Direct Imaging of Frenkel Exciton Transport by Ultrafast Microscopy

Article pubs.acs.org/accounts

Direct Imaging of Frenkel Exciton Transport by Ultrafast Microscopy Tong Zhu,# Yan Wan,# and Libai Huang* Department of Chemistry, Purdue University, West Lafayette, Indiana 47907, United States CONSPECTUS: Long-range transport of Frenkel excitons is crucial for achieving efficient molecular-based solar energy harvesting. Understanding of exciton transport mechanisms is important for designing materials for solar energy applications. One major bottleneck in unraveling of exciton transport mechanisms is the lack of direct measurements to provide information in both spatial and temporal domains, imposed by the combination of fast energy transfer (typically ≤1 ps) and short exciton diffusion lengths (typically ≤100 nm). This challenge requires developing experimental tools to directly characterize excitation energy transport, and thus facilitate the elucidation of mechanisms. To address this challenge, we have employed ultrafast transient absorption microscopy (TAM) as a means to directly image exciton transport with ∼200 fs time resolution and ∼50 nm spatial precision. By mapping population in spatial and temporal domains, such approach has unraveled otherwise obscured information and provided important parameters for testing exciton transport models. In this Account, we discuss the recent progress in imaging Frenkel exciton migration in molecular crystals and aggregates by ultrafast microscopy. First, we establish the validity of the TAM methods by imaging singlet and triplet exciton transport in a series of polyacene single crystals that undergo singlet fission. A new singletmediated triplet transport pathway has been revealed by TAM, resulting from the equilibrium between triplet and singlet exciton populations. Such enhancement of triplet exciton transport enables triplet excitons to migrate as singlet excitons and leads to orders of magnitude faster apparent triplet exciton diffusion rate in the picosecond and nanosecond time scales, favorable for solar cell applications. Next we discuss how information obtained by ultrafast microscopy can evaluate coherent effects in exciton transport. We use tubular molecular aggregates that could support large exciton delocalization sizes as a model system. The initial experiments measure exciton diffusion constants of 3−6 cm2 s−1, 3−5 times higher than the incoherent limit predicted by theory, suggesting that coherent effects play a role. In summary, combining ultrafast spectroscopic methods with microscopic techniques provides a direct approach for obtaining important parameters to unravel the underlying exciton transport mechanisms in molecular solids. We discuss future directions to bridge the gap in understanding of fundamental energy transfer theories to include coherent and incoherent effects. We are still in the infancy of ultrafast microscopy, and the vast potential is not limited to the systems discussed in this Account.

I. INTRODUCTION The Frenkel exciton, a tightly bound electron and hole pair, is a good description of the excited states of molecular light absorbers (Figure 1).1,2 The spin 0 exciton is called singlet, and the spin 1 exciton is known as triplet. The optical properties of the molecular components desirable for solar energy harvesting are dictated by excitons.2,3 Exciton migration is the primary means of energy transport in a wide variety of molecular systems and plays a crucial role in many systems, including natural light-harvesting systems, photovoltaics, and light emitting diodes.4−6 Due to the low dielectric constant of the organic materials, Frenkel excitons generally migrate at a much slower rate compared to their inorganic Wannier counterparts and have much shorter diffusion lengths, which limits the efficiency of applications such as organic solar cells.6 Direct measurements to provide quantitative results on length and time scales of exciton transport are necessary to elucidate fundamental mechanisms and provide design principle for molecular-based light harvesting materials. Despite significant efforts made toward studying exciton diffusion both theoretically and experimentally,6−9 direct measurements of exciton transport have been rare. One major challenge in © 2017 American Chemical Society

measuring exciton transport in molecular systems lies in the requirement of simultaneous ultrafast temporal resolution and nanoscale spatial resolution, imposed by the combination of fast energy transfer (typically ≤1 ps) and short exciton diffusion lengths (typically ≤100 nm). Steady-state and time-resolved photoluminescence (PL) microscopy have been utilized to visualize exciton diffusion.10−13 However, a limitation of PL based approaches is that they only reflect bright electronic states as opposed to the dark states, such as triplets. Another drawback for PL based techniques is that the time resolution is usually on the order of ∼100 ps, which is not sufficient to unravel fast energy transfer processes. Due to this challenge, many open questions remain about Frenkel exciton transport mechanisms. For instance, the most employed theory for exciton transport involves incoherently hopping between individual chromophores via Förster resonant energy transfer (FRET) mediated by dipole−diploe interactions. However, as intermolecular coupling becomes stronger, such as in photosynthetic antenna systems, excitons are delocalized over Received: March 30, 2017 Published: July 5, 2017 1725

DOI: 10.1021/acs.accounts.7b00155 Acc. Chem. Res. 2017, 50, 1725−1733

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Accounts of Chemical Research

Figure 1. Schematics of the two systems discussed in this Account. (a) Singlet and triplet exciton transport in singlet fission materials. (b) Exciton transport in tubular aggregates formed by meso-tetra(4-sulfonatophenyl) porphyrin (TPPS4).

multiple chromophores and the incoherent FRET mechanism no longer applies.14−16 Using transient absorption instead of PL as imaging contrast can address the above-mentioned challenge, which allows for investigating of both bright and dark states and improving the time resolution to better than 100 fs. The past decades have seen tremendous activities in the development of nonlinear microscopy methods to interrogate materials through their absorption, pioneered by Masuhara, Orrit, and Vallée.17−19 For a comprehensive summary on the development and applications of transient absorption microscopy (TAM), we direct the readers to two recently published review articles.20,21 In this Account, we focus on the applications of TAM as a direct approach with simultaneously high temporal resolution and spatial precision to obtain exciton transport parameters that are otherwise not possible in molecular crystals and aggregates. The Account is organized as follows. We first introduce the experimental methods and then discuss two case studies. The first example demonstrates how TAM reveals a new singletmediated triplet transport mechanism in singlet-fission polyacenes (Figure 1a) by its ability to image both bright and dark exciton states. The second example presents how the spatial and temporal information obtained by TAM is used to evaluate coherent effects in the transport of delocalized excitons in tubular molecular aggregates (Figure 1b). Finally, we close with future directions and outlook.

