Improved Electron Diffusion Coefficient in Electrospun TiO 2 Nanowires

July 8, 2017 | Autor: Chellappan Vijila | Categoría: Engineering, Technology, Nanowires, CHEMICAL SCIENCES, Diffusion Coefficient
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Improved Electron Diffusion Coefficient in Electrospun TiO2 Nanowires P. S. Archana,† R. Jose,*,† C. Vijila,‡ and S. Ramakrishna† National UniVersity of Singapore, 2 Engineering DriVe 1, 117576, Singapore, and Institute of Materials Science and Engineering, A-STAR, 3 Research Link, 117602, Singapore ReceiVed: August 26, 2009; ReVised Manuscript ReceiVed: October 15, 2009

TiO2 nanowires with a diameter of ∼150 nm, length of ∼3-4 µm, and aspect ratio of 10:1, were prepared by ultrasonically dispersing electrospun continuous nanofibers in monocarboxylic acids. The resulting pastes were used for making nanowire films on conducting glass substrates with thicknesses in the range of 500 nm to 100 µm, good adhesion, and high nanowire packing. These films were used to fabricate dye-sensitized solar cells using the D131 dye and the iodide/triiodide electrolyte. Transient photocurrent measurements showed a high electron diffusion coefficient in those nanowire films. The measured diffusion coefficient in those TiO2 nanowires was orders of magnitude higher than that observed in nanoparticles under similar experimental conditions. The charge-transport mechanism in the nanowire sample is discussed in support with the measured open-circuit voltage decay curves. 1. Introduction One-dimensional (1-D) metal oxide nanostructures, typically nanowires (NWs), are attracting much attention recently due to their unique properties exploitable for device applications.1-4 Moreover, these structures are ideal to study the dependence of physical properties on directionality. Most commonly, NWs are produced by the bottom-up approach, that is, by self-assembly of the target material from vapor, liquid, or solid phases through nucleation and growth under optimized conditions of temperature, pressure, or concentration.1 One of the emerging bottomup techniques for fabrication of NWs or even continuous 1-D nanostructures is electrospinning that works under the principle of asymmetric bending of a charged liquid jet when it is accelerated by a longitudinal electric field.5-8 The electrospinning technique is characterized by its simplicity, versatility, and cost effectiveness.5 The chemical processing of the solution for electrospinning provides controllable crystallinity and morphology, and physical processes involved, such as asymmetric bending, make the technique suitable for large-scale production of nanostructures economically. The diameter and alignment of the nanofibers could be controlled by the liquid injection rate, intensity of the electric field,8,9 and geometry of the collector surface, respectively.8,10 If the polymeric solution contains metal ions for making an inorganic solid, then appropriate postelectrospinning annealing produces continuous nanofibers of the target material.6,7,11,12 The continuous electrospun inorganic nanofibers are to be deposited on suitable substrates for fabrication of solid-state devices. Morphology, and, therefore, charge-transport properties of the final films are affected by the film fabrication technique. For example, electrospun TiO2 nanofiber based dye-sensitized solar cells (DSCs), in which photogenerated electrons are collected through diffusion, were developed on conducting glass substrates (e.g., fluorine-doped tin oxide coated glass, FTO) by several groups.13-16 TiO2 films were fabricated by electrospinning the composite fibers directly onto preheated FTO substrates, * To whom correspondence should be addressed. E-mail: [email protected] (R.J.), [email protected] (S.R.). † National University of Singapore. ‡ Institute of Materials Science and Engineering, A-STAR.

