Amorphous and Nanocrystalline Anatase Titanium Dioxide Prepared from PeroxoPolytitanic Acid and Their Electrochemical Properties
Isao Tsuyumoto, and Kazuki Kobayashi
Department of Applied Chemistry, College of Bioscience and Chemisrty,
Kanazawa Institute of Technology, Nonoichi, Ishikawa 9218501, JAPAN

Peroxo-polytitanic acid solution was obtained by a reaction
between metallic Ti powder and 30 wt% aq. H2O2. Amorphoustitanium dioxide was obtained as dried residue at 115 °C, andnanocrystalline anatase titanium dioxide was obtained by heating
the amorphous phase at 300 – 500 °C. The anatase titanium
dioxide with average particle size of 25 nm obtained by heating at
300 °C for 5h showed the capacity of 158 mAh/g as negativeelectrode for lithium ion batteries. The capacity was increased
with increasing the heating time at 300 °C. Lattice defects werereduced by heating at 300 °C without crystal growth andaggregation, and this enhanced the lithium insertion/deinsertion
performance. We also calculated site energy distribution from thedeconvolution of experimental discharge curves, and discussed therelationship between the structure and the insertion site.

Introduction
Titanium dioxides, such as anatase, rutile, hollandite, TiO2 (B), have been intensively
investigated as negative electrode materials for lithium ion batteries (1-9). Among them,anatase forms showed lithium insertion/deinsertion performance depending on thepreparation method and the resultant morphology. Small particle size compatible withfew lattice defects is favorable for the diffusion efficiency of lithium ion into and out ofparticles, and such new preparation method is highly desirable to achieve good lithium
insertion/deinsertion performance. We have developed a new method for preparing
titanium-containing aqueous solutions using a reaction between metallic titanium powder
and 30 – 70 wt% aq. H2O2 (10). The yield solution is peroxo-polytitanic acid (titaniumisopolyacid, Ti-IPA), and the precipitates from the Ti-IPA solution are used as precursors
for not only titanium oxides but also titanium complex oxides such as BaTiO3.
In the present study, we investigated lithium insertion/deinsertion properties ofamorphous and nanocrystalline anatase titanium dioxides prepared by the new method
using Ti-IPA solutions. Furthermore, we also calculated the site energy distribution fromthe experimental charge/discharge curves using a numerical deconvolution technique,because the charge/discharge curves are the function of the energy distribution of lithium
insertion site in host materials.

Experimental
Sample Preparation
Metallic titanium powder (0.36 g, 45 µm particle size) was dispersed in 150 mL of 30
wt % aq. H2O2 solution at room temperature, and the dissolving reaction proceeded
mildly with the emission of oxygen gas. A yellow transparent solution of peroxopolytitanic acid (Ti-IPA) was obtained in 24 h. After removing insolubles, Ti-IPAsolution was dried at 115 °C for 24h to yield yellow powder. The yellow powder wasamorphous TiO2. By heating the amorphous TiO2 at 300 – 500 °C in air, we obtained
anatase TiO2.
Characterization
The powder XRD patterns of the products were measured with a diffractometer usinggraphite monochromatized Cu Kα radiation (λ= 0.15406 nm). The crystalline parametersof the anatase forms were refined by the Rietveld method using the RIETAN-FP (11).
The crystallite sizes were determined by the Scherrer equation. Each sample of 16.6 –16.7 mg was intimately ground with acetylene black (AB) at weight ratio of 1:1. The
TiO2/AB composite was mixed with polytetrafluoroethylene (PTFE) binder and pressed
onto a copper mesh for the lithium insertion/deinsertion measurements. The Ag/Ag+
electrode for non-aqueous solvent (RE-7, ALS Corporation Ltd., Tokyo, Japan) was used
as a reference electrode, and LiCoO2 with AB and PTFE as a counter electrode. A 1 M
LiClO4 ethylene carbonate (EC) / diethyl carbonate (DEC) solution (EC:DEC=1:1 involume) was used as an electrolyte. The measurements were carried out in thegalvanostatic mode at 3.0 mA (1.08 C) in the range 1.0 – 3.5 V (vs Li).

Results and Discussion
Crystal Structure and Lithium Insertion/Deinsertion Properties

Figure 1. Powder XRD patterns of titanium oxides prepared from Ti-IPA (peroxopolytitanic acid). 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.

