Electrochimica Acta 83 (2012) 113–124
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(Photo)Electrochemical characterization of nanoporous TiO2 and Ce-doped TiO2 sol–gel ﬁlm electrodes Sutasinee Kityakarn a , Yingyot Pooarporn b , Prayoon Songsiriritthigul b , Attera Worayingyong a , Simone Robl c , André M. Braun d , Michael Wörner e,∗ a
Department of Chemistry, Faculty of Science, Kasetsart University, Bangkok 10903, Thailand Synchrotron Light Research Institute (Public Organization), Nakhon Ratchasima 30000, Thailand c Institute for Technical Thermodynamics and Refrigeration (ITTK) Karlsruhe Institute of Technology, Karlsruhe D-76131, Germany d Engler-Bunte-Institute, Karlsruhe Institute of Technology, Karlsruhe D-76131, Germany e Institute of Engineering in Life Sciences, Karlsruhe Institute of Technology, Karlsruhe D-76131, Germany b
a r t i c l e
i n f o
Article history: Received 19 January 2012 Received in revised form 6 July 2012 Accepted 8 July 2012 Available online 16 August 2012 Keywords: Nanoporous TiO2 ﬁlm electrode Ce-doped TiO2 Photoelectrochemistry Electrochemical impedance spectroscopy (EIS) Porous electrode model
a b s t r a c t Focusing on effects of charge separation limitations and doping on the photoactivity of TiO2 , different nanoporous TiO2 ﬁlm electrodes were prepared by the sol–gel or the suspension methods, respectively. X-ray diffraction (XRD) characterization revealed for all undoped TiO2 electrodes (TiO2 SG and TiO2 -P25) mixed phases of anatase and rutile, whereas the 2%CeTiO2 -SG electrode showed only anatase phase pattern, revealing that the incorporation of Ce ions prevented phase transformation. The (photo)electrochemical characterization of the nanoporous TiO2 ﬁlm electrodes was performed by cyclic voltammetry (CV) and electrochemical impedance spectroscopy (EIS) in the dark and under UV irradiation, respectively. A photocurrent maximum depending on the ﬁlm thickness was observed at about 13 m for all TiO2 electrodes investigated. The photocurrent responses of Ce-doped sol–gel TiO2 electrodes were comparably low, indicating an enhanced electron–hole recombination at the Ce ion levels within the band gap of TiO2 . A porous electrode model was adapted for the ﬁtting of the experimental EIS data. The potential and incident radiant power density dependence of the heterogeneous charge transfer reaction (RCT ) and the coupled transport of photogenerated electrons to the collector electrode (ZS ) were ascribed to promoted charge carrier separation and migration, i.e. electron drift dominated over diffusion. Consequently, the dependence of different discrete impedance elements was discussed, supposing a macroscopic electric ﬁeld across the 3D array of interconnected TiO2 nanoparticles that form the ﬁlm electrodes. Besides photocurrent doubling, addition of methanol as a hole scavenger revealed the limitation of the overall reaction by the heterogeneous charge transfer reaction, in particular at high radiant power densities. © 2012 Elsevier Ltd. All rights reserved.
1. Introduction Titanium dioxide (TiO2 ) is a promising material in photocatalytic applications for environmental technologies, due to its semiconductor properties and the generation of electron–hole pairs under UV irradiation. These electron–hole pairs migrate or diffuse to the TiO2 surface, where they react with adsorbed molecules. A lot of effort was made to improve the photocatalytic performance [1–4]. The photocatalytic properties of titania are sensitive to their polymorphism and microstructure. Anatase is widely used as a photocatalyst and considered to be the most active form [5,6], but high photocatalytic activity was also obtained using mixtures of aqueous suspensions of anatase and rutile particles [3,7]. In
∗ Corresponding author. Tel.: +49 721 608 46235; fax: +49 721 608 46240. E-mail address: [email protected]
(M. Wörner). 0013-4686/$ – see front matter © 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.electacta.2012.07.129
contrast to the pure dispersions, the observed increased photocatalytic activity was assumed to be due to inter-particle contacts formed between anatase and rutile particles in water and, consequently, to band bending upon a Fermi level line-up. A potential drop within the contact zone would prevent an electron ﬂow from anatase to rutile particles, whereas holes created in anatase may migrate to rutile particles. In addition, for mixed-phase TiO2 -P25 particles, an intrinsic charge separation was proposed to explain the high photocatalytic activity in particulate dispersive aqueous systems . Cerium and transition metals are added to increase the photocatalytic activity of TiO2 and to extend the absorption range into the visible. The presence of such metal ions provides trap sites for electrons and holes, in addition to those located at the particle surface (e.g. adsorbed O2 and OH− ), that may lead to higher rates of charge separation and interfacial charge transfer reactions. The photocatalytic activity of aqueous TiO2 suspensions for
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mercaptobenzothiazole degradation was signiﬁcantly enhanced by incorporation of Ce(III) . However, contradictory results were published, e.g. the doping with different metal ions leading to an increased rate of recombination of electron–hole pairs and to lower rates of substrate (4-nitrophenol) degradation . Photoelectrochemical (PEC) systems were also used to achieve an increase of the photocatalytic efﬁciency. Different methods were used to immobilize TiO2 at conductive substrates in form of nanoporous ﬁlms to permit large semiconductor surface areas [2,11–13]. The effect of the applied potential was shown for degradation of 4-chlorophenol and revealed that depletion layer conditions were needed for high rates of photocatalytic degradation . For the improvement of the performance of PEC systems based on semiconducting TiO2 , a detailed mechanistic understanding is needed. Electrochemical impedance spectroscopy (EIS) provides speciﬁc information about double layer properties, charge transfer phenomena, charge carrier diffusion and charge generationrecombination processes . The results of EIS analyses are usually discussed in terms of equivalent circuits allowing the evaluation of different physicochemical parameters of the reaction system . A number of equivalent circuits for semiconductor/electrolyte interfaces may be assembled by combinations of resistors and capacitors (i.e. Debye elements) . However, more recent studies show that it is necessary to employ constant phase elements (CPE) under conditions of the observed frequency dispersion . CPEs are associated with disorder, either in the electrode structure or in the diffusion dynamics [18,19]. In addition, a transmission line model (TLM) is introduced to describe the small signal ac-impedance of nanoporous TiO2 ﬁlm electrodes in aqueous electrolytes [20,21]. This model accounts for two transport channels, in the pores (ﬁlled with electrolyte) and in the solid (interconnected/sintered TiO2 particles), as well as for the cross reaction at the interface (interfacial charge transfer at the semiconductor/electrolyte boundary). Under UV irradiation, several coupled processes such as carrier generation and diffusion, recombination, charge transfer and mass transport in the solution have to be considered. Nevertheless, the analysis of different simultaneous processes by EIS requires adequately differing time constants. The aim of this work was to study the (photo)electrochemical properties of nanoporous TiO2 ﬁlms prepared on ITO (indium tin oxide) coated glass substrates for the improvement of the photocatalytic performance of such electrodes. A speciﬁcally developed sol–gel (SG) method was used to prepare nanoporous TiO2 -SG ﬁlm electrodes with the same anatase to rutile ratio as the one found in TiO2 -P25 (75/25), providing the possibility to compare different preparation methods and to evaluate intrinsic charge separation effects. Furthermore, the effect of Ce-doping on the anatase to rutile transformation and on the photo-electrochemical properties was studied. A model to describe the impedance behavior of nanoporous TiO2 electrodes (under UV irradiation) is presented in this work. It provides the possibility to optimize the photocatalytic activity of TiO2 -electrodes, considering morphology modiﬁcation and doping aspects.
