Controlling the Efficiency of Singlet Fission in TIPS-Pentacene

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C: Energy Conversion and Storage; Energy and Charge Transport

Controlling the Efficiency of Singlet Fission in TIPSPentacene:Polymer Composite Nanoparticles Alexandra N. Stuart, Patrick C. Tapping, Elisabeth Schrefl, David M. Huang, and Tak W. Kee J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b10163 • Publication Date (Web): 19 Feb 2019 Downloaded from http://pubs.acs.org on March 4, 2019

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The Journal of Physical Chemistry

Controlling the Efficiency of Singlet Fission in TIPS-Pentacene:Polymer Composite Nanoparticles Alexandra N. Stuart, Patrick C. Tapping, Elisabeth Schrefl, David M. Huang,∗ and Tak W. Kee∗ Department of Chemistry, The University of Adelaide, South Australia 5005, Australia E-mail: [email protected]; [email protected] Phone: +61-8-8313-5314

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Abstract Singlet fission (SF) is a process with the potential to increase the efficiency of solar cells by reducing losses from thermal relaxation of hot carriers. By generating two triplet excitons from one singlet exciton, the process effectively splits the energy of highenergy photons in two, providing a means to circumvent the Shockley–Queisser limit. While the applications of SF are promising, questions remain about the mechanistic details and practicalities of implementation in photovoltaic devices that must be resolved to exploit its full potential. In this study, we present a way to investigate the effect of average intermolecular distance on SF by embedding 6,13-bis(triisopropylsilylethynyl) pentacene (TIPS-Pn) in an amorphous polymer matrix in the form of aqueous nanoparticle dispersions. By controlling the mass ratio of TIPS-Pn to the host polymer, we systematically tune the concentration of TIPS-Pn molecules in a nanoparticle, and in turn the average intermolecular separation, leading to a range of SF quantum yields. We study this system using both steady-state and ultrafast time-resolved spectroscopic techniques, and fit the results to a kinetic model to decipher the observed behavior. The quantum yield of SF is shown to decrease with average intermolecular separation, which is explained by diffusion-limited SF and an increase in loss pathways through isolated sites. Additionally we identify an intermediate species in the SF process, and show that a significant proportion of this species decays nonradiatively without dissociating to form separated triplets, revealing a major loss pathway that has important implications for future research and applications.

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Introduction Singlet exciton fission (SF) is a spin-conserving process in which a chromophore in its first excited singlet state, S1 , shares its energy with a chromophore in the ground state, S0 , to give two triplet excitons in the T1 state. Recently SF has become of particular interest due to its potential to circumvent the Shockley–Queisser limit of conventional solar cells. 1 By increasing the range of the solar spectrum harvested and generating two excitons from a single high-energy photon, the maximum theoretical efficiency of a single-junction solar cell can be increased from 33 to 45%. 2–6 But for the process to be of substantial benefit in solar cells, the efficiency of singlet-to-triplet conversion should approach 200% (two triplet excitons for every singlet exciton), and the resultant triplets must be long-lived and able to separate so that they can be independently harvested. Details of the mechanism of SF are required to understand how to satisfy these two conditions. SF is generally agreed to proceed via a correlated triplet-pair intermediate with an overall singlet character, 1 (TT), according to the mechanism 1 −− −− S0 + S1 ) −* − (TT) ) −* − T1 + T1 ,

(1)

but further details of this mechanism are still unclear. For example, the nature of the triplet-pair state, the character and efficiency of steps to and from this intermediate, and the involvement of charge-transfer and excimer states are all factors still under debate. 7–10 A few recent studies have proposed that significant losses may occur in the SF process, leading to lower efficiencies than initially expected. 11–13 In a study on covalently linked tetracene dimers, Korovina et al. suggested that the second step of SF, the separation of 1 (TT) into individual triplets, was not efficient in isolated dimers. 11 Pensack et al. have also suggested that the separation of 1 (TT) is frustrated in amorphous nanoparticles of pentacene derivatives. 12 Recently they investigated this phenomenon in detail, and showed that only some arrangements of pentacene derivatives lead to the dissociation of 1 (TT), and that the efficiency of this step depends strongly on the degree of intermolecular coupling. 13 These findings are significant, as the triplet excitons cannot be harvested by the solar cell if the triplet-pair cannot be separated into individual triplets, potentially leading to a decrease in the solar cell efficiency rather than an increase. 14 Having been observed in several very different systems, such efficiency losses are potentially widespread. Thus there is a pressing need to understand the mechanism and causes of these losses, and therefore how they can be avoided. Morphology has a significant impact on the efficiency of SF, and understanding the effects of morphology facilitates understanding the mechanism itself. 12,15–23 As mentioned above, Pensack et al. showed that changing the packing of molecules, and therefore the intermolecular coupling, dramatically changes the yield of triplet excitons. Simply changing the packing polymorph of the same crystalline material has been shown to increase the rate of SF by more than an order of magnitude, 17,24 and can be tuned to turn off SF altogether. 18 The effect of the distance between chromophores undergoing SF is a particularly interesting factor. 25 Intuitively, it might be predicted that SF would be faster and more efficient when the S1 and S0 chromophores are closer together. However, if the coupling in a system is overly strong, the first step of SF, i.e. 1 (TT) formation, may be efficient, but the second 3



step, the dissociation of 1 (TT) to separated triplets, may not occur at all. 26 Investigating the effect of intermolecular distance on the SF efficiency can thus provide a straightforward method of obtaining insight on the mechanism of SF. Here we present a system in which we can control the concentration of TIPS-pentacene (TIPS-Pn) to systematically vary the average intermolecular separation between molecules. Not only does this shed light on the optimum conditions of SF, but by using this control to sample a range of SF efficiencies, we are also able to reveal new information about the mechanism of SF, and in particular the types of losses observed. TIPS-Pn is an attractive system that has already been characterized and shown to undergo exothermic SF, obviating considerations of the reverse triplet fusion reaction, and simplifying analysis. 2,12,15,27–32 By embedding TIPS-Pn in an amorphous polymer matrix in the form of poly(methyl methacrylate) (PMMA) nanoparticles, we vary the average concentration of TIPS-Pn molecules in a NP by controlling the TIPS-Pn:PMMA mass ratio. Thus, in NPs with low proportions of PMMA, the concentration of TIPS-Pn molecules is higher, and on average, the distance between molecules is shorter. As we increase the proportion of PMMA, we effectively increase the average intermolecular separation between TIPS-Pn molecules, and show that this in turn leads to a lower efficiency of SF. This control of the efficiency allows us to unambiguously determine the spectral features of the species involved in SF, and thoroughly describe their kinetics. A composite system of TIPS-Pn and PMMA is also of interest as embedding SF materials in a polymer matrix may be useful in thin-film fabrication, which is important for the integration of SF into photovoltaic devices. Polymers are often solution processable and form better films than small molecules, so understanding the effects of their integration with SF materials on SF efficiency is beneficial. Furthermore, using an aqueous nanoparticle dispersion allows us to gain information on a solid-state composite system without having to resort to studying films. The dispersion allows the continuous sampling of new material, avoiding effects of sample inhomogeneity and photodegradation, which are common problems associated with studying films. Using transient absorption and photoluminescence spectroscopy, we identify and model the kinetics of the triplet-pair intermediate as well as the singlet and triplet excitons for a range of TIPS-Pn concentrations. We explain the decrease in SF efficiency with TIPSPn concentration by an increase in the amount of diffusion required for excitons to reach molecules that are able to undergo SF, and an increase in the number of isolated sites that act to hinder this process. Additionally, even for the optimum TIPS-Pn concentration, we show that the quantum yield of SF is low, due to a significant proportion of the triplet-pair intermediate decaying nonradiatively rather than dissociating into independent triplet excitons. We also show that this phenomenon increases as we decrease TIPS-Pn concentration and therefore the average separation between molecules, suggesting the proximity of sites nearby those undergoing SF to which triplets can migrate is important for 1 (TT) separation.

