Brookite-Based Dye-Sensitized Solar Cells: Influence of Morphology

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C: Energy Conversion and Storage; Energy and Charge Transport

Brookite-Based Dye-Sensitized Solar Cells: Influence of Morphology and Surface Chemistry on Cell Performance Dena Pourjafari, David Reyes-Coronado, Alberto Vega-Poot, Renán Escalante, Debra Kirkconnell-Reyes, Rodrigo García-Rodríguez, Juan Antonio Anta, and Gerko Oskam J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b02384 • Publication Date (Web): 23 May 2018 Downloaded from http://pubs.acs.org on May 24, 2018

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The Journal of Physical Chemistry

Brookite-Based Dye-Sensitized Solar Cells: Influence of Morphology and Surface Chemistry on Cell Performance D. Pourjafari1*, D. Reyes-Coronado2, A. Vega-Poot1, R. Escalante1, D. Kirkconnell-Reyes1, R. García-Rodríguez1, J.A. Anta3, and G. Oskam1* 1

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Departamento de Física Aplicada, CINVESTAV-IPN, Mérida, Yucatán 97310, México. Unidad Académica Playa del Carmen, Universidad de Quintana Roo, Playa del Carmen,

Quintana Roo 77710, México. 3

Área de Química Física, Universidad Pablo de Olavide, E-41013 Sevilla, Spain.

* Email: [email protected] * Email: [email protected]

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ABSTRACT The transport and recombination properties of dye-sensitized solar cells based on phase-pure anatase and brookite nanomaterials are compared as a function of the surface chemistry and morphology. Phase-pure brookite has been synthesized from amorphous TiO2 using two different solutions at low and high pH, resulting in different size and morphology of brookite nanoparticles. The smaller short-circuit current density (JSC= 6.6 mA cm-2) for acidic brookite compared to anatase (9.8 mA cm-2) was related to the light harvesting efficiency, due to the lower amount of dye adsorbed. However, a larger open circuit voltage for acidic brookite indicates the promise of the material. The basic brookite-based solar cells gave a very low JSC (0.10 mA cm-2), which increased dramatically by a factor of about 30 after an acid treatment of the films, illustrating the effect of surface chemistry. A combination of experiments shows that the improvement is related to an increase in injection efficiency. Electrochemical impedance and intensity-modulated photocurrent and photovoltage spectroscopy show that electron transport is faster in the acid-treated basic brookite nanomaterial, related with the larger feature sizes. However, the recombination kinetics are also significantly faster, with as net result a smaller diffusion length and, hence, smaller collection efficiency.

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!

INTRODUCTION

Dye-sensitized solar cells (DSCs) are a fascinating system combining the physics and chemistry of semiconducting nanomaterials, optoelectronic properties of adsorbed dye molecules, and nonaqueous redox electrochemistry, at both the solid semiconductor surface and the molecular dye as well as at a counter electrode.1–3 The DSC is approaching the status of a mature solar cell technology with specific advantages for indoor applications and building-integrated photovoltaics with unique aesthetic features.4–6 The DSC is based on a sensitized thin film of nanostructured, mesoporous TiO2, which is an attractive low-cost, non-toxic, wide bandgap semiconductor, with excellent chemical stability and (photo)catalytic activity, specifically as a nanostructured material.1,2,7–9 A wide variety of synthesis methods have been developed in order to tune the crystal phase, nanoparticle size and morphology, and the resulting optical, physical and chemical properties.7,8,10–16 The three main crystal phases are anatase, rutile and brookite; the first two phases have a tetragonal crystal structure, while brookite is orthorhombic.7,16,17 TiO2-based DSCs are generally fabricated using pure anatase nanoparticulate films to achieve the highest efficiencies, however, other phases of TiO2 may be equally attractive.16,18–23 Several reports exist on the use of either rutile or brookite nanomaterials, but generally the efficiency is found to be lower; however, especially brookite has shown promise exhibiting a larger open circuit voltage than anatase-based solar cells.24–29 Although both materials are TiO2, significant differences may exist in several crucial parameters, including the energetic position of the conduction band, the distribution and density of trap states, electron mobility, and the rate constant for electron transfer rate to the solution.30,31 Both rutile and brookite are much more difficult to synthesize in nanoparticulate morphology related to a higher surface energy, and it is particularly complicated to obtain brookite nanomaterials of

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high purity.11,13,16,17,32 Hence, most of the reports in literature on the application of brookite in DSC actually use brookite – anatase mixed materials, which complicates the analysis of the performance. In a recent paper, the synthesis of pure brookite nanomaterials has been described, and it is concluded that a combination of lower dye loading with lower collection efficiency results in a lower solar cell efficiency for the brookite-based cells, despite a higher open circuit voltage.33 However, brookite is clearly a promising material if the cell components and materials properties can be adequately tuned. In general, it is not straightforward to determine which of the materials properties are responsible for an increase or decrease in dye solar cell performance. A useful method to analyze this is by considering that the product of three partial efficiencies determines the cell performance: the light harvesting efficiency, the electron injection efficiency, and the charge collection efficiency. The light harvesting efficiency mainly depends on the properties of the dye, the injection efficiency depends on both the dye and the oxide material, and the collection efficiency depends mainly on the oxide material and the redox electrolyte. In this work, we report methods to synthesize pure anatase and brookite by controlled transformation of amorphous titania via a hydrothermal treatment. Anatase was prepared using a mildly acidic reaction solution based on acetic acid. Brookite was prepared using two methods, based on either a strong acidic or a basic reaction solution. The two methods resulted in nanomaterials with very different morphology and surface chemistry, and the influence of these parameters have been evaluated. We perform a detailed analysis of the solar cell performance in order to elucidate the roles of the light harvesting, electron injection, and charge collection efficiencies. Particular emphasis is placed on the analysis of the collection efficiency for the different TiO2 materials using small-signal

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perturbation methods including electrochemical impedance spectroscopy (EIS) and intensitymodulated photocurrent and voltage spectroscopy (IMPS and IMVS, respectively). !