followed by hot pressing and/or solvent treatments.13,14 However, the fibrous morphology was distorted and/or the continuous nanofibers were shortened to nanorods of several hundred nanometers in length. In another method,15,16 the electrospun nanofibers were mechanically ground to nanorods, thereby compromising the initial high aspect ratio, and were sprayed onto FTO to fabricate DSCs. In both of the above methods, shortening of the nanofibers down to several hundred nanometers increased the grain boundary density and resulted in an enhanced scattering, thereby leading to poor diffusivity. Mukherjee et al.17 recently fabricated DSCs using continuous TiO2 nanofibers by directly electrospinning onto FTO substrates and hot pressed at a lower temperature and pressure than that in the previous reports.13,14 The electron diffusion coefficient (Dn) of the resulting film was lower than that of the TiO2 nanoparticles, despite the lower transport resistance observed for the nanofibers. High transit time due to the continuous fibers that were parallel to the substrate and their poor crystallinity additionally contributed to the observed lower Dn.17 The purpose of the present study is to optimize morphology by making use of the lower transport resistance in electrospun nanofibers such that higher diffusion coefficients could be achieved. Such optimized structures are inevitable in view of the increased importance of electrospinning for its ability to produce nanofibers in commercial scale as well as suitability of the 1D TiO2 nanostructures for energy harvesting and photocatalysis. Continuous nanofibers and short nanorods could be ruled out based on the previous experiences.13-16 We observed that nanowires with a length of ∼3-4 µm have an order of magnitude higher Dn compared with the continuous nanofibers in the presence of iodide/triiodide electrolyte. It was also noted that annealing the fibers for a longer time (∼24 h) increased the crystallinity without compromising much the high surface area of the fibers and resulted in an improved Dn. 2. Experimental Details The TiO2 nanofibers were prepared by reported methods with modifications.9 The sol for electrospinning was prepared from polyvinyl acetate (PVAc, Mw ) 500,000), dimethyl formamide (DMF), titanium(IV) isopropoxide, and acetic acid. The poly-

10.1021/jp908238q  2009 American Chemical Society Published on Web 10/30/2009

Electrospun TiO2 Nanowires meric solution was prepared by dissolving PVAc in DMF (11.5 wt. %). Titanium(IV) isopropoxide (2 g) was added to the PVAc solution (4.5 g) together with acetic acid (0.5 g). The resulting sol was contained in an airtight bottle and stirred for 12 h before electrospinning. Electrospinning was carried out on a commercial machine (NANON, MECC, Japan) at a 25 kV accelerating voltage and at a 1 mL/h flow rate. The polymeric fibers containing Ti4+ ions were collected on a grounded rotating drum placed ∼10 cm below the spinneret. The samples were sintered in air at 500 °C for 1-24 h to remove PVAc and allow nucleation and growth of TiO2 particles in the fiber structure. The annealed fibers were characterized by examining their morphology, surface, and crystal structure. Scanning electron microscopy (SEM, Quanta 200 FEG System, FEI Company, U.S.A.) and transmission electron microscopy (TEM, JEOL 2010Fas) of the annealed products were carried out to examine the morphology, surface, and crystallinity. The crystal structure of the nanofibers was examined by X-ray (XRD) and electron diffraction techniques. The XRD patterns were recorded by a Siemens D5005 X-ray diffractometer employing Ni-filtered Cu KR radiation. The electron diffraction was carried out during the TEM measurements. The annealed fibers were ultrasonically dispersed in various monocarboxylic and mercapto acids. Typically 0.05 g of nanofibers was ultrasonically dispersed in 0.6 mL of acetic acid for durations of 30 min to 15 h and developed into a paste. The paste was then added with ethylene glycol and ethyl cellulose and coated on FTO glass substrates (1.5 cm × 1 cm; 25 Ω/0, Asahi Glass Co. Ltd., Japan) by the doctor blade technique. The thickness of the NW films could be varied between 500 nm to 100 µm. A thin (∼100 nm) layer of TiO2 was developed on the FTO substrate by spin-coating a sol prepared from titanium isopropoxide in hydrogen peroxide before fabrication of the NW films. The films were then annealed at 500 °C for 1-24 h. The DSCs were prepared by soaking a 0.28 cm2 TiO2 NW electrode in a 1:1 volume mixture of acetonitrile and tert-butanol of D131 dye for 24 h at room temperature. Selection of D131 dye as the light harvester was due to its similarity in the LUMO surface with many of the conventional Ru-based dyes.18 The dye-sensitized samples were then washed in ethanol to remove unanchored dye and dried in air. Samples were sealed using a 50 µm spacer. Aetonitrile containing 0.1 M lithium iodide, 0.03 M iodine, 0.5 M 4-tert-butylpyridine, and 0.6 M 1-propyl-2,3dimethyl imidazolium iodide was used as the electrolyte. A Ptsputtered FTO glass was used as the counter electrode. Photocurrent measurements of the assembled DSC were performed using a solar simulator (San Ei, Japan) at AM 1.5G condition. I-V curves were obtained using a potentiostat (Autolab PGSTAT30, Eco Chemie B.V., The Netherlands). The instrument has a current sensitivity down to several nanoamperes. The electron transport in TiO2 NW films was studied using a transient photocurrent technique. Samples for the photocurrent measurements were DSCs fabricated using the TiO2 NW films with a thickness of ∼13 µm. Samples from two typical batches, viz. annealed for 1 h (S1) and 24 h (S2), were selected for photocurrent measurements. In the transient photocurrent experiments, the cells were excited with a low intensity laser pulse (532 nm Nd:YAG laser, pulse width < 5 ns) superimposed on a large background white light illumination. The intensity of the white bias light was varied in order to study the effect of photocarrier density on the Dn. The intensity of the laser light was controlled with neutral density filters to keep the magnitude of photocurrent transients less than the dc level due to the white