Methods Materials. 6,13-Bis(triisopropylsilylethynyl)pentacene (TIPS-Pn, 99.9%) was purchased from Ossila and used as supplied. Poly(methyl methacrylate) (PMMA, average MW: 120000, 4


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degree of polymerisation: 1200) and the surfactant poly(oxyethylene)nonylphenyl ether (Igepal CO-520) were purchased from Sigma-Aldrich. HPLC grade tetrahydrofuran (THF) was purchased from RCI Labscan and freshly distilled prior to use. All water used in experiments was purified using a 18 MΩ Millipore Milli-Q Reagent Water System fitted with a 0.45 µm filter. Nanoparticle Preparation. Various TIPS-Pn NP suspensions were prepared by the reprecipitation method. 33–36 A mixture stock solution of TIPS-Pn, PMMA, and surfactant was prepared by dissolving the required amount in THF (examples of concentrations and quantities used for different samples are given in Table S1 in the Supporting Information (SI)). The stock solution was then injected into 5 times the volume of water under vigorous stirring and left to stir for approximately 5 minutes. The THF was removed under reduced pressure and the NP suspension further concentrated to reach a TIPS-Pn concentration of ∼0.1 g L−1 . The samples were finally filtered through a 0.2 µm hydrophilic syringe filter (Sartorius Minisart NML). Steady-state Optical Measurements. Steady-state UV–visible absorption spectra were obtained with a Cary Varian 1E UV–visible spectrophotometer using a 2 mm path length quartz cuvette (Starna Cells 21-Q-2), and corrected for scattering using a pure PMMA nanoparticle baseline. Fluorescence spectra were taken on a Perkin Elmer LS 55 fluorescence spectrophotometer with an excitation wavelength of 590 nm, excitation slit bandwidth of 5 nm and emission slit bandwidth of 15 nm, using a 1 cm path length quartz cuvette (Starna Cells 3-Q). Absorption at the excitation wavelength was less than 0.1. Time-resolved Spectroscopy. Time-resolved spectroscopic experiments used laser pulses sourced from the output of a Ti:sapphire regenerative amplifier (Spectra Physics, Spitfire Pro XP 100F), providing pulses centered at 800 nm with 100 fs duration and a 1 kHz repetition rate. The 440 nm light was obtained with an optical parametric amplifier (Light Conversion, TOPAS-C) using the fourth harmonic of the idler. Fluorescence lifetime data were obtained using a fluorescence spectrometer (Ultrafast Systems, Halcyone) configured for either upconversion (UC) or time-correlated single photon counting (TCSPC) modes. The upconversion gate source was a small fraction of the 800 nm amplifier output, focused on to the 0.4 mm BBO crystal used for sum-frequency generation. The 440 nm excitation pulses had an energy of ∼0.25 µJ and were focused to a full-width half maximum (fwhm) spot size of ∼0.5 mm, with the polarization rotated to the magic angle (54.7◦ ) relative to the gate to negate anisotropic effects. Pump–probe spectroscopic experiments were performed on a transient absorption spectrometer (Ultrafast Systems, Helios). The 440 nm pump pulses had an energy of 1.5 µJ with a spot size of 740 µm fwhm, with a polarization rotated to the magic angle relative to the probe. The visible probe light was produced by focusing a small portion of the 800 nm amplifier output onto a 3.2 mm sapphire crystal. The white-light continuum was then split into signal and reference beams, and focused onto the sample with a fwhm spot size of 225 µm. Samples were continuously stirred throughout the experiment, and photodegradation was observed to be less than 5%. 5



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Results and Discussion Characterization of TIPS-Pn:PMMA Nanoparticles PMMA nanoparticles (NPs) embedded with TIPS-Pn were prepared using a range of different TIPS-Pn:PMMA mass ratios, which are listed in Table 1. The NPs form suspensions in water that are stable for a number of weeks at room temperature in the dark, with the addition of surfactant ensuring the stability of the more highly concentrated samples without affecting their photophysics (see sections S3 and S8 in the SI). Table 1: Range of different TIPS-Pn:PMMA mass ratios used to prepare NPs, the corresponding average concentration of TIPS-Pn molecules in a NP, and the fitting parameters for the time-resolved fluorescence upconversion data.a TIPS-Pn: TIPS-Pn PMMA conc mass ratio (mol L−1 ) 1:0 1.73 1:0.5 1.18 1:1 0.90 1:3 0.46 1:5 0.31 1:7 0.23 1:10 0.17

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τ3 (ps)c – – – 12 000 12 000 12 000 12 000

P Data fitted to a multi-exponential function f (t) = n An e−t/τn with an instrument response time of 0.45 ps. Unconstrained are shown with a 90% confidence P parameters b c interval. Amplitudes normalized so n An = 1. Fixed to natural singlet lifetime obtained from TCSPC measurements. a

The UV-visible absorption spectra of the different NPs prepared are compared with TIPSPn in THF solution in Figure 1. Previously, TIPS-Pn has been studied in crystalline forms for which the steady-state spectra reflect the types of molecular packing and strength of coupling between molecules. Aggregate features distinct from those in solution-phase have been observed in a number of studies of crystalline TIPS-Pn films, 27,29–31 as have similarly been observed for pentacene 37 and tetracene. 19 Crystalline domains of highly coupled brickwork packing have also been reported in NPs of TIPS-Pn, again resulting in distinct spectral features compared to solution. 12,15 In contrast, the spectra of the NPs in Figure 1 are nearly identical to the solution spectra, with no crystalline aggregate features, even after a number of days in storage (Section S3). This result suggests a weak electronic coupling between TIPS-Pn molecules inside the NPs due to a disordered arrangement, with negligible crystalline domain formation. We therefore conclude that TIPS-Pn is amorphously distributed inside the NP, as represented in the illustration in Figure 1.

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Figure 1: UV-visible absorption spectra of NPs with different TIPS-Pn:PMMA mass ratios and pure TIPS-Pn in solution (THF). The similarity of the NP and solution spectra suggests that the TIPS-Pn molecules form an amorphous dispersion in the NP as shown in the illustration, where the TIPS-Pn molecules are represented by dots and the PMMA chains constitute the bulk of the NP. Previous studies of neat TIPS-Pn NPs by Tayebjee et al. 15 and Pensack et al. 12,13,16,38 have also reported amorphous arrangements based on similar arguments. It should be noted, however, that the NPs prepared by Tayebjee et al. eventually experienced a morphological evolution to a more strongly coupled system, with an additional spectral feature at 700 nm. 15 This evolution was not observed here, likely due to subtle differences in the preparation procedure. A recent study by Pensack et al. was able to reproduce this evolution, and attributed it to co-precipitation with a chemical additive from the syringe used in the NP preparation. 12 The lack of this additive in our preparation is likely the reason the morphology remains unchanged over time. The series of peaks in Figure 1 at 650, 590, and 550 nm represent the S1 ←S0 0–0, 0– 1, and 0–2 vibronic transitions, and the smaller series from 440 nm represent the S3 ←S0 transitions. 39 The transitions become red shifted from those in solution as the proportion of PMMA is decreased, with the 1:10 TIPS-Pn:PMMA sample the least shifted and most solution-like. This result suggests that as the proportion of PMMA is increased, the TIPS-Pn molecules become more isolated, and thus more solution-like. We can therefore conclude that the PMMA is effectively diluting the TIPS-Pn molecules, rather than forming large separated domains of either material. Based on the densities of PMMA and TIPS-Pn we calculate the concentration of TIPS-Pn in a nanoparticle as varying from 1.73 to 0.17 mol L−1 (Table 1, SI Section S2). Note that we do not necessarily consider the TIPS-Pn molecules in the NP to be uniformly dispersed. For example, it is possible that TIPS-Pn forms small amorphous clusters within the PMMA. As the proportion of PMMA is increased, it is likely that both individual molecules become further apart, and any clusters of molecules become smaller and less abundant. The average effect is that the concentration of TIPS-Pn is decreased, so the molecules are more isolated and the average intermolecular distance is greater.

