Combined Structural, Chemometric, and Electrochemical Investigation of Vertically Aligned TiO2 Nanotubes for Na-ion Batteries.

In the challenging scenario of anode materials for sodium-ion batteries, TiO2 nanotubes could represent a winning choice in terms of cost, scalability of the preparation procedure, and long-term stability upon reversible operation in electrochemical cells. In this work, a detailed physicochemical, computational, and electrochemical characterization is carried out on TiO2 nanotubes synthesized by varying growth time and heat treatment, viz. the two most significant experimental parameters during preparation. A chemometric approach is proposed to obtain a concrete and solid multivariate analysis of sodium battery electrode materials. Such a statistical approach, combined with prolonged galvanostatic cycling and density functional theory analysis, allows identifying anatase at high growth time as the TiO2 polymorph of choice as an anode material, thus creating a benchmark for sodium-ion batteries, which currently took the center stage of the research in the field of energy storage systems from renewables.

Introduction

Current tremendously growing energy demand is pushing forward the pursuit of high-performing, cost-effective, safe and environmentally friendly energy conversion and storage systems. Indeed, electricity generated from renewable sources represents an oasis in the future to effectively meet the demand for energy supply systems characterized by as low as possible carbon footprint.[1] However, renewable sources, such as wind, solar, tidal, biomass, and geothermal, are all inherently intermittent and, often, widely scattered into isolated large-scale facilities around the globe.[2] The best way to exploit these energy resources for practical human needs is to set up smart and efficient systems to store the energy they produce.[3−7] To this purpose, secondary batteries represent a viable solution for the integration of renewable plants into the grid and will play a fundamental role to guarantee a brighter and cleaner environment for future generations.[8−12]

Whereas Li-ion batteries (LIBs) offer the highest energy density among present battery technologies,[13−17] still an amount of open challenges remains to be faced, particularly the reduced availability of global lithium resources, which are also mainly concentrated in remote and/or politically sensitive areas,[18−21] and its increasing cost due to the rising demand for smart high energy/power density storage devices. Indeed, people are now starting to consider lithium as “the new gold”,[22] as its price recently soared 300%.[23] In this respect, sodium is rapidly emerging as an alternative light metal for batteries: it is cheap and very abundant and has a uniform geographical distribution.[24−26] Its redox potential is −2.71 V versus standard hydrogen electrode (vs −3.04 V of lithium); moreover, Na+ is heavier (23 vs 6.9 g mol–1) and larger (97 vs 68 pm) than Li+. This means that—when sodium is considered—a small penalty has to be paid in terms of overall cell operating potential and gravimetric/volumetric energy densities, but it is anyway much more appealing than lithium when widespread, low-cost, and large-scale energy storage systems (ESSs) have to be implemented.[27,28] For all of these reasons, the investigation of materials for sodium-ion batteries (NIBs), along with the correct understanding of their electrochemical characteristics, has recently become hot topics within the scientific community.[29−33]

One of the main issues of NIB technology concerns the selection of suitable anode materials.[34−36] Graphite—the commercial choice anode for LIBs—cannot be used in NIBs because of its extremely low performance. Indeed, while Li+ ions are readily inserted into graphite with a final stoichiometry of LiC6 (accounting for a theoretical specific capacity of 372 mAh g–1), only a very little amount of Na+ ions can be intercalated into graphite.[37,38] Such a limited capacity can be explained from a thermodynamic viewpoint, being related to Na plating on the carbon surface before forming the graphite intercalation compounds.[39]

