Solid State Ionics 255 (2014) 60–64

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Solid State Ionics
journal homepage: www.elsevier.com/locate/ssi

Lithium ion insertion properties of nanocrystalline anatase titaniumoxides prepared from peroxo-polytitanic acid
Isao Tsuyumoto ⁎, Kazuki Kobayashi
Department of Applied Chemistry, College of Bioscience and Chemistry, Kanazawa Institute of Technology, 7-1 Ohgigaoka, Nonoichi, Ishikawa 921-8501, Japana r t i c l e

i n f oArticle history:
Received 17 June 2013
Received in revised form 31 October 2013
Accepted 27 November 2013
Available online xxxx
Keywords:
Lithium
Titanium oxide
Battery
AnatasePeroxidea b s t r a c t
Peroxo-polytitanic acid (Ti-iPA) solution was obtained by using a reaction between metallic Ti powder and
30 wt.% aq. H2O2. Amorphous titanium oxide was prepared by drying Ti-iPA solution at 115 °C, and nanocrystalline anatase titanium oxide was prepared by heating the amorphous phase at 300–500 °C. The crystal structure
was the same as that of the conventional anatase form. The anatase titanium oxide obtained by heating at 300 °C
for 5 h with an average particle size of 25 nm showed the capacity of 158 mA h/g as negative electrode for lithium ion batteries. The capacity was increased with increasing the heating time at 300 °C and reduced with increasing the heating temperature to 400–500 °C. The lithium insertion/deinsertion performance was enhancedby heating at 300 °C because lattice defects were reduced without crystal growth and aggregation. We also calculated site energy distribution from the deconvolution of experimental discharge curves, and discussed the relationship between the structure and the insertion site.
© 2013 Elsevier B.V. All rights reserved.

1. Introduction
Titanium oxides have attracted much attention as negative electrodematerials of lithium ion batteries because they accommodate lithium
ion and show lithium diffusivity in the host lattices [1–4]. Many researchers have reported new preparation methods of titanium oxides
such as anatase [5–10], rutile [11,12], hollandite [13], ramsdellite [14],TiO2 (B) [15,16], amorphous [17], and have discussed their electrochemical lithium insertion/deinsertion properties in relation to the
crystal structure, crystallinity, particle size and surface morphology[18]. The earlier reports mostly indicated that large surface area compatible with few lattice defects is essential to the good lithium insertion/deinsertion performance. Nanocrystalline titanium oxides havebeen reported to be appropriate for the lithium insertion materials, because the large surface area and small particle diameter favor the lithium diffusion across the electrolyte/electrode interface and inside theparticles. Soft-chemical processes such as the hydrothermal method[19–22], the sol–gel method [23,24], and the precursor pyrolysis method [25,26] have advantages over the conventional solid state reactions
to prepare such homogeneous nanocrystalline titanium oxides.
In our previous study, we have developed new synthetic routes ofmetal oxides from peroxo-metallic acid obtained by reaction between
metallic powder and concentrated hydrogen peroxide solution [27–36].
For example, peroxo-polytungstic acid is obtained by vigorous reaction
between metallic tungsten powder and hydrogen peroxide solution[36], and its salts with alkalis yields novel tungsten bronzes at 500–
700 °C [33]. Similarly molybdenum, niobium, vanadium and titanium⁎ Corresponding author.
E-mail address: tsuyu@neptune.kanazawa-it.ac.jp (I. Tsuyumoto).
0167-2738/$ – see front matter © 2013 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.ssi.2013.11.048

powders react with hydrogen peroxide and yield the correspondent
peroxo-metallic acids. Since the reaction of the titanium powder withhydrogen peroxide was markedly slow compared with the othermetals, we have accelerated the reaction by concentrating the hydrogen
peroxide up to 70 wt.% and have obtained the peroxo-polytitaninic
solution (titanium isopolyacid, Ti-iPA) in 6 h. Furthermore, we havesuccessfully prepared nanosized tetragonal BaTiO3 from the salt of
peroxo-polytitanic acid and Ba(OH)2 [29]. To prepare Ti-iPA solution
is a very useful method to solubilize titanium into aqueous solution,
and we found that its dry residue yields amorphous and nanocrystalline
anatase titanium oxides by heating at relatively low temperatures. In
the present study, we investigated lithium insertion/deinsertion properties of amorphous and nanocrystalline anatase titanium oxides prepared from Ti-iPA solutions under various conditions. Furthermore,
we also present the energy distribution of lithium insertion site calculated from the experimental charge/discharge curves using a numericaldeconvolution technique based on the theoretical relationship between
the charge/discharge curves and the energy distribution of lithium insertion site in host materials.
2. Experimental
2.1. Sample preparation
Metallic Ti powder (0.36 g, 45 μm particle size, as received from
Wako Pure Chemical Industries Ltd., Osaka, Japan) was dissolved in
150 mL of 30 wt.% aq. H2O2 solution (Wako Pure Chemical Industries
Ltd., Osaka, Japan) at 20 °C with stirring. The dissolving reaction
proceeded mildly with the emission of oxygen gas, and a yellow transparent solution of peroxo-polytitanic acid (denoted as Ti-iPA whereI. Tsuyumoto, K. Kobayashi / Solid State Ionics 255 (2014) 60–64

