High exciton diffusion coefficients in fused ring electron acceptor films

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High exciton diffusion coefficients in fused ring electron acceptor films Sreelakshmi Chandrabose, Kai Chen, Alex J. Barker, Joshua J. Sutton, Shyamal Prasad, Jingshuai Zhu, Jiadong Zhou, Keith C. Gordon, Zengqi Xie, Xiaowei Zhan, and Justin M Hodgkiss J. Am. Chem. Soc., Just Accepted Manuscript • DOI: 10.1021/jacs.8b12982 • Publication Date (Web): 09 Apr 2019 Downloaded from http://pubs.acs.org on April 9, 2019

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Journal of the American Chemical Society

High exciton diffusion coefficients in fused ring electron acceptor films Sreelakshmi Chandrabose#,†,, Kai Chen#,†, , Alex J. Barker¶, Joshua J. Sutton#,£, Shyamal K. K. Prasad#,†, Jingshuai Zhu¥, Jiadong Zhou§, Keith C. Gordon#,£, Zengqi Xie§, Xiaowei Zhan ¥,* and Justin M. Hodgkiss#,†,* # †

MacDiarmid Institute for Advanced Materials and Nanotechnology, New Zealand. School of Chemical and Physical Sciences, Victoria University of Wellington, New Zealand

¶

Center for Nano Science and Technology @Polimi, Istituto Italiano di Tecnologia, Milan, Italy

£

Department of Chemistry, University of Otago, New Zealand

Department of Material Science and Engineering, College of Engineering, Key Laboratory of Polymer Chemistry and Physics of Ministry of Education, Peking University, Beijing 100871, China ¥

Institute of Polymer Optoelectronic Materials and Devices, Key Laboratory of Luminescent Materials and Devices, South China University of Technology, Guangzhou 510640, China §

* Correspondence 

should be sent to J.M.H ([email protected]) and X.Z ([email protected])

S.C and K.C contributed equally

Supporting Information Placeholder ABSTRACT: Modest exciton diffusion lengths dictate the need for nanostructured bulk heterojunctions in organic photovoltaic (OPV) cells, however, this morphology compromises charge collection. Here, we reveal rapid exciton diffusion in films of a fused-ring electron acceptor that, when blended with a donor, already outperforms fullerene-based OPV cells. Temperature-dependent ultrafast exciton annihilation measurements are used to resolve a quasi-activationless exciton diffusion coefficient of at least 2 ×10-2 cm2 / s – substantially exceeding typical organic semiconductors, and consistent with the 2050 nm domain sizes in optimized blends. Enhanced 3dimensional diffusion is shown to arise from molecular and packing factors; the rigid planar molecular structure is associated with low reorganization energy, good transition dipole moment alignment, high chromophore density, and low disorder – all enhancing long-range resonant energy transfer. Relieving exciton diffusion constraints has important implications for OPVs; large, ordered, and pure domains enhance charge separation and transport, and suppress recombination, thereby boosting fill factors. Further enhancements to diffusion lengths may even obviate the need for the bulk heterojunction morphology.

INTRODUCTION

Low dielectric constants and strong electronphonon coupling in π-conjugated organic semiconductors create strongly bound electronhole states known as excitons, which control light absorption and emission, and which move as electrically neutral quasiparticles. In OPV cells, donor-acceptor heterojunctions for separating bound singlet excitons into free charge pairs must be distributed on a comparable length scale to the exciton diffusion length. This length scale is rarely more than 5–10 nm for solution processed OPVs1,2, which introduces a trade-off between exciton harvesting and subsequent charge collection efficiencies, and motivates the need to understand and control blend nanomorphology3. The apparent universality of 5–10 nm diffusion lengths in OPVs arises from several features common to solution processed organic semiconductors1,2. The diffusion length, LD is given by 𝐷𝜏, where D is the diffusion constant and τ the exciton lifetime. Since τ is intrinsically linked to the transition dipole moment (which

