Intramolecular TripletâTriplet Annihilation Upconversion in 9,10

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Intramolecular Triplet-Triplet Annihilation Upconversion in 9,10-Diphenylanthracene Oligomers and Dendrimers Damir Dzebo, Karl Börjesson, Victor Gray, Kasper Moth-Poulsen, and Bo Albinsson J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b07920 • Publication Date (Web): 22 Sep 2016 Downloaded from http://pubs.acs.org on September 23, 2016

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The Journal of Physical Chemistry

Intramolecular Triplet-Triplet Annihilation Upconversion in 9,10-diphenylanthracene oligomers and dendrimers Damir Dzeboa , Karl Börjessonb, Victor Graya, Kasper Moth-Poulsena, Bo Albinssona* a

Chalmers University of Technology/Department of Chemistry and Chemical Engineering, 41296 Gothenburg, Sweden

b

University of Gothenburg/Department of Chemistry and Molecular Biology, 41296 Gothenburg

Photon upconversion, Triplet-Triplet Annihilation Supporting Information Placeholder ABSTRACT: ABSTRACT : An important challenge when developing materials for Triplet-Triplet Annihilation upconversion (TTA-UC) is to achieve efficient and well-functioning solid state systems. We here explore the effect of intramolecular TTA in oligomers and dendrimers based on the 9,10-diphenylanthracene (DPA) chromophore. The macromolecules are sensitized using palladium porphyrin, both in solution and in solid poly(methyl methacrylate) (PMMA) demonstrating a positive effect on overall upconversion in the solid state correlating with the well-controlled size of the DPA constructs. The UC kinetics is modelled and fit to steady-state and time-resolved emission data to give further insight in the intramolecular excited state migration and annihilation in the macromolecular annihilator systems.

The mechanism of diffusion controlled triplet-triplet annihilation photon upconversion (TTA-UC), first observed by Parker and Hatchard in1962,1 starts with a sensitizer (S) that is excited from its singlet ground state with low-energy photons to its first excited singlet state. From the single state, the molecule undergoes intersystem crossing (ISC) to the first excited triplet state. Upon close proximity to an annihilator (A), Triplet Energy Transfer (TET) occurs from the sensitizer to the annihilator. In the well-established and fully intermolecular system (Figure 1a) a sufficient population of triplet-sensitized annihilators (3A*) initiates triplet-triplet annihilation (TTA) through the formation of an encounter complex between two such triplet-excited annihilators. One of the two annihilating species acquires the sum energy of two triplet states and populating its first excited singlet state (1A*), while the other annihilator returns to its ground state (1A). The now singlet excited annihilator emits a photon at a wavelength shorter than the photon used to excite the sensitizer in the first place.1-4 The described process, thus, relies on two diffusion-controlled steps, namely TET from a sensitizer to an annihilator and TTA between two annihilators. Most efficient TTA-UC experiments are carried out in liquid phase but while the liquid phase allows for fast diffusion of the sensitizer and annihilator, crucial for the two diffusion controlled intermolecular energy transfers steps to occur, it is impractical for technical applications.5-6 Before considering large scale application it would be necessary to have the liquids well sealed to prevent evaporation as well as preventing molecular oxygen to diffuse into the liquid, as it would quench the essential long-lived triplets very efficiently. TTA-UC in solid matrices could circumvent the problems of sample sealing and quenching by molecular oxygen but presently at the expense of decreasing efficiency of the process. A large number of successful examples of TTA-UC in diffusion restrictive environments have been reported in recent years7-19, in particular in polymeric matrices.20-25 Typically, systems operating under conditions

with slow diffusion has had much lower efficiencies when comparing to experiments carried out under conditions with fast diffusion. Higher efficiencies were found in rubbery or gel-like environments that apply less restriction to the mobility of the chromophores26-31 and highest in fluid systems32-35. These observations illustrate that the mobility of the chromophores in a two-fold diffusion limited TTA-UC system is crucial. Another important component for TTA-UC in general, and especially in rigid media is the dependence on concentrations of the components. High concentrations are typically needed since contact between the fluorophores is essential for transfer and annihilation of the triplet excitons.36 As a consequence, another dimension to the concentration problem that arises in solid media TTA-UC systems is aggregation and component separation.37-38 One method to circumvent this is to utilize polymer or dendrimer based chromophores.39-41 Considering the earlier work of TTA-UC systems in solid matrix and the overall loss in UC efficiency due to diffusion limitations we have set out to explore the idea of creating a supramolecular TTA-UC system where the bimolecular processes occurs intramolecularly with the objective of circumventing the diffusion limitations on the (Dexter type) TET and TTA rates. It has previously been argued that covalent coupling between sensitizer and annihilator can have an overall negative effect on UC compared to a purely bimolecular process.42 However, that particular study was conducted with an annihilator attached to the sensitizer, but without any coupling to the second annihilator necessary for the intramolecular upconversion to take place. The high proximity of the annihilator to the sensitizer in combination with its ability to rotate almost freely resulted in a Förster-type singlet-singlet back transfer of the upconverted singlet to the sensitizer, effectively short-circuiting the TTA-UC process.42 Similar attempts have been made with covalently attached dendrimer sensitizers-annihilator systems in low temperature solid matrices, but also with relative random orientations of the annihilator and sensitizer.43 We present here a first step towards a supramolecular

