Acid Adsorption on TiO2 Nanoparticles—An Electrochemical

May 3, 2008 - Sangwook Lee , In-Sun Cho , Ji Hae Lee , Dong Hoe Kim , Dong Wook Kim , Jin Young Kim , Hyunho Shin , Jung-Kun Lee , Hyun Suk Jung ...
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8476

J. Phys. Chem. C 2008, 112, 8476–8480

Acid Adsorption on TiO2 NanoparticlessAn Electrochemical Properties Study Hyun Suk Jung,† Jung-Kun Lee,*,‡ Sangwook Lee,§ Kug Sun Hong,§ and Hyunho Shin| School of AdVanced Materials Engineering, Kookmin UniVersity, Jeongneung-dong, Seongbuk-gu, Seoul 136-702, Korea, Department of Mechanical Engineering and Materials Science, Pittsburgh UniVersity, Pittsburgh, PennsylVania 15261, School of Materials Science and Engineering, Seoul National UniVersity, Shillim-dong, Seoul, 151-744, Korea, and Department of Ceramic Engineering, Kangnung National UniVersity, Kangnung, 210-702, Korea ReceiVed: December 12, 2007; ReVised Manuscript ReceiVed: March 10, 2008

The surface of TiO2 photoelectrode was treated by dipping in nitric acid and subsequently coating with solar light absorbing dye. The influence of surface-modified photoelectrodes on the performance of dye-sensitized solar cells (DSCs) was investigated. The nitric acid treatment of the photoelectrode increased DSC energy conversion efficiency from 5.4 to 6.2%, which is mainly attributed to the increase in the photocurrent rather than the change in the open circuit voltage. The comparative studies were done using hydrochloric acid treated TiO2 photoelectrode. This demonstrates that the nitric acid treated photoelectrode retards back electron transfer at the interface with the electrolyte and increases the amount of adsorbed dyes. X-ray photoemission and Fourier transform infrared spectroscopy studies show that the effect of the nitric acid treatment is due to the presence of residual nitrate ions and hydroxyl groups which decrease free surface area and strengthens physical adsorption of dyes. Introduction Dye-sensitized solar cells (DSCs) have received a vast amount of interest as a promising alternative to conventional photovoltaic devices due to their high efficiency and low production cost.1 The advanced solar cell performance has been achieved by extensive studies on optimization of dyes, semiconductor films, and redox electrolytes.2–5 One of the promising methods for improving DSC efficiency is to modify the surface of a semiconducting photoelectrode. For example, the energy conversion efficiency of the cell has been improved by employing a thin coating layer of various oxides on the TiO2 surface.6,7 The thin coating layer, which has a higher conduction band edge than TiO2, has been reported to retard the charge recombination between injected electrons and electron acceptors such as I3- ions. Another effective approach for the modification of TiO2 surface is to treat TiO2 photoelectrode with acid.8–10 However, the effect of acid treatment on DSC performance is still controversial. Hao et al.10 reported that the acid treatment of TiO2 photoelectrode was detrimental in overall energy efficiency of DSC. The 0.1 M HCl treatment of TiO2 photoelectrode reduced short circuit current density (Jsc). In contrast, Wang et al.8 showed that the 0.1 M HCl treatment enhanced Jsc, thereby improving the energy efficiency. The benefits of acid treatment were explained as the protonation effect that facilitates dye adsorption and suppresses back electron transfer to electrolytes.8 Other acid (e.g., H2SO4, HAc, and H3PO4) treatments also showed the different effects on the solar cell performance.8,10 These previous studies give rise to a demand for unveiling the correlation between the surface structure of acid-treated TiO2 photoelectrode and the * To whom correspondence should be addressed. E-mail: jul37@ engr.pitt.edu. † Kookmin University. ‡ Pittsburgh University. § Seoul National University. | Kangnung National University.

