Unraveling the Synergistic Effects of Oxygen Vacancy and Amorphous Structure on TiO2 for High‐Performance Lithium Storage

The improved electronic conductivity and ion diffusion efficiency of TiO2‐based anode materials have been extensively studied by introducing oxygen vacancies or creating amorphous structure. There has been little exploration of the synergistic effects by combining these two modification strategies into one TiO2‐based matrix. In addition, the structure–activity relationship and energy storage mechanism involved remain to be understood. Herein, a facile one‐step coreduction method is reported to successfully produce the oxygen vacancy‐doped amorphous TiO2 nanoparticles. The oxygen vacancy‐doped amorphous TiO2 anode exhibits significantly enhanced electrochemical activity and high‐rate stability (up to 87 mAh g−1 over 10 000 discharge/charge cycles at a current rate of 100 C). This outstanding electrochemical performance is attributable to the synergistic effects of amorphous structure and oxygen vacancies. Density functional theory calculations reveal the enhanced electronic conductivity and thermodynamically favorable lithium insertion architecture due to the introduction of oxygen vacancy and the construction of the amorphous skeleton. Dynamic analysis indicates that the lithium‐storage mechanism is a hybrid of surface capacitive storage and enhanced diffusion‐controlled ion insertion. This work opens up new pathways in developing novel anode materials for efficient energy storage from the wide spectrum of metal oxides.


Introduction
To resolve the increasingly serious environmental issues and meet the rapidly growing demand for green energy, the fastcharging and high-capacity energy storage has attracted widespread attention in the past decades. [1]As a result, novel materials with high-rate performance are continuously being desired and developed as anodes for Li-ion batteries. [2]Among them, titanium dioxide (TiO 2 ) is one representative material, as it is abundant, ecofriendly, and relatively stable, and has a high theoretical capacity of 335 mAh g À1 . [3]hree main TiO 2 polymorphs, including anatase, rutile, and TiO 2 -B (bronze) phases, have been widely explored as the electrode materials for Li-ion batteries. [4]However, due to their low electronic conductivity and poor ion diffusion, pristine TiO 2 anodes exhibit unsatisfactory rate and cycling performance. [5]3b,9] Oxygen vacancies can serve as the shallow donors, raising the density of states (DOS) below the Fermi level, and further improving the electronic conductivity and ion diffusion in TiO 2 materials. [9,10]3b,7a,11] In contrast, the formation of amorphous structure is another effective way to improve the electrochemical energy storage for various metal oxides. [12]he improved electronic conductivity and ion diffusion efficiency of TiO 2 -based anode materials have been extensively studied by introducing oxygen vacancies or creating amorphous structure.There has been little exploration of the synergistic effects by combining these two modification strategies into one TiO 2based matrix.In addition, the structure-activity relationship and energy storage mechanism involved remain to be understood.Herein, a facile one-step coreduction method is reported to successfully produce the oxygen vacancy-doped amorphous TiO 2 nanoparticles.The oxygen vacancy-doped amorphous TiO 2 anode exhibits significantly enhanced electrochemical activity and high-rate stability (up to 87 mAh g À1 over 10 000 discharge/charge cycles at a current rate of 100 C).This outstanding electrochemical performance is attributable to the synergistic effects of amorphous structure and oxygen vacancies.Density functional theory calculations reveal the enhanced electronic conductivity and thermodynamically favorable lithium insertion architecture due to the introduction of oxygen vacancy and the construction of the amorphous skeleton.Dynamic analysis indicates that the lithium-storage mechanism is a hybrid of surface capacitive storage and enhanced diffusion-controlled ion insertion.This work opens up new pathways in developing novel anode materials for efficient energy storage from the wide spectrum of metal oxides.
For TiO 2 -based materials, amorphous TiO 2 is known to have a lower density and looser structure than crystalline TiO 2 . [12]hen used as the anode material, amorphous TiO 2 typically has a greater accommodation for volume expansion, better electronic conductivity, and higher diffusion coefficient compared to its crystalline structure. [13]The amorphous nature could contain structure variations during the Li þ insertion/extraction process, and cause insignificant constraints on the electrode kinetics, improving the electrochemical activities. [14]Although oxygen vacancy-doped TiO 2 or amorphous TiO 2 separately enables considerable improvement of lithium storage performance, one interesting and feasible strategy worth exploring is to combine oxygen vacancies and amorphous structure in one TiO 2 material for studying their synergistic effects.Therefore, integrating the oxygen vacancy-doping with amorphization engineering to design and optimize TiO 2 -based anode materials for energy storage deserves further exploration both theoretically and experimentally.
