Synthesis and Photophysical Properties of EuS Nanoparticles from the

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Synthesis and Photophysical Properties of EuS Nanoparticles from the Thermal Reduction of Novel Eu(III) Complex Yasuchika Hasegawa,*,† Yoshiko Okada,‡ Tomoharu Kataoka,‡ Takao Sakata,§ Hirotaro Mori,§ and Yuji Wada‡ Graduate School of Material Science, Nara Institute of Science and Technology, 8916-5 Takayama-cho, Ikoma, Nara 630-0192, and Material and Life Science, Graduate School of Engineering, Osaka UniVersity 2-1 Yamadaoka, Suita, Osaka 565-0871 Japan ReceiVed: NoVember 23, 2005; In Final Form: February 2, 2006

EuS nanoparticles were synthesized by the thermal reduction of single source precursor (SSP), (PPh4)[Eu(S2CNEt2)4]‚2H2O, under microwave irradiation. The average size of the EuS nanoparticles was found to be 8 nm (3-16 nm in size). The organic products on the EuS surface were observed by using FT-IR, NMR, and MS analyses. We have found that these are resulted from the chemical reactions of SSP and cover the nanocrystal surface. A thermal reaction of SSP gave EuS nanoparticles and the organic product (•SCN(Et)2). The organic product would make a dimmer, (Et)2NC(S)-(S)CN(Et)2, by the couping of the radicals formed in the thermal reaction and/or thiopolymer in the solution through the polymerization of the radicals. The effective surface modification by the organic products led to protection of the EuS surface, resulting in the formation of the strongly luminescent EuS nanoparticles at room temperature (emission peak ) 350 nm, fwhm ) 58 nm, emission quantum yield ) 27 ( 5%).

Introduction Europium(II) sulfide (EuS) is a characteristic semiconductor having the degenerated 4f orbitals between the conduction band (5d orbitals of Eu(II)) and the valence band (3p orbitals of S2-).1 The 4f-5d electronic transition and spin configuration of EuS lead to unique photophysical and magnetooptical properties.2 These properties are strongly dependent on their sizes and the environments surrounding the particle.3 Especially, the photophysical properties of quantum-dot nanoparticles are affected by size and their surface conditions.4 A key point for creation of EuS nanoparticles having the characteristic photophysical properties is to stabilize the surface structure by surface modification. According to the protection of the nanoparticles surface, single-source precursors (SSP) have been utilized for the synthesis of nanoparticles in the presence of a suitable capping agent.5 Recently, Scholes and co-workers have reported the synthesis of EuS nanocrystals using SSP ([Eu(S2CNEt2)3](2,2′-bipyridine) or (1,10-phenanthroline) and capping agents (trioctylphosphine and oleylamine) by heating at 300 °C.6 Thermal decomposition of SSP with suitable capping agents gives monodispersed nanocrystals. Recently, we have reported that the EuS nanoparticles can be synthesized from SSP (Na[Eu(S2CNEt2)4]‚1.5H2O) without capping agents under white LED irradiation.7 This photochemical reaction gives EuS nanoparticles and organic species such as SCN(Et)2 and/or (Et)2CNS-SCN(Et)2 at room temperature. The organic species function as a capping agent on the EuS surface during the nanoparticle growth. The effective surface modification by organic species leads to protection of the EuS surface, resulting in the formation of the luminescent EuS * To whom correspondence should be addressed. † Nara Institute of Science and Technology. ‡ Graduate School of Engineering, Osaka University. § Research Center for Ultrahigh Voltage Electron Microscopy, Osaka University.