EXPERIMENTAL METHODS Chemicals and Instruments. Acetic acid (≥99.7%), titanium(IV) isopropoxide (>97%),

isopropyl alcohol, sodium hydroxide, hydrochloric acid, nitric acid (ACS reagent, 70%), ethyl cellulose (viscosity 100 cP), terpineol (anhydrous), lithium iodide (99.9%), iodine (99.8%), guanidine thiocyanate (≥ 97%), acetonitrile (99.93%), valeronitrile (99.5%) and 4-tertbutylpyridine (96%) were purchased from Sigma-Aldrich, and used as received. The N719 dye was purchased from Dyesol, and absolute ethyl alcohol (ACS Reagent Grade) was bought from Macron. An electroless platinum deposition solution (Platisol T) and 1,2-dimethyl 3propylimidazolium iodide (DMPII) were purchased from Solaronix. For TiO2 paste prepration, a rotary evaporator (BUCHI Rotavapor R-210) was used. The thickness of TiO2 films was measured by profilometry (KLA-Tencor AlphaStep D-120). To observe the deposited TiO2 film morphology, a JEOL JSM-7600F field emission scanning electron microscope was used. The crystallographic phase of TiO2 was determined with a Siemens D5000 X-ray Powder Diffraction (XRD) set-up. The BET surface area was determined using a Belsorp max II (Belsorp series, BEL Japan, Inc). The quantity of adsorbed dye molecule was calculated using UV-Vis spectra (Agilent Technologies, 8453). Photoluminescence spectra of working electrodes were obtained using a LUMINA Fluorescence Spectrometer (Thermo Scientific). Photovoltaic characterization of cells was performed using a set-up consisting of a 450 W ozone-free Xe-lamp (Oriel) with a 10 cm water filter and an AM 1.5G optical filter. The intensity was calibrated using a certified 4 cm2 monocrystalline silicon reference cell, with a KG5 filter incorporated to optimize calibration. Electrochemical impedance spectroscopy (EIS),

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intensity-modulated photocurrent spectroscopy (IMPS) and intensity-modulated photovoltage spectroscopy (IMVS) were recorded with an Autolab PGSTAT302N/FRA2 set-up, and Nova 1.10 software was used for data analysis. The impedance measurements were performed under red light LED illumination (625 nm), using an AC amplitude of 10 mV in the frequency range 10-1 to 105 Hz. EIS measurements were performed at the open circuit potential, which was varied using neutral density filters mounted in a filter wheel. The electrochemical impedance spectra were analyzed using Z-view software with the aid of an equivalent circuit corresponding to the transmission line model developed by Bisquert et al.

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IMPS and IMVS measurements were

performed at modulation frequencies between 1 mHz and 10 kHz. A red LED (625 nm) was used to illuminate the sample and it served both as the bias illumination and the small sinusoidally modulated probe beam, with an approximately 20% amplitude. In this range, the response to the modulated signal is expected to be linear. Synthesis of TiO2 materials. The TiO2 materials were synthesized from a common starting material consisting of amorphous titania and subsequent hydrothermal treatments under different conditions in order to obtain phase-pure anatase and brookite, according to Scheme 1.11 Amorphous titania was prepared as follows. A flask containing 1.14 ml of deionized water (18 MΩ cm) and 105 ml of isopropyl alcohol was placed in a salt-ice bath on a magnetic stirrer at 0 0

C. In another flask, 5 ml of titanium(IV) isopropoxide was added to 105 ml of isopropyl alcohol

(IPA). The first solution was added to the second solution while maintaining the temperature at 0 0

C and agitation. The mixed solution was kept for one hour under these conditions. Thereafter,

the suspension was maintained under stirring for 24 hours at room temperature. The amorphous titania was obtained by filtering the suspension solution three times.35

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Scheme 1. Schematic flow chart illustrating the steps in the synthesis pathway of anatase and brookite phase-pure TiO2 nanomaterials.

Pure anatase was synthesized by hydrothermal treatment of an aqueous solution containing 3 M amorphous titania and 1.5 M acetic acid in a Teflon-lined autoclave (Parr Instruments) at 200 0C for 6 hours. The final product was washed several times with deionized water and ethanol and dried at 80 0C. Brookite was synthesized using two different treatments, using either an acidic or basic solution. For the “acidic brookite” (brookite A), a solution of 3 M HCl was added to TiO2 amorphous powder under vigorous stirring to obtain a homogenous transparent solution. The final concentration of TiO2 in the solution was 3 M. The solution was then placed in a Teflon-lined autoclave and hydrothermally treated at 180 0C for 10 hours. The final product was washed and centrifuged three times with deionized water. The liquid supernatant was separated from precipitated solid residue and dried at 80 0C in order to obtain highly pure brookite. For “basic

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brookite” (brookite B), 0.09 M NaOH was added to an aqueous solution of 0.18 M amorphous TiO2 under vigorous stirring. The solution was hydrothermally treated in a Teflon-lined autoclave at 200 0C for 60 hours. The final product was washed several times with deionized water and ethanol and dried at 80 0C. A screen-printing paste was obtained by preparing two solutions: 1) 0.15 g ethyl cellulose in 10 mL of ethanol and 2) 0.5 g TiO2 powder (anatase, brookite A or brookite B) in 10 mL of ethanol. The resulting suspensions were sonicated separately for 1 h. After sonication, the two solutions were mixed and 4.1 g terpineol was added to the mixture, following by 1 hour of sonication. The excess ethanol was removed with a rotary evaporator resulting in the TiO2 screen printing paste as final product. Solar cell assembly. Fluorine-doped tin oxide (FTO) on glass with a sheet resistance of 15 Ω/

and 8 Ω/

were used as working and counter electrodes, respectively (TEC 15 and TEC

8; Xop Glass). The substrates were washed with soap, deionized water, ethanol and isopropanol in an ultrasonic bath. The FTO used for the working electrodes were immersed in an aqueous solution of 40 mM TiCl4 at 70 0C for 30 min following by heat treatment at 500 0C for 30 min.36– 39

