Design and synthesis of TiO2/C nanosheets with a directional cascade carrier transfer

Directed transfer of carriers, akin to excited charges in photosynthesis, in semiconductors by structural design is challenging. Here, TiO2 nanosheets with interlayered sp2 carbon and titanium vacancies are obtained by low-temperature controlled oxidation calcination. The directed transfer of carriers from the excited position to Ti-vacancies to interlayered carbon is investigated and proven to greatly increase the charge transport efficiency. The TiO2/C obtained demonstrates excellent photocatalytic and photoelectrochemical activity and significant lithium/sodium ion storage performance. Further theoretical calculations reveal that the directional excited position/Ti-vacancies/interlayered carbon facilitate the spatial inside-out cascade electron transfer, resulting in high charge transfer kinetics.

mm MAS probe on a Bruker AVANCE-III 500 spectrometer with a sample spinning rate of 38 kHz, a 1 H π/2 pulse length of 1.65 μs and a recycle delay of 2 s.

Photocatalytic Experiment.
To investigate the photocatalytic activity of the nanostructured TiO 2 samples, methylene blue (MB) dye was used for photodegradation. Typically, 20 mg photocatalysts were dispersed in 100 mL aqueous solution containing 3×10 -5 mol/L MB. For photocatalysis, the samples were irradiated under UV-vis light with a PLS-SXE-300D lamp (Beijing Perfectlight Technology Co., Ltd.). The photodegradation of MB was monitored by UV-visible spectrometry (UV2550, Shimadzu, Japan).
Acetone was used as a model air pollutant to measure the photodegradation ability of the TiO 2 samples obtained. The TiO 2 photocatalysts were dispersed in aqueous solution and then dispersed onto a dish with a diameter of ca. 3 cm. The dish was then dried at 80 °C for 12 h and then cooled to room temperature before being used. The weight of each catalyst was kept at 100 mg. After putting the photocatalysts into the reactor, 5 µL of acetone was injected into the reactor with a micro syringe. The reactor was kept in the dark for a certain time to reach adsorption-desorption equilibrium before irradiation. The analysis was conducted with a gas chromatograph (Agilent 2920B) equipped with a flame ionization detector (FID).

Electrochemical Measurements.
Electrochemical tests were performed using 2025-type coin cells. The working electrodes were synthesized by mixing the active materials, acetylene black, and poly (vinylidene fluoride) (PVDF) with a weight ratio of 7:2:1 in N-methyl-2-pyrrolidone (NMP) to form a slurry. The slurry was uniformly spread on a copper foil. Lithium foil was used as the counter electrode and reference electrode. A 1 mol/L solution of LiPF 6 dissolved in ethylene carbonate and dimethyl carbonate (1:1 in volume ratio) was used as the electrolyte. Na half-cells were assembled with a Na metal foil as the negative electrode and 1 mol/L NaClO 4 in ethylene carbonate and dimethyl carbonate (1:1 in volume ratio) as the electrolyte. All the half-cells were assembled in an argon-filled glovebox with both water and oxygen contents below 0.5 ppm. Galvanostatic discharge-charge curves were collected on a LAND CT2001A battery test system within a voltage range of 3.0-1.0 V (vs Li + /Li) and 3.0-0.1V (vs Na + /Na) at 1 C rate kept after first three cycles (C/5) (1 C is defined as 170 mA/g). All electrochemical measurements were carried out at 25 °C. Electrochemical impedance spectra (EIS) measurements were carried out on an electrochemical workstation (Autolab PGSTAT302N, Metrohm, Switzerland) in a frequency range of 0.1 MHz to 0.01 Hz.