nanoparticles (emission quantum yield ) 0.05%). However, photochemical reaction also gives some side reactions and complicated byproducts.8 The complicated byproducts should be obstacles to synthesis of EuS nanoparticles with photophysical properties. Here, we have successfully synthesized EuS nanoparticles by the thermal reaction of a new SSP, (PPh4)[Eu(S2CNEt2)4]‚ 2H2O (Figure 1). The thermal reaction of the SSP was carried out under 80 °C by using the microwave irradiation to avoid uncontrollable decomposition of the ligand, giving complicated byproducts. Previous SSP, Na[Eu(S2CNEt2)4], causes incorporation of impurity of Na+ cation into EuS, damaging the EuS photophysical properties. Therefore, the SSP has been improved by exchanging the cation of Na+ with a characteristic organic cation (PPh4+: tetraphenylphosphine). From the TEM analyses, the average size of the EuS nanoparticles has been found to be 8 nm. The surface modification of the EuS nanoparticles was confirmed by using of FT-IR, NMR, and MS analyses. The emission quantum yields of the EuS nanoparticles prepared in the present work have been found to be 27 ( 5% at room temperature. Experimental Section Materials. Europium(III) chloride hexahydrate (EuCl3‚6H2O) was purchased from Kanto Chemical Co. Sodium N,N-diethyldithiocarbamate trihydrate (Na(S2CNEt2)‚3H2O) and acetonitrile (CH3CN) were purchased from Nakalai Tesque. Tetraphenylphosphonium bromide (BrPPh4) and ethanol were purchased from Wako Pure Chemical Industries Ltd. Acetonitrile-d3 (CD3CN) was purchased from Aldrich. Preparation of Tetraphenylphosphonium Tetrakis(diethyldithiocarbamate)europium(III) dihydrates ((PPh4) [Eu(Et2dtc)4]‚2H2O. A solution of Na(S2CNEt2)‚3H2O (1.13 g) in 4 mL ethanol was added to EuCl3‚6H2O (0.35 g) dissolved in

10.1021/jp0567826 CCC: $33.50 © 2006 American Chemical Society Published on Web 04/19/2006

EuS Nanoparticles from a Novel Eu(III) Complex

J. Phys. Chem. B, Vol. 110, No. 18, 2006 9009

Figure 1. Schematic process for converting precursor into EuS nanoparticles.

4 mL ethanol with stirring.9 After the reaction mixture was filtered, a solution of BrPPh4 in 2 mL ethanol was added to the filtrated solution. The resulting precipitate was separated by filtration and washed several times with ethanol. Yield: 40%. FT-IR spectra (KBr): 1485-1482 (C-N) cm-1, 1442 (PPhenyl) cm-1, 1007 (C-S) cm-1. 1H NMR spectra (CD3CN): 7.91 (4H, t, J ) 6.3 Hz, [Eu(S2CNEt2)](P(C6H5)4(p)), δ7.70 (16H, m, [Eu(S2CNEt2)](P(C6H5)4(o, m)), δ3.17 (8H, q, J ) 7 Hz, [Eu(S2CNCH2CH3)2](PPh4). δ1.61 (12H, q, [Eu(S2CNCH2CH3)2](PPh4). Found: C: 47.14, H: 5.37, N: 4.99%. Calcd for C44H64EuN4O2PS8: C: 47.17, H: 5.76, N: 5.00%. Preparation of EuS Nanoparticles. The precursor, (PPh4)[Eu(S2CNEt2)4]‚2H2O, was dissolved in acetonitrile. After the solution was refluxed under microwave irradiation (by CEM Discover) for 6 h, yellowish-white powder was obtained. The reaction was monitored as a function of time by recording the optical absorption spectrum of an aliquot. The resulting yellowish-white powder was cooled to room temperature. The color might be based on the nonreacted (PPh4)[Eu(S2CNEt2)4]‚2H2O. This power was separated by centrifugation and washed with acetonitrile. After washing, white powder was obtained. Apparatus. FT-IR measurements were performed at room temperature by a Perkin-Elmer system 2000 FT-IR spectrometer. 1H NMR data were obtained with a JEOL EX-270 spectrometer. 1H NMR chemical shifts were determined using tetramethylsilane (TMS) as internal standard. 31P NMR data were obtained with a JEOL ECP-400 spectrometer. 31P NMR chemical shifts were determined using phosphoric acid (85.0%) as internal standard. Elemental analyses were performed with a PerkinElmer 240C. Fast atom bombardment mass spectra (FAB-MS) were recorded in the positive ion mode with a 3-nitrobenzyl alcohol matrix on a JEOL JMS-700 mass spectrometer. FAB mass spectroscopy was measured using a dispersion in acetonitrile under positive ion mode: FAB+ (spectrum type: normal ion). The matrix of the FAB-MS measurement is 3-nitrobenzyl alcohol. High-resolution images of the EuS nanocrystals were obtained with a Hitachi H-9000 TEM (high-resolution transmission electron microscopy) equipped with a tilting device ((10 degrees) and operating at 300 kV (Cs ) 0.9 mm). UV-vis absorption spectra were measured on a JASCO V-570 spectrophotometer at room temperature. The emission spectra were measured using a SPEX fluorolog fluorescence spectrophotometer. The emission quantum yields were obtained by using a conventional route, integrating the photoluminescence band of the sample (absorbance at 290 nm: 0.101, excitation at 290 nm) in acetonitrile and comparing the intensity to that of terphenyl10 (absorbance at 290 nm: 0.092, excitation at 290 nm, the emission quantum yield ) 95%) in acetonitrile.11 Results and Discussion Characterization of EuS Nanocrystals and Reaction Mechanism. A TEM image of the nanoparticles is shown in Figure 2a. In the high-resolution image, we found monodis-