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Fluorescence of TIPS-Pn:PMMA NPs The steady-state fluorescence spectra of the samples are shown in Figure 2a. After excita-

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Figure 2: (a) Steady-state fluorescence of TIPS-Pn:PMMA NPs. (b) Fitted time-resolved fluorescence of the NPs after 440 nm excitation. The fitting parameters for each ratio are give in Table 1. The inset of (b) shows the results in the initial 25 ps. tion at 590 nm fluorescence is detected with a peak at ∼650 nm and a shoulder ∼710 nm, reflecting the 0–0 and 0–1 vibronic transitions. As the proportion of PMMA is decreased, the fluorescence intensity decreases with negligible change in the spectral shape, and by the 1:1 TIPS-Pn:PMMA NPs is effectively quenched. To investigate the source of this quenching, the decay kinetics of the 655 nm fluorescence peak was monitored using a time-resolved fluorescence upconversion (UC) technique. The first 500 ps ofPeach time-resolved trace is shown in Figure 2b, fitted to the sum of exponentials I(t) = n An exp(−t/τn ) and convoluted with a Gaussian 0.45 ps fwhm instrument response function. Fit parameters are given in Table 1. Each fluorescence decay could be fit with 3 or fewer exponentials (n ≤ 3), with fast, intermediate, and slow decay time constants, τ1 , τ2 , and τ3 , respectively. As the UC measurements were limited to a ∼2.5 ns window, the ns-scale dynamics of the samples’ fluorescence decay was obtained using time-correlated single photon counting (TCSPC), shown in SI Figure S3. In addition to the NP samples, a 10−5 M TIPS-Pn solution in toluene was measured (SI Figure S2), which was sufficiently dilute to assume negligible intermolecular interactions between TIPS-Pn molecules over the duration of the experiment. 30 Because there are no additional singlet decay pathways such as singlet fission in this dilute sample, the decay fits to a single exponential with a time constant of τ = 12 ns. This value was assigned 8


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to the intrinsic singlet lifetime, in good agreement with other studies of TIPS-Pn. 29,30 This lifetime also matches the slowest decay observed in the TCSPC measurements of the NPs. Thus we have used it to constrain the long time constants in the fits of the time-resolved fluorescence data, which is particularly necessary for the UC data as the experimental time window is much shorter than the natural singlet lifetime. The refractive index of PMMA is nearly identical to that of toluene, so the intrinsic lifetime of TIPS-Pn would be expected to be the same in both media. 40 The two shorter time components of the UC data, τ1 and τ2 , were fit without constraints. As the proportion of PMMA is decreased, and thus TIPSPn concentration increased, the fluorescence becomes significantly more short lived, which is reflected in the fit parameters. Given that the only fluorescent species present is the S1 state, this behavior indicates a decrease in S1 lifetime due to the presence of nonradiative decay pathways, which become more dominant as the TIPS-Pn concentration increases. Only the neat 1:0 NP sample could be fit with a single, fast exponential with τ1 = 3.9 ps. The other TIPS-Pn:PMMA blend NPs required a second exponential with an intermediate time constant τ2 , indicating the presence of a second type of nonradiative decay pathway, or a second population of singlet excitons. 15,19 As the TIPS-Pn concentration decreases, the amplitude of this intermediate time constant grows, as does the natural singlet decay, τ3 . τ1 consequently becomes less dominant, and both τ1 and τ2 also become slower with decreased concentration. As the instrument response time of TCSPC is slow (650 ps), it is not used to make any significant conclusions about trends in the lifetimes of the NPs other than τ3 , which shows the same trend in amplitude as the UC data. There is a slight inconsistency in the general trend of the time-resolved fluorescence, with the decay of the 1:0.5 sample slightly faster than that of the 1:0 NPs. Because the proportion of PMMA in this sample was low, the TIPS-Pn NP concentrations for 1:0 and 1:0.5 were very similar, and the difference between decay time constants is within experimental error. We also note that these decay time constants are consistent with those measured in the neat amorphous TIPS-Pn NPs by Tayebjee et al. 15

Transient Absorption of TIPS-Pn:PMMA NPs To investigate the origin of the nonradiative decay observed in the time-resolved fluorescence, transient absorption (TA) spectra were collected over 460 to 800 nm, exciting the S3 ←S0 transition at 440 nm. Previous time-resolved studies of TIPS-Pn have shown that the excitation energy has a minor impact on exciton dynamics and decay products, as the S3 →S1 relaxation occurs rapidly. 41 Based on the energy-gap law, this relaxation should be on the order of less than 100 fs, 42,43 which is faster than the 150 fs instrument response time of the TA spectrometer. As such, we observed minimal differences in TA dynamics when exciting the S1 ←S0 transition at 590 nm instead (SI Figure S8). The transient absorption spectra of the 1:0, 1:5 and 1:10 TIPS-Pn:PMMA NPs are shown at selected times in Figure 3. Complete spectra for all samples are given in the SI (Section S5). For all samples, a negative ground-state bleach (GSB) signal is observed at ∼650, 600, and 550 nm, matching the S1 ←S0 0–0, 0–1, and 0–2 vibronic transitions seen in the steadystate absorption spectra in Figure 1. There is some overlap of these bleach bands with strong excited-state absorption (ESA) signals that dominate the 460 to 600 nm spectral window. These positive ESA signals comprise more than one spectral component. Most obvious at 9



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Figure 3: TA spectra of 1:0, 1:5 and 1:10 TIPS-Pn:PMMA NPs following 440 nm excitation. The difference in dynamics between the samples with TIPS-Pn close together and far apart allows the deconvolution of the different spectral components present. Spectra of all other ratios as well as full 3D plots are given in the SI (Section S5). early times, and in samples with a high proportion of PMMA, is a series of absorption peaks around 460, 510, and 575 nm, accompanied by a negative stimulated emission (SE) signal around 710 nm. The lifetimes of these features are consistent with the time-resolved fluorescence data, and are attributed to Sn ←S1 transitions, in agreement with previous studies. 15,16,29,30 They also match the features in the TA of the 10−4 M TIPS-Pn solution in toluene (SI Figure S4), which, as discussed above, is dilute enough that no SF occurs and thus the signal can be considered that of the singlet exciton. An additional ESA with peaks centered around 475 and 507 nm rises over tens of picoseconds, and decays at a rate much slower than that of the singlet, dominating the spectrum over the latter part of the 3 ns experimental time window. This absorption is characteristic of the TIPS-Pn T3 ←T1 transition, 22,26 indicating the production of triplet excitons. 15,16,29 Given the appearance

