Polymers are desirable optoelectronic materials, stemming from their solution processability, tunable electronic properties, and large absorption coefficients. An exciting development is the recent discovery that singlet fission (SF), the conversion of a singlet exciton to a pair of triplet states, can occur along the backbone of an individual conjugated polymer chain. Compared to other intramolecular SF compounds, the nature of the triplet pair state in SF polymers remains poorly understood, hampering the development of new materials with optimized excited state dynamics. Here, we investigate the effect of solvent polarity on the triplet pair dynamics in the SF polymer polybenzodithiophene-thiophene-1,1-dioxide. We use transient emission measurements to study isolated polymer chains in solution and use the change in the solvent polarity to investigate the role of charge transfer character in both the singlet exciton and the triplet pair multiexciton. We identify both singlet fluorescence and direct triplet pair emission, indicating significant symmetry breaking. Surprisingly, the singlet emission peak is relatively insensitive to solvent polarity despite its nominal “charge-transfer” nature. In contrast, the redshift of the triplet pair energy with increasing solvent polarity indicates significant charge transfer character. While the energy separation between singlet and triplet pair states increases with solvent polarity, the overall SF rate constant depends on both the energetic driving force and additional environmental factors. The triplet pair lifetime is directly determined by the solvent effect on its overall energy. The dominant recombination channel is a concerted, radiationless decay process that scales as predicted by a simple energy gap law.

Materials that undergo singlet fission (SF) have the potential to be exploited in solar light harvesting applications by recovering energy normally lost as heat.1–3 The SF process occurs in organic materials with strong electronic correlations, which allows a singlet exciton to relax to a multiexciton (triplet pair) state on ultrafast time scales.4,5 If the resulting triplet pair can be harvested before annihilation (in tandem, photon downconversion, or similar schemes), then the full benefit of this dynamical process can be realized.6–9 While singlet fission was initially identified in molecular crystals as a result of an intermolecular process (xSF),10–12 recent success in developing efficient intramolecular singlet fission (iSF), in which the triplet pair is produced along the backbone of a macromolecule in dilute solution, has illustrated the complexity of the multi-chromophore interactions that drive SF.13–16 The iSF approach has the benefit of being insensitive to intermolecular packing, allowing for facile tuning of chemical and electronic structures and facilitating structure–function studies.17–19 Recent successes in optimizing molecules for fast triplet pair generation and long lifetimes suggest that these systems may have practical uses as well.18–20 

While the most widely studied iSF compounds are built from chromophores that are known to undergo SF in their crystalline forms, e.g., tetracene, pentacene, and PDI derivatives among others, the first efficient iSF system observed was a low-bandgap conjugated polymer.21–24 Polymers are particularly attractive because of their demonstrated utility as the active layer in organic optoelectronic devices.25 For example, the donor–acceptor (D–A) type conjugated copolymer, polybenzodithiophene-thiophene-1,1-dioxide (PBTDO1), was found to have a very high iSF quantum efficiency (up to ∼170%) and is closely structurally related to some of the highest performing organic photovoltaic materials.26 Considering the abundant family of donor and acceptor groups, it would appear that there is a very large parameter space with which to design and optimize more efficient iSF polymer systems. However, only a few D–A copolymers with high iSF efficiency have been reported so far, primarily due to their uncertain mechanism for singlet fission.22,26,27

While the understanding of the mechanism for singlet fission in polymers is far behind what is known about small molecule xSF and iSF chromophores, uniquely distinct properties have been identified. Of prime interest is the nature of the coupled, triplet pair state 1(TT), the manner in which it couples to the photoexcited singlet to allow singlet fission, and its recombination dynamics.28–30 In SF chromophores such as TIPS-pentacene and rubrene, the two triplets in 1(TT) are relatively weakly coupled and reside on two spatially separated molecules.31 In contrast, in linear conjugated polymers, strongly coupled even parity multiexciton states (2Ag) exist, with energies close to the lowest optically allowed odd parity state (1Bu).32–34 The correlated 2Ag is often described as having multiexciton character and confusion exists about similarities and differences between the 2Ag and 1(TT). For example, it was recently proposed that the dark 2Ag state is distinct and functions as an important intermediate state for the generation of the triplet pair.35–37 Practically speaking, the 2Ag label is frequently used when the multiexciton state is optically dark, has a transient spectrum distinct from the individual triplet, and exhibits rapid non-radiative relaxation to the ground state.38 Conversely, 1(TT) label is commonly used when the multiexciton becomes weakly optically allowed and has spectral characteristics closely related to an individual triplet exciton. Still, many open questions exist as to the relationship between 2Ag and 1(TT) and the chemical factors that dictate the coupling strength and transition energy. For example, some references suggest that the mAg is an important SF intermediate,39 and others suggest that it is parasitic to the overall process.26,38

