Materials

F 2 -TES ADT was synthesized as described previously68. PC 71 BM, tetracene, rubrene, TIPS-pentacene and pentacene were purchased from Sigma Aldrich. F 2 -TES ADT and TIPS-pentacene thin film samples were spin-cast (15 mg ml−1, toluene) on polyimide precoated fused-silica substrates (the polyimide aids wetting of the organic semiconductor). For F 2 -TES ADT: PC 71 BM thin film samples, 4:1F 2 -TES ADT:PC 71 BM blend solutions (15 mg ml−1 total material, mesitylene) were spin-cast on polyimide precoated fused-silica substrates. Samples were dried on a hot-plate at 50 °C for 10 min. Tetracene, rubrene and pentacene thin-film samples were prepared via thermal evaporation at a base pressure of <6 × 10−6 mbar.

Single crystals of F 2 -ADT were grown through a physical vapour growth method. Details of the relevant method can be seen elsewhere69. We used a growth apparatus equipped with source and growth heaters that were placed side-by-side. Temperatures of the heaters were regulated in such a way that high-quality single crystals could be produced. In the present studies we set the source and growth heaters at 240 °C and 220 °C, respectively. The growth duration was 6 h.

TA and PL

For TA measurements, 90 fs pulses generated in a Ti:sapphire amplifier system (Spectra-Physics Solstice) operating at 1 kHz were used. The broadband probe beams were generated in separate home-built non-collinear optical parametric amplifiers for visible (500–800 nm) and near-infrared (800–1,100 nm) ranges. For fs-ps TA measurements, we used either narrowband <200 fs pulses from a commercial travelling-wave optical parametric amplifier of superfluorescence (TOPAS) or compressed pulses (∼40 fs, spanning 525–625 nm) from a home-built non-collinear optical parametric amplifier to excite the samples. The time delay between pump and probe pulses was controlled by a mechanical delay stage. Unless otherwise noted, pump intensities were kept below 5 μJ cm−2 to avoid bimolecular singlet–singlet annihilation effects and the pump and probe polarization were set to magic angle (54.7°) to avoid reorientation effects. For ns-TA measurements, pump pulses were generated using a frequency-doubled Q-switched ∼500 ps Nd:YVO 4 laser (532 nm). Delay times from 1 ns to 1 ms were achieved using an electronic delay generator. For time-resolved PL measurements to generate spectral maps, the samples were excited by 40 ps pulses (excitation wavelength: 470 nm) operating at a repetition rate of 2.5 MHz. PL decay dynamics were resolved using electronic gating through time-correlated single-photon counting with a temporal resolution of 180 ps and detection based on a cooled microchannel plate photomultiplier tube coupled to a monochromator. PL quantum beating measurements were performed on a separate time-correlated single photon counting system (Becker-Hickl module) system, using 100 fs pulses at 500 nm with a repetition rate of 80 MHz. Here, the emission was detected with a silicon single-photon avalanche diode, yielding a temporal resolution of around 40 ps. For all solid-state time-resolved optical measurements, samples were kept at a fixed temperature in a cryostat with dynamic helium gas flow. For solution measurements, a fused silica 1 mm path length cuvette was used.

Triplet sensitization

Blends of N-methylfulleropyrolidine (NMFP) and F 2 -TES ADT in a molar ratio of 4:1 were prepared at a concentration of 1 mg ml−1 in chloroform. The NMFP was excited by the 355 nm frequency tripled output of a Q-switched sub-ns Nd:YVO 4 laser. Following intersystem crossing on NMFP, triplet transfer to F 2 -TES ADT occurs and is monitored by TA spectroscopy. Results are shown in Supplementary Fig. 11.

Phosphorescence

To obtain samples that gave phosphorescence, the molecule of interest was spin-coated into films doped with platinum octaethylporphyrin (purchased from Sigma Aldrich). The weight ratio of target molecules to platinum octaethylporphyrin in solution was varied from 95:5 to 98:2, to give the clearest phosphorescence signal. Mixtures were spin-coated on Spectrosil at 800–1,200 r.p.m. for 1–2 min in a nitrogen-filled glove box and the films were then annealed at 60 °C for 30 min. The final samples were encapsulated to prevent sample degradation and triplet quenching by oxygen. Phosphorescence was detected using a calibrated infrared InGaAs photodiode array (ANDOR iDus 490A) coupled to a spectrograph (ANDOR Shamrock), with CW excitation at 532 nm (∼0.5 mW).

