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Feb 9, 2009 - UniVersity, SE-751 21 Uppsala, Sweden, and Department of Solid State Physics, The Ångström Laboratory,. Uppsala UniVersity, SE-751 21 ...
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J. Phys. Chem. C 2009, 113, 3810–3818

Oxygen Diffusion and Photon-Induced Decomposition of Acetone on Zr- and Nb-Doped TiO2 Nanoparticles Andreas Mattsson,† Michael Leideborg,‡ Leif Persson,† Gunnar Westin,‡ and ¨ sterlund*,†,§ Lars O FOI, SE-901 82 Umeå, Sweden, Department of Materials Chemistry, The Ångstro¨m Laboratory, Uppsala UniVersity, SE-751 21 Uppsala, Sweden, and Department of Solid State Physics, The Ångstro¨m Laboratory, Uppsala UniVersity, SE-751 21 Uppsala, Sweden ReceiVed: NoVember 11, 2008; ReVised Manuscript ReceiVed: December 22, 2008

We report on the photoinduced decomposition of acetone on Zr- and Nb-doped anatase TiO2 nanoparticles prepared by the sol-gel method in oxygen-free environment (N2) and synthetic air, respectively. Physical properties of the nanoparticles were determined by TEM, SEM, AFM, XRD, and UV-vis spectroscopy. Photoinduced surface reactions were monitored by in situ Fourier transform infrared (FTIR) spectroscopy. Acetone photo-oxidation occurs in the absence of O2 in the reaction gas and is proposed to be due to reactions with photoactivated surface oxygen. In N2 atmosphere a new parallel reaction pathway is found that stimulates surface carbonate formation. A coupled diffusion-reaction model was developed to quantitatively determine the role of O diffusion. The results yield quantitative support to an oxygen surface diffusion mechanism, which depletes the surface from oxygen and gradually deactivates the particles in the absence of external oxygen supply. The diffusion reaction pathway is significant on the doped TiO2 particles. The contribution of this reaction pathway amounts to up to 65% of the total PID rate on Nb- and Zr-doped TiO2 in synthetic air environment, while it gives only a minor contribution on pure TiO2. 1. Introduction Nanocrystalline materials are characterized by the porous structure and the large interfacial contact area with neighboring particles. In general, the latter constraint prevents the particles from obtaining their free minimum energy configuration during the material synthesis and leads to a short-range atomic order, which is different from corresponding amorphous and bulk crystalline materials. Moreover, nanocrystalline solids have a high surface-to-volume ratio, which, e.g., means that for particles with dimensions less than 10 nm more than 30% of the atoms can lie on grain or interphase boundaries. The material properties can thus be completely controlled by these interfacial properties. It has been reported that diffusion in nanocrystalline solids is largely controlled by surface and grain boundary diffusion.1,2 In particular, atoms which diffuse by vacancy mechanism in bulk (such as TiO2) are orders of magnitude more mobile due to grain boundary diffusion, whereas interstitial (volume) diffusion remains approximately the same. At low temperatures (T < 1000 K) volume diffusion is negligible for TiO2 and only surface and grain boundary diffusion is appreciable. Detailed knowledge of diffusion properties is of utmost importance in many technical applications, including ceramic processing,3 solid oxide fuel cells,4 mineral dissolution and corrosion,5 and gas sensors.6 In the search for new photocatalytic active materials, which have improved visible light photon-conversion efficiency, cation-doped TiO2 and binary metal oxides with TiO2 have been suggested.7,8 Among these materials Nb and Zr doping have * Corresponding author footnote: Email: [email protected]. Tel: +46.90.106900. Fax: +46.90.106800. † FOI. ‡ Department of Materials Chemistry, The Ångstro¨m Laboratory, Uppsala University. § Department of Solid State Physics, The Ångstro¨m Laboratory, Uppsala University.

recently attracted some attention.9-12 It is hitherto not shown whether these structural modifications result in significant changes of diffusion processes. The latter may be augmented by photon-assisted diffusion processes occurring in photocatalytic applications. Lattice oxygen has been reported to contribute to photocatalytic reactions on TiO2 nanoparticles and may give rise to alternative reaction pathways.13,14 Even though experimental evidence is lacking, it is likely that grain boundary diffusion is the dominant mechanism whereby lattice O is replenished in these experiments. Even under aerobic conditions the photoinduced reaction rate can be controlled by oxygen diffusion,15 which can affect both reaction pathways and the relative importance of minority pathways such as those involving lattice O. Lattice O may contribute to the photoinduced decomposition (PID) of acetic acid14,16-18 and formic acid.19,20 Muggli and Falconer17,18 reported different PID reaction pathways for acetic acid depending on whether O2 gas was present or not during illumination of Degussa P-25 TiO2 nanoparticles. It was argued that for the pathway that does not involve lattice O, the R-carbon in acetic acid forms CO2 and the methyl group produces methane. In a second reaction pathway, O is extracted from the TiO2 lattice and the R-carbon forms CO2 and two methyl groups form ethane. Depleted lattice O in the second pathway was replenished by either adding gas-phase O2 or by waiting in an inert atmosphere. The nature of the O source was not specified in these studies. Lee and Falconer19 reported that lattice O was extracted during PID of formic acid on Degussa P25 TiO2 nanoparticles. Lattice O depletion was also shown to cause slow deactivation of TiO2 due to slow lattice O diffusion, which was identified with bulk oxygen, which diffuses to an O deficient surface at approximately 0.008 µmol/g catalyst/s (DO ) 10-22 m-2 s-1). We note in passing that in this latter case it is more reasonable to assume that O grain boundary diffusion is the

