Dynamics of Back-Electron Transfer Processes of Strongly Coupled

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12786

J. Phys. Chem. B 2001, 105, 12786-12796

Dynamics of Back-Electron Transfer Processes of Strongly Coupled Triphenyl Methane Dyes Adsorbed on TiO2 Nanoparticle Surface as Studied by Fast and Ultrafast Visible Spectroscopy G. Ramakrishna, Hirendra N. Ghosh,* Ajay K. Singh, Dipak K. Palit, and Jai P. Mittal Radiation Chemistry & Chemical Dynamics DiVision, Bhabha Atomic Research Center, Trombay, Mumbai - 400 085, India ReceiVed: March 22, 2001; In Final Form: September 20, 2001

Electron injection and back-electron transfer (BET) dynamics of triphenylmethane (TPM) dyes adsorbed on TiO2 nanoparticles have been studied by fast and ultrafast pump-probe spectroscopy in the subpico- to microsecond time domain. TPM dyes form charge-transfer complex with TiO2 nanoparticles as they get adsorbed on the surface. Among the three TPM dyes, pyrogallol red (PGR) and bromo-pyrogallol red (BrPGR) have higher electronic coupling to or interaction with TiO2 nanoparticles compared to aurin tricarboxylic acid (ATC). Excitation of the dyes adsorbed on the TiO2 nanoparticle surface leads to electron injection into the conduction band of TiO2. Electron injection has been confirmed by direct detection of an electron in the conduction band, a cation radical of the adsorbed dye, and a bleach of the dye in real time as monitored by transient absorption spectroscopy in the visible and near-IR regions. The dynamics of BET from TiO2 to the parent cation have been measured by monitoring the recovery kinetics of the bleach of the adsorbed dye. BET dynamics have been found to be multiexponential, and it is extremely fast for the strong coupling dyes (PGR and Br-PGR). The majority of the injected electrons are found to come back to the parent cation with a time constant of ∼2 ps. BET dynamics have been compared for the strong (PGR) and moderate (ATC) coupling dyes in the microsecond time domain. Intensity dependence experiments show BET reactions for PGR- and Br-PGR-sensitized TiO2 nanoparticles follow a first-order ET rate, where as ATC-sensitized TiO2 nanoparticles follow a second-order ET rate. It has been observed that for strongly coupled dyes, BET reaction occurs much faster than that for weakly coupled dyes. Coupling elements for the BET processes from TiO2 nanoparticles to the parent cation have been determined for shallow and deep trap electrons in the above systems.

1. Introduction Interfacial electron transfer (ET) between molecular adsorbate and semiconductor nanoparticles is an intense area of current research work.1-7 Investigations in this area are strongly motivated by both its fundamental importance and the large number of practical applications, such as solar energy conversion,8 wastewater treatment,9 and nanoelectronic devices.10 Dyesensitized TiO2 nanoparticles and thin films are the most studied systems for their important application in new type of solar cells. This process involves excitation of the dye molecules with visible light and subsequent electron injection into TiO2 nanoparticles. Recent studies show that forward electron injection from strongly adsorbed dyes to TiO2 nanoparticles occur in ultrafast time scale.11-20 High efficiencies for converting absorbed light into electricity depend on fast electron injection and slow back-electron transfer (BET). It is reported in the literature that BET kinetics in different dye-sensitized TiO2 systems range from a few picoseconds to milliseconds and from single21-24 to multiexponential.16-20,25-31 However, the detailed mechanisms such as the rate of electron injection into the semiconductor as well as the factors determining the rate of BET are not well understood. Nevertheless, the main problem faced by the scientists is the low efficiency of photocurrent conversion and particularly * Corresponding author. E-mail: [email protected]. Fax: 00-91-22-5505151.

photodegradation of the dye material. Inorganic dyes, such as Ruthenium polypyridyls, have shown fairly high photocurrent conversion, ca. 10% with reasonable stability.8 However, these inorganic dye materials are comparatively expensive. On the other hand, several organic dye systems, which have good ground-state absorption in the visible region, have been studied, but none of them have shown good photo conversion efficiency as compared to the inorganic dyes. Triphenylmethane (TPM) dyes, which exhibit intense ground-state absorption in the visible region, in principle, could be suitable sunlight harvesting agents. However, the photo current efficiency of the solar cells made by using these TPM dyes (e.g., bromo pyrogallol red and pyrocatecol violet) were found to be 400 ps (Table 2). The recovery dynamics for BrPGR-sensitized TiO2 nanoparticles are shown in Figure 4B and Table 2. Transient absorption decay of PGR and Br-PGR cations have also been measured at 710 nm and are shown in panels A and B, respectively, of Figure 5. The transient

TABLE 1: Spectroscopic Parameters and the Coupling Elements (Hab) of Various Dye-TiO2 Nanoparticle Complexes dye molecule

λmax (nm)

νjmax (cm-1)

∆ν1/2 (cm-1)

max (cm-1 mol-1)

Keq (M-1)

rAB (A0)

Hab (cm-1)

PGR Br-PGR ATC coumarin-343 RuIIL2(NCS)2 alizarin

560 561 537 -

17853 17840 18622 -

4514 3736 2456 -

53431 ( 6041 19972 ( 1172 343 ( 28 -

80 81 60 -

4.1 4.2 4.9 -

10427 ( 591 5658 ( 166 527 ( 21 100a 130a 3100b

a

Taken from ref 60. b Taken from ref 47.

