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Li2O reinforced Cu nano-clusters as porous structure for Dendrite-free and Long-lifespan lithium metal anode Zhenggang Zhang, Xiaoyue Xu, Shuwei Wang, Zhe Peng, Meng Liu, Jingjing Zhou, Cai Shen, and Deyu Wang ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.6b08775 • Publication Date (Web): 20 Sep 2016 Downloaded from http://pubs.acs.org on September 26, 2016
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Li2O reinforced Cu nano-clusters as porous structure for Dendrite-free and Long-lifespan lithium metal anode Zhenggang Zhangac, Xiaoyue Xua, Shuwei Wanga, Zhe Penga*, Meng Liua, Jingjing Zhoub, Cai Shena*, Deyu Wangab*
a. Ningbo Institute of Materials Technology and Engineering, Chinese Academy of Sciences, Ningbo 315201, China. b. Materials Genome Institute of Shanghai University, Shanghai 200444, China. c. ShanghaiTech University, Shanghai 200031, China. Keywords: Lithium metal anode, Coulombic efficiency, Solid electrolyte interphase layer, Dendrite, Alkyl carbonate electrolyte, Copper oxide nano-structure.
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Abstract: A nano-structured protective structure, pillared by the copper nano-clusters and insitu filled with lithium oxide in the interspace, is constructed to efficiently improve the cyclic stability and lifetime of lithium metal electrodes. The porous structure of copper nano-clusters enables high specific surface area, locally reduced current density and dendrite suppressing, while the filled lithium oxide leads to the structural stability and largely extends the electrode lifespan. As a result of the synergetic protection of the proposed structure, lithium metal could be fully discharged with efficiency ~97% for more than 150 cycles in corrosive alkyl carbonate electrolytes, without dendrite formation. This approach opens up a novel route to improve the cycling stability of lithium metal electrodes with the appropriate protective structure.
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1. Introduction Dedicated to intensively growing market of electronic devices, high energy density batteries are urgently demanded. After decades of development, the upper energy density limitation (~300 Wh kg-1) of the Li-ion batteries (LIBs) are almost reached.1 Under this context, the innovative system of Li metal based batteries is highly preferable due to the attractive high capacity of Li metal which is 10 times higher than this of the graphite anodes.1 If a utilization ratio of 30% can be attained, Li metal could deliver normalized capacities of 1140 mAh g-1 & 610 mAh cm-3, which largely exceeds these of the graphite anodes (370 mAh g-1 & 468 mAh cm-3). However, this moderate demand is still hard to be realized to date. One of the most serious challenges is the absence of an efficient remedy to isolate Li metal from the electrolyte’s attack, which results in continuous consumption of the solvents and lithium metal until the battery failure. Inherently, the electrolyte solvents could immediately react with Li metal once in contact due to the gap between their energy levels. Part of solvents, such as carbonates and ethers, could form stable protective layers on Li metal surface in static condition, namely called the solid electrolyte interphase (SEI) layers.2,3 However, in dynamic condition upon repeated Li plating and stripping, the protective layers are continuously lacerated by the infinite surface volumetric variation and dendrite-like growth of Li metal, resulting in massive cracks through which the electrolyte permeates to react with Li metal (Scheme 1). Besides the Li loss, these reactions also result in aggregated polarization due to the accumulation of side reaction products and the dry-up of electrolyte. Various strategies have been explored to address the continuous lacerations of the surface layer on Li metal, including the reinforcement of the SEI layers4-9 and construction of artificial isolating layers10-13. As an initial attempt, the electrolyte composition has been optimized by
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varying the solvents, salts and additives to improve the quality of SEI layers.4-9 Till to date, almost none of them has shown a remarkable effect to significantly extend the cycling life of Li metal electrodes. Another approach to build artificial isolating layer, such as amorphous carbon and polymer, obviously improved the cyclic stability of Li metal.10-13 However, all of them required complicated preparative procedures, which limited their further application. In a recent effort, we proposed a porous ceramic coating layer to provide relatively rigid space for lithium growth, with aim of suppressing the volumetric variation.14 The Coulombic efficiency of Li plating/stripping has been significantly improved through this protective structure yet to be developed for its lifespan, probably due to the limited mechanical strength of binder. The origin of the growth of Li dendrites arises from the spatial inhomogeneity in charge distribution over the entire electrode surface, especially occurring at high current density causing the depletion of ion concentration nearby the electrode surface. Recently, it has been reported by Yang et al. a 3D current collector to accommodate Li metal on a