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Figure 1. SEM images of the TiO2 nanofibers sintered at 500 °C for (A) 1 h and (B) 24 h. The second panels (C, D) display a bright-field TEM image recorded using the samples heated for 1 and 24 h annealing, respectively. The insets of (C) and (D) are their corresponding SAED patterns. The third panels (E, F) display a lattice image recorded at the high-resolution mode. An enhanced grain boundary volume clearly revealed in the HREM of the sample heated for 1 h d with the other.

bias light. The cells were illuminated through the substrate side, and the photocurrent transients were recorded using a digital oscilloscope (Agilent, 1 GHz) under short-circuit conditions. The RC time constant of the setup was < 20 µs. 3. Results and Discussion Figure 1 shows the morphological and structural details of the TiO2 nanofibers obtained after heating the as-spun composite fibers for 1 and 24 h, respectively. The nanofibers maintained cross-sectional uniformity throughout the length, indicating a smooth injection of the fine TiO2 sol dispersed in the polymer matrix during electrospinning using the commercial setup. The composite polymeric and the sintered metal oxide fibers maintained similar continuous fibrous morphology; however, the diameter of the sintered fibers was less by a fraction of nearly three than that of the composite polymer fibers. No appreciable change in the fiber diameter was noted when heated for different durations; the fiber diameter remained at ∼150 nm when they were heated for 1-24 h. However, crystallinity of the fibers increased considerably due to grain growth from ∼10-15 nm (1 h) to 25-50 nm (24 h), which was well-reflected in the SAED patterns (insets of Figure 1C,D), HREM images (Figure 1E,F), and XRD (Supporting Information) patterns. The SAED pattern

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Figure 2. SEM images of the NWs obtained by ultrasonically dispersing the TiO2 nanofibers in acetic acid for 30 min and thick film developed using the NW paste. The bottom panels display magnified images of the corresponding samples.

of S1 displayed continuous rings, which are characteristics of the polycrystalline materials. As expected, a spotty pattern was obtained for S2, indicating the improvement in its crystallinity after annealing for 24 h. The lattice images shown in Figure 1E,F clearly show the difference in crystallinity; the particles grew two to four times upon prolonged heating. The SAED and XRD patterns were indexed for anatase phase. The lattice parameters calculated from the XRD pattern were a ) 3.789(4) Å and c ) 9.497(1) Å, which are consistent with the reported values and also that calculated from the SAED patterns. The TiO2 nanofibers were ultrasonically dispersed in monocarboxylic acids (formic acid, acetic acid, dichloroacetic acid, triflouroacetic acid, oleic acid, and stearic acid) and mercapto acids (mercaptosuccinic acid and mercaptopropionic acid) for time intervals ranging from 30 min to 15 h. The rationales of this selection are (i) these acids bind the TiO2 surface and could prevent the breaking down of continuous nanofibers into nanorods through molecular level interaction and (ii) acetic acid could be used for chemical sintering and to prepare high quality TiO2 paste.19 The SEM images of the nanofibers ultrasonically dispersed in acetic acid for 1-15 h well prove the first hypothesis (Figure 2). The continuous fibers were cut into NWs with an average length of 4 µm upon ultrasonic dispersion. The average aspect ratio of the NWs was 10:1. Prolonged ultrasonication of the TiO2 nanofiber suspension in the acids used here

did not appreciably reduce the length of the wires. High stability of the fibers against mechanical degradation is thought to arise from the molecular level binding of the monocarboxylic and mercapto acids with TiO2. The current method of breaking the fibers into large aspect ratio NWs also solved another crucial issue: fabrication of thick films (10-15 µm) of electrospun nanostructures with a high aspect ratio. Previous attempts compromised either the thickness and/or the aspect ratio of the electrospun TiO2 films.13-17 The efficiency of the cell was calculated from the short-circuit current density (JSC), open-circuit voltage (VOC), and fill factor (FF) determined from the J-V curves. The photovoltaic parameters of S1 (S2) are JSC ∼ 7.79 (8.46) mA/cm2, VOC ∼ 815 (815) mV, FF ∼ 59.8 (60), and η ∼ 4.12 (4.29). Both S1 and S2 showed similar dye-loading (7 × 10-8 mol/cm2), indicating the similar quantity of active surfaces and concentration of injected electrons. A small difference observed in the JSC of S2 is attributed to its improved charge transport. The effective diffusion coefficient of the electrons moving through the nanofiber film was measured by transient photocurrent measurements. Figure 3 shows the photocurrent transients observed for two devices fabricated using S1 and S2. The photocurrent was observed immediately after laser excitation in the device S1 and reaches the peak at around 0.7 ms, followed by a single exponential decay at long times. It was

