18436
J. Phys. Chem. 1996, 100, 18436-18444
Scavenging Dynamics of Photogenerated Holes in Poly(N-vinylcarbazole) Films Kazuya Watanabe, Tsuyoshi Asahi, and Hiroshi Masuhara* Department of Applied Physics, Osaka UniVersity, Suita, Osaka 565, Japan ReceiVed: March 25, 1996; In Final Form: August 30, 1996X
Diffusion-controlled scavenging of mobile holes under no applied electric field was observed directly in poly(N-vinylcarbazole) films, doped with 1,2,4,5-tetracyanobenzene (TCNB) as an electron acceptor and N,N,N′,N′-tetramethyl-p-phenylenediamine (TMPD) as a hole scavenger, by transient absorption spectroscopy. The scavenging of holes occurs mainly over several nanoseconds, and is complete within 1 µs. The mean diffusion length of the migrating holes was estimated to be ∼15 Å. A Monte Carlo simulation of 3-D diffusion in energetically disordered media was applied for analyzing the hole-scavenging behavior. The spatially restricted character of the hole migration was revealed by the simulation. A very slow (up to several tens of milliseconds) recombination of TMPD cations with TCNB anions was also observed, which was explained in terms of a long-range electron tunneling.
1. Introduction Conduction in amorphous organic films is often found to be a “dispersive” charge transport that originates from their inherent structural disorder. The disorder leads to distributions in the electronic interactions between hopping sites and to long-range electrostatic interactions between a charged site and surrounding molecules. Indeed, hole transport in molecularly doped polymers, such as tritolylamine in polycarbonate, has been extensively investigated, and a hopping transport model with both off-diagonal disorder and diagonal disorder has been confirmed to be an appropriate one.1 Here, the off-diagonal disorder means the fluctuations in the intermolecular distance and the mutual orientation of molecules at discrete sites, and the diagonal disorder means those at the molecular energy level. Since the “hopping” transport corresponds to a sequence of electron transfer (ET) steps among localized sites and since the rate of each ET process changes from one to another depending upon the above distributions, studies on the electronic state of each charge carrier site are quite important. For the investigation of the molecular nature and the electronic structure of charge carriers and the elementary intermolecular ET process,1 transient photocurrent measurements, which monitor macroscopic charge transport, are inadequate, although most of conducting materials have been studied by them. A photoluminescence measurement can provide us information on a charge recombination (CR) process, but it does not reflect the electronic states of the migrating carriers. This technique is of course inapplicable for observing nonemissive species. On the other hand, transient absorption spectroscopy is a powerful method for studying such nonemissive transient states such as ionic species. It can be used to investigate the electronic state as well as the dynamics of charged species. One more advantage of the transient absorption spectroscopy is its high potential to reveal formation and decay processes of ionic species under no applied electric field. Such studies revealing microscopic aspects of photoconduction have been provided for poly(N-vinylcarbazole) (PVCz), a representative organic photoconductive polymer. Indeed, a number of studies on its photophysical properties have been reported: photoconductivity,2 steady state and transient luminescence,3,4 single chain transient absorption in solution,5,6 and transient absorption in film states.7-9 PVCz film is known as X
Abstract published in AdVance ACS Abstracts, November 1, 1996.
S0022-3654(96)00894-5 CCC: $12.00
a hole conductor, and carbazole radical cation acts as the hole. One of the features that makes the photophysics of this material difficult to understand is the intermolecular interactions between carbazole chromophores, which cause significant changes in its excited and cationic states. These intermolecular interactions are considered to control the charge transport in the film. For some carbazole dimer compounds in solution, it has been confirmed that the absorption spectra of the dimer cation states depend on their mutual configuration.10,11 Cationic states of carbazole oligomer show overlapping of the various dimer and monomer cation bands, or of the more delocalized trimers or tetramers.6 The absorption spectra of PVCz cation in a single chain polymer in solution correspond to that of the oligomer.6 For a solid, the absorption spectra of PVCz cation resemble those of a single polymer chain in solution, which suggests that even in a solid a charge is not delocalized over more than several chromophores.7-9 However some delocalization certainly occurs as have been revealed by a measurement of a charge resonance band of PVCz cation in the near-IR region.12,13 The exact degree of delocalization is still unknown. In our previous transient absorption spectroscopic studies, we have studied