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Elucidating the Energy and Electron Transfer Dynamics of Photon Upconversion in Self-Assembled Bilayers Tristan Dilbeck, Jamie C Wang, Yan Zhou, Andrew Olsson, Milan Sykora, and Kenneth Hanson J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b07003 • Publication Date (Web): 14 Aug 2017 Downloaded from http://pubs.acs.org on August 14, 2017
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Elucidating the Energy and Electron Transfer Dynamics of Photon Upconversion in SelfAssembled Bilayers Tristan Dilbeck, Jamie C. Wang, Yan Zhou, Andrew Olsson, Milan Sykora,† Kenneth Hanson* AUTHOR ADDRESS Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida, 32306, United States †Chemistry Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
ABSTRACT
Self-assembled bilayers of acceptor (A) and sensitizer (S) molecules on a metal oxide surface is a promising strategy to facilitate photon upconversion via triplet-triplet annihilation (TTA-UC) and extract charge from the upconverted state. The hypothesized mechanism for TTA-UC in a bilayer film includes low energy light absorption, triplet energy transfer, cross surface energy migration, triplet-triplet annihilation, and electron injection into TiO2. Nonproductive processes can also occur including sensitizer-sensitizer TTA, radiative/non-radiative decay, back electron transfer, and others. Steady-state and time-resolved emission/absorption
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spectroscopy were used to determine the rate constants of these processes. The rate constants indicate that S to A triplet energy transfer as well as S and A non-radiative rates are the primary efficiency limiting processes for TTA-UC at the interface. This information is necessary to guide the design of new self-assembled UC films and is a critical stepping stone towards the long-term goal of generating a practical, UC solar cell.
INTRODUCTION Photon upconversion (UC), combining two low energy photons to generate a higher energy excited state, is of interest for a number of applications including bioimaging,1-2 oxygen sensing,2 photocatalysis,3 and solar energy conversion.4-10 For the latter, molecular UC by way of triplet−triplet annihilation (TTA-UC) is of particular interest because 1) it can be efficient even under low intensity, solar irradiation11 and 2) if successfully harnessed in a solar cell, can increase the maximum theoretical efficiencies from 33% to more than 43%.12 A key factor in dictating the efficiency of TTA-UC, is the strategy for combining sensitizer and acceptor molecules
including
in
solution,11
polymer
films,13-15
matrix
free
mixtures,16
microemulsions/vesicles/mirocapsules,17-19 and most recently in sensitizer doped amorphous films.7 Nanocrystalline metal oxides have recently emerged as a promising substrate for combining TTA-UC pairs by way of physisorption,20 codeposition,21 or heterogeneous sensitization.10, 22-23 Along this vein, our research group introduced self-assembled multilayers on a metal oxide film24 as an effective strategy for facilitating TTA-UC emission25 and generating photocurrent from the UC state.5-6 The bilayer films (Figure 1a), assembled via step-wise soaking26-27 of a nanocrystalline metal oxide substrate (TiO2 or ZrO2), are composed 4,4′-
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(anthracene-9,10-diyl)bis(4,1-phenylene)diphosphonic acid as the acceptor molecule (A), ZnII linking ions, and Pt(II)-tetrakis(4-carboxyphenyl)porphyrin as the sensitizer (S).25 The absorption spectra for the monolayer (MO2-A and MO2-S) and bilayer films (MO2-A-Zn-S) on ZrO2 can be seen in Figure 1b.
MO2
b) ZrO2
Absorbance (a.u.)
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2
λex=
ZrO2-A
360nm
ZrO2-S ZrO2-A-Zn-S
1
λex=
532 nm
0 300
350
400
450
500
550
600
Wavelength (nm)
Figure 1. (a) Schematic representation of the self-assembled bilayer with structures for A, B, and S, and (b) the UV-Vis absorption spectra for ZrO2, ZrO2-A, ZrO2-S, and ZrO2-A-Zn-S (A to S ratio is ~8:1). Blue and green arrows indicate the wavelength for preferential excitation of A and S, respectively.