Electrospun TiO2 Nanowires

Figure 3. Transient photocurrent observed for NW films with annealed TiO2 nanofibers for 1 h (S1) and 24 h (S2). Inset: diffusion coefficients of S1 and S2 as a function of photoexcitation density.

also observed that rise time of the photocurrent transient in S2 is much faster than that in S1, followed by a single exponential decay. The photocurrent collection times (τc) were extracted by fitting the photocurrent transient using a single exponential decay. The photocharge collection time (τc) for S1 was ∼4.8 ms, which increases with the decrease of bias light intensity. The τc for S2 was ∼1.5 ms, which is almost 3 times shorter than the τc estimated for S1 under similar measurement conditions. The Dn was estimated using the relation τc) d2/ 2.35Dn, where d is the thickness of the samples (∼13 µm). The Dn of the NW samples was ∼10-4 cm2/s, which showed an order of magnitude increase with the continuous nanofibers (∼4 × 10-5 cm2/s).17 The observed enhancement in the diffusion coefficient of NWs compared with continuous nanofibers, both obtained by electrospinning, is attributed to the lower photocurrent collection time due to the NW morphology. The photoexcitation density for various white light illumination intensities was calculated by numerically integrating the photocurrent transients. The inset of Figure 3 shows variation of Dn with the density of photoexcitation. An increase in Dn with photoexcitation density was observed in both the samples, similar to that observed for nanoparticles20,21 and indicative of the trap-limited

J. Phys. Chem. C, Vol. 113, No. 52, 2009 21541 diffusion process. Traps in nanocrystalline semiconductors result from their increased defects, such as unsaturated bonds, deviation from bulk bond lengths, etc. and are distributed over a broad energy range.22,23 The rate of increase of Dn with photoexcitation density changed appreciably for samples S1 and S2. The Dn of S2 (∼4.6 × 10-4 cm2/s) was nearly 3 times that of S1 (∼1.5 × 10-4 cm2/s) for a photoexcitation density of ∼2 × 1016cm-3. Note that Kopidakis et al. measured the Dn of TiO2 nanoparticles to be 10-7 cm2/s for a photoexcitation density of ∼1016/cm3.20,21,24 Recently, Jemmings et al.25 measured the Dn of 1D nanotubes using intensity modulated photoelectron spectroscopy. They observed a Dn of 10-6 cm2/s for an incident photon flux of 1016 /cm3. The Dn measured for electrospun TiO2 nanowires for a photoexcitation density of ∼1016/cm3 was ∼10-4cm2/s, which is about to 2-3 orders of magnitude higher than that measured for the nanoparticles. Many efforts have been devoted to understanding the charge transport through mesoporous TiO2 nanoparticles26 using a number of techniques, including transient photocurrent measurements.24,27 It has been generally accepted that photoinjected electrons in the mesoporous network diffuse through a well-defined conduction band minimum, EC, and is interrupted by a series of trapping and detrapping events. On the other hand, not much is known about charge transport through random 1D nanostructures except on ordered nanotubes.28,29 Figure 4 shows a schematic that explains the source of difference in Dn observed for mesoporous particles and NW samples. The smaller particle size and higher space charge region thereby in the mesoporous network lead to complete depletion of macroscopic electric fields, and therefore, the conduction band remains flat throughout the particle. On the other hand, the NWs in the present study are characterized by a dense packing of grains along their length and diameter, in contrast to the random particle network (Figure 4), which can support a small electric field due to a partially depleted space charge region within its volume. This space charge free region is thought to further accelerate the electrons. The spatial extend of the electric field increases with increase in the size of the grains composing the NWs (Figure 4). We believe that the difference in the magnitude of the depleted space region between the mesoporous network and random 1D