PVCz film doped with 1,2,4,5-tetracyanobenzene (TCNB), which forms a charge transfer (CT) complex with PVCz in the ground state and acts as an electron acceptor. We have succeeded in observing the absorption spectra of photogenerated ionic species in the films as well as the CR behavior from 1 µs to 10 ms after photoinduced electron transfer.9 A characteristic absorption intensity of ionic species was found to be proportional to t-1/2. We concluded that the mechanism of the CR is a hole-diffusion-controlled geminate recombination, namely, a CR between the fixed anion of the doped electron acceptor and a hole hopping among neighboring carbazole chromophores. However, the clues that we have obtained in our previous studies are still insufficient for a more precise description of the hole-hopping behavior, i.e., a description that includes the dimension, the mean travel path of the holes, etc. In the present work, we have added N,N,N′,N′-tetramethylp-phenylenediamine (TMPD), which works as a hole scavenger to PVCz doped with TCNB. Observation of the hole-scavenging process allows us to investigate the hole diffusion process in more detail. By picosecond transient absorption spectroscopy, it is observed that the hole-scavenging process completes in several hundreds of nanoseconds, which is very fast compared with the whole time regime of the CR behavior.9 This result © 1996 American Chemical Society
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indicates an anomalous hole diffusion, which may be a spatially restricted one. To understand our spectroscopic observation of the hole diffusion without an external electric field, we have analyzed the dynamics of photogenerated holes by means of a Monte Carlo approach, which was successfully applied to support the disorder model of charge-transporting molecularly dispersed polymers.14-16 We simulated the CR and the hole-scavenging processes with a random walk model in a 3-D regular lattice with an energy disorder. A slow CR of hole scavenger (TMPD) radical cations generated by the hole scavenging and acceptor anions, which was observed from a few tens of nanoseconds to 30 ms, was also discussed. 2. Experimental Section Transient Absorption Spectroscopy System. To measure transient absorption spectra from microseconds to milliseconds, the second harmonic (532 nm) of a Nd3+:YAG laser pulse (JK Laser HY 750, fwhm 8 ns) was used for excitation, and a pulsed Xe lamp (Hamamatsu L2187, fwhm 1 µs) was used for the probe light. The delay time between the probe and the pump pulses was stepped by a delay circuit, and the probe-light spectra were monitored by a multichannel photodiode array (Otsuka Electronics IMUC-7000). In the submicrosecond regime,8 the same exciting light source was employed and a 150 W dc Xe lamp (Wacom KXL-150F), which was additionally pulsed for ca. 200 µs in fwhm by a homemade circuit, was used. The probe light was detected by a streak camera (Hamamatsu C2830) equipped with a slow streak unit (Hamamatsu M2548) and a CCD camera (Hamamatsu C3141). A picosecond laser photolysis system17 was employed in the subnanosecond-nanosecond time regime. The second harmonic (532 nm) of a mode-locked Nd3+:YAG laser (Quantel International YG501C, 1064 nm, 30 ps) was used for excitation. A picosecond continuum generated by focusing the fundamental pulse (1064 nm) into a quartz cell containing a D2O and H2O mixture was used as the probe light, which was detected by a multichannel photodiode array (Otsuka Electronics MCPD 110A). The excitation laser wavelength (532 nm) corresponds to a charge transfer (CT) band of the TCNB-PVCz complex, and it has been confirmed that an ion pair is directly generated by the excitation.9 The excitation power of each system was several mJ/cm2, under which condition the concentration of the ionic species was less than 1 × 10-3 M at 2 µs. The concentration is low enough only to give the geminate recombination of ions.9 All measurements were performed at room temperature. Materials. PVCz (Takasago International Corp.) was reprecipitated three times from a benzene-methanol solution. TCNB (Wako, Special Grade) was recrystallized from ethanol. TMPD was obtained from TMPD dihydrochloride (Wako, Special Grade) by reduction and purified by sublimation. Sample films were cast from a 1,2-dichloroethane solution of those compounds, and the film thickness was 50-100 µm. TCNB was doped at 2 mol % of the carbazole chromophore group. The concentration of TMPD was varied from 0.04 to 0.4 mol % compared to the carbazole chromophore. Within this concentration range, no significant change in the CT absorption band between TCNB and PVCz was observed in the film doped by TMPD. 3. Results A. Steady State Fluorescence Spectra. Steady state fluorescence spectra of PVCz doped with 2 mol % TCNB and TMPD at various concentrations are shown in Figure 1. By
Figure 1. Steady state fluorescence spectra of PVCz films doped with 2 mol % TCNB and various concentrations of TMPD: (a) no TMPD; (b) 0.1 mol % TMPD; (c) 0.2 mol % TMPD. The excitation wavelength was 532 nm.
