ARTICLE pubs.acs.org/JPCA
Entropically Driven Photochemical Upconversion Yuen Yap Cheng,† Burkhard F€uckel,† Tony Khoury,† Rapha€el G. C. R. Clady,† N. J. Ekins-Daukes,‡ Maxwell J. Crossley,† and Timothy W. Schmidt*,† † ‡
School of Chemistry, The University of Sydney, NSW 2006, Australia Department of Physics and the Grantham Institute for Climate Change, Imperial College, London, United Kingdom SW7 2AZ ABSTRACT: Conventional photochemical upconversion (UC) through homogeneous triplet-triplet annihilation (TTA) is subject to several enthalpic losses that limit the UC margin. Here, we address one of these losses: the triplet energy transfer (TET) from the sensitizer to the emitter molecules. Usually, the triplet energy level of the emitter is set below that of the sensitizer. In our system, the triplet energy level of the emitter exceeds that of the sensitizer by ∼600 cm-1. Choosing suitable concentrations for the sensitizer and emitter molecules, we can exploit entropy as a driving force for the migration of triplet excitation from the sensitizer to the emitter manifolds. Thereby we obtain a new record for the peak-to-peak TTA-UC energy margin of 0.94 eV. A modified Stern-Volmer analysis yields a TET rate constant of 2.0 107 M-1 s-1. Despite being relatively inefficient, the upconverted fluorescence is easily visible to the naked eye with irradiation intensities as low as 2 W cm-2.
’ INTRODUCTION Photon upconversion (UC) is a phenomenon whereby photons with a particular energy are fused to produce a photon with higher energy. In 1961 Franken et al. generated the second harmonic of a coherent light beam focused into a nonlinear optical material.1 In the following year, Parker and Hatchard reported delayed fluorescence of anthracene sensitized by phenanthrene and explained the anti-Stokes emission via triplettriplet annihilation (TTA).2,3 The aforementioned UC mechanisms differ significantly: While second harmonic generation (SHG) requires a nonlinear optical medium and high excitation powers on the order of MW cm-2,4 TTA is an incoherent photochemical process that may proceed under low irradiation intensities (W cm-2).5 Because of this feature, photochemical UC is gaining general interest and a range of new molecular systems has been reported recently.5-24 However, compared to SHG, where double the input photon energy is obtained in the emission, the anti-Stokes shift of photochemical UC is limited by various free energy losses during the process, which serve as the driving force. In the following, we focus on the photochemical UC mechanism, where TTA proceeds in the emitter material, and denote this mechanism TTA-UC. The principal enthalpic losses of TTA-UC are depicted in Figure 1. Upon excitation of the sensitizer molecules to their S1 state, they undergo intersystem crossing (ISC) to the lower lying T1 state, whereby energy is released to the surroundings (ΔH1). Arising from the energetic difference between the respective T1 levels, the subsequent triplet energy transfer (TET) from sensitizer molecules to the emitter species is usually driven by another enthalpic loss (ΔH2). Eventually two emitter molecules in their triplet states encounter and, apart from other possible outcomes,21,25 can dissociate into one emitter in its ground state (S0) and one in its first excited singlet state S1, r 2011 American Chemical Society
Figure 1. Enthalpic losses of TTA-UC. The sensitizer molecules absorb low energy photons (hν1) and relax (ΔH1) by intersystem crossing (ISC) to their T1 state. Usually, the following triplet energy transfer (TET) to the emitter molecules is driven by the energy difference ΔH2 between the level of the sensitizer and emitter T1 states. Two emitter T1 states undergo TTA via a singlet encounter complex 1|T1 3 3 3 T1|. Dissociation of the singlet encounter complex results in internal conversion (IC) to one S0 and one S1 state. A third enthalpic loss ΔH3 is caused by the energy difference between the sum of two emitter T1 states and the emitter S1 state. The latter can relax by (delayed) fluorescence with the energy hν2.
