Thin Films of Rutile Quantum-size Nanowires as Electrodes

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J. Phys. Chem. C 2008, 112, 15920–15928

Thin Films of Rutile Quantum-size Nanowires as Electrodes: Photoelectrochemical Studies Thomas Berger, Teresa Lana-Villarreal, Damia´n Monllor-Satoca, and Roberto Go´mez* Institut UniVersitari d’Electroquı´mica i Departament de Quı´mica Fı´sica, UniVersitat d’Alacant, E-03080 Alacant, Spain ReceiVed: June 5, 2008; ReVised Manuscript ReceiVed: July 30, 2008

Transparent electrodes, formed by 50 nm bundles of rutile nanowires (NW), 2 nm in diameter, have been prepared directly by chemical bath deposition at low temperature on conducting glass. The photoelectrocatalytic behavior of such NW electrodes has been studied in acidic solutions in the presence of model organic molecules (formic acid and methanol) and has been compared with that characteristic of thin films consisting of larger (20 × 40 nm) ellipsoidal rutile nanoparticles (NP). Both UV-vis absorption and photoaction spectra evidence that the NWs are in the quantum confinement (QC) regime, as the band gap is 0.27 eV larger than that of the ellipsoidal nanoparticles. From the onset of the accumulation region, determined by voltammetry, the conduction band edge is estimated to shift upward around 0.06 eV as a result of QC. In the presence of efficient hole acceptors, significantly larger photocurrents were observed for NW films than for NP electrodes. This indicates that the morphology of the film, together with the existence of QC and the particular surface structure of the wires, confers to the corresponding electrodes particularly good photoelectrocatalytic properties. A simple model based on the electron diffusion equation is applied to rationalize the observed photoelectrochemical behavior. The results point to an efficient hole transfer and, particularly, to a diminished electron recombination due to the absence of intergrain boundaries in NW electrodes as compared to NP electrodes. Complementarily, the reactivity of the photogenerated electrons was assessed through photopotential measurements, which also reflect an increased reactivity of electrons toward oxygen in the case of NW films. 1. Introduction The (photo)electrochemical and surface properties of nanostructured oxides (for instance TiO2) determine to a great extent their applicability as photoelectrocatalysts or in devices such as sensors, solar photovoltaic cells, and water splitting devices.1,2 Only recently, the research on the electrochemistry and photocatalytic properties of nanosized metal oxides has systematically focused on the different effects of the nanoparticle morphology, including size, shape, aspect ratio, or preferential surface orientation.3-5 In fact, nanowires, forming a truly nanostructured thin film, rather than nanoparticles have been proposed to be beneficial for electron transport, thus diminishing recombination and increasing overall photoactivity.6 The reason underlying this improvement likely is the existence of straight pathways (channels) for carriers in the solid phase and for chemicals and counterions in the solution phase. Of course, both the nanoparticle shape and preferential surface orientation of its facets will play an important role in the oxide electrochemistry because these factors affect not only the reactant and/or intermediate adsorption but also the interfacial charge transfer. In this respect, it is worth mentioning that there are reports showing an effect of surface orientation on the photocatalytic behavior of TiO2.7-14 On the other hand, the preparation of TiO2 thin film electrodes formed by ultrasmall nanoparticles opens up the way to explore the effects of quantum confinement on their electrochemical and photoelectrocatalytic behavior.15 This is an almost unexplored field. In an early work, Kavan et al.16 tracked quantum size (QS) effects in nanocrystalline anatase TiO2 electrodes by UV spectroscopy and photocurrent action measurements. Sakai et al.17 investigated the (photo)electrochemical behavior of self* Corresponding author. E-mail: [email protected]; fax: +34 965903537; phone: +34 965903536.

assembled multilayer films of titania nanosheets. Only recently, we have reported on some aspects of the (photo)electrochemistry of QS rutile nanowire films.18,19 The lack of electrochemical studies on this type of nanostructured samples derives from major difficulties in the preparation of thin film electrodes consisting of TiO2 nano-objects with a size smaller than 5 nm and showing a good voltammetric response. For example, thin film preparation methods using nanostructured powders as precursors normally require a thermal annealing step in order to obtain electric conductivity throughout the film and between the film and the conducting substrate. However, in addition to particle-particle interconnection, such a thermal treatment may provoke the loss of quantum confinement (QC) due to an increase of the average particle size. In the area of photocatalysis, size quantization effects in TiO2 samples have been investigated since the mid 80s. Anpo et al.20 studied gas-phase photocatalytic processes over TiO2 samples ranging from large (micrometric) semiconductor particles to isolated Ti-oxide single site species. An improvement in the photocatalyst performance was reported upon a decrease in particle size or an increase in the degree of catalyst dispersion. Several factors were invoked to explain such a tendency. Both a diminution in carrier recombination rate and an increase in carrier reactivity could play a role in determining the behavior of quantum-sized TiO2 particles. In addition, for ultrasmall nanoparticles the time required for carrier diffusion to the surface is much shorter than the average bulk recombination time. On the other hand, an optimal value for the particle size of ∼10 nm was found for anatase TiO2 samples by Zhang et al.21 The decreased photoactivity for smaller particles was attributed to an enhanced surface charge carrier recombination, thus offsetting the beneficial effect of the higher specific surface area. Lee and co-workers22 demonstrated that size quantization improved the

