Anomalous Energy Transfer Dynamics due to Torsional Relaxation in ...

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Oct 18, 2006 - Anomalous Energy Transfer Dynamics due to Torsional Relaxation in a Conjugated Polymer. Sebastian Westenhoff,1,* Wichard J. D. Beenken ...
PRL 97, 166804 (2006)

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PHYSICAL REVIEW LETTERS

Anomalous Energy Transfer Dynamics due to Torsional Relaxation in a Conjugated Polymer Sebastian Westenhoff,1,* Wichard J. D. Beenken,2 Richard H. Friend,1 Neil C. Greenham,1 Arkady Yartsev,3 and Villy Sundstro¨m3 1

Cavendish Laboratory, University of Cambridge, Madingley Road, Cambridge CH3 0HE, United Kingdom 2 Department of Physics, Technische Universita¨t Ilmenau, 98684 Ilmenau, Germany 3 Department of Chemical Physics, Lund University, Box 124, S-221 00 Lund, Sweden (Received 8 May 2006; published 18 October 2006) In isolated conjugated polymers two explanations are in discussion for the redshift of the emission on a picosecond time scale —exciton energy transfer (EET) between conjugated segments along the chains and conformational changes of these segments themselves, i.e., torsional relaxation. In order to resolve this question we perform femtosecond time-resolved transient absorption measurements of the energy relaxation of poly[3-(2,5-dioctylphenyl)thiophene] in toluene solution. We show that torsional relaxation can be distinguished from EET by site-selectively exciting low-energy conjugated segments. We present a unified model that integrates EET and torsional dynamics. In particular, comparison to ultrafast depolarization measurements shows that torsional dynamics cannot be neglected when analyzing EET dynamics and furthermore reveals that the exciton extends itself by about 2 monomer units during torsional relaxation. PACS numbers: 72.80.Le, 62.40.+i, 71.35.Cc, 73.20.Jc

0031-9007=06=97(16)=166804(4)

Panel (a) of Fig. 1 shows that the absorption spectra of poly[3-(2,5-dioctylphenyl)thiophene] (PDOPT) are structureless in solution compared to films. Also the Stokes shift is larger in solutions (216 meV) than in films (80 meV).

Absorbance & PL

(a) Film

Solution 1.8 2.0 2.2 2.4 2.6 2.8 Energy (eV)

(b) 0 ∆OD (arb.u.)

Excitation energy transfer (EET) in conjugated polymers has attracted much scientific interest [1– 4]. The EET is interpreted as hopping of Frenkel excitons localized on extended segments of the conjugated backbone [5]. The conjugated segments are thought to be separated by conformational defects [6], but a detailed quantitative understanding has so far not been achieved. More recently, detailed simulations following a golden rule formalism have revealed that the spatial extent and geometry of hopping sites is crucial for quantitative models of EET [3,7]. Because the size of excitons and transfer distances are of comparable magnitude, methods beyond the pointdipole approximation have to be used for the calculation of the electronic coupling. Examples are the distributed monopole [3] and the line-dipole approximation [8]. We have demonstrated previously that the latter method can be used to accurately determine the size of excitons on polymer chains in solution [7]. It is widely accepted that conjugated polymers undergo conformational changes after photoexcitation, in general, from aromatic towards quinoidal geometries [9]. This modifies torsion constants between conjugated repeat units, and in general, these are increased. However, the kinetics of the torsional relaxation have never been clearly demonstrated because its signature, a dynamic Stokes shift, is masked by the energy relaxation due to EET. In this work we circumvent the problem by using frequency- and polarization-resolved femtosecond transient absorption spectroscopy to characterize the time scale of torsional relaxation and EET. Comparison of these experiments with computer simulations of EET along polymer chains shows that torsional dynamics cannot be neglected when analyzing EET kinetics. The depolarization kinetics can be reproduced only when the EET is accompanied by a dynamical increase of the size of excitons due to torsional relaxation.

(c) ∆OD (arb.u.)

