Triplet Excitation Transfer in Triphenylene Columnar Phases

trap. It is shown that triplet migration and trapping leads to the formation of the ion-pair 3(T+, TNF-), whose recombination rate constant is 5.5 × ...
0 downloads 0 Views 127KB Size
Download PDF
J. Phys. Chem. B 2001, 105, 1299-1306

1299

Triplet Excitation Transfer in Triphenylene Columnar Phases Dimitra Markovitsi,* Sylvie Marguet, and Jens Bondkowski CEA/Saclay, DRECAM, SPAM, Laboratoire Francis Perrin (CNRS FRE2298), 91191 Gif-sur-YVette, France

Sandeep Kumar Centre for Liquid Crystal Research, P.O. Box 1329, Jalahalli, Bangalore 560013, India ReceiVed: July 18, 2000; In Final Form: October 31, 2000

Triplet excitation transport occurring in the columnar liquid crystalline phase of a triphenylene derivative at room temperature is studied by transient absorption spectroscopy with nanosecond resolution. The properties of the triplet excitons are evidenced by doping the mesophase with different concentrations of 2,4,6trinitrofluoren-9-one (TNF) which is inserted in the stacks of the triphenylene cores (T) and acts as energy trap. It is shown that triplet migration and trapping leads to the formation of the ion-pair 3(T+, TNF-), whose recombination rate constant is 5.5 × 105 s-1. The comparison of the experimentally determined time dependence of the ion-pair concentration with numerically simulated curves on the basis of an one-dimensional random walk model allows the determination of the hopping time (2 ( 1 ps). The latter value is close to that found, in a previous study, for the singlet excitation transport (1.2 ( 0.5 ps) in the same mesophase. This is in agreement with the finding that interactions due to intermolecular orbital overlap, responsible for energy transport in the triplet state, are also the main driving force for singlet excitation transport. The migration length of the triplet exciton is limited by structural defects to a few hundreds of triphenylene cores.

1. Introduction Columnar liquid crystals (Figure 1) have attracted attention as one-dimensional systems for the investigation of the electronic excitation transport. The first two communications in this respect appeared in 1987.1,2 Thereafter, successive studies in this field led to a refinement of both the experimental methods and the modeling of the transport process.3-10 An important progress regarding singlet excitation transport in columnar mesophases was made recently combining timeresolved fluorescence spectroscopy, quantum chemistry calculations, and Monte Carlo simulations.12 Such a methodology allowed the determination of the various components of the electronic coupling responsible for singlet excitation transport in triphenylene columnar mesophases and provided a picture of the spatiotemporal evolution of the excitation in this system. Meanwhile, a series of conductivity and photoconductivity measurements showed that triphenylene mesophases behave as one-dimensional semiconductors.13-16 The hole mobility was found to be at least 3 orders of magnitude higher than in commercially available organic semiconductors14 making those materials promising for applications in the domain of molecular electronics and optoelectronics.14,16 The transient photocurrents recorded by the time-of-flight technique decay at the nanosecond and microsecond time scales, which are the characteristic time scales of triplet excitons. Triplet excitons and charge carriers have also in common that the electronic coupling necessary for their motion is provided by intermolecular orbital overlap which decreases exponentially with the distance. The same type of coupling may be responsible for singlet energy transfer. In a more general way, singlet excitons, triplet excitons, and charge carriers are interconnected, since triplet excitons derive from singlet ones and charge carriers may be generated from singlet or triplet excited states. Therefore, it is interesting to obtain a

Figure 1. Schematic representation of the hexagonal columnar mesophases used for the study of excitation transport. They are formed by chromophores containing an aromatic, disklike core, surrounded by flexible tails. In the present study the stacking distance d is 3.6 Å and the intercolumnar distance D is 20.7 Å.11

complete picture of the various transport processes (singlet and triplet excitation transport and charge transport) occurring in a given molecular system. With this in mind, we have undertaken a transient absorption study of the mesophase formed by the tetrameric triphenylene derivative I (Figure 2) with nanosecond resolution. Our purpose was 2-fold. On one hand, we wanted to compare the dynamical properties of the triplet excitons with those found for the singlet excitons in the same mesophase. On the other, we wanted to prepare a subsequent spectroscopic study of the charge carriers, related to the high hole mobility and performed under electric field.17 The present article is devoted only to the study of triplet excitons, whereas the spectroscopic investigation of the charge carriers will be the object of a forthcoming paper.18 The choice of the tetrameric compound was motivated by the fact that its hexagonal columnar mesophase is stable at room temperature and the mesophase f isotropic phase transition takes place at 141 °C.19 Consequently, experiments could be performed under conditions limiting local melting, which

10.1021/jp002523z CCC: $20.00 © 2001 American Chemical Society Published on Web 01/31/2001

1300 J. Phys. Chem. B, Vol. 105, No. 7, 2001

Figure 2. Studied tetrameric triphenylene derivative I and the 2,4,7trinitrofluoren-9-one (TNF) used as energy trap. Each monomeric triphenylene core bearing six oxygen atoms, noted as T, corresponds to one disk in the columnar stack.

