Intermolecular Energy Transfer across Nanocrystalline Semiconductor

Gerald J. Meyer. 2010,551-588. Anthony G. Fitch , Don Walker , Nathan S. Lewis. 2010,. Single-molecule, single-particle fluorescence imaging of TiO2-b...
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2598

J. Phys. Chem. B 2006, 110, 2598-2605

Intermolecular Energy Transfer across Nanocrystalline Semiconductor Surfaces Gerard T. Higgins, Bryan V. Bergeron, Georg M. Hasselmann, Fereshteh Farzad, and Gerald J. Meyer* Departments of Chemistry and Material Science and Engineering, Johns Hopkins UniVersity, Baltimore, Maryland 21218 ReceiVed: August 5, 2005; In Final Form: September 30, 2005

The yields and dynamics for energy transfer from the metal-to-ligand charge-transfer excited states of Ru(deeb)(bpy)2(PF6)2, Ru2+, and Os(deeb)(bpy)2(PF6)2, Os2+, where deeb is 4,4′-(CH3CH2CO2)2-2,2′-bipyridine, anchored to mesoporous nanocrystalline (anatase) TiO2 thin films were quantified. Lateral energy transfer from Ru2+* to Os2+ was observed, and the yields were measured as a function of the relative surface coverage and the external solvent environment (CH3CN, THF, CCl4, and hexanes). Excited-state decay of Ru2+*/TiO2 was well described by a parallel first- and second-order kinetic model, whereas Os2+*/TiO2 decayed with first-order kinetics within experimental error. The first-order component was assigned to the radiative and nonradiative decay pathways (τ ) 1 µs for Ru2+*/TiO2 and τ ) 50 ns for Os2+*/TiO2). The second-order component was attributed to intermolecular energy transfer followed by triplet-triplet annihilation. An analytical model was derived that allowed determination of the fraction of excited-states that follow the two pathways. The fraction of Ru2+*/TiO2 that decayed through the second-order pathway increased with surface coverage and excitation intensity. Monte Carlo simulations were performed to estimate the Ru2+* f Ru2+ intermolecular energy transfer rate constant of (30 ns)-1.

Introduction

SCHEME 1

Transition-metal compounds that have metal-to-ligand charge transfer (MLCT) excited states represent the most successful class of sensitizers for dye sensitized solar cells based on nanocrystalline TiO2 thin films.1,2 We recently reported conditions where excited-state electron transfer from the MLCT excited states of Ru(dcb)(bpy)2(PF6)2, where dcb is 4,4′(CO2H)2-2,2′-bipyridine, to TiO2 was inhibited.3 Under these conditions, long-lived MLCT excited states were observed with spectral features nearly identical to that in fluid solution. The kinetics for excited state decay were, however, more complex. It was found that at high light irradiances excited-state relaxation was second-order in nature and at lower irradiances it was nearly first-order.3 A parallel first- and second-order kinetic model was found to describe all of the relaxation data extremely well. The model shown in Scheme 1 was proposed to explain this interesting kinetic behavior. The key mechanistic steps are lateral energy transfer, bimolecular excited-state annhilation reactions, and unimolecular radiative and nonradiative decay. Direct spectroscopic evidence for lateral energy transfer was later reported.4 Here, we report the energy transfer rates and efficiencies for Os(deeb)(bpy)2(PF6)2 and Ru(deeb)(bpy)2(PF6)2, where deeb is 4,4′-(CH3CH2CO2)2-2,2′-bipyridine, anchored to nanocrystalline TiO2 thin films in a variety of solvents. Excited-state behavior was quantified by steady-state and time-resolved spectroscopy as a function of surface coverage and irradiance. The fraction of excited states that follow these pathways was determined by a shape analysis of the time-resolved excited-state decay rate. Monte Carlo simulations were used to further model the intermolecular energy transfer rates. The results demonstrate efficient lateral energy transfer across semiconductor surfaces under a variety of experimental conditions.

