Ultrafast relaxation in conjugated polymers with large optical nonlinearity

Synthetic Metals, 49-50 (1992) 565-581

565

Ultrafast relaxation in conjugated polymers with large optical nonlinearity* Takayoshi Kobayashi

Department of Physics, Faculty of Science, University of Tokyo, Hongo 7-3-1, Bunkyo-k~ Tokyo 113 (Japan)

Abstract The ultrafast relaxation of photoexcitations in conjugated polymers, polydiacetylenes (PDAs), and polythiophenes (PTs), was studied by a p u m p - p r o b e experiment using a 100 fs amplified CPM (colliding pulse mode-locked) laser to clarify the detailed mechanism and temporal response of the optical nonlinearity of conjugated polymers with large third-order susceptibility. Samples used are polydiacetylenes (PDA-3BCMU(poly[4,6-decadiyne-l,lO-diol-bis(n-butoxycarbonylmethylurethane)] (blue phase)) and PDA-4BCMU (poly[5,7-dodecadiyne-l,12-diol-bis(n-butoxycarbonylmethylurethane)] (red and blue phases))) and polythiophenes (P3MT(poly[3-methylthiophene]) and P3DT (poly[3-dodecylthiophene])). Various spectral changes due to ultrafast nonlinear optical processes are observed to appear very rapidly after or even before the pump pulse. They are perturbed free-induction decay, coherent interaction between the pump and probe (pump polarization coupling), optical (a.c.) Stark shift, induced phase modulation, and hole burning. At slightly longer delay times ( 1 0 0 - 2 0 0 fs) the formation of a self-trapped (ST) exciton from a free exciton is observed. The exponential formation times of the ST excitous are in the range 7 0 - 1 0 0 fs in PTs and 1 4 0 - 1 5 0 fs in PDAs. The time dependence of the induced absorbance change due to the ST excitons in nontluorescent polymers (PDA-3BCMU and PDA-4BCMU in the blue phase) is approximately represented by a single-exponential function after long components due to the triplet exciton, polaron, and/or bipolaron have been subtracted. The exponential decay time constants of nonfluorescent PDAs are between 1 and 3 ps in the temperature region 10-290 K. Both the formation and decay times are only weakly temperature dependent. The decay kinetics of the ST exciton in fluorescent polymers (PDA-4BCMU in the red phase, P3MT, and P3DT) deviate significantly from the single-exponential functions. A model of the relaxation of photoexcitations in the conjugated polymers is proposed to explain systematically all the experimental results. The main mechanism of the ultrafast radiationless relaxation is tunneling from the ST exciton to the ground state in the adiabatic potential description.

1. I n t r o d u c t i o n A comparison of the optical nonlinear properties between semiconductors a n d c o n j u g a t e d p o l y m e r s i s m a d e first. An extensive time-resolved study on the nonlinear optical response, such as degenerate four-wave mixing or more direct measurement of the refractive *Invited paper.

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566 index and/or absorbance change, has been carried out for various materials including semiconductors and polymers. In the experiment there are two excitation conditions: real excitation and virtual excitation. In the case of real excitation, the population (energy or longitudinal) decay time, T1, limits the speed of nonlinear optical response in the system. The excitons in various compound semiconductors have long lifetimes of the order of several hundred picoseconds. The carrier lifetimes are also long, even though they are dependent on carrier density. The response of the virtual excitation of excitons or electrons and holes is determined either by inverse detuning or by the dephasing (coherence or transverse) relaxation time, T2, depending on the ratio between the detuning and h/T2. Therefore bulk and/or quantum-well structured semiconductors are considered to have to be used under slightly off-resonance conditions to obtain an ultrafast nonlinear response not limited by T1 but by T2 and still with relatively large optical nonlinearity. Since the femtosecond laser inevitably has a broad spectxtmL the detuning must be large enough to avoid real excitation by the overlap of the tails of the pump laser and absorption spectra. In this case the resonance enhancement effect of the optical nonlinearity by the excitonic transition is not expected to be efficient. On the other hand, the efficiency of another third-order nonlinearity, namely two-photon absorption, does not change much even when the detuning is increased. Then two-photon absorption creates the real population of excitons and/or charge carriers in semiconductors, which can have long lifetimes of several hundred picoseconds. They are accumulated when highly repetitive pulses are used. For example, when a laser with a repetition rate of 100 GHz is used for the system, even if the contribution of the real excitation of excitons to the nonlinear effect is only 2% of that of virtual excitation per single pulse, the accumulation of the former becomes as large as the latter and the system cannot be used in ultrafast devices. In comparison with semiconductors, which have excitons and/or charge carriers with long lifetimes, conjugated polymers are attractive from the viewpoint of their ultrafast nonlinear optical properties. Therefore they are considered to be promising candidates for future practical applications to nonlinear optical devices, such as optical switching, optical logic, and information processing. They have large optical nonlinearity, ultrafast nonlinear responses [1-13] even under real excitation, high processibility, and high optical damage thresholds. They can also be prepared in many forms. In particular, polydiacetylenes, the group of polymers studied in the present paper, can be prepared in various forms, such as cast films, LangmuirBlodgett films, evaporated films, single crystals, solutions, and polymer alloys. In order to realize actual devices, the mechanism of the ultrafast optical nonlinearity must be clarified. For example, the factors determining the size of the third-order susceptibility and the nltrafast relaxation time must be found to obtain guiding principles for materials search and synthesis.