Figure 2. Schematics of the transient absorption microscopy set up. AOM, acousto-optic modulator; APD, avalanche photodiode; BS, beamsplitter; OPA, optical parametric amplifier. Path 1: Spatial exciton dynamics mapping, where pump and probe beams are always overlapped in spaced. Path 2: exciton transport imaging, where the pump and probe beams are scanned relatively to each other in space. Adapted with permission from ref 22. Copyright 2015 Macmillan Publishers Ltd.

beam is scanned relative to the pump beam by a pair of galvanometer scanners to generate images of the propagation of the excitonic population initially created. In such TAM images, spatial distribution of exciton density as a function of pump− probe delay is directly visualized. At 0 ps, the TAM image represents the initial photogenerated exciton population created by the pump beam. At later delay times, the TAM images reflect exciton diffusion away from the initial excitation volume.

II. ULTRAFAST TRANSIENT ABSORPTION MICROSCOPY TO VISUALIZE EXCITON MIGRATION A schematic illustration of the ultrafast TAM apparatus is shown in Figure 2, and more details can be found in our previous publication.22 To image exciton transport, the probe 1726


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Figure 3. Crystal structure, singlet and triplet energy levels, and pump and probe wavelengths for tetracene, rubrene, and TIPS-pentacene.

below. High detection sensitivity is the key for the success of the exciton transport measurements, and shot-noise limited detection can be achieved by high laser repetition rate coupled with high-speed modulation.20,23 In the measurements described below, either 400 kHz (polyacenes) or 80 MHz (molecular aggregates) laser repetition rate is used.

To quantify exciton transport, the TAM experiments can be modeled to extract exciton population in both time and spatial domains. At zero delay time, the pump beam at position (x0, y0) generates an initial population n(x, y, 0), which can be approximated as a two-dimensional (2D) Gaussian function. ⎡ (x − x )2 (y − y0 )2 ⎤ 0 ⎥ − n(x , y , 0) = N exp⎢ − ⎢⎣ 2σx ,0 2 2σy ,0 2 ⎥⎦

III. SINGLET-MEDIATED TRIPLET TRANSPORT PATHWAYS IN POLYACENES In singlet fission, an excited singlet exciton splits into two triplet excitons as illustrated in Figure 1a.24,25 Singlet fission has been intensively studied as a possible route to overcome the Shockley−Queissier limit because it could potentially double the photocurrent from high-energy photons albeit the triplet excitons provide lower open circuit voltage.26,27 A recent review on singlet fission dynamics can be found in ref 28. Transport of the triplet excitons is critical for the success of singlet fissionbased solar cells due to the need of collecting triplets at the donor−acceptor interfaces.26,27 However, the interplay between singlet fission dynamics and triplet transport is not very well understood. While long-range triplet transport has been observed by PL microscopy,10,11 it has been mainly attributed to the long triplet lifetime with modest diffusion constants via Dexter energy transfer.8 The role of singlet fission dynamics has not yet been fully taken into account. Specifically, the equilibrium between singlet and triplet population should provide a handle for modulating triplet energy transport because singlet excitons diffuse about 3 orders of magnitude faster than triplet excitons.8 There are two ways for triplet excitons to recombine to generate singlet excitons. One is through triplet pairs (Tpair) that directly fuse following singlet fission before they have time to diffuse way from their origins (geminate recombination, pathway 1 in Figure 1a).29 This pathway is independent of triplet density. The other is through free triplet excitons undergoing bimolecular triplet− triplet annihilation after they diffuse away from their origins (nongeminate recombination, pathway 2 in Figure 1a),29 which is dependent on triplet density. Singlet−triplet exciton population interconversion can be described by the following four excited state reactions.

(1)

If the excitonic motion is diffusive, then the population as a function of space and time will be governed by a diffusion equation that includes decay to the ground state: ⎡ ∂n2(x , y , t ) ∂n(x , y , t ) ∂n2(x , y , t ) ⎤ ⎥ = D⎢ + ∂t ∂x 2 ∂y 2 ⎦ ⎣ −

n(x , y , t ) τ

(2)

Here n(x,y,t) is the exciton population at time t, D is the diffusion constant, and τ is the exciton lifetime. The solution to eq 2 shows that the population profile at any later time is also ⎛ (x − x0)2 (y − y )2 ⎞ Gaussian, n(x , y , t ) = N exp⎜ − 2σ 2 − 2σ 02 ⎟, with var⎝ ⎠ x ,t y ,t iances σx(y),t2 given by σx(y),t2 = σx(y),02 + 2Dx(y)t. The exciton transport length, L, at delay time, t, is related to the variance of the exciton density profile and the exciton diffusion constant, Lx(y)2 = σx(y), t 2 − σx(y),0 2 = 2Dx(y)t