10.1021/jp8049747 CCC: $40.75  2008 American Chemical Society Published on Web 09/13/2008

Thin Films of Rutile Nanowires as Electrodes

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Figure 1. TEM images of rutile nanowires prepared by direct chemical deposition from a titanium oxysulfate solution (a) and of Sachtleben rutile nanoparticles after wet deposition of a particle suspension and thermal treatment at 450 °C (b). (c) SEM images of cross-sections for nanowire and nanoparticulate electrodes.

performance of rutile photocatalysts and attributed such an effect to an enhancement of the reducing potential of the photogenerated electrons. In the same way, QS TiO2 nanorods were found to be more effective than P25 for the inactivation of E. coli.23 Again, the observed increase in band gap was thought to underlie this behavior. In this contribution, we study the photoelectrochemical behavior of QS rutile nanowire (NW) electrodes and compare it to that typical of nanoparticulate (NP) rutile electrodes. In this way, we can focus mainly on the effects of particle morphology and size on the photoelectrocatalytic behavior of rutile. Not only the water photo-oxidation process is investigated, but also the photo-oxidation of model hole acceptors, such as formic acid and methanol. The role of grain boundaries (GBs) in the photoelectrochemical behavior of NP and NW electrodes is also discussed. 2. Experimental Section Rutile nanowire films were prepared by chemical bath deposition at 60 °C. F:SnO2-coated transparent conducting glass plates (U-type Asahi Glass Co) were immersed into aqueous titanium oxysulfate solutions for 6 h.18,19,24 Nanoparticulate electrodes were prepared by spreading an aqueous slurry of commercial rutile TiO2 nanoparticles (Nano-Rutile, Sachtleben Chemie GmbH) over 1.5 cm2 of F:SnO2-coated glass substrates.18 The suspension was prepared by grinding 1 g of rutile powder with 3.2 mL of H2O, 60 µL of acetylacetone (99+%, Aldrich), and 60 µL of Triton X100 (Aldrich). Typically, 10 µL of this suspension were applied per substrate. Afterward, the films were annealed and sintered for 1 h at 450 °C in air. Transmission electron micrographs (TEM) were obtained with a JEM-2010 (JEOL) microscope equipped with a MegaView II camera (SIS). UV-vis spectra were recorded with a Shimadzu UV-2401PC spectrophotometer equipped with an integrating sphere. Photoelectrochemical measurements were performed at room temperature in a three-electrode cell equipped with a fused silica window using a computer-controlled Autolab PGSTAT30 potentiostat. All potentials were measured against and are referred to a Ag/AgCl/KCl(sat) reference electrode, whereas a Pt wire was used as a counter electrode. In all the experiments a N2 (or O2) purged 0.1 M solution of HClO4 (Merck p.a.) in ultrapure water (Millipore Elix 3) was used as working electrolyte. A 300 W Xe arc lamp (Oriel) equipped with a water filter was used for UV-vis irradiation of the electrode from the electrolyte side (EE illumination). The applied light irradiance was measured with an optical power meter (Oriel model 70310) equipped with a bolometer (Ophir Optronics 71964) being 500 mW cm-2 in the case of polychromatic irradiation (E < 6.2