Under solar irradiance (AM1.5) passed through a 495 nm long pass filter, photocurrents of 0.158 mA cm-2 were recently demonstrated for these bilayer films28 which is the record for harnessing TTA-UC in a solar cell and is above the device relevant threshold (0.1 mA cm-2) proposed by Schmidt and coworkers.29 While promising, these values must be increased to 1 mA
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cm-2 or more to achieve notable enhancements in solar energy conversion efficiencies (i.e. a factor of 1.1 or more). Crucial to reaching this goal is to understand the rate/efficiency limiting processes in the bilayer film. The proposed mechanism and dynamics events for TTA-UC and charge separation in the TiO2-A-Zn-S can be seen in Figure 2a and 2b. These events are a compilation of the known productive and non-productive pathways in TTA-UC and dye-sensitized solar cells. This does not preclude other events from occurring but based on what is known about the above systems, these are anticipated to be the primary drivers dictating efficiencies. The productive events include low energy light absorption and intersystem crossing by S (kex and kISC in Figure 2a), S to A triplet energy transfer (kTET), cross-surface energy migration (kmig), and triplet-triplet annihilation (kTTA) yielding one ground state (1A) and one singlet excited state (1A*) acceptor molecule. There is sufficient potential in the singlet excited state of A (-1.65 V vs NHE)25 to inject an electron (kinj(1A*)) into the conduction band of TiO2 (2.0 V vs NHE)30 hinders excited state electron transfer from S* and A*, and therefore photophysical events can be quantified in the absence of electron injection. Some of the dynamic events in Figure 2a and 2b (i.e. kinj(1A*), kBET, etc.) can be measured directly using a single sample by monitoring a particular transient absorption feature. For the remainder of the samples, comparative measurements are performed such that a sample of interest will have only one additional kinetic event that is not present in the control sample (calculations are described in greater detail below).31-32 For several of the samples, triphenyl-4,4'diphosphonic acid (B in Figure 1a) is used as a photo- and electrochemically inert surrogate for A that retains the bilayer structure and MO-S spatial separation but without concerns of competitive energy or electron transfer to B.33-35 Throughout the paper, the sensitizer (S) and acceptor (A) will be preferentially excited using 532 nm 360 nm light. respectively (Figure 1b). In an effort to determine the kinetics of a the MO2-A-Zn-S bilayer under operational conditions, the A and S ratios were kept at device relevant conditions (2:1, A:S) whenever possible to account for any possible concentration dependent phenomena. The results and discussion section below is partitioned by the excited state involved (i.e. triplet sensitizer, triplet acceptor, singlet acceptor, and TiO2(e-)) and the productive and non-productive events associated with each state.
EXPERIMENTAL METHODS Materials: Zinc acetate dehydrate and Pt(II) meso-tetra(4-carboxyphenyl)porphine (S) (Frontier Scientific), were purchased from their respective suppliers, in parentheses, and used as received. All other reagents and solvents (analytical reagent grade) have been purchased and used without further purification from Alfa Aesar. Glass was purchased from Hartford Glass Co. Meltonix
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film (1170-25) and Vac’n Fill Syringe (65209) were purchased from Solaronix. Micro glass cover slides (18 × 18 mm) were obtained from VWR. TiO2 and ZrO2 solgel pastes were prepared following a previously reported procedure.27, 36-37
Dye Synthesis: 4,4′-(Anthracene-9,10-diyl)bis(4,1-phenylene) diphosphonic acid (A)25 and triphenyl-4,4'-diphosphonic acid (B)38-40 were prepared by following previously published procedures.
Sample Preparation-Cell Fabrication: Spectroscopic samples were prepared in a sandwich celltype architecture.25 Briefly, glass was cut into 2.2 × 2.2 cm pieces and an active area of 1 cm2 metal oxide was prepared by doctor blading ZrO2/TiO2 (1 layer Scotch tape) and sintering.36 Dyes were then loaded onto the metal oxide, as described below. A small hole (d = 1.1 mm) was drilled into the corner of the 2.2 × 2.2 cm glass slide. A 2 mm wide 2.2 × 2.2 cm Meltonix film was placed between the two glass slides and the entire ensemble is heated to ∼150 °C for 7 s using a home built heating/sealing apparatus described previously.33 The cells were then transferred to a glovebox (VTI Universal Purified Glovebox, N2 atmosphere) where dry and oxygen free acetonitrile was injected using a Vac’n Fill Syringe through the 1 mm hole to fill the interior of the cells. A meltonix film and small piece of micro glass cover slide were then heated to seal the hole used for solvent injection.