where the latter emits the upconverted, delayed fluorescence. In this last step the energies of the two triplet excited states are fused into one singlet excited state. Depending on the molecular energy levels of the emitter molecule, double the T1 energy usually exceeds the S0 - S1 energy gap and thereby leads to another enthalpic loss (ΔH3). Thus, the effectively upconverted energy of TTA is constrained by the sum of the enthalpic losses mentioned, 2(hν1 - ΔH1 - ΔH2) - ΔH3. Received: September 16, 2010 Revised: November 23, 2010 Published: January 25, 2011 1047
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Chart 1. Two Palladium(II) Porphyrins Employed as Sensitizer Material, PQ4Pd and PPd, and Perylene, the Emitter
Herein, we define the peak-to-peak UC margin as the energy difference between the maxima of the respective sensitizer absorption band and the emitter fluorescence spectrum. Note that this definition differs compared to reports by Singh-Rachford, Castellano, and co-workers,18,19 who considered the difference between the utilized excitation wavelength and the first maximum of the observed delayed fluorescence. While the latter method is clearly application oriented, it is imprecise for reasons of comparison. The sensitizer molecules may be excited at the red, weak end of their absorption, and the position of the maximum of the emitter delayed fluorescence depends on the amount of reabsorption (and therefore concentration) of both sensitizer and emitter species. Singh-Rachford, Castellano, and co-workers have reported the highest peak-to-peak TTA-UC margins according to our definition (and theirs) so far, 0.77 eV (0.80 eV) for a platinum(II) porphyrin derivative as sensitizer and perylene as emitter18 as well as 0.91 eV (0.86 eV) for a sensitizer molecule consisting of a bisporphyrin linked with a ruthenium(II) complex in combination with the emitter tetracene.19 In this contribution we show that a higher TTA-UC margin can be achieved by exploiting entropy as a driving force for the migration of triplet excitation from the sensitizer to the emitter manifolds. As mentioned above, the enthalpic losses limit the UC energy margin. However, the Gibbs free energy as the driving force does not rely on the enthalpic balance only. Considering TET from sensitizer to emitter, the concentrations of sensitizer and emitter molecules play an important role for the entropic driving force. Indeed, in this paper, we report a TTA-UC system, where the energy of the emitter T1 state lies above the sensitizer T1 level. The endothermic TET from sensitizer to emitter molecules is driven by the entropy of mixing, resulting in a peak-to-peak UC energy margin of 0.94 eV. Note that in contrast to recent examples where the energy of the emitter triplet state lies far above the sensitizer triplet state (ΔH2 > 2000 cm-1),5-7 in our case ΔH2 is 606 cm-1 and can therefore be overcome thermally. Our results can be explained with the modified TET dynamics arising from this enthalpic difference.
’ EXPERIMENTAL SECTION PQ4Pd and perylene (Chart 1) were dissolved in toluene to prepare a series of TTA-UC samples with similar PQ4Pd concentration (∼2.0 10-5 M) and various perylene concentrations (from 2.9 10-5 to 2.3 10-3 M). All the samples were deaerated in a custom-built vacuum cuvette through several freeze-pump-thaw cycles to remove oxygen before data acquisition. For comparison, samples of PPd (Chart 1) as the sensitizer material were prepared with similar concentrations.
Figure 2. Q-band absorption of PQ4Pd (dotted) and the perylene fluorescence (straight) in toluene. The peak-to-peak energy margin is 0.94 eV. The inset shows a photograph of the emission of a sample irradiated with a 655 nm cw diode laser (irradiation power: 1.2 mW).
In order to determine the TTA-UC quantum yield, similar to a previous study,20 two sets of measurements were performed. The first set of measurements recorded the delayed and prompt fluorescence by exciting degassed TTA-UC samples at 670 nm (530 nm) and 410 nm, corresponding to the absorption maxima of the Q-band of PQ4Pd (PPd) and perylene, respectively. The second set was a prompt fluorescence study on pristine perylene at various concentrations to provide references for a conservative estimation of the relative quantum yield. All measurements were performed by illuminating the samples with the tunable output of a TOPAS OPA laser pumped by a Clark MXR CPA 2210 femtosecond laser operating at 1 kHz. The fluorescent spots on the front face of the samples were imaged through the slits of a spectrograph consisting of a monochromator and an iCCD detector (Acton/Princeton). The spot size was ∼0.50 and ∼0.33 mm2 for the measurements on the samples containing PQ4Pd and PPd, respectively. The delayed fluorescence signal was integrated for 600 μs from 220 ns after the 670 nm laser pulse to exclude the laser pulse and any prompt perylene fluorescence signals. The prompt fluorescence signal was taken under identical imaging conditions but integrated for 500 ns from 30 ns before the 410 nm laser pulse, although the prompt fluorescence signal ceased after ∼100 ns. The employed pulse energies varied from 500 nJ to 12 μJ. The kinetics of phosphorescence and delayed fluorescence were measured in 1 μs slices, from 1 to 500 μs delay.
