J . Phys. Chem. 1986, 90, 771-774 D in benzene at 30 "C) from the dipole moment of chlorobenzene21 ( p = 1.59 D in benzene at 25 "C) and S-ethyl thioacetate2' gives a value of p = 100" which will be used in the present study. Calculations. The mean-squared dipole moment ( p 2 ) of the BTE molecule was calculated with standard procedures of the The variation of ( p 2 ) with the matrix multiplication parameters used in the calculation is summarized in Table IV; these variations were computed for small increments of each parameter from the values indicated as "main set". As Table IV shows, the most critical of the conformational energies are E,, and E,. Figure 4 shows the variation of ( p 2 ) and its temperature coefficient with these two energies; as one can see, the experimental value of ( w 2 ) is reproduced with Ed = 0.0 f 0.1 and E , = -0.2 0.2 kcal/mol; moreover, the value 103d(ln ( p 2 ) ) / d T 0.5 obtained with these energies is in very good agreement with the experimental result of 0.6. Consequently, the values of the energies associated with gauche states about S-CH, and CH2-CH2 skeletal bonds in the BTE molecule calculated from semiempirical potential functions are in satisfactory agreement with the values established for these parameters by the statistical analysis of the dipole moment and its temperature coefficient for this compound. This analysis suggests that the gauche states about CH2-CH2bonds which bring oxygen and sulfur atoms into close proximity have almost the same energy as the alternative trans state. A similar conclusion was obtained in an earlier works from the critical interpretation of the ' H N M R spectrum and dipole moments of thiodiethylene glycol dibenzoate (TDB). Therefore, the permutation of the sulfur and the labeled oxygen (0')atoms in the O=C-0'-CH2-CH2-S residue apparently does not change the rotameric population about CH2-CH2 bonds. It changes, however, the conformational energy E , associated with g states about the OCX-CH2CH2 bonds; the value of E , with respect to the corresponding t state decreases from ca. 0.5 kcal/mol for X = 0 to ca. -0.2 kcal/mol for X = S. The polarity of BTE is significantly lower than that of TDB. Thus, the mean-square dipole moment corresponding to BTE (4.1 D2) is roughly half the value of this quantity for TDB (8.5 D2).
*
(22) Flory, P. J. Macromolecules 1974, 7, 381.
77 1
The reason for this difference is the high sensitivity of ( p 2 ) to both pt and pe dipole moments and to the conformational energy E,. As Table IV shows, ( K ~ is) very sensitive to the contributions pt and pe corresponding to the dipole moments of the ester/ thioester and thioether/ether groups, respectively, and specially to p,. Both contributions are larger in the case of TDB than in BTE. Thus, in the case of TDB, these contributions p, = 1.81; pe = 1.21 D, corresponding respectively to ester and thioether residues, whereas in the case of BTE the residues are a thioester and an ether for which pt = 1.41; pe = 1.07 D, respectively. Since ( p 2 ) increases with pe and specially with p,, both contributions tend to give a higher mean-square dipole moment for TDB than for BTE. A simple way of evaluating the incidence of this effect is to calculate the dipole ratio E, = ( p 2 ) / x p o 2with xpo2 = 2(p: p:). The result for TDB (0,= 0.90) is about 38% higher than that for BTE (D, = 0.65); therefore, the combined effect of both p, and pe accounts for about 68% of the difference in mean square dipole moment of these compounds. It can be seen in Figure 2 that, when the molecule of BTE is in the all-trans conformation, the dipole moments p, of the two thioester residues are both roughly parallel to the vector obtained by addition of the two pe contributions. This positive correlation between all the contributions is diminished when either the CH2-CH, or CH2-S bonds are placed in a g state. Consequently, as Table IV shows, ( p 2 ) increases with both E , and E; (Le. with decreasing population of g states about these two bonds). As pointed out above, E; has the same value for both TDB and BTE molecules; however, E , N 0.5 and -0.2 kcal/mol for TDB and BTE, respectively; the contribution of the COX-CH2 bonds to the total polarity of the molecule will then be larger for TDB (X = 0) than for BTE (X = S). Thus, the effect of the conformational energy E,, adds up to that of the contributions p, and pe explained above, and the net result is that ( p 2 ) for TDB is roughly twice that for BTE.
