Magnetic field dependence of singlet fission in solutions of diphenyl tetracene

Abstract

Magnetic field effects provide a convenient and specific probe of singlet exciton fission within optoelectronic devices. Here, we demonstrate that this tool may also be applied to screen potential fission material candidates in solution. We characterize the phenomenon in diphenyl tetracene (DPT), which shows strong fluorescence modulation and the expected field dependence in its transient decay as a function of concentration. Solution measurements may also be used to test for the presence of an intermediate charge transfer state, but we observe no changes to the field dependence of DPT singlet exciton fission in toluene relative to chloroform.

Singlet exciton fission splits a spin zero exciton into two spin one triplet excitons and may find applications in solar energy harvesting [1–3]. But the synthetic design and testing of new singlet fission molecules have proven challenging, motivating the search for new methods to quickly screen possible fission candidates. Magnetic field modulation of fluorescence is an important existing technique for evaluating the presence of singlet fission. Molecules that perform efficient singlet fission in the solid state have low quantum efficiencies, however, as all the emissive singlet excitons are converted to triplet excitons. Here, we note that those same molecules can have high quantum efficiencies in dilute solution. With application to material screening, and prompted by recent observations of singlet exciton fission in solution [4], we report on magnetic field effects on singlet exciton fission in solution. We find that convenient magnetic field probes can be extended to the solution phase. We observed similar behaviour for soluble variants of the archetype acenes tetracene and pentacene, notably diphenyl pentacene (DPP), diphenyl tetracene (DPT), 6,13-di(2′-thienyl) tetracene (DTT) and rubrene. Of these, we most fully characterize the effect in DPT.

The magnetic field dependence of fluorescence in singlet fission chromophores originates from the nine possible pairs of spin one triplet excitons which are the combination of quintet, triplet and singlet states [5–7]. But the singlet exciton only couples to triplet pair states with some singlet character, which is redistributed under an external magnetic field. Indeed, a smaller number of triplet pair states typically exhibit stronger singlet character under a strong field [8,9]. The redistribution of singlet character within the triplet pair manifold can vary the overall fission rate if there is competition with another process, such as the separation of the triplet pair into independent triplet excitons [1]. Thus, in singlet exciton fission, an external magnetic field may be understood to shift the balance between the return of a triplet pair state back to the singlet exciton, and separation of the triplet pair. A strong external magnetic field increases the number of singlet excitons and reduces the yield of independent triplet excitons. The effect can be very large: up to 20% modulations in the fluorescence from singlet excitons are observed in acenes such as tetracene and rubrene [10].

The sensitivity and specificity of magnetic field probes of singlet exciton fission have proved to be especially useful in optoelectronic devices, because the magnetic field effect can be measured in any device geometry, and it is relatively immune to the vast range of complex electronic and excitonic processes exhibited by organic semiconductors. The magnitude of the magnetic field effect can measure the efficiency of exciton fission and its competition with loss processes [7,11]. The sign of the effect demonstrates whether a device output is dominated by singlet or triplet excitons [11,12]. For example, the effect on photocurrent in a solar cell is negative if that device generates charge from triplet excitons, but positive if it instead generates charge mostly from singlet excitons [12].

Magnetic field effects also offer an inexpensive and convenient test for the presence of singlet exciton fission in new materials. Alternative techniques include the detection of triplets using transient photo-induced absorption [13,14], or the transient observation of delayed fluorescence [15]. Such transient optical probes are typically more experimentally involved, requiring sophisticated tools and techniques, and not always suitable for in situ observations in devices.

In thin films, fission has been previously characterized by transient [8,15] and continuous wave [10] optical probes. Both show a strong magnetic field dependence in the fluorescence. To test the magnetic field dependence of fluorescence in solution various soluble polyacenes were dissolved in a solvent and sealed under a nitrogen environment using a screw cap and a polytetrafluoroethylene seal. Samples were placed between the poles of an electromagnet and illuminated using λ=365 or 420 nm light. The optical illumination was chopped mechanically and the fluorescence detected synchronously using a lock-in amplifier, as described previously [1]. In figure 1, we observe that the fluorescence of a number of polyacenes in solution depends on the external magnetic field. This strongly suggests that singlet fission is occurring between molecules in solution.

Figure 1.

Change in fluorescence in solution for soluble polyacenes. The largest change in fluorescence is observed for DPT. DPT, DTT and rubrene were measured in dichloromethane at various concentrations between 1 and 20 mg ml⁻¹ and excited with a 420 nm light-emitting diode (LED). DPP was measured in chlorobenzene at 10 mg ml⁻¹ and excited with a 365 nm LED. (Online version in colour.)

