TiO2 three-layered nanocomposite films

TiO2 three-layered nanocomposite films

Materials Science in Semiconductor Processing 21 (2014) 26–32 Contents lists available at ScienceDirect Materials Science in Semiconductor Processin...

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Materials Science in Semiconductor Processing 21 (2014) 26–32

Contents lists available at ScienceDirect

Materials Science in Semiconductor Processing journal homepage: www.elsevier.com/locate/mssp

Structure, morphology and photocatalytic activity of Cu2O/Pt/TiO2 three-layered nanocomposite films Yiming Liu a,b, Wanggang Zhang a, Liping Bian a, Wei Liang a,n, Jianjun Zhang a, Bin Yu a a b

College of Materials Science and Engineering, Taiyuan University of Technology, Taiyuan 030024, PR China Shanxi Institute of Analytical Science, Taiyuan 030006, PR China

a r t i c l e in f o

abstract

Available online 3 February 2014

Novel Cu2O/Pt/TiO2 three-layered nanocomposite films were prepared by deposition on glass substrates using the magnetron sputtering method. Their structure, surface morphology as well as optical and photocatalytic properties were examined by X-ray diffraction, Raman spectroscopy, X-ray photoelectron spectroscopy, scanning electron microscopy, UV–visible spectroscopy, and photoluminescence spectroscopy. As a comparison, Cu2O/TiO2 double-layer films were also investigated. The results show that Cu2O/ TiO2 double-layer films have relatively smooth surfaces with agglomerated Cu2O particle, whereas the surface layer of the Cu2O/Pt/TiO2 three-layered nanocomposite films was composed of fine nano-sized columnar Cu2O and they had a rough surface morphology due to the insertion of the Pt layer. The photocatalytic activity of the three-layered films is significantly higher than that of the Cu2O/TiO2 double-layered composite films. Such enhancement is closely related to the presence of the Pt layer and the rough surface, which was composed of fine nano-sized Cu2O columns; this increases the utilization of visible light as well as promotes the transfer of interfacial charge and the separation of photogenerated electron–holes. & 2014 Elsevier Ltd. All rights reserved.

Keywords: Three-layered nanocomposite films Structural properties Surface morphology Photocatalytic activity

1. Introduction The photocatalytic degradation of organic pollutants based on wide band gap semiconductors has attracted considerable attention during the past decades due to this method's capability to simultaneously harvest solar energy and drive chemical reactions via photo-excited charge carriers and activated electronic states [1,2]. Generally, the photo-catalysts are in powder form and placed in solutions that need remediation, which inevitably results in some disadvantages, such as difficult recovery, facile cohesion, low utilization rates, and secondary pollution [3]. In practice, the photocatalytic film is indeed more viable, and film-based

n

Corresponding author. Tel./fax: þ 86 351 6018398. E-mail address: [email protected] (W. Liang).

1369-8001/$ - see front matter & 2014 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.mssp.2014.01.022

photocatalytic degradation has been rapidly developed in recent years. TiO2 has become the most promising photocatalytic material due to its chemical–physical stability, thermal properties, electrical properties, low cost, and excellent ability to degrade organic pollutants [4–6]. The photocatalytic effect on the degradation of organic compounds can be explained by the presence of electron–holes in the semiconducting material. However, due to the wide band gap, TiO2 only absorbs in the near-UV region, which is only a small portion of the solar spectrum [7,8]. Due to this limitation, the development of photocatalysts that can be excited in the visible range is of great interest in order to further improve photocatalytic processes that use solar radiation for the degradation of organic pollutants [9,10]. Meanwhile, the significant recombination of the photogenerated electrons and holes is also a major

