Triaxial Nanocables of Conducting Polypyrrole@SnS2@Carbon

5 days ago - Two-dimensional (2D) SnS2 materials represent a class of high-capacity candidates as anodes of Li-ion batteries (LIBs), however, they are...
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Triaxial Nanocables of Conducting Polypyrrole@SnS2@Carbon Enabling Significantly Enhanced Li-Ion Storage Jian-Gan Wang, Huanhuan Sun, Huanyan Liu, Dandan Jin, Xing-Rui Liu, Xu Li, and Feiyu Kang ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.8b02111 • Publication Date (Web): 04 Apr 2018 Downloaded from http://pubs.acs.org on April 4, 2018

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ACS Applied Materials & Interfaces

Triaxial Nanocables of Conducting Polypyrrole@SnS2@Carbon Enabling Significantly Enhanced Li-Ion Storage †











Jian-Gan Wang, * Huanhuan Sun, Huanyan Liu, Dandan Jin, Xingrui Liu, Xu Li, Feiyu Kang‡ †

State Key Laboratory of Solidification Processing, Center for Nano Energy Materials, School of Materials

Science and Engineering, Northwestern Polytechnical University and Shaanxi Joint Lab of Graphene (NPU), Xi’an 710072, China ‡

Engineering Laboratory for Functionalized Carbon Materials and Shenzhen Key Laboratory for Graphene-based

Materials, Graduate School at Shenzhen, Tsinghua University, Shenzhen 518055, China

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ABSTRACT Two-dimensional (2D) SnS2 materials represent a class of high-capacity candidates as anodes of Li-ion batteries (LIBs), however, they are limited by inferior rate and cycling performance. Herein, we demonstrate unique triaxial nanocables of conducting polypyrrole@SnS2@carbon nanofiber (PPy@SnS2@CNF) prepared via a facile combination of hydrothermal method and vapor phase polymerization. The PPy@SnS2@CNF manifests a strong synergistic effect from its hierarchical nanoarchitecture, which provides enlarged electrode/electrolyte contact interfaces, highly electrical conductive pathways, sufficient electrolyte ingress/transport channels, as well as an intimate mechanical/electrochemical safeguard for fast electrode kinetics and good structural stability. When evaluated as binder-free anodes of LIBs, the ternary nanocomposite delivers an ultrahigh reversible capacity of 1165 mAh g-1 after 100 cycles and outstanding rate/cycling performance (880 mAh g-1 at 2000 mA g-1), which are among the best results of the previously-reported SnS2 electrodes. This work may pave a rational avenue of developing 2D materials with hierarchical structures for high efficient energy storage systems. KEYWORDS: two-dimensional structure, SnS2, ternary nanocomposite, anode, Li-ion batteries

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INTRODUCTION The social concern on the energy and environmental problems propels the scientists searching for sustainable and renewable power sources and associated energy storage systems.1-3 Rechargeable Li-ion batteries (LIBs) have been considered as one of the most promising electrochemical energy storage technologies owing to their large specific energy and long cycle life.4, 5 However, with the fast booming of electric vehicles and smart electric grid, the current graphite anode used in the commercial LIBs is hindered by its small specific capacity with a theoretical value of 372 mAh g-1 as well as sluggish lithiation/delithiation kinetics, which make it difficult to satisfy the high energy and power density requirements of next-generation LIBs.6-8 To this end, tremendous endeavors have been dedicated to develop high-performance anode materials by nanoscale design and hybrid strategy.9, 10 In recent years, the flourish of two-dimensional (2D) materials has stimulated massive fundamental scientific and technological research interest.11,

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The versatile physiochemical

properties of 2D nanostructures make them fascinating in widespread application regions from energy storage devices, sensors to catalysts.13-15 It is demonstrated that 2D nanomaterials are favorable for energy storage, because the 2D structures, compared with their bulk counterparts, are of great benefit in increasing diffusion efficiency via layered nanochannels, reducing electrolyte transport distance, and buffering strains caused by volume excursions.11,

16

Transition metal

dichalcogenides, including SnS2, MoS2, and VS2, have been considered as possible electrode alternatives of LIBs.17, 18 Among them, it should be particularly mentioned that SnS2 with a layered CdI2-type hexagonal structure stands at the core of high-performance anode materials of LIBs.19, 20 First, the layered spacing of 5.9 Å facilitates easy insertion of Li+ (0.76 Å). Second, SnS2 could store Li+ by dual mechanisms of Li alloying/dealloying with metallic Sn and conversion Li-ion reaction 3 ACS Paragon Plus Environment