Optically detected magnetic resonance

Optically detected magnetic resonance (ODMR) experiments were performed to investigate the presence of free triplets in F 2 -TES ADT. In these measurements, the change in PL is monitored under magnetic resonance. ODMR gives a direct way of identifying triplet excitons, as the dipole–dipole interaction between electron and hole spins within the triplet exciton gives rise to characteristically broad ODMR spectra, governed by the zero-field splitting Hamiltonian >, where is the triplet spin operator, and D* and E* are the zero-field splitting parameters70.

Films were placed on a microwave stripline operated at a frequency of 6.2 GHz and mounted inside an optically accessible cryostat magnet, providing the static magnetic field B. Excitation was provided by a 532 nm laser with variable intensity I. The integrated PL was collected by a photodetector, after removing the laser line with a 550 nm long-pass filter. Microwaves were square-wave modulated at frequency f M , and the change in PL due to microwave transitions ΔPL was recorded by monitoring the photodetector response at this microwave chopping frequency using lock-in detection.

Structural characterization

Specular X-ray diffraction was performed with a PANalytical Empyrean system in Bragg–Brentano geometry using a sealed copper tube (λ=1.5418 Å, 40 kV, 40 mA) and an X’Celerate detector operating in a one-dimensional mode. A variable slit optics choosing an illuminated length of 10 mm was used in combination with 0.04° Soller slits at the primary as well as at the secondary side. Low temperatures down to 85 K were reached with the low temperature attachment TTK600 from Anton Paar Ltd using vacuum (2 × 10−5 bar) conditions. Starting from room temperature the samples were cooled down in steps of 25 K with a cooling rate of 5 K min−1. After reaching a temperature of 85 K, the sample was rapidly heated up to room temperature and cooled down again in steps to a temperature of 230 K, to confirm the measurements were reproducible after thermal cycling. Careful alignment of the sample height and sample tilt were made to obtain reliable results. Peak parameters were determined by a fit of a Gaussian curve to the experimentally observed Bragg peaks.

For measurements conducted at room temperature, the out-of-plane film structure was investigated with X-ray reflectivity in a lab setup (D8, Bruker) using a wavelength of 1.5406 Å.

Photovoltaic device fabrication and characterization

Solar cells were fabricated on 10 mm × 15 mm indium tin oxide-coated glass substrates that served as the anode. The substrates were ultrasonically cleaned in detergent, deionized water, acetone and isopropanol. A layer of 30 nm PEDOT:PSS (poly(3,4-ethylenedioxythiophene):poly(styrene sulphonate) (Clevios PH 1000) was spin-coated onto the indium tin oxide substrate and dried in air at 120 °C for 10 min. Fifteen milligrams of 4:1 F 2 -TES ADT/PC71BM blend was dissolved in 1 ml of mesitylene and spin-coated on top of the PEDOT layer at 1,500 r.p.m. and annealed for 10 min at 80 °C. Finally, the LiF/Al cathode (50 nm) was vacuum-evaporated onto the annealed photoactive layer. All devices were encapsulated before testing.

A 100 W tungsten halogen lamp (500–1,500 nm) and a 120 W Xenon lamp (350–500 nm) dispersed through a monochromator (Oriel Cornerstone 260) were used for external quantum efficiency measurements. For wavelengths between 375 and 900 nm, a set of silicon diodes (ThorLabs SM05PD1A) were used. A Keithley 2635 source measure unit was used to measure the short-circuit current as a function of wavelength. The incident light was focused to a spot size of ca. 1 mm2 using a set of lenses to illuminate individual pixels of size 0.08 cm2. The current–voltage (I–V) characteristics of the devices were measured under standard AM 1.5G conditions using an Abet Sun 2000 solar simulator, at an intensity equivalent to 100 mW cm−2. Spectral mismatch correction was performed before the measurements. The dark and bright I–V characteristics were measured using the Keithley 2635 source measure unit.