TiO2 paste was deposited using a semi-automatic screen printer in an area of 0.5 cm2 (1 × 0.5

cm2). In order to reach a final thickness of about 11 µm, the deposition process was repeated 7 times with 10 min of heat treatment at 125 0C between each step. The TiO2 films were sintered at 530 0C for 1 h, using slow heating and cooling ramps.40 The final film thickness of about 11 µm was confirmed by perfilometry after heat treatment for each electrode. Four different series of working electrodes were fabricated; (i) TiO2 anatase (sample series A); (ii) TiO2 brookite synthesized at low pH (sample series BA); (iii) TiO2 brookite synthesized at

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high pH (sample series BB); and (iv) TiO2 brookite synthesized at high pH, after immersion of the electrodes in an acidic bath of 0.2 M HCl for two hours (sample series BB-ac); after the acid treatment, the substrates were rinsed with distilled water and heated at 400 0C. All substrates were sensitized by immersion at 80 0C directly after the sintering process in a 0.3 mM N719 dye solution in ethanol, and remained in the solution for 24 hours. The counter electrodes were prepared as follows. Two small holes were drilled in the FTO/glass in order to fill the cell with electrolyte after sealing of the cell. The counter electrode was covered with a thin, electroless platinum film by brushing on the Platisol solution on the same active area as the corresponding TiO2 area on the working electrode, followed by heat treatment at 400 0C for 5 min. The thermoplastic material Surlyn (DuPont, 70 µm) was used between the working and counter electrode as a sealing material. The two electrodes were assembled into a sandwich-type cell using clips, and were sealed at 215 0C for 100 s. The electrolyte solution consisted of 0.5 M LiI, 0.05 M I2, 0.6 M DMPII, 0.1 M GuSCN and 0.5 M TBP in a mixture of acetonitrile and valeronitrile (volume ratio 85:15)5,41,42, and was injected into the cells via the holes in the counter electrode, which were subsequently sealed using Surlyn and a microscope cover glass. Finally, the FTO contacts were covered with silver paint to improve the external contacts. The performance reproducibility was confirmed by fabrication of three cells for each material and no significant deviations were observed in the results. !

RESULTS and DISCUSSION Characterization of TiO2 materials. Before preparing the screen-printing paste for the

working electrodes, the synthesized TiO2 materials were characterized in powder form using Xray diffraction (XRD) to confirm the purity of the phases (see Figure S1 in the Supporting Information).

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Figure 1 shows the XRD patterns of the TiO2 films deposited onto the FTO substrates after the final sintering step, illustrating that the sintering and acid treatments do not change the material. Brookite is characterized by a (121) peak at 30.80o, which is not found for either anatase or rutile. The two other main peaks, the (120) peak at 25.33o and the (111) peak at 25.68o, overlap due to the nanoparticulate character of the films, resulting in peak broadening. In addition, these peaks are at essentially the same angle as the main anatase (101) peak at 25.28º.12,31,34,40,44

Figure 1. X-ray diffraction of TiO2 films deposited on FTO: anatase (A), brookite from acidic synthesis (BA), brookite from basic synthesis (BB), and brookite from basic synthesis after acid treatment (BB-ac). The peaks corresponding to the FTO are marked with an asterisk.

In order to confirm the phase-purity of the brookite nanomaterial, the relative intensities of the three main peaks should be compared. However, due to the peak broadening and resulting overlap, the area of the sum of the (120) and (101) peaks should be double that of the (121) peak, which was confirmed for the materials prepared. Note also that the main rutile peak at 27.45º may be masked by the FTO peak at 26.74º, however, from the powder spectra it can be concluded that no significant rutile is present in the anatase and brookite materials.

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Figure 2 shows scanning electron microscopy (SEM) images for the TiO2 films deposited on FTO after all treatments. The anatase nanoparticles are approximately spherical with an average size of about 18 nm. For brookite A, the average particle size was 40 nm and the particles are also approximately spherical. Brookite B has a significantly different elongated particle shape and the particles are somewhat larger, with an average length of about 90 nm and a width of about 25 nm. The particle size and rice-like morphology of brookite B does not change after immersion in the HCl solution.

Figure 2. SEM images of TiO2 films deposited on FTO: (a) anatase (A), (b) brookite from acidic synthesis (BA), (c) brookite from basic synthesis (BB), and (d) brookite from basic synthesis after acid treatment (BB-ac).

The differences in average particle size are reflected in the specific surface area. Films were deposited onto glass and sintered according to the protocol described previously, and the material was scraped off for gas adsorption measurements, using the BET analysis. Table 1 shows that the surface area for anatase is about 2x as high as for brookite BA, in agreement with the observation that the average nanoparticle size for anatase is about half that of brookite. The brookite BB nanoparticles are larger and of a more cylindrical shape, and the BET surface area is about half of that of brookite BA, in agreement with expectations. The available surface area for dye adsorption is an essential parameter as the light harvesting efficiency is generally proportional to the amount of dye adsorbed.7,45–47 However, dye adsorption also depends on the surface chemistry of the material, and is expected to be different for anatase and brookite. In

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addition, the different surface facets exposed for brookite BB as compared to BA related to the difference in morphology may also influence the adsorption density.18,48,49 Hence, the amount of N719 dye adsorbed was determined for each material by desorbing the dye in an aqueous 0.1 M NaOH solution. The solutions were analyzed using UV-Vis spectrophotometry, and the amount of dye was determined using the absorption coefficient and measured absorbance at 515 nm;45,50,51 the spectra are shown in Figure S2 in the Supporting Information, and the results are presented in Table 1. Table 1. Materials characteristics and adsorption properties.