’ RESULTS The Q-band absorption of PQ4Pd and the fluorescence spectrum of perylene in toluene are displayed in Figure 2 for a sample with concentrations of 2.0 10-5 and 2.3 10-3 M of sensitizer and emitter, respectively. Upon excitation to its S1 state, PQ4Pd undergoes rapid ISC (∼10-20 ps) to T1 .21 The phosphorescence from T1 of PQ4Pd is centered around 850 nm (1.46 eV),21 while the triplet state energy of perylene is known to be at 808 nm (1.53 eV).26 That is, the T1 of the emitter species lies ΔH2 ≈ 2.9kBT (76 meV, 606 cm-1) above the sensitizer T1 state, where kB is the Boltzmann constant and the temperature T = 298 K. Therefore, TET from PQ4Pd (P) to an emitter (M) 3
kTET
P þ 1M0 s F 1P0 þ 3P s R kTBT
ð1Þ
is enthalpically unfavorable, while triplet back transfer (TBT), i.e., perylene transferring a triplet excited state to a PQ4Pd 1048
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Figure 3. Kinetics of the delayed fluorescence of a mixture of PQ4Pd and perylene (a, b) and PPd and perylene (c, d) excited in the Q-band of the porphyrin, respectively. The delayed fluorescence peaks several microseconds after the excitation laser pulse and lasts for tens of microseconds. Concentrations of perylene in (a) and (c), as well as for O and ] in (b) and (d), are 2.3 10-3 M and 1.5 10-3 M, respectively. Additionally, the decay of the delayed fluorescence for the PQ4Pd sensitizer with an emitter concentration of 3.5 10-4 M (0) is depicted in (b).
molecule, is exothermic. The relationship between TET and TBT is27 kTET ΔH2 ¼ exp ð2Þ kTBT kB T resulting in a nearly 20 times higher TBT than TET rate constant for the PQ4Pd/perylene system. Note that eq 2 implies that the entropy of a single donor-acceptor pair does not change upon transfer of the triplet excited state. While changes in conformational freedom and hence in the vibrational partition function of small, flexible molecules can play a role in energy transfer dynamics,28,29 for bigger, more rigid chromophores (as investigated here) this intramolecular entropy change is negligible.30,31 However, in a toluene solution of sensitizer and emitter material, excitation of the PQ4Pd Q-band with a cw diode laser (655 nm) yields visible blue fluorescence from perylene (inset of Figure 2). In the following we will show that the endothermic TET process is driven by the differences in concentration, so that the distribution of sensitizer triplet state energies available due to thermal population can overcome the enthalpic difference. The enthalpic and entropic contributions to the Gibbs free energy balance are equal at ΔH2 = TΔS, where an equilibrium between TET and TBT would be reached (disregarding any triplet decay processes). In contrast, the phosphorescence of the second employed sensitizer PPd is located at 700 nm (1.77 eV), and TET from PPd to perylene is exothermic by ΔH2= -0.24 eV. Hence, in this case the TBT rate constant is ∼104 times smaller than the TET rate constant and therefore negligible. The kinetics of the delayed fluorescence signal for a mixture with the PQ4Pd sensitizer is displayed in Figure 3(a) as a 2-D plot. The sample was excited with a short laser pulse at 670 nm, and the emission spectrum was monitored over the following microseconds. The microsecond decay time is characteristic for TTAinduced delayed fluorescence and excludes mechanisms such as
sum frequency generation,1 two photon absorption,32 or prompt anti-Stokes fluorescence.33 Note that for both mixtures strong reabsorption due to the Soret band absorption of the sensitizer as well as the high emitter concentrations employed cut the blue part of the fluorescence spectrum of perylene. The decay kinetics of the delayed fluorescence arises from TTA and is therefore indicative of the triplet concentrations in the sample.21 A comparison of the kinetics between two different emitter concentrations, 3.5 10-4 and 2.3 10-3 M, at constant PQ4Pd concentration and irradiation is displayed in Figure 3(b). The long rise time of the delayed fluorescence is ascribed to the TET dynamics between sensitizer and emitter molecules (eq 1). The delayed fluorescence signal of the lower emitter concentration takes an even longer time to peak and decay than that of the higher one. On the other hand, in the mixtures of PPd and perylene, the delayed