Experimental Section Materials. Acetonitrile (Burdick & Jackson), hexanes (Aldrich), THF (Aldrich), CCl4 (Aldrich), CHCl3 (Aldrich), and poly(methyl methacrylate) (Aldrich) (PMM) were all reagent grade or better and used as received. Microscope slides were obtained from EM Science. Ru(deeb)(bpy)2(PF6)2 and Os(deeb)(bpy)2(PF6)2 were available from previous studies.4 Preparation of Thin Films. Transparent TiO2 thin films were prepared by a modification of a published procedure that is described elsewhere.5 Surfaces containing RuII and OsII were prepared by immersing an unsensitized TiO2 thin film in an acetonitrile solution that contained both sensitizers in the desired concentrations. The preparation of thin film actinometers based on poly(methyl methacrylate) (PMMA) has been described elsewhere.6 Spectroscopy. All spectroscopic measurements were conducted by placing the TiO2 or PMMA films diagonally in a 10 mm × 10 mm quartz cuvette, equipped with a 24/40 ground quartz joint. The thin films were then submerged in the desired solvent. The cell was closed with a PTFE stopper and purged

10.1021/jp0543680 CCC: $33.50 © 2006 American Chemical Society Published on Web 01/26/2006

Energy Transfer across Nanocrystalline Semiconductor Surfaces with argon through a two-way needle for 20-30 min at room temperature unless otherwise stated. Absorbance. Steady-state absorption data were acquired on a Hewlett-Packard 8453 diode array spectrophotometer. An unsensitized TiO2 film immersed in solution was used as a background for the surface measurements. The surface coverages were determined spectroscopically with the molar extinction coefficients  (M-1 cm-1):  (485 nm) ) 11000 M-1 cm-1 and  (650 nm) ) 2600 M-1 cm-1 for Os(deeb)(bpy)22+ and  (485 nm) ) 11000 M-1 cm-1 for Ru(deeb)(bpy)22+. Ruthenium excited-state concentrations were determined by observing the Ru2+*/TiO2 transient at 450 nm (∆450 nm ) 1.0 × 104 M-1 cm-1).6 Photoluminescence. Corrected photoluminescence (PL) spectra were obtained with a Spex Fluorolog that had been calibrated with a Optronic OL243M NIST traceable irradiance standard tungsten-halogen lamp. Time-resolved PL was measured as previously described.6 Typical irradiances for these experiments ranged from 1 to 25 mJ/cm2pulse. Time-gated PL spectra were acquired following pulsed 532 nm excitation by a Continuum Surelite II Nd:YAG, Q-switched laser (second harmonic, 8 ns fwhm, 8 mJ/cm2). Emitted light was collected in a right angle to the excitation path with a Princeton Scientific 576 G/RB intensified charge coupled device (ICCD) camera, controlled by a ST130 controller/PG200 pulse generator. Scattered light was removed using a Schott Glass OG550 long-pass filter in front of the spectrograph entrance slit. The camera was mounted on an ISA HR 320 spectrograph equipped with one 150 g/mm holographic grating, blazed at 500 nm. The camera was binned in “spectroscopy mode” with 384 pixels contributing to each data point in a spectrum. A window of approximately 250 nm was recorded over 575 pixels with each frame. Timing was achieved with a Berkeley Nucleonics BNC 555 sequence generator by sending appropriate TTL pulses to laser and camera controller. The PG 200 in turn generated 30 ns wide gated pulses. At each delay time, 100 frames were signal averaged. Data Fitting and Monte Carlo Simulations. Kinetic data was fit using Origin 7.0 (Microcal). Monte Carlo simulations of energy transfer were performed using MATLAB 6.1 (Mathworks) and MS Visual C++ 6.0. In the latter case, an implementation of the Mersenne Twister pseudo random number generator was used.7 Sensitizers were arranged in a 32 by 32 grid of either a primitive square geometry with 4 nearest neighbor sites or a hexagonal arrangement with 6 nearest neighbors. Initially, a set of random numbers was drawn that determines which of the 1024 dye molecules were in their excited states. At each time step, a random number between 0 and 1 determines whether a radiative or nonradiative decay had occurred for each excited state molecule present. If the random number was bigger than the probability of decay, one ES decay was counted. Similarly, a number was chosen for the probability that one excited state transfers its energy to a neighboring ground state, such that after 1 reciprocal hopping rate, e.g. 30 ns, 67% of excited states initially present had undergone one energy transfer step. Furthermore, the next random number determined which of the nearest neighbors accepted the excited-state energy. If two excited states were located adjacent to each other, one annihilation event was counted and one excited state was converted to a ground state while the other one remained as an excited state. The total simulation time was 5 µs, which corresponds to 5 lifetimes of Ru2+* and accounted for more than 99% total excited-state decay. A single time step in the simulation lasted one ps. The

J. Phys. Chem. B, Vol. 110, No. 6, 2006 2599

Figure 1. Absorption and photoluminescence spectra of Ru2+ (solid line) and Os2+ (dotted line) anchored to TiO2 thin films.

