J. Phys. Chem. 1990, 94, 669-672 electric response can be probed for a single magnitude of solvation. Similar models have been proposed by others. Marcus and coworkers’ discuss a similar two-dimensional potential, but the reactive motion is modeled via transition-state theory and although useful for electron-transfer reactions, does not seem appropriate for isomerization reactions that couple to the solvent mechanical friction. Agmon et al.37consider a two-dimensional model where diffusion is considered in both dimensions. However, their model is for two internal coordinates, and the potential with which they numerically solve the diffusion equation may not be appropriate in describing the polarization coordinate. Conclusions This work demonstrates the dramatic importance of both static and dynamical dielectric effects on the photoisomerization of stilbenes. In particular, polar solvents are observed to lower the barrier to isomerization over the nonpolar solvent case, hence increasing the rate dramatically. For the case of n-alkanenitriles, which are unassociated solvents, the dielectric response is rapid enough that the more polar members of the homologous series better solvate the transition state. For the case of n-alkyl alcohols, which are associated solvents, the dielectric response lags the reactive motion and the aviscous activation barrier is higher for the more polar members of the homologous series. These observations are consistent with a two-dimensional view of the reaction, consisting of the twisting coordinate and a solvent polarization coordinate. These observations hold for 4,4’-dihydroxystilbene, 4,4’-dimethoxystilbene, and trans-stilbene. Although the above behavior is observed for symmetrically substituted stilbenes, it seems likely that they would be enhanced for asymmetrically substituted stilbenes or any reactive system with an initial dipole moment. Studies of the isomerization of 4(dialkylamino)-4’-azastilbeneand 4-(dialkylamino)-4’-nitratilbene show clearly that increasing solvent polarity leads to a decrease in isomerization consistent with the results reported here. (43) GBrner, H.; Gruen, H. J . Photochem. 1985, 28, 329. (44) (a) Garner, H.; Schulte-Frohlinde,D. Ber. Bunsen-Ges.Phys. Chem. (b) GBrner, H.; Schulte-Frohlinde,D. J . Mol. Struc. 1982,
1978,82, 1102. 84, 227.
669
Comparisons of isomerization rates in different solvents indicate a general trend with solvent type. In particular, the activation barrier decreases as the solvent changes from alkane to n-alkanenitrile to n-alkyl alcohol. This trend is not consistent with the trend observed for steady-state Stokes shift, implying that a simple dipolar model may not be able to explain the trend in activation energy. Comparisons with empirical measures of polarity suggest that hydrogen bonding may be of importance. Whether a specific solute/solvent complex exists in alcohol solvents (perhaps hydrogen bonding to the T system to stabilize the charge during isomerization) cannot be addressed by these studies. Supersonic jet studies of stilbene/solvent clusters may be able to address such issues. Lastly, 4,4’-dimethoxystilbene and 4,4’-dihydroxystilbene have very similar kinetics. In fact, the barrier height parameters agree to within the experimental error, and the viscosity dependences are very similar. The oxygen atom is the primary cause of the increased barrier height over that of tilb bene.^ The presence of the methyl group makes the reduced moment of inertia higher for dimethoxystilbene over that of dihydroxystilbene but seems to have very little effect on the viscosity dependence of the rate constant. This latter observation is consistent with the motion being diffusive as opposed to inertial-however, the small change in inertial moment ( 25%) could explain the failure to observe inertial effects. Also, the solvent dependence of these two solutes is similar in nitrile solvents but significantly different in alcohol solvents, presumably from a difference in hydrogen bond accepting ability of the hydroxy and methoxy groups. N
Acknowledgment. This work was supported by the donors of the Petroleum Research Fund, administered by the American Chemical Society, and by Grant No. CHE-8613468 from the National Science Foundation. We thank J. Brady for the use of the S L M 8000 fluorimeter and Beckman DU7 absorption spectrometer as well as for numerous discussions. Registry No. 4,4’-Dihydroxystilbene, 659-22-3; propanenitrile, 10712-0; methanol, 67-56-1; ethanol, 64-17-5; propanol, 71-23-8; butanol, 71-36-3; pentanol, 71-41-0; hexanol, 111-27-3; heptanol, 11 1-70-6;octanol, 11 1-87-5;nonanol, 143-08-8; decanol, 112-30-1; acetonitrile, 7505-8; butanenitrile, 109-74-0; pentanenitrile, 110-59-8; hexanenitrile, 628-73-9; heptanenitrile, 629-08-3; octanenitrile, 124-12-9;nonanenitrile, 2243-27-8;decanenitrile, 1975-78-6.