+
Acknowledgment. Thanks are due to Mr. D. Delgado for his technical assistance. This work was supported by the CAICYT through Grant No. 513/83. Registry No. BTE, 65079-30-3.
Temperature and'Density Study of the Rayteigh Line Shape of Fluid N,O T. W. Zerda, X. Song, and J. Jonas* Department of Chemistry, School of Chemical Sciences, University of Illinois, Urbana, Illinois 61 801 (Received: August 29, 1985)
The Raman v l depolarized Rayleigh line shapes of N 2 0 are investigated at pressures varied from 8 bar to 2 kbar and over temperature range 298 to 373 K. Rotational, collision-induced,and cross-term contributions to the band shape and second moments are discussed and compared to previous results for COz, OCS, and CSz.
Introduction In recent studies of the depolarized Rayleigh scattering (DRS) of the linear molecules C02,1-5CS2,6-9and OCS,loJ'the line (1) A. De Santis and M. Sampoli, Mol. Phys., 51, 1 (1984). (2) A. De Santis and M. Sampoli, Phys. Lett. A , 101, 131 (1984). (3) H. Versmold and U. Zimmermann, Mol. Phys., 50, 65 (1983). (4) H. Versmold, Mol. Phys., 43, 383 (1981). (5) R. C. H. Tam and A. D. May, Can. J . Phys., 61, 1571 (1983). (6) B. Hegemann, K. Baker, and J. Jonas, J . Chem. Phys., 80, 570 (1984). (7) B. Hegemann and J. Jonas, J . Chem. Phys., in press. (8) P. A. Madden and T. I. Cox, Mol. Phys., 43, 287 (1981). ( 9 ) T. I. Cox and P. A. Madden, Mol. Phys., 39, 1487 (1980).
0022-3654/86/2090-077 1$01.50/0
shapes appeared to be sensitive to pressure and temperature changes. For all of these molecules the central part of the DRS spectra narrows with increasing density or decreasing temperature. In agreement with current t h e o r i e ~the ~ , ~observed effects were attributed to a diffusional type of rotational relaxation. The changes in the exponentially decaying DRS wings were explained in terms of collision-induced effects among which the dipole-ind u d dipole interaction (DID) was assumed to be the predominant mechanism. In the far wings of the DRS spectra of CS2 and OCS (IO) B. Hegemann and J. Jonas, J . Phys. Chem., 88, 5851 (1984) (11) B. Hegemann, Thesis, University of Illinois, 1984.
0 1986 American Chemical Society
772 The Journal of Physical Chemistry, Vol. 90, No. 5. 1986
Zerda et al.
another exponential part has also been distinguished and explained tentatively by quadrupole-induced dipole interaction~.6~~*'~J' Since no such region has been observed for CO,, we were prompted to study another linear molecule--N20. We will discuss the behavior with density and temperature of the N,O DRS line shape and compare it with that of CS,, OCS, and CO,. We also analyze second moments in order to evaluate the roles of the different mechanisms in determining the DRS spectrum of N 2 0 . Collision-induced scattering is also known to contribute to the Raman modes.7,10,12,13 We will study the band shape and second moments of the vl mode of N,O and compare the collision-induced contributions of the Raman band and the DRS line shape.