Sample Preparation-Dye Loading: The metal oxide films on glass were functionalized with monolayers of A and B by soaking in their respective loading solutions (200 µM A in DMSO, 150 µM B in DMSO). Surface coverages (Γ in mol cm−2) for A are described with the expression
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Γ = (A(λ)/ε(λ))/1000 where ε is the molar extinction coefficient in DMSO (1.27 × 104 M-1 cm-1 at 376 nm)25 and A(λ) is the maximum absorbance of the slides.41 Maximum surface coverage of Γ = 1.49 × 10−7 mol cm−2 was achieved for A on ~4 µm thick films of both ZrO2 and TiO2. The mixed monolayers of A and B were prepared by submerging MO2 in a mixed solution of 100 µM A and 100 µM B in DMSO. The ~50% lower absorbance of A in the mixed films, relative to A only, with similar loading time indicates co-deposition of A and B on the metal oxide. Films For bilayer film formation, MO2-A/B is then soaked in a methanol solution of 400 µM Zn(CH3COO)2, followed by a 200 µM solution of S in DMSO. After each loading step, the films were thoroughly rinsed with solvent to remove any physisorbed, not chemically bound A/B/S molecules. Surface coverages (Γ in mol cm−2) for S (ε = 1.30 × 104 M-1 cm-1 at 510 nm)25 are determined the same way as described above for A.
Sample Preparation for STTA: The metal oxide film on a loading slide was first functionalized with a full monolayer of B, then ZnII, then S (Γ = 5.0 × 10−8 mol cm−2). Following the procedure of O'Regan et al. to obtain uniform coverage,42 the fully functionalized bilayer was then submerged in dilute aqueous KOH for 5-60 seconds to desorb different quantities of S giving a range of sensitizer surface coverages from 8.8 × 10−9 mol cm−2 (18% coverage) to 4.5 × 10−8 mol cm−2 (90% coverage). Emission lifetimes were measured by submerging the films in acetonitrile in a cuvette that was then deaerated using N2 bubbling for 30 minutes.
Absorption Spectra: Data were recorded on an Agilent 8453 UV−visible photo diode array spectrophotometer. Thin film absorption spectra were obtained by placing dry, derivatized TiO2 and ZrO2 slides perpendicular to the detection beam path.
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Time-Resolved Emission: Data were collected at room temperature using an Edinburgh FLS980 fluorescence spectrometer. The emission decay traces were acquired using either multi-channel scaling (MCS) acquisition mode with 532 nm excitation from a 60 W microsecond flashlamp (pulse width < 2.5 µs) at a 100 Hz repetition rate or time-correlated single-photon counting (TCSPC; 1024 channels; 100 ns window) with data collection for 5,000 counts. Excitation for TCSPC was provided by an Edinburgh EPL-360 picosecond pulsed light emitting diode (360 ± 10 nm, pulse width - 892 ps) operated at 10 MHz. Emission was passed through the appropriate long pass filter, then a single grating (1800 l/mm, 500 nm blaze) Czerny−Turner monochromator and finally detected by a Peltier-cooled Hamamatsu R928 photomultiplier tube. As found for other dynamic processes on nanocrystalline metal oxide interfaces,43 emission decay kinetics are complex but were satisfactorily fit with a biexponential function (equation 1) using Edinburgh software package and the results are presented as a weighted average lifetime (equation 2). y = A1e-k1x + A2e-k2x +y0 τi = 1/ki
; < τ > = ΣAiτi2 / ΣAiτ
(1) (2)
Nanosecond Transient Absorption: Nanosecond transient absorption measurements were carried out by inserting sealed samples (2.2 × 2.2 cm with a 1 × 1 cm active area) perpendicular to the light source in a collinear arrangement. The spectrometer is composed of a Continuum Surelite EX Nd:YAG laser combined with a Continuum Horizon OPO (532 nm, 5-7 ns, operated at 1 Hz, beam diameter ~0.5 cm, 2.5 to 5 mJ/pulse) integrated into a commercially available Edinburgh LP980 laser flash photolysis spectrometer system. White light probe pulses generated by a pulsed 150 W Xe lamp were passed through the sample, focused into the spectrometer, then detected by intensified Andor iStar CCD camera. Time-resolved scans were passed through a 9 ACS Paragon Plus Environment
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TMS302-A monochromator (1800 grooves/mm grating) with a 300 mm focal length in Czerny Turner configuration and detected by a Hamamatsu R928 side window PMT. Detector outputs were processed using Edinburgh’s L900 (version 8.2.3, build 0) software package. As with emission, the decay kinetics were fit using a biexponential function (equation 1) and the results are presented as a weighted average lifetime (equation 2).
