One-Dimensional Exciton Diffusion in Perylene Bisimide Aggregates

ARTICLE pubs.acs.org/JPCA

One-Dimensional Exciton Diffusion in Perylene Bisimide Aggregates Henning Marciniak,† Xue-Qing Li,‡ Frank W€urthner,‡ and Stefan Lochbrunner*,† † ‡

Institut f€ur Physik, Universit€at Rostock, Universit€atsplatz 3, 18055 Rostock, Germany Institut f€ur Organische Chemie and R€ontgen Research Center for Complex Material Systems, Universit€at W€urzburg, Am Hubland, 97074 W€urzburg, Germany ABSTRACT: The dynamics and mobility of excitons in J-aggregates of perylene bisimides are investigated by transient absorption spectroscopy with a time resolution of 50 fs. The transient spectra are compatible with an exciton delocalization length of two monomers and indicate that vibrational and configurational relaxation processes are not relevant for the spectroscopic properties of the aggregates. Increasing the pump pulse energy and in that way the initial exciton density results in an accelerated signal decay and pronounced exciton-exciton annihilation dynamics. Modeling the data by assuming a diffusive exciton motion reveals that the excitons cannot migrate freely in all three directions of space but their mobility is restricted to one dimension. The observed anisotropy supports this picture and points against direct F€orster-transfer-mediated annihilation between the excitons. A diffusion constant of 1.29 nm2/ps is deduced from the fitting procedure that corresponds to a maximal exciton diffusion length of 96 nm for the measured exciton lifetime of 3.6 ns. The findings indicate that J-aggregates of perylene bisimides are promising building blocks to facilitate directed energy transport in optoelectronic organic devices or artificial light-harvesting systems.

’ INTRODUCTION Extended π-stacks formed by self-assembly of π-conjugated molecules represent a highly interesting class of supramolecular structures.1,2 Because of their order, they might be used for directed energy and charge transport in organic devices like solar cells or optoelectronic switches.3 Aggregates of dye molecules and in particular of cyanine dyes have been intensively investigated by steady-state and time-resolved spectroscopy.4-8 The electronically excited states are delocalized over several molecules due to the coupling between the chromophores and are commonly described as Frenkel excitons.9-12 In J-aggregates the transition to the lowest exciton state carries most of the oscillator strength.11 Hence it has an absorption band that shows a red shift compared to the original monomer absorption and is stronger and narrower than the corresponding monomer band.6 These spectral features have been extensively investigated, with energetic disorder and vibronic coupling taken into account.13-15 Pump-probe studies on the picosecond time scale find that the excitons of J-aggregates made from substituted cyanines are mobile and that already at moderate excitation intensities the exciton decay is dominated by bimolecular annihilation processes.8 The decay dynamics of the excitons due to annihilation depends on the frequency of interactions between them and is thereby sensitive to their mobility and density. Because the exciton density changes in the course of annihilation, the annihilation rate is a function of time. It turns out that its functional form depends on the dimensionality of the exciton mobility as well as on the rate-determining process, that is, whether the diffusive exciton motion or the annihilation interaction determines the r 2010 American Chemical Society

dynamics (see below).16-18 Accordingly, analysis of the annihilation dynamics should be a sensitive tool to investigate these properties. In this paper we explore the time dependence of the annihilation dynamics to characterize the mobility of singlet excitons in J-aggregates for a new class of self-assembling tetraphenoxy-substituted perylene bisimides.19 Perylene bisimides are excellent dyes with high oscillator strength for the S1-S0 transition and a fluorescence quantum yield of nearly 100%.20 They are versatile building blocks for supramolecular structures and organic n-type semiconductors.21 In the past few years, a broad variety of perylene bisimides have been synthesized that mostly form H-type aggregates upon self-assembly in solution.21,22 Only recently perylene bisimides became available by a self-assembly technique that exhibit the absorption characteristics of J-aggregates.19,21,23 For H-aggregates of perylene bisimides, we have recently shown that the interaction of neighboring molecules leads after optical excitation to an ultrafast relaxation to a very weakly fluorescing species and a localization of the excitation.22 They are therefore of limited use for photonic applications that rely on energy migration. To the contrary, the fluorescence from J-aggregates of the perylene bisimide N,N0 -di[N-(2-aminoethyl)-3,4, 5-tris(dodecyloxy)benzamide]-1,6,7,12-tetra(4-tert-butylphenoxy)perylene-3,4:9,10-tetracarboxylic acid bisimide (PBI, Scheme 1), which is investigated here, shows Strickler-Berg symmetry and Received: August 6, 2010 Revised: November 30, 2010 Published: December 30, 2010 648

