3936
J . Phys. Chem. 1987, 91, 3936-3938
is obtained with the highest concentration of salt and suggests an increased order of the fluid. From these data it is clear that the addition of water can greatly alter the solvating properties of C 0 2 under supercritical conditions. Water imparts sufficient conductivity to C 0 2 solutions that ionic conduction becomes possible. It is likely that this observation coincides with the formation of carbonic acid and its partial ionization in the cell. Even more dramatic is the ability of water to facilitate the dissolution of the large tetralkylammonium salt. In the presence of the salt, voltammograms at microvoltammetric electrodes are undistorted, and the voltammetric data show that the ferrocenium cation is solvated to a greater degree. The dis-
solved salt dramatically alters the properties of supercritical carbon dioxide and may exist in highly organized structures, as has been proposed in toluene solution^.'^ Finally, we note that the addition of salt to the fluid can be used to alter diffusion rates. The actions of such modifiers on supercritical C 0 2 are profound and should prove useful in various future uses of this medium.
Acknowledgment. This research was supported by the National Science Foundation (CHE 85-00529) and the Office of Naval Research (MVN). (17) Geng, L.; Murray, R. W. Inorg. Chem. 1986, 25, 3115-3120.
Laser Flash Photolysis Study of the Magnetic Field Effect on the Photodecomposition of (2,4,6-Trimethylbenzoyl)dfphenylphosphlne Oxide in Mlcellar Solution Hisaharu Hayashi,* Yoshio Sakaguchi, The Institute of Physical and Chemical Research, Wako, Saitama 351-01, Japan
Mikiharu Kamachi, Department of Chemistry, Faculty of Science, Osaka University, Toyonaka. Osaka 560, Japan
and Wolfram Schnabel Hahn-Meitner-Institut fur Kernforschung Berlin, Bereich StrahlenChemie, D- 1000 39, Federal Republic of Germany (Received: April 22, 1987)
The decay of the radical pair of the diphenylphosphonyl and 2,4,6-trimethylbenzoyl radicals in a sodium dodecyl sulfate micelle was found to be affected at room temperature by magnetic fields. The lifetime of the radical pair at 0 T was 140 ns, but an extra component with a lifetime of 680 ns appeared at 1.2 T for the decay of the radical pair other than the decay with a lifetime of 160 ns.
Introduction Recently, many chemical reactions through radical pairs and biradicals have been found to show magnetic field and isotope effects.' The effects have been proven to originate from the singlet @)-triplet (T,,,, m = 0, f l ) conversion of radicals and biradicak2-' In the course of our studies of the effects,5 we first carried out direct measurements of the magnetic field and isotope effects on the decay properties of the radicals in radical pairs with a laser flash photolysis techniqueG6 Almost all of the studies of the magnetic field and isotope effects, however, have hitherto been confined to the reactions of radicals involving atoms lighter than Ne. The spin-orbit interaction of atoms heavier than F is considered to enhance the S-T, conversion rate and then to weaken the effects on the reactions of heteroorganic radicals containing such heavy atoms. In the previous paper^,^^^ we carried out laser flash photolysis studies (1) For example, see: Molin, Yu. N., Ed. Spin Polarization and Magnetic Effecrs in Radical Reactions: Elsevier: Amsterdam, 1984. (2) (a) Hayashi, H.; Itoh, K; Nagakura, S. Bull. Chem. SOC.Jpn. 1966, 39, 199. (b) Itoh, K.; Hayashi, H.; Nagakura, S. Mol. Phys. 1969, 17, 561. (3) Closs, G. L. J . Am. Chem. SOC.1969, 91, 4552. (4) Kaptein, R.; Oosterhoff, L. J. Chem. Phys. Lett. 1969, 4, 195. (5) For example, see: Hayashi, H. Sci. Pap. Inst. Phys. Chem. Res. (Jpn.) 1986, 80, 87. (6) (a) Sakaguchi, Y.; Nagakura, S.; Hayashi, H. Chem. Phys. Lett. 1980, 72,420. (b) Sakaguchi, Y.; Hayashi, H.; Nagakura, S. J . Phys. Chem. 1982, 86, 3177.