Substrate material

A

BA

BB

BB-ac

18

40

85 × 25

85 × 25

BET surface area (m2 g-1)

177

87

45

45

Adsorbed dye* (× 10-8 mol cm-2 geometrical area)

78

53

37

50

Nanoparticle size (nm, approx.)

Dye-sensitized film*

* All films had a thickness of about 11 µm.

Table 1 illustrates that although the anatase films adsorb the largest number of dye molecules, both brookite BA and BB adsorb a significant amount of dye. If we assume a similar amount of TiO2 material per film, the adsorption density is actually higher for brookite than for anatase. An interesting effect is observed for the brookite BB sample after acid treatment: the amount of adsorbed dye increases by a factor 1.5. These results are in agreement with the visual observations from the intensity of color of the cells, as shown in Table 1. This last observation may be related to the surface chemistry of the brookite BB, implying that there is still a memory

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of the synthesis pH. In a basic solution, the adsorbed dye can be removed from the surface, related to hydrolysis of the ester-type bond between the TiO2 surface and carboxyl moiety of the dye. Hence, it can be expected that for more basic surfaces the equilibrium of dye adsorption is at lower coverage. Therefore, upon prolonged acid treatment, the surface chemistry can be adjusted to adsorb more dye. Another consequence of a memory effect of the surface chemistry related to the synthesis method would be the energetic position of the band edges. As for most oxide semiconductors, the band edges of TiO2 shift to higher energy with increasing surface pH by 59 meV per pH unit.52–58 Hence, assuming that the brookite synthesized in basic solution has retained a higher surface pH, the conduction band could be at significantly higher energy than the brookite prepared in acidic medium. This difference may affect the injection of electrons from the dye in the excited state. The acid treatment of the basic brookite results in a lowering of the surface pH and downshift of the conduction band edge and, hence, the injection efficiency may increase significantly. This interpretation can be evaluated using photoluminescence (PL) spectroscopy. When the dye-sensitized film is illuminated with light of sufficient energy, the excited state electron can either be injected into the conduction band or it can return to the ground state by radiative recombination. The photoluminescence spectra were obtained for anatase, brookite A, brookite B and brookite B after acid treatment at an excitation wavelength of 532 nm59 and the results are shown in Figure 3. All substrates had been sensitized with N719 for 24 hours. For comparison, Figure S3 in the Supporting Information shows the absorbance and photoluminescence spectra of a 0.3 mM N719 solution in ethanol, and includes a PL spectrum of N719 adsorbed to ZrO2. Due to the very negative CB edge energy, excited-state electrons cannot be injected from N719 into ZrO2

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resulting in a strong PL peak. The sensitized anatase (A) sample shows essentially no photoluminescence, in accordance with expectations of a high injection efficiency. A similar good result is observed for the brookite A (BA) sample, indicating a high injection efficiency. Brookite BB has the strongest photoluminescence, indicative of a low injection efficiency. For brookite BB-ac a significantly lower peak is observed, indicating that the acid treatment of the surface improves the injection efficiency. These differences in injection efficiency are expected to significantly affect the performance of the dye-sensitized solar cells, where the photocurrent is directly proportional to the injection efficiency.

Figure 3. Steady-state photoluminescence (PL) spectra under constant 532 nm excitation illumination for anatase (A), brookite from acidic synthesis (BA), brookite from basic synthesis (BB), and brookite from basic synthesis after acid treatment (BB-ac). The samples consisted of dye-sensitized working electrodes, and the PL intensity is weighted with respect to the quantity of dye adsorbed, as determined by subsequent desorption measurements.

The differences in injection efficiency are most likely at least partially related to the energetic position of the conduction band, which would imply that the conduction band is at highest energy for brookite BB, followed by brookite BB-ac, then brookite BA, and finally anatase A. Note however that the injection efficiency also depends on other electronic factors and may depend on the strength of the linkage of the dye to the surface.60–64

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Performance of dye-sensitized solar cells. Figure 4 shows the current density vs. voltage (J-V) curves for cells prepared with anatase, brookite BA, brookite BB and brookite after acid treatment BB-ac; the cell performance parameters are listed in Table 2.

Figure 4. J-V curves under 1 sun illumination of anatase (A), brookite from acidic synthesis (BA), brookite from basic synthesis (BB), and brookite from basic synthesis after acid treatment (BB-ac).

Figure 4 and Table 2 illustrate that the short-circuit photocurrent, Jsc, is largest for anatase, and very low for brookite BB. If we compare the results for anatase and brookite BA, it can be seen that the photocurrent scales with the amount of dye adsorbed: anatase has a factor 1.5 more dye adsorbed, and the photocurrent is also a factor 1.5 larger. However, this correlation does not hold for the brookite BB samples; although brookite BB has a factor 2 less dye adsorbed, the photocurrent is a factor 100 lower, indicating another reason for the low performance. The performance of the brookite BB is significantly improved after the acid treatment. With an increase in adsorbed dye by a factor 1.5, the photocurrent increases by a factor 32 compared to the untreated brookite BB, and becomes comparable to the results for brookite BA. However, the performance remains lower by a factor of about 2. It is clear that these results are not determined

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by the amount of dye adsorbed, i.e., the light harvesting efficiency, but rather are related to the injection and collection efficiencies. Table 2. Solar cell performance parameters under 1 sun illumination. The values are for 3 measured cells for each series and the corresponding standard deviation. Jsc

VOC

η

Fill

(mA/cm2)

(V)

(%)

Factor

A

9.83±0.61

0.74±0.017

4.9±0.17

0.67±0.023

BA

6.62±0.81

0.78±0.018

3.5±0.36

0.69±0.027

BB

0.10±0.03

0.77±0.013

0.05±0.015

0.62±0.016

BB-ac

3.18±0.18

0.77±0.005

1.7±0.061

0.68±0.026

An important observation from Figure 4 and Table 2 is that the open circuit potential, VOC, is larger for brookite than for anatase. This observation even holds for the brookite BB sample where the photocurrent is very low. A large open circuit potential points to slow recombination, indicating that the improvement of the performance of the brookite BB-ac sample is more likely to be related to the injection efficiency than to the collection efficiency. This interpretation is in agreement with the results of photoluminescence spectroscopy for the different materials shown in Figure 3. For anatase and brookite BA, the photoluminescence is low indicating efficient charge injection resulting in a large photocurrent. The strong photoluminescence observed for brookite BB indicates that the low injection efficiency is the cause of the very small photocurrent. The acid treatment results in an increase of injection efficiency and, thus, a strong increase in photocurrent and a related decrease in photoluminescence intensity. These observations are most likely mainly due to a downward shift of the conduction band, related to the change in surface acidity.

