Singlet–Singlet Exciton Annihilation in an Exciton-Coupled Squaraine

Article pubs.acs.org/JPCC

Singlet−Singlet Exciton Annihilation in an Exciton-Coupled Squaraine-Squaraine Copolymer: A Model toward Hetero-JAggregates Sebastian F. Völker,† Alexander Schmiedel,† Marco Holzapfel,† Klaus Renziehausen,‡ Volker Engel,‡ and Christoph Lambert*,† †

Institut für Organische Chemie, Center for Nanosystems Chemistry and ‡Institut für Physikalische und Theoretische Chemie, Universität Würzburg, Am Hubland, 97074 Würzburg, Germany S Supporting Information *

ABSTRACT: Low-band-gap polymers with broad spectral absorption are highly sought after for application in organic photovoltaic cells and other optoelectronic devices. Thus, a conjugated copolymer based on two different indolenine squaraine dyes SQA and SQB was synthesized by Suzuki coupling, and its steady-state and time-resolved optical properties were investigated in detail. In CHCl3 the copolymer [SQA-SQB]n shows a strongly broadened and red-shifted absorption compared to that of its monomers, which was explained by exciton coupling of localized transition moments. The theoretical background of exciton coupling theory for copolymers was worked out in detail. In toluene, [SQA-SQB]n displays a spectral narrowing of the lowest excitation band which resembles the exchange narrowing effect found in cyanine J-aggregates. In this way [SQASQB]n behaves like a one-dimensional covalently bound hetero-J-aggregate. The photoinduced dynamics of the copolymer was investigated by transient absorption pump−probe spectroscopy with femtosecond resolution. Because of the unusually high exciton diffusion constant, singlet−singlet annihilation is the rate-limiting step for deactivation of the copolymer in solution at high laser fluencies. This is unlike the situation for many conjugated polymers in the solid state, where diffusion-limited annihilation is usually found. Thus, the [SQA-SQB]n copolymer is a unique model system which combines the excitonic features of J-aggregates with the chemical robustness of a polymer.

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INTRODUCTION Since their almost parallel discovery by Scheibe and Jelly in the late 1930s, J-aggregates of cyanine dyes are a playground of numerous spectroscopic and theoretical investigations.1−4 Compared to the absorption spectra of their monomeric parent compounds, J-aggregates display sharp and red-shifted intense absorption bands. These particular optical properties have often been described by exciton coupling theory.5,6 Many other chromophores also display J-aggregate-like behavior.1 However, because aggregate formation strongly depends on external parameters such as solvent, temperature, salt concentration, pH value, and surfactants their deliberate formation and variation is limited to some extent and requires careful molecular design of interchromophore interactions.7,8 In particular, the formation of heteroaggregates from two different chromophores is difficult to achieve because self-sorting often dominates.9 Thus, our aim was to synthesize a copolymer built up from two different chromophores which are covalently connected but which nevertheless shows J-type optical properties and thus may serve as a model for a hetero-Jaggregate. To reach this goal, we used squaraine dyes because these are similar to cyanine dyes with respect to their absorption and fluorescence properties but, unlike those, are neutral and allow the synthesis of homopolymers by standard © 2014 American Chemical Society

procedures such as Suzuki or Yamamoto coupling reactions.10−12 Furthermore, squaraine dyes attracted recent interest because of their optical properties that combine a sharp absorption in the red to near-infrared spectral region with high fluorescence quantum yields.13−17 Besides their use as biolables,18−27 photoconductors,28 compounds for data imaging,29 ion sensors,30−34 NIR emitters in thin-film dye-doped organic light-emitting diodes,35 and in nonlinear optics,36−43 squaraine dyes also proved useful for photovoltaic applications12,44−66 because of their favorable absorption in the red region of the visible solar spectrum. However, in this context the relatively narrow bandwidth of their absorption is a drawback. Thus, in recent works we tried to broaden this absorption either by combining squaraine dyes with electron donors10,67 or acceptors68 or by coupling multiple squaraine chromophores in squaraine dye polymers such as homopolymers [SQA]n12 and [SQB]n11 (Chart 1) or other copolymers.10,68 Indeed, for the aforementioned homopolymers we found both a red shift of the longest-wavelength absorption and a distinct broadening of the absorption which we explain by Received: June 5, 2014 Revised: July 1, 2014 Published: July 9, 2014 17467

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knowledge there has not been any attempt to describe alternating copolymers by exciton coupling theory. Therefore, we will work out this theory for alternating polymers which should help to interpret the experimental findings. Besides broadening the absorption by exciton coupling effects, the huge molar extinction coefficient of squaraine dyes will also support fast energy transfer by dipole−dipole Förster resonance energy transfer (FRET).71 However, for the same reason squaraine dyes have a high excitation probability even at relatively low laser energy per pulse. For polymers or dye aggregates this can lead to multiple excitations which may then undergo relaxation by singlet−singlet annihilation processes to the ground state and a higher excited state. Such annihilation processes have been intensively investigated in conjugated polymers in the solid state72−78 because they may give information about exciton diffusion dynamics, which is of current interest concerning the use of these polymers in organic solar cells and other semiconductor devices. Four major mechanistic scenarios are being discussed in this context:5,74,79,80 (i) one-dimensional or (ii) three-dimensional diffusion-controlled exciton annihilation in extended chromophore aggregates such as solid films, (iii) three-dimensional dipole−dipole Förster-type annihilation over long distances without preceding diffusion, and (iv) static annihilation of equilibrated excitons in small aggregates where the size of the chromophore aggregate is small compared to the diffusion length of the exciton. Mechanisms i−iii may indeed be at work in films of conjugated polymers and dendrimers79,81 or other molecular dye aggregates82−88 because here the excitons cannot diffuse only along the conjugated polymer backbone but also in between the chains. This is different if we use conjugated polymers in dilute solution, as we will do in the present study. Here, because of the large interchain distance we assume that exciton diffusion is possible only along the conjugated polymer strand. If the exciton mobility is fast, then we may indeed deal with “small aggregates” where the annihilation process is ratelimiting. Thus, a major focus of this paper will be on singlet− singlet exciton annihilation processes which occur in this polymer because of its high molar extinction coefficient.