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with SnS2, which enable an ultrahigh theoretical storage capacity of 1230 mAh g-1. Unfortunately, the practical implementation of SnS2 is largely impeded by the inferior rate performance and poor cycling stability rendered by low electronic conductivity and huge volume variation upon charging/discharging processes, respectively. To ameliorate these crucial problems, a vast variety of research activities have been dedicated to explore various SnS2 nanostructures and/or their hybrids with conducting substrates.16, 21-32 Nevertheless, notwithstanding the established significant progress, the overall performance of these SnS2-based materials is still not satisfactory. The main reason may be ascribed to the direct exposure of SnS2 surface to the electrolyte, which gives rise to undesirable electrolyte corrosion and side reactions. Therefore, it is highly urgent and necessary to propose a new structure design strategy to achieve a full electrochemical potential of SnS2 nanomaterials by hetero-combining components with different properties and functionalities. In this study, we propose a unique triaxial nanoarchitecture of conducting polypyrrole@SnS2 nanosheet@carbon nanofiber (PPy@SnS2@CNF) nanocable prepared by hydrothermal method and vapor phase polymerization. The hierarchical configuration results in strong synergistic combination of each component to render a maximum energy harvest. In particular, the conducting PPy nanocoating enhances both the electrical conductivity and the structural integrity of SnS2 nanosheets, thereby enabling superior electrode reaction kinetics and stable cycling lifetime. Consequently, the ternary electrode delivers an ultrahigh reversible capacity of 1165 mAh g-1 along with outstanding rate performance (880 mAh g-1 at 2000 mA g-1) and excellent cycling durability, which is one of the best records on SnS2-based materials. The results demonstrate that our design strategy is effective and can be extended for the rational preparation of more2D materials with efficient energy storage. METHODS 4 ACS Paragon Plus Environment

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Materials Synthesis. All chemical agents were of analytical grade from Sinopharm, which were received without purification for the materials synthesis. CNF fabric was fabricated by a simple electrospinning technique using polyacrylonitrile (PAN, Mw=150000) as the carbon precursor according to our previous studies.33 SnS2@CNF nanocomposite were synthesized by a hydrothermal route. In a typical synthesis, 0.54 g of SnCl4·5H2O was dissolved into 30 mL of isopropyl alcohol followed by adding 0.46 g of thioacetamide. Then a piece of as-electrospun CNF (2*4 cm, ~1.6 mg cm-2) was placed vertically into the solution. Afterwards, Teflon-lined stainless steel autoclave was used to load and seal the solution. The autoclave was heated to 180 °C and maintained at this temperature overnight . When the temperature was naturally decreased to the ambient environment, the samples were rinsed with water several times, followed by drying at 80 °C overnight. For comparison, the pure SnS2 powders were synthesized under the same conditions without adding CNF. For the synthesis of PPy@SnS2@CNF, the as-received SnS2@CNF fabric was immersed in a 0.1 M FeCl3 solution for 30 min followed by drying. Subsequently, the as-treated fabric and a vial containing pyrrole monomers (500 µL) were sealed in a wide-mouth bottle. Finally, the bottle was heated to 50 °C for 24 h, during which the liquid pyrrole was gradually vaporized and penetrated into the fabric for PPy polymerization. The fabric was finally washed by water for five times to remove the residual FeCl3. The mass content of SnS2 and SnS2/PPy are about 1.8 and 2.1 mg cm-2 based on the weight difference before and after growth of active materials. The thickness of the freestanding fabrics is about 100 µm (Figure S1). Materials Characterization. The morphology and microstructure of the samples was characterized using field-emission scanning electron microscopy (FE-SEM, FEI Nano SEM 450) and transmission electron microscopy (TEM, FEI Tecnai F30G2). The crystal phase of the samples was examined 5 ACS Paragon Plus Environment

