C、N、F元素掺杂纳米二氧化钛的制备及可见光催化性能研究
详细信息    本馆镜像全文|  推荐本文 |  |   获取CNKI官网全文
摘要
纳米二氧化钛具有良好的光催化特性,在污染物降解、自清洁涂层等领域有广泛应用。但TiO_2的禁带宽度较大,需要以紫外光为激发光源,限制了其实际应用。将TiO_2的光吸收波长红移至可见光区,可以利用太阳光作为激发光源,节能环保。因此,扩展TiO_2光响应范围,使其在太阳光照射下催化降解有机物备受研究者关注。
     掺杂非金属是制备可见光响应TiO_2的重要技术途径之一。本论文以四氯化钛为原料,采用沸腾回流法,以柠檬酸为碳源,制备了碳掺杂纳米TiO_2。利用水热法,分别以硝酸铵和氟化钠为添加剂,制备了氮掺杂和氟掺杂纳米TiO_2。利用XRD、TEM、SEM、UV-Vis、XPS和X射线吸收精细结构(XAFS)等表征方法,研究了纳米TiO_2的结构、形貌、光吸收性质等。通过对甲基橙溶液的降解来测试掺杂TiO_2样品的可见光催化活性,探讨了三种元素的最佳掺杂量,分析了可见光响应机理。
     研究结果表明:(1)随着柠檬酸添加量的增大,产物中锐钛矿含量增加,球型颗粒变大,分散程度提高。未添加柠檬酸时,TiO_2的比表面积为92.232m2·g~(-1);添加柠檬酸后,样品比表面积增大到187.747m2·g~(-1)。比表面积的增大,有利于提高样品的光催化性能。(2)在反应体系中加入NH4NO3,产物为金红石相,形貌为纳米棒状颗粒组成的微球
     未掺杂TiO_2的比表面积为41.479m2·g~(-1),当NH4NO3添加量为0.4%时,比表面积为50.645 m2·g~(-1)。
     (3)在反应体系中加入少量NaF所制备样品为金红石相,是由纳米棒状颗粒组成的微球。添加2.0%NaF所得样品为混晶,锐钛矿相含量为20.7%,金红石相含量为79.3%,比表面积为40.355 m~2·g~(-1)。
     (4)与未掺杂样品和P25相比,掺杂C、N、F元素所制备TiO_2样品的吸收波长发生红移,在可见光区有吸收。以12W主波长460nm的蓝色LED灯为光源,甲基橙溶液为模拟污染物,测试样品的光催化性能。实验结果表明掺杂样品在光催化降解的过程中表现出良好的可见光活性,最佳样品的降解结果为:2.0%C-TiO_2光照3h降解率约为90%,0.5%N-TiO_2和0.4%F-TiO_2样品在光照5h时降解率约为62%,72%。
     (5)利用XAFS分析了非金属元素掺杂TiO_2中Ti原子的局域结构,获得了配位数、键长等信息,研究结果表明,随着非金属元素N和F掺杂量的增大,所得样品的配位数和Ti-O键的键长变大。XAFS和XPS结果表明C和F原子主要以替代氧或钛原子的形式掺入二氧化钛晶格中。非金属掺杂改变了二氧化钛的能带结构,增强了可见光催化活性。
Due to excellent photocatalytic properties, titanium dioxide has been widely used in many fields, such as degradation of pollutants, self-cleanning coating, and so on. However, more practical applications have been limited by its wide band gap, which require ultraviolet light as the optical excitation source. Shifting the optical response region of TiO_2 to visible spectral range means that the sun light can be used as the optical excitation source. It is helpful for saving energy and environmental protection. So many researchers are focused on enlarging the optical response region of TiO_2 to degrade organics under the sun radiation.
     It is an important way to prepare TiO_2 with visible light response by doping nonmental. In this paper, a series of TiO_2 photocatalysts were prepared using titanium tetrachloride as raw material. C-TiO_2 was synthesized using citric acid as carbon source by a simple hydrolysis method. N-TiO_2 and F-TiO_2 with visible light response were prepared using NH4NO3 and NaF as doped sources by hydrothermal method. The structure, morphology and light adsorption of such photocatalysts were characterized by XRD, TEM, SEM, UV-Vis, XPS, X-ray absorption fine structure(XAFS), etc. The photocatalytic degradation of methyl-orange was used as model reaction to evaluate the visible light activity of TiO_2 samples. It suggested that a best doping concentration existed for every dopant and the mechanism of doped TiO_2 for the visible-light activity was discussed.