eV) and 6.3 mW (diameter of the spot ∼3 mm) when using a 375 nm (3.3 eV) Gallium-nitride laser diode (Oxxius). 3. Results 3.1. Structural and Electrochemical Characterization. Figure 1 shows TEM images for the nanowires (Figure 1a) and the nanoparticles (Figure 1b) forming the electrodes. The samples were detached from thin films supported on FTO-coated glass once they had been used in photoelectrochemical experiments. The nanostructured electrode prepared by chemical bath deposition (Figure 1a) is constituted by extremely thin nanowires, around 2 nm in diameter, which form bundles around 50 nm in diameter. The nanowires are well-crystallized in the rutile phase as shown by Raman spectroscopy.19 In addition, X-ray diffractograms for these films obtained both by us19 and by Yamabi and Imai24 showed the rutile (101) and (002) peaks, which points to growth along the crystallographic c axis. The pronounced aspect ratio morphology of the rutile nanowires results from an anisotropic crystal growth due to significant differences in the interfacial free energies of different crystallographic planes. In this case, the direction of crystal growth is affected by the selective adsorption of SO42- ions on specific surfaces perpendicular to the (001) face during film deposition. As the (110) plane is thermodynamically the most stable rutile surface, the corresponding face is probably the most exposed to the electrolyte. The nanoparticulate electrode, on the other hand, is formed by 20 × 40 nm ellipsoidal particles of pure rutile phase (Figure 1b).19 It is worth noting that prior to thermal annealing, the commercial nanopowder is constituted by nanorods exposing almost exclusively (110) sites.25 After thermal annealing, the morphology is altered, but the (110) facet orientation is still expected to be the predominant one. Figure 1 also contains scanning electron microscopy (SEM) images for cross sections of the NW and NP thin films (Figure 1c). Although the nanowire film appears as a homogeneous, highly transparent thin layer, the nanoparticulate electrode is constituted by large micrometric agglomerates, which impart a light dispersive character to the film. It is remarkable that, despite their rather different thickness (the NP film is around 30 times thicker), the electrochemically active surface area of both films is similar, allowing for a more direct comparison of their respective behavior (see below). The existence of QS effects, which could be anticipated on the basis of the NW diameter, is evidenced by both absorbance (Figure 2a) and photoaction spectra (Figure 2b). The photoaction spectrum was recorded in the presence of a high concentration of formic acid under positive polarization (see below). As deduced from both curves, the apparent bandgap of the NP electrode is 2.95-3.00 eV, corresponding to bulk rutile, whereas that for the nanowires is 3.15-3.25 eV. We attribute the 0.27

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Berger et al. SCHEME 1: Schematic illustration of the electronic band structure of nanowire and nanoparticulate films. pH ) 1.1

Figure 2. (a) Diffuse transmittance UV-vis spectra for a nanowire film (dNW ≈ 5 µm) and for a nanoparticulate film (dNP ) 8 µm). In the case of the nanoporous films, uncoated FTO glass slides were used for the background measurements. The uncoated FTO glass was measured against air. (b) Action curves for the photo-oxidation of formic acid as determined from the photocurrents measured at E ) 0.8 V. The photocurrent was normalized with respect to the measured irradiance at each wavelength; electrolyte, 0.1 M HClO4; c(HCOOH) ) 4.5 M; film thickness: dNW ) 360 nm, dNP ) 11 µm.

Figure 3. Voltammograms of a nanowire electrode (NW) and a nanoparticulate electrode (NP). Electrolyte, 0.1 M HClO4; scan rate, 20 mV s-1; film thickness: dNW ) 360 nm, dNP ) 11 µm.

( 0.06 eV increase of the bandgap to the existence of QC effects. We could estimate the expected Q-effect on the basis of simple models (particle-in-a-cylindrical-box).26 However, the extremely wide range of proposed values for the carrier effective masses, together with the roughness of the theoretical model, makes the estimation quite inaccurate. More generally, size quantization effects are expected to appear when at least one of the dimensions of the nano-objects constituting the sample is smaller than the radius of the exciton. Kormann et al.27 proposed values for the TiO2 excitonic radius varying within the approximate range 0.75-1.90 nm. Such a range, which has been invoked by other groups,23,28,29 is compatible with our observation of clear QS effects for nanowires 1 nm in radius. It is also worth noting that Joo et al.23 reported a 0.13 eV band gap increase for TiO2 nanorods 1.7 nm in radius, which is in keeping with our results. Figure 3 shows typical dark voltammograms for both NP and NW electrodes. The currents (and therefore the charge exchanged) appearing at potentials lower than -0.2 V are similar, corresponding to electrodes with comparable values for the electrochemically active surface area. These currents are attributed to the accumulation of electrons in the film and to charge compensation by adsorption (insertion) of H+ from the electrolyte.30 There is, however, a drastic difference in the voltammetric behavior of the respective electrodes in the region between 0 and -0.2 V, which is characterized by the appearance of a couple of quasi-reversible peaks associated to band gap monoenergetic electron states. Recently, we have presented experimental results indicating that such electron traps are located at GBs.18,31 Although the NP electrode, because of its

