INTRODUCTION

Titanium dioxide (TiO ₂ ) is a promising anode material for lithium ion batteries (LIBs) due to high abundance of titanium, low cost and low toxicity. ^1"5 In addition, the reactions of Ti0 ₂ with lithium ions through an intercalation/de-intercalation mechanism result in remarkable reversible capacity, high chemical/thermal stability, and small volume expansion. ^5"9 Furthermore, the usual formation of solid electrolyte interface (SEI), typical of anodes based on graphite, nowadays the most commonly used anode material, is absent in Ti0 ₂ based materials owing to their high operational potential (> 1 V vs Li /Li). ^5"7 All these reasons together make Ti0 ₂ based anodes promising candidates for high power applications such as electric vehicles, hybrid electric vehicles and smart grids. ⁵ ' ^10-13

Various types of Ti0 ₂ polymorphs (anatase, rutile, brookite and bronze) have been investigated as active anode materials for LIBs. ⁵ ' ^{14 18} Among them, Ti02-Bronze (TB) has the highest capacity (335 mAh g ^"1 ) ^19"22 and additionally it undergoes pseudo-capacitive charging (due to adsorption of Li ⁺ at the TB surface and near surface region with a Ti /Ti redox reaction), which allows for higher cycling rates. ' ^" On the other hand, the low electric and ionic conductivity within TiO ₂ polymorphs have prevented the manufacturing of TiO ₂ -based LIBs as high rate anode electrodes.

To overcome these issues, nanostructuring of TiO ₂ has been proposed. ¹ ' ³ ' ^{26 28} In particular, one-dimension (ID) nano-architectures such as nano wires, nanotubes, nanorods and nanofibers have shown direct and rapid ion/electron transport, better compliance to lithiation induced stresses and short Li-ion diffusion length compared to other kinds of nanostructures. ^29"32 A further approach to improve the electrochemical performance of anode materials utilizes carbon coating and/or carbonaceous composites. For instance, 3D

33 34 21 cross-linked TiO ₂ nano web/nano fibers, ID TB nano wires, nanotubes and nanorods, ³⁵ ' ³⁶ both carbon coated and combined with reduced graphene oxide, have been proposed. However, the conductivity enhancement from carbon coating involves heat treatment at high-temperatures, which is not suitable for TB. Indeed, phase transformation to anatase and/or rutile may occur during the heat treatment. Furthermore, the use of conductive additives positively affects the electron transport but only on the surface of active electrode materials, while leaving unaltered the intrinsic electrical conductivity of Ti0 ₂ . To overcome this limitation, it was shown that doping Ti0 ₂ with metal/non-metal impurity atoms can improve its intrinsic electrical conductivity, and this leads to better lithium battery performance in terms of energy density and rate capability. In addition, doping enhances the lithium diffusion through hopping of electrons from Ti ³⁺ sites with low valence states to Ti ⁴⁺ sites with high valence states. ³⁷ In particular, Ti0 ₂ doped with metal heteroatoms such as Sn, Mo, Cr, Nb, Mn, Fe, Ni and non-metal heteroatoms like N, C, S were prepared and studied as electrodes for LIBs. ²² ' ^38-45 . Recently, Kim et al. ⁴⁶ and in a similar fashion Li et al. ⁴⁷ improved lithium battery performance by using ID Ti0 ₂ nanostructures with nitrogen doping. These results suggest that ID TB nanostructures, if doped with suitable heteroatoms, can lead to improved lithium battery performance in terms of both capacity and rate capability even though only few reports exist on this

Summary of the invention An object of the invention is to provide a simple and inexpensive synthesis procedure capable of producing nanostructures doped with heteroatoms.

A specific object of the invention is to provide C-doped Titanium bronze nano wires for use in Li-ion batteries as anode material.

The general conditions of the process of the invention are defined in the appended claims. A specific embodiment of the invention is the direct synthesis of carbon doped TB nanowires (CTB-NWs), starting from titanium carbide (TiC), via a simple hydrothermal procedure. The synthesis procedure comprises three steps, as illustrated in Figure la. TiC was used as precursor material for the primary oxidation process, which resulted in micro sized C-doped Ti0 ₂ particles (Step 1). Subsequently, micrometer- long nanowires were formed through a hydrothermal reaction in alkaline media (Step 2). The synthesis was then followed by proton exchange with diluted HCl and calcination (Step 3) resulting in the formation of CTB-NWs (see Figures lb-d).

