Facile synthesis of ultrathin-shell graphene hollow spheres for high-performance lithium-ion batteries

Electrochimica Acta 139 (2014) 96–103

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Facile synthesis of ultrathin-shell graphene hollow spheres for high-performance lithium-ion batteries Dandan Cai a , Liangxin Ding a,∗∗ , Suqing Wang a , Zhong Li a , Min Zhu b , Haihui Wang a,∗ a

School of Chemistry & Chemical Engineering, South China University of Technology, Guangzhou 510640, China School of Materials Science and Engineering, Key Laboratory of Advanced Energy Storage Materials of Guangdong Province, South China University of Technology, Guangzhou 510640, China b

a r t i c l e

i n f o

Article history: Received 30 April 2014 Received in revised form 23 June 2014 Accepted 8 July 2014 Available online 16 July 2014 Keywords: Graphene Hollow spheres Anode materials Lithium-ion batteries

a b s t r a c t In this work, ultrathin-shell graphene hollow spheres have been designed and synthesized from the graphene oxide nanosheets by a simple template assisted method without surfactant. It is found that the obtained graphene hollow spheres have a high surface area (248.3 m2 g−1 ), ultrathin porous shells (5 nm) and an interconnected structure. More strikingly, the as-prepared graphene hollow spheres exhibit outstanding electrochemical performance as an anode material for lithium-ion batteries. Even at a high current density of 5000 mA g−1 , a high reversible specific capacity of 249.3 mAh g−1 can be achieved. Furthermore, after 100 cycles, about 97.1% of the specific capacity is maintained at a high current density of 1000 mA g−1 . The excellent electrochemical properties could be attributed to the attractive structure advantages of the graphene hollow spheres including the high surface area, ultrathin porous shells and an interconnected structure. © 2014 Elsevier Ltd. All rights reserved.

1. Introduction Lithium-ion batteries (LIBs) have been widely used in portable electronic devices due to their high energy density, long cycle life and excellent safety. As the further application in hybrid electric vehicles and electric vehicles, their rate performance urgently needs to be improved [1,2]. Nowadays, graphite is the most commonly commercial anode material for LIBs owing to its high electrical conductivity and low cost. But the low theoretical specific capacity (372 mAh g−1 ) and the relatively low lithium diffusion coefficient (10−7 ∼10−10 cm2 s−1 ) restrict the further application in LIBs [3,4]. Thus, there is an urgent need to design and synthesize a highly effective anode material for high-performance LIBs. Recently, various alternative materials, such as transition metal oxides, silicon-based materials, and tin-based materials have been intensively studied as the potential anode materials for LIBs due to their high theoretical specific capacities [5,6]. Unfortunately, the above-mentioned materials are vulnerable to large volume changes during the charge/discharge processes, and consequently, resulting in poor cycling stability, which will severely restrict their practical application in LIBs. Therefore, the development of new carbon

∗ Corresponding author. Tel.: +86 20 87110131; fax: +86 20 87110131. ∗∗ Corresponding author. E-mail addresses: [email protected] (L. Ding), [email protected] (H. Wang). http://dx.doi.org/10.1016/j.electacta.2014.07.014 0013-4686/© 2014 Elsevier Ltd. All rights reserved.

materials is still considered to be the most promising strategies to meet the need of anode materials for high-performance LIBs. Up to now, a large number of novel carbon materials with various microstructures as LIBs electrodes have been investigated, such as carbon nanotubes [7–9], carbon nanofibers [10–12], hollow carbon nanospheres [13–16], graphene [17–23], and their composites [24–27]. Among these different carbon materials, graphene is considered as the most appealing alternative of graphite because of its superior electrical conductivities, high surface areas and amazing mechanical properties [28–30]. Recently, many researchers have demonstrated that the combination of 2D graphene nanosheets with porous architectures can lead to a significant enhancement in electrochemical performance [31,32]. For example, Zhao’s group [32] reported that the mesoporous graphene nanosheets used as LIBs anode materials can still deliver a reversible specific capacity of about 255 mAh g−1 , even at a large current density of 5 A g−1 . Nevertheless, the practical use of graphene nanosheets as anodes in LIBs is still facing some problems. It is well known that the graphene nanosheets tend to cause severe aggregation due to the van der Waals forces. The agglomeration will significantly decrease the electrochemical active sites and the electrode/electrolyte contact areas, which will inevitably affect the electrochemical properties of the graphene electrode. Designing ultrathin-shell and interconnected graphene hollow spheres could be considered as an effective strategy to overcome the above-mentioned drawbacks because the hollow sphere