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Scheme 1. Molecular Structure of PBI

a high quantum yield of 82%, indicating that a relaxation to localized states does not take place.19 Infrared spectra demonstrate that intermolecular hydrogen bonds involving the benzamide groups stabilize efficiently the aggregates in apolar solvents like methylcyclohexane (MCH). The basic arrangement should be a single strand of monomers sitting with a slip angle close to the magic angle on top of each other.19 MCH solutions with high concentrations, well above 10 mM, exhibit an increased viscosity and schlieren textures are observed, which result typically from extended columns that have no positional order among them. Transmission electron microscopy (TEM) measurements of PBI samples prepared from MCH solutions show loosely connected bundles of aggregate structures with lengths of several hundred nanometers.19 This points also to extended strands that agglomerate when the solvent is removed. The goal of this paper is characterization of the excitonic properties of these aggregates. We apply femtosecond pump-probe absorption spectroscopy to determine the delocalization length and, via analysis of the annihilation dynamics, the mobility of the excitons. It is discussed whether the exciton motion can be described as diffusion or as single-step F€orster resonance energy transfer and whether it occurs only in a restricted number of dimensions.

’ EXPERIMENTAL SECTION Transient absorption spectra are recorded with a setup very similar to the one described in ref 24. The samples are excited by 35 fs long pulses with a center wavelength of 545 nm, which are generated by a noncollinearly phase-matched optical parametric amplifier (NOPA)25 pumped by a 1 kHz regenerative Ti: sapphire amplifier system (CPA 2001; Clark MXR). The absorption changes are probed over the whole visible spectral range with a white light continuum generated in an eccentrically moving 4 mm thick calcium fluoride substrate. The focused pump and probe beam are overlapped at the sample. The pump polarization is adjusted relative to the probe beam with an achromatic λ/2-wave plate. The recollimated probe beam is dispersed with a prism after the sample26 and the transmitted energy is spectrally resolved and measured with a multichannel detector based on a photodiode array with 512 pixels. Steadystate absorption spectra are recorded with a UV-vis spectrophotometer (Specord 50; Analytik Jena). For data analysis, the density of excitons generated by the pump pulse has to be known. An average value of the exciton density in the probe volume is calculated according to the formula Ænævol ¼

Npump ½1 - 10 - ODðλpump Þ  2 πrprobe d

Figure 1. Steady-state absorption spectra of PBI dissolved in MCH at concentrations of 0.16 mM (black) and 0.0016 mM (gray). The molar extinction coefficient is also, in the case of the aggregates, given with respect to PBI molecules. The 0-0 bands are fitted with Gaussian peaks.