Chart 1. Squaraine Monomers SQA and SQB and Polymers [SQA]n, [SQB]n, and [SQA-SQB]n

exciton coupling theory. Thus, the coupling of transition moments of chromophores appears to be an alternative to other strategies for designing and fine-tuning the absorption properties of conjugated polymers.69 In the 1960s, exciton theory was applied to homopolymers by Kasha and McRae.70 This theory predicts an exciton bandwidth that is 4 times the electronic coupling J between adjacent chromophores. Therefore, excitonically coupled chromophores should show spectrally broader absorption. The use of two different chromophore types might lead to even broader absorption bands. Hence, in the present work we intend to even further broaden the exciton bandwidth by combining two different squaraine monomers to form an [SQA-SQB]n copolymer. However, to the best of our Scheme 1. Synthesis of Copolymer [SQA-SQB]n

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Figure 1. Exciton coupling diagram for a homodimer (A2), a heterodimer (AB), and for an infinitely long homopolymer ([A]2N) and a copolymer ([AB]N). In the polymer case, the energy levels are pairwise degenerate (not depicted) with exception of k = 0, NA/2 (homopolymer), and NA/4 (copolymer). The band diagram was calculated with eq 2 for homopolymer [SQA]n in CHCl3 with E̅ = 0, ΔE = 0, and J = −640 cm−1 (head-to-tail arrangement of transition moments) and for the alternating copolymer in toluene with E̅ = 0, ΔE = 600 cm−1, and J = −480 cm−1 (evaluated from eq 3). Coupling constants J were obtained from the respective absorption spectra and eq 3 (see the text). The transition moments at A are black and at B are red. Their length reflects the relative contribution, and their direction represents the phase relation at the band edges for a head-to-tail arrangement of chromophores. Those for a face-to-face arrangement can easily be derived analogously to the heterodimer. The experimental absorption spectrum of [SQA-SQB]n in toluene is given on the right-hand side.

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RESULTS Synthesis. Analogous to our previous work on squaraine (co)polymers, [SQA-SQB]n was readily synthesized from monomeric squaraine precursors. We used the squaraines SQ110 and SQ2,11 the diboronic ester derivative of SQA and the dibromo derivative of SQB, respectively, in a palladiumcatalyzed Suzuki coupling reaction (Scheme 1). This crosscoupling reaction was performed in an aqueous solvent mixture (THF/H2O) using Pd(PPh3)4 as the Pd(0) source and NaHCO3 as the base under reflux conditions for 6 days. Copolymer [SQA-SQB]n was purified by means of consecutive Soxhlet extractions in hexane, methanol, and acetone. Analytical gel permeation chromatography (GPC) of the purified material in CHCl3 with polystyrene standards gave Mn = 32 800, Mw = 63 400, Xn = 23.4, and PDI = 1.9. Exciton Coupling Theory for Alternating Copolymers. In order to understand some basic optical properties of alternating copolymers we use exciton coupling theory in which

the excited states of the polymers are generated by the coupling of localized excited states of monomers A and B. Before we turn our attention to copolymers we will qualitatively describe this concept for homodimers and homopolymers. The rigorous mathematical description can be found in the Supporting Information and follows essentially the work of Kasha.70,89 Exciton coupling of two identical chromophores leads to a splitting (= 2J where J measures the exciton coupling strength) of the excited states as depicted in Figure 1 if ground-state interactions are neglected. For two different chromophores (with energies EA and EB in the heterodimer) the energies of the excitonic states are further apart and can be calculated by eq 1 where E̅ = (EA + EB)/2 and ΔE = (EA − EB)/2 where EA > EB. In the case of the homopolymer the energies of the NA eigenstates can be calculated by eq 2. (In this case E̅ = EA, ΔE = 0, and the (±) has to be replaced by (−) for 0 ≤ |k/NA| ≤ 1/4 and by + for 1/4 < |k/NA| ≤ 1/2. k is a quantum number which runs from 0, ±1, ±2,...+NA/2 and NA denotes the 17469

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Figure 2. (a) Normalized absorption spectra of monomeric and polymeric squaraine dyes. (b) Normalized absorption and fluorescence spectra of [SQA-SQB]n in toluene and CHCl3 solution.

Table 1. Spectroscopic Data of Squaraine Monomers and the Polymer d

SQA

SQBf [SQA-SQB]n

λmax /nm

ṽmax /cm−1

εmax/L mol−1 cm−1

μeg/D

λfl/nm

ṽfi/nm

Φfa

639 644 685 700 766 790

15 700 15 500 14 600 14 300 13 000 12 600

336 000 340 000 207 000 236 000 204 000h 478 000h,i

11.4 11.1 10.6 10.1 14.9 15.6

649 649 706 716 785 793

15 400 15 400 14 200 14 000 12 700 12 600

0.26 0.48 (0.57)e 0.34 0.56 (0.70)g 0.013 0.12

DCM toluene DCM toluene CHCl3 toluene

τf/nsb,c 1.70 3.5 0.13 [0.73], 0.28 [0.27] 0.60 [0.51], 1.7 [0.49]

a

These values were measured relative to oxazine 1 with an absolute quantum yield of 0.15 which was measured with an integration sphere in this work. bThe values in square brackets are relative amplitudes of the corresponding lifetime. cExcitation at 656 nm. dFrom ref 10. eThis value was determined by an absolute measurement using an integration sphere. fFrom ref 11. gThis value was measured relative to SQA with the absolute quantum yield of 0.57. hThe values of the extinction coefficient are per monomer unit. iBecause we observed some solubility problems in toluene, the correct extinction coefficient was obtained by diluting a concentrated CHCl3 solution of the polymer with toluene in a 1:99 ratio.

(= band with k/NA = 0 for the polymer, see Figure 1) while all other transitions are forbidden. For the face-to-face arrangement, the transition is allowed into the highest exciton state only. For the heterodimer and the copolymer, in general, both transitions into the lowest and the highest state are allowed, depending on the individual magnitude and orientation of the localized transition moments of chromophores A and B. For the polymer, transitions into states with k/NA = 1/4 are forbidden in any case. UV/Vis/NIR Absorption and Fluorescence Spectroscopy. Before we turn to the spectroscopic properties of the [SQA-SQB]n copolymer we briefly report the spectra of homopolymer congeners [SQA]n and [SQB]n in CHCl3 as well as monomers SQA and SQB in DCM (Figure 2 and Table 1).90 The monomeric units differ in the dicyanovinylene group of SQB, which shifts the absorption maximum of the monomer (and the polymer, consequently) to lower energy compared to that of SQA. For steric reasons, monomer SQB adopts a cis configuration while SQA has a trans configuration of the indolenine groups relative to each other. Polymer [SQA]n shows a broad absorption spectrum with a prominent peak at the lowest energy. These spectral features were interpreted as being caused by a mixture of two different structures, a strongly bent zigzag structure and a herringbone structure. The herringbone structure resembles a molecular J-aggregate and gives rise to the intense lowest-energy absorption.91 In the strongly bent zigzag structure, there are two chromophores per unit cell, which leads to allowed transitions into both the lowest-energy and the highest-energy state of the excitonic manifold.92 Altogether, a broadened absorption results for the mixture of both structural alternatives in solution. In the homopolymer [SQB]n, the situation is much more complex because besides elongated zigzag structures we

number of chromophore units.) In this equation J is the electronic coupling between adjacent chromophores while all other interactions are neglected. According to the nearestneighbor approximation, the exciton bandwidth is Ebw = 4J compared to 2J for the homodimer because in a polymer each chromophore has two neighbors instead of one as in the dimer. For the copolymer, eq 2 predicts an energy region of 2ΔE where there are no states. The total bandwidth is given by eq 3 which is larger than that of the homopolymer. Thus, in principle, copolymers would allow covering a broader spectral range for light absorption. Concerning the k space, the Brillouin zone is half the size of the homopolymer because the unit cell has doubled. Therefore, quantum number k runs from 0, ±1, ±2,...NA/4. E±dimer = E ̅ ±