fluorescence signal peaks a few microseconds after the laser pulse as seen in Figure 3 (b, d). We can rationalize the differences in the kinetics by consideration of the migration of triplet excitons in the sample, where we use the word exciton to describe the localized excited states as quasi-particles to emphasize their ability to be transferred,34 despite their mobility being mostly conferred by diffusion of the carrier molecules. In particular, the change of entropy ΔS due to the triplet energy transfer depends on the difference between the concentration of sensitizer and emitter molecules in their respective states. We assume NP (NM) molecules in the sensitizer (emitter) manifold and nP (nM) triplet excitons in the respective manifold. A graphical scheme is given in Figure 4. The entropy SP (SM) of the sensitizer (emitter) subsystem consisting of nP (nM) excitons and NP (NM) molecules depends on the number of ways, W, to place the excitons in the sensitizer manifold NX ! SX ¼ kB ln W ¼ kB ln ð3Þ ðNX - nX Þ!ðnX !Þ 1049
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Figure 4. Number of triplet excitons nX in the sensitizer (X = P) and emitter (X = M) manifold distribute over the respective molecular sites NX and give rise to entropy, as described in eq 3. The migration between the manifolds by triplet energy transfer (TET) and triplet back transfer (TBT) changes the entropy of the subsystems (eq 4). The endothermic TET (ΔH2) is driven by the gain in total entropy (eq 5) due to the population of emitter sites.
where X = P, M. Applying Stirling’s approximation, ln x! ≈ x ln(x) - x, allows expansion of eq 3. Hence, the change in entropy with changing exciton population in each manifold is dSX NX - nX ¼ kB ln ð4Þ dnX nX Since nP and nM represent the T1 concentration of sensitizer ([3P*]) and emitter ([3M*]), (NP - nP) and (NM - nM) correspond to the concentrations of the ground state molecules [1P0] and [1M0], respectively, assuming that the singlet lifetimes are short (e10 ns). Hence, for TET, the change in entropy ΔS is ! dSP dSM ½1 M0 ½3 P þ ¼ kB ln 1 ΔS ¼ ð5Þ dnP dnM ½ P0 ½3 M Note that eq 4 and eq 5 do not hold for any of the concentrations approaching zero, because Stirling’s approximation is only valid for large numbers. However, we can conclude that ΔS gives high positive values at the beginning of the transfer, where most of the triplets are present in the sensitizer manifold. ΔS decreases while TET consumes 3P* and builds up [3M*]. Meanwhile, the production of 3M* leads to increasing TBT from 3 M* to 1P0 which is enthalpically favorable in the case of PQ4Pd and perylene. The dependence of the Gibbs free energy of TET on the ratio of the triplet concentrations [3M*]/[3P*] according to eq 5 for mixtures of PQ4Pd and perylene is displayed in Figure 5. The lines indicate different experimentally employed emitter concentrations, while the sensitizer concentration is held constant at ∼2.0 10-5 M. As is intuitively clear, for higher emitter concentrations TET is exergonic for a larger number of triplets already transferred to the emitter manifold. Note that for a plot of the TBT process only the sign of ΔG changes. Hence, the zero crossings of the curves are the equilibrium triplet concentrations in both manifolds. With respect to Figure 3, TET in the mixture of PPd and perylene is fast while TBT is negligible. The intensity of the delayed fluorescence is nearly instantly at its maximum, since the triplet population is readily transferred to the emitter manifold. After ∼200 μs, the decay is dominated by first order means with a time constant associated with the triplet lifetime of perylene in toluene, 310 μs. In the mixtures of PQ4Pd and perylene, on the other hand, the long rise time is indicative of the slow migration of triplet excitons to the emitter manifold. Since the entropic driving force for this process is influenced by the emitter
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Figure 5. Gibbs free energy ΔG of TET of PQ4Pd and perylene according to eq 5 dependent on the relative triplet concentrations in the sensitizer and emitter manifold. Similar to the experimental conditions, the PQ4Pd concentration is kept constant at 2.0 10-5 M for various perylene concentrations (- - 2.9 10-5 M, - - - 7.9 10-5 M, 3 3 3 3.5 10-4 M, ; 2.3 10-3 M).