The observation of singlet fission in solution was further investigated in DPT as the change in fluorescence of DPT was the largest and the solubility of DPT in toluene is excellent, allowing concentration dependence studies to span a large range. Thin films of DPT were fabricated for comparison by spinning DPT from a 50 mg ml⁻¹ solution in toluene at 2000 r.p.m. for 60 s on clean quartz. The films were sealed in a nitrogen environment between two quartz slides using UV curing epoxy and aluminium foil to shadow the active area of the film from UV light. A large modulation in DPT fluorescence is observed in both solid state and a toluene solution; however, the shape and magnitude of the effect vary (figure 2). There is a zero crossing at low field in solid state, but the solution phase effect is monotonic. The magnitude of the effect at high fields is also stronger in solid state.

Figure 2.

(a) The chemical structure of DPT together with a comparison of the magnetic field dependence of its fluorescence in thin films and concentrated solution. The low field behaviour is highlighted in (b), showing the absence of a zero crossing in solution. The DPT concentration is 100 mg ml⁻¹ in toluene. (Online version in colour.)

Singlet fission in solution is caused by the collision of a molecule in the excited singlet state with another molecule in the ground state, resulting in two triplets formed on each molecule. The random orientation of the collision changes the lineshape of the magnetic field effect compared to the lineshape of molecules in the solid state. This can be understood within the Merrifield model of the magnetic field effects of singlet fission [5,6,16,17]. The distribution of singlet character over the nine triplet pair (TT) spin eigenstates determines the magnetic field effect and its line shape; the more eigenstates with singlet character and the more even the distribution of singlet character, the greater the fission or triplet–triplet annihilation rate. The triplet pair Hamiltonian does not commute with the total spin operator of the pair, resulting in energy eigenstates that are mixtures of singlet, triplets and quintets. Ignoring intermolecular spin–spin and hyperfine interactions, the Hamiltonian of a triplet pair is given by H=H_Zeeman+H_ZFS(1)+H_ZFS(2), where H_Zeeman describes the magnetic interaction of the external magnetic field with the total spin of the pair and H_ZFS(n) describes the zero-field splitting (ZFS) of the nth triplet of the pair. ZFS is due to anisotropic dipole–dipole interactions between the unpaired electron spins of a triplet, which means that H_ZFS(n) depends on the orientation of the nth molecule with respect to the applied magnetic field [18]. In a crystal, the rapid hopping of triplet excitons (relative to the frequency of the magnetic field) results in , where describes the excitonic ZFS that is an average over the inequivalent molecules of the unit cell [19]. The parity of prohibits mixing of the triplet TT states with the singlet and quintet TT states [20]. In this case, the singlet character is distributed over three states at zero field, six states at low field and two states (or one state, at particular magnetic field orientations) at high field. In a solution, however, the orientations of two colliding molecules are random with respect to one another and with respect to the magnetic field, which must be accounted for by averaging over all possible fission-producing orientations for H_ZFS(1) and H_ZFS(2) and all orientations of the pair [21]. In this case, H_solution has no definite parity, permitting mixing of the singlet character over all of the nine eigenstates at zero and low fields [22–25]. Then, as the applied field increases in magnitude, H_Zeeman increasingly dominates H_solution, finally resulting in the same high-field distribution of singlet character over two states as in the crystal phase [26]. This can result in a monotonic magnetic field effect [27–29]. Finally, we note that depending on the solution viscosity, the orientation dependence of triplet pair interactions in solution may actually require a dynamical treatment with consideration of additional spin mixing due to spin-relaxation effects from relative and/or concerted rotational motion of the pair of molecules during a fission event; this mechanism also increases the probability of a monotonic lineshape [21,24,25,30,31].

A magnetic field could modulate the fluorescence of DPT if photoexcitation generated radical pairs. However, radical pair formation cannot be reconciled with the positive, monotonically increasing change in the fluorescence observed. Intersystem crossing in photo-generated radical pairs in solution has been shown to result in increasing changes in fluorescence with magnetic field. However, positive magnetic field effects in radical pair systems are due to the interplay of Zeeman and hyperfine splitting terms, and they consequently saturate at considerably lower field strengths (approx. 10–100 mT) than the magnetic field effects in singlet fission. The alternative mechanism in radical pair solutions—the Δg mechanism—does saturate at fields comparable to those of singlet exciton fission (approx. 1 T) but results in an intersystem crossing rate that increases with magnetic field, giving rise to a monotonically decreasing change in fluorescence [25].