Brief description of the drawings

Figure 1. (a) Schematic illustration describing the preparation of CTB-NWs starting from TiC precursor, (b) High resolution SEM image of CTB-NWs. (c) TEM image of CTB- NWs, and (d) high resolution TEM image of single CTB-NW. The inset in (d) represents the Fast Fourier Transfer (FFT) of the CTB-NWs crystal structure.

Figure 2. (a) X-ray diffraction pattern of CTB nano wires and TB nano wires. The asterisks represent the anatase peak. ICDD card 046-1237. (b) Zoom of the peaks (110) and (020) (highlighted by green dashed line in (a)), (c) Deconvoluted XPS spectra of (left) C Is, (right) Ti 2p bands of CTB-NWs and TB- NWs.

Figure 3. Electrochemical characterization of CTB-NWs and TB-NWs. (a) Cyclic voltammograms; (b) Galvanostatic charge-discharge cycling profile at the current rate of 0.1C; The Nyquist plots of electrochemical impedance spectroscopy measurements at different potentials (c) 2.6 V (OCV); (d) 1.95 V (partial lithiation); (e) 1.1V (complete lithiation) and (f) 2.2 V (complete de-lithiation) vs Li+/Li. For (c) to (f) the corresponding electrical circuits are shown.

Figure 4. Electrochemical performance of CTB-NWs. (a) Cyclic voltammograms of first 50 cycles at scan rate of O.lmV s- ¹ . (b) Cyclic voltammograms at different scan rates (mV s- ¹ ). Inset: scan rate vs current density, (c) Galvanostatic charging- discharging profile at various current rates (from C/20 to IOC), (d) capacity retention at current rates between C/2 and IOC.

Figure 5. Long-term cycling performance of CTB-NWs is displayed at a currents rate of IOC. An efficiency of 100% together with a slow decaying specific capacity

(charge and discharge) are shown. After 1000 cycles, the specific capacity had decayed of 19%.

Figure SI. SEM images of (a) TiC, (b) C-doped Ti0 ₂ , (c) Sodium titanate nanowires.

Figure S2. SEM image of undoped Ti0 ₂ -Bronze (TB-NWs) nanowires.

Figure S3. X-ray diffraction pattern of (i) TiC, (ii) C-doped TiO _¾ (iii) C-doped Na ₂ Ti ₉ Oi9, (iv) C-doped FbTisOn and (v) CTB nanowires. The asterisk represents the anatase peak.

Figure S4. Raman spectra of both CTB-NWs and TB-NWs.

Figure S5. XPS spectra of Cls and Ti2p bands for TiC (black), C-doped Ti0 ₂ (blue) and CTB nanowires (red).

Figure S6. UV-Vis absorbance measured for CTB-NWs (Black line) and TB-NWs (Red line). Figure S7. Z _Re vs ω - ^" 1/2 as obtained from the Nyquist plots at (a) OCV and (b) 1.95 V for CTB-NWs. (Black line) and TB-NWs (Red line).

Figure S8. Galvanostatic cycling performance of carbon doped TB nanowires (CTB- NWs) at currents rates (i) C/2, (ii) I C and (iii) 5 C (therein, 1 C = 335 mAh g ^"1 ).

Figure S9. Specific capacity and Columbic efficiency of undoped Ti0 ₂ -B nanowires (TB-NWs).

EXPERIMENTAL SECTION Materials. Titanium carbide (TiC) from MaTecK Material-Technologie & Kristalle GmbH, Germany, sodium hydroxide (NaOH), Hydrochloric acid, Millipore water. All chemical were used further purification. Preparation of nanowires of C-doped Ti0 ₂ -Bronze. The preparation of nanowires of C- doped Ti0 ₂ -B followed a multi-step procedure. The first step was the complete oxidation (in air atmosphere) of TiC resulting into C-doped Ti0 ₂ at 500 °C for 5 hours. Afterwards, the nanowires of C-doped TB were synthesized under hydrothermal route in alkaline solution, i.e. 10M NaOH. In particular, 0.2 grams of C-doped Ti0 ₂ were dispersed in 20 ml of 10M NaOH solution under continuous stirring, then this solution was transferred to Teflon lined autoclave and reacted at 160 °C for 48 hours. The obtained product was washed 3 times with Millipore water through centrifugation, followed by 3 times washing in 0.1M HCl solution and 6 times washing with Millipore water. Finally, it was washed with ethanol then dried under vacuum at 40 °C overnight. The resulted product was heat treated at 300 °C for 120 minutes at a heat rate of 2 °C per minute, yielding to a white powder, i.e. CTB nanowires.