     The research results were suggested as following:
     (1)The content of anatase phase of the sample rised with increasing amount of citric acid. The photocatalysts were well dispersed and their particle sizes increase with increasing amount of citric acid. The experimental result showed that the surface area of pure TiO_2 was 92.232m2·g~(-)1. After adding citric acid, the surface area of sample increased to 187.747m2·g~(-)1. The increase of surface area was helpful to improve their photocatalytic properties.
     (2)With the addition of NH4NO3, the samples were rutile phase composed of nanorods. The surface area of undoped TiO_2 was 41.479m2·g~(-)1. When the addition amount of NH4NO3 was 0.4%, its surface area was 50.645 m2·g~(-)1.
     (3)The TiO_2 samples prepared with small amount of NaF were rutile phase with the morphology of the microspheres composed of nanorods. When the mole percentage of NaF to titanium ions was 2.0%, the anatase phase could be observed in the TiO_2 powder. The content of anatase phase was 20.7% and the rutile phase was 79.3%, with the surface area of 40.355 m2·g-1.
     (4)The UV–Vis adsorption spectroscopy showed that C、N、F-doped TiO_2 appeared a certain visible light adsorption and the optical band edge exhibited a certain red-shift compared with that of undoped TiO_2 and Degussa P25. The photocatalytic activity of prepared samples were tested under 12W LED light with a major emission wavelength at 460nm as visible light source and methyl-orange as model reaction. The research suggested that the final degradation rate of the optimum samples were as following: 2.0%C-TiO_2 was found to be nearly 90% within 3h. 0.5%N-TiO_2, 0.4%F-TiO_2 were about 62% and 72% within 5h.
     (5)The XAFS technique was employed to analyse the change of the local structure around Ti atom. It showed the structure information of doping atoms, such as coordination number, bond distance, etc. With the increasing of N and F dopant, the coordination number and Ti-O bond become bigger. XPS and XAFS analysis indicated that C and F atoms had been doped in the lattice of crystalline TiO_2 by substituting the oxygen or Ti atom. Non-metal doping changed the energy band of TiO_2 and improved photocatalytic activity under visible light irradiation.
引文
[1]倪广红,丰平.纳米二氧化钛光催化的研究进展及应用[J].纳米科技, 2010, 7(2): 84-86.
    [2]S Guo, Z.B Wu, H.Q Wang, F Dong. Synthesis of mesoporous TiO2 nanorods via a mild template-free sonochemical route and their photocatalytic performances[J]. Catal.Commun, 2009, 10(13): 1766-1770.
    [3]J.H Xu, W.L Dai, J.X Li, Y. Cao, et al. Simple fabrication of thermally stable apertured N-doped TiO2 microtubes as a highly efficient photocatalyst under visible light irradiation[J]. Catal Commun, 2008, 9(1): 146-152.
    [4]V. Gombac, L.D Rogatis, A. Gasparotto, G. Vicario, et al. TiO2 nanopowders doped with boron and nitrogen for photocatalytic applications[J]. Chem. Phys, 2007, 339(1-3): 111-123.
    [5]冯彩霞. N掺杂纳米TiO2可见光催化氧化丙烯的动力学行为[J].物理化学学报, 2008, 24(4): 633-638.
    [6]王洪水.纳米银及载银纳米抗菌材料的研究[D].华中科技大学, 2006: 3.
    [7]L. Lin, R.Y Zheng, J.L Xie, et al. Synthesis and Characterization of Phosphor and Nitrogen Co-doped Titania[J]. Appl Catal B: Environ, 2007, 76(1-2): 196-202.
    [8]Y.F Zhu, L. Zhang, W.Q Yao, et al. The chemical states and properties of doped TiO2 film photocatalyst prepared using the Sol-Gel method with TiCl4 as a precursor[J]. J. Appl. Sur. Sci., 2000, 158(1-2): 32-37.
    [9]刘艳敏.可见光响应非金属掺杂纳米二氧化钛的制备及性能研究[D].河北师范大学, 2009: 3.