Figure 2. Absorption spectra of Ru2+ and Os2+ bound to TiO2 thin films. The mole fractions of Ru2+ were 1.0 (black line), 0.88 (black dash), 0.55 (black dot), 0.20 (gray line), and 0.0 (gray dash).

calculations included a circular boundary condition such that excited states that hop off the grid, reappear on the opposite side. After each time step the whole process was repeated and the simulation determined whether two excited states were within annihilation distance, an excited-state decay or a hopping step occurred. A complete simulation encompassed 10000 averaging runs. Results The spectroscopic and redox properties of Ru(deeb)(bpy)2(PF6)2 and Os(deeb)(bpy)2(PF6)2 in acetonitrile at room temperature have previously been described.3,4 The compounds are photoluminescent and have broad metal-to-ligand charge-transfer (MLCT) absorption bands in the visible region (Figure 1). For simplicity, we refer to Ru(deeb)(bpy)2(PF6)2 as Ru2+, and Os(deeb)(bpy)2(PF6)2 as Os2+, or use M2+ more generically. On base-treated TiO2, the absorption spectra of these sensitizers change to that expected for the carboxylate form of the compounds, consistent with surface-catalyzed hydrolysis of the ester groups.8 The absorption spectrum of the osmium compound displays a long wavelength absorption band (∼ 650 nm) that has been assigned to a direct singlet-to-triplet absorption.9 The absorption spectrum of a TiO2 thin film with both Os2+ and Ru2+ was well modeled by a sum of the individual Ru2+/ TiO2 and Os2+/TiO2 spectra (Figure 2). From the measured absorption spectra, it was possible to determine the overall surface coverage, Γtot, as well as those of the individual components, ΓRu, and ΓOs. The long wavelength absorption of Os2+ allows one to quantify the Os2+/TiO2 concentration, and

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TABLE 1: Photophysical Properties of Sensitzers Bound to pH ) 11 Pretreated Nanocrystalline TiO2a λabs, nmb sensitizer

λPL, nmc

φend

CH3CN

n-hexane

THF

CCl4

CH3CN

n-hexane

THF

CCl4

CH3CN

n-hexanes

THF

CCl4

[Ru(deeb)(bpy)2] χRu2+ ) 0.88 χRu2+ ) 0.55

461 462 461

457 456 442

462 463 462

461 462 455

0.46 0.84

442

442

0.97

0.98

0.96

0.93

[Os(deeb)(bpy)2]2+

442

442

442

440

658 658 642 767 640 779 783

0.65 0.92

442

675 675 e 758 660 805 810

0.61 0.89

444

665 652 648 773 652 795 795

f 0.51 0.94

χRu2+ ) 0.20

665 652 654 777 653 803 807

2+

f

a All measurements were performed at room temperature. b Absorption maxima of the visible MLCT bands observed in acetonitrile, n-hexane, THF, and CCl4, respectively. c Corrected photoluminescence maxima in the solvents mentioned, ( 2.5 nm. d Efficiency of Ru2+* f Os2+ energy transfer. e Two separate peaks were not observed. f Not applicable.

Figure 3. Corrected photoluminescence spectra of Ru2+* and Os2+* bound to TiO2 thin films. The mole fractions of Ru2+/TiO2 were 1.0 (black line), 0.88 (black dash), 0.55 (black dot), 0.20 (gray line), and 0.0 (gray dash). The inset shows an expanded view of the three lowest Ru2+/TiO2 mole fractions.

the Ru2+/TiO2 was then determined by the standard addition method. Typical saturation surface coverages were 5 × 10-8 mol/cm2, Table 1. Shown in Figure 3 are the photoluminescence (PL) spectra of Ru2+/TiO2, (Ru2+ + Os2+)/TiO2, and Os2+/TiO2 immersed in acetonitrile. The mole fractions of Ru2+ contained on the TiO2 thin films were 1.0, 0.88, 0.55, 0.20, and 0.0. The PL spectra were also quantified when these same films were immersed in CH3CN, n-hexane, THF, and CCl4, Table 1. Excitation was performed at 485 nm, where the Ru2+ and Os2+ sensitizers have nearly identical extinction coefficients. The PL spectra of the individual sensitizers anchored to TiO2 thin films were simulated with a single-mode Franck-Condon line shape analysis, eq 1.10

I(E) I(E0-0)

5

)

∑ν

[(

)

E0 - νpω 3Sν E0

ν!

