Two-Dimensional Triplet Energy Migration and Transfer in Polymer

(9) Gaines, G. L.; Robert, R. W. Nature (London) 1963, 197, 787. (10) Yamazaki, I.; Tamai, N. ..... of Education, Science, Sports and Culture of Japan...
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Two-Dimensional Triplet Energy Migration and Transfer in Polymer Langmuir-Blodgett Films Kenji Hisada, Shinzaburo Ito, and Masahide Yamamoto* Department of Polymer Chemistry, Graduate School of Engineering, Kyoto University, Sakyo-ku, Kyoto 606-01, Japan Received December 27, 1995. In Final Form: May 13, 1996X

The triplet energy migration and transfer in Langmuir-Blodgett films prepared by the copolymers of octadecyl methacrylate with 2-(9-carbazolyl)ethyl methacrylate and (4-bromo-1-naphthyl)methyl methacrylate were measured and simulated by the Monte Carlo method. At a high donor density (1.3 × 10-6 mol/m2), the triplet energy transfer takes place by a dynamic process, i.e., a few steps of energy migration among carbazole (donor) chromophores, and followed by energy transfer to bromonaphthalene (acceptor). By solving the differential equations relevant to the energy migration and energy transfer on a twodimensional square lattice of 31 × 31 ) 961 lattice points, we successfully simulated the time evolution of the triplet energy quenching. The calculated quenching efficiencies were in agreement with the experimental values observed in the LB film of poly(octadecyl methacrylate) containing both the donor and acceptor moieties.

Introduction The Langmuir-Blodgett (LB) technique is an effective method to form artificial molecular assemblies. It enables one to control the thickness of the layers by modifying the chain length of amphiphilic molecules.1-3 It is also possible to form a highly ordered film having a preferential orientation to the film plane. In the field of photochemistry in molecular architecture, Kuhn et al. studied fundamental photophysical processes for LB films of fatty acids.4 They realized that basic photoprocesses such as singlet energy transfer and electron transfer can be controlled by the “nanostructure” built-up in LB multilayers. They demonstrated that the Fo¨rster theory5 of singlet energy transfer well expresses the real photophysical processes in molecular assemblies,6,7 but the multilayers undergo irreversible degradation at an elevated temperature8 or under reduced pressure.9 Yamazaki et al. performed fluorescence spectroscopy on the LB films of fatty acids using the picosecond single-photon-counting technique.10 They found that the chromophores in the LB films of fatty acids form aggregates with a fractal distribution in the two-dimensional (2D) plane. Recently, in place of the LB films of fatty acids, some preformed polymers have been found to form a stable monolayer at the air-water interface and to be transferable to solid substrates.11-20 We have used poly(vinyl octanal acetal) (PVO) as a base polymer for realizing * To whom correspondence should be addressed: Tel 81-75-7535602; fax, 81-75-753-5632; e-mail, [email protected]. X Abstract published in Advance ACS Abstracts, June 15, 1996. (1) Kuhn, H. Thin Solid Films 1989, 178. (2) Schneider, J.; Ringsdorf, H.; Rabolt, J. F. Macromolecules 1989, 22, 205. (3) Wegner, G. Science 1994, 265, 940. (4) Kuhn, H.; Mo¨bius, D.; Bu¨cher, H. In Physical Methods of Chemistry; Weissberger, A., Rossiter, B. W., Eds.; Wiley: New York, 1972; Vol. 1 Part 3B, p 577. (5) Fo¨rster, Th. Ann. Phys. 1948, 2, 55. Fo¨rster, Th. Z. Naturforsch. 1949, 4A, 321. (6) Blodgett, K. B. Phys. Rev. 1939, 55, 391. (7) Stenhagen, E. Trans. Faraday Soc. 1938, 34, 1328. (8) Naselli, C.; Rabolt, J. F.; Swalen, J. D. Thin Solid Films 1985, 134, 173. (9) Gaines, G. L.; Robert, R. W. Nature (London) 1963, 197, 787. (10) Yamazaki, I.; Tamai, N.; Yamazaki, T.; Murakami, A.; Mimuro, M.; Fujita, Y. J. Phys. Chem. 1988, 92, 5035. Yamazaki, T.; Tamai, N.; Yamazaki, I. Chem. Phys. Lett. 1986, 124, 326. (11) Tredgold, R. H. Thin Solid Films 1987, 152, 223.