10.1021/jp809953m CCC: $40.75  2009 American Chemical Society Published on Web 02/09/2009

Decomposition of Acetone on TiO2 Nanoparticles

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dominant O transport mechanism, as we elaborate further on in this study. In the present study we report on the photoinduced decomposition of acetone on well-characterized, nanocrystalline Zrand Nb-doped TiO2 under O2 rich (synthetic air) and O2 free (N2 gas) conditions prepared by sol-gel methods. We quantify the contribution of diffusion mediated photoreactions based on a grain boundary diffusion model employing a coupled diffusion and reaction model fitted to the measured PID rates. We correlate the differences in O diffusion on the different materials with the different morphology and chemical composition of the nanoparticles. Furthermore, we show that anaerobic photoinduced decomposition proceeds via a different reaction pathway compared to the corresponding aerobic process. 2. Experimental Section 2.1. Sample Preparation. Details of the materials synthesis have been described elsewhere.9 Briefly, nanoparticles of ZrO2-TiO2 and NbO2.5-TiO2 were prepared by hydrolysis of ethanol solutions of Ti(OPri)4 (Aldrich) and Nb(OEt)5 (Aldrich) and hexane solutions of Ti(OPri)4 and Zr(OPri)4, respectively, followed by heating at 80 °C for 8 h, and hydrothermal treatment at 200 °C. The following compositions were prepared by mixing the metal alkoxides in the desired proportions: 0, 10 and 20 mol % Nb2O5 in TiO2 (denoted Nb:TiO2) and 0, 1, 2, and 5 mol % ZrO2 in TiO2 (denoted Zr:TiO2). The nanoparticles thus obtained in water were mixed with carbowax to yield pastes that were deposited on CaF2 (Zr:TiO2) and Si/SiO2 wafers (Nb: TiO2) as thin films by evaporating the 0.7 w % sol in air and subsequent heat-treatment in air at 450 °C for 30 min to yield the porous nanostructured doped titania films. The particles thus obtained are extremely well-crystallized, monodisperse, and spectroscopically contaminant free. 2.2. Materials Characterization. Structural, optical, and chemical properties of the synthesized materials were characterized by a range of different techniques as described elsewhere.9,11 Phase analysis was made by the powder X-ray diffraction patterns obtained with a Guiner-Ha¨gg focusing camera, using Cu KR1 radiation and Si as internal standard. Scanning electron microscope (SEM) images were obtained with a FEG-SEM Leo 1550 Gemini instrument. Transmission electron microscopy (TEM) was done with a Jeol 2000 FXII instrument equipped with a EDS module (Link AN 1000). High-resolution transmission electron microscopy (HRTEM) was done with a transmission electron microscope JEOL JEM 3010 operated at 300 kV (LaB6 cathode) giving a point resolution of 0.17 nm. A copper grid coated with a holey carbon support film was used to prepare samples for the TEM observation. A powdered sample was dispersed in ethanol and the suspension was treated in ultrasonic bath for 10 min. Atomic force microscopy (AFM) was done with a Nanoscope IIIa instrument (Digital Instruments) used in the tapping mode. Data extraction and image analysis were done with the software WSxM.21 UV-vis optical absorption was determined on thin films coated on R-Al2O3 or CaF2 windows by measuring the substrate corrected transmission with PerkinElmer Lambda 18 and Perkin-Elmer Lambda 19 spectrometers. The X-ray diffraction patterns all showed that the materials were of the tetragonal anatase modification and Rietveld analysis revealed a slight expansion of the cell dimensions upon doping. The a-axis and c-axis expand by up to 0.82% and 0.34%, respectively, upon Nb doping (20 wt % Nb) and by up to 0.08% and 0.35%, respectively, upon Zr doping (5 wt % Zr) from the initial values of the pure anatase phase, a ) 3.786 Å, c ) 9.500 Å. Previous XPS and XAS studies (as well as the pale yellow