increases at temperatures close to the mesophase f isotropic phase transition, and photodegradation of the chromophores whose efficiency also increases with temperature. This point is an important improvement with respect to previous studies of the mesophases formed by monomeric triphenylene derivatives carried out at much higher temperatures.1,7 As in the case of the study of the singlet excitation transport,12 we doped the mesophase with 2,4,6-trinitrofluoren-9-one (TNF, Figure 2) acting as a trap for singlet and triplet excitons. TNF forms a charge-transfer complex with the triphenylene core bearing six oxygen atoms, noted as T, and thus is inserted in the columnar stacks without segregation as shown by X-ray measurements and NMR studies.20 We followed the variation of the time dependence of the differential absorption spectra as a function of the TNF concentration. To know the behavior of noninteracting chromophores, we also studied the properties of the monomeric analogue 2,4,6,7,10,11-hexakis(n-pentyloxy)triphenylene, noted as II, in solution. The paper is organized as follows. The experimental details are given in section 2. In section 3 the spectral characterizations of noninteracting chromophores in solution and that of thin films, doped and undoped, are presented; the trapping mechanism is elucidated. In section 4 a kinetic study, performed in the nanosecond and in the microsecond time scales, is described. Then, the evaluation of the migration length (section 5) and the determination of the hopping time (section 6) are presented. A discussion on the factors which govern the hopping time values is carried out in section 7. Finally, in section 8, the main results are summarized and a comparison between the triplet and singlet transport in the examined mesophase is made. 2. Experimental Details Compounds I and II were synthesized according to the experimental procedures described in refs 19 and 7, respectively. The 2,4,7-trinitrofluorenone was obtained from Janssen Chimica and purified by 2-fold recrystallization from ethyl acetate. The TNF/I mixtures were prepared as follows. Well-defined concentrations (10-3 M or 4 × 10-5 M) of TNF in freshly distilled tetrahydrofuran were prepared. For each TNF/I mixture, an amount of ca. 15 mg of I was weighed into a glass vessel. Then,

Markovitsi et al. a certain volume of the TNF solution was added into the glass vessel by means of a microliter syringe. The solvent was evaporated under ambient conditions while stirring and gently heating (50 °C) the mixtures. Afterward the sample was dried overnight under reduced pressure (10-3 mbar). The TNF molar fraction f is defined as the number of TNF molecules per number of alkoxytriphenylene cores T, f ) (TNF)/(T). Samples with trap molar fractions equal to 5 × 10-4, 10-3, 2.5 × 10-3, 8 × 10-3, 10-2, 5 × 10-2, and 1 were prepared; the error was less than 10%. The thin films of the mesophase of I, undoped or doped, were prepared as follows. Two QS slides, typically 10 × 20 mm2, emerged, first, in dichloromethane and, then, in ethanol, were cleaned in an ultrasonic bath. After drying, they were placed on a heating stage (Heidolph MR2002) at 50 ˚C. A drop of chloroform containing 10 µm Shinshikyu silica spacers (Dodwell marketing services, Japan) was deposited on one side of each slide. When the solvent was evaporated, the spacers were sandwiched between the two slides which could slip very easily with respect to each other. A 1-2 mg amount of the powder compound was deposited on the lower slide and heated to ca. 150 °C, resulting in the formation of an isotropic liquid which filled the space between the two slides. The mesophase formed upon rapid cooling was inappropriate for optical measurements because it strongly scattered the light. Therefore, we heated the samples again to the isotropic phase and let them cool very slowly (0.1 °C/min) using a Linkam heating stage (LTS 350) equipped with a Linkam TP 92 temperature controller. The samples were checked by an Olympus BX60 polarizing microscope revealing monodomains of at least 10 µm which did not scatter the light any more. The time-resolved absorption spectrophotometer used as exciting light the third harmonic (355 nm) of a Nd:YAG laser (Spectra-Physics, Quanta Ray). The laser repetition rate was 5 Hz. The polarization of the laser beam was normal to the optical table. The laser pulses had a duration of 10 ns and their energy was measured by an energy ratiometer (Laser Precision Instruments, Rj 7200). The probing light (Xenon arc; Osram 450 W) was dispersed in a Spex 270M monochromator, detected by a Hamamatsu R928T photomultiplier, and analyzed by a Tektronix DSA 620 digitizing signal analyzer. The angle formed between the pumping and probing light was 90° for the study of solutions and 20° for the study of thin films. In the latter case, the probing light passed through a Glan Thomson prism before reaching the sample where the irradiated area was 25 mm2 and the photon density ranged from 8 × 1014 to 1016 photons/cm2. We obtained the same transient signal for parallel and orthogonal exciting and probing beams. Solutions were degassed by the freeze-thaw technique and studied in 1 cm × 1 cm QS spectroscopic cells equipped with an airtight valve. For the study of degassed thin films, the samples prepared as described above were inserted into the 1 cm × 1 cm cells used for solutions and pumped overnight at 10-3 mbar. Electrochemical experiments were carried out with a VoltaLab32 apparatus from Tacussel, equipped with a DEA332 potentiostat. Electrolysis was performed in a three-electrode cell equipped with a Pt grid working electrode, a platinum wire counter electrode, and a saturated calomel reference electrode (SCE). The working electrode plunged into a 2 mm spectroscopic cell (quartz infrasil). The electrolytic medium was 0.10 M of tetrabutylammonium tetrafluoroborate in distilled dichloroethane. All solutions were degassed by argon bubbling prior to each experiment. Oxidation of 4 × 10-4 M of II at applied

Triplet Excitation Transfer

Figure 3. Steady-state absorption spectra recorded for undoped thin films of I (...) and n-heptane solutions of II (-).

