Dependence of Photocurrent and Conversion Efficiency of Titania

Feb 23, 2008 - Biotechnology, Ritsumeikan UniVersity, Kusatsu, Shiga 528-8577, Japan. ReceiVed: NoVember 3, 2007; In Final Form: January 13, 2008...
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J. Phys. Chem. C 2008, 112, 4418-4426

Dependence of Photocurrent and Conversion Efficiency of Titania-Based Solar Cell on the Qy Absorption and One Electron-Oxidation Potential of Pheophorbide Sensitizer Xiao-Feng Wang,† Yasushi Koyama,*,† Hiroyoshi Nagae,‡ Yuji Wada,§ Shin-ichi Sasaki,|,X and Hitoshi Tamiaki|| Department of Chemistry, Faculty of Science and Technology, Kwansei Gakuin UniVersity, 2-1 Gakuen, Sanda, Hyogo 669-1337, Japan, Kobe City UniVersity of Foreign Studies, Gakuen Higashimachi, Nishiku, Kobe 651-2187, Japan, Department of Applied Chemistry, Tokyo Institute of Technology, Oh-okayama 2-12-1-S1-43, Meguro-ku, Tokyo 152-8552, Japan, and Department of Bioscience and Biotechnology, Ritsumeikan UniVersity, Kusatsu, Shiga 528-8577, Japan ReceiVed: NoVember 3, 2007; In Final Form: January 13, 2008

Titania-based solar cells were fabricated by the use of six pheophorbide sensitizers having bacteriochlorin, chlorin, and porphyrin macrocycles, to which the carboxyl or allylcarboxyl group is directly attached for binding and electron injection to TiO2. Because of structural similarity, these sensitizers are expected to have similar physical properties except for electronic-absorption and redox properties: Concerning the former, the state energies, molar extinction coefficients (), oscillator strengths ( f ), and transition-dipole moments (µ) of the Soret and Qy absorptions were determined, whereas concerning the latter, one electron-oxidation potential (Eox). Alternatively, the performance of pheophorbide-sensitized solar cells, including the incident photonto-current conversion efficiency (IPCE), short-circuit current density (Jsc), open-circuit voltage (Voc), and solar energy-to-electricity conversion efficiency (η) was determined. It was found that the Jsc and η values increased with the increasing Qy absorption and with the decreasing one electron-oxidation potential (in other words, with the increasing electron-ejection potential). To explain the clear and strong dependence, we built possible models for the pheophorbide-to-TiO2 electron injection and tried to fit the Jsc value in terms of the Qy absorption and the Eox value by the use of empirical equations. After a number of fitting trials, two successful models of reasonable fitting emerged: One, a model of parallel electron injection, that is, electron injection upon Qy excitation and redox electron transfer in the ground state, and the other, a model of electron injection simply via the excited state, in which both the Qy absorption and the Qy-state one electron-oxidation potential can contribute. These models as well as the future strategies in revealing the real mechanism of electron injection are discussed.

1. Introduction This is in a series of investigations to develop Gra¨tzel-type dye-sensitized solar cells (DSSCs) using chlorophylls (Chls) and their derivatives.1-5 In the photosynthetic systems, Chls initiate electron-transfer reactions along the redox components in the photoreaction center following charge separation at the special pair. Also, Chls play the light-harvesting function, which includes the absorption of light energy followed by singletenergy transfer from the antenna complexes eventually to the photoreaction center. Therefore, Chls are one of the most promising candidates to be used in fabricating DSSCs. The π-conjugated systems of Chls include bacteriochlorin, chlorin, and porphyrin macrocycles; the desaturation of the macrocycle proceeds in this order. In most cases, the naming of Chls and bacteriochlorophylls (BChls) is based not on the structure of macrocycles but on the kind of organisms they are extracted from.6 The history in the incorporation of chlorophyll * To whom correspondence should be addressed. E-mail: ykoyama@ kwansei.ac.jp. Fax: +81-79-565-8408. † Kwansei Gakuin University. ‡ Kobe City University for Foreign Studies. § Tokyo Institute of Technology. | Ritsumeikan University. X Present address: Nagahama Institute of Bio-Science and Technology, Nagahama, Shiga 526-0829, Japan.