Here d = 1 mm is the thickness of the sample and OD(λpump) = 0.485 is the optical density of the sample at the center wavelength of the pump pulse, λpump = 545 nm. The intensity profiles of the laser beams are assumed to be Gaussian. The probe radius rprobe = 55 μm determines the area relevant for detection and is defined as the radius where the intensity of the probe beam is 1/e2 times the maximum intensity. The number of pump photons Npump within this area is Rr 2 2 Epump λpump 0probe re - 2r =rpumpdr R ¥ - 2r2 =r 2 ð2Þ Npump ¼ pumpdr hc 0 re where Epump is the energy of the pump pulse and rpump = 125 μm is the radius of the pump beam at the sample according to the 1/e2 criterion. This results in a pump-energy-dependent average exciton density of Ænævol ¼ Epump 3 ð6:2  1022 J - 1 cm - 3 Þ

ð3Þ

When the concentration cPBI of PBI in solution (in units of centimeter-3) is taken into account, the average exciton density per PBI molecule is Ænæmol ¼

Epump ð6:2  1022 J - 1 cm - 3 Þ cPBI 3

ð4Þ

’ RESULTS AND DISCUSSION Stationary and Transient Spectra. Figure 1 shows the steadystate absorption spectra of PBI dissolved in MCH at concentrations of 0.16 and 0.0016 mM. The solution with low concentration exhibits the characteristic spectrum of monomeric tetraphenoxysubstituted PBIs, which self-assemble at higher concentration into J-aggregates.19 To analyze the spectra, Gaussian peaks are fitted to the Franck-Condon progression of the S1-S0 absorption, which extends from 475 nm (21 000 cm-1) to 650 nm (15 400 cm-1). The energetically lowest absorption band of the aggregate spectrum shows a red shift of 4 nm (110 cm-1) with respect to the monomer spectrum and peaks at 596 nm (16 770 cm-1). It was fitted with two Gaussians to account for its asymmetric line shape due to diagonal disorder.11 In aggregates, exchange narrowing results in a reduction

ð1Þ 649

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Figure 2. (Upper graph) Steady-state absorption and fluorescence spectra. The fluorescence spectrum is taken from ref 19. (Lower graph) Transient spectra of 0.19 mM PBI in MCH after optical excitation at 545 nm (18 350 cm-1) with a pump energy of 100 nJ and polarizations set to the magic angle at delay times of 1, 10, 100, and 1000 ps.

Figure 3. Decomposition of the transient spectrum measured 10 ps after excitation with 100 nJ pulses.

transient absorption measurements of the monomer (data not shown). This decomposition of the transient spectrum also indicates that the estimation of the delocalization length of two chromophores is realistic. Without delocalization the groundstate bleach and the stimulated emission would be half as large since only one instead of two chromophores would be affected. The performed subtraction of bleach and stimulated emission from the transient absorption spectrum would then result in a negative excited-state absorption, which is not reasonable. On the other hand, delocalization over more than three chromophores would enhance the ground-state bleach and stimulated emission in a way that the resulting excited-state absorption is no longer blue-shifted with respect to the ground-state absorption, in contrast to the predictions for one- to two-exciton transitions. Modeling of the Exciton Annihilation Dynamics. For analysis of the decay dynamics, the spectral integral (applying an energy scale) of the exciton feature between 590 nm (17 000 cm-1) and 625 nm (16 000 cm-1) is used as a measure of the time-dependent exciton population. In this way the population dynamics is disentangled from small spectral shifts that occur during the first 5 ps. Figure 4 shows the exciton signal on a logarithmic time axis for different pump energies measured with pump and probe polarizations set to the magic angle. At higher pump energies a more pronounced and faster decay of the exciton signal is observed than at lower energies (Figure 4, inset). This is a clear signature of exciton-exciton annihilation.7,8,16,17,29,30 The process occurs when two excitons come next to each other and their combined energy allows access to higher electronic states that have fast electronic relaxation channels. This interaction scenario results in deactivation of one of the two excitons. The exciton density n(t) then obeys the rate equation

