Ordered Multimodal Porous Carbon as Highly Efficient Counter

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Ordered Multimodal Porous Carbon as Highly Efficient Counter Electrodes in Dye-Sensitized and Quantum-Dot Solar Cells Sheng-Qiang Fan, Baizeng Fang, Jung Ho Kim, Banseok Jeong, Chulwoo Kim, Jong-Sung Yu,* and Jaejung Ko* Department of Advanced Materials Chemistry, Korea University, 208 Seochang, Jochiwon, ChungNam 339-700, Republic of Korea Received May 18, 2010. Revised Manuscript Received July 4, 2010 Ordered multimodal porous carbon (OMPC) was explored as a counter electrode in ruthenium complex dyesensitized solar cells (DSSCs) and CdSe quantum-dot solar cells (QDSCs). The unique structural characteristics such as large surface area and well-developed three-dimensional (3-D) interconnected ordered macropore framework with open mesopores embedded in the macropore walls make the OMPC electrodes have high catalytic activities and fast mass transfer kinetics toward both triiodide/iodide and polysulfide electrolytes. The efficiency (ca. 8.67%) of the OMPC based DSSC is close to that (ca. 9.34%) of the Pt based one. Most importantly, the QDSC employing OMPC material presents a high efficiency of up to 4.36%, which is significantly higher than those of Pt- and activated carbon based solar cells, ca. 2.29% and 3.30%, respectively.

1. Introduction Harvesting energy directly from sunlight using photovoltaic technology is being increasingly recognized as an essential component of future global energy production. Dye-sensitized solar cells (DSSCs) introduced by Gr€atzel and O’Regan1 two decades ago are promising devices for low-cost and large scale solar energy conversion.2,3 Power conversion efficiencies greater than 11% have been reported for DSSCs based on nanoporous TiO2 electrodes, a ruthenium-complex sensitizer (N719), and an triiodide/iodide (I3-/I-) redox system.2 In DSSCs, dye molecules absorb photons and inject excited electrons into the conduction band of a mesoporous TiO2 film where the electrons transfer to a back conducting substrate while the oxidized dye molecules are recharged by I- ions in the electrolyte, which are then regenerated by a Pt deposited counter electrode. Recently, quantum-dot solar cells (QDSCs) employing chalogenide semiconductor nanocrystals such as CdSe and PbS as sensitizers are of great interest due to the potential utilization of hot electrons in such devices and the size quantization effect of the quantum dots (QDs).4-7 The configuration of a QDSC device is similar to that of a DSSC, including a QD-loaded nanoporous TiO2 electrode, a polysulfide electrolyte, and a Pt or Au-sputtered counter electrode. Recorded power conversion efficiencies of ca. 4% for the QDSC have been obtained when applying CdS/CdSe QD multilayers.7 In both DSSCs and QDSCs, the commonly used counter electrode materials, that is, the Pt or Au noble metals, demonstrate fast electrolyte regeneration kinetics and propose high efficiencies of the devices, but their high costs inhibit the large scale applications. Inexpensive and abundant carbon material is a potential (1) O’Regan, B.; Gr€atzel, M. Nature 1991, 353, 737. (2) Nazeeruddin, M. K.; Angelis, F. D.; Fantacci, S.; Selloin, A.; Viscardi, G.; Liska, P.; Ito, S.; Takeru, B.; Gr€atzel, M. J. Am. Chem. Soc. 2005, 127, 16835. (3) Kim, S. H.; Lee, J. K.; Kang, S. O.; Ko, J. J.; Yum, J. H.; Fantacci, S.; Angelis, F. D.; Censo, D. D.; Nazeeruddin, M. K.; Gr€atzel, M. J. Am. Chem. Soc. 2006, 128, 16701. (4) Yu, W. W.; Qu, L. H.; Guo, W. Z.; Peng, X. G. Chem. Mater. 2003, 15, 2854. (5) Lewis, N. S. Science 2007, 315, 798. (6) Kongkanand; Tvrdy, K.; Takechi, K.; Kuno, M.; Kamat, P. V. J. Am. Chem. Soc. 2008, 130, 4007. (7) Lee, Y. L.; Lo, Y. S. Adv. Funct. Mater. 2009, 19, 604.