(3)

It is important to understand how exciton−exciton annihilation processes impact the spatial distribution of the excitons. Because the exciton density at the center of the spot is higher than that at the edge leading to faster exciton decay, exciton−exciton annihilation could lead to artificial broadening of σ and error in measuring D. In order to correctly account for both exciton diffusion and exciton−exciton annihilations, performing pump fluence dependent measurements is necessary. The precision in determining the exciton propagation distance L is dictated by the smallest measurable change in the population profiles and not directly by the diffraction limit. This spatial precision is ∼50 nm for the experiments described

k fission

S1 ⎯⎯⎯⎯→ Tpair 1727

(4) DOI: 10.1021/acs.accounts.7b00155 Acc. Chem. Res. 2017, 50, 1725−1733

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Figure 4. Triplet and singlet exciton propagation in a single tetracene crystal. (a) TAM images in the a−b plane pumped at 470 nm (300 fJ/pulse) with probe wavelength and polarization to select triplet excitons at different delay pump−probe delays. Color scale represents the intensity of differential transmission (ΔT) of the probe beam. The images show the spatial distribution of the ΔT signal measured at pump−probe delay time as labeled. (b) Probe wavelength and polarization to select singlet excitons at different delay pump−probe delays. (c, d) Cross sections of the TAM images fitted with Gaussian functions from panels a and b, respectively, with the maximum ΔT signal normalized. k fusion

Tpair ⎯⎯⎯⎯→ S1

Examples of TAM images of singlet and triplet exciton transport in a single tetracene crystal are shown in Figure 4. By fitting the TAM images at different delay times with a 2D Gaussian surface function, the fast and slow transport axes can be determined. The anisotropy in transport is due to the different coupling strength between the tetracene molecules along different crystal axes.8 The fast axis is assigned to the b axis, where the coupling is the strongest,8,11 and the slow axis is assigned to the a axis. All the kinetic parameters discussed below are from modeling transport along the b axis. While the intrinsic triplet diffusion constant should be similar for these three crystals based on Dexter energy transfer,8 TAM measurements show that triplet exciton transport length differs greatly in tetracene, rubrene, and TIPS-pentacene.30 Triplet migration is most rapid in tetracene, followed by rubrene, and least rapid in TIPS-pentacene (Figure 4). For tetracene and rubrene, L2 as a function of pump−probe delay deviates significantly from the linear relationship as predicted by eq 3 for a normal diffusive transport. The large difference in triplet exciton transport reflects how the triplet population is coupled to the singlet population through singlet fission process.22 Because singlet excitons diffuse about 3 orders of magnitude faster than triplet excitons,8 triplet exciton transport in the picosecond and nanosecond time scales is controlled by the probability of singlet regeneration. We used the following coupled rate equations to describe the singlet, triplet pair, and free triplet population:

(5)

kdissociation

Tpair ⎯⎯⎯⎯⎯⎯⎯⎯→ 2T1 kannh_TT

2T1 ⎯⎯⎯⎯⎯⎯⎯→ S1 + S0

(6) (7)

Using excited state absorption as the imaging contrast,22 TAM allows for tracking both the bright singlet and the dark triplet population simultaneously and can address directly triplet exciton transport in relation to singlet fission. In our recent studies, single crystals of tetracene, rubrene, and 6,13bis(triisopropylsilylethynyl) pentacene (TIPS-pentacene) were employed as model systems to investigate how singlet fission dynamics can be used to control triplet transport.22,30 Singlet fission dynamics have been extensively studied in these polyacene crystals and thin films with kinetic parameters well established, which makes them ideal model systems.31−35 Singlet fission in tetracene is the most endothermic among the three crystals with a driving force DESF = E(S1) − 2E(T1) of −(0.1−0.2) eV, followed by rubrene with a DESF of approximately −0.05 eV. The singlet energy is close to degenerate with twice the triplet energy in TIPS pentacene (DESF ≈ 0). The probe wavelength and polarization were utilized to select triplet and singlet excited state absorption.22 The triplet exciton absorption dipole (T1−T2) is known to be primarily aligned along the long axis of the molecules while the S0−S1 transition is known to align along the short axis.36 Figure 3 summarizes the pump and probe wavelengths used in the TAM experiments. 1728


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Accounts of Chemical Research Table 1. Fitting Parameters Extracted along the b Axis parameters

tetracene

rubrene

TIPS-pentacene

DT (fast), intrinsic triplet diffusion constant along the fast axis DS (fast), intrinsic singlet diffusion constant along the fast axis kfission, fission rate kfusion, fusion rate kannh_TT, triplet−triplet annihilation

0.0023 cm2 s−111 3.1 cm2 s−1 8.3 × 109 s−1 1.0 × 109 s−1 1.7 × 10−11 cm3 s−1

0.0035 cm2 s−1 2.3 cm2 s−1 1.43 × 1010 s−1 8.3 × 108 s−1 5.1 × 10−12 cm3 s−1

0.006 cm2 s−1 4.5 cm2 s−1 2 × 1011 s−1 5 × 107 s−1 5.0 × 10−12 cm3 s−1

Figure 5. (a) Experimental and simulated time evolution of the spatial profile L2 for tetracene, rubrene, and TIPS-pentacene when probing triplet. (b) Simulation of triplet yield as a function of layer thickness under solar fluences. For a given thickness, the time required for triplet excitons to diffuse is calculated, and then the singlet and triplet population at that time point is extracted from the kinetic model described in the text.