567 In the present paper, we have used femtosecond p u m p - p r o b e spectroscopy to study in detail the relaxation mechanism of the various excitations that induce nonlinear response in conjugated polymers.

2. E x p e r i m e n t a l

Cast films of blue-phase poly[4,6-decadiyne- 1,10-diol-bis(n-butoxycarbonylmethylurethane)l (PDA-3BCMU) and both blue- and red-phase poly[5,6dodecadiyne- 1,12-diol-bis(n-butoxycarbonylmethylurethane) l (PDA- 4BCMU), and electrochemically prepared films of poly[3-methylthiophene](P3MT) and poly[3-dodecylthiophene] (P3DT) prepared b y Professor Yoshino of Osaka University were used as samples. An evaporated film of PDA-3BCMU on a KC1 single-crystal surface (100) was also used. Such films form single crystals of PDA-3BCMU aligned in either the [110] or [ 1 i 0 ] direction. The sample also contains amorphous regions. The samples of PDA-3BCMU/KCI were prepared by Messrs Uemiya and Hattori of Sumitomo Electric Ind. A CPM (colliding pulse mode-locked) laser with a four-stage dye amplifier pumped by a Q-switched Nd:YAG laser was used for the femtosecond spectroscopy. The width, energy, and central wavelength (photon energy) of the amplified femtosecond pulse are typically 8 0 - 1 0 0 fs, 0.2--0.1 mJ, and 6 3 0 - 6 2 8 nm (1.97 eV), respectively.

3. R e s u l t s and d i s c u s s i o n

3.1. Experimental results of femtosecond spectroscopy Here we shall describe the experimental results of the femtosecond timeresolved spectroscopy of the polydiacetylenes (PDAs) and polythiophenes

(PWs). Figure 1 shows the transient photoinduced absorption spectra in an 11 ~ m cast film of PDA-3BCMU at 10 K after femtosecond pulse excitation at a photon density of 9.5 × 1014 p h o t o n s / c m 2 with parallel polarizations of the pump and probe [ 1 ]. Since the photon energy of the fundamental femtosecond pulse (1.97 eV) is very close to the absorption peak of the XBu excitons (1.92 eV at 10 K and about 1.95 eV at 290 K) in the blue phase and is much lower than the absorption edge in the red phase (2.2 eV), the 1.97 eV pump pulse selectively excites the 1Bu excitons in the blue phase. An oscillatory structure around 1.97 eV observed at negative delay times is due to the perturbed free-induction decay [14-17]. The sharp bleaching peak at 1.97 eV is due to hole burning affected by the coherent coupling, which sharpens the hole by the interference effect and optical (a.c.) Stark effect and induced phase modulation. The time orderings of the three electric fields to produce the third-order nonlinear polarization P(a)=eoX(3) EEE in the calculation of X (3) are as follows: perturbed free-induction decay, p r o b e - p u m p - p u m p ; pump polari-

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Fig. 1. Transient photoinduced absorption spectra o f PDA-3BCMU cast film in the blue phase with random orientation at 10 K. The spectrum of the pump--pulse laser is also shown by the dotted curve. The delay times are - 1 0 0 fs, 0 ps, and 100 fs for the three solid curves in the direction of signal increase. The dashed curve is at 500 fs. The negative-going peak at 1.97 eV between - 1 0 0 fs and 100 fs is due to the hole burning and coherent interaction in the four-wave mixing process. The negative-going peaks around 1.71 and 1.80 eV are due to Raman gain with 2090 cm -1 and 1450 cm -1 shift, respectively, from the pump laser photon energy at 1.97 eV. The excitation photon density is 9 . 5 × 10 ]4 p h o t o n s / c m 2. Fig. 2. Transient photoinduced absorption spectra of PDA-3BCMU cast film in the blue phase induced by a 1.97 eV p u m p pulse at 10 K. The excitation photon density is 3.8 × 1015 p h o t o n s / am 2.

zation coupling, p u m p - p r o b e - p u m p ; optical Stark effect, pump--pump-probe; induced phase modulation, pump-pump-probe; hole burning, pump-pump--probe. In the case of a negative delay time, where the probe comes earlier than the pump, all the above processes can take place when they overlap in time. At a longer negative delay time than the pulse width, the perturbed free-induction decay can only take place ff T2 is longer than the delay time. The pump polarization coupling and the optical Stark effect are observed only when the pump and probe overlap. The hole burning can last for TI or the spectral diffusion time. The induced phase modulation can in principle be observed for T1 but is more prominent in the case of a negative delay time, since the signal due to the effect is proportional to dn(t)/dt, n(t) being the time-dependent refractive index. The spectral region affected by the induced phase modulation extends to ±sh/td where s and td are a number of the order 2 - 1 0 and delay time, respectively. The pump polarization coupling appears in the spectral region of the pump laser and sharp transition spectrum like an exciton. The optical Stark shift is given by the photon energy derivative of the exciton transition spectrum and hole burning represents the homogeneous spectrum of the exciton transition