ΔE2 + J 2

E±(k)polymer = E ̅ ±

2 ⎛ ⎛ 2πk ⎞⎞ ΔE + ⎜⎜2J cos⎜ ⎟⎟⎟ ⎝ NA ⎠⎠ ⎝

(1)

2

(2)

where E̅ = (EA + EB)/2 and ΔE = (EA−EB)/2 where EA > EB E bw (polymer) = 2 ΔE2 + 4J 2

(3)

Whether optical transitions into excitonic states are allowed depends on the relative orientation of transition moments. These are depicted in Figure 1 for two selected cases, a head-totail arrangement (so-called J-type) and a face-to-face arrangement (so-called H-type) for the homo- and heterodimer. For the polymer, we give only the pictorial representation for the head-to-tail arrangement of chromophores. Thus, for the homodimer and the homopolymer a head-to-tail arrangement leads to a single allowed transition into the lowest energy state 17470

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Figure 3. Elongated [SQA-SQB]n polymer structure with localized transition moments indicated by gray (SQA) and red (SQB) arrows.

However, the calculation of the square of the transition moment of the whole exciton manifold with eq 4 gives comparable values, μeg2 = 222 D2 in CHCl3 and 243 D2 in toluene. This shows within experimental error that the integrated oscillator strength f ∝ μeg2 is independent of the solvent. The sum of the squared transition moments of the two squaraine components SQA (11.1 D) and SQB (10.1 D) in toluene is 225 D2, in very good agreement with that of the polymer.

postulate that there are also helix structure and other conformers present in solution, the relative amount of which is dependent on the solvent.11 Here we refer only to CHCl3 solution where the elongated zigzag structure predominates with its strong absorption at the low-energy side of the exciton manifold. Because of the dicyanovinylene group, the whole absorption band of [SQB]n is shifted to lower energy compared to [SQA]n. From the difference of peak maxima on the lowand high-energy sides of the exciton manifold (= 4J) we estimated the electronic coupling |J| = 640 cm−1 for [SQA]n. However, the point-dipole approximation (see below) yielded J = −330 to −370 cm−1 for [SQA]n.12 For [SQB]n there is no distinct peak maximum on the high-energy side, which makes the estimate of J difficult but it is assumed to be similar to that of [SQA]n. The spectra of [SQA-SQB]n are solvent-dependent in a way similar to the spectra of [SQB]n, which is probably caused by different structures in solution. In this work we consider only spectra in CHCl3 and in toluene where they are similar.93 The spectrum in CHCl3 shows a broad band between 12 000 and 18 000 cm−1 referring to the exciton manifold with a distinct maximum on the low-energy side at 13 000 cm−1 and a second maximum with lower intensity on the high-energy side at 15 300 cm−1. In comparison to the spectra of [SQA]n and [SQB]n the absorption of [SQA-SQB]n almost covers those of both homopolymers but also shows maxima on both sides that do not quite reach the energies of the low-energy side of [SQB]n and the high-energy side of [SQA]n. The somewhat lower absorption intensity between the peak maxima is in agreement with the exciton coupling theory which predicts an area with no energy states for copolymers and only the highest and lowest energy state to be allowed (see above). For systems where the transition moments of both components are similar in size and oriented head-to-tail, the lowest-energy band should be most intense, which is indeed what we find. Thus, the observed spectra speak for an elongated polymer chain where the bent SQB moiety causes a zigzag motif as sketched in Figure 3. In this schematic representation the transition moments are localized at the individual squaraine chromophores and follow their orientation but are clearly not fully parallel as was assumed in Figure 1. Nevertheless, the strongest total transition moment of excitation should be the one associated with excitation into the lowest-energy exciton state. In toluene the spectrum of [SQA-SQB]n displays some differences to that in CHCl3. The band associated with excitations into the lowest exciton state is shifted to lower energies by ca. 400 cm−1. The molar extinction coefficient per SQA-SQB monomer unit (478 000 L mol−1cm−1) is much higher than in CHCl3 (204 000 L mol−1cm−1), and the width of the low-energy band of the exciton manifold is much smaller.

μeg 2 =

3hcε0 ln 10

9n 2000π 2NAv (n2 + 2)2

∫ νε ̃ dν ̃

(4) −34

In this equation, h is Planck’s constant [6.63 × 10 J s], c is the speed of light [3 × 1010 cm s−1], NAv is Avogadro’s constant [6.02 × 1023 mol−1], ε0 is the electric field constant [8.8542 × 10−12 C2 J−1 m−1], n is the refractive index of the solvent, and ε is the extinction coefficient [L mol−1 cm−1], which yields the transition moment in C m [1D = 3.3356 × 10−30 C m]. Even more surprising is the extremely narrow width of the low-energy band in toluene (250 cm−1 at two-thirds of the maximum height compared to 820 cm−1 in CHCl3), which is reminiscent of what is called exchange narrowing in Jaggregates.6,94,95 This narrowing is caused by a coherent excitation of several chromophores, which leads to the elimination of large deviations from the mean value of the eigenstate energies. The effective coherence length Neff95−97 can be estimated by eq 598 in which Δṽ2/3(M) and Δṽ2/3(P) are the band widths at two-thirds of the maximum height of the monomer and of the polymer, respectively.99 Taking Δṽ2/3(M) = 480 cm−1 (the bandwidth of SQB in toluene which we use as an approximation for the missing SQA-SQB monomer) and Δṽ2/3(P) = 250 cm−1 for the copolymer, we evaluate Neff = 3.7. This indicates that the exciton is on average delocalized over an [SQA-SQB]3.7 section. Neff =

Δν2/3 ̃ (M) Δν2/3 ̃ (P)

(5) −1

In CHCl3 the bandwidth of the copolymer (820 cm ) is even larger than that of SQB (560 cm−1) in DCM. The difference in spectral behavior between CHCl3 and toluene solution may be caused by structural disorder in the zigzag chain in CHCl3 while in toluene there might be a higher order. The fluorescence spectra of [SQA-SQB]n in both toluene and CHCl3 (see Figure 2) are very similar and show almost mirror image behavior to the absorption spectrum of SQB in toluene. This proves that fluorescence originates form the lowest energy level of the exciton manifold only. However, Δṽ2/3 is relatively large in both solvents, 550 cm−1 in CHCl3 and 460 cm−1 in toluene. The latter value is much larger than the equivalent bandwidth of the 17471