Experimental Section The high-pressure light scattering cell, pressurizing system, and details of the data acquisition and analysis method have been described previ0us1y.l~ All the spectra were obtained by using an argon-ion laser operating at the 488-nm line at a power of 1.O W. In order to avoid a leakage of the isotropic Rayleigh scattering into the DRS a narrow slit of 0.3-cm-' width was used to measure the center of the Rayleigh line. The frequency region from 5 to 50 cm-l was detected with a 0.8-cm-' slit and for the wings expanding up to 350 cm-' with a 2.4-cm-' slit width. For the v I and vj Raman VH line measurements a 1.2-cm-' slit was used. To eliminate stray light the high-pressure cell was darkened inside, the windows were antireflection coated, and N 2 0 gas was filtered. The detailed balance correction, Z(v) = Zex&)[ 1 + exp(-hcv/kr)], and X4 scattering factor correction have been applied to all DRS spectra. The data were analyzed after the dark current signal of the photomultiplier (typically 5 counts/s) had been subtracted. No other data corrections were applied for DRS spectra, but for Raman peaks it appeared necessary to subtract also a small background. The accuracy of measurements of the VH component of the v 3 mode appeared unsatisfactory due to the very small signalto-noise ratio; thus these results will not be discussed in detail. The low-frequency side of the Raman vl band is obscured by the hot bands; therefore only the high-frequency side was analyzed. Gaseous N,O, 98% pure, was purchased from Matheson and used without further purification. The densities of N,O at pressures up to 300 bar were taken from ref 15, while the densities at higher pressures were measured in our laboratory with the high-pressure densitometer.16 The densities are accurate to within 3%. Results For linear molecules, unlike for atomic fluids, the collisioninduced effects in the DRS and Raman spectra are overshadowed by contributions due to rotational relaxation. The intensity of the scattered light is proportional to the statistical averages of the effective polarizability tensor, A = A. + AA (IAo
+ MIz)= (IAolz) + 2(IAoMl) + (lAA12)
(1)
where A , = Ea, is the molecular polarizability in the absence of interactions and A.4 is caused by intermolecular forces. The allowed DRS intensity A , is given by (IAoI2) = 4/45pS2(1
(2)
+fi)
where the quantity (1 +fi) is the static angular correlation factor and p is the number density. For molecules with large polarizability anisotropy 6 = (aIl - a I ) / ( a I , 2aI), (IAo12)is the C 0 , 5 and dominant factor in eq 1. This is the case for C02.1.5Since for N,O 6 equals 3.03 and is larger than the an-
+
N,,'9"
(12) (13) ( 198 1). (14) (15) (16) (17) (1981).
J. Schroeder and J. Jonas, Chem. Phys., 34, 11 (1978). T. W. Zerda, S. Perry, and J. Jonas, Chem. Phys. Le??., 83, 600 S. Perry, T. W. Zerda, and J. Jonas, J . Chem. Phys., 75,4214 (1981). L. J. Hirth and K. A. Kobe, J . Chem. Eng. Dara, 6, 229 (1961).
B. Wiegand and J. Jonas, unpublished results. M. Sampoli, A. De Santis, and M. Nardone, Can, J . Phys., 59, 1403
\ FREQUENCY [cm-l]
Figure 1. DRS line shape of N 2 0 at 298 K and density 0.91 g/cm3. Arbitrarily chosen regions between 40 and 110 cm-l and another above 140 cm-' were fitted to exponentially decaying functions and results are shown as broken lines.
isotropies of any of these molecules, we may expect that the allowed intensity will dominate the total intensity of the DRS spectrum. Of course the question of how the ( IAo12)intensity is distributed on the frequency scale remains unresolved, but it is believed that for linear molecules the J-diffusion model should give a reasonable a p p r o ~ i m a t i o n . ~De , ~ Santis and Sampoli' showed that even for the very dense liquid COz the orientational spectrum extends up to 200 cm-I; for N 2 0 with a smaller inertial moment (66.4 X lo-@ g cmz vs. 71.8 X g cmz for COz) this frequency limit may well be exceeded. Statistical averaging of eq 1 can be performed assuming only radial correlations but more accurate results require taking into account also angular-radial correlations. It was shown by Kielich'* that considering only density fluctuations of the liquid and ignoring any orientational statistical dependence leads to a vanishing cross-term contribution 2( IAoAAl) as only the collision-induced (CI) term ( lAAIz) will be nonzero. The importance of cross terms has been elucidated by the computer simulation studies by Frenkel and McTagueI9 and most recently by Ladanyi.20%21 CI band shape analytical calculations are very difficult even for the simplest case of atomic fluids and for molecular fluids the exact analytical calculations are virtually impossible. For atoms the center-center model of interactions can be used, but for molecules this should be replaced by the more realistic site-site model drastically increasing the complexity of calculations.20~21 Thus, CI contours for the molecular case can be found only through a computer simulation study. The results will depend upon the assumed intermolecular potential' and, more importantly, on the origin of the CI effects. The DID model is most commonly used, but there are also others such as the multipole-dipole22 or the frequently reported electronic overlap theory23which however has not been often used because of a lack of knowledge regarding this interaction as well as due to difficulties in evaluating statistical averages. There are no molecular dynamics calculations known for N,O so we may only speculate on the general intensity distribution caused by CI effects and by the cross terms assuming that they behave similarly to those found for C02.20,21The CI term contributes to the low frequency as well as to the far wing of the DRS line. The low-frequency region of CI intensity may be attributed to translational diffusion while the central and far frequency regions belong to a librational type of molecular motion.24 The (18) (19) (20) (21) (22) (23) (24) (1980).