2. Experimental 2.1. Electrode preparation 2.1.1. Nanoporous TiO2 -SG ﬁlm electrodes (TiO2 -SG and 2%CeTiO2 -SG) Nanoporous TiO2 electrodes were prepared with a sol–gel  using titianium(IV)bis(ethyl acetoacetato) method
diisopropoxide (Aldrich, technical grade) as precursor and cerium nitrate hexahydrate (Fluka, 99.0%) for doping (Table 1). The titanium alkoxide precursor solution (0.01 mol) was added drop-wise into a stirred aqueous nitric acid (pH 1.0, 36.0 cm3 ) at 296 ± 1 K. The stirred suspension was heated to 358 K and kept at this temperature for 100 min. ITO-coated ﬂoat glass (PGO, Germany) with SiO2 passivation layers, 2 cm × 3 cm (<10 /cm2 ) was used as a support for TiO2 . This support was immersed in boiling acetone (348 K) for 10 min and afterwards in 30% (v/v) HNO3 for 30 min. The pre-treated ITO glass was stored in distilled water for 1 h before coating. An area of 2 cm × 2 cm of the pretreated ITO glass was dipped into the sol for 30 s, withdrawn (within 10 s) and kept at 473 K for 10 min. This procedure was repeated several times to increase the thickness of the resulting TiO2 ﬁlm, the number of repetitions representing the number of layers. The TiO2 coated substrate was calcinated at 823 K for 4 h in air at ambient pressure. Compared to TiO2 -P25 electrodes, a higher temperature was required to obtain TiO2 -SG electrodes with the same anatase to rutile ratio as for P25 (75:25). For Ce-doping (2% CeTiO2 -SG), the corresponding amount of cerium was added to the nitric acid solution. The procedure was the same as described above for the preparation of TiO2 -SG electrodes. 2.1.2. Nanoparticulate TiO2 -P25 ﬁlm electrodes Vinodgopal’s method  to prepare nanoparticulate thin ﬁlm electrodes was modiﬁed as follows: an aqueous suspension of TiO2 -P25 (Degussa, 1.00 g in 50 cm3 water/methanol, 1/4, v/v) was dispensed on pre-treated ITO glass. The solvent was evaporated at 308 K for 2 h. The procedure was repeated to increase the number of layers, and the electrode was ﬁnally calcinated at 723 K for 4 h in air at ambient pressure. The electrical contact of all prepared electrodes was made by conductive adhesive bonding of a silver wire over the whole width of the uncovered upper part of the ITO glass substrate, and all conductive parts of the electrodes were protected by insulating epoxy glue, cutting edges included. 2.2. Characterization of TiO2 ﬁlm electrodes 2.2.1. Structure and morphology X-ray diffraction (XRD) analyses were performed with a Philips X’Pert diffractometer using Cu K␣ -radiation with an anode current of 30 mA and an accelerating voltage of 40 kV with a scanning step of 0.02◦ . The diffraction patterns were indexed by comparison with the JCPDS (Joint Committee on Powder Diffraction Standards) ﬁles number 83-2243, 78-1510 and 81-0792 for anatase, rutile and cerium oxide, respectively. The morphology of the electrodes was analyzed by ﬁeld emission scanning electron microscopy (SEM Philips XL30). An accelerating voltage in the range of 10–30 keV was used. The specimens were prepared by Au sputtering to increase the conductivity of the samples. 2.2.2. (Photo)Electrochemical characterization The (photo)electrochemical experiments were carried out with three electrode technique using the prepared TiO2 ﬁlm electrodes as working electrode, a platinum counter electrode (ﬂag of 1 cm × 1 cm) and a Ag/AgCl (in aqueous KCl, 3.0 M) reference electrode. All electrode potentials are given with respect to the reference electrode. A rectangular large cuvette (Optical Glass, 40 mm × 40 mm × 40 mm, Hellma, Germany) equipped with a selfmade Teﬂon top for positioning and ﬁxing the electrodes was used as measuring cell. Cyclic voltammograms (CV, scan rate: 25 mV/s) and electrochemical impedance spectra (EIS) were recorded with an IM6 Electrochemical Workstation (ZAHNER-Elektrik, Germany). An aqueous sodium sulfate solution (Fluka, 99.0%, 0.50 M) was
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Table 1 Sample codes and composition of different prepared TiO2 ﬁlm electrodes. Sample code
TiO2 -P25 TiO2 -SG 2%CeTiO2 -SG
Degussa Titanium(IV)bis(ethyl acetoacetato)diisopropoxide Titanium(IV)bis(ethyl acetoacetato)diisopropoxide
Suspension Sol–gel Sol–gel
100 100 97.7
– – 2.3
used as electrolyte. It was degassed with Argon (5.0) before and kept under an Argon atmosphere during experiments. Methanol (Aldrich, 98%) was added to the electrolyte solution (2.5 M of methanol) to obtain more detailed information about the effect of a hole acceptor. For EIS studies, a 5 mV ac-perturbation was applied within a frequency range of 30 mHz to 100 kHz. For comparative experiments with undoped and Ce-doped TiO2 -SG electrodes, a 250 W halogen lamp was used as irradiation source (5025AF-S, Braun, Germany). Further experiments were carried out with a halogen light source equipped with a ﬁber light guide (cold light source, KL 2500 LCD, Schott, Germany) permitting radiant power density variation. Incident radiant power densities, P0 , were determined with a calibrated ﬁber optic spectroradiometer (USB2000+, Ocean Optics, USA) and a 400 nm short pass ﬁlter (Laser 2000 GmbH, Germany) allowing to quantify the part of the emitted wavelength range that will be absorbed by the TiO2 ﬁlm electrodes. The optical ﬁber was placed at the same distance at which the TiO2 electrodes are being irradiated. Therefore, the measured values of P0 are not corrected for adsorption and reﬂection losses in cuvette glass and electrolyte solution. 3. Results and discussion 3.1. Structural and morphological characterizations The XRD patterns of ITO conducting glass, TiO2 -P25, TiO2 -SG and 2%CeTiO2 -SG ﬁlm electrodes are presented in Fig. 1. The XRD of the TiO2 -P25 ﬁlm electrode revealed characteristic peaks of anatase at 2 25.33, 48.10 and 55.14◦ (JCPDS PDF No. 83-2243) and of rutile at 2 27.51, 36.16 and 54.46◦ (JCPDS PDF No. 78-1510). The XRD pattern of the TiO2 -SG ﬁlm electrode exhibited the same pattern and almost the same intensity distribution as TiO2 -P25. The molar ratios of anatase and rutile were determined by the method described by Spurr and Myers . The rutile phase of TiO2 -SG ﬁlm electrodes was determined to be 23%, in comparison to 24% of that of the TiO2 -P25 ﬁlm electrode. It should be mentioned that calcination of TiO2 -P25 at the same temperature as for the preparation of TiO2 -SG electrodes (823 K) does not change the anatase to rutile ratio. The XRD pattern of 2%CeTiO2 -SG ﬁlm electrode was identiﬁed to be pure anatase (Fig. 1). The anatase to rutile transformation requiring temperatures above 873 K for Cedoped TiO2 , anatase was stabilized by Ce ions at a calcination temperature of 823 K. Low resolution SEM images showed signiﬁcant differences between the TiO2 ﬁlm electrodes investigated (Fig. 2a–c). The SEM image of the TiO2 -P25 electrode (Fig. 2a) showed a microstructured ﬁlm of TiO2 -P25 at low resolution, but a network of agglomerated particles, appearing as a nanoparticulate layer, became visible at high resolution (inset Fig. 2a). The particle diameter was determined to be about 50 nm. The SEM images of undoped and doped TiO2 -SG resembled compact ﬁlms at low resolution (Fig. 2b and c), but at higher resolution, tightly packed nanoparticles, forming nanoporous TiO2 ﬁlms were observed (see inset Fig. 2b and c). The particle sizes at undoped and doped TiO2 -SG electrodes were determined to be 20–30 and 10–20 nm, respectively. SEM was also used to determine the thickness of the ﬁlm to be 12–15 m for 20 layers of TiO2 -SG and for 5 layers of TiO2 -P25, respectively.
