10252
J . Phys. Chem. 1991, 95, 10252-10261
structural changes during the cycle may be regarded as a subsystem operating at constant temperature. It is convenient and instructiie to consider such isothermal subsystem cycles in terms of the energy-ntropy plane. We have recently made conjectures about the quantum mechanical nature of such cycles in biological processe~.’~The possible role of transitions of background modes associated with solvent and protein structural regions, which are coupled to the centers of primary functions (e.g., active sites), is (13) Rhodes, W. J . Mol. Liq. 1989, 41, 165-180.
now under study. Observable linear thermodynamic relations provide a valuable tool.
Acknowledgment. This paper is dedicated as a tribute to Jack Leffler, Professor Emeritus of Chemistry, Florida State University, whose scholarly approach to science-whereby academic values are held foremost in importance-is one which is rapidly losing favor in today’s society. This work was supported by Contract No. DE-FG05-86ER60473 between the Division of Biomedical and Environmental Research of the Department of Energy and Florida State University.
Temperature Dependence of Electronic Energy Transfer and Quenching in Copolymer Films of Styrene and 2-(2f-Hydroxy-5f-vinylphenyl)-2H-benzotriazole Donald B. O’Connor,+ Gary W. Scott,*’* Department of Chemistry, University of California, Riverside, Riverside, California 92521
Daniel R. Coulter, and Andre Yavrouian Space Materials Science and Technology Section, Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California 91 109 (Received: February 28, 1991)
Quenching of the emission of both the polystyrene monomer and the excimer for a series of varying composition copolymer films of styrene and 2-(2’-hydroxy-5’-vinylphenyl)-2H-benzotriazoleis reported. The preponderance of quenching for both the monomer and excimer emissions is due to interception of the migrating excitation at the quencher site, although additional quenching results via long-range dipole-dipole energy transfer from the monomer and excimer traps to the quencher trap. The quenching of the monomer fluorescence and phosphorescence and that of the excimer fluorescence were found to be temperature independent over the ranges 14-58 and 191-296 K, respectively. Most significantly, it is concluded that the energy migration process is temperature independent over the range 14-296 K.
1. Introduction Polymers have many important applications in the solar energy industry. For example, polymeric materials are utilized in solar collectors, optical elements and protective containers.’ Polymers used in such applications are susceptible to photodegradation as the result of exposure to ultraviolet light. Fortunately, there are methods of protecting the polymeric systems from photodegradationS2 One method involves the copolymerization of another molecule, a photostabilizer, into the polymer chain. A particularly effective photostabilizer is the 2-(2’-hydroxyphenyl)benzotriazole (HPB) chromophore. We have previously r e p ~ r t e d on ~ ? the ~ photophysics of polystyrene containing small amounts of this chromophore, namely, the copolymer formed by the polymerization of styrene with small amounts of 2-(2’-hydroxy-5’-vinylphenyl)benzotriazole (VHPB, Figure 1). (These copolymers will be denoted by HPB/PS.) The photostability of such copolymers is thought to be the result of electronic energy transfer processes to the photostabilizer site followed by rapid, nondestructive energy dissipation of the lowest energy excited singlet state of the photostabilizer. Previous photophysical investigations of a derivative of HPB, 2-(2’-hydroxy-5’-methylphenyl)benzotriaz01e~~’~ (MeHPB), coupled with our study of the photophysics of the HPB chromophore in an HPB/PS copolymer4 led us to conclude that the photostabilizing efficacy of this chromophore is largely due to an excited-state intramolecular proton-transfer process of HPB. Author for correspondence. ‘Present address: Department of Chemistry, University of California, Santa Cruz, Santa Cruz, CA 95064. NASA-ASEE Summer Faculty Fellow, Jet Propulsion Laboratory, 1988 and 1989.
Specifically, we found that the electronically excited HPB chromophores in an HPB/PS copolymer at room temperature undergo (1) Gebelin, C. G., Williams, D. K., Deanin, R. D., Eds. Polymers in Solar Energy Utilization; ACS Symp. Ser. 220; American Chemical Society: Washington, DC, 1983. (2) Ranby, B.; Rabek, J. F. Photodegradation, Photooxidation, and Photostabilization of Polymers: Principles and Applications; Wiley: New York, 1975. (3) Coulter, D. R.; Gupta, A.; Yavrouian, A.; Scott, G. W.; OConnor, D.; Vogl, 0.;Li, S.-C. Electronic energy transfer and quenching in copolymers of styrene and 2-(2’-hydroxy-5’-vinylphenyl)-2H-benmtriazole:Photochemical processes in polymeric systems. 10. Macromolecules, 1986, 19, 1227-1234. (4) OConnor, D. B.; Scott, G. W.; Coulter, D. R.; Gupta, A.; Webb, S. P.; Yeh, S.W.; Clark, J. H. Direct observation of the excited-state proton transfer and decay kinetics of internally hydrogen-bonded photostabilizers in copolymer films. Chem. Phys. Lett. 1985, 121, 417-422. (5) Gupta, A.; Scott, G. W.; Kliger, D. Mechanisms ofphotodegradation of ultraviolet stabilizers and stabilized polymers; ACS Symp. Ser. 151; American Chemical Society: Washington, DC, 1980 Chapter 3. (6) Otterstedt, J. A. Photostability and molecular structure. J . Chem. Phys. 1973, 53, 5716. (7) Werner, T. Triplet deactivation in benzotriazole-type ultraviolet stabilizers. J . Phys. Chem. 1979, 83, 320. (8) Huston, A. L. Mechanisms and kinetics of excited-,state relaxation in internally hydrogen-bonded aromatic molecules. Ph.D. Thesis, University of California, Riverside, 1983. (9) Flom, S.R.;Barbara, P. F. The photodynamics of 2-(2’-hydroxy-5’methylpheny1)benzotriazole in low temperature organic glasses. Chem. Phys. Lett. 1983, 94, 488. (10) Huston, A. L.; Scott, G. W.; Gupta, A. Mechanism and kinetics of excited-state relaxation in internally hydrogen-bonded molecules: 242’hydroxy-5’-methylphenyl)benmtriazole in solution. J . Chem. Phys. 1982, 76, 4978. (1 1) Huston, A. L.; Merritt, C. D.; Scott, G. W.; Gupta, A. Excited-state Absorption Spectra and Decay Mechanisms in Organic Photostabilizers. In Picosecond Phenomena; Shank, C. V., Hochstrasser, R. M., Kaiser, W., Eds.; Springer-Verlag: Berlin, 1980; Vol. 2, p 232.
