简介概要

In situ sol-gel synthesis of Ti₂Nb₁₀O₂₉/C nanoparticles with enhanced pseudocapacitive contribution for a high-rate lithium-ion battery

来源期刊：Rare Metals2020年第9期

论文作者：Guang-Yin Liu Yi-Yang Zhao Yu-Feng Tang Xiao-Di Liu Miao Liu Peng-Jiang Wu

文章页码：1063 - 1071

摘要：Ti₂Nb₁₀O₂₉/C nanoparticles with a carbon content of 13 wt% and a mean size of 50 nm were fabricated through a convenient and effective in situ sol-gel process.The small grain size and carbon modification can improve the pseudocapacitive effect of the Ti₂Nb₁₀O₂₉/C nanoparticles,leading to excellent rate capacity,especially at high current rate.Specifically,the discharge capacity of the Ti₂Nb₁₀O₂₉/C electrode is 258.3,236.0,216.6,184.5 and161.5 mAh·g^-1 at different current densities of 1C,5C,10C,20C and 30C.Nevertheless,the discharge capacity of the Ti₂Nb₁₀O₂₉ electrode is 244.9 mAh·g^-1 at 1C,which is rapidly reduced to 89.7 mAh·g^-1 at 30C.In addition,the small size and carbon layer of the Ti₂Nb₁₀O₂₉/C nanoparticles can supply abundant active sites for Li⁺storage as well as enhance the electronic conductivity and Li⁺diffusion,endowing these nanoparticles with a high discharge capacity and excellent cycle performance.

详情信息展示

稀有金属(英文版) 2020,39(09),1063-1071

In situ sol-gel synthesis of Ti₂Nb₁₀O₂₉/C nanoparticles with enhanced pseudocapacitive contribution for a high-rate lithium-ion battery

Guang-Yin Liu Yi-Yang Zhao Yu-Feng Tang Xiao-Di Liu Miao Liu Peng-Jiang Wu

College of Chemistry and Pharmaceutical Engineering,Nanyang Normal University

作者简介：*Xiao-Di Liu e-mail:liuxiaodiny@126.com;

收稿日期：18 December 2019

基金：financially supported by the National Natural Science Foundation of China (No.51802163);the National Natural Science Foundation of Henan Department of Education (No.20A480004);the China Postdoctoral Science Foundation (No.2017M622564);

In situ sol-gel synthesis of Ti₂Nb₁₀O₂₉/C nanoparticles with enhanced pseudocapacitive contribution for a high-rate lithium-ion battery

Guang-Yin Liu Yi-Yang Zhao Yu-Feng Tang Xiao-Di Liu Miao Liu Peng-Jiang Wu

College of Chemistry and Pharmaceutical Engineering,Nanyang Normal University

Abstract：

Ti₂Nb₁₀O₂₉/C nanoparticles with a carbon content of 13 wt% and a mean size of 50 nm were fabricated through a convenient and effective in situ sol-gel process.The small grain size and carbon modification can improve the pseudocapacitive effect of the Ti₂Nb₁₀O₂₉/C nanoparticles,leading to excellent rate capacity,especially at high current rate.Specifically,the discharge capacity of the Ti₂Nb₁₀O₂₉/C electrode is 258.3,236.0,216.6,184.5 and161.5 mAh·g^-1 at different current densities of 1C,5C,10C,20C and 30C.Nevertheless,the discharge capacity of the Ti₂Nb₁₀O₂₉ electrode is 244.9 mAh·g^-1 at 1C,which is rapidly reduced to 89.7 mAh·g^-1 at 30C.In addition,the small size and carbon layer of the Ti₂Nb₁₀O₂₉/C nanoparticles can supply abundant active sites for Li⁺storage as well as enhance the electronic conductivity and Li⁺diffusion,endowing these nanoparticles with a high discharge capacity and excellent cycle performance.