    [10]M.R Dhananjeyan, V. Kandavelu, R. Renganathan. A study on the photocatalytic reactions of TiO2 with certain pyrimidine bases: effects of dopants (Fe3+) and calcination[J]. J. Mol. Catal. A: Chem., 2000, 151(1-2): 217-223.
    [11]K. Wilke, H.D Breuer. The influence of transition metal doping on the physical and photocatalytic properties of titania[J]. J. Photochem. Photobiol., A: Chemistry, 1999, 121(1): 49.
    [12]W. Choi, A .Termin, M.R Hoffmann. The role of metal ion dopants in quantum-sized TiO2: correlation between photoreactivity and charge carrier recombination dynamics[J]. PhysChem, 1984, 98(5):13669.
    [13]W Li, H Lin, et al. Band gap tailoring of Nd3+-doped TiO2 nanoparticles[J]. Appl. Phys. Lett., 2003, 83: 4143-4145.
    [14]I Yasuo, K Fumitaka, Y Hideaki, et al. Structure of low concentration of vanadium on TiO2 determined by XANES and ab initio calculations[J]. Chem. Commun., 2002, 20: 2402-2403.
    [15]G. Martra. Lewis Acid and Base Sites at the Surface of Microcrystalline TiO2 Anatase: Relationships Between Surface Morphology and Chemical Behaviour[J]. Appl. Catal. A: Gen., 2000, 200(2): 275-283.
    [16]程沧沧,李太友,李华禄等.载银TiO2光催化降解2,4-二氯苯酚水溶液的研究[J].环境科学研究, 1998, 1l(6): 212-2l5.
    [17]蒋伟川,谭湘萍.载银TiO2半导体光催化剂降解染料水溶液的研究[J].环境科学, 1995, 16(2): l7-20.
    [18]施利毅,李春忠,古宏晨等. SnO2-TiO2复合颗粒的形态结构及其光催化活性[J].化学物理学报, 2000, 13(3): 336-342.
    [19]R Vogel, P Hoyer, H Weller. Quantum-Sized PbS, CdS, Ag2S, Sb2S3 and Bi2S3 particles as sensitizers for various nanoporous wide-band gap semiconductors[J]. J. Phys. Chem., 1994, 98(12): 3183-3188.
    [20]G Marci, V Augugliaro, M.J Lopez-Munoz, et al. Preparation characterization and photocatalytic activity of polycrystalline ZnO/TiO2 systems .2 .surface, bulk characterization, and 4-nitrophenol photodegradation in liquid-solid regime[J]. J. Phys. Chem. B, 2001, 105(5): 1033-1040.
    [21]张青红,高濂,孙静.氧化硅对二氧化钛纳米晶相变和晶粒生长的抑制作用[J].无机材料学报, 2002, 17(3): 415-421.
    [22]崔爱莉,王亭杰,金涌等. TiO2表面包覆SiO2和Al2O3的机理和结构分析[J].高等学校化学学报, 1998, 19(11): 1727-1729.
    [23]X.Z Fu, A.C Louis, Q Yang, et al. Enhanced photocatalytic performance of titania-based binary metal oxides: TiO2/SiO2 and TiO2/ZrO2[J]. Environ. Sci. Technol., 1996, 30(2): 647-653.
    [24]程虎民,张志颖.纳米ZrO2-TiO2复合氧化物微粉的制备研究[J].北京大学学报(自然科学版),1995, 35(2): 151-157.
    [25]R Asah., T Morikawa, T Ohwaki, et al. Visible-light Photocatalysis in nitrogen-doped titanium oxides[J].Science, 2001, 293(5528): 269-271.
    [26]H Irie, Y Watanabe, K Hashimoto. Nitrogen-Concentration Dependence on Photocatalytic Activity of TiO2-XNx Powders[J]. J. Phys. Chem. B, 2003,107(23): 5483-5486.
    [27]S Mozia, M Tomaszewska, B Kosowska, et al. Decomposition of nonionic surfactant on a nitrogen-doped photocatalyst under visible-light irradiation[J]. Appl. Catal., B: Environ, 2005, 55(3): 195-200.
    [28]H Tokudome, M Miyauchi. N-doped TiO2 Nanotube with Visible Light Activity[J]. Chem. Lett., 2004, 33(9): 1108-1109.