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Characterization

of

electron

transport

and

recombination.

Steady-state

measurements can give valuable information on the light harvesting and electron injection efficiencies, as shown in the previous sections. However, for a detailed analysis of the charge collection efficiency, small-signal perturbation methods need to be applied. Electrochemical impedance spectroscopy (EIS), intensity-modulated photocurrent spectroscopy (IMPS) and intensity-modulated photovoltage spectroscopy (IMVS) are powerful tools to obtain quantitative information on the chemical capacitance, charge transfer resistance, electron lifetime and electron diffusion coefficient.65–77 For the systems under consideration here, we have compared anatase A, brookite BA, and brookite BB-ac solar cells. The brookite BB cells could not be analyzed using these techniques due to the very low photocurrent. Electrochemical impedance measurements are generally performed under illumination at the voltage corresponding to open circuit conditions. By changing the light intensity, the voltage can be varied. Figure S4 shows representative EIS spectra for the solar cells. The chemical capacitance, charge transfer or recombination resistance, and charge transport resistance were obtained by fitting the results using Zview software to the electrical circuit model shown in the inset of Figure S4, which corresponds to the model developed by Bisquert and coworkers.66,70,73,74,77 The differential chemical capacitance describes the dependence of the density of electrons stored in the nanostructured TiO2 film, and is generally found to exponentially increase with the open circuit voltage.66,67,78,79 This can be explained by an exponential distribution of trap states below the conduction band edge, g(E), as illustrated in Scheme 2.

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Scheme 2. Exponential distribution of trap energies and illustration of the processes of electron accumulation in the traps and the generation of the open circuit photovoltage VOC.

The trap state distribution, g(E), is defined by the total density of trap states, NT, and a parameter 𝛼 that describes the average depth of the traps; at smaller values for 𝛼, the average trap depth is larger:66, 80–83 𝑔 𝐸 =

!"! !! !

exp[−𝛼(𝐸! − 𝐸)/𝑘! 𝑇]

(1)

where EC is the energy of transport level (conduction band), kB is the Boltzmann constant, and T is the temperature. The total density of electrons stored in the traps, n, as a function of the quasiFermi level for electrons, EF, can be determined by integrating the density of states using the appropriate conditions:66, 81 𝑛 𝐸! = 𝑞

!! 𝑔 !!

𝐸 𝑑𝐸 = 𝑞

= 𝑞𝑁! 𝑒𝑥𝑝 −

!!"#$% 𝑔 !!

𝐸 𝑑𝐸 +

!! 𝑔 !!"#

%$𝐸 𝑑𝐸

! !! !!!

(2)

!! !

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Note that the integral between minus infinity and ERedox describes the charge stored in the dark, n0, where the Fermi level of the TiO2 film is in equilibrium with the electrolyte solution. At the open circuit voltage under illumination, the quasi-Fermi energy is independent of position in the TiO2 film and equal to the Fermi energy of the FTO substrate. In addition, the Fermi energy of the counter electrode is equal to the redox energy in solution, hence, the solar cell voltage is given by VOC = (EF – ERedox)/e. Hence, the integral between ERedox and EF in equation (2) represents the additional charge stored under illumination. When performing an EIS experiment under illumination at the open circuit voltage, a small voltage modulation is applied, corresponding to dVOC = d(EF-ERedox) = dEF. The chemical capacitance, Cµ, is defined as the derivative of the total electron density with voltage given in equation (2), hence, for the given exponential trap state distribution: 𝐶! =

!" !!!"

=𝑞

!" !!!

=

! ! !! ! !! !

𝑒𝑥𝑝 −

! !! !!!

(3)

!! !

Taking into consideration that (EC – EF) = (EC – ERedox + ERedox – EF) = (EC – ERedox + qVOC), this equation can be converted to the more useful form:66,67,82,83 𝐶! =

! ! !! ! !! !

𝑒𝑥𝑝 −

𝛼 𝐸𝑐 −𝐸𝑅𝑒𝑑𝑜𝑥 𝑘𝐵 𝑇

𝑒𝑥𝑝

𝛼𝑞𝑉𝑂𝐶 𝑘𝐵 𝑇

= 𝐶! 𝑒𝑥𝑝


(4)

Equation (4) illustrates the exponential dependence of the capacitance on the open circuit voltage, which is generally observed experimentally. Note that the exponential trap distribution was in fact assumed based on such experimental results. It is important to realize that the prefactor C0, although independent of cell voltage, depends on three parameters that may be different when comparing systems based on different metal oxides or redox couples: (i) the total density of traps; (ii) the trap distribution parameter 𝛼; and (iii) the position of the conduction

19



band edge with respect to the redox energy.84 Although the measurement of capacitance provides a lot of information, it is not straightforward to discern between the different effects. Figure 5 shows the capacitance versus cell voltage for the three systems studied. In all cases, the capacitance is exponentially dependent on open circuit voltage in agreement with an exponential trap distribution, and significant differences between the systems are observed. The slope of the plots depends only on the trap distribution parameter 𝛼, hence, we can conclude that anatase, brookite BA and brookite BB-ac have a different trap distribution parameter. It should be noted that the capacitance depends on the surface area if we assume that the traps are mainly at the surface.33,66,67 Hence, the absolute value of the capacitance decreases from anatase, brookite BA to brookite BB-ac, in accordance with the surface area in Table 1. It is also possible that the density of traps, NT, or the position of the band edges with respect to the redox couple energy are different for the three materials. In principle, from these results only we cannot distinguish between these possibilities. However, the brookite BB-ac capacitance is an order of magnitude smaller than for brookite BA, while the BET surface area is only about a factor 2 smaller.