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obstacle inhibiting further increase in TiO2 photocatalytic activity [11]. TiO2 composited with other semiconducting materials with lower band gaps that can respond to visible light is one possible way to fix these issues. Recombination semiconductors can also increase the lifetime of charge carriers and the interfacial electron-transfer rate constant, which can improve the photoconversion efficiency for photocatalysis [12]. Cuprous oxide (Cu2O), an important p-type semiconductor with a direct band gap of 2.0 eV, has attracted extensive attention for its applications in solar energy conversion, gas sensors, electronics, magnetic storage, etc. [13]. Recently, Cu2O has been used as a visible-light-driven photocatalyst for splitting water and degrading organic contaminants [14–16]. However, pure Cu2O has relatively low catalytic activity due to its faster recombination rate between the electron and hole. Thus, photocatalysts made of TiO2 and Cu2O composites have many potential applications [17–19]. When Cu2O and TiO2 nanoparticles are coupled together to yield nanocomposite oxides, efficient electron transfer from Cu2O to TiO2 in the nanocomposite occurs under visible-light irradiation [20]. In addition, the surface modification of TiO2 may be achieved with noble metals [21]. Previous results have shown that noble metals can inhibit the charge recombination of photo-generated electron–hole pairs thereby enhancing the charge carrier density reaching the TiO2/ liquid interface and alter the surface work function of the catalyst [22–24]. Platinum is an important noble metal. Previous investigations confirmed that modified TiO2 films with platinum were a promising way for preventing the recombination of the electron–hole pairs, and this led to improved photodegradation rates for various organic compounds under visible light irradiation [25]. To the best of our knowledge, a metal combined with two semiconductors that is to be utilized as a photocatalyst has very rarely been reported. Photocatalytic films for this application indeed are more viable due to their easy separation recovery and a simple post-treatment process. In this work, Cu2O/Pt/TiO2 three-layered nanocomposite films with rough surfaces composed of fine nano-sized Cu2O columns were prepared by magnetron sputtering. The influences of the Pt metal layer on the structure, surface morphology, optical properties and photocatalytic activities of these three-layered composite films were investigated and discussed. It has been shown that the optical absorption property and the photocatalytic activities of the three-layered composite films are significantly higher than those of the Cu2O/TiO2 double-layered composite films. 2. Experimental procedures 2.1. Preparation of films The Cu2O/Pt/TiO2 three-layered composite films were prepared by magnetron sputtering. Prior to deposition, the glass substrates (6  6 cm2) were ultrasonically cleaned with acetone, absolute ethyl alcohol, and de-ionized water for 10 min. TiO2 single films were deposited on glass substrates by a high vacuum multifunctional magnetron

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sputtering equipment (JGP560I, Shenyang Scientific Instrument Co., China) using TiO2 ceramic targets at room temperature. During sputtering, the argon gas flow rate was kept at 30 sccm, the chamber pressure was maintained at 4.3 Pa, and the sputtering power was 100 W. After deposition the films were annealed at 500 1C for 2 h in an ambient atmosphere so as to form the anatase phase of TiO2. Cu was deposited onto the anatase–TiO2 films and annealed in an ambient atmosphere at 200 1C for 2 h to form Cu2O/TiO2 double-layered composite films. Cu2O/Pt/ TiO2 three-layered composite films were prepared by depositing Pt and Cu onto the anatase–TiO2 films in sequence, followed by annealing at 200 1C for 2 h in an ambient atmosphere. The reactive DC power for both the Pt and Cu targets were 100 W. During sputtering, the argon gas flow rate was kept at 30 sccm, and the chamber pressure was maintained at 6 Pa for Cu and 4.3 Pa for Pt. The thickness of the films was measured with a scanning electron microscope (JSM-6700F), and the corresponding deposition rates of the TiO2, Pt, and Cu films were then calculated to be about 10, 12, and 16 nm/min, respectively. In the three-layered structure, the thicknesses of the TiO2 and Cu2O layers were 100 nm and 90 nm, respectively, while the intermediate Pt layer was about 10 nm. For comparison, TiO2 (100 nm) single films, Pt (10 nm) single films, and TiO2 (100 nm)/Cu2O (90 nm) double-layered composite films were also investigated. 2.2. Film characterization The crystal structures of the films were analyzed with the Cu Kα line from a Rigaku D/max 2500 X-ray diffractometer (XRD) with patterns recorded in a range of 20–801 (2θ). The Raman spectra were collected on a laser microRaman spectrometer (Renishaw inVia) at a wavelength of 514 nm at room temperature. A scanning electron microscope (SEM) (JSM-6700F) operated at 10 kV was employed to investigate the morphologies of the films. Optical absorption of the composite films in the wavelength range of 300–800 nm was measured using a UV/vis spectrophotometer (Perkin-Elmer Lambda 750). The photoluminescence emission spectra of the samples were measured at room temperature with a Cary Eclipse Fluorescence Spectrophotometer (VARIAN). The binding energy was determined by X-ray photoelectron spectroscopy (XPS) (Escalab250). 2.3. Photocatalytic properties The photocatalytic activities of samples were evaluated by measuring the degradation rates of methylene blue (MB) in aqueous solution under visible light irradiation. The test samples were added to 10 ml MB aqueous solutions with concentrations of 5 mg/L in cylindrical glass reactors. Before the photocatalytic reaction, the solution was magnetically stirred in dark for 2 h to achieve an adsorption–desorption equilibrium among the photocatalyst, MB, and water. The photocatalytic reactions were carried out at room temperature, using a 300 W tungsten lamp (Philips Halogen) to simulate visible light. The degradation of MB was monitored from the intensity of