The lack of low-voltage metal oxide anodes assuring reversible storage of sodium ions at room temperature and for a sufficient amount of cycles[40,41] can be justified by the large ionic radius of Na+, the insertion of which in nanostructured electrodes requires substantial distortion of the metal oxide lattice.[42] To this purpose, titanium dioxide (TiO2) could represent a viable solution, being a stable, safe, inexpensive, nontoxic, and abundant semiconductor, able to intercalate alkali ions at moderate potential values with specific capacities comparable to graphite anodes in LIBs. Given these features, TiO2 would clearly represent an interesting material to be investigated as the anode for NIBs,[43−45] as first reported by Xu et al.[46] and Usui et al.[47] Unfortunately, it shows intrinsic low electronic conductivity, which accounts for relatively poor rate capability. As a viable solution, the use of one-dimensional TiO2 nanostructures (i.e., nanowires, nanorods, and nanotubes) provides shorter electron diffusion paths and improved conductivity values.[48,49] Among the number of approaches proposed by the scientific community for the preparation of ordered TiO2 nanostructures,[50] anodic oxidation stands out as a well-established technique that allows large area samples, along with the obtainment of uniform nanotubular arrays (namely, TiO2 NTs) characterized by interesting characteristics for various energy-related applications and relatively high specific surface.[51−53] Other two advantages of TiO2 NTs are relevant in the battery field: (i) regularly aligned inner nanopores may provide preferential pathways for the fast diffusion of the electrolyte, which can also thoroughly wet the active material surface; (ii) the growth process can be performed onto conducting flexible substrates (e.g., Ti foil), thus avoiding the use of binders and electronic conductivity enhancers, which clearly influence the overall cell energy density.[54]

Despite some research groups have recently proposed TiO2 NTs as the anode for NIBs, the scientific community does not agree on some fundamental aspects as to which is the best polymorph (e.g., amorphous or crystalline anatase/rutile) in terms of overall capacity output and/or long-term performance and which kind of modifications occur to the nanostructure during cell operation.[55,56]

Very recently, we proposed a possible explanation for the different electrochemical behavior of the amorphous and anatase phases of TiO2 nanotubes,[57] demonstrating the superior behavior of the latter upon long-term reversible cycling in lab-scale sodium cells. Here, we thoroughly investigate how the different experimental parameters, related to the growth time of the nanostructures by anodic oxidation and to different structural characteristics obtained upon annealing at different temperatures, influence the overall electrochemical response of the material, thus allowing to define the best performing polymorph. In addition, most of the research works published in the NIBs field consist in monovariate analysis; however, such a procedure often leads to error when interactions between the variables occur. As a result, we propose here an experimental design that simultaneously studies different variables to obtain not only an empirical mathematical equation for the considered factors but also a response map useful to consider the influence of all the parameters. As a result, a systematic approach to identify suitable active materials and properly optimize them to develop highly efficient sodium-based ESSs is presented.

In this work, we aim at identifying the best TiO2 polymorph for NIBs, by means of a solid and combined experimental, computational, and statistical approaches.

Results and Discussion

Morphological and Structural Characterization

X-ray diffraction (XRD) and field emission scanning electron microscopy (FESEM) analyses were performed on the different fresh samples as well as at the end of the galvanostatic cycling test. XRD profiles of the different anodized samples, that is, pristine amorphous (nonthermally treated, namely TiO2-am) and upon crystallization in air at different temperatures of 300 (TiO2-300), 450 (TiO2-450), and 600 °C (TiO2-600) are shown in Figure .

Figure 1

XRD patterns of TiO2 NTs nonthermally treated and thermally treated at 300, 450, and 600 °C. Dark colors indicate samples before cycling, while light colors refer to cycled electrodes. The growth time by anodic oxidation is kept constant at 5 min.

The TiO2-am and TiO2-300 samples show only the Ti reflections (reference JCPDS 89-5009), independently of the NTs length, thus accounting for their bare amorphous characteristics; even if some literature references report the formation of anatase at 300 °C,[58] we did not detect it in our experiments. The formation of an anatase polycrystalline structure is clearly seen in the diffraction pattern of TiO2-450 and justified by the presence of the peaks related to the (0 0 4), (1 0 1), (1 0 5), and (2 0 0) crystal planes (JCPDS 89-4921). As regards the additional peaks present in the pattern, they originate from the Ti substrate (JCPDS 89-5009). No additional peak is observable, which might be ascribable to some foreign impurity phases. Finally, TiO2-600 shows both anatase (reference JCPDS 89-4921) and rutile (reference JCPDS 87-0710) (1 1 0) and (0 2 0) peaks, thus accounting for a mixed crystalline phase structure. Indeed, the resulting material of the anodic oxidation process is polycrystalline, and there is no possibility to induce a preferred orientation by acting on the preparation parameters.