3.2. Electrochemical and photoelectrochemical characterizations 3.2.1. Cyclic voltammetry (CV) 126.96.36.199. Experiments in the dark. The voltammetric responses of a bare ITO substrate and of TiO2 -SG electrodes in 0.50 M aqueous Na2 SO4 (pH 6.3) are presented in Fig. 3a. In a degassed electrolyte solution, the bare ITO electrode could be polarized in the potential range of 1.3 to −1.1 V, the result indicating only double layer charging. For TiO2 -SG coated electrodes, a Faradaic current was observed below −0.3 V (vs. Ag/AgCl) that may be attributed to the reduction/oxidation of the Ti(IV)/Ti(III) sites of the TiO2 layer. The reduction of Ti(IV) at the hydroxylated surface is in accordance with Eq. (1) : [Ti(OH)2 ]2+ + H+ + e− → [Ti(OH)]2+ + H2 O ]2+
[Ti(OH)2 and the Ti(IV) and Ti(III) surface species of TiO2 ﬁlms, respectively. The observed current was linearly dependent on the number of layers of nanoporous TiO2 -SG (Fig. 3a). Considering redox reaction occurring only at hydroxylated surface sites, it may be assumed that the inner surface area of the porous TiO2 ﬁlm is proportional to the amount of deposited TiO2 and that the electrolyte solution may penetrate the whole pore volume of the nanoporous TiO2 ﬁlm. To verify, the charge of the anodic branch was calculated by integration of the corresponding
Fig. 1. Diffraction patterns of ITO conducting glass and different TiO2 ﬁlm electrodes (TiO2 -P25, TiO2 -SG and 2%CeTiO2 -SG; A: anatase, R: rutile, I: indium oxide).
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Fig. 2. SEM images of different TiO2 ﬁlm electrodes: (a) TiO2 -P25, (b) TiO2 -SG and (c) 2%CeTiO2 -SG.
i vs. t-plots, and thereby, the charge per mass of deposited TiO2 was plotted vs. the number of layers (Fig. 3b). Only TiO2 -SG electrodes showed the ideal behavior represented by a constant charge per mass (“charge density”), or in other terms, a linear increase of the total charge with the number of layers. For TiO2 -P25 and 2%CeTiO2 -SG, a decrease of the charge density was observed with increasing ﬁlm thickness. This deviation from the ideal behavior may be explained by gradients of active surface sites and/or by different ﬁlm morphologies. The doping with Ce ions affected the charge per mass of the 2%CeTiO2 -SG electrodes considerably. It was found to be about 10 times higher than that of the TiO2 -SG electrodes (Fig. 3b). The result might be due to the larger total surface area of 2%CeTiO2 SG as the particles were found to be smaller and forming a nanoporous ﬁlm electrode. The result is also in agreement with Alves et al.  who observed that the replacement of TiO2 by CeO2
Fig. 3. (a) Cyclic voltammograms of nanoporous TiO2 -SG ﬁlm electrodes in dependence on the number of deposited layers (in aqueous 0.5 M Na2 SO4 supporting electrode (pH 6.3)). (b) Anodic peak charge of nanoporous TiO2 electrodes in dependence of the number of deposited layers of TiO2 -P25, TiO2 -SG and 2%CeTiO2 -SG.
in IrO0.3 Ti(0.7−x) Cex O2 led to a linear increase of the total charge. The authors explained their ﬁndings by an increased effective surface area due to the decreased probability of homogeneous crystal growth. The replacement of TiO2 by CeO2 resulted in fact in the formation of a very ﬁne crystalline structure [27,28]. However, the calculated charge per mass of TiO2 -P25 ﬁlm electrodes, consisting of a network of relatively large particles, was (also) found to be about 10 times higher than that of undoped TiO2 -SG electrodes and is therefore comparable to the charge per mass of Ce-doped ﬁlm electrodes (Fig. 3b). These ﬁndings might imply that TiO2 P25 ﬁlm electrodes exhibit a signiﬁcantly higher number of active (hydroxylated) sites per surface area than electrodes prepared by the sol–gel method, as might be expected, when a lower calcination temperature is applied . 188.8.131.52. Experiments under irradiation. Irradiation of TiO2 ﬁlm electrodes with energies exceeding the band gap of TiO2 generates electron–hole pairs. The holes diffuse or migrate to the TiO2 surface and oxidize adsorbed water or surface hydroxide groups, while the promoted electrons have to cross particle grain boundaries to be withdrawn at the TiO2 network/ITO interface during anodic polarization. The observed photocurrent depends on the thickness of the TiO2 ﬁlm electrodes, as shown in Fig. 4 for TiO2 -SG electrodes under chopped irradiation. A photocurrent maximum was observed for different numbers of layers depending on the type of ﬁlm electrode: 20 layers for TiO2 -SG (12 m thick), 15 layers for 2%CeTiO2 -SG and 5 layers for TiO2 -P25 electrodes (15 m thick), respectively. The CVs of the different TiO2 ﬁlm electrodes at maximum photocurrent are presented in Fig. 5. During irradiation, a fast hole transfer to the adsorbed acceptor and into the solution takes place, whereas the promoted electrons move through a network of interconnected particles
Fig. 4. Anodic photocurrent in dependence on the number of deposited layers of nanoporous TiO2 -SG ﬁlm electrodes under chopped irradiation.
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Fig. 5. Anodic photocurrent (maximum) of different TiO2 ﬁlm electrodes under chopped irradiation; 20 layers for TiO2 -SG, 15 layers for 2%CeTiO2 -SG and 5 layers of TiO2 -P25.
