15404
J. Phys. Chem. C 2007, 111, 15404-15414
Intramolecular Exciton Relaxation and Migration Dynamics in Poly(3-hexylthiophene) Nathan P. Wells, Bryan W. Boudouris,† Marc A. Hillmyer, and David A. Blank* Department of Chemistry, UniVersity of Minnesota, 207 Pleasant Street SE, Minneapolis, Minnesota 55455 ReceiVed: June 15, 2007; In Final Form: July 24, 2007
Exciton dynamics are investigated for size selected poly(3-hexylthiophene) samples in dilute chloroform solutions using time-resolved fluorescence. The sizes range from an average of 39 monomers (Mw ) 6490 Da) to an average of 168 monomers (Mw ) 27860 Da). Both isotropic emission transients, which monitor downhill energy migration, and time-resolved emission depolarization, used to measure orientational migration of the excitons, are reported as a function of emission energy. Downhill energy migration accelerates significantly as the chains become longer. While amplitude of the initial (sub-100 fs) depolarization increases with chain length, the subsequent rate of exciton reorientation is relatively insensitive to chain length for times less than 30 ps and then slows as the chains become longer. The chain length dependence provides additional insight into the connection between spectral diffusion and exciton spatial migration. The results are considered in terms of the distribution of accessible exciton states and how this distribution changes with chain length.
1. Introduction Interest in the incorporation of conjugated polymers as a primary component in photovoltaic cells has been rapidly escalating, with efficiencies of devices reaching 5%.1-3 The conjugated polymer usually plays a dual role as one of the primary light absorbers and a charge transport medium. Photoexcitation typically results in the formation of bound electronhole pairs or excitons. In order to create charge carriers, the rate of exciton dissociation must successfully compete with relaxation and recombination.4-6 Dissociation takes place at the electron/hole carrier interface, and work to minimize the average exciton-interface distance has driven development of heterojunction based devices with increasing complexity, including bilayer and bulk heterojunction structures.1-4,7-14 In conjugated polymer films, there has been some debate over whether the primary π f π* excitation is a semiconductor bandto-band transition that leads to charged polarons or if this transition creates localized excitons on conjugated segments of the chain.15-28 More recent studies have concluded that for thin films of poly(phenylenevinylenes) (PPVs), photoexcitation leads largely to exciton formation with a binding energy of roughly 0.25 eV, and any free charge carrier generation is a result of exciton splitting due to defect sites or inadvertent dopants in the film.22-28 Compared with isolated polymer chains, studies of exciton dynamics in films are complicated by a number of additional considerations. These include the quality of the films with regard to conjugation defects and impurities, which vary with film preparation procedure, direct interchain excitation, and subsequent transfer of the excitation (exciton or polaron) between neighboring chains.24,27-32 Isolation of individual polymer chains can eliminate interchain dynamics and allow a more focused investigation of intramolecular excitation, with subsequent energy relaxation and migration.29,33-35 Such conditions can be met in dilute solutions if solvent coupling to the polymer’s electronic energy gap is * Corresponding author. E-mail:
[email protected]. † Department of Chemical Engineering and Materials Science, University of Minnesota.
relatively weak and the concentration is low enough to avoid interchain interactions.33-35 Some studies on the PPVs have suggested aggregation effects in solution that may come from distinct chains or from folding of a single chain.29,36 Aggregation can also be driven by the addition of a poor solvent, for example, adding alcohol to solutions of poly(3-alkylthiophenes) (P3ATs) creates aggregates with spectroscopic properties that resemble films.37,38 Aggregation speeds up the excitation energy transfer by allowing the excitons to transfer between subunits that belong to distinct chains or subunits on separate regions of the same chain.14,31,39,40 However, under conditions where aggregation, inter- or intramolecular, can be avoided, it becomes possible to investigate the coupling of the electronic and nuclear degrees of freedom within individual conjugated polymer chains in the absence of such complications.33-35,41 Photoexcitation of isolated conjugated polymer molecules leads to exciton formation, where the chains have enough structural disorder to cause localization onto a segment shorter than the chain length, and essentially no free charge carriers are formed.21,24,40,42-47 Conjugated polymers generally display photophysics that are challenging to properly describe because of the complexity of the electronic-nuclear coupling.23,34,35,42,48-50 Excitation and excited-state dynamics in these systems is a topic of substantial recent investigation.23,24,33-35,38-43,46-63 The developing picture includes initial excitation into a delocalized exciton state that very rapidly, sub-100 fs, localizes onto a handful of repeat units.42,49,50,63-65 For example, in the case of poly[3-(2,5-dioctylphenyl)thiophene] (PDOPT), the initial excitation localizes onto about six repeat units.33,34,41 Subsequently, the exciton relaxes via a combination of spectral diffusion within a given segment and intramolecular energy transfer to segments of lower energy.31,33-35,38,41,51-55,57-62 Spectral diffusion due to nuclear relaxation within a segment can span many time scales. Displacement of localized vibrations can relax in tens of femtoseconds to picoseconds. Torsional motions that can extend the length of a given segment by 1-2 repeat units, with concomitant lowering of the energy, have been reported to take place in approximately 20 ps.34 Resonance energy transfer along the chain, or RET, is commonly described as incoherent within
10.1021/jp074657j CCC: $37.00 © 2007 American Chemical Society Published on Web 10/03/2007
