J . Phys. Chem. 1984,88, 3165-3167
3165
In the case of Ternpol the hydrogen bonding between the hydroxyl group of Ternpol and the bulk water seems to reduce the stability of the molecular complex, and this may be a reason for the small equilibrium constant of complex formation in this system. Recently, the rate of the reduction of these aminoxyl radicals by ascorbic acid in aqueous solution was observed in the presence of 0-CDX. The reaction rates of both DTBN and Tempol lowered to '/2-'/3 of their original values (Le. in the absence of p-CDX) in the temperature range of 273-310 K. There was, however, no change in the case of Tempo.lo These observations are consistent with the models shown in Figure 3, if the effect of protection by the cavity wall of p-CDX on the reaction is considered. It is noted here that formation of inclusion complexes with p-CDX sharply discriminates these three aminoxyl radicals, though they are not so different from each other in both their molecular shape and electronic structures.
in the cavity along its y axis like DTBN. This disposition has been suggested by Rassat et al." as one of the possible structures of the complex; however, it is vitiated by the present results. The disposition depicted in Figure 3 also gives strong hydrophobic interaction because the hydrophobic trimethylene group is fully included in the cavity and the four methyl groups also in contact with the cavity wall of 0-CDX. Thus, the dispositions in the cases of Ternpol and Tempo are inclusive of the molecular sizes and the shapes of both the guest and the host molecules and the hydrophobic interaction between them. In the DTBN complex the disposition shown in Figure 3 gives the strongest hydrophobic interaction with the cavity wall of the host molecule. (10) Okazaki, M.; Kuwata, K.,to be submitted for publication. (11) Martinie, J.; Michon, J.; Rassat, A. J. Am. Chem. SOC.1975, 97, 1818.
Temperature and Site Dependence of the Rate of Hydrogen and Deuterium Abstraction by Methyl Radicals In Methanol Glassed T. Doha,$ K. U. Ingold, W. Siebrand,* and T. A. Wildmad Division of Chemistry, National Research Council of Canada, Ottawa, Ontario, Canada K1A OR6 (Received: March 9, 1984)
Rate constants are reported for hydrogen and deuterium abstraction by methyl radicals in CH30H and CD30D glasses in theranges 5-89 and 77-97 K, respectively. At each temperature, they show a distribution due to a variation of radical trapping sites. The rate constants of this distribution are analyzed theoretically to yield a quantitative relation between tunneling rate and equilibrium tunneling distance.
Introduction Hydrogen abstraction by methyl radicals in organic crystals and glasses has been studied e~tensively'-'~and is generally regarded as an outstanding example of a reaction proceeding by hydrogen t ~ n n e l i n g . ~ -In ' ~ this paper we report experimental and theoretical results for the reactions CH3. CH30H(D) CH4 .CH,OH(D) and CH3. + CD30D CH3D + .CD20D which together form a relatively simple model system for testing theoretical descriptions of the tunneling process. These reactions can be studied conveniently by generating the methyl radicals in a methanol glass. In earlier studies of this system,'-12 two types of experimental difficulties were encountered: the hydrogen transfer did not follow (pseudo-) first-order kinetics and the rate of deuterium transfer was too slow to be measured accurately. W e have recently shown how the nonexponential decay of the methyl radical can be explained as a distribution of exponential decays.I3 Using this approach, we report here new and well-defined exponential rate constants for the hydrogen transfer reaction between 5 and 89 K. In addition, we report for the first time the corresponding deuterium transfer rate constants from 77 to 97 K. These observations are used to test a recently d e ~ e l o p e d ' ~ - ' ~ two-dimensional tunneling model.
-+
+
-
Experimental Section In our experiments, methyl radicals were generated from methyl chloride by dissociative electron c a p t ~ r e . ~ - ' , 'Methanol, ~ 99.9% pure (dried over barium oxide), and C H 3 0 D , 99.5% pure, from Aldrich Chemical Co., and CD30D, 99.6% pure, from Merck Sharp and Dohme Isotopes, were used without further purification. The glassy solutions, formed at 77 K by rapid immersion into liquid nitrogen, were placed in a Dewar capable of maintaining a preset
f
Issued as NRCC No. 23478. Research Associate.
0022-3654/84/2088-3165$01.50/0
temperature ( f l K; more accurately at the boiling points of nitrogen and argon). After reaching this temperature, the samples were irradiated in the cavity of a Varian E12 X-band ESR spectrometer with light from a 1-kW mercury lamp for a period short compared to the half-life of the methyl radical signal. The reaction was monitored through the high-field line of the methyl quartet, corrected for background due to the hydroxy carbinyl radical formed in the process. As before,5-',l3 the signal was found to decay nonexponentially at all temperatures used.