Figure 4. Normalized transient absorption spectra recorded at 5 µs for undoped thin films of I (open circles) and n-heptane solutions of II (solid circles). Degassed samples are used.

potential E ) +1.15 V (vs SCE) and reduction of 4 × 10-4 M of TNF at potential E ) -0.4 V (vs SCE) were run under inert atmosphere. UV-vis and near-IR absorption spectra were recorded with a Perkin-Elmer Lambda 900 spectrophotometer. 3. Spectral Characterization Undoped Samples. The steady-state absorption spectra recorded for thin films of I (Figure 3) are similar to the spectra obtained for the mesophases of monomeric hexaalkoxytriphenylenes7 showing that the siloxane ring, located between the columns, does not affect the properties of the chromophore. Its maximum is blue-shifted with respect to the spectrum of noninteracting chromophores (II in n-heptane) by 2000 cm-1 due to strong dipolar interactions giving rise to delocalized excited states.7,21 The transient absorption experiments were performed with laser excitation located at the red edge of the spectrum and corresponding to the S0 f S1 electronic transition. The transient absorption spectra of degassed solutions of II in n-heptane present two main bands peaking at 22000 and 26300 cm-1 (Figure 4). They decay with a time constant of 62 ( 2 µs. No transient signals could be recorded for nondegassed solutions. Such a behavior as well as the relatively long decay constants shows that the species corresponding to these spectra are triplet states. In contrast to solutions, transient signals could be detected even for nondegassed thin films of I although their intensity is

J. Phys. Chem. B, Vol. 105, No. 7, 2001 1301 lower in the presence of oxygen. The decays recorded for both degassed and nondegassed samples are nonexponential. Although most of the signal intensity disappears in the microsecond time scale, a weak transient absorption signal still persists a few hundreds of milliseconds after laser excitation. The profiles of the mesophase spectra recorded at times ranging from 250 ns to 50 µs are practically identical and are the same for degassed and nondegassed samples (Figure 4). They consist of a broad band (5000 cm-1 fwmh) peaking at 17800 ( 100 cm-1. At times longer than 50 µs a progressive shift of the broad band toward lower energies is observed. At 300 µs the maximum is located at 17 300 ( 300 cm-1. We can see in Figure 4 that the maximum of the transient spectrum of the mesophase is 4000 cm-1 lower in energy than that of noninteracting chromophores in n-heptane. One could think that the spectrum in Figure 4 does not originate from triphenylene chromophores but from an impurity acting as a trap for the triplet excitons. The changes observed in the transient absorption spectra upon doping the mesophases with TNF presented below allowed us to rule out this interpretation and to evaluate the concentration of the intrinsic traps. These intrinsic traps are probably responsible for the red shift (500 cm-1) of the mesophase spectrum at long times. A plausible explanation of the observed difference between solution and mesophase transient spectra is that the mesophase absorption band corresponds to an electronic transition toward a triplet interchromophore charge transfer state (T+,T-). Doped Samples. The transient absorption spectra recorded for degassed thin films of I doped with TNF molar fraction equal to 5 × 10-4 are similar to those obtained for undoped films. When the TNF concentration reaches 10-3, the spectra recorded at times shorter than 6 µs become different from those of the undoped mesophase. They present a band peaking at 17 700 cm-1 and a second peak at 12 000 cm-1 (Figure 5a). Upon increase of the TNF molar fraction, the relative intensity of the lower energy band increases. At times longer than 6 µs, only the higher energy band is present and the spectra resemble those of the undoped samples. The transient signals recorded for samples containing a TNF molar fraction equal to 5 × 10-2 decay with the same time constant of 1.8 ( 0.2 µs whatever the wavelength (inset in Figure 5c) showing that the transient spectrum corresponds to a first-order deactivation process. No transient signal could be recorded for samples containing one TNF molecule per triphenylene core (f ) 1). This means that when the (T, TNF) charge transfer complexes are directly excited no triplet ion pair is formed. The latter finding is in agreement with a picosecond transient absorption study of the charge-transfer complexes (T, TNF) in n-heptane23 which revealed that direct excitation of (T, TNF) leads to the formation of the singlet ion-pair 1(T+, TNF-); the latter disappears with a time constant of 60 ps yielding only the ground-state complex. The fact that TNF concentrations as low a f ) 10-3 lead to the formation of detectable amounts of transient species proves that triplet migration and trapping takes place. The lowest TNF concentration capable of inducing detectable changes in the transient absorption spectra should be of the same order of magnitude as the concentration of intrinsic traps. We remark that the intrinsic trap concentration determined in the case of singlet excitons was also 10-3.12 For nondegassed samples, the intrinsic trap concentration is rather 2 × 10-2 which is reasonable since oxygen is a trap for triplet excitons. Trapping of the triplet exciton could lead either to the formation of the excited triplet state of TNF,

1302 J. Phys. Chem. B, Vol. 105, No. 7, 2001

Markovitsi et al.

Figure 6. (a) Transient absorption spectrum recorded for a TNF degassed solution in dichloroethane (10-4 M) at 1 µs. The spectrum decays with a time constant of 32 (2 µs. (b) Steady-state absorption spectra of (II)+ (-) and TNF- (...) in dichoroethane obtained by the spectroelectrochemical technique. For comparison, the transient absorption spectrum of a thin film of I doped with TNF (f ) 5 × 10-2) at 0.5 µs is shown (solid circles). Figure 5. Transient absorption spectra obtained at 0.5 µs (solid circles) and 10 µs (open circles) for degassed thin films (10 µm) of I doped with various TNF molar fractions: (a) f ) 10-3; (b) f ) 10-2; (c) f ) 5 × 10-2. In the insert are shown the transient absorption decays at 570 and 830 nm.