to the (ITO) collector electrode, where they are withdrawn as photocurrent. As long as the depth of penetration of the incident radiation exceeds the thickness of the TiO2 layer, the photocurrent increases with the layer thickness due to the higher number of photons absorbed. The diffusion length of the promoted electrons being limited mainly by the charge separation efﬁciency and the structure of the nanoporous ﬁlm, the probability of recombination processes increases with the ﬁlm thickness related to electron transport across an increased number of particles and grain boundaries. At highest photocurrents, the ﬁlm thickness (e.g. 20 layers of TiO2 -SG electrode) may reach the diffusion length of the electrons and/or the distance of penetration depth of the incident radiation. The decrease of the photocurrent for thicker ﬁlms may therefore be explained with a higher loss of promoted electrons by recombination and by charge transfer processes into the solution during diffusion across the interconnected particles to the collector electrode (back contact). It should be noticed that for 2%CeTiO2 -SG electrodes, the photocurrent was rather low and a pronounced delay in the photocurrent progression was observed (Fig. 5). Assuming that Ce4+ interstitial sites would act as effective electron scavenger for photogenerated electrons of TiO2 , the delayed photocurrent response may be explained by a fast ﬁlling of these (deep) trap sites and a subsequent diffusion of electrons via the conduction band to the back contact . Nevertheless, the low photocurrent observed for 2%CeTiO2 -SG ﬁlm electrodes might indicate an enhanced photocurrent loss, and it may be assumed that the trapped electrons efﬁciently recombine with the photogenerated holes at the Ce ion levels within the band gap of TiO2 . 3.2.2. Electrochemical impedance spectroscopy (EIS) 184.108.40.206. Equivalent circuits for EIS analysis. Impedance spectra of TiO2 -SG and 2%CeTiO2 -SG electrodes at 0.30 V in the dark and under irradiation are presented as Bode plots (amplitude, |Z|, and phase, |ϕ|, vs. frequency) in Fig. 6a and b, respectively. For experiments in the dark, the phase angle of both electrodes reaches almost −90◦ in the mid frequency range and remains almost constant at low frequencies (Fig. 6a). The ﬁndings indicate a blocking (fully capacitive) behavior of the nanoporous TiO2 electrolyte interface. For the analysis of the EIS results, a porous electrode model, corresponding to a transmission line with two transport channels and a crosswise interfacial reaction, was employed. The homogeneous porous electrode model proposed by Göhr [18,31] is implemented in the simulation and evaluation program of the used software package (Thales, ZAHNERElektrik, Germany). This model is based on a porous electrode with
Fig. 6. Impedance spectra (Bode plots) of different nanoporous TiO2 -SG ﬁlm electrodes at a potential of 0.3 V (vs. Ag/AgCl ref. electrode) (a) in the dark, (b) under irradiation (symbols: experimental data; solid lines: ﬁtted data).
uniform cylindrical pores, but assuming that the porous TiO2 ﬁlm electrode is a random network of TiO2 nanoparticles, a simpliﬁed model for the simulation procedure may be used [20,32,33]. The total impedance of the porous layer is expressed in terms of different macroscopic impedance elements (partial equivalent circuits) (Fig. 7): • • • • •
Zq for the porous TiO2 layer/pore electrolyte interface. Zs for the porous TiO2 layer of interconnected TiO2 nanoparticles. Zp for the pore electrolyte. Zn the porous TiO2 layer/ITO layer interface. Zo for the porous TiO2 surface/bulk electrolyte interface.
For nanoporous TiO2 electrodes, the impedance of the outer porous TiO2 /bulk electrolyte interface (Zo ) is thought to be very low compared to the impedance of the interior porous TiO2 /pore electrolyte interface (Zq ) due to the huge size difference of the interfacial areas and can be neglected. With this simpliﬁcation, best ﬁtting results of EIS data (recorded in the dark) were obtained by using the equivalent circuit presented in Fig. 7c. It contains partial schemes for the interfacial impedances Zn and Zq , respectively. Zn comprises two RC circuits in serial connection, the ﬁrst representing the conductive ITO bulk layer [element 1 (CPE) and 2 (RITO )], the second corresponds to the ITO/electrolyte interface at the bottom of the pores [element 3 (C3 ) and 4 (R4 )], taking into account the surface oxidation of the ITO layer by thermal treatment . The impedance of the (porous) TiO2 /pore electrolyte interface (Zq ) is described by a capacitance
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Fig. 7. Schematic and equivalent circuits of nanoporous TiO2 ﬁlm electrodes. (a) Array of TiO2 nanoparticles and corresponding distributed impedance elements according to the porous electrode model [18,31]. (b) Impedance of the porous electrode in terms of macroscopic impedance elements (Zs , Zp , Zq , Zo and Zn , as described in the main text). (c) Equivalent circuit applied for TiO2 electrodes under dark conditions. (d) Equivalent circuit for UV irradiated TiO2 electrodes.
only (element 5, CSC ). Element 6 represents the network of the differential (distributed) impedances Zpi and Zsi (i = 1, 2, 3, . . ., n, Fig. 7a). The simulation procedure allows determination of the integral pore electrolyte resistance (Zp ) and the integral solid bulk resistance, Zs (i.e. resistance of the porous TiO2 ﬁlm consisting of the interconnected TiO2 particles). Finally, the impedance of the bulk electrolyte is included as a pure ohmic resistance, element 7 (R ). The results of the ﬁtting procedure based on the proposed equivalent circuit are listed in Table 2. The resulting impedance values for Zn (elements 1–4) are different for doped and undoped TiO2 SG electrodes. This may be explained by the different interfacial structures, assuming different particle sizes and particle surface structures for undoped and doped materials. In addition, ITO surface oxidation during the calcination procedure may be affected by different colloidal structures of undoped and doped gels. Equal amounts of TiO2 being deposited on both electrodes, the higher interfacial capacitance of the pore electrolyte/TiO2 interface (CSC ) for the 2%CeTiO2 -SG may be related to the Ce-doping and/or to a larger surface area. An increased surface area for the Ce-doped material would be in accord with the results obtained from the CV experiments (3.2.1). The impedance of the 2%CeTiO2 -SG electrode is two times higher than that of the undoped material (impedance element ZS , Table 2). The argument seems to be contradictory, because the doping of the material should lead to a higher conductivity and therefore to a smaller overall impedance. However, considering that ZS is attributed to a porous TiO2 layer consisting of an assembly of interconnected TiO2 nanoparticles, the effective bulk conductivity of the porous ﬁlm depends on the intrinsic conductivity of the TiO2 particles, the geometry of the contact zone and the packing structure. In addition, the impedance of the sintered semiconductor particle network may depend primarily on discontinuities at the grain boundaries. However, the different particle surface structures of undoped and doped TiO2 -SG ﬁlm electrodes imply that ZS depends mainly on the structure of the particle sinter bridges.