Here, density functional theory (DFT) calculations were first performed to help us understand the effects of oxygen vacancy doping and amorphization engineering on the atomic structure and electronic properties of TiO 2 .Then, using a facile NaBH 4 coreduction method, the oxygen vacancy-doped amorphous TiO 2 nanoparticles (named as am-TiO 2Àx ) were successfully fabricated in one step for the first time.Such an oxygen vacancy-doped amorphous TiO 2 anode not only meets the basic requirement about high-rate and large-capacity energy storage (e.g., 246 mAh g À1 at 1 C or 92 mAh g À1 at 100 C), but also possesses remarkable cycling stability at the high-rate condition (≈95% capacity retention after 10 000 cycles at 100 C).DFT simulation and kinetic analysis provide valuable insights into the combined influences of oxygen vacancy and amorphous structure on the enhanced lithium storage performance for TiO 2 -based materials, holding great inspiration for designing other metal oxidebased anode materials with highly efficient energy storage.

DFT Calculation
To unveil the influence of oxygen vacancy and lattice distortion upon the structural and electronic properties of TiO 2 -based materials, DFT calculations were performed (details in Supporting information), and anatase TiO 2 was selected as the proof of implementation, which has been widely used as the TiO 2 -based anode material for lithium storage. [15]Figure 1a shows the representative and optimized unit cell models for anatase TiO 2 (TiO 2 (Anatase)), anatase TiO 2 with oxygen vacancy (TiO 2Àx ), amorphous TiO 2 (am-TiO 2 ), and oxygen vacancy-doped amorphous TiO 2 (am-TiO 2Àx ).The DOS was calculated using the ab initio first principles to evaluate the electronic properties of the as-constructed frameworks (Figure 1b).As presented, the valence band (VB) and conduction band (CB) of all the samples are mainly derived from O 2p and Ti 3d states, respectively.The calculated intrinsic bandgap of TiO 2 (Anatase) is about 2.72 eV.The incorporation of oxygen vacancies results in a reduced bandgap (2.66 eV) for TiO 2Àx with one intermediate band located between VB and CB.This is due to the fact that the doped oxygen vacancies generate the lone pair electrons, leading to the intermediate band and further affecting the bandgap of the oxygen vacancy-doped TiO 2 . [16]For the amorphous TiO 2 models (am-TiO 2 and am-TiO 2Àx ), both of them show the smaller band gaps than the crystalline TiO 2 models (TiO 2 (Anatase) and TiO 2Àx ).The narrowed bandgap is beneficial to improve the electronic conductivity of the as-made materials, which is conductive to the energy storage. [9,16]Two oxygen vacancyinduced intermediate bands are present at about 1.29 and 1.61 eV below the CB in am-TiO 2Àx , which can act as the springboard for the electron transport and produce a more positive impact on the conductivity of amorphous skeleton.
Furthermore, the Li insertion energy (U i ) was calculated to evaluate the electrochemical behavior of lithiation in the proposed structure (details in Supporting information).Considering the various amorphous structure and oxygen vacancy sites, different types of lithium intercalation models were screened for the stable structures with the possible lithium-ion coordination in the configuration (Figure 1c and S1, Supporting Information).As shown in Figure 1d and S1b, Supporting Information, TiO 2Àx shows three different insertion energies where the lithium ion is adjacent, near or apart from the oxygen vacancy, and finally, the value of U i is close to the energy that lithium ion intercalates into the pristine TiO 2 (Anatase) lattice.For the am-TiO 2 model, the highly disordered framework provides many nonequivalent sites and nonfixed paths for hosting lithium ions and their migration, thus a wide range of U i are achieved (Figure 1d and S1c, Supporting Information).This will be reflected as the broad lithiation/delithiation peaks in the cyclic voltammetry (CV) curves. [17]Notably, some of these values are lower than those in crystalline TiO 2 models, suggesting that there are more thermodynamically favorable lithium insertion sites in the amorphous structure compared to the crystalline phase.While for the am-TiO 2Àx model (Figure 1d and S1d, Supporting Information), the introduction of oxygen vacancies further exacerbates the degree of structural diversity, producing the large variations of chemical pair interactions in the framework, which can accommodate lithium ions with wider insertion energy characteristics compared to those in am-TiO 2 models.Therefore, as confirmed by the results from DFT analysis, the dual strategy with oxygen vacancy and amorphous framework not only can effectively adjust the electronic structure of the as-constructed TiO 2 nanostructure with the narrowed bandgap, but also offers a large number of available sites and space with thermodynamically favorable lithium insertion advantages, thereby improving the electronic conductivity and enhancing the potential energy storage characteristics.