of line widths compared to monomers by a factor N-1/2, where N is the number of molecules over which the excitons are delocalized.27 The width (full width at half-maximum, fwhm) of the lowest absorption band is 790 cm-1 for the aggregates and 1110 cm-1 for the monomers, indicating a delocalization length of approximately two monomers. To investigate the dynamics of the excitons, we turn to femtosecond pump-probe studies. Transient spectra after optical excitation at 545 nm (18 350 cm-1) with a pump energy of 100 nJ and polarizations set to the magic angle are depicted for several delay times in Figure 2 (lower graph). The transient absorption features decay on a time scale of a few hundred picoseconds but exhibit almost no changes of their spectral shape. The strong negative feature is due to the bleach of the ground-state absorption and stimulated emission from the electronically excited state, as can be seen by comparison with the steady-state absorption and fluorescence spectra (Figure 2, upper graph). Its sharp blue wing and the corresponding asymmetry results from an additional photoinduced absorption from the one- to the two-exciton state, which appears slightly blue-shifted from the ground-state absorption. To visualize this band, the ground-state bleach and the stimulated emission are subtracted from the transient spectra in Figure 3. A density of initially excited excitons of 5.42  10-2 per PBI molecule is calculated as described above. Because of the delocalization length, two molecules are affected by the generation of one exciton. This is taken into account when the timedependent fraction of excited chromophores is determined from the decay kinetics. The time-dependent bleach is calculated by scaling the absorption spectrum with this fraction. To obtain the stimulated emission, the fluorescence spectrum is multiplied by λ4 (ref 28) and scaled by a factor, which is chosen according to the assumption that the oscillator strength is equal to that of the bleach. The excited-state absorption obtained by subtracting bleach and stimulated emission shows a dominant band that is, in shape and intensity, similar to the low-energy band of the ground-state absorption (Figure 3) but slightly blue-shifted. This is the signature of a one- to two-exciton transition.4,5,10 The weaker bands at shorter wavelengths result from the vibronic structure of this transition, while the absorption band at longer wavelengths is due to an excited-state absorption that is also observed in

dnðtÞ nðtÞ ¼ - γðtÞn2 ðtÞ dt τ

ð5Þ

τ is the intrinsic lifetime of the excitons and γ(t) is the annihilation rate. γ(t) varies with time and adopts different forms, mainly depending on two factors: the dimensionality of the exciton mobility16 and the rate-determining process, which can be either the diffusive motion of the excitons or the exciton interaction itself.16,17 When diffusion of the excitons is the rate-determining process, it is assumed that the exciton-exciton annihilation interaction is 650

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dipoles. This leads to the expressions   rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2ffi 5 1 6 ð3=2Þk F RF γ1D ðtÞ ¼ Γ 6 6 τt 5 γF3D ðtÞ

ð10Þ

for interaction in one and three dimensions, respectively. It should be pointed out here that κ2 just acts as a scaling factor but does not affect the functional form of γFΔD(t), which depends only on Δ.18 From comparison of eqs 6-10, it can be seen that the time dependence of the annihilation rate is characteristic for the different models considered above. Therefore, adapting the models to the decay dynamics of the exciton signal should make it possible to draw conclusions on the nature of the exciton dynamics. This is shown in Figure 4, where eq 5, with the different expressions for γ(t) according to eqs 6-10, is numerically integrated to model the signal decay. The intrinsic lifetime τ is kept fixed in this procedure. Since the accessible time range of the applied transient absorption measurement setup is limited to 1.5 ns and annihilation processes contribute to the observed dynamics already at low pump energies, τ cannot be accurately determined by the used setup. τ is therefore calculated by scaling the monomer lifetime with the squared transition dipole moments and the fluorescence quantum yields. The monomer lifetime is determined to be 4.1 ns by transient absorption measurements in dichloromethane (data not shown). Taking into account a fluorescence quantum yield of Φmonomer = 0.78 as given in ref 19 results in a radiative lifetime of 5.3 ns, which is in good agreement with lifetimes measured for similar chromophores.33 The aggregates exhibit a fluorescence quantum yield of Φaggregate = 0.82 (ref 19) and the squared transition dipole moments for the monomers and the aggregates are calculated from the S1-S0 absorption according to the formula: Z 3hcε0 ln 10 ν~2 εð~ν Þ 2 jμj ¼ d~ ν ð11Þ 2π2 NA ν~ ν~1