Keyword：

Nanoparticles; Anode materials; Sol-gel method; Energy storage;

Received： 18 December 2019

1 Introduction

Lithium-ion batteries (LIBs) are vitally important electrochemical power sources for electric vehicles and hybrid electric vehicles (EVs/HEVs) [ 1] .Owing to the rapid development of EVs/HEVs,it is very necessary to exploit LIBs with high energy density,good rate capacity and high security.It is well known that the properties of the anodes are significant for the performance of LIBs.Graphite is widely used as an anodic material in the commercial LIBs;nevertheless,its relatively low working potential (～0.1 V vs.Li⁺/Li) can lead to the generation of Li dendrites,especially at high current density [ 2, 3] .Thus,in term of safety,graphite is not very suitable for using as anode materials in LIBs for EVs/HEVs.Accordingly,there is a great interest in exploring alternative anode materials with good safety performance and high discharge capacity.Currently,Ti₂Nb₁₀O₂₉ is considered to be a promising anode for LIBs due to its large theoretical capacity (396 mAh·g^-1) and high working potential(～1.7 V vs.Li⁺/Li),which is beneficial for achieving high energy density and improved safety [ 4] .Moreover,Ti₂Nb₁₀O₂₉ has a stable Wadsley-Roth shear structure consisting of 4×3×∞ReO₃-type blocks,leading to excellent cycle stability [ 5] .Therefore,Ti₂Nb₁₀O₂₉ has attracted tremendous research interests among the LIBs fields for EVs/HEVs.

Nevertheless,Ti₂Nb₁₀O₂₉ has a low Li⁺diffusion coefficient,which can lead to poor rate ability and accordingly severely hinder its practical application in EVs/HEVs [ 6] .Recently,the construction of nanostructured anodes has been used for solving the problem of slow diffusion of Li⁺ [ 7, 8, 9, 10] .More importantly,it has been proved that the surface-controlled pseudocapacitive effect can replace the diffusion-controlled Li⁺insertion process at high current rates,resulting in outstanding rate capability [ 10, 11, 12, 13, 14] .The smaller the size of the anode is,the higher the number of electrically charged species is on the anode surface-subsurface,which benefits charge storage via the pseudocapacitive effect and accordingly enhances the rate capacity [ 14] .Therefore,decreasing the size of the anode is a fairly promising direction for the construction of anodic materials with high energy density.Some Ti₂Nb₁₀O₂₉micro-/nanostructures have already been reported [ 15, 16, 17, 18] ;nevertheless,most of these materials are prepared at high temperature for prolonged periods,which generally leads to a large particle size and small surface area.Hence,there is still broad space to develop facile methods to prepare Ti₂Nb₁₀O₂₉ nanomaterials with smaller size and larger specific surface area.

On the other hand,Ti⁴⁺(3s²3p⁶) and Nb⁵⁺(4s²4p⁶) in Ti₂Nb₁₀O₂₉ do not have single electron,and thus,Ti₂Nb₁₀O₂₉ possesses a low intrinsic electronic conductivity,which also negatively affects its rate capability.Fortunately,carbon coating has been demonstrated to be a valid strategy for improving the electronic conductivity of anode materials [ 19, 20, 21] .Nevertheless,studies for the carbon coating of Ti₂Nb₁₀O₂₉ have been rarely reported [ 22, 23, 24] .In addition,the coating techniques that are frequently used usually require multiple steps,and post-carbon modification processes are not beneficial for the uniform coating of carbon on every nanoparticle [ 20, 25] .Thus,it is essential to explore facile methods for the direct in situ carbonization of Ti₂Nb₁₀O_29.

Herein,in consideration of both the”nanosize”and“carbon coating,”a convenient and effective in situ sol-gel method is employed to prepare carbon-coated Ti₂Nb₁₀O₂₉nanoparticles.The as-obtained Ti₂Nb₁₀O₂₉/C nanoparticles have a small size (average particle size of～50 nm) and an extremely large specific surface area (186.8 m²·g^-1);moreover,carbon is uniformly coated onto the surfaces of the Ti₂Nb₁₀O₂₉ nanoparticles.The synergistic effect between reduced particle size and uniform carbon coating can not only improve the reaction kinetics of the Ti₂Nb₁₀O₂₉/C nanoparticles but also remarkably enhance their pseudocapacitive effect,endowing them with superior electrochemical properties,especially rate performance.