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relative to their size and/or the neglect of dielectric screening. In these cases, an explicit calculation of the transition densities at the individual chromophores and their mutual interaction yields improved electronic couplings.102−104 Hence, we consider the latter value |J| = 480 cm−1 to be more reliable, and this was used to calculate the band diagram in Figure 1 where the absorption spectrum of [SQA-SQB]n in toluene is also given for comparison. This comparison shows that the bandwidth is actually quite large and also shows the gap 2ΔE where there are no states. The latter aspect is not clearly reflected in the experimental spectrum possibly because of disorder and partial localization of excitation as well as by the vibrational progression of each individual excitonic state which can be seen by the blurring of the absorption band on the highenergy side of the exciton manifold. Transient Absorption Spectroscopy. In order to probe the photoinduced dynamics of [SQA-SQB]n we recorded transient absorption spectra in toluene and CHCl3 solution with femtosecond resolution. The huge molar extinction coefficient of squaraine dyes makes it highly likely that multiple excitations will be produced in a single polymer strand within the time width of the excitation pulse. For this reason we varied the pump power to investigate the effect of multiexcitations on the dynamics. We expect that exciton annihilation will be an important contribution to the decay mechanism. However, before we describe these experiments and their analysis, we will estimate the number and distribution of excitons produced by the laser pulse in the polymer. The probability of excitation Pm is determined by the number of photons per area and the absorption cross section of the chromophore. Thus, we obtain eq 6 where the expression in parentheses appearing as the first term in the exponent is the number of laser photons per area [cm−2] and the second term is the absorption cross section [cm2]. Here, D is the diameter of the laser beam [cm], E is the energy per pulse [J], h is Planck’s constant [6.63 × 10−34 J s], c is the speed of light [3 × 108 m s−1], λ is the wavelength [m] of the laser beam, NAv is Avogadro’s constant [6.02 × 1023 mol−1], and ε is the molar exctinction coefficient [L mol−1 cm−1] of the chromophore (taken as the SQA-SQB monomer unit, see Table 1).105

absorption peak. This also demonstrates that the narrowing in the absorption spectrum is caused by coherent excitation into a delocalized Franck−Condon state while fluorescence spectra reflect a localized, more disordered nature of a relaxed excited state. While in general we do not observe any concentration dependence of absorption spectra, temperature-dependent spectra of [SQA-SQB]n in toluene show a decrease and broadening of the low-energy absorption up to 80 °C. The spectrum in toluene at 60 °C resembles that in CHCl3 at room temperature (RT) (Supporting Information, Figure S2). This effect might be caused by the formation of a double strand of two helically twinned polymer chains in toluene at RT which undergo disaggregation at elevated temperature. The twinning of polymer strands might also induce a stiffening of the polymer with a higher degree of order. On the other hand, it appears unlikely that polymer strands with a very broad length distribution form ordered aggregates. Because we lack definite proof of this aggregation hypothesis we treat the polymers in toluene solution as single-stranded in what follows. The fluorescence lifetime of the [SQA-SQB]n copolymer was measured by TCSPC (time-correlated single-photon counting) in toluene and is biexponential (τf = 0.60 and 1.7 ns) (Table 1) but is much longer than in CHCl3 (τf = 0.13 and 0.28 ns). The difference in lifetime also explains the difference in fluorescence quantum yield which is 0.013 in CHCl3 but 0.12 in toluene. The latter is significantly smaller than those of the monomeric building blocks (SQA ϕf = 0.57, SQB ϕf = 0.70 in toluene). This is surprising, as exchange narrowing in J-aggregates often goes along with an increase in the radiative decay rate (superradiance) which should lead to an increase in the fluorescence quantum yield.6,95 However, superquenching, that is, the quenching of fluorescence by defect sites preceded by very fast energy transfer, may account for the low fluorescence quantum yield.100,101 With the optical data at hand we can estimate the exciton coupling strength in copolymer [SQA-SQB]n. Here, we make use of the point-dipole approximation (eq S2 in the Supporting Information) to calculate J from the transition moments of SQA and SQB and their relative orientation. Even if we assume a 0° angle between the transition moments of SQA and SQB and a distance of 17 Å (the center-to-center distance of the two squaric acid groups in SQA and SQB estimated by a DFT computation) we obtain J = −230 cm−1. In reality, the angle is certainly larger, which would yield a weaker coupling. We can also estimate the electronic coupling by eq 3 where we use half of the peak energy difference of SQA and SQB (ESQA − ESQB = 1200 cm−1 in toluene) for ΔE = 600 cm−1 and the peak difference of the exciton manifold of [SQA-SQB]n in toluene for Ebw = 2260 cm−1. In this way we evaluate |J| = 480 cm−1. In the same way we obtain 470 cm−1 in CHCl3. Here, as with homopolymer [SQA]n (see above), the electronic coupling evaluated by analyzing the exciton manifold is about twice as large as that estimated by the point-dipole approximation. A recent estimation of the excitonic coupling of homopolymer [SQA]n by semiempirical quantum chemical calculations yielded values in quite reasonable agreement with those obtained by direct evaluation of the excitonic manifold.10 Thus, we trust in these values. However, this sheds some doubt onto whether the point-dipole approximation is applicable in cases of polysquaraines. As has been discussed by several authors, possible reasons for the breakdown of the point-dipole approximation would be too close a distance of chromophores

⎡ ⎛ ⎞⎛ ln(10)1000ε ⎞⎤ E Pm = 1 − exp⎢ −⎜ ⎟⎥ ⎟⎜ ⎢⎣ ⎝ (hc /λ)π (D/2)2 ⎠⎝ NAv ⎠⎥⎦

(6)

Since the white light continuum probe beam has a much smaller diameter than the pump beam (D = 0.053 cm at 1/e2 maximum intensity) we have to multiply the pump energy E by limx→0 (erf(x)/x)/(erf(21/2)/21/2) ≈ 1.672, which is the ratio of the energy at the center of a Gaussian-shaped laser pulse and the average energy at 1/e2 intensity. With eq 6 we obtain Pm = 0.24 at 12 700 cm−1 excitation in toluene (λ = 789 nm, ε = 478 000 M−1 cm−1) even at only 50 nJ pulse−1. The distribution of multiple excitations Pk in a single polymer strand can be evaluated by a hypergeometric distribution (eq 7) where Pm is the probability of excitation of a monomer from eq 6 in thousandths, k is the number of excitations within the polymer, and n is the number of independent monomers in the polymer (Xn = 23.4).106 17472

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Figure 4. (a) Transient absorption spectra of [SQA-SQB]n in CHCl3 at 13 100 cm−1 excitation with a 50 nJ pulse−1 pump energy at different delay times. The spectra evolve in time from blue to red. (b) Time decay traces at selected wavenumbers and global target fit (red line) according to Figure 6.

Figure 5. (a) Transient absorption time decay traces of [SQA-SQB]n in CHCl3 at a 13 100 cm−1 pump wavenumber for different pump energies pulse−1. The curves for 200 and 400 nJ pulse−1 are almost superimposed. (b) Time decay traces in toluene at the given pump energies and wavenumbers.