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Figure 1 . Jablonski diagram of a) the benchmark intermolecular TTATTA-UC mechanism, and b) the suggested intramolecular annihilating mechanism. Sensitizer and the annihilator are represented by S and A, respectively, while k represents the rate constants for the given processes. The numerals in the TET abbreviation denotes denot es the sequential order of the TET process to the same annihilator molecule while the numerals in the TTA abbreviation simply distinguishes between the intermolecular, molecular, a), and an d intramolecular, molecular, b), TTA processes respectively. respectively. TTA-UC system based on structurally rigid annihilators consisting of covalently connected DPA units. Two structurally different systems are studied, (i) linear DPA oligomer (Oligo), consisting of on average 8 phenyl anthracene sub units, thus creating electronically coupled annihilator encounter complex capable of intramolecular Triplet-Triplet Annihilation which we here call TTA2 and distinguish from the intermolecular annihilation, TTA1, as illustrated in Figure 1 and (ii) two generations of DPA dendrimers41 where, the first (G1) consisting of three DPA subunits connected via a central phenyl group and the second (G2) consisting of 9 DPA sub units. All the relevant molecular structures for this study are found in Scheme 1. A comparison of the relative UC efficiency between the established monomer annihilator DPA and our DPAmeric systems (Oligo, G1 and G2) was conducted, using Pd(II) octaethylporphyrin (PdOEP) as the triplet sensitizer. While DPA itself is upconverting most efficiently in the liquid state, in solid PMMA solution a significant increase of the relative TTA-UC efficiency with the DPAmeric systems was observed.

EXPERIMENTAL All commercially available compounds were used as provided unless stated otherwise. PdOEP, DPA, methyl methacrylate stabilized with ≤ 30 ppm Monomethyl ether hydroquinone (MEHQ), as well as thermal radical initiator 2,2′-Azobis(2-methylpropionitrile) (AIBN) were purchased from Sigma-Aldrich. Dendrimers were synthesized according to literature procedure.41

DPA oligomer synthesis Mass spectroscopy (MALDI) was performed on a Bruker Autoflex and size exclusion chromatography (SEC) was performed on a Waters Alliance GPCV2000 with a refractive index detector column: Waters Styvagel HT GE×1, Waters Styvagel HMW GE×2. The eluent was 1,2,4trichlorobenzene. The operating temperature was 135 °C, and the dissolution time was 2 h. The concentration of the samples was 0.5 mg

mL−1, which were filtered (filter: 0.45 µm) prior to analysis. The molecular weights were calculated according to calibration with polystyrene standards. 2,5-dihexyl-1,4-dibromobenzene (1.17 mmol, 272 mg), 9,10-anthracenediboronicacid bis(pinacol)ester (1.17 mmol, 503 mg, recrystalized from ethanol prior to use), Pd2(dba)3 (0.079 mmol, 71 mg) and tri(otolyl)phosphine in a 25 mL two necked reaction vessel was deaerated by several pump/argon cycles. Tetraethylammonium hydroxide (20 % in water, 11.7 mmol, 8.7 mL) and toluene (9 mL) both deaerated by argon bubbling was added and the reaction mixture and left at 95 °C under stirring for 72 h. An additional amount of the boronic ester (0.11 mmol, 50 mg), the catalyst (0.011 mmol, 10 mg) and the ligand (0.099 mmol, 30 mg) was then added and left to react at 95 °C under stirring for 6 h, to cap off eventual unreacted bromines. Finally, 2-bromoxylene (2.2 mmol, 411 mg) was added and the reaction mixture was left for an additional 16 h at 95 °C under stirring. The cooled reaction mixture was poured into methanol and the formed precipitate was filtered off, re-suspended in dichloromethane and let through a short silica plug. The off-white solid was put in a soxhlet extractor and methanol, ether, hexane, and DCM was, in that order, refluxed for at least 30 minutes each in the apparatus. The DCM fraction was found to contain the highest molecular weight polymer, having a mean molecular weight of 3300 g/mol (PDI = 1.18) according to SEC and 2100 g/mol according to MALDI. See Figure S8 for SEC chromatogram and mass spectra.

