To verify the crystalline structure of the synthesized products, the XRD patterns are presented in Fig. 2. The characteristic peaks at 25.3°, 37.8° and 48° correspond to (101), (004) and (200) planes of TiO2 (PDF#78-2486), respectively, indicating that the synthesized products have a high crystalline nature. The wide peak of Co@TiO2−xcarbon at about 26.7° indicates the success of carbon coating [19]. In the figure no other impurities are detected, confirming that the as-prepared products have high purity. Therefore, XRD showed that Co@TiO2−x-carbon and TiO2 were successfully fabricated.

Fig. 2
figure 2

XRD pattern of the synthesized samples

The characterization analysis about the basic morphological structure of Co@TiO2−x-carbon nanoparticles was conducted by SEM. It is observed that the hollow composite possessed a nearly homogeneous spherical shape and a high dispersity. (Fig. 3a). The diameter of the nanospheres is about 800 nm. As shown in Fig. 3b, Ti, O, Co and C are uniformly dispersed on the nanospheres.

Fig. 3
figure 3

a SEM image; b high-resolution SEM image and corresponding EDS mappings of Co@TiO2−x-carbon

The SEM image reveals that the as-synthesized composite forms a hollow nanospheres structure in Fig. 4a. Meanwhile, the hollow morphology of the composite has been further described by the TEM images in Fig. 4f. The porous hollow spherical structure can provide more lithium storage sites, shorter lithium ion and electron diffusion paths. At the same time, the appropriate internal cavity can well adjust the structure and volume change of the electrode. The HRTEM of Fig. 4b shows the existence of cobalt metal and TiO2. The existence of TiO2 can be further clearly observed by FFT and inverse FFT transformation of Fig. 4c–e. The existence of Ti3+ and oxygen vacancies can facilitate the migration of electron of the materials; thus, the composite electrode exhibits a superior rate performance. The linear scanning and corresponding element mapping of Fig. 4f show that TiO2 and cobalt metal are uniformly distributed on the surface of hollow nanospheres.

Fig. 4
figure 4

a SEM; b high-resolution TEM image; c FFT pattern; d the inverse FFT crystalline lattice image; e the lattice spacing profiles at selected areas in yellow and red; f linear scan and corresponding elemental mappings of Co@TiO2−x-carbon

A nitrogen adsorption experiment was used to test the pore characteristics of synthetic products, as shown in Fig. 5a. Compared with TiO2 (67.4 m2 g−1), the composite possesses a high specific surface area which was about 190.8 m2 g−1. The N2 adsorption-desorption isotherm curves of TiO2 and Co@TiO2−x-carbon belong to type-IV isotherm, indicating abundant mesopore structure (Fig. 5b). Co@TiO2−x-carbon composite has a wide range of mesoporous size distribution, which is conducive to the transport of lithium ions and can accommodate huge volume changes in the cycling process. Besides, the abundant mesoporous structure and large specific surface area provide more lithium insertion sites and voids to facilitate the storage of lithium and improve the rate ability and cycling performance of LIBs. EPR was employed to characterize the chemical states in TiO2 and Co@TiO2−x-carbon. The strong EPR signal obtained from Co@TiO2−x-carbon with a g-value of 2.003 indicates the existence of oxygen vacancies, while only a trace amount of oxygen vacancies was observed for pristine TiO2 (Fig. 5c). XPS spectra of Co@TiO2−x-carbon composites were recorded and analyzed. These peaks correspond to Co 2p3/2 and Co 2p1/2, respectively, and suggest that the reduction in Co 2p in Co(NO3)2·6H2O produced Co nanoparticles (Fig. 5d).

Fig. 5
figure 5

a N2 adsorption-desorption isotherms; b pore size distributions; c EPR spectra of Co@TiO2−x-carbon and TiO2; d XPS spectra of Co@TiO2−x-carbon

Electrochemical properties of the anode materials were further studied, as shown in Fig. 6, the lithium storage capacity was evaluated by half cells and prepared electrode. Due to the lithiation/delithiation effect of the carbon phase, the range (0.01–3 V) can lead to higher reversible capacity.