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varies little for strongly absorbing π-conjugated materials) and is suppressed via non-radiative relaxation in low bandgap materials4, the diffusion constant is the critical parameter. On the time- and length-scales governing the diffusion length, the dominant transport mechanism is incoherent resonant energy transfer hopping, with two parameters accounting for most of the variation between materials. First, the spectral overlap integral for self-energy transfer correlates strongly with diffusion length, however the vibronic progressions and Stokes shifts typical of organic semiconductors make majority of reported R0 values for self-energy transfer in the range of 1-2 nm5. Second, the energetic disorder governs the density of available sites within the transfer radius1. The energetic disorder of solutionprocessed organic semiconductors typically exceeds thermal energies at room temperature (e.g., 44 – 125 meV Gaussian disorder widths for PPV derivatives6,7), reducing density of accessible states and decreasing the exciton diffusion coefficient. The magnitude of disorder relative to thermal energy also accounts for dispersion in exciton diffusion coefficients, whereby an initial energetically downhill phase produces rapid diffusion that is not sustained for long distances1,2,11. The highest reported exciton diffusion coefficients are for polymers with a high degree of rigidity and planarity, notably ladder-type poly-p-phenylene (D = 4.4 × 10-2 cm2/s)9 and poly(9,9-di-n-octylfluorenyl-2,7-diyl) (D = 2 × 102 cm2/s)10. A high exciton diffusion constant was also reported for P3HT (D = 1 × 10-2 cm2/s)11, but this study revealed that exciton diffusion is only so high on early timescales, and not sustained when excitons relax through the density of states. The exciton diffusion constant for P3HT under quasi-equilibrium conditions is lower at D = 1.8 × 10-3 cm2/s12, similar to other OPV materials such as PPV derivatives (D = 0.3–3 × 10-3 cm2/s)7,13, PCPDTBT (D = 3 × 10-3 cm2/s)14, and even materials used in OPV devices with power conversion efficiencies exceeding 10% (PC71BM (D = 1.6 × 10-4 cm2/s)15. Exciton diffusion constants on the order of 10-3 cm2/s have been a common constraint of OPV materials throughout many generations of material advances.

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Here, we examine exciton diffusion in one of a new class of fused ring electron acceptors8, indacenodithiophene end-capped with 1.1dicyanomethylene-3-indanone (IDIC, Figure 1a)16, which was recently blended with a mid-bandgap polymer based on benzodithiophene and difluorobenzotriazole units (FTAZ)17 to create OPVs with power conversion efficiency of 12-13%18,19. XRay scattering measurements of those blends revealed large and pure phases 20-50 nm in size, consistent with the observation that charge generation dynamics lacked the ultrafast component that characterizes most fullerene blends 19. To test the hypothesis that the optimal phase size can be so large due to facile exciton diffusion, we employed ultrafast spectroscopy to measure exciton diffusion coefficients in IDIC. The measured diffusion constant is at least 2 × 10-2 cm2/s (subject to conservative assumptions), time-independent, and virtually independent of temperature. Spectroscopic and structural measurements, along with kinetic modeling, reveals that this remarkably high diffusion coefficient arises from molecular and packing factors associated with the fused-ring electron acceptor class of materials; the rigid planar molecular structure is associated with strong resonant overlap, aligned transition dipole moments, and low energetic and structural disorder – all enhancing long-range resonant energy transfer. EXPERIMENTAL DETAILS Materials. The synthesis and purification of IDIC was reported in reference16. Neat films of IDIC were prepared from chloroform (2 mg/mL) and spincoated onto spectrosil fused silica substrates in air and at room temperature at 3000 rpm. Air was not found to be detrimental when comparing complete devices cast in air versus from N2. The blend film of IDIC with polystyrene was prepared from chloroform solution of IDIC (2 mg/mL) and polystyrene (54 mg/mL) under the same conditions. The film thicknesses were measured by the Dektak, Veeco surface profiler and found to be ~90 nm for neat IDIC and ~250 nm for IDIC:polystyrene. Samples where measured under dynamic vacuum, and stored in the dark under vacuum to prevent the contact with air and light. The temperature dependent transient absorption measurements were carried out using the ‘Janis Research Model VPF 100 system’ liquid nitrogen (LN2) cryostat for five different temperatures started from 80 K to 290 K and then returned to 80 K to confirm that the sample did not change during the measurement. Optical measurements Steady state spectroscopy. The UV-Vis absorption spectra of IDIC films were recorded using a Cary 50