Spectroscopy experiments Absorption spectra were recorded on a Cary 5000 UV-Vis-NIR (Varian) spectrophotometer. Steady state luminescence spectra were recorded using a SPEX Fluorolog-3 (Horiba Jobin Yvon). For the steady state excitation intensity experiments, a 532 nm Diode Pumped Solid State Laser (DPSSL) with a measured maximum output of 106 mW was used with a beam diameter of 0.15 mm. The beam intensity was varied using a linear variable natural density (ND) filter in combination with additional non-variable ND filters.

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Scheme 1 . Chromophores used: a) sensitizer Pd(II) octaethyl porphyrin (PdOEP), b) 9,109,10 - diphenylanthracene (DPA), c) DPA oligomer (Oligo), d) 1 st generation gen eration DPA dendrimer (G1), e) 2 nd generation gen eration DPA dendrimer (G2).

excitation wavelength was obtained using a Surlite OPO (Continuum). Emission and transient absorption traces were detected using a 5 stage photomultiplier (Applied Photophysics) and recorded with an oscilloscope interfaced with a custom made LabVIEW program.

Sample preparation Liquid toluene samples as well as poly(methyl methacrylate) (PMMA) samples for power ramp experiments were measured in PYREX test tubes with an inner diameter of 1 cm. Deoxygenation of samples in toluene were carried out using freeze-pump-thaw-refill method with N2(g) of 5.0 purity as refill gas through 5 cycles. In each pumping step, a vacuum of below 5×10-5 mbar was reached and in the final step the liquid sample PYREX tubes were melt-sealed using a flame torch. The methyl methacrylate (MMA) (Sigma-Aldrich) was distilled to remove the MEHQ radical inhibitor. Thermal radical initiator AIBN was added to the distilled methyl methacrylate in a concentration of 0.02 w%. The polymerization was conducted in a forced convection heating oven (VENTI-Line 115, VWR) at 80°C for 3 hours. In order to determine the optimal concentrations for the study, two sets of five-by-five arrays of PMMA samples were prepared with five different concentrations (173 µM, 86.7 µM, 34.7 µM, 17.3 µM and 1.7 µM) of sensitizer in combination with five different concentrations (25 µM, 12.5 µM, 5 µM, 2.5 µM and 250 nM) of Oligo and (200 µM, 100 µM, 40 µM, 20 µM and 2 µM) of DPA. The DPA and Oligo concentrations were set to always have an equivalent amount of anthracene monomer units, meaning that e.g. the oligomer was dissolved at a formal concentration 8 times lower than the DPA. The samples containing the highest concentrations of sensitizer (173 µM) and annihilators DPA and Oligo (200 µM and 25 µM, respectively) proved best for upconversion with no sign of aggregation or component separation in PMMA37 and were therefore used in this study. The highest attainable concentration was limited by the solubility of the Oligo in MMA. For this array, polymerization was performed in disposable glass vials with the inner diameter of 1 cm and the produced PMMA samples were retrieved by crushing the glass vials. For every concentration combination of the sensitizer and annihilator, two reference-samples were made with pure sensitizer and each of the annihilators, respectively. As the dendrimers displayed overall higher solubility than the oligomer in MMA they were not screened in this manner and instead concentrations were set to 66.7 µM and 22.2 µM for G1 and G2 respectively, again corresponding to 200 µM of DPA monomer units to allow direct comparison between the four different samples.

RESULTS AND DISCUSSION This section will be divided into sub-sections. First the overall Spectroscopic characteristics of the investigated molecules will be presented and Sub-50 ns time-resolved emission decays were recorded using picosecond pulsed laser diode (PicoQuant) operating at 377 nm for excitation. Single-photon detection was conducted using a micro channel plate (MCP) photomultiplier from Hamamatsu R3809U-50 and a multichannel analyzer with 4096 channels (Lifespec, Edinburgh Analytical Instruments) where a minimum of 10 000 counts were recorded in the top channel. Longer time-resolved emission decay data were recorded using a nanosecond NdYAG Surlite pulsed laser with a repetition frequency of 10 Hz and a full width half-maximum (FWHM) pulse of ~7 ns. The desired

discussed. Second, upconversion measurements in low viscosity solution, hereafter called “Liquid media” will be compared to measurements in high viscosity organic glass, hereafter called “Solid media”. In the “Solid media” (PMMA) a higher UC efficiency of DPAmeric systems than for DPA is demonstrated under diffusion free conditions. Last, the Excitation intensity dependence of the two sample types will be discussed followed by an analysis of our results through Simulations and kinetics of both steady-state and time-resolved data as well as a discussion in terms of a simplified nearest neighbor model describing the probability of forming upconverting clusters of sensitizers and annihilators under diffusion free conditions.