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alternative to the Pt in DSSCs and even shows increased performance than the Au in QDSCs.8-18 To date, various carbon materials have been investigated as the counter electrode of DSSCs such as graphite,8 carbon nanotubes,9,10 activated carbon,8 carbon black,11 hard carbon spherule,12 nanocarbon,13,14 mesoporous carbon,15 and hollow core/mesoporous carbon.16 On the other hand, power conversion efficiency of the carbon based DSSC is still lower than that of the Pt based one, probably due to a higher charge transfer resistance (Rct) of the carbon counter electrode toward the I3-/I- electrolyte and a retardation of the mass transfer of the electrolyte in the carbon matrix.17 Therefore, the enhancement of Rct for the carbon counter electrode and the improvement of the electrolyte diffusion in the carbon layer require the development of novel carbon materials with superior catalytic activity and highly porous structure. Different from the case of the DSSC, the QDSC with carbon materials presents higher photovoltaic performance than its noble metal based counterpart because of a much lower Rct of the carbon counter electrode toward the polysulfide electrolyte, particularly ca. 12 Ω cm2 for the hollow core/mesoporous carbon compared with ca. 80 Ω cm2 for the Pt.18 However, an ideal Rct of the QDSC counter electrode toward polysulfide electrolyte is expected to be lower than 1 Ω cm2 for (8) Imoto, K.; Takahashi, K.; Yamaguchi, T.; Komura, T.; Nakamura, J.; Murata, K. Sol. Energy Mater. Sol. Cells 2003, 79, 459. (9) Jang, S.-R.; Vittal, R.; Kim, K. Langmuir 2004, 20, 9807. (10) Lee, W. J.; Ramasamy, E.; Lee, D.-Y; Song, J.-S. ACS Appl. Mater. Interfaces 2009, 1, 1145. (11) Murakami, T. N.; Ito, S.; Wang, Q.; Nazeeruddin, M. K.; Bessho, T.; Cesar, I.; Liska, P.; Humphry-Baker, R.; Comte, P.; Pechy, P.; Gr€atzel, M. J. Electrochem. Soc. 2006, 153, A2255. (12) Huang, Z.; Liu, X.; Li, K.; Li, D.; Luo, Y.; Li, H.; Song, W.; Chen, L.; Meng, Q. Electrochem. Commun. 2007, 9, 596. (13) Lee, W.-J.; Ramasamy, E.; Lee, D.-Y.; Song, J.-S. Sol. Energy Mater. Sol. Cells 2008, 92, 814. (14) Ramasamy, E.; Lee, W.-J.; Lee, D.-Y.; Song, J.-S. Appl. Phys. Lett. 2007, 90, 173103. (15) Wang, G.; Xing, W.; Zhuo, S. J. Power Sources 2009, 194, 568. (16) Fang, B.; Fan, S.-Q.; Kim, J. H.; Kim, M.-S.; Kim, M.; Chaudhari, N. K.; Ko, J.; Yu, J.-S. Langmuir 2010, 26, 11238. (17) Nam, J. G.; Park, Y. J.; Kim, B. S.; Lee, J. S. Scr. Mater. 2010, 62, 148. (18) Fan, S.-Q.; Fang, B.; Kim, J. H.; Kim, J.-J.; Yu, J.-S.; Ko, J. Appl. Phys. Lett. 2010, 96, 063501.

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optimal output performance, as required in a DSSC. For this purpose, ordered multimodal porous carbon (OMPC) having a unique nanostructure was explored as counter electrodes in I3-/Ibased DSSCs and polysulfide based QDSCs in this study. Interestingly and significantly, OMPC demonstrates very low Rct toward both electrolytes, yielding a very close performance of OMPC based DSSC to the Pt counterpart and a superior power conversion efficiency of QDSC to the Pt and activated carbon counterparts.