DOI: 10.1103/PhysRevLett.97.166804

Film exc 2.00 (eV)

49 ps 4.8 ps 1 ps 0.3 ps

0

Solution exc 2.13 (eV)

493 ps 301 ps 50 ps 80 fs

1.6 1.7 1.8 1.9 2.0 2.1 2.2 Energy (eV) FIG. 1. Panel (a) shows absorption and photoluminescence spectra of a spin-cast film and a toluene solution of PDOPT. Panels (b) and (c) show time-resolved transient absorption spectra the same samples.

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© 2006 The American Physical Society

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PHYSICAL REVIEW LETTERS

Both observations have been attributed to the strong coupling to low-energy (i.e., torsional) modes and are typical for many conjugated polymers and oligomers [10,11]. Karabunarliev et al. find that the low-energy modes become stiffer after excitation, which leads to the breakdown of mirror symmetry between absorption and emission [10]. These results are supported by ab initio quantum chemical calculations of biphenyl that reveal a steep torsional potential energy profile for the excited state with a minimum at a planar conformation (0 ) and a flat profile for the ground state with a minimum at around 30 – 40 [12]. Based on this, Ref. [12] concluded that the absorption is broadened, the molecules planarize after photoexcitation and that the emission is significantly more structured than the absorption. Thus, the dynamics of torsional relaxation after photoexcitation may be observed as a dynamic Stokes shift. In order to time resolve the dynamic Stokes shift we use femtosecond transient absorption (FTA) spectroscopy with site-selective excitation. Excitation and probe pulses were generated using noncollinear parametric amplifiers. For excitation we used pulses of 10 nm (FWHM) compressed to 25 fs duration. The uncompressed probe pulses spanned from 1.6 to 2.2 eV. The differential spectra were detected using a spectrograph and two diode arrays with shot-to-shot digitization. The raw data were corrected for chirp of the probe pulses by adjusting the zero time at half rise. The excitation fluence for solution measurements (1  1014 photons=cm2 ) was tested to be in the linear regime, and for films the lowest possible photon density (7  1013 photons=cm2 ) was chosen because no linear regime was found. The experimental details for the anisotropy measurements can be found elsewhere [7]. Panels (b) and (c) of Fig. 1 display time-resolved transient absorption (OD) spectra of the stimulated emission (SE) of PDOPT in film and solution. In the following, we will analyze only the second peak of the SE because it is well separated from the ground state bleach and has only minor contributions from photoinduced absorption [13]. By inspection of its position it can be clearly seen that the spectra recorded in solution show a dynamic redshift, whereas in films the spectra do not shift. In Fig. 2 the time evolution of these peak shifts are shown. It is confirmed that for films no redshift is found for excitation at 2.00 eV, which is the red onset of absorption (solid squares). For PDOPT in solution the excitation energies were 2.13 eV (open dots) and 2.33 eV (open triangles). The former corresponds to the red onset of absorption, and the latter is in the center of the absorption band. Importantly, both result in shifts on a picosecond time scale. Notably, the total magnitude of the peak shift is 15 meV for the low excitation energy, whereas for excitons in the center of the absorption band it increases to 40 meV. The latter dynamic redshift is expected, because EET leads to energy relaxation in the density of states [7,14].

2.04 Energy (eV)

PRL 97, 166804 (2006)

2.01

exc 2.33 (eV) solution exc 2.13 (eV)

1.98 1.88 1.86 0.1

exc 2.00 (eV) 1

10 Time (ps)

film 100

FIG. 2. The time evolution of the center energy of Gaussian fits to the second peak of the SE (Fig. 1) is plotted for films (solid squares) and toluene solution (open marks). Also shown are the average site energy of EET simulations as in Ref. [7] (dashed lines), with torsional relaxation in the energy domain according to Eq. (1) (dotted lines) and additional dynamical conjugation length following Eq. (2) (solid lines).