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Fig. 1. XRD patterns of TiO2 single films (a), Cu2O/TiO2 double-layered composite films (b) and Cu2O/Pt/TiO2 three-layered composite films (c).

the absorption peak of MB (664 nm) relative to its initial intensity using a Perkin-Elmer Lambda 750 UV/vis spectrometer under various illumination times. 3. Results and discussion Fig. 1 shows the XRD patterns of TiO2 single films, Cu2O/TiO2 double-layered composite films and Cu2O/Pt/ TiO2 three-layered composite films. It is observed that TiO2 single films show diffraction peaks due to the (101) and (004) of the anatase–TiO2 (JCPDS 78-2846) which demonstrates that the anatase–TiO2 film structure can be obtained after annealing at 500 1C for 2 h. It is important to note that the Cu2O/TiO2 double-layered composite films also show the (101) and (004) diffraction peaks of the anatase–TiO2 as well as additional (111) and (200) diffraction peaks due to Cu2O (JCPDS 78-2076) in Fig. 1(b), which indicates that Cu2O is formed at an annealing temperature of 200 1C for 2 h. The average crystallite size of Cu2O is 45.2 nm, according to Scherrer's equation based on the main (111) diffraction peak. As shown in Fig. 1(c), Cu2O/Pt/ TiO2 three-layered composite films also have 100% anatase–TiO2. Therefore, it can be considered that the introduction of Pt and Cu have nearly no influence on the phase structure of anatase–TiO2. Compared with double-layered composite films, the (111) and (200) diffraction peaks of Cu2O from the three-layered composite films become stronger and wider, implying an enhancement in the crystallization and formation of finer Cu2O crystallites. Meanwhile, the calculated Cu2O size of the three-layered composite films is about 31.7 nm according to the Scherrer formula. No other characteristic diffraction peaks of the Pt species except for the (111) peak are observed in the threelayered composite films due to the low amount of Pt that was present and its relatively low diffraction intensity. Raman spectroscopy is a powerful nondestructive tool for distinguishing ordered and disordered crystal structures of samples. Fig. 2 shows the Raman spectra of TiO2 single films, Cu2O/TiO2 double-layered composite films and Cu2O/Pt/TiO2 three-layered composite films at room temperature using a 514.5 nm excitation wavelength of Ar þ laser. As shown in Fig. 2(a), five bands at 142 cm  1

Fig. 2. Raman spectra of TiO2 single films (a), Cu2O/TiO2 double-layered composite films (b) and Cu2O/Pt/TiO2 three-layered composite films (c).

