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J. Phys. Chem. B 1997, 101, 5362-5369
Long-Range Singlet Energy Transfer in Perylene Bis(phenethylimide) Films Brian A. Gregg,* Julian Sprague, and Mark W. Peterson National Renewable Energy Laboratory, 1617 Cole BouleVard, Golden, Colorado 80401-3393 ReceiVed: January 27, 1997; In Final Form: March 21, 1997X
The distance over which singlet energy is transferred in polycrystalline films of perylene bis(phenethylimide), PPEI, was measured by a surface quenching technique in films ranging in thickness from 0.04 to 2.3 µm. Radiative energy transfer was not observed. Accurate values of the exciton transfer length could be obtained only with quenchers exhibiting rapid surface quenching velocities (>105 cm/s), such as poly(3-methylthiophene). The measured singlet exciton transfer length of 2.5 ( 0.5 µm is apparently the longest yet reported. Its approximate value can be inferred directly from the experimental data and is therefore essentially independent of the assumed theoretical model. Our measurements contain no direct information about the mechanism of the exciton motion; however, if it is assumed to be diffusional, the calculated intermolecular exciton hopping time, τh , 100 fs, is unusually fast. This suggests that excitons, in fact, may be delocalized over a number of molecules and that coherent energy transfer plays some role in the exciton motion. Energy is apparently transferred further and faster in PPEI films than in natural photosynthetic light-harvesting systems.
Introduction Transfer of absorbed solar energy to a site capable of converting it to chemical or electrical energy is an essential aspect of photoconversion in nature and in most organic semiconductors. In nature, light absorbed by light-harvesting antenna pigments is transferred as excitons1 to the reaction center where charge separation takes place.2-5 Light absorption by molecular semiconductor films also produces mobile excitons that eventually dissociate into electron-hole pairs or recombine.6-8 When the diffusion length is short, excitons in molecular semiconductors tend to dissociate in the bulk of the film. Photocurrent production then requires an internal electric field to separate the geminate electron-hole pairs7 in a process similar to that occurring in inorganic solar cells. But when the diffusion length is longer, excitons may dissociate primarily at interfaces in a process governed by interfacial kinetics rather than bulk electric fields.9-13 In this case, the mechanism of photoconversion more closely resembles that occurring in natural photosynthesis: the interface plays the role of the reaction center, converting the flux of energy into an electrical current. Among the molecular semiconductors, phthalocyanines typify the former class with short exciton diffusion lengths and photoconversion properties similar to inorganic semiconductors,8,14,15 while tetracene,9 porphyrins,11,12 and perylene bis(imides)8,10,13,16 exemplify the latter class. Light-harvesting pigments in natural systems transfer energy with high efficiency over hundreds of angstro¨ms to the reaction center.5,17 The mechanism of the transfer process is currently under active investigation. Simple Fo¨rster energy transfer theory may not adequately describe the motion because of the small distance and correspondingly large electronic coupling between the pigments.5,17,18 The geometrical arrangement of the chromophores, just recently elucidated for several systems,3,19,20 is complex. One question of current interest is whether the exciton is transiently localized on individual molecules, in which case the mechanism of energy transfer can be described as a hopping (diffusion) process, or whether it is best described as a delocalized excitation moving as a coherent wave.18,21-23 The same question is being asked about excitons in molecular X
Abstract published in AdVance ACS Abstracts, June 15, 1997.