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using powder X-ray diffraction (XRD, X’Pert PRO MPD, Philips) with a Cu Kα radiation. Thermogravimetric analysis (TGA) was carried out for determination of mass ratio on Mettler Toledo DSC/TGA 3+. Raman Spectrometer (Renishaw inVia) was used

to record the Raman

spectrum (laser wavelength: 532 nm).. Fourier transform infrared (FTIR) spectrum was obtained on ThermoNicolet iS50 FTIR spectrometer. The surface composition of the ternary nanocomposite was analyzed by X-ray photoelectron spectroscopy (XPS, ESCALAB 250Xi, Thermo Scientific). Electrochemical Measurement. The freestanding hybrid fabrics were punched as binder-free working electrodes for direct use. The control electrode of pure SnS2 powders was fabricated by coating the slurry containing active materials (70 wt.%), carbon black (20 wt.%), and polyvinylidene fluoride (PVDF, 10 wt.%) binder onto Cu foils. CR2016 coin-type half cells were assembled in a

glove box

filled with pure Ar gases. The Li foils were used as the counter electrode, and the polypropylene paper was used as the insulating separator. The coil cells were filled with the electrolyte of 1 M LiPF6 in ethylene carbonate/diethyl carbonate (EC/DEC, 1 : 1 (v/v)). Cyclic voltammetry (CV) was conducted on Solartron electrochemical workstation (1260 + 1287, England)

at a scan rate of 0.1

mV s−1 within a potential of 0−3 V (vs. Li/Li+). Land Battery Testing system (Land, China) was used to measure the galvanostatic charge/discharge profiles at different current densities cycled between 0.01 and 3.00 V. The electrode kinetics was analyzed by electrochemical impedance spectroscopy (EIS) at open-circuit potential, which was obtained on Solartron electrochemical workstation operated in

10−2-106 Hz frequency range. The specific capacity (C) is based on the active materials,

which is calculated by subtracting the capacity contribution of pure CNF. The pure CNF shows a low reversible capacity of about 200 mAh g-1. (Figure S2). RESULTS AND DISCUSSION 6 ACS Paragon Plus Environment

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The typical synthesis processes of the PPy@SnS2@CNF triaxial nanocables is schematically illustrated in Figure 1. Electrospinning technique was employed to obtaining a freestanding CNF fabric with excellent mechanical strength and flexibility.33 SnS2 nanosheets were subsequently growing throughout the as-spun CNF fabric via a simple hydrothermal treatment. A uniform conducting PPy nanolayer was finally in situ coated onto the surface of SnS2 nanosheets by a rational vapor phase polymerization method, and consequently, constructing the hierarchically triaxial configuration of ternary PPy@SnS2@CNF nanocomposite.

Figure 1. Schematic illustration for the preparation process of PPy@SnS2@CNF triaxial nanocables.

SEM and TEM were employed to examine the morphology and structural information of the samples. Figure 2a shows the SEM image of the pure CNF fabric, which is composed of typical interconnected porous nanofiber network with smooth surface and uniform diameter size (~200-300 nm). It is notable that the CNF fabric provides abundant void spaces for easy solution flux and the subsequent growth of SnS2. As shown in Figure 2b, nanosheet-like SnS2 structures are conformally deposited surrounding individual nanofiber exterior surface without any impurity agglomerations. The well-preservation of the void spaces in between the CNF and SnS2 nanosheets is also of great 7 ACS Paragon Plus Environment

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benefit in vapor infiltration of pyrrole monomers, thereby ensuring the homogeneous polymerization of conducting PPy nanolayer. Figure 2c exhibits the porous architecture of the ternary PPy@SnS2@CNF nanocomposite, in which the PPy nanolayers are supposed to be uniformly aligned along the SnS2@CNF. In addition, the corresponding energy dispersive X-ray (EDX) mapping shows homogeneous distribution of elemental Sn, S, C, and N (Figure S3), indicating the conformal structure of PPy@SnS2@CNF. TEM imaging provides more detailed structure information of the PPy@SnS2@CNF nanocomposite. As shown in Figure 2d and 2e, the PPy@SnS2 nanolayers are intimately connected to the CNF cores, constructing unique triaxial configuration. The diameter of the triaxial nanocables increases to ~500 nm and the hybrid PPy@SnS2 nanolayers are about 100 nm in thickness. Figure 2f displays the edge HRTEM image of a PPy@SnS2 nanosheet. Clearly, a uniform and thin PPy layer with a thickness in 5-10 nm is observed to be tightly coated on the exterior SnS2 surface. In addition, the underneath lattice fringes with an interlayer distance of 0.59 nm corresponds to the typical 2D interplanar spacing of (001) facets of the crystalline SnS2. The preferential (001) edge exposure of SnS2 is demonstrated to be favorable for enhanced electrochemical reaction kinetics, because the lithiation process of SnS2 initially occurs with the insertion of Li+ ions into these 2D interlayer nanochannels.16, 28 As a control sample, flower-like SnS2 microspheres were synthesized by a similar hydrothermal route without the addition of CNF (Figure S4).