Results We recently13 explained the observed time dependence as due to the inhomogeneity of the medium: the presence of inequivalent trapping sites for the methyl radical in the glass leads to a distribution of first-order rate constants. If N ( k , t ) is the number (1) French, W. G.; Willard, J. E. J. Phys. Chem. 1968, 72, 4604. (2) Sprague, E. D. J. Phys. Chem. 1973, 77, 2066. (3) Neiss, M. A,; Willard, J. E. J. Phys. Chem. 1975, 79, 783. (4) Neiss, M. A.; Sprague, E. D.; Willard, J. E. J. Chem. Phys. 1975, 63, 1118. (5) Bol'shakov, B. V.; Tolkatchev, V. A. Chem. Phys. Lett. 1976,40,468. (6) Stepanov, A. A.; Tkatchenko, V. A,; Bol'shakov, B. V.; Tolkatchev, V. A. In?. J. Chem. Kine?. 1978, 10, 637. (7) Bol'shakov, B. V.; Stepanov, A. A.; Tolkatchev, V. A. Int. J. Chem. Kine?. 1980, 12, 27 1. (8) Wang, J. T.; Williams, F. J. Am. Chem. SOC.1972, 94, 2930. (9) Campion, A.; Williams, F. J. Am. Chem. SOC.1972, 94, 7633. (10) Hudson, R. L.; Shiotani, M.; Williams, F. Chem. Phys. Lett. 1977, 48, 193. (1 1) Le Roy, R. J.; Murai, H.; Williams, F. J. Am. Chem. SOC.1980, 102, 2325. (12) Williams, F.; Sprague, E. D. Arc. Chem. Res. 1982, 15, 408. (13) Doba, T.; Ingold, K. U.; Siebrand, W. Chem. Phys. Lett. 1984,103, 339. (14) Siebrand, W.; Wildman, T. A.; Zgierski, M. Z. Chem. Phys. Lett. 1983, 98, 108. (15) Siebrand, W.; Wildman, T. A.; Zgierski, M. Z. J . Am. Chem. SOC., in press. (16) Siebrand, W.; Wildman, T. A.; Zgierski, M. 2. J. Am. Chem. SOC. in press.
Published 1984 American Chemical Society
The Journal of Physical Chemistry, Vol. 88, No. 15, 1984
3166
Letters
Z-E0 (A) 0.02 0.01 0.00 -0.01 -0.02-0.03
0.8
” I v
\
0.6
I
I I
I
-15 0
20
40
80
60
100
T(K)
In ( k / k o ) Figure 1. Distribution of rate constants (in s-I) for decay of methyl radicals in methanol (or methanold,,) glass as a function of In ( k / k o ) . A tenative scale of hydrogen transfer distances is given on the upper
abscissa. of methyl radicals at time t decaying exponentially with a rate constant between k and k + dk, the distribution F(k,t) = N ( k , t ) / I m0 N ( k , O ) d k = N(k,O) exp(-kt)/lmN(k,O) 0 d k (1)
Figure 2. Semilogarithmic plot of rate constants for decay of methyl radicals against temperature. Open and solid circles denote the observed most probable rate constants, ko, in methanol or methanol-d4glasses, respectively. Solid curves are calculated with R = 3.90 A. Crosses correspond to k,, indicated by the vertical bar in Figure 1. Dashed curves are calculated with the same parameters values as the solid curves, except R = 3.88 A. Squares denote rate constants taken from ref 11; they were derived under the assumption that the radical concentration in methanol decays exponentially. The error bars reflect the uncertainty (4 standard deviations) in the slopes d In [CH3.]/dt1/*,where they exceed the size of the circles. The same error bars apply to the corresponding crosses.
tance Ar, we expect k to decrease exponentially with the square of the equilibrium value of this distance, This is confirmed by model calculations. If the only difference between sites with different k is the difference in I., we can write
s.
will decay according to
f ( t ) = J m F ( k , t ) d k = l m F ( k , O )exp-(kt) d k 0
(2)
In (k/ko) = u(Go2- P)
The observed decay law5-7J3
f ( t ) = exp(-ct1/2)
(3)
implies an initial di~tribution’~ F(k,O) = c(47rk3)-’I2 exp(-c2/4k)
(4)
which reaches a maximum value F(ko,O) = (2/3~e3k&1/2for ko = c2/6. Using ko rather than c, we rewrite eq 4 in the normalized form
which is depicted in Figure 1. Since there are more sites with k = k, than with any other k value, ko is the “most probable” rate constant. It can be derived directly from a semilogarithmic plot of the methyl radical concentration against t1l2with the results shown by circles in Figure 2. For comparison, this figure also shows the rate constants derived by Williams et al.” from the initial part of the decay curve under the assumption that the radical concentration decays exponentially. Their values, indicated by squares, are much larger than the most probable rate constants and show a different temperature dependence. With one exception, discussed below, the decay law (3) was found to apply at all temperatures used. It follows that the initial distribution ( 5 ) , and hence the ratio k/ko, is temperature independent in this range of temperatures. Since the expression for k derived earlier14,15involves the square of a vibrational overlap integral between wave functions separated by the tunneling dis-
(6)
where is the distance associated with ko and u is a proportionality constant which will be temperature dependent. Although -
Ar and are also temperature dependent _ _ as a result of thermal expansion, the ratio 7 = ( E - Aro)/Arois not, provided the expansion is uniform. Since we expect 9