⎛ Pm ⎞ ⎛1000 − Pm ⎞ ⎟ ⎜ ⎟·⎜ ⎠ ⎝k ⎠ ⎝n − k Pk = ⎛1000 ⎞ ⎜ ⎟ ⎝n ⎠

energies would be decisive for ensuring single-photon excitation of the polymer strands, we are unable to measure these lower energies accurately and thus refrained from these experiments. Let us now turn our attention to the transient spectra of [SQA-SQB]n in CHCl3 at 13 100 cm−1 excitation with a 50 nJ pulse−1 pump energy (Figure 4). The spectra at early times (0− 320 fs after the beginning rise of the signals at 1.40 ps) show the evolution of a strong ground-state bleach (GSB, probably superimposed by stimulated emission (SE) on the low-energy flank) at the energy of the strongest absorption (13 100 cm−1) and an excited-state absorption (ESA) at somewhat higher energy (ca. 13 400 cm−1, see inset). This ESA decays very rapidly and leaves the GSB and very weak ESA between 16 000 and 24 000 cm−1 as the only prominent signals which then decay in a multiexponential way within ca. 1 ns (Figure 5). The GSB shows a slight red shift within the first ca. 0.5 ps which may be caused by the vibrational relaxation of torsional modes.107 After that, the shape of the GSB remains constant. Taking into account that multiple excitations are present within one polymer strand in solution, we have to consider singlet−singlet exciton annihilation as a deactivation process at early times. Indeed, while pump−probe experiments with

(7)

This yields Pk = 0.012 (k = 1), 0.044 (k = 2), 0.10 (k = 3), 0.16 (k = 4), 0.19 (k = 5), 0.18 (k = 6), 0.14 (k = 7), etc. Thus, multiple excitations with the highest probability of k = 5 result. This is essentially a consequence of the huge molar extinction coefficient of squaraine dyes. The extinction coefficient of [SQA-SQB]n in toluene is much lower at the high-energy peak of the exciton manifold at 15 000 cm−1, ε = 105 000 L mol−1 cm−1. This gives Pm = 0.050 and Pk = 0.38 (k = 1), 0.22 (k = 2), 0.079 (k = 3), 0.020 (k = 4), etc. In CHCl3, the extinction coefficient at the maximum peak (13 100 cm−1) is 204 000 L mol−1 cm−1, which gives Pm = 0.11 and Pk = 0.19 (k = 1), 0.27 (k = 2), 0.23 (k = 3), 0.14 (k = 4), etc. Thus, when we perform pump−probe experiments with the copolymer we deal in any case with multiple excitations even at a low pump energy of 50 nJ pulse−1 (= 23 μJ cm−2 ≙ 9.1 × 1013 photons cm−2 at 12 700 cm−1). While even lower pump 17473

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varying pump energies (50, 100, 200, and 400 nJ pulse−1) show almost the same spectral behavior at all times, their decay profiles at 15 000 cm−1 that are normalized at t = 0 display strong differences particularly at early times, which is indicative of annihilation processes (Figure 5). Different theories have been applied to describe annihilation processes depending on the mechanism at work. The theory widely used to describe exciton annihilation in solids (films) of polymers is based on the solution of a rate equation of the form ∂n/∂t = −kn(t) − γ(t)n(t)2 where k is the rate constant for firstorder deactivation and γ(t) is the (time-dependent) rate constant pertaining to second-order annihilation processes. In the case of the one-dimensional rate-limiting diffusion of excitons, γ is time-dependent and has the form γ = γ0/t1/2. The solution of the differential equation leads to eq 8.5,74,79,80 exp( −kt ) n = n0 1 + (2n0γ0/ k )erf( kt )

are treated as distinct species which may then recombine to yield one monomer in the ground state and the other in the singlet excited state (after very rapid relaxation from a higher excited state). The decay of a polymer strand with only noninteracting excitons (B) may then proceed via many steps (C → D (and E in toluene)) which may represent species with slightly different geometries and/or which may be caused by the distribution of chain length. We also tested alternative kinetic analyses: a fit of the bleach intensity at 15 000 cm−1 between 10 and 8000 ps with a stretched exponential function (Kohlrausch equation, I(t) = exp[−(t/τ0)β])108 gives a mean lifetime of τ0 = 63 ps and β = 0.47. However, fitting the data right after the end of the excitation pulse at ca. 0.3 ps requires the addition of two exponential functions to model the decay at early times. In this fit τ1 = 0.32 ps, τ2 = 2.65 ps, τ0 = 23 ps, and β = 0.36. While this analysis indicates that the decay at longer times has a broad lifetime distribution, a maximum entropy analysis109,110 of the same data with the MEMExp software111,112 yields five independent time components with a slightly overlapping distribution where the one with the shortest lifetime stands out both in amplitude and time separation from the other components (Supporting Information, Figure S5). This somewhat contradictory behavior may indeed point toward a mixture of discrete and distributed lifetimes. Thus, we consider the kinetic scheme (Figure 6) to be a heuristic model particularly at later times where we formulated a series of discrete species C− D which in fact may be representatives of only a distribution of states. We used this scheme and performed a global target analysis where we assume that a biexciton in A has twice the extinction coefficient as the monoexciton. For species B−D we assume the same extinction coefficient of the GSB. The global target analysis of the transient map according to Figure 6 yields species-associated difference spectra (SADS), lifetimes, and efficiencies for each species A−D which are given in Figure 7 and Table 2. In the experiment in CHCl3 there is a red shift of 90 cm−1 between the prominent GSB of the SADS of species A and B at ca. 12 900 cm−1. The SADS of species B− D are almost identical, and the bandwidth of the strong GSB at two-thirds maximum height varies between 300 and 340 cm−1, which is distinctly narrower than the absorption peak in the steady-state absorption spectrum. The most prominent difference in the decay kinetics between the various pump energies is the relative efficiency η with which biexciton A is initially formed. This efficiency increases from 0.25 for 50 nJ pulse−1 to 0.43 for 400 nJ pulse−1 (Table 2). The lifetimes of the individual species and all other efficiencies vary only a little. The transient spectra in toluene at 12 700 cm−1 excitation (Supporting Information, Figure S4) are superficially similar to the ones in CHCl3. Considering the much higher extinction coefficient in toluene, it is surprising to find that neither the spectra nor the multiexponential decay depend on the pump energies. The global target fit to the data gave five components A−E (Figure 7). The bandwidths of the strong GSB at twothirds the maximum height is 170 cm−1 even narrower than that in CHCl3. In contrast to the experiment in CHCl3 there is little variation in the efficiencies and lifetimes at different pump energies. This changes when the polymer is excited at the highenergy maximum of the exciton manifold at 15 000 cm−1 (Supporting Information, Figure S4). Besides a GSB at 15 200 cm−1 which is more pronounced than in the other experiments, the decays now strongly depend on the pump energy as can be viewed from Figure 7 and Table 2. The