Under UV irradiation, the generated photocurrent leads to a signiﬁcant decrease of the total impedance of the porous electrode in the frequency range below 10 Hz. That was also accompanied by a drop of the phase angle (Fig. 6b). Both effects were more pronounced for the undoped TiO2 -SG than for the doped 2%CeTiO2 -SG electrode. The higher photoconductivity of the TiO2 -SG electrode hence is indicated by smaller impedance and phase angle at low frequencies. These ﬁndings are in accordance with the results of CV measurements that revealed a two times higher photocurrent for the undoped material. The EIS results were simulated using a modiﬁed equivalent circuit, where charge carrier transfer and recombination processes were taken into account (Fig. 7d). The partial equivalent circuit for Zn was adjusted, because the impedance element 4 had to be eliminated, i.e. the ITO/pore ground interface was ﬁxed to be insulating (inﬁnite resistance). In fact, element 4 could no longer be ﬁtted after implementation of additional elements for Zq . Consequently and in consistence with the theory, a charge transfer reaction at this interface was excluded in the investigated potential range, and the observed current was assigned exclusively to the photogenerated electrons crossing the TiO2 particle/ITO interface. The interfacial impedance element Zq was modiﬁed by addition of elements modeling the photo-induced reactions: (i) an ohmic resistance, element 8 (RCT ) for the heterogeneous charge transfer reaction at the porous TiO2 layer/electrolyte interface, (ii) a capacitive element 10 (CIF ) for the accumulation of photoinduced charge carriers at the semiconductor surface, in parallel to the heterogeneous charge transfer reaction resistance and (iii) an ohmic resistance, element 9 (RREC ) for the charge carrier recombination. Under consideration of different models and the corresponding theoretical (physicochemical) background, several attempts to lower the number of distinct impedance elements were made. However, the equivalent circuit presented here was so far the only one to yield good ﬁtting results, especially for studies under electrode potential and radiant power density variation, be aware, that a good ﬁt does not, in itself, validate the model used. However, the use of a simpliﬁed partial equivalent circuit for Zq ,
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Table 2 Fitting results of different impedance elements for various TiO2 ﬁlm electrodes in the dark and under irradiation at an applied potential of 0.3 V (vs. Ag/AgCl ref. electrode). Dark Electrode (steady state photocurrent)/impedance element 1. CPE (uF) ␣ 2. RITO ( ) 3. C3 (F) 4. R4 (M ) 5. CSC (F) 6. Porous impedance Zp (Ohm) Zs (k ) 7. R (Ohm) 8. RCT (k ) 9. RREC (k ) 10. CIF (mF)
TiO2 -SG (38.7 nA) 14.7 0.70 11.1 30.5 3.9 2.4 8.9 240.6 16.4
often applied for mesoporous semiconductor electrodes in form of a so called chemical capacitance parallel to a resistance (which accounts for charge transfer or recombination) , yielded simulation results of low signiﬁcance and failed. Finally, Zq resulted in an equivalent circuit representative for coupled electrochemical reactions , taking into account, that heterogeneous charge transfer and recombination may take place at different interfacial electronic states. The associated capacities are attributed to (i) charge accumulation at the sc surface, CIF (associated to surface trapped holes), and to (ii) the capacitance of the semiconductor matrix considering a space charge layer (CSC ). An alternative approach for Zq would be two parallel RC combinations in serial alignment, regarding to identical electronic states for charge transfer and recombination . When comparing the modeling results of electrodes in the dark and under irradiation, elements for the interface ITO/pore ground (Zn , including elements 1–3), pore electrolyte resistance (Zp ) and electrolyte resistance (element 7, R ) remained constant (Table 2). As expected, these elements are not affected by UV irradiation, i.e. photoinduced processes. It has to be noticed that the impedances RCT , RREC and ZS were found to be signiﬁcantly smaller for the TiO2 -SG electrodes, due to their higher photoactivity. Taking into account that the same mass of TiO2 was deposited for TiO2 -SG and 2%CeTiO2 -SG electrodes, it may be concluded that the TiO2 nanoparticle network of the undoped ﬁlm electrode exhibits a higher rate constant for the heterogeneous charge transfer reaction, a smaller recombination rate and a higher conductivity. The most pronounced difference was found for the charge transfer resistance, and it seems that the overall reaction for the doped TiO2 material was limited by the rates of the hole reactions at the surface. However, the charge transfer reaction is linked to the recombination process and, therefore, cannot be seen independently. A more detailed discussion of the EIS results would require yet unavailable data concerning the inner surface area, the size and the interconnection structure of the particles.
220.127.116.11. Photoelectrochemical characterization of nanoporous TiO2 SG electrodes by EIS. TiO2 -SG electrodes yielding high photocurrents in CV experiments were prepared to study the potential dependence, the effects of the incident radiant power density and a hole acceptor/scavenger (addition of methanol), employing EIS. The irradiation system used for CV experiments was replaced by a halogen lamp coupled to a ﬁber optics to avoid emitting perturbing noise in the low frequency range of EIS measurements. In addition, by this measure the emitting power of the installation could be varied and heating of the electrolyte solution could be prevented. 18.104.22.168.1. Potential dependence of the impedance (under UV irradiation). The potential dependence of the impedance of TiO2 -SG
UV irradiation 2%Ce TiO2 -SG (51.1 nA) 11.7 0.74 16.9 28.1 2.7 3.3 7.6 524.5 14.0
TiO2 -SG (51.0 A)
2%Ce TiO2 -SG (39.5 A)
14.5 0.76 9.5 30.6
12.3 0.76 17.2 31.9
8.8 33.8 16.5 2.1 1.2 1.58
8.2 146.4 15.3 100.8 8.2 0.49
Fig. 8. Impedance spectra (Bode plots) of a TiO2 -SG electrode (20 layers) in dependence of the applied electrode potential (vs. Ag/AgCl ref. electrode in 0.5 M Na2 SO4 aqueous solution; symbols: experimental data; solid lines: ﬁtted data).
ﬁlm electrodes was investigated in the potential range from 0.0 to 0.5 V vs. reference electrode, at a ﬁxed incident radiant power density of 5.2 W/m2 . The results are presented in Fig. 8 and demonstrate the effect of the electrode potential on total impedance and phase angle in the frequency range below 1 Hz. Modeling results, presented in Fig. 9, were obtained using the equivalent circuit already described (Fig. 7d). If the anodic polarization was increased, the heterogeneous charge transfer resistance (RCT ) decreased as well as the resistive element for the recombination (RREC ) and the interconnected TiO2 particle network (ZS ). The observed strong potential dependence of the impedance of TiO2 -SG electrode shows rather the characteristics of a compact solid semiconductor ﬁlm electrode under depletion conditions than of a nanoporous electrode penetrated by the electrolyte solution, for which only a small effect is expected . The characteristics of a “classical” electrolyte–semiconductor junction under irradiation can be described by theoretical derivations, as established by Gärtner for semiconductor p–n junctions or Schottky contacts [38–40]. During anodic polarization of solid thin ﬁlm semiconductors, a space charge layer is formed that leads to an efﬁcient separation of the photogenerated charge carrier in the electric ﬁeld within the depletion zone. The photo-generated holes migrate to the TiO2 /electrolyte interface where they can be withdrawn by a heterogeneous charge transfer reaction (redox reaction), while the remaining electrons are directed to the collector electrode producing a photocurrent. When the thickness of the TiO2 ﬁlm electrode is larger than the width of the depletion layer (space charge layer),
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Fig. 9. Fitting results of different impedance elements in dependence of the applied potential for a nanoporous TiO2 -SG ﬁlm electrode (20 layers) in pure electrolyte solution (aqueous 0.5 M Na2 SO4 ) under UV irradiation.