∂nS = DS∇2 nS − k SnS − k fissionnS + k fusionnTpair ∂t

∂nTpair ∂t

+ kannh_TTn T 2

(8)

= k fissionnS − k fusionnTpair − kdissociationnTpair

(9)

The parameters that have the largest difference are the singlet fission and triplet fusion rates. The singlet fission rate constant is 8.3 × 109 s−1, 1.43 × 1010 s−1, and 2 × 1010 s−1, for tetracene, rubrene, and TIPS-pentacene, respectively. The singlet fission rates extracted for tetracene and rubrene agree well with the literature31,32 and that for TIPS-pentacene is consistent with Wong et al.35 but slower than the value reported elsewhere33 attributable to morphological difference. The fusion rate constants extracted were 1.0 × 109 s−1, 8.3 × 108 s−1, and 5 × 107 s−1 for tetracene, rubrene, and TIPS-pentacene, respectively. The triplet fusion rate constant is more than 10 times greater in tetracene and rubrene than that in TIPSpentacene leading to a much more active singlet-mediated triplet transport via pathway 1 shown in Figure 1a. Triplet− triplet annihilation rate is also slightly higher in tetracene than that in rubrene and TIPS-pentacene, indicative of a more efficient nongeminate singlet regeneration (pathway 2 shown in Figure 1a). The TAM measurements have revealed a new picture of how exciton transport is coupled to singlet fission dynamics, in which triplets can migrate as singlet excitons on time scales long after the singlet fission time constant.40 This picture adds crucial details about early time dynamics that cannot be provided by PL studies. For instance, the effective transport length L in 7 ns for triplets in tetracene is 310 nm under solar fluences. Without the singlet contribution, the time required for a triplet exciton to diffuse the same distance would be 340 ns, almost 50 times longer. From the parameters extracted from the TAM measurements, conditions under which triplet yield is optimized can be simulated.30 Triplet yield as a function of film thickness under solar fluences is plotted in Figure 5b. The lifetime of the triplet is set to 10 ns to mimic a real device situation using polycrystalline thin films. Pentacene is also simulated for comparison with the singlet fission rate fixed at 1/ 80 fs.26

∂n T = DT∇2 n T − k Tn T − 2kannh_TTn T 2 + 2kdissociationnTpair ∂t (10)

nS, nTpair, and nT are the density of singlet excitons, triplet pairs, and free triplet excitons, respectively. DT is the diffusion coefficient of the triplet exciton, and DS is that of the singlet exciton. The initial exciton densities created by the pump (on the order of ∼1019 cm−3) in the three materials inevitably led to exciton−exciton annihilation processes. To correctly account for extract exciton diffusion and exciton−exciton annihilation, pump fluence dependent measurements were performed.22,30 It is possible that triplet−triplet annihilations could result in species other than the singlet excitons; however, we did not include these pathways in the current model for simplicity. The extracted triplet annihilation rate constants were adjusted to best fit the pump-fluence dependent dynamics and the rates extracted agree well with the literature.37−39 The key parameters in governing triplet transport in tetracene, rubrene, and TIPS-pentacene are identified in Table 1.30 More details on how the parameters are obtained can be found in our previous publications.22,30 The intrinsic triplet diffusion constants extracted for tetracene, rubrene, and TIPS-pentacene were similar, with values of 0.0023 cm2 s−1, 0.0035 cm2 s−1 and 0.006 cm2 s−1, respectively. DT for tetracene was fixed using the value from delayed fluorescence microscopy measurements.11 Those for rubrene and TIPS-pentacene were adjusted to best fit the time evolution of triplet spatial profile. 1729


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Figure 6. (a) Normalized UV−vis absorption spectra of aggregate and monomer TPPS4 in solution at room temperature. (b) Exciton dynamics measured at the Q-band in the nanotube bundle in Figure 7a at different pump intensities as labeled.

R−6, where R is the separation between the states, the corresponding rate between delocalized states scales less sensitively as a function of R.14,16 Currently, the lack of capability to measure exciton transport with simultaneous nanoscale spatial resolution and femtosecond temporal resolution has prevented coherent effects to be evaluated directly. In the following, we present our initial efforts in imaging exciton transport in molecular aggregates using TAM to address coherent effects. Exciton transport in tubular molecular aggregates derived from meso-tetra(4-sulfonatophenyl) porphyrin (TPPS4) is imaged using methods established in sections II and III.45 TPPS4 aggregates are known to be cylindrical structures with a radius of approximately 16−18 nm and a length of up to several micrometers.45 Figure 1b schematically shows the geometry of a TPPS4 tubular aggregate, where the tubular shape is obtained by rolling a 2D sheet of porphyrin molecules onto a cylindrical surface. For TPPS4 monomer molecules, there are two dominant exciton bands: the high intensity B band and the low intensity Q band. The B band is split into a very narrow red-shifted peak at 490 nm (2.53 eV) and a wider peak at 423 nm (2.93 eV) in the aggregates46 (Figure 6a). The Q band is red-shifted upon aggregation from 647 to 707 and 675 nm (Figure 6a). The red-shift and narrowing of the absorption spectrum are signatures of the formation of delocalized states in J-aggregates. The exciton delocalization size is estimated by accounting for the competition between intermolecular coupling (∼300 cm−1) and static disorder (∼200 cm−1) in TPPS4 tubes, as well as the linear coupling of excitons to vibrational modes.45,47 For the optically dominant exciton states within the Q-band, the delocalization size is 208 ± 152 molecules, while at the absorption maximum of the lower component of the B-band, it reaches 1036 ± 224 molecules. Even though for the Q-band the delocalization of the optically dominant states is large, most of the Q-band excitons are delocalized over a relatively small number of molecules: >70% over less than 10 molecules. The localization is even stronger close to the band bottom: in the low-energy tail of the density of states below 1.68 eV, 99.5% are localized on less than 10 molecules. These weakly delocalized lower-energy states are the ones crucial for the exciton transport.45 Figure 6b displays the exciton dynamics in a small porphyrin nanotube bundle measured by TAM. The nonexponential exciton decay (Figure 6b) has been explained by an inhomogeneous distribution of exciton states, and the few picosecond decay component has been ascribed to the trapping of excitons by lower-energy and more localized states.45 To ensure that exciton−exciton annihilation did not play a role, we