0022-3654/91/2095-10252%02.50/00 1991 American Chemical Society
Copolymer Films of Styrene
The Journal of Physical Chemistry, Vol. 95, No. 25, 1991 10253 TABLE I: Relative Excimer Emission Intensities of HPB/PS Copolymer Films at 296 and 191 K intensity'' at 296 K intensity" a t 191 K
I
IC
I
IC
0.66 0.20 0.12 0.056
1 0.67 f 0.01 0.21 f 0.01 0.13i0.01 0.077f 0.01
1 0.67 0.22 0.12 0.054
1 0.68f 0.01 0.23 f 0.01 0.13&0.01 0.074i 0.01
mol%HPB
Figure 1. Structure of HPB/PS copolymer. (No particular tacticity or conformation is implied.)
excited-state intramolecular proton transfer in less than 10 ps followed by rapid internal conversion of the resulting protontransferred tautomer to the ground state (fluorescence lifetime of -28 ps). This is followed by ground-state proton transfer resulting in the original ground-state tautomer, which is then available t o repeat the process. This rapid photophysical decay pathway effectively competes with the deleterious photochemical pathways, such as photooxidation, resulting in a more photostabile polymer. The photostabilization process also involves several mechanisms by which the HPB chromophores are electronically excited. The HPB chromophores can directly absorb the incident UV photons and simply act as UV screens for the phenyl units of the polymer. Another, more interesting mechanism involves the absorption of UV energy by the phenyl chromophores and the subsequent transfer of electronic excitation to the HPB chromophores. This transfer is energetically possible as shown by the overlap of the emission spectrum of electronically excited polystyrene with the ground-state absorbance of HPB. Since the emission spectrum of the HPB chromophore exhibits a large Stokes shift, electronic excitation localized on a HPB chromophore is "trapped". The study of the photophysics of long-chain, amorphous polymers containing aromatic pendant chromophore^'^-^^ such as polystyrene, poly(vinylnaphthalene), and poly(vinylcarbazo1e) has led to the hypothesis that electronic energy migration occurs in the homopolymers. Electronic energy migration involves the transfer or "hopping" of electronic energy initially localized on a pendant chromophore to another chromophore. The excitation energy may become trapped at a given chromophore depending on its excited-state energy relative to that of neighboring chromophores, the distance and orientation of the chromophore with respect to its neighbors, the temperature, and other factors. In some polymers such as polystyrene, an excited-state aromatic chromophore may form an excimer with an adjacent ground-state chromophore. Since the excimer is at lower energy than a non(12)Bocian, D.; Huston, A. L.; Scott, G. W. Low temperature spectroscopy of internally-hydrogen-bonded 2-(2'-hydroxy-5'-methylphenyl)benzotriazole in a mixed crystal. J. Chem. Phys. 1983, 79, 5802-5807. (13)Woessner, G.; Goeller, G.; Kollat, P.; Stezowski, J. J.; Hauser, M.; Klein, U.K.A.; Kramer, H. E. A. Photophysical and Photochemical Deactivation Processes of Ultraviolet Stabilizers of the (2-Hydroxypheny1)benzotriazole Class. J. Phys. Chem. 1984, 88, 5544. (14)Huston, A. L.; Scott, G. W. Picosecond kinetics of excited state decay processes in internally hydrogen-bonded polymer photostabilizers. Proc. SOC. Photo-Opt. Instrum. Eng. 1982, 322, 215. (1 5 ) Huston, A. L.; Scott, G. W. Spectroscopic and Kinetic Investigations of Internally Hydrogen-Bonded (Hydroxypheny1)benzotriazole. J . Phys. Chem. 1987, 91,1408. (16)Lee, M.;Yardley, J. T.; Hochstrasser, R. M. Dependence of intramolecular proton transfer on solvent friction. J . Phys. Chem. 1987, 91,4621. (17) Guillet, J. Polymer Photophysics and Photochemistry: An Introduction to the Study of Photoprocesses in Macromolecules; Cambridge University Press: London, 1985. (1 8) Phillips, D., Ed. Polymer Photophysics: Luminescence, Energy Migration and Molecular Motion in Synthetic Polymers; Chapman and Hall: London, 1985. ( 1 9) Kloepffer, W.Aromatic Polymers in Dilute Solution. Electronic Energy Transfer and Trapping, ACS Symp. Ser. 358 (Photophys. Polym.); American Chemical Society: Washington, DC, 1987;pp 264-285. (20)Frederickson, G. H.; Andersen, H. C.; Frank, C. W. Electronic excited-state transport and trapping on polymer chains. Macromolecules, 1984, 17, 54-59. (21) O'Connor, D. B.; Scott, G . W. Laser Studies of Energy Transfer in Polymers Containing Aromatic Chromophores. In Lasers in Polymer Science and Technology: Applications; Fouassier, J. P., Rabek, J., Eds.; CRC Uniscience: Boca Raton, FL, 1990; Chapter 8. (22) MacCallum, J. R. Significance of Energy Migration in the Photophysics of Polystyrene; ACS Symp. Ser. 358 (Photophys. Polym.); American Chemical Society: Washington, DC, 1987;pp 301-307.
0 0.0114 0.0527 0.154 0.483 3.40
1
" I , is the relative intensity corrected for screening and reabsorption. See text.
interacting chromophore, it traps the excitation. In the present study we were motivated to investigate a series of copolymers of HPB/PS in order to understand more about the photophysics of polystyrene. In these copolymers the presence of a competing trap of known concentration (HPB) offers insight into the nature of the energy migration and trapping processes in the polystyrene homopolymer. We previously reported the steady-state fluorescence spectra and kinetics of a series of HPB/PS copolymers, both in dilute solution and as thin films, at room t e m p e r a t ~ r e . ~The most important features of that study of the films were (1) relatively small concentrations of the quencher HPB resulted in efficient quenching of the polystyrene excimer emission intensity with no discernible effect on the excimer fluorescence decay kinetics and ( 2 ) a t somewhat greater HPB concentrations the excimer fluorescence decay was adequately modeled by Foerster kinetics. Therefore, we concluded that there were two processes of quenching of the polystyrene excimer. One process was long-range dipoledipole (Foerster) energy transfer from the excimer to the HPB chromophores, while the other was the quenching of the excited precursor prior to excimer formation. These results are consistent with the proposition of electronic energy migration. At room temperature the polystyrene monomer emission intensity is relatively weak and is spectrally overlapped by the stronger excimer emission. Therefore, we were unable to quantify the quenching of the monomer emission due to the HPB at room temperature. However, as the temperature is lowered, the monomer emission intensity increases. The dependence of the monomer emission intensity on the HPB concentration as well as the temperature dependence of the quenching of both the monomer and excimer emissions offers additional insight into the nature of the electronic energy migration in polystyrene. Therefore, we have extended the previous work and present here the results of an investigation into the quenching of the steady-state emission intensity of the polystyrene monomer and excimer as a function of temperature and HPB concentration in a series of HPB/PS copolymer films. A brief report of our preliminary results in this area appeared p r e v i o u ~ l y . ~ ~ 2. Experimental Section 2.1. Materials. The synthesis of the copolymers of styrene and 2-(2~-hydroxy-5'-vinylphenyl)benzotriazole (VHPB) has been described in detail e l s e ~ h e r e . ~The , ~ ~concentration of the pendant HPB chromophore incorporated into each copolymer was measured spectrophotochemically. It was assumed that the extinction coefficient of the HPB chromophores in the copolymer was equal to the extinction coefficient of 2-(2'-hydroxy-5'-methylphenyl)benzotriazole (MeHPB) in methylcyclohexane. Additionally, it was assumed that the density of the copolymers was equal to the density of pure polystyrene (1.05 g/cm3). The mole percents of the copolymer films are given in Table I. Throughout this article (23)Coulter, D. R.; Gupta, A.; Miskowski, V. M.; Scott, G. W. Excitedstate Singlet Energy Transport in Polystyrene. In Phorophysics oJPolymer Systems; Hoyle, C. E., Torkelson, J. M., Eds.; ACS Symp. Ser.; American Chemical Society: Washington, DC, 1987;Vol. 358, 286-300. (24)OConnor, D. B. The photophysics of polystyrene and poly(2,3,4,5,6-pentafluorostyrene): Electronic energy processes in polymer films. Ph.D. Thesis, University of California, Riverside, 1990.