The dependency of TiO2 NTs array length on their electrochemical performance as electrodes in sodium cells was investigated. The length was controlled by acting on the time of anodization during synthesis: Figure A shows the expected linear growth of the nanotubes for 1, 5, and 10 min with corresponding FESEM images of the cross sections. The resulting lengths are about 320, 1800, and 4800 nm, respectively.

Figure 2

(A) Graph of TiO2 NTs length vs time of anodization; FESEM images showing different NT lengths are shown as insets. (B) High-magnification FESEM images of the NTs annealed at different temperatures, namely 300, 450, and 600 °C, for 1 h in ambient atmosphere.

Moreover, the effect of crystallization was considered as a parameter of interest on the final performance of the materials. Indeed, the as-grown TiO2 NTs are completely amorphous, but they can be thermally crystallized in the desired polycrystalline phase (anatase, rutile, or mixed phase) by simply selecting the right calcination temperature in ambient atmosphere. The high magnification FESEM images collected in Figure B illustrate the morphological evolution of the NTs wall during thermal treatments. Almost no difference can be appreciated up to 300 °C, but at higher calcination temperatures the nanotubes walls start exhibiting some small cracks and an increased roughness due to crystallite formation. In all cases, the TiO2 nanotube arrays demonstrate excellent mechanical robustness and self-standing ability.

Electrochemical Characterization in Sodium Cells

The evaluation of the electrochemical behavior in laboratory-scale sodium test cells was carried out at ambient temperature by means of constant current (galvanostatic) discharge/charge cycling at various current regimes, from 0.1 to 5 mA cm–2. It is worth noting that, thanks to their self-supporting ability and excellent mechanical integrity, the TiO2 NTs arrays supported on the underneath titanium foil were directly assembled in laboratory-scale sodium cells, without any addition of conductivity enhancers and/or binders, thus leading to an increased overall energy density output from the working electrode.

Representative potential versus specific capacity profiles for all the samples under study are shown in Figure . They are extracted from the ambient temperature long-term cycling tests obtained at different current regimes between 0.1 and 2.5 V versus Na+/Na (see Figure ). The formation of the solid electrolyte interface passivating film at the surface of the nanotubes is clearly visible in the initial discharge (Na-ion insertion) step as a steadily sloping pseudopotential plateau slightly below 1.0 V versus Na+/Na (black profile in all the upper plots in Figure ). It is the main responsible of the initial large irreversible capacity and corresponding low Coulombic efficiency, in agreement with literature reports.[57,59] After the initial irreversible reactions took place, the charge/discharge processes unfold into typical S-type shaped reversible sloping potential profiles, where a visible plateau is not clearly present for both discharge and charge curves, but only the expected gradual evolution associated with a continuous solid-solution reaction between sodium ions and active material, as for the typical behavior of titania upon reversible insertion/de-insertion of sodium ions.[57,60] Overall, the process is highly reversible for all the samples, as well-evidenced by the very similar Na+ ions insertion/de-insertion capabilities, even when increasing the current regimes. This observation clearly accounts for the lack of structural changes upon reversible reaction with sodium ions and the good diffusion pathways. The symmetry and shape of the constant current profiles remain almost unchanged upon cycling, which accounts for the good structural stability of the materials, as also confirmed by XRD analysis after cycling (see Figure ).

Figure 4

Ambient temperature electrochemical behavior of the different TiO2 NTs arrays under study: TiO2-am (A), TiO2-300 (B), TiO2-450 (C), and TiO2-600 (D). In particular, constant-current discharge/charge potential vs specific capacity profiles are shown between cycles 1 and 170 at different current densities from 0.1 to 5 mA cm–2 (upper plots in A–D) and between cycles 170 and 300 at fixed 0.1 mA cm–2 (lower plots in A–D).

Figure 3

Specific discharge capacity vs cycle number at different current densities (from 0.1 to 5 mA cm–2) for sodium cells assembled with TiO2 NT arrays as working electrodes, as described in Table .