2 Experimental

First,3 g P123 (E0₂₀PO₇₀EO₂₀) was added into 100 ml ethanol under vigorous stirring for 5 min.Then,5 mmol NbCl₅ and 1 mmol Ti(OC₃H₇)4 were added into the above solution and the mixture was stirred at 80℃for1 h to form a sol;the sol was then dried at 100℃for 2 h in vacuum to generate a gel.Finally,Ti₂Nb₁₀O₂₉/C nanoparticles with a black color were prepared by calcining the gel at 850℃for 8 h in N₂ atmosphere.For comparison,Ti₂Nb₁₀O₂₉ nanoparticles with white color were synthesized using the same processes except that the gel was calcined in an air atmosphere.

The morphologies,structures and electrochemical performance of the products were studied by using multiple characterization techniques:X-ray diffraction (XRD),field emission scanning electron microscopy (FESEM),transmission electron microscope (TEM),high-resolution transmission electron microscope (HRTEM),X-ray photoelectron spectroscopy (XPS),Raman spectroscopy (RS),Brunauer-Emmett-Teller adsorption isotherm (BET),thermogravimetric analysis (TG),cyclic voltammetry (CV)and electrochemical impedance spectroscopy (EIS).The corresponding instruments and methods used are shown in the Supporting Information.

3 Results and discussion

The sizes and nanostructures of the obtained Ti₂Nb₁₀O₂₉/C and Ti₂Nb₁₀O₂₉ nanoparticles were characterized by TEM,HRTEM and SEM.As shown in TEM images (Fig.1a,c),the mean size of the Ti₂Nb₁₀O₂₉/C nanoparticles is much smaller than that of the Ti₂Nb₁₀O₂₉ nanoparticles (50 vs.200 nm),which can be further confirmed by SEM results(Fig.S1).In addition,the Ti₂Nb₁₀O₂₉/C nanoparticles have good monodispersity due to the carbon coating.As shown in the HRTEM images of the Ti₂Nb₁₀O₂₉ and Ti₂Nb₁₀O₂₉/C nanoparticles (Fig.1b,d),well-resolved fringes are observed with a lattice spacing of 0.360 nm,which can be assigned to the interplanar distance of the (400) plane for the monoclinic Ti₂Nb₁₀O₂₉.It is noteworthy that the surface of the Ti₂Nb₁₀O₂₉ nanoparticles is continuously covered by a carbon layer with a thickness of～2 nm(arrowed in Fig.1d).In addition,carbon coatings do not exhibit any regular lattice fringes,indicating that they are present in an amorphous form.Benefiting from the decreasing grain size and good dispersity,the Ti₂Nb₁₀O₂₉/C nanoparticles exhibit an extremely high specific surface area of approximately 186.8 m²·g^-1 (Fig.S2).

Fig.1 TEM images of a Ti₂Nb₁₀O₂₉ nanoparticles and c Ti₂Nb₁₀O₂₉/C nanoparticles;HRTEM images of b Ti₂Nb₁₀O₂₉nanoparticles and d Ti₂Nb₁₀O₂₉/C nanoparticles

The structure of the Ti₂Nb₁₀O₂₉/C nanoparticles was firstly characterized by XRD (Fig.2a).The peaks match very well with the monoclinic-type Ti₂Nb₁₀O₂₉ (JCPDS No.40-0039).Compared to pure Ti₂Nb₁₀O₂₉ nanoparticles,no diffraction peaks attributed to crystalline carbon can be found,so the carbon coatings likely exist in anamorphous state.RS (Fig.2b) can be used to further identify the structure of the carbon layer because the Raman spectra for crystalline and amorphous carbon possess D (disorder or defect) and G (graphite) bands with different intensities and positions [ 26] .In Fig.2b,two peaks at wavenumbers of 1333.5 and 1588.1 cm^-1 agree with the D and G-bands of carbon,respectively.The ratio of the D-band and G-band intensities (I_D/I_G) is～1.23,which convincingly demonstrates that the carbon layer has an amorphous structure [ 27, 28] ;moreover,the high intensity of the D-band reflects a high degree of disorder in the carbon layer,which can effectively improve the electrical conductivity of Ti₂Nb₁₀O₂₉ [ 26, 29] .