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structure can act as an effectively barrier to suppress agglomeration of graphene nanosheets [33]. In addition, compared to other conventional hollow carbon spheres, the ultrathin-shell and interconnected graphene hollow spheres not only retain the superior performance of graphene nanosheets but also show the following additional advantages: i) ultra-thin graphene shell could significantly reduce the diffusion length for lithium ions during insertion/extraction process; ii) the superior electronic conductivity and interconnected network structure of graphene hollow spheres could provide a highway network for fast electron transport; iii) the wrinkled and porous structure of graphene could provide more lithium storage sites. The graphene hollow spheres are generally synthesized by template method and hydrothermal method [33–36]. Among them, template method is more favourable because the size of graphene hollow spheres is uniform and could be controlled by tuning the diameter of templates particle size. However, expensive surfactant is generally needed by functionalizing/modifying the template due to the incompatibility between the template surface and shell material, resulting in the complicated fabrication process and high cost. Moreover, hydrothermal process is usually along with high temperature and high pressure which will inevitably increase the cost. Thus, it is essential to synthesize ultrathin graphene hollow spheres by simple and facile methods and study their lithium storage properties. Herein, we successfully develop a facile and efficient template assisted method without surfactant to fabricate ultrathin-shell and interconnected graphene hollow spheres. Notably, the as-prepared graphene hollow spheres with ultrathin-shell and interconnected structure as an advanced electrode material can endow many apparent advantages, such as high surface area, short ion diffusion length and convenient electronic transmission path. As expected, as an anode material for LIBs, the ultrathin-shell and interconnected graphene hollow spheres exhibit an excellent electrochemical performance. 2. Experimental section 2.1. Synthesis of graphene oxide nanosheets and colloidal SiO2 Graphene oxide nanosheets (GOs) were prepared through the modified Hammer’s method. Detailed preparation procedure can be found in our previous report [19]. Colloidal SiO2 was synthesized by using the classical Stöber method [37]. In a typical experiment, 4.5 mL Tetraethyl orthosilicate (TEOS, 98%) (Guangzhou Chemical Reagent Factory, China) was added into a mixed solution containing 9 mL ammonia solution (Guangzhou Chemical Reagent Factory, China), 61.75 mL ethanol (Sinopharm Chemical Reagent Co., Ltd., China) and 24.75 mL deionized water under vigorous stirring. Then, the mixture was stirred at room temperature for 2 h. Subsequently, the resulting product was washed with ethanol and deionized water for several times by centrifugation. Finally, the white colloidal SiO2 in water with 250 nm in diameter was obtained. 2.2. Synthesis of the ultrathin-shell graphene hollow spheres The as-prepared GOs and colloidal SiO2 were uniformly mixed by ultrasonic dispersion in deionized water. Then, water in the mixture was removed by vacuum freeze drying process, resulting in obtaining the SiO2 @GOs core-shell composite powders. In order to reduce the surface oxygen functional groups of GOs, the above-mentioned powders were annealed at 800 ◦ C in argon gas atmosphere. Finally, the SiO2 template was removed by immersing 20% hydrofluoric acid (HF) solution with stirring for 4 h. After washed with deionized water, the ultrathin-shell graphene hollow spheres can be successfully obtained.