569 including the phonon side band. The induced phase modulation is represented by _ dS(oJ)/deo, where S(¢o) is the probe spectrum. The plus and minus signs correspond to the sign of dn/dt. The optical Stark shift and the induced phase modulation will be discussed in a little more detail later. Two small but reproducible negative peaks at 1.79 and 1.71 eV at zero delay time are due to the probe amplification by the Raman gain process [1, 2l, corresponding to the Stokes Raman shifts of 1450 cm -1 ( C = C stretching) and 2100 cm -1 ( C - C stretching) [1-5]. The Raman gain appears when the pump and probe temporally overlap and the signal appears at the Stokes-shifted position. The inverse Raman effect also appears at the antiStokes shifted frequencies, but it is usually more complicated than the Raman gain because of the interference among several contributing terms to the signal in the expression of the frequency dependence of X (3) corresponding to the process. The same vibrational modes as in the present study were found to be coupled strongly with the excitons in the inverse Raman effect of PDA-TS (poly[2,4-hexadiyne-l,6-diol-bis(p-toluene sulfonate)l) [6l. The intensity dependence of the inverse Raman spectrum was not studied even though the spectrum was explained in terms of the phonon-mediated optical Stark shift. We have for the first time observed a shift of the Raman gain spectrum from a single-crystal sample of another polydiacetylene (poly[1,4bis(2,5-bis(trifluoromethylphenyl))butadiyne)(PDA-MADF) by increasing the pump intensity [13]. This verifies directly for the first time the phononmediated optical Stark effect. The asymmetric bleaching near 1.97 eV in the transient spectrum of PDA-3BCMU, shown in Fig. 2, is induced by a high excitation photon density of 3.8 X 10 ~ p h o t o n s / c m 2 at 10 K. This is partially due to the optical (a.c.) Stark effect, which has been discussed for several condensed-phase materials [5, 6, 14-21]. The pump photon energy in the present study is higher than the exciton transition energy, in contrast to the previous reports [5, 6, 14-21 ]. This leads to the red shift as theoretically expected, and was recently reported for another system of semiconductors by Hulin et al. [22]. The derivative-type spectrum is also partially due to the induced phase modulation [23]. This can be verified by the observed spectral change for PDAs (red phase), which does not have an exciton peak near 2 eV. The spectrum represents the photon energy derivative of the probe spectrum, which has a sharp peak at 1.97 eV [4]. There are common features in the transient adsorption spectra of both PDAs (blue-phase PDA-3BCMU and PDA-4BCMU and red-phase PDA-4BCMU) and PTs either in randomly oriented films or in well-oriented films. One feature is a very broad absorption spectrum in the 1.2-1.9 eV region observed just at excitation (0 ps). The broad width suggests the transition to a continuum state, i.e., the free exciton to the conduction band [1, 2]. On the broad background there are two peaks near 1.4 eV and 1.8 eV, which appear after a few hundred femtoseconds. The peaks at 1.4 eV corresponds to the transition of the 1Bu self-trapped exciton to 1Au exciton and that at 1.8 eV can be assigned to the transition of the ZBu self-trapped exciton to the

570

excitonic molecule (or biexciton) with 1A~ symmetry. Another feature is the peak around 1.4 eV due to the triplet exciton, which has a long delay time and appears only when the laser intensity is high in the case of PDAs [24, 25]. Figure 3 shows the transient absorption spectrum of PDA-3BCMU/KCI. Because of the smaller inhomogeneity due to the higher quality of the sample, a narrow bleaching spectrum is exhibited due to absorption saturation of the excitonlc transition. A very clear Raman gain spectrum is seen at 0 ps delay. The bleaching peak at 1.97 eV at 0 ps is due to pump polarization coupling and that at 1.95 eV is due to hole burning. This means that the h o m o g e n e o u s width of the zero-phonon line of this sample is narrower than 0.02 eV HFHM. The absorption peaks at 1.8 and 1.4 eV are typical in the femtosecond transient absorption spectra of the conjugated polymers studied, i.e., polydiacetylenes and polythiophenes, at delay times of a few hundred femtoseconds. The peak at 1.4 eV corresponds to the 'Bu exciton -~ lag 0.1

