Exfoliation of layered Na-ion anode material Na2Ti3O7 for enhanced capacity and cyclability

We report the exfoliation of layered Na2Ti3O7, a promising anode material for Na-ion batteries, and restacking using HNO3 and NaOH to form H-Ti3O7 and Na(x)-Ti3O7 compositions, respectively. The materials were characterised by a range of techniques (SEM, TEM, solid-state NMR, XRD, PDF). Although the formation of aggregated nanoparticles is favoured under acidic restacking conditions, the use of basic conditions can lead to control over the adherence between the exfoliated layers. Pair distribution function (PDF) analysis confirms that the local TiO6 connectivity of the pristine material is maintained. The lowest sodium-containing Na(1)-Ti3O7 phase, which is the stable product upon Na+ leaching after consecutive washing steps, displays the best performance among the compositions studied, affording a stable reversible capacity of about 200 mAh/g for 20 cycles at a C/20 rate. Washing removes the excess of free/reactive Na+, which otherwise forms inactive Na2CO3 in the insufficiently-washed compositions.


Introduction
The discovery of atomically-thick graphene has recently aroused great interest in the properties and phenomena exhibited by two-dimensional (2D) materials, which in general can be considered as the exfoliation products of layered structures to form either single or few layers. The exfoliation of layered structures to individual or few nanosheets can be advantageous for applications requiring high surface activity, such as catalysis, electrochemistry and photoelectrochemistry. [1,2] In the extended family of layered inorganic structures, including metal oxides, metal chalcogenides (for example, reduced TiS2, MoS2 and WS2), LiCoO2 and others, [1,2] interlayer counterions are often required to preserve/maintain the electroneutrality. This is advantageous for ion-exchange properties, but makes their exfoliation to generate individual layers more challenging than for graphite [1,3,4] , because of the strong Coulombic forces that hold them together. [1] In general, Na-ion batteries are considered as a lower-cost alternative to their Li-ion counterparts, which operate in a similar manner. This is in part due to the high natural abundance of sodium, along with the option to use aluminum current collectors on the anode side, instead of the more expensive copper used for Li-ion batteries. One of the key challenges for implementation of the Naion technology is related to discovering new anode materials since graphite, the anode of choice for Li-ion batteries, does not show electrochemical activity in Na-ion batteries. [5,6] Hard (non-graphiteable) carbon can however reversibly intercalate Na + ions via a combined mechanism of Na + insertion between the nearly parallel layers and into nanopores but much of this storage takes place close to the sodium-plating voltage, raising potential safety concerns. [7,8] Other potential anode materials are also being explored, [9,10] among them, a variety of titanium-based structures, but these show low specific capacity in part due to the limited Na storage sites within the host structures. [9][10][11] Titanium-based structures are often preferred for various anode applications due to their lack of toxicity and relatively low cost compared to other transition metals, such as cobalt or manganese, and the redox activity of titanium being in the appropriate voltage window. [12] Layered Na2Ti3O7 is a well-known potential anode material for Na-ion batteries demonstrating good electrochemical properties at a low intercalation potential of around 0.3 V vs. Na + /Na. [13,14] It is built up of corrugated (Ti3O7) 2layers (formed by series of corner-sharing tri-octahedral ribbons) and Na + ions sitting in the interlayer space. The low intercalation potential of Na2Ti3O7 is advantageous when coupled with a highvoltage cathode in a full cell to achieve a higher energy density. For example, Na2Ti3O7 nanotubes have recently been tested as anode materials in full-cell batteries using the highvoltage cathode material VOPO4 (V= 3.75 V vs. Na + /Na), demonstrating promising electrochemical performance. [15] It is generally believed that reduction of Na2Ti3O7 occurs via the reversible intercalation of two additional Na + ions in the structure, forming Na4Ti3O7, [14] with 2/3 of the Ti(IV) ions being reduced to Ti(III). [13] Several studies have attempted to enhance the electrochemical capacity of this material by generating sodium vacancies within the crystal structure [16] and by fabrication of carefully controlled nanostructures. Recent advances in the field showing promising performance include bottom-up (BU) techniques for growing Na2Ti3O7 based structures, such as growth of nanotube arrays [17] , formation of a 3D spiderweb architecture assembled by nanotubes [18] , and growth on carbon-coated hollow spheres [19] . Promising results have also been reported when techniques favouring reduced particle size are used; these include crystalline rods prepared by microemulsion [20] and microspherical particles prepared by spray-drying [21] . Limited reports exist for preparing Na2Ti3O7 via top-down (TD) facile techniques. It has been recently reported that exfoliation of bulk Na2Ti3O7 can be achieved by ion exchange using alkyl ammonium ions. With some Na + ions remaining from the parent material, alongside propylamine ions added during the exfoliation process, a mixture of nanosheets and nanoplatelets was formed. This process led to an improvement in the charge storage kinetics and cyclability compared to the bulk material. [22] In this study, we sought to entirely exfoliate Na2Ti3O7 into nanosheets by complete removal of Na, along with the alkyl ammonium ions used during the process, followed by re-insertion of Na ions to restack the layers in a more disordered fashion. This was envisioned to create additional sites for Na + ion insertion, allowing for complete reduction of Ti 4+ to Ti 3+ , thus increasing the capacity. [1][2] In addition, surface effects, as a result from exfoliation to thinner nanosheets, may favour further enhancement of the electrochemical performance in terms of the rate performance. We explored the effect of the exfoliation/restacking conditions on the structural chemistry, morphology and electrochemical properties of the phases obtained.