The transient decay of DPT fluorescence is characterized in figure 3. The decay in figure 3a represents the wavelength integrated emission as measured by a streak camera using a 400 nm excitation. The excitation source was 127 μm in diameter and approx. 100 fs in duration. Measurements were performed at a pump fluence under which no change in kinetics was observed. The emission was taken from the front of the vial and passed through a dichoric filter. As noted by Bardeen and co-workers [8], the magnetic field dependence of the transient fluorescence in tetracene is expected to appear after the triplet pair states are first populated from the initial singlet exciton. The field varies the yield of singlet exciton recovery relative to the generation of independent triplets on isolated DPT molecules. Indeed, the transients recorded in the presence and absence of a magnetic field diverge after a couple of nanoseconds. This time scale is comparable to the characteristic decay time constant for singlet exciton fission in DPT solutions at the 45 mg ml⁻¹ concentration of 4.2 ns. The decay was determined by fitting a single exponential to the decay without magnetic field starting at time zero.

Figure 3.

(a) Transient measurements of the fluorescence decay of 45 mg ml⁻¹ DPT in toluene. The decay in the absence of a magnetic field is shown in black, and the red data are recorded in the presence of a 0.5 T magnetic field. A single exponential fit to the decay in the absence of a magnetic field is shown in green. As expected the magnetic field effect appears after the initial decay has commenced as the magnetic field modulates the yield of singlet excitons returning from the triplet pair state. (b) Comparison of the transient lifetime and magnetic field effects as a function of the concentration of DPT demonstrates that the bimolecular fission process saturates at high concentrations of DPT. At high concentration, singlet fission presumably becomes rate limited by the speed of the intrinsic fission process in DPT rather than the probability of DPT collisions. (Online version in colour.)

Furthermore, the magnitude of the steady-state magnetic field effect and transient decay rate are a function of the concentration of DPT (figure 3b). This signifies that the underlying phenomenon is bimolecular, as expected. The fission rate and magnetic field effects are limited at low DPT concentrations by the low probability of DPT–DPT collisions. But at higher concentrations of DPT, a larger number of photoexcited molecules collide with ground state molecules leading to magnetic field-sensitive fluorescence due to the reformation of the singlet exciton from the triplet pair. At high enough concentrations, the fission rate and magnetic field effects saturate at a limit defined by the intrinsic rate of DPT fission.

Finally, solution phase measurements may also be used to probe the mechanism of singlet exciton fission [24]. It has been speculated that the process may be mediated by a charge transfer state shared between the two molecules that eventually support the triplet pair [24]. If so, the energy of the charge transfer state should depend on solvent dielectric constant and polarity. In figure 4, we test for the presence of charge transfer state in DPT fission by comparing the magnetic field effects in toluene (ε=2.38, μ=0.43) and chloroform (ε=4.81, μ=1.15). We find no notable differences. Prior measurements of the magnetic field effect on delayed fluorescence showed strong dependencies on solvent viscosity but no consistent dependence on solvent dielectric constant and polarity for either 1,2-benzanthracene or pyrene [24]. Future studies may instead probe the effect in materials with notably fast fission rates [32].

Figure 4.

Comparison of the magnetic field effect on DPT fluorescence at 10 mg ml⁻¹ in toluene (circles) and the more polar solvent chloroform (squares). No dependence on solvent polarity is observed. Changing solvent may be used to test for the presence of an intermediate charge transfer state in the fission process as the energy of an intermediate charge transfer state is expected to depend on the polarity and dielectric constant of the solvent. (Online version in colour.)

To conclude, we have found that magnetic field probes can be used to screen materials in solution for singlet fission activity. The necessary experiment does not require pulsed lasers or transient detection. The material must exhibit detectable fluorescence, however. Thus, we have found it to be most effective in the tetracene series of materials where the fission rate is relatively slow. While not a comprehensive alternative to delayed fluorescence or photo-induced absorption due to this limitation, solution-based magnetic field effect measurements may still provide a convenient indication of potential fission activity, especially in potential tetracene-based partners for silicon solar cells.

Funding statement

This work was supported as part of the Center for Excitonics, an Energy Frontier Research Center funded by the US Department of Energy, Office of Science, Office of Basic Energy Sciences under award no. DE-SC0001088.