Cu template with surfacedeposed Cu nanowire,15 in which a higher specific surface could enable a better current distribution for Li plating to hinder the dendrite growth, compared to the planar current collector, such a 3D current collector exhibited a stable Coulombic efficiency of ~97% for 50 cycles at 0.5 mA cm−2. In this work, we prepared a more advanced, long-lifespan, 3D porous current collector with intrinsically integrated structure, pillared by the copper nano-clusters with in-situ filled lithium oxide in the interspace, to improve the stability of Li plating and stripping, as shown in Scheme 1. Through the electrochemical reduction of CuO nano-clusters by Li+ ions, the reduced Cu nanoclusters could largely raise the specific surface area and supply a porous space for Li metal accommodation than the planar Cu, resulting in locally reduced current density and dendrite
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suppressing; on the other hand, the filled Li2O could efficiently reinforce the porous structure and enable a lifespan much longer than that of planar Cu electrode and the electrode only constituted of Cu nano-clusters. The SEI layer formed on this 3D composite layer effectively isolates the lithium metal from electrolyte’s attack, even in corrosive alkyl carbonate electrolytes. The cyclic stability of the protected system could be improved for more than 150 cycles with an average columbic efficiency as high as ~97%.
Scheme 1. Illustration of the different Cu substrates and related Li deposition morphologies.
2. Experimental section 2.1 Electrode preparations
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To obtain the CuO nano-clusters based electrode, a Cu foil (3.5×3.5×0.0015 cm3) was cleaned by performing consecutive ultrasonication in acetone, ethanol, and distilled water, and then in 1.0 M HCl solution for 10 min. Then, the prepared Cu foil was immersed in a 0.1 M NaOH solution to 50% volume filling in a 100 mL autoclave. Finally, the autoclave was sealed and maintained at 80℃ for 4 h, and then cooled naturally to room temperature to obtain the CuO nano-clusters covered electrode. The ex-situ reduced Cu nano-clusters based electrode was obtained through the chemical reduction of CuO to Cu nano-clusters under H2:Ar (5:95) atmosphere, at 250℃ for 12h, with temperature ramping of 5℃ min-1. 2.2 Electrochemistry Cycling tests were performed using a battery testing system (LandCT2001 from LAND electronics Co., Ltd.). Cu electrodes were used as working electrodes. Li foils were used as counter electrodes. Coin cells CR2032 were used for cell assembly, with Celgard separator film (diameter: 18 mm; thickness: 20 µm) in which an electrolyte amount of 70 µL was deposed. The electrolytes consisted of a commercial electrolyte (1M LiPF6 in 1:1 ethylene carbonate, EC and dimethyl carbonate, DMC, Guotai-Huarong New Chemical Materials Co., Ltd.), with addition of Vol. 2% Fluoroethylene carbonate, FEC (Sigma-Aldrich Co. LLC.) as additive. The cyclic voltammetry (CV) curves and electrochemical impedance spectroscopy (EIS) spectra were measured using a potentiostat/galvanostat 1470E equipped with a frequency response analyzer, FRA 1455A from Solartron. For the CV, the voltage sweep rate was 0.05 mV s-1 between 0 and 2 V vs Li/Li+. The EIS measurements were performed on the frequency range of 10-1-105 Hz with a voltage perturbation of 5 mV. 2.3 In-situ AFM characterizations
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In-situ atomic force microscopy (AFM) experiments were conducted in an argon-filled glovebox (MBRAUN, H2O ≤0.1 ppm, O2≤0.1 ppm) at room temperature. The CuO-NC/Cu electrode was used as working electrode (WE) and Li wires were used as counter and reference electrodes (CE and RE). The electrolytes consisted of a commercial electrolyte (1M LiPF6 in 1:1 ethylene carbonate, EC and dimethyl carbonate, DMC, Guotai-Huarong New Chemical Materials Co., Ltd.), with addition of Vol. 2% Fluoroethylene carbonate, FEC (Sigma-Aldrich Co. LLC.) as additive. In order to study the CuO structure evolution, the cell was studied by cyclic voltammetry (CV) at a scanning rate of 0.25 mV s−1 from 3 to 0 V. AFM topography was collected simultaneously in ScanAsyst mode using nitride coated silicon probes (tip model: SCANNASYST-FLUID with k = 0.7 N m-1). 2.4 Electrode characterizations After being cycled, the cells with Cu electrodes were carefully disassembled in glove box. The Cu electrodes were rinsed with pure DMC in order to eliminate residual trace of solvents and salts, and then stored in glove box for further characterization. The microscopy analysis of the surface morphology was performed using scanning electron microscopy (SEM, FEI, QUANTA 250 FEG) and transmission electron microscopy (TEM, FEI, Tecnai F20, 200 kV). The crystalline phase of the prepared samples was characterized by X-ray diffraction (XRD) with a Bruker D8 advanced diffractometer using CuKα (λ = 1.5406 Å) radiation (Bruker axs, D8 Advance) between 10° and 80° in 0.02° step per second. Surface analysis was conducted with a PHI 3056 X-ray photoelectron spectrometer (XPS), which was excited by an MgKα radiation source at a constant power of 100 W (15 kV and 6.67 mA). Nitrogen gas adsorption measurement was carried out on an ASAP2020 analyzer from Micromeritics, Inc.