12790 J. Phys. Chem. B, Vol. 105, No. 51, 2001

Figure 4. Bleach recovery kinetics at 570 nm of pyrogallol red (A) and at 590 nm bromo pyrogallol red (B) TiO2 nanoparticle. (Inset: recovery kinetics in the shorter time scale).

TABLE 2: Life Times of the Transients of PGR and Br-PGR Monitored up to 400 ps after Excitiation with 620 nm (fwhm ∼ 300 fs) Laser Pulsea wavelength (nm)

PGR/TiO2

Br-PGR/TiO2

590

τ1 ) 2.49 ps (65.3%) τ2 ) 127.3 ps (7.4%) τ3 > 400 ps (27.3%) 〈τ〉 ) 15.19 ps τ1 ) 2.64 ps (72.4%) τ2 ) 109.7 ps (6.9%) τ3 > 400 ps (20.7%) 〈τ〉 ) 11.96 ps τ1 ) 2.41 ps (52.5%) τ2 ) 32.8 ps (16.3%) τ3 > 100 ps (32.2%)

τ1 ) 2.52 ps (51.5%) τ2 ) 134.6 ps (7.7%) τ3 > 400 ps (40.8%) 〈τ〉 ) 19.7 ps τ1 ) 2.85 ps (55.4%) τ2 ) 123.6 ps (7.3%) τ3 > 400 ps (37.3%) 〈τ〉 ) 16.91 ps -

710

790

Ramakrishna et al.

Figure 5. Decay kinetics of the cation radical of Pyrogallol red at 690 nm (A) and Bromo pyrogallol red (B) at 710 nm exciting with 620 nm laser pulse. (Inset: decay kinetics in the shorter time scale).

a 〈τ〉 is calculated considering the faster 2 components and using eq 12.

absorptions at these wavelengths are both due to transient absorption of the cation radical and also due to the electron in the nanoparticle. So the decay contains two contributions: one is the true decay of the cation radical of PGR, and the other is the decay of the electron signal. The decays are seen to follow multiexponential functions with typical time constants of 2, 110, and >400 ps and 2, 130, and >400 ps for the cation radicals of PGR and Br-PGR respectively (Table 2). We have already discussed and shown in Table 1 that the interaction between TiO2 nanoparticles and ATC dye is weaker as compared to that between TiO2 nanoparticles and PGR or Br-PGR. The optical density of the ATC /TiO2 system at 620 nm was very low. As a result, we could not perform the femtosecond time-resolved measurements for ATC/TiO2 system. However, time-resolved experiments using picosecond flash photolysis have been carried out to study the electron-transfer processes in ATC-sensitized TiO2 nanoparticles exciting by 532 nm (fwhm 35 ps) laser light. The time-resolved transient absorption spectra of ATC-sensitized TiO2 colloid at different time delays following the 532 nm photoexcitation are shown in Figure 6. The spectrum at each time delay consists of a bleach from 450 to 580 nm peaking at 540 nm and a broad positive feature in the whole spectral region (600-800 nm). The broad feature in the 600-800 nm region is assigned to the electrons injected in TiO2 nanoparticles.41-44 To find out the cation absorption spectra, we have carried out pulse radiolysis experiments40 for ATC in water, as described earlier. The transient absorption spectrum for the cation radical of ATC shows a peak

Figure 6. Transient absorption spectra of aurin tricarboxylic acid (ATC) sensitized TiO2 nanoparticles in water at 0, 33, 132, 330, and 660 ps and 1.32 ns after excitation with 532 nm (fwhm ) 35 ps). (Inset: bleach recovery kinetics at 540 nm).