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571

exciton transition. Hence the energy of the lag exciton is 1.95 + 1.4 = 3.35 eV. It is very interesting that the absorption peak of the triplet exciton is near that of the ~Ag exciton. This means that the transition energies from the self-trapped 11Bu exciton to m l A , exciton (m/> 2) and that from the selftrapped 13B, triplet exciton to the higher n3Bu triplet exciton (n>~2) are close to each other. The peak at 1.8 eV may be due to the biexciton (or excitonic molecule). If this is the case, the binding energy of the biexciton is calculated to be 1 . 9 5 - 1 . 8 = 0 . 1 5 eV. This is the upper limit of the binding energy, since the peak of the 'biexciton' is shifted to lower energy because of the bleaching in the 2 eV region. Figure 4 shows the time dependence of the absorbance change due to the self-trapped excitons in several PDAs and PTs, after the components with very long lifetimes, such as polarons, bipolarons, and triplet excitons, have been subtracted. As can clearly be seen in the Figure, the decays of nonfluorescent PDA-3BCMU in the blue phase and PDA-4BCMU also in the blue phase are approximately represented by exponential functions except the early stage within about 500 fs. The fluorescent polymers are known to have nonexponential decay until 30 ps from the data with extremely high S/N. The initial decay times, defined by the slope of the semilogarithmic plot of absorbance change against delay time just after excitation, are determined as 890 _ 160 fs, 620 +_60 fs, and 450 +- 50 fs in PDA-4BCMU in the red phase, P3MT, and P3DT, respectively, at 10 K. The decay becomes slower at longer

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-',,2-'& Delay Time (ps) Fig. 4. Time d e p e n d e n c e of the absorbance change due to the formation of self-trapped excitolls in several PDAs and PTs at 10 K, after the very long-lived c o m p o n e n t has b e e n subtracted. The photon energy and pulse width for PDA-4BCMU (red-phase cast film) are 3.94 eV and 300 fs, respectively. They are 1.97 eV and 100 fs otherwise. The probe photon energies are 1.92, 2.30, 1.63 and 2.3 eV for PDA-3BCMU (blue-phase cast film), PDA-4BCMU (red-phase east film), P3MT, and P3DT, respectively.

572

delay times. This will be explained later using a model of potential curves as being due to the less efficient tunneling through the barrier with thicker width and larger height of excitons. The formation and decay times and photoluminescence properties of the ST excitons in several PDAs and PTs studied are summarized in Table 1. 3.2. M e c h a n i s m o f exciton se~f-trapping in a one-dimensional system Since there is no barrier in the potential curve between free and selftrapped (ST) excitons in a one-dimensional system [26-28], as shown in Fig. 5, the formation of the ST excitons is expected to take place within the period T~-- 2~r/a~ of the coupled phonon cycle. The experimental results TABLE 1

The formation time a (vf) and the decay time (Vd) or serf-trapped (ST) excitons in several polymers Polymer

~f (fs) (290 K)

PDA-3BCMU (blue) PDA-4BCMU (blue) PDA-4BCMU (red) P3MT P3DT

150 ± 140 ± <200 70 ± 100 ±

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7d (ps) (10 k)

Fluorescent (f) or nonfluorescent (n)

1.9 ± 0.2 2.1 ± 0.1 0.96±0.09 b 0.62 ± 0.07 b 0.45 ± 0.06 b

n n f f f

"The formation o f ST excitons m e a n s the process of emission of the p h o n o n strongly coupled to the excitonic transition. The process is associated with a change in the transient spectrum. bThe values are determined by the slope of the semilogarithmic plot of a b s o r b a n c e change just after excitation, since the decay kinetics of the ST excitons in the fluorescent (f) polymers deviate substantially from single-exponential functions as shown in Fig. 4.

pump

G Fig. 5. Potential curves of the ground state (G), free exeiton (FE), and serf-trapped exeiton (STE) of the nonfluorescent polydiacetylenes. There is no barrier between the free-exciton (FE) and self-t~pped-exciton potential curves. Numbers 1,2 and 3 indicate FE, hot STE, and STE before thermal equilibration, respectively. Part of this Figure is enlarged and shown in Figs. 6 and 7.