T + TNF f T + 3TNF

Kerr ellipsometry in the picosecond time scale upon excitation of the charge-transfer band.23 At this point we can conclude that the trapping of triphenylene triplet excitons leads to the formation of a triplet ion-pair 3(T+, TNF-) whose lifetime is 1.8 µs.

3

or to the formation of the triplet ion-pair,

T + TNF f 3(T+, TNF-)

3

In the former case, the transient spectra of the highly doped films should present the spectral features of 3TNF. We can see in Figure 6a that the absorption spectrum of 3TNF is characterized by a main band peaking at 19 600 cm-1; the spectrum is very different from that shown in Figure 5c which is also represented in Figure 6b. Thus, the first possibility has to be ruled out. The absorption spectrum of the triplet ion-pair 3(T+, TNF-) is expected to exhibit the absorption bands corresponding to the donor radical cation (T+) and to the acceptor radical anion (TNF-). These spectra were recorded using the spectroelectochemical technique (Figure 6b). The spectrum of the triphenylene radical cation (T+) presents three main absorption bands at 23 400, 15 800, and 12 000 cm-1. A broad band peaking at 18 600 cm-1 characterizes the TNF- spectrum. The transient spectrum recorded for strongly doped mesophase (f ) 5 × 10-2) contain the spectral features of the two radical ions. The discrepancy observed at higher energies is explained by the fact that the transient spectrum is a differential one and, therefore, it contains the bleaching of the ground-state charge-transfer absorption band.22 Such an assignment is further supported by the great similarity between the transient spectrum in Figure 6b and those of the singlet ion-pair 1(T+, TNF-) obtained by

4. Kinetic Study After having elucidated the trapping mechanism, we will try to find out the characteristic times of energy migration and trapping. To this end, we focus our attention on the profiles of the transient absorption signals recorded, first, in the microsecond and, then, in the nanosecond time scale. Microsecond Time-Scale Behavior. The transient absorption decay kinetics observed for undoped samples and for samples containing TNF molar fractions lower than 5 × 10-2 are quite complex. However, a clearer picture appears when these decays are normalized at 10 µs (Figure 7). They are all composed of a rapid component whose intensity increases with increasing the TNF concentration and of a slower one which is identical for all the samples, both doped and undoped. The rapid component is, therefore, related to the trapping by TNF whereas the slower one corresponds to the triphenylene triplet excitons. To get more information about this process, we subtract the normalized curve corresponding to the undoped sample from the normalized curves of the doped ones. The remaining transient absorption signals decay all exponentially with the same rate constant of (5.5 ( 0.5) × 105 s-1. The same value is determined for degassed and non-degassed thin films both at 12 000 cm-1, where the radical cation T+ absorbs, and at 18 300 cm-1, corresponding to the absorption band of TNF-. Those findings show that no matter the TNF concentration the triplet ion-pair 3(T+, TNF-) decays with the same characteristic time, 1.8 µs. The recombination of the radical ions is

Triplet Excitation Transfer

J. Phys. Chem. B, Vol. 105, No. 7, 2001 1303 TABLE 1: Degassed Thin Films of I (10 µm): Variation of the Differential Optical Density (∆OD) at 560 nm Recorded at 10 µs as a Function of the TNF Molar Fraction TNF molar fraction f ) (TNF)/(T)

∆ODa (560 nm, 10 µs)

∆ODdoped/∆ODundoped (560 nm, 10 µs)

0 5 × 10-4 1 × 10-3 2.5 × 10-3 8 × 10-3 1 × 10-2 5 × 10-2

0.0116 0.0120 0.0090 0.0056 0.0036 0.0016 0

1.00 1.03 0.78 0.48 0.31 0.14 0

a

Figure 7. Transient absorption decays recorded at 560 nm for degassed thin films of I doped with various TNF molar fractions (0, 2.5 × 10-3, 8 × 10-3, 10-2, and 5 × 10-2) and normalized at 10 µs.

Estimated error: 30%.

The transient signals of the samples containing 8 × 10-3 and TNF molar fractions present a rise in the absorption (Figure 8b). The time needed for the signal to reach its maximum value is 80 ( 20 ns for f ) 10-2 and 105 ( 25 ns for f ) 8 × 10-3. We correlate this rise time to the formation of the ion-pairs 3(T+, TNF-) following migration of the triplet excitons. Although the triphenylene triplet states 3T absorb at 830 nm (Figures 4), for the examined TNF concentrations, the absorption of the radical cations predominates at early times (Figure 6). For f ) 5 × 10-2, only the slow decay is observed (Figure 8c). In this case, migration and trapping are probably too fast to be detected. 10-2

5. Determination of the Migration Length

Figure 8. Transient absorption signals recorded at 830 ( 10 nm for degassed thin films of I doped with TNF molar fractions (a) 0, (b) 10-2, and (c) 5 × 10-2.

practically completed at 6 µs. Therefore, the transient absorption signals recorded after that time correspond to triphenylene triplet excitons which are not trapped by TNF. Nanosecond Time-Scale Behavior. The transient absorption signals recorded at the blue side of the spectrum at times shorter than 250 ns were distorted by the intense and broad triphenylene fluorescence.7 Therefore, our study at the nanosecond time scale was carried out at 830 nm where 10 nm slits had to be used because of the weak signal. Signals recorded for undoped samples show, at early times, a rapid component decaying within the laser pulse duration, followed by a slower one (Figure 8a). The rapid component is probably due to the absorption of the singlet excited states whose lifetime is 14 ns.12 Upon increase of the TNF molar fraction, the relative intensity of the rapid component diminishes because singlet excitons are trapped by TNF;12 the resulting singlet ionpairs 1(T+, TNF-) disappear too rapidly23 to be detected with this experimental setup.