TABLE I. Structural Parameters refined by the Rietveld Method and Crystallite Sizes. Tetragonal,Space Group; I 41 / amd (144). All occupancies are fixed at unity.
Heating Condition

Lattice Parameter

300 °C, 1 ha=3.789, c=9.512

300 °C, 5 ha=3.796, c=9.527

400 °C, 1 ha=3.793, c=9.521

400 °C, 5 ha=3.787, c=9.512

500 °C, 1 ha=3.786, c=9.515

500 °C, 5 ha=3.790, c=9.524

Site Coordinate andAtomic position
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

Crystallite Size
22 nm
25 nm
22 nm
26 nm
25 nm
27 nm

Figure 1 shows the XRD patterns of amorphous TiO2 obtained as the residue of TiIPA solution dried at 115 °C for 24 h and of nanocrystalline anatase TiO2 obtained byheating the amorphous TiO2 at 300 or 400 °C. Table I shows structural parametersrefined by the Rietveld method and crystallite sizes. The space group, I 41/amd, and thesite cooridinates were the same as that of the conventional anatase TiO2 (12,13). The
amorphous phase crystallized into the anatase form over around 300 °C. By theextension of heating time from 1 h to 5 h at 300 °C, the lattice parameter c was increased
from 0.9512 nm to 0.9527 nm, and the former parameter was close to the conventional
anatase form. The crystallite sizes of heating time 1 h and 5 h at 300 °C were 22 nm and25 nm, respectively, indicating that crystal growth hardly proceeds around 300 °C.
The amorphous TiO2 showed steep potential changes without plateau regions uponlithium insertion and deinsertion as shown in Figure 2 (a). The capacity was about 60
mAh/g much lower than the theoretical value 168 mAh/g. This indicates that the lithium
insertion sites in the amorphous phase are heterogeneous and more than half of them are
unsuitable for lithium insertion due to spatial or energetic reason. Figures 2 (b), (c) and(d) show charge/discharge curves of nanocrystalline anatase TiO2 obtained by heating at
300 °C for 1 h, at 300 °C for 5 h, and at 400 °C for 1 h, respectively. A plateau region
was observed in each charge/discharge curve, indicating homogeneous lithium insertion
sites. The capacity was increased from 109 mAh/g to 158 mAh/g with increasing theheating time from 1 h to 5 h. The capacity 158 mAh/g close to the theoretical value wasachieved at rather high rate 1.08 C using the nanocrystalline anatase TiO2 obtained at
300 °C for 5 h. Additionally, as shown in Figures 2 (e) and (f), the capacities of theanatase TiO2 obtained at 400 °C and 500 °C for 5 h were 143 mAh/g and 121 mAh/g,
respectively. Elevating the heating temperature resulted in the reduction of the capacity,
because crystal growth and aggregation to form secondary particles at elevating
temperatures are not favorable for the diffusion of lithium ion into and out of the particles.
We can say that heating the amorphous precursor at 300 °C is the most appropriate route
to prepare nanocrystalline anatase TiO2 for lithium insertion and deinsertion, because
crystal growth and aggregation are suppressed and lattice defects are reduced at 300 °C.

Figure 2. 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,5h; and (f) 500 °C, 5 h.

Theoretical Relationship between Site Energy Distribution and OCV Curves
The electrode potential E (vs. Li) of lithium insertion materials is determined by thechemical potential difference between the inserted Li in host electrode µ Li, host and the Li
metal electrode µ Li, metal. When we set the chemical potential of the Li metal electrodeµ Li, metal at zero, and consider the electrode potential E and the chemical potential of theinserted Li µ Li, host as a function of Li content x in host electrode, the electrode potential
isE (x) = −µ Li ,host (x )F,[1]where F is the Faraday constant. Thus, the theoretical OCV (open circuit voltage) curves
are derived by the calculation of the chemical potential of Li in host electrode as afunction of Li content x.

If the host material has insertion sites with homogeneous site energy ε (< 0) andtotal number N, and n sites among N are occupied by inserted Li, the internal energychange by the insertion is⊿U = nε,[2]

and the entropy change by the insertion is⊿S = k ln

N!
,n! ( N − n )!

[3]

where k is the Boltzmann constant. In the present case, ⊿H is considered to be equal to⊿U , because the volume change is negligibly small. The Gibbs energy change is⊿G = nε − kT ln

N!
.
n! ( N − n )!