Morphological and Structural Characterization
To verify the results deduced from DFT calculations, commercial white TiO 2 (Anatase) nanoparticles were used as the raw material in our experiments.As shown in Figure 2a and S2a,b, Supporting Information, the pristine TiO 2 (Anatase) nanoparticles possess a spherical microstructure with a particle size ranging from 20 to 50 nm.The polycrystalline anatase structure with a d 101 -spacing of 0.35 nm is clearly revealed in the highresolution transmission electron microscopy (HRTEM) image (Figure 2b).The selected area electron diffraction (SAED) pattern with obvious diffraction dots proves the good crystallinity of the commercial anatase nanoparticles (inset of Figure 2b).Figure 2c, d and S2c,d, Supporting Information, display the TEM and scanning electron microscopy (SEM) images of TiO 2Àx , which are consistent with TiO 2 (Anatase).The spherical microstructure and the particle size distribution were also found to be retained for am-TiO 2Àx (Figure 2e and S2e,f, Supporting Information) and am-TiO 2 (Figure 2g and S2g,h, Supporting Information).The amorphous feature of am-TiO 2Àx and am-TiO 2 is clearly evidenced in HRTEM images (Figure 2f,h), as there are no lattice fringes on the nanoparticles.The phase transition can further be supported by the SAED patterns.As shown in the inset of Figure 2f, the SAED pattern of am-TiO 2Àx shows ambiguous diffraction halos, indicating its amorphous nature.After calcinated in air, the prepared am-TiO 2 exhibits the similar diffraction halos with some bright dots due to the presence of little amount of anatase nanoparticles.
The structures of the as-made samples were further analyzed by X-ray diffraction (XRD) patterns (Figure 3a).The pristine TiO 2 (Anatase) exhibits the typical characteristic peaks of anatase phase (JCPDS 21-1272).All peaks in TiO 2Àx are identical to the standard anatase phase, and the color changes from white to blue (inset in Figure 3a), indicating the presence of oxygen vacancies. [9,18]Am-TiO 2Àx shows the color similar to that of TiO 2Àx .However, the total disappearance of characteristic anatase peaks confirms the amorphous nature of am-TiO 2Àx after the high-temperature NaBH 4 coreduction reaction.For am-TiO 2 nanoparticles, the complete oxidation turns the blue color of am-TiO 2Àx to grayish white, while the amorphous structure is largely retained with some low-intensity anatase peaks due to the presence of a small amount of anatase phase formed during the calcining process (Figure 3a).In addition, the structural differences of these samples were further revealed in Raman spectroscopic results (Figure 3b).Four characteristic anatase peaks at 142 cm À1 (E g ), 394 cm À1 (B 1g ), 516 cm À1 (A 1g ), and 639 cm À1 (E g ) are identified for TiO 2 (Anatase). [19]All these distinct peaks are maintained in TiO 2Àx nanoparticles duo to the well-preserved anatase phase.Moreover, TiO 2Àx nanoparticles display the obvious blue-shift of the Raman-active modes as the introduction of oxygen vacancies can reduce the bonding symmetry of Ti-O bonds. [20]However, for am-TiO 2Àx and am-TiO 2 , the intensities for the above peaks almost disappear, indicating their amorphous property. [21]Specifically, the obvious blue-shift and broadening of the relatively low-intensity E g peak in am-TiO 2Àx highlight the coexistence of oxygen vacancies and structure distortion induced by the high-temperature NaBH 4 coreduction process. [22]After annealing in air, a weak E g peak appears in am-TiO 2 at the same position of TiO 2 (Anatase) due to the existence of small amount of anatase phase in am-TiO 2 , while its broadening nature remains due to the retained amorphous structure.