Experimental
Synthesis: The pristine layered Na2Ti3O7 materials were made by solid-state synthesis, according to previous reports. [13] Stoichiometric amounts of Na2CO3 (Alfa Aesar, anhydrous, 99.5% purity) and TiO2 (anatase, Sigma Aldrich, 99.8% purity) were ball-milled in isopropanol using a highenergy mill, and after evaporation of the solvent the mixture was sintered at 800 o C for 20 h in air, followed by grinding and a second sintering step under the same conditions. The same synthesis protocol was followed for the Na2Ti6O13 and Na2TiO3 model compounds.
The protonated H2Ti3O7 form was made by ion-exchange of pristine Na2Ti3O7 via a solvothermal reaction in HNO3 (aq) in an autoclave at 60 ο C for 12 h. The material was isolated by filtration (Durapore PVDF membrane, pore size 0.22 μm, diam. 47 mm), washed with copious deionized (DI) water until neutral pH was achieved, and dried in an oven at 60 o C. The proton analogue H2Ti3O7, was then gradually swollen by ion exchange in two steps of increasing size alkyl ammonium ions in aqueous solutions of amines (MA: methylamine and PA: propylamine). Each reaction was performed solvothermally at 120 o C for 48 h in an autoclave, with the concentrations used as reported previously. [23] The resulting colloidal suspensions were centrifuged at 6000 rpm for 5 min and the precipitates were washed and centrifuged for a further three times, until neutral pH. The MA-Ti3O7 and PA-Ti3O7 samples were then dried in an oven at 60 o C prior to further characterisation. The final titanate product of amine swelling (PA-Ti3O7) was then dispersed in water (0.1 g in 50 ml H2O), followed by sonication in order to exfoliate to titanate layers/nanosheets. The non-exfoliated material was collected as the precipitate of centrifugation at 6000 rpm for 5 min. The supernatant suspension, containing the dispersed exfoliated nanosheets, was then restacked by mixing with HNO3 or NaOH aqueous solutions, in 1:1 ratio by volume. After being left overnight to settle, the precipitates were easily separated by centrifugation (3000 rpm, for 3 min). In the case of restacking by NaOH, the washing procedure of the precipitate was carefully controlled, resulting in different amounts of inserted Na in the exfoliated/restacked samples. All the samples were dried, initially in air at 60 o C and finally at 100 o C in a vacuum oven.
Transmission electron microscopy (TEM) images were recorded at magnification between 40,000X and 800,000X in a JEOL JEM-3011 electron microscope operated at 300 kV, with objective lens characteristics Cs = 0.6 mm and Cc = 1.2 mm. With a LaB6 emitter these produced an interpretable resolution limit of 0.17 nm and an absolute information limit of 0.14 nm. Scanning electron microscopic (SEM) images were recorded with a Hitachi S-5500 in lens field emission electron microscope.
Pair Distribution Function (PDF) analysis: Data of the samples, packed into kapton capillaries, were collected at the I15 beamline at Diamond Light Source, Didcot, UK. An X-ray beam of energy of 76 keV (λ = 0.1631 Å) was used in conjunction with an amorphous silicon area detector (Perkin-Elmer).
The sample geometry and the sample-to-detector distance were determined using a CeO2 standard. The data were converted to intensity vs Q using the Data Analysis WorkbeNch (DAWN). [24] Standard corrections (background subtraction, Compton scattering, detector effects) were applied, and the data were Fourier transformed to obtain G(r) using the software PDFGetX2 using a Qmax of 24 Å −1 . [25] Refinements against known TiO2 phases were performed in PDFGui. [26] Refinements against single-layer models were performed in the Diffpy-CMI complex modeling framework. [27] The starting model was simulated from supercells of the Na2Ti3O7 structure, where all atoms except for a single-layer in the middle of the unit cell were removed. The structure function was simulated from the Debye scattering equation [28] which was then Fourier transformed over a range of 1−24 Å −1 . The model was refined using a least-squares approach; unit cell parameters, a, b, c and β, an isotropic thermal parameter, Uiso, for each atomic species and a scale factor were allowed to refine. Solid-state NMR: All solid-state 1 H and 23 Na NMR spectra were acquired on a 16.4 T Bruker Avance III spectrometer using a 1.3 mm HX probe head. A rotor-synchronized Hahn-echo (for 1 H) and a single-pulse sequence (for 23 Na) were used to acquire magic-angle spinning (MAS) spectra with spinning frequencies of 55-60 kHz, recycle delays of 5 and 5-40 s (for 1 H and 23 Na, respectively), and radiofrequency (rf) field strengths of 125 and 140 kHz, respectively. 1 H and 23 Na shifts were externally referenced to solid adamantane at 1.87 ppm and solid NaCl at 7.21 ppm, respectively. Simulations of 23 Na MAS powder spectra were performed with SIMPSON. [29] First-principles calculations: DFT computations were performed using CASTEP with on-the-fly generated pseudopotentials. [30][31][32] For the electron-electron exchange and correlation interactions, the functional of Perdew, Burke and Ernzerhof (PBE) [33][34][35][36] was employed. Non-spin-polarized calculations were performed for the geometry optimization of the Na2Ti3O7 system. The kpoints mesh used was 3x3x3 with cutoff energy of 700 eV.