However, this explanation cannot be applied when the lowenergy segments are site-selectively excited. We propose that in PDOPT torsional relaxation of the excited conjugated segments results in this dynamical Stokes shift. In the ground state the chains are torsionally disordered due to the shallow torsional potential with a nonplanar equilibrium position. After vertical excitation the steep profile of the potential energy surface in the excited state initiates torsional relaxation into planar conformations with quinoid character. The absence of the redshift in films (Fig. 2) strongly supports our interpretation. Here, the chains are locked in a crystalline arrangement and may already be planarized in the ground state [15,16]. Therefore torsional relaxation may not take place. Furthermore, our results for PDOPT agree well with findings for oligothiophenes in solution, where a redshift of the photoluminescence (PL) was found on the same time scale [17]. We note that the time scale of relaxation is relatively slow compared to the vibrational cooling along high-energy stretching modes, which is found to be faster than 100 fs [18]. In conclusion, the site-selective FTA experiments show that the redshift of PL in PDOPT consist of two components that are identified as EET and torsional relaxation. We have shown earlier that the EET dynamics on conjugated polymer chains can be analyzed quantitatively by Monte Carlo simulations [7]. In these computer experiments, polymer chains are generated as a sequence of conjugated segments with length lseg . Conformational disorder is simulated by rotating each conjugated segment randomly in space with respect to the previous one [19]. The rotation angle is taken from a Gaussian distribution with standard deviation !  0:8 [7]. An energy Ei taken from the inhomogeneous density of states is assigned to

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PHYSICAL REVIEW LETTERS

Ei tocc;i   Ei  Etor exptocc;i =tor ;

(1)

where tocc;i is the residence time of the exciton on the conjugated segment i, tor is the time constant of planarization, and Etor is the amplitude of the energy relaxation. Note that we do not take any torsional relaxation in the ground state into account. For tor  15 ps and Etor  15 meV the agreement with the magnitude and kinetics of the experimental peak shift is greatly enhanced at red excitation (dotted lines). We note that even at this lowenergy excitation the exciton still migrates along the polymer chain by thermally activated energy transfer steps (see anisotropy below), but this results in only a very small redshift. Thus, the energy relaxation is in this case almost entirely due to torsional relaxation, and we can determine tor and Etor with good certainty. Torsional relaxation in the energy domain [Eq. (1)] influences the average excitation energy directly and also modulates the magnitude of the spectral overlap IDA that determines the EET rates. Since only the excited segment is allowed to relax while the photoexcitation migrates along the polymer, the decays seen in Fig. 2 are not simply monoexponential, but nontrivial convolutions of the torsional relaxation with the energy transfer dynamics. While the dynamic redshift is a sensitive probe of EET and torsional dynamics in the energy domain, a truly quantitative spatial account of EET can be given only by comparing the simulations to polarization anisotropy data [2,7,19]. When excitations migrate along conformationally

disordered polymer chains they lose their initial polarization and cause a decay of the anisotropy. Figure 3 compares the simulated anisotropies (lines) with experimental data (open dots). Panels (a) and (b) show data for blue and red excitation, respectively. It can be seen that for both excitation energies neither the conventional model (dashed lines) nor the simulations taking into account the effect of torsional relaxation in the energy domain using Eq. (1) (dotted lines) reproduce the measured decay of anisotropy. Both methods give very similar anisotropy decays, indicating that the EET rates are not sensitive to the small dynamical Stokes shift related to torsional relaxation. Directly after photoexcitation the excite states relaxes along the high-energy stretching modes on a femtosecond time scale [18]. However, the conjugated backbone is still torsionally disordered around nonplanar equilibrium position as in the ground state, which limits the delocalization of the exciton [8]. After torsional relaxation on a picosecond time scale into planar geometries, the number of conformational defects will be greatly reduced and the exciton can be expected to be more delocalized. We have included this effect into the simulations by using a timedependent conjugation length