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2.3. Materials characterization The structure and morphology were characterized by field emission scanning electron microscopy (FE-SEM) (JSM-6330F) and high resolution transmission electron microscope (HRTEM) (JEM2010HR). Nitrogen adsorption-desorption measurements were carried out at 77 K with a Micromeritics ASAP 2020 system. The Brunauer-Emmett-Teller (BET) method was used to calculate the specific surface area. The functional groups of SiO2 powders and GOs were analyzed by Fourier transform infrared (FTIR) spectra using a Bruker Vector 33 spectrophotometer. Raman spectra were obtained using a Horiba Jobin Yvon LabRam Aramis Raman spectrometer at a wavelength of 632.8 nm. 2.4. Electrochemical measurements The electrochemical experiments were carried out in CR2025 coin-type half cells. The working electrodes were prepared by coating the slurry of the active materials (the graphene hollow spheres) (80 wt.%), Super P (10 wt.%), and poly(vinylidene fluoride) (PVDF, Kureha, Japan) binder (10 wt.%) dissolved in an N-methyle2-pyrrolidone (NMP, Tianjin Kermel Chemical Reagent Co., Ltd., China) solvent onto a copper foil, and dried at 100 ◦ C in a vacuum oven (DZF-6020, shanghai Qi Xin Scientific Instrument Co., Ltd., China). The weight of active material in the electrode is ca. 0.45 mg, which was obtained by the highly accurate electronic balance (METTLER TOLEDO, MX5, 0.001 mg). Then, the lithium foil was used as the counter electrode, and the celgard 2325 membrane was used as the separator. The electrolyte was composed of 1 mol L−1 LiPF6 dissolved in a mixture of ethylene carbonate (EC) and diethylcarbonate (DEC) (1:1 by volume) (Beijing Institute of Chemical Reagents, China). The coin cells were assembled in an argon-filled glove box (Mikrouna, super 1220) where the oxygen and moisture contents were less than 1 ppm. The cells were galvanostatically discharged and charged using a Battery Testing System (Neware Electronic Co., China) between 0.01 and 3.0 V at different current densities. Cyclic voltammetry (CV) measurements were performed on an electrochemical workstation (Zahner IM6ex) at the scan rate of 0.2 mV s−1 over the potential range of 0.01-3.0 V vs. Li/Li+ . Electrochemical impedance spectroscopy (EIS) studies of cells after discharge/charge 30 cycles were carried out on the electrochemical workstation (Zahner IM6ex) by applying an amplitude voltage of 5 mV in a frequency range of 10 mHz to 1 MHz. 3. Results and discussion 3.1. Microstructure characterization Fig. 1 illustrates the overall synthetic procedure of graphene hollow spheres. The two main synthetic steps are the formation of the SiO2 @graphene core-shell spheres and the removal of the SiO2 template spheres. The colloidal SiO2 would be tightly wrapped by GOs with abundant surface functional groups due to electrostatic attractions. As a result, the GOs circle around the colloidal SiO2 spheres to form the SiO2 @GOs core-shell structure. After heat reduction, the SiO2 @graphene core-shell spheres were formed. Finally, the SiO2 spheres were removed by acid etching, and then the graphene hollow spheres were obtained. It should be pointed out the colloidal SiO2 spheres were chosen as the sacrificial template due to their obviously structural advantages including high dispersion, smooth surface and controllable in size [14,34]. Moreover, GOs were used as the precursor for the graphene hollow spheres because of the large scale preparation and the abundant surface oxygen functional groups [38,39].

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Fig. 1. Overall synthetic procedure of the graphene hollow spheres.

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XRD patterns of graphite, GOs and graphene hollow spheres are displayed in Fig. 2. For the graphite, the XRD pattern shows a typical (002) diffraction peak at 26.6o . Compared with XRD pattern of graphite, the (002) peak of GOs disappears and an additional (001) peak at 10.8o appears, which results from the introduction of oxygenated functional groups [40]. The XRD diffraction peak of graphene hollow spheres is hardly found relative to the XRD peaks of graphite and GOs. After the XRD patterns were magnified, a new and broad diffraction peak is observed at 15-30o for graphene hollow spheres (see inset Fig. 2), indicating the successful reduction of GOs. In order to clarify the synthetic process, the FE-SEM images of the colloidal SiO2 nanospheres, the GOs, the SiO2 @graphene and graphene hollow spheres are shown in Fig. 3. From Fig. 3a, it is observed that the colloidal SiO2 is uniform and smooth sphere with an average diameter of about 250 nm. Fig. 3b shows a FE-SEM image of typical GOs, revealing a thin curled paper-like structure, which is consistent with the previous report [39]. As shown in Fig. 3c, the SiO2 nanosphere was tightly wrapped by graphene nanosheets, leading to form the ultrathin-shell SiO2 @graphene core-shell spherical structure. As displayed in Fig. 3d, the graphene hollow spheres were interconnected and the sample exhibits hollow spherical morphology with the diameter of about 250 nm. The hollow sphere originates from the near-perfect replication of the microstructure of the spherical colloidal SiO2 . Thus, the hollow spherical size can be easily adjusted by controlling the size of colloidal SiO2 sphere. It is noteworthy that some broken spheres can be observed in Fig. 3d, which fully proves the formation of the hollow structure. To further examine the unique structure of the graphene hollow spheres, the morphologies and microstructures were investigated by the TEM and HRTEM techniques. As shown in Fig. 4a, the hollow spherical structure could be clearly seen, which indicates that