concentration, the delayed fluorescence of the mixture with the higher emitter concentration peaks earlier and decays faster compared to the mixture with the lower emitter concentration. So far we have discussed TTA in the emitter species only. We note that there are examples of photochemical upconversion in which the emitter triplet level lies well above the sensitizer triplet energy and TET cannot proceed.5-7 Different mechanisms have been proposed to explain the observed delayed fluorescence from the respective emitter species. Generally, TTA between two sensitizer molecules and subsequent energy transfer from the higher excited sensitizer state to an emitter molecule5,6 is unlikely due to the fast relaxation of the higher excited singlet state of the sensitizer.7 A more plausible explanation for these cases is exciplex formation between a triplet sensitizer and a ground state emitter molecule, followed by TTA of this exciplex with another triplet sensitizer.7 However, this mechanism seems to be unlikely for the present work because our sensitizer molecules were designed to have bulky di(tert-butyl)phenyl groups to hinder aggregation sterically. This is supported by quantum chemical calculations using the semiempirical method AM135 within the program package HyperChem Pro 6 to obtain the geometries of the porphyrins and perylene. The H-H distance of the long axis of the latter is found to be 9.3 Å, while the pocket above (below) the porphyrin’s inner cycle appears to be unsuitable for πstacking partners bigger than ∼8 Å due to the periphery. In contrast, heterogeneous TTA between sensitizer and emitter molecules in their respective triplet states could be an important process for our system, especially since the triplet exciton population is split between the sensitizer and emitter manifolds. Heterogeneous TTA could yield one excited senisitizer or emitter singlet state; however, we can only speculate upon the respective probabilities. Even for heterogeneous TTA, the migration of triplet excitons from the sensitizer to the emitter manifold is a precondition. Usually, to reveal the TET rate (that is, the quenching of the sensitizer triplet state by perylene), a Stern-Volmer experiment based on the first order triplet decay rate of the sensitizer as a function of quencher concentration is performed.7,18,21 For the samples containing PPd and perylene, monoexponential phosphorescence decays are obtained, as illustrated for one example in Figure 6(a). From the Stern-Volmer plot, displayed in Figure 6(b), we obtain a TET rate constant of 2.7 109 M-1 s-1, about onefourth of the diffusion limit in toluene at room temperature.36 1050
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TTA (k3), and TBT may play an important role. Especially at longer times TBT is significant, where the overall triplet concentration is low and therefore the triplet decay is dominated by first order processes. Since the triplet lifetime of PQ4Pd (130 μs) is 2-3 times shorter than that of perylene, the triplets in the emitter manifold act as a reservoir for the sensitizer phosphorescence. In order to obtain a reliable measure for kTET for the PQ4Pd mixtures, uninfluenced by heterogeneous TTA or TBT, we used an alternative Stern-Volmer approach that focuses on the initial decay of the phosphorescence, where no triplet emitter molecules are present. The triplet decay of PQ4Pd at zero time can be expressed as d½3 Pt 2 3 3 ð7Þ ¼ - k0 ½ P0 - k2 ½ P0 dt 0
0
Figure 6. (a) Phosphorescence decay and monoexponential fit of a sample containing 2.8 10-5 M PPd and 3.2 10-4 M perylene. (b) Stern-Volmer plot for the PPd/perylene system.
Figure 7. Phosphorescence decay of pristine PQ4Pd (Δ) in toluene and with 2.3 10-3 perylene (O). The phosphorescence of the mixture lasts for several hundreds of microseconds. Both decays show TTA between two PQ4Pd molecules as a second order process at early times, as indicated by the nonlinear behavior.