We have seen, on one hand, that the trapping of triplet excitons by TNF takes place in the nanosecond timescale and, on the other, that the spectra recorded for doped samples at times longer than 6 µs are very similar to those of undoped samples. Consequently, we conclude that there are two different populations of triplet excitons, one which is trapped by TNF and another which decays without being perturbed by the presence of TNF. The fraction of triplet excitons nontrapped by TNF can be evaluated from the ratio ∆ODdoped/∆ODundoped. ∆ODdoped and ∆ODundoped denote the differential optical density at 560 nm band at 10 µs recorded for doped and undoped samples, respectively (Table 1). This ratio diminishes by increasing the TNF concentration, and it becomes zero for f equal to 5 × 10-2. The fact that the population of long-lived excitons decreases upon increasing the TNF concentration proves that they are mainly mobile and not self-trapped. We explain the existence of two types of mobile excitons as follows. Columnar phases do not consist of infinite perfectly ordered one-dimensional stacks, but they are characterized by various types of structural defects.24 Moreover, as we mentioned above, intrinsic traps are also present in the mesophase. Therefore, we can schematically represent the columnar phase as an ensemble of well-ordered one-dimensional segments delimited by reflecting barriers. The triplet exciton whose mobility is due to orbital overlap performs, within the segment where it was created, a random walk from nearest neighbor to nearest neighbor. When it reaches the edge of the stack, it can hardly come out because of lack of orbital overlap. Thus, it will be reflected and will continue its random walk within the same segment. If the segment contains a TNF molecule, the exciton will be eventually trapped. If not, it will continue its random walk until it decays naturally; it can also be trapped by an intrinsic trap. According to the above reasoning, for a given TNF concentration, the fraction of excitons which are not trapped by TNF at 10 µs is equal to the probability to find an one-dimensional segment which does not contain TNF. Those probabilities,

1304 J. Phys. Chem. B, Vol. 105, No. 7, 2001

Markovitsi et al.

TABLE 2: Probabilities To Find a Columnar Segment without TNF for Various TNF Molar Fractionsa f ) (TNF)/(T)

N ) 50

N ) 100

N ) 200

N ) 300

N ) 400

0 5 × 10-4 1 × 10-3 2.5 × 10-3 8 × 10-3 1 × 10-2 5 × 10-2

1.00 0.98 0.95 0.88 0.67 0.60 0.08

1.00 0.95 0.90 0.78 0.45 0.37 0.01

1.00 0.90 0.81 0.61 0.20 0.13 0.00

1.00 0.86 0.74 0.47 0.09 0.05 0.00

1.00 0.82 0.67 0.37 0.04 0.02 0.00

a N is the number of triphenylene cores (T) per columnar segment The traps are assumed randomly distributed within the mesophase. The probability of having x TNF molecules in a columnar segment consisting of N aromatic cores is given by the binomial distribution B(x) ) N![x!(N - x)!]-1f x(1 - f )N-x. The probabilities in this table are calculated as B(0) ) (1 - f )N.

calculated for various TNF concentrations and various lengths of columnar segments, are shown in Table 2. A comparison between the values in Tables 1 and 2 shows that the fractions of the excitons which are not trapped by TNF, evaluated as ∆ODdoped/∆ODundoped, are close to the probabilities obtained for segments consisting of 200 aromatic cores. The estimated error is (100 cores. It is worth noticing that correlation lengths of the order of 100 aromatic cores have been determined by X-ray diffraction for the columnar phases formed by monomeric25 and dimeric26 triphenylene derivatives. 6. Determination of the Hopping Time In this section we fit the experimentally deduced curves for the time dependence of the concentration of the ion-pair 3(T+, TNF-), resulting from migration and trapping of the triplet excitons within the mesophase, with simulated ones using the hopping time as fitting parameter. Our simulations are based on a one-dimensional random walk model with hops only to the two nearest neighbors with equal probability; traps are randomly distributed and the trapping efficiency is equal to one. The rate of change of the 3(T+, TNF-) concentration has two contributions. The ion pair is formed by the migration and trapping process but is depleted at a rate k[3(T+, TNF-)]t with k ) 5.5 × 105 s-1. The net rate of change is therefore

d[3(T+, TNF-)]t/dt ) d(1 - Φt)/dt - k[3(T+, TNF-)]t (1) where Φt denotes the survival probability of the triplet excitons as a function of time, Φt ) [3T] t/[3T]0. The solution of the above first-order differential equation is

[3(T+, TNF-)]t ) Kt exp(-kt)

(2)

with Kt ) ∫[(dΦt/dt) exp(-kt)]dt and the condition Kt)0 ) 0. Φt is calculated by the Anlauf expression including the second-order term:27

Φn ) (8/π)(2/3π)1/2x3/2 exp(-3x/2)[1 + (17/18)(1/x) + (205/648)(1/x2)] (3) Here x ) [-π ln(1 - f)]2/3n1/3 and t ) nτh, where n denotes the number of steps and τh the hopping time. The above equation provides a good approximation of the exciton survival probability in the frame of the considered model and for the experimental conditions used.27 Although the assumption of trapping efficiency equal to one was experimentally confirmed for the trapping of singlet triphenylene excitons by TNF,7 it has not been possible to check it for triplet excitons.