S1089-5647(97)00326-X CCC: $14.00
semiconductors.24 Strong intermolecular electronic coupling and a high degree of structural and energetic order among chromophores tend to promote delocalization of excitons. Molecular semiconductors provide a convenient and easily manipulated system in which to study energy transfer processes. Although simpler than natural light-harvesting systems, they are still not well understood.6,25 The most common technique for measuring singlet exciton transport parameters involves fitting time-resolved fluorescence decays to a theoretical model of the system.24,26-30 In some cases, a small quantity of dopant (guest) is added to an otherwise pure crystal and the increase in fluorescence decay rate caused by the guest, or the fluorescence of the guest, is fit to theory. In less well-defined cases, the fluorescence decay is assumed to be governed by a population of unknown impurities and the fit to theory provides both the exciton motion parameters and the concentration of impurities. The fluorescence decay rate in such experiments depends on two parameters, however, the capture rate of the exciton by the guest and the diffusion coefficient of the exciton in the host, neither of which can be measured independently.27 Assuming that the capture rate is essentially infinite within some radius of the guest can lead to a substantial underestimation of the exciton transfer length. Transient grating techniques avoid this problem but require single-crystal samples, high laser intensities, and a careful accounting for the acoustic waves produced in the crystal simultaneously with the grating.31,32 Measuring the fluorescence quenching or photocurrent caused by a quencher contacting one side of a molecular semiconductor film is one of the conceptually simplest techniques and employs the geometry most relevant to solar cells.9,33-37 Assuming that the exciton concentration at the quenching surface is zero can again lead to an underestimate of the transfer length. On the other hand, it can be overestimated if radiative transfer dominates diffusion.26 Here, we employ a variation of the surface quenching technique in which the steady state fluorescence of perylene bis(phenethylimide) films in contact with a quencher is measured as a function of film thickness. Although our measurements contain no direct information about the mechanism of exciton transfer, they do provide an unambiguous and intuitive measure of the transfer length, apparently the longest yet reported for a singlet exciton. We discuss some possible © 1997 American Chemical Society
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reasons for the unusually long-range and rapid exciton transfer in these films. Experimental Section Perylene bis(phenethylimide), PPEI (structure shown in the inset to Figure 6), was synthesized and purified as reported previously.38 SnO2-coated glass plates (Libby Owens Ford, 10 Ω/square) were cleaned by immersion in a solution of KOH in 2-propanol, rinsed with deionized water, dried in a stream of nitrogen, and dehydrated immediately before use by heating to 200 °C. Poly(3-methylthiophene),39 PMT, films were electropolymerized onto one half of each SnO2 plate by oxidizing a 0.3 M solution of 3-methylthiophene (Aldrich) in dry acetonitrile containing tetrabutylammonium perchlorate at 1.6 V vs SCE for 70 s. The potential was then scanned back to 0 V and held for 60 s before the electrode was removed, rinsed thoroughly with ethanol, and dried. The PMT films were approximately 100 nm thick. They were in the reduced (low conductivity) form.39 PPEI was evaporated at ca. 10-7 Torr onto both the PMTcoated and bare halves of the SnO2 plates. Four plates were arranged in the evaporator at increasing distances from the source to effect a thickness gradient of PPEI across each plate and from plate to plate. Three sets of plates were coated in this fashion giving a series of films with PPEI thicknesses ranging from 40 nm to 2.3 µm as determined optically.38 The films were annealed by exposure to methylene chloride vapor for 3 h.38 The fluorescence intensity was measured on both the PMT-coated and the bare halves of each plate at several positions (thicknesses). A series of PPEI films on nonquenching substrates, both bare microscope slides, and poly(4-vinylpyridine)-coated microscope slides, were made similarly. The PMT films are cross-linked and insoluble as formed;39 but to rigorously exclude the possibility that fluorescence quenching may be caused by some species diffusing from the PMT into the PPEI during the annealing process, several PMT films were specially treated to remove possible diffusing species. After electropolymerization, they were soaked in pure ethanol for 2 h, then in pure methylene chloride for 3 h, then cycled electrochemically from oxidized to reduced forms 10 times in acetonitrile/tetrabutylammonium perchlorate, and finally soaked for another 3 h in pure methylene chloride. These films gave results comparable to the others, and data from them is included with the rest. For some experiments, evaporated films of titanyl phthalocyanine (TiOPC, H. W. Sands), N,N′-diphenyl-N,N′-ditolylbenzidine (called tetraphenyldiamine or TPD, H. W. Sands), or other quenchers were employed in place of the PMT films. One set of films was made by evaporating TiOPc onto preannealed PPEI films, so the TiOPc was not exposed to methylene chloride vapor. Another set was made by first evaporating TiOPc, annealing the films for 2 days in methylene chloride vapor, and then evaporating the PPEI films and reannealing for 3 h. The two sets gave comparable results. Since TPD is soluble in methylene chloride, the usual annealing process could not be employed. In this case, the TPD was evaporated onto the PPEI films, and they were then thermally annealed for 5 min at 180 °C. Absorption spectra were measured on an HP 8452A spectrophotometer. Fluorescence emission spectra were measured with an Aminco Bowman AB2 spectrofluorometer employing a front face cell holder for solid samples. Spectra were corrected for the instrument response. For the intensity vs film thickness measurements, the emission was measured at 710 nm with 16 nm slits and a 700 nm long pass filter on the emission
Figure 1. Schematic representation of the experimental geometry. Light was incident on the PPEI/air interface. Io is the incident intensity, and R is the absorption coefficient at the excitation wavelength. Some fraction of the excitons traverse the PPEI film of thickness d and reach the quencher, Q, on the opposite surface. Excitons reaching d can either be quenched by Q at a rate of S cm/s or reflected back into the bulk.
