Experimental Study on Adsorption and Photocatalytic Decomposition

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Experimental Study on Adsorption and Photocatalytic Decomposition of Isopropyl Methylphosphonofluoridate at Surface of TiO2 Photocatalyst Tsutomu Hirakawa,*,† Keita Sato,‡ Asuka Komano,‡ Shintarou Kishi,‡ Chifumi K. Nishimoto,† Nobuaki Mera,† Masahiro Kugishima,§ Taizo Sano,† Hiromichi Ichinose,§ Nobuaki Negishi,† Yasuo Seto,*,‡ and Kouji Takeuchi† National Institute of AdVanced Industrial Science and Technology (AIST), Tsukuba-west 16-1, Onogawa, Tsukuba, Ibaraki, 305-8569, Japan, National Research Institute of Police Science (NRIPS), 6-3-1 Kashiwanoha, Kashiwa, Chiba, 277-0882, Japan, and Saga Ceramic Research Laboratory (SCRL), 3037-7 Arita, Saga, 844-0024, Japan ReceiVed: NoVember 17, 2009; ReVised Manuscript ReceiVed: December 16, 2009

The adsorption and photocatalytic degradation of nerve agent, isopropyl methylphosphonofluoridate, Sarin (GB) on powdery TiO2 film has been investigated using attenuated total reflection-infrared Fourier transform spectroscopy (ATR-FTIR) in ambient atmosphere. Producing innocuous isopropyl methylphosphonic acid as a consequence of GB adsorption at the surface of TiO2 indicates that powdery TiO2 film is effective to hydrolyze GB. The adsorbed GB and IMPA were quickly decomposed by TiO2 photocatalysis to give isopropanol, acetone, formate, and methylphosphonic acid, and finally completely mineralized to phosphoric acid, water, and carbon dioxide. We also elucidated a plausible adsorption structure and photocatalytic decomposition mechanism of GB at the surface of TiO2 photocatalyst. 1. Introduction Decontamination of the environmental area contaminated by chemical warfare agents, CWAs, has been studied.1–5 Use of metal oxide as a catalyst has been greatly focused on for the decontamination of the CWAs including the case of chemical terrorism.6–13 For instance, an important study on adsorption and hydrolysis of isopropyl methylphosphonofluoridate, Sarin as nerve agent (GB, illustrated in Scheme 1), was originally investigated on γAl2O3 and MgO by Fourier transform infrared spectroscopy (FTIR).6 The hydrolysis mechanism of GB at the surface of them was studied, and it was found that the Lewis acid site at the metal oxide surface has an important role in hydrolyzing the adsorbed GB to the innocuous reagent isopropyl methylphosphonic acid (IMPA). Such a study on adsorption, hydrolysis, and decomposition of organophosphonate compounds including GB molecules at the metal oxide surface has been well summarized.7 In recent years, the detailed kinetics of hydrolysis and decomposition of trimethylpropyl methylphosphonofluoridate, tabun (GD), S-[2-(diisopropylamino)ethyl]-O-ethyl methylphosphonothioate (VX) as a nerve agent, and sulfur mustard (HD) as a blister agent at the surface of γAl2O3, MgO, CaO, and TiO2 has been strenuously investigated by nuclear magnetic resonance (NMR) and gas chromatographymass spectroscopy (GC-MS), and the hydrolysis mechanism of them on the metal oxide has also been suggested.8–11 One of the subjects which has to be solved is slow hydrolysis decontamination that needs several days and an accumulation of toxic production.12,13 Titanium dioxide, TiO2, has been shown to be an effective photocatalyst for the decomposition of a large number of organic * To whom correspondence should be addressed. E-mail: t-hirakawa@ aist.go.jp. Fax: +81-29-861-8051. † National Institute of Advanced Industrial Science and Technology (AIST). ‡ National Research Institute of Police Science (NRIPS). § Saga Ceramic Research Laboratory (SCRL).

SCHEME 1: Isopropyl Methylphosphonofluoridate, Sarin as Nerve Agent (GB)

compounds.14–24 However, few studies on the photocatalytic decomposition for CWAs have been reported and a detailed study on the photocatalytic reaction mechanism for these CWAs has never been reported.25–29 In contrast, a number of studies using CWA simulants have examined the reaction of gas and liquid phase.30–56 For CWAs simulant, dimethyl sulfide (DMS), diethyl sulfide (DES) and 2-chloroethyl ethyl sulfide (2CEES) as HD simulant,30–40 and dimethyl methyl phosphonate (DMMP) and di-isopropylfluorophosphate (DFP) as GB and GD simulant46–56 have been known for major simulants used in the study on the photocatalysis. Complete decomposition of these simulants by TiO2 photocatalysis indicates that TiO2 has an advantage as a photocatalyst compared with γAl2O3. It is clearly elucidated that the photocatalytic decomposition mechanism depends on each chemical structure of simulant and an accumulation of products affects the photocatalytic activity.30–56 Even though the photocatalytic decomposition for the CWA simulant is evidently elucidated as stated above, the photocatalytic decontamination methods have not been recognized yet. The reason is that experimental verification to decompose real CWAs by TiO2 photocatalysis has never been reported yet. Because the chemical structure of real CWAs absolutely affects the photocatalytic decomposition rate and mechanism, the haphazard use of TiO2 photocatalysts for CWA decontamination