Migration Dynamics in Poly(3-hexylthiophene) a Fo¨rster type model.29,33,35,41,49,66 The transfer rate is time dependent, as downhill energy transfer also leads to changes in the average distance and spectral overlap between neighboring segments.35,57 Poly(3-hexylthiophene) (P3HT) is one of the most common and most successful conjugated polymers in recent optoelectronic implementations.3,4,10,67,68 Here, we report the timeresolved intramolecular exciton dynamics in dilute P3HT solutions using ultrafast time-resolved fluorescence. Timeresolved spontaneous emission allows for a clean probing of the initially excited state without interference from excited-state absorption. We present the time-resolved isotropic emission dynamics for three distinct molecular weight distributions of P3HT at three emission energies to better understand the exciton relaxation processes. Energy transfer is probed using timeresolved fluorescence anisotropy. From this data, we are able to characterize the intramolecular exciton dynamics and better understand the connection between spectral diffusion and RET. The energy relaxation dynamics are more strongly dependent on the chain length distribution than the RET dynamics, and this is considered in terms of the distribution of available chromophore segments. 2. Experimental Section Laser System. The time-resolved emission experiments were performed using a home-built, amplified, ultrafast Ti:sapphire laser system. This laser is similar in design to one we have previously described.69 A mode-locked oscillator, pumped by 2.7 W from a CW Nd:YVO4 (Spectra Physics, Mellenia Pro) laser, produces seed pulses with a typical bandwidth of 60 nm and an average power of 200 mW at 85 MHz. The seed pulses are stretched to a few hundred picoseconds with a home-built single grating stretcher and amplified by a Ti:sapphire regenerative amplifier. The regenerative amplifier is pumped at 2 kHz, 1.4 mJ/pulse, with a Q-switched Nd:YAG laser (Lightwave Electronics Series 612). Following compression, the pulses have an energy of 170 µJ, 30 nm of bandwidth centered about 815 nm, and a 65 fs full width at half maximum (fwhm) assuming a Gaussian profile. Excitation pulses are created with a homebuilt two stage noncollinear optical parametric amplifier (NOPA) driven with the output of the regenerative amplifier. The design is based on that of Riedle and co-workers.70,71 A schematic diagram of our home-built NOPA is available in Supporting Information. The NOPA is tunable throughout the visible light region (450-700 nm), and the output is compressed with a pair of SF10 prisms. The residual 815 nm pulse is extracted from the NOPA with a dichroic mirror and used as the upconverting gate pulse. The gate pulse is compressed by a pair of SF11 prisms to 85 fs intensity fwhm assuming a Gaussian profile. Fluorescence Upconversion. The tunable output of the NOPA is used to excite the sample in a 1 mm flow cell that sits at one focus of an elliptical reflector (Melles Griot 02 REM 001). The sample was flowed at a rate of 0.25 mL/s. The excitation beam is focused to a spot size of 300-400 µm by a 15 cm lens. The emission is collected by the elliptical reflector and imaged to a 0.5 mm thick type I BBO crystal (Super Optronics) which sits at the second focus of the elliptical reflector. The upconversion crystal is cut for SFG between 450 and 750 nm. The emission is imaged to a spot size of 0.5 mm and is gated with the residual 815 nm pulse. The gate pulse is focused by a 40 cm lens and overlapped with the image of the emission. A computer controlled delay stage (Newport UMT150PP.1) with submicrometer resolution is used to control the timing between the gate and the pump pulses. The excitation
J. Phys. Chem. C, Vol. 111, No. 42, 2007 15405 TABLE 1: Characterization of P3HT Samples; See Figure 1 for Complete Distributions sample I sample II sample III
Mn (Da)
Mw (Da)
PDI
% HT Coupling
Nn
Nw
4100 7730 13050
6490 18130 27860
1.6 2.3 2.1
> 98.5 > 98.5 95
25 47 85
39 109 168
was linearly polarized with a Glan laser polarizer (CLPA, CVI Laser), and the final polarization orientation was set with an achromatic waveplate (10RP52-1, Newport). Polarization contrast exceeded 800:1. The upconversion signal is spatially masked from the pump and gate pulses and recollimated by a 10 cm lens. The signal is dispersed with a fused-silica prism and the frequency of interest is isolated spatially using a slit between the dispersing prism and the input slit of the monochromator. The fluorescence signal is focused to the entrance slit of a 0.3 m single grating UV monochromator (McPherson 218) by a 30 cm lens and detected using a photomultiplier tube (PMT; Hamamatsu R636-10). The output of the PMT is monitored using a lock-in amplifier (Stanford Research 810) synchronized to the laser repetition rate. The instrument response function, IRF, is determined by setting the upconversion apparatus to the sum-frequency of the excitation and gate pulses. Isotropic data was collected by setting the pump polarization to the magic angle (54.7°) with respect to the gate polarization. When collecting data for the anisotropy measurements, signals were collected with the excitation set both parallel and perpendicular to the gate polarization. The data sets represents 12-16 time delay scans at each polarization, with the polarization rotated after every other scan. The time width of the IRF is 140 fs fwhm assuming a Gaussian profile. Typical excitation energies for the presented data are 30-40 nJ/pulse. The experiments were repeated with excitation energies that ranged from 10 to 100 nJ/pulse, and within this range, the observed dynamics were found to be independent of irradiance. Time Correlated Single Photon Counting. Time correlated single photon counting (TCSPC) was used to determine the excited-state lifetimes. Briefly, the samples are excited by pulses at 3.32 eV, 40 MHz, 220 mW from a diode laser (Picoquant LDH-P-C-375). Subsequent emission is focused into a double monochromator (Jobin-Yvon TRIAX-320) and detected by an avalanche photodiode. Emission events are counted as a function of time (Picoquant TimeHarp 200). The instrument response function is 0.55 ns fwhm. By using a convolute and compare fitting algorithm, decays as fast as 0.35 ns can be determined with reasonable confidence. Poly(3-hexylthiophene) (P3HT) Samples. Three P3HT samples of differing size distributions were investigated. Throughout the manuscript, we refer to these as samples I-III, in ascending order of molecular weight. A characterization summary is presented in Table 1. The two lower molecular weight samples were synthesized via the Grignard metathesis (GRIM) method.72 In a typical procedure, 150 mL of anhydrous tetrahydrofuran (THF) was transferred via cannula to an evacuated 300 mL three-neck round-bottom flask under argon. To this solvent, 2,5-dibromo-3-hexylthiophene (4.9 g, 14.9 mmol) was added by syringe under argon. A 1 M solution of tert-butylmagnesium chloride in THF (15 mL, 15 mmol) was transferred into the solution by syringe under argon. This mixture was refluxed for 1.5 h under inert atmosphere and then cooled to room temperature. At this point, 1,3-bis(diphenylphosphino)propane nickel(II) chloride [Ni(dppp)Cl2] (0.143 g, 0.26 mmol) was added as a solid under argon. The solution was allowed to stir at room temperature for 45 min and was then precipitated in methanol. The polymer was then filtered and
15406 J. Phys. Chem. C, Vol. 111, No. 42, 2007
Figure 1. Molecular size distribution of samples I-III against the number of monomer repeat units, i, in a given molecule. The number of molecules with i monomer repeats is given by ni. The black line is sample I; the red line is sample II, and the blue line is sample III. Statistics from the plot are provided in Table 1.