0022-3654/87/2091-3936$01.50/0
of the reactions of germanium- and sulfur-centered radicals and found some magnetic field effects on their dynamic behavior. In the present Letter, we report on the results of a magnetic field effect on the photodecomposition of (2,4,6-trimethylbenzoy1)diphenylphosphine oxide (TMDPO) in a micellar solution of sodium dodecyl sulfate (SDS) at room temperature. To the best of our knowledge, this is the first observation of the effect on a reaction of a phosphorus-centered radical by a laser flash photolysis technique. Experimental Section Laser flash photolysis experiments in the presence and absence of a magnetic field were performed with the same apparatus that has been described el~ewhere.~Degassed solutions of TMDPO were excited at room temperature by the fourth harmonic (266 nm) of a Nd:YAG laser. The pulse width of the fourth harmonic was 5 ns. The time dependence of the transient absorbance ( A ( t ) ) was recorded with a transient recorder (10 ns/division). Here, the time of laser excitation is taken as t = 0 ns. The lowest magnetic field generated by a counter current for canceling the residual field of the employed electromagnet was less than 0.2 mT. Hereafter, the experiments under the lowest field are denoted (7) Hayashi, H.; Sakaguchi, Y.; Mochida, K. Chem. Lett. 1984, 79. (8) Hayashi, H.; Sakaguchi, Y.; Tsunooka, M.; Yanagi, H.; Tanaka, M. Chem. Phys. Lett. 1987, 136, 436. (9) Sakaguchi, Y.; Hayashi, H. J. Phys. Chem. 1984, 88, 1437.
0 1987 American Chemical Society
The Journal of Physical Chemistry, Vol. 91, No. 15, 1987 3937
Letters
(TMDPO)
* 0.2
2z
C
3
e
ow - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
0 \
~
W 0
I
0
z 0.1 a
I
I
I
-
I
I
1
I
I
t / p
m
Figure 2. The time dependence of the transient absorbance ( A ( t ) )for
2
a micellar SDS solution of TMDPO observed at 340 nm (a) in the absence and (b) presence of a magnetic field of 1.2 T. The concentrations of SDS and TMDPO are 0.08 and 0.00135 mol dm-), respectively.
5
0 3 00
350
(a1 B = O T
LOO
X/nm Figure 1. Reaction scheme for the photodecomposition of (2,4,6-tri-
methylbenzoy1)diphenylphosphine oxide (TMDPO) and the transient absorption spectrum observed at a time delay of 40 ns after excitation of a micellar SDS solution of TMDPO. The concentrations of SDS and TMDPO are 0.08 and 0.00067 mol dm-', respectively.
as those in the absence of a magnetic field.
c
'1 C
3
-a 0.5 7 c
Results and Discussion Kamachi et al.1° studied the photodecomposition of TMDPO in benzene with the transient ESR technique and found signals due to the diphenylphosphonyl and 2,4,6-trimethylbenzoyl radicals in the submicrosecond to microsecond time range. The former radical has a g value of 2.0035 and a hyperfine (HF) structure of 36.5 mT (31P)and the latter has a g value of 2.0008 and no HF structure. Therefore, a radical pair of these radicals is considered to be produced upon photolysis of TMDPO as shown in Figure 1. A ( t ) curves of a micellar SDS solution of TMDPO were measured in the wavelength region 325-600 nm. Figure 1 shows the time-resolved absorption spectrum observed in the absence of a magnetic field at a delay time of 40 ns after laser excitation. The intensity of this spectrum decreased monotonously with increasing delay time until 9 ws and no other transient species appeared in the delay time range 0-9 ps. The position and shape of the transient spectrum shown in Figure 1 are almost the same as that already obtained by Sumiyoshi et a1.I' with laser flash photolysis of TMDPO in dichloromethane. Since they assigned their spectrum to the diphenylphosphonyl radical, the spectrum observed in the present study can also be assigned to the same radical. No precursor of this radical could be observed in both studies. Therefore, the precursors of this radical are considered to be too short-lived to be detected with the nanosecond-laser flash photolysis techniques. A ( t ) curves a t 340 nm were measured in the magnetic field range 0-1.2 T. The curves observed in the absence and presence of a magnetic field of 1.2 T are shown in Figure 2. Each of these curves has an initial decay component and nearly constant part at later times. In comparison with our previous results on the magnetic field effects on A(t) curve^,^ the initial decay and nearly constant components are considered to correspond to the decay of the diphenylphosphonyl radical in the generated radical pair (10) Kamachi, M.; Kuwata, K.;Sumiyoshi, T.; Schnabel, W. J . Chem. SOC.,Perkin Truns. 2, submitted for publication. (1 1) (a) Sumiyoshi, T.; Henne, A.; Lechtken, P.; Schnabel, W. Z . Nuturforsch. A 1984, 39, 434. (b) Sumiyoshi, T.; Schnabel, W.; Henne, A,; Lechtken, P. Polymer 1985, 26, 141.