Figure 2. TEM image of EuS nanoparticles. (a) HRTEM image of nanoparticles. (b) Size distribution histogram. (c) Electron diffraction pattern image.

persed EuS nanoparticles with clear lattice fringes. The crystallinity was clear and well-resolved and lattice planes of EuS (0.29 nm (200)) were observed. The average diameter of the nanoparticles was found to be 8 nm (Figure 2b). The electron diffraction pattern of the nanocrystals revealed spacings of 2.98, 2.11, 1.80, and 1.34 dÅ, corresponding to (200), (220), (311), and (420) planes of NaCl-type EuS nanocrystal, in agreement with those reported previously for EuS nanoparticles (Figure 2c).3,7 The results indicated that thermal reaction of SSP under microwave irradiation gave the EuS nanoparticles at 80 °C. To observe the reacting solution, the absorption spectrum of the sample including SSP (5.0 mM) in acetonitrile was recorded at time intervals. The absorption spectra are shown in Figure 3. The peak of the absorption band of SSP was located at 420 nm and assigned to the S f Eu LMCT transition of the SSP, (PPh4)[Eu(S2CNEt2)4], due to the comparison with Eu(III) dithiocarbamate complexes reported previously.9 Strong absorption below 400 nm should be due to the π-π* transition of [S2CNEt2]- ligands. After microwave irradiation, we could follow the reaction by observing the decrease of the LMCT band. The LMCT band was gradually decreased during the first 1 h. We propose the thermal reaction of SSP as follows (Figure 3). First, this reaction gives Eu(II) ion and •S2CNEt2 through the electron transfer from the ligand to Eu(III). The •S2CNEt2 moiety gives S2- and •SCNEt2. The EuS nanoparticles might be formed by the reaction of Eu(II) with S2-, followed by particle growth. Figure 3 shows appearance of reactive solvent under microwave irradiation. The reactive solution includes EuS nanoparticles and nonreacted yellow reagents, (PPh4)[Eu(S2CNEt2)4]‚2H2O. After washing with acetonitrile, white powder without absorption at 400 nm was obtained. It is known that the microwave irradiation is a useful tool for nanocrystal formation with narrow size distributtion.12 This advantage was also realized in the present work. Surface Analyses of EuS Nanoparticles. The organic products on the EuS surface were observed by using FT-IR, NMR, and MS analyses. An FT-IR spectrum of the sample is shown in Figure 4a. The vibration band at 1075 cm-1 was assigned to C-S stretching of the organic products. The wavenumber of this broad band was shifted to longer than that of corresponding SSP (Eu dithiocarbamate complex: 1007 cm-1). This result suggests that the C-S bonds transform from single bond character to double bond. We also observed the vibration bands between 1600 and 1400 cm-1 (C-N stretching). In the FAB-MS spectrum, we found the signal at 116.1 for an acetonitrile solution containing EuS nanoparticles. This signal

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Figure 5. Emission and excitation spectra of EuS nanoparticles in acetonitrile at room temperature. Excitation wavelength for measurement of emission spectrum is a 290 nm. Monitor wavelength for measurement of excitation spectrum is a 360 nm.

Figure 3. (a) UV-vis absorption spectra of the experimental solution in each reaction time. The absorption at 420 nm shows S f Eu LMCT. (b) Variation of the absorption at 420 nm taken at different time intervals. (c) Decomposition mechanism of (PPh4) [Eu(S2CNEt2)4] precursor.