Material Characterization. The powder X-ray diffraction patterns were recorded on a Rigaku SmartLab 9 kW diffractometer equipped with Cu Ka X-ray source operated at 40 kV and 150 mA. Transmission electron microscopy images were obtained using a JEOL JEM 1011 (Jeol, Tokyo Japan) operating at 100 kV acceleration voltage, equipped with a W thermionic electron source and a FEI TECNAI G2 F20 instrument, equipped with a Schottky field emission gun (FEG), operating at 200 kV acceleration voltage. High resolution scanning electron microscopy images were obtained using a JEOL JSM 75 OOF A (Jeol, Tokyo, Japan) equipped with a cold FEG, operating at 15 kV acceleration voltage.

Raman spectroscopy measurements were carried out with Renishaw in Via Micro Raman equipped with laser source at 785 nm through a 50x objective (LEICA N PLAN EPI 50/0.75). X-ray photoelectron spectroscopy (XPS) analysis was performed on a Kratos Axis Ultra DLD spectrometer, using a monochromatic Al Ka source (15 kV, 20 mA). High resolution narrow scans were performed at constant pass energy of 10 eV and steps of 0.1 eV. The photoelectrons were detected at a take-off angle Θ = 0° with respect to the surface normal. The pressure in the analysis chamber was maintained below 7 x 10 ⁹ Torr for data acquisition. The data were converted to VAMAS format and processed using Casa XPS software, version 2.3.16. The binding energy (BE) scale was internally referenced to the C Is peak (BE for C-C = 284.8 eV). Electrochemical Measurements. Electrochemical 2032 coin cells were fabricated inside a MBraun glovebox with < 0.1 ppm H ₂ 0 and < 0.1 ppm 0 ₂ . The working electrode was prepared by mixing the active materials (CTB nanowires, super P carbon and polyvinylidene difluoride (PVDF)) in the weight ratio of 70:20: 10, casted onto copper current collector then dried overnight at 120 °C under vacuum. The mass of the composite electrode materials was between 2.5 and 3.0 mg. Lithium metal was used as counter and reference electrode and 1.0M of LiPF ₆ in ethylene carbonate/dimethyl carbonate (1 : 1 v/v) from BASF was used as the electrolyte. All electrochemical measurements were carried out with Biologic MPG-2 multichannel battery unit and PARSTAT 4000 Potentiostat/galvanostat at room temperature (-25 °C).

RESULTS AND DISCUSSIONS

In order to verify the contribution from the carbon doping and identify the crystal structure and morphologies, the CTB-NWs were examined by scanning and transmission electron microscopy (SEM and TEM), X-ray diffraction (XRD), X-ray photoelectron spectroscopy (XPS) and Raman spectroscopy. Similarly, the intermediate synthesis products were studied by XRD. For comparison, the undoped TB nanowires (TB-NWs) were prepared from Ti0 ₂ particles (see Supporting Information, SI). Finally, both the CTB-NWs and the TB-NWs were tested as anode materials for LIBs. The results demonstrate superior performance of CTB-NWs in terms of capacity, rate capability, and better cycle life stability than the TB-NWs. Indeed, during cycling experiments, the CTB-NWs exhibited lithium storage capacity of -306 mA h g ^"1 (91% of the theoretical capacity) at the current rate of 0.1C as well as excellent discharge capacity of -160 mAh g ^"1 even at the current rate of IOC after 1000 charge/discharge cycles.

