Efficient up-conversion by triplet-triplet annihilation

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Efficient up-conversion by triplet-triplet annihilation

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The 8th Asian International Seminar on Atomic and Molecular Physics Journal of Physics: Conference Series 185 (2009) 012002

IOP Publishing doi:10.1088/1742-6596/185/1/012002

Efficient up-conversion by triplet-triplet annihilation Josie E. Auckett1 , Yuen Yap Chen1 , Tony Khoury1 , Rapha¨ el G. C. R. Clady1 , N. J. Ekins-Daukes2 , Maxwell J. Crossley1 and Timothy W. Schmidt1 1

School of Chemistry, The University of Sydney, NSW 2006, Australia Department of Physics and the Grantham Institute for Climate Change, Imperial College London, U.K 2

E-mail: [email protected] Abstract. Following experimental determination of kinetic parameters governing the upconversion of light by triplet-triplet annihilation (TTA-UC), we develop a kinetic model to determine the conditions required for efficient up-conversion. We discuss the assumptions underpinning statistical arguments for an upper limit to TTA-UC and argue that no such limit exists.

1. Introduction Single threshold photovoltaic convertors suffer from an inability to harvest photons of an energy less than the threshold, restricting their efficiency to about 30%.[1] One possible improvement to the single threshold device is to place an up-converting material behind the cell which can efficiently convert the low sub-threshold photons into usable light.[2] The limiting efficiency of a cell utilizing an up-conversion (UC) system is over 50% with a threshold energy of 2 eV.[3] However, using rare-earth containing phosphors, the best UC quantum efficiency recorded is ∼ 10−6 .[4] Recently, a way to up-convert red light using triplet-triplet annihilation (TTA) in organic molecules has been developed.[5, 6] In TTA-UC, efficiently emitting molecules, “emitters”, are placed in their long lived triplet states through collisions with triplet sensitizer molecules. The sensitizers are chosen such that they undergo intersystem crossing from the S1 state to the T1 state following absorption of a low energy photon. When two triplet emitter molecules encounter another, a complex is formed which may take on singlet, triplet or quintet spin states. Due to the degeneracies of these states, they are statistically weighted, respectively, 1:3:5, such that there is only a 1/9 statistical chance of producing a singlet encounter complex. When formed, the singlet undergoes internal conversion to a lower energy state whereby one emitter moiety is in its S1 state and the other is in its ground state (S0 ). The excited moiety then promptly fluoresces, yielding up-converted light. The general scheme is given in Figure 1. The limiting efficiency of TTA-UC is not known, but it is widely held that it cannot exceed 11%, the statistical weighting of singlet encounter complexes. However, in 2008 we showed that 28% UC efficiency is possible using a palladium tetrakisquinoxalinoporphyrin as the sensitizer and rubrene as the emitter.[7] Using a pulsed laser source and time-resolved spectroscopy, we measured the rate constants indicated in Figure 1. In this article, we present the kinetic model which emerged from the previous study and discuss how spin statistics and the various kinetic parameters affect the predicted TTA-UC efficiencies. c 2009 IOP Publishing Ltd

1


S1

S1

S1

hν

ISC

hν

T1

kφ

T1 kp

kTTA

T1 kTET

knr

S1 ISC

T1

kTET

S0


kp

kφ

knr

S0

S0

sensitizer

hν

emitter

emitter

sensitizer

Figure 1. Kinetic scheme of TTA-UC.