Figure 5. Chemical capacitance vs. open circuit voltage for solar cells prepared with anatase (A), brookite from acidic synthesis (BA), and brookite from basic synthesis after acid treatment (BB-ac).

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Very often, the capacitance curves for different systems are displaced to overlap, thus correcting for the shift of the band edges, but it is important to realize that this is only possible for systems with the same density of traps and trap distribution parameter.71,82,85 In addition, the capacitance is generally found to be proportional to surface area, hence, if materials with different active surface areas are used, care must be taken with the interpretation of shifts. The voltage correction resulting in overlap of the capacitance curves is generally performed in order to compare the recombination kinetics at the same electron density, which provides a way to separate thermodynamics from kinetics. In order to be able to compare the results obtained for materials with differences in NT and 𝛼, the electron density has to be calculated from the capacitance results. To ensure an appropriate comparison of parameters and interpretation of results, the total charge at a given voltage can be obtained by integration of the capacitance: since dn = Cµ dVOC, the total charge can be obtained as a function of voltage by integration of equation (4), which leads to the following result: 𝑛 𝑉𝑂𝐶 =

!! ! !"

𝐶! 𝑒𝑥𝑝


=

!! ! !"

𝐶!

(5)

Equation (5) illustrates that the capacitance is linear with electron density, hence, if the results are graphed in a log – log plot, a straight line with a slope of 1 is obtained, and the intercept is given by 𝛼: this is illustrated in Figure S5. In this figure, it can be seen that the capacitance for the brookite BB-ac is much smaller than for the other two materials, and the horizontal displacement between the straight lines are due to the differences in 𝛼. The lower values for the capacitance (at the same voltage) observed for both brookite materials appear to be caused by the combination of a higher value of EC, as suggested by the more intense photoluminescence, and a lower surface area as a consequence of a larger particle size. These

21



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two effects are difficult to separate due to the different values of 𝛼, but it does not hinder us from discussing the recombination and transport data at the same values of the electron density. Hence, using this method, for each solar cell the total electron density can be determined using the measured capacitance and the value for 𝛼. In addition, other fundamental properties such as the recombination resistance and electron lifetime can be evaluated both versus cell voltage and versus total electron density. The recombination resistance, Rrec, describes the charge transfer kinetics of electrons to the acceptor in the electrolyte solution, and can give information on whether the recombination process is faster or slower for certain materials, surface facets or redox electrolytes.66,70,76 The recombination resistance is generally found to be exponential with the cell voltage, with a slope that is defined by a recombination parameter, 𝛽, which is generally smaller than 1. This observation demonstrates the influence of the trap-limited character of the fundamental processes in the DSC:33,66,70,86,87 𝑅!"# 𝑉!" = 𝑅!"#,! 𝑒𝑥𝑝(−

!"!!" !! !

)

(6)

In Figure 6, the recombination resistance is plotted vs. VOC and n, respectively. The recombination resistance decreases exponentially with increasing open circuit voltage, and the slope is similar for the three materials. The value for 𝛽 is about 0.65, which results in a diode ideality factor m = 1/𝛽 of about 1.6; this is generally observed for DSCs.76,88–92 At a constant voltage, the recombination resistance is much larger for both brookite BA and BB-ac as compared to anatase, in accordance with the observation that the open circuit voltage is larger for the brookite cells. In Figure 6b, the recombination resistance is shown versus the electron density. It can be observed that the brookite BB-ac curve is shifted to lower electron density,

22


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which is related with the much smaller capacitance observed for this material. The recombination resistance at the same electron density is significantly smaller for the brookite BB-ac cells, which suggests faster recombination in this case.

Figure 6. Recombination resistance versus (a) the open circuit voltage, and (b) the total electron density for solar cells prepared with anatase (A), brookite from acidic synthesis (BA), and brookite from basic synthesis after acid treatment (BB-ac).

The relative effects of the parameters that determine cell performance can be evaluated using the lifetime, which can be obtained under open circuit conditions using either electrochemical impedance spectroscopy (EIS) or intensity-modulated photovoltage spectroscopy (IMVS).82 From EIS, the electron lifetime can be obtained from 𝜏! = 𝑅!"# 𝐶! . One of the advantages of this parameter is that it does not depend on the surface area, as the area dependence of the capacitance and resistance cancel out. Hence, this allows for a separation of the geometrical effects and fundamental mechanistic effects. IMVS is also performed at the open circuit potential and, in general, a single semicircular arc is observed. The lifetime is obtained from the frequency at the apex, τIMVS=1/ωmin.66,71,78,82 Figure S6 shows representative spectra for the three materials.

23



Figure 7 shows the electron lifetime obtained from both EIS and IMVS versus the open circuit potential and the electron density, respectively, for the three systems.

Figure 7. Lifetime versus (a) the open circuit voltage, and (b) the total electron density for solar cells prepared with anatase (A), brookite from acidic synthesis (BA), and brookite from basic synthesis after acid treatment (BB-ac). The open and solid symbols correspond to the IMVS and EIS results, respectively.

Approximately the same results are obtained from both techniques. As a function of voltage, the lifetimes obtained for the brookite-based solar cells are larger, especially for the brookite BA system. However, the results as a function of electron density tell a different story. The lifetime for the brookite BB-ac system is significantly smaller than for the other two systems, which confirms the faster recombination rate suggested by the resistance data. The brookite BA system has a larger lifetime than the anatase A system, however, the slope versus electron density is larger for the brookite BA system. These observations indicate that at higher light intensities, where the electron density is larger, the anatase system may become the system with the longest lifetime. The different slopes for the lifetime versus electron density plots illustrate the importance of the trap distribution parameter: the optimal materials system may depend on the light intensity.