The presence of oxygen vacancy in TiO 2Àx and am-TiO 2Àx was further verified using electron paramagnetic resonance (EPR) spectrometry.Figure 3c and S3, Supporting Information, present a weak EPR signal with g-value of 1.979 for TiO 2 (Anatase), assigned to the rhombic Ti 3þ center in the bulk of the pristine TiO 2 material. [23]For TiO 2Àx , a sharp resonance signal at g-value of 2.003 was obtained.It is believed that two residual electrons in an oxygen vacancy are usually transferred to the adjacent Ti 4þ to form Ti 3þ (Figure 3d), Ti 3þ species tend to adsorb atmospheric O 2 , which will be reduced to a surface oxygen radical (O 2 À ) (Figure S4a, Supporting Information), showing a resonance signal at g = 2.003. [23,24]Whereas a broad and strong EPR intensity with a g-value of 1.958 can be clearly identified for am-TiO 2Àx .This peak is originated from the formation of bulk Ti 3þ sites upon the high-temperature reduction process. [25]A further step about the formation energy of the oxygen vacancies at different sites was evaluated through DFT calculation. [26]As shown in Figure 3e and S4, S5, Supporting Information, the corresponding oxygen vacancy formation energy in the surface is larger than that in either the subsurface or bulk region, that is, oxygen vacancies tend to form from the surface toward the subsurface and bulk region, creating more oxygen vacancies in the subsurface and bulk region and yielding a large number of Ti 3þ sites. [27]24a] However, in am-TiO 2 , only a small signal at g-value of 1.979 can be found, suggesting the successful removal of oxygen vacancies and the formation of small amount of anatase TiO 2 after the calcination process.The X-ray photoelectron spectroscopy (XPS) studies were also performed to investigate the defective structures (Figure 3f and S6, Supporting Information).The high-resolution Ti 2p spectrum of TiO 2 (Anatase) exhibits two peaks at 458.6 and 464.4 eV, attributable to Ti 2p 3/2 and Ti 2p 1/2 of Ti 4þ , respectively.27b] Upon the removal of oxygen vacancies in the subsequent calcination process, am-TiO 2 exhibits the same Ti 4þ binding energies as those in TiO 2 (Anatase).These evolutionary trends indicate the successful introduction and removal of the gen vacancies in am-TiO 2Àx . [9,28]All these results strongly prove the successful synthesis of oxygen vacancy-doped amorphous TiO 2 nanoparticles by our one-step NaBH 4 coreduction route.

Lithium-Ion Storage Performance
14b] In the first redox CV curve at 0.1 mV s À1 (Figure 4a), TiO 2 (Anatase) anode shows the typical cathodic/anodic peaks around 1.70/2.10V versus Li þ /Li, corresponding to the Li insertion and extraction processes into the TiO 2 lattice. [29]The irreversible cathodic peak at 0.70 V is reported to be caused by the irreversible intercalation of Li ions into the TiO 2 crystal, the decomposition of the electrolyte and the formation of solid electrolyte interface (SEI) layers. [30]In the subsequent cycles, the cathodic/anodic peak current diminishes gradually, indicating the electrochemical instability of TiO 2 (Anatase) anode.For TiO 2Àx anode (Figure 4b), the CV curves display the similar shape and peak positions that belong to the typical TiO 2 -based anodes. [11]However, the more pronounced cathodic/anodic peaks and the retention of the peak intensities in the succedent cycles verify the enhanced electrochemical activity and reversible reduction/oxidative process (Figure S7a, Supporting Information), proving that the introduction of oxygen vacancies improves the kinetics of TiO 2Àx anode. [9]istinct from TiO 2 (Anatase) and TiO 2Àx anodes, the redox process for amorphous TiO 2 anodes (am-TiO 2Àx and am-TiO 2 anodes) shows quite different CV curves scanning at 0.1 mV s À1 .As presented in Figure 4c,d, two obvious cathodic peaks around 1.55 and 0.70 V appear in the first scanning cycle and disappear upon cycling.Except for the same peak at 0.70 V as shown in TiO 2 (Anatase) anode assigned to the formation of SEI films, the peak around 1.55 V is attributed to Li þ insertion into the amorphous TiO 2 structure upon reduction of Ti 4þ to Ti 3þ , and the associated extraction process points to the anodic peak at 1.75 V. [14b,31] Besides, the small cathodic/anodic peaks at ≈1.70/2.10V also appear in the cathodic/anodic sweeps for am-TiO 2 anode (Figure 4d and S7b, Supporting Information), which is related to the small components of anatase phase in am-TiO 2 particles.In the subsequent scans, amorphous TiO 2 anodes exhibit broad cathodic/anodic peaks due to the wide range of nonequivalent lithiation and delithiation sites available in the amorphous structure as mentioned in the earlier DFT analysis (Figure 1d and S7c, Supporting Information).Besides, the overlap of the subsequent curves in am-TiO 2Àx and am-TiO 2 anodes shows the good reversibility of the insertion/extraction process in the amorphous