10254 The Journal of Physical Chemistry, Vol. 95, No. 25, 1991
O'Connor et al.
0
250
275
wavelength (nm) Figure 2. Room temperature absorption spectra of polystyrene in cyclohexane solution (thin line; lo-' M phenyl unit concentration) and neat polystyrene film (thick line). The ordinate scale is relative intensity for the PS film spectrum.
a copolymer whose photostabilizer mole percent content = x will be referred to as x%-HPBIPS. 2.2. Methods. The methods of obtaining absorption spectra, temperature-dependent steady-state emission spectra, and emission anisotropy spectra have been described e l s e ~ h e r e . ~ ~ , ~ ~ The technique of determining the absolute quantum yields of emission of neat polystyrene film at several temperatures is an extension of a method used to determine quantum yields of powdered samples.26 The spectrofluorimeter used previously25 (Spex Fluorolog 2, Model 212) was utilized in making the necessary measurements. The method involves (1) determining the diffuse reflectance of the sample at an energy where it does not absorb, (2) measuring the diffuse reflected light at a second energy where some absorption occurs, and (3) recording the emission spectrum while exciting at this second energy. It was assumed that the diffuse reflectance of the sample would be the same at both energies provided the excitation intensities were the same at the two energies. The expected diffuse reflected light intensity at the second energy is calculated from the measured value at the first energy and the relative output of the excitation source. The absolute quantum yield 4 is given by
300
325 350 wavelength (nm)
375
400
Figure 3. Room temperature absorption spectra of MeHPB in methylcyclohexane (thick line; t = 15063 cm-' M'' at 340 nm) and 3.4%HPB/PS copolymer in cyclohexane (thin line).
wavelength (nm) Figure 4. Emission spectra of neat polystyrene film (Aex = 260 nm) a t 15 K (-), 30 K 58 K (-), 93 K (---), 143 K (-), and 296 K (-). (.e.),
3. Results 3.1. Absorption Spectra. The absorption spectra of polystyrene M-' phenyl unit confilm and polystyrene in cyclohexane ( centration) are shown in Figure 2. These spectra show a weak
band with a maximum near 260 nm (t = 202 cm-' M-' at 260 nm in cyclohexane). The intensity, location, and structure of this band indicate that it is due to phenyl a-a* absorptions such as are also seen in benzene and t o l ~ e n e . ~ ~ ? ~ ' The absorption spectrum of MeHPB in methylcyclohexane is shown in Figure 3. The absorption spectrum of 3.4%-HPB/PS copolymer in cyclohexane is also shown in Figure 3. The general shapes of the two spectra are the same for wavelengths greater than 280 nm. Above this wavelength only the photostabilizer chromophores absorb. The HPB chromophores incorporated into the copolymers are assumed to have the same extinction coefficient as the MeHPB. 3.2. Steady-State Emission Spectra. The emission spectra of neat polystyrene film (kx = 260 nm) at several temperatures over the range of 15 K to room temperature are shown in Figure 4. The room-temperature spectrum shows a highly Stokes shifted, structureless band (A,, 325 nm) which is due to excimer f l u ~ r e s c e n c e . *As ~ ~the ~ ~ temperature decreases, the spectra show increasing intensity emission bands due to the monomer (A,, = 285 nm at 15 K). The monomer fluorescence band is at higher energies than the excimer and exhibits vibronic structure, The monomer phosphorescence also exhibits structure and is at lower energies (Amx = 410 nm at 15 K) than the excimer fluorescence. The monomer emissions decrease dramatically as the temperature increases from 15 K to about 143 K. Above this temperature there is very little additional decrease in the monomer fluorescence while the monomer phosphorescence continues to decrease noticeably.
(25)OConnor, D.B.; Scott, G. W.; Coulter, D. R.; Miskowski, V. M.; Yavrouian, A. The Photophysics of Poly(2,3,4,5,6-pentafluorostyrene)Film. J. Phys. Chem. 1990, 94, 6495-6503. (26)Wrighton, M. S.;Ginley, D. S.; Morse, D. L. A technique for the determination of absolute emission quantum yields of powdered samples. J. Phys. Chem. 1974, 78, 2229-2233.
(27) Berlman, I. B. Handbook of Fluorescence Spectra of Aromatic Molecules, 2nd ed.; Academic Press: New York, 1971. (28)Basile, L. J. Effect of styrene monomer on the fluorescence properties of polystyrene. J. Chem. Phys. 1962, 36, 2204. (29)Yanari, S. S.;Bovey, F. A.; Lumry, R. Fluorescence of styrene homopolymers and copolymers. Nature 1963,200, 242.
where E and D2 are the integrated emission intensity and integrated diffuse reflectance intensity, respectively, while exciting at the second energy. Dl is the integrated diffuse reflectance intensity obtained while exciting at the first energy where the polymers do not absorb, corrected for the difference in the excitation source intensity at the two energies. The numerator and denominator of eq 1 are proportional to the number of photons emitted and absorbed by the sample, respectively. The proportionality constant, the collection efficiency of the spectrofluorimeter, is the same for both. E and Dl were both obtained while exciting at 260 nm, while D2 was obtained with 310-nm light. The diffuse reflectance of the polymers films was found to vary by less than *25% from 280 to 350 nm. The assumption that the diffuse reflectance a t 260 nm, in the absence of absorption, is equal to the reflectance at 310 nm i s an extrapolation of this result. The accuracy of this technique was estimated to be *25% for powdered
The Journal of Physical Chemistry, Vol. 95, No. 25, 1991 10255
Copolymer Films of Styrene
270
310
270 310 350 390 430 470 510 550 590 630 670
wavelength (nm) Figure 5. Emission spectra of 0.0527%-HPB/PScopolymer film (Aex = 260 nm) at 15 K (-), 30 K 58 K (-), 93 K (---), 143 K (-),and (ma-),
296 K (-).
350 390 wavelength (nm)
430
470
Figure 7. Room-temperature emission spectra (Aex = 260 nm) of x%HPB/PS copolymer films where x = 0 (-), 0.01 14 0.0527 (---), (.-e),
0.154 (-),and 0.483 (---). 1
-.2
’
I
310
330 wavelength (nm)
350 wovelength (nm) Figure 8. Emission spectra (Aex = 260 nm) at 191 K of x%-HPB/PS 0.0527 (---), 0.154 (-), copolymer films where x = 0 (-), 0.014 and 0.483 (- --). (as.),
TABLE II: Screening and Reabsorption Correction Factors for Polystyrene Excimer Fluorescence mol % ’ HPB S R SR
0
-. 2
280
320
360 400 wavelength (nm)
440
480
Figure 6. Emission polarization anisotropy spectra (Aex = 260 nm) of neat polystyrene film at (a) room temperature and (b) 14 K.