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Figure 2. SEM images of (a) CNF, (b) SnS2@CNF, and (c) PPy@SnS2@CNF samples. (d-e) TEM and (f) HRTEM images of PPy@SnS2@CNF nanocomposite.

The phase structure and its crystallinity of the samples are investigated by XRD, Raman, and FTIR measurements. As shown in Figure 3a, the three samples share one set of diffraction peaks, which corresponds well to the SnS2 with typical layered hexagonal structure.34, 35 It is worth to note that the peaks of the nanocomposites are of broad feature and low intensity, suggesting the SnS2 particle sizes are smaller than the pure SnS2 counterpart.36 The result agrees well with the SEM observation. In addition, no trace of other peaks is found, indicating a high purity of the materials. Raman spectra provide more details of the structural information (Figure. 3b). The strong Raman band at 311 cm-1 can be attributable to the A1g band of the SnS2 component.37 Additionally, the SnS2@CNF exhibit two wide peaks of graphitic band (G) and defect-induced band (D)of carbon structure at 1596 and 1354 cm-1, respectively. The introduction of PPy leads to a significantly enhanced D/G peak intensity due to the strong Raman-activity of the PPy aromatic backbone. The 9 ACS Paragon Plus Environment

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presence of PPy is further confirmed by the characteristic FTIR peaks (Figure S5).38, 39 Specifically, the adsorption bands at 1542/1446 cm-1 can be ascribed to the C-C/C-N stretching vibrations of pyrrole structure. Additionally, the peaks at 1300, 1168, 1093, and 1038 cm-1 belong to the in-plane deformation modes of C-N, C-H, NH+, and N-H bonds, respectively. The peaks at 965, 913, and 785 cm-1 are attributed to the C-C and C-H out-of-plane ring deformation vibrations. The mass ratio of SnS2/PPy and SnS2 is estimated by TGA analysis, which is about 54.9 wt.% and 52 wt.%, respectively (calculation details see Figure S6).

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Figure 3. (a) XRD and (b) Raman spectra of CNF, SnS2@CNF, and PPy@SnS2@CNF samples. XPS was measured to probe the surface chemistry and its elemental valence states of the ternary PPy@SnS2@CNF nanocomposite. The survey spectrum (Figure 4a) clearly shows main signal peaks belonging to the Sn, S, N, C, and O elements. The core-level Sn 3d spectrum (Figure 4b) presents a Sn 3d5/2 componenet at 486.2 eV and a Sn 3d3/2 component at 494.6 eV, which are characteristic of Sn4+ species.29, 40 The high-resolution S2p spectrum (Figure 4c) displays a shoulder peak that can be fitted into S 2p3/2 and S 2p1/2 subpeaks of S2-, suggesting the successful formation of SnS2 phase.41, 42 The N 1s spectrum (Figure 4d) exhibits a single pyrrolic-N peak with a binding energy at 399.5 eV, demonstrating the existence of PPy nanolayer.20 10 ACS Paragon Plus Environment

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Figure 4. XPS spectra of PPy@SnS2@CNF nanocomposite: (a) survey spectrum; and core-level spectra of (b) Sn 3d, (c) S 2p, and (d) N 1s. The as-prepared PPy@SnS2@CNF nanocomposite is served as binder- and additive-free anodes for LIBs to investigate the Li-ion storage performance. Binary SnS2@CNF paper and pure SnS2 powders are also examined for comparison. Figure 5a and Figure S7-S8 display the galvanostatic charge/discharge profiles of the three electrodes. During the first discharge process, the short voltage plateau at around 1.70 V can be attributed to the intercalation of Li+ into the 2D interlayer nanochannels of SnS2 accompanying with the generation of LixSnS2 phase (Eq. (1)).28,