Figure 1. High-resolution TEM micrograph of a representative anatase TiO2 nanocrystal.

color) show that Nb is almost entirely in the pentavalent state.9 The TEM and HRTEM studies showed homogeneous Zr and Nb doping of the titania particles with mainly perfect, grain boundary free nanocrystals (Figure 1) throughout the different materials series within the accuracy of the analytical technique. This, together with the diffraction data, shows that the dopants have been introduced into the anatase structure. The TEM analysis showed further that the entire sample was crystalline with well-developed crystal facets. The SEM images showed a homogeneous metal composition nanostructure over the samples. SEM and AFM images of the Zr- and Nb-doped TiO2 samples are shown in Figures 2 and 3, respectively. They show that with increasing doping the particles develop an elongated shape, from the initial tetrahedral shape (I41/amd) shown in Figure 3. Even though the tip convolution effect rounds off the particles and enlarges the particle size in AFM, the AFM measurements allow for evaluation of the height distribution and hence the tilt of the particles. This makes it possible to extract the 3-dimensional geometrical shape of a large number of particles. To extract simple dimensional properties from the AFM images we simply assume that the nanoparticle particles are shaped as an ellipse and ignore tip deconvolution processing. The length of the major and minor axis has been determined from the SEM, TEM, and AFM measurements. This procedure is sufficient for the present purpose since we are here only interested in the relative size of the particles and the dependence of diffusion rate on dimensional properties. To obtain the surface area and volume of the particles we further assume that the particles are symmetrical around its major axis (prolate spheroid). For a prolate spheroid the surface area, S, is given by

(

S ) 2πb2 1 +

a arcsin(e) be

)

where e )

√a2 - b2 a

and

a > b (1)

The volume is given by

4 V ) πb2a 3

(2)

where a and b are half the length of the major and minor axis, respectively.

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Figure 2. SEM images of pure TiO2 and 1% Zr-, 2% Zr-, 5% Zr-, 10% Nb-, and 20% Nb-doped TiO2, respectively. The size of the particles increases upon doping with Nb and Zr. The shape of the particles also changes with doping and becomes elongated.

Figure 3. AFM images of pure anatase TiO2 and Zr- and Nb-doped TiO2, respectively. The images were recorded in the tapping mode.

TABLE 1: Physical Properties of the ZrO2 and NbO2.5 Doped TiO2 Particlesd SEM data material

XRD 〈d〉 (nm)

TiO2 (Zr batch) TiO2 (Nb batch) 1% Zr:TiO2 2% Zr:TiO2 5% Zr:TiO2 10% Nb:TiO2 20% Nb:TiO2

20 20 20 21 18 24 37

a

b

b

AFM data c

c

2a (nm)

2b (nm)

surface area (nm2)

particle vol (nm3)

2ab (nm)

2bb (nm)

UV-vis optical band gap (eV)

28 30 32 33 46 49 55

22 20 24 23 19 27 38

1804 1692 2223 2160 2293 3604 5938

7096 6283 9651 9140 8695 18703 41584

53 50 52 47 48 53 69

41 41 38 28 32 35 39

3.25 3.15 3.25 3.29 3.34 3.11 3.02

a

Mean diameter from Scherrer analysis of XRD data ((101) peak). b The value indicates the mean length of the major and minor axis of an elliptically shaped particle. c Mean surface area or volume of ellipsoidally shaped particles. d The SEM and optical data for Nb:TiO2 are taken from ref 9.

For each sample the particle dimension, surface area, and volume of an average aggregate have been calculated by averaging over 30-40 particles for AFM and 120-800 particles for SEM. The average geometrical properties of the particles from SEM, XRD, and AFM respectively are shown in Table 1. In the following we will use the SEM data for further analysis, since Scherrer analysis of the XRD data does not take into

account the asymmetrical shape of the particles, and the AFM show poorer precision and statistics. The optical absorption edge Eg can be related to the absorption coefficient, R, by the relation RhV ) (hV - Eg)n, where n ) 0.5 for direct-gap transitions and n ) 2 for indirect-gap transitions. We find a linear relationship for all materials with n ) 2 near the optical band gap and conclude that in our dopant regime

Decomposition of Acetone on TiO2 Nanoparticles

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Figure 4. In situ FTIR transmission spectra of acetone adsorbed on TiO2 and Zr-doped TiO2 thin films acquired at different times during illumination in a flow of 100% N2. The sample temperature was 299 K in all experiments. Highlighted are absorbance bands due to acetone and intermediate species showing photocatalytic degradation of acetone in O2 deficient conditions.