The elusiveness of the multiexciton state in polymers is partially a result of the negligible matrix elements coupling the singlet and triplet pair that makes SF difficult to observe, except under certain special conditions. In fact, coupling between 1(TT) and the singlet only becomes significant when they become nearly resonant due to strong electron correlations.36 As carbon atoms in the polymer backbone become more inequivalent (due to functionalization with electron withdrawing or donating groups), singlet fission is facilitated by singlet–triplet pair mixing and the optically forbidden 1(TT) state becomes weakly emissive, borrowing oscillator strength from the singlet state.26,27 We note that the resonance conditions are in direct contrast to small molecule SF, where energetically downhill SF (ΔES-TT = ES1 ETT, large and positive) is strongly allowed and fast, e.g., as in pentacene and hexacene.14,15,40 A similar symmetry breaking effect has been previously discussed in the context of molecular crystals (Herzberg–Teller mechanism) where coupling to odd-symmetry vibration permits weak radiative transition from the triplet pair state.31,41,42 Recent studies have shown that additional environmental considerations are important as well in determining the SF properties of molecules.27,43–45 Alvertis et al. identified the importance of solvent-induced symmetry breaking in which changes to the molecular conformation result in switching between a coherent and incoherent mechanism, depending on the solvent polarity.43 These authors showed that because the charge-transfer state is an essential intermediate for promoting singlet fission, the solvent effects become an essential key factor in determining the rate constant and SF yield.

Here, we investigate the role of solvent effects in determining the formation and decay rate of the triplet pair in a high efficiency singlet fission polymer PBTDO1. We find that similar to theoretical predictions, the triplet pair state is directly emissive, indicating significant symmetry breaking and mixing with the singlet state. Importantly, we observe that the triplet pair emission energy varies considerably with changing solvent polarity, while the singlet exciton emission energy is largely insensitive. This suggests a larger amount of charge transfer character in the triplet pair than the singlet, despite the nominal donor–acceptor character of the singlet states. As a result, the energy separation between the singlet and triplet pair increases systematically with the solvent polarizability. However, the singlet fission rate is less correlated with the solvent properties, suggesting a complex process involving several chemical and electronic factors. The scaling of the triplet pair lifetime is more straightforward, showing a strong correlation with the solvent polarizability consistent with a direct decay process. Overall, this study suggests that while CT intermediate states may play a role in singlet fission, other important contributing factors need to be considered.

The synthesis and characterization of PBTDO1 were reported previously.26 For spectroscopic measurements, PBTDO1 were dissolved in different aprotic solvents.

Computations

The ground state geometry of PBTDO1 is optimized using density functional theory (DFT), and the relaxed lowest triplet state is further optimized using an unrestricted DFT calculation. The transition of excited states is calculated with time-dependent DFT (TDDFT) at the optimized ground state geometry. Then, natural transition orbital (NTO) approach is used to characterize the transition of the lowest singlet and triple states.46 All calculations in the gas phase were performed using the Gaussian 16 package at the B3LYP/6-31G(d) level.47 