2. Experimental Section 2.1. Fabrication and Characterization of OMPC. The OMPC was fabricated through inverse nanocasting of ordered hierarchical nanostructured silica (OHNS) as described previously.19,20 In detail, the OHNS was synthesized using monodisperse polystyrene (PS) spheres as a template with colloidal dispersion of small silica particles as follows. First, monodisperse PS spheres were mixed with a colloidal dispersion of much smaller silica particles. Upon gradual drying of the mixture, the PS spheres self-assemble themselves into an ordered lattice where the meso-sized smaller silica particles are forced to pack closely at the interstices between the PS spheres, which leads to the generation of particulate silica gels around the ordered PS lattice. Next, the resulting composite was slowly heated to 500 °C and kept for 6 h under air to remove the PS colloids and to sinter the silica nanoparticles at their contact points, which resulted in rigid OHNS composed of particulate silica gels in the wall of the ordered macropore array. Interestingly, the voids between the sintered silica particles in the resulting OHNS also provide fully interconnected mesopores. OMPC was synthesized using the OHNS as a sacrificial template and furfurylalcohol (FFA) as a carbon precursor. The OHNS was dried at 70 °C for 4 h prior to the impregnation with FFA. During the impregnation period, FFA was adsorbed into the mesopore voids between silica particles of the OHNS through the capillary effect. Oxalic acid was added as an acidic catalyst. OMPC was obtained after carbonization of the carbon precursor and subsequent dissolution of the OHNS framework. The removal of the meso-sized silica particles in the carbon/OHNS composite resulted in corresponding mesopores embedded in the carbon wall in addition to the macropores generated by removal of the PS particles. The as-produced OMPC was characterized through measuring the N2 adsorption and desorption isotherms at 77 K on a KICT SPA-3000 gas adsorption analyzer after the carbon was degassed at 423 K to 20 μTorr for 12 h. The specific surface area was determined from nitrogen adsorption using the BrunauerEmmett-Teller (BET) equation. Total pore volume was determined from the amount of gas adsorbed at the relative pressure of 0.99. Micropore volume was calculated from the analysis of the adsorption isotherm using the Horvath-Kawazoe method. Pore size distribution (PSD) was derived from the analysis of the adsorption branch using the Barrett-Joyner-Halenda (BJH) method. Scanning electron microscopy (SEM) images were obtained using a Hitachi S-4700 microscope operated at an acceleration voltage of 10 kV, and transmission electron microscopy (TEM) was conducted on an EM 912 Omega instrument at 120 kV. 2.2. Electrode Preparation. The OMPC counter electrodes for both DSSCs and QDSCs were fabricated as follows. First, 100 mg of OMPC was dispersed in 10 mL of ethanol and ultrasonicated for 30 min followed by overnight magnetic stirring. Then the carbon colloidal dispersion was coated onto a FTO glass substrate with a carbon loading of ca. 120 μg cm-2 by using a doctor blade. Finally, the electrodes were heat-treated at 400 °C in air for 5 min by using a hot-wind gun (Leister CH6060 Sarnen, Switzerland). For comparison, activated carbon (Duksan Pharm. (19) Chai, G. S.; Shin, I. S.; Yu, J. -S. Adv. Mater. 2004, 16, 2057. (20) Fang, B.; Kim, J. H.; Kim, M.-S.; Yu, J.-S. Chem. Mater. 2009, 21, 789.

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Co., Korea) counter electrodes with a loading of ca. 120 μg cm-2 on FTO glass were fabricated by the same procedures. Pt counter electrodes with an optimized Pt loading of ca. 50 μg cm-2 on FTO glass were prepared according to a previous method.3 The dye-sensitized TiO2 electrodes for DSSCs were prepared as reported elsewhere.3 Typically, first, TiO2 films of 10 μm in thickness were fabricated on FTO glass plates by using a doctor blade printing TiO2 paste (Solaronix, Ti-Nanoxide T/SP). Scattering layers were deposited by doctor blade printing a paste containing 400 nm sized anatase particles (CCIC, PST-400C). After being sintered at 500 °C for 30 min, the films were treated with 40 mM TiCl4 aqueous solution followed by heat treatment at 500 °C for 30 min. TiO2 electrodes were fabricated by immersing TiO2 films into a N719 (Solaronix) ethanol solution (0.3 mM) at room temperature for 24 h. The CdSe QD electrodes for QDSC were fabricated according to the protocol developed by our group,21 which included a process of assembling 3.5 nm sized CdSe QDs onto a mesoporous TiO2 matrix followed by chemical bath seedgrowing, ZnS coating, and postsintering at 400 °C. 2.3. Cell Configuration and Photovoltaic Tests. The DSSC was prepared by assembling the dye-adsorbed TiO2 electrode (surface area: ca. 0.2 cm2) and the counter electrode (surface area: ca. 0.2 cm2) into a sealed sandwich-type cell, which were separated by using a 50 μm thick hot-melt ionomer film (Surlyn) as a spacer. The I3-/I- electrolyte contained 0.6 M 1,2-dimethyl3-n-propylimidazolium iodide (DMPII), 0.05 M I2, 0.1 M LiI, and 0.5 M 4-tert-butylpyridine in acetonitrile. The QDSC was a similar sandwich-type with the as-prepared QD-sensitized electrodes and the counter electrodes separated by a 50 μm thick Surlyn film. The electrolyte was a polysulfide containing 0.5 M Na2S, 0.5 M sulfur, and 0.1 M KCl in the mixed solution of methanol and H2O (7:3 in volume ratio). Electrochemical impedance spectroscopy (EIS) measurements were conducted with an impedance analyzer (Parstat 2273, Princeton) at zero bias potential and 10 mV of amplitude over the frequency range of 0.1 Hz to 100 kHz at a constant temperature of 20 °C. A sandwich cell consisting of two identical electrodes (0.5 cm2), a spacer of 100 μm thick Surlyn film, and a polysulfide electrolyte was used in the EIS measurements. The measurements of J-V curves of the solar cells conducted at 20 °C can be seen in detail elsewhere.3