the electronic transitions are indirect as for pristine TiO2. The optical absorption edges determined in this manner are shown in Table 1. 2.3. In Situ Fourier Transform Infrared Spectroscopy. Fourier transform infrared (FTIR) transmission measurements were made in a vacuum pumped spectrometer (Bruker IFS66v/ S) equipped with a LN2 cooled narrow band HgCdTe detector as described elsewhere.9 All FTIR measurements were performed in a modified transmission gas cell (Specac) allowing for in situ reaction studies with simultaneous gas deposition, light illumination, and IR spectroscopy of the thin solid films. FTIR spectra were recorded in transmission mode with 4 cm-1 resolution and 135 scans (corresponding to 30 s measurement time per spectra) and 30 s dwell time between consecutive spectra. All spectra were smoothed with a Savitzky-Golay algorithm, using a 9 point window. Absorbance peak areas were obtained after appropriate baseline corrections of the spectra. 2.4. Photodegradation Experiments. Simulated solar light was generated by a Xe arc lamp source operated at 200 W and filtered through a set of air mass filters (AM1.5). To reduce the infrared part of the emission spectrum, the light was first directed through a 75 mm long water filter (deionized water, 18.2 MΩ). The light was collected into a fused silica fiber bundle and directed on to the sample cell through a CaF2 window at an angle of 25° to the surface normal. The measured photon power at the sample was measured to be 166 (200 < λ < 800 nm) and 19 mW cm-2 (200 < λ < 400 nm). FTIR spectra were acquired with the samples kept at 299 K in a 100 mL min-1 feed flow in pure nitrogen gas through the reaction cell, and controlled by a set of mass flow controllers. Prior to each measurement the samples were cleaned in situ at 673 K in the reaction cell for 15 min in synthetic air and subsequently cooled to 299 K in the same feed and after cool down the system was purged with 100% N2 for 30 min. This procedure removed all organic contaminants from the surface as determined by in situ FTIR spectrometry before, during, and after the cleaning procedure. Research grade gases were used without further purification. Acetone (GC purity, Scharlau) was added to the gas feed through a home-built gas generator.9 The independently calibrated acetone injection in the feed obtained with these parameters was 0.29 ( 0.02 or 0.19 ( 0.02 mg min-1 for the Nb- and Zr-doped series, respectively, which corresponds to an ideal steady-state concentration of 1232 ( 109 or 795 ( 70 ppm in the feed, respectively. No other gas species than acetone were detected mass spectrometrically with this gas evaporation setup. After acetone dosing (ca. 15 min) the sample was kept for ca. 20 min in a pure feed gas before solar light

illumination. In all measurements the FTIR background was collected on a (spectroscopically) clean sample during 1 min (265 scans) in 100% N2 feed at 299 K. 2.5. Simulations. A kinetic model discussed in the following sections was constructed to describe the experimental results. A set of differential equations describing the reaction kinetics was expressed as a dimensionless system and discretized in the spatial variable, and the semidiscretized system is simulated by using the Matlab ODE solver ode15s, a solver for stiff ODE’s using a variable order method. The simulation code was verified by using the method of manufactured solutions.22 The spatial domain was truncated such that the boundary condition (eq 7, below) was well approximated during the entire simulation time. Spatial grid convergence was also verified. The asymptotic behavior of the solutions was independently checked by comparison with the analytical solutions of the ODE. 3. Results and Discussion 3.1. Photodegradation of Acetone. Figures 4 and 5 show FTIR spectra as a function of illumination time under oxygen deficient conditions (in 100% N2 gas) on Zr:TiO2 and Nb:TiO2 films, respectively, with increasing Zr and Nb concentration. Similar to previous studies it is evident that even in the absence of O2 in the gas phase illumination results in decomposition of adsorbed organic molecules.14 Inspection of the OH absorbance region reveals that the integrated ν(OH) band intensity does not follow the acetone degradation. The OH band intensity slightly increases indicating a buildup of hydroxyls, while acetone degradation proceeds throughout the experimental cycle (60 min). The dissimilar trend for OH and acetone surfaces concentrations suggests that acetone degradation is not coupled to reactions with reminiscent OH surface groups. The new absorption bands that appear and grow with illumination time at ∼1735, ∼1717, ∼1668, ∼1590, ∼1557, 1441, 1380, and 1358 cm-1 can be attributed to intermediate decomposition products (acetate, formaldehyde, formate, and carbonates) that form on the surface.9,23-26 In particular, different formate groups with typical (coordination dependent) bands at∼1590 (ions), ∼1557 (µ-coordinated), ∼1380, and ∼1358 cm-1 typically form25,27 on TiO2 and are stable intermediates, whose further decomposition limits the complete oxidation of acetone in synthetic air.26 It is also evident that acetone degradation (compare the 1695 and 1240 cm-1 bands due to the ν(CdO) and ν(C-C) modes, respectively) is faster on the Zr-doped TiO2 than on either Nb-doped TiO2 or pure TiO2. Moreover, it is seen that significant carbonate formation

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Figure 5. In situ FTIR transmission spectra of acetone adsorbed on TiO2 and Nb-doped TiO2 thin films acquired at different times during illumination in a flow of 100% N2. The sample temperature was 299 K in all experiments. Highlighted are absorbance bands due to acetone and intermediate species showing photocatalytic degradation of acetone in O2 deficient conditions.