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of the triplet signal occurs much faster than the rate of S1 →T1 intersystem crossing, 30 we attribute the nonradiative decay of singlets observed in the time-resolved experiments to triplet production through SF. This is consistent with previous observations of SF in amorphous TIPS-Pn NPs. 12,13,15,16 As the proportion of PMMA increases, there is a decrease in the rate of formation of the T1 ESAs and concurrent decay of the S1 ESAs. In the TA spectra of the 1:0 NPs (Figure 3a), a well-defined T3 ←T1 peak is present by 5 ps, with minimal features of the singlet exciton. In contrast, for the 1:10 NP sample the spectral shape at 5 ps differs significantly, with relatively weak triplet ESA and obvious singlet exciton presence (Figure 3c). These trends are consistent with the increase in the long-lived signal in the fluorescence UC data (Figure 2b, Table 1), and demonstrate the reduced rate of SF as TIPS-Pn concentration decreases. To highlight the difference in SF rates with concentration, Figure 4 shows the TA at 5 ps for all the TIPS-Pn:PMMA ratios. Two isosbestic points are present at 540 and 670 nm, characteristic of the conversion from one kinetic species to another. As the proportion of PMMA increases, and hence TIPS-Pn concentration decreases (red to blue lines), the triplet-dominated region around 507 nm decreases and the singlet ESA increases, indicating a slower conversion from singlets to triplets. The isosbestic point at 670 nm similarly shows a decrease in magnitude of the GSB region with an increase in intensity of the SE at 710 nm, indicative of less exciton multiplication by SF as the proportion of PMMA increases. The strengthening of the broad ESA band around 750 nm as singlet excitons are depleted is worth noting. While there is some overlap with the SE at 710 nm, the appearance of this feature is neither correlated to the observed singlet exciton decay, nor the growth of the triplet ESA peaks, suggesting another component may be present. 10 -3 TIPS-Pn:PMMA

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Figure 4: TA spectra at 5 ps for different TIPS-Pn:PMMA mass ratio NPs. The shape of the spectra at early times is significantly different for the different TIPS-Pn separations. GSB is ground state bleach, SE is stimulated emission, and ESA is excited-state absorption. It should be noted that there is significant overlap of the T3 ←T1 and Sn ←S1 ESAs around 475 to 525 nm, and of the Sn ←S1 ESA and the GSB features around 550 to 625 nm. Additionally, the observed SE signal at 710 nm corresponds to the weak 0–1 shoulder in the steady-state fluorescence (Figure 2a), implying that there must also be a significant 0–0 SE component to the negative signal band around 650 nm, overlapping the GSB. Hence in this 11



system it is not reliable to use solely the magnitudes of the GSB or ESAs to quantitatively analyze SF rates or yields, although other studies of SF have done so. 31,44,45

Efficiency and Mechanism of SF in TIPS-Pn:PMMA NPs Spectral Analysis Because of the extent of overlap of different features in the TA spectra, there are no regions that can be solely assigned to S1 or T1 , and thus no single wavelength can be used as a kinetic trace for either population. To extract the kinetics from the TA data, the spectra should be resolved into their respective components or “basis spectra” following the terminology of Roberts et al. 19 The TA spectra can then be fit to a linear combination of the basis spectra to give the concentrations of each component as a function of time. Note that these fits are not constrained to any kinetic scheme. To avoid confusion with the concentrations that are later given by fitting the data using a kinetic model, we refer to the fits obtained from this method as “spectral fits”. Full details of the extraction of the basis spectra and subsequent spectral fitting are given in the SI (Section S9). Briefly, the T1 basis spectrum was obtained using the TA of the 1:0 TIPS-Pn:PMMA NPs at late times (e.g. 3 ns) when negligible singlets were present, and the S1 basis spectrum was extracted using an additional 1:100 TIPS-Pn:PMMA sample, in which, as with the dilute solution, the concentration of TIPS-Pn molecules was sufficiently low to eliminate intermolecular TIPS-Pn interactions such that only singlets were present (see SI Sections S4 and S5). Additionally, given that the fluorescence decay is a reflection of the S1 lifetime, the time evolution of the S1 populations were constrained to match the fluorescence UC data, and only the magnitude of the concentration, CS1max , was fit. The resulting S1 and T1 spectra are given in Figure 5a. Initially a two-component fit (only singlet and triplet excitons) to the TA was attempted, but the fits were poor at times before 2 ns (SI Figures S11 and S12), and SF yields were much lower than what has previously been reported for TIPS-Pn. 15,16,29–31,44 Even at late times, after the S1 population has completely decayed, there are still some regions of the TA spectra the T1 basis spectrum is unable to fit. For example, the broad band at 750 nm persists after the singlet has decayed, and cannot be accounted for by the triplet. As mentioned previously, the lifetimes of some of the features in the TA spectra suggest the presence of an additional species. The inability of the T1 spectra to fit the shape of the TA at intermediate times is further indication of this conclusion. Therefore to improve the fits to the TA spectra a third species was considered. Recent studies have reported the identification of the triplet-pair intermediate, 1 (TT), in various kinds of systems. 7,9,11,38,46–49 While the exact nature and formation of 1 (TT) is still unclear, the suggestion that 1 (TT) is actually observable in some systems, and the fact that our proposed third species exists at intermediate times between the S1 and T1 states, leads to the assignment of this component to the 1 (TT) intermediate. The basis spectrum of 1 (TT) was determined from the 1:0 sample at 40 ps, when the S1 population has decayed but 1 (TT) and T1 are evidently both present. There are multiple possibilities for the 1 (TT) spectrum, depending on how rapidly we assume the T1 population decays over time. For simplicity we only show a rational estimate here as an example, which assumes the T1 population decays by 15% between 40 ps and 3 ns, but we note the full range of possibilities were considered, and as such the singlet fission yields reported here are a 12