hollow spherical structure is successfully formed by the template method without surfactant. The crinkly shell structure further confirms the presence of the graphene nanosheets [17,28]. Furthermore, we also found that the neighboring spheres are linked together to form interconnected structure which will facilitate the fast transportation of electrons in the electrode materials [13]. The blurred electron diffraction pattern (inset in Fig. 4a) indicates that the hollow spheres have a low level of crystallinity which is well consistent with the above XRD result. The magnified TEM image in Fig. 4b indicates that the thickness of the shell is uniform and only ∼5 nm, which is thinner than those in the previous reports [13–15]. For instance, the previously reported nanographene-constructed hollow carbon spheres have a shell thickness of around 70 nm [14]. The researchers generally think that the thinner shell could provide a shorter lithium-ions diffusion distance and a larger electrode/electrolyte contact area [15]. Thus, it is reasonable to deduce that the ultrathin-shell structure can improve the electrochemical performance for LIBs. More interestingly, the porous structure in the shell can be clearly observed in the inset of Fig. 4b. Moreover, the pore size is about 1.0 and 3.0 nm, which is consistent with the following results of pore size distribution (see inset in Fig.4b). The phenomenon suggests that the shell of graphene hollow spheres is made up of the few-layers nanoporous graphene sheets. Moreover, the ultrathin and porous shell structure could lead to a short transport length of lithium ions and electrons when being used as anode materials for LIBs. In order to find the possible reason of the formation for graphene hollow spheres, the FTIR spectra of as-prepared the colloidal SiO2 and the GOs are shown in Fig. 5. For the colloidal SiO2 , the absorption peaks around 3432 and 1630 cm−1 are attributed to the silanol group and adsorbed water. Moreover, bands located at 1099, 948, 800 cm−1 are associated with the transverse-optical mode of the Si-O-Si asymmetric bond stretching vibration, the Si-OH stretching vibration, and the network Si-O-Si symmetric bond stretching vibration, respectively. In addition, The spectra of GOs indicate that there are carbonyl groups (C = O stretching vibrations) at about 1638 cm−1 , and hydroxyl groups (O-H stretching vibrations) at 3390 cm−1 on the surface of graphene oxides. Thus, it is reasonable to assume that the colloidal SiO2 could be tightly wrapped by GOs due to the existence of abundant oxygen-containing functional groups in GOs and silanol group in colloidal SiO2 . The existence of these functional groups may be one of the reasons that the graphene hollow spheres are formed without surfactant. The nitrogen adsorption-desorption isotherm of the graphene hollow spheres is showed in Fig. 6. The isotherm exhibits a typical IV-type curve with type-H3 hysteresis loop, suggesting the presence of mesopores structure [41]. The specific surface area of the graphene hollow spheres is calculated to be 248.3 m2 g−1 by the BET measurement. The high specific surface area could introduce the extra lithium storage sites for LIBs. The pore distribution curve was derived by the density functional theory (DFT) method. The major pore sizes are distributed at 1.2 and 3.2 nm from the pore size distribution curve (see inset of Fig. 6). The structure of the micropores and mesopores is beneficial for the diffusion and transport of

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Fig. 3. FE-SEM images of (a) the colloidal SiO2 spheres, (b) the GOs, (c) the SiO2 @graphene, and (d) graphene hollow spheres.

lithium-ions and electrons and could enhance the electrochemical properties for LIBs [32]. Additionally, these pore sizes are totally different from the particle diameter of the SiO2 sphere templates (250 nm), indicating that these pores are not from pores of hollow spheres. Thus, we could conjecture that these pores may be generated in the process of the thermal reduction process of SiO2 @GOs

composite powders. And these pores also could be ascribed to the spaces between the graphene nanosheets. Raman spectroscopy is one of effective tools to characterize the structure of graphene materials. It is generally considered that the intensity ratio of D band and G band (ID /IG ) represents the disorder degree of graphene[18,19,21,23]. The Raman spectrum of graphene

Fig. 4. a) TEM image of graphene hollow spheres, the inset image shows the selected area electron diffraction pattern; b) high-resolution TEM image of graphene hollow spheres, the inset image is the microstructure of the ultrathin shell.