Figure 6. Comparisons of in situ FTIR transmission spectra of acetone adsorbed on Zr- and Nb-doped TiO2 thin films acquired at different times during illumination in a flow of synthetic air and 100% N2, respectively. Measurements on niobium-doped samples in synthetic air are obtained from ref 9. Distinct differences can be seen for the doped and pure TiO2 when comparing reactivity in O2 excess and deficient conditions.

Figure 7. Logarithmic plot of the normalized absorbance, ln(A(t)/A(t)0)), where t is the UV illumination time in both O2 excess (solid markers) and N2- for Zr-doped samples (a) and Nb-doped samples (b) during the first 10 min of illumination. The solid lines are least-squares curve fits to the experimental data.

(ν(C-O) band at ∼1120 cm-1) occurs in the absence of O2 in the feed gas. Figure 6 shows a compilation of FTIR spectra obtained after t ) 0 and 60 min of illumination on pure anatase TiO2, 5% ZrO2:TiO2, and 20% Nb:TiO2 films, respectively, in synthetic air and in 100% N2 gas, respectively. In Figure 7 is shown a logarithmic plot of the corresponding decrease of the ν(C-C) absorption band due to acetone as a function of illumination time for all materials. From Figures 6 and 7 it is obvious that

the PID rate (as expected) proceeds much faster in presence of O2 gas than without O2 (cf. Figures 4 and 5). It can also be seen that the acetone degradation rates on the Zr- and Nb-doped TiO2 materials in synthetic air and in N2 gas, respectively, differ much less compared to those in pure TiO2. It is seen that aldehyde and asymmetric Ti-CO2 groups are formed on TiO2 in synthetic air and ν(CdO) at 1735 and 1718 cm-1,28 which does not occur in the absence of O2 in the reaction gas. Only on the doped TiO2 materials are these species detected in oxygen

Decomposition of Acetone on TiO2 Nanoparticles

J. Phys. Chem. C, Vol. 113, No. 9, 2009 3815

TABLE 2: Extrapolated Oxygen Diffusion Coefficients for TiO2 at 299 K diffusion coeff (m2 s-1)

material nanocrystalline rutile-grain boundary rutile single crystal O self-diffusion O vacancy a

∼10-21 a ∼10-51;b10-55 c 10-44 d

Ho¨fler.2 b Arita.29 c Derry30 (c-axis). d Iguchi40 (a and c-axis).

free environment. The different reaction kinetics with and without molecular oxygen suggest that oxidation of acetone with photoexcited lattice O and O2 radicals opens up an energetically favorable reaction pathway that produces carbonates. A possible pathway discriminating the two situations may be realized by considering the oxidation of the methoxy groups, which are formed after the initial nucleophilic oxygen radical attack on the acetone carbonyl bond. We propose that successive reactions of O-• with the CH3-O-Ti groups yield carbonates, while reaction with O2-• directly yields CO2 and water (leaving a proton behind). Similar distinctions between lattice O and O2 mediated reaction pathways have been suggested by Muggli and Falconer.18 2, where X ) Zr or Nb (with specified The PID rate, kX:TiO dec dopant concentration), of acetone on the different materials was derived from the integrated peak area of the ν(C-C) acetone absorption band at 1240 cm-1 for the Zr:TiO2 and at 1244 cm-1 for the Nb:TiO2 samples, respectively. The ν(C-C) absorption band is used instead of the strong carbonyl ν(CdO) absorption band, since this band appears well-isolated in the FTIR spectra, and is least affected by overlapping carbonyl bands due to intermediate reaction products. The acetone surface coverage, θAc(t), was estimated from the ν(C-C) absorption band after saturation dosing and evacuation.9 Briefly, monolayer and multilayers of acetone can be distinguished spectroscopically by the chemical shift of the ν(CdO) absorption band. For accurate determination, it is also necessary to take into account the (small) acetone desorption rate at room temperature, which can be done by independent measurements.9 In this manner a good estimate of the acetone coverage can be obtained; typically, θAc(t)0) ) 0.8 ( 0.2. Thus the absorbance, A, can be related to the acetone surface coverage θAc(t). A plot of ln(A(t)/A(t)0)), where t is the UV illumination time, yields a linear curve at t < 10 min (Figure 7). This indicates that the initial photoinduced acetone decomposition can be described by pseudo-first-order reaction kinetics, viz.

