J. Phys. Chem. 1985, 89, 3-4
is very likely as well that oscillatory convection is at the origin of the oscillations in emission (or absorption) intensity reported earlier in other photochemical systems.'-' This conclusion is to be related to the one that some of us reached about spatial dissipative structures previously supposed to be photochemically induced." Their Occurrence can also be interpreted as convective instabilities induced by evaporative cooling. Plessar also reached similar conclusions concerning some aspects of the fluorescence analysis of shallow layers of NADH solutions.I2
Olsen and Rosenberger'O for gases. For liquids such as chloroform, Epstein et a1.8 have estimated that a temperature gradient as small as A T / h = 0.015 OC/cm should be large enough to induce a time-dependent convection. This temperature gradient can be estimated from an approximate solution of the heat equation, provided one has access to experimental values of the heat loss, JQ, at the upper free surface. However, since
JQ = r,Lv
(1)
where Ja is the heat loss (cal-s-l), rethe rate of evaporation (gd), and Lv the latent heat of evaporation (cal-g-I), these values can be obtained from the data of Figure 2. On that basis, we estimate the gradient across a column of chloroform 4 cm high to be 0.05 OC/cm. This value is therefore consistent with the onset of time-dependent convection in unstoppered DMA/CHCI3 solutions. As a conclusion, it can be stated that the body of evidence in favor of the hydrodynamic hypothesis is now overwhelming in the case of the DMA/CHCI, system. As suggested by Epstein et it (10)
J. M. Olsen and F. Rosenberger, J . FIuid Mech., 92, 609 (1979).
3
Acknowledgment. We thank Dr. Dewel, Dr. Borckmans, and Dr. Walgraef to the Universitg Libre de Bruxelles for fruitful discussions. M.G. acknowledges a scientific and technical grant from the European Communities Committee. Registry No. DMA, 781-43-1; CHCl,, 67-66-3. (1 1) J. C. Micheau, M. Gimenez, P. Borckmans, and G. Dewel, Nature (London),305, 43 (1983). (12) S. C. Muller and T. Plesser in "Modelling of Patterns in Space Time", W. Jager, Ed., Lecture Notes in Biomathematics (1983), Springer, to be published.
Torsional Oscillation of the Isooctyl Radical in the Thiourea Canal Complex Studied by ESR Yasurii Hori, Hiroshi Ohno, Shigetaka Shimada, and Hisatsugu Kashiwabara* Nagoya Institute of Technology, Showa- ku, Nagoya 466, Japan (Received: August 1 , 1984)
Isotropic ESR spectra of the isooctyl radical, (CH,),CCH,C(CH,),, have been observed in the irradiated thiourea-isooctane complex in the temperature range between 77 and 318 K. The structure of the isooctyl radical has been determined and the temperature dependence of the hyperfine splittingswas explained by the simple formulation developed for torsional oscillation. The frequency of torsional oscillation of -C(CH3), group has been estimated to be 58 f 2 cm-l.
Introduction For unstable free radicals, a great amount of ESR studies have been reported. However, many of these studies were carried out at low temperature and poorly resolved spectra have been observed. In order to obtain highly resolved ESR spectra for unstable radicals, one may need a rather difficult technique; e.g., a continuous irradiation apparatus' or the adamantane matrix method.2 On the other hand, use of the thiourea canal complex is expected to give a useful simple method to observe the highly resolved ESR spectra, because this complex can be made very easily and the radical trapped in the canal may be very stable, and because the trapped radical is expected to undergo random motion since the diameter of canal is large. By using the thiourea complexes, isotropic ESR spectra have already been observed by Helcki and Fantechi, for cyclohexane and cycloheptane complexes, but they used a continuous irradiation apparatus. This report gives an example of the usefulness of thiourea complex to observe the isotropic spectra stably at high temperatures by a rather simple procedure, namely annealing of the irradiated sample. Experimental Section Samples were prepared by adding a desired quantity of isooctane (2,2,4-trimethylpentane) to a saturated methanol solution of thiourea at 5 OC. Complex formation was confirmed by DSC measurements. The complexes were sealed off in an ESR tube at -40 OC and y irradiated at liquid nitrogen temperature. (1) R. F. Fessenden and R. Shuler, J . Chem. Phys., 39, 2147 (1963). ( 2 ) S . DiGregoris, M. B. Yim, and D. E. Wood, J . Am. Chem. Soc., 95, 8455 (1973). (3) G. A. Helcke and R. Fantechi, Mol. Phys., 18, 1 (1970).
0022-3654/85/2089-0003$01 S O / O
First-derivative ESR spectra were recorded with 100-kHz modulation.