However, for mixtures of PQ4Pd and perylene, the phosphorescence persists for several hundreds of microseconds, as displayed in Figure 7. The simple Stern-Volmer approach does not accurately describe its dynamics, since the sensitizer triplet population [3P*] is dependent on several processes d½3 Pt 2 ¼ - k1 ½3 Pt - kTET ½3 Pt ½1 M0 t - k2 ½3 Pt dt - k3 ½3 Pt ½3 Mt þ kTBT ½1 Pt ½3 Mt ð6Þ Besides the natural decay of the triplet state of the porphyrin (k1) and TET, TTA between two porphyrins (k2, also present in the pristine sensitizer solution as seen in Figure 7), heterogeneous
where k = k1 þ kTET[M] is the total first order and k2 the total second order decay rate constant due to TTA between porphyrin molecules. To obtain the initial triplet decay rates, eq 7 is normalized by dividing the derivative by the initial triplet concentration [3P*]0, which is proportional to the initial phosphorescence signal d½3 Pt dt 0 ¼ - k0 - k2 ½3 P0 ¼ - k ð8Þ ½3 P0 Equation 8 demonstrates the linear relationship between the normalized initial decay rate and the initial triplet concentration. Thus the slope of the tangent to the normalized phosphorescence decay curve approaching zero time yields -k. Assuming a linear relationship between the irradiation and the initial triplet concentration, the two terms k 0 and k2[3P*]0 can be obtained from the y-intercept and slope of a linear fit to a plot of k against the respective irradiation intensity. For high irradiation intensities, this precondition does not hold (Figure 8(a)); therefore, these points were omitted from the fitting procedure. We note that the resulting slope k2[3P*]0 is constant within (10% for the different employed perylene concentrations. Due to significant propagation of the laser beam into the sample cuvette, in turn due to the necessarily low sensitizer concentration, it is unclear exactly which range of triplet concentrations is imaged into the detection apparatus. However, the extrapolation of the initial decay rate, k 0 , to zero triplet concentration is unaffected. The alternative Stern-Volmer plot can be acquired from k 0 as a function of [M] (Figure 8(b)). This plot provides the PQ4Pd natural decay rate, k1 and kTET, from its y-intercept and slope, which are 7400 s-1 and 2.0 107 M-1 s-1, respectively. Considering the relationship between forward (kTET) and backward (kTBT) triplet energy transfer eq 2, we can calculate kTBT. The enthalpically favored kTBT is obtained to be 3.7 108 M-1 s-1. This value is similar to triplet energy transfer rates from PQ4Pd to rubrene (3.1 108 M-1 s-1) found in a previous study.21 To obtain the relative TTA-UC quantum yield, we used a procedure similar to a previous TTA-UC study.20 The TTA-UC signal per input photon is compared to that from the prompt fluorescence triggered by blue photon excitation obtained under identical experimental conditions. However, the maximum excitation energy used for obtaining the prompt fluorescence was 6 μJ. 1051
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time of the delayed fluorescence). In comparison, the PPd-perylene system with a perylene concentration of 3.2 10-4 M gives 2.7% and 4.2% relative yield under 1 and 5 μJ pulse excitation (equivalent to 4 and 20 W cm-2 cw excitation), respectively. Compared to PQ4Pd, high excitation energies are required to obtain high TTA-UC yields in the latter system, because of the relatively low extinction coefficient of PPd (∼17 000 M-1 cm-1). Moreover, since the TTA-UC yield depends on the triplet concentration, we expect higher TTA quantum yields from the PPd/perylene system for higher PPd concentrations.20
Figure 8. (a) Dependence of the PQ4Pd triplet decay rate on the laser pulse energy from a TTA-UC sample consisting of 2.4 10-5 M of PQ4Pd and 2.9 10-5 M of perylene. The intercept as a function of emitter concentration is used for the Stern-Volmer plot. (b) Alternative Stern-Volmer plot by plotting the y-intercepts (kphos) from different samples against the corresponding perylene concentrations.