Transient emission spectroscopy

Time-resolved photoluminescence (TRPL) was measured by ultrafast spectroscopy using optical Kerr gating.48 A 1 kHz Ti:sapphire based regenerative amplifier (Spitfire, Spectra-Physics) is employed to create pulses around 800 nm with 100 fs duration. The output from the amplifier is used to pump, and an optical parametric amplifier (TOPAS-C) is used from which an excitation and gating pulse is produced. For all transient emission measurements reported here, the parametric generation process was tuned to generate a signal at 1400 nm and an idler at 1866 nm. The 1400 nm signal pulse was used as a gate pulse for the Kerr medium. The idler (1866 nm) was mixed with a portion of the residual 800 nm fundamental to create a sum frequency generated signal at 560 nm that was used to excite the sample (pulse fluences ∼100 μJ/cm2). A set of interference filters was used on the gate (1064 nm longpass) and excitation (560 nm bandpass) beams to remove residual harmonics. The fluorescence emitted by the sample is collected by a pair of off-axis parabolic mirrors and focused onto a 1 mm path length cuvette of benzene that functions as the optical Kerr medium. For our measurements, benzene provided the best compromise between gating efficiency and time resolution (∼500 fs). For detection, a liquid nitrogen cooled CCD camera is utilized to resolve and simultaneously collect data over the 600 nm–900 nm wavelength range.

Transient absorption spectroscopy

Transient absorption spectroscopy was conducted using a Ti:sapphire laser system. Excitation light at 530 nm (pulse fluences ∼100 μJ/cm2) was generated by a commercial optical parametric amplifier (TOPAS-C, LightConversion). The white probe light was generated by focusing the 800 nm fundamental into a sapphire disk. The pump–probe delay was controlled by means of a mechanical delay stage. The data are from dilute solutions using different solvents.

Kinetic analysis

The transient data were globally analyzed using the publicly available program Glotaran based on the statistical fitting package TIMP.49,50 The analysis was performed using a sum of exponential decays convoluted with the instrument response function (IRF). In transient emission measurements, where only emissive species are detected, we employ global analysis with a sequential model to analyze the transient emission data. In transient absorption measurements, a branched model is used to account for some parasitic generation of a dark charge separated state.

The singlet fission dynamics of PBTDO1 [Fig. 1(a)], an iSF polymer with strong charge transfer character and a low triplet energy, was recently examined in detail in both solution26 and thin films.51 The criteria for identifying the triplet pair state are discussed in detail in these references. Briefly, it involves the identification of the triplet pair spectra to the one-triplet spectra using triplet sensitization measurements and quantification of the multiplication yield from the determination of the triplet–triplet absorption coefficient. This polymer is representative of a well-established strategy for obtaining low bandgap polymers using push–pull or donor–acceptor type interactions. In these compounds, the lowest-energy optical excitation arises due to delocalization across the push–pull interface with significant charge-transfer character. This effect can be clearly observed in PBTDO1 compared with the unoxidized thiophene analogs. Oxidation of the thiophene unit increases the acceptor (pull) strength and leads to large redshifts and broadened absorption.26,38 Small but measurable shifts in the absorption spectra are observed for polymers dissolved in different solvents [Fig. 1(b)]. While there is no consistent trend with solvent polarity [the lowest shift occurs in 1,2-dichlorobenzene (DCB), which has an intermediate polarity], we generally observe that the solvents with highest polarity [e.g., dichloromethane (DCM)] exhibit a blue-shifted absorption edge. These small shifts are consistent with what is observed in the solid-state, where relatively small changes in the absorption energy (redshift by ∼ 100 meV) and line shape features are observed.51 Interestingly, the blueshift indicates that the excited state is less polar than the ground state, despite its charge transfer character. This insensitivity of the absorption to the solvent polarizability is in contrast to a simple description of the charge transfer character of the exciton. However, other push–pull type macromolecules exhibit a similar insensitivity of the absorption to the solvent, even in small oligomers where the effect of delocalization is minimized.52 

FIG. 1.

(a) Molecular structure of low-bandgap polymer PBTDO1. The low-energy optical absorption is derived from hybridization of the benzodithiophene “push” (electron-donating) and thiophene dioxide “pull” (electron-withdrawing) unit. (b) Normalized UV–vis absorption spectra of PBTDO1 in xylenes (XYL), chlorobenzene (CLB), 1,2-dichlorobenzene (DCB), and dichloromethane (DCM). The solvents have orientational polarizabilities ranging from 0 to 0.22. (c) Natural transition orbital analysis of the electron and hole for singlet and triplet states.