Pressure Effect on the Lifetime of Singlet Oxygen in Solutions Masami Okamoto,**tFujio Tanaka,* and Hiroshi Teranishit Faculty of Engineering and Design, Kyoto Institute of Technology, Matsugasaki, Sakyo- ku, Kyoto 606, Japan, and College of Integrated Arts and Science, University of Osaka Prefecture, Mozu-umemachi. Sakai, Osaka 591, Japan (Received: April 19, 1989)
Lifetimes of singlet oxygen (IO2; la,) were measured in four solvents as a function of pressure in the range of 0.1-400 MPa at 25 OC. It was found that the lifetimes decrease monotonically with increasing pressure in solvents examined. The activation volumes for the quenching by solvent fall in the range of -4 to -9 cm3/mol depending on solvent. The magnitude of which was well interpreted by taking into account the pressure dependence on the collision frequency estimated by the hard sphere model. From the analysis, it was concluded that the influence of pressure on the lifetime is attributed not only to the increase of collision frequency due to the increased solvent concentration by pressure but also to the extra increase of collision frequency characteristic to a given solute-solvent pair depending on the packing fraction and the size of molecules.
Introduction Although most studies on the reaction in solution under high pressure are concerned with thermal reactions, the influence of pressure on the photophysical and photochemical processes has recently begun to appear.l In particular, time-resolved studies give us invaluable information about the quenching mechanism Institute of Technology. *University of Osaka Prefecture.
+ Kyoto
0022-3654/90/2094-0669%02.50/0
and reactivity of excited states.24 To date, there have been no reports in the literature concerned with the pressure effect on the lifetime of oxygen in solution. (1) Schimidt, R.; Brauer, H.-D. Organic High Pressure Chemistry; Le Noble, w.J . 2 Ed.; Elsevier: Amsterdam, 1988; P 357. (2) Okamoto, M.; Teranishi, H. J . Phys. Chem. 1984, 88, 5644. (3) Okamoto, M.; Tanaka, F.;Teranishi, H. J. Phys. Chem. 1986, 90,
1055.
(4) Okamoto, M.; Teranishi, H. J . Am. Chem. Soc. 1986, 108, 6378.
0 1990 American Chemical Society
610
The Journal of' Physical Chemistry. Vol. 94, No. 2, I990
Singlet oxygen (IO2; la,) is the lowest energy electronically excited state and an important intermediate in photophysical and photochemical reactions. The lifetime in solution has been evaluated from observing the rate of bleaching of optical absorption of an oxidizable solute such as diphenylisoben~ofuran,~-~ and recently by observing directly infrared emission decay of IO2at ca. 1270 nm.p-14 Now, it is confirmed that the lifetime of singlet oxygen in solution depends strongly on the nature of solvent. Several mechanisms have been proposed to account for the marked solvent dependence and the solvent isotope In these studies, the decay process of IO2 has been recognized as electronic-to-vibrational energy transfer from IO2 to oscillators in surrounding solvent molecules. The most probable model is a relaxation based on exchange energy transfer which is independent of optical transition moments of oscilIators.llJ3 High pressure changes continuously the density of the solvent without changing temperature or solvent. The solvent-induced collisional quenching of lo2may be related to solvent density, so that it is of current interest to measure the influence of pressure on the magnitude of the lifetime of singlet oxygen in different solvents.