0.4 Anisotropy

each segment. Excitons are placed site-selectively taking into account the homogenous line shape [20]. EET rates between two conjugated segments (D and A) are calculated 2 using the golden rule kDA  2 @ IDA VDA , where the spectral overlap (IDA ) is computed from the normalized homogeneous spectral line shapes. The excitonic coupling matrix element (VDA ) is calculated using the line-dipole approximation [8]. Within this approximation the electronic coupling depends sensitively on the length and shape of the conjugated segments. If EET is predominantly intrachain as it is the case on dissolved polymer chains, the linedipole EET simulations are a sensitive probe for the delocalization of excitons. We have previously determined the length parameter to be lseg  2:9 nm for PDOPT in solution [7]. Figure 2 compares the simulated average site energies with the experimental peak position of the SE. It can be clearly seen that the EET simulation with the conventional model described above (dashed lines) reproduces neither the magnitude nor the kinetics of the experimental peak shift (open dots) for redmost excitation. This strongly supports our interpretation that conventional EET alone is not a valid explanation for the redshift of the SE after excitation of low-energy sites, but that torsional relaxation has to be considered. We included this into the model by using time-dependent site energies:

exc 2.47 (eV) 0.3 0.2 (a) 0.4

Anisotropy

PRL 97, 166804 (2006)

exc 2.21 (eV)

0.3

0.2 0.1

(b) 1 Time (ps)

10

FIG. 3. The simulated (lines; for assignments see caption of Fig. 2) and measured anisotropies (open dots) are plotted for red and blue excitation in panel (a) and panel (b), respectively. The experimental anisotropy is defined as rexp t  ODk  OD? =ODk  2OD?  and the simulated anisotropy was calculated as rsim t  h15 3cos2 t  1 i, where t is the angle of the occupied segment at time t with respect to the initially excited segment.

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PHYSICAL REVIEW LETTERS

lseg;i tocc;i   lseg  ltor exptocc;i =tor ;

(2)

where ltor is the overall lengthening of the segments by planarization and is the only adjustable parameter. We recall that the segment length lseg;i tocc;i  sensitively controls the energy transfer rates between segments in in-line geometry. The planarization time (tor  15 ps) is still rigorously determined by the spectral kinetics as above, i.e., Eq. (1). Using ltor  0:7 nm, which corresponds to approximately 2 monomer units, gives the solid lines in Figs. 2 and 3. The agreement with the experimental anisotropy decay in Fig. 3 is dramatically improved when the dynamical lengthening of the segments is taken into account. Also the kinetics of energy relaxation in Fig. 2 are best fit using this assumption. Furthermore, the simulations agree well with either red or blue excitation for both the frequency and polarization-resolved experiments, which provides further assurance that the choice of parameters is realistic. Our findings suggest that the excitons expand in size during torsional relaxation by about two monomeric units. It would be interesting to compare this to excited state quantum chemical calculations, but because of the large size of conjugated polymers these computations have not been achieved yet. In order to illustrate the effect of the dynamical conjugation length on the EET times (DA  1=kDA ) we computed the quantity for two conjugated segments with in-line geometry. Isoenergetic transfer between torsionally relaxed segments (lseg  2:9 nm) yields DA  23 ps. We expect faster rates for downhill EET [3]. For example, an EET step of 0:12 eV (twice the inhomogeneous broadening) between the relaxed segments reduces the transfer time to DA  3 ps. Furthermore, our model demonstrates faster EET due to enhanced electronic coupling between shorter, torsionally disordered segments. For lseg  2:2 nm we calculate an isoenergetic transfer time DA  4 ps. Both effects together can yield EET as fast as DA  0:5 ps. This situation occurs at early times after photoexcitation at high energy. Our model calculations highlight that the electronic coupling is very sensitive to small variations in exciton size, which cannot be neglected when analyzing the energy transfer dynamics. As a consequence, analytical models describing EET are likely to fail for polymer chains in solution as long as they do not take torsional relaxation into account [1]. In conclusion, we have found that dissolved chains of PDOPT undergo torsional relaxation on a picosecond time scale. The process is shown to have a direct impact on exciton migration. Energy transfer simulations on chains with time-dependent site energies and conjugation lengths show that the average exciton size increases by about 2 monomer units during torsional relaxation. The authors thank Professor Erich Runge for a critical reading of the manuscript, and Professor Mats R. Andersson for providing the PDOPT samples. S. W. thanks

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the Oppenheimer Fund and the Lund Laser Center for financial support, and A. Y. and V. S. acknowledge the Swedish Research council, the Knut and Allice Wallenberg Foundation, and the Crafoord Foundation for funding.