[4]

The chemical potential µ Li, host is obtained by differentiating Eq. 4 with respect to nµ Li, host (x) = ε + kT lnx,1− x[5]where x = n/N (14). This equation bears close analogy to the Langmuir adsorption
isotherm.
Let us consider a host material whose site energy has a wide distribution. In case ofamorphous host materials, innumerable kinds of insertion sites exist and each site energy
is different from the other kinds of sites in varying degrees. The inserted Li is distributed
among the sites so that the chemical potential of Li in each site becomes equal to eachother.
If we denote each site energy by ε 1, ε 2, ε 3, ･･･ and the occupancy of each site by f1,f2, f3, ･･･, the chemical potential of Li in each site is equally given byµ = ε 1 + kT ln

f1
1 − f1f2= ε 2 + kT ln
1− f2
f3= ε 3 + kT ln
1 − f3･･･.

[6]

By transforming Eq. 6, we obtain
 µ − εi 
1 + exp −kT 
1fi =( i = 1, 2, 3, ･･･ ).

[7]

This equation indicates that the inserted Li obeys the Fermi distribution function in eachsite. 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 obtainn =ΣNi( i = 1, 2, 3, ･･･ ).
 µ − εi 
1 + exp −kT [8]

If we define a density function g (ε ) = dN (ε ) / dε by assuming Ni shows a continuous
distribution as a function of ε i, Eq. 8 givesn = ∫∞−∞g (ε )dε .
 µ −ε 
1 + exp − kT [9]

Eq. 9 is a theoretical derivation of OCV curves, because the capacity corresponds to nand the potential to －µ /e. It is interesting to note that the capacity is a convolution of
the density function g (ε ) and the fermi function
f (x) =as1,
 x 
1 + exp − kT n (µ) = ∫ f (µ − ε )g (ε )dε .
∞−∞

[10]

[11]

Thus, we can calculate the density function g (ε ) from the OCV curve using adeconvolution method. In dataprocessing, 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 of n (µ) is the product of matrices denoting f (x) and g (ε ),we obtain the dataset of g (ε ) by multiplying an inverse matrix of f (x) with the dataset ofn (µ). We calculated the inverse matrix of f (x) by the Gauss - Seidel method so as toyield the dataset of g (ε ).

Energy Distribution Curve of Lithium Insertion Sites Calculated from Discharge Curve
Figure 3 shows energy distribution curves of lithium insertion sites calculated fromthe discharge curves using Eq. 11. The abscissa is proportional to the number ofinsertion sites and the peak area is proportional to the total number of insertion sites. The
nanocrystalline anatase TiO2 had uniform site energy distributions around 2.1 V,
indicating that the insertion sites are homogeneous in the nanocrystalline anatase form.
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. Our results indicate that the amorphous phase has a
disadvantage in lithium insertion and deinsertion, because the insertion sites areenergetically and spatially heterogeneous. Here we demonstrate that energy distribution
curves are numerically calculated from discharge curves and very useful to discuss therelationship between crystal structures and discharge properties.

Figure 3. Energy distribution curves of lithium insertion sites calculated by the numericaldeconvolution of the discharge curves.

ConclusionsAmorphous and nanocrystalline anatase TiO2 were prepared through a new routeusing peroxo-polytitanic acid (Ti-IPA). The capacity of anatase TiO2 with average
particle size of 25 nm prepared by heating the amorphous precursor at 300 °C for 5 h was
158 mAh/g at rather high rate 1.08 C. Elevating the heating temperature to 400 °C or
500 °C resulted in the reduction of the capacity. Heating at 300 °C is favorable forlithium insertion and deinsertion, because crystal growth and aggregation to form
secondary particles are suppressed and lattice defects are diminished. We also presented
a theoretical discussion on the relationship between energy distribution of insertion sites
and discharge curves, and developed a numerical calculation method of the energy
distribution of insertion sites from the discharge curves. The nanocrystalline anatase

TiO2 showed uniform site energy distributions reflecting the homogeneous insertion sites,
whereas the amorphous phase had a broad energy distribution reflecting theheterogeneous structure. The energy distribution curves calculated from the discharge
curves will be very useful to discuss the insertion sites in crystal structures.

Acknowledgments
The authors are grateful to Prof. Tetsuichi Kudo for helpful advice and to Messrs.
Kazuki Iwata and Kazuki Sakamoto for their assistance in the preliminary experimentsof this work.

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