exciting the CT absorption band at 532 nm, a broad CT fluorescence spectrum from excited CT states of the PVCzTCNB complex was observed as previously reported.4 Since sample thickness varies in each film, the fluorescence intensity was divided by the corresponding absorbance at 532 nm, which would be proportional to the film thickness, to compare each fluorescence intensity. For all samples examined here, absorbance at 532 nm was in the range 0.1-0.3, so this treatment may be appropriate. When TMPD was doped, the CT fluorescence was strongly quenched, which is eventually ascribed to the hole-scavenging effect by TMPD; the hole-scavenging process by TMPD interrupts the CR between the hole and TCNB anion and reduces the fluorescence intensity. This doping also results in slight blue shifts of the CT fluorescence spectra. The CT fluorescence is contributed by CT complexes with various mutual configurations between donor and acceptor. The spectral shift observed in the quenching experiment indicates that holes, which would result in an energetically lower CT complex, are scavenged relatively efficiently. CT complexes with a delocalized (dimer or trimer) PVCz cation may have a lower energy than that with a carbazole monomer cation, and therefore, it can be said that a CT complex with a delocalized cation brings about a migrating hole, which is scavenged by TMPD, preferentially. B. Transient Absorption Spectra (10-11 to 10-7 s). The hole scavenging was observed directly by transient absorption spectroscopy. Figure 2 shows the picosecond absorption spectra of PVCz film doped with 2 mol % TCNB and 0.2 mol % TMPD. For a comparison, transient spectra of PVCz film doped with 2 mol % TCNB and without TMPD are also given. Immediately after excitation in the CT band, the TCNB anion (465 nm) and the hole (carbazole cation) (700-850 nm) are directly generated in both films.18 In the film with TMPD, an absorption band around 550-650 nm ascribed to the TMPD cation19,20 arises after several tens of picoseconds. The contribution of the hole slightly decreased compared to the sample without TMPD. Thus, the spectral change can be interpreted as a hole-scavenging process by TMPD. It has been found that after a photoinduced CT, the hole hops to the neighboring carbazole chromophores away from the TCNB anion in ca. 2 ns.18 Thus, the generation of the TMPD cation can be considered as due to a scavenging of mobile holes by TMPD. TMPD has a low ionization potential (5.70 eV in glassy n-hexane at 77 K),21 while the ionization potential of PVCz in the solid is ∼6.1 eV.22 Therefore, it is conceivable that the
18438 J. Phys. Chem., Vol. 100, No. 47, 1996
Figure 2. Transient absorption spectra of PVCz film doped with 2 mol % TCNB in picosecond-nanosecond time regime: no TMPD (dots); 0.2 mol % TMPD (solid lines). The delay times are indicated in the figure. Both spectra are normalized at 465 nm.
Watanabe et al.
Figure 4. (a) Decay curves of the hole (750 nm) in PVCz film doped with 2 mol % TCNB in several nanoseconds time regime: no TMPD (cross); 0.4 mol % TMPD (triangles). The decay curves are normalized around the peaks. The solid curves are a guide for the eyes. (b) Formation kinetics of the TMPD cation (590-640 nm) in PVCz films doped with 2 mol % TCNB and various concentrations of TMPD in several nanoseconds time regime. The concentration of TMPD is 0.4 mol % (triangles), 0.2 mol % (asterisks), and 0.1 mol % (filled circles). The vertical axis is proportional to the hole-scavenging yields. The solid curves are a guide for the eyes.
Figure 3. Transient absorption spectra of PVCz films doped with 2 mol % TCNB and various concentrations of TMPD at 2 µs after excitation. The spectra are normalized at 465 nm. Each spectrum is composed of the TCNB anion (465 nm), TMPD cation (550-650 nm), and the hole (PVCz cation) (700-800 nm). The concentrations of TMPD are indicated in the figure.
hole transfer from PVCz to TMPD occurs by the encounter of the PVCz cation and TMPD. We also examined a PVCz film doped with only TMPD (no TCNB) under the same conditions and observed no significant absorption in the 550-650 nm region. The triplet state of TMPD has a large extinction coefficient in this wavelength region. Hence, a two-photon excitation of TMPD or an energy transfer from biphotonically excited carbazole leading to the TMPD triplet state is negligible. Also, in transient absorption spectra with different TMPD concentrations, the hole scavenging by TMPD is clearly shown. Figure 3 shows the transient absorption spectra of PVCz films doped with 2 mol % TCNB and at various concentrations of TMPD at 2 µs after excitation. The spectra were normalized at 465 nm, and this figure demonstrates that hole-scavenging yields strongly depend on the concentration of TMPD. Figure 4a shows decay curves of the hole (at 750 nm) without TMPD and with 0.4 mol % TMPD. We recognize that the decay of the hole with TMPD becomes faster at the initial stage owing to the scavenging of mobile holes. Formation curves of the TMPD radical cation under three different concentrations
Figure 5. Same decay (a) and formation (b) curves as in parts a and b of Figure 4 immediately after excitation.
of TMPD are depicted in Figure 4b. Since in the wavelength region the absorption band of the hole is included in the spectra, these curves are obtained by averaging the absorbance in the 590-640 nm wavelength region after subtracting the contribution of the hole by the following procedures. It was assumed that the absorbance of the TMPD cation around the peak of the hole absorption band (longer wavelength than 730 nm) is negligible and that the spectral shape of the hole is independent of TMPD doping. The obtained formation curves were very similar to each other after normalization for the films with TMPD concentrations of 0.4 and 0.2 mol % (Figure 4b). Parts a and b of Figure 5 show the same transient curves of the hole and TMPD cation, respectively, immediately after excitation. In Figures 4 and 5, the formation curves of the TMPD cation have a fast (a few hundreds of picoseconds) and a slow (several nanoseconds) time constant, and the change in the hole decay kinetics induced by TMPD doping is consistent with it. The formation of the TMPD cation in Figure 5b is surely slower than the response of the detection system so that the generation of the TMPD cation is not due to a direct excitation of the TCNB-TMPD CT complex.
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Figure 6. Formation kinetics of the TMPD cation (590-640 nm) in PVCz films doped with 2 mol % TCNB and various concentrations of TMPD in the submicrosecond time regime. The concentrations of TMPD are indicated in the figure.