an efﬁcient electron/hole recombination during the diffusion of the photogenerated electrons to the back contact must be considered. Under these conditions and for the given incident radiant power density, the photocurrent can be increased with increasing anodic polarization yielding a thicker depletion layer, where efﬁcient charge separation may take place. However, in the present study, the electrode is composed by very small TiO2 particles forming a nanoporous layer that is penetrated by the electrolyte solution. Assuming individual nanoparticles, the width of the space charge layer cannot exceed the particle radius, and for maximum depletion conditions, the voltage difference between the surface and the center of the nanosized TiO2 particles cannot exceed several tenths of millivolts . The results obtained with TiO2 -SG electrodes support the hypothesis of the formation of a macroscopic electric ﬁeld between the ITO collector electrode and the outer part of the nanoporous TiO2 ﬁlm. It seems that for these nanoporous ﬁlm electrodes, an apparent space charge layer becomes operative. With increasing anodic polarization (i.e. extended macroscopic electric ﬁeld), migration of photogenerated electrons to the electrode contact and the redox reactions of holes at the semiconductor/electrolyte interface are enhanced, and a decrease of the charge transfer resistance (RCT ) and of the impedance element for the recombination reaction (RREC ) is expected. In fact, RCT decreased steadily with increasing anodic potential (Fig. 9a). The drop of RREC was less pronounced, most probably due to the characteristics of the applied equivalent circuit, as discussed below. A macroscopic electric ﬁeld across a semiconductor nanoparticulate network was also suggested by Hagfeldt et al. to explain the high photocurrent quantum efﬁciencies of colloidal TiO2 ﬁlm electrodes . In contrast to this picture, models of the potential distribution in semiconducting porous electrodes, penetrated by an electrolyte solution, showed a potential drop within a spatial resolution of few particle layers next to the collector electrode
(ITO layer surface) [37,43]. Alternatively, the observed potential dependence might be due to an electric ﬁeld induced by photogenerated charges. Assuming very fast hole removal reactions, negative charges may shift the band edges to higher energy, due to remaining electrons trapped in interfacial band-gap states. Taking the spatial absorption characteristic into account, such a shift of band edges would result in an electric ﬁeld component driving electrons to the collector electrode, when the nanoparticulate TiO2 ﬁlm would be irradiated from the electrolyte (front) side. Nevertheless, it has been published that light-induced electric ﬁeld effects should not alter the electron-transport characteristics in a fundamental way . Both effects, potential drop next to the collector electrode and light-induced electric ﬁeld, should have a strong impact on the photo-response of the nanoparticulate TiO2 ﬁlm, when irradiation is changed from electrolyte (front) to back side. The experimental results of this work with nanoparticulate TiO2 -SG ﬁlm electrodes (20 layers) revealed only small changes for all ﬁtted impedance elements (mean error 1.0 ± 0.5%) and cannot support these alternative approaches [37,43,44]. Compared to dark conditions, the impedance of the particle network (ZS ) dropped by a factor of about 8 during UV irradiation. This can be explained by a high (excess) concentration of electrons in the transport state (conduction band) due to excitation of the porous TiO2 electrode in combination with the fast removal of the holes. In contrast, the observed potential dependence of ZS in the dark was small, and varied only by a factor of 1.5 in the potential range between 0.0 and 0.5 V vs. ref. electrode. Only biasing TiO2 SG electrodes in the cathodic potential region towards the conduction band edge potential induced a pronounced drop of ZS as predicted by the theory, which based on an exponential increase of the density of states (DOS) approaching the conduction band [21,45]. Focusing on the photocatalytic performance of nanoporous electrodes, we excluded the cathodic potential region (vs. ref) for the experiments of UV irradiated electrodes. Hence, under idealized conditions, ZS would only depend on the incident radiant power density, considering the low conductivity (DOS) und the small potential dependency for the dark situation, respectively. Therefore, the observed potential dependence (see Fig. 9a) of the impedance of the particle network (ZS ), i.e. the resistive channel of electron transport to the collector electrode, was unanticipated. It seems that the applied equivalent circuit is oversimpliﬁed with respect to RREC , implemented as an element of the interfacial impedance Zq only. Charge carrier recombination may also take place in the bulk material (nanoparticle array) and at grain boundaries. In fact, lower charge carrier recombination rates at the grain boundaries would affect the impedance of the nanoparticle network (ZS ) resulting in the observed decrease of ZS with increasing anodic polarization. This interdependence might be ascribed to an extended diffusion length of photo-generated electrons. The partial equivalent circuit for Zq comprises two capacitive elements, CIF and CSC (see Fig. 7d). The twofold increase of CIF with increasing anodic polarization implies that a higher number of surface trapped holes cannot be removed by heterogeneous charge transfer reactions leading to an accumulation of photogenerated charge at the semiconductor surface. This seems to contradict the enhanced charge transfer conditions when increasing the anodic bias, but the steady state photocurrent increased by a factor of 5 simultaneously. CSC also depends on the applied potential and decreases steadily with increased anodic biasing. A Mott–Schottky plot yielded a linear dependence of C−2 vs. electrode potential, see Fig. 10. The ﬂat band potential under irradiation was determined to be −0.22 V vs. ref. electrode. The results are consistent with respect to the theoretical prediction for a wide band gab bulk semiconductor. The Schottky behavior of CSC underlines that an apparent space charge layer could be responsible for the enhanced charge separation efﬁciency by increasing the anodic bias, indicated by
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Fig. 10. Mott–Schottky plot of CSC for a nanoporous TiO2 -SG ﬁlm electrode (20 layers) in pure electrolyte solution (aqueous 0.5 M Na2 SO4 ) under UV irradiation.
the decrease of RCT and ZS , and the increase of the steady state photocurrent by a factor of 5 in the investigated potential range. It seems that CSC behaves not as a chemical capacitance, often used to describe the (exponential) potential dependence of charge accumulation in mesoporous semiconductors . Nevertheless, it should be taken into account that a switch between different mechanism in dependence of the applied potential may occur, and in addition that the generation of charge carriers (electron and holes) by excitation of the semiconductor material itself may require a more complex model than established for dye sensitized solar cells [21,46]. 22.214.171.124.2. Effect of incident radiant power density (P0 ). Photoinduced processes at (nanoporous) TiO2 semiconductor electrodes depend on various parameters such as morphology and absorption characteristics of the ﬁlm, the thickness of space charge layer with respect to the ﬁlm dimension and the spectral emission of the irradiation source. Investigating the rate determining process, as e.g. limitations by the heterogeneous charge transfer or by the recombination process, the incident radiant power density (P0 ) was varied. Bode plots of TiO2 -SG electrodes for different incident radiant power densities applying an electrode potential of 0.3 V are presented in Fig. 11. Obviously, the variation of the radiant power density affected only the impedance below 1 Hz. With increasing P0 , the decrease of the overall impedance was accompanied by a pronounced phase angle bending. Impedance spectra taken at different incident radiant power densities were simulated with the same high accuracy employing the outlined equivalent circuit (Fig. 7d). Elements, supposed not to be affected by photo-induced processes, remain almost constant: (i) Zn (elements 1–3), (ii) Zp
Fig. 12. Fitting results of different impedance elements and steady state photocurrent in dependence of the incident radiant power density (P0 ) for a TiO2 -SG electrode (20 layers) in pure electrolyte solution (aqueous 0.5 M Na2 SO4 ) and after addition of methanol (2.5 M) at an applied potential of 0.3 V (vs. Ag/AgCl ref. electrode).
Fig. 11. Impedance spectra (Bode plots) of a TiO2 -SG electrode (20 layers) in dependence of the incident radiant power density at 0.3 V vs. Ag/AgCl ref. electrode in 0.5 M Na2 SO4 aqueous solution (symbols: experimental data; solid lines: ﬁtted data).