Experimental Section Zone refined grade anthracene (A; Tokyo Kasei) was used as supplied. Solvents were hexane, methylcyclohexane (MCH), methanol, and acetonitrile of spectroscopic grade from Dojin and used without further purification. Diphenylisobenzofuran (DPBF Aldrich) was purified by recrystallization from methanol/water. A laser photolysis experiment at high pressure was carried out with the 8-11spulse of a nitrogen laser (337 nm), at right angles to a xenon analyzing flash lamp. The details are described el~ewhere.~ Singlet oxygen (IO2;'Ag) was created by irradiating an aerated anthracene solution (ca. M) with the laser pulse. In the bleaching experiment of DPBF, the transmitted analyzing light intensities were monitored by a Hamamatsu R 928 photomultiplier terminated with 2 0 0 4 load resister, the output of which was offset to observe a small change in the transmitted light intensities and digitized with an lwatsu TS 8123 storagescope. All data were analyzed with a microcomputer that was interfaced to a digitizer. The sample solutions for photolysis were replaced by a new one every two or three shots of the laser pulse. The change in the concentration of DPBF with increasing pressure was corrected by taking into account the known compressibility of s01vents.l~ Temperatures were controlled at 25 f 0.1 "C. Pressures were measured with a calibrated manganin wire. Results The sensitized singlet oxygen creation and its decay in the presence of DPBF have been established5s6 A 3A*
hu
1A* + 3A*
-
.-+
+ 302 (32;) IO, (]A,)
'02('Ag)
kd
+ DPBF
+ IO2 ('Ag)
A
302 02;)
kr
IOSS of DPBF
4
(1)
(2) (3)
(4)
(5) Merkel, P. B.; Kearns, D. R. J . Am. Chem. SOC.1972, 94, 7244. (6) Adams, D. R.; Wilkinson, F. J . Chem. Soc., Forodoy Trans. 2 1972, 68, 586. (7) Peters, G.; Rogers, M . A. J. J . Am. Chem. SOC.1981, 103, 6759. (8) Gotman, A . A,; Gauld, I. R.; Hamblett, I . J . Am. Chem. SOC.1982, 104, 7098. (9) Krasnovsky, A. A., Jr. Photochem. Photobiol. 1979, 29, 29. ( I O ) Ogilby, P. R.; Foote, C . S. J . Am. Chem. SOC.1983, 105, 3423. ( 1 1 ) Hurst, J. R.; Schuster, G.B. J . Am. Chem. SOC.1983, 105, 5756. (12) Rogers, M. A. J. J . Am. Chem. SOC.1983,105, 6201. ( 1 3 ) Schmidt, R.; Brauer, H.-D. J . Am. Chem. SOC.1987, 109, 6976. (14) Hurst, J. R.; McDonald, J . D.; Schuster, G . B. J . Am. Chem. SOC. 1982. 104,2065. (15) Bridgman, P. W . The Physics of High Pressure; Bell: New York, 1958; p 128. Jonas, J.; Hasha, D.; Huang, S . G. J . Chem. Phys. 1979, 71, 3996. Schroeder. J.; Schiemann, V. H.; Sharko, P. T.; Jonas, J. J. Chem. Phys. 1977,66, 3215. Brazier, D. W.; Freeman, G. R. Con.J . Chem. 1969, 47, 893.
Okamoto et al. E
+
0
E 0 W
1.5c
1
0.1 MPa
TINE
NICROSECONO
/
Figure 1. Plots of relative transmittance against time for the bleaching of DPBF in M C H at two pressures. The solid curves were calculated by use of eq 5 by a nonlinear least-squares method. [DPBF] = 8.43 X M. TABLE I: Lifetimes of Singlet Oxygen (k,-') and Rate Constants for the Reaction between Singlet Oxygen and DPBF (k,)in Various Solvents at 25 OC and 0.1 MPa solvent kd-I/fis (lit.) k,/lO* M-I s-l (lit.) hexane 26 (3 1.4") 2.6 MCH 21 3.7 methanal 6.2 (10.4," 10: 7: Sd) 7.2 (8.1,b 8') acetonitrile 53 (35; 61: 54.4/778) 14.2 12.88) Reference 12. Reference 8. Reference 5. 'Reference 14. /Reference IO. EReference 7.
dReference 6.
TABLE 11: Values of A VD*and A VD*(Hs)for the Quenching of Singlet Oxygen by Solvent Molecules in Various Solvents at 25 O C and 0.1 MPa
hexane MCH methanol acetonitrile
0.60 0.61 0.40 0.45
0.52 0.55 0.51 0.53
-9 -6 -4 -6
f2 f2 f 1
i3
-9.7 -7.8 -5.4 -7.5
"The hard sphere diameter of oxygen do was estimated to be 0.35 nm.'* bValues at 25 OC and 0.1 MPa.
When reactions 1 and 2 are much faster than those of 3 and 4, and the initial concentration of IO2 is much smaller than that of DPBF [DPBF], the absorbance change of DPBF with time A ( t ) is given from the scheme as follows: A(t) = A ( a )
k,,
+ (A(0)-A(..)] = kd
exp(-k,,t)
+ k,[DPBF]
(5)
(6)
where A ( 0 ) and A ( m ) are the absorbances at t = 0 and t = a, respectively. As a preliminary experiment, we measured the triplet lifetime of anthracene in aerated MCH solution at high pressures. It was found that the lifetime of 3A* is less than 0.2 MUSat 300 MPa, which is much shorter than kob-l. Figure 1 shows the time dependence of relative transmittance at 420 nm in the bleaching of DPBF. The value of kob was determined by a nonlinear least-squares method based on eq 5 (Figure 1). The plots of kob against [DPBF] according to eq 6 yielded slopes k, and intercepts kd (Figure 2). The results at 0.1 MPa are listed in Table I together with published data. The solvent dependence on kd and
Pressure Effect on the Lifetime of Singlet Oxygen
The Journal of Physical Chemistry, Vol. 94, No. 2, 1990 671
I I
T 0
"y T
0
I
I
I
[DPBF] I
r M
I
GO
120
I
I
I
200
300
400
pressure I MPa
I
t a0
Figure 2. Plots of kobs against [DPBF] in MCH at various pressures.