10.1021/jp910911x  2010 American Chemical Society Published on Web 01/19/2010

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without experimental verification causes a grievous accident such as a fatal accident in the scene contaminated by CWAs. Hence, experimentally verifying the adsorption and photocatalytic decomposition mechanism of real CWAs is necessary to pave the way to develop the photocatalytic decontamination systems. In the present paper, we focus on the nerve agent GB for one of the CWAs and report the results of analysis of the adsorption and photocatalytic decomposition of vaporized GB at the surface of TiO2 photocatalyst by using ATR-FTIR spectroscopy. 2. Experimental Section 2.1. Sample. TiO2 powder (P25, Nippon aerojil, 32 nm primary particle size, 49 m2/g BET surface area, 20% rutile and 80% anatase crystal component)57 was used as a photocatalyst. Isopropyl methylphosphonofluoridate, GB (the purity was >97% according to the supplier), was obtained from TNO Prince Maurits Laboratory, Rijswijk, The Netherlands. GB was used without further purification. Isopropyl methylphosphonic acid (IMPA) was synthesized in our laboratory.58 Methyl phosphonic acid (MPA) (Aldrich, purity 98%), phosphoric acid (PA) (Wako for HPLC grade, purity 85%), iropropanol (Wako, purity 99.9%, cGC grade), acetone (Wako, purity 99.5%, GR grade), formaldehyde (SIGMA-Aldrich, purity 37%, 10-15% methanol), NaF (>99% purity, Wako), NaCl (>99.5% wako), and HCl (35%, wako) were used without further purification. 2.2. ATR-FTIR Analysis. 2.2.1. ATR Accessory for CWAs. The adsorption and the photocatalytic decomposition of GB at the surface of TiO2 were analyzed by ATR-FTIR spectroscopy. A special ATR accessory was made of stainless steel and aluminum for handling GB gas and was equipped with a quartz window to irradiate UV light into the photocatalyst. The volume of the photocatalytic reactor part was 180 mL. The ATR accessory possesses a gas flow pipe in both the photocatalytic reactor and IR beam path. The IR beam path was purged by air passed through soda lime and a charcoal filter to remove humidity and CO2. ZnSe was used as the ATR crystal. The incidence angle and number of IR beam reflection are 45° and 5 times, respectively. An IR spectrum was measured by FT-IR spectroscopy (FT/IR-610, JASCO) equipped with a MCT detector. The IR frequency was recorded with 2 cm-1 resolution and 32 times scan. 2.2.2. Photocatalysis. P25 was suspended in Milli-Q water and agitated by sonication for 15 min. After agitation, the suspension was applied to ZnSe crystal of 2.5 cm × 1.1 cm and was slowly dried in air on a warm plate; finally, powdery TiO2 film was obtained. The film thickness of TiO2 applied to the surface was adjusted to 1.5 µm. The powdery TiO2 film at the ZnSe crystal was put on the special ATR accessory. Typically, the powdery TiO2 film was exposed to UV light for 1 h before experiment under the same air as the flow air in the IR beam path to remove a small amount of organic contamination from the surface. UV irradiation was carried out by an UVLED irradiator (ZUV-C30H, OMRON, center wavelength: 360 nm). The light intensity on the powdery TiO2 film, which was measured with a photometer (UV Ceramate Pro, Fuji Xerox), was 2.0 mW · cm-2; it was passed through the quartz window of the ATR accessory. Of the undiluted GB, 3 µL was injected into a glass tube (volume of 500 mL, GL science) equipped with a gas flow cock and was completely vaporized by heating the GB liquid spot in the tube with a heat blower. Then, the temperature of the glass tube was usually 60.5-61 °C. The vaporized GB in the glass tube was pumped into the photocatalytic reactor part in the ATR

Hirakawa et al. accessory by an air cylinder at a flow rate of 200 mL/min for 2 min. Then, the exhaust cock of the gas pipe in the ATR accessory was opened in order to keep the pressure of the photocatalytic reactor. After pumping, the inlet and exhaust cock of the gas pipe in the photocatalytic reactor part were closed. The residual vaporized GB in the photocatalytic reactor was then used as an initial concentration in this study. The humidity and temperature of gas containing the vaporized GB in the photocatalytic reactor were 21% and 18 °C, respectively. Photocatalysis started after observing the evaporated GB adsorption at the surface of TiO2 for 30 min. UV light was irradiated by an UV-LED irradiator at a 2.0 mW · cm-2 light intensity passed through the quartz window, and the ATR-FTIR spectrum was measured in situ under UV irradiation. 2.2.3. IMPA, MPA, PA, and F- Adsorption. IMPA, MPA, PA, and F- adsorption was carried out under TiO2 suspension conditions by ATR-FTIR in order to verify the formation of them in the adsorption and photocatalytic decomposition of the GB molecule. A 1.37 mM solution of each reagent IMPA, MPA, and PA was prepared in acetonitrile. A 30 µL portion of the acetonitrile solvent was applied at the powdery TiO2 film. After applying, the photocatalytic reactor part was purged by air passed through soda lime and a charcoal filter to remove the acetonitrile for 5 min and the IR frequency was measured as described in section 2.2. The application of each reagent and the measurement of the IR frequency were repeated four times. One gram per liter of TiO2 suspension was prepared in 10 mM NaCl solution, and the pH was adjusted to 4 by 0.1 M HCl. The TiO2 suspension of 0.5 mL was injected into the special ATR accessory where the powdery TiO2 film was already prepared at the ZnSe. A 10 mM NaF solution was prepared in 10 mM HCl solution, and 50 µL of the NaF solution was injected into the TiO2 suspension. The IR frequency was measured as described in section 2.2. Caution: In the present study, all experiments were carried out under ambient atmosphere. However, GB as CWAs and IMPA used in these experiments are highly toxic by both inhalation or ingestion. These compounds should always be handled with special care in a special experimental room under reduced air pressure and should be immediately destroyed with sodium hypochlorite after use. Every experiment was performed by trained personnel and using applicable safety procedures in a special laboratory of NRIPS with the permission of the Ministry of Economy, Trade and Industry of Japan. 3. Result 3.1. GB Adsorption at Powdery TiO2 Thin Film. By pumping the vaporized GB into the photocatalytic reactor part, the IR band in the 1000-1800 and 2500-3800 cm-1 ranges corresponding to the IR adsorption of GB molecule gradually appeared for 30 min in ATR-FTIR spectra of the powdery TiO2 film. Figure 1 shows the GB adsorption process at the surface of TiO2 in the dark. The PdO stretching mode, ν(PdO), first appeared broadly at 1252 cm-1, and the intensity of the IR frequency decreased with GB adsorption. The IR frequency at 1210 cm-1 newly appeared broadly, and the IR intensity increased. The IR frequency of the ν(PdO) mode under liquid and gas conditions GB usually appears in the 1255-1277 cm-1 range, and the frequency shifts to the low side with adsorption at the surface of γAl2O3, as listed in Table 1.6,59 The shift of the ν(PdO) mode on DMMP by adsorption from gas and liquid

Study on Isopropyl Methylphosphonofluoridate

Figure 1. ATR-FTIR spectra of the adsorption process of the vaporized GB. Adsorption time after injection of the vaporized GB: (a) 0.5 min, (b) 1 min, (c) 3 min, (d) 5 min, (e) 10 min, (f) 15 min, (g) 20 min, (h) 25 min, and (i) 30 min. The IR band shown here is from the 1000 to 1470 cm-1 range.