XPS was used to analyze the chemical states of the samples.The Ti 2p core level spectrum of the Ti₂Nb₁₀O₂₉/C nanoparticles (Fig.3a) is composed of two peaks that can be confirmed as Ti⁴⁺(2p3/2) and Ti⁴⁺(2p1/2) at 459.5and 465.3 eV,respectively [ 30] ;moreover,for the Nb 3d XPS spectrum (Fig.3b),two peaks at 207.9/210.8 eV can be attributed to Nb 3d_5/2/Nb 3d_3/2,which verifies the existence of Nb in its highest oxidation state of 5+ [ 31] ,whereas the Ti 2p and Nb 3d peaks for the Ti₂Nb₁₀O₂₉nanoparticles are clearly shifted toward lower values by0.8 eV compared to the Ti₂Nb₁₀O₂₉/C nanoparticles,whichmay be caused by the absence of carbon [ 32] .As depicted in Fig.3c,the C 1s spectra for Ti₂Nb₁₀O₂₉/C and Ti₂Nb₁₀O₂₉ all show three peaks.Namely,the dominant peak appearing at 284.8 eV is attributed to C-C,and another two peaks located at 286.0 and 288.3 eV can be assigned to C-O and C=O,respectively [ 33, 34] .The O 1s spectrum of the Ti₂Nb₁₀O₂₉ nanoparticles (Fig.3d) can be split into two peaks.In contrast,the O 1s spectrum of the Ti₂Nb₁₀O₂₉/C nanoparticles is composed of three peaks at531.1,532.3 and 533.5 eV,which are due to M-O(M=Nb,Ti),C-O and C=O,respectively [ 35] .Additionally,based on the results from TG results (Fig.S3),the content of carbon in Ti₂Nb₁₀O₂₉/C nanoparticles is confirmed to be 13 wt%.

It is known that the sol-gel process is an important technology for the synthesis of nanomaterials [ 36, 37, 38] .Ti₂Nb₁₀O₂₉ precursors with small size can be produced by the sol-gel process under mild reaction conditions (low temperature and short reaction time);moreover,P123 can absorb onto the Ti₂Nb₁₀O₂₉ precursors surfaces,which is beneficial to prevent the growth of the precursors [ 39, 40] .Then,after the calcination of the precursors in an air atmosphere,pure Ti₂Nb₁₀O₂₉ nanoparticles are obtained,whereas Ti₂Nb₁₀O₂₉ nanoparticles with a uniform carbon layer coating can be easily prepared under an insert atmosphere of N_2.Hence,it is reasonable to conclude that carbon is produced from the pyrolysis of P123.More importantly,carbon coatings can effectively inhibit the further growth and aggregation of nanoparticles in the calcination process,so Ti₂Nb₁₀O₂₉/C nanoparticles with small particle size and good dispersity can be obtained [ 28] .The growth mechanisms for the Ti₂Nb₁₀O₂₉/C and Ti₂Nb₁₀O₂₉ nanoparticles are illustrated in Fig.4.

The CV method was used to investigate the electrochemical discharge/charge reactions of the Ti₂Nb₁₀O₂₉/C electrode.It can be seen that the CV curve for the first cycle (Fig.5) exhibits a pair of main redox peaks (1.71/1.59 V) and two pairs of minor redox peaks (1.19/1.10 and1.93/1.88 V),corresponding to Nb⁵⁺/Nb⁴⁺,Nb⁴⁺/Nb³⁺and Ti⁴⁺/Ti³⁺,respectively [ 41] .Hence,Ti₂Nb ₁₀O₂₉exhibits a high theoretical capacity due to the three-electron transfer.In the following two cycles,the positions of the three pairs of redox peaks remain almost unchanged,indicating excellent cycling stability,which can be further verified from the corresponding discharge-charge curves(Fig.S4).In addition,according to the major cathodic/anodic peaks,the operating voltage of the Ti₂Nb₁₀O₂₉/Celectrode is as high as 1.65 V,which can restrain the generation of Li dendrites and accordingly result in a high level of security for the Ti₂Nb₁₀O₂₉/C electrode [ 42] .