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a random chromophore distribution in a 2D plane, in which the chromophores were attached to the polymer chain with covalent bonds.21,22 The singlet energy transfer in the polymer LB films was well characterized and controlled by the layered structure, while the structure itself became disordered by thermal motion of the polymer chain. To estimate the degree of disordering, the fluorescence decay curve was analyzed by a chromophore distribution model with Gaussian form in the direction of plane normal; the chromophores are distributed with a standard deviation ranging from 1 to 2 nm even immediately after the deposition.21 Triplet energy transfer takes place at a short interchromophore distance (0.6-1.5 nm) so that more strict regulation of the chromophore distribution is required to control triplet energy transfer. Mumby et al.23,24 and Arndt et al.25 studied the orientation of alkyl side chains of poly(octadecyl methacrylate) (PODMA) by polarized IR spectroscopy. They concluded that the orientation of alkyl side chains is approximately perpendicular to the substrate. Mumby et al. suggested that four to eight methylene units are needed as the spacer units between the amorphous chains to maintain the architecture of multilayer in a highly ordered structure. We studied the chromophore distribution in LB films of (12) Shigehara, K.; Murata, Y.; Amiya, N.; Yamada, A. Thin Solid Films 1989, 179, 287. (13) Erdelen, C.; Laschewsky, A.; Ringsdorf, H.; Schneider, J.; Schuster, A. Thin Solid Films 1989, 180, 153. (14) Watanabe, M.; Kosaka, Y.; Oguchi, K.; Sanui, K.; Ogata, N. Macromolecules 1988, 21, 2997. (15) Hayden, L. M.; Anderson, B. L.; Lam, J. Y. S.; Higgins, B. G.; Storoeve, P.; Kowel, S. T. Thin Solid Films 1989, 160, 379. (16) Shimomura, M.; Song, K.; Rabolt, J. F. Langmuir 1992, 8, 887. (17) Jark, W.; Russel, T. P.; Comelli, G.; Sto¨hr, J.; Erdelen, C.; Ringsdorf, H.; Schneider, J. Thin Solid Films 1991, 199, 161. (18) Naito, K. J. Colloid. Interface Sci. 1989, 131, 218. (19) Miyashita, T.; Matsuda, M.; Van der Auweraer, M.; De Schryver, F. C. Macromolecules 1994, 27, 513. (20) Menzel, H. Macromol. Chem. Phys. 1994, 195, 3747. (21) Ohmori, S.; Ito, S.; Yamamoto, M. Macromolecules 1991, 24, 2377. (22) Ohmori, S.; Ito, S.; Yamamoto, M. Macromolecules 1990, 23, 4047. Ohmori, S.; Ito, S.; Yamamoto, M.; Yonezawa, Y.; Hada, H. J. Chem. Soc., Chem. Commun. 1989, 1293. (23) Mumby, S. J.; Rabolt, J. F.; Swalen, J. D. Thin Solid Films 1985, 133, 161. (24) Mumby, S. J.; Swalen, J. D.; Rabolt, J. F. Macromolecules 1986, 19, 1054. (25) Arndt, T.; Schouten, A. J.; Schmidt, G. F.; Wegner, G. Makromol. Chem. 1991, 192, 2215.

© 1996 American Chemical Society

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Table 1. Compositions of Poly(octadecyl methacrylate) Copolymers and Chromophore Densities in the LB Films sample P(CN-OD)L-1 P(CN-OD)L-2 P(CN-OD)L-3 P(CN-OD)L-4 P(CN-OD)L-5 P(CN-OD)H-1 P(CN-OD)H-2 P(CN-OD)H-3 P(CN-OD)H-4 P(CN-OD)H-5

[Cz]2D, [BN]2D, CzEMA, BNMMA, mol %a 10-7 mol m-2 b 10-8 mol m-2 b mol %a 5.3 5.2 5.1 5.0 5.2 15.7 15.4 15.3 15.2 14.7

0 0.47 1.1 2.1 4.1 0 0.14 0.75 1.3 3.4

3.87 3.98 4.00 4.32 4.26 13.1 12.9 13.2 11.7 11.5

3.62 8.17 18.2 33.5 1.18 6.09 10.1 26.4

a Determined by UV absorbance. b Chromophore density in the surface films (mol m-2) at deposition.