The direct carbon doping of bronze Ti0 ₂ was achieved by a multi-step hydrothermal synthesis (see Figure la). The first step is the transformation of the TiC precursor into C- doped Ti0 ₂ (CT) by heat treatment, which is followed by the synthesis of C-doped sodium titanate nanowires (Na-CT NWs) via hydrothermal approach in alkaline media. In the last step, the wires undergo an acid treatment, by which sodium is replaced by hydrogen, yielding to hydrogen titanate nanowires (H-CT NWs), followed by calcination at 300 °C (in the present context carbon is the heteroatom). It is important to note that no additional carbon source was used. For comparison, TB-NWs were synthesized by using Ti0 ₂ (anatase and rutile) particles, following the synthesis protocol discussed in the Supporting Information. Morphological and Structural studies. The wire like morphology of the particles was evidenced from both high resolution SEM and TEM (Figure lb-c). All the synthesized nanowires are between 2 μιη and 10 μιη long with width in the range of 20-200 nm. Furthermore, no agglomeration was observed. The high resolution TEM image of a single nanowire (Figure Id) evidences two sets of well-defined lattice fringes, with interplanar distances of 0.35 nm and 0.58 nm that are related to the (110) and (100) planes of TB, respectively. Both the Fast Fourier Transform (FFT, Figure Id) and the high resolution TEM image prove that the wires have a bronze phase. SEM images of the TiC (Step 1), C- doped Ti0 ₂ (Step 2) and C-doped sodium titanate nanowires are reported in Figure SI a, Sib and Sic of the SI, respectively. These images suggest that the nanowires formation occurs during the hydrothermal reaction in alkaline media and it is not affected by proton exchange and calcination. Undoped TB-NWs were synthesized too and their SEM images are presented in Figure S2.

The XRD patterns of both TB-NWs and CTB-NWs, reported in Figure 2a, match the monoclinic TB, with space group C2/m(12) (ICDD card number 046-1237), and they both show the presence of a small quantity of anatase (asterisk). Importantly, the CTB-NWs diffraction peaks at (110) and (020) are slightly shifted to lower angles with respect to the corresponding TB-NWs diffraction peaks: the (110) peak shifted from 24.88° to 24.70° and the (020) peak shifted from 48.32° to 48.20° (Figure 2b). It has been already suggested ⁵¹ that this shift originates from lattice expansion occurring when carbon is introduced in the Ti0 ₂ crystal lattice, similarly to the doping of sulphur in Ti0 ₂ ⁵² and of fluorine in Sn0 ₂ ⁵³ . Furthermore, X-ray diffraction was used to investigate the different synthesis steps reported in Figure 1, namely the complete transformation of TiC in CT under thermal annealing conditions, the formation of C-doped sodium titanate nanowires in alkaline media followed by their hydrogenation (C-doped hydrogen titanate nanowires) and the final transformation into crystalline and highly pure CTB-NWs phase, as shown in figure S3 of the SI.

The surface composition and chemical state of the different constituents of both CTB-NWs and TB-NWs were studied by XPS. Figure 2(c) shows XPS spectra collected from CTB- NWs and TB-NWs powders over the binding energy (BE) range typical for Cls and Ti 2p core levels. From Figure 2c, the peaks located at the BE values of 284.8 eV, 286.6 eV and 288.9 eV for both CTB-NWs and TB-NWs correspond to the elemental carbon C-C, C-0 and 0-C=0 bonds, respectively. ⁵⁴ ' ⁵⁵ It was also reported that the presence of the 288.9 eV peak can result from the formation of C-0 bonds through the replacement of Ti atoms by carbon in the Ti0 ₂ lattice, resulting in the formation of Ti-O-C/O-Ti-C structures ^55"58 . Therefore, the peak at 288.9 eV could be the summation of contributions from 0-C=0 bonds due to adventitious carbon ⁵⁹ ' ⁶⁰ and C-doping into the Ti0 ₂ lattice. These considerations, together with the result that CTB-NWs peak at 288.9 eV has an amplitude significantly higher than the corresponding peak for the TB-NWs structure, suggests a significant presence of carbon doping in the CTB-NWs. This conclusion is also supported by the XPS spectra around the Ti 2p band region (Figure 2c) where a shift of ~ 0.2 eV between the Ti 2p _3/2 peaks of CTB-NWs (458.6 eV) and TB-NWs (458.8 eV) can be observed. Indeed, the insertion of carbon in the Ti0 ₂ lattice results in a shift of Ti 2p towards lower binding energy values, due to the lower electronegativity of carbon with respect to oxygen ^61"63 , and it represents an increase of Ti ⁺³ species due to charge compensation mechanism in the carbon doped Ti0 ₂ -B sample. ³⁷ Quantitative analysis was carried out to estimate the carbon content in the sample, using the C Is (288.9 eV) region. According to the analysis, the percentage of carbon content in the CTB-NWs is 1.0% higher than in the TB-NWs. ⁵⁵ XPS was employed to analyze the CT powder obtained by thermal annealing of TiC (Step 1 in Figure la). This spectrum, together with the corresponding XPS analysis of the TiC precursor and of the CTB-NWs, is reported in