Table 1

Experimental Matrix of Variables (x1 = Growth Time of TiO2 NTs by Anodic Oxidation, x2 = Annealing Temperature) and Corresponding Experimental and Predicted Responses To Optimize the Specific Capacity of the Samples

cell	x1 (min)	x2 (°C)	measured specific capacity (μAh cm–2)	predicted specific capacity (μAh cm–2)
N1	1	25	11.6	12.3
N2	1	300	6.6	7.9
N3	1	450	1.8	2.1
N4	1	600	1.1	0.3
N5	5	25	57.7	56.4
N6	5	300	36.1	38.9
N7	5	450	11.5	10.8
N8	5	600	0.4	0.8
N9	10	25	89.4	90.9
N10	10	300	67.9	67.0
N11	10	450	57.0	58.0
N12	10	600	25.0	27.2
N13	5	450	11.2	10.8
N14	5	450	12.0	10.8

The potential drop at below 0.6 V versus Na+/Na, which is visible in TiO2-450 and, particularly, in TiO2-600, is attributed to the reversible sodiation/desodiation process in rutile TiO2 host, which is consistent with previous reports.[61,62] The process is visible, even if much reduced, in the following cycles and, in particular, at lower current regimes; this may suggest that the reaction between rutile TiO2 and Na+ is a surface-confined charge-transfer process.[63]

The comparison of the constant current profiles of the different samples clearly enlightens that TiO2-450 and TiO2-600, calcined at higher temperature, demonstrate a remarkable increase in the specific capacity output at 0.1 mA cm–2 and upon long-term cycling (lower plots in Figure ). This reflects an increased material utilization upon reversible cycling of highly crystalline samples, which is not the case for the materials having a higher degree of amorphicity.

Nanostructure-Performance Correlation by a Design of Experiments (DoE) Approach

The experimental parameters behind the preparation (and related characteristics) of vertically aligned TiO2 NTs and the resulting performances in lab-scale sodium cells were investigated by means of a chemometric approach. The proposed multivariate mathematical analysis represents a powerful tool if the aim is that of optimizing functional materials, especially when it is required to determine variables as others are modified in the experimental work. By means of this statistical-mathematical approach, the operational variables (i.e., the growth time of TiO2 NTs by anodic oxidation and the annealing temperature) can be concurrently varied to identify the relative weight of each one and the relation between them, particularly indicating synergies and antagonisms. This approach aims at challenging the strong imbalance that now exists between the technical ability to generate a large amount of excellent experimental data and the human ability to interpret them properly.

Fourteen sodium cells were assembled to investigate the experimental domain in the proposed chemometric approach. The overall constant-current cycling behavior at various current densities (0.1–5 mA cm–2) of the series of TiO2 NTs arrays under study is shown in Figure , where the influence of the growth time on the overall materials performance as well as the peculiar opposite behavior of amorphous and crystalline TiO2 NTs samples is well-evidenced. Only specific capacity values upon discharge are plotted to simplify the figure and facilitate the understanding.

The chemometric matrix shown in Table was filled with the experimental responses corresponding to the specific capacity values of the assembled sodium cells at the 85th cycle. The interpolation parameters derived from the multiple linear regression were Q2 = 0.79 (i.e., the fraction of the variation of the response that can be predicted by the model) and R2 = 0.95 (i.e., the fraction of the variation of the response explained by the model). In other words, these parameters provide the summary of the fit for the studied model, representing overestimated (R2) and underestimated (Q2) measures of the quality of chemometric model fitting. In the present study, R2 and Q2 are close to 1 (R2 in particular), which indicates that an excellent description of the relationship between the response and the independent variables is provided by the regression model; this is also clear when predicted specific capacity values listed in the last column of Table are considered.

The set of experiments permitted the achievement of a maximum specific capacity of 90.9 μAh cm–2 for the cell assembled with the amorphous TiO2-am sample, which was grown for 10 min and clearly not annealed. Figure A shows how much each variable influences the experimental response, with 95% confidence. From the coefficient plot shown in this figure, it is possible to write the modeling equation, which represents an empirical relationship between the variables and the response expressed in polynomial form:where y is the specific capacity of the various sodium cells. The numerical values of the coefficients in the equation indicate the importance of each factor in the equation. It is worth noticing that the coefficients of x1 and x2 are positive, while those of the respective quadratic effects are one positive and one negative. It means that a slight increase in x1 and x2 leads to an increase in specific capacity, but high values of these factors lead to opposite effects on cells performance. Lastly, the interaction term x1·x2 is negative, and this indicates that there is absence of synergistic effects between these two variables.