2. Kinetic Model of TTA-UC Under continuous illumination, there is a continuous pumping of population from the S0 level into the S1 level of the sensitizer. This rate is given by kφ = φ²0 , where φ has units of moles of photons dm−2 s−1 , and the molar extinction coefficient, ²0 =R² log(10), is in M−1 dm−1 . In the case of solar irradiation, the rate is given by the integral kφ = dλρ(λ)²0 (λ), where ρ is given in moles of photons dm−2 s−1 nm−1 . The S1 state of the sensitizer lives only ∼ 2 ps as the molecules undergo intersystem crossing to T1 .[7] In the following, X represents the sensitizer molecules, and Y represents the emitter species. The kinetics of the triplet energy transfer and triplet-triplet annihilation procedure proceed as d[3 X] dt d[3 Y ] dt

¡ ¢ d[1 X] = kφ [1 X] − kT ET [1 Y ][3 X] − kp [3 X] − kT T A 2[3 X]2 + [3 Y ][3 X] = − dt 1Y ] ¡ ¢ d[ = kT ET [1 Y ][3 X] − knr [3 Y ] − kT T A 2[3 Y ]2 + [3 Y ][3 X] = − dt

where kT ET and kT T A represent the rate constants for the triplet energy transfer and triplettriplet annihilation respectively. The constants kp and knr represent the total first-order decay constants for the sensitizer and emitter triplets respectively. The kinetic processes are also shown schematically in Figure 1. These equations are solved to find steady state conditions. The efficiency, e, is given by kT T A [3 Y ]2 . (1) e=2 kφ [1 X] In all simulations, kinetic rate constants and concentrations were held at our experimental values: [X] = 1.16 × 10−4 M, [Y ] = 2.30 × 10−3 M, kT ET = 3.33 × 108 M−1 s−1 , kT T A = 1 × 108 M−1 s−1 , knr = 9000 s−1 , kp = 2.5 × 104 s−1 and kφ = 10 s−1 unless specified otherwise. 3. Results and Discussion Our modelling reveals a threshold behaviour for efficiency as a function of kT ET and [Y ]. Essentially, efficient TTA-UC can proceed if kT ET [1 Y ] À kp , as seen in Figure 2. When this is satisfied, the efficiency comes down to the competition between knr [3 Y ] and kT T A [3 Y ]2 . We require that kT T A [3 Y ] & knr . In Figure 3, a plot of photon absorption rate against photon emission rate is presented. On the double-logarithmic plot, the order of the process is revealed by the slope. Interestingly, the slope of the plot is very sensitive to the value of knr , the rate of spontaneous decay of emitter triplets. At high values of knr , say 104 s−1 , the process is seen to exhibit a quadratic nature 2



0.18

quantum efficiency

0.16

Figure 2. Quantum efficiency of the TTA

0.14 0.12 0.10 0.08 0.06 0.04 0.02

kp = 101 s-1 kp = 102 s-1 kp = 103 s-1 kp = 104 s-1 kp = 105 s-1

0.00 -1 0 1 2 3 4 5 6 7 8 9 10 10 10 10 10 10 10 10 10 10 10 10 10 kTET.[1Y] /s-1

system over several values of kp , showing competition between the desired triplet energy transfer process (TET) and alternative sensitizer triplet decay pathways. The quantity kT ET .[1 Y ] describes the transfer between sensitizer triplets and emitter triplets per second. At very low values, emitter triplet production is negligible and TTA efficiency approaches zero regardless of the value of kp . At very high values, sensitizer triplet “loss” mechanisms cannot compete with TET; kp becomes insignificant and efficiency reaches an upper limit set by the values of knr , kφ and kT T A .