Figure 4. Time dependence of the integrated exciton signature for four different pump energies between 10 and 100 nJ on a logarithmic time axis. The pump and probe polarizations were set to the magic angle. Solid lines [1D/3D (F)] show simulations with a model that accounts for one-dimensional diffusion as well as for F€orster-type interaction in three dimensions. The broken lines depict fits of a three-dimensional diffusion model (3D) and a one-dimensional F€orster-type interaction model [1D (F)] to the 100 nJ data (see text for details). (Inset) Different decay dynamics of the normalized signal for different pump energies.

much faster and can be neglected in modeling the deactivation dynamics. Depending on the dimensions, in which the diffusion takes place, the annihilation rate γ(t) can be written as rffiffiffiffiffiffi 2D ð6Þ γ1D ðtÞ ¼ πt for one-dimensional diffusion and   R γ3D ðtÞ ¼ 4πRD 1 þ pffiffiffiffiffiffiffiffiffiffi 2πDt

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi   1 1 ð3=2Þk2 3 πRF ¼ Γ 2 3 τt

ð9Þ

ð7Þ

for three-dimensional diffusion.16 D is the diffusion constant and R denotes the critical distance between two excitons at which annihilation takes place. It is usually assumed that R is on the order of the distance between adjacent molecules if the annihilation dynamics is diffusion-controlled and of three-dimensional character.16,30 In the one-dimensional case, a critical distance does not enter in the annihilation rate. Equation 7 holds also for anisotropic diffusion since the coordinate space can be transformed so that the reaction surface for annihilation is conformal with the diffusion tensor.31,32 In the other case, when the rate-determining process for annihilation is a long-range exciton interaction, the diffusive motion is assumed to be too slow to have an impact on the deactivation dynamics. The exciton interaction is modeled as a long-range F€orster-type interaction. The time variation of γ(t) is then a result of the distribution of distances between the excitons and depends on the number of dimensions Δ in which the excitons can interact.18 In this case γ(t) reads      1 Δ 3 2 - 1 Δ=6 Δ Δ=6 - 1 kτ ð8Þ γFΔD ðtÞ ¼ VΔ Γ 1 t 2 6 2 6

where ε is the molar extinction coefficient in dependence on the wavenumber ν~, h is the Planck constant, c is the speed of light, ε0 is the dielectric constant, and NA is Avogadro's number. This leads to an overall scaling factor of (Φaggregate/Φmonomer) 3 |(μmonomer/μaggregate)|2 = 0.88 and thus to an intrinsic aggregate lifetime of τ = 0.88(4.1 ns) = 3.6 ns. The models with γ1D(t) and γF3D(t) lead to the same dynamics due to the same t-1/2 time dependence and yield good agreement with the measured data. For the highest pump pulse energy of 100 nJ, the initial exciton density per molecule n0 is calculated as described pffiffiffiffiffi in the Experimental Section. The parameters D and RF3 k2 are optimized, 2 -1 3 resulting pffiffiffiffiffi in 5.61 molecule ps for D or 49.9 molecule for 3 RF k2 in units of the monomer volume. The time traces at lower pump pulse energies are fitted with the same parameters and only the initial exciton densities n0 are adapted. The results for n0 are given in Table 1. They scale very well with the pump pulse energies, demonstrating that the model can consistently describe all time-resolved measurements taken at the magic angle configuration. The other models with different time dependences of γ(t) can clearly be distinguished and show, even with optimized parameters, strong systematic deviations from the

The upper index F indicates a F€orster-type annihilation process. VΔ is the Δ-dimensional sphere that defines the interaction distance and is thus related to the F€orster radius RF. The factor κ2 accounts for the average relative orientation of the transition 651

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Table 1. Initial Exciton Density Dependence on Pump Pulse Energya Epump (nJ)

n0 (10-2 3 molecule-1)