573 of the absorption spectra, the Raman gain [1, 2], the resonance Raman scattering, and the phonon-mediated optical nonlinearity [6] show that the singlet excitons in polydiacetylene are coupled with the C = C and C = C stretching modes. The coupled stretching mode frequencies are about 1500 c m - i ( C = C stretching and 2100 cm-1 (C---C stretching), corresponding to the oscillation periods of 20 and 15 fs, respectively, both of which are much shorter than the experimentally observed appearance times of ST excitons, for example, 150 fs in PDA-3BCMU, 100 fs in PDA-4BCMU, 70 fs in P3MT, and 100 fs in P3DT. In the following, the terminology 'self-trapping' is used in two ways. One is the change in the adiabatic potential for excitons, which have the same energy as the free excitons. The self-trapping time estimated above from the oscillation period is used in this sense. After this self-trapping, the free exciton is converted to a non-thermal self-trapped exciton. The other meaning includes the above process followed by the emission of the phonon (intramolecular vibration) with high frequency. After this the exciton energy is lower than that of the free excitons, and the population of the thermalized ST excitons is distributed near the bottom of the ST exciton (STE) potential in Fig. 5. According to Jortner [26], the rate of the self-trapping process in the second sense in rare-gas solids such as Ne and Ar at low temperatures is given by ksw----o~ e x p ( - O~/eOD), where a~ and CODare the frequency of the most strongly coupled mode and the Debye frequency, respectively. Using the values of a~D in the literature and O~M given above, the calculated rate ksw is several orders of magnitude smaller than the observed rate in the polymers [ 1 ]. This is because of the over-simplified phonon structure in the model, which is only suited to rare-gas solids. The much longer self-trapping time can be explained by the geometrical reorganization (relaxation) involving the lower-frequency modes than the oscillation period of the strongly coupled modes. The lower-frequency modes may include those associated with the structural change in the bulky side chains, which are lacking in rare-gas solids. There is a difference in the formation time of the second meaning of ST excitons, namely the self-trapping time, between PDAs and PTs. The formation times are 150 fs in PDA-3BCMU and 140 fs in PDA-4BCMU in the blue phase, 70 fs in P3MT, and 100 fs in P3DT. This can be explained by the difference in the chemical structures of these two groups of polymers. The urethane-derivative-substituted polydiacetylenes, PDA-3BCMU and PDA4BCMU, have side groups with hydrogen bonds connecting neighboring side chains, while P3MT and P3DT have rigid structures of thiophene rings conjugated with each other. PTs have helical noncoplaner structures due to the steric hindrance among the side groups [29, 30]. There is the van der Waals interaction between the neighboring side chains and between the main chain and side chains. The interactions are more intense in P3DT than in P3MT because of the longer side chains in the former. This is consistent with the longer formation time in the former.

574 In contrast to the PTs, both PDA-3BCMU and PDA-4BCMU have bulky substituent groups attached to the main PDA chains. They extend a few tens of gmgstroms from the backbone main chain and form a sheet in the backbone plane assisted by the hydrogen bonding between two neighboring side chains in the blue-phase PDA-3BCMU and PDA-4BCMU. After electronic excitation, the whole side-group structure must be reorganized so that they can fit the new configuration with the lowest energy in the 1Bu exciton state. This change must be associated with the conformational reorganization of all the substituent side groups in the polymer. It is expected to take longer in PDA-3BCMU and PDA-4BCMU with bulky side groups, which are connected with neighboring side chains by the hydrogen bonds, than in P3MT and P3DT with small side groups and no strong interaction between neighboring side chains. From the experimental results, the reorganization of the whole configuration takes place after five to twenty periods of the oscillation induced by photogeneration of excitons in PDA-3BCMU and PDA-4BCMU because of the strong elect r o n - p h o n o n coupling. The self-trapping time constant of excitons in P3MT is 70 fs, which differs from 150 fs in PDA-3BCMU only by a factor of two, even though the differences in the structure and size of the side chains are very large. This may be due to the following three possible mechanisms: (1) Finite time is needed for the hot self-trapped exciton to start sliding down along the adiabatic potential because the slope of the potential curve of the self-trapped exciton is flat with zero derivative at the point where it starts from the bottom of the free exciton potential curve [27, 31 ]. (2) According to Sumi's theory of the self-trapping process in reduced dimensionalities [27, 28, 31 ], the spontaneous geometrical relaxation, which takes place from the infinitely extending free exciton to the self-trapped exciton of any size, follows a reaction pathway with a very small slope along the reaction coordinate. (3) Because of the interchain interaction, the conjugated polymer may not be an ideal one-dimensional system. Then there may be a very low barrier between two minima in the potential curves of the ground state and the ST exciton state. These three mechanisms can also explain the relatively small (0.01-4). 15 eV) Stokes shift observed for fluorescent polymers. The small Stokes shift may also be explained as follows. There may be a shallow minimum in the ground-state potential curve of the polymers under the same configurations as the ST excitons. The Franck-Condon configurations of PDAs and PTs corresponding to the bottoms of ST exciton potentials are butatriene-like and quinoid-like forms, respectively.

3.3. Decay kinetics of self-trapped excitons in conjugated polymers [32] The following properties are addressed here concerning the excited-state dynamics in conjugated polymers, especially polydiacetylenes.