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3. Result and Discussion The common copper foil is appropriately roughed through a simple hydrothermal route,16 and the formation of CuO nano-clusters on the substrate surface has been verified. As shown in Figure 1, after treatment, the copper foil was covered by the black products (Figure 1a), for which the morphology is presented as nano-clusters with 40-60 nm in diameter, shown by scanning electron microscopy, SEM images (Figure 1b and c) and transmission electron microscopy, TEM (Figure 1d). The tilted view of SEM (Figure 1e) demonstrates that this oxidized layer is ~1 ߤm. The surface of the CuO nano-clusters based copper substrate (denoted as CuO-NC/Cu) was confirmed with X-ray diffraction, XRD pattern (Figure 1f), in which the CuO-NC/Cu sample was composed of the copper metal as the dominant phase (JCPDS card No. 41-0254) and cupric oxide as the second phase (JCPDS card No. 41-0254), showing obvious diffraction peaks at 36 and 38.6o indexed to CuO, and a peak at 32.5o indexed to Cu2O indicating a transitional Cu2O layer between Cu substrate and CuO nano-clusters. Neither the CuO nor the Cu2O peaks in XRD pattern can be observed on the bare Cu substrate. The ionic state of copper in CuO was also confirmed with X-ray photoelectron spectrometer, XPS (Figure 1g), with the Cu 2p shakeup satellite lines at 938.2, 942.3, and 962.2 eV, which were not present on the bare Cu substrate. For comparison, an ex-situ reduced Cu nano-clusters based substrate (denoted as CuNC/Cu), was also obtained, by reducing the CuO-NC/Cu under H2:Ar atmosphere. The same XRD patterns and XPS spectra between the Cu-NC/Cu and bare Cu indicate the successful conversion of CuO into Cu at the substrate surface (Figure 1f and g). As a result, the substrate surface was converted to Cu nano-clusters (Figure 1h) with slightly agglomerated morphology (Figure 1i and j). Both of the samples with nano-clusters have very close BET surface areas,
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1.034 and 1.06 m2 g-1 for CuO-NC/Cu and Cu-NC/Cu, respectively, which are ~2 times higher than that of the bare Cu foil (0.456 m2 g-1, Figure S1).
Figure 1. (a) Digital photo of the Cu substrate covered by CuO nano-clusters; (b-c) SEM top view of the CuO nano-clusters; (d) TEM image of the CuO nano-clusters; (e) SEM tilted view of the surface of CuO nano-clusters; (f) XRD and (g) Cu 2p XPS spectra of the bare Cu, the
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substrates covered by Cu and CuO nano-clusters; (h) Digital photo of the Cu substrate covered by Cu nano-clusters; (i-j) SEM top view of the Cu nano-clusters.