dried under vacuum (P < 100 mTorr) overnight prior to use. Sample III was obtained from Rieke Metals. Molecular weights were determined by size-exclusion chromatography (SEC) data collected on a Hewlett-Packard 1100 series equipped with a Hewlett-Packard 1047A refractive index detector and three Jordi poly(divinylbenzene) columns of 104, 103, and 500 Å pore sizes. Tetrahydrofuran (THF) at 40 °C was used as the mobile phase at a flow rate of 1 mL/min. The SEC was calibrated with polystyrene standards (Polymer Laboratories) and appropriate corrections based on published Mark-Houwink parameters of P3HT.73 The average molecular weights, polydispersity indexes (PDIs), and percent head to tail (HT) coupling (as determined by 1H NMR spectroscopy) are given in Table 1. The complete molecular weight distributions, plotted as the number of monomer repeat units, for all three samples are shown in Figure 1. The samples used in all experiments were dissolved in chloroform (Mallinckrodt Chemicals, ACS grade, used as received) at concentrations between 0.1 and 0.2 mg/mL. For sample I with Mn ) 4.1 KDa, this corresponds to a chain concentration of 49 µM. This concentration is nearly 2 orders of magnitude below the overlap concentration as estimated from the Mark-Houwink parameters.73 The absorption and emission spectra were collected on a Cary 14 and Spex Fluoromax-III respectively, and the fluorescence spectra were corrected for the frequency dependent detection sensitivity. These are shown in Figure 2. The absorption spectra show no evidence of a lowenergy tail that might indicate the presence of aggregates. From these considerations, we believe that interchain interactions are minimized under these conditions. All samples were dissolved within 8 h of use and were continuously degassed with argon during the experiments. The shape of the absorption spectrum of the samples remained unchanged after the upconversion measurements were conducted. Under long collection times (>6 h) the samples would show a very minor increase in the optical density. This is attributed to slow evaporation of the solvent during the experiment. All experiments were performed at room temperature. 3. Results and Analysis 3.1. Absorption, Emission, and Excited State Lifetimes. The normalized absorption and emission spectra of the three
Wells et al.
Figure 2. Absorption and fluorescence spectra for P3HT samples in chloroform. The black is sample I; the red line is sample II, and the blue line is sample III. Samples are defined in Table 1. The dashed black line shows the experimental excitation spectrum, and the three vertical lines indicate the detected emission energies.
P3HT samples are shown in Figure 2. Samples II and III, with the two largest molecular weights, have nearly identical spectra with an absorption maximum at 2.76 eV and an emission maximum at 2.14 eV. The emission spectra show a shoulder around 2.00 eV that is due to an unresolved vibrational progression. For sample I, with the smallest molecular weight, there is a small shift to higher energy of 37 meV in the absorption maximum as compared with the other two samples. No spectral shift is observed as a function of molecular weight in the maxima of the fluorescence spectra. However, the fluorescence onset of the smallest molecular weight polymer is at a slightly higher energy than the two larger molecular weight samples. Excited-state lifetimes were determined by time correlated single photon counting. Measurements on all three samples at an emission energy of 2.18 eV are shown in Figure 3. The data was fit with a single-exponential decay convoluted with the instrument response function. Optimized fit parameters are given in Table 2 for the three emission energies used in the upconversion experiment and for all three molecular weight distributions. Within the experimental accuracy, the excitedstate lifetime is independent of both emission energy and molecular weight. 3.2. Time and Energy Resolved Isotropic Emission. Figure 4 presents time-resolved spontaneous emission polarization selected at 54.7° relative to the excitation pulse. Isotropic fluorescence reflects the exciton population in a selected energy window. Emission was measured for all three molecular weight distributions on the high-energy side of the fluorescence maximum at 2.30 eV, near the maximum at 2.18 eV, and on the low-energy side at 2.05 eV (see Figure 2). As shown in Figure 4, the measurements involve both rising and decaying intensity on multiple time scales, and this reflects excitons coming into and/or out of the spectral detection window because of energy relaxation. The data was fit with a model that separates the effects of spectral diffusion and excited-state lifetime,
P(t) ) S(t) exp(-t/tLT)
(3.1)
In eq 3.1, P(t) is the population of excitons with energy and S(t) provides the influence of spectral diffusion at a given
Migration Dynamics in Poly(3-hexylthiophene)
J. Phys. Chem. C, Vol. 111, No. 42, 2007 15407 TABLE 3: Fitting Parameters: Isotropic Emission Detected at 2.30 eV; Excitation at 2.64 eV
sample I sample II sample III
t1 (ps)
t2 (ps)
t3 (ps)
t4 (ps)
tLT (ps)
A
B
C
D
E
0.11 0.10 0.10
1.88 1.38 0.50
11.1 9.2 5.2
80.0 77.7 40.0
500 500 500
0 0 0
107 107 113
81 80 90
49 40 42
29 20 15
TABLE 4: Fitting Parameters: Isotropic Emission Detected at 2.18 eV; Excitation at 2.64 eV
sample I sample II sample III
t1 (ps)
t2 (ps)
t3 (ps)
t4 (ps)
tLT (ps)
A
B
C
D
E
0.13 0.12 0.12
2.05 1.33 1.10
23.3 11.3 10.0
200 200 200
500 500 500
0 0 0
102 103 105
94 93 95
86 83 78
80 63 47
TABLE 5: Fitting Parameters: Isotropic Emission Detected at 2.05 eV; Excitation at 2.64 eV Figure 3. TCSPC data, P3HT in chloroform. Excitation at 3.32 eV, emission measured at 2.18 eV. The solid line is sample I; the dashed line is sample II, and dot-dashed line is sample III. Samples are defined in Table 1. The open circles are the instrument response function.
TABLE 2: Single-Exponential Time Constants from Fitting TCSPC of P3HT at the Indicated Emission Energy: Excitation at 3.32 eV sample I sample II sample III
2.05 eV
2.18 eV
2.30 eV
508 ps 482 ps 494 ps
514 ps 496 ps 502 ps
503 ps 488 ps 486 ps
sample I sample II sample III
t1 (ps)
t2 (ps)
t3 (ps)
tLT (ps)
A
B
C
D
0.14 0.14 0.13
2.88 1.89 0.65
739 139 75
500 500 500
0 0 0
89 90 89
101 102 100
87 90 80
dynamics within this time frame are largely the result of spectral diffusion. To facilitate comparisons and discussions of energy relaxation time scales, the influence of spectral diffusion on the relative emission amplitude at a given detection energy, S(t), is modeled as a series of first-order events,
a(t)A 9 8 b(t)B 9 8 c(t)C 9 8 d(t)D 9 8 e(t)E t t t t 1
detected emission energy. The exponential accounts for the excited-state lifetime, and tLT is fixed at 500 ps on the basis of the photon counting results summarized in Table 2. Since the upconversion experiments only extend to 300 ps, the observed
2
3
(3.2)
4
The capital letters, A-E, represent the signal amplitude, and t1-t4 are the time constants for transition between each value. The time dependent coefficients a(t)-e(t) are constrained to a sum of 1 and determined by solving the associated differential equations.74 Initial conditions are set to a(t ) 0) ) 1 and A ) 0. The signal amplitude as a function of time is the sum of the values weighted by the time dependent coefficients,
S(t) ) a(t)A + b(t)B + c(t)C + d(t)D + e(t)E (3.3)
Figure 4. Time and energy resolved isotropic emission. Note the broken time axis with linear scale for t < 3 ps and a logarithmic scale for t > 3 ps. The excitation energy is 2.64 eV. Circles are emission at 2.30 eV; squares are emission at 2.18 eV, and diamonds are emission at 2.05 eV. The top panel is sample I; the middle panel is sample II, and the bottom panel is sample III. Samples are defined in Table 1. The lines are the fits to the data, and the associated residuals as described in the text.