materials.14b,32] Galvanostatic discharge/charge test at C-rates from 0.25 to 100 C (1 C = 168 mA g À1 ) was performed to evaluate the rate performance of the as-made TiO 2 anodes (Figure 4e).The am-TiO 2Àx anode presents an initial discharging capacity of 787 mAh g À1 and retains a charging capacity of 374 mAh g À1 at 0.25 C, higher than those of am-TiO 2 anode (596 and 312 mAh g À1 ), TiO 2Àx anode (581 and 295 mAh g À1 ), and TiO 2 (Anatase) anode (563 and 271 mAh g À1 ) (Figure S8, Supporting Information).The initial capacity loss is commonly attributed to the irreversible decomposition of the electrolyte and the formation of SEI films. [33]With respect to TiO 2 (Anatase) and TiO 2Àx anodes (Figure S8a,b, Supporting Information), two broad plateaus occur around 1.7 and 2.0 V during the discharge/charge process, in accordance with the lithiation/delithiation peak positions observed in the CV curves (Figure 4a,b).However, a significant capacity attenuation occurs in the following cycles for pristine TiO 2 (Anatase) anode, while a slower dropping trend is presented for TiO 2Àx anode.This improved cycling performance of TiO 2Àx anode can be credited to the presence of oxygen vacancy.Figure S8c,d, Supporting Information, displays the discharge/charge profiles of the am-TiO 2Àx and am-TiO 2 anodes with larger specific capacities.As expected, no plateau-like features appear in the discharge/charge curves of amorphous TiO 2 anodes.
Additionally, the cycling performance was also evaluated under the high current densities.The specific capacity of am-TiO 2Àx anode is about 300 mAh g À1 after 200 cycles at 1 C (Figure 4f ), which is larger than that of am-TiO 2 anode (245 mAh g À1 ), TiO 2Àx anode (189 mAh g À1 ), and TiO 2 (Anatase) anode (138 mAh g À1 ).Obviously, the amorphous TiO 2 anodes (am-TiO 2Àx and am-TiO 2 ) have relatively larger capacities compared to the crystalline TiO 2 anodes (TiO 2 (Anatase) and TiO 2Àx ).Such enhancement on the electrochemical properties can be attributed to the more reversible trapping sites inside the amorphous structure.Moreover, the gradual increase of capacity upon cycling can be ascribed to the electrochemical activation process, which results in an improved accessibility of Li ions into the inner area of the electrode. [34]The more distinct capacity increase in the oxygen vacancy-doped TiO 2 anodes (am-TiO 2Àx and TiO 2Àx ) implies the advantages of the oxygen vacancy doping in respect to the cyclability.For the cyclability at 10 C, the am-TiO 2Àx electrode gives a specific capacity of 217 mAh g À1 after 2 000 cycles (Figure S9, Supporting Information).Notably, when discharging/charging at ultra-high rate of 100 C (Figure 4g), the am-TiO 2Àx anode can retain a marvelous specific capacity of 87 mAh g À1 even after 10 000 cycles, while the corresponding values for am-TiO 2 , TiO 2Àx , and TiO 2 (Anatase) anodes are just 46, 51, and 21 mAh g À1 , respectively.In detail, the capacities for TiO 2Àx anode climb from 41 to 51 mAh g À1 , while the capacities for TiO 2 (Anatase) anode fade from 27 to 21 mAh g À1 , further revealing the effective impact of oxygen vacancies for the enhancement of the cyclability for TiO 2 nanoparticles.Besides, the amorphous TiO 2 anodes (am-TiO 2Àx and am-TiO 2 ) yield the obvious higher capacities at the beginning of the cycling test, apparently disclosing that the disordered phase could serve more lithium storage.However, the large decay of the high-rate performance for am-TiO 2 anode from 88 to 46 mAh g À1 upon 10 000 cycles at 100 C may point to the instability of amorphous structure under high-rate conditions.Compared to am-TiO 2 anode, the highly conductive oxygen vacancy-doped framework in the am-TiO 2Àx anode may eliminate the conductivity limitation for a high-power delivery, resulting in the amorphous lattice being able to withstand more radical changes of current density.Furthermore, the Coulombic efficiency keeps around 100% even after cycling 10 000 times (Figure 4g), further verifying the favorable reversibility and sturdy structure of the oxygen vacancy-doped amorphous framework.As can be seen from the postmortem SEM and TEM images (Figure S10, Supporting Information), the morphology of am-TiO 2Àx nanoparticles is not significantly changed after 10 000 cycles at 100 C, indicative of a robust material property in the long-term cycling.However, for am-TiO 2 anode (Figure S11, Supporting Information), many holes were found in the nanoparticles after the cycling test at 100 C, which may be pointed to the instability of am-TiO 2 nanoparticles.The significant differences in high-rate performance among am-TiO 2Àx , am-TiO 2, TiO 2Àx , and TiO 2 (Anatase) anodes unambiguously signify the crucial roles of the amorphous structure in realizing the large capacity and the doping of oxygen vacancies in maintaining the stability during the fast discharge/charge process.