Figure 5b illustrates that triplet yield close to 200% is achievable for all four materials if the appropriate layer thickness is employed. Due to the short exciton diffusion length, the optimal device thickness for pentacene is around 10−25 nm, which is in good accord with the optimized 15 nm device thickness reported.26 In contrast, long-range triplet transport facilitated by singlet-mediated pathways allows for much thicker optimal device thickness of 150 and 260 nm for rubrene and tetracene, respectively. The optimal device thickness on hundreds of nanometer length scale does not contradict the micrometer rubrene single crystal triplet diffusion length predicted by photoconductivity measurements in ref 41 because the triplet lifetime used in our simulation (∼10 ns) for polycrystalline thin films is orders of magnitude shorter than that of the single crystal because of nonradiative quenching and static traps. These results demonstrate that by employing TAM with kinetic modeling, the underlying mechanism of the interplay between dark and bright Frenkel excitons can be revealed.

IV. UNRAVELING COHERENT EFFECTS IN EXCITON TRANSPORT Coherent effects resulting from strong intermolecular coupling are expected to play an important role in exciton transport in molecular aggregates and photosynthetic antenna systems.4 Self-assembled molecular aggregates are suitable candidates to attain long-range transport, because they offer the potential to control coherent and incoherent motions through modulating intermolecular coupling.13 In these aggregates, excitons are delocalized over part of the system and the delocalization (coherent) length is defined by the competition between intermolecular coupling strength and disorder.42 Micrometer long exciton transport has recently been visualized by PL microscopy in one-dimensional H-aggregate molecular fibers at room temperature, where transport is postulated to be predominantly coherent.13 Such long-range exciton transport in molecular assemblies is remarkable because it demonstrates that macroscopic transport is possible in lower dimensional aggregates by controlling intermolecular coupling. Recent measurements by exciton−exciton annihilation in molecular aggregates have inferred diffusion constant as high as 55 cm2 s−1,43 also suggesting the importance of coherent effects. In principle, delocalized excitons accelerate energy transfer and facilitate long-range transport in three ways. First, within each delocalized segment the excitation energy propagates ballistically, compared to the diffusive hopping described FRET.44 Second, the energy transfer between two delocalized segments is enhanced by the supertransfer effect.15 Lastly, while the classical FRET rate between two localized states scales as 1730


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Figure 7. (a) TAM image of the sample area at 0 ps pump probe delay. Pump and probe beams are overlapped in space. Scale bar 1 μm. (b) TAM images of exciton propagation at different pump−probe delay times for the bundle of nanotubes as marked in panel a. The images show the spatial distribution of the ΔT signal measured at pump−probe delay times as labeled. Scale bar 0.5 μm. (c) Cross sections of the TAM images along the long axis fitted with Gaussian functions at different delay times with the maximum ΔT signal normalized to unity. (d) L2 as a function of pump− probe delay time (symbols), with a linear fit to eq 3 (line), which yields a diffusion constant of 6.4 ± 0.2 cm2 s−1.

aggregates by employing ultrafast TAM with simultaneous spatial and temporal resolution. Such an approach establishes an initial step toward discerning the underlying excitation energy transport mechanisms in organic materials. An important future direction is to elucidate coherent and incoherent pathways in exciton transport. Understanding exciton transport with mixed coherent and incoherent characteristics is important for achieving desirable long-range transport because energy transfer in this regime could be enhanced compared to the incoherent hopping mechanism assumed by FRET.15,44 As shown by our initial work on molecular aggregates that coherent effects play a role even when exciton delocalization is not extensive, further work will be needed to quantify the coherent and incoherent contributions. Future measurements on systems with more extensive exciton delocalization, such as in double-walled carbocyanine tubular aggregates43 and one-dimensional Haggregate molecular fibers,13 will allow for differentiating coherent and incoherent transport regimes. Other systems such as molecular π-stacks where both long-range coupling and short-range coupling48 are tunable will also be useful for the further elucidation of coherent effects. Performing ultrafast microscopy measurements over a wide temperature range with improved temporal resolution will be necessary for differentiating coherent and incoherent pathways. Because scattering of excitons by phonons (vibrations) is less efficient at low temperature, coherence size (delocalization) of exciton increases as temperature decreases. In addition, coherent and incoherent energy transport should exhibit different temperature dependence; coherent transport should increase as temperature decreases while the opposite is true for incoherent transport. Further expansion of ultrafast microscopy toolsets will also be desirable. Combining two-dimensional electronic spectroscopy with microscopy techniques49 can be a powerful means to provide phase-sensitive information that can measure the spatial extent of the coherent transport directly. Finally, direct measurements of exciton transport in both the spatial and temporal domains can provide important parameters to refine energy transfer theories. A unified theoretical treatment for exciton transport that includes both coherent and incoherent effects to satisfactory degrees is yet to be attained. Further improving these theories of energy transfer with the aid of new experimental techniques to provide a detailed picture of dynamics and transport of exciton will be timely.

