Single Lévy States–Disorder Induced Energy Funnels in Molecular

Letter pubs.acs.org/NanoLett

Single Lévy States−Disorder Induced Energy Funnels in Molecular Aggregates Aboma Merdasa,† Á ngel J. Jiménez,‡ Rafael Camacho,† Matthias Meyer,† Frank Würthner,‡ and Ivan G. Scheblykin*,† †

Chemical Physics, Lund University, P.O. Box 124, 22100 Lund, Sweden Institut für Organische Chemie and Center for Nanosystems Chemistry, Universität Würzburg, , Am Hubland, 97074 Würzburg, Germany

‡

S Supporting Information *

ABSTRACT: Using fluorescence super-resolution microscopy we studied simultaneous spectral, spatial localization, and blinking behavior of individual 1D J-aggregates. Excitons migrating 100 nm are funneled to a trap appearing as an additional red-shifted blinking fluorescence band. We propose that the trap is a Frenkel exciton state formed much below the main exciton band edge due to an environmentally induced heavy-tailed Lévy disorder. This points to disorder engineering as a new avenue in controlling light-harvesting in molecular ensembles

KEYWORDS: J-aggregates, Lévy distribution, super-resolution microscopy, single molecule spectroscopy, Frenkel excitons, energy funneling

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technology, particularly in ordered molecular systems for organic photovoltaics. J-aggregates are highly ordered, self-assembled ensembles of dye molecules. Resonance interaction between the dye molecules leads to delocalization of the excited states over many molecules resulting in a bathochromic shift of the absorption band. J-aggregates can be understood as lowdimensional molecular crystals, having Frenkel excitons as excited states.8−11 Because Nature employs J-aggregates for energy transport in photosynthetic systems,12 they are of significant importance and are much discussed in literature,13 recently often in relation to the role of electronic coherences for light-harvesting.14−17 Classical J-aggregates are formed by aggregation of cyanine dyes in aqueous solutions containing high concentrations of salts.13,18−20 For many applications, one needs to create conditions for J-type self-assembly in other media (e.g., organic solvents) than highly polar salt-containing aqueous solutions. In fact, this is much more difficult to realize than aggregates characterized by H-type excitonic coupling. The reason is given by the fact that the dyes need to be displaced from the abundant cofacial stacking arrangement directed by van der Waals interactions,21 which can be achieved by suitably

he issue of randomness versus order in Nature definitely invites a discussion hard to tame. Over two centuries ago, renowned mathematicians Adrian, Gauss, and Laplace formulated the normal distribution and central limit theorem, which since have been used to describe a vast diversity of natural phenomena. However, over recent years there has been a growing understanding that a correct description of many physical phenomena requires thinking beyond Gaussian statistics, namely application of so-called heavy-tailed probability distributions. Because of the heavy (slowly decaying) tails, highly improbable (if one thinks in terms of Gaussian statistics) events can occur, and often such events play the most crucial role in the system behavior. This is the reason, for example, for stock market crashes,1 and biodiversity where long-range spatial interactions of a species cause drastic sustainability issues to the ecosystem as a whole.2 In physics, heavy-tailed distributions, for example, are involved when atoms come to rest in laser cooling,3 power laws in fluorescence intermittency,4 and anomalous diffusion.5 One of the fundamental reasons of non-Gaussian statistics is the presence of hidden correlations (or interactions) between fluctuating systems, which is nicely illustrated by non-Gaussian spectral lineshapes of impurities in crystals.6,7 Because of the crucial role non-Gaussian statistics can play in material properties, it is important to understand where and why such heavy-tailed distributions arise and how these can be controlled in order to be used for high-impact © XXXX American Chemical Society

Received: June 6, 2014 Revised: October 10, 2014

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Figure 1. Schematics showing aggregates in different environments and their respective fluorescence spectra (a1−a4). The single-aggregate sample spectrum is a normalized sum of 217 individual aggregate spectra. The spectrum is cut at 660 nm due to the long-pass filter used to block the 640 nm excitation light. For all other samples, 514 nm excitation was used. From the aggregates in solution (a1) to the drop-cast sample at room temperature (a2), we observe a red-shift of the fluorescence band. Cooling the drop-cast sample to 77 K induces an additional red shift of the peak (a3). The single aggregate sample at 77 K (a4) shows an additional 5 nm red shift in comparison to the drop-cast sample. There is also a progressive broadening of the band from aggregates in the solution to single-aggregates on the substrate. (b) Molecular structure and packing of PBI-1 Jaggregates in a 1D aggregate.20 The gray and light blue “insulation” around the aggregate (shown in red) is formed by the side groups of each PBI-1 molecule. Such insulation preserves 1D structure of the aggregate.