Internal quantum efficiency plots were calculated from external quantum efficiency (λ)/A(λ), where A is the absorbance of the photoactive layer, which was computed with a transfer matrix approach, where A was modelled according to published literature procedures71. The required values for the refractive index n and the extinction coefficient k were determined via ellipsometry, see Supplementary Fig. 25. The real and imaginary part of the complex refractive index were determined using variable angle spectroscopic ellipsometry (M-2000, Woollam Co.) using an optically isotropic layered optical model. The thickness was determined by fitting the data in the transparent wavelength range using the Cauchy model to describe the real part of the complex refractive index, assuming the imaginary part is zero. Film thicknesses were further determined via AFM.

Spectral decomposition techniques

To identify the spectral species present in the TA measurements and to determine their individual evolution over time, we used a combination of singular value decomposition and a spectral deconvolution code45. This code generates a given number of spectra that best reproduce the original data, while satisfying basic physical constraints such as spectral shape and population dynamics. The optimization of these spectra is done by a genetic algorithm. Once the code has minimized the residual between the obtained spectra and the original data the output is a set of spectra and kinetics for the species identified. The advantage of this optimization method over other approaches is that the genetic algorithm starts from random initial spectra and does not require a starting kinetic scheme, such as in global analysis methods. In brief, the genetic algorithm is an example of an evolutionary algorithm that factors TA spectra into a pre-determined number of spectral components. The idea is based on natural selection of genes in a population; random spectra or parents are mixed until they give separate spectra that best reproduce the original data, which constitutes a test for genetic fitness. The advantages of a genetic algorithm for our purpose over other optimization methods, such as gradient search methods, is that it is more capable of modelling a multidimensional data space that can be noisy and contain several overlapping features. Gradient search methods, on the other hand, are much more likely to get stuck in local minima.

Here, this optimization code was used to analyse the separate spectral components of TA and PL spectra. Singular value decomposition was used to give an initial estimation of the number of principal components in each spectrum. From here the optimization code was run to look for the same number of species. We assumed that the initially photogenerated species primarily contains only singlets that evolve into other excited states at later time. Once it was determined whether two or three species best fit the data, the genetic algorithm was run several times on the same TA measurement to assess the reproducibility of the results. Unless otherwise mentioned, for fs–ps TA measurements, the algorithm was run over 200 fs to 2 ns. The precise dynamics of the sub-200 fs region are hard to assess due to the numerous fluctuations in the early-time signal and a time resolution of ∼200 fs. For ns-TA measurements, the algorithm was run over 3–2,000 ns, omitting the instrument response region. For ps-PL measurements, the algorithm was run over 200 ps–20 ns.

We assess the reliability of the results of the optimization in three ways: (1) by testing the reproducibility of the results from >10 runs of the genetic algorithm data, as shown in Supplementary Fig. 26; (2) by comparing the spectra obtained from the optimization to the raw data obtained from both TA and PL measurements; and (3) by comparing the kinetics of population decay and/or spectra with independent measurements, for example, comparing the singlet and 1(TT) intermediate state kinetics in the TA measurements with that in the transient PL measurements. These two measurements are both conducted in the linear regime at similar excitation fluence to ensure the same photophysics are observed in both measurements.

Ab initio calculations

PL from the triplet pair state: to clarify the origin of 1(TT) PL, we analyse the bright exciton component in the 1(TT) state based on ab initio excited-state calculations. The 1(TT) states of π-stacked dimers are calculated using the complete active space self-consistent field (CASSCF) method, where the active orbitals consist of the highest-occupied molecular-orbital and lowest-unoccupied molecular-orbital of two monomers, that is CASSCF(4,4). The doubly excited 1(TT) diabatic state is optically dark and thus the 1(TT) PL necessitates mixing with singly excited bright exciton states. Yet, as found for the acene crystals16, the bright exciton component to the adiabatic 1(TT) states completely vanishes due to the relative phase factor of the wavefunctions in H-aggregates. In this case, the symmetric 1(TT) mixes only with the dark exciton and charge transfer states, which do not contribute to PL. However, the bright exciton can be mixed with 1(TT) via symmetry-breaking effects due to intra-molecular vibronic coupling. We model this in the simplest way possible by displacing the geometry of one of monomers from the triplet minimum to the ground state minimum, (see Fig. 2f in the main text for results and discussion). Such a scenario is consistent with intensity borrowing induced by coupling to vibrational modes, that is, the Herzberg–Teller mechanism.