Following convolution over the instrument response function, P(t) is compared with the data, and A-E and t1-t4 are simultaneously adjusted to minimize the square of the residuals using a standard simplex algorithm. The fits and associated residuals are shown in Figure 4. The optimized fitting parameters are listed in Tables 3-5. All measured responses are arbitrarily scaled to a maximum value of 100. For each emission energy, a spectral diffusion function with the minimum number of kinetic steps needed to obtain a reasonable fit of the entire data was used. When two steps in the kinetics would lead to redundant time scales under optimization, the number of kinetic steps would be reduced by one. In this procedure four steps were required to obtain a satisfactory fit at 2.30 and 2.18 eV, and a good fit was possible with only three steps for data at 2.05 eV. In some cases, the last time scale begins to approach or exceed the exciton lifetime determined by TCSPC, for example, t4 for emission detected at 2.18 eV. Inclusion of these longer decays noticeably improves the fits. However, time constants larger than approximately 150 ps are underdetermined because of the limited time range of the data sets (t < 300 ps). All three samples show the same general trend in the energy dependent exciton relaxation. The two highest emission energies
15408 J. Phys. Chem. C, Vol. 111, No. 42, 2007
Wells et al.
show a one step rise with a time constant near 100 fs that brings the population to the maximum value. From there, a multiphase decay is seen with time constants of roughly 1, 10, and 100 ps. -1 The second and third decay rates (t-1 3 and t4 ) tend to slow down at 2.18 eV compared with 2.30 eV. At the lowest emission energy measured, 2.05 eV, a change in the initial dynamics is seen with a biphasic rise, and this is followed by a small amplitude decay to 80-90% of the signal maximum. The rest of the decay is accounted for by the lifetime component associated with exciton recombination. At 2.05 eV, the two component rise occurs with a slightly slower initial rise, around 140 fs, and a small amplitude (10%) secondary rise with a time constant comparable to the t2 decay seen at 2.30 and 2.18 eV. As the average molecular weight of the sample increases, there is a general decrease in the time constants. The only exception is the initial approximately 100 fs rise, which is insensitive to molecular weight but is also approaching the experimental time resolution in the 2.30 and 2.18 eV emission data. This trend toward faster energy relaxation with increasing average molecular weight is reflected at all observed emission energies. For the emission at 2.30 and 2.18 eV, there is a faster decay of the signal as the chain length increases, and there is a correlated faster rise in the low-energy emission, reported as the t2 time constant at 2.05 eV. 3.3. Time-Resolved Emission Depolarization. Time dependent decay in the correlation between the absorption and the emission transition moment directions was determined from independent measurements of the emission intensity parallel, I|(t), and perpendicular, I⊥(t), to the excitation polarization. The time dependent anisotropy for an isotropic sample is typically defined as
R(t) )
I|(t) - I⊥(t) I|(t) + 2I⊥(t)
(3.4)
This can be constructed directly from our measurements of I|(t) and I⊥(t). However, as discussed by Cross and Fleming, care must be taken when extracting the anisotropy from data taken with a finite instrument response.75 The anisotropy constructed point-by-point from the measured I|(t) and I⊥(t) is not equivalent to direct convolution of the impulsive limit anisotropy, which we will label r(t), with the instrument response function, IR(t). Direct construction of R(t) from the raw data becomes more accurate for time scales that are long compared with the instrument response. However, at short delay times, and when determining the amplitude of any initial depolarization that is comparable to the instrument response time, failure to properly account for the instrument response can introduce significant error. Repeating the same experiment on a series of consecutive days, a day-to-day variance of 1%-3% in the relative measured I|(t) and I⊥(t) intensities was determined. This propagates to an error of up to 10% when constructing R(t). To more accurately determine trends in the anisotropy, measurements were made at single fixed time delays while cycling though the different samples or detected emission energies in rapid succession. The top panel of Figure 5 presents the results of this procedure for sample III at a time delay of 20 ps comparing the three different detection energies. The bottom panel of Figure 5 compares the three different samples at a series of three time delays and an emission energy of 2.18 eV. Since all of the delay times are much larger than the instrument response time, the anisotropy was calculated directly using eq 3.4. The error bars are given at the 95% confidence limit. Although there could be a small
Figure 5. Top: anisotropy at 20 ps for sample III. Bottom: anisotropy at three time delays for the three P3HT samples. The excitation energy is 2.64 eV, and the emission energy is 2.18 eV. The circles are sample I; the squares are sample II, and the diamonds are sample III. Samples are defined in Table 1.