Figure 4. Schematics showing the diffusion process in nanoparticle and nanowire systems. The bottom and top panel display the morphologies and energy levels, respectively. The red arrow indicates the diffusion process, and the blue curves indicate the recombination processes. (A) Mesoporous nanoparticle system in which the conduction band is flat throughout the particle. Typically, 25 nm particles have an effective surface area of ∼100 m2/g. The mesoporosity of the films has the advantage of large dye-anchoring, consequently, with increased recombination. (B) A nanowire with an average diameter of 150 nm composed of particles of ∼12 nm; in the present experiment, similar structures were obtained by annealing the as-spun composite polymeric fibers for 1 h. These fibers had an effective BET surface area of ∼60 m2/g. The dyes could be anchored only on their surface, consequently, with a reduced recombination rate. Close packing of nanoparticles in the nanowires leads to a depleted space charge region in the volume of the nanowires and, therefore, with an improved diffusion process. (C) A nanowire with an average diameter of 150 nm composed of particles of ∼50 nm; in the present experiment, similar structures were obtained by annealing the as-spun composite polymeric fibers for 1 h. These fibers had an effective BET surface area of ∼50 m2/g. Enhanced particle size further reduced the space charge region, thereby leading to an improved diffusion process.

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Archana et al. electric field in dense NWs due to a partially depleted space charge region within its volume. The width of this space charge free region increases with increase in the particle size, which further enhanced the Dn. Thus, electrospinning offers a possibility to enhance the charge mobility without compromising much to the specific surface area of the nanostructures thereby produced. The high electron diffusion coefficient observed in annealed electrospun metal oxide NWs in the present study provides opportunities to fabricate electronic devices with better performance. Acknowledgment. This project is financially supported by the Clean Energy Program Office, National Research Foundation, Singapore.

Figure 5. OCVD curve measured for the samples S1 (black dots) and S2 (red dots).

NWs is the source of the improved effective Dn in the latter structure. Annealing the samples for a long time increases the particle size, thereby removing the surface traps. Therefore, the high Dn observed for S2 is assigned to its enhanced crystallinity compared with that of S1. Removal of surface traps upon increasing the particle size was further studied by measuring the open-circuit voltage decay (OCVD)30,31 of the two samples, S1 and S2. The OCVD measures the lifetime of the electrons as a function of the opencircuit voltage. The OCVD curves were recorded by turning off the illumination in a steady state and monitoring the subsequent photovoltage decay. As the measurement is performed in the dark, recombination with the oxidized dye molecule does not take place, but this is acceptable because the electrolyte accounts for the majority of the recombination even under illumination. Thus, assuming a first-order recombination reaction, the electron lifetime is given by τn ) -(kT/e)(dVOC/dt)-1,30,31 where kT is the thermal energy, e is the positive elementary charge, and dVoc/dt is the first-order time derivative of the VOC. Figure 5 shows the electron lifetime as a function of VOC for S1 and S2. The shape of the OCVD curve for S1 shows a dependence on the quasi-fermi level, confirming a trap-assisted conduction mechanism similar to those of nanoparticles. Similar OCVD was reported for electrospun continuous nanofibers directly spun on FTO, followed by annealing for 1 h.17 The depression seen in the curve at around 0.3 V indicates the presence of surface trap states that could result in recombination of electrons with the electrolyte through tunneling. Furthermore, the strength of the deviation from linear suggests a high rate constant for such recombination. Interestingly, the dependence of τn on VOC was found to be linear for the sample S2, indicating the removal of the surface traps, thereby accounting for its larger Dn compared with that of S1. 4. Conclusions In conclusion, smooth, porous, and thicker TiO2 NW films of high aspect ratio were developed on conductive glass substrates by combining coordination chemistry and electrospinning. Electrospun metal oxide nanofibers were coordinated using organic acids, which prevented breaking of nanofibers into tiny submicrometer nanorods during the film fabrication process. The Dn of the resulting NW shows an order of magnitude enhancement d with the random continuous nanofibers that are parallel to the substrate. The observed enhancement in Dn is attributed to a small