PODMA by phosphorescence spectroscopy.26 At a low chromophore density, the chromophores in the LB films were analyzed in a planar manner with deviation of a few angstroms in the direction of the plane normal. However, the active sphere model27 adopted in the previous study26 could not be applied to the high chromophore density system in which triplet excitons migrate among the donors. To analyze such a high chromophore density system, a model adopting the hopping process of excitons is necessary. For the singlet energy transfer in 2D systems, Klafter and Blumen derived similar analytical solutions when the acceptor groups were distributed in a 2D plane with a fractal dimension d h .28 In this theory, an analytical equation was obtained also for the case in which both energy migration and transfer take place (multistep trapping). The direct trapping of the exciton depends on the fractal dimension d h , while the multistep trapping is given in terms of another dimension called a spectral dimension d ˜ . Sisido et al. simulated the time evolution of the distribution of the excited state on a 2D square lattice, taking into account both energy migration and energy transfer.29 In the present study, we have simulated triplet exciton diffusion on a 2D square lattice by solving the differential equations relevant to energy migration and transfer. The rate constants for both energy migration and energy transfer were obtained from Dexter’s formula. By the simulation, we derived the time profile of survival probability of the excited donor and the quantum efficiency of energy transfer to acceptors. The dynamic processes of energy migration and transfer as well as direct energy transfer from a donor to an acceptor (static process) could be described by this simulation. Experimental Section Materials. Poly[2-(9-carbazolyl)ethyl methacrylate-co-4bromo-1-naphthylmethyl methacrylate-co-octadecyl methacrylate] (P(CN-OD)) was prepared by the copolymerization of octadecyl methacrylate with 2-(9-carbazolyl)ethyl methacrylate (CzEMA) and (4-bromo-1-naphthyl)methyl methacrylate (BNMMA). Detailed preparative methods for PODMA, P(CN-OD), and PVO were as described previously.22,26 The composition of copolymers and the chromophore densities in a plane for the LB films are listed in Table 1. We prepared two series of octadecyl methacrylate copolymers with a fixed content of CzEMA (x ∼ 5 and 15) but with various contents of BNMMA, abbreviated as P(CN-OD)L-n (n ) 1-5) and P(CN-OD)H-n (n ) 1-5), respectively. We assumed that the chromophore density is maintained during the deposition procedure. The chromophore density at the surface pressure of the deposition was employed as that in the LB film. It is a reasonable assumption because the LB films (26) Hisada, K.; Ito, S.; Yamamoto, M. Langmuir 1995, 11, 996. (27) Perrin, F. C. R. Seances Acad. Sci. 1924, 178, 1978. (28) Klafter, J.; Blumen, A. J. Chem. Phys. 1984, 80, 875. (29) Sisido, M.; Sasaki, H.; Imanishi, Y. Langmuir 1991, 7, 2788.

Figure 1. Schematic illustration of single chromophoric layer sandwiched by protective layers for emission measurements. Circles represent carbazole chromophores, and squares represent bromonaphthalene chromophores. of P(CN-OD) maintains a highly order structure due to the crystallization of the alkyl side chain.

P(CN-OD)