and porphyrin derivatives into DSSCs as dye sensitizers, taking advantage of their remarkably high potentials of light harvesting and electron ejection, can be summarized as follows: (1) As a pioneering work in the usage of Chl derivatives and related porphyrins, Kay and Gra¨tzel7 found that those compounds containing copper as the central metal gave rise to the highest incident photon-to-current conversion efficiencies (IPCEs): Cu mesoporphyrin IX exhibited an IPCE value as high as 83% at the Soret absorption, that is, a unit quantum yield of charge separation when the loss of light by reflection and scattering was taken into account, while Cu chlorophyllin gave rise to performance with a short-circuit photocurrent density (Jsc) of 9.4 mA‚cm-2, open-circuit photovoltage (Voc) of 0.52 V, and a solar energy-to-electricity conversion efficiency (hereafter, abbreviated as “conversion efficiency”, η) of 2.6%. (2) A comparison between the porphyrin and ruthenium bipyridyl dye sensitizers was made by Tachibana et al.8 concerning the electron-injection and charge-recombination dynamics. Interestingly, they found that large difference in the photophysics and redox chemistry of these dyes gave rise to rather little influence on the interfacial electron-transfer kinetics, when they were adsorbed onto TiO2 nanocrystals. (3) It was shown by Nazeeruddin et al.9 that Zn porphyrins exhibit much better performance than Cu porphyrins. Among tetraphenyl porphyrin-type com-

10.1021/jp710580h CCC: $40.75 © 2008 American Chemical Society Published on Web 02/23/2008

Dependence of Photocurrent and Conversion Efficiency

Figure 1. Chemical structures of pheophorbide sensitizers used in the present investigation. The arrows indicate the direction of Qy transitiondipole moment.

J. Phys. Chem. C, Vol. 112, No. 11, 2008 4419 showed that this type of molecular structure is not always necessary to obtain a high performance. We are going to compare the performance of these DSSCs, including their IPCE, Jsc, and η values, by the measurement of the IPCE profiles and the I-V curves. Thus, a first question we have addressed in the present investigation is the following: Which pheophorbide sensitizer gives rise to the best performance, including photocurrent and conversion efficiency? We tried to collect a complete set of data concerning the electronic-absorption and redox properties of these pheophorbides. We determined the state energies, molar extinction coefficients, transition-dipole moments of the Soret and Qy absorptions, and the one electron-oxidation potentials. Then, we addressed a second question: Which molecular parameters of the pheophorbide sensitizers correlate with the above parameters showing the performance of DSSCs? We actually identified the dependence of photocurrent of DSSC not only on the Qy absorption but also on the one electron-oxidation potential of pheophorbide sensitizer. Finally, we have addressed a third question: What is the mechanism by which these physical parameters determine the performance of DSSC? 2. Experimental Section

pounds tested, tetraxylporphyrinato Zn(II) ethenyl benzonic acid (“compound 2”) showed the best performance, that is, Jsc ) 9.7 mA‚cm-2, Voc ) 0.66 V, and η ) 4.8%. (4) The performance of a wide variety of porphyrins was compared, and its structural dependence was analyzed by Campbell et al.10 The above compound turned out to be the best. (5) A series of Zn tetraphenyl porphyrins having a conjugated peripheral chain having the carboxyl end was synthesized, their electronicabsorption and redox properties were determined, and their performance as dye sensitizers was examined.11 The solar cell sensitized by Zn tetraphenylporphyrinatocyanoacrylic acid (“Zn3”) yielded the following remarkable performance: the maximum IPCE ) 85%, Jsc ) 13.0 ( 0.5 mA‚cm-2, Voc ) 0.61 ( 0.05 V, and η ) 5.6%. This is the most efficient porphyrin-sensitized solar cell reported to date. (6) The effects of the central metal in this methylphenyl-carboxyphenyl porphyrin on the photocurrent generation were examined:12 The photocurrent yield, that is, the charge-injection yield (Φinj) multiplied by the charge-collection efficiency (ηc), increased when the one electron-oxidation potential (Eox) was increased, which was ascribed to the suppression of the reverse electron transfer from TiO2 to the porphyrin sensitizer. (7) Most recently, a DSSC that we fabricated by the use of Chl c2 exhibited a performance, that is, Jsc ) 13.7 mA‚cm-2, Voc ) 0.57 V, and η ) 4.6%.5 (8) Dr. Nazeeruddin tested our Phe a sensitizer that is used in the present investigation and obtained Jsc ) 14.4 mA‚cm-2, Voc ) 0.5 V, and η ) 5.1% (personal communication); the performance of this pheophorbide sensitizer is much higher than that of DSSC we fabricated (3.1%);1 the conversion efficiency (η ) 5.1%) is approaching the best porphyrin sensitizer mentioned above (η ) 5.6%).11 In the present investigation, we have fabricated DSSCs by the use of a set of pheophorbide sensitizers, which include one having the bacteriochlorin skeleton, three having the chlorin skeleton, and two having the porphyrin skeleton (see Figure 1). The sensitizers include the derivatives of pheophorbides and intact pheophorbides c1 and c2; we call them “pheophorbides (Phe)” collectively. We used such pheophorbides that contain a carboxyl group directly attached to the conjugated macrocycle at different positions to facilitate the binding and electron injection of the sensitizer to TiO2, although Kay and Gra¨tzel7

