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Recombination rate between dye cations and electrons in N719-sensitized nanocrystalline TiO2 films under substantially weak excitation conditions
Chemical Physics Letters 471 (2009) 280–282
Contents lists available at ScienceDirect
Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Recombination rate between dye cations and electrons in N719-sensitized nanocrystalline TiO2 films under substantially weak excitation conditions Ryuzi Katoh a,*, Motohiro Kasuya a, Akihiro Furube a, Nobuhiro Fuke b, Naoki Koide b, Liyuan Han b a b
National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba Central 5, 1-1-1 Higashi, Tsukuba, Ibaraki 305-8565, Japan Sharp Corporation, 282-1 Hajikami, Katsuragi, Nara 639-2198, Japan
a r t i c l e
i n f o
Article history: Received 27 October 2008 In final form 18 February 2009 Available online 21 February 2009
a b s t r a c t We evaluated the charge recombination rate in N719-sensitized nanocrystalline TiO2 films after photoinduced charge separation under substantially weak excitation conditions. We found that the recombination rates did not reach a constant value but instead decreased with decreasing light intensity. Ó 2009 Elsevier B.V. All rights reserved.
1. Introduction Recombination between oxidized dye and electrons in dyesensitized solar cells is extensively studied, since recombination is one of the key processes that govern the performance of these solar cells. Specifically, to obtain a high photocurrent yield, the recombination time must be slower than the time needed for regeneration of oxidized dyes by a redox mediator, such as I =I 3. To determine a reliable means by which to evaluate recombination rates, transient absorption (TA) techniques have been examined in the last 15 years [1–3]. Early reported recombination rates varied widely among different studies, but in 2000, Durrant and co-workers reported very important TA results that help to explain these reported variances [2]. The researchers carefully measured recombination rates as a function of varying experimental conditions, such as excitation light intensity and electrochemical bias. According to their studies, the number of electrons per particle, Ne, is a key parameter limiting the recombination rate. They reported that the recombination rate became constant for Ne < 1. This phenomenon can be explained as follows: the recombination of an electron-oxidized dye pair occurs in the particle without interparticle hopping; in other words, geminate recombination occurs in the particle. On the basis of this concept, the recombination rate has been evaluated under sufficiently low excitation densities (Ne < 1) to investigate the origin of this slow recombination process [3]. Time-resolved microwave conductivity (TRMC) is an alternative method to TA for evaluating the recombination process for dye-sensitized nanocrystalline films [4–6]. In TRMC, the analytical signal is generated from mobile electrons in the TiO2 particles and is proportional to the product of the electron mobility and the number of electrons. For dye-sensitized nanocrystalline TiO2 films, the TRMC signal normalized by light intensity (Iex) decreases with * Corresponding author. Fax: +81 29 861 4517. E-mail address: [email protected] (R. Katoh). 0009-2614/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2009.02.053
decreasing excitation intensity for Ne < 1, indicating that effective mobility is affected by Iex [4–6]. This can be explained in terms of the ‘trap-filling effect,’ in which injected electrons immediately occupy deep traps in the particles. As a result, the effective mobility of other electrons decreases, and then small TRMC signals are observed. From these findings, one can expect that the recombination rate decreases with decreasing Iex even for Ne < 1; such a trend contradicts the opinion proposed by Durrant and co-workers [2,3] as mentioned above. To reconcile this discrepancy, we carefully measured the recombination rate of N719-sensitized nanocrystalline TiO2 (N719/TiO2) films under substantially weak excitation conditions with a highly sensitive TA spectrometer. 2. Experimental Nanocrystalline TiO2 films were prepared from a commercially available TiO2 paste (Solaronix SA, T/SP). The paste was painted on a glass plate substrate with a screen printer. Nanocrystalline films were prepared by calcination of the painted substrate for 1 h at 450 °C. The films obtained had an area of 10 10 mm2 and a thickness of 13 lm. N719 (Fig. 1, Solaronix) was dissolved at a concentration of 0.3 mM in 1:1 tert-butylalcohol:acetonitrile. The nanocrystalline TiO2 films were immersed in the dye solution for 0.5 h, so that the dye could adsorb onto the semiconductor surface. The films then were rinsed with ethanol and dried in air. For TA measurements, a Nd3+:YAG laser (HOYA Continuum, Surelite II) was used as the pumping light source. The repetition rate of the laser was 10 Hz. The second-harmonic pulse (532 nm) was used for excitation of the dye-sensitized TiO2 films. A halogen lamp (100 W) was used as the probe light source. The probe light was incident to sample films after through a long-pass filter (>650 nm for the spectrum measurements and >750 nm for the decay measurements) to eliminate excitation of the sample by the probe light. The light transmitted through the sample films was detected with a Si photodiode (Hamamatsu, S-1722) after