100

5.42b

50 25

2.91c 1.30c

10

0.55c

a

Fitted values are obtained by adopting the model, that is, eq 5, in combination with eq 6 or eq 10 to the measured data. b Calculated. c Fitted.

measurements. This is demonstrated in Figure 4 for the 100 nJ data. These findings indicate that neither exciton diffusion in three dimensions (eq 7) nor direct F€orster energy transfer between excitons in one dimension without prior approach by diffusion (eq 9) is responsible for the observed annihilation dynamics. The structure of the aggregates hints at a limitation of the exciton mobility along one dimension. Due to the substituents of the PBI molecules at the bay and terminal positions, a hydrogenbond-directed aggregation of the chromophores is taking place in solvents of low polarity like MCH.19 Accordingly, the aggregates should have a rodlike, one-dimensional structure and the excitons might move only along this direction. In this case the annihilation dynamics should be governed by one-dimensional exciton diffusion. If a center-to-center distance of 0.48 nm between monomers in an aggregate is assumed (see Supporting Information of ref 19), the parameter D would translate into a one-dimensional diffusion constant of 1.29 nm2/ps and results with τ = 3600 ps in a diffusion length LD = (2Dτ)1/2 of 96 nm for the excitons. This would be about 10 times larger than in disordered polymers29,30 but on the same order of magnitude as in perylene-based molecular crystals of 3,4,9,10-perylenetetracarboxylic dianhydride, where LD was found to be 61 nm,16 or in tetracene crystals, where the diffusion constant for singlet excitons was determined to be 4 nm2/ps.34 To determine the F€orster radius RF from the simulation for the case of annihilation by direct energy pffiffiffiffiffi transfer in three dimensions, that is, from the expression RF3 k2 , one has to take into account the relative orientations of the aggregates and the intermolecular distances. The distances are limited by the dimensions of the monomers, which we estimate as 0.48 nm  2 nm  3 nm = 2.88 nm3. The relative orientations govern the factor κ2, which in principle can adopt values between 0 and 4 for the energy transfer between two molecules.35 For a three-dimensional molecular assembly, extreme values are highly unlikely for the averaged factor κ2. For a wide range of κ2 values from 0.1 to 4, reasonable F€orster radii between 7.7 pffiffiffiffi ffi and 4.2 nm result from a value of 49.9 molecule3 for RF3 k2 found by the fitting procedure. Thus at a first glance this model seems also to be consistent with the data. Polarization Dependence. From measurements with different relative polarization orientations of pump and probe pulse, the transient anisotropy r(t) of the absorption properties can be calculated according to36 rðtÞ ¼

Sigjj ðtÞ - Sig^ ðtÞ Sigjj ðtÞ þ 2Sig^ ðtÞ

Figure 5. Anisotropy decay for various pump pulse energies between 10 and 100 nJ. Solid lines depict simulations for diffusion-controlled exciton-exciton annihilation in one dimension.