carried out pump intensity dependent studies by measuring TAM dynamics (Figure 6b). Negligible pump intensity dependence was found on the experimental range of 0.4−4.1 μJ/cm2, and therefore exciton−exciton annihilation was insignificant. The probe wavelength was in resonance with the lowest-energy exciton band (Q-band) and the polarization was set to be parallel to the porphyrin nanotube long axis for exciton transport for a small porphyrin nanotube bundle as marked in Figure 7a. The broadening of the exciton profile (Figure 7b,c) was found only to occur along the aggregation axis of the porphyrin tube.45 Although the number of data points is limited, Figure 7d suggests a linear dependence of L2 on time, indicative of diffusive exciton transport on the picosecond time scale. D = 6.4 ± 0.2 cm2 s−1 is obtained for the particular bundle of tubes imaged in Figure 7. The TAM results for two other bundles of nanotubes result in diffusion constants of 3.0 ± 0.2 and 5.4 ± 2.3 cm2 s−1. We compare the experimentally measured exciton diffusion constant to the simulation by the incoherent Haken− Strobl−Reineker (HSR) model.7 Assuming the limit where dephasing has rendered the transport process to an entirely incoherent hopping between individual molecules, the transport is diffusive, and within the HSR model, a simple expression can be obtained for the diffusion tensor.7 The details of the theoretical simulation can be found in our recent publication.45 As a result, a theoretical estimate for the incoherent diffusion constant along the axis of a porphyrin nanotube of 1.20 cm2 s−1 can be obtained. The measured exciton diffusion constants of 3−6 cm2 s−1 in tubular TPPS4 aggregates, 3−5 times higher than the lower bound incoherent hopping limit, suggest that coherent effects play a role, albeit that they do not lead to a huge enhancement. The exciton diffusion constants measured by TAM for the TPPS4 aggregates are about an order of magnitude smaller than those estimated from exciton−exciton annihilation for doublewalled carbocyanine tubular aggregates by Caram et al.43 This is consistent with the overall lower static disorder (115 cm−1) and higher intermolecular coupling (688 cm−1) in the carbocyanine tubular aggregates, which leads to larger exciton delocalization sizes.43 Caram et al.43 also found a good agreement between their experiments and estimates from a disorder-based model.

V. CONCLUSIONS AND OUTLOOK In this Account, we described the progress in directly visualizing Frenkel exciton motion in molecular crystals and 1731