DSC performance. Although the protonation was generally suggested to be a reason of treated by various acid treatments, the surface structure of acid-treated TiO2 photoelectrode and related functional properties were not fully understood. In particular, the effect of anions on the surface of TiO2 has been relatively ignored. Given that anion groups can be adsorbed on the surface, more investigation on surface structure of TiO2 using various characterization tools is required to understand the effect of acid treatment on energy conversion efficiency on DSC. In the present study, we demonstrate that a change in surface structure of TiO2 photoelectrode by nitric acid treatment improved energy conversion efficiency of DSC. The comparative study using a HCl-treated photoelectrode was done to separate the role of anion groups from that of the protonation and to understand the efficiency improvement mechanism of DSC underlying anion adsorption effect. The surface of the photoelectrodes was analyzed using surface characterization tools including X-ray photoelectron spectroscopy (XPS) and Fourier-transform infrared (FTIR) spectroscopy, which clearly shows that the residual anion groups affect the functional properties of the photoelectrode. Experimental Section Preparation of TiO2 Photoelectrodes. TiO2 photoelectrodes were prepared using nanocrystalline TiO2, which was synthesized with the method described in the Supporting Information. TiO2 films (0.5 cm × 0.5 cm) were screen printed on transparent conducting glass (F-doped tin oxide, Pilkington, England) with a size of 1.5 cm × 2 cm. The screen-printed films were dried at 80 °C and then were annealed at 450 °C for 1 h. The thickness of the TiO2 electrode was approximately 12 µm as measured by an R-step apparatus. We used a modified acid treatment method proposed by Wang et al.11The TiO2 films were immersed in a 0.1 M HCl and HNO3 solution in deionized water for 10 min, respectively. The bare TiO2 films were immersed in deionized water for balancing experimental conditions of acid

10.1021/jp711689u CCC: $40.75  2008 American Chemical Society Published on Web 05/03/2008

Acid Adsorption on TiO2 Nanoparticles

J. Phys. Chem. C, Vol. 112, No. 22, 2008 8477 TABLE 1: Cell Parameters of the DSCs Based on Bare TiO2 and HCl-Treated and HNO3-Treated TiO2 Electrodes

Figure 1. Photocurrent-voltage curves of DSCs, composed of the bare, HCl-, and HNO3-treated TiO2 photoelectrodes.

treated photoelectrodes. Consequently, the films were rinsed with water and dried at 70 °C. Photovoltaic Measurements. The bare, HCl-treated, and HNO3-treated TiO2 photolectrodes were dipped in the solution of N3 dye [ruthenium(2,2’bipyridyl-4,4′-dicarboxilate)2(NCS)2, SOLARONIXTM, Switzerland, dissolved in ethanol] at 50 °C for 2 h. Then, the dye-adsorbed electrode was assembled with a Pt counter electrode to form a sandwich-type dye-sensitized solar cell. A drop of electrolyte solution (Iodolyte AG-50, SOLARONIXTM, Switzerland) was infiltrated between the two electrodes of the cell. Photovoltaic properties and electrochemical impedances of the fabricated solar cells were measured under the illumination of air mass 1.5 (ORIEL 91193 1000 W xenon lamp; intensity: 100 mW/cm2) with the aid of a potentiostat (CHI 608C, CH Instruments). Impedance of the cells under 100 mW/cm2 illumination and reversely biased open circuit voltage was also measured by a potentiostat (CHI 608C, CH Intruments). Characterization. Surface states of the TiO2 films were analyzed using XPS (model: SIGMA PROBE, ThermoVG, U.K). The XPS spectra were acquired using monochromatic Al KR (100 W), and the binding energy of the O (1s) peak was calibrated with respect to the C (1s) peak at 284.6 eV. The TiO2 powders, which were taken from the prepared photoelectrodes, were mixed with KBr and pressed into pellets for IR spectroscopy analysis. IR transmittance spectra in the range of 1000-2000 cm-1 were measured at room temperature using a FTIR spectrometer (Bomem, Model DA8-12, Canada). The dye molecules were desorbed from photoelectrodes by soaking then in alkaline alcoholic solutions. The optical absorption of the dye solutions was also characterized to compare the degree of adsorbed dye molecules by using a UV-vis spectrophotometer (Perkins-Elmer, U.S.A.).

sample

Voc (V)

Jsc (mA/cm2)

FF (%)