3. Results and Discussion Figure 1 shows the typical SEM and TEM images of the asproduced OMPC. They reveal a unique multimodal porous carbon framework with highly ordered hierarchical nanostructure. The macropores are a highly ordered hexagonal array with a diameter of approximately 440 ( 10 nm and are interconnected through small pores (i.e., connecting pores) of approximately 100 ( 10 nm, and the mesopores in the wall are approximately 20 ( 3 nm. The nitrogen adsorption-desorption isotherms of the OMPC are shown in Figure 2, which are of type IV with a H2 hysteresis according to the IUPAC classification, corresponding to framework mesopores. The pore size was estimated from the PSD maximum as approximately 20 nm. The OMPC exhibits a large BET surface area of 1023 m2 g-1 and a total pore volume of 1.87 cm3 g-1, mainly attributable to the presence of the mesopores in the framework (mesopore volume: 1.65 cm3 g-1). As a reference, the activated carbon is mainly composed of micropores of less than 2 nm and the BET surface area is ca. 1084 m2 g-1.18 Featured structural characteristics such as ordered hierachiacal nanostructure with uniform pore sizes were not observed for the activated carbon. Instead, carbon particles with uneven particle sizes agglomerate (21) Fan, S.-Q.; Kim, D.; Kim, J.-J.; Jung, D. W.; Kang, S. O.; Ko, J. Electrochem. Commun. 2009, 11, 1337.

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Figure 3. Electrochemical cell used for EIS measurements (a), equivalent circuit (b), and typical Nyquist plot (c). Figure 1. Typical SEM (a) and TEM (b) images of OMPC.

Figure 2. Nitrogen adsorption-desorption isotherms at 77 K and derived PSD for the OMPC.

heavily together. The large surface area and particularly the unique ordered hierarchical nanostructure for the OMPC material were expected to lower the resistances of charge transfer and electrolyte diffusion, which are determining factors that influence the solar cell performance. To compare the resistances existing in the counter electrode and the electrolyte, EIS spectra were measured with the sandwichtype electrochemical cells (shown in Figure 3a) comprising two (22) Kim, S.-S.; Nah, Y.-C.; Noh, Y.-Y.; Jo, J.; Kim, D.-Y. Electrochim. Acta 2006, 51, 3814.

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identical carbon (or Pt) electrodes.22 Figure 3b shows the equivalent circuit for this type of cell, where Rh is the ohmic serial resistance mainly related to the FTO glass, Rct is the charge transfer resistance, Cdl is the capacitance of electrical double layer, and Zw is the Nernst diffusion impedance of the electrolyte. As shown in Figure 3c, Rh can be determined by the impedance at high frequency of around 100 kHz, while Rct and Zw are derived from the semicircles in the high and low frequency ranges, respectively, through fitting the plots with Z-VIEW software. Figure 4a shows typical Nyquist plots for the Pt, OMPC, and activated carbon counter electrodes toward the I3-/I- electrolyte. From the inset, which shows the semicircles in the high frequency range, the Rct is determined for various counter electrodes and is summarized in Table 1 where other parameters derived from the plot fitting by using the equivalent circuit shown in Figure 3b such as equivalent series resistance (Rh), double layer capacitance (Cdl), and Zw are also listed. It is found that the Rh values are at the same level for the various counter electrode materials while a large difference was observed in the Cdl values; namely, the carboncoated electrodes exhibit much larger (ca. 2-5 times) Cdl values than that of the Pt electrode, even though the Cdl values were calculated based on their specific surface areas. Although the increased Cdl values probably suggest larger electrochemically active areas for the carbon-coated electrodes, it is still somewhat difficult for scientists to correlate quantitatively the Cdl values with the electrochemically active areas. In contrast, the other two parameters Rct and ZW have been frequently used by scientists to evaluate the influence of the electrode materials on the performance of the solar cells.18,22 Evidently, the Rct values of the OMPC and activated carbon electrode, ca. 0.4 and 0.6 Ω cm2, respectively, are very close to that Langmuir 2010, 26(16), 13644–13649