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(9) Lunt, R. R.; Benziger, J. B.; Forrest, S. R. Relationship between Crystalline Order and Exciton Diffusion Length in Molecular Organic Semiconductors. Adv. Mater. 2010, 22, 1233−1236. (10) Irkhin, P.; Biaggio, I. Direct Imaging of Anisotropic Exciton Diffusion and Triplet Diffusion Length in Rubrene Single Crystals. Phys. Rev. Lett. 2011, 107, 017402. (11) Akselrod, G. M.; Deotare, P. B.; Thompson, N. J.; Lee, J.; Tisdale, W. A.; Baldo, M. A.; Menon, V. M.; Bulović, V. Visualization of exciton transport in ordered and disordered molecular solids. Nat. Commun. 2014, 5, 3646. (12) Clark, K. A.; Krueger, E. L.; Vanden Bout, D. A. Direct Measurement of Energy Migration in Supramolecular Carbocyanine Dye Nanotubes. J. Phys. Chem. Lett. 2014, 5, 2274−2282. (13) Haedler, A. T.; Kreger, K.; Issac, A.; Wittmann, B.; Kivala, M.; Hammer, N.; Köhler, J.; Schmidt, H.-W.; Hildner, R. Long-range energy transport in single supramolecular nanofibres at room temperature. Nature 2015, 523, 196−199. (14) Jang, S.; Newton, M.; Silbey, R. Multichromophoric Förster Resonance Energy Transfer. Phys. Rev. Lett. 2004, 92, 218301. (15) Chuang, C.; Knoester, J.; Cao, J. Scaling relations and optimization of excitonic energy transfer rates between one-dimensional molecular aggregates. J. Phys. Chem. B 2014, 118, 7827−7834. (16) Chuang, C.; Lee, C. K.; Moix, J. M.; Knoester, J.; Cao, J. Quantum Diffusion on Molecular Tubes: Universal Scaling of the 1D to 2D Transition. Phys. Rev. Lett. 2016, 116, 196803. (17) Tamai, N.; Porter, C. F.; Masuhara, H. Femtosecond transient absorption spectroscopy of a single perylene microcrystal under a microscope. Chem. Phys. Lett. 1993, 211, 364−370. (18) Van Dijk, M. A.; Lippitz, M.; Orrit, M. Detection of Acoustic Oscillations of Single Gold Nanospheres by Time-Resolved Interferometry. Phys. Rev. Lett. 2005, 95, 267406. (19) Muskens, O. L.; Del Fatti, N.; Vallée, F. Femtosecond response of a single metal nanoparticle. Nano Lett. 2006, 6, 552−556. (20) Huang, L.; Cheng, J.-X. Nonlinear Optical Microscopy of Single Nanostructures. Annu. Rev. Mater. Res. 2013, 43, 213−236. (21) Devadas, M. S.; Devkota, T.; Johns, P.; Li, Z.; Lo, S. S.; Yu, K.; Huang, L.; Hartland, G. V. Imaging nano-objects by linear and nonlinear optical absorption microscopies. Nanotechnology 2015, 26, 354001. (22) Wan, Y.; Guo, Z.; Zhu, T.; Yan, S.; Johnson, J.; Huang, L. Cooperative singlet and triplet exciton transport in tetracene crystals visualized by ultrafast microscopy. Nat. Chem. 2015, 7, 785−792. (23) Chong, S.; Min, W.; Xie, X. S. Ground-state depletion microscopy: detection sensitivity of single-molecule optical absorption at room temperature. J. Phys. Chem. Lett. 2010, 1, 3316−3322. (24) Merrifield, R. E.; Avakian, P.; Groff, R. P. Fission of singlet excitons into pairs of triplet excitons in tetracene crystals. Chem. Phys. Lett. 1969, 3, 386−388. (25) Smith, M. B.; Michl, J. Singlet fission. Chem. Rev. 2010, 110, 6891−6936. (26) Congreve, D. N.; Lee, J.; Thompson, N. J.; Hontz, E.; Yost, S. R.; Reusswig, P. D.; Bahlke, M. E.; Reineke, S.; Van Voorhis, T.; Baldo, M. A. External quantum efficiency above 100% in a singlet-excitonfission-based organic photovoltaic cell. Science 2013, 340, 334−337. (27) Ehrler, B.; Wilson, M. W. B.; Rao, A.; Friend, R. H.; Greenham, N. C. Singlet exciton fission-sensitized infrared quantum dot solar cells. Nano Lett. 2012, 12, 1053−1057. (28) Piland, G. B.; Burdett, J. J.; Dillon, R. J.; Bardeen, C. J. Singlet Fission: From Coherences to Kinetics. J. Phys. Chem. Lett. 2014, 5, 2312−2319. (29) Bayliss, S. L.; Chepelianskii, A. D.; Sepe, A.; Walker, B. J.; Ehrler, B.; Bruzek, M. J.; Anthony, J. E.; Greenham, N. C. Geminate and Nongeminate Recombination of Triplet Excitons Formed by Singlet Fission. Phys. Rev. Lett. 2014, 112, 238701. (30) Zhu, T.; Wan, Y.; Guo, Z.; Johnson, J.; Huang, L. Two Birds with One Stone: Tailoring Singlet Fission for Both Triplet Yield and Exciton Diffusion Length. Adv. Mater. 2016, 28, 7539−7547.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Libai Huang: 0000-0001-9975-3624 Author Contributions #

T.Z. and Y.W. equally contributed.

Notes

The authors declare no competing financial interest. Biographies Tong Zhu is a graduate student in the Department of Chemistry at Purdue University. She received her B.S. degree from Harbin Institute of Technology, China. She is currently a Ph.D. candidate and looking forward to receiving her Ph.D. degree in summer 2017. Her current research interests focus on imaging Frenkel exciton transport in molecular systems as well as studying charge and energy transfer at organic−inorganic van der Waals heterostructures interfaces using ultrafast pump−probe microscopy. Yan Wan received his B.S. in 2004 from Tsinghua University (Beijing) and his Ph.D. from Institute of Chemistry, Chinese Academy of Sciences, in 2010. He is currently a postdoctoral research associate in the Department of Chemistry at Purdue University. His research currently focuses on energy transport in organic semiconductors visualized by ultrafast microscopy. Libai Huang is currently an Assistant Professor in the Department of Chemistry at Purdue University. She received her B.S. from Peking University in 2001 and her Ph.D. from University of Rochester in 2006. She joined the Purdue faculty in 2014. Her research program is aimed at directly imaging energy and charge transport with femtosecond time resolution and nanometer spatial resolution to elucidate energy and charge transfer mechanisms.

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ACKNOWLEDGMENTS We acknowledge the support from US National Science Foundation through Grant NSF-CHE-1555005. We thank our collaborators, Dr. Justin Johnson, Dr. Anna Stradomska, and Prof. Jasper Knoester, for contributing to the research discussed in this Account.

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REFERENCES

(1) Davydov, A. S. Theory of Molecular Excitons; Springer US: Boston, MA, 1971. (2) Bardeen, C. J. The structure and dynamics of molecular excitons. Annu. Rev. Phys. Chem. 2014, 65, 127−148. (3) Scholes, G. D.; Rumbles, G. Excitons in nanoscale systems. Nat. Mater. 2006, 5, 683−696. (4) Scholes, G. D.; Fleming, G. R.; Olaya-Castro, A.; Van Grondelle, R. Lessons from nature about solar light harvesting. Nat. Chem. 2011, 3, 763−774. (5) Gregg, B. Excitonic solar cells. J. Phys. Chem. B 2003, 107, 4688− 4698. (6) Mikhnenko, O. V.; Blom, P. W. M.; Nguyen, T.-Q. Exciton diffusion in organic semiconductors. Energy Environ. Sci. 2015, 8, 1867−1888. (7) Haken, H.; Strobl, G. An exactly solvable model for coherent and incoherent exciton motion. Z. Phys. A: Hadrons Nucl. 1973, 262, 135− 148. (8) Yost, S. R.; Hontz, E.; Yeganeh, S.; Van Voorhis, T. Triplet vs Singlet Energy Transfer in Organic Semiconductors: The Tortoise and the Hare. J. Phys. Chem. C 2012, 116, 17369−17377. 1732