Compositional analysis: For C/H/N analysis, an Exeter analytical CE440 analyser was used. Typically, 1-2 mgs of sample were combusted at 950 o C in oxygen. For the ICP analysis, a Thermo scientific iCAP 7400 OES instrument was used. Samples were digested at 80 o C for four hours in 2 ml aqua regia. They were then made up to 50 ml using Millipore 18 M water. The ICP was calibrated using 10 ppm and 1 ppm standard samples.
Electrochemical testing was carried out in CR2032 coin cells vs. sodium metal, in a galvanostatic mode. The electrolyte used 1M NaPF6 in propylene carbonate (PC, >99% Aldrich) and glass fibre (Whatman GF B 55) was used as a separator. The working electrode was prepared by mixing 70% active materials, with 30% carbon Super C-65 (Timcal) and 10% binder (PVdF-HPF copolymer) in NMP in a mortar and pestle. The mixed slurries were casted on copper foil using the doctor blade technique. A cell containing only carbon was also prepared for comparison reasons in a similar way, but the electrode slurry consisted of 70% carbon Super C-65 (Timcal) and 30% binder to ensure adequate adhesion to the copper foil and between particles. The laminates were vacuum dried at 100 o C for 12 h prior to punching and pressing the electrodes, followed by further drying at 100 o C under vacuum for 12 h. The cells were assembled in a glovebox under argon atmosphere (O2 < 0.1 ppm and H2O < 0.1 ppm). The typical electrode loading was 20-25 mg.

Results and Discussion
Pristine Na2Ti3O7 was made by solidstate synthesis, as reported previously [13] , and was characterized by PXRD (SI, Figure S1 and Table S1, also included in Figure 1B in red) and 23 Na NMR (SI, Figure S2 and Table S2, spectrum also shown in Figure 3C). SEM shows that the pristine material comprises well-shaped nanorods of approximately 2.5 μm length and 0.1 μm thickness ( Figure 2A).
The Na2Ti3O7 exfoliation protocol used in this study is a modified version of previous reports for liquid exfoliation of titanates, niobates and titanoniobate nanosheets [23] and is illustrated in Figure 1A. It consists of the three successive processes of swelling, exfoliation and restacking. Na2Ti3O7 swelling was accomplished via ion-exchange steps and the effect on the interlayer spacing (d) was monitored by PXRD ( Figure 1B), based on the position of the 001 reflection. Na2Ti3O7 was initially ion-exchanged to its protonated H2Ti3O7 form. Complete ion exchange was achieved, in agreement with the literature [37] , as confirmed by 23 Na NMR (SI, Figure S2) and 1 H NMR (SI, Figure S3).
Although the interlayer distance (d) in the proton analogue H2Ti3O7 (d =7.87 Å) is smaller than in pristine Na2Ti3O7 (d = 8.46 Å), the former is more reactive towards acid-base reactions and the layers may consequently be swollen by incorporation of protonated organic bases. This was done by ion exchange in two steps involving aqueous solutions of amines of increasing size (MA: methylamine, PA: propylamine) forming first MA-Ti3O7 and then PA-Ti3O7. Chemical analysis (SI, Table  S3, C:N ratio) confirmed that the alkyl ammonium ions were intercalated as whole ions and did not decompose under the reaction conditions. The ion exchange was complete for the first amine exchange step, while the final product after intercalation of PA (PA 1.7±0.2 )Ti3O7 was slightly amine deficient. 1 H NMR of these materials (SI, Figure S3) confirm the presence and the stability of the alkyl ammonium ions; in the case of the PA-Ti3O7, a residual amount of protons remain in the structure bound to the Ti3O7 host. The yield of the exfoliation protocol strongly depends on the amount of sufficiently swollen titanate; the nonexfoliated content is removed at a later stage. The amine-driven swelling of the titanate framework results in general broadening of the reflections in the XRD patterns. The progressive shift of the 001 reflection position to lower angle indicates the increase of the interlayer spacing (d) upon intercalation of the alkyl ammonium ions (d= 10.13 Å and 13.55 Å for H2Ti3O7-MA and H2Ti3O7-PA, respectively). Upon enlargement of the interlayer distance along the a-axis, all the (hk0) reflections of Na2Ti3O7 are expected to remain intact, with the 020 reflection at approximately 2θ (Cu Kα) = 48 o being the most intense. The (001) and (020) planes of pristine Na2Ti3O7 are displayed in Figure 1F.