Figure 9. Time dependence of the ion-pair 3(T+, TNF-) concentration within the mesophase of I containing TNF molar fractions (a) f ) 10-2 and (b) f ) 5 × 10-2. A comparison of the experimental curves (noisy lines) with the curves simulated for different hopping time values (smooth lines) is shown.

Therefore, the values deduced from the fit must be considered as an upper limit for the triplet hopping time. In this model we implicitly assume that the intrinsic trap molar fraction is negligible with regard to the TNF molar fraction, since we consider that the probability to form the ionpair 3(T+, TNF-) is equal to the probability to trap the triplet exciton. Figure 9 shows the [3(T+, TNF-)]t curves for 10-2 and 5 × 10-2 TNF molar fractions. They were calculated according to the eqs 2 and 3 for different hopping time values and convoluted with a Gaussian curve (10 ns fwhm) accounting for the laser pulse duration. We can see in Figure 9a that, when the TNF concentration is equal to 10-2, hopping time values equal to 0.1, 1, 2, 5, and 10 ps result to clearly distinguishable curves; a decrease in the hopping time leads to an increase in the rise time. When f ) 5 × 10-2, the curves calculated for hopping time values ranging from 0.1 to 10 ps appear quite similar at the examined time scale. In Figure 9 are also represented the experimentally determined profiles of [3(T+, TNF-)]t. We have seen in section 5 (Tables 1 and 2) that, for f ) 10-2, 14% of the columnar segments do not contain TNF. Consequently the transient absorption signal recorded at 830 nm has two contributions, one due to the triplet excitons weakly absorbing at this wavelength and the other to the ion-pairs 3(T+, TNF-). Therefore, the profile of [3(T+, TNF-)]t presented in Figure 9a was obtained from the transient signal recorded at 830 after subtraction of the contribution of the nontrapped excitons. For f ) 5 × 10-2, the experimental curve (Figure 9b) is directly obtained from the transient signals recorded at 830 nm (Figure 8c) because all the columnar segments contain TNF. The comparison of simulated curves with the experimental ones was limited to those obtained for 8 × 10-3, 10-2, and 5 × 10-2 TNF molar fractions for which the intrinsic molar fraction (ca. 2 × 10-3) can be neglected. The experimental curve obtained for TNF molar fraction equal to 10-2 (Figure 9a) is close to the simulated one obtained for a hopping time of 2 ps. The error in the determination of this value, estimated from a series of measurements, is (1 ps. For TNF molar fraction equal to 5 × 10-2, the comparison between the experimental curve and the simulated curves leads only to

Triplet Excitation Transfer

J. Phys. Chem. B, Vol. 105, No. 7, 2001 1305

an upper value for the hopping time (τh < 10 ps). This means that, for such a high trap molar fraction, the trapping process becomes very fast compared to the temporal resolution of our experiment and only the recombination of the formed ion pairs is observed.

calculated by quantum chemistry methods, are respectively 19 and 18 cm-1. Therefore, long-distance hops which take place with low probability for singlet transport can be neglected and eqs 4 and 5 yield

τhsinglet ) h/[4πTvib[(1/V1) 2 + (1/V2)2]]

(6)

7. Discussion on the Hopping Time The hopping time value of 2 ( 1 ps found for the triplet excitons in the studied mesophase is quite similar to that found for singlet excitons (1.2 ( 0.2 ps) in the same system.12 This contrasts with what is described for another widely studied model system, anthracene crystals,28-30 in which the singlet hopping time at room temperature is much shorter (58 fs)31 than the triplet hopping time (20 ps).32 Regarding the magnitude of triplet hopping time in other molecular systems, values ranging from hundreds of femtoseconds5 to microseconds33,34 are reported in the literature. To understand the origin of such discrepancies, we discuss below the way the hopping time is related to the electronic coupling V, which is the driving force for excitation transport. The probability density per unit time wi for the energy to hop from an excited molecule to a molecule i is given by the Fermi’s golden rule:

wi )

∂Pi 4π2 ) T V2 ∂t h vib i

(4)

Here Tvib is a vibronic term. For a system consisting of identical chromophores, from chemical and energetic point of view, Tvib has the same value for all hops. Under these conditions, the probability density per unit time w for the excitation to leave a given chromophore is independent of this chromophore. The hopping time, which is in fact an average residence time, is defined as the reciprocal of w:

th ) 1/w ) 1/Σwi

(5)