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Bio UV-Vis spectrometer over the range 190 – 1100 nm. A Horiba Fluorolog – 3 spectrometer was used to collect the steady state photoluminescence. Temperature dependent PL data of neat IDIC film were recorded by a polychromator (SP2300 by Princeton Instruments) and an intensify CCD camera (PIMAX 3 by Princeton Instruments) following 680 nm laser excitation. The PL quantum yield of an IDIC

film was measured by using a Hamamatsu C11347-11 absolute fluorescence quantum yield spectrometer. The film of IDIC was prepared from chloroform (12 mg mL-1) and spin-coated onto quartz plate at 3000 rpm. Transient absorption spectroscopy. Exciton diffusion and recombination in IDIC films were studied by femtosecond transient absorption (TA) spectroscopy using the output of an amplified Ti:Sapphire laser (Spitfire, Spectra Physics, 800 nm, 3 KHz, 100 fs) where the TA system has been described previously30,31. The neat IDIC films were excited by 100 fs, 716 nm laser pulses that were generated in an optical parametric amplifier (TOPAS) and then chopped at 1/2 (1.5 kHz). Excitations were probed via a broadband white light continuum generated by focusing a portion of the fundamental to an undoped YAG crystal. The polarization of the pump and the probe pulses were set to the magic angle (54.7o) at the sample in order to prevent orientational dynamics, aside from in the polarisation anisotropy measurement. After passing through the sample, the probe pulses were spectrally dispersed using a prism spectrometer and then collected using an InGaAs photodiode array (for NIR) or CMOS camera (for visible). The differential transmission signals are calculated from the sequential probe shots corresponding to the pump on versus off. The pump – probe time delays up to nanoseconds are produced via a retroreflector on a motorised translational stage. For the measurements, 6000 shots were averaged for each time delay and were repeated for at least 4 times. The data saved as binary files were processed via MATLAB which is used to correct the chirp, background and also for combining the visible and IR components. We confirmed that photoproduct buildup did not affect the measured dynamics by confirming the correspondence of signals and dynamics from sequential TA scans.

The polarization anisotropy measurements were performed using the same system described above. Here we used a waveplate to selectively excite the parallel and perpendicularly oriented dipoles in the film and then isolated the corresponding TA signals using a fixed broadband polariser applied to the probe.

The extent of polarization is described in terms of anisotropy (r) defined by, ∆𝑇

𝑟=

[𝑇 ] ― [

∆𝑇 𝑇 ⊥]

∆𝑇

∆𝑇

∥

[𝑇 ] + 2[𝑇 ∥

Where

∆𝑇 𝑇 ∥

and

∆𝑇 𝑇 ⊥ are

⊥

(1)

]

the

differential

transmission signals corresponding to the parallel and perpendicularly oriented chromophores. Transient photoluminescence spectroscopy. The transient PL experiments used the setup previously described32. Here, instead of a Ti:sapphire laser, we used a 100-kHz fiber amplifier (Tangerine by Amplitude Systèmes)33with 130 fs pulse width and 200 uJ/pulse. The 1030-nm fundamental output of the fiber laser was used to generate a transient grating in an undoped Yttrium Aluminum Garnet crystal, which makes the near IR region accessible, where IDIC emits. The IDIC samples were excited at 515 nm (second harmonic of the fundamental output). A pair of offaxis parabolic mirrors collected and then focused PL of the samples to the transient grating gate. The spectra of the diffracted transient PL were measured by a spectrometer equipped with back-illuminated CCD camera. The time resolution of the system is ~250 fs, characterised by measuring the scattering of 515 nm. All the samples were measured under vacuum to prevent photodegradation. Computation of reorganization energy. Reorganization energies for electron transfer were calculated using the equation given by, 𝜆𝐼𝑅𝐸 = 𝜆𝑁 + 𝜆𝐶 = (𝐸𝑁―1 ― 𝐸0𝑁) + (𝐸0𝐶 ― 𝐸𝐶―1 ) where 𝜆𝐼𝑅𝐸 is the internal reorganization energy, 𝐸𝑁 and 𝐸𝐶 indicate, respectively, the energies for the optimized geometries of the neutral molecule and of its charged counterpart; the superscripts refer to the molecular charge. Geometry optimizations with both a neutral and anionic charge, alongside single point calculations with alternate charge for that of the optimization were carried out in Gaussian, using B3LYP/6-31G(d) parameters. For all calculations, a dichloromethane solvent field was applied. Analysis Spectral fitting. Absorption and PL spectra were modelled by a Frank-Condon progression of Gaussian line shapes displaced by the phonon energy of a single vibrational mode (C=C stretch) given by,