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range bounded by the two extreme cases. The lower bound assumes the triplets do not decay at all between 40 ps and 3 ns (0%), and the upper bound assumes there is no 1 (TT) absorption at the 507 nm T1 peak, and thus all of the decay of this peak is due to triplets (27%). Further details of the extraction of the basis spectrum and subsequent fitting with three spectral components are given in the SI (Section S9.2). The 1 (TT) basis spectrum is given in Figure 5a, and the resultant concentrations and fit for the 1:5 sample are given as an example in Figure 5b and c. The slight dip in the 1 (TT) spectrum at 500 nm is a result of the method used to extract the basis spectra from the experimental spectra. There is likely some spectral broadening of T1 around 500 nm between 40 ps and 3 ns, and its effect is reflected in the basis spectrum of 1 (TT). Apart from this artifact, it appears that 1 (TT) also exhibits ESA features around 460 to 550 nm, as well as the weak and broad 750 nm band. The shape of this spectrum is consistent with previous assignments of triplet pairs in pentacene derivatives, including the weak 750 nm band. 13,50 The fits to all other samples are given in SI Figures S14, S16, and S17, and in all cases the fits are significantly improved by including a third component. The reconstructed TA (SI Figures S16 and S17) are practically coincident with the experimental TA at all times for the 1:0 to 1:1 samples, and only slight deviations are observed for the 1:3 to 1:10 samples at early times. Small discrepancies in the fits at short times are to be expected, as there is some approximation in extracting the S1 basis spectrum, and S1 is most prevalent at early times. For this same reason the 1:10 data show the least satisfactory fit among the data sets, as this has the most long-lived S1 component. Even so, the 1:10 three-component fit still shows significantly better agreement with experiment than the two-component fit. To confirm this agreement was not a result of the fit method, the TA spectra of the samples were also de-convoluted using global analysis methods (SI Section S10). The spectra used in the global analysis are the best fits to the TA data, rather than being manually extracted and assigned as is the case here. Even with this additional freedom, the TA data could not be fit using only singlets and triplets, but require three components. This good agreement indicates the reliability of the spectral analyses used in this study. The time-dependent species concentrations in SI Figure S14 show the amount of triplet produced increases with increasing concentration of TIPS-Pn in the NP. The SF quantum yields, max([T1 ]) , (2) φSF = max([S1 ]) reflect this (Figure 8a and SI Table S5), but they are still much lower than previous reported values for TIPS-Pn, which have been as high as 2 in some cases. 15,16,29–31,44 We note that this definition of a quantum yield neglects the proportion of triplets that decay before the maximum has reached. However, the triplet decay rate is slow enough here that this proportion should be low, so for efficient SF this number should still be close to 2. To explain the low yields, we examined the time-dependent concentrations of 1 (TT) and T1 (SI Figure S14). For all of the samples, the T1 population reaches a maximum at relatively early times, from approximately 20 ps for 1:0 to 200 ps for 1:10. The 1 (TT) component, however, continues to decay past this time, i.e., the decay of 1 (TT) is not correlated with the rise of T1 . This implies that there is an alternate decay pathway for the 1 (TT), and that they do not all dissociate to form T1 . This observation is consistent for all variations of 1 (TT) spectra (SI 13



10

a

6

(L mol-1 cm -1 )

4

S1 0.5 1 (TT) T1

4 2 0

500

Concentration (M)

10

550

600

650

b

8

700

750

S1

1:5

6 8 6 4 2 0

4 2

0

0 0

800

Wavelength (nm)

-7

1000

40

1

(TT) T1

80

Time (ps)

120

2000

3000

Time (ps)

c

Exp Fit

1:5

5 ps A

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

Page 14 of 29

100 ps 3000 ps 500

550

600

650

700

750

800

Wavelength (nm)

Figure 5: (a) Basis spectra of S1 , 1 (TT), and T1 states of TIPS-Pn. The S1 spectrum was obtained from the TA spectra of a 1:100 TIPS-Pn:PMMA sample, the T1 spectrum from TA of the 1:0 sample at long times (3 ns), and the 1 (TT) spectrum from the 1:0 sample at an intermediate time (40 ps). Note that the spectra include GSB contributions, resulting in the negative values in the 600 to 700 nm region. (b) The extracted concentrations of S1 , 1 (TT), and T1 states obtained by fitting linear combinations of the basis spectra in (a) to the 1:5 TA data, giving the fitted TA spectra in (c). The inset in (b) shows detail of the concentrations over the first 120 ps. Figure S18). To quantify the effect of this behavior we define a second quantum yield, φSF0 ,

14


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which takes into account the 1 (TT) intermediate: φSF0 =

max([T1 ] + 2 × [1 (TT)]) . max([S1 ])

(3)

Several reviews on SF have emphasized that SF should not be considered to be complete unless individual separated triplets are produced. 2,26,41 We therefore do not term φSF0 a quantum yield of singlet fission. Instead, this quantity represents the amount of singlets that begin to undergo SF to form 1 (TT), i.e. the efficiency of the first step(s) of SF. The values of φSF0 for low proportions of PMMA are much closer to 2 than φSF , as is expected for TIPS-Pn SF quantum yields (Figure 8a and SI Table S5). This result suggests the low values of φSF are due to the failure of the 1 (TT) state dissociation, rather than any decay pathways of the triplets. That is, for the samples with φSF0 close to 2, most singlets begin to undergo SF as expected from past studies, but they do not all separate into T1 . No additional S1 population is observed to form, so the decay of 1 (TT) is unlikely to be the reverse reaction of SF. Instead we propose that 1 (TT) decays nonradiatively to the ground state, as has previously been suggested for nanoparticles of pure amorphous acenes by Scholes and coworkers. 12,13 As the proportion of PMMA increases and TIPS-Pn concentration decreases, both quantum yields decrease, indicating that there are losses other than the 1 (TT) state not separating for these samples. Additionally, the long lifetime of the S1 and 1 (TT) states, and the slow formation of T1 suggests SF is much slower in samples with low TIPS-Pn concentrations. In order to explain these phenomena we fit the TA data to a kinetic model, as described in Figure 6. Kinetic Analysis Slong kS1

klong

kD

SD

kS1

kSFA 1(TT)

k1(TT)

klong(t)

SSF

A

1(TT)

SSF

SD

Slong

kSFB

kD(t) kSFA 1

B

kdiss

k S1

kS1

(TT)A

k S1

kSFB 1

(TT)B

k1(TT)

T1

T1+T1 kT1

S0

Figure 6: Schematic and energy-level diagram of the kinetic scheme used to fit the TA data. klong and kD are given by Smoluchowski diffusion, kS1 is assumed to be 8.33 × 10−5 ps−1 from time-resolved fluorescence data, and kT1 is set as 6.67 × 10−5 ps−1 . Given the multiexponential decay of the fluorescence signal (Figure 2b), we used a kinetic model with multiple singlet populations. 15,19,47 Following the example of Roberts et al., 19 we 15


kdiss

kT1


Page 16 of 29

propose that SF in the NPs is diffusion limited; that is, only a subset of the singlet exciton population will be located on TIPS-Pn molecules with a neighbor that has a separation and orientation favorable for SF. The remaining excitons must therefore diffuse to these “SF sites” in order to undergo fission. We denote singlet excitons located on SF sites as SSF , and those that are not, i.e., the diffusing population, as SD . Some number of SF sites will be populated directly by the laser excitation pulse, giving an initial concentration of singlet excitons able to undergo fission, [SSF ]0 . Further SF sites can be populated by the diffusion of SD , which we model using a Smoluchowski diffusion rate, 51,52 kD (t) = 4πRDcSF (1 + √

R ), πDt

(4)

where R is the trapping radius of a SF site, D is the diffusion constant of singlet excitons, and cSF is the total number of SF sites. Initially the data were fit using just these two singlet populations (Figures S26 and S28 in the SI), but these models were not able to reproduce the data. The time-resolved fluorescence of the samples fit to a combination of three different time constants, τ1 (fast), τ2 (intermediate), and τ3 (slow) (Table 1). Diffusion-limited SF accounts for the rapid decay time, τ1 , and gives a distribution of intermediate decay times to account for τ2 . However, diffusion alone is insufficient to account for the longest time component, τ3 . The presence of this component, and the fact that it fits well to the intrinsic 12 ns singlet lifetime for all samples, implies the existence of a third population of singlet excitons that can neither undergo SF, nor diffuse to eventually reach a site where they can on the 3 ns timescale. The only decay pathways available to this population are the intrinsic decay pathways to the ground state. We call this third population of long-lived singlet excitons Slong . As with the SF sites, Slong can either be populated from the initial excitation or filled by the diffusion of SD . The total concentration of singlet excitons is then given by [S1 ] = [SD ] + [SSF ] + [Slong ].