Figure 4. (a) IR spectra of nanoparticles, (b) 1H NMR spectra, and (c) 31P NMR spectra of spectra of EuS nanoparticles and SSP.

was assigned to C3H10NS. These results indicate that the organic product has the structure •SCN(Et)2. Therefore, we propose that the organic product, •SCN(Et)2, is formed by a thermal reaction of Eu (III) dithiocarbamate complex. 1H NMR spectra of EuS nanoparticles and SSP (Eu dithiocarbamate complex) in acetonitrile-d3 are shown in Figure 4b. The two resonance signals at 3.10 and 1.19 ppm for an acetonitrile solution containing EuS nanoparticles were assigned to ethyl groups of the organic product (•SCN(Et)2). These signals were shifted to higher magnetic field than those of the corresponding peaks at 3.16 ppm (triplet, 3H) and 1.59 ppm (quartet, 2H) for an SSP solution. We observed the shift of the

signals of the organic cation, tetraphenylphosphine, for a EuS nanoparticle solution (7.10, 6.58 and 3.97 ppm) in comparison with those for an SSP solution (7.90 (triplet, 1H) and 7.70 (multiplet 4H) ppm). 31P NMR spectra of EuS nanoparticles and SSP in acetonitrile-d3 are also shown in Figure 4c. The signal of tetraphenylphosphine for a EuS nanoparticle solution (-12.22 ppm) was also shifted to higher magnetic field than that for SSP (24.47 ppm). In general, NMR signals of organic compounds on surface of nanoparticles are shifted to higher magnetic field.13 We propose that EuS nanoparticles are coordinated by organic products, such as the Eu complex. This supposition is caused by an upper-field shift of NMR data of tetraphenylphosphonium. Suppositional compounds, •SCN(Et)2 or their derivatives, would also coordinate on the EuS nanoparticle surface. However, discussion about higher magnetic field signals of the suppositional compounds is not clear at the present time because the chemical structures of suppositional compounds are different from that of corresponding SSP, (PPh4)[Eu(S2CNEt2)4]‚2H2O. Furthermore, we have measured elemental analysis of our surface-modified EuS nanoparticles (Found: C: 11.91, H: 2.17, N: 0.56%). These data suggest the presence of organic products on the EuS surface. A small percentage of nitrogen might be caused by small amount of •SCN(Et) or derivatives. We propose that EuS nanoparticles 2 have a sulfide-rich surface, assuming that the nanoparticles plus ligands, Ph4P+, is overall neutral. In this work, a thermal reaction of SSP gave EuS nanoparticles and the organic product (•SCN(Et)2). The organic product may make a dimmer, (Et)2NC(S)-(S)CN(Et)2, by the couping of the radicals formed in the thermal reaction and/or thiopolymer in the solution through the polymerization of the radicals. We could not observed the dimmer or polymer, however, Wei and co-workers have suggested dithiocarbamate assembly on nanoparticles, recently.14 Then we propose that the EuS nanoparticle surface is covered with the dimer or the polymer. Optical Properties. The emission and the excitation spectra of EuS nanoparticles in acetonitrile are shown in Figure 5. When the sample was irradiated at 290 nm, the emission spectrum exhibited a peak at λ ) 350 nm. This emission band is due to a 4f-5d transition. The energy gap in nanoparticles of 8 nm was estimated by a zero-zero band between the emission and excitation spectra, giving the energy gap of 3.7 eV. This shows a blue shift in comparison with previous EuS nanoparticles (of ca. 10 nm: 3.1 eV).15 The level of the conduction band constructed from 5d orbitals should be affected by the particle