Fig.2 a XRD patterns of Ti₂Nb_i0O₂₉/C nanoparticles (TNO/C) and Ti₂Nb₁₀O₂₉ nanoparticles (TNO);b Raman spectrum of Ti₂Nb_i0O₂₉/C nanoparticles

Fig.3 a Ti 2p,b Nb 3d,c O 1s and d C1s XPS spectra of Ti₂Nb₁₀O₂₉/C nanoparticles (TNO/C) and Ti₂Nb₁₀O₂₉ nanoparticles (TNO)

Fig.4 Growth mechanism of Ti₂Nb_i0O₂₉/C nanoparticles (TNO/C) and Ti₂Nb₁₀O₂₉ nanoparticles (TNO)

Fig.5 CV curves of Ti₂Nb₁₀O₂₉/C nanoparticles at a scanning rate of0.1 mV·s^-1 in potential range between 1.0 and 2.5 V (vs.Li⁺/Li)

Figure 6a,b shows the first discharge-charge curves for the two samples at various current rates.With current density increasing,the first discharge capacities for the Ti₂Nb₁₀O₂₉/C electrode are slowly reduced from 280.7 to223.9,209.4,175.7 and 151.6 mAh·g^-1.In contrast,the discharge capacities of the Ti₂Nb₁₀O₂₉ electrode aregreatly reduced;for instance,the discharge capacity is259.2 mAh·g^-1 at 1C,which is reduced to just 85.9mAh·g^-1 at a high current density of 30C.The long-term cycling stability of the Ti₂Nb₁₀O₂₉/C and Ti₂Nb₁₀O₂₉electrodes for 300 cycles at a current density as high as 10C is shown in Fig.6c.The Ti₂Nb₁₀O₂₉/C electrode exhibits large first discharge/charge capacities of 200.0/198.9mAh·g^-1 and accordingly possesses a high initial coulombic efficiency (99.5%),which favors stable cycle performance [ 43] .Actually,after 300 cycles,the discharge capacity of the Ti₂Nb₁₀O₂₉/C electrode is maintained at181.3mAh·g^-1 (90.7%of the first discharge capacity).In contrast,the Ti₂Nb₁₀O₂₉ electrode exhibits a lower discharge capacity of 127.6 mAh·g^-1 and a lower capacity retention of 79.3%.The carbon layer modification,small size and large surface area of the Ti₂Nb₁₀O₂₉/C nanoparticles can stabilize the structure,reduce Li⁺diffusion paths and supply a large number of active sites;therefore,the Ti₂Nb₁₀O₂₉/C electrode has high discharge capacity and good cycle performance [ 44, 45] .In addition,the Ti₂Nb₁₀O₂₉/C electrode exhibits a longer activated process than the Ti₂Nb₁₀O₂₉ electrode,which may be caused by the insufficient contact of the electrode materials with the electrolyte in the fresh cells [ 46, 47, 48] .

Fig.6 Initial discharge-charge curves of a Ti₂Nb₁₀O₂₉/C nanoparticles and b Ti₂Nb₁₀O₂₉ nanoparticles at 1C,5C,1OC,20C and 30C;c cycle performance of Ti₂Nb₁₀O₂₉/C nanoparticles (TNO/C) and Ti₂Nb₁₀O₂₉ nanoparticles (TNO) in voltage range of 1.0-2.5 V at 10℃