281
R. Katoh et al. / Chemical Physics Letters 471 (2009) 280–282 COOR HOOC
N Ru
Iex = 50 µJ cm
-2
N
HOOC
COOR R = TBA (tetrabutylammonium)
0.4
0.0007
NCS
0.0006 0.0005 0.0004
0.3
0.0003
0.2
0.0002
0.1
0.0001
0 400
500
600
700
800
900
Absorbance change
0.5
Absorbance
N
Absorbance change
0.6
NCS
N
0.7
10-3
-4
10
Slope = 1
10-5 0 10
0 1000
1
Iex / µJ cm-2
Wavelength / nm Fig. 1. Absorption spectrum of an N719/TiO2 film in the ground state (solid line) and TA spectrum of an N719/TiO2 film excited by 532-nm light and integrated within 20–40 ls (closed circles). Molecular structure of N719 dye is also shown.
Fig. 1 shows the absorption spectrum of an N719/TiO2 film in the ground state. The distinct peak at 540 nm is attributed to the metal-to-ligand charge transfer absorption band of the N719 dye. The number of dye molecules per unit area of the film (Ddye) was estimated to be 1.6 1016 cm2 under the assumption that the absorption coefficient of N719 was the same as that of N3 dye (e = 14 000 dm3 mol1 cm1). The number of particles per unit area of the film (Dparticle) was estimated to be 1.5 1014 cm2 for a TiO2 particle radius (rp) of 10 nm, a film thickness (dfilm) of 13 lm, and a film porosity (P) of 0.5. Accordingly, approximately 100 dye molecules were adsorbed on one particle, and the area S occupied by an N719 dye molecule was estimated to be 13 nm2. This value is markedly larger than the molecular size of N3 (1 nm2) [7,8], suggesting that the N719 dye molecules were well dispersed on the surface. Fig. 1 also shows the TA spectrum of N719/TiO2 excited by 532nm light. The spectrum was integrated within 20–40 ls. The peak position in this spectrum, 800 nm, is similar to that of N3/TiO2 [9]. Since the molecular structure of N719 is similar to that of N3, this spectrum was assigned to the oxidized N719 dye (N719+). Fig. 2 shows the absorbance change caused by the production of N719+ at the peak of the TA signal as a function of Iex observed at 800 nm. Clearly, the observed signals were proportional to Iex. This indicates that no fast recombination occurs within the time resolution of our TA system (5 ls). The efficiency of electron injection (Uinj) from excited N719 dye to nanocrystalline TiO2 films can be estimated from the values of the absorbance change caused by the generation of N719+ (DAcation) and its molar absorption coefficient ecation:
DAcation
ecation ð1 TÞN0
ð1Þ
:
In this equation, T and N0 represent the transmittance of excitation light and the number of incident excitation photons per unit area (cm2), respectively. We have already estimated ecation for N3 dye at its peak absorbance as 6000 mol1 dm3 cm1 (=1 1017 cm2) [9]. Assuming that N719 has the same value, which is a reasonable assumption because the molecular structure of N3 dye is very similar to that of N719, the injection efficiency of electrons was estimated to be about 0.7. We considered this value to be reasonable since it agreed with values obtained in our previous experiments [9]. Fig. 3 shows the decay profiles observed at 800 nm. The profiles are normalized by the peak value of the TA signal. Clearly, the recombination rate decreased with decreasing Iex. To discuss the electron density effect on the recombination kinetics, we estimated Ne from the number of oxidized dyes per unit area (Dcation) using the equation Ne = (Dcation/Dparticle) = (Uinj(1 – T)Iex)/Dparticle). From this equation, Ne = 1 occurred at Iex = 3 1014 photons cm2 (100 lJ cm2). To evaluate recombination time, the time required to observe 50% of the initial absorbance (t1/2) is often used. Thus, we plotted t1/2 as a function of Iex (open circles in Fig. 4). Although the decay curves observed in the present study were not precisely fitted by conventional second-order kinetics, it would be significant to discuss with such ideal simple kinetics. For simple second-order
1.25 6 µJ cm-2 12 24 48 95 190
1
Absorbance / Iex
3. Results and discussion
10
Fig. 2. Absorbance change caused by the production of N719+ in an N719/TiO2 film, recorded at the maxima of the TA signals as a function of Iex observed at 800 nm.