at 470 nm and no absorption beyond 600 nm. Inset of Figure 6 shows the bleach recovery kinetics at 540 nm and found to be multiexponential function with time constants 150 ps, 1.2 ns, and >5 ns. To ensure that the observed transient absorption spectra are due to the photoexcitation of ATC-sensitized TiO2 colloid, blank experiments such as ATC/water and TiO2/water have been performed. No transient signals have been observed from these blanks following 532 nm excitation. Transient absorption studies have also been carried out in microsecond time domain for all the dye-TiO2 nanoparticle systems following 532 nm excitation. Transient absorption signals in microsecond time domain are similar in nature, as observed in femto- and picosecond transient measurements. Shown in Figure 7 are the bleach recovery traces of the PGR/ TiO2 system at 590 nm (Figure 7A) and of the ATC/TiO2 system at 540 nm (Figure 7B). The recovery kinetics can be fitted by a multiexponential function with time constants 0.368 µs (60%) and >10 µs (40%) for the PGR/TiO2 system and 0.978 µs (41.5%) and >10 µs (58.5%) for the ATC/TiO2 system at the lowest pump power used (5 mJ/pulse) (Table 3). The bleach recovery kinetics for the Br-PGR/TiO2 system at 590 nm is also determined to be 0.452 µs (58.3%) and >10 µs (41.7%). It has been observed that the bleach recovers faster for PGR/

Triphenyl Methane Dyes Adsorbed on TiO2

J. Phys. Chem. B, Vol. 105, No. 51, 2001 12791 nanoparticles and at 570 nm of PGR-sensitized TiO2 nanoparticles in the microsecond time domain. We did not observe any pump power dependency of bleach recovery kinetics for PGRand Br-PGR-sensitized TiO2 nanoparticles both in pico and microsecond time domains. However, it is seen in Figure 8A that the bleach recovery kinetics in ATC-sensitized nanoparticles strongly depend on the excitation intensity. The rate constants for the bleach recovery kinetics for both ATC- and PGRsensitized TiO2 nanoparticles have been shown in Table 3. 4. Discussion

Figure 7. Bleach recovery kinetics of pyrogallol red (PGR) at 590 nm (A) and aurin tricarboxylic acid (ATC) at 540 nm (B) on TiO2 in the microsecond time domain after excitation with 532 nm (fwhm ) 35 ps) laser pulse, at the same laser intensity (5mJ per pulse).

Figure 8. Bleach recovery kinetics of (A) aurin tricarboxylic acid (ATC) at 540 nm and (B) pyrogallol red (PGR) at 590 nm adsorbed on TiO2 nanoparticles at different laser intensities. Excitation was at 532 nm, and the intensity was 5 (a), 8 (b), 12 (c), and 16 mJ (d) per pulse. The traces have fitted by biexponential kinetics and shown in Table 3.

TABLE 3: Life Times of the Transients of ATC- and PGR-Sensitized TiO2 Nanoparticles Monitored up to 10 µs after Excitation with 532 nm Laser Pulse at Different Laser Intensity energy/ ηe × 10-18 pulse (mJ) (electrons/cm3) 5

5.4

8

8.6

12

13

16

17.3

lifetimes (µs) ATC/TiO2a PGR/TiO2b τ1 ) 0.978 (41.5%) τ2 > 10 (58.5%) τ1 ) 0.784 (42.9%) τ2 > 10 (57.1%) τ1 ) 0.575 (42.1%) τ2 > 10 (57.9%) τ1 ) 0.474 (42.4%) τ2 > 10 (57.6%)

τ1 ) 0.358 (60%) τ2 > 10 (40%) τ1 ) 0.338 (62.5%) τ2 > 10 (37.5%) τ1 ) 0.376 (56.3%) τ2 > 10 (43.7%)

a Bleach recovery is monitored at 540 nm. b Bleach recovery is monitored at 570 nm.

TiO2 and Br-PGR/TiO2 systems as compared to that for the ATC/TiO2 system. To gain more insight into the nature of recombination kinetics, pump power dependence studies have been carried out for PGR-, Br-PGR-, and ATC-sensitized TiO2 nanoparticles. Shown in panels A and B of Figure 8 are the pump power dependency of the bleach recovery kinetics at 540 nm of ATC-sensitized TiO2

(A) Assignment of Steady-State Optical Absorption Spectra and Formation of Charge-Transfer Complex. To study the dye-sensitized electron-transfer reaction in the excited state, it is very important to know the type of interaction of the dye molecules when they adsorb on the nanoparticle surface. Shown in Figure 1 are the steady-state optical absorption spectra of PGR in water and in TiO2 colloidal solution. It has been observed that with increasing TiO2 concentration, the optical density of the adsorbed dye increases, and also, a new peak appears. At high concentrations of the TiO2 nanoparticle (15 g/L), the optical absorbance goes beyond 800 nm. It has already been observed by Tennakone et al.32 that upon addition TiO2 nanoparticles in Br-PGR, the optical absorbance spectrum of Br-PGR becomes broad and red-shifted. The interaction between TiO2 and Br-PGR is explained to be charge transfer in nature. In the present study, the interaction between PGR and Br-PGR dyes and TiO2 nanoparticles have been attributed to the charge transfer interaction. With the assumption that the optical density at 650 nm is directly proportional to the adsorbed dye, the variation of optical density at 650 nm with TiO2 nanoparticle concentration, the Benesi-Hilderband equation,45 is used to determine the Keq (equilibrium constant). For chargetransfer interaction, it can be represented as Keq