Figure 5

(A) Coefficient plot for the D-optimal DoE; (B) response surface showing the effect of the two experimental parameters on the specific capacity at the 85th cycle of lab-scale sodium cells assembled with the different vertically aligned TiO2 NTs under study.

The response surface of the quadratic matrix of 14 experiments is shown in Figure B, where the maximum response zone for specific capacity is observed at x1 = 10 min and x2 = 25 °C. Two hypotheses were analyzed to validate the chemometric experimental model:

H1: a dependency between the variables exists.

H0: a dependency between the variables does not exist.

By using the quadratic differences between the results and their average, the Student’s t-test was applied, and it gave a probability of 5% for H0 and of 95% for H1, therefore corroborating H1 and underlining that a dependency between the variables exists.

We decided not to stop cell testing at the 85th cycle (although it was already enough to extract information on the most promising electrodes, i.e., those with the growth time of 10 min). Surprisingly, when we resumed the initial current regime (0.1 mA cm–2), we clearly observed the inversion of the behavior of the amorphous and the anatase electrodes. Specifically, as clearly visible in Figure A, the samples calcined at 450 °C and above were much more stable upon long-term operation, while the amorphous sample and TiO2-300 calcined at low-temperature showed a rapid decay of the specific capacity values. This is also clearly detectable from the contour plot shown in Figure B, obtained by fitting the DoE at the 250th cycle. The best performance was obtained by anatase titania samples (i.e., calcined at 450 °C, TiO2-450), which were grown for 10 min.

Figure 6

(A) Specific discharge capacity values under 0.1 mA cm–2 for sodium cells assembled with TiO2 NTs array working electrodes (growth time = 10 min) between the 250th and 300th cycle; (B) response surface showing the effect of annealing temperature and growth time on the specific capacity at the 250th cycle of lab-scale sodium cells.

Summing up, the chemometric approach enabled the following observations on the investigated system. A direct correlation between growth time and specific capacity output of the cell was evidenced: higher specific capacity values were provided by longer TiO2 NTs, which were also able to retain very long-term cycling stability. It accounted for the high quality and excellent mechanical robustness of the TiO2 NTs prepared by anodic oxidation in this work. This might be considered as an “expected” result, but it is not trivial: very often, longer 2D nanostructures lack by proper structural stability that causes a rapid performance decay upon prolonged operation.[64,65] As already discussed,[57] TiO2-am showed an increase of performance in the very initial cycles at low current, which was then followed by a constant capacity decrease at all of the tested current densities. The TiO2-300 sample showed likely the same cycling behavior. This was independent on the growth time, as both longer and shorter nanotubes had the same behavior. Highly crystalline samples TiO2-450 and TiO2-600 showed a rapid specific capacity increase at low current density during initial operation; the specific capacity gain remained constant even at higher current densities. It is worth noting that the specific capacity of the crystalline samples relentlessly and monotonously increased when the current was reduced back to low 0.1 mA cm–2, which is a completely different behavior if compared to amorphous samples. It confirms the superior long-term cycling performance of anatase TiO2 NTs over their amorphous counterparts. The presence of rutile phase, which was obtained upon calcination at 600 °C, in the material did not influence the overall cycling behavior but was clearly not beneficial to the overall specific capacity output.

Nanostructure-Performance Correlation by a Theoretical Approach

From the previous sections, a distinction in the performance between anatase, rutile and amorphous TiO2 clearly emerged. In our previous work,[57] we demonstrated the superior behavior of the anatase phase upon long-term reversible cycling in lab-scale sodium cells. This is confirmed here, as the single-phase anatase polymorph, obtained by calcination at 450 °C, provides the highest specific capacity value after 300 reversible discharge/charge cycles. The growth time also affects the electrochemical response of the material, and, in particular, notwithstanding the calcination temperature, the best results are obtained at longer growth time. In the present work, we also demonstrate that the presence of foreign phases of TiO2 other than pure anatase negatively affects the electrochemical performance. In this respect, the TiO2-600 sample shows a sizeable amount of rutile, which is formed upon calcination at 600 °C (see XRD diffraction patterns in Figure ), thus resulting in a mixed anatase/rutile structure. It shows a substantial decrease in the overall specific capacity output at all of the different current regimes if compared to the single-phase anatase (TiO2-450), which suggests the limited reversible insertion/de-insertion capability of the rutile polymorph.