61

iPA stands for isopolyacid) was obtained in 24 h. After removing insolubles by ﬁltration, Ti-iPA solution was dried at 115 °C for 24 h to yield
yellow amorphous powder. Amorphous and nanocrystalline TiO2 wereprepared by heating the yellow powder as a precursor in air at the desired temperatures speciﬁed by thermal and structural analyses.
2.2. Characterization
The thermal behavior of the amorphous precursor was investigatedby thermogravimetry (TG) and differential thermal analysis (DTA; DTG50 Shimadzu, Kyoto, Japan) in air at a heating rate of 20 °C/min. The
XRD patterns of the products were measured with a diffractometer(XD-D1, Shimadzu, Kyoto, Japan) using graphite-monochromatized Cu
Kα radiation (λ = 0.15406 nm) at 30 kV and 30 mA. The X-ray proﬁleswere collected between 2° and 120° of 2θ angles with a step interval of
0.02° and a count time of 1 s/step. The crystalline parameters were reﬁned by the Rietveld method using the RIETAN-FP program [37], andthe crystallite sizes were determined by the Scherrer equation. For lithium deinsertion/insertion measurements, each sample of 16.6–16.7 mg
was intimately ground with acetylene black (AB) at a weight ratio of
1:1, and the composite, after mixing with 15.0 mg of polytertraﬂuoroethylene (PTFE) as a binder, was pressed onto a copper mesh. The
Ag/Ag+ electrode for non-aqueous solvent (RE-7, ALS Corporation
Ltd., Tokyo, Japan) was used as a reference electrode, and its potential
was determined at 3.84 V vs Li. The counter electrode was a mixtureof 61 mg LiCoO2, 12 mg AB, and 5 mg poly(vinylidene diﬂuoride)(PVDF) as a binder. The active material in the counter electrode wasthree times in excess compared to that in the working electrode. The
lithium deinsertion/insertion measurements were carried out in thegalvanostatic mode at 3.0 mA (1.08 C rate) in the range 1.0–3.5 V (vsLi). Discharge curves were also measured at 0.06 mA (0.022 C rate)in order to use as OCV (open circuit voltage) curves in theoretical
calculations.
3. Results and discussion
3.1. Formation of amorphous and nanocrystalline TiO2 from Ti-iPA solution
Fig. 1 shows the TG and DTA curves for the residue obtained by drying Ti-iPA solution at room temperature. The weight decreased monotonously by 25% up to around 400 °C and remained almost constant overaround 400 °C. An exothermic peak appeared at 396 °C, around which
the weight ceased to decrease. These indicate that the condensation ofhydroxyl group, the decomposition of peroxo group, and the volatilization of H2O and H2O2 proceed continuously up to around 400 °C, andthat crystallization occurs at around 396 °C after the completion of therelease of H2O, H2O2 and O2. Fig. 2 shows the XRD patterns of amorphous titanium oxide obtained at the residue of Ti-iPA solution driedat 115 °C for 24 h and of nanocrystalline anatase TiO2 obtained by

Fig. 2. Powder XRD patterns of titanium oxides prepared from Ti-iPA. Amorphous phase is
the residue of Ti-iPA aq. dried at 115 °C for 24 h, and nanocrystalline anatase forms are obtained by heating the amorphous phase.