Uinj ¼ being dispersed with a monochromator (Acton Research, SpectraPro-150). The photocurrent from the detector was amplified with an amplifier (NF Electronic Instruments, 5305). Signals were processed with a digital oscilloscope (Tektronix, TDS380) and analyzed with a computer. The DC offset of the photocurrent from the detector was subtracted by means of an electric frequency filter (NF Electronic Instruments, FV-628B), and therefore small absorbance changes (<10–5) could be detected. The time resolution of the system was about 5 ls. The intensity of the laser pulse was measured with a pyroelectric energy meter (Ophir, PE25-SH-V2). All measurements were carried out at 295 K.
2
10
0.75 0.5 0.25 0 -5 10
10-4
Time / s
10-3
10-2
Fig. 3. TA decay profiles of an N719/TiO2 film observed at 800 nm. The profiles are normalized by the peak value of the TA signal.
282
R. Katoh et al. / Chemical Physics Letters 471 (2009) 280–282
Ne
1
s
0.1
Recombination time t1/2
0.001
Slope = -0.3
0.0001
Slope = -1 1
10
100
1000
Iex / µJ cm-2 Fig. 4. Recombination time t1/2 as a function of Iex for an N719/TiO2 film used in the present study (open circles) and t1/2 as a function of Ne for films studied by Durrant and his co-workers [2] (closed squares).
kinetics, t1/2 is inversely proportional to the number of electrons produced primarily, meaning that t1/2 is proportional to I1 ex . This simple expectation is consistent with the trend observed at higher Iex values (Fig. 4), and t1/2 seems to be proportional to I1 ex in our experiments. A deviation from linearity was observed at around 100 lJ cm2 (Fig. 4), which corresponds to Ne = 1. Below that intensity, t1/2 tended to saturate but still increased with decreasing Iex. This trend was not consistent with the results reported by Durrant’s group, who argued that the recombination rate became constant below Ne = 1. The t1/2 values reported by Durrant’s group [2] are plotted as a function of Ne (closed squares) in Fig. 4. These data points did not coincide with the data points observed in the present experiments. This discrepancy was probably caused by small differences between the specimens used for our experiments and those used by Durrant’s group. Actually, the relation between t1/2 and Iex observed by Durrant’s group after multiplication by a factor of 0.5 is similar to the relationship observed from the present results. Therefore, there was no substantial difference between the present results and Durrant’s results, except for the range of electron density. As shown in Fig. 4, t1/2 deviated downward from the linearity for Ne < 1, indicating that the recombination times became faster than the values predicted from simple second-order kinetics. There are two possible explanations for this tendency: an increase in electron mobility and the presence of ion-pair correlation between