FIG. 1.

(a) Molecular structure of low-bandgap polymer PBTDO1. The low-energy optical absorption is derived from hybridization of the benzodithiophene “push” (electron-donating) and thiophene dioxide “pull” (electron-withdrawing) unit. (b) Normalized UV–vis absorption spectra of PBTDO1 in xylenes (XYL), chlorobenzene (CLB), 1,2-dichlorobenzene (DCB), and dichloromethane (DCM). The solvents have orientational polarizabilities ranging from 0 to 0.22. (c) Natural transition orbital analysis of the electron and hole for singlet and triplet states.

Close modal

Calculations of a PBTDO1 segment (a tetramer, Fig. 1) indicate that the singlet exciton is delocalized over several monomer units along the conjugated backbone. Density functional theory (DFT) calculations up to four repeat units show that the lowest singlet transition energy is 1.72 eV based on the optimized ground state geometry. Unrestricted DFT results show that the energy of the optimized lowest triplet state is 0.95 eV above the ground state. These calculations suggest that the energy of S1 is less than double the energy of T1 by approximately 0.18 eV. However, the triplet pair binding energy (Eb = 2 × ET1 − ETT) is also important in determining the overall SF energetics, which previous calculations have estimated to be on the order of the calculated singlet–triplet gap.35,36 We use the time-dependent DFT method to determine the natural transition orbitals (NTOs) of the electron and hole in the S1 and T1 excitons and find the high degree of spatial overlap between electron and hole orbitals in both the singlet and triplet manifolds [Fig. 1(c)].46 The resulting orbitals are consistent with the idea that a large spatial overlap enhances the exchange interactions and leads to a large singlet–triplet energy gap.26,53 In agreement with the previous studies, we find that both the electron and hole in the singlet exciton reside over several segments. This delocalization may explain the absorption blueshift that is seen in polar solvents, reducing the amount of localized charge transfer character. In addition, this delocalization provides the multi-chromophore character needed to induce coupling of the S1 and 1(TT) states. The individual triplet exciton is more strongly localized than the singlet, extending over the central ADADA block with a majority of the amplitude on the central acceptor (TDO). While the triplet pair state cannot be readily determined using this approach, a study on this polymer using density matrix renormalization group theory suggested that the triplet pair is highly delocalized, similar to the high energy 2Ag state observed in other conjugated polymer systems such as polyphenylenes.35,54

To explore the relaxation dynamics of the singlet exciton and triplet pair, we use transient emission measurements based on an optically gated technique that has been described previously.48 This technique is capable of resolving broadband emission transients (no phase matching restriction) and provides the time resolution (∼500 fs) sufficient to resolve the fundamental decay processes and spectral dynamics in these polymers and determine their relative contribution to the steady-state (time-integrated) emission spectrum. Although transient absorption approaches have been previously used to understand the singlet fission dynamics in this material, it is difficult to identify states that are weakly emissive due to overlapping stimulated emission and photoinduced absorption bands.26 

A dilute solution of PBTDO1 in DCB (∼100 µg/ml) shows emission on multiple time scales, extending out to ∼100 ps, with a systematic redshift concomitant with the increasing time delay [Figs. 2(a) and 2(b)]. Using previous transient absorption studies as a guide, we analyze the transient emission data by a sequential global model in which a singlet exciton is directly converted to a triplet pair, followed by recombination back to the ground state.26 Using this approach, we perform spectral decomposition on the raw emission data and obtain two primary species [Fig. 2(c)]. We assign the first species to prompt fluorescence from the singlet exciton due to its coincidence with the time scale for decay of the singlet–singlet photoinduced absorption near 775 nm (∼5 ps) obtained in transient absorption experiments (Fig. S6) and its relatively small Stokes shift (∼680 nm emission maximum). The second species is assigned to direct emission from the 1(TT) triplet pair state due to the coincidence of the decay time for the triplet–triplet photoinduced absorption feature near 675 nm (∼50 ps) observed in transient absorption (Fig. S6) and its relatively large Stokes shift (max located at ∼ 725 nm). The TA and PL dynamics were compared over the range of solvents reported here. The corresponding population evolutions are shown in Fig. 2(d), with a concomitant decay of the singlet emission and growth of the triplet pair emission. Due to the long lifetime of the triplet pair compared with the singlet, the steady-state emission spectrum is dominated by the triplet pair emission [Fig. 2(b)].

