Preparation and spectroscopic characterization of quantum-size titanium dioxide

Zhang Yuhong , Wu Ming , Xiong Gouxing , Yang Weishen
(State Key Laboratory of Catalysts, Dalian Institute of Chemical Physics,The Chinese Academy of Sciences, Dalian 116023, China)

Received Nov. 24, 1999; Supported by the National Natural Science Foundation of China (Grant No. 29873050) and the Chinese Academy of Sciences (Grant No. KJ951-A1-505).

Abstract A new method for the preparation of TiO₂ sol by directly peptizing commercial powder has been reported in this paper. It was found that the particle size which was defined by atomic force microscopy (AFM) could be controlled effectively by acidity of the peptized solution. Their absorption spectra showed a typical Q-size effect and two pronounced exciton peaks at 260nm and 310nm, respectively. A strong fluorescence peak at 340nm could be assigned to the transition of the surface Ti-OH groups, suggesting the existence of abundant surface hydroxy groups on the surface of the small TiO₂ particles. The relationship between the bandgap and particle size was also discussed through several calibration curves obtained from quantum mechanical calculations.
Keywords sol-gel, titanium dioxide, quantum-size, UV-absorption, fluorescence

1.INTRODUCTION
TiO₂ is a semiconductor that has been often investigated in photoelectro-chemistry and photocatalysis ^[1]. The understanding of its photophysical and photochemical properties in aqueous media is of particularly interest because of its extensive application in the detoxification of polluted ecosystems ^[2].
    It has been known that the electronic band structure of a semiconductor oxide is size dependent when its dimension is comparable with the exciton (Bohr) radius (the so-called Q-size effect). The development of the preparation and stabilization method for monodispersed semiconductor nanoparticles in transparent colloids is very important as offering a nice opportunity of experimental verification for theoretical predictions. Systematic studies of the size-dependence of the photo-properties of TiO₂ sol, however, have not kept pace with the studies in heterogeneous photocatalysis where TiO₂ play a significant role. The preparation of quantum-size (< 3nm) TiO₂ colloidal particles was reported by Kormann et al ^[3] where a blue shift of the UV absorption edge was observed with the decrease of the particle size. Anpo et al ^[4] had reported the preparation and thereafter the properties of TiO₂ powders with controlled particle size in the range of 5.5-200nm (rutile) and 3.8-53nm (anatase). They have found distinct Q-size effects even for relatively large crystallites, for instance, the band gap increased by 0.07 eV relative to the bulk bandgap (3.0 eV) for 12-nm-sized rutile particles and about 0.16eV relative to the bulk value of 3.2eV for 3.8-nm-sized anatese particle.
    In this article we describe a method for the preparation of colloidal TiO₂ solution with different particle size from a commercial powder. Their Q-size effects were shown by UV-vis absorption and fluorescence spectra. The relationship between the particle size and the wavelength of the absorption threshold was discussed in more detail by several calibration curves obtained from quantum mechanical calculations.
2.EXPERIMENTAL
Commercial powder TiO₂ assigned as T-25 in this paper (made by Taixing, China) in deioned water was hydrated for 1 hour, then was peptized with HCl solution followed by refluxing for 48 hours under vigorous stirring at 30^oC. After filtering off the unpeptized powder, an aqueous colloidal solution was obtained. This colloidal solution was stable for weeks at room temperature.
    Particle sizes were determined by atomic force microscopy (AFM). UV-vis absorption spectra were recorded on HITACHI 200-10 spectrophotometer equipped with an integrating sphere accessory for diffuse reflectance and transmission measurement. Fluorescence spectra were measured by exciting samples with a 280nm light beam on a HITACHI MPF-4 fluorescence spectrophotometer.
3. RESULTS AND DISCUSSION
3.1 Preparation of colloidal TiO₂
T-25 powder is commercial TiO₂, which contains mainly anatase structure and only a few rutile as defined by XRD analysis. The UV-vis absorption and fluorescence spectra of T-25 powder were shown in Figure 1. A broad absorption continuum appears at the range 420nm to 200nm. The onset of absorption is about 410nm, approaching the energy gap of bulk rutile TiO₂ (3.0eV, 410nm). This probably results from a few rutile in T-25 powder. The fluorescence spectrum shows a broad continuum at 400nm, which belongs to the fluorescence of Ti-O bond ^[5], and another weak peak at 340nm. Spectral assignments will be discussed in the following section. All the above results suggest that the physical and chemical properties of T-25 powder are similar to those of bulk TiO₂ (anatase: E_g=3.2ev,l_onset=388nm; rutile: E_g=3.0ev, l_onset=410nm).