thickness and configuration, possesses a high density of such states, their concentration is very low in the case of NW electrodes. This can be understood as a consequence of the low NW film thickness and, even more decisively, of its nanostructure, constituted by bundles of aligned nanowires, which offers little opportunity for particle interconnection in comparison with the NP films. Another significant difference between the voltammograms shown in Figure 3 is the onset of the accumulation region, which is shifted 0.06 ( 0.02 V toward more negative potentials in the case of the NW film. Importantly, dark cyclic voltammetry in the accumulation potential region has been employed to study the electronic structure of nanoparticulate films (including quantum dots).32-34 Neglecting electron trapping at band gap states, electron accumulation in the film begins when the substrate electrode potential approaches that corresponding to the rutile conduction band edge. The accumulation region onset can thus be roughly associated with the conduction band (CB) edge. On the basis of our experimental findings, we assume that the CB edge of the NW sample is located ∼0.06 eV higher than in the case of the NP sample. Such a behavior also reflects the existence of QC and indicates that the nanowires behave as individual particles electronically isolated from one another. This conclusion is in agreement with the low density of band gap traps, attributed to defect states at GBs, found in the case of NW electrodes. The value for the CB edge shift, together with the corresponding increase in the band gap energy reported above, allows one to sketch the energy level diagram for the nanowires in comparison with that of the nanoparticles and macroscopic rutile samples. To locate the position of the band edges in the electrode potential scale, we consider that the conduction band edge is situated at the photocurrent onset potential in the presence of an efficient hole scavenger (Scheme 1). As can be seen in the Supporting Information section, such a potential value is approximately equal to -0.55 V. In addition, the CB edge seems to be located 0.06 V more positive for the NP film than for the NW film as deduced from Figure 3. As mentioned above, the effective masses of electrons and holes for TiO2 are not accurately known. The effective electron mass for TiO2, (me) has been reported to lie between 5 mo and 30 mo whereas for

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Figure 4. Voltammograms of a nanowire electrode (NW) and a nanoparticulate electrode (NP) under polychromatic EE illumination; 300 W Xe lamp: I ) 500 mW cm-2; electrolyte, 0.1 M HClO4; scan rate, 20 mV s-1; film thickness: dNW ) 360 nm, dNP ) 11 µm.

holes, mh values are estimated to be 2 mo or >3 mo.29 In any case, me is considered to be substantially larger than mh, which would explain the larger shift deduced for the valence band edge. On the other hand, the charge integrated in the accumulation region is proportional to the inner surface area of the thin film.18 The values obtained by integration down to -0.6 V are 5.5 and 6.3 mC cm-2, respectively, for the NW and NP electrodes used in Figure 3. They are quite similar in spite of the large differences observed in film thickness (Figure 1), implying that the electrochemically active surface area of both films is similar. 3.2. Photoelectrochemical Behavior. NW electrodes as well as rutile NP electrodes show very low photocurrents for water oxidation in 0.1 M HClO4 solution (Figure 4). This finding differs from results obtained under equivalent conditions with anatase and anatase+rutile nanoparticulate electrodes, which give rise to water photo-oxidation currents 1-2 orders of magnitude larger.31 However, preliminary results using electrodes consisting of ultrathin anatase nanowires also show low activity for water photo-oxidation. Several factors should be taken into consideration in order to explain this huge difference in photoelectrocatalytic behavior, for instance, electronic structure or particle size and shape (morphology), but the question needs further investigation. In any case, it should be mentioned that, for nanoporous electrodes, the magnitude of the photocurrent is determined by the relative rates of recombination, charge transport within the solid, and charge transfer to solution. The low activity found toward water photo-oxidation should not be attributed to a slow transport of the photogenerated electrons, because such a factor would equally limit the photocurrent for organics oxidation (see below). Moreover, one could think that the low photocurrent developed for water photooxidation is linked to an enhanced reactivity of CB electrons with evolved O2. In such a case, the photocurrent transients (at any potential in the current plateau) would be characterized by an initial spike and a progressive photocurrent decrease resulting from the build-up of product (oxygen) concentration in the vicinity of the electrode. However, the observed transients (see Supporting Information) do not show such a trend, being characterized by a constant photocurrent. Hence, the limitation should originate from a slow charge transfer to water. Figure 5 shows a series of voltammograms recorded under UV-vis illumination for the NW electrodes, corresponding to the photo-oxidation of methanol (Figure 5a) and formic acid (Figure 5b). Related information on the NP electrode is given as Supporting Information as well as photocurrent transients and voltammograms obtained under chopped illumination. As observed, the introduction of the organic substances gives rise to the development of significant photocurrents, especially in the case of formic acid. Using the 375 nm light of a Gallium-

Figure 5. Voltammograms of a nanowire electrode under polychromatic illumination in the presence of methanol (a) and formic acid (b). The insets show the photocurrents for low and high concentrations of the respective organic molecule; 300 W Xe lamp EE illumination: I ) 500 mW cm-2; electrolyte, 0.1 M HClO4; scan rate, 20 mV s-1; film thickness: dNW ) 360 nm, dNP ) 11 µm.