(5)

We also modeled the triplet-pair intermediate using multiple populations. Using only one triplet-pair intermediate, as in Figure S26 in the SI, the rapid formation of T1 cannot be reconciled with the long lifetime of 1 (TT) observed in the spectral fits. These features can only be reproduced if a second triplet-pair population is introduced. This allows one population, 1 (TT)A , to slowly decay with rate constant k1 (TT) , while in parallel the other population, 1 (TT)B , is able to rapidly dissociate with the rate constant kdiss to form separated triplets. We then have [1 (TT)] = [1 (TT)A ] + [1 (TT)B ], (6) where SSF begins to undergo SF to give either 1 (TT)A or 1 (TT)B with rate constants kSFA and kSFB , respectively. Finally, we also modeled the decay of T1 with a unimolecular rate constant kT1 . Given SF is exothermic in TIPS-Pn, 2,26 and since no delayed fluorescence is observed, we excluded the reverse reactions. The full model, which we show in Figure 6, can

16


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be expressed as the following series of coupled differential equations: d[SD ] dt d[Slong ] dt d[SSF ] dt 1 d[ (TT)A ] dt d[1 (TT)B ] dt d[T1 ] dt

= −kS1 [SD ] − klong (t)[SD ] − kD (t)[SD ]; = −kS1 [Slong ] + klong (t)[SD ]; = −kS1 [SSF ] + kD (t)[SD ] − (kSFA + kSFB )[SSF ]; = kSFA [SSF ] − k1 (TT) [1 (TT)A ]; = kSFB [SSF ] − kdiss [1 (TT)B ]; = 2kdiss [1 (TT)B ] − kT [T1 ].

(7)

The model was fit using an iterative least-squares method, in which the equations were solved using a fourth-order Runge–Kutta scheme, and the solution was used to reconstruct the TA data. The intrinsic rate constant of decay of S1 to the ground state, kS1 , was constrained to be 8.33 × 10−5 ps−1 , which was obtained from the time-resolved fluorescence results. The decay of T1 takes much longer than the 3 ns time window of the experiment, so the rate of decay of T1 can not be deduced with accuracy. Therefore, to simplify the fitting process, kT1 was constrained to 6.67 × 10−5 ps−1 after initial observations that this value fit the data well. The time-resolved fluorescence of the 1:0 sample fits to a single exponential decay, with a time constant of 3.9 ps or rate constant of 0.256 ps−1 , indicating that SF in this sample was not diffusion limited (i.e., all neighboring pairs of TIPS-Pn molecules acted as SF sites). If the SD population is zero, then all of the S1 decay can be attributed to SF, so we can constrain the total rate constant for the first step of SF, kSFA + kSFB to be 0.256 ps−1 . We then assumed the difference in rates of formation of 1 (TT) and T1 between the different samples to be due to diffusion, and that the total rate constant of the first step of SF does not change. As such kSFA + kSFB was constrained to be 0.256 ps−1 for every sample. Despite the single exponential decay, it is possible there is actually some small amount of diffusion in the 1:0 sample, however attempting to include this would result in too many degrees of freedom to fit the rest of the model reliably. This total rate constant of SF is therefore likely an underestimate of the actual rate of SF. Initial fits to the data found that the trapping radius, R, and singlet-exciton diffusion constant, D, could not be fit independently. To obtain physically meaningful values for D, R was fixed to 1.4 nm, which was obtained by relating the proportion of TIPS-Pn molecules that were SF sites (2 × cSF /ctotal ), to the probability that the separation between two molecules would be less than R. This relation relies on the assumption that TIPS-Pn molecules are uniformly distributed within the NP, which is unlikely to be the case. As such, the R reported here represents an upper bound on the trapping radius, and therefore D is a lower bound on the diffusion constant. Full details of this and other constraints on the kinetic model are given in the SI (Section S11). Fitting the kinetic model with these constraints gives the results in SI Figure S23 and fitted parameters in Table 2 for all samples. The fit to the 1:7 sample is shown in Figure 7 as

17



an example. The quality of the fits is significantly better than the alternative kinetic models Concentration (x10-7 M)

8

a

S1

1:7

1

(TT) T1

6 4 2 0

0

500

1000

1500

2000

2500

3000

Time (ps)

b

1:7

Exp Fit

5 ps A

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

Page 18 of 29

100 ps 3000 ps 500

550

600

650

700

750

800

Wavelength (nm)

Figure 7: (a) Concentrations of S1 , 1 (TT), and T1 obtained by fitting the model in Figure 6 to the 1:7 TA data. The dashed lines are the kinetic fit and the solid lines are the spectrally extracted concentrations (spectral fits). The fit parameters are given in Table 2. (b) The kinetically fitted TA data compared with the experimental curves for the 1:7 sample. Fits to all other samples are given in the SI Section S11 along with a comparison to fits without the Slong and 1 (TT)A populations. considered without three singlet and two intermediate populations (Figures S26 and S28 in the SI). In general the residuals are lower, and importantly the singlet-exciton population is well described. The discrepancies in the samples with larger proportions of PMMA are due to the increased amounts of inhomogeneity in these systems. This inhomogeneity leads to a broader distribution of different rate processes, which is difficult to fully capture using a simple kinetic model. The parameters for these systems would be better described using a distribution of values rather than a single constant, but this is complicated to fit, and beyond the scope of the work here. For the 1:0 and 1:0.5 samples, the initial concentration of SD is very close to 0, so little to no singlet-exciton diffusion occurs for these samples. The value of the singlet exciton diffusion constant, D, therefore has no physical relevance in these cases; that is, it could take any value and not impact the residuals, so this quantity is omitted from the corresponding parts of Table 2. The average of D for the rest of the samples is (8 ± 3) × 10−5 cm2 s−1 , which is comparable to the 1.5 × 10−5 cm2 s−1 diffusion constant observed in disordered films of 18


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Table 2: Fitted parameters describing singlet population and singlet-fission kinetics for the model in Figure 6. TIPS-Pn:PMMA 1:0 1:0.5 1:1 1:3 1:5 1:7 1:10

D (cm2 s−1 ) -c -c 6.7 × 10−6 1.2 × 10−4 5.9 × 10−5 9.4 × 10−5 1.3 × 10−4

kSFA kSFB kdiss k1 (TT) SD (0) SSF (0) Slong (0) rC a rA b −1 −1 −1 −3 −1 −7 (ps ) (ps ) (ps ) (10 ps ) (%) (%) (%) (10 M) ( 10−3 ) 83.4 3.21 0.0 100.0 0.0 100 8.8 0.107 0.149 92.7 2.45 0.1 99.9 0.0 108 8.7 0.117 0.139 92.8 6.52 12.8 87.2 0.0 170 10.4 0.126 0.130 80.1 7.86 72.7 26.4 0.9 271 11.6 0.138 0.118 92.8 10.29 56.9 40.0 3.1 254 10.3 0.138 0.118 92.8 11.80 73.9 23.2 2.9 275 9.7 0.136 0.120 92.8 14.01 71.1 24.7 4.2 404 14.3 0.160 0.096