    [29]J Geng, D Yang, J Zhu, et al. Nitrogen-doped TiO2 nanotubes with enhanced photocatalytic activity synthesized by a facile wet chemistry method [J]. Mater Res Bull, 2009, 44: 146-150.
    [30]C Burda, Y Lou, X Chen, et al. Enhanced Nitrogen Doping in TiO2 Nanoparticles[J]. Nano. Lett., 2003, 3(8): 1049-1051.
    [31]H Irie, Y Watanabe, K Hashimoto. Carbon-doped anatase TiO2 powders as a visible-light sensitive photocatalyst[J]. Chem. Lett., 2003, 32(8): 772-773.
    [32]C Lettmann, K Hildenbrand, H Kisch, et al. Visible light photodegradation of 4-chlorophenol with a coke-containing titanium dioxide photocatalyst[J]. Appl. Catal. B: Environ., 2001, 32(4): 215-227.
    [33]S Khan, M Al-Shahry, W.B Ingler, et a1. Efficient Photochemical Water Spliting by a Chemically Modified n-TiO2[J]. Science, 2002, 297 (5590): 2243-2245.
    [34]K Nagaveni, M S. Hegde, N Ravishankar, et al. Synthesis and structure of nanocrystalline TiO2 with lower band gap showing high photocatalytic activity[J]. Langmuir, 2004, 20(7): 2900-2907.
    [35]V.C Di, G Pacchioni, A Selloni Theory of Carbon Doping of Titanium Dioxide[J]. Chem. Mater, 2005, 17(26): 6656-6665.
    [36]T Ohno, T Mitsui, M Matsumura. Photocatalytic activity of S-doped TiO2 photocatalyst under visible light[J]. Chem Lett, 2003, 32(4): 364-365.
    [37]T Umebayashi, T Yamaki, H Itoh, et al. Band gap narrowing of titanium dioxide by sulfurdoping[J]. Appl. Phys. Lett., 2002, 81(3): 454-456.
    [38]朱启安,王树峰,张平等.硫掺杂纳米TiO2可见光催化剂的制备及光催化活性[J].精细化工, 2007, 24(6): 526-530.
    [39]A Hatori, M Yamamoto, H Tada, et al. A promoting effect of NH4F addition on the photocatalytic activity of sol-gel TiO2 films[J]. Chem. Lett., 1998, 27: 707-708.
    [40]J.C Yu, J.G Yu, W.K Ho, et al. Effects of F-doping on the photocatalytic activity and microstructures of nanocrystalline TiO2 powders [J]. Chem Mater, 2002, 14(9): 3808-3816.
    [41]陈恒,龙明策,徐俊等.可见光响应的氯掺杂TiO2的制备、表征及其光催化活性[J].催化学报, 2006, 27(10): 890-894.
    [42]H.M Luo, T Takata, Y Lee, et al. Photocatalytic Activity Enhancing for Titanium Dioxide by Co-doping with Bromine and Chlorine[J]. Chem. Mater. 2004, 16(5): 846-849.
    [43]X.T Hong, Z.P Wang, W.M Cai, et al. Visible-Light-Activated Nanoparticle Photocatalyst of Iodine-Doped Titanium Dioxide[J]. Chem. Mater. 2005, 17(6): 1548-1552.
    [44]S Usseglio, A Damin, D Scarano, et al. (I2)n Encapsulation inside TiO2: A Way To Tune Photoactivity in the Visible Region[J]. J. Amer. Chem. Soc., 2007, 129(10): 2822-2828.
    [45]L Lin, W Lin, J.L Xie,et al. Photocatalytic properties of phosphor-doped titania nanoparticles[J]. Appl Catal B: Environ, 2007, 75(1-2): 52-58.
    [46]M Bettinelli, V Dallacasa, D Falcomer, et al. Photocatalytic activity of TiO2 doped with boron and vanadium[J]. J. Hazard. Mater., 2007, 146 (3): 529-534.
    [47]Y.L Su, X.W Zhang, S Hang, et al. F-B-codoping of anodized TiO2 nanotubes using chemical vapor deposition[J]. Electrochem Commun, 2007, 9(9): 2291-2298.
    [48]A Masakazu. Photocatalysis on titanium oxide catalysts: Approaches in achieving highly efficient reactions and realizing the use of visible light[J]. Catal Surv Japan, 1997, 1(2): 169-179.