The rate capabilities for the two samples are compared,and the results are shown in Fig.7a.It is clear that,as the current densities are increased from 1C to 5C,10C,20C and 30C,the Ti₂Nb₁₀O₂₉/C electrode exhibits excellent rate capability with discharge capacities of 258.3,236.0,216.6,184.5,and 161.5 mAh·g^-1,respectively,whereas the corresponding value for the Ti₂Nb₁₀O₂₉ electrode is244.9 mAh·g^-1 (1C),which is greatly reduced to89.7 mAh·g^-1 at high current density (30C).Subsequently,as the current density is reduced to 1C,a high discharge capacity of 257.3 mAh·g^-1 is recovered,suggesting that the Ti₂Nb₁₀O₂₉/C electrode has good structural stability.Additionally,compared with other Nb-based electrodes(Fig.S5),the Ti₂Nb₁₀O₂₉/C electrode possesses outstanding rate capacity.

Fig.7 a Rate capacity and b Nyquist plots of Ti₂Nb₁₀O₂₉/C nanoparticles (TNO/C) and Ti₂Nb₁₀O₂₉ nanoparticles (TNO),and inset in b being equivalent electrical circuit model

Fig.8 CV curves of a Ti₂Nb₁₀O₂₉/C nanoparticles and d Ti₂Nb₁₀O₂₉ nanoparticles at different scanning rates from 0.1 to 5 mV·s^-1 with potential window of 1.0-2.5 V vs.Li/Li⁺;lgi-lgv plots of b Ti₂Nb₁₀O₂₉/C nanoparticles and e Ti₂Nb₁₀O₂₉ nanoparticles;pseudocapacitive and diffusion-controlled contributions of c Ti₂Nb₁₀O₂₉/C nanoparticles and f Ti₂Nb₁₀O₂₉ nanoparticles at different scanning rates

The electrical conductivity of the Ti₂Nb₁₀O₂₉/C electrode can be prominently improved due to the carbon layer,so the rate capability is greatly improved [ 49] .EIS tests were then performed to further prove the enhancement of the electronic conductivity.The Nyquist plots for the two samples are displayed in Fig.7b.Both Nyquist plots show semicircles and sloping lines in the high-frequency and low-frequency regions,respectively.The inset in Fig.7b shows the equivalent circuit model,in which R₁,R₂,W₁and CPE₁ are the Ohmic resistance of the cell,chargetransfer resistance,Warburg impedance for the Li⁺diffusion resistance in the electrode and constant phase element,respectively.According to the fitted results,the Ti₂Nb₁₀O₂₉electrode possesses a larger R₂ compared to the Ti₂Nb₁₀O₂₉/C electrode (83.8 vs.64.4Ω),demonstrating that the Ti₂Nb₁₀O₂₉/C electrode has good electron and Liion transport during cycling due to the carbon coating [ 9, 50] .In addition,the Li⁺-diffusion coefficient (D) for the two samples is further researched based on the following equations [ 51] :

where Z',σ,ω,R,T,A,n,F and C are the real part of the impedance,Warburg factor,angular frequency,gas constant,absolute temperature,surface area,number of electrons transferred in the redox reactions,Faraday constant and concentration of Li⁺in Ti₂Nb₁₀O₂₉,respectively.According to the slopes of the Z'-ω^-0.5 plots (Fig.S6),Ti₂Nb₁₀O₂₉ nanoparticles have a largerσvalue than the Ti₂Nb₁₀O₂₉/C nanoparticles (294.14 vs.94.41Ω·cm²·s^-0.5).Therefore,based on Eq.(2),the D value for the Ti₂Nb₁₀O₂₉ nanoparticles is smaller than that for the Ti₂Nb₁₀O₂₉/C nanoparticles,and eventually the kinetics for the lithium-ion and electron transfer in the Ti₂Nb₁₀O₂₉/C electrode become faster than that for the Ti₂Nb₁₀O₂₉electrode [ 52] .In order to get more electrochemical information,EIS measurements of the Ti₂Nb₁₀O₂₉/C and Ti₂Nb₁₀O₂₉ electrodes after 50 cycles were also carried out,and the results are shown in Fig.S7.As we can see,the Ti₂Nb₁₀O₂₉/C/Li cell exhibits a lower R₂ value (110.2Ω)after 50 cycles compared to the Ti₂Nb ₁₀O₂₉/Li cell(150.1Ω),indicating that the carbon layer in Ti₂Nb₁₀O₂₉/C has maintained a fairly good electronic conductivity even after 50 cycles.In addition,the enlarged R₂ value of the Ti₂Nb₁₀O₂₉/C and Ti₂Nb₁₀O₂₉ electrodes after 50 cycles may be attributed to the developed internal resistance upon charge/discharge cycle,which is a common phenomenon observed in the electrodes of Li-ion battery [ 53] .