fluctuations of the intermolecular interaction due to, for example, local geometrical distortion of the aggregate. Usually, the fluctuations are assumed to obey Gaussian distributions. The level of the disorder is then characterized by the ratio of the standard deviation (σ) of the corresponding distribution and the resonance interaction (J) between the monomers. Large disorder in natural aggregates like LH2, FMO, chlorosomes etc. (σ/J ≈ 1) leads to fast exciton trapping and very strong dephasing. Conjugated polymers have even larger disorder but still exhibit pronounced J- and H-aggregate characteristics in some cases.25−29 Classical J-aggregates,18 however, possess much lower disorder and stronger interaction in comparison to the natural antenna systems. There are examples of J-aggregates where the σ/J ratio is as small as 0.1,10 meaning that excitons can propagate as coherent wave-packets over large distances before dephasing. This has been observed at low temperatures,24,30 making J-aggregates very interesting model systems for understanding energy transfer mechanisms over large distances.31 Further, it has been theoretically

positioned hydrogen bonds or metallosupramolecular interactions.20 However, the efforts encountered by the design of such dye aggregates are justified because J-aggregation is probably the only way to realize extremely high concentrations of chromophores (essentially as dense as one can possible pack them) without the penalty of severe concentration quenching.22 J-aggregates often possess a high fluorescence yield together with a very large transition dipole moment and offer extremely efficient energy migration.23,24 Accordingly, J-aggregates are of interest for many photonic applications and are also becoming relevant in emerging photovoltaic technology due to the need of systems with defined spectral properties, high absorption cross-section and excellent mobility of excitations and charges. Properties of the exciton states in molecular aggregates depend heavily on so-called disorder, which is the variation of transition energies of the aggregated monomers and/or variations of the resonance intermolecular interactions (J) between the monomers. The origin of the disorder is in the variation of the local environment of the monomers leading to fluctuations of the monomer transition energies and/or B

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Figure 2. (a) Fifteen fluorescence spectra of individual aggregates (red curves, averaged over the whole observation period) compared to the dropcast sample spectrum (black curves), all at 77 K. A reference line is drawn at 700 nm in each graph. (b) Spectra for each frame for the aggregate #78 where the two colors represent the two clusters extracted with the SVD and Hierarchical Clustering methods. (c) Result of the double-peak Gaussian−Lorentzian fit applied to the spectra of cluster 2. The width of the red band is ∼900 cm−1.

consisting of a couple of hundreds of molecules in an organic solvent, which can be transferred to a surface.40 The relatively small length of the isolated aggregates allowed us to observe the excitonic phenomena hidden behind the ensemble averaging. Moreover, the true 1D geometry allows direct comparison between experiment and theory because most of the theoretical studies of J-aggregates consider 1D systems. In our study, we combined spectroscopy and superresolution localization imaging.41−44 We were not only able to see that energy transfer happens but also determine its distance and direction. We inferred an extremely efficient longrange exciton migration within an aggregate on the order of 100 nm in length to a single localized exciton state. Using a theoretical model, we showed that a single low-energy exciton state cannot be formed if the disorder in the aggregate obeys the commonly used Gaussian statistics. Instead, so-called heavytailed distributions, often referred to as Lévy α-stable distributions, must be used. J-aggregates of PBI-1 dye are formed via hydrogen bonding and π−π stacking interaction when the dye is dissolved in low polarity solvents such as methylcyclohexane (MCH); dissolving in more polar solvents, such as dichloromethane (DCM), keeps the dye in its monomeric form.20 We prepared samples of PBI-1 J-aggregates at high and low concentration on Si/SiO2 substrates with a 109 nm thick thermal oxide layer. The highly concentrated sample, hereafter referred to as the drop-cast sample, was prepared by dropcasting a 1 mM MCH solution of PBI-1. The low concentrated sample, hereafter referred to as the single-aggregate sample, was prepared by spin-casting a 1 μM solution at 3000 rpm. The solution was spin-cast immediately after its preparation from

discussed that there is a potential to control the exciton migration direction through the local environment.32 The ability to control the optical response of an artificial nanosystem through chemical and morphological engineering has been vital for the development of organic photovoltaics. A number of these systems are used for light-harvesting where absorption and emission features are altered through morphological engineering. Currently, much effort is being put toward manipulating a nanosystem’s size and shape for desired optical properties.33 However, the control of energy funneling direction is probably the most important for creating light-driven molecular chemical machines. Could disorder engineering be a complementing factor to control the excitation transport and optical properties of organic materials? Single molecule spectroscopy has proven to be the most powerful tool to reveal underlying physical mechanisms behind the commonly observed ensemble averaged properties of molecules, aggregates, and other nanosystems.34 Single molecular aggregate spectroscopy allows extracting information about individual exciton levels.35−38 The difficulty, however, is that classical J-aggregates formed in aqueous solutions usually do not keep their structure when cast on a surface. It has been recently demonstrated that individual tubular J-aggregates immobilized on a surface can be studied experimentally.39 However, the reported excitonic properties of these tubular aggregates were still ensemble averaged due to a single aggregate consisting of tens of thousands of the dye molecule and having only a quasi 1D (tubular) geometry. Here we present an experimental study of isolated Jaggregates having a pure 1D structure. A perylene bisimide dye (PBI-1, Figure 1b)20 forms very stable 1D aggregates C