The behaviors of three electrodes, bare Cu, Cu-NC/Cu, and CuO-NC/Cu, on lithium deposition and dissolution are evaluated within Cu/Li batteries for a capacity density of 1 mAh cm-2, with a current density of 0.5 mA cm-2. In the first cycle, the Coulombic efficiency for bare Cu electrode is 83.2%, which is close to our previous results (Figure 2a).14 Cu-NC/Cu sample delivered a much higher value of the 1st Coulombic efficiency ~91.3%, revealing that the side reactions were obviously suppressed under the nano-clusters based porous structure (Figure 2b).15 As for CuO-NC/Cu sample, it exhibited the lowest efficiency ~59% (Figure 2c). The latter should correspond to the conversion of CuO + 2 Li+ + 2 e- → Cu + Li2O, which was identified by the redox peaks in cyclic voltammetry, CV (Figure S2),17-19 and the absence of CuO signals in XRD patterns for the reduced CuO-NC/Cu electrode (Figure S3). Also, the peak of metal-oxide bonding at 530.6 eV in the O 1s XPS spectrum corresponding to CuO disappeared after the reduction, while the appearance of Li 1s peak and large contribution of oxygen-containing organic species at 532.1 eV in the O 1s spectrum justified the formation of SEI layer with Li2O and other lithium-containing species (Figure S4).
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Figure 2. Charge-discharge profiles of (a) the bare Cu, (b) the Cu-NC/Cu, and (c) the CuONC/Cu electrodes, with a current density of 0.5 mA cm-2.
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The morphological transition in the conversion of CuO + 2 Li+ + 2 e- → Cu + Li2O was observed though the in-situ observation by atomic force microscopy, AFM. Figure 3a-c show the surface layer of CuO-NC/Cu electrode at different discharge potentials. After a discharge down to 1.68-1.46 V (vs. Li/Li+), the initial pillar shaped grains “meltdown” and were no more visible but a smooth surface with compact and uniform morphologic surface was detected. The formation of such structure could be due to the formation and filling of Li2O on the electrode during reduction. Upon further reduction to 0 V, the surface morphology continues to change. Note that such variation of the surface morphology may be caused by the formation of SEI and/or the conversion reaction as the insertion of Li+ ions induces volume expansion. It has been reported the theoretical volume expansion is equal to 80% when CuO is fully converted into Cu/Li2O. The line profiles in Figure 3d corresponding to the lines in (a) and (c) clearly showed that after reduction the surface morphological changed significantly and became very smooth. An overview of the 3D surface structure of the CuO-NC/Cu electrode before/after the reduction is given in Figure S5. One should be mentioned that the nano-structured CuO is only electrochemically active in the first cycle for its reduction into nano-structured Cu and Li2O. Once the reduction is accomplished, the substrate is no more active since the applied potential of the anode is below the re-oxidation potential of Cu.
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Figure 3. In-situ AFM images of CuO-NC/Cu electrode at various discharge stage. (a) The opencircuit voltage, 3.0 V; (b) 1.68-1.46 V; (c) 0.19-0 V; (d) line profiles correspond to images (a) to (c), scale bar: 1 µm.
The surface-modified samples present much better cyclic stability than that of bare copper foil. The Coulombic efficiency of the CuO-NC/Cu electrode was stabilized at ~96.7% for more than 150 cycles, while the bare system only achieved an average value of 74.3% before the cell failure at the 50th cycle (Figure 4a). Intermediately, the Cu-NC/Cu electrode exhibited an average efficiency of ~94% before the start of fluctuating state at the 36th cycle. Obviously, although the generated nano-structure kept the columbic efficiency to a higher level, the better performance
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still required the Li2O filling into the interspace between Cu pillars to stabilize the porous structure and the above-formed SEI layer.
The charge-discharge profiles of the bare Cu cell are shown in Figure 4b, fluctuant and increased polarizations (the potential difference between the plating and stripping plateaus) were observed in the bare Cu cell (~0.2 V for the 50th cycle). In contrast, the polarizations of the CuNC/Cu ~0.025 V were not affected upon cycling, while its Coulombic efficiency dropped to 61.5% at the 50th cycle (Figure 4c). The latter could probably due to an unstable electrode/electrolyte interface during cycling. Again, as mentioned before, the stable cycling of the Li metal need the Li2O filling into the interspace of the generated nano-structure, as shown by the polarization remained at 0.03 V for more than 150 cycles in the CuO-NC/Cu based cell (Figure 4d).