In order to exfoliate the titanate layers/nanosheets, the amine-swollen titanate product (PA-Ti3O7) was dispersed in water and then sonicated. After centrifugation to remove the precipitate containing nonexfoliated material, the supernatant containing the dispersed nanosheets was collected. The difference between the TEM of the exfoliated and the pristine material is striking. While the latter shows clearlydefined flakes and particles (SI, Figure S4), typical TEM images of the exfoliated (and dried) material ( Figure 1C) are indicative of individual and multiple layers which have coalesced and collapsed as the solvent is removed, coming together in an extremely disordered arrangement with greatly reduced flake thickness. Arrays of layers can be seen in the high-contrast regions at the edges of the specimen ( Figure 1D), but their arrangement is mostly irregular. In the regions where they form some sort of ordering, as for example at the very bottom of Figure 1D, no more than six layers with regular spacing are found. In these areas, the spacing between layers is in the order of 8 -9 Å, similar to the regular layer spacing observed for the pristine material, indicating the structural similarity upon removal of the solvent. The exfoliated suspension was then restacked by NaOH; a representative SEM picture is displayed in Figure 1E showing layers stacked in a rather disordered fashion. swelling of pristine layered Na2Ti3O7 by alkyl ammonium ions, by using aqueous solutions of amines of increasing size (MA: methylamine, PA: propylamine), 2. exfoliation by agitation and 3. restacking by NaOH; (B) Powder X-ray diffraction (PXRD) data monitoring the swelling, the dashed box highlighting the interlayer spacing (d), as derived from the 001 reflection. The pristine Na2Ti3O7 was initially ionexchanged to form the protonated H2Ti3O7, which was then gradually swollen by ion exchange of the increasing size alkyl ammonium ions (MA, PA). The upturned triangle denotes the 020 reflection, which is retained upon swelling of the structure in the a-direction. (C, D) TEM images of exfoliated titanate nanosheet suspension, (E) representative SEM image of an exfoliated/ restacked specimen, (F) Crystal structure of pristine Na2Ti3O7, highlighting the (001) and the (020) planes, the unit cell and the interlayer distance (d). Red spheres represent Na atoms and green TiO6 octahedra form the layered framework.
In order to control and understand the restacking process, a careful investigation of the effect of different restacking conditions was made, with two series of experiments being performed. In the first method, HNO3 (either 1 M or 2 M) was added to the nanosheet suspension, with the obtained white precipitate separated by centrifugation. For the second method, a large excess of NaOH (aq) was added to the nanosheet solution, followed by washing under different conditions.
The morphology of the products was determined by SEM ( Figure 2). The nanorods observed for pristine (Na2Ti3O7, Figure 2A) are still observed, but their shape is mostly irregular once the structure is swollen by the incorporation of alkyl ammonium ions (PA-Ti3O7, Figure 2B), which is the last step to exfoliation. Subsequent exfoliation and restacking changes drastically the morphology of the products, which varies according to the restacking conditions. Restacking by HNO3 (H-[Ti3O7], Figure 2C) favours the formation of aggregated nanoparticles as also evidenced by the broad PXRD patterns, with the patterns fitting quite well with those for mainly TiO2 anatase with some small amount of brookite (H(a)-[Ti3O7]) and rutile (H(r)-[Ti3O7]) polymorphs, for restacking by 1 M and 2 M HNO3 respectively (SI, Figure S5). This is consistent with literature observations that different TiO2 polymorphs can be formed hydrothermally from amorphous titania by varying the acidic conditions. [38] The fact that TiO2 nanoparticles are the products of the exfoliation/(nominal) restacking process by HNO3 suggests that the drying process used here results in structural transformation likely upon removal of structural water; this is reported to happen at temperatures above 80 °C . [39] However, restacking by NaOH (aq) results in the formation of stacked nanosheets. The stacking order seems to be strongly dependent on the washing procedure, with reduced order observed as the samples are further washed ( Figure 2D, E and F). The composition of the nanosheets restacked by NaOH was first determined by ICP/OES ( Table 1). The composition was also determined indirectly by converting the poorly crystalline Na(x)-[Ti3O7] phases at high temperatures into more well-defined crystalline phases; the Na:Ti ratio of the resulting phases as determined by PXRD (SI, Figures S6-S8) and confirmed by solid-state NMR (SI, Figure S10) provides a second estimate of Na content (assuming all the titanate material has been converted to crystalline material).