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The results obtained at the open circuit voltage mainly describe the recombination kinetics, while the collection efficiency may also depend on the electron transport properties. Intensitymodulated photocurrent spectroscopy (IMPS) performed under short-circuit conditions is the most suitable method to characterize transport. The spectra generally consist of a single semicircular arc, and the transport time constant can be determined from the frequency at the apex. Figure S7 shows representative IMPS spectra for the three systems. An important characteristic of the DSC under short-circuit conditions is that the quasi-Fermi level in the TiO2 film is not equal to that of the FTO contact. In fact, although the cell voltage is zero, the quasiFermi energy inside the nanostructured film is about 0.5 eV higher than in the FTO contact, related to the trapped charge in the film and the relatively slow extraction rate.87 The corresponding kinetics depend on the light intensity, where at higher intensity more charge remains trapped, thus maintaining the quasi-Fermi level at higher energy. As a consequence, the energy needed for the de-trapping of electrons from the quasi-Fermi energy to the conduction band is smaller, and transport is faster. This is reflected in a light intensity or electron density dependence of the measured effective diffusion coefficient, Dn, which is generally expressed as follows:66,93–96 𝐷! =

!!

(7)

! !!"#$

where d is the film thickness and 𝛾 is a constant, that is taken to be 2.35 for TiO2 and depends on film thickness, absorption coefficient and illumination direction.90,93 Figure 8 shows the results of the analysis of the IMPS measurements for the three systems. It can be observed that the diffusion coefficient depends on the incident light intensity for all systems, in agreement with the multiple trapping transport model, and the value of Dn depends on the system.

25



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Figure 8. Diffusion coefficient versus light intensity obtained from IMPS measurements under short circuit conditions for solar cells prepared with anatase (A), brookite from acidic synthesis (BA), and brookite from basic synthesis after acid treatment (BB-ac).

Figure 8 shows that the transport properties for the acid-treated basic brookite are better than for the acidic brookite, which is most likely related to the larger particle size and lower capacitance. The diffusion coefficients for anatase and acid-treated basic brookite are essentially the same, while the diffusion coefficient for acidic brookite is significantly lower, implying that for similar morphologies charge transport in brookite slower than in anatase. The balance of recombination and charge transport kinetics determine the collection efficiency of the solar cell, and the results from EIS, IMVS, and IMPS illustrate that each system behaves differently. In order to compare the three systems, it is useful to analyze the diffusion length, Ln, which can be determined from 𝐿! =

𝜏! 𝐷! , where 𝜏! and 𝐷! are the electron lifetime and

electron diffusion coefficient, respectively, obtained from EIS. The value for 𝐷! is determined from the charge transport resistance, Rt, which is obtained from the fit of the impedance spectra !!

(see Figure. S4 in the Supporting Information), using 𝐷! = !

!

26


!!

.

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Figure 9. Diffusion length obtained from EIS measurements versus open circuit voltage for solar cells prepared with anatase (A), brookite from acidic synthesis (BA), and brookite from basic synthesis after acid treatment (BB-ac).

Figure 9 shows the diffusion length for the three materials versus the open circuit voltage, illustrating that for both anatase and acidic brookite, the diffusion length is significantly larger than the film thickness (11 µm) in the entire voltage range. However, the diffusion length for the acid-treated basic brookite solar cell is less than the film thickness. As a consequence, the collection efficiency for the acid-treated basic brookite solar cell is significantly less than 100%, which may explain the lower short circuit current density obtained for this system. !

CONCLUSIONS

We have compared the solar cell performance of three types of TiO2 nanomaterials: anatase, brookite prepared by an acidic synthesis route, and brookite prepared under basic reaction conditions. The solar cell performance of the acidic brookite nanomaterial was very similar to that of the anatase-based solar cell, with a smaller short-circuit current density of 6.6 mA cm-2

27



vs. 9.8 mA cm-2, limited by the light harvesting efficiency and proportional to the amount of dye adsorbed. The brookite-based solar cells show a somewhat larger open circuit voltage of 0.78 V vs. 0.74 V for anatase, illustrating the promise of the material. The basic brookite nanomaterial gave a very low short circuit photocurrent of 0.10 mA cm-2, which increased dramatically to 3.2 mA cm-2 after an acid treatment, illustrating the effect of surface chemistry. A combination of experiments, including BET surface area, dye desorption and photoluminescence spectroscopy, show that the improvement is related to an increase in injection efficiency. A detailed analysis of electrochemical impedance and intensity-modulated photocurrent and photovoltage spectroscopy measurements show that electron transport is faster in the acid-treated basic brookite nanomaterial, related with the larger feature sizes. However, the recombination kinetics are also significantly faster resulting in a smaller diffusion length and, hence, smaller collection efficiency. It can be concluded that the solar cell efficiency is a balance of the light harvesting, electron injection and collection efficiencies, which depend on the crystal structure, morphology, and surface chemistry of the TiO2 nanomaterials. !

ASSOCIATED CONTENT Supporting Information. XRD patterns of powder materials, UV-Vis spectra, EIS

spectra and representative circuit model, chemical capacitance versus total accumulated charges, IMVS and IMPS spectra. !

AUTHOR INFORMATION Corresponding Authors

Dena Pourjafari:E-mail: [email protected] Gerko Oskam: E-mail: [email protected]

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Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

!

ACKNOWLEDGEMENTS

The authors gratefully acknowledge CONACYT, SENER and IER-UNAM for funding through the Mexican Center for Innovation in Solar Energy (CeMIE-Sol), Project P-27. DP acknowledges CONACYT-SENER for a post-doctoral fellowship. This work was partially

supported by Conacyt under Grant No. CB-2012/17850 and by Programa de Mejoramiento al Profesorado (PROMEP) UQROO-PTC-106. We would like to thank Beatriz Heredia Cervera, Leny Pinzón Espinosa, Dora Huerta, and Daniel Aguilar for technical assistance. !

