). As seen in Fig. 3a, the TEM image of the TNAs shows a smooth nanowire with a diameter of about 85 nm, which agrees well with the aforementioned SEM images. A wellcrystallized structure of the nanowire is observed from the HRTEM image (Fig. 3c) of the TNAs. The measured lattice spacings of about 0.36 and 0.62 nm correspond well to the (110) and (001) planes of TiO2-B, respectively [43,45]. Additionally, the lattice spacing of about 0.35 nm is in agreement with the (101) plane of anatase. Evidently, the TiO2-B is the primary crystal phase, consistent well with the XRD and Raman spectra studies. Compared

with the pristine TNAs, the TVNAs nanowire sample (Fig. 3b) exhibits a rougher surface, indicating the VS2 has successfully grown onto TNAs. It is noted that the VS2 nanoparticles show layered structure and uniformly distribute on the surface of TiO2-B nanowire. The HR-TEM image taken from the heterojunction region of the heterogeneous nanowire is shown in Fig. 3d. The measured lattice spacings of 0.36 and 0.62 nm are in agreement with the (110) and (001) planes of TiO2-B, respectively. Meanwhile, the measured interlayer spacing of 0.57 nm corresponds well to the c parameter of crystalline hexagonal phase VS2 [31,41]. The electrochemical performance of TNAs and TVNAs electrodes were evaluated in half-cells utilizing metallic lithium plates as the counter electrode. Fig. 4 compares cyclic voltammogram (CV) curves of TNAs and TVNAs electrodes at a scan rate of 0.2 mV s1 in the voltage range of 0.01e3.0 V. As depicted in Fig. 4a, each of the curves exhibits three pairs of characteristic anodic/cathodic peaks at around 1.61/1.47 V, 1.74/1.53 V and 2.10/1.70 V for the TNAs electrode. The two pairs of peaks at around 1.61/1.47 V and 1.74/ 1.53 V correspond to pseudocapacitive lithium storage of TiO2-B and the pair of peaks at around 2.10/1.70 V is ascribed to the solidstate lithium diffusion in anatase [16,46]. The overall lithium insertion/extraction process for the TNAs electrode could be described as reaction (1). Additionally, a broad cathodic peak at around 0.41 V can be detected in the first CV curve of the TNAs electrode, which attributes to the formation of a solid electrolyte interface (SEI) layer. Compared to the CV curves of the TNAs electrode, two more anodic/cathodic peak pairs appearing at around 2.70/2.10 V and 0.70/0.61 V in the CV curves of the TVNAs electrode

Fig. 2. FESEM images of (a, b) TNAs and (c, d) TVNAs.

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Fig. 3. TEM images of (a) TNAs and (b) TVNAs, HR-TEM images of (c) TNAs and (d) TVNAs.

Fig. 4. CV curves (first three cycles) of (a) TNAs electrode and (b) TVNAs electrode.

can be attributed to the lithium intercalation and deintercalation of VS2 according to the reaction process (2) [35,47]. Interestingly, the cathodic peak at around 2.10 V in the first cycle transfers to about 2.50 V in the followed cycles. This may derive from the irreversible structure change of VS2 crystal in the first cycle.

TiO2 þ xLiþ þ xe 4Lix TiO2

(1)

VS2 þ xLiþ þ xe 4Lix VS2

(2)

Fig. 5a and b show the first three charge and discharge curves for TNAs and TVNAs electrodes at a current density of 1 C (335 mA g1) in the voltage range of 0.01e3.0 V. The initial discharge capacity is 430.0 mA h g1 (0.516 mA h cm2) for the TNAs electrode and 513.7 mA h g1 (0.771 mA h cm2) for the TVNAs electrode. The

increased initial discharge capacity is mainly ascribed to the extra capacity contribution of the deposited VS2. The initial coulombic efficiency is 46.6% for the TNAs electrode and 54.8% for the TVNAs electrode, indicating large irreversible capacity losses for both electrodes. These capacity losses are mainly due to the formation of SEI layers on the electrode surface and the irreversible lithium insertion into TiO2-B and VS2 crystals. Fig. S3 shows the first charge and discharge curves of TVNAs-S1 and TVNAs-S2 electrodes. The initial discharge capacities of the TVNAs-S1 and TVNAs-S2 electrodes are 469.0 and 544.8 mA h g1, respectively, with coulombic efficiencies of 54.1% and 55.3%. Based on the above results, we can conclude that the electrodes with more VS2 not only deliver larger capacities but also show higher coulombic efficiencies, which are due to the higher capacity and conductivity of VS2 compared to TNAs. However, the optimal content of VS2 should be determined