S. Kielich, J . Phys., 43, 1749 (1982). D. Frenkel and J. P. McTague, J . Chem. Phys., 72, 2801 (1980). B. Ladanyi, J . Chem. Phys., 78, 2189 (1983). B. Ladanyi and N. E. Levinger, J . Chem. Phys., 81, 2620 (1984). A. D. Buckingham and G. C. Tabisz, Mol. Phys., 36, 583 (1978). J. A . Bucaro and T. A. Litovitz, J . Chem. Phys., 54, 3846 (1971). B. Guillot, S. Bratos, and G. Birnbaum, Phys. Rea. A , 22, 2230
The Journal of Physical Chemistry, Vol. 90, No. 5, 1986 773
Rayleigh Line Shape of Fluid NzO TABLE I: DRS Line Shape Analysis Parameters for N20at Different Temperatures and Pressures AI,
M(2),
M(2)/ Mh(2)
N4)/ M(2)
25.3 25.1 28.7 31.2 35.2
1260 1280 1290 1390 1460
1.20 1.22 1.23 1.33 1.40
3568 3644 4290 4680 5195
0.74 0.80 0.91 1.oo 1.05
25.4 25.4 30.3 31.9 35.6
27.6 28.1 29.0 29.6 30.5
1360 1420 1490 1510 1580
1.20 1.25 1.31 1.33 1.39
3842 4018 4585 4692 5241
0.74 0.80 0.91 1.oo 1.05
29.1 29.3 30.8 32.8 34.1
27.5 29.5 30.1 31.2 31.2
1460 1490 1580 1610 1660
1.20 1.22 1.30 1.32 1.36
3992 4147 4652 4786 5289
0.74 0.80 0.91
28.4 31.5 33.4 33.9 35.3
28.7 29.9 30.5 31.5 32.0
1525 1580 1690 1720 1770
1.20 1.21 1.29 1.32 1.35
3959 4272 4643 5039 5349
g/cm3
cm-I
298
0.74 0.80 0.91 1.oo 1.05
323
348
373
41,
cm-' 26.1 27.9 28.1 28.6 29.8
P,
T, K
1.oo
1.05
lo
I
+ Mc'(2) + McR(2)
c
~ " ' ~ ~ " " " " ' ' ~ ' 50
0
100
I50
200
FREQUENCY [crn-l]
Figure 2. The depolarized Raman band shape of u1 mode of N 2 0at 323 K, density 1.05 g/cm3, and slit width 1.2 cm-I. The exponentially decaying wing was fitted to A exp(-u/ARAM)function and is shown as a
broken line.
cross terms have an important effect on the central part of the DRS spectrum, but due to their slow decay they also contribute to the intensity in the wings.'qZ0 Although this picture is helpful, it does not provide us with the information on how to separate these different contributions. Thus, we will discuss only the overall DRS line shape. In order to present our experimental data in an analytical form, the far wings and intermediate regions were fitted to two exponential functions of the form of A exp(-v/A) as illustrated in Figure 1. The decaying constants AI (found in the frequency region between 40 and 110 cm-') and A,, (for frequencies above 140 cm-') are presented in Table I. Of course, the boundary limits as well as the exponential forms of the fitting functions have been arbitrarily chosen. Similarly to the total intensity (eq l), the experimental second M(2) and fourth M(4) moments are sums of three contributions collision-induced f11(2),and due to orientational motion wR(2), cross McR(2) terms: M(2) = M O R ( 2 )
k-
TABLE 11: v I Raman Band of N 2 0 Second Moments M ( 2 ) , Reduced Moments M(2)/Mtb(2),and Slopes of the High-Frequency Wings, ARAM. Mtb(2)= 6kT/I T, K D. a/cm3 ARAM,cm-I M(2). cm-* M ( 2 ) / M h ( 2 ) 298 0.74 23.3 1050 1.01 0.80 23.9 1100 1.05 0.91 24.6 1130 1.08 1.oo 25.1 1100 1.05 1.05 27.3 1 I70 1.12 323
1.05
25.0 25.8 26.1 27.4 28.1
1150 1170 1250 1300 1320
1.01 1.03 1.10 1.15 1.16
348
0.74 0.80 0.91 1 .oo 1.05
27.8 28.1 28.1 29.6 32.5
1330 1350 1400 1450 1500
1.09 1.10 1.15 1.19 1.23
373
0.74 0.80 0.91 1.oo 1.05
29.8 28.6 29.3 29.9 29.4
1450 1470 1550 1600 1640
1.11 1.12 1.18 1.22 1.25
1.oo
(3)
In Table I we present the total second moment of the DRS along with the M(2)/iMth(2)ratio which measures the role of nonorientational effects as well as the ratio of M(4)/M(2) where @(2) = 6 k T / I is the orientational second moment for isolated molecule. The analysis of collision-induced effects in the Raman spectra is similar to that of DRS, except that the depolarized I V H component of Raman scattering also includes a contribution due to vibrational relaxation. Fortunately, the depolarization ratio of the v , mode of NzO is small (7 = 0.15) and the ZvH spectrum is more than 20 times broader than Ivv, so we may assume vibrational relaxation to be Consequently, the whole I V H spectrum may be attributed to rotational relaxation processes and collision-induced phenomena. Thus, the M(2) values for the v , band reported in Table I1 are composed only of orientational, CI, and cross contributions. When the v1 Raman band is displayed on a logarithmic scale (Figure 2) the experimentally decaying wings can be distinguished. The decay constants found via a fitting procedure are also enclosed in Table 11. The second moments of the Raman and DRS bands of NzO increase with density and temperature (Tables I and 11). This is a typical observation for small linear molecules'~7~20~21 but not necessarily for polyatomic symmetric top molecule^.^^^'^ The temperature dependence of M(2) can be partially explained as being due to rotational contributions which are a function of (25) T. W. Zerda, X.Song, and J. Jonas, Chem. Phys., 94, 427 (1985).