Polynomials were fit to the plots of the prompt fluorescence signal versus excitation energy obtained from different samples. The linear terms yield the prompt fluorescence signal per absorbed photon in each sample allowing a comparison with the delayed fluorescence. The delayed fluorescence signal per two input photons was the reference point for 100% relative TTA-UC quantum yield, since two low energy photons can generate one upconverted photon at most. Measurements in this study, however, are expected to provide a measure for the relative TTA-UC quantum yield due to differences in excitation propagation of different PQ4Pd and perylene concentrations. The maximal decadic extinction coefficient of perylene is 23 306 M-1 cm-1, so that 90% of photons with a wavelength of 410 nm are absorbed at the first 1 mm of the cuvette, if the concentration exceeds 4 10-4 M. In this scenario, the prompt fluorescence on the sample surface can be imaged properly through the slits. In contrast, the extinction coefficient of PQ4Pd at 670 nm is approximately 105 M-1 cm-1, and the concentration used is only 2 10-5 M; thus, the 670 nm laser pulse can propagate much deeper into the sample. As a consequence, the delayed fluorescence occurring inside the sample is partially reabsorbed. Moreover, according to eq 5, ΔS is inversely proportional to the natural logarithm of [P]. That is, to ensure a significant entropical driving force, the PQ4Pd concentration has to be low compared to [M]. The consequence of a low PQ4Pd concentration is, however, a low triplet supply for perylene and therefore a low overall TTA-UC yield.37 The sample with the highest perylene concentration (2.3 10-3 M) gives a relative yield of 0.59% under 2.5 μJ pulse excitation (equivalent to 10 W cm-2 cw excitation based on the spot size of the excitation beam and decay
’ CONCLUSION We have explored one of the intrinsic enthalpic losses of TTAUC by combining an emitter species (perylene) with a slightly higher triplet energy level than that of the sensitizer (PQ4Pd). As a result of the enthalpic gain in the TET process, we achieve the highest reported peak-to-peak UC margin of 0.94 eV. Similar to the anti-Stokes fluorescence observed by Wood in 1928,33 the thermal energy present is sufficient to overcome the enthalpic barrier of the TET process, while the thermodynamic driving force results from the gain in entropy by distributing the triplet excitons between the sensitizer and emitter manifolds. The rate constants of the triplet migration dynamics have been revealed by an analysis that focuses on the initial phosphorescence decay of the sensitizer. We find rate constants of 2.0 107 and 3.7 108 M-1 s-1 for the sensitizer to emitter and for the emitter to sensitizer triplet energy transfer, respectively. From a comparison with samples containing perylene and a sensitizer with higher triplet energy, we conclude that the kinetics of the delayed fluorescence and the phophorescence are strongly influenced by the triplet energy migration dynamics. However, the UC phenomenon is clearly observable with an excitation intensity as low as 100 mW cm-2. The sample with the highest emitter concentration (2.3 10-4 M) gave the highest relative quantum yield for the entropically driven TTA-UC of 0.59% under irradiation equivalent to 10 W cm-1.
’ AUTHOR INFORMATION Corresponding Author
*E-mail
[email protected]; phone þ61 2 9351 2781; fax þ61 2 9351 3329.
’ ACKNOWLEDGMENT Y.Y.C. acknowledges The University of Sydney for a Gritton Fellowship. B.F. acknowledges the Alexander von Humboldt foundation for a Feodor Lynen fellowship. This work was supported by The University of Sydney (2008-00511 Efficient Upconversion for Photovoltaic Devices) and the Australian Research Council (LE0668257). ’ REFERENCES (1) Franken, P.; Hill, A.; Peters, C.; Weinreich, G. Phys. Rev. Lett. 1961, 7, 118. (2) Parker, C.; Hatchard, C. Proc. Chem. Soc. 1962, 147. (3) Parker, C.; Hatchard, C. Proc. Chem. Soc. 1962, 386. (4) Shen, Y. The Principles of Nonlinear Optics; Wiley: New York, 2002. (5) Baluschev, S.; Miteva, T.; Yakutkin, V.; Nelles, G.; Yasuda, A.; Wegner, G. Phys. Rev. Lett. 2006, 97, 143903. (6) Baluschev, S.; Yakutkin, V.; Wegner, G.; Minch, B.; Miteva, T.; Nelles, G.; Yasuda, A. J. Appl. Phys. 2007, 101, 4. 1052
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