EuS Nanoparticles from a Novel Eu(III) Complex size of EuS (a quantum size effect). It seems that the 3p orbitals of sulfides are also affected by the quantum size effect. However, the emission bands are dependent on the transition between 5d orbitals of Eu(II) and degenerated 4f orbitals, f-d transition. The emission spectrum with higher energy gap (3.7 eV) might be based on the 5d orbitals. The effective mass of EuS is estimated at 0.3-1.1 by previous reports.16 Therefore, the electron Bohr radius is calculated to be 0.7-2.3 nm. EuS nanoparticles with smaller size (diameter ∼5 nm) would be affected by the quantum effect, strongly. We propose that larger energy gap of prepared EuS nanoparticles (3-16 nm in size) might be due to the quantum size effect. Particle size from single source precursor depends on the condition of thermal reduction. Smaller EuS nanoparticles (average diameter < 5 nm) would be prepared by improvement of solvent, temperature, concentration, and structure of SSP. Concerning the emission process of EuS nanoparticles, we are now trying to analyze the emission lifetime. The detailed analysis of the emission lifetimes would lead to demonstration of the emission process of EuS nanoparticles soon. The emission quantum yield of EuS nanoparticles was found to be 27 ( 5% at room temperature. This was higher than that of corresponding EuS prepared by white LED irradiation (0.05%).7 We also measured photophysical properties of EuS nanoparticles from Na[Eu(S2CNEt2)4]‚1.5H2O. The emission spectrum exhibited a peak at λ ) 340 nm. We propose that the average size of EuS nanoparticles from Na[Eu(S2CNEt2) 4]‚1.5H2O is similar to that of corresponding EuS nanoparticles from (PPh4)[Eu(S2CNEt2) 4]‚2H2O. However, The quantum yield of EuS from Na[Eu(S2CNEt2)4]‚1.5 H2O was found to be 0.53%. These results indicate that tetraphenylphosphonium cations play an important role of enhanced luminescence. We suggest that this strong emission comes from the following two reasons: (1) absence of impurities cation, Na+ ions, (2) perfect protection on the EuS nanoparticle surface by organic products, (3) less amount of the organic byproducts. As a result, EuS nanoparticles synthesized from a thermal reaction of SSP should show strong luminescent properties with high emission quantum yield. Conclusion Luminescent EuS nanoparticles were successfully synthesized by the thermal reaction of a new single-source precursor (SSP). We identified the organic product on the EuS surface using NMR, FT-IR, and mass spectra. The emission quantum efficiency of the EuS nanoparticles with the organic product was the highest one among reported EuS crystals at room temperature. We suggest that luminescent EuS nanoparticles are obtained by the perfect protection of the surface. The surfaceprotected condition using the organic product can be manipulated by molecular design of SSP, especially ligands. The manipulation of the surface-protected condition of EuS nanoparticles would be linked to advanced applications such as magnetoopto devices, isolators, and photomagnetic memories. Acknowledgment. This work was supported partly by NEDO (New Energy Industrial Technology Development