The high performances of the CuO-NC/Cu electrode should originate from the very stable electrode/electrolyte interface. To illustrate the interfacial state evolution, the repeated electrochemical impedance spectra, EIS were measured after each Li plating/striping with a capacity density of 1 mAh cm-2. As shown in Figure 4e and f, both of the bulk (Rb) and interfacial (Ri) resistances in the cell with bare copper foil were quickly augmented, i.e., 7.3 & 18.2 Ω for Rb & Ri in the 1st cycle and 115.7 & 243.9 Ω for Rb & Ri in the 15th cycle. It suggests a quick rate of electrolyte consumption and fast reparation of the interfacial layer, rooted in the continuous cracking of the SEI layer. In contrast, the CuO-NC/Cu electrodes exhibited relatively stable resistances, 2.4 & 48.6 Ω for Rb & Ri in the 1st cycle and 8.6 & 45.2 Ω for Rb & Ri in the 100th cycle. The high Ri value of CuO-NC/Cu sample at initial cycles should be related to Li2O’s filling in the interspace.
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Figure 4. (a) Coulombic efficiency of the Cu/Li cells with the bare Cu, the Cu-NC/Cu and the CuO-NC/Cu electrodes; Charge-discharge profiles of (b) the bare Cu, (c) the Cu-NC/Cu and (d) the CuO-NC/Cu electrodes in Cu/Li cells; (e) EIS spectra and (f) the bulk (Rb)/interfacial (Ri) resistances of the bare Cu and CuO-NC/Cu electrodes in Cu/Li cells.
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To further compare the interfacial characteristics, the surface morphologies of the investigated electrodes after 10 cycles are shown in Figure 5a-f. Largely generated products islanded on the electrode surface were observed for the bare Cu sample (Figure 5a and b), while more compact side-products were still observed for the Cu-NC/Cu sample (Figure 5c and d). It is interesting to note that the much rugged surface on the inter wall of the pores was formed for Cu-NC/Cu (the inset of Figure 5d), which suggests that the inhomogeneity still persisted during the formation and reparation of the SEI layers onto the Cu nano-clusters structure. No side-products accumulation was observed on the CuO-NC/Cu electrode. It seems that a dense surface-film covered the electrode (Figure 5e and f).
The SEM images of disassembled electrodes after the cycling tests (Figure 5g-l) showed highly developed dendrites at micro-scale length on the bare Cu substrate (Figure 5g and h). In contrast, dense and flat morphology of deposited Li was observed both on the Cu-NC/Cu (Figure 5i and j) and CuO-NC/Cu electrode (Figure 5k and l), however, with larger cracks found on the Cu-NC/Cu. The latter demonstrated that the Li2O filling into the interspace between Cu pillars could effectively conduct to better stability of the SEI layers. These results suggest that a dense and stable composite layer formed on our nano-structured CuO-NC/Cu electrode can well protect the Li metal form electrolyte’s attack, which is consistent with the EIS results.
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Figure 5. SEM images of (a-b) the bare Cu, (c-d) the Cu-NC/Cu (with tilted view in the inset of d), and (e-f) the CuO-NC/Cu electrodes after 10 cycles (1 mAh cm-2 Li was plated/stripped during 1 cycle); SEM images of (g-h) the bare Cu, (i-j) the Cu-NC/Cu, and (k-l) the CuO-NC/Cu electrodes dissembled after the long-cycling tests.
Performances at different capacity loading on the CuO-NC/Cu electrode was compared and shown in Figure 6a, high Coulombic efficiency ~97% was attained in all of the three capacity loading (1, 2 and 4 mAh cm-2). It suggested that the Li2O filled Cu nano-clusters layer was capable to accommodate the thickness change of deposited Li metal. As shown by the Figure S6a, after the 1st cycle of the CuO reduction, the as-formed protective layer reserved an interfacial space towards the Cu substrate which should be auto-adjusted to protect different thickness of deposed Li metal. As for the shorter working life of the samples with high capacity loading of 4
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mAh cm-2, it should be related to higher electrolyte consumption on both of the working and counter electrodes. The latter could be illustrated by the quickly increased polarization during cycling (Figure 6b). As well, SEM images of the CuO-NC/Cu electrode surface after the long cycling with high capacity loading of 4 mAh cm-2 show cracks and growth of dead Li out of the structure, suggesting that a too high capacity loading can still lead to the structure collapse beyond the mechanical tolerance of this protective structure (Figure S6b).