2.1. Preparation of Chlorophyll and Bacteriochlorophyll Derivatives. 3,7,8-Carboxy derivatives were prepared by oxidation of the formyl group in the corresponding methyl (bacterio)pyropheophorbides: Methyl 3-devinyl-3-carboxy-pyropheophorbide a (Phe a), methyl 7-deformyl-7-carboxy-pyropheophorbide b (Phe b), and 3-deacetyl-3-carboxy-bacteriopyropheophorbide a (BPhe a) were prepared as reported previously.13 3-Devinyl3-ethyl-8-deethyl-8-carboxy-pyropheophorbide a (Phe x) was prepared as described in Section S-1 of the Supporting Information. Pheophorbide c1 (Phe c1) and pheophorbide c2 (Phe c2) were prepared as follows by the removal of the central Mg atom from chlorophylls c1 and c2, whose isolation procedure has been described elsewhere.5 Chl c1 or c2 was dissolved into pyridine and diluted with chloroform (1:4). The pigment solution and 5% aqueous HCl solution were mixed and rigorously shaken in a separation funnel for the demetallation reaction. After a while, the lower chloroform layer containing pheophorbide was collected and washed with distilled water three times. Phe c1 or c2 was purified further by the use of the polyethylene column (MW ) 4 × 106 Da, particle size 59 µm, provided by Asahi Kasei, Okayama Prefecture, Japan) and an eluent, 10% pyridine in acetone. 2.2. Fabrication of DSSCs and Measurements of Their Performance. DSSCs using pheophorbide sensitizers were fabricated, and their performance was determined by the measurement of the IPCE profiles and the I-V curves as described previously.1 3. Results 3.1. Characterization of Pheophorbide Sensitizers. 3.1.1. Molecular Structures. Figure 1 shows the chemical structures of six different types of pheophorbides that were used in the present investigation. They can be characterized as follows: BPhe a consists of the bacteriochlorin skeleton having a carboxyl group at position C3 on ring A. Phe a consists of the chlorin skeleton with a carboxyl group at the same position. The structures of BPhe a and Phe a are the same except for the C7 to C8 chemical bond of ring B, which is saturated in the former and unsaturated in the latter. (We previously called Phe a “PPB

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TABLE 1: Electronic-Absorption and Redox Parameters of Pheophorbide Sensitizers: Parameters Include Molar Extinction Coefficients (E), Oscillator Strengths ( f ), Transition Dipole Moments (µ), and One Electron-Oxidation Potentials (Eox) /cm-1M-1

µ/debye

f

sensitizer

Soret

Qy

Soret

Qy

Soret

Qy

Eox vs NHE/V

BPhe a Phe a Phe x Phe b Phe c1 Phe c2

53 000 (0.64) 83 000 (1) a 166 000 (2) 156 000 (1.88) 148 000 (1.78) 130 000 (1.57)

32 000 (0.57) 56 000 (1) a 47 000 (0.84) 36 000 (0.64) 12 700 (0.23) 10 200 (0.18)

0.70 (0.39) 1.80 (1) a 2.84 (1.58) 3.23 (1.79) 4.39 (2.44) 3.47 (1.93)

0.45 (0.45) 0.99 (1) a 0.56 (0.57) 0.50 (0.51) 0.17 (0.17) 0.12 (0.12)

7.3 (0.58) 12.6 (1) a 16.1 (1.27) 17.2 (1.37) 20.1 (1.60) 17.9 (1.42)

8.5 (0.71) 12.0 (1) a 8.9 (0.74) 8.4 (0.70) 4.5 (0.38) 3.8 (0.32)

0.92 1.18 1.20 1.24 1.30 1.33

a

Relative values when the value of Phe a is normalized.