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Figure 4. Nyquist plots of Pt, OMPC, and activated carbon electrodes toward I3-/I- (a) and polysulfide electrolytes (b). Table 1. Rh, Rct, Zw, and Cdl Values of the Pt, OMPC, and Activated Carbon Based Counter Electrodes toward the I3-/Iand Polysulfide Electrolytes electrolyte

counter electrode

I3-/II3-/II3-/Ipolysulfide polysulfide polysulfide

Pt OMPC activated carbon Pt OMPC activated carbon

Rh Rct Zw Cdl (Ω cm2) (Ω cm2) (Ω cm2) (μF cm-2) 7.3 7.4 7.2 6.4 6.7 6.3

0.5 0.4 0.6 96.4 3.5 36.9

2.1 3.3 9.8 14.1 36.9

10.3 17.7 23.6 3.5 17.8 4.9

of the Pt one, ca. 0.5 Ω cm2. It suggests that the two carbon materials have similarly high electrocatalytic activities compared with the Pt toward the same I3-/I- electrolyte, which are likely due to the high specific surface area of the carbon materials. On the other hand, the Zw of these three electrodes, which are determined from the semicircle in the low frequency range in Figure 4a and summarized in Table 1, are significantly different. The much higher Zw (ca. 9.8 Ω cm2) for the activated carbon electrode implies a much higher resistance for the I3-/I- electrolyte diffusing in the activated carbon layer, which probably resulted from the small-sized micropores and the irregular pore structure of the activated carbon material. In comparison, the OMPC electrode shows decreased Zw, ca. 3.3 Ω cm2, which is close to that of the Pt, ca. 2.1 Ω cm2. The low Zw of the OMPC electrode indicates an improved electrolyte diffusion capability in the OMPC layer, which is likely attributed to the unique ordered hierarchical nanostructure of the OMPC, namely, the multimodal structure consisting of macropores, connecting pores, and mesopores. From Figure 4b, Rct and Zw of the Pt, OMPC, and activated carbon electrodes toward the polysulfide electrolyte are determined and are listed in Table 1. Pt and activated carbon materials Langmuir 2010, 26(16), 13644–13649

Figure 5. J-V curves of DSSCs (a) and QDSCs (b) based on the Pt, OMPC, and activated carbon counter electrodes.

present high Rct values of several tens of Ω cm2, implying much lower electrochemical catalytic activity toward the polysulfide electrolyte, which is consistent with the reported results.18 Interestingly and importantly, the OMPC electrode presents significantly decreased Rct, ca. 3.5 Ω cm2. Such low Rct in the OMPC is even less than that of the other hierarchiacal porous carbon materials, that is, hollow core/mesoporous shell carbon (HCMSC) toward the same polysulfide electrolyte,18 indicating that the OMPC material is very promising to improve the photovoltaic performance of the QDSC further. The highly enhanced electrochemical catalytic activity of the OMPC material compared with the activated carbon is mainly related to its multimodal porous nanostructure. In addition, Zw of the OMPC electrode decreased to 14.1 Ω cm2 compared with that (ca. 36.9 Ω cm2) of the activated carbon electrode, demonstrating that the particularly ordered porous structure of the OMPC material provides the electrode with a much faster transfer kinetic of polysulfide electrolyte. From Table 1, it is also interesting to note that the Rct values of various carbon materials, that is, the OMPC and activated carbon, toward I3-/I- electrolyte are almost the same (i.e., ca. 0.4 and 0.6 Ω cm2, respectively) and much smaller compared with their Rct values determined in a polysulfide electrolyte. In addition, it is further found that OMPC demonstrates a Rct value of ca. 3.5 Ω cm2 which is much smaller compared with activated carbon in a polysulfide electrolyte. The small and close Rct values observed in I3-/I- electrolyte suggest that these carbon materials are highly efficient (i.e., catalytically active) and comparable to Pt when they are used as the counter electrode in a DSSC probably due to their large specific surface areas. Due to their DOI: 10.1021/la1019873