across the ranges of kφ employed here. A value of kφ = 104 s−1 corresponds to monochromatic light intensity of about 10 Wcm−2 , for the molecules employed here. Typically, sunlight would bring about kφ ∼ 10 s−1 . The quadratic dependence of the TTA-UC across several orders of magnitude of irradiance is due to the short life of the triplet states. Where the dominant triplet decay mechanism is non-radiative, rather than TTA, the amount of up-converted light will depend quadratically on the concentration of triplets which is controlled linearly by the level of irradiation. However, where the non-radiative processes are cut-off, so that knr = 0, the process is entirely linear. In this case, triplets always have the time to react by TTA and thus the TTA-UC output is linearly dependent on the irradiation level, bringing about a slope of unity. At intermediate values of knr , the process changes smoothly from quadratic to linear as the input light is increased, as opposed to exhibiting a threshold.[8] This behaviour has been recently observed.[9] It is only where the process deviates from quadratic towards linear that the TTA-UC is significantly efficient. At typical solar excitation rates of kφ ∼ 10 s−1 , knr must be below about 1000 s−1 to achieve significant TTA-UC. One contaminant that likely increases knr is dioxygen. Being a triplet ground state, when it encounters a triplet emitter molecule in solution it can undergo TTA to yield singlet oxygen and a ground state emitter, short circuiting the TTA-UC process. With concentrations of dioxygen as low as 10−7 M (one atmosphere is 10−2 M), knr will be enhanced by a contribution on the order of 1000 s−1 . As such, dioxygen concentrations must be kept low to achieve efficient TTA. In our experiments concerning TTA-UC kinetics in degassed toluene, the measured knr value of 9000 s−1 is too high to achieve efficient TTAUC under solar illumination. It is likely that our experiments were affected by trace levels of oxygen, foreshortening the lifetime of the rubrene triplet state. Nevertheless, the high efficiencies obtained under pulsed-laser illumination (28%) and the excellent agreement with our kinetic model suggests that higher efficiencies could be obtained with more careful deoxygenation.[7] The competition between intramolecular and intermolecular processes will be more important still when implementing TTA-UC in solid polymer films.[10, 11] In such environments, the rates kT T A and kT ET will be reduced by a factor consistent with the increased viscosity of the environment. Solving for a steady-state population of triplets, we find that the condition kT T A [3 Y ] & knr translates to the condition q 2 + 8k [1 X]k knr (2) T T A /knr & 5. φ

3

100 10-1 10-2 10-3 10-4 10-5 10-6 10-7 10-8 10-9 10-10 10-11 10-12

(a) slope = 1

quantum efficiency

photons emitted /M s-1


slope = 2

knr = 0 knr = 101 s-1 knr = 102 s-1 knr = 103 s-1 knr = 104 s-1 0.01

0.1

1

10

100

1000 10000

1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0


(b)

0.01

kφ /s-1

0.1

1

10

kφ /s-1

100

1000 10000

Figure 3. (a) Photon output of the rubrene emitter in the TTA process over several values of knr , the rate constant for decay of the rubrene triplet state via all pathways other than TTA, including quenching by molecular oxygen. The slopes for knr = 103 and = 104 s−1 at moderate values of kφ are close to 2, yet knr = 0 has a slope of 1, suggesting that if loss mechanisms of the emitter triplet can be suppressed, such as by careful removal of all oxygen from the system, TTA proceeds with linear dependence on the light intensity.(b) The corresponding quantum efficiencies, defined as the percentage of sensitizer triplet pairs that successfully undergo TTA to place one emitter molecule in its S1 state. At very high kφ , all curves approach the maximum efficiency given by knr = 0, showing that triplet loss mechanisms cannot compete with TTA when sensitizer triplets are being regenerated very quickly. 4. Final remarks Our kinetic model predicts that efficient TTA-UC can proceed providing that certain conditions are met: triplet energy must be rapidly transfered to the emitter molecules, and the emitter triplet states must be long lived with respect to the TTA rate. We find no evidence in support of a spin-statistical limitation on TTA. Indeed, our experiments, on which the present model is based, suggest that TTA can proceed with high efficiency. If quintet encounter complexes are to decay non-radiatively, rather dissociating back into triplets, the the question remains: since there is no lower quintet state, to which state does the encounter complex decay? Indeed, if it does decay, then due to the energy-gap law, it is likely to decay to a state which subsequently fluoresces. The only possible quenching process is if the triplet encounter complex decays into the lower triplet state which then dissociates into a triplet and a ground state emitter. In this case the limiting efficiency is 40%. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]

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