conditions to the surface of metal oxide has also been reported.48,49,60 Thus, the changes of the IR frequencies at 1252 and 1210 cm-1 are attributed to GB molecules in the gas phase or in a physisorbed water layer at the powdery TiO2 film for free PdO groups and the adsorbed GB molecule at the surface of TiO2, respectively. With the frequency shift of the ν(PdO) mode, the IR frequency at 1320 cm-1 which corresponds to the δs(CH3-P) mode was also shifted to 1313 cm-1, expecting that IMPA was formed. Figure 2 shows the IR spectrum of the IMPA adsorbed at the surface of TiO2 in the dark. As you can clearly see in the IR spectrum, the δs(CH3-P) mode of IMPA appeared at 1312 cm-1, indicating that the shift of the IR frequency from the 1320 to 1313 cm-1 range was corresponding to the formation of IMPA. The other assignment of IMPA adsorbed at the surface of TiO2 was listed in Table 2 (Figure S1 in the Supporting Information). The formation of IMPA was also identified with a shift of the frequency from 1025 to 1018 cm-1, attributed to vibration mode νs(C-O-(P)) of GB and IMPA, as shown in Figure 1 and Table 2. The IMPA formation is brought by hydrolyzing GB with surface hydroxyl groups. In fact, the IR frequencies at 3406 cm-1, which are attributed to the ν(OH) mode, as shown in Figures 3 and 4, were decreased with adsorption of the vaporized GB at the surface of TiO2. Especially, the negative IR frequency at 3693 cm-1 attributed to isolated OH groups of the TiO2 surface appeared. The isolated OH groups at 3693 cm-1 are well-known as the surface species for hydrolyzing DMMP,48,49,52 clearly indicating that GB molecules were hydrolyzed to IMPA by the surface hydroxyl groups with consumption of the surface water molecules at the crystal surface of TiO2 (Figure S2 in the Supporting Information). The IR frequencies at 1081 (F(CH3-C)), 1142 (F(CH3-C)), 1178 (F(CH3-C)), 1379 (δs(CH3C)), 1385 (δs(CH3C)), 1459 (δas(CH3C)), and 1468 (δas(CH3C)) cm-1 appeared and were attributed to isopropyl groups of GB (Figure 1 and Table 1). Acetone was also observed as IR frequencies at 1230, 1674, 1678, 1701, and 1720 cm-1, and the low intensity IR frequencies attributed to formate at the surface of TiO2 also appeared in the 1500-1580 cm-1 range (Tables S1 and S2 in the Supporting

J. Phys. Chem. C, Vol. 114, No. 5, 2010 2307 Information). This acetone and formate might be contamination and/or product catalytically produced with adsorbing GB molecules at the surface of TiO2. By GB adsorption, the IR frequencies at 1117, 1652, and 1658 cm-1 also appeared, as shown in Figures 1 and 3. The similar IR frequencies at 1120, 1652, and 1658 cm-1 were observed from IMPA adsorption, as shown in Figure 2, indicating that the IR frequency was corresponding to the formation of IMPA from the hydrolyzed GB (Table 3 and the inset of Figure S1 in the Supporting Information). 3.2. GB Decomposition by TiO2 Photocatalysis. After observation of GB adsorption for 30 min, UV irradiation started. Dramatic changes were observed in the 1000-1800 and 2700-3800 cm-1 ranges of the IR spectra. As shown in Figure 5a, the IR intensities of 1018 and 1081 cm-1, which were attributed to vibration mode νs(C-O-(P)) and the F(CH3) mode of IMPA, were decreased, indicating that IMPA was oxidized by TiO2 photocatalysis. With the disappearance of the vibration mode, the δs(CH3-P) mode of IMPA at 1313 cm-1 also shifted to a higher frequency at 1320 cm-1. The IR frequency of the δs(CH3-P) mode on MPA usually develops at higher frequency than that of IMPA (Figure S3 and Table S6 in the Supporting Information). In addition, new IR frequencies at 1123 and 1204 cm-1 appeared at 10 min and developed in process of UV irradiation time. The IR frequency at around the 1204 cm-1 range is attributed to the overlapped mode of δs(OH) and δas(OH),61 indicating that the IR frequencies at 1320 and 1204 cm-1 are attributed to MPA. It is known that PA has characteristic IR frequency at 1125, 1086, 1055, and 1008 cm-1 62 (Figure S4 and Table S7 in the Supporting Information). As seen in the inset of Figure 5a, broad IR frequency at around the 1000-1070 cm-1 range developed with UV irradiation for 30-50 min, clearly indicating that the IR frequency at 1123 cm-1 is attributed to PA. The developing rate of the IR frequency of MPA was faster than that of PA, as shown in Figure 5b. The difficulty in decomposing the CH3-P structure of MPA reflects the appearance order. Slow decomposition of the CH3-P structure by photocatalysis is also verified by DMMP decomposition.52 This result supports the result of an assignment of MPA because of the fact that the PA has no IR frequency attributed to the δs(CH3-P) mode. Hence, the adsorbed IMPA is stepwise oxidized to MPA and PA by TiO2 photocatalysis. For 10 min of UV irradiation, the IR frequency of isopropyl groups on GB and IMPA at 1081 (F(CH3-C)), 1142 (F(CH3-C)), 1178 (F(CH3-C)), 1379 (δs(CH3C)), 1385 (δs(CH3C)), 1459 (δas(CH3C)), and 1468 (δas(CH3C)) cm-1 became broad and stepwise disappeared, as seen in Figures 5a and 6, indicating that the isopropyl groups of GB and IMPA were decomposed by the photocatalysis. As the decomposition progressed, the formation of acetone was also observed at 1646, 1663, and 1733 cm-1 and the IR frequency from the 1300 to 1600 cm-1 range attributed to formate appeared newly and developed in the process of UV irradiation time (Table S3 in the Supporting Information). At 1360 cm-1, the broad and strong IR frequency also developed and was corresponding to the overlapping range of isopropanol, acetone, and formate at the surface of TiO2. The decomposition of isopropyl groups also can be seen from a disappearance of the IR frequencies at 2933 (νs(CH3)) and 2981 (νas(CH3C)) cm-1 and an appearance of new IR frequencies at 2940 (νs(CH3)), 2973 (νs(CH3)), 3012 (νas(CH3-P)), and 3028 (ν(CH)) cm-1, as shown in Figure 7a. The IR frequencies at around 1600, 3240, and 3331 cm-1, which are attributed to surface O-H stretching vibrations of