an electron and a dye cation undergoing recombination. An increase in electron mobility was discarded as a possible explanation, because the mobility of electrons decreases with decreasing Iex for Ne < 1 as determined by TRMC measurements [4]. The presence of ion-pair correlation is likely, namely geminate recombination occurs. Geminate recombination occurs if no interparticle hopping of electrons occurs before their recombination with cations as proposed by Durrant’s group. In such condition, however, the recombination time becomes constant at the low density region, which is not consistent with present results. Nelson and Chandler presented theoretical model for the recombination rate at low electron density region [10]. They showed the model calculation including preliminary experimental results and found that the recombination time still increases with decreasing electron density in the low density region if interparticle electron transfer occurs between weakly coupled particles [10]. Recent results of temperature dependence of TRMC also suggests that interparticle transfer occurs before recombination [6]. As mentioned above, the geminate recombination model was applicable to our present system, but the recombination time still increased with decreasing electron density, even for Iex below Ne = 1. In other words, the recombination time did not reach a constant value even for Ne < 1. Namely, there are no suitable parameters to characterize the recombination rate, such as a rate constant and therefore, it is difficult to discuss the origin of the difference of the recombination rates obtained in various dye-sensitized nanocrystalline films. Acknowledgment We gratefully acknowledge financial support from the New Energy and Industrial Technology Development Organization (NEDO) of Japan. References [1] J.R. Durrant, S.A. Haque, E. Palomares, Chem. Commun. (2006) 3279. [2] S.A. Haque, Y. Tachibana, R.L. Willis, J.E. Moser, M. Grätzel, D.R. Klug, J.R. Durrant, J. Phys. Chem. B 104 (2000) 538. [3] J.N. Clifford et al., J. Am. Chem. Soc. 126 (2004) 5225. [4] J.E. Kroeze, T.J. Savenije, J.M. Warman, J. Am. Chem. Soc. 126 (2004) 7608. [5] R. Katoh, A. Huijser, K. Hara, T.J. Savenije, L.D.A. Siebbeles, J. Phys. Chem. C 111 (2007) 10741. [6] T.J. Savenije, A. Huijser, M.J.W. Vermeulen, R. Katoh, Chem. Phys. Lett. 461 (2008) 93. [7] V. Shklover, Y.E. Ovchinnikov, L.S. Braginsky, S.M. Zakeeruddin, M. Grätzel, Chem. Mater. 10 (1998) 2533. [8] A. Sasahara, C.L. Pang, H. Onishi, J. Phys. Chem. B 110 (2006) 4751. [9] T. Yoshihara et al., J. Phys. Chem. B 108 (2004) 2643. [10] J. Nelson, R.E. Chandler, Coord. Chem. Rev. 248 (2004) 1181.
Contents lists available at ScienceDirect
Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Recombination rate between dye cations and electrons in N719-sensitized nanocrystalline TiO2 films under substantially weak excitation conditions Ryuzi Katoh a,*, Motohiro Kasuya a, Akihiro Furube a, Nobuhiro Fuke b, Naoki Koide b, Liyuan Han b a b
National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba Central 5, 1-1-1 Higashi, Tsukuba, Ibaraki 305-8565, Japan Sharp Corporation, 282-1 Hajikami, Katsuragi, Nara 639-2198, Japan
a r t i c l e
i n f o
Article history: Received 27 October 2008 In final form 18 February 2009 Available online 21 February 2009
a b s t r a c t We evaluated the charge recombination rate in N719-sensitized nanocrystalline TiO2 films after photoinduced charge separation under substantially weak excitation conditions. We found that the recombination rates did not reach a constant value but instead decreased with decreasing light intensity. Ó 2009 Elsevier B.V. All rights reserved.