Sample Preparation. Water in the subphase was deionized, distilled, and passed through a water purification system (Barnstead Nanopure II). The sample was spread on the surface of pure water from a dilute benzene solution (ca. 0.1 g/L) at 20 °C, and then the solvent was allowed to evaporate. The surface film was compressed at a rate of 15 cm2/min and transferred vertically onto a substrate at a surface pressure of 20 mN/m for PDOMA and PVO and of 17.5 mN/m for P(CN-OD). For PODMA and P(CN-OD), the deposition rate was 15 mm/min in the down mode and 2 mm/min in the up mode. For PVO, the rate was 15 mm/min in both up and down modes. A quartz plate used as a substrate was cleaned in sulfuric acid containing a small amount of potassium permanganate, dipped in 10% hydrogen peroxide solution, and then rinsed with water. The transfer ratio was nearly unity and the transfer mode was in Z-type for PODMA and P(CN-OD) and in Y-type for PVO. Figure 1 illustrates the structure of the LB films for the spectroscopic measurements. On quartz, polymeric layers were deposited in the following order: (1) two layers of PODMA; (2) a layer of P(CN-OD); (3) four layers of PVO. Note that P(CNOD) takes a Z-type deposition, then the intralayer interaction of chromophores is dominant. The layers of PODMA and PVO were deposited to remove the effects of the interface. Measurements. The phosphorescence spectra were recorded with a Hitachi 850 spectrophotometer equipped with a phosphorescence attachment involving a rotating light chopper between the excitation light source and the sample holder. The use of the chopper and a gated electric circuit allowed us to collect selectively the delayed emission later than 1 ms after the excitation. The total emission including both the phosphorescence and the prompt fluorescence could be recorded when the chopper was turned off. All the emission spectra were recorded with an excitation wavelength of 340 nm; this wavelength could excite the carbazole chromophore selectively. The lowest singlet state of bromonaphthalene is at a higher energy level than that of carbazole, so that bromonaphthalene does not quench the singlet excited state of carbazole. The phosphorescence decays were measured with a phosphorimeter assembled in our laboratory. Details of the system have been described elsewhere.30 (30) Ito, S.; Katayama, H.; Yamamoto, M. Macromolecules 1988, 21, 2456.

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Figure 2. Delayed emission spectra for the LB films of P(CNOD)H copolymers. The LB films were immersed into liquid nitrogen in a quartz Dewar vessel for the emission measurements.

Results and Discussion The delayed emission spectra of polymer LB films are summarized in Figure 2. The intensity was normalized by the carbazole fluorescence intensity at 365 nm measured without the rotating light chopper. This procedure effectively reduces the errors in the phosphorescence intensity measurement due to the difference of optical geometry. The emission band with peaks at 412, 440, and 460 nm is the carbazole phosphorescence and that with peaks at 500 and 535 nm is the bromonaphthalene phosphorescence. With the increase of bromonaphthalene content, the carbazole phosphorescence was quenched by the acceptor and the intensity of the bromonaphthalene phosphorescence increased. The quenching efficiency of carbazole phosphorescence (Q) was determined from the phosphorescence intensity at 412 nm compared with the fluorescence intensity. Figure 3 provides a plot of Q against the 2D acceptor density in a plane, [A]2D. The quenching efficiency observed (Qobsd) increased with [A]2D and was larger than the estimated value from the active sphere model in which the quenching radius of the active sphere (RA) was assumed to be 1.57 nm.28 The LB film of P(CN-OD)H-1 shows both phosphorescence and delayed fluorescence around 360 nm. These findings indicate that in this system a carbazole triplet is quenched by a dynamic process, i.e., a few steps of energy migration among the donors followed by energy transfer to an acceptor. The active sphere model cannot be applied to such a high donor content system involving the diffusion of triplet excitons. To analyze this system, we simulated time evolution of the triplet energy diffusion process in a 2D plane by solving the differential equations relevant to the energy migration and the energy transfer. The simulation procedure is described below. Computer Simulation for Triplet Energy Migration and Triplet Energy Transfer. Both the donors and the acceptors were randomly distributed in a square lattice as Figure 4 shows. The position of each chromophore was fixed, at least during the lifetime of the excited donor. The lattice interval was taken to be 0.5

Hisada et al.

Figure 3. Acceptor density dependence of the quenching efficiency of carbazole phosphorescence for P(CN-OD)H LB films. Simulated quenching efficiencies with energy migration are compared with the experimental results (O). The simulation made for Lda was 0.086 nm (9), 0.094 nm (b), and 0.101 nm ((). A quenching efficiency curve estimated from an active sphere model (- - -) is also illustrated (RA ) 1.57 nm).

Figure 4. Schematic illustration of chromophore distribution in a 2D lattice: [D]2D ) 1.2 × 10-6 mol/m2 and [A]2D ) 9.7 × 10-8 mol/m2. Open circles and filled circles represent the donors and the acceptors, respectively.

nm, which was estimated from the unit size of P(CNOD)H monolayer at the deposition.26 All distances between the donors and the acceptors were calculated. The energy-migration rates and the energytransfer rates at the distances, Rji and Rsi, are given by the Dexter formula,31

kji ) νdd exp(-2Rji/Ldd)

(1)

ksi ) νda exp(-2Rsi/Lda)

(2)

where kji is the energy-migration rate from the ith donor to jth donor, ksi is the energy transfer rate from the ith donor to sth acceptor, νdd and νda are the prefactor constants, and Ldd and Lda are the constants called the (31) Dexter, D. L. J. Chem. Phys. 1953, 21, 836.