Equations 4 and 5 show that the hopping time is proportional to the sum of the couplings between the excited chromophore and any other chromophore in the system. Therefore, it depends both on the electronic structure of the chromophores and the molecular arrangement and may have quite different values for different systems. For systems for which the lowest triplet and singlet excited states have the same electronic configuration, the singlet hopping time is expected, in general, to be smaller than the triplet one. This happens because triplet energy transport is induced only by intermolecular orbital overlap interactions (Vioo) whereas for singlet transfer both Coulombic interactions (dipolar Vdip and multipolar Vmult) and intermolecular orbital overlap interactions are operative.35-39 Thus, the stronger the singlet-singlet dipolar transition, the larger the difference between the triplet and singlet hopping times. Since the So f S1 transition is allowed for anthracene40 and symmetry forbidden for tiphenylene,7,21 the triplet hopping time is expected to be closer to the singlet one in triphenylene columnar phases but quite longer for anthracene crystals. In the case of the examined mesophase, it is possible to estimate the triplet hopping time (τhtriplet) from the singlet hopping time (τhsingle) and the values of the various components of the electronic coupling. In our previous study,12 we showed that singlet excitation transport occurring in the lowest singlet excited state is dominated by interchromophore orbital overlap interactions acting only between nearest neighbors. The strength of those interactions was found equal to 135 cm-1 whereas dipolar and multipolar interactions between nearest neighbors,

The subscripts 1 and 2 denote the two nearest neighbors. Since these neighbors are identical, V1 ) V2 ) Vdip + Vmult + Vioo and eq 6 becomes

τhsinglet ) h/[2πTvib(Vdip + Vmult + Vioo) 2]

(7)

In the same way, we can write

τhtriplet ) h/[2πTvib(Vioo)2]

(8)

The intermolecular orbital overlap interactions are expected to be similar for the lowest singlet and the triplet excited state because (i) the S1 is mainly built on the HOMO f LUMO monoexcitation and (ii) the HOMO and LUMO are large in the same region.7,21 Consequently, the T1 should also build on the HOMO f LUMO monoexcitation. Moreover, the vibronic factors Tvib should also be similar for S1 and T1. Under these conditions eqs 7 and 8 give

τhtriplet ) τhsinglet(Vdip + Vmult + Vioo)2/(Vioo)2

(9)

Equation 9 yields a hopping time value of 1.9 ps for the triplet exciton in perfect agreement with the value of 2 ( 1 ps deduced from Figure 9. Finally, it is worth noticing that the hopping time value of triplet excitons determined for the ordered hexagonal mesophase of I is somewhat longer than that found for the same type of mesophase formed by a zinc phthalocyanine (0.4 ps).5 A faster transport process in the latter mesophase is explained by a better interchromophore orbital overlap due to the larger size of the aromatic cores and the existence of the axial d orbitals of the zinc atoms. 8. Summary and Comments The work reported in this communication regarding triplet excitation transport in the columnar liquid crystal formed by the tetrameric triphenylene derivative I is the counterpart of previous work describing singlet excitation transport in the same mesophase.12 Therefore, here we summarize and compare the findings of these two studies, combining experiments and numerical simulations. A global scheme depicting the various discussed processes is shown in Figure 10. The present investigation was carried out by transient absorption spectroscopy with nanosecond resolution whereas the previous one was based on fluorescence spectroscopy performed by means of the single photon counting technique with picosecond resolution. In both studies, which were carried out at room temperature, excitation transport was analyzed as a random walk process because of the weak electronic coupling involved. Both singlet and triplet incoherent excitons are trapped by TNF molecules inserted in the columnar stacks resulting in the formation of 1(T+, TNF-) and 3(T+, TNF-) ion pairs. They recombine with time constants of 60 ps and 2 µs, respectively, to yield the ground-state complex (T, TNF). The hopping time value found for the triplet excitons (2 ( 1 ps) is very close to that determined for singlet excitons (1.2 ( 0.2 ps). This is in agreement with the finding that the electronic

1306 J. Phys. Chem. B, Vol. 105, No. 7, 2001

Figure 10. Global scheme of the various processes related to the roomtemperature singlet (1T) and triplet (3T) excitation transport and trapping in the mesophase formed by the tetrameric triphenylene derivative I doped with TNF.

coupling responsible for singlet transport, related to a symmetryforbidden electronic transition, is dominated by interactions due to orbital overlap between neighboring chromophores in the stacks. Those interactions are the only operative in the case of triplet transport which is hindered by the existence of structural defects. The average length of well ordered columnar segments delimited by such defects was evaluated to 200 ( 100 aromatic cores, which is somewhat larger compared to the migration length of the singlet exciton (ca.100 aromatic cores) during its lifetime. Triplet excitations remain imprisoned within the columnar segment in which they are created whereas singlet excitations can escape due to the weak but nonnegligible longrange dipolar interactions. Acknowledgment. This work has been performed in the frame of a European COST D14 project entitled “Experimental and Modeling Aspects of Electron and Energy Transfer in Organized Molecular Materials”. The authors wish to thank Dr. P. Argyrakis, Dr. L. Gallos and Dr. Ph. Millie´ for helpful discussions. References and Notes (1) Markovitsi, D.; Rigaut, F.; Mouallem, M.; Maltheˆte, J. Chem. Phys. Lett. 1987, 135, 236. (2) Blanzat, B.; Bartou, C.; Tercier, N.; Andre´e, J. J.; Simon, J. J. Am. Chem. Soc. 1987, 109, 6193. (3) Blasse, G.; Dirksen, G. J.; Meijerink, A.; Van der Pol, J. F.; Neelman, E.; Drenth, W. Chem. Phys. Lett. 1989, 154, 420. (4) Gregg, B. A.; Fox, M. A.; Bard, A. J. J. Phys. Chem. 1989, 93, 4227.