Figure 7. Transient absorption spectra of PVCz film doped with 2 mol % TCNB in microsecond-millisecond time regime: no TMPD (dots); 0.1 mol % TMPD (solid lines). The delay times are indicated in the figure.
TABLE 1: Hole Scavenging Yield at 15 ns TMPD concentration (mol %) [TMPD+] (15 ns)/[PVCz+] (0 ns) (%)
0.4 19
0.2 8
0.1 5
From the absorbance at various TMPD concentrations, we estimated the hole-scavenging yield. We assumed that the molar extinction coefficient of the TCNB anion9 at 465 nm and TMPD cation20 at 620 nm were 10 000 M-1 cm-1. Since the ratio of of the TCNB anion (at 465 nm) and the hole (at 750 nm) is 2:1 (see Figure 7, dotted lines), of the hole at 750 nm is considered to be 5000 M-1 cm-1. By use of these values, the TMPD cation relative to the initial concentration of the hole at 15 ns is given in Table 1. The scavenging yields change almost linearly with the TMPD concentration. Figure 6 shows the kinetics of the TMPD cation in the submicrosecond regime obtained in a similar manner. At 0.04 mol % TMPD, the scavenging lasts for several hundreds of nanoseconds, but further formation of the TMPD cation was not observed despite the existence of many holes. The features of the hole-scavenging process can be summarized as follows. (a) The scavenging yield strongly depends on the TMPD concentration. (b) The formation kinetics of the TMPD cation (Figure 3b) cannot be fitted with a singleexponential function, which suggests that the scavenging is not described as a pseudo-first-order reaction in a homogeneous system. (c) The scavenging is complete within 1 µs, which is
Figure 8. Decay curves of ionic species in PVCz film doped with 2 mol % TCNB and 0.1 mol % TMPD. Observation wavelengths were 455-475 nm (TCNB anion), 550-630 nm (TMPD cation), and 730800 nm (the hole). The solid line is a smoothed decay kinetics of the TMPD cation. The decay curve of the TCNB anion have two components: one is a fast decay component to 30 µs, which corresponds to the hole decay, and the other one is a slow decay, which is in accordance with TMPD cation.
fast compared to the whole CR process of the TCNB anion and a hole (to several millisecond).9 C. Transient Absorption Spectra (10-6 to 10-3 s). Figure 7 shows the transient absorption spectral change of the TCNBPVCz film doped with 0.1 mol % TMPD. The hole decays faster than other species and could not be observed at several hundreds of microseconds after excitation, while the TCNB anion and TMPD cation live up to a few tens of milliseconds. The absorption decay curves of each species are shown in Figure 8. Around the peak of the TCNB anion (465 nm), absorption of the TMPD cation is considered to overlap with that from the TCNB anion. From the absorption spectrum of the TMPD cation in acetonitrile,20 of the TMPD cation band at 465 nm is about 20% of that at 620 nm. We subtracted this component in Figure 8. For the TMPD cation, the absorption band of the hole should be eliminated, and this has been done by the procedure described above. The decay behavior of the hole obeys approximately the t-1/2 law, which is close to the behavior reported in the same film without TMPD dopant.9 This indicates that the hole is not scavenged in this time regime. The faster disappearance of the hole compared with other species indicates that hole detrapping from TMPD to PVCz chromophores is negligible. The decay kinetics of the TCNB anion and TMPD cation in TMPD-doped films are slower than that of the hole and TCNB anion in the film without TMPD.9 Such a dramatic change of the decay kinetics of ionic species is very unusual, and this slow decay dynamics indicates a long-range CR in the TMPD-doped polymer. 4. Discussion A. Monte Carlo Simulation of Hole Scavenging. It is considered that the observed hole diffusion and scavenging dynamics are due to a random walk of charged species. As mentioned in the Introduction, a hole transport in molecularly dispersed polymers has been well characterized as a hole hopping under the diagonal and the off-diagonal disorder.1 In those studies, the diagonal (energy) disorder was assumed to have a Gaussian distribution. The photocurrent in the PVCz film was described by a multiple trapping formalism,23 although the band model does not seem to hold. Here, we have applied the hopping transport description that is similar to that used for the molecularly dispersed polymers. According to Ba¨ssler et
18440 J. Phys. Chem., Vol. 100, No. 47, 1996
Watanabe et al.