η (%)

bare TiO2 HCl-treated TiO2 HNO3-treated TiO2

0.65 0.64 0.65

12.9 13.7 14.8

64.5 65.2 64.5

5.4 5.7 6.2

is 12.9 mA/cm2. The Jsc of HCl-treated photoelectrode is 13.7 mA/cm2 in between the bare and HNO3-treated ones. The open circuit voltage (Voc) and fill factor do not change significantly after the acid treatment. The Voc of the bare and HNO3-treated photoelectrodes is approximately 0.65 V, and that of HCl treated one is 0.64 V. These results indicate that the increase in Jsc is responsible for the improvement in the overall energy conversion efficiency and that the HNO3 treatment is more effective in improving the solar cell performance than the HCl treatment. To understand the origin of the increase in Jsc, dye-adsorptive characteristics of TiO2 photoelectrodes were investigated. Figure 2 shows UV-vis absorption spectra of solutions in which dye molecules from bare, HCl-, and HNO3-treated TiO2 photoelectrodes were dissolved. The absorbance of 540-nm peaks associated with metal-to-ligand charge-transfer (MLCT) is larger for the HCl- and HNO3-treated TiO2 photoelectrodes than for the bare TiO2. The absorbance of the dye solution from the HCland HNO3-treated photoelectrodes is almost identical. This change in the UV-vis absorption indicates that the amount of adsorbed dye of the HNO3- and HCl-treated photoelectrode is larger than that of the bare photoelectrode by about 10% The enhancement in dye adsorption has been suggested to result from surface protonation.8,12 The acid treatment changes the surface of TiO2 nanoparticles to be positively charged. Then, the electrostatic attraction between the negatively charged end of dye molecules and the positively charged TiO2 surface strengthens their bond and increases the amount of dye molecules adsorbed on the photoelectrode.8 Since HNO3- and HCl-treated photoelectrodes show the similar level of the increase in the dye adsorption, the protonated surface is attributed to be the origin for it. Figure 3 illustrates XPS spectra of O (1s) from bare, HCl-, and HNO3-treated TiO2 photoelectrodes. The O (1s) spectrum is composed of two peaks whose binding energies are 530.2 eV (Ti-O) and 532.0 eV (Ti-OH).13 A new peak of 532.0 eV is observed in both the HCl and HNO3 treated TiO2 photoelectrodes, indicating that the TiO2 surface is significantly hydroxylated and protonated by the acid treatment.13 The almost same intensity of OH peaks in Figure 3 show that HNO3 and HCl treatments have the similar effect on the surface protonation of

Results and Discussion Photocurrent-voltage curves of DSCs using the bare, HCl-, and HNO3-treated TiO2 nanoparticles are compared in Figure 1. A HNO3-treated TiO2 photoelectrode shows the best solar cell performance; the cell efficiency is increased from 5.4 to 6.2% by using HNO3-treated nanoparticles. HCl treatment also shows the improvement of energy conversion efficiency. However, it is noted that the increase in cell efficiency for the HNO3-treated TiO2 photoelectrode is more significant than that for the HCl-treated one. As summarized in Table 1, the short circuit current density Jsc for the HNO3-treated photoelectrode increases to 14.8 mA/cm2, while that of the bare photoelectrode

Figure 2. UV-vis absorption spectra of the desorbed dye solution from bare, HCl-, and HNO3-treated TiO2 photoelectrodes.

8478 J. Phys. Chem. C, Vol. 112, No. 22, 2008

Figure 3. XPS spectra of O (1s) from bare, HCl-, and HNO3-treated TiO2 photoelectrodes.

Figure 4. Impedance spectra of DSCs employing the bare, HCl-, and HNO3-treated TiO2 photoelectrodes: (a) Nyquist and (b) Bode plots.

TiO2 nanoparticles and the enhancement of dye adsorption, which explains the results of Figures 1 and 2 consistent with previous studies. We note that the protonation effect does not fully explain the solar cell performance in Figure 1. Although the enhancement of dye adsorption by HCl and HNO3 treatments was similar, the HNO3 treatment increases Jsc more effectively. Since the amount of adsorbed dye determines the number of carriers produced by light irradiation, HCl- and HNO3-treated photoelectrodes must have the same capability in making photogenerated carriers. However, the short circuit current (Jsc) is different, which implies that the efficiency in transferring carriers to the external load is affected by the kind of surface treating acid. Impedance analysis of solar cells composed of bare, HCl-, and HNO3-treated TiO2 photoelectrodes was performed at Voc of each cell under illumination. Figure 4a shows Nyquist plots of DSCs. Three arcs are observed in the frequency regime of 103-105 (ω1 or ω2), 1-103 (ω3), and 0.1-1 (ω4) Hz, from left to right. These arcs are associated with resistances at conducting layer/TiO2 (ω1) or Pt/electrolyte interface (ω2), TiO2/dye/ electrolyte interface (ω3), and diffusion of I3-/I- redox electrolyte (ω4), respectively.14,15 Identical ω1/ω2 semicircles for three samples indicate that HCl and HNO3 treatment do not impact the charge transfer at either FTO/TiO2 or Pt/electrolyte interface. In addition, no change in ω4 arcs is expected because only TiO2 nanoparticles are treated with HCl or HNO3 acid

Jung et al.