𝐼(𝜔) ∝ (ℏ𝜔)3 𝑛(𝜔) ×

∑

𝑆𝑚 Γ (𝐸0 ― 0 ± 𝑚𝐸𝑝ℎ,𝜎) (3) 𝑚!

𝑚=0


(2


where ℏω is the Einstein coefficient of spontaneous emission, n(ω) is the refractive index at a frequency ω (which is taken here as a constant throughout the frequency range), S is the Huang-Rhys factor, m is the vibrational transition index, Eph is the phonon energy of the C=C stretch and Γ is a Gaussian line shape with full width half maximum σ. In the fitting procedure S, E0-0 and σ were the free parameters while n(ω) and Eph were fixed. Calculation of Förster radius. FRET radius, which is the distance at which the energy transfer efficiency is 50%, is given by,

𝑅60

=

9000 (ln 10) 𝜅2 𝑄𝑌 128 𝜋5 𝑁𝐴𝑉 𝜂4

𝐽

(4)

where J is the spectral overlap integral between the emission (normalized) and absorption (in the unit of M-1 cm-1) of dipoles, QY is the quantum yield of the material (0.03 for IDIC), η is the refractive index of the medium and κ2 is the relative orientation between the emissive and absorptive dipoles (which is 1 for parallel dipoles and 4 for head to tail dipoles). In the calculation of FRET radius for exciton diffusion, the spectral overlap integral, J, is taken as the spectral overlap between emission and absorption of the ground state acceptor (J = 1.524 × 1016 nm4). When considering a FRET mechanism for exciton-exciton annihilation, the spectral overlap integral (J = 1.863 × 1016 nm4) is calculated from the overlap of emission and absorption spectra of excited state (overlap between steady state emission and exciton PIA, where the PIA peak is normalized to the same peak extinction coefficient as the ground state absorption). RESULTS Static and time-resolved optical spectra of IDIC. Figure 1b shows the UV-visible absorption and photoluminescence (PL) spectra for solutions and thin films of IDIC. The absorption spectrum of the thin film peaks at 712 nm and is dominated by the 0-0 vibronic peak. While the film absorption spectrum displays the expected red-shift compared with solution, their similar spectral shape suggests that aggregate coupling effects do not play a major role. Absorption and PL spectra of dilute solid films of IDIC in a polystyrene matrix (Supporting Information Figure S1) reveal similar spectral shapes. Electronic structure calculations matched to experimental Raman spectra (Supporting Information Figures S2, S3) depict the S1 state of IDIC as a strongly absorbing π-π* excited state (oscillator strength 2.87) that is delocalized along the molecule with minimal

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structural distortion (excited state bond length alternation shown in Supporting Information Figure S4). The minimal structural distortion in the excited state is also consistent with the low reorganization energy associated with charge transfer. Using the same computational approach as Swick et al, a reorganization energy of 0.17 eV was obtained for reduction, in line with the low reorganization energies recently found for other members of this class of fused-ring electron acceptors34.