upward trend in the anisotropy as a function of emission energy, this trend only emerges from the experimental uncertainty below the 50% confidence limit. Within the experimental error, the measured anisotropy is independent of emission energy. There is a measurable difference in the anisotropy between the different samples, with the anisotropy at a given delay time decreasing as the molecular weight increases. For analysis of the depolarization dynamics, the complete time domain transients were scaled to minimize the combined difference of the measured values at the three time points determined in the bottom panel of Figure 5. This scale factor was typically in the range 0.96-1.04. As discussed above, while this procedure may retain 10% errors in the absolute values of the anisotropy, errors in the relative values between the three samples are much lower. The data was checked for consistency by plotting the measured isotropic data against an isotropic data set constructed from the parallel and perpendicular data sets. In all cases, the measured isotropic data matched the constructed data within experimental error. The time dependent anisotropy decays in the impulsive limit, r(t), are determined by fitting the data using the procedure outlined by Cross and Fleming.75 The parallel and perpendicular intensities are constructed from a model r(t) using the following expressions,
1 i|(t) ) P(t)[1 + 2r(t)] 3
(3.5)
1 i⊥(t) ) P(t)[1 - r(t)] 3
(3.6)
The time dependent population of the excited state at the detection energy, P(t), is determined from the isotropic emission data as described in the previous section. The impulsive parallel and perpendicular responses are convoluted over the instrument response function,
I|(t) )
∫0tIR(t - τ)i|(t) dτ
(3.7)
I⊥(t) )
∫0tIR(t - τ)i⊥(t) dτ
(3.8)
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J. Phys. Chem. C, Vol. 111, No. 42, 2007 15409
TABLE 6: Fitting Parameters: Fluorescence Depolarization; Excitation at 2.64 eV; Emission Detected at 2.18 eV t1 t2 t3 (ps) (ps) (ps) sample I 0.97 27 sample II 0.97 30 sample III 1.22 34
A1
A2
A3
A4
219 0.030 0.036 0.078 0.127 290 0.041 0.042 0.090 0.080 328 0.041 0.040 0.070 0.069
r0 ) A1+ A2+A3+A4 0.271 0.253 0.220
and compared with the measured I|(t) and I⊥(t). The anisotropy decay function, r(t), is iteratively adjusted to simultaneously fit the time dependent emission intensities measured both parallel and perpendicular to the excitation polarization. The anisotropy decay was modeled as the sum of three exponential decays and a time independent offset,
r(t) ) A1 exp(-t/t1) + A2 exp(-t/t2) + A3 exp(-t/t3) + A4 (3.9) The optimized amplitudes, A1-A4, and time constants, t1-t3, for all three samples at an emission energy of 2.18 eV are reported in Table 6. An example of the resulting simultaneous fit to the parallel and perpendicular emission signals is presented in Figure 6 for sample I. Data and fits at the other energies and for the other samples are available in Supporting Information. The sum of exponential decays was chosen as a model for r(t) simply because of the ability to provide a reasonable fit to the measured data set over the entire range of time delays. A minimum of three decay components were required to fit the data. The combination of a time independent offset and a single stretched exponential, which has been successfully employed in fitting depolarization dynamics in thin films of MEH-PPV,57 did generate good fits to our data for time delays restricted to 1 ps < t < 30 ps but did not provide satisfactory fits over the entire range of measured delays. The optimized anisotropy decays are reconstructed with our finite instrument time resolution from the determined r(t) decays and plotted as the lines in Figures 7 and 8. The anisotropy decays constructed directly from the raw data using eq 3.4 are also shown in these figures for comparison. Figure 7 demonstrates the independence of the anisotropy decay from emission energy within our experimental accuracy. All three samples show very
Figure 7. Time dependent fluorescence anisotropy. The lines are the anisotropy decays, constructed from r(t) and determined as described in the text. The symbols are the anisotropy decays constructed directly from the raw data for comparison: Circles are sample I; squares are sample II, and triangles are sample III. Excitation is at 2.64 eV. Blue symbols are emission at 2.30 eV; green symbols are emission at 2.18 eV, and red symbols are emission at 2.05 eV. Samples are defined in Table 1.
Figure 8. Time dependent fluorescence anisotropy. The lines are the anisotropy decays, constructed from r(t) and determined as described in the text. The symbols are the anisotropy decays constructed directly form the raw data for comparison: Excitation is at 2.64 eV, and emission was detected at 2.18 eV. Circles are sample I; squares are sample II, and triangles are sample III. Samples are defined in Table 1.
Figure 6. Sample I upconversion signals and fits for pump polarization parallel (circles) and perpendicular (squares) to the gate polarization. The lines are the optimized fits as described in the text. Excitation is at 2.64 eV, and emission is detected at 2.18 eV. The inset shows the data and fits from -2 to 5 ps. Samples are defined in Table 1.
similar decays on multiple time scales where the decay rate slows with time. The associated time constants are relatively insensitive to the molecular weight with the largest difference appearing in last measured depolarization rate which slows from 0.0046 to 0.0030 ps-1 between samples I and III. Although these time scales are comparable to the time range of the measurements and are therefore not accurately determined, the trend with molecular weight is consistently required to obtain good fits to the data. In all cases, the initially determined anisotropy, r0 ) r(t ) 0), is significantly below the theoretical maximum of r0 ) 0.4 for an isotropic sample. The determined values of r0 ∼ 0.25 (see Table 6) indicate rotation of the transition moment by approximately 30° within the time resolution of our experi-
15410 J. Phys. Chem. C, Vol. 111, No. 42, 2007 ment ( 98), Mn ) 1.7 × 104 Da, P3HT in dilute chloroform solution. This persistence length corresponds to ∼120 monomers if the polymer chain is fully extended.37 Given that samples in our study are, on average, shorter than or comparable to (less than 1.5×) the persistence length, we conclude that the polymer chains are best described as more rodlike than coiled in dilute chloroform solution. This conclusion includes the assumption that intramolecular throughspace interactions will not contribute substantially to the observed dynamics. Even though the molecular weight distribution for sample III extends to a few times the persistence length, there is no evidence for intra- or intermolecular aggregation in the measured absorption spectrum of any of the samples. Aggregation is known to significantly shift the absorption to lower energy analogous to the absorption in thin films.78 4.2. Time Integrated Absorption and Emission. Many conjugated polymers in solution show an unstructured absorption and a narrowed emission spectra exhibiting vibrational structure similar to that shown for P3HT in Figure 2.21-23,78,79 The narrowing and enhanced resolution of the emission