Figure 5. FT-IR spectra of bare, HCl-, and HNO3-treated TiO2 powders. The HNO3 treated TiO2 powder, which was subsequently dye adsorbed, is also plotted.

before fabricating the solar cells. It is interesting that the ω3semicircle of HNO3 treated solar cell gets larger than the HCl treated and bare photoelectrodes. At open circuit, the electrons which are injected from the adsorbed dye to the TiO2 nanoparticles partially accumulate at the interface of TiO2/dye/electrolyte and react with the electrolyte, thereby decreasing the impedance of ω3.14 Therefore, the larger ω3 of HNO3-treated photoelectrode shows that the recombination of photogenerated electrons with the electrolyte by the backward transfer is retarded by the HNO3treatment. The electrons produced by the dye are extracted to the external load rather than being consumed at the interface of TiO2/dye/electrolyte.8,14 Figure 4b illustrates Bode plots of DSCs with bare, HCl-, and HNO3-treated TiO2 photoelectrodes. Two peaks associated with the transfer of the photogenerated electrons at the surface of TiO2 nanoparticles and the conducting electrodes, are clearly observed. The trace of the peak below 1 kHz is due to Nernstian diffusion in the electrolyte. The overall shape of Bode plot is consistent with the Nyquist plot of Figure 4a. The frequency of the maximum phase shift in the midfrequency peak ranging from 1 to 1000 Hz is inversely proportional to the electron lifetime that is determined by the backward transfer of electrons to the electrolyte. The peak frequency of HNO3 treated photoelectrode is 30% smaller than that of bare photoelectrodes. This indicates that the HNO3 treatment increases the electron lifetime by 30%, which is ascribed to the surface adsorption of nitrate ions and the retarded reaction of the electrons with I3- in the electrolyte.15 We investigated TiO2 surfaces to understand the origin of the retarded backward transfer in the HNO3 treated TiO2 photoelectrode by using FT-IR measurements. Figure 5 presents FT-IR spectra of bare, HCl-, and HNO3-treated TiO2 powders, which are the materials of the photoelectrodes. The combined effect of the HNO3 treatment and following dye adsorption is also measured by FT-IR. The increase in the peak of 1624 cm-1 (HOH bending mode) from both HCl and HNO3 treated TiO2 supports that the surface of TiO2 nanoparticles is hydroxylated and protonated during the acid treatment. This is in good agreement with XPS data in Figure 3 and previous research by Wang et al.8 It is noteworthy that the HNO3-treated TiO2 powder exhibits a sharp and intensive peak at 1385 cm-1, which is associated with the presence of NO3- group.16 The FT-IR spectrum exhibit that a large amount of NO3- group as well as protons is adsorbed on the TiO2 surface during HNO3 treatment. HNO3 reaction on TiO2 particles has been reported as an irreversible and dissociative process forming surface nitrate, which is not removed under vacuum.17 In this study, newly

Acid Adsorption on TiO2 Nanoparticles

J. Phys. Chem. C, Vol. 112, No. 22, 2008 8479

Figure 6. Schematic diagram of NO3- ions adsorbed on to the TiO2 photoelecrode. (proton ions are not illustrated in this figure).