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expected from Stern-Volmer kinetics. The time-resolved UC data displays a strong and more prompt UC emission generation with the smallest, most mobile and abundant DPA annihilator and a weaker but more long-lived UC emission for the larger and more slowly diffusing annihilators.

Upconversion in Solid media In order to demonstrate the intramolecular TTA2 process in the

Figure 2 . Absorption (solid) and emission (dashed) spectra recorded in toluene for all chromophores used in this study. study .

System characteristics The PdOEP and DPA upconversion pair is well-studied and was therefore chosen as a benchmark system.3, 26, 35, 37, 44-46 Interestingly the optical properties of the Oligo, G1 and G2 display very little perturbation of the general characteristics of the DPA subunit. As can be observed in Figure 2, apart from a slight alteration of the vibronic peak intensities, the absorption and emission spectra look very similar with little to no spectral shift and no apparent signs of exciton coupling interactions in contrast to what has been observed for other oligomeric structures.47 Furthermore, their fluorescence quantum yields are very similar and close to unity while the singlet and triplet lifetimes (values in Table 1 and measured decays with corresponding fitting in the SI) do differ slightly in both toluene and PMMA. Molar absorptivities for the compounds in toluene are found in Table S1.

Upconversion in Liquid media To facilitate comparison, all samples contain an equal concentrations of sensitizer (173 µM, vide supra) and an equal amount of DPA-units. This results in the monomeric DPA system getting a sensitization advantage in the TET-step (Figure 1), due to higher molecular concentration compared to Oligo, G1 and G2, which contain 8, 3 and 9 times less annihilator molecules, respectively. This in turn contributes to slightly higher upconversion emission of the DPA reference sample compared to the DPAmeric annihilators in a low viscosity medium (Figure 3). In liquid media, very similar upconversion emission intensity dependence with ramping of excitation intensity is observed (Figure 3a). DPA displays a slightly higher UC efficiency in the steady-state data compared to the other DPA derivatives, which is attributed to the higher DPA molecular concentration and thus more efficient TET-step (Figure 1). This is also further supported by time-resolved measurements (Figure 3b) in which DPA has the highest quenching efficiency of the sensitizer emission. It is evident (Figure 3b) that the quenching of the sensitizer scales well with the annihilator molecular concentrations, as

DPAmeric molecules (Figure 1), PMMA solubilized samples was used to eliminate molecular diffusion. Remarkably, the steady-state excitation intensity ramping data in Solid media (Figure 3a) display a clear positive effect on upconversion emission intensity with increasing annihilator size. This despite the fact that the amount of annihilator molecules is consequently smaller which in turn makes the TET-steps less efficient. The obvious and dramatic lowering of the UC emission is expected as the sensitizer has no affinity to the annihilators, and thus, the observed UC emission occurs only from positions within the sample where one or several sensitizers happen to be close enough to at least one DPAmeric molecule or several DPA, forming a functioning UC cluster. As the DPA system adds another requirement for a successful UC event, namely that there should also be two or more DPA molecules in very close proximity to each other, it is not entirely surprising that the UC intensity produced using DPA is much weaker in the solid matrix compared to the Oligo and dendrimers that lack this requirement. The low UC emission intensity in the Solid media made time-resolved measurements difficult, however the parameters obtained in the steady-state simulations fitting of the Solid media (Table 1) can be used to simulate and illustrate the expected weak and long lived kinetic traces (Figure S7, SI).

Excitation intensity dependence The UC emission dependence on excitation intensity in Liquid media is very similar for all four annihilator molecules. There is however a clear difference in thresholds between the apparent quadratic and linear regions as illustrated by the solid vertical lines in Figure 3a. When expressing the apparent “Quadratic” and “Linear” regions without simplifications, for our systems we obtain (see Excitation intensity dependence section in SI for full derivations)

 I exc − 3k TTAS [3 S * ]2 − k PS [3 S * ]   I UC , Lin = Φ FA    2  

(1)

I UC ,Quad = 2   I exc − 3k TTAS [ 3 S * ]2 − k PS [ 3 S * ]      k + TTA 1    Φ FA  k PA      k TTA 2 [3 A ** ]   

(2)

where

I exc ≡ k exc [1 S ] ∝ [ 3 S * ]