1. Introduction Recombination between oxidized dye and electrons in dyesensitized solar cells is extensively studied, since recombination is one of the key processes that govern the performance of these solar cells. Specifically, to obtain a high photocurrent yield, the recombination time must be slower than the time needed for regeneration of oxidized dyes by a redox mediator, such as I =I 3. To determine a reliable means by which to evaluate recombination rates, transient absorption (TA) techniques have been examined in the last 15 years [1–3]. Early reported recombination rates varied widely among different studies, but in 2000, Durrant and co-workers reported very important TA results that help to explain these reported variances [2]. The researchers carefully measured recombination rates as a function of varying experimental conditions, such as excitation light intensity and electrochemical bias. According to their studies, the number of electrons per particle, Ne, is a key parameter limiting the recombination rate. They reported that the recombination rate became constant for Ne < 1. This phenomenon can be explained as follows: the recombination of an electron-oxidized dye pair occurs in the particle without interparticle hopping; in other words, geminate recombination occurs in the particle. On the basis of this concept, the recombination rate has been evaluated under sufficiently low excitation densities (Ne < 1) to investigate the origin of this slow recombination process [3]. Time-resolved microwave conductivity (TRMC) is an alternative method to TA for evaluating the recombination process for dye-sensitized nanocrystalline films [4–6]. In TRMC, the analytical signal is generated from mobile electrons in the TiO2 particles and is proportional to the product of the electron mobility and the number of electrons. For dye-sensitized nanocrystalline TiO2 films, the TRMC signal normalized by light intensity (Iex) decreases with * Corresponding author. Fax: +81 29 861 4517. E-mail address: [email protected] (R. Katoh). 0009-2614/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2009.02.053
decreasing excitation intensity for Ne < 1, indicating that effective mobility is affected by Iex [4–6]. This can be explained in terms of the ‘trap-filling effect,’ in which injected electrons immediately occupy deep traps in the particles. As a result, the effective mobility of other electrons decreases, and then small TRMC signals are observed. From these findings, one can expect that the recombination rate decreases with decreasing Iex even for Ne < 1; such a trend contradicts the opinion proposed by Durrant and co-workers [2,3] as mentioned above. To reconcile this discrepancy, we carefully measured the recombination rate of N719-sensitized nanocrystalline TiO2 (N719/TiO2) films under substantially weak excitation conditions with a highly sensitive TA spectrometer. 2. Experimental Nanocrystalline TiO2 films were prepared from a commercially available TiO2 paste (Solaronix SA, T/SP). The paste was painted on a glass plate substrate with a screen printer. Nanocrystalline films were prepared by calcination of the painted substrate for 1 h at 450 °C. The films obtained had an area of 10 10 mm2 and a thickness of 13 lm. N719 (Fig. 1, Solaronix) was dissolved at a concentration of 0.3 mM in 1:1 tert-butylalcohol:acetonitrile. The nanocrystalline TiO2 films were immersed in the dye solution for 0.5 h, so that the dye could adsorb onto the semiconductor surface. The films then were rinsed with ethanol and dried in air. For TA measurements, a Nd3+:YAG laser (HOYA Continuum, Surelite II) was used as the pumping light source. The repetition rate of the laser was 10 Hz. The second-harmonic pulse (532 nm) was used for excitation of the dye-sensitized TiO2 films. A halogen lamp (100 W) was used as the probe light source. The probe light was incident to sample films after through a long-pass filter (>650 nm for the spectrum measurements and >750 nm for the decay measurements) to eliminate excitation of the sample by the probe light. The light transmitted through the sample films was detected with a Si photodiode (Hamamatsu, S-1722) after
281
R. Katoh et al. / Chemical Physics Letters 471 (2009) 280–282 COOR HOOC
N Ru
Iex = 50 µJ cm
-2
N
HOOC
COOR R = TBA (tetrabutylammonium)
0.4
0.0007
NCS
0.0006 0.0005 0.0004
0.3
0.0003
0.2
0.0002
0.1
0.0001
0 400
500
600
700
800
900
Absorbance change
0.5
Absorbance
N
Absorbance change
0.6
NCS
N
0.7
10-3
-4
10
Slope = 1
10-5 0 10
0 1000
1
Iex / µJ cm-2
Wavelength / nm Fig. 1. Absorption spectrum of an N719/TiO2 film in the ground state (solid line) and TA spectrum of an N719/TiO2 film excited by 532-nm light and integrated within 20–40 ls (closed circles). Molecular structure of N719 dye is also shown.