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effective average Bohr radii.

∑jkji)pi - (∑sksi)pi + ∑j(kijpj) dps/dt ) ∑i(ksipi)

dpi/dt ) -(

(3) (4)

where pi (ps) is the survival probability for the ith (sth) donor (acceptor). The intrinsic lifetime of donor τd ) kii-1 was taken to be 6.4 s, which was the value of 9-ethylcarbazole in a 2-methyltetrahydrofuran rigid solution at 77 K.32 The values νda and Lda are 1.3 × 1012 s-1 and 0.117 nm for the intramolecular triplet energy transfer from carbazole to naphthalene at 77 K.32 We assumed that the parameters νda and Lda for the triplet energy transfer from carbazole to bromonaphthalene are equal to that from carbazole to naphthalene. For many triplet donors, such as benzophenone and phenanthrene, the radius of active sphere is insensitive to the kind of acceptor, e.g., whether it is naphthalene or 1-bromonaphthalene.33 Since the value of RA is reflected on νda and Lda, the parameters νda and Lda take similar values for the triplet energy transfer from a donor to naphthalene or 1-bromonaphthalene. The parameters for the energy migration, νdd and Ldd, are unknown. In this study, we employed the same value of ν for both the energy transfer and energy migration processes (νdd ) νda). On this assumption, Ldd, the only variable, was used as an adjustable parameter for the following fitting procedure. The simultaneous differential equations, eqs 3 and 4, can be expressed in the following form

dp/dt ) kp

(5)

where p is a column vector consisting of pi and ps and k is the matrix of rate constants. The set of differential equations, eq 5, has a formal solution that includes the eigenvalues of the rate constant matrix ki

pi(t) )

∑i

Ai exp(-kit)

Figure 5. Phosphorescence decay curves for the LB films of P(CN-OD)H at 77 K: n ) 2 (s), n ) 3 (- - -), n ) 4 (- - -), and n ) 5 (- - -).

time, the time profile of Q(t) for the longer times was approximated by triexponential curves with eq 7 3

Q(t) ) Q∞ -

(32) Katayama, H.; Ito, S.; Yamamoto, M. J. Phys. Chem. 1992, 96, 10115. (33) Birks, J. B. Photophysics of Aromatic Molecules; Wiley; New York, 1970; p 605. (34) The differential equations were solved numerically according to the Runge-Kutta-Verner method. The subroutine IVPRK included in the IMSL mathematical library (IMSL, Inc., Houston, TX) was used.

(7)

where Q∞ is the probability that triplet excitons are trapped by acceptors during the intrinsic lifetime and Ri is the apparent lifetime of donor exciton. Using eq 7, the phosphorescence decay curve is expressed as eq 8.

I(t)) I0{1 - Q(t)} exp(-t/τd) 3

) I0{1 - Q∞ +

∑ Ai exp(-t/Ri)} exp(-t/τd)

(8)

i)1

(6)

The pre-exponential factors Ai can be calculated from the eigenvector of the matrix. Practically, the differential equations were solved directly by numerical integration for the reduction assumed and the number of chromophores was set from the real chromophore density in each LB film. The simulation yields the trapped probability ps(t) of excitons for each acceptor at position s. The summation of all ps(t) values gives the population of trapped excitons at time t. This value was divided by the initial number of triplet excitons, giving the quenching efficiency at time t, Q(t). These calculations were repeated for 5-12 patterns of random distribution of chromophores to obtain a statistical average. The obtained Q(t) vs t curves were added and the sum was normalized by the number of initially excited chromophores. The calculation was performed until 4 ms after excitation. Figure 5 shows the phosphorescence decay curves observed for the LB films of P(CN-OD)H. Each phosphorescence decay has a similar time profile after 10 ms. This indicates that the exciton capture by acceptors was finished within this period. Although the major quenching process was expressed by the above simulation, a minor portion of quenching occurs after the calculation time. To reduce the computation

∑ Ai exp(-t/Ri)

i)1

When the apparent lifetime Ri is much smaller than the intrinsic lifetime (Ri , τd), eq 9 holds.