43

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subsequent voltage plateau locating at ~1.25 V is related with the conversion reaction between LixSnS2 and Li+ to produce Li2S and metallic Sn (Eq. (2)).25, 27 The long sloped curve below 1.0 V can be due to the inevitable formation of solid-electrolyte-interface (SEI) layers caused by the 11 ACS Paragon Plus Environment

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decomposition of electrolyte and the multi-step reactions of Li+ alloyed with the Sn (Eq. (3)).16, 44 Upon charging, the voltage plateau below 0.9 V corresponds to the reversible process of Eq.(3), while the long sloped curve is related to the reverse formation of electro-active SnS2 via Eqs. (1-2). It is observed that the plateau at about 1.25 V (Eq. (2)) is well maintained in the ternary electrode during the extended cycles while that of the control electrodes fade away quickly, indicating that the introduction of PPy could help to retain the electrochemical activity and reversibility of SnS2.

SnS2 + xLi+ + xe ↔ LixSnS2

(1)

LixSnS2 + (4-x)Li+ + (4-x)e ↔ Sn + 2Li2S

(2)

Sn + 4.4Li+ + 4.4e ↔ Li4.4Sn

(3)

Figure 5b presents the cycling performance of the test electrodes. It is noted that the PPy@SnS2@CNF electrode delivers high specific capacities of 1469 and 1092 mAh g-1 in the first discharge/charge cycle, respectively, corresponding to an initial Coulombic efficiency as high as 74.3%. The Li-ion storage reversible capacity is higher than that of the control electrodes of SnS2@CNF (1009 mAh g-1) and pure SnS2 (794 mAh g-1), indicating the conducting PPy and CNF components could collectively improve the electrochemical utilization of SnS2. More remarkably, the ternary electrode manifests a much larger initial Coulombic efficiency than the binary SnS2@CNF electrode (61.2%) and pure SnS2 electrode (58.7%). It is believed that the enhanced Coulombic efficiency can be ascribed to the uniform PPy nanolayers, which enables uniform generation of SEI layers and minimizes the undesirable reactions of SnS2 with electrolyte.45-47 The irreversible capacity in the first cycle is primarily resulting from the inevitable generation of SEI layers and the unfavorable side reactions. The Coulombic efficiency of the ternary electrode dramatically increases to 97.7% from the second cycle and retains at >99% in the extended cycles (Figure 5b). Impressively, 12 ACS Paragon Plus Environment

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the ternary electrode does not show any capacity degradation over the cycling operations with a high reversible capacity of 1165 mAh g-1 being sustained after 100 cycles. In sharp contrast, the control electrodes suffer from serious capacity decay rate of 56% and 69% for the binary and pure SnS2 electrodes, respectively. The outstanding cycling stability demonstrates the importance of conducting PPy nanolayer to preserve the structural stability of the ternary electrode. As shown from Figure S9, the triaxial nanocable morphology of the ternary composite is well preserved after 100 cycling test, confirming the strong electrode stability. To highlight the significant advantage of the ternary composite, we compare the specific capacity of the recent previously-reported SnS2-based materials. As summarized in the Table S1 (supporting information), the electrochemical properties of the ternary electrode outperforms most of the reported results, which stands the top-level performance. The conducting PPy nanolayers are believed to be beneficial to promoting the electron transfer kinetics. Rate capability is examined to validate this enhanced electrode kinetics. Figure S10 displays the charge/discharge profiles of the ternary electrode at various current densities. The high-rate voltage profiles are consistent with those at low-rates, manifesting small polarization and high kinetic reversibility of the electrode. Figure 5c compares the rate capability of the three electrodes. It is worth noting that the ternary electrode could maintain average reversible capacities of 1065, 1033, 1009, and 880 mAh g-1 when the current rate increases to 200, 500, 1000, and 2000 mA g-1, which are much better than those of the binary and pure electrodes. The high rate retention of 80% from 100 to 2000 mA g-1 reveals excellent rate capability. In addition, a high and stable specific capacity of ~1200 mAh g-1 is regained as the current density is reduced to 100 mA g-1, again elucidating superior cycling stability of the ternary electrode. Electrochemical impedance spectrum (EIS) is used to obtain an insightful investigation of the enhanced electrode reaction kinetics. As exhibited in 13 ACS Paragon Plus Environment