R-O- + tTisOH2+ 98 dTisOsR + H2O

(4)

Since the concentration of surface hydroxyl groups (tTisOH2+) is proportional to the concentration of TiO2 nanoparticle, we can define the equilibrium association constant

Keq )

[Ti-OR] [R-O-][TiO2]

(5)

where [R-O-] is the equilibrium concentration of the nonadsorbed dye i.e., remaining in solution, [TiO2] is the particle concentration, and [Ti-OR] is the concentration of the complex. This equation can be written as

Keq )

CTi-OR 0 (CR-O -

0 - CTi-OR)(CTiO - CTi-OR) 2

(6)

0 0 Here CTiO and CR-O - are the initial concentrations of TiO2 and 2 free dye, respectively, and CTi-OR is the concentration of the complex formed. When optical absorption of free dye is very small compared to that of the CT complex and the experimental 0 0 . CR-O condition CTiO - is fulfilled, then the following 2 Benesi-Hildebrand equation can be easily derived using the relation CTi-OR ) l D/Ti-OR, where D and Ti-OR are the optical density and molar absorption coefficients due to the complex, respectively, and l is the path length of the cell:

12792 J. Phys. Chem. B, Vol. 105, No. 51, 2001

( )

0 CRO 1 1 1 + ) 0 D KeqTi-OR C Ti-OR TiO2

Ramakrishna et al.

(7)

From the Benesi-Hilderband plot (Figure 1 Inset), the values of Keq and Ti-OR of the PGR-TiO2 complex having a band maximum at 560 nm have been determined to be 80 M-1 and 53 431 ( 6041 L cm-1 mol-1 (Table 1). Figure 2 shows the change in optical absorption spectrum of ATC in the presence of TiO2 nanoparticles. It has been observed that the free dye shows absorption peak at 521 nm and the dye adsorbed on TiO2 nanoparticles shows absorption peak at 531 nm. But the dye-nanoparticle complex peak absorbs at 537 nm (Table 1). We have determined the complex peak, just from the absorption spectra of the dye on nanoparticles by subtracting the absorption spectra of the free dye and TiO2 nanoparticle. The dye-nanoparticle interaction has been found to be weaker for ATC as compared to those of PGR and Br-PGR. From the Benesi-Hilderband plot, the values of Keq and Ti-OR for ATCTiO2 complex have been determined and presented in Table 1. From the optical absorbance measurements, the spectroscopic quantities of dye-TiO2 complex the molar extinction coefficient (max), CT band maximum (λmax), νjmax , and the bandwidth (∆νj1/2) have been determined for all the dyes and are shown in Table 1. The electronic coupling matrix Hab of ground state to a charge-transfer excited state can be calculated using Mulliken-Hush equation.33,34 Using the spectroscopic quantities obtained from the absorption spectrum of the surface complex and donor-acceptor separation rDA calculated out of the molecular volume,46 Hab’s for all the dye-TiO2 systems have been calculated and are given in Table 1. It is observed that the values of Hab’s are very high for PGR-TiO2 and Br-PGRTiO2 complexes, but that of ATC-TiO2 is 1 order of magnitude lower (Table 1). The electronic matrix element Hab for the alizarin-TiO2 complex has been reported to be 3.1 × 103 cm-1 by Huber et al.47 It has already been discussed by Moser et al.48 that surface complexation for catechol is stronger than salicylate compounds with colloidal TiO2 solution. Catechol type of complexation forms a five-membered ring, which is very stable compared to a six-membered salicylate type of complex (Scheme 2). In the present investigation, both PGR and BrPGR form catechol type complex with TiO2 nanoparticles; on the other hand, ATC forms a salicylate-type complex with TiO2 nanoparticles. (B) Femtosecond Laser Flash Photolysis Studies of TPM Dyes and Assignments of the Transients. It has been demonstrated by many workers that optical excitation of dye molecules adsorbed on TiO2 nanoparticle surface injects electrons into the conduction band of the nanoparticle.11-31 In the present investigation, we have carried out subpicosecond laser flash photolysis experiments exciting the TPM dye (PGR and Br-PGR) sensitized TiO2 nanoparticle at 620 nm to study the electron-transfer dynamics on semiconductor surface. Figure 3 shows the time-resolved transient absorption spectra of PGRsensitized TiO2 nanoparticles in water. The spectrum at each time delay consists of a bleach in 520-600 nm wavelength region with a maximum at 570 nm, a positive absorption band with maxima at ∼690 nm, and a broad positive feature in the spectral region (750-900 nm). The bleach peak appears due to disappearance of ground state of the dye-TiO2 complex upon excitation by the laser pulse. The broad spectral absorption in the 750-900 nm regions is attributed to the conduction band electrons in the nanoparticle. It has already been shown by many workers that the conduction band electrons can be detected both by visible30,31,41-44 and infrared absorption.15-19 The band having