The temperature dependence of the emission spectra of one of the copolymers, 0.0527%-HPB/PS, is shown in Figure 5 . The general temperature-dependent trends for this copolymer and the others as well are the same as those seen in pure polystyrene (Figure 3). The steady-state emission anisotropy spectra of a neat polystyrene film at room temperature and 14 K (hex 260 nm) are shown in Figure 6. The polarization anisotropy has a constant, within experimental error, value of r = 0.02 f 0.02 throughout the emission spectra at both temperatures. 3.2.1. Excimer. A detailed analysis of the quenching of the polystyrene excimer fluorescence in HPB/PS polymer films at room temperature was presented earlier.3 We have repeated some of the experiments and present the results here for comparison with the results at other temperatures. The room-temperature results presented here agree within experimental error with those previously p ~ b l i s h e d . ~ Since we are interested in the quenching of the polystyrene emission as a function of the concentration of HPB, it is illustrative to plot the emission intensities of the films of varying HPB content
=
0.01 14 0.0527 0.154 0.483
1 1.oo 1.oo
1.01 1.04
1
1
1.01 1.03 1.10 1.32
1.01 1.03 1.11
1.37
at a particular temperature. Figures 7 and 8 show that the excimer emission spectral intensities decrease monotonically with increasing HPB content at room temperature and at 191 K, respectively. The relative integrated intensity, normalized to the pure polystyrene value, of the excimer emission (300-360 nm) for each of these films a t room temperature and at 191 K is shown in Table I. One mechanism resulting in decreasing excimer emission with increasing HPB concentration is competitive direct absorption by the HPB chromophores of the incident 260-nm photons. Since HPB absorbs at the excitation wavelength (Figure 3), the excimer emission decreases with increasing HPB concentration due to an effective attenuated source. To account for direct HPB absorption of 260-nm photons, the emission intensity of each film can be normalized to a constant excitation intensity by a corresponding screening factor S, where
S = (ODHPB+ ODPS)/ODPS
(2) s = [ € ~ p ~ ( 2 nm)CHpB 60 + eps(260 nm)Cps] /Eps(260 nm)CB in which € ~ p ~ ( 2nm) 6 0 = 1578 cm-l M-’ and ~ ~ ( 2 nm) 6 0 = 202 cm-’ M-I. These screening correction factors are tabulated in Table 11. Another mechanism that results in a decrease in the relative excimer emission intensity with increasing HPB content is ‘trivial”
10256 The Journal of Physical Chemistry, Vol. 95, No. 25, I991
O’Connor et al.
radiative energy t r a n ~ f e r . ~ ’ This . ~ ~ radiative energy transfer involves the absorption by HPB chromophores of photons emitted by the excimers. As we are primarily interested in aspects of nonradiative energy transfer, the relative emission intensities need to be corrected for this radiative quenching mechanism. For this correction it is assumed that the excimer is an isotropically emitting point source in a given copolymer film. The fraction of the total emission reaching the detector is dependent upon the f number of the optical system, the concentration of HPB, the depth z of the point source, and the indexes of refraction of air and of polystyrene. If we assume that the excimer emission emanates from an isotropically emitting line source, perpendicular to the film surface, then an expression relating the detected emission intensity Id to the total emission intensity I can be derived:
.2 .3 . 4 . s M o l e % HPB F w e 9. Dependence of the ratio of the polystyrene excimer fluorescence intensity, Io, to the corrected excimer fluorescence intensity, I, on the content of the HPB chromophore in the copolymer film at 296 K (+) and 191 K (0). .1
in which tps(260) = 202 cm-‘ M-I, Omax = na,,/(2np& and eHPB(325)= 12264 cm-I M-I. The instrumentalfnumber is 4, the refractive index of neat polystyrene film, rips, is 1S920, and the refractive index of air, nair,is 1.00. Simpson’s rule was used to numerically evaluate the denominator of eq 3. A practical value of infinity is the depth at which 99.9% (OD = 3) of the exciting radiation has been absorbed by the film. In this case, infinity was taken to be 1.5 X cm. The correction factor for each film is obtained by merely normalizing the value obtained from eq 3 to the value obtained for neat polystyrene using eq 3. These radiative correction factors R are shown in Table 11. It should be noted that the R correction factors are wavelength dependent since the absorption of HPB is obviously wavelength dependent. The extinction coefficient of HPB varies by less than 25% over the spectral range of the excimer emission (see Figure 3). The extinction coefficient value at 325 nm was chosen because it corresponds to the maximum in the excimer emission as well as a nearly average value of the HPB extinction coefficient over the range of the excimer emission. The correction factor R at 340 nm was calculated for each of the films and found to vary from the corresponding value at 325 nm by less than 4%. For example, R = 1.12 at 340 nm for the O.l54%-HPB/PS film, a change of less than 2% from the 325-nm value of R = 1.10. This wavelength, 340 nm, corresponds to a maximum in the HPB absorption and the point at which the greatest variation in the correction factor R from the reported value is expected. Therefore, we conclude that the factors reported in Table I1 are valid in analyzing the integrated data. The total correction factor for each film is the product of the screening factor S and the reabsorption factor R . These are tabulated in Table 11. The total correction to the integrated excimer emission is less than 10% for films containing less than 0.16 mol % HPB. The integrated excimer emission intensity values, corrected for screening and reabsorption, at room temperature and 191 K are tabulated in Table I. It is illustrative to plot the data from Table I (Figure 9) as the ratio of the room temperature corrected emission intensity of the excimer in pure polystyrene film, Io,to the corresponding value of each of the copolymers, I, as a function of the HPB content. Clearly, the quenching of the excimer emission is significant even after considering the reabsorption and screening mechanisms. Also plotted in Figure 9 is the corresponding ratio I o / I versus HPB content at 191 K. It is important to note that the plots are the same within experimental error. 3.2.2. Monomer. The emission spectra of the copolymer films at 15, 30, and 58 K are shown in Figure 10. The general trend shown is a monotonic decrease in the emission intensity with (30) Birks, J. B. Photophysics of Aromatic Molecules; Wiley-Interscience: London, 1970; p 354.
TABLE 111: Relative Monomer Fluorescence Intensities of HPB/PS Cowlvmer Films at 15, 30. and 58 K intensity‘ intensity” intensitya mol at 15 K at 30 K at 58 K m.0
HPB 0 0.0114 0.0527 0.154 0.483
I
I,
I
1 0.74 0.28 0.29 f 0.01 0.26 0.12 0 . 1 3 f 0 . 0 1 0.12 0.052 0.066 f 0.01 0.048
1
1
I, 1 0.75 f 0.01 0.27 f 0.01 0.13f0.01 0.061 f 0.01
I 1 0.59 0.22 0.11 0.056
I, 1
0.60 f 0.01 0.23 f 0.01 0.12i0.01 0.071 f 0.01
“ I , is the relative intensity corrected for screening and reabsorption. See text.
increasing HPB content. We are particularly interested in quantifying the dependence of the quenching of the monomer fluorescence (Amx = 285 nm at 15 K) as a function of the HPB content of the films. Due to the spectral overlap of the monomer fluorescence and excimer fluorescence, it is necessary to subtract out the excimer emission in order to quantify the relative monomer fluorescence intensity directly from these spectra. It is known that the excimer emission intensity in pure polystyrene films varies by less than 25% over the temperature range 15 K to room t e m p e r a t ~ r e . ~ ~The . ~ ’spectra of neat polystyrene shown in Figure 4 are consistent with this. Furthermore, the spectrum of each copolymer as a function of temperature (e& O.O527%-HPB/PS shown in Figure 5) demonstrate that the temperature dependence of the excimer emission in the copolymers is the same as that in pure polystyrene. This information was used to obtain the emission spectra of the polystyrene monomer only. The room temperature spectrum of polystyrene was multiplied by the relative emission intensity at a particular t e m p e r a t ~ r e , ~ ~ normalized to the room-temperature value, to obtain the spectrum of the excimer at a particular temperature. These factors, the excimer emission intensity normalized to the room-temperature value, are 0.97 (143 K), 0.90 (93 K), 0.83 (58 K), 0.77 (30 K), and 0.76 (15 K). This excimer emission spectrum was then subtracted from the polystyrene spectrum at the corresponding temperature. The resulting spectrum is considered to be the emission spectrum of the polystyrene monomer only. These difference spectra of neat polystyrene over the temperature range 15-143 K are shown in Figure 11. These difference spectra of neat polystyrene closely resemble those of ethylbenzene in dilute solution, which do not exhibit excimer fluore~cence.~’ The same (31) Frank, C. W.; Harrah, L. S . Excimer formation in vinyl polymers. 11. Rigid solutions of poly(2-vinylnaphthalene) and polystyrene. J. Chem. Phys. 1974, 57, 534.