-

dθAc 2 θAc(t) ) kX:TiO dec dt

(3)

2 determined The experimentally determined values for kX:TiO dec from eq 3 are shown in Table 3. 3.2. Oxygen Diffusion Mediated Reaction. The results in Figure 9 and Table 3 which compare the PID rate in N2 and synthetic air, respectively, suggest that photon-induced activation of reactive species coupled with diffusion are important pathways for PID reactions in general in doped TiO2 materials and may contribute significantly to the measured PID rates. Indeed, the magnitude of the diffusion mediated reaction rate in N2 gas is up to ca. 65% of the rate in synthetic air for the cation-doped samples. Note that we can exclude minority OH groups present on the surface after the in situ high-temperature preoxidation as the main oxidation agent that obeys different kinetics (section 3.1).

Figure 8. Schematic drawing of the diffusion model used for the simulations of the photoinduced coupled reaction between oxygen and acetone. The O atoms diffuse along the spherical surface defined by the coordinates r and ϑ, with a characteristic diffusion length δ along the diffusion path r · (∆ϑ), and deplete available O atoms in a diffusion zone around the acetone molecules upon photon illumination.

The diffusion mechanism may in principle be either due to hot O atoms or acetone molecules diffusing to hot O sites. The model outlined below is applicable for both (symmetrical with respect to diffusing species), but the quantitative results we obtain and comparisons with literature data suggest that O diffusion is the more likely active mechanism. The model below is therefore outlined in terms of an O diffusion model. Oxygen diffusion may in principle occur by either bulk diffusion (interstitial), surface, or grain boundary diffusion (interfaces). A comparison of experimentally determined diffusion coefficients from the literature is given in Table 2. Data for the anatase phase are lacking. Table 2 includes both self-diffusion and O vacancy diffusion, obtained by measuring the concentration of 18O in the sample with SIMS,29 and nuclear techniques.30 The diffusion constant has also been determined in nanocrystalline rutile with SIMS detection of 18O.2 Measurements of the diffusion constants are typically made at elevated temperatures between 700 and 1400 K, and values of DO given in Table 3 were therefore extrapolated to 299 K by using the following Arrhenius relationship, DO ) D0 exp(-Ea/kT). This procedure introduces an additional source of error in the comparisons, and assumes that the same diffusion mechanism is valid also at low temperatures. The results in Table 2 reveal that there is a large spread of DO in the literature for the different types of proposed diffusion mechanisms. It is clear from these data that bulk O diffusion is (as expected) very small in comparison to grain boundary diffusion and can be ignored. A coupled diffusion and reaction model was developed to quantify the role of lattice O in the O2 free experiments and quantify the role of lattice O in the photoreaction of acetone. We assume that O diffusion, DO, is the main oxygen source and is rate determining in the photodegradation of acetone. Since O diffusion via interfaces is orders of magnitude larger than volume (bulk) diffusion in TiO2 at low temperatures, as illustrated in Table 2,1,2,30-32 and since most particles have welldeveloped crystal structure with no or few internal grain boundaries (Figure 1), it is safe to ignore bulk O diffusion and simply use DO to denote interfacial (surface) O diffusion. The films consist of crystalline nanoparticles, whose dimensions are known. We assume that the acetone molecules are adsorbed at

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Figure 9. Simulated (solid line) and measured (circles) acetone coverage θAc(t) as a function of illumination time. The simulation results are given for pure TiO2 (2 sets of samples from each of the Nb- and Zr-series), 2% Zr:TiO2, 5% Zr:TiO2, 10% Nb:TiO2, and 20%Nb:TiO2. The values for 2, and the O diffusion length, δ, obtained from the simulation are shown as well as the effective oxygen diffusion constant, DO, rate constant, kX:TiO dec 2 obtained from the sum of the squares of the residual errors, R2. Initial values for the simulations are DO ) 10-22 m2 s-1, δ ) 5 Å, and kX:TiO dec eq 3. X:TiO2 TABLE 3: Simulated Effective Oxygen Diffusion Coefficient (DO), Rate Constant (kdec ), and Diffusion Length (δ) As Obtained from a Global Least-Squares Fit of the 3-Parameter Model to the Experimental Dataa 2 (s-1) exptl rate coeff kX:TiO dec