[DPBF] was corrected by taking into account the known compressibility of solvent^.'^
k , in Table I is in good agreement with the results reported previously. As seen in Figure 3, the pressure dependence on kd is not large, but distinct. Since the application of high pressure changes considerably the molar concentration of solvent [SI, the intrinsic pressure dependence on kd is given by the bimolecular decay constant kD ( = k d / [ S ] as ) will be described below. The volume of activation AvD* was evaluated from the plots of In kDagainst pressure according to eq 7 , where K is the isothermal compresRT(d In kD/dP)T = -AVD* - R T K
I
100
(7)
sibility of the solvent. The values of RTKat 25 OC and 0.1 MPa were calculated from the available data.I5 The results are listed in Table 11. The pressure dependence on k, has a maximum value with increasing pressure, which may reflect the fast reaction of IO2 with DPBF competing with diffusion controlled process; i.e. the bimolecular reaction is accelerated with increasing pressure while the diffusion is retarded by the increase in solvent viscosity with increasing pressure. The kinetics and the mechanism of the reaction from the pressure dependence on k, will be described elsewhere. The present work focuses on the influence of pressure On kd.
Discussion The solvent dependence on the lifetime has been recognized as the radiationless process from IO2 to the solvent molecules. The earlier approach was made by Kearns et aleswho have proposed a Forster type energy transfer from electronically excited oxygen to vibrational levels of solvent molecules. Their theoretical consideration was supported by an empirical expression between the lifetime and the optical density of solvent in the infrared wavelength region. However, a number of the lifetimes in various solvents have revealed that the Kearns correlation is held only qualitatively in spite of various modifications.10J1*13J4 Concurrently, it has been experimentally found that the decay rate constant of IO2 is expressed as a sum of the quenching constant k x y intrinsic to the individual terminal oscillator XY in the solvent molecule^'^-'^
where Nxu is the number of times a particular X-Y pair occurs per one solvent molecule. Hurst and Schuster" have found for
Figure 3. Plots of In kd against pressure in various solvents. The activation volumes AV,' were evaluated from the slopes of the least-squares plots of In &/[SI) against pressure according to the equation In &/[SI) =A
+ BP + C P ~ .
a series of compounds containing a C-H bond in solvent that a correlation between kd and [C-HI is much better than that between kd and the Kearns optical solvent properties and proposed an alternative mechanism analogous to exchange energy transfer since the exchange mechanism is independent of optical transition moments. According to their theory, the bimolecular quenching rate constant for an oscillator in the solvent molecule is given by
kxy = zC FmFsR,
(9)
m.s
--
where Z is a term independent of the specific nature of solvent. F,,, and Fs are the Franck-Condon factors for the (0 m) vibronic s) vitransition of IO2 (lA ) to the ground state and the (0 brational transition ofthe oscillator X-Y in the solvent molecule, respectively. R,, is an off-resonance factor. They successfully interpreted the decreasing tendency of kxu for oscillators X-Y, 0-H > C-H > 0-D > C-D, by comparing the energy for the highest fundamental vibration of solvent with that for the oxygen vibronic transition. This idea was supported by Schmidt and Brauer,13 who interpreted quantitatively the solvent effect on the lifetime by estimating the parameters in eq 9. In these treatments by the exchange mechanism, k x y does not depend on the nature of solvent but only depends on the relative energy difference between oxygen and the oscillator. In the present high pressure study, the lifetime of IO2decreased definitely with increasing pressure in solvents examined. This is sharp contrast to the very small or neglegible temperature effect on the lifetime.'0J1~13 The decay constant of singlet oxygen is clearly related to the frequency of collision Z, between lo2and the solvent molecules and also to the energy transfer probability per collision P,. kd may be written as We consider the energy transfer process in hard sphere solvent since simple liquids are well approximated by the hard sphere liquid. When we suppose the energy transfer between a hard sphere solute molecule (diameter do) and a hard sphere solvent molecule (diameter ds), the bimolecular decay constant kD is written by eq 11, since Z , is given by using the radial distribution where p and function g(d,) at the closest approach distance &,I6