The resulting compositions were expressed via the simplified formula Na(x)-[Ti3O7], so as to focus only on the Na(x) content (   Table 1). 8 The Na(x) content in the Na(x)-[Ti3O7] exfoliated/ restacked specimens was found to be approximately Na(6), Na(2) and Na(1) based on the PXRD analysis. Slightly lower Na contents were systematically determined by ICP/OES, which may be due to the techniques reported low sensitivity for Na, due to weak emission of alkali metal ions in general and interference issues for Na. [40] However, it may also reflect the presence of (amorphous) Na-deficient phase not seen by PXRD. The information obtained regarding the Na(x) content of the Na(x)-[Ti3O7] compositions demonstrate that washing induces leaching of Na + accommodated in the titanate exfoliated layers. Hence, control over washing can determine both the composition and the stacking order of the Na containing nanosheets. For easy reference, all of the exfoliated/restacked samples, and samples prepared with subsequent heat treatments and washings are listed in Table 2, along with the synthesized model compounds. The PXRD patterns of all exfoliated/ restacked Na(x)-[Ti3O7] compositions are plotted together in Figure 3(A) and compared with those of crystalline NaOH.H2O and Na2CO3 references, to exclude the presence of excess NaOH, as well as H2O and CO2 adsorption from the atmosphere. All the Na(x)-[Ti3O7] samples display very broad reflections, demonstrating their inherent disordered nature and absence of the 001 reflection at low angles, indicating that there is no significant ordered stacking of the layers. The PXRD pattern of the low-sodium phase Na(1)-[Ti3O7] only displays the 020 reflection at about 48 o 2θ, which appears to be indicative of the structural coherence of the TiO6 octahedral layered framework upon swelling ( Figure 1B). This characteristic reflection is also observed in the patterns of the higher sodium containing phases Na(2)-[Ti3O7] and Na(6)-[Ti3O7], along with increasing amount of crystalline Na2CO3. PDF analysis In order to probe the local connectivity of the exfoliated materials, pair distribution functions (PDF) were extracted from total scattering data for Na(1)-[Ti3O7], Na(2)-[Ti3O7] and the pristine Na2Ti3O7. These are shown in Figure 3B. Peaks are observed in the PDF beyond 50 Å (SI, Figure  S11), implying that some long-range order exists and the material is not amorphous. Peak intensity dampens more quickly with increasing distance, r, in the exfoliated material compared to the pristine material; we assign this principally to the presence of disordered interlayer correlations (i.e. between Ti3O7 layers) resulting in a zero contribution to the total G(r). At longer interatomic distances, as the proportion of interlayer vs intralayer distances increases and, therefore, the total intensity of G(r) will decrease. In addition to this, the finite size/limited coherence of the nanosheets will also contribute to the drop of intensity with increasing distance. Below 5 Å, peaks in the experimental PDF for Na(1)-[Ti3O7] appear at very similar distances to the pristine Na2Ti3O7 material (as shown by the dashed lines in Figure 3B), indicating that the immediate connectivity of the TiO6 framework remains the same as the parent material.
Furthermore, the peak positions in the experimental data for Na(1)-[Ti3O7] are a poor match to all TiO2 polymorphs (SI, Figure S12), and the residual factors obtained from leastsquares refinements of TiO2 polymorph structures against the experimental data for Na(1)-[Ti3O7] are very high (SI , Table S4). This confirms that the basic exfoliation/restacking conditions have not converted the material into other TiO2 polymorphs, as was observed in acid conditions.
To further probe the extent to which the [Ti3O7] layers remain intact in the exfoliated material, a model of a single [Ti3O7] layer, approximately 50 x 50 Å in size was constructed (SI, Figure S13(a)). Only the contributions from Ti and O are considered in the model; no Na atoms were placed in the model because the 23 Na NMR data indicate that a range of sodium environments exist (see below) and so are unlikely to contribute well-defined peaks to the PDF. Peak positions in the one-layer model show a good match to the experimental data, including the intense peak at 9.8 Å, which results from Ti-Ti interactions within the titanate layer. When this model was refined against experimental data for Na(1),a reasonable fit was obtained (SI, Figure S13 (a), Rw = 0.39,), indicating that the structure of the exfoliated/restacked material is similar to that of a single layer of the Na2Ti3O7 parent phase.
The fit remains imperfect; peaks in the residual of the refinement (G(r)model -G(r)experiment , grey line in SI, Figure S13 (a)) remain, indicating that some aspects of the structure are not captured by the current model and, therefore, the exfoliated/restacked materials structure shows some differences to Na2Ti3O7-like Ti3O7 layers. There are several possible sources for these differences including: (a) additional broad contributions from the disordered sodium which are not accounted for in this model; (b) the presence of some inter-layer correlations, which although likely to be disordered, may lead to some changes in intensity; (c) additional structural complexity induced by defects in the exfoliated material, and; (d) a possible range of sheet sizes and connectivities. The fit to experimental data can be slightly improved by using a fragment with smaller dimensions, where some connectivity between the corner-sharing octahedra has been broken. Of the models tried (see SI, Section S4), a fragment with extended connectivity along the b-axis, but only a single set of corner sharing octahedra shows the best fit to the data (SI, Figure  S13(b), Rw= 0.35). This implies that some breakdown/modification of the layers may have taken place during the exfoliation/restacking, either from sheet termination, or from defective areas within sheets. However, the calculated PDF for a single unit of six edge-sharing TiO6 octahedra, the basic building block of the Ti3O7 layers shows no peaks beyond approximately 10 Å (SI, Figure S13 (d)). As interatomic correlations are observed well beyond this distance in the experimental PDF, this confirms that the sheets have not been broken down into very small units of the starting material. More detailed structural characterization will be the subject of another paper.
