J . Phys. Chem. 1990, 94. 8861-8863 4
A
7
t
3.3
8861
3.4
3.5
3.6 .10-J
'
+(K-')
25.54
3.3
3.4
3.5
3,6 a
- 3
'
f(K-1)
Figure 2. Logarithm of the velocity c of plane waves divided by T3I4 plotted vs l / T (T = absolute temperature), according to eq 6b.
Figure 3. Logarithm of the diffusion coefficient D divided by vs l / T (T = absolute temperature), according to eq 3.
In Figure 2 the logarithm of the plane wave velocity divided by T3I4is plotted versus 1 / T. As expected from eq 6b, one can derive the activation energy of wave propagation by a linear fit to the data, yielding 37.10 f 1.26 kJ/mol. This value is in close agreement with data given in the literature (34.9 f 1.2 kJ/mol in ref 9) as obtained for planar waves in a similar reaction mixture. Figure 3 shows the logarithm of the diffusion coefficient D divided by the temperature T as a function of I / T . According to eq 3 we calculated from the slope of the regression line the activation energy of diffusion to be 13.4 f 1 .OkJ/mol. This value is in the same order as the activation energy for the diffusion of CuS04 ( 1 5.3 f 1.3 kJ/molI0), which we use for comparison because of the similar size of this molecule. With E, = ' / z ( E D E k ) the activation energy Ek is determined to be 60.8 kJ/mol, and with E R = '/Z(Ek - E D ) , E R becomes 23.7 kJ/mol. The corresponding values for the critical radius, Rcrit(Table I), show that with increasing temperature smaller initiation radii are necessary so that propagation of circular waves will take place. In previous work5 we have obtained RCri,directly at room temperature by using thin, silver-coated electrodes. It should be of interest to perform such direct measurements also at different
temperatures, so that the temperature dependence of Rcritcould be obtained directly and the lower limit for this quantity determined. The results are further experimental proof for the theoretically predicted relationship between the normal velocity and the curvature of wave fronts. In the case where the assumptions of the model in ref 2 concerning the predominant influence of the autocatalytic species HBrOZin eq 1 are correct, we obtain in this way details about the diffusion coefficient of an important intermediate of the BZ reaction. For this intermediate, so far no direct data are available because its concentration in the BZ reaction is too low for direct measurements. Usually, the data documented for substances of comparable size have to be used for numerical calculations. Our results for the activation energies have also some practical use, because they allow the comparison of velocity measurements reported by different groups at different temperatures. The measured temperature effects show the increasing reactivity of the reaction solution and the enhancement of the diffusion processes with increasing temperature. In this context, it would be interesting to vary the relevant diffusion coefficients in this reaction, e.g., by increasing the viscosity of the solution. One could expect a critical transition point when the process of wave propagation becomes diffusion-limited, which needs future experimentation.
+
(9)Kuhnert, L.; Krug, H.-J.; Pohlmann, L. J . Phys. Chem. 1985,89, 2022-2026. (IO) Lundo/r-B6rnstein; Springer: New York. 1969; Vol. 11, part 5, p 631.
T plotted
Zero-Field Splitting of the First Excited Triplet State in Biradicals Estimated from Magnetic Effects on the Fluorescence Decays V. Lejeune, A. Despres, and E. Migirdicyan* Laboratoire de Photophysique Moliculaire du CNRS, Bdtiment 21 3, UniversitC Paris-Sud. 91405 Orsay, France (Received: October 31, 1990)
The fluorescencedecay of matrix-isolated m-xylylene biradicals is nonexponential and attributed to the emission from different sublevels of the first excited triplet state. In the presence of a magnetic field, the lifetime of the slow decay component decreases. Its dependence as a function of a weak magnetic field can be caiculated for different values of the zero-field splitting parameter D. The best fitting value is 1 0 1 = 0.04 0.01 cm-'. This D value is found to be significantly larger in the first excited triplet state than in the ground state of the m-xylylene biradicals.
*
Introduction The conventional electron paramagnetic resonance (EPR) method has commonly been used to determine the zero-field splitting (zfs) parameters D and E of the ground triplet state in matrix-isolated biradicals and carbenesl,z and of the lowest m* ( I ) Murray, R. W.; Trozzolo, A. M.; Wasserman, Chem. SOC.1962,84, 3213.
E.;Yager, W. A. J . Am.
excited triplet state of aromatic hydrocarbons having lifetimes of several second^.^ Unfortunately, this method cannot be used for halogenated aromatic molecules and aromatics with lowest n r * triplet states that have triplet lifetimes Of the order Of mil(2) Brandon, R. W.; Closs, G. L.;Davoust, C. E.;Hutchison, Jr., C. A.; Kohler, B. E.; Silbey, R. J . Chem. Phys. 1965,43. 2006. (3) Hutchison, Jr., C. A.; Mangum, B. W. J . Chem. Phys. 1961,34,908.
0022-3654/90/2094-886 1 %02.50/0 0 I990 American Chemical Society
8862
Letters
The Journal of Physical Chemistry, Vol. 94, No. 26, 1990 I
Magnetic Field Effects of the Decay Rate Constants of the T,-To Transitions of Biradicals Magnetic effects in the triplet state are described by the well-known spin Hamiltonian Hspinincluding the fine structure and Zeeman terms. In our labeling of molecular axes, the T , sublevel described in zero field by the eigenfunction IT,) is separated by the amount D from the nearly degenerate T~ and T , sublevels ( E