    [49]谭礼林,甘佐华,孙振范. Fe元素掺杂二氧化钛纳米薄膜的光物理化学性质[J].海南师范大学学报(自然科学版), 2009, 22(4): 418-424.
    [50]宋海燕.新型光催化材料的制备与催化性能研究[D].中国科学技术大学,2006: 76.
    [51]吴道新,陈启元,李洁,尹周澜.钽掺杂金红石型二氧化钛光催化分解水的析氧活性[J].中国有色金属学报, 2009, 19(2): 360-365.
    [52]顾虹,许波连,周静,李远志,范以宁.负载型Pd/TiO2和Pd-Ag/TiO2催化剂的乙炔选择性加氢催化性能[J].物理化学学报, 2006, 22(6): 712-715.
    [53]E Barborin, et al. Nanostructured TiO2 films with 2eV optical gaps[J]. Adv. Mater., 2005, 17(15): 1842-1846.
    [54]D Li, H Haneda, S Hishita, N Ohashia, N.K Labhsetwar. Fluorine-doped TiO2 powders prepared by spray pyrolysis and their improved photocatalytic activity for decomposition of gas-phase acetaldehyde[J]. J. Fluorine Chem., 2005, 126(1): 69-77.
    [55]D Li, H Haneda, N.K Labhsetwar, S Hishita, N Ohashi.Visible-light-driven photocatalysis on fluorine-doped TiO2 powders by the creation of surface oxygen vacancies[J]. Chem. Phys. Lett., 2005, 401(4-6): 579-584.
    [56]高濂,郑珊,张青红.纳米二氧化钛光催化材料及应用[M].化学工业出版社.
    [57]Z.D Zhang, Z.B Hu, Q.L Liu. The applications of EXAFS spectroscopy in bioinorganic chemistry. Progr Chem, 1996, 8(3): 213-219.
    [58]S.Q Wei, Y.N Xie, F.Q Xu, T.D Hu, W.H Liu, T Liu. Synchrotron radiation XAFS station and its applications. Physics, 2002, 31(1): 40-44.
    [59]钟文杰,贺博,李征,韦世强. USTCXAFS 2.0软件包[J].中国科学技术大学学报, 2001, 31(3): 328-333.
    [60]I.C Kang, Q.W Zhang, S Yin, T Sato, F Saito. Preparation of a visible sensitive carbon doped TiO2 photo-catalyst by grinding TiO2 with ethanol and heating treatment [J]. Appl. Catal., B: Environ, 2008, 80(1-2): 81-87.
    [61]M.S Wong, S.W Hsu, K.K Rao, C.P Kumar. Influence of crystallinity and carbon content on visible light photocatalysis of carbon doped titania thin films[J]. J. Mol. Catal. A: Chem.,2008, 279(1): 20-26.
    [62]S Sakthivel, H Kisch. Daylight photocatalysis by carbon-modified titanium dioxide[J]. Angew Chem Int Ed, 2003, 42: 4908-4911.
    [63]Z.Y Jiang, C.Q Lu, H Wu. Photoregeneration of NADH using carbon-containing TiO2[J]. Ind. Eng. Chem. Res., 2005, 44(12): 4165-4170.
    [64]S Yin, R.X Li, Q.L He, et al. Low temperature synthesis of nanosize rutile titania crystal in liquid media[J]. Mater Chem Phys, 2002, 75(1-3): 76-80.
    [65]X Qi, L Ouyang. Photocatalytic activity and hydroxyl radical formation of carbon-doped TiO2 nanocrystalline: Effect of calcination temperature[J]. Chem. Eng. J, 2009,148 (2/3):248-253.
    [66]Y.C Jimmy, W Ho, J.G Yu, S.K Hark, and K Iu. Effects of Trifluoroacetic Acid Modification on the Surface Microstructures and Photocatalytic Activity of Mesoporous TiO2 Thin Films[J]. Langmuir, 2003, 19(9): 3889-3896.
    [67]Y Huang, W Ho, S Lee, L Zhang, G Li, J.C Jimmy. Effect of Carbon Doping on the Mesoporous Structure of Nanocrystalline Titanium Dioxide and Its Solar-Light-Driven Photocatalytic Degradation of NOx[J]. Langmuir, 2008, 24(7): 3510-3516.