The series of transient absorption (TA) spectra for an IDIC film shown in Figure 2a are explained by one species; singlet excitons. The positive differential transmission feature around 1.6–2.0 eV can be largely attributed to groundstate bleaching, but it extends further to the red, which is explained by stimulated emission from the S1 state (assigned based on its coincidence with the PL spectrum). The TA spectrum also features a sub-gap excitonic photoinduced absorption peak around 1.45 eV. The spectrum displays negligible change with time (Supporting Information Figure S5), and its apparent half-life of only ~5 ps already reflects substantial exciton annihilation at this fluence, as confirmed from the 126 ps lifetime measured in a dilute polystyrene blend film, and 90 ps amplitude weighted lifetime at the lowest fluence (vide infra). Figure 2b shows normalized ultrafast PL spectra measured using the transient grating PL spectroscopy method (non-normalized shown in Supporting Information Figure S6). The highenergy PL edge red-shifts by 10 nm tend to be for 1D diffusion, and in materials that are not particularly suited for OPV cells, for example perylene bisimide aggregates (96 nm) 23, or ladder-type PPP derivatives (11-14 nm)9,24. The comparatively long exciton diffusion length measured for IDIC also explains an intriguing observation in previously reported OPVs using IDIC as an acceptor. In FTAZ:IDIC blends with 1213% power conversion efficiency18,19, scattering measurements revealed phases sizes 20-50 nm19, and in contrast to typical polymer:fullerene blends, charge generation kinetics lacked an ultrafast component associated with excitons generated at interfaces. With such a high exciton diffusion coefficient, diffusion from the center to the edge of a 20-50-nm IDIC phase can easily occur on the picosecond timescale. Structural and energetic order. In order to probe structural order, we measured the Raman spectrum of an IDIC film in the sub 100 cm-1 frequency range, where Raman scattering comes from intermolecular phonon modes, and the occurrence of sharp peaks signifies long-range structural order. The Raman spectrum shown in Supporting Information Figure S7 shows weak, but distinct peaks below 25 cm-1, as opposed to a broad, featureless, vibronic density of states. This is consistent with the solution processed IDIC adopting some level of ordered packing arrangement. The presence of distinct low frequency bands is consistent with a greater level of ordering or crystallinity, as has been observed for other semiconducting materials25. This finding is in agreement with previous X-Ray scattering measurements that revealed a domain size of 20-50 nm19. Polarization-resolved TA spectroscopy shows that excitons predominantly hop between

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aligned chromophores as they diffuse. The polarization anisotropy dynamics in Supporting Information Figure S8 reveal that, beyond an ultrafast decay – commonly observed and attributed to localization of the initial delocalized excitation – the polarization anisotropy is maintained above 0.1 for its entire lifetime, over which excitons are shown above to be undergoing rapid diffusion. The structural order that creates arrays of near parallel transition dipole moments is well-suited for rapid, longrange the resonant energy transfer. In order to test whether low energetic disorder contributes to substantially enhanced exciton diffusion, we measured the temperaturedependence of PL spectra and exciton annihilation rates. The inset of Figure 4a shows PL spectra measured over the range 80–290 K. Each spectrum is fit to a vibronic progression, and the 0-0 peak position can be taken as a measure of the mean exciton energy for each temperature, assuming they achieve an equilibrium distribution within their lifetime. The Gaussian energetic disorder experienced by excitons, σ, is obtained from the slope of a plot of E0-0 vs 1/T (Figure 4a). The data exhibits pronounced curvature, with an apparently higher slope at high temperature. This is consistent with the activated diffusion model and data previously shown for PPV6, but the magnitude of disorder is substantially lower in this case – in the range of σ = 10–23 meV. Comparably low disorder widths are rarely observed in organic semiconductors, generally only in structurally rigid molecules such as ladder-type conjugated materials26. Importantly, the measured disorder is less than thermal energy at room temperature (26 meV), consistent with the lack of dispersive exciton transport observed for IDIC. The temperature dependence of the exciton diffusion coefficient was measured by extending the series of fluence-dependent measurements and analysis described for Figure 3 as a function of temperature (fluence dependent plots and fits at each individual temperature shown in Supporting Information Figure S9). The temperature dependence of the exciton diffusion coefficient is shown in Figure 4b. In contrast to typical disordered organic semiconductor films whose exciton transport is suppressed at low


