J . Phys. Chem. 1984,88, 773-777
773
Absolute Rate Constants for Radical Rearrangements in Liquids Obtained by Muon Spin Rotation Peter Burkhard, Emil Roduner, Jiri Hochmann, and Hanns Fischer* Physikalisch- Chemisches Institut der Universitaet Zurich, CH-8057 Zurich, Switzerland (Received: July 13, 1983)
By addition of muonium (Mu = p'e-), a light hydrogen isotope, the hepten-2-yl radicals CH2=CHCH20C.H2CHCH2Mu and CH2=CHCH2C(CH3)2CH2CHCH2M~, and the cyclopropylcarbinyl radicals C3H,CHCH2Mu and C3H5C(CH3)CH2Mu are generated. Their Fourier transform muon spin rotation (BR)spectra show line widths increasing with increasing temperature which are attributed to the processes of ring closure for the former and ring fission for the latter two radicals, well-known from the chemistry of the species. Analysis yields the Arrhenius parameters for the reactions which agree well with previous estimates for the protiated species obtained by other methods. Advantages and limitations of the technique are discussed.
Introduction Rates of radical-molecule reactions in liquids are often studied in competition experiments relative to those of unimolecular radical rearrangements which serve as internal 'free radical clocks".'s2 Much effort has therefore been devoted to the calibration of the clocks,2i.e., the determination of reliable rate constants for radical rearrangements, and a series of data is now a ~ a i l a b l e . However, ~ most of these rate constants were not measured directly but again relative to those of other processes, mostly radical self-terminations since the experiments employed conditions of rather high radical concentrations where terminations and rearrangements compete. In this work we determine absolute rate constants and their temperature dependencies for several chemically well-characterized free-radical rearrangements by muon spin rotation (pSR), a method utilizing extremely low radical concentrations and avoiding competition by self-termination. The pSR technique rests on the following principles: 46 Spin-polarized positive muons are stopped in the targets of interest. Their spins then undergo precession in an external magnetic field B, here transverse to the initial spin direction, and/or internal magnetic fields. Independent of their environments the muons decay, emitting positrons preferentially along the instantaneous spin directions. The time evolution of the spin polarization is detected in the form of time-differential histograms which consist of numbers of positrons counted in given telescope directions as a function of the time elapsed since the stops of the corresponding muons. The pSR histograms are thus radioactive decay curves modulated by the muon precessions. Direct fitting to theoretical expressions or Fourier analysis reveals the frequencies, their amplitudes, phases, and relaxation rates. If muons are stopped in liquid unsaturated compounds, precession frequencies are observed which correspond to muons incorporated in diamagnetic compounds and to muons in muonium-substituted radicals. They arise from the addition of muonium (p'e- = Mu) to the molecules. In high external fields ( B 1 1 kG) each radical species exhibits two precession frequencies from which the isotropic electron-muon hyperfine coupling constant is determined. We and others have recently generated a large variety of such radicals and have obtained unambiguous assignments of radical structures from coupling ~
(1) A. L. J. Beckwith and K.U. Ingold in 'Rearrangements in Ground and Excited States", Vol. 1, P.de Mayo, Ed., Academic Press, New York, 1980, p 161. (2) D. Griller and K. U. Ingold, Acc. Chem. Res., 13, 317 (1980). (3) A. L. J . Beckwith in 'Radical Reaction Rates in Liquids", LandoltBbrnstein, New Series, Group 11, Vol. 13, H. Fischer, Ed., Springer, West Berlin, in press. (4) Vols. 1-3, V. W. Hughes and C. S. Wu, Eds., "Muon Physics", Academic Press, New York, 1975. (5) D. C. Walker, J . Phys. Chem., 85, 3960 (1981). (6) P. W. Percival, Radiochim. Acta, 26, 1 (1979). (7) E. Rcduner and H. Fischer, Chem. Phys., 54, 261 (1981).
0022-3654/84/2088-0773$01.50/0
Reactions of the radicals during the muon lifetime of 2.2 ps cause a chemical relaxation of the precessions. Since at any instant of the experiment the sample contains only one muon and since the muon fluxes are low (1105 s-l), chemical relaxation by radical-radical reactions is extremely unlikely to compete with pseudo-first-order radical-molecule reactions or with first-order radical rearrangements. Thus, rate constants for such reactions can be extracted from B R relaxation rates unperturbed by radical self-terminations. Unfortunately, the chemical reaction mechanism is not obtained since the reaction products are unobservable, and one has to rely on systems with known chemistry. Therefore, we apply the method here to established radical rearrangements. Radicals are generated from liquid diallyl ether, 4,4-dimethylheptadiene-1,6, cyclopropylethene, and 2-cyclopropylpropene. From previous experiments7,*we expect the dominant formation of radicals by muonium addition to the unsubstituted ends of the olefins and the following rearrangements:
An asterisk denotes the position of muonium. In fact, the cyclization (eq 1) of the protiated 4-oxa-6-hepten-2-yl radical has been studied by Beckwith,I2 and a rate constant of 8.8 X lo6 has been estimated for n-pentane solution at 338 K.) The analogous ring closure 2 is known from work on related radicals such as the unsubstituted 6-hepten-2-yl radicalI2-l4( k 7.6 x los at 338 K in n-pentane3) and the 3-methyl-5-hexenyl radical15 ( k = 1.65 X IO6 s-' at 353 K in benzene). Further, the ring fission rearrangements 3 and 4 are well established for a variety of cyclopropylalkyl radicals, and for reaction 3 a rate
=
(8) E. Roduner, W. Strub. P. Burkhard, H. Hochmann, P. W. Percival, H. Fischer, M. Ramos, and B. C. Webster, Chem. Phys., 67, 275 (1982). (9) E. Roduner, G. A. Brinkman, and P. F. Louwrier, Chem. Phys., 73, 117 (1982). (10) J. M. Stadlbauer, B. W. Ng, D. C. Walker, Y. C. Jean, and Y. Ito, Can. J. Chem.. 59. 3261 (1981). (1 1) A. Hili, G.' Allen,'G. Stirling, and M. C. R. Symons, J . Chem. Soc., Faraday Trans. 1 , 78, 2959 (1982). (12) A. L. J. Beckwith, I. A. Blair, and G. Phillipou, J. Am. Chem. Soc., 96. 1613 (1974). ':13) C: Waliing and A. Cioffari, J. Am. Chem. Soc., 94, 6059 (1972). (14) Y. Maeda and K. U. Ingold, J . Am. Chem. Soc., 101,4975 (1979). (15) A. L. J . Beckwith, T. Lawrence, and A. K. Serelis, J . Chem. Soc., Chem. Commun., 484 (1980).