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TABLE 1: Observed and Calculated Infrared Absorption Bands and Mode Assignment for GB. IR frequency, cm-1 a

vibration mode

GB/TiO2 0 min (30 min)

GBliquidb

νas(CH3C) νs(CH3C) ν(CH) ν(CdO) acetoned δas(CH3C) i-Pr-P δas(CH3C) i-Pr-P δas(CH3) δs(CH3C) i-Pr-P δs(CH3C) i-Pr-P δ(CH) δs(P-CH3) ν(PdO) F(CH3-C) i-Pr-P F(CH3-C) i-Pr-P F(CH3-C) i-Pr-P νs(C-O-(P))

2985 (2981) 2933 2881 1739 1468 1459 1420 1385 1379 1363 1320 (1313) 1252 (1210) 1178 1142 1077 (1081) 1025 (1018)

2985 2932 2878 1724 1468 1461 1419 1390 1380 1351 1320 1277 1180 1145 1106 1014

GBadsb 2980 2930 2870 1730 1465 1455 1415 1380 1350 1320, 1315 1245 1170 1135 1090 1020

GBgas.cal.c

GBads.cal.c

3016 2940 2970

3015 2941 3068

1479 1466 1434 1393 1381 1342 1329 1255 1168 1126 1101 971

1471 1463 1428 1386 1379 1349 1335 1169 1176 1139 1089 1007

a This study. b Assignments from ref 6. c The IR peak was calculated from RHF and DFT in ref 59. d The IR frequency is composed of νs(C-O-(P)) + νs(P-O-(C)) suggested from ref 6. However, in this study, we assigned the IR frequency to acetone.

TABLE 2: Infrared Absorption Bands and Mode Assignment for IMPA.

Figure 2. ATR-FTIR spectra of the adsorption process of the IMPA. A 0.12 µM IMPA-acetonitrile solvent was applied at the powdery TiO2 film. The IMPA-acetonitrile solvent was applied four times, and the IR spectra obtained are shown in this figure. The IR band shown here is from the 1000 to 1500 cm-1 range. The whole band of IMPA which is adsorbed at the surface of TiO2 is shown in Figure S1 of the Supporting Information.

TiOH, TiOH2, Ti2OH, and water molecules, developed as a consequence of decomposing GB and IMPA molecules in the process of UV irradiation time (Figure 7a). Parallel to the water production, CO2 production was also observed (Figure S5 in the Supporting Information). These results clearly indicate that GB molecule is completely decomposed to H2O, CO2, and PA. 4. Discussion 4.1. GB Adsorption Mechanism. As seen in Figure 1, the broad IR frequency of ν(PdO) at 1252 and 1210 cm-1 was observed. In the present study, because the powdery TiO2 film was preirradiated before ATR-FTIR measurement, the surface of TiO2 became hydrophilic with decomposition of the small amount of organic contamination63 (Figure S6 in the Supporting Information). Namely, GB molecule first adsorbs at the waterrich surface which is composed of a physisorbed water layer,

vibration mode

IR frequency, cm-1 IMPA/TiO2a

νas(CH3C) νs(CH3C) ν(CH) ν(CdO) δas(CH3C) i-Pr-P δas(CH3C) i-Pr-P δas(CH3) δs(CH3C) i-Pr-P δs(CH3C) i-Pr-P δ(CH) δs(P-CH3) ν(PdO) F(CH3-C) i-Pr-P F(CH3-C) i-Pr-P F(CH3-C) i-Pr-P νs(C-O-(P))

2979 2931 2875, 2857 1734 1469 1453 1414 1388 1375 1361 1312 1207, 1215 1177 1140 1085 1011

a Of the IMPA/acetonitrile solvent, 120 µL was applied at the powdery TiO2 film. A total of 0.17 µmol of IMPA was adsorbed.

indicating that the broad IR frequency is corresponding to a mixed frequency of the simultaneous GB molecules in the gas phase, in the physisorbed water layer, and at the crystal surface of TiO2. If GB molecules were hydrolyzed in the physisorbed water layer at the TiO2 surface, which has been suggested at a pH of 7, the half-life time was calculated to 19.8 h.64 As shown in Figures 1 and 8, the IR peaks assigned to νs(C-O-(P)) and δs(CH3-P) of GB were largely shifted to that of IMPA, indicating that the hydrolysis of GB molecules gradually started at around 5-15 min adsorption time in the dark. Hence, we suggested that the GB hydrolysis to produce IMPA is dominantly carried out by the hydroxyl groups at the crystal surface as the Bro¨nsted acid site.6,48,52,53 We estimated the ratio of the concentration of GB to the total concentration of water molecules and surface hydroxyl groups at the surface of TiO2. The concentration of GB adsorbed was calculated by using the IR intensity at 1018 cm-1 assigned to νs(C-O-(P)) of IMPA so that the concentration of GB adsorbed was hydrolyzed to IMPA (Pre-UV Irradiation section in the Supporting Information). The concentration of GB adsorbed at the surface was calculated to be 0.086 µmol (5.2 × 1017


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TABLE 3: Infrared Absorption Bands and Mode Assignment at around 1120 and 1660 cm-1 vibration mode

IR frequency, cm-1

GB/TiO2a IMPA/TiO2b Al-Fc F-/TiO2d

1117, 1652, 1658 1120, 1652, 1657 1120, 1660 1640, 3065d

a The IR frequency was taken from this study, as shown in Figures 1 and 3. b The IR frequency was taken from Figure 2 in this study. c Assignments from ref 6. d NaF/NaCl/HCl solution was added into TiO2 suspension composed of NaCl/HCl, as shown in Figure S8 in the Supporting Information. The IR frequency at around 3065 cm-1 was visually transparency with addition of F- ion.

molecules), that is, one GB molecule adsorbed at 1 nm2 if it was assumed that the GB molecule adsorbed all over the surface. The total amount of water molecules and the surface hydroxyl groups was estimated to 6.02 × 1017 molecules, meaning that