(3)

we can see that the “Linear” component eq. (1) has a clear quadratic excitation dependence through the presence of the triplet excited sensitizer squared in the channel of triplet-triplet annihilation of the sensitizer

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Figure 3 . a) SteadySteady-state UC emission power ramp experiment with DPA, Oligo, G1 and G2 dissolved in toluene (“Liquid”) and in PMMA (“Solid”). Straight gray regions in the the background are a guide for the eye, highlighting the quadratic and linear dependencies of the data. Vertical solid lines indicate estimated breaks between trend regions in the UCUC-Photon flux dependency. b) Time resolved sensitizer (PdOEP; top) and TTATTA-UC (bottom) emission performed in liquid media. In all cases the sensitizer (PdOEP) concentration was 173 µM, and the annihilator concentrations were 200 µM (DPA), (DPA), 25 µM (Oligo), (Oligo), 67 µM (G1) and 22 µM (G2). Fitting was conducted globally on steadysteady- state and time t imeime-resolved data for the Liquid media while the Solid media simulation was optimized only to the steadysteady-state emission data. (TTAS). The apparent “Quadratic” component given in eq. (2) has excitation dependence to the power of 2, 3 and 4 through the same channel in combination with the phosphorescence decay channel of the sensitizer (PS). By numerically finding the intercept between eq. (1) and (2) we obtain a threshold excitation intensity which is converted to threshTh old photon flux Pexc through the relation in eq. (3) and

k exc = α ⋅ Pexc

(4)

where α is the absorption cross-section of the sensitizer at excitation wavelength in cm2 and Pexc is the photon flux in Photons/cm2/s. Normally however, a fluid upconversion system is prepared with an abundance of the annihilator relative to the sensitizer to ensure efficient TET from the sensitizer to the annihilator. Due to this effective quenching of the triplet excited sensitizer the TTAS channel is practically inactive. Furthermore it is assumed that

I exc >> k PS [ 3 S * ]

(5)

implying that excited sensitizer triplets are produced at a higher speed than they are lost through natural decay and finally due to the low viscosity of a fluid system the TTA2 channel can be assumed to be negligible (vide supra). With these simplifications, eqs. (1) and (2) can be reduced to truly represent a linear and a quadratic region. By equating the two equations one obtains the threshold intensity Ith which is rewritten to threshold photon flux marking the transition point between the two regions for an ideal system Th , Ideal Pexc =

k PA 2 2k TTA1⋅α [1 S]

as demonstrated by others as well.48-50

(6)

The ideal threshold estimation for all annihilators in Liquid media is at most 6 % lower than the one obtained numerically without simplifications. This suggests that even though the non-simplified region describing components (eq. (1) and (2)) are not of pure linear and quadratic nature, the deviation of the threshold intensity is almost negligible when compared to an approximate estimation. In contrast, for the Solid media a clear difference in UC emission is observed. The largest annihilators produce higher UC emission than the smaller ones, with DPA being the least emissive. At low excitation intensities the UC emission in solid media displays a sub-linear dependence on increasing excitation intensity (Figure 3a). This is attributed to exceptionally low UC efficiency resulting from naturally decaying excited triplet sensitizers and annihilators at a speed proportional to that of forming the excited triplet sensitizers (eq. (3)). With increasing excitation intensity a quadratic-like region appears, described well with equation (2) before significant sensitizer ground state bleach occurs, effectively capping the UC emission at high intensities well before the actual crossing of the “Quadratic” and “Linear” UC emission components. To estimate the expected crossing of the regions given by the intersection of eq. (1) and (2) as if sensitizer ground state bleach did not occur, a linear and quadratic projection is made numerically along the nonbleach-perturbed regions of eq. (1) and (2) and the crossing point is numerically located, see Figure S9 and Table S2 in SI. These threshold values are however separated from the ideal ones (eq. (6)) by several orders of magnitude in excitation intensity. This indicates that the necessary approximations for deriving the expression in equation (6) are not valid, and in extension that equation (1) and (2) do not even approximately have a pure linear and quadratic nature in the solid media. This outcome may be attributed to the fact that the sensitizers and annihilators have no affinity to each other (Figure S11, and S12) and thus a successful TET event relies on that a sensitizer happens to be close enough to an annihilator, resulting in most excited sensitizer decaying to their ground state

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without energy transfer. In other studies where the solid matrix, unlike PMMA, exhibits exciton migration properties, a better agreement with the predicted threshold intensity has been obtained.16, 51 The conclusion drawn here is that it is essential to motivate the simplifications necessary for the derivation of equation (6) before characterizing the excitation intensity dependence of a TTA-UC system as linear and/or quadratic. In an optimally prepared TTA-UC system in low viscosity liquid medium the approximations often hold but this may not always be true for systems at higher viscosity.