0 1984 American Chemical Society
Burkhard et al.
114 The Journal of Physical Chemistry, Vol. 88, No. 4, 1984 constant of k, z 7 X lo6 s-I at 273 K in Decalin has been rep ~ r t e d . ~ .Since ’ ~ the muon-bearing methyl group is not directly involved in reactions 1-4, we expect the substitution to cause only minor changes in the rate constants. These, as given above, made reactions 1-4 particularly suited for a pSR study since the muon lifetime restricts measurable relaxation rates to k 2 lo5 s-I.
Experimental Section Diallyl ether and 2,3-dimethylbutene- 1 were purchased from Fluka, Buchs and distilled before use. n-Propyl allyl ether was prepared via Williamson synthesis.I7 Cyclopropylethene and 4,4-dimethylheptadiene- 1,6 were synthesized according to ref 18 and 19. 2-Cyclopropylpropene was obtained from dimethylcyclopropylcarbinol by dehydration, the latter synthesized by Grignard reaction from cyclopropyl methyl ketone. The pure liquids were freed from dissolved oxygen and sealed in spherical glass bulbs? By aid of a cryostat the sample temperature during runs was held constant to h0.2 K. The temperature inhomogeneity over the samples was less than 0.2 K. All pSR experiments were carried out at the muon channels of SIN (Schweizerisches Institut fur Nuklearforschung, Villigen) using a standard transverse field pSR assembly7 with B = 2 kG and four separate simultaneously operating telescopes for positron detection. Their relative sensitivities were determined with a standard CCl, sample from the amplitudes of the precession frequency of muons in diamagnetic environment.6 During each run corresponding to one sample and temperature (70-80) X lo6 good events were accumulated in about 4 h and stored in 4 X 2 K time channels of memory with width of T = 1.7 ns/channel to obtain four independent histograms. Analysis was performed off-line at the Rechenzentrum of the Eidgenossische Technische Hochschule Zurich. The muon polarization found on radical precession frequencies corresponded to about 20% of the polarization of muons incorporated in diamagnetic compounds (asymmetry 0.02 for one radical line).
with grossly different amplitudes occur. In particular, for the present case of low radical amplitudes a fit in frequency space is more suitable since there individual lines can be treated separately and the relevant information is condensed into a smaller number of points. The corresponding procedures, developed in this work, are as follows. To increase the apparent resolution of the frequency spectra g(n) was extended to N = 4096 points by zero-filling,20Le., g(n) = 0 for N‘ In IN - 1. It then was multiplied by exp(-AonT) with Xo = 0.67 X lo6 s-I. This filtering reduces the noise in the Fourier transforms (Appendix). Discrete transformation via21*22 “-1
F(m) =
n=O
g(n) exp(-2?rimn/w
(9)
using a fast routine gives the N points 0 Im IN - 1 of the complex frequency spectrum with resolution D = 2 ? r / N ~ . It is easy to show analytically that one term of eq 6 yields a contribution to F of F = F+ F(10)
+
where T = N’T is the length of the histogram and A‘ = A + io. For A’T N' are too small by a factor of ( N / N ' ) ' / * .The errors given in the text are values corrected accordingly. Registry No. Mu, 12587-65-4; diallyl ether, 557-40-4; 4,4-di-
+
methyl-1,6-heptadiene, 22146-18-5; cyclopropylethene, 693-86-7; 2cyclopropylpropene, 4663-22-3; diallyl ether muonium adduct, 82904muonium adduct, 88412-14-0; cyclo68-5; 4,4-dimethyl-l,6-heptadiene propylethene muonium adduct, 884 12- 15- 1 ; 2-cyclopropylpropene mucnium adduct, 82904-65-2; dimethylcyclopropylcarbinol, 930-39-2; cyclopropyl methyl ketone, 765-43-5. (31) P.R. Bevington, 'Data Reduction and Error Analysis for the Physical Sciences", McGraw-Hill, New York, 1969.