*Electronic address: [email protected] [1] G. D. Scholes, Annu. Rev. Phys. Chem. 54, 57 (2003). [2] D. Beljonne et al., J. Phys. Chem. B 109, 10 594 (2005). [3] D. Beljonne, G. Pourtois, C. Silva, E. Hennebicq, L. M. Herz, R. H. Friend, G. D. Scholes, S. Setayesh, K. Mu¨llen, and J. L. Bre´das, Proc. Natl. Acad. Sci. U.S.A. 99, 10 982 (2002). [4] C. Madigan and V. Bulovic, Phys. Rev. Lett. 96, 046404 (2006). [5] S. Heun, R. F. Mahrt, A. Greiner, U. Lemmer, H. Ba¨ssler, D. A. Halliday, D. D. C. Bradley, P. L. Burn, and A. B. Holmes, J. Phys. Condens. Matter 5, 247 (1993). [6] S. N. Yaliraki and R. J. Silbey, J. Chem. Phys. 104, 1245 (1996). [7] S. Westenhoff, C. Daniel, R. H. Friend, C. Silva, V. Sundstro¨m, and A. Yartsev, J. Chem. Phys. 122, 094903 (2005). [8] W. J. D. Beenken and T. Pullerits, J. Chem. Phys. 120, 2490 (2004). [9] S. Tretiak, A. Saxena, R. L. Martin, and A. R. Bishop, Phys. Rev. Lett. 89, 097402 (2002). [10] S. Karabunarliev, E. R. Bittner, and M. Baumgarten, J. Chem. Phys. 114, 5863 (2001). [11] G. Heimel, M. Daghofer, J. Gierschner, E. J. W. List, A. C. Grimsdale, K. Mullen, D. Beljonne, J. L. Bredas, and E. Zojer, J. Chem. Phys. 122, 054501 (2005). [12] W. J. D. Beenken and H. Lischka, J. Chem. Phys. 123, 144311 (2005). [13] A. Ruseckas, M. Theander, L. Valkunas, M. R. Andersson, O. Inganas, and V. Sundstrom, J. Lumin. 76 –77, 474 (1998). [14] S. C. J. Meskers, J. Hubner, M. Oestreich, and H. Bassler, J. Phys. Chem. B 105, 9139 (2001). [15] K. E. Aasmundtveit, E. J. Samuelsen, W. Mammo, M. Svensson, M. R. Andersson, L. A. A. Pettersson, and O. Ingana¨s, Macromolecules 33, 5481 (2000). [16] H. Sirringhaus et al., Nature (London) 401, 685 (1999). [17] G. Lanzani, M. Nisoli, S. DeSilvestri, and R. Tubino, Synth. Met. 76, 39 (1996). [18] T. E. Dykstra, V. Kovalevskij, X. J. Yang, and G. D. Scholes, Chem. Phys. 318, 21 (2005). [19] M. M. L. Grage, T. Pullerits, A. Ruseckas, M. Theander, O. Ingana¨s, and V. Sundstro¨m, Chem. Phys. Lett. 339, 96 (2001). [20] As in our previous study we described the inhomogeneous density of states as a Gaussian with standard deviation inh  60 meV. The homogeneous line shape was composed from three Gaussians spaced by the energy associated with the main vibrational mode (0.179 eV) and standard deviation hom;abs  75 meV for absorption and hom;PL  60 meV for PL.

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