TABLE 2: Electronic Absorption of Pheophorbide Sensitizers Bound to TiO2 Layer and Performance of PheophorbideSensitized Solar Cells: The Former Include Integrated Qy and Overall Absorptions and the Latter Include Integrated IPCE (∫IPCEdνj), Short-Circuit Photocurrent Densities (Jsc), Open-Circuit Photovoltage (Voc), Fill Factors (FF), and Conversion Efficiencies (η)

a

sensitizer

Qy absorption/ OD‚cm-1

overall absorption/ OD‚cm-1

∫IPCEdV h/ cm-1

Jsc/ mA‚cm-2

Voc/V

FF

η /%

BPhe a Phe a Phe x Phe b Phe c1 Phe c2

648 (1.00) 650 (1) a 464 (0.71) 252 (0.39) 182 (0.28) 153 (0.24)

2149 (0.71) 3014 (1) a 5306 (1.76) 3822 (1.26) 6312 (2.09) 4159 (1.38)

5001 (0.99) 5055 (1) a 4979 (0.98) 4270 (0.84) 3209 (0.63) 2860 (0.57)

11.9 (1.04) 11.4 (1) a 10.7 (0.94) 7.6 (0.67) 6.5 (0.57) 5.0 (0.44)

0.49 0.55 0.50 0.53 0.39 0.38

0.63 0.61 0.58 0.60 0.60 0.58

3.7 (0.97) 3.8 (1) 3.1 (0.82) 2.4 (0.63) 1.5 (0.39) 1.1 (0.29)

Relative values when the value of Phe a is normalized.

a der.”1 and “PPB a”.3 Here, we have renamed it to differentiate it from the following two compounds having similar pyropheophorbide structures.) Phe x consists of the chlorin skeleton with a carboxyl group at position C8 on ring B, and Phe b consists of the chlorin skeleton with a carboxyl group at position C7 on ring B. All of these compounds have a methyl ester group on ring D. The structures of Phe a, Phe x, and Phe b are basically the same except for the positions where the carboxyl group is attached. Natural pheophorbide c1 (Phe c1) and pheophorbide c2 (Phe c2) have very similar structures, having an ethenylcarboxyl group at position C17 on ring D and a methyl ester group at position C13 on ring E. The only difference is concerned with a group attached to position C8 on ring B, that is, the ethyl group in the former and the vinyl group in the latter. The particular position of the carboxyl group may give rise to differences not only in the electronic-absorption and redox properties of the sensitizer but also in the molecular assembly on TiO2; all of these differences can affect the photocurrent and conversion efficiency of DSSCs using the particular sensitizers. However, the latter difference may not be too drastic, a fact that hopefully allows us to elucidate the correlation between the electronic-absorption and redox properties of a sensitizer and the performance of DSSC fabricated. 3.1.2. Electronic-Absorption and One Electron-Oxidation Potential of Sensitizers in Solution and Electronic Absorption of Sensitizers Bound to TiO2. The electronic-absorption spectra of BPhe a, Phe a, Phe x, Phe b, Phe c1, and Phe c2 in tetrahydrofuran (THF) solution (Figure S-1) are presented and characterized in Section S-2 of the Supporting Information. Table 1 lists the electronic-absorption parameters concerning the Soret and Qy absorptions of pheophorbides in THF solution, which include the molar extinction coefficients (), oscillator strengths ( f ), and transition-dipole moments (µ). These parameters provide us with additional characterization: (v) In the case of the Soret absorption, the oscillator strength ( f ) and transition dipole moment (µ) are in the order BPhe a < Phe a < Phe x > Phe b > Phe c1 > Phe c2, whereas in the Qy

absorption, these parameters are in the order BPhe a < Phe a > Phe x > Phe b > Phe c1 > Phe c2. Table 1 also lists the one electron-oxidation potentials (Eox) of the pheophorbides. The Eox value systematically increases in the order BPhe a < Phe a < Phe x < Phe b < Phe c1 < Phe c2. The electronic-absorption spectra of BPhe a, Phe a, Phe x, Phe b, Phe c1, and Phe c2 that were adsorbed on the TiO2 layer are presented (Figure S-2) and characterized in Section S-2 of the Supporting Information. Table 2 lists the values of the integrated Qy and overall absorptions; their rankings are quite different from each other. 3.2. Performance of Pheophorbide-Sensitized Solar Cell. 3.2.1. IPCE Profiles. Figure 2 shows the IPCE profiles of DSSCs using BPhe a, Phe a, Phe x, Phe b, Phe c1, and Phe c2 as sensitizers. They are quite different from the profiles of electronic-absorption spectra of pheophorbides bound to the TiO2 layer (Figure S-2). The difference originates from the fact that much larger amounts of pheophorbides were adsorbed in fabricating the DSSCs (the electronic-absorption peaks are practically saturated) and also from the effects of the scattering layer in the DSSCs, which enhances the IPCE profile in the 500-600 nm region. The IPCE profiles of pheophorbides can be characterized as follows: (i) The bacteriochlorin skeleton of BPhe a extends the IPCE profile toward the near-infrared region, a unique property of this sensitizer. (ii) The IPCE profiles in the Qy region are broader in BPhe a, Phe a, Phe c1, and Phe c2 than those in Phe x and Phe b, suggesting a heterogeneity of the aggregate in the former. (iii) The IPCE profile in the Soret region, relative to that in the Qy region, is much higher in Phe x, Phe b, Phe c1, and Phe c2 in comparison to BPhe a and Phe a. All of these characteristics of IPCE profiles stem from the electronicabsorption spectra of the set of pheophorbides free in solution (Figure S-1 in the Supporting Information) and when bound to the TiO2 layer (Figure S-2). Table 2 also lists the IPCE values that are integrated over the wavelength region shown in Figure