φSF

φSF0

1.16 1.08 0.99 0.87 0.83 0.78 0.60

1.94 1.95 1.77 1.46 1.22 0.96 0.84

rC is the sum of squared residuals between the fitted and spectrally extracted concentrations b rA is the sum of squares of residuals between the experimental and reconstructed TA. c Does not affect the quality of the fit and has no physical significance. a

diphenyl tetracence 19 and the 5 × 10−4 cm2 s−1 diffusion constant in crystalline pentacene films. 37 The rate constants of the first step of SF, kSFA and kSFB , vary slightly between the different samples. On average kSFA and kSFB are the same within error ((0.13 ± 0.01) ps−1 , compared with (0.12 ± 0.01) ps−1 , respectively), corresponding to around half of the SSF population forming 1 (TT)A , and half 1 (TT)B . The prevalence of the 1 (TT)A pathway accounts for the low quantum yields of SF observed, as on average half of the singlet excitons that begin to undergo SF (SSF ), decay as a triplet-pair intermediate instead of dissociating to give T1 . It is difficult to compare these rate constants with other rates of triplet-pair formation in the literature, as each are modeled or defined in subtly different ways. We only note that they are on the same order of magnitude to what is generally reported for these kinds of processes in TIPS-Pn NPs and films, being slightly on the slower side due to the disordered arrangement and variations in preparation procedure. 12,15,16,22,27,28,38 There is a weak trend in the SF rate constants as the concentration of TIPS-Pn in the NP is decreased. kSFA becomes larger with decreasing concentration, and kSFB becomes smaller, implying more SF to form triplet-pair intermediates that decay rather than dissociate. The proportion of decay through the 1 (TT)A pathway increases from 42 to 62% as concentration decreases. A lower concentration implies, on average, a larger intermolecular separation between TIPS-Pn molecules, suggesting that the formation of triplet-pairs that do not dissociate is facilitated by larger average intermolecular separations. Given we assume that the nature of SF sites does not change significantly with TIPS-Pn concentration, we hypothesize that this trend is due to the neighboring TIPS-Pn molecules of the SF sites being further away. A possible interpretation of this result is that 1 (TT) dissociation and T1 formation is promoted by hopping of separated triplets away from SF sites. Then, if 1 (TT)B represents triplet-pairs on SF sites that are close to neighboring TIPS-Pn molecules, hopping from these sites is likely and the triplet-pair can dissociate. As concentration is decreased, and intermolecular separation is increased, the number of SF sites that are more isolated from their neighbors and do not dissociate, 1 (TT)A , will also increase, explaining the increase in kSFA . A similar conclusion was made in a study on intramolecular SF in cova19



lently linked alkynyltetracene dimers, which also identified a 1 (TT) intermediate, and found that 1 (TT) decayed through a radiationless pathway in isolated dimers, implying energy transfer to a nearbly molecule is necessary for free triplet production. 11 Another explanation for having two populations of triplet-pair intermediates is that there may be particular relative geometries of TIPS-Pn molecules that facilitate separation, and others that do not. Pensack et al. identified two types of SF sites in NPs of amorphous pentacene derivatives: sites that act like individual chromophores, and H-aggregate-like sites. They suggested the triplet-pairs on H-aggregate-type sites fail to separate to individual triplets. 13 In light of this report, 1 (TT)A may also represent intermediates on H-aggregate-like sites, and 1 (TT)B the “monomer-like” sites. While this is a plausible explanation, we note that Pensack et al. modeled the pentacene derivatives with two parallel pathways of SF, and that the two types of sites had spectrally distinct singlets, triplets, and triplet-pair intermediates. The kinetics of the systems of the pure pentacene derivatives in that work were not limited by exciton diffusion, and therefore the evolution of the species is likely spatially localized to specific sites with distinct spectral signatures. In contrast, in the diluted systems studied here, exciton diffusion plays a significant role, and so the site at which a singlet is initially formed can be spatially quite different from that at which the triplets are eventually produced. Other than this, our model is consistent with that of Pensack et al. The rate constant of dissociation of 1 (TT)B , kdiss , is practically the same for all samples (Table 2). It is much faster than the first step of SF, with a time constant of only ∼0.01 ps, which is interestingly similar to values measured for crystalline pentacene derivatives. 12,38 The first step of forming the triplet-pair intermediate thus appears to be the rate-limiting step in the formation of separated triplets. Fitted values of kdiss are consistently significantly faster than kSFB , so can not be expected to be fit with much sensitivity. The rate constant for the decay of 1 (TT)A , k1 (TT) , on the other hand, varies significantly between the samples. With the exception of the 1:0 and 1:0.5 samples, this rate constant appears to increase with decreasing TIPS-Pn concentration. The reason for 1 (TT)A to decay at different rates for different samples is unclear, but we note that in all cases k1 (TT) is much smaller than kdiss , accounting for the the long-lived component of the triplet-pair intermediate. The fitted initial concentrations of each S1 population are also given in Table 2, as a percentage of the total number of singlet excitons. The proportion of excitons initially excited onto Slong sites increases with decreasing TIPS-Pn concentration, indicating that the total number of these types of sites in a NP must also increase. We propose that these long-lived singlet excitons are caused by the sites they occupy having a combination of a large intermolecular separation and unfavorable geometry for exciton hopping. As the concentration is decreased, the number of particularly isolated molecules would increase, and so there is more of this long-lived population. The number of SF sites, on the other hand, decreases with TIPS-Pn concentration. The explanation for this trend is similar to long-lived excitons: SF sites consist of TIPS-Pn molecules that are relatively close together and have a favorable orientation, but as the TIPS-Pn concentration decreases, less molecules have the necessary separation and so the total number of SF sites decreases. Finally, we can use the fitted concentrations of S1 and T1 to determine a quantum yield of SF, φSF , for each sample. These yields are given in Table 2 and plotted against the proportion of PMMA to TIPS-Pn in Figure 8b. The quantum yields are generally consistent with those determined from the spectral fits (Figure 8a), but are slightly greater due to the 20


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higher maximum T1 and 1 (TT) concentrations fitted in the kinetic model. The decrease in yields with proportion of PMMA can be explained by the proportions of Slong sites and SF sites. As the proportion of PMMA increases, the TIPS-Pn molecules become more dilute and the number of isolated sites increase, meaning more long-lived singlet excitons that cannot undergo SF. At the same time, the number of SF sites decreases, so singlet excitons must diffuse further before they can reach a SF site and undergo SF. This diffusion allows more time for competing processes, such as diffusion into isolated sites and decay of S1 , resulting in less triplets formed and a lower φSF . As observed with the spectral fits, even the highest yield, found in the 1:0 sample, is approximately 1 instead of 2. This is despite the 1:0 NP sample comprising entirely SF sites, with no long-lived population. This low yield can now be explained by the decay of the triplet-pair intermediate, 1 (TT)A . 42% of singlets undergoing SF form 1 (TT)A , meaning only 58% actually form triplets, giving a yield of 2 × 0.58 = 1.16, which is exactly what is observed. We note that this is similar to the yields reported for neat amorphous TIPS-Pn NPs by Pensack et al., where a significant proportion of 1 (TT) decay leads to a low triplet yield of 1.28. 13 All of the samples have between 42 and 62% of SSF decaying through 1 (TT)A instead of dissociating to triplets, so the yields for all the samples are significantly less than 2. To further illustrate this point, we calculated the modified SF quantum yield, φSF0 (Figure 8b). As this yield includes T1 and 1 (TT), φSF0 accounts for all of the S1 population for the 1:0 sample, so the observed value is close to 2 (slightly below because of the decay of 1 (TT) and T1 ). This result indicates that all singlets of the 1:0 sample begin to undergo SF, but only a portion actually complete the process to dissociate to T1 . The trend of φSF0 with TIPS-Pn concentration thus indicates the proportion of losses that are solely due to the nonradiative decay of diffusing and long-lived excitons. With respect to previous studies of TIPS-Pn that have reported SF quantum yields much closer to 2, it may be the case that the failure of 1 (TT) to dissociate to T1 is unique to amorphous TIPS-Pn, 13 but many previous studies have not made an attempt to identify and model 1 (TT) as was done here. 15,27,30,31,44 Potentially this means that any 1 (TT) features present in the TA spectra were attributed to T1 , resulting in an overestimate of the amount of triplet produced. Essentially, it is possible that previous yields reported were φSF0 , rather than φSF . Another study by Pensack et al. 12 comparing crystalline and amorphous TIPS-Pn NPs similarly found that the dissociation of 1 (TT) was frustrated in the amorphous systems, but did not observe this behavior in the crystalline NPs. In light of this result, the SF quantum yields of TIPS-Pn in crystalline films are potentially higher than those of the NPs presented here, but it would nevertheless be interesting to re-examine the results of previous studies by taking 1 (TT) into consideration, particularly for TIPS-Pn in solution. The results here also serve as an example that a high rate of SF does not necessary equate to a high efficiency. Here, the rate of triplet formation was rapid, but the SF yield was low. Given the growing number of studies that only report a rate of SF rather than a yield, this is an important consideration. It should be noted that we have assumed 1 (TT)A and 1 (TT)B are different populations of the same species; that is, that their spectral identity is the same. However, the fits show 1 (TT)B dissociates to form T1 extremely rapidly, on the order of 0.01 ps. Hence, this population contributes negligibly to the TA spectra. The 1 (TT) component observed in the TA is only due to the 1 (TT)A population, meaning that these two populations do not necessarily have to have the same spectrum or, in other words, be the same species. 1 (TT)A 21