FIG. 2.

Transient emission data of PBTDO1 in diluted DCB solution. (a) Transient emission shown in a pseudo-color plot. (b) The emission spectra of different time delays, compared with the steady emission (gray solid curve). (c) Spectral decomposition of the raw data shows two species, assigned to the emission from the singlet and triplet pair states. (d) The population decay of S1 and TT is determined using global analysis and a sequential decay model.

FIG. 2.

Transient emission data of PBTDO1 in diluted DCB solution. (a) Transient emission shown in a pseudo-color plot. (b) The emission spectra of different time delays, compared with the steady emission (gray solid curve). (c) Spectral decomposition of the raw data shows two species, assigned to the emission from the singlet and triplet pair states. (d) The population decay of S1 and TT is determined using global analysis and a sequential decay model.

Close modal

The large spectral differences between the singlet and triplet pair emissions (>100 meV) allow us to rule out a delayed fluorescence resulting from triplet–triplet annihilation back to the singlet state. Although photoluminescence from the triplet pair state is forbidden in an independent electron picture, our observation of weak direct triplet pair emission is consistent with calculations that account for the enhanced electron correlations in this material and similar to what has been observed in other SF systems.27,30,31,42 Following these works, we propose that the variation in the site energies along the backbone of the polymer and vibronic coupling effectively breaks the symmetry of the triplet pair state, enabling coupling and intensity borrowing from the allowed singlet excited state, imparting nonzero oscillator strength.43 This mechanism is analogous to the Herzberg–Teller mechanism that has been invoked in molecular crystals. The weak emission of the one-photon-forbidden 2Ag state in carotenoids is also explained by a similar mechanism. These similarities are unsurprising since the 2Ag state, like the triplet pair, contains the totally symmetric irreducible representation (parity-forbidden) and has significant multiexciton character (dipole-forbidden).30 

Given the “push–pull” electronic structure of the polymers, it is expected that environmental factors have a particularly large influence on the singlet fission dynamics. For one, the inherent CT character of the singlet state has been proposed to be essential for mediating singlet fission.4,26,55 In addition, it has been shown theoretically that even high lying CT states can have non-trivial effects on the SF rate constant.56 As the energy of the CT is a strong function of the solvent orientation polarizability, we would expect a quantifiable change in the dynamics as a function of polarity of the solvent. Finally, we expect that solvent interactions can non-trivially affect the symmetry breaking process that couples the singlet and triplet pair. Based on our DFT calculations, the singlet state extends over the push–pull backbone of PBTDO1. In quadrupolar molecules based on push–pull–push and pull–push–pull architectures, which are representative of the photoactive fragment of our polymer, excited-state symmetry breaking from solvent effects was observed by transient IR and fluorescence upconversion spectroscopy.57–59 Similarly, solvent-induced symmetry breaking has been shown to modulate the electronic structure of a SF dimer, affecting the relative contribution of coherent vs incoherent singlet fission.31 Taken together, it is clear that understanding the nature of the CT state and its relevance in both the singlet and triplet pair states is of great importance.