Figure 5. (A) Changes in ATR-FTIR spectra of the adsorbed GB during photocatalytic oxidation. Time after the start of UV irradiation: (a) 0 min, (b) 0.5 min, (c) 1 min, (d) 3 min, (e) 5 min, (f) 10 min, (g) 15 min, (h) 18 min, (i) 20 min, (j) 25 min, and (k) 30 min. The IR band shown here is from the 1000 to 1350 cm-1 range. The inset shows an enlarged figure of the IR band from 1000 to 1100 cm-1, and the UV irradiation time is for 30, 40, and 50 min. (B) Kinetics plot of the appearance of the IR frequency at 1204 cm-1 of MPA and 1123 cm-1 of PA of spectral intensities observed during the photocatalysis of the adsorbed GB at the surface of TiO2.

the total number of them is 12.3-13 molecules/1 nm2 (Pre-UV Irradiation section in the Supporting Information). Hence, the ratio of the total amount of water and surface hydroxyl groups to GB will be 12:1 at least in this study, indicating that the amount of water and surface hydroxyl groups fully adsorbs at the surface of TiO2 to hydrolyze GB. The physisorbed water layer then has a role to supply water molecules to the crystal surface and to hold GB molecules at the surface of TiO2 as a consequence of dissolving it in the water layer. By taking into account our surroundings, since the surface of TiO2 is usually hydrated, the hydrated surface of TiO2 and superhydrophilicity as an intrinsic property of TiO2 are one of the advantages as an ability to hold highly toxic GB molecules and to supply water molecules to the crystal surface in order to be hydrolyzed to innocuous reagent IMPA.

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Figure 6. Changes in ATR-FTIR spectra of the adsorbed GB during photocatalytic oxidation. Time after the start of UV irradiation: (a) 0 min, (b) 0.5 min, (c) 1 min, (d) 3 min, (e) 5 min, (f) 10 min, (g) 15 min, (h) 18 min, (i) 20 min, (j) 25 min, (k) 30 min, (l) 40 min, and (m) 50 min. The IR band shown in here is from the 1350 to 1800 cm-1 range.

When GB molecule is hydrolyzed to IMPA, Ti-F formation at the surface of TiO2 is expected as well as that observed from F- adsorption at the surface of γAl2O3 where the IR frequency appeared at 1120 and 1660 cm-1 6 (Table 3). In order to verify the Ti-F formation, F- ion was injected into a TiO2 suspension at the ATR accessory. As stated above, GB molecule is first adsorbed at the water-rich surface as a physisorbed water layer and is hydrolyzed to produce F- ion. Hence, F- adsorption at the crystal surface of TiO2 takes place in the physisorbed water layer. Consequently, no IR frequency at 1120 cm-1 appeared. Instead of that, the IR frequency at 3065 and 1630 cm-1 in the ν(OH) and δ(H2O) modes became transparent; a new IR frequency at 1640 cm-1 appeared, and every IR frequency developed in the progress of time, as shown in Figure 9 (Table 3). The change in the IR frequency with addition of F- ion corresponds to some contribution from the surface of solvated F- ions displacing water molecules in an electrical double layer of positively charged TiO2 surface and a deprotonation of surface OH groups. Usually, the water molecules at the surface of TiO2 show two frequencies such as Ti-OH2 (Ti-H2O) at around 1623 cm-1 and ν(OH) similar to bulk water molecules at around 3200 cm-1. From neutral to acid conditions, the IR frequencies of Ti-OH2 broadly shift from 3200 to 3100-3000 cm-1.65 Furthermore, the IR frequency at 3065 cm-1 is also attributed to the surface proton adsorbed at the oxygen site of the crystal lattice.65 On the basis of these assignments, the appearance of negative IR frequency with addition of F- under acidic conditions indicates that these water molecules and proton at the oxygen lattice are substituted by F- ion as a consequence of F- adsorption, as shown in eqs 1 and 2.

Ti-OH2+ + F- T Ti-OH2+-F- T Ti-OH-F--H+ (1) TiO2-OH2 + F- T TiO2-F- + H2O

(2)

As stated above, we could not directly recognize the Ti-F formation at the surface of TiO2 as well as Al-F. However, we believe

Figure 7. (A) Changes in ATR-FTIR spectra of the adsorbed GB during photocatalytic oxidation. Time after the start of UV irradiation: (a) 0 min, (b) 0.5 min, (c) 1 min, (d) 3 min, (e) 5 min, (f) 10 min, (g) 15 min, (h) 18 min, (i) 20 min, (j) 25 min, (k) 30 min, (l) 40 min, and (m) 50 min. The IR band shown here is from the 2700 to 3900 cm-1 range. (B) An enlarged section of part A. The IR band is from 3600 to 3800 cm-1.

the Ti-F formation based on our results and other reports, such as the IMPA formation, F- adsorption at surface hydroxyl groups, the Al-F formation at the surface of γAl2O3 with adsorbing GB,6 and Ti-F formation at the surface of TiO2 with adsorbing DFP.55,56 Since the IMPA molecules have OH groups as a consequence of GB hydrolysis, the Ti-O-P-O-Ti bond can be formed and the new IR frequency as a ν(O-P-O) mode may appear. The IR frequency of the ν(O-P-O) mode depends on the substitution on the phosphorus atom and always appears within the frequency range 1300-1000 cm-1. For instance, the ν(O-P-O) mode on DMMP was assigned to 1100 cm-1.48 It is also suggested that the IR frequency of the ν(PdO) mode splits into two frequencies, forming the O-P-O bond at the surface of γAl2O3, where the new frequency appears 90-100 cm-1 lower.6 On the basis of these suggestions, the IR frequency assigned to the ν(O-P-O) mode may appear at around the 1107-1125 cm-1 range. Hence, we suggest that the IR frequency at 1117-1120 cm-1 observed from GB adsorption is attributed to the Ti-O-P-O-Ti bond of an adsorbed IMPA molecule (Figure S7 and Assignments of IR frequency of



Figure 8. (A) Kinetics plot of the shift of IR frequency assigned to νs(C-O-(P)) of GB and IMPA. The open and closed diamonds mark νs(C-O-(P)) of GB and IMPA that appeared at 1025 and 1018 cm-1, respectively. The peak intensity of 1025 cm-1 of GB gradually shifts to 1018 cm-1 of IMPA within 15 min. (B) Kinetics plot of the shift of IR frequency assigned to δs(CH3-P) of GB and IMPA. The open and closed circles mark δs(CH3-P) of GB and IMPA that appeared at 1320 and 1313 cm-1, respectively. The peak intensity of 1320 cm-1 of GB gradually shifts to 1313 cm-1 of IMPA within 15 min.