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Fan et al. Table 2. Photovoltaic Parameters of DSSCs and QDSCs Based on Pt, OMPC, and Activated Carbon Counter Electrodes

solar cell

counter electrode

Jsc (mA cm-2)

Voc (V)

FF

η (%)

DSSC DSSC DSSC QDSC QDSC QDSC

Pt OMPC activated carbon Pt OMPC activated carbon

17.16 ( 0.4 16.86 ( 0.2 15.92 ( 0.4 11.65 ( 0.4 12.34 ( 0.3 11.85 ( 0.3

0.74 ( 0.02 0.75 ( 0.02 0.75 ( 0.01 0.59 ( 0.02 0.63 ( 0.01 0.61 ( 0.02

0.73 ( 0.01 0.69 ( 0.01 0.65 ( 0.02 0.33 ( 0.04 0.56 ( 0.01 0.46 ( 0.03

9.34 ( 0.3 8.67 ( 0.3 7.65 ( 0.2 2.29 ( 0.2 4.36 ( 0.2 3.30 ( 0.3

small values which are close to the limiting value (i.e., 0 Ω cm2) of Rct, the difference in catalytic activity for the OMPC and activated carbon is somewhat difficult to be exactly and clearly observed. These Zw values of the both carbon electrodes are significantly different, and a much smaller value (ca. 3.3 Ω cm2) is observed for the OMPC compared with that (ca. 9.8 Ω cm2) for the activated carbon electrode, implying a much smaller resistance for the I3-/I- electrolyte diffusing in the OMPC layer due to its fantastic hierarchical nanostructure of OMPC. As for a polysulfide electrolyte, much higher Rct values were observed compared with I3-/I- electrolyte, suggesting that the former is less sensitive (i.e., electrochemically active) for all the employed counter electrodes. In such a system, an electrode material with high catalytic activity is highly desirable. As evident from the Rct and Zw values, the OMPC not only facilitates faster mass transport but also possesses higher catalytic activity toward the electrolyte. Enhanced catalytic activity is probably related to its multimodal porous nanostructure of the OMPC, which deserves further study. The enhancement in the mass transfer is expected to improve the photovoltaic performance in DSSCs by increasing the fill factor (FF) of the solar cell and the short-circuit current density (Jsc). Figure 5a presents the J-V curves of the DSSCs using various counter electrode materials. For clarity, the derived photovoltaic parameters are summarized in Table 2. Although the efficiency of the OMPC cell (ca. 8.67%) is a slightly lower than that of the Pt one (9.34%), it is obviously higher than that of the activated carbon based cell (ca. 7.65%). The improved efficiency for the OMPC in comparison with the activated carbon is mainly attributed to the enhancement in the FF and the Jsc. As for the QDSC, improved solar cell performance (Figure 5b) is clearly observed for the OMPC counter electrode compared with the activated carbon and Pt ones. A high efficiency of up to 4.36% (Table 2) was obtained, resulting from a slight increase in the JSC and a significant improvement in the FF (ca. 0.56 for the OMPC compared with ca. 0.33 and ca. 0.46 for the Pt and activated carbon, respectively). The high FF of the OMPC based DSSC and QDSC, which makes the solar cells highly efficient, should be mainly attributed to the low Rct and Zw of the OMPC counter electrodes, as evident from the EIS-derived data shown in Table 1. The two parameters, Rct and Zw, can influence the solar cell performance through increasing the total series resistance (Rs) of the cell by the equation Rs = Rh þ Rct þ Zw, where Rh is mainly related to the sheet resistance of the FTO glass.23,24 The corresponding J-V curves of the photoelectrochemical cells including DSSC and QDSC are well fitted with the diode equation given below, "  #  V þ JRs V þ JRs -1 ð1Þ I ¼ Iph - I0 exp q nkT Rsh

(23) Han, L.; Koide, N.; Chiba, Y.; Mitate, T. Appl. Phys. Lett. 2004, 84, 2433. (24) Murayama, M.; Mori, T. Jpn. J. Appl. Phys. 2006, 45(1B), 542.