nitride laser diode, the absorbed-photon-to-current-efficiency (APCE) was roughly estimated to be at least as high as 0.5. Remarkably, the multiplication factor, defined as the ratio between the maximum photocurrent found for the organics photo-oxidation and that corresponding to the photo-oxidation of water, attains values as high as 200. This reflects, in part, the low activity of both NW and NP rutile electrodes toward water photo-oxidation. From the insets of Figure 5, a different voltammetric behavior can be observed for formic acid and methanol. For the latter, the photo-oxidation wave shifts toward more negative potentials (0.08 V) as the concentration increases (from 0.1 to 4.5 M), whereas it does not shift in the case of formic acid. In this potential region, the transport of electrons toward the back contact is retarded because of the negative potential being applied, and the probability of carrier recombination is increased. Obviously, an increase in the concentration of the hole acceptor (methanol) favors charge transfer to solution over recombination, which is reflected in the observed potential shift of the photocurrent wave. The situation is different in the case of formic acid, which is known to be adsorbed. In the concentration range being used, the surface coverage does not suffer drastic variations, explaining why the photocurrent onset is not altered.35 In Figure 6 the saturation photocurrent (jsat photo) is plotted versus the organics concentration for both NP and NW rutile electrodes. Under equivalent illumination conditions, the photocurrent delivered by the NW electrode is around 1 order of magnitude

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Berger et al. 4.1. Methanol: Indirect Hole Transfer Mechanism. The reaction scheme for the indirect photocatalytic oxidation of nonspecifically adsorbed RH2 species via photogenerated surface O · + radicals is described by the following equations: hν

TiO2 98 h++edOS + h+fdOS•+

r0 ) RΦ0 exp(-Rx)

(1)

r1 ) k1[h+]N(1 - f)

(2)

dOS•+ + RH2fRH• + dOS + H+ dOS•+ + e-fdOS

riox ) kiox[RH2]Nf (3)

rr ) kr[e-]Nf

RH•fR + e- + H+

rinj ) riox

(4) (5)

where R is the absorption coefficient (cm-1), Φ0 is the incident photon flux (cm-2 · s-1), N is the concentration of hole trapping sites at the surface (cm-2), Nf is the concentration of surface O•+ radicals (cm-2), and x is the spatial coordinate (with x ) 0 at the solid/solution interface and x ) d at the back contact). The rate constants for hole trapping, indirect oxidation, and recombination of the intermediate RH• radical are given by k1, kiox and kr, and the respective reaction rates by r1, riox and rr. The rate for electron injection from RH• is given by rinj. Under steady state conditions43,45 and making n ≡ [eS-], Nf can be obtained as:

Figure 6. Saturation photocurrent densities at E ) 0.8 V as a function of methanol and formic acid concentration for (a) nanowire and (b) nanoparticulate electrodes.

larger than in the case of the NP electrode for both organics in spite of the fact that the NW film is much thinner and harvests a limited amount of light. Incidentally, it is noteworthy that the electrochemical doping of the NP electrode31 leads to an important increase in its photoactivity (by 1 order of magnitude after 2 h of electrochemical doping at -0.6 V in 0.1 M HClO4). In any case, the photocurrent never exceeds that of the NW electrode. To complete the photoelectrochemical study of the NW film in comparison with the NP film, we measured the open circuit potential under interrupted illumination for both samples (Figure 7) in the presence of either formic acid or methanol and oxygen. As observed, upon illumination, there is in all cases an abrupt decrease in the open circuit potential. In the following we call photopotential the difference between the rest potential in the dark and the open circuit potential under illumination. As observed, the photopotential is larger by 0.10-0.15 V for the NW electrode, and even more importantly, its relaxation upon light interruption is faster. 4. Discussion The behavior reported in Figure 6 can be explained by means of a simple kinetic model43-47 assuming an indirect hole transfer mechanism for methanol photo-oxidation and a direct hole transfer in the case of formic acid. It should be noted that the nomenclature has been slightly changed with respect to previous reports by us (particularly ref 45) to take into account recent works suggesting that surface-trapped holes are located at terminal oxygen lattice sites instead of being OH radicals resulting from the oxidation of adsorbed water.36

Figure 7. Open circuit potential measurements of nanowire electrodes (NW) and nanoparticulate electrodes (NP) in the presence of either methanol (a) or formic acid (b). 300 W Xe lamp EE illumination, I ) 500 mW cm-2; electrolyte, O2-saturated aqueous 0.1 M HClO4 solution; c(HCOOH) ) 4.5 M, c(CH3OH) ) 4.5 M; film thickness: dNW ) 360 nm, dNP ) 11 µm.