Femtosecond Transient Absorption Spectroscopy: The TA spectra were recorded using a commercial femtosecond pump–probe TA spectrometer (Helios, Ultrafast Systems). The pump pulses at energy of 3.1 eV (400 nm) were generated by focusing a portion of the 800 nm output from 1 kHz regenerative amplifier (Spectra Physics) onto a BBO crystal. The probe pulse, a white light continuum, was generated by passing the second portion of the 800nm output through a delay line and a 2 mm sapphire crystal. The instrument response time of the system (as determined by pump-probe cross-correlation in a BBO crystal) was 430 fs (FWHM). The diameter of the probe beam focused onto the sample was 0.25 mm. The pump fluence was 26 µJ cm-2 per pulse. To minimize the potential effects of photo-degradation and local heating, the samples were moved (speed of 1 mm/s) continuously back and forth along the length of the film during the experiment. A 435nm long pass filter was placed in front of the detector to reject any potential scattered light generated by the sample. Singular Value Decomposition (SVD) was performed to obtain the decay associated spectra using the commercial software package Surface Xplorer Pro (Ultrafast Systems, LLC).
Applied Potential Nanosecond Transient Absorption: The nanosecond transient absorption spectra were taken as described above while applying a negative bias potential to a sealed cell
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(TiO2-A-Zn-S with 0.1 M LiClO4 in MeCN) using a CH Instruments CHI630E electrochemical analyzer with a three-electrode configuration (TiO2 working, FTO counter, Pt reference) with extended Pt electrodes submerged in an external electrolyte solution (0.1 M LiClO4 in MeCN). The negative bias was applied for one minute before starting the transient absorption acquisition to ensure the TiO2 reached steady state electron concentrations before the measurement was started.
RESULTS AND DISCUSSION 1. Sensitizer Triplet Excited State For platinum porphyrin compounds, the generation of the triplet excited state (3S*) via excitation (kex : 1S + h →1S*) and intersystem crossing (kISC :1S*→3S*) is known to occur on ultrafast time scales (< 1 ps) and in near unity efficiency.44-45 Once generated, several relaxation pathways for 3S* can be envisioned including triplet energy transfer (kTET), radiative (kr(3S*)) and non-radiative (knr(3S*)) decay, S-S triplet-triplet annihilation (kSTTA) and electron injection (kinj(1/3S*)) as summarized in equations 3-7. kTET:
3 *
S + 1A → 3A* + 1S
(3)
kr(3S*):
3 *
(4)
knr(3S*):
3 *
(5)
kSTTA:
3 *
(6)
kinj(1/3S*):
TiO2-3S* → TiO2(e-)-S+
(7)
S → h + 1S S → heat + 1S S + 3S* → 1S + 1S*
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For TTA-UC the only productive process from this list is interlayer S to A triplet energy transfer (S-A TET), eq. 3. To determine kTET we compare two samples with the same sensitizer concentration, which was kept low to prevent any possible STTA (ΓS = 1.26 × 10−8 mol cm−2, 10 A:1 S), one in which S-A TET can occur (ZrO2-A-Zn-S) and a control sample where triplet energy transfer does not occur (ZrO2-B-Zn-S). Terphenyl-4,4''-diylbisphosphonic acid (B) is a photo- and electrochemically inert structural analogue to A that will retain the bilayer structure/distance, but, due to its high energy, is inert towards energy or electron transfer.33-35 The excited state lifetime for ZrO2-B-Zn-S (τs) and ZrO2-A-Zn-S (τs(bl); bl = bilayer) can be described using equations 8 and 9 respectively.