t'/ps 1.o
1
( b ) B =1.2 T
t'/p Figure 3. An analysis of the observed time dependence of the transient
absorbance ( A ( t 3 )using the method of least squares: (a) at B = 0 T, the A(r? curve is analyzed by a set of two exponential functions; (b) at E = 1.2 T, the A(?? curve is analyzed by a set of three exponential functions. Here, t' is taken as t - 70 ns and E is the strength of the applied magnetic field. and a combination of escaping radicals and cage products, respectively. As shown in Figure 2, a magnetic field of 1.2 T was found to reduce the decay rate of the radical pair but not to change the nearly constant part appreciably. The A ( t ) curves observed below 0.1 T were almost the same as that at 0 T; the curves observed in the magnetic field range 0.75-1.2 T were almost the same as that at 1.2 T; and the curves observed in the magnetic field range of 0.1-0.75 T lie between the curves observed at 0 and 1.2 T. The magnetic field effects observed in a low magnetic field (usually below 0.1 T) can usually be explained by the HF coupling mechanism.'J* The effect on the A ( t ) curves of the present study
3938
J . Phys. Chem. 1987, 91, 3938-3943
is much smaller than those observed in the photoreduction of carbonyl molecule^.^^^ Thus, the effect due to the HF coupling mechanism is considered to be too small to be detected in the present reaction in spite of the large HF coupling constant of P (36.5 mT). The decrease in the decay rate of the A ( t ) curve observed above 0.1 T in the present study can be explained by a relaxation mechanismI2 as shown in the following paragraph. The A ( t ) curves observed in the time range t = 70 ns to 9 ps in the absence and presence of a magnetic field of 1.2 T could be analyzed well by sets of two and three exponential functions, respectively. The results of the analysis using the method of least squares are shown in Figure 3 and by the following equations: at 0 T A(t’) = 0.8923 exp(-t’/139 ns)
+ 0.1077 exp(-t’/75
ps)
(1)
at 1.2 T A(?’)= 0.7296 exp(-t’/l60 ns)
+ 0.1498 exp(-t‘/677
ns)
+
0.1206 exp(-t’/100
ps)
(2)
Here, t ’ = t - 70 ns. Because the S/N ratios of the nearly constant components with lifetimes of 75 and 100 ps, respectively, are very small, the magnetic field effect on these components is considered to lie within the experimental errors. However, an extra decay component with a lifetime of about 680 ns appeared at 1.2 T for the decay of the radical pair other than the decay with a lifetime (12)Hayashi, H.;Nagakura, S. Bull. Chem. SOC.Jpn. 1984,57, 322.
of about 160 ns. Such an extra component could not be observed at 0 T, where the decay of the radical pair can well be represented by an exponential function with a lifetime of about 140 ns: The appearance of the second decay component upon application of a magnetic field is characteristic of a magnetic field effect due to a relaxation mechanism in the case when a radical pair is prepared from a triplet precursor.I2 Thus, the radical pair produced in the photodecomposition of TMDPO in an SDS micelle can be shown to be prepared more efficiently from the triplet state of TMDPO than from its singlet excited states. Sumiyoshi et al. estimated the lifetime of triplet TMDPO as 0.3 ns.” Indeed, such a triplet state is considered to be too short-lived to be detected with conventional nanosecond-laser flash photolysis techniques. The second decay component observed in the presence of a magnetic field originates from the relaxation from the T+l levels of a radical pair to its To and S levels.I2 Thus, for the present reaction, such an extra component was found to be induced by a magnetic field. From an analysis of the 31PH F coupling tensor of the diphenylphosphonyl radical trapped in a single crystal,13 the 3s and 3p characters of 31Pwere obtained to be 0.1 1 and 0.60, respectively. Thus, the odd electron of this radical was found to be nearly localized on 31P. Therefore, in the present study, we could observe an appreciable magnetic field effect on the rate of reaction between phosphorus- and carbon-centered radicals with the laser flash photolysis technique. (13)Geoffroy, M.; Lucken, E. A. C. Mol. Phys. 1971,22, 257.