(Eg), 197 cm  1 (Eg), 394 cm  1 (B1g), 514 cm  1 (A1g), and 637 cm  1 (Eg) are observed in the Raman spectra of pure TiO2 films, which are the characteristic Raman modes of the anatase phase [26]. The Raman signal of composite films is a combination of two independent material signals verifying the efficient crystalline formation [27]. Fig. 2(b) shows that two weak characteristic peaks at about 109 cm  1 and 218 cm  1 for the Cu2O structures are observed in the Raman spectrum of the Cu2O/TiO2 double-layered composite films, which correspond to the well-documented inactive Raman mode and the secondorder Raman-allowed mode [28]. While comparing the shifts in peak positions between TiO2 single films and Cu2O/TiO2 double-layered composite films, the peak at 142.28 cm  1 from the double-layered films shifts to 147.97 cm  1, which is close to the characteristic peaks of Cu2O. The shifted peak is also significantly broader in the double-layered composite films, expanding from 360 nm to 700 nm; the broadening region also contains characteristic peaks of Cu2O and TiO2, which may be related to a charge transfer between the Cu2O and TiO2 conductions bands [29]. In fact, the Raman spectra of the Cu2O/TiO2 double-layered films show a combination of the two semiconducting characteristic bands. Fig. 2(c) shows the positions and intensities of the Raman active modes of the three-layered composite films, and they agree well with the double-layered composite films. These observations show that the Cu2O/Pt/TiO2 three-layered composite films only consist of the Cu2O and anatase–TiO2 phase, because the single Pt metal itself has no Raman peak. In order to further characterize the Pt particle in the Cu2O/Pt/TiO2 three-layered composite films, XPS was used to examine a Cu2O/Pt/TiO2 three-layered composite film with a thinner Cu2O film thickness of 5 nm. As shown in Fig. 3(a), it is found that Pt 4f5/2 and 4f7/2 peaks are present and correspond to bonding energies of 74.3 and 71.2 eV, respectively, which is expected for metallic Pt0 [30]. Similarly, as shown in Fig. 6(b), Cu 2p3/2 and 2p1/2 peaks are present at 932.4 eV and 952.2 eV, respectively, which indicates that Cu in the three-layered composite film exists in the Cu þ form [31]. This further confirms the presence of metal Pt (Pt0) and Cu2O (Cu þ ) in the threelayered composite film.

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Fig. 3. XPS data of 5 nm Cu2O/Pt/TiO2 three-layered composite films: Pt-4f and Cu-3p (a) and Cu-2p (b).

Fig. 4. SEM images of TiO2 single films (a), Pt/TiO2 double-layered films (b), Cu2O/TiO2 double-layered composite films (c), Cu2O/Pt/TiO2 three-layered composite films (e), cross-sectional SEM micrograph of Cu2O/TiO2 double-layered composite films (d) and Cu2O/Pt/TiO2 three-layered composite films (f).

Fig. 4(a) presents SEM images of the TiO2 single films, which show a dense, smooth coating with regularly arranged particles that are about 70–80 nm in diameter, which can be attributed to the crystal growth and densification during the heating process at 500 1C. For the Pt/TiO2 double-layered films, however, fine Pt particles on the top layer of the film are about 10 nm in diameter and they are homogeneously distributed over the TiO2 films which are discrete and have a high volume fraction of interspaces, as shown in Fig. 4(b). Fig. 4(c)–(f) shows the surface morphologies and high-magnification cross-section of Cu2O/TiO2 double-layered composite films and Cu2O/Pt/TiO2 three-layered composite films. Although both surfaces are covered by Cu2O layers, their surface

morphologies are very different. As shown in Fig. 4(c) and (d), the surface layer of the double-layered Cu2O/TiO2 composite films consists of about 50 nm Cu2O particles that have a strong agglomeration tendency, and a relatively smooth surface is present. In contrast, the surface layer of the Cu2O/Pt/TiO2 three-layered nanocomposite films was composed of uniformly distributed fine nano-sized columnar Cu2O that were about 15–30 nm in diameter and the films exhibited a rough surface morphology due to the insertion of the Pt layer, as shown in Fig. 4(e) and (f). Interestingly, there is no obvious particle agglomeration observed in Fig. 4(e). This indicates that the Pt insertion has significant influence on the growth mechanism and growth pattern of the top layer Cu2O crystals. The double-layered