Supporting Information Available: X-ray diffraction patterns of the NW samples under different annealing conditions. This material is available free of charge via the Internet at http:// pubs.acs.org. References and Notes (1) Xia, Y. N.; Yang, P. D.; Sun, Y. G.; Wu, Y. Y.; Mayers, B.; Gates, B.; Yin, Y. D.; Kim, F.; Yan, Y. Q. AdV. Mater. 2003, 15, 353–389. (2) Hochbaum, A. I.; Chen, R.; Delgado, R. D.; Liang, W.; Garnett, E. C.; Najarian, M.; Majumdar, A.; Yang, P. Nature 2008, 451, 163–167. (3) Heath, J. R. Acc. Chem. Res. 2008, 41, 1609–1617. (4) Palmer, L. C.; Stupp, S. I. Acc. Chem. Res. 2008, 41, 1674–1684. (5) Greiner, A.; Wendorff, J. H. Angew. Chem., Int. Ed. 2007, 46, 5670– 5703. (6) Shui, J.; Li, J. C. M. Nano Lett. 2009, 9, 1307–1314. (7) Sigmund, W.; Yuh, J.; Park, H.; Maneeratana, V.; Pyrgiotakis, G.; Daga, A.; Taylor, J.; Nino, J. C. J. Am. Ceram. Soc. 2006, 89, 395–407. (8) Li, D.; Xia, Y. N. AdV. Mater. 2004, 16, 1151–1170. (9) Kumar, A.; Jose, R.; Fujihara, K.; Wang, J.; Ramakrishna, S. Chem. Mater. 2007, 19, 6536–6542. (10) Teo, W. E.; Ramakrishna, S. Nanotechnology 2006, 17, R89–R106. (11) Ramasheshan, R.; Sundarrajan, S.; Jose, R.; Ramakrishna, S. J. Appl. Phys. 2007, 102, 111101. (12) Li, D.; Xia, Y. Nano Lett. 2003, 3, 555–560. (13) Song, M. Y.; Ahn, Y. R.; Jo, S. M.; Kim, D. Y.; Ahn, J. P. Appl. Phys. Lett. 2005, 87, 113113. (14) Onozuka, K.; Ding, B.; Tsuge, Y.; Naka, T.; Yamazaki, M.; Sugi, S.; Ohno, S.; Yoshikawa, M.; Shiratori, S. Nanotechnology 2006, 17, 1026–1031. (15) Fujihara, K.; Kumar, A.; Jose, R.; Ramakrishna, S.; Uchida, S. Nanotechnology 2007, 18, 365709. (16) Jose, R.; Kumar, A.; Thavasi, V.; Ramakrishna, S. Nanotechnology 2008, 19, 424004. (17) Mukherjee, K.; Teng, T. H.; Jose, R.; Ramakrishna, S. Appl. Phys. Lett. 2009, 95, 012101. (18) Jose, R.; Kumar, A.; Thavasi, V.; Fujihara, K.; Uchida, S.; Ramakrishna, S. Appl. Phys. Lett. 2008, 93, 023125. (19) Park, N.-G.; Kim, K. M.; Kang, M. G.; Ryu, K. S.; Chang, S. H.; Shin, Y. J. AdV. Mater. 2005, 17, 2349–2353. (20) Benkstein, K. D.; Kopidakis, N.; van de Lagemaat, J.; Frank, A. J. J. Phys. Chem. B 2003, 107, 7759–7767. (21) Kopidakis, N.; Schiff, E. A.; Park, N. G.; van de Lagemaat, J.; Frank, A. J. J. Phys. Chem. B 2000, 104, 3930–3936. (22) Bisquert, J. Phys. Chem. Chem. Phys. 2008, 10, 49–72. (23) Jose, R.; Thavasi, V.; Ramakrishna, S. J. Am. Ceram. Soc. 2009, 92, 289–301. (24) Kopidakis, N.; Benkstein, K. D.; van de Lagemaat, J.; Frank, A. J.; Yuan, Q.; Schiff, E. A. Phys. ReV. B 2006, 73, 045326. (25) Jennings, J. R.; Ghicov, A.; Peter, L. M.; Schmuki, P.; Walker, A. B. J. Am. Chem. Soc. 2008, 130, 13364–13372. (26) Bisquert, J. Phys. Chem. Chem. Phys. 2008, 10, 3175–3194. (27) Walker, A. B.; Peter, L. M.; Martinez, D.; Lobato, K. Chimia 2007, 61, 792–795. (28) Zhu, K.; Vinzant, T. B.; Neale, N. R.; Frank, A. J. Nano Lett. 2007, 7, 3739–3746. (29) Zhu, K.; Neale, N. R.; Miedaner, A.; Frank, A. J. Nano Lett. 2007, 7, 69–74. (30) Zaban, A.; Greenshtein, M.; Bisquert, J. ChemPhysChem 2003, 4, 859–864. (31) Bisquert, J.; Zaban, A.; Greenshtein, M.; Mora-Sero, I. J. Am. Chem. Soc. 2004, 126, 13550–13559.

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