monochromator. The fluorescence was monitored at 710 nm to avoid any reabsorption of emitted photons by the PPEI film. Excitation was at 464 nm where 90% of the light is absorbed in the first 300 nm. The films were excited through the PPEI/ air interface (see Figure 1), and emission was measured at 90° from the excitation beam. Fluorescence decays were measured by time-correlated single-photon counting. A cavity-dumped synchronously-pumped dye laser (Spectra Physics 3500) operating at 600 nm provided pump pulses of 10 ps. A Hamamatsu microchannel plate detector afforded a typical instrument response function of 70 ps. Theoretical Model The theory of exciton transfer to an interface between a molecular semiconductor and an “end detector” (a fluorescent film), and the subsequent fluorescence of the detector has been given by Kenkre and Wong.34,35 Their expression is easily recast in a form appropriate to our experiments in which the exciton is quenched by the “detector”. A schematic drawing of the experimental geometry is shown in Figure 1. The theory is based on a master equation approach, but Kenkre and Wong showed that when the continuous limit is taken, their result is identical to that obtained by solving the differential equation
∂n(x,t) n ∂2n ) - + D 2 + RIoe-Rx ∂t τ ∂x
(1)
where n(x,t) is the concentration of excitons, τ is the lifetime of the unquenched exciton, D is the exciton diffusion coefficient, R is the absorption coefficient, and Io is the incident light intensity. This model assumes the diffusive transport of excitons. We briefly discuss the possibility of coherent transfer later and note that the approximate exciton transfer length can be directly inferred from our results and does not depend on the assumed mechanism of energy transfer. Kenkre and Wong’s theory includes a term for the escape of the exciton from the fluorescent detector back into the semiconductor film. In our case the detector (poly(3-methylthiophene), PMT) is nonfluorescent, and its excited state is higher in energy than the exciton in PPEI by ∼0.5 eV. Exciton quenching occurs by exothermic hole transfer from PPEI to the PMT,40 rather than by energy transfer, therefore we neglect the exciton escape term. The resulting equation describing the quenched fluorescence intensity at the probe wavelength, Flq, in terms of the maximum fluorescence intensity observed at that wavelength for optically thick, unquenched films, Flmax, is
[ { [ (
SτL tanh(d/L) R Sτ + L tanh(d/L) 1 - e-Rd 1 R cosh(d/L) + sinh(d/L) (2) L
Flq ) Flmax(1 - e-Rd) 1 L csch(d/L) 2
2
R L -1
R - e-Rd
)]}]
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Figure 3. Absorption (solid lines) and fluorescence (dashed lines) spectra of perylene bis(2,5-di-tert-butylphenylimide), a soluble analog of PPEI in CH2Cl2, and of a polycrystalline PPEI film. The left axis shows the absorption coefficient (to the base 10) of the PPEI film; all other spectra are in arbitrary units. Also shown (dot-dashed) is the absorbance of the poly(3-methylthiophene) film.