Fig.1 The absorption and fluorescence spectra of T-25 powder

    During the preparation process, the size and the stability of colloidal particles are determined by several factors such as the acid type, acidity (H⁺/Ti mole ratio) and temperature. Four samples named T-1, T-2, T-3 and T-4 were prepared when H⁺/Ti mole ratio was 1.2, 1.0, 0.7 and 0.4, respectively. The particle size could be effectively controlled by acidity in the peptized solution ^[6]. The particle size of TiO₂ sol decreases with the increase of H⁺/Ti ratio. Moreover, the transparency of these samples T-1 to T-4 became worse and worse, providing further evidence that the particle size decreases with the increase of H⁺/Ti ratio.
    In order to prove this point, we measured the exact particle size of T-1 and T-4 samples by AFM (see to Fig.2). Fig.2a is the AFM pictures of sol particles. Fig.2b shows the size distribution of T-1 and T-4. The mainly particle size of T-1 is 1.2nm while that of T-4 is 10.8nm. Their size distributions are both uniform, but the distribution range of T-4 is broader than that of T-1. The particle size of T-1 is in the range of 0.2-2.3nm while T-4 has a particle size in the range of 5-30nm. We thus concluded that the acidity (H⁺/Ti mole ratio) should be one important factor in controlling the size of sol particles.

(a)
(b)	Fig.2 (a) AFM characterization and (b) height histogram of sample T-1 and T-4

3.2 UV-vis absorption spectra
Figure 3a shows the UV-vis absorption spectra of TiO₂ colloids obtained with different particle size. The absorption of TiO₂ sol has significant difference from that of T-25 powder. The onset of absorption was obtained by extrapolating the steep part of the rising absorption curve. The onsets of absorption of T-1, T-2, T-3 and T-4 appear at l_onset=342nm, 348nm, 359nm and 369nm, respectively, which exhibit large blue shifts relative to the onset of bulkanatase (l_onset=388nm). Moreover, the onset (l_onset) is more and more rapidly shifted toward shorter wavelength with the increase of the H⁺/Ti mole ratio. It is interesting that two pronounced peaks appear at 260nm and 310nm, respectively, and also their sites keep uncharged with different samples. However, the relative contents of the two peaks vary with the samples (see to the fitted curves in Fig. 3a). When the particle size is smaller, the relative content of peak at shorter wavelength 260nm becomes higher.
The absorption onsets of the four different colloids are shifted by 0.4~0.2eV with respect to the absorption onset of the TiO₂ anatase crystalline phase. In principal, this could be due to the small quantum size of our colloidal particles whose radii are comparable to the exciton Bohr radius. It is well known that the concentration of colloids and the variety of solvent affect the onset of absorption. Kormann ^[3] found that neither variation of the concentration nor dialyzing of TiO₂ colloid solution has any effect on the curve of lnα versus the photon energy, E. Figure 3b shows the plot of lnα versus the photon energy, E=hcl^-1, for the four samples. The absorption coefficient α has been calculated from the measured absorbance (A) via
　
where p stands for the density of TiO₂, 3.9 g.cm^-3; M, the molecular weight, 79.9 g.mol^-1; c, the molar concentration of TiO₂ and l is the optical path length. The linear partition of curves of colloids was found between ln α =8 and ln α =13. Urbach’s rule suggests to use the values between ln α =6 and 10 for the determination of semiconductor bandgaps. Taking these curves, the linear partition of T-1 and T-2 is between ln α =8.7 and ln α =9.4 (the circles in Fig. 3b), and the bandgaps of T-1 and T-2 are calculated in 3.4eV and 3.3eV, respectively. However, for T-3 and T-4 samples, the onsets of linear partition are not obvious and a continual curve appears between ln α =6 and ln =10, which suggest that the bandgaps of T-3 and T-4 are about 3.0eV. Therefore, we can conclude that a TiO₂ colloid prepared by H⁺/Ti=1.2 has particle sizes small enough to result in a bandgap shift of 0.2ev without solvent effect.