Fig. 1 shows the absorption spectrum of an N719/TiO2 film in the ground state. The distinct peak at 540 nm is attributed to the metal-to-ligand charge transfer absorption band of the N719 dye. The number of dye molecules per unit area of the film (Ddye) was estimated to be 1.6 1016 cm2 under the assumption that the absorption coefficient of N719 was the same as that of N3 dye (e = 14 000 dm3 mol1 cm1). The number of particles per unit area of the film (Dparticle) was estimated to be 1.5 1014 cm2 for a TiO2 particle radius (rp) of 10 nm, a film thickness (dfilm) of 13 lm, and a film porosity (P) of 0.5. Accordingly, approximately 100 dye molecules were adsorbed on one particle, and the area S occupied by an N719 dye molecule was estimated to be 13 nm2. This value is markedly larger than the molecular size of N3 (1 nm2) [7,8], suggesting that the N719 dye molecules were well dispersed on the surface. Fig. 1 also shows the TA spectrum of N719/TiO2 excited by 532nm light. The spectrum was integrated within 20–40 ls. The peak position in this spectrum, 800 nm, is similar to that of N3/TiO2 [9]. Since the molecular structure of N719 is similar to that of N3, this spectrum was assigned to the oxidized N719 dye (N719+). Fig. 2 shows the absorbance change caused by the production of N719+ at the peak of the TA signal as a function of Iex observed at 800 nm. Clearly, the observed signals were proportional to Iex. This indicates that no fast recombination occurs within the time resolution of our TA system (5 ls). The efficiency of electron injection (Uinj) from excited N719 dye to nanocrystalline TiO2 films can be estimated from the values of the absorbance change caused by the generation of N719+ (DAcation) and its molar absorption coefficient ecation:
DAcation
ecation ð1 TÞN0
ð1Þ
:
In this equation, T and N0 represent the transmittance of excitation light and the number of incident excitation photons per unit area (cm2), respectively. We have already estimated ecation for N3 dye at its peak absorbance as 6000 mol1 dm3 cm1 (=1 1017 cm2) [9]. Assuming that N719 has the same value, which is a reasonable assumption because the molecular structure of N3 dye is very similar to that of N719, the injection efficiency of electrons was estimated to be about 0.7. We considered this value to be reasonable since it agreed with values obtained in our previous experiments [9]. Fig. 3 shows the decay profiles observed at 800 nm. The profiles are normalized by the peak value of the TA signal. Clearly, the recombination rate decreased with decreasing Iex. To discuss the electron density effect on the recombination kinetics, we estimated Ne from the number of oxidized dyes per unit area (Dcation) using the equation Ne = (Dcation/Dparticle) = (Uinj(1 – T)Iex)/Dparticle). From this equation, Ne = 1 occurred at Iex = 3 1014 photons cm2 (100 lJ cm2). To evaluate recombination time, the time required to observe 50% of the initial absorbance (t1/2) is often used. Thus, we plotted t1/2 as a function of Iex (open circles in Fig. 4). Although the decay curves observed in the present study were not precisely fitted by conventional second-order kinetics, it would be significant to discuss with such ideal simple kinetics. For simple second-order
1.25 6 µJ cm-2 12 24 48 95 190
1
Absorbance / Iex
3. Results and discussion
10
Fig. 2. Absorbance change caused by the production of N719+ in an N719/TiO2 film, recorded at the maxima of the TA signals as a function of Iex observed at 800 nm.
Uinj ¼ being dispersed with a monochromator (Acton Research, SpectraPro-150). The photocurrent from the detector was amplified with an amplifier (NF Electronic Instruments, 5305). Signals were processed with a digital oscilloscope (Tektronix, TDS380) and analyzed with a computer. The DC offset of the photocurrent from the detector was subtracted by means of an electric frequency filter (NF Electronic Instruments, FV-628B), and therefore small absorbance changes (<10–5) could be detected. The time resolution of the system was about 5 ls. The intensity of the laser pulse was measured with a pyroelectric energy meter (Ophir, PE25-SH-V2). All measurements were carried out at 295 K.
2
10
0.75 0.5 0.25 0 -5 10
10-4
Time / s
10-3
10-2
Fig. 3. TA decay profiles of an N719/TiO2 film observed at 800 nm. The profiles are normalized by the peak value of the TA signal.