Figure S5. From the figure we can conclude that there are no longer the characteristic C ls and Ti 2p peaks of TiC, hence revealing the complete oxidation of TiC into CT. Furthermore, the effect of the C-doping on the optical band gap was examined by recording UV- Visible spectra of CTB-NWs and TB-NWs (see Figure S6 in SI). The CTB- NWs exhibited slightly red-shifted absorbance, therefore a narrowing on the band gap, with respect to the TB-NWs. This is expected due to carbon doping. ^63"65

Electrochemical Performance. The performance of the CTB-NWs as anode material for lithium-ion batteries was extensively evaluated by electrochemical measurements. CTB- NWs and TB-NWs electrodes were fabricated and assembled in 2032 type coin cells using lithium metal as counter and reference electrode. The cells preparation was performed in a glove box under argon atmosphere (< 0.1 PPM of 0 ₂ and H ₂ 0). A standard solution of 1M LiPF ₆ in ethylene carbonate/dimethyl carbonate (1 : 1 v/v) was used as electrolyte. The cells were characterised by cyclic voltammetry, electrochemical impedance spectroscopy and galvanostatic charging-discharging studies. Electrodes based on CTB-NWs and TB-NWs were tested at the scan rate of 0.1 mV s ^"1 between 1.0 V and 2.5 V vs Li ⁺ /Li, as shown in Figure 3a. For both the CTB-NWs and the TB-NWs, the voltammograms exhibited two pairs of cathodic and anodic peaks at the potentials of ~ 1.57 V, 1.49 V and 1.55V, 1.62 V vs Li ⁺ /Li, respectively. Electrodes from the CTB-NWs exhibited higher current densities than TB-NWs, which was related to their higher ionic and electronic conductivity. The observed peaks are the signatures of Ti0 ₂ -bronze phase (TB), also known in literature as SI and S2 surface adsorption peaks. ²⁴ In this article, Graetzel et al. reported that SI and S2 peaks are due to the different energy barriers for Li-ions transfer at the (100) and (001) faces of Ti0 ₂ -B and/or might be associated with two distinct super-structures of Li _x Ti0 ₂ - B. This finding is in good agreement with both the Raman spectra (Figure S4) and with the XRD pattern of Figure 2a, where the TB phase was first identified. Minor reversible peaks at potential of -1.76 V and 1.95 V vs Li ⁺ /Li were observed for both CTB-NWs and TB-