×

( (

exp -4 ln 2

)]

E - E0 + νpω ∆ν0,1/2

2

0 (1)

In this equation the energy dependence of the emission is expressed in terms of four parameters: E0, pω, S, and ∆νj0,1/2. The energy term, E0 is the energy difference between the ν* ) 0 f ν ) 0 vibrational levels of the excited and ground state. Vibronic contributions are then included as a single, averaged mode of quantum spacing, pν, and an electron-vibrational coupling constant, S. The full width at half-maximum, ∆νj0,1/2, includes contributions from low-frequency modes treated clas-

Figure 4. Uncorrected time-gated photoluminescence spectra measured following 532 nm excitation of a (Ru2+ + Os2+)/TiO2 thin film. The mole fraction of Ru2+ was 0.57. The spectra were obtained by integration over the following time scales: 0-30 ns (black line), 1040 ns (black dash), 20-50 ns (black dot), 50-80 ns (gray line), and 100-130 ns (gray dash) delay times.

sically and the solvent. Spectral data, like that shown in Figure 3, were converted to energy units and corrected by the technique of Parker and Rees.10b When the emission spectral profiles of surfaces containing both Ru2+ and Os2+ were analyzed, a sum of the single-component Ru2+*/TiO2 and Os2+*/TiO2 was employed. This method allowed for the determination of an individual sensitizer’s emission profile and hence its integrated PL intensity. The quantum yield for energy transfer was determined with a comparative method. The integrated PL intensity of Ru2+*/TiO2 was compared to that of a mixed (Ru2+ + Os2+)/TiO2 thin film. All Ru2+*/TiO2 quenching was assumed to have resulted from energy transfer to Os2+/TiO2. The results of the calculations are given in Table 1. Time-gated PL spectra after pulsed 532 nm excitation were acquired for a (Ru2+ + Os2+)/TiO2 thin film, and the results are displayed in Figure 4. The thin film contained a mole fraction of Ru2+ of 0.57. The normalized PL contributions from Ru2+*/ TiO2 and Os2+*/TiO2 to the observed spectra were delay time independent with no evidence for spectral shifts with surface coverage or irradiance. Time-resolved PL decays were collected for Ru2+ and Os2+ in acetonitrile at room temperature. Both excited states exhibited exponential decays with lifetimes of 1 µs and 50 ns, respectively. These lifetimes were independent of the incident irradiance and solution concentration. The decay kinetics of Os2+*/TiO2 were also exponential within experimental error and were surface coverage independent, with a measured lifetime similar to that in solution. The excited-state decay of Ru2+*/TiO2 was non-

Energy Transfer across Nanocrystalline Semiconductor Surfaces

Figure 5. Normalized excited-state decay for Ru2+*/TiO2 in CH3CN observed at 650 nm with 532 nm excitation. The irradiances shown are as follows: 2.0 mJ/pulse (black line), 4.5 mJ/pulse (gray line), 8.8 mJ/pulse (black dashed line), 13.6 mJ/pulse (gray dashed line), 23.0 mJ/pulse (black dotted line), and 29.5 mJ/pulse (gray dotted line). The inset displays five different surface coverages of Ru2+/ TiO2 at a fixed irradiance of 4.0 mJ/pulse: 1/2 (black line), 2/3 (gray line), 4/5 (black dashed line), 9/10 (gray dashed line), and full saturation surface coverage (black dotted line).

exponential and was well described by a parallel first- and second-order kinetic model,3 Equations 2 and 3

PLI(t) ) B

(

k1 exp(-k1t)

)

k1 + p - p exp(k1t)

p ) k2[Ru2+*]t)0

(2) (3)

where k1 is a first-order rate constant analogous to solution and B is a constant. The parameter, p, is the product of the observed second-order rate constant, k2, and the initial concentration of ruthenium excited states, [Ru2+*]t)0. The decay kinetics of Ru2+*/TiO2 were found to be dependent upon surface coverage and irradiance, Figure 5. The average first-order rate constant determined from a large number of Ru2+*/TiO2 samples was (1.0 ( 0.5) × 106 s-1. The time-resolved photoluminescence data does not allow one to directly determine the second-order rate constant. The analysis only gives the product of the observed second-order rate constant, k2, and the initial concentration of ruthenium excited states, [Ru2+*]t)0. We therefore simulated the observed decays by independently varying both the energy transfer rate constant and the initial excited-state concentration. Figure 6 shows the results of this analysis. At an infinitely slow energy transfer “hopping” rate, first-order decays were simulated. As the hopping rate was increased to 1 ns, the decay became second-order. For a large number of samples at saturation surface coverage, the best agreement with experimental data (as determined by residuals and sum of square errors) was for an energy hopping rate constant of (30 ns)-1. When the hopping rate was fixed and the initial excited-state concentration was varied, best fits were obtained with 1.95% of the ground states converted to excited states. This value was consistent with actinometry measurements and expectations based on groundstate absorption and the excitation irradiance. The fraction of excited-states that decay by the first-order pathway was modeled as a function of time (eq 4 and Figure 6)