Vibrational Modes of Several Kinds of Organic Compound Composed of GB Molecule section in the Supporting Information). The plausible GB adsorption mechanism at the surface of TiO2 proposed in the present study is summarized in Scheme 2. 4.2. Photocatalytic Decomposition Mechanism of GB. In general, it has been known that the TiO2 photocatalytic reactions proceed mainly by photoinduced valence band hole (h+) and hydroxyl radical (OH•) that they are major oxidative species to decompose many hazardous chemical compounds.14–24 Hence, the adsorbed GB and IMPA molecules are oxidized by OH• and/or h+, as has also been reported by the study of the photocatalytic decomposition mechanism of DMMP and DFP.46–56 Acetone and iropropanol production then may be carried out with almost equal probability (path A and path B in Scheme 3).46,47,49–54 The acetone molecule is adsorbed at the surface and is oxidized to formate. Superoxide radical, O2•-, as one of the active oxygen species may also contribute to oxidizing GB and IMPA molecules because it has been suggested that O2•- is reduced to OH• in the TiO2 photocatalysis, as shown in eqs 3-10.14–24,66–68

TiO2 + UV T e- + h+ +

-

+

h + OH (H2O) f OH•(OH•+H ) +

Figure 9. (A) ATR-FTIR spectrum of TiO2 suspension with addition of F- solution. Kinetics plot of the change in the IR frequency at 1640 (B) and 3065 (C) cm-1 of spectral intensity observed during the Fadsorption at the surface of TiO2.

(3)

O2•- + O2•- + H+ f HO2- + O2

(8)

(4)

O2•- + H+ + e- f HO2-

(9)

h + GB, IMPA f oxidation OH•+GB, IMPA f oxidation

(5) (6)

e- + O2 f O2•-

(7)

-

+

-

-

HO2 + H + e f OH•+OH -

(10)

where e represents photoinduced conduction band electrons. Here, as proposed in Scheme 3, although it is expected that the

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Hirakawa et al.

SCHEME 2: The Plausible GB Adsorption Mechanism at the Surface of TiO2 Proposed in the Present Study

SCHEME 3: The Plausible Production Mechanisms of Acetone and Iropropanol (Paths A and B)a

a Isopropyl groups of IMPA may be directly oxidized to acetone molecules (path A), the isopropanol production process may be carried out in the TiO2 photocatalysis, and isopropanol gradually oxidizes to acetone (path B).

methyl groups of P--CH3, isopropyl groups of IMPA and GB are oxidized by the TiO2 photocatalysis with almost equal probability, we suggest that the oxidation of isopropyl groups is dominantly carried out, based on our experimental results. Figure 7b shows enlarged IR spectra in the range 3600-3800 cm-1 in Figure 7a. The IR frequencies at 3748 and 3693 cm-1 kept on negative IR absorbance despite the ν(OH) mode and water vibration developed with decomposing GB by TiO2 photocatalysis. These IR frequencies correspond to isolated OH groups (Bro¨nsted acid site), indicating that the isolated OH groups are not regenerated by producing IMPA, MPA, and PA and even water is produced. Hence, we suggest that the products such as IMPA, MPA, and PA adsorb at the site of isolated OH groups. Namely, the surface site for the adsorption, which is formed by consuming OH groups with adsorbing IMPA, MPA, and PA, besides Ti4+, Ti3+, and Ti2+ depending on the degree of the surface reduction condition, is similar to the Lewis acid site. Here, an accumulation of MPA and PA at the surface of TiO2 is expected as a consequence of adsorption of them at the Lewis

acid like site. After UV irradiation for 50 min, a fresh air flowed to displace the air contained GB if remaining and intermediates in the photocatalytic reactor (Figure S8 in the Supporting Information). The decrements of the IR intensities at 1035, 1360, and 1725 cm-1 which were assigned to i-PrOH, acetone, and carbon dioxide were observed. The slight decrement of the IR intensity at around 1000-1300 cm-1 might be attributed to overlapped IR frequencies of carbon hydrate such as i-PrOH and acetone, while the IR frequencies of MPA and PA were stable. By taking into account the low volatility of MPA and PA, they certainly remain and are accumulated at the surface of TiO2. The MPA and PA accumulation deactivates the TiO2 photocatalyst because they occupy the site for adsorption of the next GB molecules.47,48 The IR frequency at 1739 cm-1, which was suggested to be attributed to the overlapped vibration mode of νs(C-O-(P)) and νs(P-O-(C)) of GB,6 also disappeared by the fresh air flow, but the change in the IR frequency as a consequence of the decrement of residual vaporized GB if remaining was not observed. If the vaporized GB would sufficiently remain in the



SCHEME 4: The Plausible Photocatalytic Decomposition Mechanism of GB Proposed in the Present Study

gas phase, the precise shift of the IR frequency as shown in Figures 1, 5a, and 7a would not be observed; instead, the broad shoulder spectra would appear. The result clearly indicates that the vaporized GB does not remain in the gas phase and is completely decomposed (Exchanging gas for clean air after end of the Photocatalysis Section in the Supporting Information). This discrepancy leads us to one of the suggestions that the IR frequency at 1739 cm-1 is not corresponding to the overlapped vibration mode of νs(C-O-(P)) and νs(P-O-(C)). What kind of species appear in this IR frequency range? The CdO vibration mode of acetone in the gas phase or the physisorbed one appears at 1739 cm-1.69 Acetone has high volatility, and the chemical structure is unfit to adsorb at the TiO2 surface. In fact, the vaporized acetone decomposition had a longer irradiation time, and it was stable in the photocatalysis (Figure S9 in the Supporting Information). This suggestion could be supported by the result of ab initio calculations, as listed in Table 1; that is, the IR frequency at 1739 cm-1 was not calculated from GB molecules.59 Hence, we suggest that the possibilities of appearance of acetone are as follows: (I) original GB solvent supplied is already contaminated by acetone which may be used as purification, (II) acetone is formed with adsorbing GB molecules at the surface of TiO2 as suggested in Scheme 3 so that GB molecule is hydrolyzed by the surface hydroxyl groups. As stated above, GB underwent complete destruction into inorganic products such as phosphoric acid, H2O, and CO2 according to the following equation.