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Figure 2. IPCE profiles of DSSCs using BPhe a, Phe a, Phe x, Phe b, Phe c1, and Phe c2 as sensitizers. Dotted line indicates IPCE after correction against the light intensity of the solar simulator (AM 1.5) in arbitrary ordinary scale.

Figure 3. I-V curves of DSSCs using BPhe a, Phe a, Phe x, Phe b, Phe c1, and Phe c2 as sensitizers.

S-2 (∫IPCEdνj). Their ranking among pheophorbides parallels not the ranking of the overall absorption but that of the Qy absorption. 3.2.2. I-V CurVes. Figure 3 exhibits the I-V curves, and Table 2 lists the values of short-circuit photocurrent (Jsc), opencircuit photovoltage (Voc), fill factor (FF), and conversion efficiency (η) derived from them. They can be characterized as follows: (i) The Jsc value is in the order BPhe a g Phe a > Phe x > Phe b > Phe c1 > Phe c2, whereas the Voc value is not in a systematic order, BPhe a < Phe a > Phe x < Phe b > Phe c1 ≈ Phe c2. As a combination, the η value becomes in the order Phe a g BPhe a > Phe x > Phe b > Phe c1 > Phe c2. Importantly, the Jsc and η values give rise to the same ranking. (ii) The ranking of the Jsc values among pheophorbides roughly

parallels that of ∫IPCEdνj, both reflecting the photocurrent (if we regard BPhe a ≈ Phe a). (iii) The values of Voc may reflect, at least partially, the packing of the pheophorbide molecules on the surface of the TiO2 layer. The decreasing photocurrent (Jsc) and conversion efficiency (η) of DSSCs using sensitizers except for BPhe a, that is, Phe a > Phe x > Phe b > Phe c1 > Phe c2, will be correlated with the intrinsic electronic-absorption and redox properties of the sensitizer mentioned in the previous section. 3.3. Dependence of the Photocurrent and Conversion Efficiency of DSSC on the Qy Absorption and the One Electron-Oxidation Potential of Pheophorbide Sensitizer. 3.3.1. Dependence on the Qy Absorption. In Table 2, the relative magnitudes of the photocurrent (Jsc) and conversion efficiency (η) are shown for comparison among the pheophorbide sensitizers (in parentheses), the values for Phe a being normalized to 1. It turns out that the rankings of all of the ∫IPCEdνj, Jsc, and η values relevant to photocurrent are the same; their averaged values being in the order BPhe a (1) ) Phe a (1) > Phe x (0.9) > Phe b (0.7) > Phe c1 (0.5) > Phe c2 (0.4). Importantly, the ranking of the Qy absorption, that is, BPhe a (1) ) Phe a (1) > Phe x (0.7) > Phe b (0.4) > Phe c1 (0.3) > Phe c2 (0.2), is the same as that of the above averaged values. Figure S-3a in the Supporting Information depicts the dependence of each of the ∫IPCEdνj, Jsc, and η values on the integrated Qy absorption. Each value exhibits a more or less similar dependence. The possible reasons for the predominant contribution of the Qy absorption are as follows: (i) It is naturally expected that the lowest and the most long-lived Qy state plays the major role in the electron injection into TiO2. The Soret and Qx states, that

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Figure 4. Schematic presentation of the relative positions of the conduction band and the valence band of TiO2 and the one electron-oxidation potentials (Eox) of the sensitizers including BPhe a, Phe a, Phe x, Phe b, Phe c1, and Phe c2, the redox potential being positive downward. The Soret, Qx and Qy energies of the pheophorbides are also shown in reference to their one electron-oxidation potential (Eox) that is regarded as the HOMO level, the energy being upward positive.