0.74 0.80 0.91
temperature, and for isolated molecules is given by Mh(2)= 6kT/Z. The ratio M(2)/Mh(2)indicates the temperature dependence of the other processes. This ratio for the v1 mode increases by 10% when the temperature is raised from 298 to 378 K, but for the DRS the M(2)/Wh(2) ratio is constant at low densities and decreases at highest densities. Basically the same mechanisms are responsible for both Raman and DRS line shapes so this finding is surprising at first glance. Raman scattering detects rotational relaxation of individual molecules while Rayleigh is also due to collective motion. In order to compare rotational second moments, the one obtained from the DRS line should be divided by a factor (1 +fz), where f2
= c ' / 2 ( 3 COSz%,,- 1)
(4)
is orientational pair correlation factor and Oil is the relative orientation of two molecules. This value is not known for N 2 0 but typically for linear molecules f2is small and does not exceed a value of 0.1. NzO has a small dipole moment which is responsible for the short-lived alignment between the molecules.z5 At constant density when the temperature is increased this coupling becomes weaker and one may expect that f 2 will slightly decrease with temperature. In the center-center interaction approximation, De Santis and Sampoli' showed the M'(2)contribution to DRS to
774
J. Phys. Chem. 1986, 90, 714-778
be much more density dependent than f l ' ( 2 ) contribution to the Raman second moment. Although the center-center model cannot be valid for N20,this observation by Sampoli made questionable any attempts for an evaluation of the f2factor from the measured M ( 2 ) values. This different @ ( 2 ) behavior also explains the larger second moments obtained from DRS than from Raman spectra. It is clear that we cannot limit the second moments density dependence to CI effects only. It was shown for 0, and COto-21 that cross terms can be even more sensitive to density increase. As this finding does not depend on the applied model of interaction, it may be regarded as a general rule and as such applicable also to N 2 0 . But any quantitative conclusions have to be based on theoretical calculations, preferably a molecular dynamics study. Of the three components of the ratio M ( 2 ) / W h ( 2 )(eq 3) the first two, orientation and CI, may be assumed to be temperature independent, so the temperature changes observed for the Raman band are attributed to the cross terms. This observation further confirms the importance of the w R ( 2 )to the total second moment. For DRS temperature dependence of the ratio M ( 2 ) / M h ( 2 ) is additionally perturbed by f 2 which as discussed previously is also a function of T . The physical meaning of the ratio M ( 4 ) / M ( 2 ) is not clear as the presence of collision-induced scattering precludes any meaningful evaluation of mean square torques from this quantity.' It is also more convenient to use this ratio rather than M ( 4 ) values only, since it partially reduces the collision-induced effects in the fourth moment. We choose to enclose this quantity in Table I as it may provide a useful criteria of comparison with possible future molecular dynamics calculations. The DRS second moments are basically determined by the intensity distribution in the far wings, where CI and cross terms are important and may overshadow the rotational term (we estimated previously that the orientational component extends beyond 200 cm-'). Thus, we assume that the slopes AI, describe with fair accuracy the frequency distribution of CI and cross terms. The slopes of the DRS and Raman wings (Tables I and 11) agree within 20%, but we should not expect them to be identical. Although mechanisms responsible for Raman and DRS scattering are similar, the DRS line is determined by the polarizability tensor while the Raman band by its derivative of normal coordinates. Also, in Raman wings the rotational component is probably more
pronounced than in the DRS region where the A,, slopes were found. Since the temperature and pressure dependence of the decaying constants A for both experiments are almost identical, this is an indication that CI and cross intensities are important in Raman wings.