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Figure 3. Correlation between the fluorescence spectral (a), intensity (b), and spatial (c) dynamics of aggregate #78; (a,b) share the same horizontal scale. The data points belonging to clusters 1 and 2 are shown by blue and red color, respectively. In (b), each frame is plotted as either a blue square (cluster 1) or red circle (cluster 2). (d) Schematic of how the mean position drastically jumps by tens of nanometers as the red band switches on and off; the arrows illustrate energy transfer (see the text for details). The video corresponding to this data is called SI-M78 and can be found in Supporting Information SI−IV.

the 1 mM solution because such strong dilution leads to disaggregation of the molecules within a shorrt period of time.40 We found that treating the silica substrate surface with UV radiation prior to spin-casting (the standard procedure for removing residual luminescence45) reduced the fluorescence quantum yield of the J-aggregates significantly (5−10 times). We also know that any contact with water interferes with the hydrogen bonding between the dyes and deforms the supramolecular J-aggregate architecture.46 Therefore, the silica substrates were used directly out of the box without any treatment or cleaning. The sample was placed in vacuum at 77 K using a liquid nitrogen cryostat. Its fluorescence was detected by an inverted fluorescence microscope with a dry objective lens (40× Olympus LUCPlanFl, NA = 0.6). A 640 nm diode laser and 514 nm line of an argon-ion laser were used for fluorescence excitation. Sequential series of images (“movies”) were acquired at 100 ms exposure time per image (referred to as acquisition frames). A transmission grating was placed in front of the camera where the zero order (image) and first order (spectrum) diffractions were imaged onto different parts of the EMCCD chip. Therefore, the setup was able to simultaneously measure fluorescence spectra, intensity, as well as the emission pattern of an individual aggregate, allowing spatial localization of the emission centroid position with nanometer accuracy using a postprocessing technique. The intensity of individual aggregates was also measured as a function of the orientation of the polarization plane of the excitation light (633 nm) and orientation of a fluorescence analyzer placed in front of the EMCCD camera. This method,

called two-dimensional polarization imaging (2D-POLIM), is explained in detail elsewhere.47 Figure 1a shows fluorescence spectra of PBI-1 J-aggregates in different environments and at different temperatures (see Supporting Information Figure SI-1 for absorption spectra of the monomers and aggregates in solution). In comparison with the solution sample spectrum, J-aggregates dispersed at high concentration on a silica substrate showed a red-shifted spectrum. An additional red shift was observed when cooling the samples down to 77 K. This illustrates the influence of the environment on the J-aggregate spectral characteristics. Individual aggregates exhibited large spectral fluctuations throughout the entire observation time period as well. Figure 2a shows the emission spectra of 15 individual aggregates (singleaggregate sample) plotted against the ensemble spectrum of the highly concentrated drop-cast sample at 77 K. These Jaggregates possess different spectra with a tendency to have an additional second red-shifted band. This must be due to each aggregate in the single-aggregate sample experiencing a different local environment. We investigated these spectral fluctuations by looking at the spectral dynamics of individual aggregates throughout the acquisition time. The 15 aggregate spectra shown in Figure 2a possessed the largest spectral fluctuations. They were sorted out using statistical methods including singular value decomposition (SVD) and Hierarchical Clustering outlined in detail in Supporting Information SI−II. Among all investigated aggregates, the one labeled #78 in Figure 2a had the largest fluctuations according to the analysis. The analysis procedure divided all spectra from all frames of D