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temperature, we find that high exciton diffusion coefficients are maintained at least as low as 80 K. Long-range resonant energy transfer model. We modelled energy transport in order to investigate whether the long exciton diffusion lengths observed in IDIC can be attributed to resonant energy transfer. A simple analytical expression for LD in terms of R0 has been developed and applied with some success,5 however, it only considers transfer to nearestneighbours. This assumption is valid in the vast majority of systems whose R0 values have been evaluated at around 1-2 nm, however, longer transfer steps should clearly be considered in our system with R0 = 4.7 nm (corresponding to a volume containing hundreds of IDIC chromophores, Supporting Information). A sum of rates approach for all accessible chromophores could be employed based on the known crystal structure. We went a further step and used a numerical Monte-Carlo approach, which also enabled the effect of energetic disorder to be modeled. Here, incoherent resonant transport is considered to be a stochastic memoryless process, where at each step, a random number is used to determine the outcome from either energy transfer to one of a list of potential acceptors or relaxation to the ground state. The probability for each of these outcomes is determined using the modified Förster expression described below, considering the relative positions and dipole orientations of the donor and each potential acceptor in the IDIC lattice. These geometric parameters were taken from the X-ray crystal structure of IDIC (Supporting Information Table S1, Figure S14), superimposed with transition dipole moment orientations determined from TD-DFT calculations (Table S2). The rate kT of fluorescence resonance energy transfer (FRET) between a given donor-acceptor pair was originally described in a point-dipole approximation by Förster27. Wong et al.28 have since shown how the point-dipole approximation breaks down when the effective length scale of chromophores is similar to the interchromophore spacing, as is the case for IDIC thin films. They propose a modified version of the Förster expression,

1

𝑅0

( )

𝑘T(𝑟) = 𝜏D

𝑙+𝑟

6

(8)

where τD is the excited state lifetime of the donor in the absence of acceptor, r is the donoracceptor distance, l is effective chromophore length, and R0 is the distance at which energy transfer takes place with 50% efficiency (calculations provided in the Supporting Information Information). Finally, we need to consider energetic disorder, which can be approximated as a Gaussian distribution of excitonic energies with full width at half maximum σ, referred to as the disorder factor1. For a given value of σ, the fraction of chromophores that are energetically unavailable for energy transfer is equal to 1 ― 2 exp( ― 𝜎 2(𝑘B𝑇)2). For each step, we therefore approximate disorder by setting the probability for transfer to an appropriate fraction of randomly selected acceptors to zero. Figure 5a presents a typical path taken by a single excitation calculated using the above framework following absorption of a photon at (𝑥,𝑦,𝑧) = 0. The distance of the exciton from its origin is shown in Figure 5b, where we can see that while more than 700 transfer events took place before the excitation relaxed to ground, the maximum distance from the origin was 112 nm, which occurred after approximately 600 energy transfer steps. By repeating this simulation many times, we are able to accumulate a set of statistics to compare to our measured value of diffusion length. Figure 5c is a histogram showing the distribution of maximum distances achieved after 10,000 simulated absorbed photons. The median value of these maximum distances represents the distance at which 50% of excitations would be quenched in a volume quenching measurement, and therefore can be directly compared to the diffusion length LD obtained from our transient absorption measurements. We find a predicted LD of 87.7 nm for a perfect IDIC lattice, with LD decreasing to 85.8 and 72.0 nm when applying our measured limits for disorder of σ = 10 and 23 meV, respectively (Figures 5b and c, Table S3). These values indicate that the enhanced energy transfer in IDIC thin films (due to excellent molecular



packing, strong spectral overlap, and low disorder) can sufficiently account for a long exciton diffusion length. In the disorder-free case, the results of the MC would be equivalent to that found by simply summing the rates to all sites. The use of MC methods allows us to introduce the effect of energetic disorder, which was important for comparison to experimental results for this study. The possibility of obtaining crystal structures for this class of compounds means that in future, measured and predicted diffusion coefficients might be correlated with specific packing structures. In addition, we also find evidence for some degree of anisotropic transport, with significantly longer diffusion along the tightly packed z-axis direction (i.e. perpendicular to the substrate in the case of flat packing), as shown in Supporting Information Figure S10. In order to obtain a simple comparison to corresponding values in ‘traditional’ conjugated polymers, we repeat our calculation with R0 = 1.5 nm and σ = 80 meV (Supporting Information Figure S11). In this case, even when retaining the tightly packed IDIC lattice structure, LD is reduced to 4.6 nm, consistent with diffusion lengths and optimal domain sizes in well-established organic semiconductors5. There are two likely reasons that the simulations overestimate the measured diffusion lengths for IDIC; i) the Gaussian approximation of disorder is surely oversimplified, and the real system is likely to be rather sensitive to deviations given that long diffusion arises from a large number of FRET events, ii) the short distance correction to the point dipole approximation may begin to fail at such high packing densities, where it applies to a large number of acceptor sites. DISCUSSION The high exciton diffusion coefficient observed for IDIC is well-described via a simple resonant energy transfer hopping model; the same physics previously used to describe materials with substantially slower diffusion. Aggregate effects like supertransfer29 do not appear to play a role, when considering the similar spectral shapes for neat films and dilute