To confirm this statement, we have performed state-of-the-art density functional theory (DFT) calculations of Na+ insertion in TiO2 rutile bulk phase, following the same approach as for the case of TiO2 anatase bulk.[57] We employed a 96-atom structural model for TiO2 rutile, corresponding to a 2 × 2 × 4 supercell. The relaxed structural parameters are in good agreement with the experimental values, as listed in Table .

Table 2

DFT-PBE Minimum-Energy Structural Parameters for TiO2 Rutile Bulk Phase (Space Group No. 136: P42/mnm), Lattice Vectors ( = , ) in Å and u Coordinate of the 4f Wyckoff Position for the Oxygen

	this work	exp.a
a = b (Å)	4.6364	4.5936
c (Å)	2.9862	2.9862
uO	0.3047	0.3048

Reference (66).

The rutile structure presents a cavity that forms a channel along the [001] direction: in this cavity, it is possible to accommodate a Na+ cation, as depicted by Figure .

Figure 7

(A) Structural model of the relaxed 96-atom 2 × 2 × 4 supercell of TiO2 rutile, view along the [001] direction, color code: Ti (cyan) and O (red). (B) Minimum-energy structure for the insertion of a Na+ cation (yellow) inside the TiO2 rutile. (C) Zoom over one Ti6O6 host “cage” for Na+ showing six coordination oxygen atoms. The size of this cage is determined by the two closest oxygen atoms (d1 in orange), while two other equivalent O–O pairs (d2 in red) lie at a higher distance: d1 goes from 3.36 Å in pristine TiO2 rutile to 4.01 Å in the presence of sodium (Na0.03TiO2), and d2 goes from 4.49 to 4.41 Å.

The insertion energy has been computed according to the following equation:where E(Na:TiO2) is the total energy of the system with the inserted Na+ cation; E(TiO2) and E(Nam) are the reference energies for titania and sodium metal, respectively. The computed Eins for the insertion of the first sodium in rutile is 0.988 eV. This positive value means that the insertion is not energetically favorable, and the reason is to be found in the distortions of the Ti6O6 cavity that accommodates the sodium: the oxygen–oxygen distances (see d1 and d2Figure C) are perturbed by the large Na+ cation and especially d1 is elongated by ∼20% to make room for sodium.

The rutile unfavorable insertion energy should be compared to the Eins value of −0.14 eV computed for the anatase phase.[57] We also computed the insertion energies for a second Na+ cation in different relative positions with respect to the first cation; Figure depicts the different configurations.

Figure 8

Structural models for a second Na+ cation placed in different configurations: (A) as next-neighbor along the same [001] channel; (B) in the furthest position within the 96-atom supercell; (C) in an adjacent site of a parallel [001] channel; (D) in a parallel [001] channel bridged by a TiO6 moiety: the central Ti of such moiety strongly goes off-center upon relaxation. Color code as in Figure .

The insertion of the second sodium is always unfavorable; the computed insertion energies Eins for the different configurations are (A) 1.379, (B) 1.725, (C) 0.855, and (D) 3.074 eV. These high-energy values correspond to very unfavorable insertion for a second Na+ cation. For the C configuration, the computed Eins is the least unfavorable, while the most unfavorable is the D configuration where there is a strong displacement of a Ti atom in a TiO6 moiety in between two insertion sites. These computed values in rutile are much higher than the anatase counterparts, where the computed Eins values for the second sodium are within ∼0.5–0.7 eV.