Various current densities have been considered to assess the charge transfer through the CuONC/Cu electrodes. Increased polarizations were observed with increased current densities (Figure 6d). However, the changes were not immense, for example, at the 5th cycle, the polarizations are 0.03, 0.05 and 0.08 V for 0.5, 1 and 2 mA m-2, respectively. Since the Li2O is an insulating material, the maintained polarizations should be due to the reduced Cu nanoclusters pillaring the protective structure which enables a locally reduced current density. The Coulombic efficiencies were decreased at 94% and 89% over 90 cycles for 1 and 2 mA cm-2, respectively (Figure 6c). The affected cycling stability could be due to a high reaction rate which results in Li+ concentration depletion nearby the electrode surface, and particularly, at the counter electrode side (Li foil) where the dendrite could be quickly generated and consume high amount of the electrolyte.
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Figure 6. (a) Coulombic efficiencies and (b) Charge-discharge profiles of the CuO-NC/Cu electrodes for different capacity loading; (c) Coulombic efficiencies and (d) Charge-discharge profiles of the CuO-NC/Cu electrodes for different current densities.
To identify the influence of surface morphology, the copper foil was directly burned under air to generate CuO layer. As shown in the Figure S7a, a foam surface structure was obtained through this simple method. The cycling performances were kept to the 48th cycle with an average columbic efficiency of 55.3%, even lower than that of the bare Cu and much lower than CuO-NC/Cu sample (Figure S7e). Observed with SEM, some side-products were found on the reduced Cu surface (Figure S7b) after the electrochemical reduction, and massive cracks were scattered on the electrode surface after cycling test (Figure S7c). Obviously, this type of CuO did not possess ability to protect the Li metal from the electrolyte’s attack, and in contrast, leaded to
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the formation of a very thick Li2O layer which impeded the ion transfer resulting in high polarization (Figure S7d). Thus, the unique protection could be suggested for the morphology of CuO nano-clusters.
4. Conclusion We have studied the influence of several substrate structures on the stability of lithium stripping & plating. Among the investigated samples, the copper oxide nano-clusters based copper substrate, CuO-NC/Cu, evolved to the copper nano-clusters pillaring the interspace that was in-situ filled with lithium oxide, presented the best ability to protect the lithium from the electrolyte’s attack. Li metal deposited on such a substrate could be fully discharged with efficiency as high as ~97% for long lifespan, without dendrite formation. Our approach provided an easily scale-up method to improve the cyclic stability of lithium metal with the appropriate protective structure, which sheds light on the practical application of lithium metal electrodes.
ASSOCIATED CONTENT Supporting Information Supplemental BET, CV, XPS, XRD, AFM and SEM results, electrochemical performance of CuO layer generated by burning a copper foil. This material is available free of charge via the Internet at http://pubs.acs.org.
AUTHOR INFORMATION
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Corresponding Author *Zhe Peng, E-mail:
[email protected] *Cai Shen, E-mail:
[email protected] *Deyu Wang, E-mail:
[email protected] Notes The authors declare no competing financial interests. ACKNOWLEDGMENT This work was supported by the 863 project (Grant No. 2013AA050906), the “Strategic Priority Research Program” (Grant No. XDA09010403), the National Natural Science Foundation of China (Grant No. 21303236), and Zhejiang Province Key Science and Technology Innovation Team (Grant No. 2013PT16). Zhe PENG thanks the financial support from the China Postdoctoral Science Foundation funded projects (Grant No. 2015M570530 and 2016T90556) and Ningbo Natural Science Foundation (Grant No. 2016A610278). Cai SHEN thanks the financial support from the Ningbo 3315 plan, the Youth Innovation Promotion Association, CAS. REFERENCES (1) Bruce, P. G.; Freunberger, S. A.; Hardwick, L. J.; Tarascon, J. M. Li-O2 and Li-S Batteries with High Energy Storage. Nat. Mater. 2012, 11, 19-29. (2) Winter, M.; Appel, W. K.; Evers, B.; Hodal, T.; Moller, K. C.; Schneider, I.; Wachtler, M.; Wagner, M. R.; Wrodnigg, G. H.; Besenhard, J. O. Studies on the Anode/Electrolyte Interface in Lithium Ion Batteries. Monatsh. Chem. 2001, 132, 473-486.
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