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blinking or spectral and spatial localization fluctuations. Fluorescence detected linear dichroism (FDLD) of individual aggregates showed a broad distribution, indicating that the aggregates were not straight but rather possessed wormlike conformations in agreement with previous AFM studies.20,46 The fluorescence emission polarization degree of the aggregate was usually higher than the FDLD of the same aggregate, suggesting energy funneling (see Supporting Information SI− V). Quantitatively, energy funneling can be characterized by applying the single funnel approximation.51 This analysis (Figure 4) showed a large fraction of individual aggregates

aggregate #78 into either cluster 1 (blue lines) or cluster 2 (red lines) as shown in Figure 2b. For each cluster the mean spectrum is plotted in yellow. It becomes evident that the spectra belonging to cluster 2 all contain the characteristic spectrum of cluster 1 (centered at 665 nm) and an additional band centered at ∼700 nm. To separate these two bands we applied a double-band (blue and red) mixed Gaussian− Lorentzian fit to the spectra (see Figure 2c and Supporting Information Figure SI-2). The emission of the aggregate therefore appears to always consist of emission from the “blue” band, while the contribution of the “red” band fluctuates with time (see Supporting Information SI−II). Figure 3 shows the time-evolution of the spectra (a) and total intensity (b) where the red band fluctuations become clear. The fluorescence intensity was normalized to the excitation power density and expressed in the units of Brightness and showed pronounced blinking.40 Applying a super-resolution microscopy technique, the spatial localization of the emission was acquired by fitting a 2D Gaussian surface to the emission profile of the aggregate in each frame and is plotted in Figure 3c. As one can see, the centroid coordinates form the same well-separated clusters in space as the corresponding data points form in the spectral and intensity measurement domains. The clusters are marked in red and blue color in the figure. The collective blinking behavior, when the fluorescence of a multichromophoric systems switches “on” and “off”,43,48,49 has already been reported for J-aggregates of PBI-1, which is a signature of efficient energy transfer over the aggregates to a photogenerated quencher.40 Here we observed that blinking clearly correlates with the spectral and spatial localization fluctuation (Figures 3a−c). Correlated fluctuations in intensity, spectral, and spatial domains were not only seen in aggregate #78. A statistical analysis of the individual aggregates plotted in Figure 2a showed similar results, detailed in Supporting Information SI− III. Aggregate #78 was selected only for showing the clearest correlations. Supporting Information SI−IV contains additional movies and descriptions of analyzed aggregates where correlations are clearly observed. It is evident that the “blue” fluorescence band for aggregate #78 was always present in the emission throughout the entire acquisition while the “red” band was solely responsible for the intensity fluctuations (Figures 3a,b). The difference between the mean spatial position of the two clusters was about 50 nm, which is substantially larger the experimental accuracy.50 The evident “on−off” behavior in the intensity, spectral, and spatial domains suggests that there is a single state responsible for the red fluorescence band, whereas the stable blue-band emission is typical for emission from many independent sites. As schematically illustrated in Figure 3d, because the emission of cluster 1 was coming from many sites, the 50 nm jump of the mean position suggests that the aggregate #78 could easily be 100 nm or longer. The emission of the red band contributes approximately 50% to the total fluorescence signal, meaning that the excitons from approximately a half of the aggregate were funneled to a single low energy state, which works as a fluorescent trap. The 2D-POLIM measurement of individual J-aggregates was used to verify the presence of localized low-energy emissive traps and obtain independent information about the exciton migration. The advantage of this method is that it allows an assessment of energy transfer without relying on fluorescence

Figure 4. Histograms showing (a) the modulation depth of funnel (Mf) and (b) energy funneling efficiency (ε) for 223 individual aggregates, as well as the correlation between Mf and ε (c). Average values of Mf and ε are indicated. There is a large fraction of aggregates where nearly all excitons emit from a single localized trap with Mf ≈ 1.

possessing energy funneling with large, often 100% efficiency (ε = 1), toward fluorescent traps having a strongly linearly polarized emission (emission polarization degree or modulation depth of the funnel, Mf ≈ 1). A high Mf is only possible if the emitting state is indeed localized on a small, straight part of a curved, wormlike 1D aggregate, which is in agreement with our hypothesis. One could argue that the “red” band is the emission of a localized defect site, for example, a chemically modified PBI-1 molecule. We think that it is unlikely that a chemical defect would accidentally have the properties of a perfect exciton trap, namely possessing not only the transition energy slightly lower than the excitonic transition (on the contrary, chemical modification often leads to absorption and emission spectral shift toward shorter wavelengths52) but also a high fluorescence quantum yield. However, the most important observation that demonstrates the excitonic nature of the red band is that it is even narrower than the blue excitonic peak, which we already know exhibits motion narrowing due to wave function delocalization over several PBI-1 monomers.53 Previous measurements of isolated PBI-1 dyes on a glass surface46 yielded a fluorescence spectral width of nearly 2400 cm−1, which is 2.5 times larger than the spectral width of the “red” fluorescence (see Figure 2c). Thus, we conclude that the nature E