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Figure 5d, the Nyquist curves possess similar feature of depressed semicircles and sloped lines in the medium-to-high and low frequency regions, respectively. The charge-transfer resistance (Rct) of electrode can be obtained from the semicircle diameter. Notably, the Rct of the ternary electrode (97 Ω) is much smaller than that of binary electrode (162 Ω) and pure electrode (490 Ω). As the lithiation/delithiation processes require a simultaneous charge collection and transport, charge transfer capability becomes an important factor of the whole electrochemical reaction. Therefore, the reduced Rct of the ternary electrode suggests a significant kinetic enhancement in the high-rate

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Figure 5. (a) Galvanostatic charge/discharge curves of PPy@SnS2@CNF electrode at 100 mA g-1. (b) Cycling stability (100 mA g-1), (c) Rate capability, and (d) EIS spectra of CNF, SnS2@CNF, and PPy@SnS2@CNF electrodes.

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Figure 6 illustrates the energy storage characteristics of the triaxial PPy@SnS2@CNF nanocable electrode to enable the prominent Li-ion storage properties. First of all, the uniform conducting PPy nanolayer coating plays a significant tri-functional role of (i) electron pathways to boost the interfacial charge transfer kinetics (high rate capability), (ii) surface mediator to minimize the irreversible side reactions (high initial Coulombic efficiency), and (iii) robust shield to accommodate the huge volume variation of the underneath SnS2 (long cyclic stability). Secondly, the 3D hierarchical network architecture allows for rapid electrolyte ingress/diffusion and sufficient electrode/electrolyte contact area. Thirdly, the nanoscaled SnS2 sheets could reduce the electron/ion transport distances and provide preferential 2D nanochannels for Li-ion insertion. Fourthly, the ultralong conductive CNF core assists in the long-range charge collection and transfer throughout the whole electrode. Finally, the freestanding hybrid eliminates the use of insulating binders that may bring sluggish kinetics and invalid sites. Overall, the ternary electrode ensures good electrical and mechanical bridge between each nanoscaled components, thereby resulting in strong synergistic effect with high and stable electrochemical utilization.

Figure 6. Energy storage characteristics of PPy@SnS2@CNF nanocomposite. 15 ACS Paragon Plus Environment

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CONCLUSIONS In summary, we have successfully fabricated triaxial nanocables of PPy@SnS2@CNF through a facile hydrothermal approach and a subsequent vapor phase polymerization. The CNF fabric provides excellent porous network scaffold for the growth of edge-terminated SnS2 nanosheets and the uniform coating of conducting PPy nanolayers. The ternary nanocomposite, when examined as binder-free anodes of LIBs, delivers an ultrahigh reversible capacity of 1165 mAh g-1, outstanding rate performance (880 mAh g-1 at 2000 mA g-1) and long-term cyclic durability. The superior Li-ion storage performance can stem from the unique 3D hierarchical nanoarchitecture, which is of great benefit in promoting the lithiation/delithiation reaction kinetics, enlarging the electrode/electrolyte contact interfaces, and safeguarding the mechanical/electrochemical stability of the ternary electrode. The present work may pave a rational strategy on the development of hierarchically-structured 2D hybrid materials for high-efficient energy storage.

Supporting Information Additional data, including: SEM images of pure SnS2 sample. FTIR spectra of PPy@SnS2@CNF materials. Vvoltage profiles of SnS2@CNF and SnS2 electrodes. SEM image of PPy@SnS2@CNF after cycling test. Voltage profiles of the PPy@SnS2@CNF electrode at various current densities. A table summary of Li-storage performance. This material is available free of charge via the Internet at http://pubs.acs.org. AUTHOR INFORMATION Corresponding Authors *E-mail: [email protected] (J.-G. Wang) 16 ACS Paragon Plus Environment

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ACKNOWLEDGMENTS The authors want to acknowledge the research supports from the National Natural Science Foundation of China (51772249, 51521061), the Hong Kong Scholars Program (XJ2017012), the Program of Introducing Talents of Discipline to Universities (B08040), the Research Fund of the State Key Laboratory of Solidification Processing (NWPU), China (Grant No.: 123-QZ-2015), and State Key Laboratory of Control and Simulation of Power System and Generation Equipment (Tsinghua University, SKLD17KM02), and the Fundamental Research Funds for the Central Universities (G2017KY0308).

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