Photo-electrochemical Measurements.
Photocurrent tests were carried out in a conventional three-electrode system using on a Autolab PGSTAT302N electrochemical workstation (Metrohm, Switzerland) with a Pt foil as the counter electrode and a Ag/AgCl reference electrode under a PLS-SXE-300D lamp. The working electrodes were prepared by dispersing catalysts (5 mg) and Nafion solution (100 µL, 0.5 wt%) in water/ethanol mixed solvent (1 mL, 1:1 v/v) at least 30 min of sonication to form a homogeneous ink. The working electrode was synthesized by drop-casting the above ink (40 µL) onto FTO glass with an area of 1 cm 2 .

Density Functional Theory Calculations.
The generalized gradient approximation (GGA) with the Perdew-Burke-Ernzerhof exchange correlation functional (adding Grimme method for DFT-D3 correction were performed to study the formation mechanism of Ti-vacancy) and a 520 eV cutoff for the plane-wave basis set were employed to perform all the density functional theory (DFT) computations of the materials within the frame of Vienna ab initio simulation package (VASP). The convergence threshold was set as 10 -5 eV in energy and 0.02 eV/Å in force. 1×3×1 Monkhorst-Pack grid kpoints were employed for geometric optimization. In this study, the C are represented by C42 and the anatase TiO 2 (001) surface is represented by the anatase TiO 2 (001) surface model.   a The peak area of sp 2 carbon is the total amount of the fitted peaks in S sp2 in Fig. S9. b The peak area of sp 3 carbon is the total amount of the fitted peaks in S sp3 in Fig. S9. c It has to be pointed out that the numerical values of the calculated sp 2 /sp 3 ratio here don't mean the exact amount of the sp 2 /sp 3 ratio in the samples. They can be regarded as reference for the comparison of their relative amount in TiO 2 /C Inter and TiO 2 /C Surf .

Results and Discussion
where E total is the total energy of the model, E C is the energy of carbon layer, and E TiO2 is the energy of TiO 2 . 13 For where E total defect and E total host host are the total energies of the models with and without Ti vacancies, respectively, and μ Ti FERE is the standard state Ti chemical potential, the value of μ Ti FERE is -5.52 eV. [14][15] Fig. S1. TG and DTA curves of Ti-G.

Detailed descriptions of TGA-DTA.
Thermogravimetric analysis-differential thermal analysis (Fig. S1) of titanium glycerolate (designated as Ti-G) was used to determine the calcination profile. The slight weight loss below 300 °C is due to the loss of absorbed water, the weight loss of 38% in the range of 300-          Table S2.  XPS of TiO 2 /C Inter and TiO 2 /C Surf are recorded for further investigation (Fig. 2b, Fig. S11a, b).
The O1s core-level XPS of TiO 2 /C Inter (Fig. S11b)  Surface C/Ti ratio and Surface C content. The surface C/Ti atomic ratio can be calculated from the Ti 2p and C 1s peaks of the samples (Fig. S11a, f, Table S2). The C/Ti atomic ratio is calculated to be 6.42±0.1 for Ti-G, 0.69±0.1 for TiO 2 /C Inter , 0.69 for the sample calcined at 550 °C, 0.88±0.1 for the sample calcined at 750 °C and 3.12±0.1 for TiO 2 /C Surf (Fig. S11d and         S17b). Moreover, the TEM images of TiO 2 /C Inter after the lithium/sodium-ion cycling performance for 300 cycles (Fig. S18) show that their nanostructure is well-maintained, indicating their good structural stability.
According to the rate performance of lithium-ion storage shown in Fig. S19a, TiO 2 /C Inter displays high capacities of 200, 194, 185, 172, 153 and 131 mAh/g at current densities of 0.2 C, 0.5 C, 1 C, 2 C, 5 C and 10 C, respectively, and also a reversible capacity of 180 mAh/g at 0.2 C, which is obviously higher than TiO 2 /C Surf . For the rate performance of sodium-ion storage, TiO 2 /C Inter also displays high capacities of 217, 184, 168, 152, 133 and 118 mAh/g at current densities of 0.2 C, 0.5 C, 1 C, 2 C, 5 C and 10 C, and also a reversible capacity of 197 mAh/g at 0.2 C (Fig. S19b).
The excellent stability and high rate performance of TiO 2 /C Inter could be attributed to its unique structural features. Firstly, the very thin nanosheet could shorten the diffusion length for Li + /Na + , which allows for fast insertion/extraction of Li + /Na + . 22 Secondly, the amorphous interface between TiO 2 crystals could be a more effective structure to increase the capacity of Li + due to less structural confinement for the Li + ions in the insertion/extraction reaction. 23 Thirdly, the interlayered carbon and the titanium vacancies could endow it with good electronic conductivity and enhance the mobility and diffusion of Li + /Na + . 24 These structural advantages are favorable for the increased Li + and Na + reversible capacities.