All these theoretical results support a worsening of Na+ insertion capability for TiO2 nanostructures going from anatase to rutile, in agreement with electrochemical experiments. Moreover, these experimental and theoretical results are in agreement with previous observations independently obtained for a different polymorph (TiO2@C nanospheres) by Wang’s group.[67] However, the anodic oxidation process here proposed for nanotubes is faster and cheaper with respect to the hydrothermal method used to design nanospheres by a template approach.

Conclusions

The best nanostructure based on TiO2 nanotubes as the anode for sodium batteries has been identified by a combined physicochemical, electrochemical, computational, and chemometric approach. The experimental design made it possible to identify anatase electrodes grown for longer anodic oxidation times as the best choice to this purpose, and the DFT study allowed to justify this behavior. Anatase is the most stable polymorph upon cycling, because it is not perturbed by the insertion of new Na ions and the channels directed along the [001] direction guarantee a favorable path for Na ion diffusion. Conversely, the insertion in the rutile structure is not energetically favorable because of the distortions of the Ti6O6 cavities that accommodate sodium ions.

The combined approach proposed in this work allowed obtaining a state-of-the-art benchmark as an optimized anode for sodium batteries, an increasingly investigated electrochemical technology for the storage of energy produced from renewable sources. Right now, as the TiO2 comprises only a small fraction of the Ti foil used, the energy density for full battery cells of size for commercialization will be quite low when considering the mass of the entire cell: a proper choice of Ti foil thickness and an evaluation of its application also in the field of sodium-ion microbatteries will be challenging further steps in this field; alternatively, a thin Ti layer can be deposited onto a standard current collector, subsequently proceeding with the anodization process.

Experimental Section

Preparation of Vertically Aligned TiO2 Nanotubes

TiO2 nanotube arrays were directly grown on titanium foils (thickness 70 μm, 99.96% purity, Goodfellow) by anodic oxidation. Before use, foils were cleaned by ultrasonication in acetone and soft HF etching (3 wt % HF in aqueous solution for 1 min) to remove the native oxide layer. The electrochemical process was conducted in an electrolytic solution containing NH4F 0.5 wt % and deionized water 2.5 wt % in ethylene glycol, using a platinum sheet as the counter electrode (thickness 250 μm, 99.99% purity, Goodfellow) at the constant temperature of 25 °C in a Peltier thermostat (LAUDA Omnicool unit 62 Plus) under magnetic stirring. The anodization time was varied in the 1–10 min range applying a constant voltage of 60 V (using a dc power supply, GW Instek SPD-3606) to obtain nanotubes with lengths ranging from approximately 300 nm up to about 5 μm. Samples were then rinsed in distilled water and dried under nitrogen flow. To investigate the effect of the crystallization on the electrochemical performance, the as-grown TiO2 nanotubes were thermally treated at 300, 450, and 600 °C for 1 h in ambient atmosphere into a laboratory furnace by Abb Furnace Co.

Chemometric Approach

The first step of our chemometric approach entails the selection of the variables to be investigated and their relative experimental domain. In agreement with the purpose of this work, we selected the following experimental variables and related ranges of values: the growth time of TiO2 NTs by anodic oxidation (x1, which ranged between 1 and 10 min) and their annealing temperature (x2, which ranged between 25 °C non-annealed, i.e., amorphous samples, and 600 °C, crystalline samples). The two variables were codified in 3 and 4 levels, respectively.

To carry out a multivariate DoE, the software MODDE (version 11.0.2.2309, Umetrics) was adopted, which is widely used in the chemistry field.[68] An experimental domain as the one considered here can be investigated by means of a D-optimal design, with the goal of achieving the maximum information within a well-determined set of experiments with respect to a stated mathematical model. In detail, if a specified regression model is considered, such aswhere y is a (N × 1) vector representing the measured responses (i.e., NIB specific capacity), X is a (N × p) extended design matrix that includes all of the n experiments plus additional columns for the p model terms (e.g., interaction terms, constant term, square terms, etc.), β is a (p × 1) vector related to coefficients that are unknown and to be determined by fitting the model to the measured responses, ε is a (N × 1) residuals vector indicating the differences between the predicted and observed values of the response y, and the D-optimal design constitutes the statistical mean that permits the maximization of the X′X matrix determinant, being an overall measure of the information in X.[69]