Thin Films of Rutile Nanowires as Electrodes

Nf )

J. Phys. Chem. C, Vol. 112, No. 40, 2008 15925

BRΦ0 exp(-Rx)

(6)

krn + kiox[RH2]

with B being the total-volume-to-inner-surface-area ratio for the thin film. Assuming that diffusion is the main electron transport mechanism, the continuity equation can be written as eqs 7 and 8,

D

d2n 1 1 + RΦ0 exp(-Rx) + kiox[RH2]Nf - krnNf ) 0 (7) 2 B B dx -D

2kiox[RH2] d2n dJ RΦ0 exp(-Rx) ) ) dx2 dx krn + kiox[RH2]

(8)

where J is the electron flux, which is directly proportional to the photocurrent, and D is the diffusion coefficient. We assume both that the Fermi level at the back contact (x ) d) is determined by the external applied potential and that there is equilibrium between the conducting glass substrate and the contacted TiO2 particles:37,38

(

dark e(E - EOC ) n(d) ) n0(d)exp mkT

)

(9)

where n0(d) is the stationary concentration of electrons in the dark (at the rest potential Edark oc ) and n(d) is the electron concentration for the particles directly contacted by the substrate once a potential E is applied. The value of the ideality factor (m) was obtained by fitting the experimental behavior at the onset of the photocurrent wave, that is, in the region where the photocurrent depends strongly on the applied potential. For the NW electrodes, such a value is approximately equal to 2. Furthermore, we assume that at the solid/solution interface (at x ) 0):

( dndx )

x)0

)0

remarkable that the ratio kiox/kr was the only parameter used in order to fit the experimental results. The values taken for the different constants are given in the caption. The differences observed in the methanol photo-oxidation behavior with NW and NP electrodes may therefore be attributed to significant differences in the respective kiox/kr values, such a ratio being significantly larger (by a factor of ∼6) in the case of the NW electrode. 4.2. Formic Acid: Direct Hole Transfer Mechanism. To describe the formic acid photo-oxidation, eq 3 in the reaction scheme presented above needs to be substituted by the following equation.

(10)

In Figure 8, we plot, against methanol concentration, the experimental saturation photocurrent density jsat photo for methanol photo-oxidation for both NP and NW electrodes. The data for NW electrodes was taken from Figure 6, and equivalent data is plotted against the concentration of methanol. In addition, theoretical values for the saturation photocurrent as determined by numerical solution of eq 8 with n(d) ) 0 (using a shooting method to derive n(x ) 0) and a fourth order Runge-Kutta method to solve the differential equation) are also plotted. It is

h+ + RH2,SfRH• + H+ rdox ) kdox[RH2,S][hS+]

(11)

At steady state, assuming low stationary concentration of surface trapped holes, (i.e., f , 1), Nf can be obtained by eq 12.

Nf )

(

BRΦ0 exp(-Rx)

)

(12)

kdox 1+ [RH2,S] krn Nk1

One could conceive that step 3 can coexist with step 11, thus defining a mixed hole transfer mechanism. However, our previous work with compact43 and nanoparticulate45 TiO2 electrodes indicates that this is not needed in the case of formic acid oxidation; all the experimental results could be accounted for by considering that step 3 is negligible with respect to step 11. In this case, the continuity equation is given by eq 13.

D

d2n 1 1 + RΦ0 exp(-Rx) + kdox[RH2,S][hS+] - krnNf ) 0 2 B B dx (13)

Therefore, the incoming flux of electrons to the FTO substrate J(d) is given by eq 14,

dn dx

( )

J(d ) ) -D

x)d

)

2Φ0kdox[HCOOHS] Nk1 + kdox[HCOOHS]

(1 - exp(-Rd )) (14)

by assuming that the stationary surface concentration of formic acid follows the Langmuir isotherm, that is:

[HCOOHS] )

aK[HCOOH] 1 + K[HCOOH]

(15)

where a is the surface density of formic acid adsorption sites, and K is the adsorption constant, one arrives at:

J(d) )

2Φ0(akdox ⁄ Nk1)K[HCOOH] 1 + [1 + (akdox ⁄ Nk1)]K[HCOOH]

(1 - exp(-Rd)) (16)

Figure 8. Experimental and simulated values for the saturation photocurrents of methanol oxidation for NP and NW electrodes; R ) 5 × 103 cm-1; Φ ) 5 × 1016 cm-2 s-1; D ) 10-5 cm2 s-1; n0,NW ) 2.56 × 1015 cm-3; n0,NP ) 1.02 × 1015 cm-3; dNW ) 360 nm; dNP ) 11 µm.

Figure 9 shows the experimental values for the saturation current density corresponding to the oxidation of formic acid on both NP and NW electrodes as taken from Figure 6. The solid lines correspond to the best fit of the experimental results obtained from eq 16, in each case using as a sole parameter the value of (akdox/Nk1), which may be interpreted as the ratio of the cross section for hole capture at an adsorbed formic acid molecule and at an intrinsic surface site (terminal oxygen lattice site). The same value for the formic acid adsorption constant

15926 J. Phys. Chem. C, Vol. 112, No. 40, 2008

Berger et al.