Triplet pair separation rate: we analysed the transfer rate from the bound 1(TT) to free triplets based on the Marcus–Levich–Jortner rate theory parameterized against ab initio calculations. The electronic coupling for the intermolecular triplet transfer, V T−T , (see Fig. 5c in the main text) was estimated using time-dependent density functional theory as applied to π-stacked dimer models. The intramolecular reorganization energy, λ intra , for the triplet diffusion was computed on the monomers at the DFT level. The enthalpy change, ΔH, for the 1(TT) separation was obtained from CASSCF(4,4)/ CASPT2 calculations on π-stacked trimer models, with the monomers adopting either the fully relaxed triplet geometry (T) or the ground-state geometry (G). Thus, in this notation, the bound and separated triplet pairs correspond to TTG and TGT configurations, respectively.

The 1(TT) separation rate, K T−T , is evaluated by the Marcus–Levich–Jortner theory:

where k, T and S are the Boltzmann constant, temperature and entropy change, respectively. The Franck–Condon factor for the intramolecular effective mode, 〈0|0〉 intra , is evaluated from the reorganization energy, λ intra , and the frequency of 0.18 eV corresponding to the usual breathing/stretching mode in aromatic/conjugated molecules. The low-frequency intermolecular reorganization energy, λ inter , is small for covalent excitations such as triplets and its calculation cumbersome. Here we take a conservative value of 0.05 eV; modifying it in a reasonable range (up to a factor of 3) hardly affects the conclusions below. eW account for ΔS considering the numbers of spatial and spin configurations for the bound 1(TT) and separated triplets. The 1(TT) separation pathway for π-stacked TIPS-pentacene, F 2 -TES ADT and rubrene can be regarded as a one-dimensional chain; in this case, the spatial ΔS from the bound 1(TT) to nearest-neighbour T+T is unity. Considering the dissipation of spin correlation, the number of spin configurations of the separated T–T (3 × 3) is three times as many as the total-singlet 1(TT), that is exp(ΔS/k)=3.

The calculated ΔH indicates that the 1(TT) separation is endergonic for the three molecular materials investigated (see Fig. 5d in the main text). The bound 1(TT) is stabilized by orbital delocalization as well as the admixture of singly excited electronic configurations into the nearest-neighbour TT pairs (TTG), both contributions vanishing in the case of separated triplets (TGT). The free-energy stabilization going from TGT to TTG completely dominates the activation energy ΔE. Although these are overestimated by the calculations, the predicted trends in the ΔE values (namely larger in TIPS-pentacene compared to rubrene) match reasonably well with the measurements. It is interesting to point out that for rubrene in its equilibrium crystal structure at 0 K, the singlet-triplet mixing is strictly null because of symmetry20; thus, the finite (yet smaller) ΔE value computed in that case reflects only the energy stabilization associated with direct wavefunction overlap between neighbouring triplets. The relatively large 1(TT) separation rate of TIPS-pentacene compared with F 2 -TES ADT and rubrene is rationalized by the difference in electronic coupling for triplet diffusion. Thus, based on these theoretical results, we believe the measured activation energies reported in Fig. 5 essentially reflect the energy stabilization of bound vs free triplet pairs, rather than the reorganization energy for the migration of free triplets. This is borne out by the fact that measurements in anthracene single crystals have demonstrated that the triplet diffusion coefficient is quasi temperature-independent in the range 100–300 K (ref. 72) (see also references therein).

Data availability

The data that support the findings shown in both the main figures and Supplementary Figures in this study are available with the identifier https://doi.org/10.17863/CAM.9032.