= +
( )
(8)
= + +
(9)
Assuming the only additional decay pathway in the bilayer film is TET, then kTET can be calculated by combining equations 8 and 9, giving equation 10. =
( )
−
(10)
Time-resolved emission spectroscopy was used to determine τs and τs(bl) by selectively exciting S at 532 nm (Figure 1b) and monitoring the emission at 670 nm (Figure 3) giving τs = 59 ± 2 µs, τs(bl) = 33 ± 5 µs, and a kTET of 1.3 × 104 s-1. These, and subsequent lifetimes, are the average of three different measurements for three different samples with the error being the standard deviation. The average lifetimes are then used to calculate the rate constants (k = 1/τ).
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10000
ZrO2-A-Zn-S (33 µs)
8000
ZrO2-B-Zn-S (59 µs)
Counts
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6000 4000 2000 0 0
100
200
300
Time (µs)
Figure 3. Time-resolved emission traces of ZrO2-A-Zn-S (black) and ZrO2-B-Zn-S (red) excited at 532 nm and monitoring S emission at 670 nm (532 nm notch filter).
Radiative and non-radiative decay rates of 2.7 × 102 s-1 and 1.7 × 104 s-1, respectively, from the 3S* state were calculated using equations 11 and 12: =
(11)
=
( )
(12)
where Φs is the emission quantum yield (Φs = 0.016)25 and τs is the emission lifetime (59 ± 2 µs) for ZrO2-B-Zn-S. As an aside, it is interesting to note that the lifetime of S from ZrO2-B-ZnS in MeCN is longer than we observe for S solvated in DMSO (41.08 µs).25 Presumably the difference can be attributed to either the solvent or the local environment decreasing the nonradiative rates in the former. Non-productive STTA is dependent on the proximity of two 3S* states. Since kSTTA is presumed to be a surface loading/concentration dependent phenomena, the excited state lifetime
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(τs) of ZrO2-B-Zn-S was measured with respect to surface loading and the results can be seen in Figure 4. 80 70 60
Lifetime (µ s)
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50 40 30 20 10 0 -8
1.0x10
2.0x10
-8
3.0x10
-8
4.0x10
-8
5.0x10
-8
-2
Surface Coverage (mol cm )
Figure 4. Emission lifetime for ZrO2-B-Zn-S at 670 nm with respect to surface coverage of S (λex=532 nm). To determine kSTTA, we compared the lifetime of a sensitizer in a film with the lowest sensitizer concentration ( ; i.e. with minimal S-S TTA) to one that has a high, device operational sensitizer concentrations ( ), using equation 13, whose derivation is similar to that of equation 10:
= −
(13)
the lifetime for the low (Γ = 8.8 × 10−9 mol cm−2) and high (Γ = 4.9 × 10−8 mol cm−2) sensitizer concentration films were within film to film error at 57.2 µs and 58.5 µs, respectively. The small change in lifetime with respect to S loading and relatively slow rate constant indicates that STTA is a negligible process in the bilayer films, regardless of concentration, giving a value for kSTTA of ~0 s-1. This is in contrast to solution or heterogeneous TTA-UC strategies where increased sensitizer concentration can inhibit UC emission via non-productive TTA.10,
22, 46
The spatial 14
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separation and the limited mobility of S in the bilayer architecture likely inhibits STTA and allows for exceptionally high sensitizer concentrations and reduced Ith values (vide infra) in the bilayer film without decreases in efficiency.5 In an ideal TTA-UC solar cell, the sensitizer will absorb sub-band gap light and have insufficient potential to directly transfer electrons into the conduction band of TiO2. In fact, previous device measurements indicate that minimal photocurrent is generated from the TiO2-S only device.5 However, electron transfer from hot excited states (kinj(1/3S*))47 or into low energy trap states of TiO2 represents an additional non-productive decay pathway for 3S*. To probe this event, the excited state lifetime for S at 670 nm was measured in both ZrO2-B-Zn-S (τZrO2 = 59 ± 2 µs) and TiO2-B-Zn-S (τTiO2 = 39 ± 1 µs) where the only additional excited state quenching process in the latter is electron transfer from
1/3 *
S to TiO2 (Figure S1). A kinj(1/3S*) value of 8.7 ×
103 s-1 was calculated using equation 13. (/ ∗ ) =
!"#
−
(13)
$%"#
Taking into account the rates/processes in equations 3-7, a S to A triplet energy transfer quantum yield (ΦTET) of 0.33, or 33%, was calculated using equation 14 with knr (1.7 × 104 s-1) being one of the primary drivers behind reducing ΦTET. & = '
' ( (
)'% )'*% )'
(14) !*+(
/ ∗ )
The ΦTET value is lower than our previous estimates that were based on steady-state emission quenching (70%).6 However, it is important to note that, due to the inhomogeneous nature of the samples and the limited temporal resolution of the measurement, S-A TET events
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prior to 1 µs are not accounted for in the above calculation. Therefore, the kTET and ΦTET values mentioned above are low-end estimates of the true value. Measurement of kTET by fs−ps timeresolved emission/absorption will be necessary to directly determine the energy transfer rate constant and efficiency. Regardless, the residual emission from S in ZrO2-A-Zn-S indicates that TET is less than 100% efficient, suggesting that energy transfer losses could be a large contributor to lowering the solar energy conversion efficiency of the TTA-UC bilayer. Increasing kTET by increasing the driving force for energy transfer and reducing the distance between S-A or alternatively, using new dyes with lower knr will help increase the energy transfer efficiency.