Simulations and kinetics

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macromolecular annihilators. This is, however, a trivial result of the DPA concentration being higher than the molecular concentration of the Oligo and the dendrimers resulting in the TET-step being more efficient for DPA (vide supra). The effect disappears when setting all the annihilator concentrations to equate that of DPA and repeating the simulation, as illustrated in Figure S8 in SI. It should be noted that normally, the component concentrations of an efficient TTA-UC system are set with the annihilator concentration being significantly higher than that of the sensitizer, ensuring that the sensitizer is efficiently quenched. However, this mixing ratio did not produce the best UC signal in the Solid media (vide supra).

Fitting of simulated kinetics in Liquid media was performed on steadystate and time-resolved data simultaneously with kTTA1, kTET2 and τPA as sample-individual fitting parameters. Since the concentration of the sensitizer and the sensitizer itself is the same in all cases, the sensitizer-parameter kTTAS was fitted globally. In Solid media, the simulations were fit only to steady-state data with the effective annihilator concentrations as the only sample individual parameter. The rate constants and the sensitizer concentration were fitted globally, as indicated in Table 1. While the Oligo and the dendrimers are capable of intramolecular TTA (TTA2), the path generating their excited singlets is dominated by the diffusion-controlled TTA1 process in a low viscosity media such as toluene. The reason for this is that a secondary sensitization through Triplet Energy Transfer (TET2) would require an abundance of the triplet excited annihilator (3A*) in close proximity to a triplet excited sensitizer (3S*), both of which are effectively dispersed and consumed through diffusion controlled processes in low viscosity medium explaining the insignificant difference between the UC emission in Liquid media. This is further illustrated in eq. (7)

d [1 A * ] 2 = kTTA1 [ 3 A * ] − k FA [1 A * ] + kTTA 2 [ 3 A ** ] dt

(7)

where it can be seen that if the intermolecular rate constant kTTA1 is in the same order of magnitude as the rate of diffusion (kd ≈ 109 M-1s-1) then single sensitized annihilators are predominantly consumed at a higher rate proportional to [3 A* ]2 and produce singlet excited annihilator mainly through the TTA1 channel. However, if the diffusion rate, and consequently kTTA1 are significantly lower than kd, the single-sensitized annihilator triplets are not consumed as rapidly and thus more of them are available for a second sensitization described by the kTET2 part of eq. (8),

d [ 3 S* ] 2 = k isc [1 S* ] − 2kTTAS [ 3 S* ] − k PS [3 S* ] dt − kTET 1 [3 S* ][1 A ] − kTET 2 [ 3 S* ][ 3 A * ]

(8)

which is a prerequisite for the intramolecular annihilation described by kTTA2 part of eq. (7). To illustrate this point simulations were performed with all bimolecular diffusion controlled rate constants set to kd and ramped over the region of 100-109 M-1s-1 while the remaining parameters were kept as given in Table 1, Liquid media. The result seen in Figure 4 demonstrates how the Oligo- and the dendrimer-generated UC emission is expected to exceed that of DPA at high viscosities (low kd) when the mechanisms for generation of upconverted singlet annihilator through double-sensitization (TET2) and intramolecular TTA (TTA2) become more dominant. Further, the simulations indicate that there is a lower viscosity region (~105 -109 M-1s-1) where the system containing the small DPA annihilator displays higher efficiency than those with the

Figure 4 . Simulated steady s teadyteady- state singlet excited annihilator concentrations with all diffusion controlled rate constants set to kd and ramped from high to low viscosity. All other parameters are as given in Table 1 under the Liquid media headline. Excited singlet annihilator concentrations are extracted at an excitation intensity corresponding to the linear excitation dependence at both high and low viscosities viscosit ies (10 18 Photons/cm2 /s). The Oligo simulation is overlapped overlapped by the simulation of G1 due to a similar value of the product between the molecular concentrations and annihilator triplet excited state lifetimes (Table (Table 1) 1). Instead the best signal was obtained with the sensitizer concentration in the same order of magnitude or higher than the annihilator without signs of aggregation. At high sensitizer concentration and at high enough excitation intensity sensitizer decay will be influenced by its own triplettriplet annihilation. Therefore the simulations also incorporate TripletTriplet Annihilation of the Sensitizer (TTAS) as seen in eq. (8) (see Simulations and Fitting section in SI). The sensitizer triplet lifetimes in Table 1 for samples in the Liquid media were obtained, for consistency, through a measurement with excitation conditions similar to those of the time-resolved data in Figure 3b. The excitation intensity was varied in an attempt to separate the effects of the natural sensitizer decay lifetime from the TTAS deactivation pathway. Since the effect of the sensitizer’s natural decay is not very prominent in the time-resolved data in Figure 3b, it was decided that it would be set to the obtained value throughout the simulation. The rate of TTAS was however kept as a fitting parameter and it is encouraging that the kTTAS = 2.6·109 M-1s-1 determined through optimization of the simulations (Table 1) is very close to the independently determined value of