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films where aggregates cannot form. The facile exciton diffusion for IDIC thus results from many FRET parameters being optimized for long-range transport. Here, we consider the molecular basis of these factors, their intrinsic limits, and the possibility of further enhancements. The most important factor is the spectral overlap for transfer between the same chromophore. When expressed as the FRET radius, R0 (assuming random dipolar alignment for comparison with published results), our R0 value of 4.7 nm substantially exceeds previously reported values, which are in the range of 1.0-2.0 nm)5. Since resonant overlap between the absorption and PL of IDIC comes from the 0-0 vibronic peaks, the dominance of the 0-0 peaks for absorption and PL in IDIC (i.e., low HuangRhys factor, low reorganization energy) mean that its high oscillator strength is concentrated in the overlapping region. The strong self-overlap ultimately arises from the rigidity imparted by the fused ring structure of IDIC and other fused ring electron acceptors – again reminiscent of ladder-type polymers.9 We estimate that the spectral overlap integral would be further increased by a factor of 2.6 if the energy offset between 0-0 peaks in absorption and PL were completely eliminated, which would enhance the diffusion length by the same factor. The low energetic disorder of IDIC is an important factor for its facile exciton diffusion, and is another consequence of it being a rigid, crystalline small molecule. Dispersive exciton transport is a hallmark of disordered materials, whereby excitons undergo diffusion only while relaxing within the density of states, before running out of spatially and energetically accessible transfer sites. Since the Gaussian disorder for IDIC – spectroscopically measured from excited state energies is lower than thermal energy, excitons in IDIC can sustain long-range energy transfer throughout their lifetime. When incorporating the 23 meV Gaussian disorder, the modeled diffusion length was ~18% shorter than for a model without energetic disorder, and the suppression of diffusion length would be substantially worse with greater disorder. The parameters outlined above benefit substantially from the fused ring molecular structure IDIC, yet there is room for further


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enhancement. With optimized BHJ domain sizes already 20-50 nm, further increases in selfspectral overlap and energetic order may push the diffusion length towards the optical absorption length of ~100 nm. An exciton diffusion length exceeding the optical absorption length would obviate the need for a BHJ morphology and introduce the possibility of solution-processed bilayer devices. Bilayer devices with sharp interfaces, or even BHJs with very large domains, may not suffer from morphology-dependent effects like reduced fillfactor, variability in morphology, and the requirement to tune sidechains and deposition conditions to optimize morphology. Moreover, new low bandgap semiconductors are expected to require enhanced exciton diffusion coefficients to compensate for their generally shorter exciton lifetimes4. Finally, we note that care must be taken when undertaking time-resolved spectroscopy on fused ring electron acceptor materials like IDIC. Facile exciton diffusion means that their excitonexciton annihilation thresholds are substantially lower than expected for most OPV materials. Indeed, annihilation still dominates the picosecond dynamics of IDIC at fluences as low as ~1 µJ/cm2. CONCLUSION We have shown that the fused-ring electron acceptor, IDIC, has a remarkably high exciton diffusion coefficient of at least 2 × 10-2 cm2/s, perhaps as high as 1 × 10-1 cm2 / s. This property is consistent with the 20-50 nm domains found in optimized BHJ devices with 12-13 % power conversion efficiency, and it is a consequence of molecular factors favoring long-range resonant energy transfer. The rigid planar structure of the molecule focuses its absorption and emission oscillator strength into overlapping 0-0 vibronic

peaks, enhancing resonant energy transfer. Low energetic disorder means that facile diffusion is sustained throughout the exciton lifetime, and structural order also boosts the orientation factor. These results challenge long-held assumptions of exciton diffusion constraints and raise the prospect of high performing solutionprocessed bilayer OPV devices.