measured with perpendicular polarizations. The anisotropy is shown in Figure 5 for different pump pulse energies. The observed anisotropy not only decays with time, but its dynamics also depends on the pump pulse energy. The decay implies a dependence of the measured dynamics on the relative orientation of pump and probe polarization. Such dependence can be caused either by reorientation of exciton transition dipole moments or by different decay dynamics of excitons with differently oriented transition dipole moments. The former can be realized by a rotation of the aggregates, which, however, is very unlikely on the time scale investigated here. The rotation of the monomers in solution occurs with a time constant of 500 ps (data not shown); rotational diffusion of the larger aggregates is expected to be much slower. Another mechanism would be exciton transfer to molecules with differently oriented transition dipole moments. This is excluded within each of the two models considered here: in the three-dimensional F€orster transfer model, annihilation is assumed to take place within a single step, and in the one-dimensional diffusion-controlled model, the transition dipoles within one aggregate are assumed to be parallel. Although these are idealizations, the effect of exciton transfer between differently oriented molecules on the anisotropy cannot account for the strength of the decay and in particular not for the dependence on pump pulse energy.36 The second above-mentioned possibility of different decay dynamics for differently oriented transition dipoles can account for the energy dependence and is in agreement with the onedimensional diffusion model. In this case only excitons on the same aggregate, where the transition dipoles are assumed to be parallel, can interact and the annihilation dynamics depends on the exciton density on the isolated aggregate, analogous to the case of polymer chains discussed in ref 36. Because aggregates with transition dipoles parallel to the pump pulse polarization interact more strongly with the laser field than aggregates with perpendicular transition dipoles, more excitons are created on the former ones. Accordingly, they exhibit more pronounced annihilation dynamics and a faster exciton decay. They contribute dominantly to the signal when pump and probe polarization are parallel, resulting in a signal decrease faster than the average. With perpendicular probe polarization, aggregates with transition dipoles strongly tilted to the excitation field contribute dominantly to the transient absorption. They interact more weakly with the pump field and the

ð12Þ

Sig||(t) is the absorption change measured with the probe pulses polarized parallel to the pump pulses, and Sig^(t) is the signal 652

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generated exciton density is lower, leading to slower annihilation dynamics. To be somewhat more quantitative, we apply the following crude simulation of the effect. It is assumed that annihilation due to one-dimensional exciton diffusion takes place and that Sig||(t) ∼ n||(t) and Sig^(t) ∼ n^(t). Equation 5 can be evaluated analytically when γ(t) ∼ t-1/2, resulting in16 n0 e

- t=τ

pffiffiffiffiffiffiffiffiffiffi ð13Þ 1 þ n0 C erf ½ ðt=τÞ pffiffiffiffiffiffiffi where C ¼ γ1D ðt Þ 3 πτt is a constant. Using eq 13 for n||(t) and n^(t) separately and replacing Sig||(t) and Sig^(t) in eq 12 by n||(t) and n^(t) gives the expression nðtÞ ¼

rðtÞ ¼

0:4 1 þ 1:08n0 C erf ½

pffiffiffiffiffiffiffiffiffiffi ðt=τÞ

ð14Þ

Here we assume in addition that the anisotropy is maximal at time zero [r(0) = 0.4]36,37 and that the initial exciton density n0 = 1 /3(n||,0 þ 2n^,0) is an average of the initial exciton densities n||,0 and n^,0 probed with parallel and perpendicular polarization with respect to the pump pulse.37 This treatment neglects that a distribution of exciton densities contributes to the respective signals. The resulting simulations are shown in Figure 5 (solid lines). The parameters used are given in Table 1 and τ was again set to 3.6 ns. No further optimization was made. The simulations are able to describe the principal behavior of the anisotropy, including the dependence on excitation energy. As mentioned above, neither rotation of the aggregates nor exciton transfer between differently oriented molecules, which may occur due to some degree of conformational disorder, is considered in this model. Since both processes would enhance the anisotropy decay,36 this might explain the systematic deviations from the measured data. Nevertheless, the results demonstrate that a certain degree of structural order within the molecular assemblies exists. Such an order can be expected along one-dimensional strands of aggregated molecules. In the case of F€orster energy transfer in three dimensions, on the other hand, an analogous effect can occur only if three-dimensional assemblies with a high degree of structural order are formed, which are characterized by preferential transition dipole orientations. Otherwise the exciton density on all probed molecular assemblies would be the same. In that case the observed dynamics should be insensitive to the orientation of the probe polarization with respect to the pump polarization, and the decay of the anisotropy should not be affected by annihilation processes. As can be seen in Figure 5, our experiments are not in agreement with this consideration. In case of a three-dimensional ordered assembly, one has to assume a regular structure of several strands. Interaction between short strands would be weak and unspecific since the substituents, that is, the tert-butylphenoxy group and the long C12H25 alkane chains, expose only C-H bonds to the outside. The chromophores and the nitrogen and oxygen atoms, which are good acceptors for hydrogen bonds, are hidden inside the strand.19 The formation of bundles is therefore expected only for long strands. Accordingly, many molecules are needed to form threedimensional ordered objects. Such objects should result in significant stray light from the excitation. However, not more stray light than from diluted solutions is observed. Due to these