To probe the effect of solvent on the exciton energies and singlet fission dynamics, we measured the transient emission characteristics of PBTDO1 in 11 different solvents, including three binary mixtures, with orientation polarizabilities ranging from 0.006 (xylenes) to 0.25 (cyclohexanone). A list of solvents used, their properties, and the resulting emission dynamics is summarized in Table I. The raw transient emission data (including detailed spectra and kinetics) are available in the supplementary material. The qualitative dynamics are similar for all solvents, though the details of their rate constants and emission energies vary. A set of representative emission spectra for the singlet state in four solvents, from nonpolar XYL to polar DCM, is obtained using spectral deconvolution analysis and shown in Fig. 3(a). Interestingly, we note that the maximum of the singlet emission is nearly solvent-independent [Fig. 3(b)], despite the measurable blueshifts observed in the linear absorption spectra. This implies that the blueshift of the singlet in the ground state geometry (vertical energy) is exactly canceled by an increase in the energy stabilization from geometric relaxation (adiabatic energy). The net result is that the emission energy of PBTDO1 is ∼1.82 eV, with a variation of <10 meV for all solvents.

TABLE I.

Fitting parameters for transient emission in different solvents.

SolventsaΔfbES1c (eV)ETTd (eV)ΔES-TTe (eV)kSFf (×1011 s−1)kTTg (×1010 s−1)
XYL 0.006 1.83 1.76 0.07 1.93 1.06 
TOL 0.015 1.83 1.76 0.08 2.24 1.47 
1:3 (DCM:XYL) 0.111 1.82 1.73 0.09 2.04 1.36 
CLB 0.143 1.82 1.72 0.10 2.50 1.82 
CLF 0.148 1.81 1.71 0.10 2.77 1.80 
1:1 (DCM:XYL) 0.162 1.81 1.70 0.11 3.79 1.83 
DCB 0.186 1.81 1.71 0.10 2.27 2.19 
3:1 (DCM:XYL) 0.194 1.81 1.69 0.12 3.80 2.21 
THF 0.210 1.83 1.72 0.12 3.06 1.50 
DCM 0.218 1.81 1.69 0.13 5.62 2.72 
DCE 0.228 1.80 1.67 0.13 3.02 2.74 
CHO 0.249 1.82 1.71 0.11 3.10 2.35 
SolventsaΔfbES1c (eV)ETTd (eV)ΔES-TTe (eV)kSFf (×1011 s−1)kTTg (×1010 s−1)
XYL 0.006 1.83 1.76 0.07 1.93 1.06 
TOL 0.015 1.83 1.76 0.08 2.24 1.47 
1:3 (DCM:XYL) 0.111 1.82 1.73 0.09 2.04 1.36 
CLB 0.143 1.82 1.72 0.10 2.50 1.82 
CLF 0.148 1.81 1.71 0.10 2.77 1.80 
1:1 (DCM:XYL) 0.162 1.81 1.70 0.11 3.79 1.83 
DCB 0.186 1.81 1.71 0.10 2.27 2.19 
3:1 (DCM:XYL) 0.194 1.81 1.69 0.12 3.80 2.21 
THF 0.210 1.83 1.72 0.12 3.06 1.50 
DCM 0.218 1.81 1.69 0.13 5.62 2.72 
DCE 0.228 1.80 1.67 0.13 3.02 2.74 
CHO 0.249 1.82 1.71 0.11 3.10 2.35 
a

Solvents: XYL (p-xylene), TOL (toluene), CLB (chlorobenzene), CLF (chloroform), DCB (o-dichlorobenzene), THF (tetrahydrofuran), DCM (dichloromethane), DCE (dichloroethane), and CHO (cyclohexanone).

b

Orientation polarizability.

c

Emission maximum of the singlet state.

d

Emission maximum of the triplet pair state.

e

ΔES-TT = ES1 ETT.

f

Singlet fission rate constant.

g

Triplet pair decay rate constant.

FIG. 3.

(a) (Top) Singlet emission and (bottom) direct triplet pair emission spectra in XYL (black), CLB (red), DCB (dark blue), and DCM (light blue). (b) The energy of singlet and triplet pair state is determined from the peak maxima and plotted as a function of solvent polarizability. Solid lines are provided as guides to the eye.

FIG. 3.

(a) (Top) Singlet emission and (bottom) direct triplet pair emission spectra in XYL (black), CLB (red), DCB (dark blue), and DCM (light blue). (b) The energy of singlet and triplet pair state is determined from the peak maxima and plotted as a function of solvent polarizability. Solid lines are provided as guides to the eye.