material

rate constant (N2) simulated 2 (s-1) kX:TiO dec

effective diffusion coeff, DO ( m2 s-1) -24

-4

6.0 × 10 3.8 × 10-24 1.8 × 10-23 5.5 × 10-23 4.5 × 10-23 3.1 × 10-24 1.0 × 10-24

TiO2 TiO2 1% Zr 2% Zr 5% Zr 10% Nb 20% Nb

4.5 × 10 4.4 × 10-4 6.1 × 10-4 1.2 × 10-3 1.1 × 10-3 3.8 × 10-4 7.1 × 10-5

O diffusion length δ (Å) 5.7 5.6 5.5 6.5 6.1 7.5 4.9

inert atm. (N2) -4

2.3 × 10 3.0 × 10-4 7.1 × 10-4 1.3 × 10-3 1.1 × 10-3 2.8 × 10-4 7.7 × 10-5

synthetic air 4.8 × 10-3 1.1 × 10-2 2.5 × 10-3 2.3 × 10-3 1.8 × 10-3 6.9 × 10-4 1.2 × 10-4

a For comparison is given the experimental value of the rate constants from a pseudo-first-order analysis of the acetone decomposition rate. The rate coefficients in synthetic air for the Nb-doped samples are obtained from ref 9.

the surface of the crystalline particles and that O atoms diffuse on the surface of the particles (Figure 8).

dθAc 2 θAc(t)θO(t, 0), t > 0 (t) ) -kX:TiO dec dt DO ∂θO 2 θAc(t)θO(t, 0), t > 0 (t, 0) ) kX:TiO dec δ r∂ϑ ∂θO ∂2θO (t, θ), (t, ϑ) ) DO 2 ∂t r ∂ ϑ2 lim θO(t, ϑ) ) 2,

zf∞

θO(O, ϑ) ) 2,

t > 0, t>0

ϑ>0

θ>0

(4) (5) (6) (7) (8)

where δ is the characteristic diffusion length along the diffusion path r∆ϑ on the spherical surface (a hopping length comparable to the unit cell dimension), ϑ is the polar angle, and r is the radius of the particle. The site area density coverage on the

sample of acetone and oxygen, θAc(t) and θO(t,θ), respectively, is defined by

θx(t) )

nx(t) Ns

(9)

where nx(t) is the site area density of specie x and Ns is the maximum site area density. For efficient computation the diffusion model described by eqs 4-9 is written in dimensionless form. On the basis of the diffusion model described by eqs X:TiO2 , δ, and DO were optimized to best fit the input 4-9, kdec parameter, the measured acetone coverage versus time. The experimentally determined values of θAc(t) obtained in this manner were used as input in the simulations. The results from the model simulations are in good agreement with the experimental data, using a minimum of fitting parameters (DO, 2, and δ). Moreover, the results are robust and yield kX:TiO dec consistent and physically reasonable values for all materials

Decomposition of Acetone on TiO2 Nanoparticles

J. Phys. Chem. C, Vol. 113, No. 9, 2009 3817 mobility due to the Zr-V-(O) cation-oxygen vacancy associations is larger. It should also be noted that the oxygen selfdiffusion rate is larger in ZrO2 compared to TiO2.29,30,35,36 These considerations stress that modulation of O diffusion by substitution doping of cations is expected to be important in order to assess PID rates on cation-doped TiO2. It also implies differences in the thermal stability of the anatase structure, which indeed has been reported for both Zr- and Nb-doped TiO2 and Ti alloys.33,37-39 4. Conclusions

Figure 10. Left ordinate: Photoinduced decomposition (PID) rate 2 normalized to band gap illumination power [per unit area], total kX:TiO dec particle surface area, and O diffusion constant (DO/area). Right ordinate: 2 normalized to band gap illumination power [per unit area] and kX:TiO dec particle surface area. All PID rates are normalized to pure TiO2 from the Zr batch, which defines the horizontal solid line. The error bars indicate the accumulated relative errors of the measured PID rate (15%), illumination power (5%), particle area and volume (10%), and (for the right ordinate) simulated diffusion constant (25%).

parameters (Table 3 and Figure 9). The results yield independent values of the grain boundary O diffusion constant in TiO2, which is in remarkable good agreement with reported data (Table 3). In particular, the results are in good agreement with reported values for grain boundary diffusion in nanocrystalline TiO2,2 and previously inferred values of oxygen diffusion in anatase-rutile mixtures (Degussa P25) based on measurements with isotope labeled oxygen.14 Assuming that O surface diffusion is the dominant reaction pathway in oxygen free environment scaling with the diffusion coefficient (or more precisely (DO/area) according to eq 5) 2 should yield a constant value. In Figure 10 the scaled kX:TiO dec 2. In both cases the (left ordinate) is compared to the kX:TiO dec 2 have been normalexperimentally determined values of kX:TiO dec ized to the incident photon flux (taking into account the different optical band gaps in Table 1), and the total particle surface area (per unit volume given in Table 1). The results show that scaling 2 to a constant value. This corroborates the initial forces kX:TiO dec assumption that O mediate surface diffusion is the dominant 2. contribution to kX:TiO dec The diffusion coefficient reported in Table 3 varies more than an order of magnitude. This points to an inherent material specific difference in photoactivated O diffusion on Nb- and Zr-doped TiO2, respectively. One reason may be found in the different valency of the Zr and Nb ions. Since diffusion of oxygen in TiO2 occurs by a vacancy mechanism,29-32 substitution of Nb5+ into the TiO2 can in principle decrease the oxygen vacancy concentration and hence suppress O diffusion.33 In contrast, it has earlier been shown that small concentrations of cation doping of TiO2 also can increase the oxygen diffusion.29 Studies of titania dissolved in yttria tetragonal zirconia polycrystalline solid solutions show two kinds of cation-oxygen ¨ and Ti-VO ¨ with different vacancy associations: Zr-VO 34 diffusion dynamics, from which it can be inferred that the O