Figure 2. Plots of eq 2 showing the relative fluorescence vs film thickness assuming (a) an exciton diffusion length, L ) 1.0 µm, and (b) L ) 2.5 µm. Values of the surface quenching velocity, S, in cm/s are shown on the curves.
where d is the film thickness (cm), S is the exciton quenching velocity (cm/s) at the surface, and L is the exciton diffusion length (cm). S is equivalent to the surface recombination velocity in inorganic semiconductors.41,42 Plots of eq 2 are shown in Figure 2 for two values of the exciton diffusion length and for surface quenching velocities ranging from 0 to 107 cm/s. The exponential absorption coefficient and the fluorescence lifetime appropriate to the PPEI films, R464 ) 7.37 µm-1 and τ700 ) 0.87 ns were used in the calculations, where the subscripts on R and τ denote the excitation and emission wavelengths, respectively. The plots show that the lowest resolvable value of the surface quenching velocity is S ≈ 500 cm/s, while the highest resolvable value is S ≈ 107 cm/s. The fluorescence versus thickness curves are insensitive to variations in the exciton diffusion length when the quenching velocity is low. Therefore, an unambiguous determination of the diffusion length requires a fast quencher. Spectral and Morphological Characteristics of PPEI Films The absorption and fluorescence spectra of perylene bis(2,5di-tert-butylphenylimide), a soluble analog of PPEI, in CH2Cl2 and of a polycrystalline PPEI film are shown in Figure 3. The fluorescence spectrum of the solution species shows the expected mirror-image symmetry with the absorption spectrum. The quantum yield for fluorescence of the soluble perylene derivative in CHCl3 is reported to be 99% while its fluorescence lifetime is 3.7 ns.43 The polycrystalline film of PPEI shows two absorption maxima, one 310 meV (2500 cm-1) above and one 310 meV below the (0-0) band of the solution species. The large shift in excited state energy between the monomer and the solid film is evidence of the unusually strong intermolecular
electronic interactions in this material.38,44 PPEI molecules crystallize in coplanar stacks with a stacking distance between aromatic cores of 3.5 Å.44,45 The requirements for efficient singlet energy transfer26,46,47 seem to be well satisfied by the polycrystalline PPEI films: the films are highly fluorescent, the emission spectrum somewhat overlaps the absorption spectrum, and there is strong intermolecular electronic coupling between the tightly-packed chromophores. On this basis, we might expect to observe unusually facile exciton motion through the PPEI films. Also shown in Figure 3 is the absorption spectrum of the PMT quencher. The excited state energy of the PMT is substantially higher than that of the PPEI; therefore, radiative transfer from PPEI to PMT can be neglected. Although they are relatively highly ordered for evaporated thin films of molecular semiconductors, the PPEI films still have numerous structural defects. The morphology of a typical PPEI film is shown in the scanning electron micrographs of Figure 4: Figure 4a looks directly down on the exposed PPEI surface, while Figure 4b shows the cross section of the PPEI and PMT films. The outside surface of the film shows rodlike crystallites with their long axes lying primarily in the plane of the substrate. Typical crystallite dimensions are approximately 50 × 50 × 400 nm. The cross section shows that the film is quite densely packed. The two most important results obtained from these micrographs are (1) that excitons created near the outside surface of the film probably must traverse a large number of crystallite grain boundaries to arrive at the PMT quencher and (2) that the geometry of the films is essentially that as shown in Figure 1, that is, there is an approximately planar interface between the PPEI and the PMT quencher and that the bulk PPEI is dense enough to prevent a significant fraction of the incident light from penetrating, through cracks or pinholes, to points near the quencher. The energetic disorder in the PPEI films, caused partially or wholly by the remaining structural disorder, is apparent in timeresolved fluorescence emission measurements. The fluorescence decays are multiexponential and become progressively slower as lower emission energies are monitored; that is, the fluorescence spectra shift to lower energy with time after a laser pulse (Figure 5). This “spectral diffusion” is characteristic of a material with a distribution of energy levels, rather than a single exciton level, and indicates that excitons created by the laser pulse fall into ever lower energy levels with time as they move through the film. Therefore, a single exciton lifetime, or
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Figure 6. Fluorescence decays monitored at 700 nm of an unquenched 750 nm thick PPEI film (hashes, with fit) and of a 2.3 µm PPEI film quenched by PMT (diamonds). Excitation was at 600 nm; the decays were independent of excitation wavelength. The fit of the unquenched decay to the sum of three exponentials, the corresponding residuals, and the average of the three lifetimes and their relative populations are shown. The structure of PPEI is shown in the inset. Figure 4. Scanning electron micrographs of a 0.95 µm thick PPEI film after exposure to CH2Cl2 vapor for 3 h. (top) The exposed surface of the PPEI film. Micrograph shows an area of 1.1 × 0.8 µm. (bottom) Cross section showing the PPEI film on top of the 0.2 µm thick PMT film.