575 (1) Many conjugated polymers are nonfluorescent or only weakly fluorescent. In particular, the quantum efficiency of the nonfluorescent bluephase polydiacetylenes is estimated to be lower than 10 -5 and that of the fluorescent red-phase polydiacetylenes is only of the order of 10 -4. The relatively high quantum efficiency of poly(p-phenylenevinylene)(PPV) is only about 0.08. This is in remarkable contrast to low-molecular-weight aromatic molecules, some of which have an efficiency higher than 0.95. (2) A triplet exciton cannot be f or m e d directly from the singlet exciton. T h e y are f o r med only at high-density excitation of excitons or by chargecarrier creation by the interband transition. To obtain a model which can explain the above characteristic properties t o g e t h e r with the present experimental results on f e m t o s e c o n d - p i c o s e c o n d s p e c t r o s c o p y and n a n o s e c o n d - m i c r o s e c o n d spectroscopy, I would like to summarize the results and discuss t h e m as foUows. The lifetime of the ST IBu excitons in PDAs in the blue phase is m u c h shorter than the radiative lifetime estimated from the oscillator strength of the transition. This means there is a p r e d o m i n a n t radiationless relaxation in the exciton decay process. Excitons in many sem i conduct ors and organic molecular crystals have lifetimes between several h u n d r e d p i c o s e c o n d s and several h u n d r ed n a n o s e c o n d s at low temperatures. More than one order of magnitude differences in the lifetime of these excitons and the fluorescence q u a ntu m efficiency are usually found between low t e m p e r a t u r e s and room temperature. The activation potential barrier is very often invoked to explain the t e m p e r a t u r e dependence in m os t excitons in semiconductors, organic molecular crystals, and also in ionic crystals. The relaxation of photoexcitations in polymers in general can be described as follows using PDAs and PTs as examples [1, 2, 4, 32]. The differences in the relaxation kinetics of excitons in nonfluorescent PDA-3BCMU and PDA-4BCMU in the blue phase, fluorescent PDA-4BCMU in the red phase, and P3DT and P3MT described in Section 3.1 can be discussed based on Toyozawa's th eo r y [28, 33l. Figures 6 and 7 show the potential curves of

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G[

Fig. 7. Potential curves of the ground state (G), free exeiton (1~), and self-trapped exeiton (S'rE) of the fluorescent polymers. Numbers 1, 2 and 3 are the same as in Fig. 5. Number 4 means STE after thermal equilibration among intramolecular vibrational modes to a local (within a chain) temperature higher than the bulk experimental temperature of the samples. Number 5 indicates the STE after the local temperature is lowered to the bulk experimental temperature.

the ground state (G) and self-trapped exciton (STE), and the free exciton (FE) band of the nordluorescent (Fig. 6) and fluorescent (Fig. 7) polymers, respectively. The curvature radius of the potential of the STE is shown to be larger than those of the G and FE states in order to take into account the discussion about the reaction coordinate by Sumi et al. [31 ] and of the small Stokes shift observed for the fluorescent polymers. The electronic structures of the polymer systems are too complicated to be represented by the one-dimensional potential curves. The small Stokes shift may also be explained by the ground-state potential having two minima with a small barrier in between, corresponding to the acetylenic and butatrienic configurations or to the aromatic and quinoid configurations in the cases of PDAs and PTs, respectively. The relaxation processes of photoexcitations in the polymers can be described as follows. In Figs. 6 and 7, a self-trapping process from FE (indicated by the number 1 in the Figures) to STE (indicated by 2) is the process 1-~2, followed by the emission of a phonon of strongly coupled modes to the excitonic transition. The STEs after the phonon emission process still remain in the unthermalized states (3). The unthermalized STEs (3) are coupled with phonon modes (intramolecular vibrations) of low frequencies and thermalize to states where temperatures of the intramolecular vibration can be defined. The thermalization process (3--* 4) is observed at the spectral change at delay times from 0.5 to 5.0 ps. The time constant of the thermalization can be determined by the time dependence of the absorbance-change ratio among several different wavelengths. The obtained time constant of the thermalization process is about 1 ps in both red-phase PDAs and P3DT. However, the temperature of the STEs defined from equilibrated vibrational modes after this 1 ps thermalization process may be still higher than the bulk temperature of the polymer sample. Therefore the cooling-down process (4--~ 5) with a

577 time constant of several or a few tens of picoseconds is expected to take place after the observed thermalization process. However, the spectral change due to the cooling-down process of the STEs could not be clearly detected in this study because of the limited signal-to-noise ratio of the spectral data. The change of the decay rate observed in the red-phase PDA-4BCMU and P3DT can be explained by the competition between the thermalization and tunneling processes. The STEs relax to the ground state mainly by tunneling through the barrier between the STEs and ground-state potentials. The initial fast decay is the relaxation from the nonthermal STEs (indicated by 3 -* 4 in Fig. 7) with a time constant of about 1 ps. After the thermalization the STEs come down near the bottom of the potential and the loss rate by tunneling becomes slower. The decay time constant of about 5 ps is due to the tunneling from the thermalized STE (indicated by 4 in Fig. 7). The time needed for the STE thermalization is estimated as about 1 ps from the time dependence of the spectral change. The wavelength dependence of the decay curve can be explained by the thermalization process. The absorbance change at 2.00 eV in the red-phase PDAs is mainly due to the nonthermal STEs and the thermalized STEs have an absorption peak at 1.6 eV. Therefore, the decay curve at 2.00 eV can be fitted to a single exponential function with a time constant of about 1 ps. The time constant of the absorbance change below 1.8 eV is longer than that of the bleaching, because the nonthermal STEs thermalize with a time constant of 1 ps and the absorption peak due to the thermalized STEs appears at 1.6 eV. The observed data of P3DT can be explained in the same way. The decay of the nonthermal STE (after emission of the phonons with high frequencies) in the blue-phase PDAs is faster than in the red-phase ones, because the crossing point is lower than that in the latter. The major fraction of the STEs relaxes to the ground state before the thermalization. The decay rate from the nonthermal STEs to the ground state is not much slower than the decay rate from the unrelaxed STEs. Therefore, the decay curves in the blue-phase PDAs can be fitted to single-exponential functions. The wavelength dependence of the time constant is due to contributions of signals from the STEs with different degrees of relaxation. The bleaching signal exhibits the unrelaxed and relaxed (i.e., after large-frequency phonon emission) but unthermalized STEs, while the absorption around 1.8 eV is due to the unthermalized STEs. Therefore, the observed decay time constant of the bleaching is shorter. The difference between fluorescent and nonfluorescent polymers is in the tunneling rate from the nonthermal and thermalized STEs to the ground state. The time constants in the blue-phase PDAs are between 1 and 3 ps and they are shorter than that in the red-phase PDAs. Therefore the number of remaining STEs at the bottom of the STE potential curves in the bluephase PDA is smaller and the luminescence cannot be detected. The fast component of the luminescence in the red-phase PDAs is considered to be due to the STEs and the slow component is due to the traps in the polymer