Dynamic Analysis
To gain deep insights into the synergistic effects of oxygen vacancy and amorphous structure on the underlying lithium insertion and extraction kinetics, CV experiments were further performed at different sweep rates varying from 0.2 to 100 mV s À1 (Figure 5a-d).
In general, two typical storage mechanisms, diffusion-controlled faradaic behavior and capacitive pseudo-capacitance, have been commonly considered for lithium-ion storage in TiO 2 -based anodes.The following equation between the measured current (i) and the scan rate (ν) can be used to distinguish the storage mechanism worked on the electrode: where the b-value of 0.5 indicates a total diffusion-controlled process and 1.0 for a surface-controlled behavior and capacitive process. [35]or TiO 2 (Anatase) anode (Figure 5e), the b-values obtained from the fitting lines are 0.61 and 0.59 for the cathodic and anodic peaks, respectively.35b,c] In the case of the TiO 2Àx anode, the corresponding values reduce to 0.58 and 0.57, respectively, indicating a more obvious diffusioncontrolled process caused by the doping of oxygen vacancy.As presented in Figure 5f, the b-value of amorphous TiO 2 anodes (am-TiO 2Àx and am-TiO 2 ) ranges from 0.70 to 0.76, indicating the coexistence of the diffusion-controlled and capacitive processes.Interestingly, all the oxygen vacancy-doped anodes display the relatively lower b-values compared to their counterparts (am-TiO 2Àx vs am-TiO 2 , TiO 2Àx vs TiO 2 (Anatase)), implying the promotion effect of oxygen vacancies on ion mobility. [11,36]oreover, the dependence of the b-value on the voltage potential had also been plotted to gain a better understanding on the storage mechanism during the whole lithiation/delithiation process. [37]35c,38] Unsurprisingly, the am-TiO 2Àx anode shows the smaller b-values in the whole potential range compared to am-TiO 2 anode due to the improved ion diffusion kinetics.
In contrast, based on the equation between the measured current [i(V )] and the scan rate (ν) at a fixed potential (V ): (2) the total capacity can be divided into the surface capacitive and diffusion-controlled insertion capacities. [29]The quantified results demonstrate that the surface capacitive capacity is enhanced with the increase of the scan rate for all the electrodes (Figure 5g).The higher diffusion-controlled contribution in the total capacity for oxygen vacancy-doped anodes (am-TiO 2Àx vs am-TiO 2 , TiO 2Àx vs TiO 2 (Anatase)) is consistent with the electrochemical features obtained from Equation (1).Electrochemical impedance spectroscopy (EIS) analysis was also employed to further understand the effects of oxygen vacancies and amorphous structure on the impedance properties of the asmade anodes.From Figure 5h and Table S2, Supporting Information, the R ct of the am-TiO 2Àx (134 Ω) or TiO 2Àx (161 Ω) is smaller than that of am-TiO 2 (170 Ω) or TiO 2 (Anatase) (192 Ω).In addition, the calculated ion diffusion coefficient (D 0 ) deduced from Nyquist plots demonstrates that the amorphous TiO 2 anodes (am-TiO 2Àx and am-TiO 2 ) or the oxygen vacancy-doped TiO 2 anodes (am-TiO 2Àx and TiO 2Àx ) have the larger values of D 0 than their counterparts, and am-TiO 2Àx anode has the largest value of D 0 (3.01 Â 10 À12 cm 2 s À1 ), implying a higher Li þ diffusion rate and an efficient ion and current delivery for rapid electrode reactions (Figure S12c and Table S2, Supporting Information).Furthermore, the galvanostatic intermittent titration technique (GITT) test was used to elucidate the diffusion coefficients (D Li þ ) during the lithiation/delithiation process (Figure 5i).Just as expected, the amorphous TiO 2 anodes or the oxygen vacancydoped TiO 2 anodes also possess the larger values of D Li þ than their counterparts, and am-TiO 2Àx anode exhibits the relatively higher D Li þ values than other anodes, indicating the faster diffusion kinetics of Li þ ions inside am-TiO 2Àx nanoparticles (Figure 5j and Table S2, Supporting Information).In addition, unlike the significant drop of D Li þ values in TiO 2Àx and TiO 2 (Anatase) anodes at ≈1.8 V, the change of D Li þ values for am-TiO 2Àx and am-TiO 2 anodes is gentle, implying a comparatively stable and efficient lithium ion diffusion process during the discharge/charge steps in the amorphous structure.