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However, this theory holds true only in cases of diffusioncontrolled processes in large aggregates of chromophores or solid films of conjugated polymers. The same equation is applicable if the diffusion of excitons is infinitely slow and annihilation occurs via long-range 3D dipole−dipole Förster energy transfer. In fact, attempts to fit the whole decay curves in Figure 5 by eq 8 failed, also when only early time intervals are considered (e.g., 0−20 ps). In cases of small aggregates (such as polymers in dilute solution) where the annihilation is determined by the static rate of equilibrated excitons, Paillotin et al.106 and Larsen et al.79 showed that annihilation can be expressed as a sum of exponential functions. This theory is valid in cases where the mean diffusion length of excitons LD is large compared to the average distance of the excitons. Thus, based on this assumption we developed a kinetic scheme (Figure 6) that

Figure 6. Kinetic scheme for the deactivation of excited polymer strand with biexcitons (red) and monoexcitons (blue). M stands for monomer unit SQA-SQB. Photoexcitation leads to a mixture of polymer strands with an overall relative population of biexcitons ηAB and monoexcitons 1 − ηAB. The efficiencies ηBC etc. refer to the given step while the remainder 1 − η is the direct deactivation to the ground state which is not depicted explicitly.

assumes the formation of single excitons (marked in blue in A) and biexcitons (marked in red in A) within the instrument response time after the excitation of the polymer. With biexcitons we assign an excited-state entity in which two monomers are excited which are in close proximity so that singlet−singlet annihilation (SSA) may occur. The biexcitons 17474

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Figure 7. (a−c) SADS from the global fits of transient maps of [SQA-SQB]n obtained with 50 nJ pulse−1. (d) Normalized SADS B, inverted fluorescence spectrum (divided by ṽ2), inverted absorption spectrum, and difference of SADS and absorption spectrum to simulate the ESA spectrum.

Table 2. Lifetimes of the Spectral Components and Efficiencies for the Processes in Figure 6 Obtained from a Global Target Fit to the Transient Maps of [SQA-SQB]n at the Given Pump Energy per Pulse E/nJ pulse−1

η

CHCl3 @ 13 100 cm−1 50 0.25 100 0.31 200 0.39 400 0.43 toluene @ 15 000 cm−1 50 0.11 100 0.16 200 0.24 400 0.35 toluene @ 12 700 cm−1 50 0.45 100 0.47 200 0.38 400 0.41

τA/ps

τB/ps

ηBC

τC/ps

ηCD

τD/ps

0.61 0.54 0.40 0.57

6.4 4.9 4.2 5.9

0.50 0.52 0.47 0.45

46 38 44 96

0.38 0.40 0.38 0.21

260 270 360 1000

0.82 0.66 0.62 0.56

5.0 3.9 3.4 2.9

0.65 0.65 0.64 0.62

54 54 50 42

0.55 0.60 0.62 0.67

0.29 0.26 0.31 0.29

1.8 1.5 1.2 1.5

0.51 0.51 0.52 0.53

20 18 17 16

0.58 0.57 0.55 0.59

bandwidths of the strong GSB at two-thirds the maximum height is again ca. 170 cm−1. There is a spectral GSB

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ηDE

τE/ns

670 720 700 600

0.12 0.14 0.18 0.27

3.4 2.6 2.3 2.0

290 290 260 200

0.37 0.42 0.48 0.53

1.2 1.6 1.5 1.5

DISCUSSION AND CONCLUSIONS

Exciton coupling theory predicts for alternating copolymers with elongated zigzag structure allowed transitions into the bottom and top bands of the exciton manifold. Indeed for [SQA-SQB]n we found a strong transition on the low-energy side and a weaker but still significant transition on the highenergy side of the absorption manifold. However, there is no real gap between these transitions, which may be caused by vibrational progression of these transitions but is more likely due to disorder and deviation from a fully regular zigzag structure. In toluene solution the lowest-energy transition is

component with 3.4 ns which has a much different shape than the other GSB bands at earlier times. In this spectrum the positive signal at 12 500 cm−1 is caused by residual stray light. As in the case of excitation in CHCl3, the efficiency for biexciton formation ηAB varies strongly with excitation energy (0.11 to 0.35 on going from 50 to 400 nJ pulse−1). Lifetimes τB and τE also vary somewhat. 17475

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on the order of 100 fs.114 The observation that the annihilation rates are not really constant and independent of the pump energy points toward deficiencies in our model assumptions. A more sophisticated theory of exciton annihilation involves Hamiltonians which incorporate one- and two-exciton manifolds, see e.g. refs 115−118. Here we employ just a heuristic model, leaving the more detailed theoretical analysis to future studies. In CHCl3 the exciton annihilation time is not much different (0.4−0.6 ps) from that in toluene. These times are in the same range as the annihilation rate in recently investigated helical πstacks of perylene diimides aggregates.119 Also all other lifetimes and efficiencies of [SQA-SQB]n do not deviate much in the two solvents besides the longest component in toluene which is in the nanosecond regime. This finding is surprising given the more narrow lowest-energy transition which indicates much stronger exciton delocalization in toluene than in CHCl3. Obviously this exciton delocalization does not lead to faster SSA processes. This emphasizes that at shorter times exciton diffusion is not the rate-limiting step for exciton annihilation but the static annihilation process of two already adjacent singlet excitons. The exciton diffusion may be explained by Förster-type energy-transfer process between concomitant dipole allowed relaxation (≙ fluorescence) and dipole allowed excitation (≙ absorption) processes at chromophores located at nearby sites m and n according to (n) (n) S(m) → S(m) 1 0 /S1 ← S0 . To be fast, this mechanism requires spectral overlap between the absorption (here GSB) and the emission (SE) spectrum. Because of the small Stokes shift and the highly allowed transitions this is clearly the case and should lead to very fast energy transfer. On the other hand, the SSA process can be understood by the dipole interaction of dipole allowed relaxation (≙ fluorescence) and dipole allowed excitation from S1 to a higher excited state (≙ excited state 84 (n) absorption) according to S(m) → S(m) ← S(n) This 1 0 /Sx 1 . process also requires spectral overlap, and we have found such an ESA a little shifted to higher energies than the prominent GSB. However, because of this blue shift there is a much smaller spectral overlap with the fluorescence (Figure 7d). Thus, the annihilation is probably much slower than singlet energy transfer and is the rate-limiting process. To substantiate this interpretation we estimated the energy transfer rate kFT by Förster theory which is based on the golden rule expression of eq 9a, where J is the electronic coupling and ρ(ṽ) is the density of interacting initial and final states.102,120