Figure 5. “Spectral diffusion”: the change in the (uncorrected) fluorescence emission spectrum of a 730 nm PPEI film with time after a 10 ps laser pulse at 600 nm. Spectra are normalized. The corrected steady state emission spectrum is shown in Figure 3. Spectral diffusion was observed in all films studied, from 100 nm to 2.3 µm in thickness.
diffusion coefficient, cannot be assigned to these films. A complete description would require characterizing the distribution of these quantities. Existing dynamical theories28,41,42,48 are not adequate to describe exciton transfer and quenching processes in films that show spectral diffusion. This is one reason we have chosen a steady state method of measuring the
(average) exciton transfer length in the films. The fluorescence versus film thickness measurements reported here are timeaveraged, and to some extent, wavelength-averaged. Spectral diffusion is also known to occur in optically thick films as a result of fluorescence reabsorption.49 However, only a small fraction of the PPEI fluorescence is reabsorbed because the overlap between the fluorescence and absorption spectra is small (Figure 3). Furthermore, spectral diffusion is observed even in optically thin, 100 nm PPEI films with an absorbance at 680 nm, the fluorescence maximum, of 0.02. Therefore, the spectral diffusion observed in PPEI films cannot be caused by fluorescence reabsorption. A value for the (average) exciton lifetime is required in eq 2. Therefore, the fluorescence decay at 700 nm (Figure 6) was fit to the sum of three exponentials and the population-weighted average lifetime,42 τ ) 0.87 ns, was used in eq 2. Note that only the product of the lifetime and the surface quenching velocity appears in eq 2; thus any error in τ will inversely affect the value of S. The fitted value of the diffusion length is not directly affected by uncertainties in τ. The fluorescence decay rates for unquenched films were independent of film thickness in all films studied, from 100 nm to 2.3 µm in thickness. The fluorescence decay of a quenched 2.3 µm film is also shown in Figure 6. Fluorescence vs Thickness Before interpreting the fluorescence versus thickness experiments in the presence of a quenching film, the surface quenching velocity in its absence must be measured. Any quenching at the PPEI/substrate or PPEI/air interfaces would complicate interpretation of the results with an added quencher. Measurements of the fluorescence intensity versus film thickness for PPEI films prepared on nonquenching substrates (poly(4-
5366 J. Phys. Chem. B, Vol. 101, No. 27, 1997
Figure 7. Fluorescence of unquenched PPEI films evaporated onto bare microscope slides (triangles) and onto poly(4-vinylpyridine)-coated microscope slides (circles). Emission was measured at 700 nm where emission reabsorption by the film is negligible. The curve is a fit to eq. 2.