The Journal of Physical Chemistry, Vol. 95. No. 25, 1991 10257
Copolymer Films of Styrene
"270 300 330 360 390 420 450 480 510 540 570
wavelength (nm)
270 310 350 390 430 470 510 550 590 630 670
wavelength (nm) Figure 11. Difference emission spectra due to the monomer of neat polystyrene film after subtracting the excimer emission (Aex = 260 nm) at 15 K (-), 30 K (-.-), 58 K (---), 93 K (-), 143 K (---). 1 1
1
wavelength (nm)
I
1 1
-
270 300 330 360 390 420 450 480 510 540 570
wavelength (nm) Figure 12. Difference emission spectra due to the monomer at 15 K of x%-HPB/PS copolymer films after subtracting the excimer emission (kX = 260 nm) where x = 0 (-), 0.0527 0.154 (- - -), and 0.483 (-). (.e.),
TABLE I V Screening and Reabsorption Correction Factors for Polystyrene Monomer Fluorescence
270 300 330 360 390 420 450 480 510 540 570
mol 7% HPB
S
R
SR
0 0.01 14 0.0527 0.154 0.483
1 1.oo 1.oo 1.01 1.04
1 1.01 1.02 1.07 1.22
1 1.01 1.02 1.08 1.27
Wavelength (nm) n P r e 10. (a) Emission spectra (Aex = 260 nm) at 15 K ofx%-HPB/PS copolymer films where x = 0 (-), 0.0527 (. s), 0.154 (- - -), and 0.483 (-). (b) Emission spectra (Aex = 260 nm) at 30 K of x%-HPB/PS copolymer films where = 0 (+, 0.01 14 (...), 0.0527 0.154 (-), and 0.483 (c) Emission spectra = 260 nm) at 58 K ofx%~ p ~ / copolymer p s films where = 0 (-), 0.0114 (...), 0.0527 (.-.), 0.154 (-), and 0.483 (---).
-
e--),
procedure was used to obtain the temperature dependence of the monomer emission in the copolymer films. The emission intensity of the x%-HPBIPS copolymer films resulting from the monomer only at 15 K is shown in Figure 12. The relative integrated (270-3 10 nm) monomer fluorescence intensities at 15 K as well as those at 30 and 58 K are tabulated in Table 111. As with the excimer, it is necessary to correct these relative intensities for the competitive screening of the excitation photons and reabsorption of the monomer fluorescence by the HPB chromoDhores. The screening correction factors. S. are the same as thosd calculated for the eicimer. Implicit in' this calculation is the assumption that the absorption spectra of the copolymers are temperature independent. For a particular copolymer, the reabsorption correction factor R is smaller for the monomer fluorescence than the excimer because the absorption of the HPB chromophores is relatively weaker in the region of the monomer
fluorescence (see Figure 3). These correction values were obtained using 3 with the additional factor that = 8271 cm-l M-l at 285 nm. The correction factors are tabulated in Table IV. The relative fluorescence intensities of the m o n c n " multiplied by the corresponding correction factor and the corrected relative fluorescence intensities, are also given in Table 111. Figure 13 is a plot of the ratio of the corrected integrated monomer fluorescence intensity of the pure polystyrene fiim, I,,, to that of each of the copolymers, I , as a function of the HPB molarity. Figure 13 contains three plots corresponding to 15, 30, and 58 K. It is noteworthy that these plots are, within experimental error, the same. 3.2.3. Theoretical Foerster Energy Transfer. The "theoretical" Foerster critical radius Ro associated with dipole-dipole energy transfer from the polystyrene excimer trap to the HPB chromophores was calculated previously3 by a method detailed by Berlman3*using the following equation: Ro6 =
9000K2(h 1O)4D 128rSn4N
-
d3 FD(P)CA(B)
v4
(4)
(32) F l m a n , I. B. Energv Transfer Parameters of Aromatic Compounds; Academic Press: New York, 1973.
10258 The Journal of Physical Chemistry, Vol. 95, No. 25, 1991
.I.
.2
.3
.4
O'Connor et al.
.1
.5
Mole % HPB Figure 13. Dependence of the ratio of the polystyrene monomer
fluorescence intensity, I,, to the corrected monomer fluorescence intensity, I , on the content of the HPB chromophore in the copolymer film at 15 K (+) and 30 K (0)and 58 K (*). in which 4Dis the quantum yield of emission of the donor in the absence of the acceptor, n is the index of refraction of the solvent, N is Avogadro's number, FD(ij)is the emission spectral intensity of the donor normalized such that .fFo(ij) dv = 1, and eA(v) is the molar extinction coefficient of the acceptor as a function of ij. In the solid state the orientation factor K~ is usually taken to be 0.475 such as would be expected for a random distribution of the transition dipole orientations of the donor and acceptor molecules. The Foerster critical radius Ro is indicative of the distance over which dipole-dipole energy transfer may be significant. Specifically, Ro is the separation distance between the donor and acceptor at which the probability of energy transfer is 0.5. The values of the parameters needed to obtain Ro are n = 1.592, K~ = 0.475, and 4D= 0.06 f 0.03. With these parameter values, the value of Ro obtained was 17 f 2 8,. The Foerster critical radius of energy transfer from the polystyrene monomer traps to the HPB chromophores was also calculated from the overlap of the monomer emission and quencher absorption. Since the quantum yield of emission of the monomer is temperature dependent (see Figure 1l ) , the Foerster critical radius is as well. The quantum yields of fluorescence of the monomer in neat polystyrene film obtained using the diffuse reflectance method were 0.17 f 0.08, 0.14 f 0.06, 0.07 f 0.04 at 15, 30, and 58 K, respectively. Using these values and the same values for n and K ~ the , Foerster critical radii at 15, 30, and 58 K were determined to be 18 f 2, 17 f 2, and 16 f 2 A, respectively. These values are all essentially the same as the excimer-HPB value of 17 f 2 A. The increased fluorescence quantum yield of the monomer compensates for the decrease in the monomer-HPB overlap compared to the excimer-HPB overlap (see eq 4). 4. Discussion
At room temperature and at 191 K, the polystyrene excimer emission intensity is quenched dramatically in copolymer films containing relatively small amounts of the photostabilizer HPB as seen in Figure 9. As shown previously,' it is possible to predict the extent of this quenching that is due to Foerster dipole-dipole energy transfer from the donor, the excimer, to the quencher, the HPB chromophore. The pertinent expression^^^-^^ relating the ~
(33) Stryer, L.; Haugland, R. P. Energy transfer: a spectroscopic ruler. Proc. Natl. Acad. Sci. U.S.A. 1967, 58, 719. (34) Foerster, Th. 10th Spiers memorial lecture: transfer of electronic excitations. Discuss. Faraday SOC.1959, 27, 7. (35) Eisenthal, K. B.; Siegals, S. Influence of resonance transfer on 1uminescence decay. J . Chem. Phys. 1964, 41, 652.