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composite contains a Cu2O layer (about 90 nm) and an anatase–TiO2 layer (about 100 nm), as shown in Fig. 4(d). Fig. 4(f) also shows a notable three-layered structure with Pt thin layer having a thickness of approximately 10 nm between the top Cu2O layer (about 90 nm) and bottom anatase–TiO2 layer (about 100 nm). UV–visible spectra of TiO2 single films, Cu2O/TiO2 double-layered composite films and Cu2O/Pt/TiO2 threelayered films are shown in Fig. 5. It is obvious that the TiO2 single films absorb mainly UV light with wavelengths of less than 400 nm. The small fluctuations of the absorption spectra came from interferences occurring at the interface of the thin film and the glass substrate [32]. Due to the visible light response of Cu2O, the Cu2O/TiO2 doublelayered composite films exhibited a clear absorption redshift into the visible-light range. Compared with the double-layered composite films, the absorption spectrum of the three-layered composite films also has an obviously enhanced optical absorption property, which can be attributed to the insertion of the Pt layer and rough surface morphology. Therefore, the introduction of Pt can effectively enhance visible-light absorption. The photoluminescence (PL) emission spectra were used to reveal the efficiency of trapping, migration, transfer, and separation of charge carriers, and to investigate their lifetime in the semiconductor since PL emissions result from the recombination of electron/hole pairs [33]. When electron–holes recombination occurs after photocatalyst irradiation, photons are emitted and this results in photoluminescence. It is generally believed that a lower stimulated PL intensity indicates an enhanced separation and transfer of photoinduced electrons in the photocatalyst, thus resulting in a higher photocatalytic activity [34,35]. In this study, Fig. 6 shows the PL spectra for Cu2O/Pt/TiO2 three-layered composite films and Cu2O/ TiO2 double-layered composite films at an excitation wavelength of 430 nm, which exhibits similar spectral patterns in the wavelength range of 500–650 nm. In contrast, quenching of the PL intensity in the threelayered composite films is more drastic than that in the double-layered composite films, indicating a markedly enhanced charge separation in the three-layered composite films. The reason for this is the presence of Pt in the

three-layered composite films, which favors the migration of photo-produced electrons and hence promotes the electron–hole separation. To evaluate the photoactivity properties of the samples, MB decomposition studies were performed in a reactor system at room temperature. Fig. 7 shows the photocatalytic degradation of MB as a function of time with different kinds of the films under visible irradiation. For comparison, the blank test was also conducted under the same reaction conditions (Fig. 7(a)). There is little change in the MB concentration after irradiation by visible light for 120 min, indicating that the photolysis of the MB solution without any photocatalyst is negligible under the employed experimental conditions. The photocatalytic reactivity of different kinds of films is quantified by the ratio of the residual concentration (C) to the initial concentration (C0) of MB, denoted as 1  C/C0. It can be seen in Fig. 7(b) that there is no obvious degradation of MB for the pure Pt sample. The photo-degradation efficiency is very obvious for the Cu2O/TiO2 double-layered composite films (only 50% of MB is bleached within 120 min), as shown in Fig. 7(c). As for the Cu2O/Pt/TiO2 three-layered composite films (Fig. 7(d)), the photo-degradation efficiency is even higher than that of the double-layered composite films,

Fig. 5. UV–visible absorption spectra of TiO2 single films, Cu2O/TiO2 double-layered composite films and Cu2O/Pt/TiO2 three-layered films.

Fig. 7. Photocatalytic degradation behaviors of methylene blue (MB) when exposed to the films under visible light irradiation.

Fig. 6. Photoluminescence (PL) spectra of Cu2O/TiO2 double-layered composite films and Cu2O/Pt/TiO2 three-layered composite films.

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reaching up to about 65% within 120 min due to the introduction of Pt. To summarize, a novel Cu2O/Pt/TiO2 semiconductor– metal–semiconductor nanocomposite film with a rougher surface formed by finer aligned columnar Cu2O crystals was successfully prepared, and it exhibits improved optical absorption and photocatalytic reactivity compared to the Cu2O/TiO2 double-layer composite film. The reasons for this can be explained as follows. It has been reported that the crystallization extent of Cu2O was different on different substrates [36]. In our experiment, the Cu2O in the Cu2O/Pt/TiO2 three-layer film had a higher extent of crystallization than that in the Cu2O/TiO2 double-layer film and it had a different morphology due to the differences in the grown substrates. The reason why the substrates have this effect on the Cu2O deposition is not well known, but it may be related to the surface crystal structure of the substrates and thin film growth modes. For the Cu2O/TiO2 double-layer film, the Cu thin film grows on a dense and smooth TiO2 substrate and finally forms a relatively smooth Cu2O thin film surface morphology after annealing. However, when the Pt layer was introduced in the Cu2O/Pt/TiO2 three-layer film, the Cu thin film grew on a dispersed Pt nanoparticle substrate which did not completely cover the surface of the TiO2 single films. Pt and Cu, which have infinite miscibility with each other, are very similar in structure and both are facecentered cubic materials. Therefore, in the Cu2O/Pt/TiO2 three-layer film, Pt nanoparticles may act as nucleation sites for Cu, and Cu crystals preferentially grow on the Pt particles resulting in the formation of a series of well-aligned nanoCu2O columns. Such columnar structures produce a rougher surface which increases the number of available surface active sites and leads to higher photocatalytic efficiency [37]. The introduction of the Pt layer and surface morphology also enhances the visible-light absorption of the Cu2O/ Pt/TiO2 three-layered composite films compared with the Cu2O/TiO2 double-layered composite films. The intense absorption in the UV–vis light region indicates that more photo-generated electrons and holes can be produced to participate in photocatalytic reactions [38]. Generally speaking, single TiO2 has no response to visible light, but photogenerated electrons can be generated in Cu2O under irradiation. When they are combined together, it is generally recognized that the potential difference between TiO2 and Cu2O forced the migration of photogenerated electrons from Cu2O to TiO2, because the conduction bands of TiO2 are positioned below those of Cu2O [17,39]. Thus, under visible light excitation, photogenerated electrons from Cu2O accumulate in the conduction band of TiO2, whereas holes can accumulate in the valence band of Cu2O, which restrains the recombination of the photogenerated electrons with the holes. The PL measurement results show that the Pt layer in the threelayered composite films leads to the separation of photogenerated charge carriers, and favors the migration of photogenerated electrons. The metal particles act as electron wells allowing a more efficient separation of the charges, assisting the electron transfer to electron acceptors and thus preventing a higher degree of electron–hole recombination [24]. The Pt metal core benefits the charge