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of the red trap must be excitonic. Can this be rationalized in the framework of excitons in disordered systems? Exciton states and optical transitions of a 1D J-aggregate can be described by the Frenkel exciton Hamiltonian of a disordered molecular chain in the nearest-neighbor approximation.54 The disorder is introduced as fluctuations of the monomer transition energy (diagonal disorder) or the intermolecular interactions (off-diagonal disorder). We modeled our system using Gaussian distributions for both types of disorder and as expected,55 the resulting excitonic band structure was similar whether the disorder was diagonal or off-diagonal. With rising disorder-to-interaction ratio (σ/J) we saw a broadening of the exciton band as well as a decrease of the exciton delocalization length. However, the simulation with the Gaussian disorder did not yield any state that could be indicative of a preferential trapping state observed in our experiments. The reason we did not obtain a single state that is significantly different in energy from the rest of the exciton states is that Gaussian distributions do not allow fluctuations significantly larger than the distribution width. Therefore, a different distribution of the disorder must be used (see Supporting Information SI−VI). The Gaussian distribution belongs to a family of symmetric distributions referred to as the Lévy α-stable distributions (hereafter referred to as just Lévy distributions) with mathematical expressions for the characteristic function and distribution according to

Figure 5. A summary of one realization of the exciton Hamiltonian for an aggregate consisting of 250 monomers. The monomer transition energies (a) are distributed according to the Lévy distribution with α = 1.5 (b). The dashed vertical line indicates the monomer number with the lowest transition energy. (c) Exciton state wave functions vertically shifted according to their transition energy are shown. The 60 lowest states are plotted. (d) The oscillator strengths of all plotted exciton states are shown.

ϕα , s(υ) = exp( −s α |υ|α ) P(E) =

1 2π

∞

∫−∞ ϕα ,s(υ)eiEυ dυ

(1)

We suggest that the Lévy-state acts as an energy trap to which excitons are funneled from a large part of the aggregate. The trapping occurs due to the large (several kTs) difference between the energy of the Lévy-state and the rest of exciton states of the band. Emission of the Lévy-state is observed as the extra red-shifted band in the fluorescence spectrum. Excitons that cannot reach the trap emit from the lowest locally accessible exciton states with energy corresponding to the “normal” or, as we call it, “blue” band of the emission spectrum. This is summarized schematically in Figure 6. Because the excitons are funneled to the Lévy-state from a large part of the aggregate, acting as a light-harvesting antenna, it has more emissive events in any given time-interval than any other “normal” exciton state. Thus, the chance of the Lévy-state getting quenched by a photogenerated quencher is much greater. Once this happens, excitons that initially emitted through the Lévy-state become quenched and the red emission completely disappears (only the blue emission is left), intensity drops significantly, and the mean position of the localization shifts greatly in space (as schematically shown in Figure 3d).58 A quencher may also form at the location of any other exciton state responsible for the blue spectral band, however, due to the emissive events being spread out over many states, each has a lower probability of being quenched and the event of collective quenching is unlikely. Therefore, at any given time it would lead to only small fluctuations of the total “blue” fluorescence. Thus, our model of exciton trapping on a state induced by a large local perturbation of the aggregate explains the observed fluctuations in fluorescence intensity, spectrum and emission localization.59

where α (0 < α ≤ 2) is the index of stability defining the asymptotic behavior, and s is a scale parameter determining the distribution width.56 The probability distribution, P(E), is generated by taking the Fourier transform of the characteristic function φα,σ(υ). For α = 2, P(E) is a Gaussian distribution possessing an exponentially decaying tail. For α < 2, P(E) decays as 1/Eα+1 for large E, meaning that the distributions possess so-called heavy (slowly decaying) tails. The Lorentzian (or Cauchy) distribution is the special case for α = 1. Recent theoretical work56,57 considered 1D J-aggregates where the monomer energies were taken from such heavytailed distributions and found drastically different properties related to the formation of so-called “outliers”−exciton states with significantly lower energy than the states dominating the absorption spectra. We carried out similar modeling by substituting the Gaussian disorder distribution with a Lévy distribution with α = 1.5 and choosing J and s to fit our experimentally observed spectral shift between the monomer and J-aggregate, and the J-aggregate absorption width (details in Supporting Information SI−VI). One of the realizations of the exciton band is shown in Figure 5 where one can clearly see a single outlier state, referred to hereafter as a Lévy state, which is substantially lower in energy than the rest of the states. This state is localized around the monomer possessing the transition energy substantially different from the mean value. Note also that in spite of the large energy difference, the Lévy state still has oscillator strength nearly 3 times larger than that of the monomer. F