∫0∞ I(t) dt ≈ ∫0∞ I0(1 - Q∞) exp(-t/τd) dt ) I0(1 - Q∞)τd (9) Then total quenching efficiency, Qcalcd, is obtained as eq 10.

Qcalcd ) 1 -

∫0∞ I(t) dt/∫0∞ I0 exp(-t/τd) dt ) Q∞

(10)

The obtained Qcalcd value was compared with the quenching efficiency, Qobsd, experimentally observed. Figure 6 shows an example of time evolution for the triplet excited state. At the initial stage, donors at 11 × 11 lattice points around the center were excited (pi(t) ) 1). Triplet excitons are spread over the plane and trapped by the acceptors. At first, the acceptor near the initially excited donors, e.g., (x,y) ) (17,20) and (17,21), trap the excitons. The population of triplet excitons on the acceptors located on the route of triplet diffusion, e.g., (x,y) ) (4,12), grows with the elapse of time. Figure 7 shows the time profile of the calculated Q(t), and the solid lines are the exponential expression with eq 7. Each time profile was expressed by the triexponential function. First, the simulation was made at [A]2D ) 9.7 × 10-8 mol/m2 for three different Ldd (0.086, 0.094, and 0.101 nm). When Ldd is 0.094 nm, Qcalcd is in agreement with the experimentally observed value as given in Figure 3. Next, Qcalcd was calculated for a wide range of acceptor densities keeping Ldd ) 0.094 nm. The simulation

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Hisada et al.

Figure 6. Time evolution of the population of triplet exciton in a 2D square lattice: [D]2D ) 1.2 × 10-6 mol/m2 and [A]2D ) 9.7 × 10-8 mol/m2. The chromophore distribution was the same as that in Figure 4. The interval of the contour line is 0.2.

were also simulated. As described previously,26 the [A]2D dependence of Qobsd for the LB films of P(CN-OD)L can be explained by an active sphere model.27 When chromophores are distributed exactly in one plane, the quenching efficiency was calculated from eq 11

Q ) 1 - exp{-(πRA)2 NA[A]2D}

(11)

where RA is a quenching radius of an active sphere and NA is Avogadro’s number. Quenching efficiency was also obtained by the Monte Carlo simulation. For this system, the energy-migration term in eq 3 can be omitted because the donor densities in the LB films were low. To calculate the probability of a donor in the excited state, the following simultaneous differential equations were solved.

∑sksi)pi dps/dt ) ∑i(ksipi)

dpi/dt ) -( Figure 7. Plot of the simulated quenching efficiencies as a function of time. Solid lines are the curvs calculated by eq 7. The donor density in a plane is fixed to be 1.2 × 10-6 mol/m2 and acceptor densities in a plane are indicated in the figure.

reproduced the experimentally observed quenching efficiencies at various acceptor densities in a fairly good manner. Although the simulated value is smaller than the observed one at a low acceptor density, this deviation probably comes from the experimental error in the phosphorescence intensity measurements, because the intensity difference between P(CN-OD)H-1 film and P(CNOD)H-2 film is small at low [A]2D. To confirm the validity of parameters, Lda and νda, the data for the low donor densities ([Cz] ∼ 4 × 10-7 mol/m2)

(12) (13)

Figure 8 shows that Qobsd was also reproduced by this simulation. From this result, we confirmed the validity of energy transfer parameters, νda and Lda. This means that the triplet energy transfer in the polymer LB films take place in a similar manner to that in the threedimensional (3D) system although the LB film is a highly ordered system. In other words, the orientation of chromophores in the LB films is not restricted in a 2D plane and gives the averaged parameters Lda and νda in analogy with the 3D system. Therefore, the triplet energy transfer in the polymer LB films can be simulated by the

Triplet Energy Migration in Films

Figure 8. Comparison of experimentally observed quenching efficiency (4) with the simulated one without energy migration (2) for P(CN-OD)L copolymers. Quenching efficiency curve estimated from active sphere model (- - -) is also illustrated. The radius of active sphere for the triplet energy transfer in this system is 1.57 nm.