χ1st(t) ) 1 -

p exp(-k1t) k1 + p

(4)

J. Phys. Chem. B, Vol. 110, No. 6, 2006 2601 Both k1 and p were obtained from spectral fitting of the PL decays. Figure 7 shows the results of the analysis using six values for the shape parameter, p, ranging from 2.38 × 106 s-1 to 4.06 × 106 s-1. An integrated expression was derived (see the Appendix) that allows the fraction of excited-states that decay through the first∞ χ1st is a order process to be abstracted, eq 5, where ∫t)0 function of the first-order rate constant and shape parameter that were obtained from spectral analysis (eqs 2 and 3). For three different surface coverages, the net fraction of ruthenium excited-states that decayed via the first-order pathway was plotted versus the fraction of excited states created (Figure 8). The initial concentration of ruthenium excited-states created was determined by actinometry. Analysis of the transient data indicated that the fraction of excited-states relaxing via firstorder pathways increased with decreasing irradiance and surface coverage. The results of Monte Carlo simulations were overlaid with the experimental results (Figure 8).

k

∫t)0∞ χ1st ) p1ln

( ) k1 + p k1

(5)

It was also of interest to simulate the net random walk path of the energy transfer. Shown in Figure 9 are the results of Monte Carlo simulations wherein an excited state was placed in the center of a 32 × 32 sensitizer grid and allowed to randomly hop with a (30 ns)-1 rate constant. Simulations were done for a sensitizer with a 1 µs lifetime, like that of Ru2+*/ TiO2, and a 50 ns lifetime like that of Os2+*/TiO2. The amplitudes reflect the probability that the excited state would decay at that site at the given delay time. It was found that after four lifetimes (data not shown), there was a finite probability for excited-state decay of Ru2+*/TiO2 at all sites. In fact, after 1.5 µs the Ru2+*/TiO2 had migrated efficiently across the surface and pictorial histograms, like that in Figure 9, were of little use for visualizing energy transfer. For Os2+*/ TiO2, the excited-state decay after four lifetimes was most probable within 10 sensitizers of the initial excitation, Figure 9E. Discussion We recently reported an “interfacial charge-energy transfer switch” wherein ruthenium(II) and osmium(II) polypyridyl complexes anchored to a nanocrystalline TiO2 thin film could be switched between interfacial charge transfer and intermolecular energy transfer simply by tuning the nature and concentration of cations in the external solution.4 This behavior appears to emanate from cation adsorption induced shifts in the semiconductor conduction band edge energy. In the absence of potential determining cations (such as the alkali and alkaline earth cations), the conduction band edge lies energetically above the excited-state reduction potential of the sensitizers and interfacial electron transfer is energetically unfavorable.3 Under these conditions, we found evidence for efficient lateral energy transfer among the sensitizers.4 The high sensitizer surface coverages facilitate energy transfer and are necessary for solar energy conversion applications. The adsorption isotherm data is consistent with monolayer surface coverage,2 although precise demonstration of this was difficult due to the ill-defined surface area of the mesoporous films.2 Therefore, we prefer to discuss sensitizer surface coverages relative to the ‘saturation value’. In any event, the surface coverage was undoubtedly high and theoretical calculations based on a Dexter formalism indicated

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Figure 6. Overlay of experimental (monitored at 650 nm) and simulated photoluminescence decays. (A) Constant initial excited state concentration and the following energy-transfer hopping rates: infinitely slow hopping (black, straight line), (100 ns)-1 (gray, straight line), experimental data (black, dashed line), (30 ns)-1 (gray, dashed line), (10 ns)-1 (black, dash dot line), and (1 ns)-1 (gray, dash dot). The inset in panel A shows only the experimental data (black) and the best fit (gray). (B) Constant hopping rate (30 ns)-1 and different initial excited state concentrations. 1.17 % (gray, dashed line), 1.95 % (black, straight line), experimental data (gray, straight line), 3.125 % (black, dash dot). The inset in panel B shows only the experimental data (gray) and the best fit (black).

Figure 7. Instantaneous fraction of excited-states that decay through first-order pathways. These results were determined using the irradiance dependence data in Figure 5. The first-order rate constant used in lineshape analysis of the decay of the excited state was fixed at 1 × 106 s-1. See the text for additional details.