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Table 1 . Parameters for both steadysteady- state and timetime- resolved simulations. simu lations. Arrows indicate global variables. Values without footnote are determined from complementary experiments. Liquid media (Toluene) [Sensitizer] (µ ( µ M)

DPA

Oligo

G1

G2

173

173

173

173

25

67

22

0.89

b 1.00

b

[Annihilator] (µ (µ M) 200 b 0.97

Φ FA

kTTAS ( M-1 s-1) τ PS (ms) kTET1 (M-1 s-1) ×10-9 1.6 kTTA1 (M-1 s-1) ×10-9 d 0.37 kTET2 kTTA2 (s-1) ×10-9 τ PA (ms) τ FA (ns) (M-1 s-1)

×10 -9

Solid media (PMMA)

0

d 2.6×109

← ←

G1

d 24×10-6

d 61×10-6

←

→ 2.5

d 0.56

d 0.94

d 0.25

d0

d0 a 1000

d 32×10-6 c 1.00

←

1.9

→

→

← ←

→

1.6

→

d 7.5

→

d 220

d 65×10-6

→

d 2.0×105

←

d 0.33

G2

d 0.031

←

→

0.32

←

Oligo

0.99

2.5

0

DPA

→

0

←

d 0.13

0

←

c1000

→ →

d 3.4

d 5.5

d 1.4

d 1.8

18

24

20

20

b 7.0

4.9

b 5.3

b 4.5

9.1

6.4

8.2

6.0

a Estimated value. b Ref 41. c

Set value, based on values from liquid samples. d Optimized values of simulation variables.

1.75·109 M-1s-1 (Sensitizer characterization section, Figure S2, in SI) from pure sensitizer samples. The kTTA1 obtained from the simulations was approximately one order of magnitude lower50 than the experimentally determined kTET1 (see Table 1 and Stern-Volmer-section including Figure S1 in SI) even though both processes are expected to be diffusion controlled. This could be attributed to the fact that our model does not include the effect of spin statistics in the TTA-steps.52 The experimental data is the UC emission and thus only reflects the end-state of the TTA-UC process. It should, however, be noted that while spin-statistics may be applied with relative ease to the TTA process between two freely diffusing annihilators where all geometrical collisions may be close to or equally probable it is not entirely clear which interaction is dominating in the intramolecular TTA2 process of the DPAmeric molecules thus we excluded the spin-statistical parameters in the simulations. The optimized kTET2 for G1 and G2 is approximately zero supporting the hypothesis that the TTA2-channel is or is close to inactive in Liquid media. The triplet lifetimes of the annihilators in toluene are in the same order of magnitude for all molecules, which is expected. The triplet lifetime of the DPA (3.4 ms) agrees well with the reported 1-5 ms.53-54 The determined triplet lifetime of the sensitizer (318 µs) is determined at a sensitizer concentration of 173 µM using varied and pulsed high excitation intensity up to the equivalents of the excitation intensity for the time resolved measurements in Figure 3b to also probe the effects of TTAS (see Sensitizer characterization section in SI). While acknowledging that our mathematical model of the UC process is based on a purely diffusive system the Solid media steady-state data (Figure 3a) was fitted with effective annihilator concentration as the only individually varying sample parameters, while the rest of the variables; sensitizer concentration and rate constants for TTAS, TET1 and TTA1, were fitted globally for all annihilators in Solid media. TET2 was set as global variable for the DPAmeric annihilators and to 0 for DPA (Table 1). The singlet and triplet lifetimes of the annihilators were determined experimentally as well as the triplet lifetime of the sensitizer (see Sensitizer and Annihilator characterization sections as well as Figures S2-S6 in SI). The rate constant for the intramolecular TTA2 process was assumed to be large and kept the same among the DPAmeric