(a)	Fig.3 (a) Absorption spectra (solid lines) and fitted-cruves (dashed lines) of TiO2 colloids and (b) absorption spectra of TiO2 colloids deducting the solvent effect.
(b)

    In addition, it is notable that the photon energy corresponding to the two inflection points (see the arrow in Figure 3b) is same as the energy of the two pronounced peaks at 260nm and 310nm respectively in the absorption spectra. Moreover, their sites in the absorption spectra do not show difference even for the different samples. Henglein ^[7] suggested that the maxima which appeared in the absorption spectrum of very small particles (Figure 3a) corresponded to the optical transition to the first excited state in quantized particles of different size and thus to the "magic" agglomeration numbers existed in the size distribution of the sample. This suggests that two agglomeration numbers exist in our colloids, which produce two kinds of primary particle corresponding to two peaks in optical absorption. With the decrease of the H⁺/Ti ratio, the particles including larger agglomeration number increase so that the contents of peak at 260nm decrease.
3.3 Fluorescence spectra
Fluorescence spectra recorded in colloidal samples are presented in Figure 4. The emission increases sharply after 330nm and reaches a maximum at 340nm. A broad and weak peak appears at 370nm. The spectra extend to 500nm. The relation of the relative content of the two peaks is same as the results of the absorption spectra.
    Fluorescence has been described as transitions from surface states. Among the three crystalline polymorphs: rutile, anatase and brookite, the nature and spectral position of anatase have not come to a common conclusion and agreement. Broad asymmetric UV emission at 375nm (Dl_fwhm=100nm) has been observed in  m m-size anatase colloids ^[8]. In recent publication ^[9], more complex fluorescence spectra of TiO₂ colloidal nanoparticles in the range between 300 and 500nm have been observed.
    As one can see that only in UV range, two fluorescence continual peaks have been observed in our samples. It is reasonable to assign the UV emission spectrum observed at 370nm in the present study to interband transitions. The excited state of TiO₂ can be considered as Ti³⁺...O^- and the emission may be due to electron exchange leading to Ti⁴⁺. Another fluorescence of TiO₂ at 340nm has not been reported. In many hydroxides, a fluorescence peak at 340nm usually appears if 280nm excitation is used, while this continuum disappears in corresponding oxides. So we suggest that the fluorescence at 340nm results from the transition of surface Ti-OH bond.
    Since emission is mostly a particle surface phenomenon, differences in emission intensities must originate from differences in surface properties of the particles. In figure 4, the decrease of the content of peak at 340nm indicates that the surface hydroxy groups decrease with the increase of the particle size. Comparatively, the peak intensity at 340nm is stronger than that of T-25 powder, suggesting that the Ti-OH groups are rich in our colloids.

Fig.4 Fluorescence spectra (solid lines) and fitted-cruves (dashed lines) of TiO₂ colloids
3.4 Quantum mechanical calculations
Quantum mechanical calculations of the band gap shift in small semiconductor particles were first made by Efros ^[10] and Brus ^{[11, 12]}. Brus has described the analytical formula based on effective mass approximation (m_{e, h}=const):

where E_g and E_g^s are the particle and solid-state band gap energies; R is radius of the particle;  m ^-1=m_e^*-1+m_h^*-1 is the reduced mass of the exciton, here m_e^* is the effective mass of the electron and m_h^* is the effective mass of the hole; e is dielectric constant of the material. Another approach based on quantum mechanical variation calculation has been described by Kayanuma:^[13]

    In this paper, the dielectric constant e =12^[14] and the electron and hole masses of 10m_e and 0.8m_e^[14], respectively (where m_e is a free electron mass), have been used. The calculated calibration curves are presented in Figure 5. Anpo's results ^[4] (+ ) and our experimental point ( with solvent effect and n deducting solvent effect) are given in Figure 5. The calculated results are used to compare with our results of AFM and Anpo's results. Experimental results with solvent effect deviate to the calculations by Kayanuma and Brus. After excluding the effect of solvent, our experimental results are in agreement with theoretical predictions by Brus (dashed line), though they deviate to the calculation described by Kayanuma (solid line).

Fig.5 Calibration curves lonset(R): according to the Kayanuma's variational calculation (solid line); according to Brus formula (dashed line); Anpo's result (+) and our experimental point (. with solvent effect and n deducting solvent effect).

4. CONCLUSION
A small and stable TiO₂ sol can be obtained by peptizing commercial TiO₂ powder. The particle size can be effectively controlled by acidity of the peptized solution. The smallest particle size is 1.2nm in H⁺/Ti=1.2 measured by AFM. Small TiO₂ particles show typical Q-size effects. The onset of UV-vis absorption shifts to shorter wavelengths with the decrease of the particle size, and the exciton energy becomes pronounced. A fluorescence peak appeared at 340nm is assigned to the transition of surface Ti-OH groups. Moreover, their intensities are consistent with size distribution. In addition, our results are in agreement with the quantum mechanical calculations by Brus.

ACKNOWLEDGMENT
We are also with to express our thanks to Dr. Xiaohui Qiu for AFM experimental assistance.

REFERENCES
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