spectrum has been attributed to a dynamic exciton localization and energy transfer to polymer segments with the longest conjugation length.50,58,61,80,81 Given the largely extended conformation of regioregular P3HT in dilute solution, the initial excitation at 2.64 eV will create intrachain excitons that are dynamically localized to individual segments of the polymer.42 On the basis of theoretical and experimental absorption spectra of thiophene oligomers, the segment length for intrachain excitation correspond to ∼6 monomers, while on the basis of the emission spectrum of thiophene oligomers and the measured emission spectra of P3HT, the fully relaxed emissive segment length in P3HT is >7 monomers.82,83 For conjugated polymers, the effective segment model agrees well with spectroscopic observables.42,45,81,84 Absorption is described as a superposition of effective segment lengths with comparable homogeneous line shapes.21,44,52,85 Site selective fluorescence has demonstrated that below a certain excitation energy only the longest chains are excited and the peak of the emission spectrum is dependent on the excitation energy.21,44,52,86 Above this energy, the initial excitation involves segments of shorter length, with subsequent energy relaxation that can include extending the segment length and migration to longer segments. With relaxation to longer
Wells et al. segments preceding the majority of the spontaneous emission, the time integrated fluorescence spectrum is independent of excitation. 4.3. Exciton Relaxation and Migration. The time-resolved isotropic emission and anisotropy dynamics presented in section 3 show that the energy relaxation of the initially created excitons is multifaceted. The energy selected emission transients in Figure 4 are typical of molecular systems undergoing spectral diffusion.43,87-90 For small dye molecules in solution, the transient spectral shift is caused by a combination of structural relaxation in the excited state and solvent motions coupling to the electronic transition. In dilute solutions of conjugated polymers, spectral diffusion is dominated by intramolecular dynamics, including nuclear rearrangement of the polymer chain and migration of the excitation to lower energy segments defined by longer effective conjugation lengths.33,34,47,54,55,57 Emission anisotropy decay measurements can help isolate exciton migration when associating reorientation of the transition moment with relocation of the exciton. For conjugated polymers, emission anisotropy decay can be interpreted in terms of energy transfer between chromophoric segments.33,34,53,57,59 However, the initial anisotropy dynamics can be complicated by significant nuclear reorganization on sub-100 fs time scales after excitation.29,65,91,92 4.3.1. Ultrafast Relaxation and Localization. The data in Figures 4, 6, and 7 indicate that significant exciton relaxation takes place within the first 100 fs after excitation. The initial rise at all measured emission energies shows that a large fraction of the spectral shift is accounted for in less than 100 fs (t1 values in Tables 3-5). The initial fluorescence anisotropy values, r0, demonstrate a 30% reduction from the theoretical maximum within our experimental time resolution. This indicates significant reorientation (ca. 30° rotation) of the transition moment in less than 100 fs. Similar rapid depolarization has been reported for other conjugated polymers, poly[3-(4-octylphenyl)-(2,2′)bithiophene], PTOPT, and MEH-PPV, and this was attributed to localization of the initially prepared more diffuse excitation.29,63,65,92 Scholes and co-workers have also assigned localization to the approximately 30 fs decay of the electronic energy gap correlation function in MEH-PPV as measured by three pulse photon echo peak shift.58,64 We assign the sub-100 fs spectral migration and depolarization that we observe in isolated P3HT chains to the strong coupling between the electronic excitation and the intramolecular nuclear degrees of freedom that are also responsible for rapid dynamic exciton localization.23,42,49,63,64 Consideration of the structural reorganization associated with transition to a more planar quinoidal structure in the excited state suggests that the primary motions involved are C-C stretching, around 1300 cm-1, and torsional motions, around 100 cm-1.35,82,93,94 The stretching mode is commonly observed as a vibrational progression in the time integrated emission spectrum of conjugated polymers.21-23,78,79 Exciton localization can be exhibited in the emission anisotropy decay. For example, when the initially delocalized excitation spans a kink in the polymer chain, subsequent localization favoring one side of the kink will rotate the transition moment.42,65 In films and both intermolecular and intramolecular aggregates, a similar rotation of the transition moment can follow localization from an initial excitation delocalized through space between adjacent polymer segments.29,58,92,95 However, localization of an initial excitation that spans segments of differing spatial alignment is not required for substantial rapid initial decay in the fluorescence anisotropy. For terthiophene in dilute solution, Yang et al. found initial
Migration Dynamics in Poly(3-hexylthiophene) depolarization to an anisotropy value of r0 ) 0.24 within the 200 fs time resolution.91 The lack of analogous spatial localization available in terthiophene and an initial depolarization that is comparable to our measurements for P3HT suggests that ultrafast rotation of the transition moment in P3HT is largely due to structural reorganization along displaced vibrational coordinates. Depolarization due to localization about a bend or kink in the chain, driven by the same nuclear motions, is difficult to isolate in these measurements. An indication that this mechanism of depolarization is also active in our P3HT measurements comes from the dependence of the initial depolarization on the polymer size. As shown in Table 6, the r0 values decrease with increasing chain length. This trend is consistent with the transition to a less rigid rodlike structure of the polymer chain as the average length goes from well below to comparable with the persistence length. Interestingly, the r0 value of ∼0.27 for sample I likely represents the localization contribution in the absence of excitations around bends or kinks since the chain length that corresponds to Nw is well below the persistence length. The decrease in r0 from ∼0.27 follows the increase in the probability that the initial delocalized excitation spans a bend in the chain. 