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3.2. Electrochemical properties of the graphene hollow spheres

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hollow spheres was shown in Fig. 7 and the ID /IG value is 1.25. The value is higher than the previously reported [19], indicating that the three-dimensional graphene hollow spheres constructed by twodimensional graphene nanosheets have more defect, edge sits and pores. These sites could provide the storage space for lithium-ions and the result also further prove the probability of the promising electrochemical performance for the graphene hollow spheres.

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Fig. 8a depicts the first three discharge/charge curves of the graphene hollow spheres at a current density of 100 mA g−1 . The first reversible specific capacity of the graphene hollow spheres is as high as 824.2 mAh g−1 at a current density of 100 mA g−1 . The reversible specific capacity is superior to those reported previously for hollow carbon spheres and hollow graphene oxide spheres [13–15,42]. For example, the reported hollow carbon spheres delivered a first reversible capacity of 713 mAh g−1 at a rate of 0.2 C [14] The hollow graphene oxide spheres by a water-in-oil emulsion technique and the spheres exhibited a reversible capacity of 485 mAh g−1 [42]. The high reversible capacity of graphene hollow spheres could be attributed to the hollow structure and the ultrathin graphene shells. It should be pointed that the irreversible capacity for the graphene hollow spheres could be associated with the formation of the solid electrolyte interphase (SEI) films at the electrode/electrolyte interface in the first cycle. No obvious voltage plateau in the three charge/discharge curves could be attributed to the disordered stacking of graphene nanosheet. Moreover, the specific capacity of the voltage region below 0.5 V (vs. Li/Li+ ) is mainly due to the lithium-ions intercalation into the graphene layers [17,18]. The cyclic voltammograms of the as-prepared graphene hollow spheres at a scanning rate of 0.2 mV s−1 are presented in Fig. 8b. The shape of cyclic voltammograms matches well with the above-mentioned discharge/charge profiles. It is worth noting that the cyclic voltammograms of the following two cycles are almost overlapped, indicating that the material shows a high reversibility during the lithium-ions insertion/extraction process. The rate capabilities of the graphene hollow spheres at different current densities are observed in Fig. 9a. The first ten cycles of the as-assembled coin cell were cycled at a low current density of 100 mA g−1 , and then the following cycles was stepwise increased to the high current density of 5000 mAh g−1 . At a low current density of 100 mA g−1 , the reversible specific capacity of the graphene hollow spheres is as high as 649.7 mAh g−1 after 10 cycles. The reversible specific capacity of 434.1, 382.1, 316.9, and 286.9 mAh g−1 were still obtained at the current densities of 500, 1000, 2000, and 3000 mA g−1 , respectively. More significantly, even at a high current density of 5000 mA g−1 , a high stable capacity still reached to about 249.3 mAh g−1 . Notably, the rate capacity is much better than that of the reported hollow carbon spheres [13–15]. The superior rate capability could originate from the ultrathin and porous shell structure, the interconnected hollow structure and the high electronic conductivity of graphene. Additionally, when the current density go back to 100 mA g−1 after cycling at different current densities, the specific capacity could still back to 754.1 mAh g−1 , indicating that the as-prepared graphene hollow spheres have a good electrochemical stability. The cycle performance and coulombic efficiency at a high current density of 1000 mA g−1 were also investigated and shown in Fig. 9b. It should be pointed that the cell was discharged and charged for three cycles at a low current density of 100 mA g−1 before cycling performance measurement at a high current density of 1000 mA g−1 . As shown in Fig. 9b, the first reversible specific capacity of 437.4 mAh g−1 could be achieved at a high current density of 1000 mA g−1 , which is still higher than the theoretical capacity of graphite (372 mAh g−1 ). In addition, the slight increase in capacity after 20th cycle is due to the activating process of the porous carbon materials [43]. More strikingly, at the high current density of 1000 mA g−1 , the capacity retention of the electrode material can be as high as 97.1% after 100 cycles. The cycle stability is superior to that of the graphene nanosheets obtained by chemical approach [18]. Moreover, the coulombic efficiencies approach 100% after the second cycle at the current density of 1000 mA g−1 . The results demonstrated that the graphene hollow spheres show an excellent cycling performance at the high