are slightly higher in energy than the Qy state and have small energy gaps with each next lower-lying singlet-excited state, must internally convert more rapidly than the Qy state having a larger energy gap down to the ground state. As a result, these higher excited states must be too short-lived to efficiently inject electrons to TiO2. (ii) The Qy to the ground transition is a welldefined single transition, and therefore it should give rise to a specifically oriented transition-dipole moment to facilitate efficient electron injection into TiO2 rather than the transition from the Soret state that is actually a composite of various transitions.14,15 In order to establish the dependence of photocurrent and conversion efficiency on the Qy absorption, we used a set of optical filters to excite each pheophorbide sensitizer selectively to the Qy state: Figure S-3b in the Supporting Information shows the photocurrent (Jsc) and the conversion efficiency (η) as functions of the integrated Qy absorption. On the basis of the results shown in Figure S-3a and b, we simply assumed a linear relation between the photocurrent upon the Qy excitation (J excite) and the integrated Qy absorption as

Jexcite ∝ Qy absorption

(1)

3.3.2. Dependence on One Electron-Oxidation Potential. Table 1 also shows the one electron-oxidation potential (Eox) of the pheophorbide sensitizers, and Table 2 shows the parameters relevant to photocurrent mentioned above (∫IPCEdνj, Jsc, and η). Figure S-4 in the Supporting Information depicts the dependence of these parameters on the Eox value. Each parameter exhibits a more or less similar, linear dependence on Eox. The correlation that the more negative one-electron oxidation potential (i.e., the smaller Eox value) gives rise to the larger photocurrent suggests redox electron transfer from the pheophorbide sensitizer to TiO2. In order to evaluate the contribution of

one electron-oxidation potential to photocurrent, we have tried to derive an equation based on the Marcus theory:16 According to this theory, the rate of electron transfer from the donor (D) to the acceptor (A+) can be given by

WDA+fD+A ) 2π |T |2 p DA

1

x4π kBT λ

[

exp -

]

(∆G + λ)2 (2) 4kBT λ

with ∆G ) GD+A - GDA+ where TDA is the electron tunneling matrix, kB is the Boltzmann constant, T is the absolute temperature, and λ is the so-called reorganization energy. The standard redox potentials of D and A, that is, E0D and 0 EA, are related to their Gibbs energies as

E0D ) const +

1 (G0 - G0D) |e| D+

E0A ) const +

1 (G0 - G0A) |e| A+

(3)

where e is the electronic charge. Then, we have

E0A - E0D )

1 (G0 + GA0 + - G0A - GD0 +) |e| D

)

(4)

1 (G0 - GD0 +A) |e| DA+

Substituting this relation to eq 2, we obtain

WDA+fD+A ) 2π |T |2 p DA

1

x4π kBT λ

(

exp -

)

[λ - (E0A - E0D)|e|]2 (5) 4kBT λ

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J. Phys. Chem. C, Vol. 112, No. 11, 2008 4423

Taking the values of kBT and E0A to be 0.025 and 2.86 eV (the edge of the valence band), respectively, we obtain the following relation for the redox electron transfer in the ground state

J

redox

(

)

[λ - (2.86 - Eox)]2 ∝ exp 0.1λ

(6)

where Eox() E0D) is the one electron-oxidation potential of pheophorbide. 4. Discussion 4.1. Empirical Equations for Electron Injection Obtained by Fitting Trials Based on Possible Models. One of the most important findings of the present investigation is the dependence of photocurrent (Jsc) not only on the integrated Qy absorption (Figure S-3a) but also on Eox (Figure S-4 in the Supporting Information). We have tried to find out empirical fitting equations (or in other words, electron injection models) for fitting to Jsc by the use of Qy absorption and Eox. We have actually tried a number of fittings; we present some examples giving rise to reasonable agreement. 4.1.1. Models of Parallel Electron Injection from the Excited and Ground States. Here, we assumed the presence of two pathways of electron injection, that is, one from the Qy state of sensitizer to the conduction band (CB) of TiO2, and the other, from the ground state of sensitizer to the valence band (VB) of TiO2. We call the former “A: electron injection upon Qy excitation” and the latter “B: redox electron transfer in the ground state”. Figure 4 presents an energy diagram showing the conduction band (CB) and the valence band (VB) of TiO2 as well as the low-lying singlet-excited states and the ground state of pheophorbide sensitizers; the two pathways of A and B are indicated by solid and broken arrows. A: All of the Qy states of the sensitizers are energetically above the conduction band edge (CBE) to facilitate electron injection upon Qy excitation. Here, we assumed that the excitation of pheophorbides to the Qy state is enough for electron injection. Alternatively, the injected electron in the CB of TiO2 has a lifetime (∼1 ms under full sunlight condition17) long enough to reach the electrode, although some of them can either be trapped by Ti4+ center or oxygen or lost through the chargerecombination reaction.18-20 The density of states in the CB of TiO2 can be considered to be more or less similar in the Qy energy region.21 We have experimentally established the presence of this pathway by the excitation of the pheophorbide sensitizers specifically to the Qy state blocking the TiO2 excitation by filters (see Figure S-3b in the Supporting Information). B: To facilitate electron transfer in the ground state, the presence of holes in the VB of TiO2 is absolutely necessary. After excitation of TiO2 from the VB to the CB, holes are generated in the former, whereas electrons, in the latter. However, all of the holes including free and trapped as ‚OH radical or O2•- can be quenched quickly by charge recombination especially at room temperature.18-20 Therefore, constant irradiation of the TiO2 absorption in the UV region must be necessary to keep supplying holes in the VB. We have shown that the contribution of TiO2 to photocurrent (Jsc) is very small (see the blue line in Figure S-3b). We also examined the effect of selective masking of the TiO2 absorption band in the UV region by filters (cut UV < 370 nm), while irradiating the rest of the spectral region (until 850 nm); decrease in the Jsc values was Phe x & Phe b > Phe c1 & Phe c2. Here, we just take into account the relative magnitude of the Qy transition-dipole moment (µ) that is approximately proportional to xQyabsorption. The one electron-oxidation potential: In the model of two pathways of electron injection, we have taken into account the one electron-oxidation potential only for electron transfer via the ground state. However, the one electron-oxidation potential in the Qy state may play a role in electron injection via the excited state as well. We assumed that this electron injection takes place through the tunneling electron transfer across a barrier, which can be given by