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Figure 6. Theoretical J-V curves simulated from the diode equation at different Rs values.

where Iph is the photo current, I0 is the initial current, Rsh is the parallel (shunt) resistance, n is the diode factor, q is the elementary electric charge, k is the Boltzmann constant, and T is temperature. The diode equation describes a theoretical relationship between the Rs value and the shape of the J-V curve. When Rsh is 2000 Ω cm2, and other parameters in the diode equation employ the values reported in previous papers,23,24 the derived J-V curves with different given Rs values can be drawn. The typical Rsdependent J-V curves are demonstrated in Figure 6. It is clear that Rs influences greatly the deviation of the area below the J-V curve from a rectangle, which represents the FF of the solar cell. With a larger Rs, the FF becomes lower. When Rs is increased further, that is, up to 90 Ω cm2, both the FF and Jsc drop dramatically. This theoretical effect of the Rs on the solar cell performance is well consistent with the experimental results shown in Figure 5. In this point of view, it is deduced that the decrease of the total Rs is beneficial to the improvement of the efficiency for an actual solar cell. Therefore, it is reasonable that the high efficient solar cells employing the OMPC material, particularly the QDSC, is ascribed to the low Rs, particularly the low Rct and Zw of the OMPC counter electrodes. To obtain low-resistance carbon counter electrodes with improved electrochemical catalytic activity and fast electrolyte diffusion rate, novel carbon materials with particular nanostructure and high specific surface area as well as ordered stacking form of carbon particles in the carbon electrode are required.17 In this study, both the OMPC and the activated carbon materials have similar specific surface area, ca. 1023 and 1084 m2/g, respectively. According to the roughly optimized loading amounts of ca. 120 μg cm-2 for the two carbon counter electrodes, the roughness factors of the two counter electrodes were calculated up to 1227 for the OMPC electrodes and 1301 for the activated carbon ones. Evidently, the two carbon electrodes present very close roughness factors, while the OMPC one demonstrates lower Rct and Zw, particularly toward the polysulfide electrolyte, as shown in Table 1. The lower resistances of the OMPC are probably due Langmuir 2010, 26(16), 13644–13649

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to its unique structural characteristics such as the interconnected multimodal pore framework consisting of larger macropores, smaller connecting pores, and mesopores, as shown in Figure 1. This featured structure-property relationship of the OMPC is similar to that of the HCMSC whose bimodal pore structure endowed its electrode with high catalytic activity.18 Interestingly, the OMPC used in this study demonstrates a significantly lower Rct of ca. 3.5 Ω cm2 than that (ca. 12 Ω cm2) of the HCMSC toward the same polysulfide electrolyte and presents a higher FF and thus a higher efficiency of ca. 4.36% than that (ca. 3.90%) of the HCMSC.18 The high performance of the OMPC electrode reflects the favorable porous nanostructure of such a material. The larger macropore arrays and the interconnected smaller macropores of the OMPC provide an open highway network for fast mass transport. In addition, the large volume mesopore channels in the wall serve as local pathways for efficient diffusion of the reactants and products. The effect of the multimodal pore network in the OMPC on electron transfer and electrolyte diffusion kinetics is expected for the design of more efficient carbon electrodes and solar cells.

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4. Conclusions It has been demonstrated that the OMPC electrode presented a similar Rct toward the I3-/I- electrolyte and an exponentially decreased Rct toward the polysulfide electrolyte compared with those of the conventional Pt and activated carbon ones. Such a superb characteristic is likely related to the well-developed 3-D interconnected ordered multimodal pore structure, which simultaneously results in a low resistance for the electrolyte diffusion and electron transfer. The investigation on the efficiencies of DSSC and QDSC proved that the OMPC is very interesting and of particular significance not only because of the great improvement in the performance of QDSCs but also due to the expected considerable decrease in the cost of fabricating DSSCs. A detailed understanding of the relationship between the carbon porous nanostructure and the electron transfer and electrolyte diffusion needs further investigation through other advanced technologies. Acknowledgment. This work was supported by the WCU (the Ministry of Education and Science) program (No. R31-2008-00010035-0). Special thanks are given to KBSI at Jeonju, Daejon and Chunchoen for SEM and TEM measurements.

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