considerations, the formation of three-dimensional assemblies consisting of several extended and interacting strands seems unlikely. Thus the dependence of the anisotropy decay dynamics on pump pulse energy supports the notion of one-dimensional exciton diffusion.

’ SUMMARY AND CONCLUSIONS We investigated the exciton dynamics and mobility in PBI J-aggregates by transient absorption spectroscopy with a time resolution of 50 fs. The transient spectra are compatible with an exciton delocalization length of two monomers and indicate that vibrational and configurational relaxation processes are not relevant for the spectroscopic properties of the aggregates. Excitation density-dependent experiments reveal pronounced annihilation dynamics. Quantitative analysis of the time-dependent exciton density indicates that the exciton mobility is restricted to one dimension. It should be mentioned that numerical simulations show significant deviations from the one-dimensional behavior as soon as an exciton can jump one time from one strand to another within its lifetime.32 The observation of γ(t) ∼ t-1/2 is apparently a sensitive indicator for purely one-dimensional behavior. A diffusion constant of 1.29 nm2/ps was deduced from the fitting procedure. From the intrinsic exciton lifetime of 3.6 ns and the diffusion constant, a maximal diffusion length of 96 nm is estimated, which is about 10 times larger than in disordered polymers29,30 but on the same order of magnitude as in molecular crystals16,34 and in excellent accordance with another class of highly ordered one-dimensional PBI J-aggregates where the diffusion length was found to be 70 nm by single-molecule spectroscopy.38 The value for the diffusion length is an upper limit and valid only if the aggregate strands have a length of at least 96 nm. This is unlikely for the investigated solution. However, one can expect this diffusion length if large aggregates or films are prepared. Direct F€orster energy transfer between excitons in three dimensions would also be compatible with the measured time dependence of the exciton density. However, the observed anisotropy can be explained only by the notion of large and structurally ordered assemblies of PBI consisting of several strands, which seems unlikely for the investigated samples. Additional support for one-dimensional diffusion comes from a simple estimation of the diffusion constant by calculating the resonant energy transfer rate between neighboring exciton sites of the aggregate according to35 kET ¼

4π2 jV j2 JðλÞ ch2

ð15Þ

V is the dipole coupling between two monomers, corresponding to the 110 cm-1 red shift of the steady-state absorption spectrum of the aggregate relative to the monomer (Figure 1), and J(λ) is the spectral overlap of the area-normalized aggregate absorption and fluorescence spectra. From that the diffusion constant can be calculated via: D ¼ kET

a2 2

ð16Þ

Taking a = 0.96 nm, which corresponds to the estimated average exciton size along the strand of two chromophores, leads to D = 1.3 nm2/ps, in excellent agreement with the value deduced from fitting the diffusion model to the data. 653

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The findings indicate that J-aggregates of PBIs are promising building blocks to facilitate directed energy transport in optoelectronic organic devices or artificial light-harvesting systems. The large diffusion length simplifies the construction of wellabsorbing layers, and the one-dimensional mobility results in energy migration along a preferential direction without trapping effects as encountered in PBI H-aggregates.22,39 Even photonic wires on the nanometer scale might be feasible with this class of molecules if one succeeds in the preparation of long and singlestranded aggregates. The results also demonstrate that femtosecond absorption measurements are a powerful tool to analyze mobilities on the molecular length scale and to gain valuable insights into the topology of supramolecular structures and the resulting effects.

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’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

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dx.doi.org/10.1021/jp107407p |J. Phys. Chem. A 2011, 115, 648–654