Figure 8. Fraction of excited state that decayed through a first-order (radiative or nonradiative decay) pathway as a function of the fraction of Ru2+/TiO2 sensitizers excited. Simulated decays on a hexagonal array: 100 ns (up-triangle), 30 ns (diamonds), 10 ns (squares), and 1 ns (open circles) hopping rates. Experimental data obtained at 1/2 (stars), 2/3 (hexagons), and full (right triangle) saturation surface coverage.

isoenergetic energy transfer could occur on monolayer surfaces with rate constants of 2 × 1011 s-1.3 Here we have detailed the effects of surface coverage and external environment on the quantum yields for energy transfer

(φen). In addition, we have described a method by which the fraction of excited states that undergo triplet-triplet annhiliation reactions can be quantified from a shape analysis of the excitedstate decay. Monte Carlo simulations were used to gain insight into the rate constant for intermolecular energy transfer on the surface of the TiO2 nanoparticles. Intermolecular Ru2+*-Os2+ Energy Transfer. Inter- and intramolecular Ru* f Os energy transfer is well-known.11-15 Intermolecular energy transfer across nanocrystalline TiO2 surfaces was clearly demonstrated by the enhanced emission of Os2+*/ TiO2 on surfaces that contained both Ru2+ and Os2+. The emission quantum yield for Ru2+* is about 80 times larger than that for Os2+* in fluid solution.4 Yet on TiO2 thin films that contained equal concentrations of both compounds, drastically enhanced PL intensity from Os2+* was observed, consistent with a near quantitative Ru2+* f Os2+ energy transfer, φen ≈ 1 (Table 1). The φen for Ru2+* f Os2+ energy transfer was studied while varying the solvent in which the sensitized thin film was immersed. Within experimental error there was no noticeable effect of solvent on the energy transfer yields at low Ru2+/TiO2 surface coverages. At high Ru2+/TiO2 surface coverages, a measurable change in the energy transfer yields with solvent was noted but the effect was small. This suggests that the external solvent makes a small contribution to the total reorganization energy for energy transfer. It also indicates that efficient energy transfer in these materials is expected in most environments. We note that Ru2+* f Os2+ energy transfer, -∆G ∼ 400 meV, was energetically favored under all these conditions. Efficient Ru2+* f Os2+ energy transfer is also observed at lower mole fractions of Os2+. A probable mechanism for this is isoenergetic intermolecular energy transfer Ru2+* f Ru2+ (ken) across the nanocrystalline TiO2 surface occurs until the excited-state encounters an Os2+ compound. While there is clear spectroscopic evidence for Ru2+* to Os2+ energy transfer there is no such direct evidence for iso-energetic Ru2+* to Ru2+ energy transfer as the reactants and products are spectroscopically indistinguishable. However, there is some indirect kinetic evidence to suggest its existence. Previous research has demonstrated that excited-state decay of Ru2+*/TiO2 is primarily first-order at low irradiance and second-order at high irradiance.3 At intermediate irradiances, a parallel first- and second-order kinetic model accurately described the dynamics of Ru2+*/TiO2 excited-state relaxation (eqs

Energy Transfer across Nanocrystalline Semiconductor Surfaces

J. Phys. Chem. B, Vol. 110, No. 6, 2006 2603

Figure 9. Position of decay of an excited state initially placed at the center of a 32 by 32 square planar array of sensitizers where energy migration takes place at a (30 ns)-1 hopping rate constant. The panels on the left show the decay coordinates for an excited-state lifetime of 50 ns, such as Os*/TiO2, at (A) 2 ns, (C) 42 ns, and (E) 200 ns delay times. The panels on the right correspond to an excited-state lifetime of 1 µs, such as Ru*/TiO2, at (B) 40 ns, (D) 400 ns, and (F) 1.4 µs delay.

2 and 3). In this model, the first-order rate constant (k1) is comprised of radiative (kr) and nonradiative (knr) decay components, analogous to exponential decay in solution (eq 6) k1

Ru2+* 98 Ru2+ + hν, ∆

(6)

Here, we find that the first-order rate constant was independent of surface coverage and the excitation irradiance. While a distribution of first-order rate constants may exist, we found no reason to resort to dispersive kinetics. Interestingly the decays of Os2+*/TiO2 were surface coverage and irradiance independent. Presumably the lifetime of the osmium excited-state limits the distance the excited-state can travel on the TiO2 thin film. The observed second-order component (k2) was modeled as iso-energetic intermolecular energy migration (ken) across the TiO2 thin film, followed by bimolecular excited-statesexcitedstate annihilation reactions (kann), Scheme 1. Conceptually, this is similar to molecular diffusion in solution to form an encounter complex, followed by a bimolecular reaction where two reactants form two products. The second-order relaxation pathways demand that the excited-state decay rate from Ru2+*/ TiO2 is dependent on the initial concentration of Ru2+*/TiO2.