NWs, which were related to small amounts of anatase Ti0 ₂ . This was expected because minor anatase Ti0 ₂ phase was observed in XRD patterns of both electrode materials (Figure 2a). Importantly, the disappearing of the peaks was observed upon cycling. The performances of both CTB-NWs and TB-NWs were studied by galvanostatic charging-discharging tests, reported in Figure 3b. The cell made with CTB-NWs electrodes exhibited charge and discharge capacities for the first cycle of ~ 345 and 292 mAh g ^"1 , respectively, and columbic efficiency of ~ 85% at current rate of 0.1C. The cells fabricated with TB-NWs showed first cycle charge and discharge capacities of ~ 342 and 285 mAh g ^"1 , respectively, with a columbic efficiency of ~ 83% at 0.1 C current rate. Upon cycling, the cells reached a columbic efficiency close to 99%. The loss of capacity for both CTB-NWs and TB-NWs in the first cycles is attributed to the irreversible interaction between the TB nano wires and the electrolyte ⁶² . While the capacity retention of both electrodes were similar during the initial three cycles, upon further cycling a capacity fading was observed for the TB-NWs electrode, which reached a capacity of ~ 203 mAh g ^"1 after 40 cycles. On the contrary, the CTB-NWs electrode exhibited higher stability, with lower capacity fading and a discharge capacity of 280 mAh g ^"1 after 40 cycles. This better performance of CTB- NWs due to carbon doping leads to high electrical conductivity and higher lithium ion diffusion with hopping of electrons from Ti ³⁺ sites with low valence states to Ti ⁴⁺ sites with high valence states. ³⁷ In order to investigate the electrochemical kinetics, electrochemical impedance spectroscopy measurements were carried out for both CTB-NWs and TB-NWs electrode materials at several different states of charge in a frequency range from 100 kHz to 0.1 Hz with an amplitude of 10 mV. The Nyquist plots of both CTB-NWs and TB-NWs electrodes with their corresponding electrical circuits are presented in Figure 3 (c to f) at potentials of 2.6 V (open circuit voltage, OCV), 1.95 V (partial lithiation), 1.1 V (complete lithiation) and 2.2 V (complete de-lithiation). From these plots, the intercepts of both materials at the highest frequency range are related to the internal resistance (R _s ) of the electrolyte, separator and currents collector. The semicircle in the range from high to mid frequency is instead related to the charge-transfer process defined by the charge-transfer resistance (Ret) and by the double layer capacitance (Cdi). At low frequencies, the semicircle is followed by a sloping line, which defines the Warburg (W) region related to the Li-ion diffusion. In particular, Figures 3c-f show that R _s from CTB-NWs and TB-NWs plots are quite similar to each other and lie between 3.8 Ω to 8.5 Ω at all potentials, indicating that the resistance due to the electrolyte, separator and current collector is approximately the same in both cells. Furthermore, the R^ and Warburg region have similar profiles for both electrodes, with the Ret value for the CTB-NWs smaller than TB-NWs. This result was related to the presence of C-doping, which increases the electrical conductivity of CTB-NWs material. The behaviour of depends on the electric potential. In particular, at 1.95 V, where Li- ions start to be intercalated in the active TB material (Figure 3d) is lower than under OCV conditions. At 1.1 V we observe an increase of with the concomitant appearance of a second semicircle which, according to previous reports, ²⁵ ' ^{66 70} is related to the bulk resistance Rb defined as the resistivity of the electrolyte trapped in the pores of the composite electrode material (such as active material, conductive carbon and binder). At 2.2 V (Figure 3f) the data showed similar profiles and similar Rc _t (between 17 Ω and 25 Ω, where R _s about 5 Ω is considered) with respect to the cell measured at OCV, hence implying a reversible system. Importantly, the impedance studies show that CTB-NWs at various charge-discharge potentials have lower values than the undoped counterpart, while galvanostatic studies evidence higher reversible capacity than TB-NWs, indicating improved electrical conductivity by carbon doping, namely better CTB-NWs cycling performances. These results have been confirmed by the calculation of the ratio between the Li-ion diffusion coefficients (D _L i) for CTB-NWs and TB-NWs. Indeed, from the Nyquist plots at OCV (Figure 3c), the DLi of the CTB-NWs was found to be about 2.9 times higher than the DLi of the TB-NWs (see Figure S7a of SI), whereas at 1.95 V, CTB- NWs showed 3.2 times higher DLi compared to TB-NWs. In addition, the DLi of both CTB-NWs and TB-NWs at 1.95 V was about 70 times higher than DLi at OCV (see Figure S7). ^71"72

The long cycling and high rate performances of CTB-NWs electrode materials were examined by cyclic voltammetry and galvanostatic charge-discharge cycling studies at various scan rates and current rates. The first 50 voltammograms, measured at 0.1 mV s ^"1 , are showed in Figure 4a. The cycling voltammetry shows good reversibility for the CTB- NWs electrode along with stable anodic and cathodic currents. The characteristic peak of anatase seen in Figure 4a (asterisk) disappears from the 5 ^th cycle on. This behaviour suggests that the irreversible capacity from the initial cycles might be related to the presence of small impurity of anatase Ti0 ₂ . Similarly, cyclic voltammograms at different scan rates are shown in Figure 4b. The peak current increases linearly with increasing the scan rate (see inset Figure 4b) according to the pseudo capacitive charge storage behaviour of the TB electrode reported in the literature. ¹⁹ ' ²⁴ The rate performance of the CTB-NWs electrode was examined at various current rates and the data are shown in Figure 4c. The discharge capacities of ~ 290, 273, 265, 262, 258, 228, 203, 180 and 172 mAh g ^"1 were recorded at an increasing current rates of C/20, C/10, C/5, C/2.5, C/2, C, 2C, 5C and IOC, respectively. In particular, the long cycling performance of CTB-NWs electrodes was studied at C/2, 1C and 5C current, and yielded capacities of 220, 205 and 180 mAh g ^"1 after 250 cycles, respectively (SI, Figure S8). For all of the cases a columbic efficiency of ~ 100% was attained. Cycling performances for a single CTB-NWs cell was examined at various current rates of charge and discharge. The capacity retention of symmetrical charge and discharge at C/2, 1C, 2C, 5C, IOC and again back to initial rate of C/2 showed discharged capacities of 265, 240, 220, 185, 145 and 250 mAh g ^"1 , respectively and a columbic efficiency around ~ 100% (see Figure 4d). Similarly, single cell of TB-NWs was examined at various current rates of charge and discharge with their corresponding columbic efficiencies (see Figure S9 in SI). The analysis evidenced the higher specific capacity and capacity retention of the CTB-NWs over the TB-NWs. These results prove that CTB-NWs is a suitable active material for applications requiring fast charging and discharging LIBs.