Based on the above theoretical calculations, experimental results, and dynamic analysis, the incorporation of amorphous configuration into the TiO 2 lattice can effectively improve the poor electronic conductivity and reduce the charge transfer resistance, which are beneficial to the ion/electron transport.Moreover, the loosely packed skeleton can provide more free space and open spatial channels as the facile lithium-ion diffusion pathways, thus obtaining multiple accommodation sites with well-dispersed insertion energies.In contrast, the loosely packed structure caused by the absence of long-term ordering and the relatively lower ion diffusion ability may also make the as-made anode material unable to withstand the rapid unremitting and random Li þ insertion/extraction, leading to poor cyclability under large current density.The introduction of oxygen defects in the disordered structure can further improve the electronic conductivity, reduce the charge transfer resistance, boost the ion diffusion coefficient, and cause the wider distribution of thermodynamically active Li þ accommodation sites, which together guarantee that the material can withstand the high and rapid lithium diffusion flux for efficient lithium storage especially under the ultra-high current densities.As expected, am-TiO 2Àx anode expresses the impressive electrochemical performance and stability even after 10 000 cycles at 100 C. Thus, the expanded internal storage sites with the help of oxygen vacancies are able to acclimate the rapid insertion and removal of lithium ions with accelerated storage kinetics, and preserve the amorphous structure.

Conclusion
In summary, oxygen vacancy-doped amorphous TiO 2 nanoparticles have been successfully realized via the one-step coreduction method.The oxygen vacancy-doped amorphous TiO 2 anode shows the superior energy storage performance, delivers a reversible capacity about 300 mAh g À1 at 1 C and excellent long-term cyclability over 10 000 cycles at 100 C. Furthermore, our results elucidate the coexistence of the capacitive and enhanced diffusion-controlled lithium storage process.Through the DFT calculations and kinetic analysis, the high-rate and large-capacity energy storage of am-TiO 2Àx can be possibly attributed to its disordered structure with loose atomic packing and various favorable insertion sites; in contrast, the long-term stability of am-TiO 2Àx is related to the high conductivity and the weakened kinetic constraints endowed by the doping of oxygen vacancies, promoting the ion/charge transport and the structural stability ever under the ultra-high rate condition.This work opens new directions in designing functional materials for high-capacity and fast-charging electrodes with long-term stability for practical applications.

Experimental Section
Materials Synthesis: Oxygen vacancy-doped TiO 2 and oxygen vacancydoped amorphous TiO 2 nanoparticles were synthesized by NaBH 4 coreduction method.In a typical reaction, 1 g pristine TiO 2 (Anatase) nanoparticles were ground with 0.2 g NaBH 4 .Then, the mixture was transferred into a 25 mL glass bottle and placed in a tubular furnace, heated in argon atmosphere at 350 °C for 0.5 h with a heating rate of 2 °C min À1 .After being naturally cooled down to ambient temperature, the blue product was washed with deionized water and 1 M hydrochloric acid several times to remove unreacted NaBH 4 and dried at 80 °C overnight.The obtained blue TiO 2 nanoparticles will be named as TiO 2Àx .To prepare the oxygen vacancy-doped amorphous TiO 2 , 1 g pristine TiO 2 (Anatase) nanoparticles were mixed with 0.5 g NaBH 4 and thoroughly oscillated for 5 min at room temperature.Then, the mixture was transferred into a 25 mL glass bottle and placed in a tubular furnace, heated in argon atmosphere at 500 °C for 4 h with a heating rate of 2 °C min À1 .After being naturally cooled down to ambient temperature, the blue product was washed with ethanol, deionized water, and 1 M hydrochloric acid several times to remove unreacted NaBH 4 and dried at 80 °C overnight.The obtained blue TiO 2 nanoparticles will be referred to am-TiO 2Àx .For the synthesis of oxygen vacancy-free amorphous TiO 2 nanoparticles, the as-prepared oxygen vacancy-doped amorphous TiO 2 was further annealed in air under 500 °C for 2 h, and the as-made sample was donated as am-TiO 2 .