The principal difference between the two PDFs of the two restacked compositions is the intensity of the first peak, which is likely related to the presence of a low scattering component Na2CO3 in Na(2)-[Ti3O7] (as evidenced from XRD and NMR measurements) and/or difference in the amount of oxygen vacancies present.

NMR Analysis
The 23 Na NMR spectra of the three exfoliated/restacked (Na(x)-[Ti3O7]) compositions are shown in Figure 3C and compared with pristine Na2Ti3O7 and NaOH and Na2CO3 references. The 23 Na NMR spectrum of Na2Ti3O7 consists of two signals in agreement with previously reported data [41] and the Density Functional Theory (DFT) calculations performed in this work (SI, Figure S2). These are assigned to the two different Na coordination environments in the Na2Ti3O7 layered structure, [42][43][44] the Na1 site at lower chemical shift (at around -10 ppm, nine-fold coordinated, coordination number (CN) = 9) with a significant second order quadrupolar broadening effect and the Na2 site (at approximately +3.2 ppm, sevenfold coordinated, CN=7). While the spectrum of the high sodium containing Na(6)-[Ti3O7] phase is a good match with that of the reference Na2CO3 spectrum, in agreement with PXRD for high carbonate content, the low sodiated Na(1)-[Ti3O7] phase only shows a single resonance with a shift at about -10 ppm.
Although not displaying the characteristic second order quadropolar broadening, this resonance was labelled Na1' to reflect the similarity in shift position to that of the Na1 site (CN=9) in the pristine material. We do not necessarily assign this resonance to the same crystallographic site, but merely suggest that it has a similar CN. It is anticipated that there is some variation in the Na-O bond lengths in the disordered titanate network resulting in a distribution of slightly different chemical shifts and broader 23 Na NMR resonances compared to the pristine material. The intermediate sodium containing Na(2)-[Ti3O7] phase has a spectrum that appears to correspond to a mixture of Na2CO3 and Na1', displaying the most intense shift for Na2CO3 at +5.5ppm and an asymmetric resonance at lower frequency (around -9 ppm), due to the presence of overlapping carbonate and Na1' signals.
All exfoliated/restacked compositions, display one 1 H NMR resonance with a shift at around +6 ppm (SI, Figure S14). This resonance could not be assigned to NaOH, and this signal is assigned to protons incorporated into the titanate network. H2Ti3O7 gives rise to 1 H NMR shifts above +10 ppm (SI, Figure S3) and thus the proton signal is likely due to H2O/H3O + molecules/ions that are incorporated into the structure [45] (along with residual amine groups); the slightly displaced shift of +4.8 ppm is assigned to free water molecules. Spatial constraints associated with the order of nanosheet stacking ( Figure 2D-F), which is enhanced with increasing the Na(x) content, could dictate the amount of water intercalated into the titanate network.
The absence of excess NaOH in the Na(6)-[Ti3O7] and Na(2)-[Ti3O7] phases is explained by the observation of Na2CO3, formed by reacting with H2O and CO2 from the atmosphere; with Na2CO3 presumably crystallizing on the surface upon drying. A proposed mechanism is demonstrated in SI ( Figure S15), which involves the formation of a Na2[Ti3O7]* metastable phase (for x≥2), which transforms to the more stable Na(1)-[Ti3O7] phase and liberates the excess Na + . The excess Na2CO3 can cleanly be removed on washing, leaving Na(1)-[Ti3O7] as the final stable phase. The Na atoms in Na (1) Figure S16). The titanate framework in the asmade Na(1)-[Ti3O7] composition is preserved as shown from the PDF analysis. In order to maintain charge neutrality in this phase, oxygen vacancies may be present or more likely, the Na ions are coordinated by both water and OH3 + ions, the charge compensating protons being lost as water on heating. A transition to crystalline Na2Ti6O13 (Na1Ti3O6.5) is expected to occur once sintered at temperatures above 600 o C [39] and is observed in this study as well when heated at 800 o C (SI, Figure S8 and Figure S10 for Na(1)-[Ti3O7]) consistent to the cation ratio present in the exfoliated phase.
Electrochemistry: The exfoliated/restacked H(x)-[Ti3O7] and Na(x)-[Ti3O7] compositions were evaluated as anode materials for Na-ion batteries in the 0.005 -2.5 V range, at a C/20 rate (corresponding to the addition of 2 Na + in 20 hours). Preliminary data were also collected at C/10 and 1C for some of the compositions. The protocol initially adopted for pristine Na2Ti3O7 with 30% carbon as a conductive additive was used for all samples to ensure consistency with the literature, and hand-grinding as opposed to mechanical milling was using to mix the reagents was used to avoid any structural rearrangement within the electrode materials. [13] Thus, the cycling behaviour of the cell containing only carbon was also investigated for comparison. The cycling data over 20 cycles of both H(a) and H(r)-[Ti3O7] compositions are shown in Figure 4A, where closed and open symbols correspond to discharge and charge steps respectively. The first discharge capacity is notably high for both materials (≥1000 mAh.g -1 ), indicating that a large amount of Na + atoms are consumed irreversibly by forming the solid electrolyte interphase (SEI) layer.