Detailed descriptions of theoretical calculations
To investigate the role of interlayered carbon in charge transfer, three models are built including TiO 2 with Ti-vacancies (TiO 2 -V Ti ) (Fig. S20b), TiO 2 with Ti-vacancies and surface carbon (TiO 2 -V Ti -C Surf ) (Fig. S20d), and TiO 2 with Ti-vacancies and interlayered carbon (TiO 2 -V Ti -C Inter ) (Fig. 3e). Notably, an obvious charge accumulation can be observed in the interlayered carbon layer of TiO 2 -V Ti -C Inter (Fig. S20a). Moreover, a relatively weak charge accumulation is also observed at the neighbouring oxygen atoms of both interlayered carbon and titanium vacancies, which indicates a cascade transfer path from titanium vacancies to the interlayered carbon. The charge density difference of TiO 2 -V Ti show that titanium vacancies could also affect the charge distribution of the neighbouring atoms (Fig. S20c), but the influence is relatively weaker compared with that of TiO 2 -V Ti -C Inter , which indicates that a junction of interlayered carbon and titanium vacancies is more beneficial for the charge transfer. There is no charge accumulation in the surface carbon layer in TiO 2 -V Ti -C Surf , which indicates that interlayered carbon is more efficient for charge transfer compared with surface carbon (Fig. S20e). To have a better understanding of the charge transfer path, we further investigated the charge density difference of the section model of (010) facet in TiO 2 -V Ti -C Inter . From Fig. 3f and 3g, it can be clearly observed that there is charge accumulation of the atoms around interlayered carbon and titanium vacancies. Therefore, they can act as bridge for the efficient charge transfer from TiO 2 lattice to titanium vacancies and to interlayered carbon.
The stability of TiO 2 with surface carbon and interlayered carbon are investigated by calculating the formation energy of different models. The calculation is based on the formula listed in Table S5. TiO 2 -V Ti -C Inter show a lower formation energy (-45 eV) compared with TiO 2 -V Ti -C Surf (-36.8 eV) (Table S5), which indicates that the interlayered carbon structure is relatively stable than TiO 2 -V Ti -C Surf . Besides, the formation energy of titanium vacancies are further calculated to understand the stability of titanium vacancies in different models. To calculate the formation energy of titanium vacancies, three modes without defects are firstly constructed and opitimized. The calculation details are listed in Table S6. It can be seen that the formation energy of titanium vacancies in TiO 2 -V Ti -C Inter model is the lowest among the three models (Table S6), which indicates that titanium vacancies are more easily to form and more stable in TiO 2 -V Ti -C Inter structure. 25 The low formation energy of titanium vacancies in TiO 2 -V Ti -C Inter could be attributed to the existence of interlayered carbon, which could affect the electron distribution and orbital hybridization of the neighbouring atoms. These theoritical Detailed description of the formation of interfacial defects expressed by Kröger-Vink notation.
The formation of titanium vacancy can be described as: Where represents titanium vacancy, and represents hole.
Titanium vacancy is acceptor-type defect, which means O 2near titanium vacancy will change to Oto balance the charge.
The related formation of Ocan be described as: Where represents O -.

•
The lattice charge neutrality at the interface can be described as: → ' + ℎ •