Therefore the PL from Ru2+*/TiO2 was studied while varying the incident irradiance or surface coverage (Figure 5). Under higher irradiances and surface coverages we observed a faster relaxation time for Ru2+*/TiO2. A similar irradiance dependence was observed by Shaw et al. with ruthenium(II) polypyridyl compounds chemically bound to a polystyrene backbone.14 Therefore, assignment of the second-order process as a triplettriplet annihilation reaction appears to be well grounded. The reaction between two Ru triplet excited-states may proceed to form a ground state and an excited singlet state.16 The excited singlet state would be expected to rapidly intersystem cross to yield the emissive triplet state (eq 7). In addition, the Ru excited state is known to be unstable with respect to disproportionation, (eq 8).17 We do not directly observe any of these products from the triplet-triplet annhilation reactions so neither processes can be completely ruled out. We note however, that the disproportionation reaction produces an equivalent of Ru+/TiO2, which is a potent reducing agent that would likely transfer an electron to the TiO2 thin film to yield RuIII/ TiO2(e-).18 There is no experimental evidence for such a process so we slightly favor the annhilation reactions and have employed it in the Monte Carlo simulations.

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kann

2(Ru2+*/TiO2) 98 1Ru2+*/TiO2 + kisc

Ru2+/TiO2 98 3Ru2+*/TiO2 + Ru2+/TiO2 (7) kann

2(Ru2+*/TiO2) 98 Ru+/TiO2 + RuIII/TiO2

(8)

Parallel first- and second-order kinetic pathways for relaxation of triplet states have been long known.16 However, determination of the fraction of excited states that follow each pathway, i.e., the relative amplitiudes of the two components, has received remarkably little attention.19 The problem is nontrivial as the two processes are occurring in parallel. We have therefore derived an expression (see the Appendix) that allows one to extract this information from the shape of the observed excitedstate decay. In addition, one can calculate the percentage of excited states that follow each pathway at any time after the laser pulse, a quantity we term the instantaneous percentage. Not surprisingly, at times just following the laser pulse, where the concentration of excited states is highest, the second-order process is dominant while at long times excited state decay is predominantly first-order (Figure 6). The fraction that follow the second-order pathway can be systematically increased with the sensitizer surface coverage or the incident irradiance in a predictable manner (Figure 7). Monte Carlo simulations were contrasted with experimental results to better understand intermolecular excited-state energy transfer across the nanocrystalline TiO2 surfaces (Figure 7). We estimate that there are about 800 sensitizers anchored to an ∼20 nm anatase particle at the maximum surface coverage and have used a 32 by 32 grid of sensitizers to model this. The sensitizers were packed in either a primitive square geometry with four nearest neighbor sites or a hexagonal arrangement with six nearest neighbors. The calculations included a circular boundary condition such that when an energy transfer step required the excited state to move beyond the grid, it reappeared on the opposite side. This allowed all sensitizer sites to be treated equally and could correspond to either the case where the grid corresponded to energy transfer between sensitizers on the same TiO2 particle or described the continuous surface of the nanoparticle film. A (30 ns)-1 hopping rate constant was found to be most consistent with the time-resolved photoluminescence data. Such kinetics modeled the observed excited-state decay of Ru2+*/ TiO2 at saturation surface coverages and moderate irradiances. It is also consistent with the fact that the second-order component was absent for Os2+*/TiO2. The relatively short Os2+* lifetime relative to this energy hopping rate did not allow for significant excited state-excited-state encounters. Based on a (30 ns)-1 energy transfer rate, the Monte Carlo simulations show that an individual Ru2+* excited state, or any sensitizer with long-lived microsecond lifetimes, could transfer energy to any of the ∼800 sensitizers on an anatase nanoparticle surface. This long range energy transfer coupled with the strong light harvesting is important for photocatalysis applications as energy could be efficiently delivered to a remote catalytic surface site. In practice, encounters with impurity quenchers or other excited states will lower the energy transport distances substantially. At intermediate irradiances (0.005 < χex < 0.015), where χex is the fraction of sensitizers excited, Monte Carlo simulations of Ru2+*/TiO2 close-packed in hexagonal arrays gave better fits to experimental data than did the primitive arrangement. However, at very high and very low irradiances, the Monte Carlo simulations did not agree as well with experimental results regardless of the packing arrangement (Figure 8). This is