vinylpyridine)-coated microscope slides and bare microscope slides) are shown in Figure 7. The best fit of the combined data to eq 2, with S and Flmax as fitting parameters, gives S ) 144 cm/s, within experimental error ((500 cm/s) of S ) 0 cm/ s. This shows that excitons are not quenched at interfaces between PPEI and air, glass or poly(4-vinylpyridine), and the fluorescence intensity is therefore directly proportional to the amount of light absorbed in the film. This conclusion is further supported by the fact that the fluorescence decay rates are independent of film thickness. If surface quenching were occurring at a measurable rate, the decays in thinner films would be faster because excitons would have a greater probability, or frequency, of encountering the surface. These experiments clearly demonstrate that, in marked contrast to inorganic semiconductor electrodes,41,42 the surface recombination velocity in the PPEI films is near zero. This is presumably a result of the low surface state density expected at molecular semiconductor surfaces where no high-energy bonds are broken (“dangling”), in contrast to the situation at inorganic semiconductor surfaces. Moreover, because of the change in polarizability at the interfaces, the exciton energy at the surface of a molecular semiconductor may be higher than that in the bulk,50 causing excitons to be reflected back into the bulk before reaching the interface. The consequences of this fundamental difference in interfacial character between molecular semiconductors and inorganic semiconductors remain largely unexplored. Fluorescence versus thickness data of PPEI evaporated onto SnO2-coated glass plates half-covered with PMT are shown in Figure 8. In this case both the bare and the PMT-coated halves of the SnO2-coated plates act as quenchers. The solid lines show the best fits to eq 2. Excitation was at 464 nm where 90% of the light is absorbed in the first 0.3 µm. The value of Flmax was taken from the fit to the unquenched data shown in Figure 7. Quenching at the SnO2 surface was measurable but slow, with a rate of S ) 6 × 103 cm/s. In this case, S was too low to permit an accurate determination of the diffusion length, so the value of L obtained in the fit to the PMT-quenched half of the films was employed. The PMT-coated surface strongly quenches the PPEI fluorescence even for the thickest (2.3 µm) film. This surface shows a quenching velocity of 8 × 105 cm/ s. The best fit to the exciton diffusion length is L ) 2.5 µm. To illustrate the sensitivity of the fit to variations in L, the dashed and dot-dashed lines show the best fit to these data using just S as a fitting parameter when L is constrained to be 1.8 µm and 4.0 µm, respectively. The former fit underestimates the data
Gregg et al.
Figure 8. Fluorescence of PPEI films evaporated onto the bare halves of SnO2-coated glass plates (diamonds) and onto the poly(3-methylthiophene)-coated halves of the plates (circles). Excitation was at 464 nm; emission was measured at 700 nm. The solid curves are the best fits to eq 2. The dashed and dot-dashed lines through the PMT-quenched data are the best fits to eq 2 with the diffusion length fixed at L ) 1.8 µm and L ) 4.0 µm, respectively. The dashed line through the SnO2quenched data illustrates the error that would result from assuming that S ) ∞ for this quenching surface. In this case the best fit to eq 2 gives L ) 0.07 µm.
for thin films (due to a higher quenching velocity, S ) 1.6 × 106 cm/s) and overestimates the data for thicker films. When L is set to 4.0 µm, the best fit gives S ) 5.6 × 105 cm/s, and the fit errs in the opposite sense. We estimate the accuracy of the fitted exciton diffusion length to be L ) 2.5 ( 0.5 µm. The dashed line through the SnO2-quenched data illustrates the severe underestimation of the exciton transfer length that would result from the common assumption that the quenching rate is infinite at the quenching surface. This assumption is usually expressed as a boundary condition on the differential equation that sets the exciton concentration at the quenching surface to zero. The error is particularly large when this assumption is applied to poorly quenching substrates, such as SnO2 in our system. A relatively good fit to the SnO2-quenched data can be obtained for S ) ∞ and L ) 0.07 µm. However, this value of L underestimates the actual value by a factor of 36 and is clearly incompatible with the results obtained with faster quenchers (Figures 8 and 9). Normalized fluorescence versus thickness curves for three different quenchers are shown in Figure 9. The quenchers are PMT (same data as shown in Figure 8), tetraphenyldiamine (TPD), and titanylphthalocyanine (TiOPc). The magnitude of the quenching observed for thick films shows that TPD and TiOPc are also efficient quenchers of excitons in PPEI. However, in