578 chains. A detailed study using highly oriented samples is also consistent with the above model [4]. The proposed relaxation model predicts that the decay rate of the STE in conjugated polymers depends on the exciton energy. Conjugated polymers with large exciton energy are considered to have excitons with long lifetime and to be more fluorescent. For example, poly(p-phenylenevinylene)(PPV), which has an absorption peak at 2.5 eV, has relatively strong luminescence with a quantum yield of several percent [34]. Recently, a Langmuir-Blodgett film of PDA-(12,8), which has an exciton peak at 1.88 eV, has been studied and the decay time constant of the STE is estimated as 1 . 3 ± 0 . 1 ps at 290 K [35]. It is slightly shorter than that in blue-phase PDAs, which have an exciton peak at 1.97 eV. These results are consistent with the model proposed above. The low fluorescence quantum efficiency of the one-dimensional polymers is systematically explained by the proposed model shown by Figs. 6 and 7. In fluorescent polymers such as PDA-4BCMU in the red phase, P3MT, and P3DT, the crossing points are higher than in PDA-3BCMU and PDA-4BCMU in the blue phase because of the higher energy of free and ST excitons. In red-phase PDA-4BCMU a larger fraction (probably ten to several tens percent) of free excitons are relaxed to thermalized ST excitons with 3 ps lifetime at 10 K. This is represented in Figs. 6 and 7 as tunneling through the potential barrier between the ST excitons and the ground state.

3.4. F o r m a t i o n o f triplet excitons The formation of a triplet exciton, which has a characteristic absorption peak around 1.4 eV, observed for PDAs does not take place when the photon energy is smaller than the band-gap energy, Eg. When the photon energy exceeds Eg, the transient absorption due to the triplet exciton starts to appear [37]. When the intensity of the laser, whose photon energy is smaller than Eg, is increased, a triplet exciton can also be observed. The signal intensity due to the triplet exciton was nearly proportional to the laser intensity. In the case of PTs, and also of poly(thienylenevinylene)(PTV) [36], the triplet exciton appears near 1.4-1.5 eV even though the ST exciton decay kinetics of PTs are similar to those of the fluorescent PDAs and that of the nonfluorescent PTV (quantum efficiency of less than 10 -5) is represented by a single exponential decay function as in the nonfluorescent PDAs. This can be explained as follows. The CPM laser photon energy is in resonance with the exciton transition in PTs and PDAs, but since the excitons formed in PTs and PTV are easily ionized by the disorder, as discussed by Baessler and co-workers [37], triplet excitons are formed from the electrons and holes created as in the case of the interband transition in PDA. Therefore it the samples of PTs and PTV are synthesized without a substantial amount of disorder, they will show activation energy spectra of the both the photoconduction and triplet exciton formation different from each absorption spectrum.

579 Recently a detailed investigation of the intensity dependence of the photoinduced reflectance change of PDA-MADF (poly-l-(3-(methylamino)phenyl)-4-(3,5-bis(trifluoromethyl)phenyl)-l,3-butadiyne) has been done [38]. It was clarified that the Auger process induced by the dipole interaction between two singlet excitons creates the (higher) excited state of the selftrapped excitons; the two triplet excitons are then formed by the fission of the latter [39]. The equations which represent the processes are So+hv

) $1

(1)

81 "~-S1

)

Sn+80

(2)