al.,14,16,24 we take into account the diagonal (energy) disorder, which has a Gaussian distribution. Different from the molecularly dispersed conducting polymers, the distribution of the mutual distance of neighboring chromophores is not so severe in PVCz film. Therefore, for simplicity, we neglect the offdiagonal disorder in this study. We examined a 3-D diffusionlimited scavenging on a regular lattice. The Monte Carlo simulation is known to be a powerful method for investigating hopping transport in a disordered system, and we employed this simulation. The current simulations were performed on a cubic lattice consisting of 30 × 30 × 30 sites with a lattice constant of 6 Å. The anion was placed at the center position (15, 15, 15), and a hole started a random walk from the nearest neighbor site of the anion. Scavengers, which correspond to TMPD in our experiment, were distributed randomly at a certain concentration and were assumed to be fixed. The hole hopping, namely ET, occurs from a site to one of the nearest sites. The ET rate (k) was determined by
k ) k0 exp (-G+/(kBT))
(1)
where G+ is the activation energy for the ET and k0 is the rate constant for hole hopping between the nearest neighbor sites when G+ equals zero. According to the Marcus theory,25 G+ is given by
G+ ) (G0 + λ)2/(4λ)
(2)
where G0 is the difference in Gibbs energy between the reactant and the product and λ is the reorganization energy. As the first model, we examined the case in which only a Coulombic field was considered (without energy disorder). The Coulombic energy at each site ri with respect to the anion placed at re ) (15, 15, 15) is
U(ri) ) -e2/(4π0|ri - re|)
(3)
and G0 for the hole hopping is given by the difference of the values of U(ri) at each site. 0 is the permittivity of the vacuum, and is the relative permittivity. was set to be the value of PVCz ( ) 3.38) in the bulk.2e λ was assumed to be 0.10 eV (see below) and to be the same at every site. Every holehopping process was conducted in the following manner. First, the direction of hopping was chosen randomly among the neighboring sites contained in the 3 × 3 × 3 cube, 26 sites, around the hole site. For simplicity, we neglected the possibility of ET directly to the outside of the neighboring 3 × 3 × 3 cube. Second, the hole transfer probability was calculated with eq 1 for the hopping in the chosen direction. For the hopping to diagonal positions, the rate was estimated by multiplying a distance dependence factor, exp(-|ra - rb|/a)/(exp[(-6 Å)/a]), to the k obtained from eq 1, where a is a constant that was assumed to be 1 Å and ra and rb are the initial and the final position of the hole with the hopping, respectively. Third, a random value was obtained between 0 and 1, and if it was below the hopping probability, the hopping occurred, and if not, the hole stayed on the same site. It was also assumed that a hole scavenging occurred immediately if a hole was on a scavenger site. In the vicinity of the anion only, a CR was set to occur at a rate of 3 × 108 s-1, which is close to the CR rate of a CT complex between N-ethylcarbazole and TCNB in toluene solution, 2.8 ×108 s-1.18 The calculation step was 0.05 ps, and the calculations were performed up to 15 ns unless a hole was scavenged or recombined. Temporal changes of the number of survival holes were recorded as well as the distributions of the distance between a hole and an anion. The position of the
Figure 9. (a) Monte Carlo simulation result of decay curve of the hole and (b) temporal change of the ionic distance under no scavenger condition. The parameters are k0 ) 1012 s-1 and λ ) 0.10 eV.
scavengers was reset for each anion-hole pair, and the results were accumulated 2000 times per every set of parameters. In Figure 9a, a simulated decay curve of holes considering only a Coulombic field is plotted. Distribution of the distances between anion and holes is plotted in Figure 9b. In this case, the simulation cannot reproduce the experimental result of the decay kinetics of the PVCz cation. Holes cannot escape from the position next to the anion, and the decay curve was determined only by the rate of CR between the adjacent anion and hole and became a single-exponential curve, even in the case with a k0 value of 1012 s-1, which is a considerably large value for this type of ET process. It is obvious that the decay kinetics is not affected by the existence of the hole scavenger with this model. As the second model, we examined an effect of the disorder in the energy of each site. Ba¨ssler et al. assumed a Gaussian function as the density of states for charge carriers in PVCz film and estimated that its width was σc = 0.1 eV from spectroscopic results.24,26 The origin of this fluctuation was considered to be a difference of the van der Waals interaction energy, of the ion-induced dipole interaction, or of the ionpermanent dipole interaction depending on each site. We introduced the effect simply as follows. The energy fluctuation of each site Ei was chosen randomly between -5σc and 5σc with the probability proportional to a Gaussian function (eq 4).