C4H10PO2F +

/2O2 + TiO2 f H3PO4 + 4CO2 + 3H2O + F/TiO2

13

(11)

The plausible photocatalytic decomposition mechanism of GB proposed in the present study is summarized in Scheme 4. 5. Conclusions We have investigated the adsorption and photocatalytic decomposition of isopropyl methylphosphonofluoridate, Sarin (GB), at the surface of TiO2 photocatalyst by attenuated total

reflection-infrared Fourier transform spectroscopy. One of the advantages of the hydrated TiO2 photocatalyst in our surroundings is an ability to hold highly toxic GB molecules and to supply water molecules to the crystal surface in order to be hydrolyzed to innocuous reagent IMPA. Especially, the fact that GB molecules are quickly mineralized to PA, CO2, and H2O by photocatalysis as demonstrated in our study guarantees an advantage of the TiO2 photocatalyst and photocatalysis to decontaminate CWAs. Exploring the utilization of photocatalyst for decomposing real CWAs can pave the way for designing novel CWA decontamination systems. Acknowledgment. This work was supported by a grant from Research and Development Program for Resolving Critical Issue, commissioned by Ministry of Education, Culture, Sports, Science and Technology. Supporting Information Available: Tables showing the IR characteristics of acetone, formate, IMPA, isopropanol, mesityl oxide, MPA, and PA (Tables S1-S7), figures containing the ATR-FTIR spectrum of undiluted and diluted IMPA, MPA, and PA (Figures S0, S1, S3, and S4), kinetic plot of the change in the IR frequency of isolated Ti-OH groups with adsorption of the vaporized GB molecules (Figure S2), CO2 production in TiO2 photocatalysis as a consequence of photocatalytic mineralization of the adsorbed GB molecules (Figure S5), hydrophilic phenomenon in UV irradiation for pretreatment before experiment (Figure S6), NMR analysis of IMPA synthesized in our laboratory (Figure S7), change in ATR-FTIR spectrum by after exchanging from the gas phase after UV irradiation to clean air (Figure S8), the ATR-FTIR spectra of photocatalytic decomposition of acetone in the gas phase (Figure S9), and the plausible hydrolysis mechanism of isopropyl groups of IMPA (Scheme S1). This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Mario, F. S. Chem. ReV. 1951, 48, 225–257. (2) Yang, Y.-C.; Baker, J. A.; Ward, J. R. Chem. ReV. 1992, 92, 1729– 1743.

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(3) Bizzigotti, O. G.; Castelly, H.; Hafez, M. A.; Smith, B. H. W.; Whitmire, T. M. Chem. ReV. 2009, 109, 236–256. (4) Rauk, A.; Shishkov, I. F.; Vilkov, L. V.; Koehler, K. F.; Kostyanocsky, R. G. J. Am. Chem. Soc. 1995, 117, 7180–7185. (5) Hazardous Materials Toxicology; Clinical Principles of EnVironmental Health; Sulivan, B. J., Jr., Krieger, R. G., Eds.; Williams and Wilkins: 1992; pp 990-992. (6) Kuiper, A. E. T.; Bokhoven, J. J. G. M.; Medema, J. J. Catal. 1976, 43, 154–167. (7) Ekerdt, J. G.; Klabunde, K. J.; Shapley, J. R.; White, J. M.; Yates, J. T., Jr. J. Phys. Chem. 1988, 92, 6182–6188. (8) Wagner, G. W.; Bartram, P. W.; Koper, O. B.; Klabunde, K. J. J. Phys. Chem. B 1999, 103, 3225–3228. (9) Wagner, G. W.; Koper, O. B.; Erik, L.; Decker, S.; Klabunde, K. J. J. Phys. Chem. B 2000, 104, 5188–5123. (10) Wagner, G. W.; Procell, L. R.; Conner, R. J.; Munavalli, S.; Carnes, C.; Kapoor, P. N.; Klabunde, K. J. J. Am. Chem. Soc. 2001, 123, 1636– 1644. (11) Wagner, G. W.; Procell, L. R.; Munavalli, S. J. Phys. Chem. C 2007, 111, 17564–17569. (12) Gershonov, E.; Columbus, I.; Zafrani, Y. J. Org. Chem. 2009, 74, 329–338. (13) Brevett, C. A. S.; Sumpter, K. B.; Pence, J.; Nickol, R. G.; king, B. E.; Giannaras, C. V.; Durst, H. D. J. Phys. Chem. C 2009, 113, 6622– 6633. (14) Serpone, N.; Pelizzetti, E.; Hidaka, H. Photocatalytic Purification and Treatment of Water and Air; Ollis, D. F., Al-Ekabi, H., Eds.; Elsevier: London, 1993; pp 225-250. (15) Fox, M. A.; Dulay, M. T. Chem. ReV. 1993, 93, 341–357. (16) Hoffmann, M. R.; Martin, S. T.; Choi, W.; Bahnemann, D. W. Chem. ReV. 1995, 95, 69–96. (17) Mills, A.; Hunte, L. S. J. Photochem. Photobiol., A 1997, 108, 1– 35. (18) Fujishima, A.; Hashimoto, K.; Watanabe, T. Photocatalysis; BKC Inc.: Tokyo, 1999. (19) Fujishima, A.; Rao, T. N.; Tryk, D. A. J. Photochem. Photobiol., C 2000, 1, 1–35. (20) Photocatalysis; Kaneko, M., Ohkura, I., Eds.; Kodansha-Springer: Tokyo, 2002; pp 123-155 and 157-173. (21) Ollis, D. F.; Hsiao, C.-Y.; Budiman, L.; Lee, C.-L. J. Catal. 1984, 88, 89–96. (22) Matthews, W. R. J. Catal. 1988, 111, 264–272. (23) Ibusuki, T.; Takeuchi, K. Atoms. EnViron. 1986, 20, 1711–1715. (24) Ibusuki, T.; Takeuchi, K. J. Mol. Catal. 1994, 88, 93–102. (25) Zuo, G.-M.; Cheng, Z.-X.; Li, G.-W.; Shi, W.-P.; Miao, T. Chem. Eng. J. 2007, 128, 135–140. (26) Zuo, G.-M.; Cheng, Z.-X.; Shi, W.-P.; Zhang, X.-H.; Zhang, M. J. Photochem. Photobiol., A 2007, 188, 143–148. (27) Yang, Y.-C. CRDEC 1989, 83–89. (28) Fox, M. A.; Kim, Y.-S.; Abdel-Wahab, A. A.; Dulay, M. Catal. Lett. 1990, 5, 369–376. (29) Fox, M. A.; Abdel-Wahab, A. A. Tetrahedron Lett. 1990, 31, 4533– 4536. (30) Vorontsov, A. V.; Savinov, E. V.; Davydov, L.; Smirniotis, P. G. Appl. Catal., B 2001, 32, 11–24. (31) Vorontsov, A. V.; Savinov, E. N.; Claude, L.; Smirniotis, P. G. Appl. Catal., B 2003, 44, 25–40. (32) Kozlov, D. V.; Vorontsov, A. V.; Smirniotis, P. G.; Savinov, E. N. Appl. Catal., B 2003, 42, 77–87. (33) Martyanov, I. N.; Klabunde, K. J. EnViron. Sci. Technol. 2003, 37, 3448–3453. (34) Vorontsov, A. V.; Claude, L.; Savinov, E. N.; Smirniotis, P. G. J. Catal. 2003, 220, 414–423. (35) Panayotov, A. D.; Yates, T. J., Jr. J. Phys. Chem. B 2003, 107, 10560–10564. (36) Panayotov, A. D.; Paul, D. K.; Yates, T. J., Jr. J. Phys. Chem. B 2003, 107, 10571–10575.