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separation of the photocatalyst. At the same time, the relatively low resistance of the Pt metal core is convenient for photo-electron transfer from the excited Cu2O to TiO2 [40]. Therefore, the excited electrons first transfer from the valence band to the conduction band of Cu2O under visible light irradiation in the three-layered composite films, then they transfer to the Pt layer, and finally to the conduction band of TiO2. It is the Pt metal layer that pushes more photogenerated electrons to transfer to the conduction band of TiO2, and the recombination of electrons and holes is further suppressed in the three-layered composite films. Simply, the presence of Pt metal particles plays an important role in the separation of photogenerated charge carriers, which increases the available surface active sites and enhances the visible-light absorption, prolonging the lifetime of the excited electrons and improving the photocatalytic performance. 4. Conclusion In this work, a novel Cu2O/Pt/TiO2 three-layered nanocomposite film with a rough surface composed of nano-scale columnar Cu2O was successfully prepared using magnetron sputtering followed by annealing in air. Various characterization approaches confirmed the formation of the novel threelayered Cu2O/Pt/TiO2 nano-junction system. The introduction of the Pt layer reduced the size of the surface crystallite, restrained the agglomeration of surface nanoparticles, enhanced the visible-light absorption of the films, prohibited the combination of electron–hole pairs, and facilitated the interfacial charge transfer resulting in significantly enhanced photocatalytic activity compared with that of the doublelayered composite film. The enhanced photocatalytic activity can be attributed to the small crystalline size, greater surface roughness, increased visible-light absorption, enhanced charge separation, and enhanced electron transfer in the three-layered composite films. This work may provide new insights into the design of novel multi-component photocatalyst systems with efficient visible light activity.

Acknowledgments The authors gratefully acknowledge the financial support of this study by the National Natural Science Foundation of China (Grant nos. 51175363 and 51274149), the Program for Chang Jiang Scholar and Innovative Research Team in University (IRT0972), the Outstanding Innovation Project in Shanxi Province (20133027) and Taiyuan University of Science and Technology Innovation Fund (2013A004). References [1] D.W. Chu, Y. Masuda, T. Ohji, K. Kato, Langmuir 26 (2010) 2811–2815. [2] A. Houas, H. Lachheb, M. Ksibi, E. Elaloiu, C. Guillard, J.M. Herrmann, Appl. Catal. B: Environ. 31 (2001) 145–157. [3] G.D. Wu, W. Zhai, F.Q. Sun, W. Chen, Z.Z. Pan, W.S. Li, Mater. Res. Bull. 47 (2012) 4026–4030. [4] M. Pelaez, N.T. Nolan, S.C. Pillai, M.K. Seery, P. Falaras, A.G. Kontos, P.S.M. Dunlop, J.W.J. Hamilton, J.A. Byrne, K. O’Shea, M.H. Entezari, D.D. Dionysiou, Appl. Catal. B: Environ. 125 (2012) 331–349.

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