2

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spectral fit spectral fit

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Mass ratio (PMMA/TIPS-Pn) 2

b

kinetic fit

SF SF'

kinetic fit

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1

0.5

0

2

4

6

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Mass ratio (PMMA/TIPS-Pn)

Figure 8: Yields determined from (a) spectral fits and (b) kinetic fits. φSF is defined as the max[T1 ]/max[S1 ] and φSF0 is a modified yield that takes the triplet-pair intermediate into account, defined as max([T1 ]+2×[1 (TT)])/max[S1 ]. could alternatively be described as some sort of trap state that is distinct from 1 (TT). For example, previous studies of SF have identified excimer trap states. 53,54 We can rule out the possibility of excimers in our case, since no emission was observed due to the decay of 1 (TT)A , but there may be some form of non-emissive trap. Given other studies have now recognized a large portion of the 1 (TT) state decays rather than dissociates, we surmise that calling 1 (TT)A a triplet-pair intermediate is reasonable. 11–13 Further investigation is needed to clarify the nature of the 1 (TT) intermediate and how it is formed. It may be possible to elucidate the role of charge-transfer states by studying this system with a host polymer of different polarities. A polymer with a higher dielectric constant than PMMA, for example, may have the effect of stabilizing any charge-transfer intermediates as has been documented for substituted pentacene dimers, 9 resulting in significantly different kinetics than what was observed here. Lastly, we note that we have neglected triplet-triplet annihilation (TTA) in our model. The decay of the triplets occurs on a significantly longer time scale than the time window of the experiments studied here, so we cannot make any conclusions about the validity of 22


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this assumption with confidence, but no such evidence is seen in the decay of T1 . Triplet fusion (T1 + T1 → S1 + S0 ) is endothermic in TIPS-Pn, 29,55 so is not expected to occur. Additionally, no delayed fluorescence is observed in the TCSPC experiments, which were performed over tens of nanoseconds. Bimolecular TTA to give a higher energy triplet excited state (T1 + T1 → Tn + S0 ) is unlikely, as we do not observe any power dependence of the triplet peak in the transient absorption and the decay of the triplet excitons appears to be first order. Additionally, if bimolecular TTA were to play a major role, we would expect higher TIPS-Pn concentrations to facilitate more efficient TTA, and therefore a lower SF quantum yield. Given the highest concentration shows the highest SF yield in this study, we expect bimolecular TTA to be insignificant. Geminate triplet-triplet annihilation on the other hand, cannot be ruled out, and may act to shorten the observed triplet lifetime. It would be interesting to study these NPs over a larger time window to determine if TIPS-Pn concentration or intermolecular separation has an effect on the triplet decay (or to study a system where triplet fusion is significant, such as tetracene). However, ultimately any loss in efficiency due to the slow decay of T1 will be negligible compared to the loss from the failure of 1 (TT) to dissociate into individual triplets.

Conclusions Aqueous dispersions of TIPS-Pn/PMMA NPs were prepared with various TIPS-Pn:PMMA mass ratios, in which the arrangement of TIPS-Pn in the NPs was shown to be amorphous, with no formation of crystalline domains. All NP dispersions were shown to undergo SF, with the rate of triplet formation comparable with the fast rates of SF reported for TIPSPn. Fitting and deconvolution of the TA spectra showed that the quantum yields of SF were lower than previously reported, and that an increase in the number of isolated sites and level of diffusion required to undergo SF led to a decrease in quantum yield with the concentration of TIPS-Pn. A major loss of efficiency present for all concentrations of TIPS-Pn was that approximately half of all correlated triplet-pair intermediates, 1 (TT), decayed to the ground state rather than dissociating into separated triplets. Thus, even in the pure TIPS-Pn (1:0) sample, in which there were no isolated sites and SF was not diffusion limited, the quantum yield of SF was 1 instead of the theoretical maximum of 2. The proportion of 1 (TT) that decayed without separating decreased slightly with increasing TIPS-Pn concentration, suggesting the formation of triplets may be facilitated by the ability to hop away from the SF site, as has previously been suggested in studies of tetracene dimers. 11 The loss of efficiency due to the decay of 1 (TT) is likely not unique to this system. As mentioned, the phenomenon has also been observed in tetracene dimers, 11 and in an independent study on amorphous TIPS-Pn NPs. 12,13 Many other spectroscopic studies on SF have not considered 1 (TT) in their analysis, so it is possible that SF quantum yields that had previously been attributed to triplet formation may in fact be a combination of the triplet and triplet-pair, and SF may not be as efficient in these systems as initially thought. Additionally our results serve as an example that a fast rate of triplet formation is not synonymous with a high yield. The composite TIPS-Pn/polymer NPs presented here are a useful system in which to study SF. Ultimately, fine control over the concentration of TIPS-Pn in a NP and by extension the kinetics of SF was achieved, allowing insight into the efficiency of SF in TIPS-Pn. 23



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Unless a way to promote full 1 (TT) dissociation can be established, these amorphous NPs are not ideal for application in solar cells, although the ease of solution processing polymer NP suspensions would be beneficial. However, the system in this study can be modified in a number of ways, and there is potential to use the control demonstrated here to elucidate further aspects of the mechanism of SF and competing processes.

Acknowledgement This research was supported by research grants from the Australian Research Council (LE0989747, DP160103797) and an Australian Government Research Training Program (RTP) Scholarship. We also thank Emi Schutz for her contributions to this work.

Supporting Information Available Additional experimental details, the chemical and colloidal stability of the TIPS-Pn/PMMA nanoparticles, time-correlated-single photon counting data, transient absorption data, power and pump wavelength dependence studies, effect of the surfactant on the NPs, details of the spectral deconvolution of the transient absorption data and the global target analysis of the transient absorption data, and details on the kinetic fitting.

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Controlling the Efficiency of Singlet Fission in TIPS-Pentacene

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