When chemometrics is adopted in materials chemistry studies, the D-optimal design is typically built up by choosing N experiments (runs) from a candidate set, representing the discrete set of “all potential good experiments” included in the experimental domain that is initially defined by the operator. After this step, the best design is constructed by a selection process that depends on the number of runs that can be carried out by the operator (some experiments can be performed easily, others are costly) and on a statistical criterion. On the basis of our previous experiences in the field, we selected G-efficiency (Geff) as the statistical criterion, which is defined by this mathematical equationwhere p is the number of terms in the model, n the number of experiments in the design, and d the maximum relative prediction variance over the candidate set. The higher the numerical value of Geff criterion, the higher is the probability to obtain the maximum amount of information from the experimental setup defined with the software and performed in the laboratory. In the present case, the highest value of Geff was obtained for a D-optimal design built with 14 runs, which will be described in the following. A thorough discussion of the mathematical and statistical basis behind the selected DoE can also be found elsewhere.[70] The experimental matrix generated by the software is shown in Table . Our selected experimental response (y) was the specific capacity of the lab-scale sodium cells at the 85th galvanostatic cycle, thus having a clear idea about the performance of each device assembled with the TiO2 NTs electrodes prepared accordingly to the experimental protocol described above.

To evaluate the experimental reproducibility following the standard criteria of DoE techniques, three replicates (named N7, N13, and N14 in Table ) of the central point were carried out.

Characterization of the Materials, Fabrication of the Devices, and Electrochemical Tests

The morphology of the as-grown nanotubes was studied by FESEM analysis using a MERLIN ZEISS instrument, equipped with an energy dispersive X-ray spectrometer for compositional analyses. XRD analysis was used to assess the structural characteristics of the materials. A PANalytical X’Pert MRD Pro instrument, equipped with a Cu Kα X-ray source and a curved graphite secondary monochromator, was used to study the samples both before and after galvanostatic cycling.

The electrochemical behavior of the vertically aligned TiO2 NTs upon reversible insertion/de-insertion of Na+ ions was studied in three-electrode T-cells made of polypropylene and assembled by contacting in sequence a working electrode (i.e., Ti foil-supported TiO2 NTs disk, with an area of 20 mm2), a separator (that was a Whatman Grade GF/A product soaked into a 1.0 M solution of sodium perchlorate—NaClO4 by Solvionic—in propylene carbonate—PC, Solvionic), and a counter electrode (a sodium metal foil by Sigma-Aldrich). NaClO4/PC was selected as the preferred electrolyte solution as we found it to be the most performing in terms of Coulombic efficiency and specific capacity output and is also low cost and easily available.[71]

Constant current (galvanostatic) discharge (Na+ insertion)/charge (Na+ de-insertion) cycling was conducted at ambient temperature (≈20 °C) using the battery testing system model BT2000 by Arbin Instruments. Discharge/charge cycles for all the cells were set at the same rate ranging from 0.1 to 5 mA cm–2 and keeping a cut off potentials: 0.2–2.5 V versus Na+/Na. Procedures of devices assembly were carried out under inert and controlled atmosphere by using a GP Dry-Glove Box Workstation by Jacomex (H2O and O2 content lower than 0.1 ppm), filled with extra pure Ar 6.0. Before assembly, all samples were prepared and stored in an environmentally controlled dry-room (10 m2, relative humidity <2% ± 1 at 20 °C) produced by Soimar Group.

Computational Details

We performed spin-polarized Kohn–Sham DFT[72,73] calculations by means of the generalized-gradient approximation with the exchange−correlation density functional of Perdew, Burke, and Ernzerhof (PBE),[74] as implemented in the VASP code.[75−77] The projector-augmented wave potentials were used to describe nuclei and core electrons.[78,79] The pseudo-wave functions was expanded in a plane-wave basis set with a kinetic energy cut-off of 600 eV and a k-point sampling based on Γ-centered 3 × 3 × 3 grid for the 96-atom TiO2 2 × 2 × 4 supercell. With these numerical parameters the achieved convergence for total electronic energies is within 5 meV per formula unit. Furthermore, structural optimization were carried out until the convergence of Hellmann−Feynman forces with a threshold of 10 meV Å−1.