Close modal

In contrast, the triplet pair emission maximum is highly dependent on the solvent polarity. The broad emission of the triplet pair spectrum implies a lot of intrachain disorder and makes it difficult to assign vibronic bands. Instead, we use the peak of triplet pair emission as a proxy for the energy level. Again, we show the emission spectra obtained from the spectral deconvolution analysis for the triplet pair in a series of representative solvents spanning the full range of polarity [Fig. 3(a)]. The energy of triplet pair decreases with the increasing polarity of solvents, shifting from ∼1.76 eV in nonpolar solvents to ∼1.66 eV in polar solvents. To analyze the effect of solvent on the emission spectra of molecular chromophores, the Lippert equation is commonly employed,60,61 which separates the contributions from electronic polarizability (instantaneous) and solvent reorientation (∼1 ps time scale): EabsEemc*Δf*μ*μ2, where c represents a set of constants and μ (μ*) represents the dipole moment in the ground (excited) state. The orientation polarizability, Δf, is defined using static dielectric constants (ε(0)) and optical refractive indices (n) of the solvents by the following expression:

Δf=ε(0)12ε(0)+1n212n2+1.
(1)

As the dipole moment of the ground state is expected to be small due to the centrosymmetry of the polymer along the backbone, the change in the emission energy with solvent orientation polarizability should be directly proportional to the excited state dipole moment. Surprisingly, this implies that the dipole moment of the triplet pair state is larger than that of the relaxed singlet state. This result is not expected if one considers the localized individual triplet, which has a wavefunction that is highly localized on the pull TDO unit. However, it suggests that the nature of the triplet pair in polymers is not well understood and that the triplet pair may contain significant charge transfer character. The CT character of the triplet pair state has been explicitly discussed in pentacene dimers, though not in polymers.62 

The singlet and triplet emission spectra can be used to directly determine the singlet fission driving force (ΔES-TT), defined here as the difference between the relaxed (adiabatic) singlet energy and the triplet pair energy. As we have discussed, the relaxed singlet energy is nearly independent of the solvent orientation polarizability (Δf), and the triplet pair energy varies linearly with Δf. As a result, ΔES-TT linearly increases as a function of Δf and ranges from 70 meV to 130 meV [Fig. 4(a)]. In addition to the spectral dynamics, transient emission measurements allow us to quantify the rate of singlet fission and its variation in different solvents. The singlet lifetime can be roughly visualized from the raw data by taking a kinetic slice on the blue edge of the emission [Fig. 4(b)]. For example, kinetic traces at 625 nm have minimal contribution from the triplet pair decay and show that the rate constants systematically increase in going from less polar solvents (XYL) to more polar solvents (DCM). To confirm the time constants and the assignments, transient absorption measurements were performed as a function of solvent and time constants were determined using target analysis with the branched kinetic model to account for some parasitic charge formation (see the supplementary material). The rates extracted using transient emission and transient absorption experiments are in strong agreement (Fig. S10). We find that a general trend holds for a wide range of solvents, with more polar solvents tending to promote fast singlet fission, the relationships between Δf [Fig. 4(c)] or ΔES-TT [Fig. 4(d)] and the decay constants are non-monotonic and contain quite a bit of scatter. The resulting SF time constants ranging from 1.8 ps (DCM) to 5.2 ps (XYL) are in agreement with the previous studies and TA measurements (see the supplementary material).26 An apparent outlier is DCM, which exhibits a notably faster singlet fission rate than other solvents of comparable polarity. Interestingly, the viscosity of DCM is less than other solvents of comparable polarity. Although the influence of the viscosity to the SF rate is not strongly correlated (Fig. S5), it appears likely that the SF rate is a multivariate function of several solvent properties.44 

FIG. 4.

(a) The singlet fission driving force ΔES-TT increases continuously as a function of solvent polarization, Δf. (b) The singlet decay dynamics can be isolated from the raw emission dynamics using kinetic cuts on the blue edge of the emission spectra (625 nm). The decay dynamics are strongly solvent dependent. The SF rate determined by global analysis is only weakly correlated with the solvent polarizability (c) and driving force (d).