Markovitsi et al. (5) Markovitsi, D.; Le´cuyer, I.; Simon J. J. Phys. Chem. 1991, 95, 3620. (6) Ecoffet, C.; Markovitsi, D.; Millie´, P.; Lemaistre, J. P. Chem. Phys. 1993, 177, 629. (7) Markovitsi, D., Germain, A.; Millie´, P.; Le´cuyer, P.; Gallos, L.; Argyrakis, P.; Bengs, H.; Ringsdorf, H. J. Phys. Chem. 1995, 99, 1005. (8) Lemaistre, J. P.; Ecoffet, C.; Markovitsi, D. J. Lumin. 1996, 66, 67, 327. (9) Sigal, H.; Markovitsi, D.; Gallos, L. K.; Argyrakis, P. J. Phys. Chem. 1996, 100, 10999. (10) Lemaiste, J. P. Chem. Phys. 1999, 246, 283. (11) Sigal, H. Ph.D. Thesis, Ecole Normale Supe´rieure de Cachan, Cachan, France, 1997. (12) Markovitsi, D.; Marguet, S.; Gallos, L. K.; Sigal, H.; Argyrakis, P.; Ringsdorf, H.; Kumar S. Chem. Phys. Lett. 1999, 306, 163. (13) Boden, N.; Bushby, R. J.; Clements, J. J. Chem. Phys. 1993, 98, 5920. (14) Adam, D.; Schuhmacher, P.; Simmerer, J.; Ha¨ussling, L.; Siemensmeyer, K.; Etzbach, K. H.; Ringsdorf, H.; Haarer, D. Nature 1994, 371, 141. (15) Warman, J.; Schouten, P. G, J. Phys. Chem. 1995, 99, 17181. (16) Christ, T.; Glu¨sen, B.; Greiner, A.; Kettner, A.; Stu¨mpflen, V.; Tsukruk, V.; Wendorff, J. AdV. Mater. 1997, 9, 48. (17) Bondkowski, J. Ph.D. Thesis, Universite´ de Paris Sud, Paris, France, 2000. (18) Marguet, S.; Markovitsi, D.; Bondkowski, J.; Kumar, S. Manuscript in preparation. (19) Kumar, S.; Schuhmacher, P.; Henderson, P.; Rego, J.; Ringsdorf, H. Mol. Cryst. Liq. Cryst. 1996, 288, 211. (20) Ringsdorf, H.; Wu¨stefeld, R.; Zerta, E.; Ebert, M.; Wendorfff, J. Angew. Chem., Int. Ed. Engl. 1989, 28, 914. Kranig, W.; Boeffel, C.; Spiess, H. W.; Karhaus, O.; Ringsdorf, H.; Wu¨stefeld, R. Liq. Cryst. 1990, 8, 375. (21) Marguet, S.; Markovitsi D.; Millie´, P. Sigal, H. Kumar, S. J. Phys. Chem. B 1999, 102, 4697. (22) Markovitsi, D.; Bengs, H.; Ringsdorf, H. J. Chem. Soc., Faraday Trans. 1992, 88, 1275. (23) Markovitsi, D.; Pfeffer, N.; Charra, F.; Nunzi, J. M.; Bengs, H.; Ringsdorf, H. J. Chem. Soc., Faraday Trans. 1993, 89, 37. (24) Chandrasekhar, S.; Ranganath, G. S. Rep. Prog. Phys. 1990, 53, 57. (25) Levelut, A. M. J. Phys. Lett. 1986, 124, 478. (26) Zamir, S.; Poupko, R.; Luz, Z.; Hu¨ser, B.; Boeffel, C.; Zimmermann, Z. H. J. Am. Chem. Soc. 1994, 116, 3148. (27) Anlauf, J. K. Phys. ReV. Lett. 1984, 52, 1845. (28) Silinsh, E. A. Organic Molecular Crystals; Springer-Verlag: Berlin, 1980. (29) Avakian, P.; Merrifield, R. E. Mol. Cryst. 1968, 5, 37. (30) Levine, M.; Jortner, J.; Szo¨ke, A. J. Chem. Phys. 1966, 45, 1591. (31) Braun, A.; Mayer, U.; Auweter, H.; Wolf, H. C.; Schmidt, D. Z. Naturforsch. A 1982, 37A, 1013. (32) Von Burg, K.; Altwegg, L.; Zschokke-Gra¨nacher, I. Phys. ReV. B 1980, 22, 2037. (33) Mo¨hwald, H.; Sackmann, E. Solid State Commun. 1974, 15, 445. (34) Blagoy, Y. P.; Levitsky, I. A.; Rubin, Y. V. J. Mol. Struct. 1993, 294, 123. (35) Dexter, D. L. J. Chem. Phys. 1953, 21, 836. (36) Forster, T. Discuss. Faraday Soc. 1959, 27, 7. (37) Robinson, G. W.; Frosch, R. P. J. Chem. Phys. 1963, 38, 1187. (38) Scholes, D. G.; Ghiggino, K. P. J. Phys. Chem. 1994, 98, 4580. (39) Scholes, D. G.; Harcourt, R. D.; Ghiggino, K. P. J. Chem. Phys. 1995, 102, 9574. (40) Berman, I. B. Handbook of Fluorescence Spectra of Aromatic Molecules; Academic Press: New York, 1965.