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by further considering the cycling stability and rate capability. Fig. 5c compares the cycling performance of TNAs and TVNAs electrodes at 1 C rate. Owing to extra capacity contribution of VS2, the TVNAs electrode displays much higher capacities in all the cycles compared to the TNAs electrode. Besides, the TVNAs electrode shows high coulombic efficiencies of around 99.3% except in the first several cycles, revealing highly reversible lithium insertion and extraction. Impressively, the capacity of the TVNAs electrode becomes larger during cycling, which may result from electrochemical activation of the VS2 [48]. After 500 cycles, the reversible capacity of the TVNAs electrode reaches to 365.4 mA h g1 with a capacity retention efficiency of 129.9%. Meanwhile, the corresponding capacity of the similarly cycled TNAs electrode is 192.7 mA h g1 with a capacity retention efficiency of 96.1%. The high capacity retention efficiencies of the two electrodes reveal their good structural stability, which can be verified by the morphological evolutions of both the electrodes. As shown in Fig. S4, the nanowire morphology and their array structure are maintained after 500 cycles for both the electrodes. Fig. S5a depicts cycling performance of TVNAs-S1 and TVNAs-S2 electrodes. Though the TVNAs-S1 electrode demonstrates favorable cycling stability, it delivers lower capacity than the TVNAs electrode due to its lower VS2 content. Meanwhile, the TVNAs-S2 electrode displays rapid capacity fading in the cycling process. This may result from too much VS2 onto TNAs forming an unstable coating layer. After 500 cycles, the reversible capacities of the TVNAs-S1 and TVNAs-S2 electrodes are 249.8 and 112.7 mA h g1, respectively, with capacity retention efficiencies of 98.4% and 37.4%. By comparing the cycling performance of the electrodes with different VS2 contents, it is found that an optimal VS2 content is important for improving both the capacity and cycling stability of the electrodes. For comparison, the pure VS2 powder was prepared and its cycling performance for

LIBs was measured. As shown in Fig. S6, the pure VS2 powder consists of aggregated nanoparticles. The pure VS2 powder exhibits inferior cycling stability with a capacity retention efficiency of only 14.4% (Fig. S7). These results indicate the cycling stability of VS2 is largely depended on its morphology and structure, and the selfsupported one-dimensional heterogeneous nanostructure plays a vital role in enhancing the cycling stability of VS2. Fig. 5d shows the rate performance of TNAs and TVNAs electrodes. Due to the presence of VS2, the TVNAs electrode delivers higher capacity with discharge capacities of 536.9, 294.6, 253.5, 216.1 and 171.2 mA h g1, respectively, at 0.5 C, 1 C, 2 C, 5 C and 10 C rates. Meanwhile, the TNAs electrode maintains discharge capacities of only 499.4, 219.8, 168.6, 124.5 and 90.9 mA h g1, respectively, at 0.5 C, 1 C, 2 C, 5 C and 10 C rates. When the current density is set back to 1 C, the TVNAs electrode is still able to provide a capacity of 272.3 mA h g1 (corresponding to an initial capacity retention of 92.4%), manifesting good rate reversibility. Fig. S5b presents the rate performance of TVNAs-S1 and TVNAs-S2 electrodes. Compared to TVNAs electrode, the TVNAs-S1 electrode delivers lower capacities at a certain current density, which is ascribed to the lower VS2 content. Owing to the unstable VS2 coating layer on TNAs surface, the TVNAs-S2 electrode shows rapid capacity fading with increasing the current density. These results indicate an optimal VS2 content is necessary to maintain the higher rate capability of the electrodes, which is similar to the cycling stability investigation. To testify the enhanced electronic conductivity of TVNAs electrode, EIS was carried out and the corresponding Nyquist plots are depicted in Fig. 6. Both the Nyquist plots for the TNAs and TVNAs electrodes show a semicircular loop at high-to-medium frequencies, corresponding to the charge transfer resistance. A sloped straight line is observed at low frequencies, which represents the diffusion resistance. The radius of the

Fig. 5. First three charge and discharge curves of (a) TNAs electrode and (b) TVNAs electrode at a current density of 1 C. (c) cycling performance comparison of TNAs electrode and TVNAs electrode at a current density of 1 C. (d) rate performance of TNAs electrode and TVNAs electrode at various current densities from 0.5 C to 10 C.

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Fig. 6. Nyquist plots of TNAs electrode and TVNAs electrode after first cycle.

semicircular loop of the TVNAs electrode is much smaller than that of the TNAs electrode, suggesting that the TVNAs electrode shows a much lower charge transfer resistance, which supports the significantly enhanced rate performance of TVNAs electrode compared to the TNAs electrode. 4. Conclusions In summary, TiO2-B@VS2 heterogeneous nanowire arrays (TVNAs) have been prepared through a facile two-step hydrothermal process and applied as additives-free anodes for LIBs. The VS2 nanoparticles show a layered structure and uniformly distribute on the surface of TiO2-B vertical nanowire arrays (TNAs). The TVNAs electrode has effectively integrated the well electrochemical functionalities of the individual components, including the outstanding cycling stability of TNAs and high capacity and conductivity of VS2. As a result, the TVNAs electrode demonstrates superior lithium storage performance with a reversible capacity of 365.4 mA h g1 over 500 cycles at a current density of 1 C as well as a high rate capability of 171.2 mA h g1 at 10 C rate. Our study has verified the superior lithium storage performance of the TiO2-B@VS2 heterogeneous nanowire arrays, which may accelerate the development of other heterogeneous nanoarrays serving as high-performance electrodes in electrochemical energy storage. Acknowledgements Financial support from the National Basic Research Program of China (2014CB643506 and 2013CB922104), the Natural Science Foundation of Hubei Province (No: ZRZ2015000203), Technology Creative Project of Excellent Middle & Young Team of Hubei Province (No.: T201511) are acknowledged. The authors thank the Analytical and Testing Center of HUST and the Center of MicroFabrication and Characterization of WNLO for the measurements. Appendix A. Supplementary data Supplementary data related to this article can be found at http:// dx.doi.org/10.1016/j.jpowsour.2017.03.070. References [1] J.M. Tarascon, M. Armand, Nature 414 (2001) 359e367.

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