Sn -I- 8o

> TI q- T,

(3)

where So, $1, Sn, and T1 are the ground state (llAe.), the lowest self-trapped singlet exciton (11B~), the higher excited state exciton (mlAg), and the lowest self-trapped triplet exciton (laB~), respectively. In the early stages of the study of triplet excitons, an electron-hole pair was considered as a higher-lying state [39], since the quantum yields of photoconductivity and the triplet exciton formation showed a similar photon energy dependence in a single crystal of PDA-TS [401. However, Winter et al. [41l observed the triplet excitons in PDA-TS by pulsed ESR after photoexcitation at 3.68 eV and suggested that the triplet excitons are generated from a triplet pair state, which is directly excited via one-photon absorption. Recently Austin e t al. [42] measured the magnetic-field dependence of the triplet-exciton production and decay in PDA-4BCMU, and found that the triplet excitons are created by fission of the higher-lying singlet excitons. The higher excited singlet state reached by the Auger effect of singlet excitons is lAg because of the dipole-allowed transition from the 'Bu exciton state. Then two triplet excitons are generated via the fission of the higherlying miig exciton state (S~). The fission of a singlet exciton into two lowest triplet excitons (laB~) is known to occur in organic crystals such as anthracene and tetracene [43-45]. The population of the triplet excitons generated was found to be proportional to the squared population of the self-trapped excitons. The reason why triplet excitons are not formed from the singlet-exciton formation under low-density excitation of PDAs can be explained as follows. In ordinary molecular crystals without a heavy atom the intersystem crossing takes place with a time constant between 1 /xs and 1 ns. Since the lifetimes of the free exciton, nonthermal STE and the thermalized STE are 10-20fs, 100-200 fs and 1-3 ps, respectively, in PDAs, there is no time for the singlet excitons to change their spin state. The time needed for the intersystem crossing is between 10/~s and 1 ns in ordinary aromatic molecules without heavy atoms such as bromine or iodine. Because of this short lifetime of the singlet excitons, triplet excitons cannot be directly formed from them. The triplet-exciton formation in PTs and PTV is due to the intersystem crossing of electron-hole pairs created by the ionization of excitons induced by the disorder in these polymers.

580

4. Conclusions In t h e p r e s e n t p a p e r w e h a v e clarified t h e m e c h a n i s m o f the low f l u o r e s c e n c e q u a n t u m yield in PDAs, PTs, a n d in PTV a n d t h a t t h e r e is n o t r i p l e t - e x c i t o n f o r m a t i o n f r o m t h e singlet e x c i t o n in PDAs. This is b e c a u s e of the v e r y s h o r t lifetime o f t h e singlet e x c i t o n in t h e c o n j u g a t e d p o l y m e r s . T h e s h o r t lifetime is c a u s e d b y t h e e l e c t r o n - p h o n o n c o u p l i n g in a o n e d i m e n s i o n a l s y s t e m , w h i c h is e x p l a i n e d a s follows. Since the c o n j u g a t e d p o l y m e r s are o n e d i m e n s i o n a l , t h e s p o n t a n e o u s g e o m e t r i c a l r e l a x a t i o n t a k e s p l a c e w i t h o u t a n y a c t i v a t i o n b a r r i e r in the a d i a b a t i c p o t e n t i a l b e t w e e n the free e x c i t o n a n d the s e l f - t r a p p e d exciton. B e c a u s e o f this, the a d i a b a t i c p o t e n t i a l s o f the s e l f - t r a p p e d e x c i t o n a n d t h e g r o u n d s t a t e c r o s s at a p o i n t l o w e r t h a n in o r d i n a r y t h r e e - d i m e n s i o n a l s y s t e m s . T h e r e f o r e the r e l a x a t i o n o f t h e s e l f - t r a p p e d e x c i t o n s b y t u n n e l i n g is efficient. P a r t o f t h e p r e s e n t p a p e r h a s a l r e a d y b e e n p u b l i s h e d [ 1 - 3 ] . A detailed s t u d y o f o r i e n t e d a n d u n o r i e n t e d films o f PDA-4BCMU in t h e b l u e a n d r e d p h a s e s , t h e difference in d e c a y kinetics b e t w e e n a m o r p h o u s c a s t film a n d e v a p o r a t e d film o f PDA-3BCMU on KC1, a n d t h e triplet e x c i t o n f o r m a t i o n in PDA-MADF will be d e s c r i b e d in refs. 4, 4 6 a n d 38, respectively.

Acknowledgements The a u t h o r w o u l d like t o e x p r e s s t h a n k s to Dr M. Yoshizawa f o r his essential c o n t r i b u t i o n to t h e s t u d y a n d also t o Drs K. I c h i m u r a and U. S t a m m a n d Mr M. Taiji f o r t h e i r c o l l a b o r a t i o n in t h e f e m t o s e c o n d t i m e - r e s o l v e d e x p e r i m e n t . H e also is i n d e b t e d to P r o f e s s o r K. Yoshino for p r o v i d i n g the PDA-3BCMU s a m p l e s . H e also t h a n k s D r Y. H a t t o r i f o r the gift o f t h e PDA3BCMU/KC1 s a m p l e s . T h e a u t h o r t h a n k s P r o f e s s o r s Y. T o y o z a w a , E. H a n a m u r a , H. B a e s s l e r a n d H. Sumi a n d Dr S. A b e for t h e i r v a l u a b l e discussions.

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