maximum at 690 nm is assigned to PGR cation radical (PGR‚ +). Assignment of this band has been made on the basis of the results obtained in separate pulse radiolysis experiments,40 where PGR‚+ was generated selectively by the reaction of N3• radical with PGR molecule in N2O saturated aqueous solution. The transient spectrum obtained from the above experiment shows an absorption peak at 690 nm with a shoulder at 625 nm. The pulse radiolysis measurements gave the transient absorption peak for the Br-PGR cation radical at 710 nm. To ensure that the observed transient absorption spectra are due to the photoexcitation of PGR-sensitized TiO2 colloid, experiments with unsensitized TiO2/water and PGR/water were performed. No transient signals have been observed from these blanks following 620 nm excitation. It should be noted that the ground-state UV/ vis spectrum of TiO2 colloid shows no absorption at 620 nm. The electron-transfer reaction in the present study can be presented as hν

8 e- (TiO2) + dye+• [TiO2 -dye]adsorb 9 electron injection cb Where dye+• is the cation radical of the dye and ecb is the conduction band electron in TiO2 nanoparticle. However, the bleach at 590 nm recovers with time (Figure 4), and this is due to the back reaction involving recapture of the conduction band electrons by the dye cation radical recombination

+• e98 [TiO2 -dye]adsorb cb(TiO2) + dye

The recovery kinetics have been found to be a multiexponential function with the time constants of 2.5 ps (65.3%), 130 ps (7.4%), and >400 ps (27.3%)(Table 2), although up to 400 ps (maximum time limit of detection of our subpicosecond spectrometer) only 70% of the bleach recovers. At longer time scale measurements (nano- and microsecond), the recombination process is also found to be a multiexponential process (next section). The BET dynamics in the case of Fe(CN)64--sensitized TiO2 nanoparticles studied by Lian group17,20 were also found to be nonexponential. The origin of the nonexponential recombination was attributed to the spatial and energetic distribution of trap states of the injected electrons in the nanoparticle. The rate of BET reaction can also be determined by monitoring the cation peak at 710 nm (Figure 5A). The decay of the observed signal can be fitted by a multiexponential function with time constants of 2.64 ps (72.4%), 110 ps (6.9%), and > 400 ps (20.7%)(Table 2). However, the transient absorption at 690 nm is due to both transient absorption of PGR cation radical as well as the conduction band electron. So, for recombination reactions, we have preferred to monitor the bleach recovery kinetics. Time-resolved studies in subpicosecond time domain have also been carried out for Br-PGR dye-sensitized TiO2 nanoparticles following excitation by 620 nm laser pulse. The timeresolved spectrum of the transients recorded at each time delay contains a bleach in 450-610 nm wavelength region, a positive peak at 710 nm for cation radical, and a broad positive absorption band in the 750-950 nm wavelength region for conduction band electron. Bleach recovery kinetics have been compared with the PGR-TiO2 system and are shown in Figure 4B. The bleach recovery kinetics have been fitted multiexponentially with time constants 2.5 ps (51.5%), 130 ps (7.7%), and >400 ps (40.8%) (Table 2). Figure 5B shows the transient absorption decay for the cation radical of Br-PGR at 710 nm, and the kinetics have been fitted multiexponentially with time