    [68]L Zhang, R.V Koka. A study on the oxidation and carbon diffusion of TiC in alumina–titanium carbide ceramics using XPS and Raman spectroscopy[J]. Mater. Chem. Phys., 1998, 57(1): 23-32.
    [69]王振华.掺杂改性纳米TiO2光催化剂的制备、表征及光催化活性的研究[D].山东大学, 2007: 42.
    [70]F.Y Wei, H.L Zeng, et al. Various TiO2 microcrystal: Controlled synthesis and enhanced photocatalytic activities[J]. Chem. Eng. J, 2008, 144:119-123.
    [71]秦好丽,古国榜,柳松等.尿素为氮源制备氮掺杂二氧化钛及其光催化性[J].华南理工大学学报(自然科学版), 2006, 34(12): 78-82.
    [72]P Cheng, C Deng, M Gu, et al. Effect of urea on the photoactivity of titania powder prepared by sol-gel method [J]. Mater. Chem. Phys., 2008, 107(1): 77-81.
    [73]J.H Xu, J.X Li, W.L Dai, et al. Simple fabrication of twist-like helix N, S-codoped titania photocatalyst with visible-light response[J]. Appl. Catal ,B: Environ, 2008, 79(1): 72-80.
    [74]M Janus, M Inagaki, B Tryba, et.al. Carbon-modified TiO2 Photocatalyst by Ethanol Carbonization[J]. Appl. Catal ,B: Environ, 2006, 63(3-4): 272-276.
    [75]S.F Chen, L Chen, S Gao, et al. The Preparation of Nitrogen-doped Photocatalyst TiO2-xNx by Ball Milling[J]. Chem. Phys. Lett., 2005, 413(4-6): 404-409.
    [76]李川,李兆华,柳松,古国榜.氟掺杂纳米氧化钛的制备及日光敏催化活性的研究[J].科技创新导报, 2009 (17): 1-2.
    [77]李发堂,赵地顺,郝勇静,刘瑞红,殷蓉.氟掺杂纳米TiO2粉体的合成及光催化活性研究[J].化学工程, 2009, 37 (2): 54.
    [78]D Li, H Haneda, S Hishita, N Ohashi. Visible-Light-Driven N?F?Codoped TiO2 Photocatalysts. 2. Optical Characterization, Photocatalysis, and Potential Application to AirPurification[J]. Chem. Mater., 2005, 17 (10): 2596–2602.
    [79]J.K Zhou, L Lv, J.Q Yu, H.L Li, P.Z Guo, H Sun, X.S Zhao. Synthesis of Self-Organized Polycrystalline F-doped TiO2 Hollow Microspheres and Their Photocatalytic Activity under Visible Light[J]. J. Phys. Chem., 2008, 112(14): 5316-5321.
    [80]赵振国.接触角及其在表面化学研究中的应用[J].化学研究与应用, 2000, 12(4): 370-374.
    [81]W.J Ren, Z.H Ai, F.L Jia, L.Z Zhang, X.X Fan, Z.G Zou. Low temperature preparation and visible light photocatalytic activity of mesoporous carbon-doped crystalline TiO2[J]. Appl. Catal., B: Environ, 2007, 69(3-4): 138–144.
    [82]T Ihara., M Miyoshi, Y Iriyama, et al. Visible-light-active titanium oxide photocatalyst realized by an oxygen-deficient structure and by nitrogen doping[J]. Appl. Catal., B: Environ, 2003, 42(4): 403-409.
    [83]C Minero, G. Mariella, V Maurino, et al. Photocatalytic Transformation of Organic Compounds in the Presence of Inorganic Anions.1.Hydroxyl-Mediated and Direct Electron-Transfer Reactions of Phenol on a Titanium Dioxide-Fluoride System[J]. Langmuir, 2000, 16(6), 2632-2641.
    [84]L.X Chen, T Rajh, Z.Y Wang and M.C Thurnauer. XAFS Studies of Surface Structures of TiO2 Nanoparticles and Photocatalytic Reduction of Metal Ions[J]. J. Phys. Chem. B, 1997, 101(50): 10688-10697.
    [85]L Soriano, M Abbate, J Vogel, J.C Fuggle. Chemical changes induced by sputtering in TiO2 and some selected titanates as observed by X-ray absorption spectroscopy[J]. Surf. Sci., 1993, 290(3): 427-435.