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TOC Graphic

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Scheme 1. Schematic flow chart illustrating the steps in the synthesis pathway of anatase and brookite phase-pure TiO2 nanomaterials. 81x113mm (300 x 300 DPI)


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Figure 1. X-ray diffraction of TiO2 films deposited on FTO: anatase (A), brookite from acidic synthesis (BA), brookite from basic synthesis (BB), and brookite from basic synthesis after acid treatment (BB-ac). The peaks corresponding to the FTO are marked with an asterisk. 82x72mm (300 x 300 DPI)



Figure 2. SEM images of TiO2 films deposited on FTO: (a) anatase (A), (b) brookite from acidic synthesis (BA), (c) brookite from basic synthesis (BB), and (d) brookite from basic synthesis after acid treatment (BBac). 163x28mm (300 x 300 DPI)


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Figure 3. Steady-state photoluminescence (PL) spectra under constant 532 nm excitation illumination for anatase (A), brookite from acidic synthesis (BA), brookite from basic synthesis (BB), and brookite from basic synthesis after acid treatment (BB-ac). The samples consisted of dye-sensitized working electrodes, and the PL intensity is weighted with respect to the quantity of dye adsorbed, as determined by subsequent desorption measurements. 82x62mm (300 x 300 DPI)



Figure 4. J-V curves under 1 sun illumination of anatase (A), brookite from acidic synthesis (BA), brookite from basic synthesis (BB), and brookite from basic synthesis after acid treatment (BB-ac). 89x76mm (300 x 300 DPI)


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Scheme 2. Exponential distribution of trap energies and illustration of the processes of electron accumulation in the traps and the generation of the open circuit photovoltage VOC. 82x90mm (300 x 300 DPI)



Figure 5. Chemical capacitance vs. open circuit voltage for solar cells prepared with anatase (A), brookite from acidic synthesis (BA), and brookite from basic synthesis after acid treatment (BB-ac). 82x65mm (300 x 300 DPI)


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Figure 6. Recombination resistance versus (a) the open circuit voltage for solar cells prepared with anatase (A), brookite from acidic synthesis (BA), and brookite from basic synthesis after acid treatment (BB-ac). 82x65mm (300 x 300 DPI)



Figure 6. Recombination resistance versus (b) the total electron density for solar cells prepared with anatase (A), brookite from acidic synthesis (BA), and brookite from basic synthesis after acid treatment (BB-ac). 82x68mm (300 x 300 DPI)


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Figure 7. Lifetime versus (a) the open circuit voltage for solar cells prepared with anatase (A), brookite from acidic synthesis (BA), and brookite from basic synthesis after acid treatment (BB-ac). The open and solid symbols correspond to the IMVS and EIS results, respectively. 82x68mm (300 x 300 DPI)



Figure 7. Lifetime versus (b) the total electron density for solar cells prepared with anatase (A), brookite from acidic synthesis (BA), and brookite from basic synthesis after acid treatment (BB-ac). The open and solid symbols correspond to the IMVS and EIS results, respectively. 82x68mm (300 x 300 DPI)


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Figure 8. Diffusion coefficient versus light intensity obtained from IMPS measurements under short circuit conditions for solar cells prepared with anatase (A), brookite from acidic synthesis (BA), and brookite from basic synthesis after acid treatment (BB-ac). 82x67mm (300 x 300 DPI)



Figure 9. Diffusion length obtained from EIS measurements versus open circuit voltage for solar cells prepared with anatase (A), brookite from acidic synthesis (BA), and brookite from basic synthesis after acid treatment (BB-ac). 82x71mm (300 x 300 DPI)


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TOC Graphic 84x47mm (300 x 300 DPI)



Figure S1. X-ray diffraction of TiO2 different phases as powder for anatase (A), brookite from acidic synthesis (BA), and brookite from basic synthesis (BB). 82x70mm (300 x 300 DPI)


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Figure S2. UV-Vis spectra of desorbed dye for anatase (A), brookite from acidic synthesis (BA), brookite from basic synthesis (BB), and brookite from basic synthesis after acid treatment (BB-ac). The samples consisted of dye-sensitized working electrodes. 82x67mm (300 x 300 DPI)



Figure S3. UV-Vis spectra (red) and PL spectrum (black) for N719. The inset shows the PL spectrum at 532 nm excitation for ZrO2 films sensitized with N719.

82x65mm (300 x 300 DPI)


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Figure S4. EIS spectra for solar cells prepared with anatase (A), brookite A (BA), and brookite B after acid treatment (BB-ac). 82x68mm (300 x 300 DPI)



The inset shows the equivalent circuit generally used for the interpretation of EIS measurements on DSSCs: Rs is the FTO series resistance; RFTO and CFTO correspond to the substrate not covered by the TiO2 nanoparticles; Rt represents the resistance for electron transport; Rrec is the charge transfer or recombination resistance; Cµ is the chemical capacitance; Zd is the Warburg impedance corresponding to diffusion of the redox species in the electrolytic solution; Rpt stands for the charge transfer resistance; and Cpt for the Helmholtz capacitance at the counter electrode/electrolyte interface. 191x101mm (300 x 300 DPI)


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Figure S5. Chemical capacitance vs. total accumulated charge for solar cells prepared with anatase (A), brookite from acidic synthesis (BA), and brookite from basic synthesis after acid treatment (BB-ac). 218x179mm (300 x 300 DPI)



Figure S6. IMVS spectra for anatase (A), brookite from acidic synthesis (BA), and brookite from basic synthesis after acid treatment (BB-ac).

82x64mm (300 x 300 DPI)


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Figure S7. IMPS spectra for anatase (A), brookite from acidic synthesis (BA), and brookite from basic synthesis after acid treatment (BB-ac).

82x65mm (300 x 300 DPI)


Brookite-Based Dye-Sensitized Solar Cells: Influence of Morphology

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