(pore electrolyte resistance) and (iii) element 7, R (bulk electrolyte resistance). Impedance elements which showed a corresponding dependence of the incident radiant power density are presented in Fig. 12. The observed photocurrent is due to the coupling of the interfacial charge transfer (RCT ) and the resistive electron transport channel (ZS ). Under idealized conditions, the photoconductivity of TiO2 -SG ﬁlm electrodes is expected to be proportional to the rate of absorbed photons. Assuming a constant absorption coefﬁcient across the TiO2 ﬁlm and, a ﬁxed correlation between the incident radiant power density and the rate of absorbed photons, RCT and ZS should show a linear reciprocal dependence on the incident radiant power density, if the efﬁciency of charge separation and the electron diffusion length are not affected by irradiation. In fact, the charge transfer resistance RCT (element 8) decreased with increasing incident radiant power density up to 3.0 W/m2 (58% of maximum power). At higher values of P0 , RCT remained constant within the experimental error of ±5%, implying that the heterogeneous charge transfer reaction starts to limit the
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photocurrent (overall reaction). When the electrode is irradiated on the front side (semiconductor/electrolyte interface), the penetration depth of the photons, i.e. the space, where the charge carriers are produced, has to be related to the width and the position of the supposed space charge layer, where an efﬁcient charge separation can take place. The experimental results may be interpreted in a way that the penetration depth reaches the thickness of the apparent space charge layer at an incident radiant power density of about 3.0 W/m2 . Based on these idealized assumptions, at low radiant power densities all charge carriers will be produced within the zone of efﬁcient charge separation. Through this, the number of charge carriers would depend linearly on the incident radiant power density. Assuming that holes can be removed quantitatively by surface redox reactions, RCT should drop reciprocally with the incident radiant power density. For values ≤3.0 W/m2 the experimental results corroborate with the assumed interdependence. Nevertheless, this hypothesis does not imply the effect of charge recombination reactions (RREC ) that may also depend on P0 . In fact, the impedance element for recombination (RREC ) decreases with increasing incident radiant power density, showing a linear reciprocal dependence (Fig. 12a). The observed dependence suggests that a certain percentage of photo-generated charge carriers are lost by recombination. Nevertheless, this ﬁnding has to be related to the implementation of RREC , see discussion below. A reciprocal dependence on the incident radiant power density (for idealized conditions) is also observed for ZS , again limited to values ≤3.0 W/m2 . At higher P0 , the ﬁtting procedure resulted in higher values of ZS , as displayed by the drop of the slope in the plot of the reciprocal resistance of the particle network (ZS−1 ) vs. the incident radiant power density (P0 ) (Fig. 12b). Interestingly, the deviation of ZS from the idealized behavior was observed at the same incident radiant power density, where RCT became constant (>3.0 W/m2 ), implying that the same process is decisive for the observed dependence on the incident radiant power density. In accord with the discussion concerning RCT , at moderate P0 the penetration depth of the irradiation does not exceed the width of the supposed space charge layer. Under these considerations, when the charge carriers are generated within an electric ﬁeld, the expected reciprocal dependency can be observed. Then again, when at high P0 the irradiated volume exceeds the zone of supported charge carrier separation, a higher rate of recombination is expected. A reduced electron diffusion length due to enhanced charge carrier recombination in the bulk and at the grain boundaries would affect ZS negatively. As a consequence, this suppressed incident radiant power density dependency would result in a decreased slope in the ZS−1 vs. P0 plot at high power densities as displayed in Fig. 12b. 126.96.36.199.3. Effect of methanol addition. The experiments aimed at possible limitations of the overall reaction (photocurrent) by heterogeneous charge transfer processes under conditions of high incident radiant power densities. Further, the possible effect of a hole-scavenger was studied. The addition of e.g. citrate, formic acid or methanol to the supporting electrolyte solution accelerates the hole reaction at the semiconductor surface, leading to a faster removal of the holes and, therefore, to a more efﬁcient charge separation process . In this study, the steady state photocurrent increased by a factor of about two, when 2.5 M methanol in 0.5 M Na2 SO4 aqueous solution was used (Fig. 12c). This result may be explained by an effect introduced as “current doubling” [47,48] that was not a topic of our experimental studies. Current doubling was described to a reaction sequence, where methanol is oxidized by a hole (Eq. (2)) (or by a surface hydroxyl radial), the intermediate C-centered
radical injecting subsequently an electron into the conduction band of TiO2 (Eq. (4)): ··
CH3 OH + h+ → CH3 OH ·+
CH3 OH → CH3 O· + H+
CH3 O· → CH2 O + H+ + e−
To determine the impedance elements, the EIS data were processed as before. The addition of methanol affected primarily the heterogeneous charge transfer resistance (RCT ) that dropped by a factor of about 2.2. This effect is more pronounced at high radiant power densities (Fig. 12a). Expectedly, heterogeneous charge transfer reactions are, in the case of nanoporous TiO2 -SG ﬁlm electrode in indifferent aqueous electrolyte solution, a key limiting factor of the efﬁciency of the overall reaction. As the hole reaction rate at the semiconductor surface is increased, the coupled charge recombination rate is expected to drop. In fact, RREC decreased by a factor of about 1.8 due to the addition of methanol. For the resistive pathway of electrons to the electrode back contact (impedance of the particle array, ZS ), an almost linear radiant power dependence was found. The addition of methanol led to experimental results from which a better reciprocal correlation between ZS and the incident radiant power density (idealized conditions) could be obtained. Compared to the results in the pure electrolyte solution, the most pronounced effect of methanol addition was found at high radiant power densities (Fig. 12b). The evolution of the ZS−1 vs. P0 plot for pure electrolyte solutions was explained by a higher loss of electrons due to an enhanced charge carrier recombination under irradiation, where the penetration depth of light exceeds the width of the (supposed) macroscopic electric ﬁeld. Under such conditions, it may be assumed that an improved photocurrent is mainly due to a very efﬁcient removal of holes by addition of methanol, independent of where the charge carriers are generated, and the effect can be dragged down to the level of individual nanoparticles. Besides the current doubling effect of methanol, the results support the hypothesis that the photoelectrochemical response of TiO2 -SG electrodes may be increased by hole scavenging. For environmental applications, e.g. waste water remediation, a strong dependence of the process efﬁciency on chemical nature and adsorption characteristics of substrates and intermediates is to be expected. 4. Conclusion Nanoporous TiO2 -SG and 2%CeTiO2 -SG ﬁlm electrodes were prepared by sol–gel method, and TiO2 -P25 electrodes were prepared by suspension method. XRD characterization revealed for all undoped TiO2 electrodes (TiO2 -SG and TiO2 -P25) a phase mixture of anatase and rutile, whereas 2%CeTiO2 -SG electrodes exhibited only anatase phase pattern. The result indicates that the incorporation of Ce ions prevented the transformation from anatase to rutile. The (photo)electrochemical properties of nanoporous TiO2 ﬁlm electrodes were studied by CV and EIS. The Faradaic current under cathodic polarization in the dark increased with the number of TiO2 layers, and the result may be linked to the reduction of hydrated Ti(IV) surface sites within the ﬁlm electrodes that are penetrated by the electrolyte solution. The doped 2%CeTiO2 electrodes showed higher dark currents per deposited mass compared to TiO2 -SG electrodes, a result generally explained by a higher interior surface area due a decreased probability of homogeneous crystal growth, caused by Ce addition.