|TDA|2 ∝ e-κ‚r

(11)

where TDA is the tunneling matrix (see eq 5), κ is a constant,

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and r is the distance between the redox components.23 If κ is a function of a physical parameter, x, for example, then it can be written as

|TDA|2 ) C1 e-C2x

(12)

Proposition of an empirical equation: Thus, we have tried fitting by the use of the following empirical equation

Jsc ) C1 exp[C2Eox ×

xQy absorption] × Qy absorption

(13)

taking into account the above considerations: The Qy absorption at the end of the equation reflects the efficiency of excitation, whereas xQyabsorption in the exponential function reflects the Qy transition-dipole moment. We simply assumed that the relative Eox values in the excited state are proportional to those in the ground state among the set of pheophorbides whose structures are similar to one another. The results of fitting are shown numerically in Table S-1d of the Supporting Information and pictorially in Figure 5d. Here, it is important that the constant C2 is determined as a negative value because the smaller Eox value (the higher energy) should give rise to the more efficient electron injection in the tunneling mechanism through a barrier. The disagreement is small, except for Phe c1, even by the use of only two constants to fit. 4.2. Toward Determination of the Electron-Injection Mechanism. It is important to keep in mind that if the model and the fitting equation are correct and the physical parameters used have been determined correctly then a successful fitting should be obtained. However, a successful fitting does not necessarily mean that the fitting equation based on the particular model is real. The above-mentioned fittings may be used as a guide to elucidate the mechanism of electron injection, although they are still of limited implication. Here, the data points used for the fitting originate from only five different pheophorbides. The following considerations are necessary to obtain a more reliable fitting: First, to increase the number of different pheophorbide sensitizers that have been obtained by extraction or by organic synthesis, and second, to correctly determine the relevant physical parameters by repeating measurements under the suitable experimental conditions. The results of the above-mentioned fitting provide us with some insight into the electron-injection mechanism, which needs to be founded on more solid physical basis: Fittings a and b. Fittings based on the models of parallel electron injection from the ground and excited states gave rise to reasonable agreement, although the relative contributions of the Qy absorption (A) and the redox (B) terms still could not be fit completely. It is challenging to establish the pathway via the ground state (see Figure 1b of ref 24). However, the present experimental condition, that is, the photon density for the VB to CB excitation of TiO2 is much lower than that for the ground to Qy excitation of pheophorbides, must have caused difficulty in the present fitting analysis. It is absolutely necessary to introduce a light source that generates UV light stronger than the conventional solar simulator and to systematically change the relative contribution of the UV excitation of TiO2 and the NIR Qy excitation of pheophorbides to establish this pathway. Here, it is most important to solve the issue of strong correlation between the two physical parameters. We have actually observed a systematic correlation of the one electronoxidation potential with the integrated Qy absorption (semiexponential, upper panel) and with the molar extinction