Material Characterization: The XRD pattern was collected by Bruker D8 High Resolution with Cu radiation (Cu Kα = 0.15406 nm).The Raman spectra were recorded on a Raman microscope system (Horiba Jobin Yvon Modular Raman Spectrometer) with laser excitation wavelength of 514 nm.EPR spectra of the samples were collected at room temperature using a Bruker EMX spectrometer.The surface electronic states were conducted by XPS (ESCALAB 250Xi).All the values of binding energy are calibrated by using C 1s = 284.8eV as calibration.Field-emission scanning electron microscopy, TEM, HRTEM, and were performed on Hitachi SU8010, Tecnai G2 20, and FEI Tecnai G2 F20 S-TWIN machines, respectively.
Electrochemical Measurement: Electrochemical experiments were tested at room temperature using standard CR2032 type coin cells.The cells were assembled in an argon-filled glove box consisting of a working cathode, a metallic Li anode, a PP separator (Celgard 2400), and an electrolyte.The working electrodes were prepared by mixing the as-prepared blue TiO 2 , carbon black (Super P), and polymer binder (polyvinylidene fluoride) in a weight ratio of 70:20:10 and pasted on pure Cu foil.The mass loading of each circular electrode is about 0.8 mg cm À2 .The electrolyte consisted of a solution of 1.0 M LiPF 6 in ethylene carbonate (EC)/dimethyl carbonate (DMC)/ethyl methyl carbonate (EMC) (1:1:1 by volume).The galvanostatic discharge-charge experiments were tested on a NEWARE multichannel battery testing system at different current densities in a voltage range of 0.01-3.0V. CV measurements of the electrodes were carried out on an CHI660E electrochemical station with a voltage window of 0.01-3 V. EIS analysis was recorded in the frequency of 0.01-10 5 Hz with a 5 mV AC amplitude on an AUTOLAB electrochemical station.GITT test was measured on a NEWARE multichannel battery testing system at the current density of 0.25 C for 0.5 h and then rested for 1 h.

Figure 1 .
Figure 1.DFT calculation and atomic structure analysis.a) The atomic models of TiO 2 (Anatase), TiO 2Àx , am-TiO 2 , and am-TiO 2Àx .b) The corresponding DOS of the constructed models.c) The representative atomic configurations for the insertion of Li and d) the calculated U i at different sites in TiO 2 (Anatase), TiO 2Àx , am-TiO 2 , and am-TiO 2Àx .

Figure 3 .
Figure 3. Structural analysis of the as-prepared nanoparticles.a) XRD patterns.The inserts are the optical images.b) Raman spectra.c) EPR spectra.d) Schematic illustration of the excess electrons on the Ti atoms with the existence of one oxygen vacancy.e) Oxygen vacancy formation energies in different parts of anatase TiO 2 .The inserts are the atomic structures of anatase TiO 2 with oxygen vacancy on the surface, subsurface or bulk.f ) High-resolution Ti 2p XPS spectra of TiO 2 (Anatase), TiO 2Àx , am-TiO 2Àx , and am-TiO 2 .

Figure 4 .
Figure 4. Electrochemical evaluations on the prepared TiO 2 (Anatase), TiO 2Àx , am-TiO 2Àx , and am-TiO 2 anodes in half cells.a-d) CV curves from 1 st to 5 th cycles at a scan rate of 0.1 mV s À1 .e) Rate performance at different current densities from 0.25 to 100 C, and then return to 0.25 C (1 C = 168 mA g À1 ).f ) Cycling performance at 1C. g) Long-term performance at 100C, and the Coulombic efficiency of am-TiO 2Àx anode at 100 C.

Figure 5 .
Figure 5. Kinetic analysis of the electrochemical behavior for TiO 2 (Anatase), TiO 2Àx , am-TiO 2Àx , and am-TiO 2 anodes.a-d) CV curves at different scan rates varying from 0.1 to 100 mV s À1 .b-value analysis using the relationship between peak currents and scan rates from 0.1 to 100 mV s À1 for e) TiO 2 (Anatase) and TiO 2Àx anodes, and f ) am-TiO 2Àx and am-TiO 2 anodes.g) Contribution ratio of the diffusion-controlled and capacitive capacity.h) Nyquist plots at room temperature.The inset is the corresponding equivalent circuit.i) The charge/discharge profiles in GITT test, and j) the calculated Li þ ion diffusion coefficients at the second and third discharge/charge cycles.