contrast to the PMT-quenched case, the fluorescence does not approach zero as the film thickness goes to zero. We interpret the nonzero intercept as evidence for a lack of uniform physical or electrical contact between the polycrystalline PPEI film and the polycrystalline quencher films, as explained in more detail below. PPEI seems to make an almost perfect contact to the noncrystalline PMT film, resulting in a zero intercept in Figure 9. The curves through the TPD and TiOPc data are fits to a modification of eq 2 in which the term in braces, the fraction of fluorescence quenched by the surface, was multiplied by a fractional effective contact area. For the fits, the transfer length was assumed to be 2.5 µm and the fitting parameters were S and the effective contact area. The effective contact area was 0.65 for TiOPc and 0.83 for TPD; the quenching velocities were S ) 4 × 105 cm/s and S ) 6 × 105 cm/s, respectively. Although these fits are not as compelling
Long-Range Singlet Energy Transfer in PPEI Films
Figure 9. The quenched fluorescence, normalized by dividing by the maximum fluorescence and by the amount of light absorbed in the film, versus thickness. Unquenched films have a constant value of 1 in this representation. The quenchers are poly(3-methylthiophene) (PMT, same data as shown in Figure 8), tetraphenyldiamine (TPD) and titanylphthalocyanine (TiOPc, open circles and fit are from PPEI evaporated on TiOPc and then annealed, filled circles without fit are from TiOPc evaporated onto preannealed PPEI). The curves are fits to a modification of eq 2 that accounts for the imperfect contact between PPEI and the quenchers TPD and TiOPc.
as the fit to the PMT data, because of the additional fitting parameter and the lack of data on thicker films, they lend further support to the existence of an unusually long exciton transfer length in the PPEI films. Discussion The measured exciton transfer length, L ) 2.5 ( 0.5 µm, is apparently the longest yet reported for a singlet exciton. It should be compared to L < 0.2 µm for single-crystal naphthalene, anthracene, and phenanthrene26,32,33 and L ≈ 0.25 µm for thin films of perylene dianhydride and perylene bis(benzimidazole).10,37 Why is the measured value of L so long in PPEI compared to other materials? In this section we discuss (1) the possibility that our surface quenching experiments overestimated the transfer length; (2) the possibility that some previous measurements underestimated the transfer length in other materials, (3) differences between the PPEI films used in this study and the previously studied materials, and (4) the intuitive nature of our results that makes the measured value of L essentially independent of the assumed theoretical model. Finally, we briefly discuss the significance of our results in relation to the mechanism of exciton motion through PPEI films. In optically thick films, exciton motion may occur primarily by long-range radiative transfer rather than by diffusion or coherent transfer.26,49 This effect can lead to an overestimation of the exciton transfer length. Radiative transfer occurs when an exciton created near the outer surface of a film emits a photon toward the quenching surface. If the photon is reabsorbed near the quencher, it will appear that the exciton has moved through most of the film. This problem is well known and must be accounted for when making measurements on optically thick crystals.26,41 However, only a small fraction of the emitted fluorescence is reabsorbed in PPEI films because of the relatively weak overlap between absorption and emission spectra (Figure 3); therefore, radiative transfer is not expected to be significant in thin PPEI films.49 The following results show that radiative transfer is of negligible importance in the PPEI films studied here: (1) The reabsorption of emitted photons characteristically results in an apparent increase in emission lifetime with film thickness, since a photon may be emitted and reabsorbed numerous times before escaping the film and being detected.49 The PPEI films, however, showed no change in the
J. Phys. Chem. B, Vol. 101, No. 27, 1997 5367 fluorescence decay rate with increasing film thickness from 100 nm (optically thin) to 2.3 µm. (2) Radiative transfer is a slow process, necessarily occurring on the same time scale as fluorescence emission from thin films. Figure 6 shows, however, that the fluorescence of a quenched 2.3 µm PPEI film decays much more rapidly than the unquenched fluorescence of a 0.75 µm film. (3) Radiative transfer occurs only in optically thick films and therefore could not account for the strong quenching observed in the thinner films in which reabsorption is unlikely. PPEI films below ∼0.5 µm may be considered optically thin in this context because their absorbance at 680 nm, the peak of the fluorescence spectrum, is