The long term and high rate cycling of CTB-NWs was carried out at the current rate of IOC for 1000 cycles (Figure 5). The result shows capacity retention of ~ 81% (160 mAh g ^{" l} ) of the initial state after 1000 cycles. This remarkable performance, both in the long cycling capability and high rate of CTB-NWs, can be related to the 1-Dimentional nanowire morphology along with carbon doping. Indeed, the carbon doping increases the electrical conductivity as well as it decreases the Li-ions diffusion length. Accordingly, the invention provides a simple and inexpensive method to implement carbon direct doping into TB nanowires by hydrothermal approach without using any external carbon source. For comparison undoped TB nanowires were prepared by the same protocol. The formation of TB nanowires was confirmed by XRD, SEM/TEM, and Raman, while XRD and XPS spectroscopy proved the presence of carbon doping. Both doped and undoped TB nanowires were electrochemically characterized by Cyclic Voltammetry,

Electrochemical Impedance Spectroscopy and galvanostatic charging-discharging techniques. It was found that carbon doped TB nanowires exhibited lower RCT and better cycling performances than the undoped counterpart. In particular, carbon doped TB nanowires revealed remarkable electrochemical performance with considerable lithium storage capacity, high rate performance during charge and discharge, and a significant capacity retention (81% of the initial value) at IOC rate after 1000 cycles.

The carbon-doped TB nanowires of the invention find further application and use for Sodium ion batteries, for the production of supercapacitors and pseudo capacitors, for dye sensitized solar cells and in photo catalysis and photo degradation of organic molecules. SUPPORTING INFORMATION

Synthesis of undoped TiO ₂ -Bronze nanowires (TB-NWs)

The nanowires of TB were synthesized through multi step procedure from titanium-(iv) iso propoxide. In particular, 2.842 grams of titanium-(iv) iso propoxide were added to 10 ml of anhydrous ethanol. Furthermore, deionized water was continuously added to the above solution while stirring. The result was an immediate colour change of the solution, from colourless to milk white colour, indicating the formation of titanium dioxide. After 2 hours of continuous stirring, white colour powder (Ti0 ₂ ) was obtained from centrifugation, and annealed at 500 °C for five hours (as followed for the synthesis of CTB-NWs, Step 1). Finally, TB nanowires were synthesized under hydrothermal route in alkaline solution (NaOH). In particular, 0.2 grams of Ti0 ₂ were dispersed, while stirring, in 20 ml solution of 10 M NaOH, to be transferred to Teflon lined autoclave and brought to 160 °C temperature for 48 hours. The obtained product was washed 3 times with Millipore water through centrifugation, procedure followed by 3 times washing in 0.1 M HC1 solution, 6 times with Millipore water and again with ethanol. Finally, drying procedure was performed under vacuum at 40 °C overnight. The resulting product was heat treated at 300 °C for 120 minutes at a heat rate of 2 °C per min, yielding a white powder, i.e. TB nanowires. The morphology and crystal structure were examined by using scanning electron microscopy, X-ray diffraction pattern and X-ray photoelectron spectroscopy as presented in Figure S2 and Figure 2a/2c, respectively. X-Ray Diffraction.