D(Ei) ) exp(-Ei2/2σc2)
(4)
Then G0 of the hopping from site j to site i was given by
G0 ) U(ri) + Ei - U(rj) - Ej
(5)
The hole-hopping rate was determined by substituting (5) into (2) and then into (1). The energy fluctuation was set at the beginning of each random walk and kept fixed during a survival of a hole. The value of λ was set to be less than 0.20 eV and to be the same at every site in our simulation. Ba¨ssler et al. also estimated a stabilization energy of a carrier generated at a defect in the PVCz film to be 0.10 eV from a fluorescence Stokes shift measurement.26 They deemed the defect as a dimer cation site
Poly(N-vinylcarbazole) Films where carbazole chromophores overlap and considered that the stabilization energy at most of other sites would be smaller than that value. The stabilization energy of 0.10 eV would provide 0.20 eV as the reorganization energy. This is derived as follows. In the small polaron-hopping model, the polaron binding energy corresponds to twice of the activation energy of a hopping between two energetically equivalent sites,27 while in the Marcus theory, the activation energy of the ET between energetically equivalent sites (G0 ) 0) is given by λ/4. This leads to the fact that the polaron binding energy is twice the reorganization energy. Thus, we used the value of λ less than 0.20 eV. Using the value of k0 less than 1012 s-1, we varied σc, λ, and k0 in order to fit the experimental hole decays. The best fit simulation result under no scavenger concentration is plotted in Figure 10a with a solid line, together with the experimental result (triangles). The parameters used are σc ) 0.3 eV, λ ) 0.05 eV, k0 ) 3 × 1011 s-1, and the simulation decay curve reproduces the experimental result well. The σc value was larger than that estimated by Ba¨ssler et al. With σc less than 0.3 eV, the number of the holes that escapes the Coulomb attraction was insufficient, and the simulated hole decay became faster than the experimental results. It is worth noting that owing to the energy disorder, the holes can escape the Coulomb attraction of the counteranion, namely, the energy disorder is an essential and sufficient condition for the charge separation process. Figure 10b shows the simulation curves of holes with various scavenger concentrations, together with the experimental results obtained under no TMPD and 0.4 mol % TMPD conditions. The scavenging yield at 15 ns was ca. 18% in the simulation with 1.8% scavenger, which was close to the experimental value obtained with the film doped with 0.4 mol % TMPD. The simulated decays reproduce the change of the decay kinetics of the hole induced by the scavenging process observed in the experimental results. However, the scavenger concentrations in our simulation are 4-5 times larger than the experimental concentrations. This means that the actual scavenging yields are higher than that expected by the simulation. Although a larger k0 value would bring a larger scavenging yield, the employed k0 value in our simulation was almost the largest one, which would be expected in this type of ET reaction. Varying the parameters in the range 0.3 eV < σc < 0.5 eV, 0.05 eV < λ < 0.15 eV, and 1011 s-1 < k0 < 1012 s-1, we found several parameters that fit the experimental hole decay curve, and the parameter values σc ) 0.3 eV, λ ) 0.05 eV, and k0 ) 3 × 1011 s-1 give the highest scavenging yields among them. Parts c and d of Figure 10 show formation curves (normalized at 15 ns) of scavenged holes simulated with the same parameters as in Figure 10b, together with the experimental formation curves of the TMPD cation of 0.4 mol % TMPD concentration. The experimental curve was normalized to fit the simulation results. The simulation results of the formation kinetics reproduce the experimental results well. The reason for the discrepancy of the scavenging yield between the simulation and the experiment may be attributed to the fact that the energy fluctuation at each site is very severe and holes get immobile too rapidly in our simulation. An introduction of a spatial correlation of the energy disorder might improve the model. Of course, an inclusion of an effect of hole delocalization over a few chromophores will also increase the scavenging yield. Also, about 3 times the value of σc that is expected from the spectroscopic study26 was necessary to fit the experimental results. This may be attributed to the neglect of orientational disorder of carbazole chromophores in our model. Slowik et al. calculated the effect of the mutual configuration of two carbazole chromophores on the ET integral
J. Phys. Chem., Vol. 100, No. 47, 1996 18441
Figure 10. Monte Carlo simulation results obtained with a Gaussian distribution of energy. The parameters are k0 ) 3 × 1011 s-1, σc ) 0.3 eV, and λ ) 0.05 eV. Part a shows the simulation results without the hole scavenger. The solid curve is a decay of the hole, and the broken curve is that of the remaining hole in the initial position. The initial part to 50 ps of the broken line was omitted, and the curve was normalized to the solid curve. The triangles are the experimental decay kinetics of the hole in the film without TMPD. Part b shows the hole decay curves at scavenger concentrations of 1.8%, 0.85%, 0.54%, and 0% (lower to upper solid curves). The triangles and filled circles are the experimental decay kinetics of the PVCz cation without TMPD and with 0.4 mol % TMPD, respectively. Parts c and d show the formation kinetics of scavenged holes at various concentrations of scavenger in the nanosecond time regime (c) and subnanosecond time regime (d). The scavenger concentrations are 1.8% (solid line), 0.85% (broken line), and 0.54% (dots). Open squares indicate the experimental kinetics of the TMPD cation at 0.4 mol % TMPD concentration.
and concluded that the transfer integral changes 2 or 3 orders of magnitude, depending on the relative angle of the molecular plane.28 Thus, orientational disorder results in a larger distribution of each ET rate. In our simulation, a larger σc value might be necessary in order to reflect the distribution caused by the disorder. Shown in Figure 10a is a decay curve (broken line) of holes that remain at the nearest neighbor site of the anion without a recombination or a hopping away. Though this decay curve has a fast component within 50 ps, we omitted the component
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Watanabe et al. simulation, the scavenged holes distribution would be more spread than what is expected in a 3-D homogeneous medium (eq 6). This accordance between the scavenged hole distribution and eq 6 indicates that the dimension of the hole diffusion in our simulation is close to 3-D. From the absorption spectra at 2 µs (Figure 3), we can estimate the total yield of the hole scavenging. In the case of 0.1 mol % TMPD concentration, from a decay curve of the hole over the subnanosecond and microsecond regions, the initial concentration of the hole is estimated to be 8 times larger than that in Figure 3. Assuming that the decay of TMPD cation to 2 µs is negligible, the total yield is estimated to be about 7% with 0.1 mol % TMPD concentration. The mean diffusion length of the hole was estimated as follows. The probability for the migrating hole not to be scavenged during n steps is given as
(1 - 0.001)N(n) Figure 11. (a) Monte Carlo simulation results on time evolution of the interionic distance under no scavenger condition. The delay times are indicated in the figure. The parameters are the same as those of Figure 10a. (b) Monte Carlo simulation result of the distribution of scavenged holes at 15 ns with 1.8% scavenger concentration (thin solid line). The parameters are the same as those of Figure 10b. Also, the distribution function of eq 6 at 1.8% scavenger concentration is plotted with a bold curve.