Results and Discussion ESR spectra were observed at 77 K after annealing the irradiated sample at various temperatures, and parts a and b of Figure 1 show the spectral change caused by annealing. The spectral shape of Figure l b was unchanged when annealed at a temperature between 233 and 313 K. Spectrum Ib has been assigned to the isooctyl radical as described later. From Figure l a it can be shown that the y irradiation at 77 K produces a small amount of isooctyl radicals and a large amount of unknown paramagnetic species in the thiourea-isooctane complexes. This unknown species decays by annealing faster than the isooctyl radical and gives a singlet-like spectrum with a peak-to-peak width of 3.2 mT and with a g value of 2.0104 which was obtained by the subtraction of spectrum l b from la. After the sample was annealed at 233 K, temperature-dependent ESR spectia were observed at various temperatures ranging from 77 to 318 K, and an example is shown in figure IC. The spectra observed at high temperatures have a narrower line width such as 0.16 mT at 293 K compared with 0.38 mT at 77 K. This result indicates that the radical is rather randomly rotating in the canal. All of the spectra were successfully simulated by assuming that the radical has six equivalent p protons and two equivalent /3 protons, and these hyperfine couplings are isotropic. At 77 K . the obtained hyperfine constant for six protons (hereafter named as aM)is 2.30 mT and that for two protons (a,) is 1.18 mT. The obtained g value is 2.0030 and the temperature dependence of the hyperfine coupling constants is shown in Figure 2. From these data, we asigned this radical to the isooctyl radical (CH,),CCH,C(CH,),, since no methyl radical was observed. This 0 1985 American Chemical Society
4
Letters
The Journal of Physical Chemistry, Vol. 89, No. I, 1985
'Hni
Figure 3. Conformation of the i s w t y l radical: solid lines and boxed etc., equilibrium state; dotted lines and H, etc., oscillating state.
where 0 is the dihedral angle between the p orbital and C-H bond, and Bo and B2 are empirical parameters. The contribution of BO was neglected, and B2 can be calculated as 4.60 mT since the methyl group is freely rotating and its splitting, aM,is 2.30 mT. Then the following equation was obtained for the methylene proton splitting:
1
3 mT
Figure 1. FSR spectra of the irradiated thiourea-isooctane complex: (a) observed at 77 K as irradiated: (b) observed at 77 after annealing at 233 K; (c) observed at 293 K.
a, = 1.15
(2) where 6, is a torsional oscillation amplitude and 62 represents the projected amplitude of vibration of the methylene proton (see Figure 3 ) . From eq 2, a, can be calculated if one knows (SI2) and ( 622) which are functions of the temperature and the frequencies based on Boltzmann statistics. Under the assumption that all of the oscillations are harmonic, we obtain the following equation: (fj2)
'
~
too
"
'
'
'
200
-Temperature(K
'
'
'
'
300
~
1
Figure 2. Temperature dependence of the hyperfine coupling constants of isooctyl radical: (0) methyl proton; ( 8 )methylene proton. Lines are calculated curves (see text).
isooctyl radical is produced by abstraction of a proton from the tertiary carbon of isooctane, and the dihedral angle of the methylene proton has been concluded to be 60' at the equilibrium state as shown in Figure 3 because a, N aM/2.The methyl groups of the radical are concluded to be freely rotating even at 77 K because aMis independent of the observation temperature as seen in Figure 2. The temperature dependence of a, can be explained by a torsional oscillation of the -C(CH3)2 group as follows. It is well-known that the magnitude of the P-proton splitting can be calculated from the following equation4 ag = Bo
+ B2 cos2 0
(1)
+ 2.3O((fjl2)+ ( ~ 3 ~ ~ ) )
= (h/8?r2vp)coth (hv/2k77)
(3)
where Y is the frequency and p is the reduced mass. In the calculations, we assumed that only two vibronic modes (rocking and wagging) are important and that these frequencies are 726 and 1465 cm-I, respectively, from the data for polyethylene.' The calculated curves are given in Figure 2 for several frequencies of torsional oscillation including the contribution of the methylene proton vibrations which is shown by the line denoted as /3Hin the figure. From these calculated curves, we have concluded that 58 f 2 cm-l is the frequency of torsional oscillation of -C(CH3)2, and this 58 cm-I means that Vo = 9.0 kcal/(mol-rad2) when the twofold potential is written in the standard form, V(@)= 'lzV0(1 - cos 269, and the mean amplitude of torsional oscillation was estimated to be 10.5 O at 300 K. For a torsional oscillation, there have been several studies by ESR and these can be classified into two groups. The first treated ionic radicals6,' which have small activation energies for torsional oscillation and the second is a group of neutral radicals which have rather large energies.*v9 Our result is belonging to the second group.
Acknowledgment. The partial support by a Grant-in-Aid for Scientific Research from the Ministry of Education, Science, and Culture of Japan is greatly acknowledged. Registry No. Thiourea isooctane complex, 39109-23-4; thiourea isooctyl complex, 93304-19-9.
(4)C. Heller and H. M. McConnell, J . Chem. Phys., 32, 1535 (1960). (5) S. Mizushima and T. Shimanouchi, "Infrared Absorption and Raman Effect", Kyoritu Shuppan, 1965 (in Japanese). (6) E. W. Stone and A. H. Maki, J. Chem. Phys., 37, 1326 (1962). (7) F. Nemoto, F. Shimoda, and K. Ishizu, BUN.Chem. Soc. Jpn., 48,2627 (1975); F. Nemoto and K. Ishizu, J. Phys. Chem.. 79, 1730 (1975). (8) M. Kashiwagi and Y. Kurita, J. Chem. Phys., 39, 3165 (1963). (9) M. D. Sevilla and G. Vincow,J . Phys. Chem., 72, 3647 (1968).