Triphenyl Methane Dyes Adsorbed on TiO2 constants 2.85 ps (55.4%), 123.6 ps (7.3%), and >400 ps (37.3%) (Table 2). (C) Pico- and Microsecond Laser Flash Photolysis Studies of TPM Dyes and Assignment of the Transients. Timeresolved picosecond flash photolysis experiments have been carried out on ATC-sensitized TiO2 nanoparticles after excitation with 532 nm laser pulse. Figure 6 shows the transient absorption spectra at different time delays, which consist of a band due to bleach in 450-590 nm region with a peak at 540 nm and a broad positive feature in 600-800 nm wavelength region, which is assigned to the conduction band electron. No signal for the cation radical is observed beyond 600 nm. It can be explained from the fact that the cation radical observed in pulse radiolysis measurements showed transient absorption peak at 470 nm, and the transient does not absorb beyond 600 nm. The bleach recovery kinetics monitored at 540 nm has been shown in Figure 6 inset. The recovery kinetics can be fitted by a multiexponential function with time constants 150 ps (26.7%), 1.2 ns (43.9%), and >5 ns (29.4%). Time-resolved picosecond experiments have also been carried out for PGR- and Br-PGR-sensitized TiO2 nanoparticles using 532 nm laser pulse. The nature of the spectra is similar, as we observed due to excitation by 620 nm femtosecond laser pulse. The results of the above systems have already been discussed in the previous section. To compare the bleach recovery kinetics for all the TPM dyesensitized TiO2 nanoparticle systems at longer time scale, flash photolysis experiments have been carried out at microsecond time domain. The bleach recovery kinetics of PGR-sensitized TiO2 nanoparticles monitored at 570 nm and ATC-sensitized TiO2 nanoparticles monitored at 540 nm have been shown in panels A and B, respectively, of Figure 7. It has been observed that back-electron transfer is much faster in the case of PGRsensitized TiO2 nanoparticles compare to that in ATC-sensitized TiO2 nanoparticles. We have already mentioned that the coupling constant for the ground-state complex of the PGR/TiO2 system is ∼20 times higher as compared to that of the ATC/TiO2 system (Table 1). Free energy change (-∆G) for the BET reaction for all the TPM dye-sensitized TiO2 nanoparticles is found to be very similar (discussed in the section E). Now, from the experimental data, it can be concluded that coupling strength for the back-electron-transfer reaction for the PGR/TiO2 system must be higher than that of the ATC/TiO2 system. The detailed mechanism of back-electrontransfer reaction for the above systems has been discussed in the section E. (D) Intensity Dependence of Recombination Kinetics. To find out the order (first or second) of electron-transfer rate for all the above systems, we have carried out experiments by changing the pump intensity. Panels A and B of Figure 8 show the bleach recovery kinetics as a function of laser intensity for ATC-sensitized TiO2 nanoparticles at 540 nm and PGRsensitized TiO2 nanoparticles at 570 nm, respectively. It has been observed that both for PGR- and Br-PGR-sensitized TiO2 nanoparticle systems, the bleach recovery kinetics do not dependent on the excitation intensity both in pico- and microsecond time domain. The linear pump power dependency of recombination dynamics for FeCN)64--sensitized TiO2 naoparticle was also observed by Lian and co-workers.20 They concluded that charge-separated ionpair behaves as a geminate pair. In the present investigation, both PGR and Br-PGR form strong charge-transfer complex and show linear dependency with pump power in bleach recovery kinetics. It indicates that charge separated ionpairs for both the systems behave as geminate pairs. So the recombination reaction rate will be first-order in the pair.

J. Phys. Chem. B, Vol. 105, No. 51, 2001 12793 SCHEME 3: Mechanistic Scheme for Electron Transfer from the Electronically Excited Dye to the TiO2 Nanoparticlea

a Here S*/S+ is the excited sensitized dye/cation radical couple, E c the conduction band edge (-0.5 V), Ev the valence band, and SS the surface states.

Under these conditions, the back reaction lifetime will be unaffected by changes in laser excitation power, as we observed for PGR-sensitized TiO2 naoparticle in Table 3. However, we have observed strong pump power dependence recombination kinetics for the ATC-sensitized TiO2 nanoparticle in microsecond time domain. The recovery kinetics can be fitted by two exponentials. It has been observed that lifetime of the shorter component decreases with increasing laser intensity, but the relative contributions do not change (Table 3). The recombination reaction for the ATC-sensitized TiO2 nanoparticle follow second-order electron-transfer rate and has been discussed in detail in next section. (E) Back-Electron Transfer. According to semiclassical theory,49 formulation for the back-electron-transfer rate constant kBET can be given in eq 8 as

kBET )

( )

{

}

(∆G0 + Λ)2 2π 1 exp [HAB]2 p 4ΛkT x4πΛkT

(8)

∆G° is the overall free energy of reaction ) (EC - ES/S+), EC is the potential of electrons in the conduction band of the semiconductor (-0.52 V),7 and ES/S+ is the redox potential of the adsorbed dye (Scheme 3). One can use eq 8 if the reaction follows first-order electron-transfer rate. But for a second-order reaction (in this case, for recombination between conduction band electrons and the oxidized sensitizers), a model for the distribution of reactant distances during the charge-transfer process, is required to extract the electronic coupling constant from second-order rate constant.50,51 Assuming a random distribution of distances between the electrons in the nanoparticle and the adsorbed acceptors, the second-order electron-transfer rate constant (kBET) can be expressed as

kBET )

( )

2π [Hab]2 p d

lSC 2/3 SC

(6/π)

1 1/3

x4πΛkT

{

exp -

}

(∆G0 + Λ)2 4ΛkT

(9)

12794 J. Phys. Chem. B, Vol. 105, No. 51, 2001

Ramakrishna et al.