in the figure and multiplied it by 6 in order to normalize the curve to the hole decay curve. Miyasaka et al. examined picosecond transient absorption and dichroism decays of a PVCz film doped with 3 mol % TCNB and found that the dichroism of the PVCz cation decays with a time constant of about 1 ns.18 They ascribed the decay to the hole migration from the vicinity of the counteranion to neighboring sites. The broken line curve in Figure 10a may be related to the dichroism decay, while our simulated result has a fast component (up to 50 ps, which is not shown in the figure) that is absent in the experimental result. Because the pump and probe pulse widths were about 16 ps in their experiment, this fast component may be hidden by the time resolution in the dichroism measurement. Without this fast component, our simulated result (broken line in Figure 10a) shows behavior similar to that indicated by the decay curve of dichroism in ref 18. Figure 11a shows a temporal evolution of the interionic distances up to 15 ns without a hole scavenger. It is clearly shown that holes do not migrate very far from their initial positions, and this is responsible for the slowly rising components apparent in the hole-scavenging kinetics (parts c and d of Figure 10). Figure 11b shows a simulation result of a distribution of scavenged holes at 15 ns with 1.8% scavenger concentration. It is obvious that the hole scavenging occurs mainly within several sites, and this agrees with the restricted migration of the holes indicated by Figure 11a. The bold curve in Figure 11b is a calculation of the distribution of nearest neighbor scavengers P(R) by eq 6 at 1.8% scavenger concentration.29
P(R) ) 4πR2c exp(-(4/3)πR3c)
(6)
where R is the distance and c is a multiplex of a concentration of the scavenger and Avogadro’s number. This curve is multiplied by a certain factor in order to compare with the simulation. The bold curve approximately corresponds to the distribution of scavenged holes. If the dimension of the hole diffusion is heavily restricted by the energy disorder in our
(7)
in the case of 0.1mol % TMPD concentration, where N(n) is the number of distinct sites visited during n steps. Then, N(n) should satisfy the next equation,
(1 - (1 - 0.001)N(n)) ) 0.07
(8)
This gives the N(n) value as ca. 70. Thus, the holes mainly migrate in a volume in which 70 sites are contained, and we can estimate the mean diffusion length from the scale of this volume. There is a possibility that the disorder modifies the dimension of the hole migration, and if so, it is not easy to calculate the mean diffusion length, since the site density depends on the actual shape of the system.30 As suggested by the agreement of eq 6 and the simulation result of the scavenged hole distribution, the hole scavenging in our simulation model may be close to that in a 3-D homogeneous medium. The higher scavenging yield obtained in the experiment compared with the simulation indicates that the actual hole diffusion in the film is not so spatially restricted as that in our simulation. If we approximate this volume by a sphere in 3-D homogeneous medium, its radius is about 2.5 sites, which corresponds to ∼15 Å. Therefore, roughly speaking, we can say that the mean diffusion length is ∼15 Å, and the distribution of holes at 2 µs is not very different from that at 15 ns (Figure 11a). This suppression of the further spread of the holes corresponds to our observation that the hole scavenging is completes at 1 µs. Thus, the hole migration turned out to be limited within small domains, at most several sites away from TCNB anion, over the whole CR process. From these considerations, the hole diffusion manner is described as follows. Within several tens of nanoseconds, there exist holes that migrate as if they were in a 3-D homogeneous medium and are scavenged, and after that most of surviving holes hop down into the bottom of the potential valley and become immobile, leading to the saturation of the scavenging. We summarize the result brought by this random walk model. First, the existence of energy disorder of each hopping site makes a hole escape from its counteranion. Second, hole diffusion seems to be restricted to ∼15 Å, which results in the saturating behavior of hole scavenging. Third, a faster hole migration process or a more efficient delocalization of a hole compared to the description in our model is suggested. B. CR Process between TCNB Anion and TMPD Cation. As mentioned above, the hole-scavenging process is complete in 1 µs, although the holes are not be scavenged completely and the number of holes remains considerable at that time. In this section, we deal with the recombination of ions left after
Poly(N-vinylcarbazole) Films
J. Phys. Chem., Vol. 100, No. 47, 1996 18443
Figure 12. Decay curves of TMPD cation in PVCz films doped with 2 mol % TCNB and various concentrations of TMPD. The concentrations of TMPD are 0.2 mol % (filled circles), 0.1 mol % (squares), and 0.04 mol % (triangles). The solid curves are obtained by calculation with eqs 6 and 9 (see text).