4.3.2. Energy Transfer and Dynamic Exciton Extension. Following the initial ultrafast (sub picosecond) dynamics, the next regime of exciton relaxation and migration takes place in 1-30 ps. In this time window, the measured isotropic fluorescence decays on the high-energy side of the fluorescence maximum, 2.30 and 2.18 eV, and exhibits a correlated rise on the low-energy side at 2.05 eV. There is a similar decay in the measured fluorescence anisotropy. In our fitting of the timeresolved anisotropy, we have represented this portion of the dynamics as bimodal, with time scales around 1 ps and around 10 ps. However, as mentioned in section 3.3, reasonable fits between 1 and 30 ps could also be obtained using a stretched exponential. Our data is not sufficient to distinguish between independent contributions with different rates and a single process with a time-dependent declining rate. We believe that both mechanisms are represented, including an energy transfer between segments that slows with time and torsional relaxation that extends the effective conjugation length lowering the energy.33-35,47,57,59,84,96 Prior studies of related conjugated polymers have interpreted energy transfer along the polymer chain in terms of resonant energy transfer (RET) between adjacent segments via a Fo¨rster mechanism.29,31,33,35,47,66,81,97 Extension of the Fo¨rster approach beyond the point dipole approximation and inclusion of a time dependence of the overlap between the donor and the acceptor spectra has shown very good agreement with the type of time dependent decay we observed between 1 and 30 ps.33,34,57,96 The RET rate is initially faster as a result of a better spectral overlap and, because of a shorter average segment length at higher energy, a shorter average transfer distance. The Fo¨rster hopping picture is in good qualitative agreement with our observed dynamics. However, we note that this model relies on weak donor-acceptor coupling, and the small dependence of the electronic coupling in P3HT on molecular structure could compromise the quantitative accuracy of this representation.42 The initial decay in the anisotropy and isotropic fluorescence are similar at around 1 ps, t2 in Tables 3 and 4 and t1 in Table 6, respectively. The correlation between energetic relaxation and transition moment reorientation is consistent with energetically downhill RET between segments of differing orientation. Comparison of the next decay in both cases, t3 in Tables 3 and 4 and t2 in Table 6, indicates that energetic relaxation is
J. Phys. Chem. C, Vol. 111, No. 42, 2007 15411 somewhat faster than energy transfer. This is consistent with the fact that energetically downhill RET is faster than RET between segments of comparable energy. Once the initially localized exciton transfers to a low-energy segment, potential acceptors become kinetically restricted to neighboring segments lower than or within kBT in energy. Simulations of PDOPT by Westenhoff et al. found that downhill RET is initially ∼7 times more probable than uphill RET, and the two rates become equivalent after about 20 ps.33 In addition to RET, torsional relaxation can extend the effective conjugation length and rotate the transition moment.34 Unlike the rapid reorganization driven by displacement and tightening of the torsional potential immediately following excitation implicated above in section 4.3.1 as part of the first 100 fs, here, we are referring to thermally activated torsional motion. Comparison between simulation and experiment on PDOPT concluded that this is reflected in both anisotropy and isotropic emission on a picosecond time scale, with a time constant for torsional relaxation assigned at 15 ps.34 In the absence of simulations, we are not able to separate RET and torsional relaxation in our measurements on P3HT. On the basis of comparison with related work, we conclude that both processes contribute to exciton relaxation and migration in the intermediate 1-30 ps region. There is a clear difference in the dependence of the dynamics on polymer size when comparing the isotropic emission and the emission anisotropy decay. A substantial increase in the rate of energy relaxation follows increasing average molecular weight, while the rate of anisotropy decay is nearly independent of molecular weight (see Tables 3-6). The anisotropy measurements indicate very little change in the RET rates as a function of average molecular weight. Our hypothesis is that the apparent acceleration in the energy relaxation reflects the greater probability of a kinetically accessible path to a low-energy segment per created exciton in a longer polymer molecule. Figure 9 contrasts three different excitation events in a sample of longer molecules (represented as excitation localizing to three different locations in the same molecule) with the analogous three excitations taking place in individual shorter molecules (represented as pieces of the longer molecule adjacent to the initial localization). Comparing the two cases, one can see how excitation on a longer polymer chain has a higher probability of access to a lower energy segment via RET, primarily because of the higher probability that a lower energy segment initially exists on the molecule. In shorter polymer chains, kinetically accessible RET is more likely to end at a higher energy segment. This leaves the balance of the exciton relaxation to take place via the relatively slower mechanism of thermally activated segment structural relaxation/elongation. While some excitons created on longer chains will be initially trapped on a highenergy segment because of two higher energy neighbors, when averaged over an ensemble, the longer polymers have a larger fraction of the exciton relaxation take place via migration along the chain. Shorter polymer chains have a larger fraction of the relaxation take place via slower segment structural relaxation. Assuming the distribution of segment energies is independent of molecular weight, for polymer chains that are only long enough to support approximately 2 segments, the reduction of nearest neighbors by half should proportionally reduce the probability of an initial energetically downhill RET event. Although a relatively small fraction of the total distribution is observed here, Figure 1 shows that the probability of exciting a polymer molecule which is only the length of two to three effective segments drops by half from sample I to sample II.
15412 J. Phys. Chem. C, Vol. 111, No. 42, 2007
Wells et al.
Figure 9. Illustration summarizing the proposed exciton dynamics and comparing three different excitation events in a longer polymer chain (a) to the same excitations in shorter polymers taken from pieces of that chain (b). The parabolas represent individual segments within a polymer chain. The events are categorized and labeled as (1) excitation to a state initially delocalized over more than one segment, (2) rapid relaxation and localization due to strong coupling of the electronic transition to nuclear degrees of freedom, < 0.1 ps, (3) RET, or “hopping”, between segments, roughly 1-10 ps, and (4) thermally activated structural relaxation that extends the segment length, roughly 10-100 ps. Note that in this example all three excitations in the longer chain can take advantage of downhill RET to reach the lower energy segment. The same three excitations in the shorter chains are less likely to have RET access to segments at the lower end of the energy distribution. When averaged over the ensemble, this results in faster exciton relaxation in samples of larger average chain length.