Langmuir, Vol. 12, No. 15, 1996 3687

energy transfer at 1.5 nm. This means that the distance 1.2 nm is regarded as the critical distance for the migration process among carbazole chromophores. Previously, the critical distance for triplet energy migration between carbazole chromophores was obtained as 1.0-1.2 nm for the system of carbazole chromophores in polymer films at various concentrations.30,36 The similar results for the energy migration distance assure that the value of the parameter Ldd used in the present simulation is reasonable. Previously, we analyzed the one-step transfer from carbazole to bromonaphthalene in PODMA LB films.26 The LB films were estimated to make the chromophores located in a planar distribution including the distribution in the direction of plane normal; the deviation from a complete planar distribution was less than a few angstroms. The reason why the chromophores can be fixed at a certain position by using LB films of PODMA, is explained as follows. Mumby et al. and Arndt et al. observed that the orientation of the alkyl side chains in the PODMA monolayer and multilayer on a solid substrate are approximately perpendicular to the substrate and the four to eight methylene units are needed as the spacer units to fix the amorphous polymer backbone to the crystallized portion of alkyl side chains.23-25 The crystalline region of the side chains maintains the structure of multilayer in a highly ordered state. The chromophores are closely attached to the main chain and they will be located in the amorphous region. The crystallized methylene units maintain the chromophores in a planar manner with a deviation of a few angstroms in the direction of the plane normal. The triplet energy migration and transfer in PODMA LB films were well expressed by the present simulation on the assumption of a planar distribution of chromophores, because of this high quality of LB film. Conclusion

Figure 9. The dependence of the rate constants upon the interchromophore distances: νda ) 1.3 × 1012 s-1 and Lda ) 0.117 nm (s), νdd ) 1.3 × 1012 s-1 and Ldd ) 0.094 nm (- - -). The radius of active sphere for the triplet energy transfer from carbazole to bromonaphthalene (RA) is indicated in the figure.

Dexter formula. Then, by using such a simulation we can predict Q for other donor-acceptor pairs in the LB film. As described by eqs 1 and 2, the rates of triplet energy migration and transfer decrease with the increase of interchromophore distance. Figure 9 illustrates the dependence of the rates of triplet energy migration and transfer on the interchromophore distances: The parameters were Ldd ) 0.094 nm and νdd ) 1.3 × 1012 s-1 for the triplet energy migration between carbazole chromophores, Lda ) 0.117 nm and νda ) 1.3 × 1012 s-1 for the triplet energy transfer. For the energy transfer from carbazole to naphthalene, RA is known to be 1.5 nm.32,35 When the interchromophore distance is 1.2 nm, the rate constant of energy migration is approximately equal to that for the (35) Ermolaev, V. L. Sov. Phys. Dokl. 1962, 6, 600.

Triplet exciton capture in a 2D plane was simulated by solving the differential equations relevant to energy migration and energy transfer. The calculated results well reproduced the quenching efficiencies obtained experimentally for both P(CN-OD)L and P(CN-OD)H LB films. This indicates that the triplet energy migration and transfer in a 2D plane can be described by the mechanism described in the above simulation. The best fit parameters were Ldd ) 0.094 nm and νdd ) 1.3 × 1012 s-1 for the triplet energy migration between carbazole chromophores, and Lda ) 0.117 nm and νda ) 1.3 × 1012 s-1 for the triplet energy transfer from carbazole to bromonaphthalene. The triplet energy transfer process is mechanistically equivalent to the electron transfer process because it takes place through the electron exchange interaction. Therefore similar molecular systems involving an electron transfer process can be built by using polymeric LB films. Acknowledgment. Computation time was provided by the Supercomputer Laboratory, Institute for Chemical Research, Kyoto University. This work was supported by a Grant-in-Aid for Scientific Research on Priority Areas, Photochemical Reactions (No. 06239107) from the Ministry of Education, Science, Sports and Culture of Japan. LA951570T (36) Hisada, K.; Katayama, H.; Ito, S.; Yamamoto, M. J. Photopolym. Sci. Technol. 1993, 6, 105. Katayama, H.; Hisada, K.; Yanagida, M.; Ohmori, S.; Ito, S.; Yamamoto, M. Thin Solid Films 1993, 224, 253.