the scavenging. After a few microseconds after photoexcitation, a hole that does not undergo scavenging decays by a CR process with the TCNB anion. After the hole decays, the TCNB anion (455-475 nm) and TMPD cation (550-630 nm) decay by longrange electron transfer. The absence of the hole absorption after a few microseconds suggests that a hole-detrapping process from TMPD cation is negligible. It is well-known that the distance R dependence of the charge transfer rate constant k can be written as follows:31
k(R) ) V0 exp(-R/a)
(9)
where V0 stands for an ET rate at a contact state and a is a parameter concerning the attenuation of the molecular electronic wave function. Figure 12 shows the decay curves of the TMPD cation with various TMPD concentrations. Since the holescavenging process is considered to be over in 1 µs, the decay curves in Figure 12 reflect only the CR process between the TMPD cation and the TCNB anion through the time regime shown. The solid lines depict the results of numerical integration of eq 9 with suitable parameters. We used a nearest neighbor distribution function P(R) given by eq 6 as an ionic distance distribution function. In Figure 12, the experimental results can be reproduced with this model, changing only the concentration of scavenger. The values used in the calculation were 1012 s-1 for v0 and 1.5 Å for a. The concentration of carbazole chromophores in the film state is considered to be ca. 6 M, so we set the concentrations of the scavenger to be 0.012, 0.006, and 0.0024 M, which correspond to 0.2, 0.1, and 0.04 mol % TMPD concentration, respectively. When the parameter a is changed from 1.5 to 1.8 Å, the most suitable value of V0 changes from 1012 to 109 s-1, and the same decay curves were obtained also with the different values. Owing to the lack of knowledge of these values, we cannot determine the appropriate parameters uniquely, but at least we could show the applicability of the long-range electron transfer model between a fixed anion and a TMPD cation to this slow recombination dynamics. 5. Conclusion In this paper, we have reported on the direct observation of the hole-scavenging process in a PVCz film by a transient absorption spectroscopy. The hole-scavenging process occurs mainly within several nanoseconds after photoexcitation and is
over in a microsecond. The scavenging yields depend on the scavenger concentration linearly. We also performed a Monte Carlo simulation to examine the applicability of random walk model in a 3-D regular lattice. In the simulation, introducing an energy disorder at each site was necessary to reproduce the experimental results, and this suggests that the disorder inherent in this polymer film permits a hole to escape from the Coulomb field by the anion and determines the recombination dynamics. The origin for the distribution in energy is the structural disorder and the formation of various dimers or more delocalized cation states. This is related to a free volume distribution of the polymer chain in the film, which brings a distribution of van der Waals, ioninduced dipole, or ion-permanent dipole interactions. The distribution was assumed to be a Gaussian function, and a width that is about 3 times wider than that of a Gaussian function expected from a spectroscopic estimation was necessary to fit the experimental data. This may be due to a neglect of the off-diagonal disorder in our simulation; in addition to the energy distribution, a distribution of the electron transfer integral caused by an orientational distribution of each carbazole chromophore would affect the hole-hopping rate and bring a wider distribution of the hopping rate. The Monte Carlo simulation revealed a spatially restricted hole diffusion (Figure 11), which may make the hole-scavenging dynamics slower with time (Figure 4 and 5). From the holescavenging yield obtained from experiment, the hole migration was found to be spatially restricted within ∼15 Å away from the anion. This characteristic behavior is brought about by the structural disorder. The simulation was able to reproduce the hole-scavenging process qualitatively. However, the experimental results show 4-5 times higher scavenging yields than the simulation. The energy distribution in our simulation is so large that holes become extremely immobile, and this is also considered as the reason for the discrepancy. An introduction of a spatial correlation in the energy distribution would improve the simulation model. The neglect of hole delocalization in the simulation is also a candidate of the cause of the discrepancy. We also observed a dramatic increase of the lifetimes of ionic species, which was brought about by the hole scavenging. The decay curves of the TMPD cation extend up to several tens of milliseconds, which is much longer than the CR dynamics of a migrating hole. This slow CR process was interpreted in terms of a long-range electron transfer model between the TCNB anion and the TMPD cation. A study of the temperature dependence of the CR dynamics and a study under higher initial concentrations of photogenerated ions are now in progress, and we will try a more unified description of the CR process with these results. Acknowledgment. The authors thank Takasago International for their kind gift of PVCz. The present work was partly supported by a Grant-in-Aid on priority-area-research “photoreaction dynamics” from the Japanese Ministry of Education, Science, Sports, and Culture (06239101) and by a Grand-inAid from the Japanese Ministry of Education, Science, Sports, and Culture (1985). K. Watanabe is a research fellow of the Japanese Society for the Promotion of Science. We are indebted to Mr. Y. Yoshikawa (Osaka University) for his help. Thanks are also due to Otsuka Electronics Co. for providing us use of the IMUC-7000. References and Notes (1) Van der Auweraer, M.; De Schryver, F. C.; Borsenberger, P. M.; Ba¨ssler, H. AdV. Mater. 1994, 6, 199.
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