formed surface nitrate group also makes a strong bond with the TiO2 surface and the peak of NO3- groups still remains after the HNO3 treated TiO2 powder are soaked in the dye solution and are annealed at 300 °C (Supporting Information). In contrast, a peak related to the Cl- ion is not found in the FT-IR spectrum of HCl-treated TiO2. The adsorption strength of Cl- ions on TiO2 is relatively weaker than that of NO3ions.18 In the previous study, we also found that the residual Cl- ions of TiO2 nanopowders, synthesized from TiCl4 were removed after washing.19 Figure 6 illustrates the surface of the TiO2 nanoparticles after HNO3 treatment and dye adsorption. HNO3 treatment makes the surface of the TiO2 nanoparticles be covered by protons and HNO3. Since a carboxyl group (-COO-) in a dye molecule has stronger anchoring affinity with the surface of the of TiO2 than an NO3- group, the pre-existent nitrate ions do not prevent the dye adsorption process.8 Given that 72% of the surface of the bare TiO2 is covered by N3 dye, a part of surface NO3- is replaced by the N3 dye molecules.9 However, tiny NO3- molecules can still stay on the significant portion of the surface of the HNO3-treated TiO2 where the bulky dye molecules do not fit well. The occupation area of a single dye molecule is 1.3 nm2, while that of a single NO3- ion is about a few angstroms.2,9,20 We believe that the coverage of NO3- ions on TiO2 surface blocks the path of the electron backward transfer, thereby improving the solar cell performance. The effect of anion adsorption is previously reported. Murayama and Mori have shown that the carboxylic molecules that are adsorbed on TiO2 surface block the backward electron reaction, which demonstrates that the anion adsorption is effective in retarding back electron reaction.9 Since the Cl- ion is not adsorbed strongly on the surface of TiO2, the similar improvement in the cell performance is not observed in the HCl-treated TiO2. The lifetimes of electrons in the bare and the HNO3 treated TiO2 photoelectrodes were measured to confirm the correlation between the NO3- ions adsorption and the retarded back electron transfer. Figure 7 presents the carrier lifetimes for the bare and HNO3-treated TiO2-based DSCs, which were obtained from the decay of Voc as a function of time (the inset of Figure 7).21 These data demonstrate that carrier lifetime of HNO3-treated TiO2-based DSC is significantly improved, suggesting the suppressed back electron transfer of the NO3- ion adsorbed TiO2. The retardation of back electron transfer can improve Voc as well as Jsc.22 However, the change in Voc was observed after the acid treatment, as shown in previous studies on the acid treament.8,23 Wang et al.8 suggested that surface protonation, induced by acid treatment, leads to the positive shift of a TiO2 flat band and counterbalances the increase in the Voc by the enhanced dye adsorption.24 The positive shift of TiO2 flat band reduces the energy difference between the redox potential of electrolyte and Fermi level of electrons, thereby decreasing the upper limit of Voc.8 Therefore, there is a compromise of three

Figure 7. Electron lifetimes as a function of Voc for the bare and HNO3treated TiO2-based DSCs.

changes in dye adsorption, electron backward transfer, and flat band potential, maintaining Voc to be the same. We measured the flat band potentials of bare and HNO3-treated TiO2 photoelectrodes and observed the significant positive shift of flat band potential by the HNO3 treatment. This result confirms that the increase in Voc due to the enhanced dye adsorption and the retardation of back electron transfer in the HNO3-treated photoelectrode is nullified by the positive shift of the flat band. In summary, the improved energy conversion efficiency of DSC was achieved by a simple acid treatment of TiO2 photoelectrode. The acid treatment was found to enhance Jsc of solar cell, ascribed to enhancement in dye adsorption by surface protonation. Especially, the energy conversion efficiency of HNO3 treated DSC was superior to that of the HCl-treated one. A comparative study on HCl- and HNO3-treated photoelectrodes demonstrates that the benefit of HNO3 treatment is to suppress backward electron transfer by uptaking NO3- anions on TiO2 surface, thereby collecting more charge carriers. These results indicate that the anion adsorption on TiO2 surface as well as surface protonation is also effective to improve the performance of TiO2-based DSCs. Acknowledgment. This work was supported by the ERC (CMPS, Center for Materials and Processes of Self -Assembly) program of MOST/KOSEF (R11-2005-048-00000-0) and the new faculty research program 2006 of Kookmin University in Korea. This work was also supported by Seoul R&BD Program and the Korea Science and Engineering Foundation (KOSEF) grant funded by the Korean government (MOST) (R01-2007000-11075-0). Supporting Information Available: Preparation of TiO2 nanocrystyals, FT-IR spectra of HNO3-treated TiO2 powders, and Mott-Schottky plots of bare and HNO3-treated TiO2 electrodes. This information is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) O’Regan, B.; Gra¨tzel, M. Nature 1991, 353, 737. (2) Nazeeruddin, M. K.; Pe´chy, P.; Renouard, T.; Zakeeruddin, S. M.; Humphry-Baker, R.; Comte, P.; Liska, P.; Cevey, L.; Costa, E.; Shklover, V.; Spiccia, L.; Deacon, G. B.; Bignozzi, C. A.; Gra¨tzel, M. J. Am. Chem. Soc. 2001, 123, 1613. (3) Adachi, M.; Murata, Y.; Takao, J.; Jiu, J.; Sakamoto, M.; Wang, F. J. Am. Chem. Soc. 2004, 126, 1613.