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surface and funnel the light energy absorbed by the aggregate to a desired spatial location. Aggregate #78 is an ideal case because it only has one Lévystate, which is why we could use the correlated fluctuations of intensity, spectra, and emission localization to build our hypothesis. Our sample preparation procedure resulted in the formation of J-aggregates of very different length and conformations. Therefore, it is possible that more than one Lévy-state forms in a single aggregate as it all depends on the aggregate length and parameters of the disorder distribution. In this scenario, the red-shifted emission would originate from several Lévy states with different energies. This is actually the case for the majority of the studied aggregates. In this partially ensemble-averaged situation it is obviously much harder to infer the properties of the hidden Lévy-states from the spectroscopy and spatial localization data. Note that the ensemble averaged spectra of J-aggregates cast on the surface (Figure 1, a2,3) showed an additional red-shifted shoulder, which most probably originates from the Lévy-states emission. Similar to how single molecule spectroscopy methods reveal additional information compared to ensemble measurements, we emphasize the importance of using single Lévy-state spectroscopy to conclude efficient energy funneling and hidden exciton level structure in these 1D multichromophoric systems. To summarize, it is the first time when theoretically predicted “outliers”, or Lévy states (Frenkel exciton states with substantially lower energy than all other exciton states), were observed in J-aggregates experimentally. Studying 1D Jaggregates at the single aggregate level allowed us to directly observe energy funneling over ca. 100 nm toward a single Lévy state acting as a fluorescent trap. A Lévy state occurs when the disorder in the J-aggregate obeys a heavy-tailed Lévy rather than a Gaussian distribution. Possible origins of the heavy-tailed disorder include a dipole−dipole interaction with a random environment or the presence of special sites on the surface. Our results show a new avenue in energy transport engineering when exciton transport through nanoantennas can be directed to a desired spatial location by manipulating the environment rather than the antenna itself.

Figure 6. Schematic illustration showing the impact of a Lèvy-state on the fluorescence properties of a J-aggregate. (a) Disordered chain of monomers, the color codes the monomer transition energies. (b) Fluorescence spectrum possessing fluorescence from the “normal” exciton states (blue) and fluorescence of the Lévy-state (red). (c) Cartoon of the exciton band structure of the aggregate shown in (a). Exciton relaxation pathways to the “normal” exciton states (blue) and the Lévy-state (red) are shown by the corresponding color. Switching the Lévy-state on and off would give the observed blinking of the red fluorescence band.

What is the physical origin of the heavy-tail disorder distribution in molecular aggregates? We can actually rephrase the question and ask why one would think that the disorder should be Gaussian? We do not have a definitive answer regarding the particular PBI-1 J-aggregates studied here; however, the several examples that will be discussed below should be sufficient to clarify our ideas concerning this issue. Indeed, it is common practice to use Gaussian distributions to account for inhomogeneous broadening induced by the environment, however, spectral lines in condensed matter very often possess long tails that cannot be fitted by a Gaussian function.60 A very nice illustration that this “paradigm” must be changed was recently pointed out by Vlaming et al.61 The authors considered a dipole (representing a chromophore) in a gas of other dipoles (representing the solvent) possessing random orientations and positions in space. They analytically showed that the solvent-induced energy shift of the chromophore is given by a Lorenztian, a heavy tailed Lévy distribution with α = 1 (eq 1). An aggregate on a surface experiences even stronger random electrostatic forces due to the presence of a rough interface between low and high refractive index media, and the interactions are mostly static. Even if one does not consider the dipole−dipole interaction that leads to Lorentzian disorder, a deviation from the Gaussian distribution can be induced by non-Gaussian roughness of the surface at the nanoscale. It is well-known that surfaces can possess so-called special or active sites having drastically different properties from the rest. These sites can be due to a different chemical composition or special local topology. For example, even a surface of a crystal possesses steps from one atomically flat crystal layer to another. An ordered molecular aggregate laying on such a surface and crossing the step would have large fluctuation of the monomer transition energy at the location close to the step in comparison with all others. This gives an idea of how, by changing the properties of the surface (for example, by an AFM tip or lithography), one can manipulate local disorder of an aggregate situated on the

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ASSOCIATED CONTENT

S Supporting Information *

Details on experimental results, analytical methods, theoretical simulations, and additional data. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Author Contributions

A.M. did the experiments and data analysis. A.M. and I.S. wrote the manuscript. I.S. interpreted the results (together with A.M.) and took part in the experiments. A.J. synthesized the molecule. R.C. developed the 2D-POLIM analysis method, wrote the analysis software (together with M.M.), and participated in writing. M.M. took part in the 2D-POLIM data acquisition. F.W. designed the molecule, took part in the data interpretation, and writing of the manuscript. Funding

The work was sponsored by the Swedish Research Council, Knut & Alice Wallenberg foundation, and the Bavarian State Ministry of Science, Research, and the Arts within the G

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Collaborative Research Network ‘‘Solar Technologies go Hybrid’’.