Conclusions Similarly to other linear triatomic molecules (CO,, CS,, OCS), we have found collision-induced effects in both the Raman and Rayleigh scattering of N20. There are some discrepancies between the N20results and those obtained for CS,. In CS2 rotational relaxation is highly hindered due to its large moment of inertia and therefore the time scales for rotational motion and CI contributions are widely different and separable. This allows the assumption that only the CI component is responsible for the observed contour, and it may be separated into regions with different molecular motions responsible for collision-induced scattering (compare ref 6 ) . In N20with a smaller inertia moment, the situation is quite different as all the components are present and may not be separated. We were not able to distinguish separate regions in DRS spectra, but we observed exponentially decaying wings, another characteristic feature of the DRS lines is the shoulder observed at about 60 cm-I. The physical origin of this is not completely clear due to the reasons mentioned above. The slope A, reported in Table I may be assumed to characterize the shoulder's low-frequency side. We have not found other characteristic regions, as, for example, the one reported for OCS and CS, in the very far wings and attributed to higher-order multipole interactions. P r e ~ i o u s l y ,we ~ ~have ~ ' ~ found that second moments for depolarized Raman bands of chloroform and propine decrease with increasing density. Present findings of increase of M ( 2 ) with density for N20, along with the data reported in literature for COz, CS2, OCS, and N,, suggest that different mechanisms are responsible for line broadening in the case of linear triatomic and spherical top molecules. Acknowledgment. This work was supported in part by the National Science Foundation under Grant N S F CHE 8 1- 1 1 176 and the Department of Energy under Grant DOE DEFG 22-82 PC 50800. Registry No. N,O, 10024-97-2.
Radiative and Nonradiative Decay of Electronically Excited Ketyl Radicals of Some Substituted Benzophenones Hiroshi Hiratsuka,* Tatsuya Yamazaki, Yasuhiko Maekawa, Takumi Hikida, and Yuji Mori Department of Chemistry, Faculty of Science, Tokyo Institute of Technology, Ohokayama, Meguro-ku, Tokyo 152, Japan (Received: September 12, 1985)
Fluorescence spectra and fluorescence lifetimes have been measured for several substituted benzophenone ketyl radicals in poly(viny1 alcohol) films at 77 K. Fluorescence spectra were similar to that of the benzophenone ketyl radicals. Fluorescence lifetimes for most derivatives of the benzophenone ketyl radical are shorter than that of benzophenone ketyl radicals. An exceptionally strong intensity and long lifetime of fluorescence were observed for the ketyl radicals of dibenzosuberone. Radiative and nonradiative decay rate constants have been estimated for these radicals from fluorescence lifetimes and fluorescence intensities relative to that of benzophenone ketyl radicals. The slow nonradiative decay rate for dibenzosuberoneketyl radicals is discussed on the basis of the molecular structure.
Introduction The benzophenone ketyl radical is known to be an important intermediate in the photoreduction of benzophenone. A number of investigations have been reported on the optical absorption spectrum and the electronic structure of the ketyl The 0022-3654/86/2090-0774$01.50/0
dynamics of the excited states of the benzophenone ketyl radical have been studied by Some groWs.'5-'9 (1) G. Porter and F. Wilkinson, Trans. Faraday SOC.57, 1686 (1961). (2) A. Beckett and G . Porter, Trans. Faraday SOC.,59, 2038 (1963).
0 1986 American Chemical Society