2. Acceptor Triplet Excited State After triplet energy transfer, the 3A* can undergo cross surface migration (kmig), A-A triplet-triplet annihilation (kTTA), non-radiative (knr(3A*)) decay, and electron injection (kinj(3A*)) as summarized in equations 15-18. kmig :
3
A* + 1A → 1A + 3A*
(15)
kTTA :
3
A* + 3A* → 1A* + 1A
(16)
knr(3A*) :
3
A* → 1A + heat
(17)
TiO2-3A* → TiO2(e-)-A+
(18)
kinj(3A*) :
The rate of migration/diffusion and TTA are not trivial to deconvolute. For example, many upconversion systems are limited by diffusion through the medium and thus the kTTA is often not determined.29 A common alternative is use of the excitation intensity dependence
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measurements to determine the Ith value, the crossover point between quadratic and linear regimes.48 For a ZrO2-A-Zn-S sample (Γs = 1.15 x 10-8 mol/cm2; ~10:1 A to S ratio to limit inner filtering of emission by S) an Ith value of 469 mW/cm2 was determined by measuring the steadystate integrated emission from 460 to 480 nm with respect to 532 nm excitation power density (Figure S2). From the Ith value the second order rate constant for the TTA-UC process (γTTA) can be calculated using equation 19: ,-. =
( ∗/()∗(0 )# ∗1
(19) 0
where α(E) is the absorption coefficient for the sensitizer (575 cm-1), τ3A is the lifetime of the anthracene triplet state (2.04 ms, vide infra), and ΦTET is the S to A triplet energy transfer yield (0.33). The γTTA for the bilayer film was found to be 1.0 × 10-15 cm3 s-1. This value is about 4 orders of magnitude slower than seen in a solution of PtOEP/DPA molecules48 and two orders of magnitude slower than that for the exciton dynamics seen with rubrene TTA-UC systems.49 It is important to note that γTTA does not differentiate migration and triplet-triplet annihilation events it also largely focuses on 3D diffusion events and may not be appropriate to describe the bilayer system. Efforts are currently underway in our lab to model TTA-UC emission from the bilayer film using Monte Carlo simulations to determine kmig, kTTA, and the site-to-site hopping rate constant but that work is beyond the scope of the current manuscript. Due to the spin forbidden nature of the 1A 3A*transition, the triplet state of anthracene in the ZrO2-A-Zn-S films must be generated via excitation of S followed by TET to A. Emission from 3A* was not observed at room temperature and attempts to directly monitor the 3A* lifetime (i.e. the non-radiative decay constant for (knr(3A*))) by transient absorption were unsuccessful due
17 ACS Paragon Plus Environment
The Journal of Physical Chemistry
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to strong spectral overlap between 3S* and 3A* features. (Figure S3) As an alternative, knr(3A*) was determined using equation 20 following the method of Li et al.50
( ∗ ) = 2 ×
(20) 45
where τUC is from tail fitting the emission decay at 430 nm following excitation of S in a solution of 1000 µM A and 0.1 µM S in DMSO at 532 nm. From an upconverted emission lifetime measurement of 1.02 ± 0.09 ms a knr(3A) of 491 s-1 was calculated. While not directly measured, the driving force for electron transfer from 3A* to TiO2 (equation 18) is more than 400 mV lower than for 3S*. Therefore, we anticipate that the electron transfer rate will be