compounds. This approach is in accordance with our hypothesis that the UC emission in Solid media is only produced by a small subset of molecules, a critical concentration of sensitizer and annihilators operating with similar energy transfer rates as in Liquid media. The satisfactory fit resulted in rate constants for TET1 and TET2 in similar range to those seen in Liquid media. The rate constant for the TTA1 process in Solid media is a factor of 103 higher than those in Liquid media suggesting that if, while not very likely, two annihilators are in close proximity the regular intermolecular annihilation may occur at a rate that is comparable to the intramolecular TTA2 process. The rate constant for TTAS in Solid media is significantly lower than the same in Liquid media, which seems reasonable considering that the recorded UC emission in Solid media originates only from locations where enough sensitizers and annihilators are in close enough proximity. It stands to reason that if these few TTAUC clusters function, they do so relatively well and therefore other depletion channels would be less effective in these instances. The optimized effective sensitizer and annihilator concentrations are in the pM range (Table 1) further supporting the hypothesis of very few active molecules producing the observed UC emission in Solid media. Since samples in Solid and Liquid media contain the same bulk concentrations one can obtain the fraction of the UC-active annihilators proportional to the probability of forming successful UC clusters by dividing the fitted annihilator concentrations in Solid media with those of the bulk

PUC ∝

[1 A ]active [1 A ]bulk

(9)

Then using a probability density function for the Nearest-Neighbor (NN) distances of finite particles with ideal-gas approximation in 3 dimensions 55

f ( ρ , r ) = ρ ⋅ 4π ⋅ r

2

 − ρ ⋅4π ⋅r 3      ⋅ e 3 

(10)

where r is the distance between the particles and ρ is the particle density, an inter-particle distance distribution can be obtained for all bulk concentrations. Integrating the distance distribution function, eq. (10),

7



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

yields the probability function P(r). As the shape of the annihilator molecules is not accounted for in the NN-distribution, the inter-particle distances are only proportional to those between the neighboring molecules. Extracting the distances at probabilities proportional to the fractions in equation (9) and normalizing them to the intermolecular distance obtained for the Oligo to 8, yields relative distance ratios of 1.5, 8, 3.5 and 9 for DPA, Oligo, G1 and G2, respectively.56 These relative distances scales very well with the content of DPA subunits in the annihilators suggesting that the more DPA subunits there is in an annihilator molecule the larger intermolecular distances are tolerated to achieve successful UC in a rigid environment such as PMMA. This finding, in combination with the correlating stronger UC emission for the fewer larger annihilators than the many smaller ones, as illustrated in Figure 5 as well as the increased TTA2-channel contribution in higher viscosity medium (Figure 3) supports the hypothesis that there is a working intramolecular Triplet-Triplet Annihilation (TTA2) channel to be exploited in larger DPAmeric annihilator complexes.

Page 8 of 10

ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge via the Internet at http://pubs.acs.org Molar absorption, Stern-Volmer quenching, Sensitizer characterization, Annihilator characterization, Simulation and Fitting, Excitation intensity dependence, DPA oligomer synthesis analysis, Investigation of possible intermolecular interactions in Solid media.

AUTHOR INFORMATION Corresponding Author * E-mail: [email protected] , Phone: +46 (0)31 772 30 44 , Fax: +46 (0)31 772 38 58, Web site: http://www.chalmers.se/en/Staff/Pages/bo-albinsson.aspx

ACKNOWLEDGMENT We acknowledge financial support from the Swedish Energy Agency, the Swedish research council, the Swedish Strategic Research council and Knut and Alice Wallenberg foundation for financial support. KMP acknowledge support from Chalmers Material and Energy AoA. The authors would also like to acknowledge Dr. Nikola Marković for valuable input on Nearest-Neighbor statistics of finite particles.

REFERENCES

Figure 5 . Mean of the relative relative TTATTA-UC emission of Solid media in the excitation intensities range between 3.7·10 3.7 ·1017-1.6·1018 pho2 tons/cm /s from Figure 3 a.

CONCLUSION We have shown that UC efficiencies are increased in solid state matrix by covalently connecting DPA monomers to form an Oligomer and two generations of dendrimers (Scheme 1). This effect correlates well with the increasing size of the annihilator and is only visible if double-sensitization occurs to a significant degree from the sensitizer to the DPAmeric units which at the moment requires a high sensitizer concentration and high viscosity to be clearly distinguished from intermolecular annihilation. Thus the highest UC emission in the solid matrix was achieved with the largest molecules (Oligo and G2) followed by G1 and the lowest emitting DPA. It seems that the larger the annihilator structures are the better the upconversion performance will be. The general conclusions drawn from this study should aid further work in exploring means for efficient TET from the sensitizer to the annihilator while circumventing the expected problems of non-radiative UC short-circuiting through singlet back energy transfer. This is work presently being pursued in our laboratory.

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