partially due to the fact that it was not possible to experimentally quantify the fractions of excited states that follow each pathway at very low irradiances (χex < 0.005) due to poor signal-tonoise. At higher irradiances (χex > 0.015) annihilation immediately following the laser pulse could account for the discrepancies, since there is a much greater chance for two excited-states to be located adjacent to one another. Therefore, it is possible that the population of excited-states had already been reduced on a time scale that our instrumentation could not resolve (k > 108 s-1). Consequently, it would then appear as if a lesser overall percentage of excited-states were decaying through the second-order pathway. A second possible explanation is that the assumption of identical sensitizers on the nanocrystalline surfaces is not correct. Transmission electron microscopy analysis of the TiO2 thin films shows necking regions between the nanoparticles where the sensitizer environment is likely to be very different.2 Therefore, the sensitizers may be inhomogeneously spaced such that isolated regions exist within the films. In this scenario, excited states formed in the “island regions” would not be able to access every sensitizer on the nanoparticle. This would lead to a decreased number of excited-states decaying through the secondorder annihilation pathway. Trammell et al. have seen a similar effect in energy-transfer studies on insulating metal oxide particles as a function of the ruthenium surface coverages.13e Conclusion Highly efficient excited-state Ru2+* f Os2+ energy transfer across nanocrystalline TiO2 surfaces was quantified in various ambient media. Relaxation rates of Ru2+*/TiO2 were described with a parallel first- and second-order kinetic model to account for both unimolecular radiative and nonradiative decay and bimolecular excited-state annihilation reactions occurring at the surface. The instantaneous and overall percentages of excited-states that decayed through these two pathways were evaluated and compared to the fraction of molecules excited. Comparing these experimental results with appropriate modeling data allowed us to estimate a rate constant of (30 ns)-1 for isoenergetic Ru2+* f Ru2+ energy transfer across the nanocrystalline TiO2 surface at saturations surface coverages. Appendix Decay of the excited state occurs through a parallel first- plus second-order model.

-

d[Ru2+*] ) k1[Ru2+*] + k2([Ru2+*])2 dt

The integrated rate expression is given as follows:

[Ru2+*](t) )

k1[Ru2+*]t)0 exp(-k1t) k1 + k2[Ru2+*]t)0 - k2[Ru2+*]t)0 exp(-k1t)

Experimentally, we measure a fraction of the emitted photons and represent the photoluminescence intensity with PLI, where PLIt)0 ) Rkr[Ru2+*]t)0 and p ) k2[Ru2+*]t)0. Here, “R” is a multiplicative constant comprised of instrument responses, and kr is the radiative rate constant.

PLI )

PLIt)0k1 exp(-k1t) k1 + p - p exp(-k1t)

Energy Transfer across Nanocrystalline Semiconductor Surfaces Integration with respect to time, evaluated from t ) 0 to t ) ∞, gives a value proportional to the total amount of emitted photons. Further division by PLIt)0 results in the yield for a ∞ first-order decay process,∫t)0 χ1st.

k

∫t)0∞ χ1st ) p1ln

( ) k1 + p k1

The instantaneous efficiency for the first-order process at a particular time, χ1st(t), depends on the parameter “p”, and upon k1. One can derive an expression for χ1st(t) by a ratio of the differential rates.

χ1st(t) )

k1[Ru2+*]t k1[Ru2+*]t + k2([Ru2+*]t)2

Further simplification and substitution gives the following result:

χ1st(t) ) 1 -

p exp(-k1t) k1 + p

Acknowledgment. The Division of Chemical Sciences, Office of Basic Energy Sciences, Office of Energy Research, U.S. Department of Energy is gratefully acknowledged for research support. References and Notes (1) O’Regan, B.; Gra¨tzel, M. Nature 1991, 353, 737-739. (2) For recent reviews, see: (a) Gra¨tzel, M. Nature 2001, 414, 338342. (b) Watson, D. F.; Meyer, G. J. Ann. ReV. Phys. Chem. 2005, 56, 119-156. (3) (a) Kelly, C. A.; Farzad, F.; Thompson, D. W.; Meyer, G. J. Langmuir 1999, 15, 731-737. (b) Kelly, C. A.; Thompson, D. W.; Farzad, F.; Stipkala, J. M.; Meyer, G. J. Langmuir 1999, 15, 7047-7054.

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