Hirakawa et al. (37) Panayotov, D.; Kondratyuk, P.; Yates, J. T., Jr. Langmuir 2004, 20, 3674–3678. (38) Thompson, L. T.; Panayotov, A. D.; Yates, T. J., Jr. J. Phys. Chem. B 2004, 108, 16825–16833. (39) Thompson, L. T.; Panayotov, A. D.; Yates, T. J., Jr.; Martyanov, I.; Klabunde, K. J. Phys. Chem. B 2004, 108, 17857–17865. (40) Davidson, S. R.; Pratt, J. E. Tetrahedron Lett. 1983, 24, 5903– 5906. (41) Gratzel, C. K.; Jirousek, M.; Gratzel, M. J. Mol. Catal. 1987, 39, 347–353. (42) Gratzel, C. K.; Jirousek, M.; Gratzel, M. J. Mol. Catal. 1990, 60, 375–387. (43) Harada, K.; Hisanaga, T.; Tanaka, K. New J. Chem. 1987, 11, 597– 600. (44) Harada, K.; Hisanaga, T.; Tanaka, K. Water Res. 1990, 24, 1415– 1417. (45) Lu, M.-C.; Roam, G.-D.; Chen, J. N.; Huang, C. P. J. Photochem. Photobiol., A 1993, 76, 103–110. (46) O’Chea, K. E.; Beightol, S.; Garcia, I.; Aguilar, M.; Kalen, D. V.; Cooper, W. J. J. Photochem. Photobiol., A 1997, 107, 221–226. (47) Obee, T. N.; Satyapal, S. J. Photochem. Photobiol., A 1998, 118, 45–51. (48) Rusa, C. N.; Yates, J. T., Jr. J. Phys. Chem. B 2000, 104, 12292– 12298. (49) Rusa, C. N.; Yates, J. T., Jr. J. Phys. Chem. B 2000, 104, 12299– 12305. (50) Vorontsov, A. V.; Dayvdov, L.; Reddy, E. P.; Lion, C.; Savinov, E. N.; Smirniotis, P. G. New J. Chem. 2002, 26, 732–744. (51) Vorontsov, A. V.; Chen, Y.-C.; Smirniotis, P. G. J. Hazard. Mater. 2004, B113, 89–95. (52) Moss, J. A.; Szczepankiewicz, S. H.; Park, E.; Hoffmann, M. R. J. Phys. Chem. B 2005, 109, 19779–19785. (53) Trubistyn, D. A.; Vorontsov, A. V. J. Phys. Chem. B 2005, 109, 21884–21892. (54) Panayotov, D. A.; Morris, J. R. Langmuir 2009, 25, 3652–3658. (55) Kiselev, A.; Andersson, M.; Mattson, A.; Shchukarev, A.; Sjoberg, S.; Palmqvist, A.; Osterlund, L. Surf. Sci. 2003, 584, 98–105. (56) Kiselev, A.; Andersson, M.; Mattson, A.; Shchukarev, A.; Sjoberg, S.; Palmqvist, A.; Osterlund, L. J. Photochem. Photobiol., A 2006, 184, 125–134. (57) Hirakawa, T.; Nakaoka, Y.; Nishino, J.; Nosaka, Y. J. Phys. Chem. B 1999, 103, 4399–4403. (58) Kataoka, M.; Tsunoda, N.; Ohta, H.; Tsuge, K.; Takesako, H.; Seto, Y. J. Chromatogr., A 1998, 824, 211–221. (59) Bermudez, V. M. J. Phys. Chem. C 2007, 111, 3719–3728. (60) Bertisson, L.; Engquist, I.; Liedberg, B. J. Phys. Chem. B 1997, 101, 6021–6027. (61) van der Veken, B. J.; Herman, M. A. J. Mol. Struct. 1973, 15, 225–236. (62) Tejedor-Tejedor, M.-I.; Anderson, M. A. Langmuir 1990, 6, 602– 611. (63) Wang, R.; Hashimoto, K.; Fujishima, A.; Chikuni, M.; Kojima, E.; Kitamura, A.; Simohigoshi, M.; Watanabe, T. Nature 1997, 288, 431– 432. (64) Gustafson, L. R.; Martell, E. A. J. Am. Chem. Soc. 1962, 84, 2309– 2316. (65) Connor, A. P.; Dobson, D. K.; McQuillan, J. A. Langmuir 1999, 15, 2402–2408. (66) Hirakawa, T.; Nosaka, Y. Langmuir 2002, 18, 3247–3254. (67) Hirakawa, T.; Yawata, K.; Nosaka, Y. Appl. Catal., A 2007, 325, 105–111. (68) Hirakawa, T.; Nosaka, Y. J. Phys. Chem. C 2008, 112, 15818– 15823. (69) Xu, W.; Raftery, D.; Francisco, S.-J. J. Phys. Chem. B 2003, 107, 4537–4544.

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Experimental Study on Adsorption and Photocatalytic Decomposition

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