much narrower than in CHCl3 and that of the monomeric parent compounds, which indicates delocalization of excitation over several [SQA-SQB] monomer units in toluene as a consequence of a more ordered structure in this solvent. This exchange narrowing emphasizes the essential J-aggregate-like behavior of the polymer and has not been observed before for any conjugated polymer to the best of our knowledge. The interesting observation in the transient spectra that the bandwidth at two-thirds the maximum height is much smaller in the GSB signal at ca. 12 700 cm−1 of the SADS than the analogous steady-state absorption bands needs explanation. A comparison of the normalized SADS in toluene at 15 000 cm−1 excitation with the negative steady-state absorption spectrum and the fluorescence spectrum in toluene is given in Figure 7d. From this comparison we see that the GSB of species B (and also C and D) can be superimposed on the low-energy side of the prominent negative signal with the steady-state spectrum. Interestingly, there is no stimulated emission visible which should appear as a negative signal at lower energy than the GSB signal, as can be seen from comparison with the steady-state emission spectrum divided by ṽ2.113 Calculating the difference between the steady-state absorption spectrum and SADS yields a rough estimate for the ESA spectrum. This spectrum has a distinct absorption on the high-energy side above ca. 13 000 cm−1 which might be caused by two-photon states which should have somewhat higher energy than the lowest band in a J-aggregate exciton manifold.95 This superposition of ESA of this two-photon state and GSB appears to be responsible for the narrow GSB in the transient spectra. The fluorescence lifetimes both in CHCl3 and in toluene agree very well with the decay times obtained from transient absorption spectroscopy at later times. The strong GSB is the most prominent signal in the transient maps in both solvents and decays multiexponentially. The pump energy dependence in CHCl3 at 13 100 cm−1 and in toluene at 15 000 cm−1 clearly proves annihilation processes to be responsible for the rapid signal decay at early times. The observation that the pump energy at 12 700 cm−1 excitation in toluene has no influence may be understood by the fact that there are multiple excitations present in one polymer strand caused by the high extinction coefficient at the pump wavenumber. This leads to a saturation effect. When plotted together, the decay profiles in toluene at 15 000 cm−1 excitation (50 → 400 nJ pulse−1) and the one at 12 700 cm−1 excitation with 50 nJ pulse−1 (Figure 5) show that the SSA in the latter experiment is even more pronounced than at 400 nJ pulse−1 in the former. From Table 2 we can see that in this series of experiments the efficiency of biexciton formation increases from 11 → 35% and then to ca. 45%. In the same series the lifetime of biexciton τA decreases from 0.82 to 0.29 ps. All other lifetimes and efficiencies also show a monotonous trend along this series even at very late decay times. This shows that the variation of pump energy influences processes not only at early times but also at later times. One possible explanation is that at later times when geometry relaxations have taken place and have led to the localization of excitons, the diffusion of these localized excitons is much slower, which then also retards the formation of new biexcitons which thus apparently annihilate more slowly because it is now an exciton diffusion-controlled process. In any case we can assign the first prominent decay time τA to the rate of exciton annihilation in toluene. However, one should be aware that parallel to exciton annihilation, other relaxation processes such as the localization of excitation may take place

kFT =

2π 2 J ρ(ν)̃ [in SI units] ℏ

(9a)

kFT = 4π 2cJ 2 ρ(ν)̃ = 1.18(ps−1)(J /cm−1)2 (ρ(ν)/cm) ̃ (9b)

kcoh =

2J [in SI units] h

kcoh = 0.06(ps−1)j/cm−1

(10a) (10b)

For practical application we use eq 9b where the electronic coupling J is given in cm−1. This quantity was evaluated from the exciton coupling energy (see above and Supporting Information) which is ca. 480 cm − 1 in toluene. Furthermore, c is the speed of light (3 × 1010 cm s−1) and ρ(ṽ) [cm] is approximated by the spectral overlap ρ(ṽ) ≈ ∫ If(ṽ) ε(ṽ)ṽ−4 d(ṽ) of reduced and area-normalized 17476

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diimide dyes or cyanine dyes.82,87 Because of the very high exciton diffusion constant, singlet−singlet annihilation is the rate-limiting step for deactivation of the copolymer in solution at high laser fluencies. This is unlike many conjugated polymers in the solid state where diffusion-limited annihilation is usually found. In this way copolymer [SQA-SQB]n is a unique model system which combines the excitonic features of J-aggregates with the chemical robustness of a polymer.

emission and absorption spectra, respectively, on the wavenumber scale. Because in the present case the absorption spectrum is broad as a result of excitonic interactions, we adjusted the intensity of ε(ṽ)ṽ−1 at its maximum to those of the reduced and area-normalized fluorescence spectrum If(ṽ)ṽ−3. By this procedure we obtain ρ(ṽ) = 4.1 × 10−4 cm and with that kFT = 110 ps−1 for toluene. Using the appropriate values in CHCl3 (J = −470 cm−1 and ρ(ṽ) = 2.6 × 10−4 cm) we evaluate kFT = 68 ps−1 for CHCl3. These rates are about an order of magnitude faster than those calculated for the intrachain exciton transfer in polyindenofluorene, which is a rather stiff conjugated polymer,121−123 or other conjugated polymers in solution124 such as MEH-PPV.125 It is questionable whether a theory describing an incoherent process gives accurate rates for a system for which we assume at least partially coherent energy migration126 (which is equivalent to exciton coupling). In the latter case eq 10 applies, which yields 29 ps−1 for toluene and 28 ps−1 for CHCl3.89 In any case, our estimate shows that in [SQA-SQB]n energy migration is faster than exciton−exciton annihilation (rates of ca. 1−3 ps−1) which supports our view of static annihilation processes to dominate the deactivation at high pump energies in [SQA-SQB]n polymer. The above estimated exciton transfer rates kFT = 110 ps−1 in toluene and kFT = 68 ps−1 in CHCl3 allow us also to estimate the diffusion constant for excitons by eq 11 in which we use a = 3.5 nm as the end-to-end distance of an SQA-SQB monomer as the minimum size of an exciton which then gives D = 670 nm2 ps−1 (= 6.7 cm2 s−1) in toluene and D = 420 nm2 ps−1 (= 3.1 cm2 s−1) in CHCl3.

a2 2

(11)

2Dτ ̅

(12)

D = kFT LD =

R 0 = a 6 kFTτ ̅

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EXPERIMENTAL PART Gel permeation chromatography (GPC) was performed in CHCl3 at room temperature with polystyrene standards on a Shimadzu instrument (model SPD-M20A diode array detector, CBM-20A system controller, LC-20AD solvent delivery unit, DGU 20A9 online degasser). An SDV column (PSS SDV linear S, dimension 8 × 300 mm2, particle size 10 μm) from PSS/ Mainz, Germany was used. UV/vis/NIR absorption spectroscopy was performed with a Jasco V670 UV/vis/NIR spectrometer or a Cary 5000 UV/vis/ NIR spectrophotometer. The compounds were dissolved in Uvasol solvents from Merck and were measured in 1 cm quartz cuvettes in a concentration range from ∼1 × 10−5−1 × 10−7 mol L−1 to exclude aggregate formation. As reference, the pure solvent was used. Fluorescence spectroscopy was performed in 1 cm standard cuvettes with a Photon Technology Instruments (PTI) QM fluorescence spectrometer with a cooled photomultiplier (model R928P) or an InGaAs detector. The compounds were dissolved in Uvasol solvents from Merck and degassed in a stream of argon for 10 min prior to the experiment. As a fluorescence reference, oxazine 1 in ethanol (Φf = 0.151 ± 0.0025) was used.130 The quantum yield of oxazine 1 was determined in an absolute way at four different concentrations with an integration sphere and an Edinburgh Instruments FLS980 fluorescence spectrometer equipped with double monochromators and corrected for self-absorption.131 In the same way, the absolute quantum yield of SQA was determined to be 0.573 ± 0.0065 in toluene. To determine the relative quantum efficiency, the following equation was used,