Although crystallising as different TiO2 polymorphs, both specimens demonstrate similar electrochemical performance after the initial 10 cycles, both reaching about 150 mAh.g -1 after 20 cycles, at C/20 rate. During the initial 10 cycles, the capacity values diverge with slightly higher values for H(r)-[Ti3O7] than H(a)-[Ti3O7] during discharge, and converge during charge steps. The capacity values for H(r)-[Ti3O7], with particle size distribution between 3-10 nm ( Figure 2C and SI, Figure S5), are significantly improved when compared to commercial rutile TiO2 (Sigma Aldrich #224227, particle size< 5 μm) measured at the same conditions for this study ( Figure 4B). This demonstrates that nano-structuring TiO2 has a significant effect on the electrochemical properties and it is the first report of nano-rutile being tested as a material for a Na-ion anode to the best of the authors' knowledge. [9,10] Among the several TiO2 polymorphs, the bronze-type TiO2(B) has the most open crystal structure, followed by anatase, rutile and brookite in decreasing order, and is able to accommodate 1 Li+ per Ti giving a capacity of 335 mAh.g -1 for Li ion batteries in both bulk and nanostructured forms [46] ; much lower capacity values are observed for sodium ion batteries due to the larger size of the Na ions. [47] Nanosized TiO2 typically shows poor cycling performance in Na-ion batteries; this is attributed to the formation of unstable SEI and side-reactions while cycling. [48][49][50]

13
The cycling data over 20 cycles of Na(x)-[Ti3O7] compositions are shown in Figure 4C. The capacity increases with reduced Na(x) content, with Na(1)-[Ti3O7] displaying the best performance and attaining the highest stable capacity of about 200 mAh.g -1 over 20 cycles. Despite the high first discharge irreversible capacity, similar to that obtained by other nanostructuring methods, [17][18][19][20][21] all the exfoliated/restacked Na(x)-[Ti3O7] compositions demonstrate improved cycling performance compared to pristine Na2Ti3O7, which was measured under the same conditions and suffers from poor capacity retention [51] ; this is a common problem for many potential materials used as anodes in Na-ion batteries. [10,52] We note however that we have not attempted to optimize the electrode formulation. Further studies would be required to understand the effect that the first cycle losses have on long-term cyclability and in full cells.
The reduced capacity values observed for the Na(2)-[Ti3O7] and Na(6)-[Ti3O7] compositions compared to Na(1)-[Ti3O7] are ascribed to the increasing Na2CO3 content. However, the presence of Na2CO3 in these phases is not detrimental to the properties when compared to pristine and/or the model crystalline compounds, with the same Na:Ti ratio ( Figure 4D for Na(1) and SI, Figure  S17(A) and S17(B) for Na (6) and Na(2) respectively). This suggests that Na2CO3 is inactive and the improved capacity is related to the available space for Na intercalation and the amount of the active Na(1)-[Ti3O7] component.
Reduction of all the Ti(IV) content would be expected to occur via the intercalation of three sodium atoms and formation of Na5Ti3O7 (Ctheor= 267 mAh.g -1 ) during cycling. In bulk Na2Ti3O7, two sodium atoms are reversibly intercalated in the structure with concomitant reduction of 2/3 of the Ti(IV) to Ti(III) in Na4Ti3O7 (Ctheor= 177 mAh.g -1 ). [13] The diverse values in the literature for pristine Na2Ti3O7 depend largely on the formulation of the electrode, the additives and the choice of electrolyte, which has not as yet been standardized. [ and Na(1)-[Ti3O7] end members, such as Na(ca.1.7), (SI, Figure S9 and Figure S10 for Na(ca.1.7)-[Ti3O7]) display higher capacities for initial cycles (e.g. about 240 mAh.g -1 after 10 cycles) but these values are not stable and decrease to about 200 mAh.g -1 after 20 cycles (SI, Figure S17(C)).