We have investigated the photoinduced degradation of acetone on Zr- and Nb-doped anatase TiO2 nanoparticles. It is concluded that substitutional doping of anatase TiO2 with Nb and Zr results in inferior PID rates in O2 atmospheres, while in inert (N2) atmospheres Zr-doped TiO2 is superior to both pure TiO2 and Nb-doped TiO2. In general the ratio of the PID rate in synthetic air and in inert atmosphere is much larger for pure TiO2 than cation-doped TiO2. It is shown that PID reactions in inert gas are due to a photoinduced O surface diffusion pathway. The latter pathway leads to an additional reaction pathway that yields carbonate formation. Quantification of the O diffusion constant, DO, based on a phenomenologically simple model supports an O surface diffusion model. The values of DO show good quantitative agreement with previous reports of grain boundary diffusion in nanocrystalline TiO2 and reveal that O diffusion is enhanced upon Zr doping while it is suppressed upon Nb doping. The absolute values of DO and PID rate constants in inert atmosphere show that the photoactivated O diffusion mechanism is important to assess PID rates for cation-doped TiO2 in general (not only in inert gas). Acknowledgment. We thank Snejana Bakardjieva for the ¨ . acknowledge HRTEM measurements. A.M., L.P., and L.O financial support by the Swedish Department of Defence (grant nos. E4005 and E4024). G.W. and M.L. acknowledge financial support by the Swedish Research Council. References and Notes (1) Brossmann, U.; Wurschum, R.; So¨dervall, U.; Schaefer, H.-E. J. Appl. Phys. 1999, 85, 7646. (2) Ho¨fler, H. J.; Hahn, H.; Averback, R. S. Defect Diffus. Forum 1991, 75, 195. (3) Chen, I.-W.; Wang, X.-H. Nature 2000, 404, 168. (4) Rupp, J. L. M.; Infortuna, A.; Gauckler, L. J. Acta Mater. 2006, 54, 1721. (5) Cabrera, N.; Mott, N. F. Rep. Prog. Phys. 1948, 12, 163. (6) Wu, N.-L.; Wang, S.-Y.; Rusakova, I. A. Science 1999, 285, 1375. (7) Carp, O.; Huisman, C. L.; Reller, A. Prog. Solid State Chem. 2004, 32, 33. (8) Anpo, M. Bull. Chem. Soc. Jpn. 2004, 77, 1427. ¨ sterlund, (9) Mattsson, A.; Leideborg, M.; Larsson, K.; Westin, G.; O L. J. Phys. Chem. B 2006, 110, 1210. (10) Herna´ndez-Alonso, M. D.; Tejedo-Tejedor, I.; Coronado, J. M.; Soria, J.; Anderson, M. A. Thin Solid Films 2006, 502, 125. ¨ sterlund, L.; Mattsson, A.; Leideborg, M.; Westin, G. Photode(11) O composition of acetone on ZrO2-TiO2 thin films in O2 excess and deficit conditions In Ceramic Engineering and Science Proceedings; Mathur, S., Ed.; Wiley & Sons: New York, 2007; Vol. 28. (12) Hirano, M.; Matsushima, K. J. Nanosci. Nanotechnol. 2006, 6, 762. (13) Larson, S. A.; Widegren, J. A.; Falconer, J. L. J. Catal. 1995, 157, 611. (14) Muggli, D. S.; Falconer, J. L. J. Catal. 2000, 191, 318. (15) Krysa, J.; Bouzek, K.; Stollberg, C. J. Appl. Electrochem. 2000, 20, 1033. (16) Sclafani, A.; Palmisano, L.; Schiavello, M.; Augugliaro, V. New J. Chem. 1988, 12, 129. (17) Muggli, D. S.; Keyser, S. A.; Falconer, L. J. Catal. Lett. 1998, 55, 129. (18) Muggli, D. S.; Falconer, J. L. J. Catal. 1999, 187, 230. (19) Lee, D. L.; Falconer, J. L. Catal. Lett. 2000, 70, 145.

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