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current density of 1000 mA g−1 . The better cycling stability could be attributed to the structural stability of the graphene hollow spheres. Fig. 10 represents cycle performance of the graphene hollow spheres at a low current density of 100 mA g−1 . After 35 cycles, it is observed that the electrode still maintains a reversible sepecific capacity of 760 mAh g−1 , which is higher than the previous reports [14,20]. More strikingly, the reversible sepecific capacities remain stable from the second cycle, showing an excellent cycle stability, which should originate from the stable structure

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of graphene hollow spheres. It is should be pointed out that the low initial coulombic efficiency is common phenomenon for the carbon-based materials, which is ascribed to the formation of SEI films [13,14,19,20]. In order to evidence the stable structure of the graphene hollow spheres, the FE-SEM image of the graphene hollow spheres electrode after 100 cycles at the current density of 1000 mA g−1 were presented in Fig. 11. It is observed that the interconnected hollow structure is obviously observed, suggesting that the graphene hollow spheres have an excellent structural stability. It should be pointed out that the obscure layer on the surface spheres could be associated with the formation of SEI films. To show the conductivity of the graphene hollow spheres, EIS measurement for the electrode after 30 cycles was carried out and corresponding Nyquist plot was shown in Fig. 12. The semicircle at the high-to-medium frequencies is associated with the charge-transfer resistance, while the straight sloping line is related to diffusion resistance through the bulk of the active material [20,44,45]. What’s more, EIS results were fitted using an equivalent circuit (inset in Fig. 12). In the equivalent circuit, R represents the uncompensated bulk resistance of electrolyte, separator and electrode. RSEI and C1 are the resistance and capacitance of the SEI films formed on the electrode surface, respectively. Rct is associated with the charge-transfer resistance at the active material interface and Cd represents the double layer capacitance. Zw is the Warburg impedance related to the diffusion of lithium-ions into the bulk electrode. For the graphene hollow spheres, the values of the uncompensated bulk resistance and charge-transfer resistance

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4. Conclusions In summary, we have proposed a facile template assisted approach and without using surfactant for the large scale synthesis of the ultrathin-shell graphene hollow spheres from the graphene oxide nanosheets. The as-prepared graphene hollow spheres were employed as an advanced anode material for LIBs and exhibited superior electrochemical performance, especially the excellent rate capacity (249.3 mA h g−1 at 5000 mA g−1 ) and very high reversible lithium storage capacity (824.2 mA h g−1 at 100 mA g−1 ). The superior electrochemical performances are mainly ascribed to the porous, ultrathin shell and the interconnected hollow spheres structure. The results suggest that the graphene hollow sphere might be a great promising anode material for the next generation high-performance LIBs. Furthermore, the present graphene hollow spheres also can be used as a competitive support for electrochemically active materials such as transition metals, oxides, and precious metals in the pursuit of high-performance electrode materials or electrocatalyst. Fig. 11. FE-SEM image of the graphene hollow spheres after 100 cycles at a high current density of 1000 mA g−1 .

are 4.13  and 68.57 , respectively. According to the equation [45,46] ␴=L/(RA), where ␴, L, A and R represent the electronical conductivity, thickness, area and fitted resistance of electrode pellets. The electronical conductivity for the graphene hollow spheres electrode calculated is 2.43 × 10−4 S cm−1 , which is higher than the previously reported [45]. Therefore, the graphene hollow spheres electrode exhibits a good electronical conductivity. The pronounced electrochemical performance could be based on the following reasons. Firstly, the ultrathin graphene shells not only provide good conductivity but also greatly shorten diffusion length for lithium ions, and consequently lead to improved rate capability. Secondly, the high surface area and porous structure can provide large quantity of accessible active sites for lithiumion insertion, which can increase the reversible specific capacity of graphene hollow spheres. Thirdly, the interconnected graphene hollow spheres can ensure the continuous and fast transportation of electrons in the electrode. The exciting results indicate that the interconnected hollow structure, ultrathin shell and porous morphology play an important role in improving the electrochemical performance, and make the graphene hollow spheres a promising anode material for high-performance LIBs.

Fig. 12. Nyquist plot of graphene hollow spheres, the inset shows equivalent circuit for the Nyquist plot.

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