Fig. 6
figure 6

CV curves of a Co@TiO2−x-carbon and c TiO2; Charge–discharge voltage profiles of b Co@TiO2−x-carbon and d TiO2 at 0.2 A g−1; e Cyclic stability and f rate capabilities of as-synthesized products; g Long cycling performance of as-synthesized products at 1 A g−1; h Nyquist plots of as-synthesized products before cycling

The lithium storage behaviors of the synthesized samples were investigated in half cells at a scanning rate of 0.1 mV s−1 and in a scanning range of 0.01–3 V. The curves show the initial five cycles of the as-prepared products are shown in Fig. 6a, c. The first small reduction peak of the composite at 1.75 V during the first discharge can be attributed to the insertion of Li+ into TiO2 to form Li0.5TiO2 (The inset images in Fig. 6a). As we all known, due to the existence of TiO2−x, the conductivity of LixTiO2 formed in situ is also improved [20, 21]. Meanwhile, in subsequent cycles, the reduction/oxidation peak of 1.50/1.70 can be attributed to TiO2−x and the reduction/oxidation peak of 1.75/2.02 can be attributed to TiO2 [22]. The CV curves of TiO2 sample displays one oxidation peak at approximately 2.10 V and a reduction peak at approximately 1.70 V, which are in agreement with anatase TiO2 (Fig. 6c) [23].

Discharge/charge profiles of lithium-ion battery with two samples are exhibited in Fig. 6b, d at 0.2 A g−1 under a voltage window of 0.01–3 V. The first discharge capacity of the composite electrode is 323 mAh g−1, superior to TiO2 electrode (214 mAh g−1). Simultaneously, the result of the first cycle shows that the composite electrode exhibits low initial coulombic efficiency (ICE), which may be associated with the construction of a solid electrolyte interface (SEI) membrane [24]. Furthermore, the complex anode delivers a discharge specific capacity of 302 mAh g−1 in the following cycle, whereas TiO2 electrode in the same process only 209 mAh g−1. Compared with TiO2 electrode, the charge-discharge curve of the composite electrode shows a similar and clear potential platform and is stable, which reveals the prominent reversibility of electrochemical reactions for the composite anode [25].

As shown in Fig. 6e, Co@TiO2−x-carbon provides the highest discharge specific capacity during the test at 0.2 A g−1. After 100 cycles, the composite material delivers a higher reversible capacity of 242 mAh g−1 than TiO2 nanoparticles (139 mAh g−1), demonstrating that the composite material possesses an outstanding reversibility [26]. The introduction of the carbon layer can increase the capacity of LIBs. In addition, the design of porous hollow nanospheres, the introduction of oxygen vacancies and metal cobalt can promote cycle stability.

The rate capability of the electrodes is further compared in Fig. 6f. Compared with TiO2, the electrochemical performance of the composite electrode has a higher reversible capacity and better cycling performance at different current densities. The discharge capacities under the conditions of 0.1, 0.2, 0.5 and 1 A g−1 were 379, 291, 253 and 217 mAh g−1, respectively. Electron conductivity and diffusion path determine the rate performance of LIBs [27, 28]. The structure of hollow nanospheres of the Co@TiO2−x-carbon shortens the diffusion path of Li+ and electron, and the existence of VOs, carbon coating and cobalt metal improve the conductivity essentially.

It is worth noting that Co@TiO2−x-carbon exhibits strong cycle stability (no significant capacity degradation and close to 100% coulombic efficiency) at a high current density at 1 A g−1 and maintains 173 mAh g−1 after 1000 cycles. Obviously, the composite electrode displays uch better cycle performance than TiO2, and the reversible specific capacity of the composite material is much higher than that of TiO2 (42 mAh g−1 at the 1000 th cycle) in Fig. 6g. Due to the specific hollow structure of the as-prepared product, which can inhibit the volume expansion during the cycling process and obtain excellent cycling performance.

Figure 6h shows the EIS of anode materials. The two Nyquist plots are both consisted of a compressed semicircle at the high-frequency region followed by a sloping line in the low frequency region. The low-frequency region represents the Warburg diffusion process which might be attributed to the diffusion of the lithium ions, and the semicircle at high frequency corresponds to the charge-transfer resistance [29]. Clearly, the composite has lower resistance and better conductivity than the TiO2 sample, which are caused by the Li-ion insertion/extraction rates. Therefore, the composite product exhibits superior electrochemical reaction kinetics.

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