heating the amorphous titanium oxide at 300 or 400 °C. The nanocrystalline anatase TiO2 was formed by heating the amorphous titaniumoxide under such conditions as at 290 °C for 10 h or at 300–500 °C for
1 h or more, while the products remained amorphous after heating at
280 °C for 1–10 h or at 290 °C for 1–5 h. In the XRD patterns, the crystallization into anatase form occurred in the temperature range of 290–
300 °C, whereas the exothermic crystallization peak was observed
around 396 °C in the DTA curve at the heating rate of 20 °C/min. This
discrepancy is due to the difference of the heating time. The crystallization was triggered below 396 °C, because the condensation of hydroxyl
group, the decomposition of peroxo group, and the volatilization of H2O
and H2O2 in the amorphous phase were completed by prolonging theheating time to 10 h at 290 °C or 1 h at 300 °C. Table 1 shows structuralparameters and crystallite sizes reﬁned by the Rietveld method. The
space group, I41/amd, and the site coordinates were the same as thatof the conventional anatase TiO2 [19,38]. As mentioned above, theamorphous phase crystallized into the anatase form over around
300 °C. The crystallite sizes of heating time 1 h and 5 h at 300 °C were
22 nm and 25 nm, respectively, indicating that crystal growth hardly
proceeds around 300 °C. Elevating the heating temperature to 400 °C
and 500 °C also resulted in a little increase in crystallite size.

3.2. Lithium insertion and deinsertion properties
Fig. 3 shows charge/discharge curves of the titanium oxides prepared from Ti-iPA. The amorphous titanium oxide prepared by heating
at 115 °C for 24 h showed a steep potential change without a plateau
region by lithium insertion and deinsertion, as shown in Fig. 3(a). The
amorphous titanium oxides prepared by heating at 280 °C for 1 h, 5 h,and 10 h also showed the same charge/discharge curves as the one
Table 1
Structural parameters reﬁned by the Rietveld method and crystallite sizes. Tetragonal,
space group; I41/amd (144). All occupancies are ﬁxed at unity.

Fig. 1. DTA and TG curves for the residue obtained by drying Ti-iPA solution at room
temperature.

Heating
condition

Lattice parameter

Site coordinate
and atomic position

Crystallite size

300 °C, 1 h

a = 3.789, c = 9.512

22 nm

300 °C, 5 h

a = 3.796, c = 9.527

400 °C, 1 h

a = 3.793, c = 9.521

400 °C, 5 h

a = 3.787, c = 9.512

500 °C, 1 h

a = 3.786, c = 9.515

500 °C, 5 h

a = 3.790, c = 9.524

Ti 4a (0, 3/4, 1/8)
O 8e (0, 1/4, u), u = 0.208
Ti 4a (0, 3/4, 1/8)
O 8e (0, 1/4, u), u = 0.206
Ti 4a (0, 3/4, 1/8)
O 8e (0, 1/4, u), u = 0.207
Ti 4a (0, 3/4, 1/8)
O 8e (0, 1/4, u), u = 0.205
Ti 4a (0, 3/4, 1/8)
O 8e (0, 1/4, u), u = 0.208
Ti 4a (0, 3/4, 1/8)
O 8e (0, 1/4, u), u = 0.207

25 nm
22 nm
26 nm
25 nm
27 nm

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I. Tsuyumoto, K. Kobayashi / Solid State Ionics 255 (2014) 60–64

Fig. 3. Charge/discharge curves of the titanium oxides prepared from Ti-iPA by heat treatment of (a) 115 °C, 24 h; (b) 300 °C, 1 h; (c) 300 °C, 5 h; (d) 400 °C, 1 h; (e) 400 °C, 5 h; and (f)500 °C, 5 h.

prepared at 115 °C. The capacities were about 60 mA h/g much lower
than the theoretical value 168 mA h/g, suggesting that the lithium insertion sites are heterogeneous and more than half of them are unsuitable for lithium insertion due to spatial or energetic reason. The steep
change of the potential also suggests the heterogeneous lithium insertion sites in the amorphous phase. These are consistent with the experimental fact that the crystallization occurs after the completion of therelease of H2O, H2O2 and O2. The remaining hydroxyl and peroxo groups
and the caged molecules such as H2O, H2O2 and O2 in the amorphousmatrix probably make the insertion sites spatially or energetically inaccessible to the lithium. Fig. 3(b)–(f) shows charge/discharge curves ofnanocrystalline anatase TiO2 obtained by heating at 300–500 °C. A plateau region was observed for all the nanocrystalline TiO2, indicating thatthe insertion sites are homogeneously formed in the nanocrystals. The
capacity varied depending on the preparative conditions. The capacity
was increased from 109 mA h/g to 158 mA h/g with increasing theheating time from 1 h to 5 h at 300 °C. On the contrary, the capacity
was decreased to 143 mA h/g and 121 mA h/g with elevating theheating temperature to 400 °C and 500 °C, respectively. Interestingly,
the anatase TiO2 obtained at 300 °C for 5 h showed the largest capacity
158 mA h/g at rather high rate 1.08 C, and this is close to the theoreticalvalue 168 mA/g. Similar performance has been reported for anatase
TiO2 with crystallite size 30–40 nm prepared at 400 °C from oxalatopolytitanate by Yagi et al. [7], but the current density, 25 mA/g, fortheir case was much smaller than that for our case, 181 mA/g. We cansay that we ﬁrst achieved the capacity 158 mA h/g at rate 1.08 C
using the anatase TiO2 obtained at 300 °C. Elevating the heating temperature to 400–500 °C brought about the reduction of the capacity, because crystal growth and aggregation to form secondary particles are
not favorable for the diffusion of lithium ion into and out of the particles.
Prolonging the heating time from 1 h to 5 h at 300 °C contributed to the