where lSC is the effective coupling length between the oxidized dye and the nanoparticle and dSC is the density of the atoms that contribute to the density of states in the band concern. Comparison of eqs 8 and 9 shows that the electronic coupling for a second-order reaction is modified by the term lSC/[dSC2/3 - (6/π)1/3], which has units of cm3, so that kBET is measured in units of cm3 s-1. The redox potential values of PGR, Br-PGR, and ATC in aqueous solution are measured to be 0.478, 0.458, and 0.475 V, respectively, against the Ag/AgCl half electrode. The free energy changes (-∆G°) of BET reaction calculated for these dyes are seen to be very similar value. Now, from the data obtained, we can say that all electron-transfer parameters for all the dyes are very similar except the coupling element |HAB|2. The difference in BET rates for the above systems can be attributed to the difference in coupling strengths of the injected electrons and the parent cation. Once the electron is injected into the conduction band, it relaxes very fast to the conduction band edge. As the time progresses, the electron relaxes to different trap states (shallow and deep) (Scheme 3). Earlier, many authors17-20,25-31 attributed the multiexponential recombination dynamics to the distribution of coupling strengths for the BET reaction of shallow and deeply trapped electrons and the parent cation. We too expect different coupling constants between the differently trapped electrons (shallow and deep) and the parent cation. To determine the coupling elements of the above systems using eqs 8 and 9, we need to know the value of Λ (where Λ ) λs + λv). Here λv and λs are the internal and solvent reorganization energies, respectively. λv depends on frequency ν of the vibrational mode associated with the electron transfer. In the present investigation, PGR-TiO2 and Br-PGR-TiO2 have active vibration mode similar to that of alizarin-TiO2.47 So we use the same value for λv (0.32 eV) as that calculated for alizarin-TiO2 by Moser and Gratzel.47 We have used the same value for λv (0.30 eV) for ATC-TiO2 as that calculated by Moser and Gratzel47 for coumarin-343-TiO2 because both ATC and coumarin 343 have similar kind of binding (salicylate type) with TiO2 nanoparticle. According to the Marcus equation in electron-transfer heterogeneous media,49 the solvent reorganization energy λs depends on the diameter of the dye molecule (d), the mean electron-transfer distance, i.e., the separation of the molecule from the surface (r), the static dielectric constant of the solvent (), and the high-frequency dielectric constant, which is given by its refractive index squared (n2):

(

)(

2

λs )

)

1 (∆e) 2 1 1 1 2 4π0 d 2r n2 

(10)

However, the reorganization energy λS for redox-active ions at a semiconducting electrode-liquid interface52 can be expressed as:

[(

(

)]

n 2 - n2 2 1 (∆e) 2 1 1 1 TiO2 1 TiO2 -  1 λs ) 2 4π0 d n2  2r n 2 + n2 n2 TiO2 +   TiO

)

2

(11)

where nTiO2 and TiO2 are the refractive index and dielectric constants for the electrode material (nTiO2 ) 2.5 and TiO2 ) 86 for anatase TiO2).53 In the present investigation, we have used eq 11 to determine λS for all the dye molecules at the nanocrystalline TiO2 surface. For PGR-TiO2 and Br-PGR-

TiO2, the diameters of the dye molecules are calculated to be 0.41 and 0.42 nm, respectively (Table 1). The mean electrontransfer distance r for both the systems is considered to be 0.22 nm, which is same as used in the case of alizarin-TiO2.54 For ATC-TiO2, d is calculated to be 0.49 nm, and r is 0.3 nm. Using eq 11, the λ s for PGR and Br-PGR are calculated to be 0.406 and 0.408 eV and, for ATC, 0.415 eV. Hence, using these values of λ s and λ v, the values of Λ are calculated to be 0.726 eV for PGR, 0.728 eV for Br-PGR, and 0.713 eV for ATC. As BET reactions for the above systems are multiexponential processes, a reasonable comparison would be the average or characteristic rates. We adopted a commonly used definition of average life 〈τ〉 of the form55,56

〈τ〉 )

∫01∆A(t) dt ∆A(t′) - ∆A(0)

(12)