(13)

With an average natural lifetime of τ ̅ ≈ 1.4 ns in toluene and τ ̅ ≈ 0.20 ns in CHCl3 (from the average fluorescence lifetime τ ̅ = Σiαiτi2/Σiαiτi at very low excitation energies in Table 1), we estimate the average exciton diffusion length by eq 1280 to be LD = 1370 nm in toluene (LD = 410 nm in CHCl3). This distance works out even considerably longer when we use the exciton length of 3.7 × SQA-SQB monomer units in toluene for a in eq 11. Taking the rate for coherent energy transfer from eq 10 we evaluate D = 180 nm2 ps−1 (LD = 710 nm) in toluene and D = 170 nm2 ps−1 (LD = 260 nm) in CHCl3. In any case, in both solvents the exciton diffusion length of [SQA-SQB]n is distinctly larger than the average polymer length (23.4 × 3.5 nm = 82 nm), which simply means that an exciton may travel several times back and forth along the polymer chain until it decays to the ground state by either exciton annihilation or by first-order relaxation processes. It is instructive to estimate the Förster radius R0 for this energy transfer process by using eq 13 which yields 26 nm in toluene and 17 nm in CHCl3. In conclusion, compared to other conjugated polymers, [SQA-SQB]n behaves much differently in terms of spectral narrowing of the lowest excitation band and in the high exciton diffusion length. The latter is about 2 orders of magnitude longer than in standard conjugated polymers. 103 Even polymeric cyanine dyes127 or regioregular poly-3-hexylthiophene which display highly ordered structural domains do not show similar properties.128,129 The squaraine copolymer studied in this work resembles more typical J-aggregates of perylene

⎛ I(v )̃ × OD × (n 20)2 ⎞ Ref D ⎟ Φf = Φf,Ref ⎜ 20 2 I ( v ) OD ( n × × ⎝ ̃ Ref D) ⎠

where I(ṽ) is the integral of the emission band, OD is the optical density at the excitation wavelength, n20 D is the refractive index of the solvent, and Φf is the fluorescence quantum yield. Fluorescence lifetimes were measured with an Edinburgh Instruments TCSPC fluorescence lifetime spectrometer FLS980. A 656 nm laser diode was used for excitation and colloidal silica in deionized water was used as a scatter solution to determine the instrument response. The decay curve was fitted with a biexponential decay function to obtain the fluorescence lifetime. Solvent and solution were used as in the steady-state experiment. Femtosecond Transient Absorption Pump−Probe Spectroscopy. The setup consists of a Helios transient spectrometer from Ultrafast Systems and a Solstice femtosecond laser from Newport Spectra Physics which has a pulse duration of 100 fs. The pump wavenumbers of 12 700, 15 000, and 13 100 cm−1 are generated by an OPA (TOPAS-C) with a pulse duration of about 140 fs. To probe the excited sample the laser fundamental of 12 500 cm−1 is used to generate a white light continuum from 25 000 to 12 500 cm−1. For the detailed 17477

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Notes

setup, see ref 132. All experiments were performed in quartz cuvettes from Spectrocell (Oreland, PA) with an optical path length of 2 mm, equipped with a microstirrer. All samples were dissolved in CHCl3 or toluene and filtered. Before the measurement the solution was purged with pure argon for at least 30 min. The concentration of the samples was ∼1 × 10−6−5 × 10−6 mol (monomer unit)−1 L−1. Before analysis the transient maps were corrected for stray light contributions which is particularly important because the GSB is strongest at the pump wavenumber. Then, the timeresolved spectra were analyzed by global fitting with GLOTARAN133 by employing a target model (i.e., branched model) modeling the IRF (ca. 150 fs), the white light dispersion (chirp), and the coherent artifact (the model used has the time characteristics of the IRF plus an additional exponential function) at time zero to yield the speciesassociated difference spectra (SADS) together with their corresponding lifetimes. Syntheses were performed in standard glassware, and chemicals were purchased from commercial suppliers and used without further purification. The reaction was carried out under a nitrogen (oxygen removal via copper catalyst R3-11 from BASF; drying via Sicapent from Merck) atmosphere in flame-dried glassware, and the THF was dried according to common literature procedures and stored under nitrogen. The preparation of compounds SQ110 and SQ211 is described in previous publications. Copolymer [SQA-SQB]n. Squaraines SQ1 (170 mg, 183 μmol), SQ2 (162 mg, 183 μmol), and NaHCO3 (615 mg, 7.32 mmol) were dissolved in dry and peroxide-free THF (16 mL) and water (4 mL) under a nitrogen atmosphere. The mixture was degassed in a stream of nitrogen for 10 min, and Pd(PPh3)4 (4.23 mg, 3.66 μmol) was added. The solution was stirred at 105 °C for 6 days. Brine (20 mL) and CHCl3 (20 mL) were added, and the layers were separated. The organic layer was washed with brine (2 × 20 mL) and water (20 mL), and the solvent was evaporated under reduced pressure. The residue was dissolved in CHCl3 (10 mL), and the solution was dripped into MeOH/water (4:1, 500 mL). The precipitate was filtered off and washed with MeOH (50 mL) and water (50 mL). The crude product was purified by subsequent Soxhlet extractions using MeOH, hexane, and acetone. The remaining solid was dissolved in a little CHCl3 and dripped into MeOH. The precipitate was filtered off and washed with MeOH to obtain 88.0 mg (62.9 μmol, ∼34%) of a ruby-colored solid. 1H NMR (400 MHz, CDCl3): δ 7.62−7.47 (8 H), 7.14−7.01 (4 H), 6.55 (2 H), 6.01 (2 H), 4.26−3.88 (8 H), 1.97−1.76 (24 H), 1.76− 1.46 (16 H), 1.46−1.11 (24 H), 1.11−0.98 (12 H), 0.93−0.77 (24 H); Mn = 32 800; Mw = 63 400; Xn = 23.4; PDI = 1.93.

■

The authors declare no competing financial interest.

ACKNOWLEDGMENTS

■

REFERENCES

We acknowledge funding by the Deutsche Forschungsgemeinschaft within the Research Group FOR 1809 and the Bavarian State Ministry of Science, Research and the Arts within the SolTech network. We thank Hamamatsu Photonics and Edinburgh Instruments for generous support.

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ASSOCIATED CONTENT

S Supporting Information *

Transient absorption spectra in toluene and time decay traces at selected wavenumbers, time-dependent steady-state absorption spectra, 1H NMR spectrum, maximum entropy analysis of pump−probe spectra in CHCl3, and a rigorous mathematical description of the exciton model for the copolymer. 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]. 17478

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