Article

Accounts of Chemical Research (31) Burdett, J. J.; Bardeen, C. J. The Dynamics of Singlet Fission in Crystalline Tetracene and Covalent Analogs. Acc. Chem. Res. 2013, 46, 1312−1320. (32) Ma, L.; Zhang, K.; Kloc, C.; Sun, H.; Michel-Beyerle, M. E.; Gurzadyan, G. G. Singlet fission in rubrene single crystal: direct observation by femtosecond pump-probe spectroscopy. Phys. Chem. Chem. Phys. 2012, 14, 8307−8312. (33) Yost, S. R.; Lee, J.; Wilson, M. W. B.; Wu, T.; McMahon, D. P.; Parkhurst, R. R.; Thompson, N. J.; Congreve, D. N.; Rao, A.; Johnson, K.; Sfeir, M. Y.; Bawendi, M. G.; Swager, T. M.; Friend, R. H.; Baldo, M. A.; Van Voorhis, T. A transferable model for singlet-fission kinetics. Nat. Chem. 2014, 6, 492−497. (34) Wilson, M. W. B.; Rao, A.; Johnson, K.; Gélinas, S.; di Pietro, R.; Clark, J.; Friend, R. H. Temperature-Independent Singlet Exciton Fission in Tetracene. J. Am. Chem. Soc. 2013, 135, 16680−16688. (35) Wong, C. Y.; Cotts, B. L.; Wu, H.; Ginsberg, N. S. Exciton dynamics reveal aggregates with intermolecular order at hidden interfaces in solution-cast organic semiconducting films. Nat. Commun. 2015, 6, 5946. (36) Tavazzi, S.; Raimondo, L.; Silvestri, L.; Spearman, P.; Camposeo, A.; Polo, M.; Pisignano, D. Dielectric tensor of tetracene single crystals: The effect of anisotropy on polarized absorption and emission spectra. J. Chem. Phys. 2008, 128, 154709. (37) Poletayev, A. D.; Clark, J.; Wilson, M. W. B.; Rao, A.; Makino, Y.; Hotta, S.; Friend, R. H. Triplet Dynamics in Pentacene Crystals: Applications to Fission-Sensitized Photovoltaics. Adv. Mater. 2014, 26, 919−924. (38) Biaggio, I.; Irkhin, P. Extremely efficient exciton fission and fusion and its dominant contribution to the photoluminescence yield in rubrene single crystals. Appl. Phys. Lett. 2013, 103, 263301. (39) Ryasnyanskiy, A.; Biaggio, I. Triplet exciton dynamics in rubrene single crystals. Phys. Rev. B: Condens. Matter Mater. Phys. 2011, 84, 193203. (40) Roberts, S. T. Energy transport: Singlet to triplet and back again. Nat. Chem. 2015, 7, 764−765. (41) Najafov, H.; Lee, B.; Zhou, Q.; Feldman, L. C.; Podzorov, V. Observation of long-range exciton diffusion in highly ordered organic semiconductors. Nat. Mater. 2010, 9, 938−943. (42) Fidder, H.; Knoester, J.; Wiersma, D. A. Optical properties of disordered molecular aggregates: A numerical study. J. Chem. Phys. 1991, 95, 7880−7890. (43) Caram, J. R.; Doria, S.; Eisele, D. M.; Freyria, F. S.; Sinclair, T. S.; Rebentrost, P.; Lloyd, S.; Bawendi, M. G. Room-Temperature Micron-Scale Exciton Migration in a Stabilized Emissive Molecular Aggregate. Nano Lett. 2016, 16, 6808−6815. (44) Lloyd, S.; Mohseni, M. Symmetry-enhanced supertransfer of delocalized quantum states. New J. Phys. 2010, 12, 075020. (45) Wan, Y.; Stradomska, A.; Knoester, J.; Huang, L. Direct Imaging of Exciton Transport in Tubular Porphyrin Aggregates by Ultrafast Microscopy. J. Am. Chem. Soc. 2017, 139, 7287−7293. (46) Stradomska, A.; Knoester, J. Shape of the Q band in the absorption spectra of porphyrin nanotubes: Vibronic coupling or exciton effects? J. Chem. Phys. 2010, 133, 094701. (47) Wan, Y.; Stradomska, A.; Fong, S.; Guo, Z.; Schaller, R. D.; Wiederrecht, G. P.; Knoester, J.; Huang, L. Exciton Level Structure and Dynamics in Tubular Porphyrin Aggregates. J. Phys. Chem. C 2014, 118, 24854−24865. (48) Yamagata, H.; Maxwell, D. S.; Fan, J.; Kittilstved, K. R.; Briseno, A. L.; Barnes, M. D.; Spano, F. C. HJ-Aggregate Behavior of Crystalline 7,8,15,16-Tetraazaterrylene: Introducing a New Design Paradigm for Organic Materials. J. Phys. Chem. C 2014, 118, 28842− 28854. (49) Hildner, R.; Brinks, D.; Nieder, J. B.; Cogdell, R. J.; Van Hulst, N. F. Quantum coherent energy transfer over varying pathways in single light-harvesting complexes. Science 2013, 340, 1448−1451.

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