. 2 .3 . 4 . 5 Mole % HPB
Figure 14. Dependence of the ratio of the polystyrene excimer fluorescence intensity, I,, to the corrected excimer fluorescence intensity, I , on the content of the HPB chromophore in the copolymer film at 296 K (+) and 191 K (0). The lowest solid line is the calculated quenching efficiency due to long-range dipole-dipole energy transfer from the excimer to HPB. The points marked by the asterisks are indicative of precursor quenching at 296 K.
Foerster critical radius Ro to the steady-state emission intensities are
f = A'+
exp(y2)[ 1 - erf(r)]
f = (40 - 41/40 Co = 3 0 0 0 / ( 2 ~ ~ / ~ N R 2 ) in which $o and 4 are the emission quantum yields of the donor in the absence and presence of an acceptor of concentration C, y is termed the quenching efficiency, and N is again Avogadro's number. Using the "theoretical" Foerster critical radius of 17 8, (see section 3.3.3), the lower curve in Figure 14 was obtained by numerical evaluation of eq 5. The large difference between this curve and the experimental points indicates that other energy-transfer mechanisms are significant in these polymers. The significance of these other mechanisms in quenching the excimer emission can be seen by simply dividing the experimentally obtained Io/I values by the corresponding 'theoretical" values from the lower curve in Figure 14. The resulting data points at 296 K are shown in the figure also. The corresponding 191 K points are the same within experimental uncertainty. In our previous work3 we found that the fluorescence decay kinetics of films at room temperature containing less than about 0.0527 mol % HPB were essentially the same as that of pure polystyrene and therefore concluded that the dipole-dipole mechanism of quenching was not significant in films spanning the 0 . 5 2 7 mol % range. Furthermore, any mechanism of direct quenching of the excimer should result in a change in the fluorescence decay kinetics. Since the kinetics and the predicted steady-state quenching (the lower curve in Figure 14) both indicate that the dipoledipole mechanism is not significant over this range, then we must conclude that another mechanism is responsible. Since the kinetics do not change over this range, we must conclude that the quenching is the result of inhibiting the formation of the excimer, Le., quenching of the precursor of the excimer. This finding of precursor quenching of the excimer in polystyrene validates the notion that excimers are formed as the result of electronic excitation migrating in polystyrene to an excimerforming site. These data are consistent with the hypothesis that the HPB traps this mobile excitation and thus inhibits the formation of the excimers. Therefore, the data points in Figure 14, formed from the ratio of the experimental values of I o / I and the
Copolymer Films of Styrene predicted values of l o / I , are indicative of the degree of precursor quenching. Further examination of Figure 14 indicates that about 15% of the excimer emission cannot be quenched by precursor quenching at room temperature or 191 K, i.e., the slope of the precursor quenching curve seems to approach zero for HPB contents greater than about 0.2 mol %. If we assume that the copolymer films are homogeneous throughout and that the energy migration process is accurately modeled by a three-dimensional random walk, then the most straightforward explanation of this experimental result is that about 15% of the excimer emission results from the direct excitation of phenyl units in excimer-forming sites, which subsequently rapidly form excimers. This would suggest that the percentage of phenyl units in excimer forming sites is about 8%, since an excimer-forming site contains two phenyl units. This is much larger than previously estimated concentrations of excimer forming If, as is more likely, the polymers are not homogeneous throughout, then there are several other possible explanations of the limit in quenching of the excimer emission. For example, if the distribution of the quencher HPB in the copolymers becomes increasingly less random as its content is increased, then we might expect regions of relatively high and low HPB content. This could result from polymerization reactivity differences of the initial materials or from increased coiling and clustering of similar pendant groups during the casting process. The excimer emission from the areas of low HPB content would not be efficiently quenched. Additionally, the model of a three-dimensional random walk may not be valid when the excitation lies near the surface of the film or, perhaps, near the end of a polymer segment. In our previous work3 we obtained an estimate of the fraction of phenyl units in excimer-forming sites based on data such as those in Figure 14. The fraction obtained of 1 X is 2 orders of magnitude smaller than the estimate based on the proposition that 15% of the excimer emission results from direct absorption into excimer-forming sites. This suggests that the 15% limit is largely due to reasons related to the inhomogeneities of the samples or end/edge effects of the copolymers. This suggestion is consistent with our finding that polystyrene excess precursor quenching is more complete in a copolymer of styrene with 2,3,4,5,6-pentafl~orostyrene,~~ a polystyrene copolymer with a more uniformly homogeneous distribution of extrinsic traps. Figure 13 demonstrates that the monomer fluorescence intensity is also quenched significantly in copolymer films containing relatively small amounts of the quencher HPB at 15, 30, and 58 K. As with the case of the excimer, it is possible to predict the extent of this quenching resulting from Foerster dipole-dipole energy transfer from the donor, the monomer, to the quencher, the HPB chromophore using eq 5. Using the "theoretical" Foerster critical radii of 18 and 17 A (see section 3.3.3), the lower curves in Figure 15 were obtained by numerical evaluation of eq 5. The two curves predict the extent of dipole-dipole quenching at 15 and 30 K, respectively. The large difference between each of these curves and the corresponding experimental points suggests that precursor quenching of the monomer is also prevalent in these copolymers at low temperatures. This offers further validity to the notion of electronic energy migration in these polymers. The degree of this precursor quenching was obtained by dividing the experimentally obtained vahes by the corresponding "theoretical" values given by the lower curve in Figure 15. The resulting data points at 15 and 30 K are shown in the figure also and are the same within experimental uncertainty, as are the data at 58 K, which are not shown. As with the excimer, about 15% of the (36) Gelles, R.;Frank, C. W. Energy Migration in the Aromatic Vinyl Polymers. 2. Miscible Blends of Polystyrene with Poly(viny1 methyl ether). Mocromolecules 1982, 15, 741-747. (37) Sienicki, K.;Bojarski, C. Studies of Electronic Energy Migration and Trapping in Styrene Copolymers. Macromolecules 1985, 18, 2714-2719. (38) Sienicki, K.;Bojarski, C. Studies of electronic energy migration and trapping in polystyrene. Polym. Photochem. 1985, 6, 205-213. (39) O'Connor, D. 6.; Scott, G. W.; Coulter, D. R.; Yavrouian, A. Emission Spectra and Kinetics of Copolymer Films of Styrene and 2,3,4,5,6-Pentafluorastyrene.Macromolecules 1991, 24, 2355-2360.