Additionally,as the size of anode is reduced to nanoscale dimensions,a fairly large amount of stored charges and a fast charge/discharge rate can be easily obtained [ 49, 54] .The total stored charges are mainly composed of contributions from the diffusion-controlled Li⁺insertion process and the surface-controlled pseudocapacitance.As the grain size is reduced to the nanoscale regime,pseudocapacitance is important to the total stored charge due to the large number of surface atoms [ 55] .The contribution of the pseudocapacitive effect can be determined by CV tests conducted at different sweep rates (Fig.8a,d) on the basis of the following equations [ 56] :

where i and v is the measured current intensity and sweep rate,respectively,and a and b are the appropriate constants.There are two well-defined cases:for b=1.0,i is proportional to v and the process is limited by the pseudocapacitive effect;for b=0.5,i is proportional to v^1/2and the electrochemical reaction is controlled by Li⁺diffusion.According to the slopes of lgi vs.Igv plots(Fig.8b,e),b is equal to 0.847/0.808 and 0.818/0.784,for the middle cathodic and anodic peaks of the two electrodes,respectively,indicating that Li⁺storage reactions of the two electrodes are controlled by two Li⁺-storage mechanisms:the Li⁺-insertion process and pseudocapacitive effect [ 57, 58] :

where i(V) is the total current response,k₁ and k₂ are adjustable parameters,and k₁v and k₂V^1/2 are the current contributions from the surface-controlled pseudocapacitive effect and diffusion-controlled Li⁺insertion process,respectively.Based on Eq.(6),k₁ and k₂ correspond to the slope and intercept of the plot of i(V)/v^1/2 vs.v^1/2.As shown in Fig.8c,k₁v at specific scan rates can be calculated to be 52.2%,60.8%,70.9%,77.6%,83.1%and88.6%,respectively.Obviously,k₁v is gradually enlarged with scan rate increasing,indicating that the total stored charge for the Ti₂Nb₁₀O₂₉/C electrode is mostly controlled by the pseudocapacitive process at high sweep rates.For comparison,the pseudocapacitive contributions for the Ti₂Nb₁₀O₂₉ electrode at various scan rates were also studied,and it was found that the Ti₂Nb₁₀O₂₉ electrode possesses smaller pseudocapacitive contributions compared to the Ti₂Nb₁₀O₂₉/C electrode (Fig.8f).Specially,k₁v for the Ti₂Nb₁₀O₂₉ electrode is 37.8%,46.3%,57.6%,65.8%,73.1%and 81.1%.Thus,it can be demonstrated that the pseudocapacitive contributions can be significantly enlarged by decreasing the particle size and decoration of the carbon layer [ 43, 50] .

4 Conclusion

In summary,Ti₂Nb₁₀O₂₉/C nanoparticles with good dispersity were synthesized by a simple and effective in situ sol-gel process.A large specific surface area and small grain size can decrease Li⁺diffusion length and offer plenty of accessible active sites for Li⁺storage,leading to a large discharge capacity and superior rate capability.Meanwhile,the carbon layer not only improves the pseudocapacitive effect and electric conductivity,but also serves as an elastic barrier to buffer the stress of the volume change generated in the discharge and charge processes,leading to excellent rate capacity and good cycle performance.

Acknowledgments This study was financially supported by the National Natural Science Foundation of China (No.51802163),the National Natural Science Foundation of Henan Department of Education (No.20A480004) and the China Postdoctoral Science Foundation (No.2017M622564).