This is consistent with the reduced amplitude, with no measurable change in the rate, of the initial 1 ps contribution to the anisotropy decay of sample I compared with sample II (see Table 6). The last observed phase in the energy relaxation and depolarization in free chains of P3HT occurs on a time scale of 200 ps or greater. In our measurements, this time scale is not accurately determined since our data only extends to 350 ps. Our reported anisotropy decay time scales around 300 ps are in good qualitative agreement with down chain hopping time previously seen in some conjugated polymers.29,35 Our measured anisotropy time constants increase with molecular size from 219 to 328 ps in samples I and III, respectively. Again acknowledging the limited accuracy of these values, we find the trend with molecular weight was consistently required for good quality fits of the data. These dynamics could be related to larger scale molecular reorganization, such as concerted reorientation of multiple monomers, that can mediate RET or spatially extends individual excitons. 5. Conclusions Intramolecular energy relaxation and migration was investigated for a series of three P3HT samples of increasing molecular weight in dilute solution using time and energy resolved fluorescence. An illustration summarizing the primary aspects of the dynamics associated with exciton energy relaxation in both long and short chains is shown in Figure 9. Excitation can initially span multiple segments of the polymer chain and a significant portion of the relaxation of the initially created exciton takes place on an ultrafast time scale. A large fraction
of the exciton cooling (total Stokes shift) is seen within 100 fs, and this rapid relaxation is driven by strong coupling between the electronic excitation and nuclear motions. The rapid nuclear reorganization results in localization on an individual segment. Rapid reorientation of the transition moment during this time period is largely associated with transition to a more quinoidal structure in the excited state and is analogous to the ultrafast anisotropy measured in terthiophene.91 The decrease of the initial anisotropy with molecular weight indicates that there is a component of the sub-100 fs depolarization originating from reorientation following localization of the exciton about a kink or bend in the chain. The exciton then cools, representing a small fraction of the total Stokes shift, on an approximately 1 ps time scale via downhill RET to adjacent segments and continues to relax on an approximately 10 ps time scale via a combination of subsequent RET to lower energy segments and thermally activated torsional relaxation that extends the segment conjugation length. Although observed RET rates are independent of molecular weight, increasing availability per molecule of downhill RET pathways to low-energy segments leads to a substantial increase in average exciton relaxation rate with molecular weight in the picosecond time regime (compare the top and bottom of Figure 9). The observed time scales are similar to investigations by others of both solution and films of other conjugated polymers, indicating that the intramolecular exciton dynamics in P3HT are competitive with intermolecular energy transfer in films of related materials. Acknowledgment. This work was funded in part by the Initiative for Renewable Energy and the Environment at the University of Minnesota and in part by the Xcel Energy
Migration Dynamics in Poly(3-hexylthiophene) Renewable Development Fund. D.A.B. gratefully acknowledges support from the David and Lucille Packard Foundation. The authors thank Dr. Sean Shaheen at the National Renewable Energy Laboratory for providing sample III. We thank Dr. Rajeswari Kasi for help with polymer synthesis. Supporting Information Available: Parallel and perpendicular data and fits detected for samples I-III and noncollinear optical parametric amplifier and upconversion setup. This material is available free of charge via the Internet at http:// pubs.acs.org. References and Notes (1) Li, G.; Shrotriya, V.; Huang, J.; Yao, Y.; Moriarty, T.; Emery, K.; Yang, Y. Nat. Mater. 2005, 4, 864. (2) Ma, W.; Yang, C.; Gong, X.; Lee, K.; Heeger, A. J. AdV. Funct. Mater. 2005, 15, 1617. (3) Coakley, K. M.; McGehee, M. D. Chem. Mater. 2004, 16, 4533. (4) Brabec, C. J.; Sariciftci, N. S.; Hummelen, J. C. AdV. Funct. Mater. 2001, 11, 15. (5) Arkhipov, V. I.; Emelianova, E. V.; Barth, S.; Ba¨ssler, H. Phys. ReV. B 2000, 61, 8207. (6) Muller, J. G.; Lupton, J. M.; Feldmann, J.; Lemmer, U.; Scharber, M. C.; Sariciftci, N. S.; Brabec, C. J.; Scherf, U. Phys. ReV. B 2005, 72, 195208/1. (7) Hoppe, H.; Sariciftci, N. S. J. Mater. Res. 2004, 19, 1924. (8) Chasteen, S. V.; Harter, J. O.; Rumbles, G.; Scott, J. C.; Nakazawa, Y.; Jones, M.; Horhold, H. H.; Tillman, H.; Carter, S. A. J. Appl. Phys. 2006, 99, 033709/1. (9) White, M. S.; Olson, D. C.; Shaheen, S. E.; Kopidakis, N.; Ginley, D. S. Appl. Phys. Lett. 2006, 89, 143517/1. (10) Vanlaeke, P.; Vanhoyland, G.; Aernouts, T.; Cheyns, D.; Deibel, C.; Manca, J.; Heremans, P.; Poortmans, J. Thin Solid Films 2006, 511512, 358. (11) Waldauf, C.; Scharber, M. C.; Schilinsky, P.; Hauch, J. A.; Brabec, C. J. J. Appl. Phys. 2006, 99, 104503/1. (12) Peumans, P.; Uchida, S.; Forrest, S. R. Nature 2003, 425, 158. (13) Podhajecka, K.; Pfleger, J. Eur. Phys. J. Appl. Phys. 2006, 36, 241. (14) Nguyen, T.-Q.; Kwong, R. C.; Thompson, M. E.; Schwartz, B. J. Appl. Phys. Lett. 2000, 76, 2454. (15) Bradley, D. D. C.; Colaneri, N. F.; Friend, R. H. Synth. Met. 1989, 29, E121. (16) Colaneri, N. F.; Bradley, D. D. C.; Friend, R. H.; Burn, P. L.; Holmes, A. B.; Spangler, C. W. Phys. ReV. B 1990, 42, 11670. (17) Gomes da Costa, P.; Conwell, E. M. Phys. ReV. B 1993, 48, 1993. (18) Pakbaz, K.; Lee, C. H.; Heeger, A. J.; Hagler, T. W.; McBranch, D. Synth. Met. 1994, 64, 295. (19) Chandross, M.; Mazumdar, S.; Jeglinski, S.; Wei, X.; Vardeny, Z. V.; Kwock, E. W.; Miller, T. M. Phys. ReV. B 1994, 50, 14702. (20) Cornil, J.; Beljonne, D.; Bre´das, J. L. J. Chem. Phys. 1995, 103, 842. (21) Rauscher, U.; Ba¨ssler, H.; Bradley, D. D. C.; Hennecke, M. Phys. ReV. B 1990, 42, 9830. (22) Sariciftci, N. S., Ed. Primary Photoexcitation in Conjugated Polymers: Molecular Exciton Versus Semiconductor Band Model; World Scientific Publishing Co. Pte. Ltd.: Singapore, 1997. (23) Bre´das, J.-L.; Cornil, J.; Beljonne, D.; Dos Santos, D. A.; Shuai, Z. Acc. Chem. Res. 1999, 32, 267. (24) Hendry, E.; Schins, J. M.; Candeias, L. P.; Siebbeles, L. D. A.; Bonn, M. Phys. ReV. Lett. 2004, 92, 196601/1. (25) Pichler, K.; Halliday, D. A.; Bradley, D. D. C.; Burn, P. L.; Friend, R. H.; Holmes, A. B. J. Phys.: Condes. Matter 1993, 5, 7155. (26) Pichler, K.; Halliday, D. A.; Bradley, D. D. C.; Friend, R. H.; Burn, P. L.; Holmes, A. B. Synth. Met. 1993, 55, 230. (27) Im, C.; Emelianova, E. V.; Ba¨ssler, H.; Spreitzer, H.; Becker, H. J. Chem. Phys. 2002, 117, 2961. (28) Arkhipov, V. I.; Emelianova, E. V.; Ba¨ssler, H. Chem. Phys. Lett. 2003, 372, 886. (29) Nguyen, T.-Q.; Wu, J.; Doan, V.; Schwartz, B. J.; Tolbert, S. H. Science 2000, 288, 652. (30) Brown, P. J.; Thomas, D. S.; Ko¨hler, A.; Wilson, J. S.; Kim, J.-S.; Ramsdale, C. M.; Sirringhaus, H.; Friend, R. H. Phys. ReV. B 2003, 67, 064203/1. (31) Beljonne, D.; Pourtois, G.; Silva, C.; Hennebicq, E.; Herz, L. M.; Friend, R. H.; Scholes, G. D.; Setayesh, S.; Mu¨llen, K.; Bre´das, J. L. Proc. Natl. Acad. Sci. U.S.A. 2002, 99, 10982. (32) Schwartz, B. J. Ann. ReV. Phys. Chem. 2003, 54, 141. (33) Westenhoff, S.; Daniel, C.; Friend, R. H.; Silva, C.; Sundstro¨m, V.; Yartsev, A. J. Chem. Phys. 2005, 122, 094903/1.
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