The Journal of Physical Chemistry, Vol. 95, No. 25, 1991 10259
r 16
c
14 12
I
9
10
I , 6 4
2 .2 .3 .4 .5 Mole % HPB Figure 15. Dependence of the ratio of the polystyrene monomer fluorescence intensity, Io,to the corrected monomer fluorescence intensity, I, on the content of the HPB chromophore in the copolymer film at 15 K (+) and 30 K (0). The two lowest solid lines are the calculated quenching efficiency due to long-rangedipoledipole energy transfer from the monomer to HPB at 15 K (the upper one) and 30 K. The points marked by the dollar signs and asterisks are indicative of precursor quenching at 15 and 30 K, respectively. .1
fluorescence intensity of the monomer cannot be quenched by quenching the precursor. It is reasonable that this value would be the same as was observed in the excimer quenching data if structural inhomogeneities are underlying the phenomena. Examination of the precursor quenching curves in Figures 14 and 15 indicates that the precursor quenching efficiency is independent of temperature. Assuming that the precursor quenching is the result of energy migration followed by single step dipoledipole energy transfer to a trap, then this suggests that energy migration in these polymers is also independent of temperature since the dipole-dipole energy-transfer rate is independent of t e m p e r a t ~ r e . ' ~ J ~(This ~ * ~assumes * ~ ~ that the pure radiative rate constant of the donor, the absorption spectrum of the acceptor, and the shape of the emission spectrum of the donor are approximately temperature independent.) Temperature independent energy migration is expected if the migration consists of a series of single-step dipole-dipole energy transfers from phenyl unit to phenyl unit. The precursor quenching curves of Figures 14 and 15 are approximately linear over a range of HPB content of 0 to -0.05 mol %. This linear dependence of l o / Z with quencher concentration is indicative of Stern-Volmer q u e n ~ h i n g . ~The ' ~ ~Stern-Volmer ~ model is applicable when the relative diffusion of the donor and acceptor is appreciable during the excited-state lifetime of the donor. Johnson41concluded, on the basis of studies of energy transfer to perylene and dimethyl terephthalate from n-isopropylcarbazole dispersed in polystyrene films, that energy migration functions similarly to diffusion at high donor concentrations. The donor (monomer) concentration in these copolymers is relatively high. The precursor quenching curves suggest that the energy migration in these films is similar to diffusion for relatively low quencher (HPB) content. Kilp and Guillet$2 while studying energy transfer in poly(viny1 phenyl ketone), observed curved Stern-Volmer plots. This curvature is expected if energy migration is rapid such that statistical mixing of the donor and acceptor does not occur during the excited state lifetime of the donor. This may be particularly pertinent for the copolymers of (40) Stern, 0.;Volmer, M. The extinction period of fluorescence. Phys. Z . 1919, 20, 183. (41) Johnson, G. E. Energy Migration and Transfer in Molecularly Doped Polymers. Macromolecules 1980, 13, 145.
(42) Kilp, T.; Guillet, J. E. Triplet Energy Migration in Poly(acrylophenone): Dependence on Polymeric Tacticity. Macromolecules 1981, 14, 1680.
10260 The Journal of Physical Chemistry, Vol. 95, No. 25, 1991
O'Connor et al. CHART I
+.-
M + hv 4 'MI* HPB hu HPB* ' M I * 'M,* 'Mn* 'MT* M hul 'MT* 'MT* M 'MT* ]MT* 'MT* M hY2 M 'MT*
a
+
monomer absorption
photostabilizer screening (absorption) energy migration populating of monomer trap + monomer trap fluorescence monomer trap nonradiative decay monomer trap intersystem crossing + monomer trap phosphorescence monomer trap triplet nonradiative decay lMn* EFS populating of excimer-forming site EFS E excimer formation E M + M + hu] excimer fluorescence E-M+M excimer nonradiative decay M + HPB* precursor quenching 'M,* + HPB 'MT* + HPB M + HPB* dipole-dipole transfer (monomer trap to HPB trap) E + HPB M+M+ dipole-dipole transfer (excimer trap to HPB* HPB trap) HPB* HPB + hu4 HPB fluorescence HPB* HPB HPB nonradiative decay
--+
-C
I
-C
,
00
.
, 50
I,
, e ,
100
. n r
150
200
T (K)
+
--
L
OO
20
40
60
1/T x 1000
Figure 16. (a) Plot of the relative phosphorescence intensity (0)and the relative fluorescence intensity (%) of the polystyrene monomer versus temperature. (b) Plot of the relative phosphoresence intensity (0)and fluorescence intensity (1)of the polystyrene monomer versus 1 / T . The solid line is the best fit of eq 8 to the phosphorescence data.
relatively high HPB content if the degree of nonuniform distribution of the quenchers increases with increasing quencher content as suggested earlier. We suggest that at least a portion of the curvature of the precursor quenching curves in Figures 14 and 15 is the result of incomplete statistical mixing of the donors and quenchers during the donor excited-state lifetime. Examination of Figure 12 shows that the polystyrene monomer fluorescence and phosphorescence both decrease with increasing temperature. A plot of the integrated phosphorescence intensity (370-570 nm) vs T i s shown in Figure 16a. If we assume that the total decay rate of the triplet state is the sum of a temperature-independent pure radiative rate constant, a temperature-independent nonradiative rate constant, and a temperature-dependent nonradiative rate constant, then we can write
where knr(7') is the temperature-dependent nonradiative rate constant. Ipand Ioare the phosphorescence intensities at temperature T and absolute zero, respectively. If we assume that the temperature-dependent term has an Arrhenius form Ae-€IRT,then l/Ip = l/Io
+ A'e-EIRT
(7)
A three-parameter (1 /Io, A', and E ) nonlinear least-squares fit of eq 7 to the data did not yield a satisfactory fit. Guillet et al.43
proposed the existence of two significant temperature-dependent nonradiative rate constants to explain the temperature dependence of phosphorescence emission intensity for a wide range of polymers. If we assume both temperature-dependent rates are of Arrhenius form, then eq 6 can then be written
+ A'exp(-E,/RT) + B'exp(-E2/RT)
l / I p = 1/I0
-
--
are A' = 3.3 f 0.3 and B' = 780 f 7 1 and fo = 1.02 f 0.02. The best fit is shown with the data vs 1 / T in Figure 16b. The smaller activation energy E , is in good agreement with the reported frequency of a torsional mode of the pendant phenyl groups in p o l y ~ t y r e n e . ~ ~The ? ~ ~larger activation energy E2 is in good agreement with the reported value of an out-of-plane vibrational mode of the phenyl groups of polystyrene."*45 Our single activation energy analysis of preliminary data23yielded a value intermediate between E , and E2. The integrated monomer fluorescence intensity is also plotted in Figure 16. The temperature dependence of the fluorescence is very similar to that of the polystyrene phosphorescence. The temperature dependence of the monomer emission intensity and the temperature independence of the precursor quenching suggest that the fluorescing monomer is a trap and different from the phenyl units involved in the energy migration. If we assume a perfectly homogeneous and uniform distribution of phenyl units in a polymer, then all phenyl units are essentially the same and each, when excited, has fixed probabilities for energy transfer to a neighbor or fluorescing or decaying by some nonradiative mechanism. The probability of each of these events is the same for all the phenyl units. In such a system, if the nonradiative decay rate is increased, for example by raising the temperature, then the relative fluorescence intensity will decrease as is the case with pure polystyrene. Additionally, the relative efficiency of energy migration to a neighbor will decrease with increasing nonradiative decay rate. However, in these copolymers, the precursor quenching efficiency, which is a measure of the energy migration efficiency, is temperature independent. Therefore, we conclude that the monomer fluorescence is associated with phenyl units which act as traps of the mobile excitation. Webber and Pratte similarly proposed the existence of mobile and nonmobile monomers in other poly(viny1 aromatic) systems to explain the saturation effects observed in singlet-singlet annihilation studies.46 The steady-state emission anisotropy spectra offer further evidence of electronic energy migration in these polymers. The polarization anisotropy of PS emission was constant within experimental error throughout the emission spectra at both 296 and 14 K (see Figure 6) in spite of the fact that two species are responsible for the emission, namely, the excimer and monomer. Moreover the emission is essentially depolarized. Since rotational reorientation of the chromophores is expected to be slow relative
(8)
A five-parameter (1 / I o , A', E , , B', and E2) nonlinear least-squares fit of eq 8 to the data yielded activation energies of E , / h c = 58 f 10 cm-l and E2/hc = 378 f 40 cm-I. The preexponential values (43) Somersall, A. C.; Dan, E.; Guillet, J . E. Photochemistry of Ketone Polymers. 1 I . Phosphorescence as a Probe of Subgroup Motion in Polymers at Low Temperatures. Macromolecules 1974, 7, 233-244.