Adiabatic vs. Nonadiabatic Electron Transfer and Longitudinal Solvent Dielectric Relaxatton: Beyond the Debye Model Massimo Sparpaglione and Shad Mukamel*+ Department of Chemistry, University of Rochester, Rochester, New York 14627 (Received: April 29, 1987)
A theory for electron-transfer rates in a polar medium is developed using an expansion of the density matrix in Liouville space and utilizing the analogy with the problem of nonlinear optical line shapes. A separation of time scales between the populations and coherences (diagonal and off-diagonal elements of the density matrix, respectively) allows us to carry an approximate summation of the rate to infinite order in the nonadiabatic coupling. A closed expression for the rate and a novel criterion for adiabaticity, involving the entire frequency and wavevector-dependent dielectric function of the solvent c(k,w) are derived. A proper definition of the relevant solvent time scale in terms of c(k,w), which is not restricted to the Debye model, is obtained. The role of the solvent longitudinal dielectric relaxation in inducing the crossover from the nonadiabatic to the adiabatic regimes is analyzed.
I. Introduction The effects of solvation dynamics and relaxation on the rates of electron-transfer (ET) processes had received considerable attention It has long been recognized that the ET rate is usually controlled by the dynamics of dielectric fluctuations in the surrounding medium (the Favorable fluctuations, which make the initial and the final states temporarily isoenergetic, are crucial in inducing the electron transfer. The theory of Marcus6 uses a classical dielectric continuum formulation to express the rate to second-order perturbation theory in the electronic coupling matrix element Vbetween the initial and the final states. This theory had remarkable success in predicting the electron-transfer rate in terms of the static and the high-frequency dielectric constants of the solvent (to and E-, respectively). A parabolic dependence of the logarithm of the reaction rate (the activation free energy) on the exothermicity has been predicted and ~ o n f i r m e d . ~As the coupling matrix element V increases, Camille and Henry Dreyfus Teacher-Scholar.
this perturbative expression in V will no longer be valid. It is expected that for large V, or when the solvent motions are suf(1) Kosower, E. M. Acc. Chem. Res. 1982,15,259;J . Am. Chem. SOC. 1985,107,1 1 14. Kosower, E.M.; Huppert, D. Chem. Phys. Lett. 1983,96, 423. Kosower, E. M.; Huppert, D. Annu. Rev. Phys. Chem. 1986,37,127. (2) Wang, Y.; Eisenthal, K. B . J. Chem. Phys. 1982,77,6067. Millar, D. P.; Eisenthal, K. B. J. Chem. Phys. 1985,83,5076. (3) Heisel, F.;Miehe, J. A. Chem. Phys. 1985,98,233. (4) Weaver, M. J.; Gennett, T. Chem. Phys. Letf. 1985,113, 213. (5) McGuire, M.; McLendon, G. J. Phys. Chem. 1986,90,2549. (6)Marcus, R. A. J. Chem. Phys. 1956, 24, 966. For a review, see: Marcus, R. A. Annu. Reu. Phys. Chem. 1964,15, 155. Sumi, H.; Marcus, R. A. J. Chem. Phys. 1986,84,4894. (7) Levich, V. In Physical Chemistry: An Aduanced Treatise; Eyring, H., Henderson, D., Jost, W.,Eds.; Academic: New York, 1970;Vol. 9B. Dogonadze, R.,In The Chemical Physics of Solvation; Part A ; Dogonadze, R., Kalman, E., Kornyshev, A. A., Ulstrup, J., Eds.; Elsevier: Amsterdam, 1985; VOl. 1. (8) Jortner, J.; Ulstrup, J. J. Am. Chem. SOC.1979,101,3744. Redi, M. H.; Gerstman, B. S.; Hopfield, J. J. Biophys. J. 1981,35,471. (9)Miller, J. R.; Calcaterra, L. T.; Closs, G. L. J. Am. Chem. SOC.1984, 106, 3047.
0022-365418712091-3938$01,5010 0 1987 American Chemical Society