(31) Scheblykin, I. G. In J-Aggregates; Kobayashi, T., Ed.; World Scientific Pub Co, Singapore: Singapore, 2012; pp 309−342. (32) Vlaming, S. M.; Malyshev, V. A.; Knoester, J. J. Chem. Phys. 2007, 127, 154719. (33) Scholes, G. D.; Rumbles, G. Nat. Mater. 2006, 5, 683−696. (34) Kozankiewicz, B.; Orrit, M. Chem. Soc. Rev. 2014, 43, 1029− 1043. (35) Kulzer, F.; Orrit, M. Annu. Rev. Phys. Chem. 2004, 55, 585−611. (36) Yoo, H.; Furumaki, S.; Yang, J.; Lee, J.-E.; Chung, H.; Oba, T.; Kobayashi, H.; Rybtchinski, B.; Wilson, T. M.; Wasielewski, M. R.; Vacha, M.; Kim, D. J. Phys. Chem. B 2012, 116, 12878−12886. (37) Van Oijen, A. M.; Ketelaars, M.; Köhler, J.; Aartsma, T. J.; Schmidt, J. Science 1999, 285, 400−402. (38) Lang, E.; Sorokin, A.; Drechsler, M.; Malyukin, Y. V.; Köhler, J. Nano Lett. 2005, 5, 2635−2640. (39) Eisele, D. M.; Knoester, J.; Kirstein, S.; Rabe, J. P.; Vanden Bout, D. A. Nat. Nanotechnol. 2009, 4, 658−663. (40) Lin, H. Z.; Camacho, R.; Tian, Y. X.; Kaiser, T. E.; Würthner, F.; Scheblykin, I. G. Nano Lett. 2010, 10, 620−626. (41) Habuchi, S.; Onda, S.; Vacha, M. Chem. Commun. 2009, 4868− 4870. (42) Galbraith, C. G.; Galbraith, J. A. J. Cell Sci. 2011, 124, 1607− 1611. (43) Bolinger, J. C.; Traub, M. C.; Adachi, T.; Barbara, P. F. Science 2011, 331, 565−567. (44) Muls, B.; Uji-i, H.; Melnikov, S.; Moussa, A.; Verheijen, W.; Soumillion, J. P.; Josemon, J.; Mullen, K.; Hofkens, J. ChemPhysChem 2005, 6, 2286−2294. (45) Ruzyllo, J.; Duranko, G.; Hoff, A. J. Electrochem. Soc. 1987, 134, 2052−2055. (46) Tian, Y.; Stepanenko, V.; Kaiser, T.; Würthner, F.; Scheblykin, I. G. Nanoscale 2012, 4, 218−223. (47) Mirzov, O.; Bloem, R.; Hania, P. R.; Thomsson, D.; Lin, H. Z.; Scheblykin, I. G. Small 2009, 5, 1877−1888. (48) Van den Bout, D. A.; Yip, W. T.; Hu, D. H.; Fu, D. K.; Swager, T. M.; Barbara, P. F. Science 1997, 277, 1074−1077. (49) Hofkens, J.; Maus, M.; Gensch, T.; Vosch, T.; Cotlet, M.; Kohn, F.; Herrmann, A.; Mullen, K.; De Schryver, F. J. Am. Chem. Soc. 2000, 122, 9278−9288. (50) Because of the lower number of photons when the red band was “off” (cluster 1), the localization precision was worse, leading to larger spread of localizations for cluster 1 in comparison with cluster 2. (51) Camacho, R.; Thomsson, D.; Yadav, D.; Scheblykin, I. G. Chem. Phys. 2012, 406, 30−40. (52) Liao, Z.; Hooley, E. N.; Chen, L.; Stappert, S.; Müllen, K.; Vosch, T. J. Am. Chem. Soc. 2013, 135, 19180−19185. (53) Fennel, F.; Lochbrunner, S. Phys. Rev. B 2012, 85, 094203. (54) Bednarz, M.; Malyshev, V.; Knoester, J. Phys. Rev. Lett. 2003, 91, 217401. (55) Fidder, H.; Knoester, J.; Wiersma, D. A. J. Chem. Phys. 1991, 95, 7880−7890. (56) Vlaming, S. M.; Malyshev, V. A.; Eisfeld, A.; Knoester, J. J. Chem. Phys. 2013, 138, 214316. (57) Möbius, S.; Vlaming, S. M.; Malyshev, V. A.; Knoester, J.; Eisfeld, A. 2014, arXiv:1404.4475v1. (58) Here it is assumed that when the Lévy-state is quenched it still acts as a trap for excitons as before, but its emission yield is zero. (59) Note that in order to describe our particular observation one does not need to assume any specific distribution of the disorder. The only condition is that it should have a long tail, or even just one extra “bump” at the low energy tail which is substantially shifted from the distribution center. (60) Peach, G. Adv. Phys. 1981, 30, 367−474. (61) Vlaming, S.; Malyshev, V.; Knoester, J. Phys. Rev. B 2009, 79, 205121.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS

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REFERENCES

Much appreciation to Dr. Yuxi Tian for fruitful discussions in regard to the optical behavior of the PBI-1 molecule.