8480 J. Phys. Chem. C, Vol. 112, No. 22, 2008 (4) Park, N. G.; Kang, M. G.; Kim, M. K.; Ryu, K. S.; Chang, S. H.; van de Lagemaat, J.; Benkstein, K. D.; Frank, A. J. Langmuir 2004, 20, 4246. (5) Kambe, S.; Nakade, S.; Kitamura, T.; Wada, Y.; Yanagida, S. J. Phys. Chem. B 2002, 106, 2967. (6) Jung, H. S.; Lee, J.-K.; Nastasi, M.; Lee, S.-W.; Kim, J.-Y.; Park, J.-S.; Hong, K. S.; Shin, H. Langmuir 2005, 21, 10332. (7) Wang, Z. S.; Yanagida, M.; Sayama, K.; Sugihara, H. Chem. Mater. 2006, 18, 2912. (8) Wang, Z. S.; Yamaguchi, T.; Sugihara, H.; Arakawa, H. Langmuir 2005, 21, 4272. (9) Murayama, M.; Mori, T. Jpn. J. Appl. Phys. 2006, 45, 542. (10) Hao, S.; Wu, J.; Fan, L.; Huang, Y.; Lin, J.; Wei, Y. Sol. Energy 2004, 76, 745. (11) Wang, Z. S.; Li, F. Y.; Huang, C. H. Chem. Commun. 2000, 2063. (12) Wang, Z. S.; Li, F. Y.; Huang, C. H. J. Phys. Chem. B 2001, 105, 9210. (13) Jung, H. S.; Shin, H.; Kim, J. R.; Kim, J. Y.; Hong, K. S.; Lee, J. K. Langmuir 2004, 20, 11732. (14) Hoshikawa, T.; Yamada, M.; Kikuchi, R.; Eguchi, K. J. Electrochem. Soc. 2005, 152, E68.

Jung et al. (15) Kern, R.; Sastrawan, R.; Ferber, J.; Stangl, R.; Luther, J. Electrochim. Acta 2002, 47, 4213. (16) Musiæ, S.; Gotiæ, M.; Ivanda, M.; Popoviæ, S.; Turkoviæ, A.; Trojko, R.; Sekuliæ, A.; Furiæ, K. Mater. Sci. Eng., B 1997, 47, 33. (17) Goodman, A. L.; Bernard, E. T.; Grassian, V. H. J. Phys. Chem. A 2001, 105, 6443. (18) Rinco´n, A.-G.; Pulgarin, C. Appl. Catal. B 2004, 51, 283. (19) Youn, H. J.; Ha, P. S.; Jung, H. S.; Hong, K. S.; Park, Y. H.; Ko, K. H. J. Colloid Interface Sci. 1999, 211, 321. (20) Gro¨nbeck, H.; Hellman, A.; Gavrin, A. J. Phys. Chem. A 2007, 111, 6062. (21) Zaban, A.; Greenshtein, M.; Bisquert, J. Chem. Phys. Chem. 2003, 4, 859. (22) Yanagida, M.; Yamaguchi, T.; Kurashige, M.; Hara, K.; Katoh, R.; Sugihara, H.; Arakawa, H. Inorg. Chem. 2003, 42, 7921. (23) Hore, S.; Palomares, E.; Smit, H.; Bakker, N. J.; Comte, P.; Liska, P.; Thampi, K. R.; Kroon, J. M.; Hinsch, A.; Durrant, J. R. J. Mater. Chem. 2005, 15, 412. (24) O’regan, B.; Gra¨tzel, M.; Fitzmaurice, D. Chem. Phys. Lett. 1991, 183, 89.

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