672 The Journal of Physical Chemistry, Vol. 94, No. 2, 1990 kBare the reduced mass and the Boltzmann constant, respectively. We assume here that P, is equal to CNxukxu, which is independent of solvent at 0.1 MPa as mentioned above. The application of high pressure causes spectral shifts in electronic and vibrational transition" that may affect the parameters in eq 9. However, such shifts induced by pressure up to a few hundred megapascals is similar in magnitude to that in solvents with different polarity at 0.1 MPa." Thus, we may reasonably assume that P, is independent of solvent and pressure. As a result, the pressure-dependent term in eq 1 1 is only g(d,). In previous work the contribution of g(d,) is not explicitly allowed, but in the present work we should take into account the pressure dependence on g(d,) relating to the solvent density. From eq 7 and 1 1 , we can obtain the activation volume by the hard sphere model AVD'cHS) = -RT[a In g(d,)/aP], - RTK
(12)
Hence, the pressure effect on the lifetime is attributed to the problem of that on g(d,). The radial distribution function has been applied to the systems such as vibrational relaxation'* and the chemical reactionsrgin solution. A suggestive application to the volume change for the contact-complex formation in hard sphere liquid has been made by Yoshimura and Nakahara," who used the radial distribution function at infinite dilution in hard sphere solvent. In the present case, the analytical expression of g(d,) at infinite dilution of IO2 is written as2'
where y is the packing fraction, given in terms of the solvent density p s by (16) Einwohner, T.; Alder, B. J. J . Chem. Phys. 1972,24, 269. (17) Offen, H. W. Organic Molecular Phorophysics; Birks, J. B., Ed.; Wiley: New York, 1973; Vol. I , p 103. Brauer, H.-D.; Schmidt, R.; Kelm, H. High Pressure Chemistry; Kelm, H., Ed.; D. Reidel: Boston, MA, 1978; p 521. (18) Delalande, C.; Gale, G. M. J . Chem. Phys. 1979,71,4804. Chesnoy, Chem. Phys. 1984,83, 283. Wild, E.; Klingshirn, H.; Maier, M. J . Photochem. 1984, 25, 131. Chatelet, M.; Tardieu, A,; Spreitzer, W.; Maier, M. Chem. Phys. 1986, 102, 387. (19) Northrup, S. H.; Hynes, T. J . Chem. Phys. 1979, 71, 871. Yoshimura, Y.; Nakahara, M. Bull. Chem. SOC.Jpn. 1987,60,69, and references cited therein. (20) Yoshimura, Y.; Nakahara, N . J . Chem. Phys. 1984, 81, 4080. (21) Grunke, E. W.; Henderson, D. Mol. Phys. 1972,24,269. Lebowitz, J. L.; Helfand, E.: Praestgaard, E. J . Chem. Phys. 1965, 43, 774.
Okamoto et al. (14) In eq 14, AIA and M , are Avogadro's number and the molecular weight of solvent, respectively. The values of d, and do were estimated from van der Waals volumes.22 The results are listed in Table 11. The packing fractions at 0.1 MPa and 25 OC calculated from eq 14 are also listed in Table 11. The value of g(d,) calculated increases with increasing pressure, for example, the value at 400 MPa is 2.12 times larger than that at 0.1 MPa in hexane. The activation volumes by the hard sphere model were evaluated from the plot of In g(d,) against pressure according to eq 12. The results are listed in Table I1 together with the experimental ones. As shown in Table 11, both values are in good agreement with each other, and the solvent dependence on the activation volume is also well interpreted by the simple hard sphere model. We may therefore conclude that the enhanced decay constant of the singlet oxygen by pressure is attributed not only to the increase of collision frequency due to the increased solvent concentration with compression but also to the extra increase of collision frequency characteristic to a given solventsolute pair depending on the packing fraction and the size of molecules. In conclusion, we have demonstrated that an approach from the density dependence of solvent by the application of pressure at constant temperature is hopeful for the study of photophysical processes. The present high pressure study tells us that the collision frequency is a factor that governs the lifetime of singlet oxygen in solution. Finally, it is noted that very small temperature dependence on the collision frequency a t 0.1 MPa was calculated in hard sphere liquid, for example, in methanol it increased by 20% on going from 27 to -38 O C . Similar magnitude of temperature dependence on the lifetime has been observed in a few solvents.i0.11s'3 Systematic and accurate measurements of the lifetime on the temperature effect may reveal the other factors controlling the lifetime in solutions as well as the collision frequency.
Acknowledgment. This work was partly supported by a Grant-in-Aid for Scientific Research from the Ministry of Education of Japan (No. 62540331). Registry No. MCH, 108-87-2; DPBF, 5471-63-6; oxygen, 7782-44-7; hexane, 110-54-3; methanol, 67-56-1; acetonitrile, 75-05-8; anthracene, 120-12-7. (22) Bondi, A. J . Phys. Chem. 1964,68, 441.