282
R. Katoh et al. / Chemical Physics Letters 471 (2009) 280–282
Ne
1
s
0.1
Recombination time t1/2
0.001
Slope = -0.3
0.0001
Slope = -1 1
10
100
1000
Iex / µJ cm-2 Fig. 4. Recombination time t1/2 as a function of Iex for an N719/TiO2 film used in the present study (open circles) and t1/2 as a function of Ne for films studied by Durrant and his co-workers [2] (closed squares).
kinetics, t1/2 is inversely proportional to the number of electrons produced primarily, meaning that t1/2 is proportional to I1 ex . This simple expectation is consistent with the trend observed at higher Iex values (Fig. 4), and t1/2 seems to be proportional to I1 ex in our experiments. A deviation from linearity was observed at around 100 lJ cm2 (Fig. 4), which corresponds to Ne = 1. Below that intensity, t1/2 tended to saturate but still increased with decreasing Iex. This trend was not consistent with the results reported by Durrant’s group, who argued that the recombination rate became constant below Ne = 1. The t1/2 values reported by Durrant’s group [2] are plotted as a function of Ne (closed squares) in Fig. 4. These data points did not coincide with the data points observed in the present experiments. This discrepancy was probably caused by small differences between the specimens used for our experiments and those used by Durrant’s group. Actually, the relation between t1/2 and Iex observed by Durrant’s group after multiplication by a factor of 0.5 is similar to the relationship observed from the present results. Therefore, there was no substantial difference between the present results and Durrant’s results, except for the range of electron density. As shown in Fig. 4, t1/2 deviated downward from the linearity for Ne < 1, indicating that the recombination times became faster than the values predicted from simple second-order kinetics. There are two possible explanations for this tendency: an increase in electron mobility and the presence of ion-pair correlation between
an electron and a dye cation undergoing recombination. An increase in electron mobility was discarded as a possible explanation, because the mobility of electrons decreases with decreasing Iex for Ne < 1 as determined by TRMC measurements [4]. The presence of ion-pair correlation is likely, namely geminate recombination occurs. Geminate recombination occurs if no interparticle hopping of electrons occurs before their recombination with cations as proposed by Durrant’s group. In such condition, however, the recombination time becomes constant at the low density region, which is not consistent with present results. Nelson and Chandler presented theoretical model for the recombination rate at low electron density region [10]. They showed the model calculation including preliminary experimental results and found that the recombination time still increases with decreasing electron density in the low density region if interparticle electron transfer occurs between weakly coupled particles [10]. Recent results of temperature dependence of TRMC also suggests that interparticle transfer occurs before recombination [6]. As mentioned above, the geminate recombination model was applicable to our present system, but the recombination time still increased with decreasing electron density, even for Iex below Ne = 1. In other words, the recombination time did not reach a constant value even for Ne < 1. Namely, there are no suitable parameters to characterize the recombination rate, such as a rate constant and therefore, it is difficult to discuss the origin of the difference of the recombination rates obtained in various dye-sensitized nanocrystalline films. Acknowledgment We gratefully acknowledge financial support from the New Energy and Industrial Technology Development Organization (NEDO) of Japan. References [1] J.R. Durrant, S.A. Haque, E. Palomares, Chem. Commun. (2006) 3279. [2] S.A. Haque, Y. Tachibana, R.L. Willis, J.E. Moser, M. Grätzel, D.R. Klug, J.R. Durrant, J. Phys. Chem. B 104 (2000) 538. [3] J.N. Clifford et al., J. Am. Chem. Soc. 126 (2004) 5225. [4] J.E. Kroeze, T.J. Savenije, J.M. Warman, J. Am. Chem. Soc. 126 (2004) 7608. [5] R. Katoh, A. Huijser, K. Hara, T.J. Savenije, L.D.A. Siebbeles, J. Phys. Chem. C 111 (2007) 10741. [6] T.J. Savenije, A. Huijser, M.J.W. Vermeulen, R. Katoh, Chem. Phys. Lett. 461 (2008) 93. [7] V. Shklover, Y.E. Ovchinnikov, L.S. Braginsky, S.M. Zakeeruddin, M. Grätzel, Chem. Mater. 10 (1998) 2533. [8] A. Sasahara, C.L. Pang, H. Onishi, J. Phys. Chem. B 110 (2006) 4751. [9] T. Yoshihara et al., J. Phys. Chem. B 108 (2004) 2643. [10] J. Nelson, R.E. Chandler, Coord. Chem. Rev. 248 (2004) 1181.