(1) Bates, D. S. J. Financ. Econ. 2012, 105, 229−259. (2) Wang, D.; Zhuang, Q.; Fan, Y.; Di, Z.-R. Chin. Phys. B 2013, 22, 128702. (3) Burnett, K. Levy Statistics and Laser Cooling: How Rare Events Bring Atoms to Rest; Cambridge University Press: Cambridge, 2002; pp 793−794. (4) Cichos, F.; Vonborczyskowski, C.; Orrit, M. Curr. Opin. Colloid Interface Sci. 2007, 12, 272−284. (5) Bouchaud, J.-P.; Georges, A. Phys. Rep. 1990, 195, 127−293. (6) Barkai, E.; Naumov, A. V.; Vainer, Y. G.; Bauer, M.; Kador, L. J. Lumin. 2004, 107, 21−31. (7) Barkai, E.; Silbey, R.; Zumofen, G. Phys. Rev. Lett. 2000, 84, 5339−5342. (8) Würthner, F.; Kaiser, T. E.; Saha-Möller, C. R. Angew. Chem., Int. Ed. 2011, 50, 3376−3410. (9) Spano, F.; Mukamel, S. J. Chem. Phys. 1989, 91, 683−700. (10) Fidder, H.; Terpstra, J.; Wiersma, D. A. J. Chem. Phys. 1991, 94, 6895−6907. (11) Fidder, H.; Knoester, J.; Wiersma, D. Chem. Phys. Lett. 1990, 17, 529−536. (12) Ganapathy, S.; Oostergetel, G. T.; Wawrzyniak, P. K.; Reus, M.; Gomez Maqueo Chew, A.; Buda, F.; Boekema, E. J.; Bryant, D. a; Holzwarth, A. R.; de Groot, H. J. M. Proc. Natl. Acad. Sci. U.S.A. 2009, 106, 8525−8530. (13) Kobayashi, T.. J-Aggregates; Kobayashi, T., Ed.; World Scientific Pub Co: Singapore: Singapore, 2012. (14) Hildner, R.; Brinks, D.; Nieder, J. B.; Cogdell, R. J.; van Hulst, N. F. Science 2013, 340, 1448−1451. (15) Olaya-Castro, A.; Scholes, G. D. Int. Rev. Phys. Chem. 2011, 30, 49−77. (16) Dostál, J.; Mančal, T.; Augulis, R.; Vácha, F.; Pšenčík, J.; Zigmantas, D. J. Am. Chem. Soc. 2012, 134, 11611−11617. (17) Brixner, T.; Stenger, J.; Vaswani, H. M.; Cho, M.; Blankenship, R. E.; Fleming, G. R. Nature 2005, 434, 625−628. (18) Jelley, E. E. Nature 1936, 138, 1009−1010. (19) Scheibe, G.; Schontag, A.; Katheder, F. Naturwissenschaften 1939, 27, 499−501. (20) Kaiser, T. E.; Wang, H.; Stepanenko, V.; Würthner, F. Angew. Chem., Int. Ed. 2007, 46, 5541−5544. (21) Chen, Z.; Lohr, A.; Saha-Möller, C. R.; Würthner, F. Chem. Soc. Rev. 2009, 38, 564−584. (22) Walter, B. Ann. Phys. 1888, 270, 316−326. (23) Scheblykin, I. G.; Sliusarenko, O. Y.; Lepnev, L. S.; Vitukhnovsky, A. G.; Van der Auweraer, M. J. Phys. Chem. B 2000, 104, 10949−10951. (24) Spitz, C.; Daehne, S. Int. J. Photoenergy 2006, 2006, 84950. (25) Tilgner, A.; Trommsdorff, H. P.; Zeigler, J. M.; Hochstrasser, R. M. J. Chem. Phys. 1992, 96, 781−796. (26) Yamagata, H.; Hestand, N. J.; Spano, F. C.; Köhler, A.; Scharsich, C.; Hoffmann, S. T.; Bässler, H. J. Chem. Phys. 2013, 139, 114903. (27) Barford, W. J. Phys. Chem. A 2013, 117, 2665−2671. (28) Spano, F. Acc. Chem. Res. 2009, 43, 429−439. (29) Hestand, N.; Spano, F. J. Phys. Chem. B 2014, 118. (30) Lebedenko, A. N.; Grynyov, R. S.; Guralchuk, G. Y.; Sorokin, A. V.; Yefimova, S. L.; Malyukin, Y. V. J. Phys. Chem. C 2009, 113, 12883−12887. H

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