J. Phys. Chem. B, Vol. 110, No. 18, 2006 9011 Organization) and by a Grant-in-Aid for Scientific Research on Priority Area A of “Panoscopic Assembling and High Ordered Functions for Rare Earth Materials” from the Ministry of Education, Culture, Sports, Science, and Technology, Japan. References and Notes (1) (a) Wachter, P. Handbook on the Physics and Chemistry of Rare Earths, 2nd Ed.; North-Holland: Amsterdam, 1979; p 189. (b) Kasuya, T.; Yanase, A. ReV. Mod. Phys. 1968, 40, 684. (c) Eastman, D. E.; Holtzberg, F.; Methfessel, S. Phys. ReV. Lett. 1969, 23, 226. (2) Recent papers of optomagnetic properties of bulk EuS. (a) Muller, C.; Lippitz, H.; Paggel, J. J.; Fumagalli, P. J. Appl. Phys. 2004, 95, 7172. (b) Schoenes, J. J. Phys.: Condens. Matter 2003, 15, S707. (c) Umehara, M. Phys. ReV. B 2002, 65(20), 205208/1. (d) Muller, C.; Lippitz, H.; Paggel, J. J.; Fumagalli, P. J. Appl. Phys. 2002, 91, 7535. (e) Tanaka, K.; Tatehata, N.; Fujita, K.; Hirao, K. J. Appl. Phys. 2001, 89, 2213. (f) Uspenskii, Y. A.; Harmon, B. N. Phys. ReV. B 2000, 61, R10571. (3) (a) Thongchant, S.; Hasegawa, Y.; Wada, Y.; Yanagida, S. J. Phys. Chem. B 2003, 107, 2193. (b) Thongchant, S.; Hasegawa, Y.; Wada, Y.; Yanagida, S. Chem. Lett. 2003, 32, 706. (c) Thongchant, S.; Hasegawa, Y.; Tanaka, K.; Fujita, K.; Hirao, K.; Wada, Y.; Yanagida, S. Jpn. J. Appl. Phys. 2003, 42, L876. (4) Recent papers on surface chemistry of luminescent nanoparticles (a) Chan, Y.; Zimmer, J. P.; Stroh, M.; Steckel, J. S.; Jain, R. K.; Bawendi, M. G. AdV. Mater. 2004, 16, 2092. (b) Talapin, D. V.; Mekis, I.; Goetzinger, S.; Kornowski, A.; Benson, O.; Weller, H. J. Phys. Chem. B 2004, 108, 18826. (c) Wang, Y.; Tang, Z.; Correa-Duarte, M. A.; Pastoriza-Santos, I.; Giersig, M.; Kotov, N. A.; Liz-Marzan, L. M. J. Phys. Chem. B 2004, 108, 15461. (d) Gu, F.; Wang, S. F.; Lue, M. K.; Zhou, G. J.; Xu, D.; Yuan, D. R. J. Phys. Chem. B 2004, 108, 8119. (e) Shavel, A.; Gaponik, N.; Eychmueller, A. J. Phys. Chem. B 2004, 108, 5905. (f) Wei, S.; Lu, J.; Yu, W.; Qian, Y. J. Appl. Phys. 2004, 95, 3683. (g) Borchert, H.; Talapin, D. V.; Gaponik, N.; McGinley, C.; Adam, S.; Lobo, A.; Moeller, T.; Weller, H. J. Phys. Chem. B 2003, 107, 9662. (5) (a) Revaprasadu, N.; Malik, M. A.; O’Brien, P.; Wakefield, G. Chem. Commun. 1999, 1573. (b) Pickett, N. L.; O’Brien, P. Chem. Record 2001, 1, 467. (c) Mikulec, F. V.; Kuno, M.; Bennati, M.; Hall, D. A.; Griffin, R. G.; Bawendi, M. G. J. Am. Chem. Soc. 2000, 122, 2532. (d) Malik, M. A.; O’Brien, P.; Helliwell, M. J. Mater. Chem. 2005, 15, 1463. (6) Scholes, G. D.; Mirkovic, T.; Hines, M. A. Chem. Mater. 2005, 17, 3451. (7) Hasegawa, Y.; Mohanmad. A.; O’Brien, P.; Wada, Y.; Yanagida, S. Chem. Commun., 2005, 242. (8) (a) Cuquerella, M. C.; Bosca, F.; Miranda, M. A.; Belvedere, A.; Catalfo, A.; de Guidi, G. Chem. Res. Toxicol. 2003, 16, 562. (b) Banerjee, A.; Falvey, D. E. J. Org. Chem. 1997, 62, 6245. (c) Ci, X.; Silveira da Silva, R.; Nicodem, D.; Whitten, D. G. J. Am. Chem. Soc. 1989, 111, 1337. (d) Kurz, M. E.; Lapin, S. C.; Mariam, K.; Hagen, T. J.; Qian, X. Q. J. Org. Chem. 1984, 49, 2728. (9) Kobayashi, T.; Naruke, H.; Yamase, T. Chem. Lett., 1997, 907. (10) (a) Hasegawa, Y.; Yamamuro, M.; Wada, Y.; Kanehisa, N.; Kai.; Yanagida, S. J. Phys. Chem. A 2003, 107, 1697. (b) Lesiecki, M. L.; Drake, J. M. Appl. Opt. 1982, 21, 557. (11) (a) Zhengtao D.; Bingsuo, Z. J. Phys. Chem. B 2005, ASAP. (b) Cumberland, S. L.; Hanif, K. M.; Javier, A.; Khitrov, G. A.; Strouse, G. F.; Woessner S. M.; Yun, C. S. Chem. Mater. 2002, 14, 1576. (c) Demas, J. N.; Crosby, G. A. J. Phys. Chem. 1971, 75, 991. (12) (a) Yamamoto, T.; Wada, Y.; Yin, H.; Sakata, T.; Mori, H.; Yanagida, S. Chem. Lett. 2003, 964. (b) Yamamoto, T.; Wada, Y.; Miyamoto, H.; Yanagida, S. Chem. Lett. 2004, 33, 246. (13) Yin, H.; Wada, Y.; Kitamura, T.; Sumida, T.; Hasegawa, Y.; Yanagida, S. J. Mater. Chem. 2002, 12, 378. (14) Zao, Y.; Perez-Segarra, W.; Shi, Q.; Wei, A. J. Am. Chem. Soc. 2005, 127, 7328. (15) Eastman, D. E.; Holtzberg, F.; Methfessel, S. Phys. ReV. Lett. 1969, 23, 226. (16) (a) Xavier, R. M.; Fac. Sci., O., Phys. Lett. A, 1967, 25, 244. (b) Thompson, W. A.; Penney, T.; Holtzberg, F.; Kirkpatrick, S., Proc. Int. Conf. Phys. Semicond., 11th, 1972, 2 1255.