FIG. 4.

(a) The singlet fission driving force ΔES-TT increases continuously as a function of solvent polarization, Δf. (b) The singlet decay dynamics can be isolated from the raw emission dynamics using kinetic cuts on the blue edge of the emission spectra (625 nm). The decay dynamics are strongly solvent dependent. The SF rate determined by global analysis is only weakly correlated with the solvent polarizability (c) and driving force (d).

Close modal

We note that the recombination rate of the triplet pair state scales directly with the overall energy of the triplet pair. The lifetime of the triplet pair can be measured by fitting the long-lived tail of the decay of the red-shifted and longer-lived direct triplet pair emission and shows a strong solvent effect [Fig. 5(a)]. The time constant ranges from ∼35 ps in polar solvents to ∼100 ps in non-polar solvents [Table I and Fig. 5(b)]. The dominant contribution to the triplet pair decay appears to be non-radiative losses in which both triplets are lost: 1(TT) → S0. We rule out other possible triplet–triplet annihilation processes since no other long-lived species are observed in transient absorption measurements (ruling out annihilation via T1 + T1 → S0 + T2), and no delayed recovery of the singlet emission is observed (ruling out annihilation via T1 + T1 → S1). In the limit where non-radiative decay dominates, the lifetime of the triplet pair should follow an energy gap law in which the rate constant increases as the triplet pair energy decreases: knr ∼ exp(−γΔE), where γ is a material specific constant.63 This effect has been previously observed for molecular triplets and for triplet pairs in which the recombination is dominated by a radiationless concerted decay process involving both triplets.15,40,64 Indeed, we find a nearly monotonic behavior for the PBTDO1 triplet pair decay rate that scales with the total triplet pair energy. Furthermore, the overall range of decay rates follows the expected scaling behavior for a total energy variation of ∼100 meV [dashed line in Fig. 5(b)]. From this analysis, we conclude that the primary effect of the solvent on the decay rate is its effect on the total triplet energy.

FIG. 5.

(a) The triplet pair decay kinetics of PBTDO1 can be isolated from the raw emission dynamics using kinetic cuts on the red edge of the emission spectra (750 nm). The emission rate is a function of solvent. (b) The decay of the triplet pair dominated by a radiationless process in which the rate constant scales as knr ∼ exp(−γΔE) (dashed line fit).

FIG. 5.

(a) The triplet pair decay kinetics of PBTDO1 can be isolated from the raw emission dynamics using kinetic cuts on the red edge of the emission spectra (750 nm). The emission rate is a function of solvent. (b) The decay of the triplet pair dominated by a radiationless process in which the rate constant scales as knr ∼ exp(−γΔE) (dashed line fit).

Close modal

In summary, the results presented here suggest the need for a refined description of charge transfer states in both the singlet exciton and the triplet pair multiexciton in iSF polymers. Tuning the solvent environment has a moderate to negligible effect on the singlet exciton energies, but a rather pronounced effect on the triplet pair energy, opposite to what is suggested by simple descriptions of these states. While the rate of singlet fission shows a complex dependence on both the exciton energetics and environmental factors, the triplet pair decay is more straightforward. The dominance of the non-radiative decay of the triplet pair further reinforces the idea that dephasing out of the net singlet spin coupled triplet pair—1(TT)—is necessary to achieve long lived multiexciton states in SF materials. Unlike in small molecule SF compounds and pendent polymer arrangements of molecular chromophores,17 this feat has not been accomplished in conjugated singlet fission polymers or star macromolecules.65 A better understanding of the intrinsic character of the triplet pair state can lead to molecular engineering concepts to control the dynamics of the multiexciton in polymeric systems.

See the supplementary material for the raw transient emission and transient absorption data discussed in this manuscript in addition to supporting data analysis.

G.H. and E.B. contributed equally to this work.

This work was supported by the National Science Foundation under Grant Nos. DMR-2004683 and DMR-2004678. This research used resources of the Center for Functional Nanomaterials, which is a U.S. DOE Office of Science Facility, at the Brookhaven National Laboratory under Contract No. DE-SC0012704.

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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