Figure 9. Experimental and simulated values for the saturation photocurrents of formic acid oxidation for NP and NW electrodes; R ) 5 × 103 cm-1; Φ ) 5 × 1016 cm-2 s-1; D ) 10-5 cm2 s-1; n0,NW ) 2.56 × 1015 cm-3; n0,NP ) 1.02 × 1015 cm-3; dNW ) 360 nm; dNP) 11 µm; K ) 1.8 × 10-20 cm3.

was taken for both electrodes on the basis of experimental results obtained by means of infrared spectroscopy, indicating a similar adsorption equilibrium constant in both cases.39 As observed, a reasonably good fit was obtained by using, in the case of the NW electrode, a value of (akdox/Nk1) 2 orders of magnitude larger for the NW than for the NP electrode. The ratio a/N is not expected to change in a drastic way for rutile samples with the same preferential surface orientation, especially if one takes into account that an increase in the step and kink sites may equally increase the concentration of surface hole traps40 and formic acid adsorption sites. It is likely that the difference between both samples results from a much larger value of the ratio kdox/ k1 in the case of the NW electrode. As observed, we have not explicitly considered in the kinetic model the recombination rate at the particle boundaries for the sake of simplicity. The introduction of additional equations to consider the specific recombination at GBs does not significantly alter the kinetic analysis presented above. Mainly, the hole transfer and the recombination/capture rate constants would become effective, if the contribution of the GBs were included (see the Supporting Information). 4.3. Photopotential Measurements. Our discussion will focus on the potential relaxation curves as recorded after light interruption. These measurements allow us to complement the information derived from the voltammograms obtained under illumination. Although the latter allow us to determine the hole reactivity (transfer to solution), the photopotential decay measurements contain valuable information on electron reactivity, particularly with molecular oxygen present in solution.41 Both processes are equally important for determining the efficiency of a certain photocatalyst. The faster the photopotential relaxation, the faster the electron concentration decay and, therefore, the larger the value of the kinetic constant (kred) for the process:

H++O2+eS- f HO•2

(17)

As observed in Figure 7, in the presence of both methanol and formic acid, the photopotential relaxation is faster for NW electrodes, which indicates that photogenerated electrons in the nanowires exhibit a higher reactivity for oxygen reduction than those in NP samples. This increased reactivity can be understood on the basis of the diagram in Scheme 1. As a consequence of quantization, the conduction band edge gets displaced toward more negative potentials, which renders photogenerated electrons stronger reductants, having an increased avidity for dissolved oxygen.

4.4. General Discussion. According to the preceding, a diminished recombination rate and/or an enhanced hole transfer rate seem to underlie the higher efficiency of the NW electrode toward the photo-oxidation of organics. Regarding recombination, one should note that, for this type of sample, bulk recombination is diminished, even almost eliminated, because the bulk of the nanowires is virtually nonexistent. On the other hand, and because of their particular morphology, NW electrodes are characterized by a very low concentration of GBs as reflected in the low intensity of the quasi-reversible peaks shown in the cyclic voltammetry at around 0.2 V. Such GB sites act as electron traps, but due to their location they will also favor their recombination with photogenerated holes due to electrostatic attraction.31,41 In fact, such an electrostatic interaction is enhanced by the fact that the charges trapped at these sites are not screened by ions in solution, as would occur in the case of surface-trapped charges. Because the concentration of particle interconnections in NW films is low, the number of potential recombination centers is diminished in these electrodes as compared to NP films. Regarding hole transfer,20-23 it is worth noting that for NW films the increase in band gap should be accompanied by an enhanced reactivity of the photogenerated carriers. CB electrons become more reductant whereas VB holes become more oxidant. Such an effect is particularly important in the case of holes, because of their lower effective mass in the case of TiO2 (see above). For species that do not interact strongly with the surface, such as methanol,42 normally the photo-oxidation takes place via an indirect mechanism, that is, photogenerated holes will be captured at the surface prior to their attacking of organic species in the vicinity of the TiO2 surface.43-45 In the case of the NW electrodes, once the photo-oxidation process begins with the generation of the methoxy radical, the probability of subsequent electron injection in the conduction band of the semiconductor (current doubling mechanism) will increase due to the short distance between the radical and the neighboring nanowires, thus leading to a maximization of formaldehyde production. In addition, the spatial constriction of the solution species within the nanochannels will facilitate its full mineralization as illustrated in Scheme 2. Formaldehyde molecules (presumably not strongly adsorbed at the rutile surface) in their way out of the channel toward the solution bulk will have a high probability of hole capture and subsequent electron injection, leading to the formation of formic acid, which would become adsorbed and photo-oxidized. On the other hand, in the case of species that get photooxidized directly via hole capture,43-47 for instance formic acid, the increased activity with respect to the NP electrode can be associated to the fact that the inelastic hole capture by the organics would become more exoergic, but additional aspects, such as electrode adsorption properties, should also be considered. Even if the (photo)electrochemically active surface area is similar in both cases (see above, Figure 3), major differences in the geometry of surface sites are expected for the two types of electrodes. In principle, in very small nano-objects, there will be a larger fraction of surface sites with tetrahedral coordination for the Ti atoms.48-50 Species adsorbed at titanium surface sites of low coordination are probably more reactive than those adsorbed at sites of high coordination. However, the adsorption constants of formate species on NW films and on layers of Sachtleben rutile nanocolumns were found to differ only by a factor of less than 2 both for 4-fold and 5-fold Ti sites.39 Clearly, additional effects, as discussed above, have to be taken into