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For UV irradiated electrodes, a photocurrent maximum was observed for ﬁlm electrodes consisting of 20 layers of TiO2 -SG, 15 layers of 2%CeTiO2 -SG and 5 layers of TiO2 -P25, respectively. The dependence of the photocurrent on the number of deposited layers may be a consequence of a combination of the penetration depth of light and the free diffusion length of electrons in relation to the ﬁlm thickness. In the presence of Ce ions in titania, the observed photocurrent was comparably small with a delayed signal response. The addition of Ce ions may lead to an enhanced charge carrier trapping at the Ce levels within the band gap of TiO2 , resulting in an unwanted higher electron–hole recombination rate. Comparing irradiated undoped and doped TiO2 -SG ﬁlm electrodes, modeling results revealed a higher rate constant for the heterogeneous charge transfer, a smaller recombination rate and a higher conductivity for undoped TiO2 -SG ﬁlm electrodes. In addition, the potential dependence, the effect of the incident radiant power density and methanol addition on the photocurrent response of TiO2 -SG electrodes (20 layers) were studied. The potential dependence led to the hypothesis, that a macroscopic electric ﬁeld across the nanoporous ﬁlm electrode is required to explain the ﬁtting results concerning the heterogeneous charge transfer (RCT ) and electron transportation to the electrode back contact (ZS ) which favors drift over diffusion. Such a hypothesis would ask for a macroscopic space charge layer promoting the drift of electrons to the back contact that would not be restricted to individual particles or few particle layers next to the contact (ITO collector electrode). To receive more information about the rate determining process, the incident radiant power density (P0 ) was varied. Under idealized conditions, it may be expected that the photocurrent density of TiO2 -SG ﬁlm electrodes is proportional to the rate of absorbed photons. In fact, a reciprocal dependence of ZS , the resistive pathway of electron motion to the back contact, on moderate values of radiant power densities were determined. At high radiant power density, the ﬁtting procedure yielded higher values for ZS , explained by enhanced recombination losses of excited electrons when the penetration depth of light exceeds the zone of promoted charge separation as a consequence of implementation of RREC as surface related impedance element only. The same dependence on the incident radiant power density was obtained for the heterogeneous charge transfer reaction (RCT ). For P0 of up to 3.0 W/m2 , a drop of RCT with increasing values of P0 implies that holes could be removed by surface redox reaction in an efﬁcient way. At high radiant power densities, the heterogeneous charge transfer reaction rate leveled off. This was ascribed to conditions, where the electron–hole recombination affected the photocurrent response notably. Again, when at high P0 the irradiated volume exceeds the zone of supported charge carrier separation, a higher rate of recombination is expected, which would lead to the observed dependency of RCT . Addition of methanol as hole-scavenger doubled the steadystate photocurrent of TiO2 -SG electrodes. The linear reciprocal dependency of RCT on the photon ﬂux was much more consistent, in particular at high incident radiant power densities. Under these conditions, the heterogeneous charge transfer reaction plays a decisive role in the limitation of the overall reaction under anodic bias. The removal of holes by their reaction with methanol suppressed the competing electron–hole recombination in an efﬁcient way, as shown by a remarkable drop of RREC , in particular at high radiant power densities. In summary, the photochemical characterization gave evidence that nanoporous TiO2 -SG ﬁlm electrodes can be considered as a hybrid of individual nanoparticles and solid crystalline semiconducting material. Current doubling disregarded, the pronounced effect of methanol addition, especially at high incident radiant power densities, on the heterogeneous charge transfer reaction
is a feature of individual nanoparticles. The high photocurrent of relatively thick ﬁlm electrodes at moderate radiant power densities would then be the result of nanoparticles surrounded by the electrolyte solution which favors a fast hole removal by surface reactions. Alternatively, the observed dependence of the heterogeneous charge transfer reaction (RCT ) on the electrode potential, and the radiant power density dependence of RCT and the ZS (impedance of the TiO2 particle network) could be explained by a 3D array of nanoparticles that behave as a collective like a solid crystalline electrode. Future work will deal with the validation of the hypotheses by EIS characterization of TiO2 -SG electrodes with different ﬁlm thickness, investigating potential dependence, direction and power of incident irradiation, as well as hole scavenging reactions. Focusing at the possible effect of intrinsic charge separation on the photoactivity of TiO2 , nanoporous ﬁlm electrodes with different anatase to rutile ratios will be prepared by sol–gel method. Furthermore, a new photoelectrochemical set-up featuring monochromatic irradiation with tunable output will enable investigations on the spectral response of the semiconductor electrodes and the determination of photocurrent quantum yields. Acknowledgments The authors acknowledge gratefully support from Synchrotron Light Research Institute (Public Organization), Thailand (Grant Number: 2548/05) and the former Chair of “Umweltmesstechnik”, University of Karlsruhe, now KIT (Karlsruhe Institute of Technology), Germany. Further, we acknowledge support from Deutsche Forschungsgemeinschaft (DFG). References  M.R. Hoffmann, S.T. Martin, W. Choi, D.W. Bahnemann, Chemical Reviews 95 (1995) 69.  K. Vinodgopal, S. Hotchandani, P.V. Kamat, Journal of Physical Chemistry 97 (1993) 9040.  B. Sun, P.G. Smirniotis, Catalysis Today 88 (2003) 49.  U.I. Gaya, A.H. Abdullah, Journal of Photochemistry and Photobiology C 9 (2008) 1.  S.-I. Nishimoto, B. Ohtani, H. Kajiwara, T. Kagiya, Journal of the Chemical Society, Faraday Transactions 81 (1985) 61.  Z. Ding, G.Q. Lu, P.F. Greenﬁeld, Journal of Physical Chemistry 104 (2000) 4815.  T. Ohno, K. Sarukawa, K. Tokieda, M. Matsumura, Journal of Catalysis 203 (2001) 82.  B. Sun, A.V. Vorontsov, P.G. Smirniotis, Langmiur 19 (2003) 3151.  F.B. Li, X.Z. Li, M.F. Hou, K.W. Cheah, W.C.H. Choy, Applied Catalysis A 285 (2005) 181.  K. Nagaveni, M.S. Hegde, G. Madras, Journal of Physical Chemistry B 108 (2004) 20204.  A. Fujishima, K. Honda, Nature 238 (1972) 37.  H. Bartkova, P. Kluson, L. Bartek, M. Drobek, T. Cajthaml, J. Krysa, Thin Solid Films 515 (2007) 8455.  D. Jiang, H. Zhao, Z. Jia, J. Cao, R. John, Journal of Photochemistry and Photobiology A 144 (2001) 197.  M. Radecka, M. Wierzbicka, M. Rekas, Physica B 351 (2004) 121.  I.D. Raistrick, D.R. Franceschetti, J.R. Macdonald, in: E. Barsoukov, J.R. Macdonald (Eds.), Impedance Spectroscopy: Theory, Experiment, and Applications, Second Edition, John Wiley & Sons, Inc, Hoboken, NJ, USA, 2005.  P.J. Boddy, Journal of Electroanalytical Chemistry 10 (1965) 199.  M. Tomkiewicz, Electrochimica Acta 35 (1990) 1631.  J.R. MacDonald, Journal of Electroanalytical Chemistry 223 (1987) 25.  J.-B. Jorcin, M.E. Orazem, N. Pébère, B. Tribollet, Electrochimica Acta 51 (2006) 1473.  J. Bisquert, G. Garcia-Belmonte, F. Fabregat-Santiago, N.S. Ferriols, P. Bodganoff, E.C. Pereira, Journal of Physical Chemistry B 104 (2000) 2287.  F. Fabregat-Santiago, G. Garcia-Belmonte, J. Bisquert, A. Zaban, P. Salvador, Journal of Physical Chemistry B 106 (2002) 334.  Y. Pooarporn, A. Worayingyong, M. Wörner, P. Songsiriritthigul, A.M. Braun, Water Science and Technology 55 (2007) 153.  Radiant power density (P0 ) equates to emitted, transferred, or received radiant energy per time and area.  R.A. Spurr, H. Myers, Analytical Chemistry (Washington, DC, U. S.) 29 (1957) 760.  B. Liu, X. Zhao, N. Zhang, Q. Zhao, X. He, J. Feng, Surface Science 595 (2005) 203.
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