to obtain the average ET rate. In the present study, we do not have data at delay times over 400 ps, so we can only calculate the average lifetime within 400 ps, by integrating the kinetics up to 400 ps. The calculated 〈τ〉 are shown in Table 2. We have already discussed that bleach recovery kinetics for PGR- and Br-PGR-sensitized TiO2 nanoparticles show linear dependence with laser intensity both in pico- and microsecond time domain. Using eq 8, we have calculated the values of HAB for the BET reactions and found to be 24.2 and 19.6 cm-1 between the shallow trapped electrons and the parent cation for PGR- and Br-PGR-sensitized TiO2 nanoparticle systems, respectively. In the present investigation, the coupling matrix element determined by bandwidth analysis is designated as Hab, and determined by kinetic analysis as HAB. We can make a comparison of the coupling matrix elements for these two dyes as determined by two processes. Hab’s for PGR and Br-PGR are determined to be 10427 and 5658 cm-1, respectively (Table 1), and the ratio of them is found to be 1.84. On the other hand, HAB’s ratio for PGR and BR-PGR is found to be 1.23. HAB’s for PGR and Br-PGR systems have been calculated from eq 8, which depends on kBET, Λ, and -∆G°. As both Λ and -∆G° are different for the above systems, it is not necessary that Hab’s ratio and HAB’s ratio to be similar. However, it is important to see that the trend, i.e., Hab of PGR is higher than Hab of BrPGR, is carried through so that HAB of PGR is higher than HAB of Br-PGR. We have already discussed that the coupling elements of the shallowly trapped electron will be different from deeply trapped electron with the parent cation. We have attributed the recombination dynamics in faster time scale (picosecond time domain) as recombination between shallowly trapped electron and parent cation and in longer time scale (micro-second time domain) as recombination between deeply trapped electron and parent cation. After electron injection in the conduction band, the electrons relax very fast to the conduction band edge, and then they go to shallowly trapped states and at longer time move to deeply trapped states. In the case of strong complexes (PGR/ TiO2 and Br-PGR/TiO2), the recombination rate follows a firstorder ET rate, so in these cases, different binding modes of the dye molecule do not come into the picture. If different binding modes were there, then recombination rate would follow secondorder ET rate. The coupling constant of deeply trapped electron for PGR/TiO2 and Br-PGR/TiO2 systems have been determined to be 0.16 and 0.13 cm-1, respectively, using kET as 0.364 µs for PGR/TiO2 and 0.452 µs for Br-PGR/TiO2 and eq 8. On the other hand, the bleach recovery kinetics for ATCsensitized TiO2 nanoparticles show laser intensity dependence

Triphenyl Methane Dyes Adsorbed on TiO2

J. Phys. Chem. B, Vol. 105, No. 51, 2001 12795

Figure 9. Plot of apparent rate constant for back ET to ATC cation radical (ATC+‚) versus ηe, the number of injected electrons per unit volume of TiO2.

behavior in the microsecond time domain. To determine the coupling strength for BET in ATC-sensitized TiO2 nanoparticles, second-order electron transfer rate equation (eq 9) can be used. The data obtained from recovery kinetics can be fitted reasonably well with two exponentials, but the fit produced different rate constants for each excitation intensity (Table 3). Figure 9 shows a representative power dependence or reaction order plot for the sensitizer, ATC. The plot is formulated as k1,app versus ηe, the number of injected conduction band electrons per unit volume of TiO2. The required ηe values are obtained by first determining the concentration of the injected electrons for each sample (∆A/A[Dye]) and dividing by the molarity of TiO2 particles (determined from concentration and estimated size and density) and the volume of the TiO2 particles. Even with the lowest intensity of the excitation pulse, we have calculated that more than one electron is injected into the nanoparticle. Figure 9 shows that the apparent rate constant is a linear function of the electron concentration. The results are consistent; therefore, the overall rate constant for ATC-sensitized TiO2 follows second order. Following Lewis and co-workers,57,58 the BET rate can be written as

rate ) (1/τ1)[ATC+] ) k1,app[ATC+] ) kBETβηe[ATC+] (13) where [ATC+] is the concentration of the oxidized ATC dye on the semiconductor surface (mol cm-2) and β is the electronic coupling attenuation factor (value unknown, but for molecular ET system, it is estimated as 0.4 < β < 1.5 Å-1). In this formulation, the units of kET are cm4 s-1, as expected for a second-order interfacial process. As the value of β is unknown, we have chosen to report the composite quantity kETβ obtained from the slopes of best fit lines of plots of k1,app versus ηe. We get the value of kETβ from Figure 9 as 9.34 × 10-14 cm3 sec-1 for the ATC-sensitized TiO2 nanoparticle system. Now following the second-order rate equation in dye semiconductor nanoparticle surface, eq 9 can be written as50

kETβ )

( )

{

}

(∆G0 + Λ)2 2π 1 [HAB]2 exp p 4ΛkT x4πΛkT

(14)

where

HAB ) HAB

x

lSC

dSC (6/π)1/3 2/3

Using eq 14, HAB for ATC-sensitized TiO2 nanoparticles has been calculated to be 3.75 × 10-15 eV cm3/2. Considering the lSC the effective coupling length as 3 × 10-8 cm, the HAB has

been calculated to be 6.04 cm-1. As we have measured the recombination dynamics of ATC/TiO2 in the microsecond time scale and in that time the electrons go to the deeper trapped state, HAB gives the coupling matrix of the recombination reaction of parent cation and deeply trapped electrons. (F) Energy Conversion Implications. The significant application of the knowledge of BET reaction of dye-sensitized nanoparticles is to design and optimization of dye-sensitized solar cell. The solar cell designed by Tennakone et al.32 using organic triphenyl methane (bromo-pyrogallo red and pyrocatechol violet) dyes was found to give low photo current conversion efficiency (