Thin Films of Rutile Nanowires as Electrodes SCHEME 2: Schematic illustration of the methanol photo-oxidation on nanowire electrodes

consideration to explain the large difference in the photocatalytic activity of NW and NP electrodes. We should mention at this point that the efficiency of nanostructured photoanodes could also depend on the transport of electrons and oxidizable matter through the nanostructure. On the one hand, the distance to be traveled by the photogenerated electrons is shorter for the NW electrodes. Likewise, the electron diffusion coefficient is probably larger for the NW electrode because of both the existence of straight pathways to the substrate and the virtual absence of GB traps. In the case of indirect hole transfer (methanol photo-oxidation), considering a larger value for the electron diffusion coefficient in the NW electrode would also allow us to fit the experimental photocurrent data, even keeping the ratio kiox/kr constant for both electrodes. However, attributing a decisive importance to this factor would render the data for formic acid photo-oxidation not understandable, as they do not depend on the electron diffusion coefficient. As occurs for electrons, the distance to be traveled by the reactants and products is also minimized. However, the narrowness of the pores (around 1 nm in diameter) could hinder the transport of these species, yielding this process ratedetermining. The fact that the voltammogram under illumination presents a well-defined plateau (there is no photocurrent decay vs time or potential) indicates that these channels are efficient enough not to convert mass transport into the rate-determining step in the organics oxidation.

J. Phys. Chem. C, Vol. 112, No. 40, 2008 15927 as well as by a relatively sharp voltammetric feature associated to grain boundary traps. The density of the latter states is very low in comparison with that found in conventional nanoparticulate electrodes. Importantly, both UV-vis and photocurrent action spectroscopies reveal that the band gap for such electrodes is around 0.27 eV larger than for conventional rutile samples, which is considered to be a quantum size effect. Under illumination, the voltammograms for the nanowire electrode are virtually the ideal ones for an electrode where carrier transport is purely diffusive. The photocurrent developed in the presence of simple organics such as methanol or formic acid is remarkable: the quantum efficiency in the presence of a high concentration of formic acid (4.5 M) is at least as high as 0.5. The photocurrents for nanoparticulate electrodes having similar inner surface areas are significantly smaller (up to 1 order of magnitude). These results have been rationalized by means of a simple model based on the electron diffusion equation. Fitting the model to the experimental data points to the fact that the ratio of the hole transfer rate constant to the recombination rate constant is significantly higher in the case of the NW electrode. On the other hand, the photopotential measurements reveal that the photogenerated electrons are transferred to solution molecular oxygen faster for the NW electrodes than for the NP ones. The increased reactivity of both electrons and holes in the NW samples could derive from the fact that they possess, respectively, a lower and higher redox potential than those of the nanoparticulate electrodes, as a direct consequence of the increased band gap. In addition, the recombination in the nanowire electrodes is probably reduced because of a very low concentration of grain boundaries, which are thought to be effective sites (traps) for carrier recombination. Undoubtedly, important changes at the surface level, with a higher concentration of surface sites with low coordination and different electron and mass transport properties could also have a significant role in determining the apparently superior performance of the nanowire electrodes. More research is underway to address these issues. Acknowledgment. This work was financially supported by the Spanish Ministry of Education and Science (MEC) CTQ200606286 (FONDOS FEDER) and HOPE CSD2007-00007(Consolider-Ingenio2010) and the Generalitat Valenciana (ACOMP07095). T. B. gratefully acknowledges the support of the Austrian Science Fund (Project J2608-N20). D.M.-S. thanks the MEC for the award of a FPI grant. We thank C. Almansa and A. Amoro´s Rodrı´guez for performing the TEM and SEM measurements, respectively. Supporting Information Available: Photocurrent transients for water oxidation, voltammograms in the presence of organics for NP electrodes, determination of the photocurrent onset, and discussion on the effect of considering the GB traps in the kinetic model. This material is available free of charge via the Internet at http://pubs.acs.org.

5. Conclusions Transparent nanowire electrodes can be prepared on conducting glass by one-step chemical bath deposition from acidic solutions of titanyl sulfate. These films are hierarchically organized as bundles of 30-50 nm composed of nanowires, around 2 nm in diameter. In the dark, their voltammograms are characterized by a well-defined accumulation region of very high capacitance, which is shifted 0.06 V toward more negative potentials as compared to that of the nanoparticulate electrodes,

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