(44) Sears, W. M.; Hunt, J. L.; Stevens, J. R. Raman spectra at low temperatures and depolarization ratios for styrene and polystyrene. J . Chem. P h p . 1982, 77, 1639-1644. (45) Sears, W. M.; Hunt, J . L.; Stevens, J. R. Raman scattering from polymerizing styrene. I. vibrational mode analysis. J . Chem. Phys. 1981, 75, 1599-1602. (46) Pratte, J. F.; Webber, S.E. Excited-State Annihilation Processes in Poly(viny1 aromatics) in Solution: Poly(2-vinylnaphthalene) and Poly(4vinylbiphenyl). Macromolecules 1984, 1 7 , 21 16-2123.
J . Phys. Chem. 1991, 95, 10261-10266
to the emission lifetimes particularly at 14 K, this suggests that the emission is from chromophores that were not initially excited but rather received their electronic excitation by electronic energy transfer. It should be emphasized that this result does not suggest that the average number of electronic energy-transfer steps is especially large since even an average of one or two steps would lead to essentially depolarized emi~sion.~'*~*
5. Model and Summary Chart I shows the photophysical model of energy-transfer processes in the HPB/PS copolymers. (47)Craver, F. W.;Knox, R. S. Theory of polarization quenching by excitation transfer 11. Anisotropy and second-neighbor considerations. Mol. P h p . 1971,22 ( 5 ) , 385-402. (48)Galanin, M. D. Trudy Fiziol. Inst. I . P. Pavlova 1950,5, 341.
10261
These studies of HPB/PS copolymer films have shown that relatively small amounts of HPB result in efficient quenching of the excimer and monomer emission at temperatures ranging from room temperature to 15 K. The preponderance of the quenching is the result of quenching of the precursor, the mobile exciton, with additional quenching the result of long-range dipole-dipole energy transfer from the monomer and excimer traps to the HPB. The energy migration process is temperature independent.
Acknowledgment. The research described in this paper was carried out by the University of California, Riverside, and the Jet Propulsion Laboratory, California Institute of Technology, and was sponsored by the Committee on Research, University of California, Riverside, and the National Aeronautics and Space Administration. Registry No. VHPB/S (copolymer), 81273-49-6.
On the Theory of Photoinduced Intramolecular Electron Transfer Reza Islampour+ and Sheng H. Lin* Department of Chemistry and Center for the Study of Early Events in Photosynthesis, Arizona State University, Tempe, Arizona 85287-1604 (Received: March 4, 1991; In Final Form: April 29, 1991)
A quantum mechanical theory of the photoinduced electron-transfer process in electron donor and acceptor systems in condensed media is developed using the time correlation function formalism followed by the cumulant expansion of Kubo. The flexibility of the theory allows one to easily incorporate displacement and rotation of potential energy surfaces, frequency shifts, and anharmonicity effects. The effect of anharmonicity on ET rate is examined on the assumption that the anharmonic motion can be described by the Morse potential.
Introduction The transfer of electrons from one molecule to another is one of the most fundamental processes in chemical and biological systems. Thus experimental and theoretical research on the subject has been actively pursued for many decades.IJ The theoretical developments include semiclassical extensions of the classical formalisms as well as quantum mechanical treatments. The classical theory of ET was developed in the late 1950s by Marcus.) From the consideration of the nonequilibrium polarization of the medium employing a dielectric continuum model for the solvent and with the aid of the transition-state theory, he derived an Arrhenius expression for the rate of ET processes. The same problem was investigated by Dogonadze and Levich4in terms of the polaron model. Levich and Dogonadze also advanced a completely quantum mechanical formulation using the generating function technique of Kubo and Toyozawa.s In quantum mechanical description, the nonadiabatic ET process is conceptualized as radiationless transitionsbs between vibronic levels. H ~ p f i e l d , ~ in a semiclassical treatment, by using the Forster-DexterlO energy-transfer theory as a model, derived an expression for the rate of the electron-transfer processes in the biological systems. For further work on the theory, the reader is referred to ref 11. It should be noted that in these theoretical treatments the vibration modes of the system are described in the harmonic approximation, and it is assumed that there is no distortion for the potential energy surfaces during the E T process. In the present paper, we are concerned with the theoretical treatment of intramolecular electron-transfer processes. The theory is developed by using the time correlation function formalism followed by the cumulant expansion of Kubo. Without 'On sabbatical leave (1990-1991)from Department of Chemistry, Teacher Training University, 49 Mofateh Ave., Tehran, Iran. *To whom correspondence should be addressed at the Department of Chemistry.
referring to a particular vibration model for the nuclear motions, it is shown that the thermal average of the vibrational gap between two electronic states can be interpreted as the reorganization energy, which for the displaced oscillator is reduced to the conventional definition of this quantity. In contrast to the previous works, the flexibility of the present work allows one to easily incorporate the distortion, rotation, and anharmonicity effects of the potential surfaces. Numerical calculations will be performed to demonstrate the effect of anharmonicity, distortion, and rotation of potential surfaces on electron transfer. General Consideration The dynamical behavior of a quantum mechanical system is described by ( I ) Ulstrup, J. Charge Transfer Processes in Condensed Media; Berlin: Springer-Verlag, 1979;No. IO in the series "Lecture Notes in Chemistry". (2)For a brief survey of references, see: Mikkelsen, K. V.; Ratner, M. A. J. Chem. Phys. 1989,90, 4237. (3)Marcus, R.A. J. Chem. Phys. 1956,24,966;Annu. Rev. Phys. Chem. 1964,15, 155. (4)For a review, see: Levich, V. G. Adv. Electrochem. Electrochem. Eng. 1966,4,249. (5) Kubo, R.; Toyozawa, Y. Prog. Theor. Phys. 1955,13, 161. (6)Lin, S.H.J. Chem. Phys. 1966,44,3759. Lin, S.H.;Bersohn, R. J. Chem. Phys. 1968,48,2132.Freed, K.F.;Lin, S. H. Chem. Phys. 1975,1I, 409. Lin, S. H., Ed. Radiationless Transitions; Academic Press: London, 1980. (7)Henry, B. R.; Kasha, M. Annu. Rev. Phys. Chem. 1968, 19, 161. (8) Freed, K.F.; Jortner, J. J. Chem. Phys. 1970,52,6272. Engleman, R.; Jortner, J . Mol. Phys. 1970,18, 145. (9)Hopfield, J. J. Proc. Natl. Acad. Sei. U.S.A.1974,71, 3640;Biophys. J . 1977. 18. 311. (IO) Forster, T. Narunvissenschaften 1946,33, 166. Dexter, D. L. J. Chem. Phys. 1953,21,836. (11) Kestner, N.R.; Logan, J.; Jortner, J . J. Phys. Chem. 1974,78, 21. Ulstrup, J.; Jortner, J. J. Chem. Phys. 1975,63, 4358. Jortner, J. J. Chem. Phys. 1976,64,4860.
0022-365419 1 12095- 10261~ $02.50 10-.1 @~1991 American Chemical Society ---, I
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