The changes in the crystal structure at different synthesis steps were investigated by X-ray diffraction. As previously described, the formation of CTB-NWs involved the complete oxidation of TiC into micron sized CT (both anatase and rutile) and the transformation of these particles into nanowires structures. In this regard, Figure S3 shows the XRD pattern of TiC precursor and of the reaction intermediates CT, C-doped sodium titanate nanowires (C-Na ₂ Ti ₉ 0i9; Na-CT NWs, Step 2), C-doped hydrogen titanate nanowires (H ₂ Ti ₈ 0i7; H- CT NWs, Step 3 before performing calcination) and CTB-NWs. The figure clearly evidences the different phase transition of Ti0 ₂ during the synthesis steps. Particularly descriptive of the process is the phase transformation of sodium titanate (2Θ - 11°, ICDD card number 078-1598) into hydrogen titanate (2Θ ~ 9.8°, ICDD card number 036-0656). Importantly, both Na and H are not present in the XRD spectra of CTB-NWs ¹³ ' ¹⁹ . Finally, the peak at 2Θ equal to 14.10° (ICDD card number 046-1237) is representative of TB phase, hence confirming the crystallographic phase of CTB-NWs. Similar considerations are valid for TiC precursor, indeed none of its characteristic peaks can be found in CT, sodium titanate, hydrogen titanate and CTB-NWs XRD spectra. From the latter pattern it can also be observed a very small amounts of anatase Ti0 ₂ (indicated by the asterisk in the Figure S3). The presence of anatase may originate either from the raw residual of precursor before the hydrothermal process or from the phase transformation of Ti0 ₂ -Bronze phase during the calcination.

Raman Spectroscopy Figure S4 shows the Raman spectra of both CTB-NWs and TB-NWs. The primitive cell of

S 1

TB contains 36 Raman active modes (18A _g and 18B _g ) . These vibrations are due to the bonding interactions of Ti-Ti, 0-0 and Ti-0 . The figure reveals quite similar characteristic vibrations modes for both CTB-NWs and TB-NWs at 162, 170, 196, 248, 294, 412, 466 and 645 cm ^"1 of TB phase and it is in excellent agreement with previous reports of either bulk or nanowires ^" .

Furthermore, the high purity of TB phase is confirmed by the absence of the characteristic peak associated to anatase-Ti0 ₂ (i.e. at 144 cm ^"1 ). The Raman spectroscopy could not provide any clear evidence of carbon doping in CTB-NWs, which is explained through the very low percentage of carbon doping with respect to TB. Similar results were reported in Fe containing TB nanowires ⁴⁵ .

X-ray Photoelectron Spectroscopy

Figure S5 shows that the TiC peak at -281.6 eV for C Is band, and the peaks at 454.9 eV and 460.8 eV for Ti 2p band (indicated with asterisk in the figure) completely disappear in both CT and CTB-NWs spectra. Based on these data and XRD patterns from Figure 2a, we can conclude that TiC is completely oxidized into CT by thermal annealing.

UV- Visible Spectroscopy To estimate the effect of carbon doping on the band gap of Ti0 ₂ -B nanowires, UV- Visible absorption spectra were measured. As shown in Figure S6, a noticeable shift of absorption peak to the higher wavelength region was observed for the CTB-NWs in comparison with undoped TB-NWs. It is known that successful carbon doping into Ti0 ₂ lattice yields red

S8-S 10

shift in the absorbance ^" . The approximate band gaps of CTB-NWs and TB-NWs result to be 2.83 and 2.96 eV respectively. These evidences prove the carbon doping in CTB-

NWs which indeed leads to absorbance peak at higher wavelength and band gap narrowing of CTB-NWs compared to TB-NWs.

Diffusion Coefficient calculation

The Li-ion diffusion coefficient can be calculated according to the following formulas ^{sl l} ' ^S12 :

Z _Re = R _ct + R _s + ff &J ^"1/2 (1)

R ² T ²

^{Li ~} 2A ⁴ CV ^{( )}

where Z _Re is the real component of the impedance and σ is the Warburg prefactor which can be obtained from combining Eq. (1) and Figure S7 In Eq. (2) the quantity R is the Regnault gas constant, T the absolute temperature, A the electrode area, n the number of electrons transferred in the redox couple, F the Faraday's constant and C the Li-ion concentration. From Eq. (2) the ratio between the diffusion coefficients of CTB-NWs and TB-NWs simplifies as the ratio between the corresponding Warburg prefactors. From Fig. S7 at OCV are found to be σ Ω S ^~1/2 and at 1.95 V are Ω s ^~1/2 and

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