FIGURES



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Figure 1. Chemical structure and steady-state spectra. (a) Chemical structure of IDIC and (b) steady state absorption and photoluminescence spectra of IDIC in both solution and thin film along with their fits to the vibronic progression model.


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Figure 2. Transient absorption and photoluminescence spectra of neat IDIC film (a) Series of transient absorption spectra of IDIC film at different time delays (excited at 716 nm, at a pump fluence of 6.56 µJ/cm2) along with the normalized steady state absorption and photoluminescence spectra and (b) Transient photoluminescence spectra of IDIC film at various time delays (excited at 515 nm, at a fluence of 7.8 µJ/cm2).



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Figure 3. Singlet–singlet exciton annihilation in neat IDIC film. Fluence dependent singlet exciton decays (extracted from the singular value decomposition) of neat IDIC film fitted to the singlet-singlet exciton annihilation model. The reference kinetics from a film of IDIC diluted in a polystyrene matrix are also shown.


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Figure 4. Effect of low energetic disorder on exciton diffusion. (a) Temperature dependence of 0-0 emission peak energy (extracted from fits to vibronic progression) of neat IDIC film after 680 nm excitation. The range of Gaussian energetic disorder is obtained from the slopes at each extreme (which are noted in the figure) along with the temperature dependent steady state emission spectra in the inset and (b) Arrhenius plot of exciton– exciton annihilation constants versus reciprocal temperature.



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Figure 5. Monte-Carlo simulations of resonant transport in IDIC thin films. (a) Typical path taken by a single excitation beginning at (x,y,z) = 0, with (b) corresponding distance from origin. (c, d, and e) show histograms of maximum distance from origin and resulting diffusion length LD (red dashed lines) after 10,000 simulated absorbed photons for disorder parameter σ = 0, 10, and 23 meV respectively.


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ASSOCIATED CONTENT Supporting Information. Figures including transient absorption spectra and kinetics of IDIC:polystyrene film with 665 nm excitation, Raman spectroscopy, electronic structure and excited state structural distortion in IDIC film, additional information from TA and TRPL, low frequency Raman, ultrafast polarization anisotropy result, temperature dependent exciton annihilation fittings and further details from Monte-Carlo simulations. This material is available free of charge via the Internet at …. AUTHOR INFORMATION Corresponding Authors [email protected] [email protected] Notes The authors declare no competing financial interest. ACKNOWLEDGMENTS JMH and KC acknowledge support from the Marsden Fund and a Rutherford Discovery Fellowship to JMH. XZ acknowledges support from NSFC (No. 21734001 and 51761165023). REFERENCES (1) Mikhnenko, O. V.; Blom, P. W.; Nguyen, T.-Q. Energy Environ. Sci. 2015, 8, 1867-1888. (2) Menke, S. M.; Holmes, R. J. J. Energy Environ. Sci 2014, 7, 499-512. (3) Liu, F.; Gu, Y.; Shen, X.; Ferdous, S.; Wang, H.W.; Russell, T. P. Pro. Polym. Sci. 2013, 38, 1990-2052. (4) Dimitrov, S. D.; Schroeder, B. C.; Nielsen, C. B.; Bronstein, H.; Fei, Z.; McCulloch, I.; Heeney, M.; Durrant, J. R. Polymers. 2016, 8, 14. (5) Lunt, R. R.; Giebink, N. C.; Belak, A. A.; Benziger, J. B.; Forrest, S. R. Appl. Phys. 2009, 105, 053711. (6) Mikhnenko, O.; Cordella, F.; Sieval, A.; Hummelen, J.; Blom, P.; Loi, M. J. Phys. Chem. B. 2008, 112, 11601-11604. (7) Markov, D.; Tanase, C.; Blom, P.; Wildeman, J. Phys. Rev. B. 2005, 72, 045217.

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TOC FIGURE


High exciton diffusion coefficients in fused ring electron acceptor films

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