The galvanostatic curves of all exfoliated/ restacked Na(x)-[Ti3O7] compositions during the first cycle are shown in Figure 5A and compared with those of parent Na2Ti3O7 and carbon cells. All the cells exhibit irreversible plateaus at about 0.6 -1.0 V vs. Na + /Na and at lower voltages (0.1-0.2V) during the first discharge. These are not observed during the first charge or in subsequent cycles, demonstrated here for the second cycle ( Figure 5B) and the twentieth cycle ( Figure 5C). The differential dQ/dV plots are shown in SI, Figure S18. These irreversible plateaus are believed to be due to reaction of Na + with the carbon additive and to the SEI formation from electrolyte decomposition. [13,22,51] It should be noted that the existence of Na2CO3 in the Na(2)-[Ti3O7] and Na(6)-[Ti3O7] compositions may have an additional effect on the nature of the SEI forming during operation, due to its solubility in the electrolytes commonly used for sodium-ion batteries. [51] Moreover, the water molecules, whose existence was evidenced by 1 H NMR (SI, Figure S14), likely participate to the processes occurring at the first discharge step. These intercalated water molecules were only removed upon further drying/treatment at 400 °C (SI, Figure S16), which is likely to have an effect to the nanosheet stacking. The capacity values of Na(x)-[Ti3O7]-400 compositions were reduced by about 100 mAh.g -1 during the first discharge step compared to as-made samples, while there was no significant difference for the subsequent cycles (SI, Figure S19). Although the incorporation of water molecules would be expected to influence the electrochemical performance while cycling by continuously reacting with the electrolyte, this was not observed for these samples under the conditions tested. It is however anticipated that the existence of intercalated water molecules might affect further high rate capability studies. After the formation of SEI during the first discharge step, the electrochemical processes for the pristine Na2Ti3O7 occur at distinct active sites in the bulk favoring a two-phase reaction, accompanied by flat voltage plateaus at around 0.2 and 0.4 V vs. Na + /Na during discharge (sodiation) and charge (de-sodiation) steps, respectively [13] ( Figure 5B and Figure 5C for the 2 nd and 20 th cycles, respectively, dQ/dV plots in SI, Figure  S18). The additional small plateau at about 0.1 V vs. Na + /Na, observed for pristine and all exfoliated/restacked compositions, is believed to be related with the carbon additive (SI, Figure S18(D)). On the contrary, all the cells containing the exfoliated/restacked Na(x)-[Ti3O7] compositions display sloping discharge/ charge potential profiles (shown separately for Na(1) in Figure 5D) compared to the pristine material, with a very broad plateau at average voltage about 0.6 V vs. Na + /Na, most intense for Na(1)-[Ti3O7] composition (also observed at dQ/dV plots, SI, Figure S18). This plateau is likely to be related to the existence of the Na intercalation sites (as evidenced by 23 Na NMR, Figure 3C) and is not observed for the H-[Ti3O7] compositions (SI, Figure S20).
In general, sloping potential profiles are indicative of single-phase behaviour, where the intercalation/deintercalation processes occur at non-equivalent sites with different energies, in part due to the disorder of these systems and the large exposed surfaces of reduced particle-size materials. [53,54] The overall surface area of the exfoliated/restacked materials in this study, is expected to be higher than for the pristine crystalline Na2Ti3O7 (BET = 1.3 m 2 .g -1 ); reliable BET measurements would require synthesis on a larger scale. In the general case of nanosized materials, the intercalation/ deintercalation processes are accompanied by shortened diffusion/ transport distances, which is often advantageous for the overall specific capacity. [54] For the restacked Na(x)-[Ti3O7] nanosheets, the existence of Na intercalation sites is likely related to the observed improved capacity retention. Although higher rate data were not collected for Na(1)-[Ti3O7], preliminary data for Na(2)-[Ti3O7] indicate that the capacity of about 120 mAh.g -1 remains stable when cycled at C/20 and 1C for 40 cycles (SI, Figure  S20(F)). Clearly, there is further scope for optimization and high rate studies.

CONCLUSIONS
In summary, we report the exfoliation and subsequent restacking of Na2Ti3O7 using HNO3 and NaOH to form H-[Ti3O7] and Na(x)-[Ti3O7] compositions, respectively; these were tested as potential Na-ion anode materials. The formation of aggregated TiO2 (rutile and anatase) nanoparticles is favoured upon drying of the H-[Ti3O7] compositions, resulting in high capacity materials, but which suffer from poor capacity retention. In the case of the Na(x)-[Ti3O7] compositions, the local connectivity of the titanate framework was retained. Control over the composition can be achieved by washing, which induces gradual Na leaching from the titanate network resulting in reduced degrees of adherence between the exfoliated layers. The final composition is Na(1)-[Ti3O7], washing removing the excess of "free/reactive" Na + , which otherwise forms inactive Na2CO3 in the insufficiently washed compositions. All the exfoliated/restacked Na(x)-[Ti3O7] compositions show significantly improved capacity retention compared to the pristine Na2Ti3O7 and/or the crystalline compounds with the same Na:Ti ratio. This is likely related to enhanced kinetics due to nanosize effects and the formation of a more open titanate framework. The optimal electrochemical performance among the series of exfoliated/restacked Na(x)-[Ti3O7] compositions studied is demonstrated for the Na(1)-[Ti3O7] phase, where Na atoms likely occupy a range of slightly different Na intercalation sites, Na(1)-[Ti3O7] displaying a stable capacity of about 200 mAh.g -1 after 20 cycles at C/20 rate. In-situ and/or postcycling studies would be required to conclude whether the intercalation of additional sodium atoms compared to pristine Na2Ti3O7 is dominating over surface factors.

SUPPORTING INFORMATION
Further details about the characterization of materials (pristine, intermediates and products) by chemical and NMR measurements, PDF, XRD and TGA analysis, DFT calculations and TEM images, as well as supplementary electrochemical data and analysis, including Tables S1-S4 and Figures S1-S20.

NOTES
Additional data related to this publication are available at the Cambridge data repository: https://doi.org/10.17863/CAM.18615