reduction of lattice defects without crystal growth and secondary particle formation. Heating the amorphous precursor at 300 °C is the mostappropriate route to prepare nanocrystalline TiO2 for lithium insertionand deinsertion, because crystal growth and aggregation are suppressed and lattice defects are reduced at 300 °C. Low temperature process around 300 °C is appropriate for preparation of lithium insertionmaterials because it can provide nanocrystals with fewer lattice defects.
3.3. Theoretical relationship between site energy distribution and
OCV curve
The electrode potential E (vs. Li) of lithium insertion materials is determined by the chemical potential difference between the inserted Li in
host electrode μLi, host and the Li metal electrode μLi, metal. When we set
the chemical potential of the Li metal electrode μLi, metal at zero and consider the electrode potential E and the chemical potential of the inserted
Li μLi, host as a function of Li content x in host electrode, the electrode potential isEðxÞ ¼ −μ Li;host ðxÞ
;
F

ð1Þ

where F is the Faraday constant. Thus, the theoretical OCV curves are derived by the calculation of the chemical potential of Li in host electrodeas a function of Li content x.
If the host material has insertion sites with homogeneous site energyε(b0) and total number N, and n sites among N are occupied by inserted
Li, the internal energy change by the insertion is⊿ U ¼ nε;ð2ÞI. Tsuyumoto, K. Kobayashi / Solid State Ionics 255 (2014) 60–64

asand the entropy change by the insertion is⊿ S ¼ k ln

N!
;n!ðN−nÞ!

ð3Þ

where k is the Boltzmann constant. Here we neglected repulsive forcesamong the inserted Li ions. In the present case, ⊿ H is considered to beequal to ⊿ U, because the volume change is negligibly small. The Gibbs
energy change is⊿ G ¼ nε−kT ln

N!
:n!ðN−nÞ!

ð4Þ

The chemical potential μLi, host is obtained by differentiating Eq. (4)with respect to n as
μ Li;host ðxÞ ¼ ε þ kT ln

x
;
1−x

ð5Þ

where x = n/N [39]. This equation bears close analogy to the Langmuiradsorption isotherm.
Let us consider a host material whose site energy has a wide distribution. In the case of amorphous host materials, innumerable kinds ofinsertion sites exist and each site energy is different from the otherkinds of sites in varying degrees. The inserted Li is distributed among
the sites so that the chemical potential of Li in each site becomesequal to each other.
If we denote each site energy by ε1, ε2, ε3, ⋯ and the occupancy ofeach site by f1, f2, f3, ⋯, the chemical potential of Li in each site is equally
given byf1
1− f 1f2¼ ε2 þ kT ln
1−f 2
f3¼ ε3 þ kT ln
1−f 3
…:

μ ¼ ε1 þ kT ln

ð6Þ1 μ−ε i
1 þ exp −kT

ði ¼ 1; 2; 3; ⋯Þ :

ð7ÞThis equation indicates that the inserted Li obeys the Fermi distribution function in each site. If we denote the number of each site by N1, N2,
N3, ⋯, the number of each occupied site by n1, n2, n3, ⋯, and the total
number of the occupied sites by n, we obtainn¼