coefficient (linear, lower panel). The correlations are shown in Figure S-5 in the Supporting Information, although their implications are not clear at this moment. If such a correlation is physically established, then it should be taken into account in formulating empirical equations. Fitting c. Fitting based on the model including electron transfer from the I-/I3- couple suggests that this electron-transfer process may also be relevant in the stationary state. However, this electron-transfer reaction is diffusion-limited, and it is completely different from the electron transfer from carotenoid to Phe a (PPB a), where the pair of pigments were physically bound to each other.3 It is also different from the abovementioned pheophorbide-to-TiO2 electron transfer via the ground state, where the pair of redox components are coordinated or chemically bound. This electron-transfer pathway from the I-/I3couple may be of secondary importance, even though it cannot be completely excluded at the present stage. Fitting d. Fitting based on the model assuming the tunneling electron injection via the excited state gave rise to reasonable agreement, suggesting the roles of the one electron-oxidation potential and the polarization of pheophorbide in the Qy state. However, this is still a working hypothesis. To establish the role of the Qy-state one electron-oxidation potential in electron injection via the Qy state of the sensitizer, it is crucial to determine these values. It would be an intriguing attempt to observe the ground-state and excited-state one electron-oxidation reactions of pheophorbides by means of electronic-absorption and fluorescence spectroscopy for the ground and Qy states, respectively. Whether the Eox values in the Qy states of pheophorbides can energetically inject electron to the CB or not is a key question. 5. Conclusions The following answers to the questions addressed in the Introduction section have been obtained: (1) Which sensitizer gives rise to the best performance, including photocurrent and conversion efficiency? BPhe a and Phe a gave rise to the best performance among the pheophorbide sensitizers tested, although the former looked unstable. (2) Which molecular parameters of pheophorbide sensitizers correlate with the above parameters determining the performance of DSSCs? Clear dependence of the photocurrent on the Qy absorption as well as on the one electron-oxidation potential has been observed, indicating that these physical parameters play key roles in determining the performance of DSSCs. A set of pheophorbides having similar structures and physicochemical properties has played a key role in elucidating these key parameters. (3) What is the mechanism by which these physical parameters of pheophorbide sensitizers determine the photocurrent of DSSC? We have tried various fittings to find out reasonable empirical equations based on possible models. Two reasonable models emerged, that is, one, a model of parallel electron injection via the excited and ground states, and the other, a model of electron injection simply via the Qy state. These models suggested that one electron-oxidation potential plays a role in the redox electron transfer via the ground state and also in the electron injection via the excited state. The real mechanism of electron injection explaining the dependence on the one electronoxidation potential still remains as an open question. The results of present investigation, however, have led us to the following line of research in the future: (a) To establish (or negate) the redox electron-transfer pathway via the ground state: When the TiO2 absorption in

4426 J. Phys. Chem. C, Vol. 112, No. 11, 2008 the UV region is efficiently excited to generate holes, there is a good chance of this electron-transfer pathway to be activated. This pathway may have been overlooked by the usage of a conventional solar simulator. (b) To establish the role of one electron-oxidation potential of the dye sensitizer in the excited state. The electron injection through a barrier via the excited state has been suggested in the present simulation together with the effect of polarization of the dye sensitizer upon excitation. (c) To establish the correlation between the Qy absorption and the one electron-oxidation potential. The determination of one electron-oxidation potential by opt-electrochemical measurements using electronic-absorption for the ground state and fluorescence for the relevant singlet state can be a promising method to determine the redox potentials in both states. It will become possible to correlate these values with the Qy absorption. These results will provide us deeper insight into the mechanisms of electron injection from the dye sensitizer to TiO2. In addition to the above two physical parameters we have found experimentally in the present investigation, another important parameter can be electronic coupling between the carboxyl group of Phe sensitizers and the surface of TiO2, as one of the reviewers has pointed out. He/she kindly suggested to try DFT calculations to elucidate the overlap of the HOMO and the LUMO between the two components. Infrared and resonance-Raman spectroscopy of the vibration(s) of the carboxyl group can be an experimental counterpart of this investigation. Acknowledgment. This work has been supported by grants (to Y.K.) from the Ministry of Education, Culture, Sports, Science and Technology (an Open Research Center Project, “The Research Center of Photo-Energy Conversion”) (to Y.W), a Grant-in-Aid for Scientific Research on Priority Areas (417) (no. 17029038) from MEXT, an Academic Frontier Project as well as Grants-in-aid for Scientific Research from MEXT and JSPS (to H.T.) and a grant (to X.-F.W) from JST project “Research for Promoting Technological Seeds” (no. 11-121). Supporting Information Available: S-1, Preparation of 3-devinyl-3-ethyl-8-deethyl-8-carboxy-pyropheophorbide a (Phe x). S-2, Electronic-absorption spectra of sensitizers in solution and bound to TiO2. S-3, Dependence of ∫IPCEdνj, Jsc, and η on the Qy absorption and Eox. S-4, The results of fitting trials to photocurrent (Jsc) as functions of Qy absorption and one

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