XN i μ−ε i1 þ exp −kT

ði ¼ 1; 2; 3; ⋯Þ :nðμ Þ ¼Z ∞−∞f ðμ−εÞg ðεÞdε:ð11ÞThus, we can calculate the density function g(ε) from the OCV curveusing a deconvolution method. In data processing, when n(μ) and g(ε)
are the datasets consisting of m values, we denote n(μ) and g(ε) by(m × 1) matrices and f(x) by (m × m) matrix. Because the dataset ofn(μ) is the product of matrices denoting f(x) and g(ε), we obtain thedataset of g(ε) by multiplying an inverse matrix of f(x) with the datasetof n(μ). We calculated the inverse matrix of f(x) by the Gauss–Seidel
method so as to yield the dataset of g(ε).
3.4. Energy distribution of lithium insertion sites
Energy distribution curves of lithium insertion sites were calculated
from the discharge curves using Eq. (11), as shown in Fig. 4. Here weassumed that a single phase material was formed by the reaction between Li and TiO2 and approximately regarded the discharge curves at
0.022 C rate as OCV curves. The abscissa is proportional to the numberof insertion sites and the peak area is proportional to the total numberof insertion sites. The nanocrystalline anatase TiO2 showed sharp energy
distributions around 2.1 V, indicating that the insertion sites arehomogeneous in the host. On the other hand, the amorphous phase
had a broad energy distribution from 1.3 V to 3.5 V peaking at about
1.6 V. The site energy ε(b0) of the amorphous phase was calculated ataround −1.6 eV larger than that of the anatase form −2.1 eV. The energy distribution curves as well as the charge/discharge curves indicatethat the amorphous phase has a disadvantage in lithium insertion anddeinsertion because the insertion sites are energetically and spatiallyheterogeneous. Here the energy distribution curves were numericallycalculated from the discharge curves on the assumption that the repulsive forces among the inserted lithium ions are neglected, and they
proved to be very useful to discuss the relationship between crystal
structures and discharge properties.
4. Conclusions

By transforming Eq. (6), we obtain
fi ¼

63

Titanium was solubilized into aqueous solution by using a reaction
between metallic Ti powder and 30 wt.% aq. H2O2 to yield peroxopolytitanic acid (Ti-iPA) solution. Amorphous titanium oxide was obtained as dried residue of Ti-iPA solution at 115 °C, and nanocrystalline
anatase titanium oxide was formed by heating the amorphous phase at
300–500 °C. The largest capacity 158 mA h/g as negative electrode forlithium ion batteries was observed for the anatase titanium oxide obtained by heating at 300 °C for 5 h with an average particle size ofð8Þ

If we deﬁne a density function g(ε) = dN(ε) / dε by assuming thatNi shows a continuous distribution as a function of εi, Eq. (8) gives
n¼

Z ∞

g ðεÞ
 μ−εdε:−kT−∞ 1 þ exp

ð9Þ

Eq. (9) is a theoretical derivation of OCV curves, because the capacity
corresponds to n and the potential to −μ/e. It is interesting to note thatthe capacity is a convolution of the density function g(ε) and the Fermi
functionf ðxÞ ¼

1
 x ;
1 þ exp −kT

ð10ÞFig. 4. Energy distribution curves of lithium insertion sites numerically calculated from thedischarge curves. The inset shows discharge curves at 0.022 C rate used for theoretical
calculations.

64

I. Tsuyumoto, K. Kobayashi / Solid State Ionics 255 (2014) 60–64

25 nm at rather high rate 1.08 C. Any other preparative condition suchas shorter heating time at 300 °C and higher temperature 400–500 °C
resulted in reduction in capacity, because lattice defects are reducedby heating at 300 °C and crystal growth and aggregation proceed at
higher temperature 400–500 °C. In general, nanocrystals with few lattice defects are favorable for lithium insertion and deinsertion, because
large surface area and small particle diameter facilitate the lithium diffusion across the electrolyte/electrode interface and inside the particles.
Low temperature synthesis is highly desirable for the preparation ofelectrode materials. We found that heating the amorphous precursor
at 300 °C is the most appropriate method for the preparation of anatasetitanium oxide for lithium ion batteries. We also presented a theoretical
discussion on the relationship between energy distribution of insertion sites and discharge curves, and showed that the energy distribution of insertion sites are numerically calculated from the discharge
curves. The nanocrystalline titanium oxide showed uniform site energy
distributions reﬂecting the homogeneous insertion sites, whereas theamorphous phase had a broad energy distribution reﬂecting the heterogeneous structure. The energy distribution curves calculated from thedischarge curves will be very useful to discuss the insertion sites in crystal structures.
Acknowledgments
The authors express their grateful thanks to Dr. Tetsuichi Kudo,
Emeritus Professor at the University of Tokyo, for the helpful advice
and to Messrs. Kazuki Iwata and Kazuki Sakamoto for their assistancein the experiments in this work.
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