J. Phys. Chem. 1081, 85, 1326-1332
1328
+ I, 0.08;HI, 0.
In CHI they were as follows: 02,0.04; Ht If competition of H and I with O2 and CO for reaction with the diffusing H is responsible for the low H 0 2 and HCO yields in the Xe experiments, the relatively high C2H5 yields with C2H6 and C2H4 as solutes (Table I) imply that the rate constants at 50 K for reaction of H with these molecules are higher than for the reactions with O2 and CO. As this work was nearing completion, a paper by Iwasaki and co-workers4on the competitive reactions of H with C2H6, c2D6, and HI in Xe matrices appeared? Their data show that the ratio kH/kD of the rate constants for abstraction from C2H6 and CzD6 is -1 at the lowest temperature at which Ht species are detrapped and diffuse but increases with increasing temperature, as does the relative probability of reaction with HI. This is interpreted to indicate that, when the rates of diffusion are sufficiently slow, all encounters of an H with a CzH6, C&, or HI last long enough for the probability of tunneling abstraction to be high but that, as the rate of diffusion increases, and the duration of the encounters decreases, this probability falls off faster for the c2D6 than for the C2& and HI. This analysis introduces an important concept for the understanding of competitive reactions of diffusing species with different solutes in solid matrices. In their experiments on in Xe, the Iwasaki group used 0.1 mol% HI and 1 mol% C2& and photolyzed only a small fraction of the HI, while we used 0.04 mol% HI and 0.1 and 0.5 mol% C2H6 and decomposed all of the HI. The results can be compared in Table I. Both laboratories find no observable
+ I, 0.00024; HI, 0.04.
attack of H on CHI in Xe, either during photolysis at 4-5 K or on warming. The attack on C2H6 during photolysis increases with C2H6concentration, as expected, and is consistent with the conclusion from a near-neighbor analysis4 that most of the yield results from the reaction of a freshly thermalized H with a c2H6 molecule in the wall of its cage. The fraction of the Ht which reacts with C2H, on warming to 50 K increases in the sequence 0.38,0.63, and 0.7 for the C2H6 concentration sequence 0.1,0.5,and 1.0 mol%. For the 0.1 and 0.5 mol% experiments there was no HI present to compete with the C2H6 for the H. Therefore the competition must have been limited to the H2, H + I HI, and H + CZH6.* reactions H + H C2H5 + Hz. In the 0.1 mol% system the ratios of the inital concentration of [HI + [I] to [C,He] was 0.8. Thus it appears that the rate constants for reaction with the molecules and with the atoms at 50 K are similar. Another conclusion from the data of Table I is that the fraction of the Ht produced by photolysis of HI in Xe which recombines with geminate I partners is 60.3. This follows from the value of 0.7 for Ht converted to C2H5a t 1mol% C2H6. Since some H may have reacted with HI in this system, the 0.3 is a maximum value. I t contrasts with the -60% geminate H + I recombination yield reporteda for CHI matrixes. A precise calculation of relative rate constants for reaction of Ht with different solutes in these systems, based on measurements of the ratio of radicals produced to Ht consumed, must take into account the fraction of the Ht predestined to combine with geminate I atoms.
-
-
Reactions of Thermal Hydrogen Atoms at Cryogenic Temperature below 77 K As Studied by ESR. 4.+ Abstraction from C3H8and I-C4HI0 and Addltion to C2H4in Xenon Matrixes Machlo Iwasakl, Karuml Torlyama, Hachlzo Muto, Kelchl Nunome, and MHsuharu Fukaya Government Industrial Research Institute, Nagoya, Hkate, Kite, Nagoya, Japan (Received: November 13, 1080)
Previously we have demonstrated that thermal H atoms easily abstract H from C2H6 at 10-20 K in methane matrixes and at 35-50 K in Xe matrixes contrary to the ordinary assumption that they must be unreactive below 77 K because of the high activation energy of this reaction at ordinary temperature. In the present work, we have further confirmed that thermal H atoms abstract H from C9H8and i-C4HI0as well at 35-50 K in Xe matrixes, whereas they are unreactive with CHI in the same matrixes. It has also been found that the ease of H abstraction from CzH6is not largely different from that of H addition to C2H4 forming C2HP The results can be understood if the reactions of H atoms in such low-temperature solids are strongly diffusion controlled and the tunnel process allows such reactions to proceed during the first encounter. The rate-constant ratio for the abstractions from the secondary (tertiary) and the primary C-H bonds is estimated to be ca. unity for the reactions during photolysis at 4 K, while it is 6(14)for the reactions of H atoms detrapped at -50 K. The intramolecular site preference in abstraction at -50 K may be ascribable to the onset of rotational diffusion of the solute molecules.
Introduction In recent years chemical reactions at low temperature below 77 K have drawn increasing attention because of the involvement of the tunnel process and of some other reaction channels characteristic of low-temperaturesolids.l-12 'References 4,18, and 19 in this paper are considered to be parts
1-3 of this series of studies. 0022-3654/81/2085-1326$01.25/0
For example, we have reported that the conversion of iminoxy radical pairs, which involves hydrogen-atom (1) Toriyama, K.; Nunome, K.; Iwasaki, M. J. Am. Chem. SOC.1977, 99,5823. (2) Toriyama, K.; Iwasaki, M. J. Phys. Chem. 1978,82, 2056. (3) Toriyama, K.; Iwasaki, M. J. Am. Chem. SOC.1979, 101, 2516. (4) Iwasaki, M.; Toriyama, K.; Muto, H.; Nunome, K. Chem. Phys. Lett. 1978,66,494.
0 1981 American Chemical Society
Reactions of Thermal Hydrogen Atoms below 77 K transfer, proceeds even at 4.2 K.l From leveling off of the Arrhenius plot below 50 K and a large deuterium isotope effect, it was concluded that the reaction proceeds by the hydrogen-atom tunneling. Such reactions in low-temperature solids reported so far are mainly for the inter- or intramolecular H-atom transfer, which might have some favorable situations in orientations and distances. If hydrogen abstraction reactions by diffusive hydrogen atoms take place in the low-temperaturesolids below 77 K, it may be of much wider and general significance. Reactions of hydrogen atoms with alkanes are one of the most important and fundamental reactions in radiation and photochemistry as well as in reaction dynamics. Since the activation energy of hydrogen abstraction by hydrogen atoms is of the order of kcal/mol at ordinary temperatures, thermal hydrogen atoms have long been postulated to be unreactive at low temperature below 77 K. However, to interpret low-temperature irradiation effects on hydrocarbon radiolysis,13we came to the conclusion that thermalized hydrogen atoms must be reactive below 77 K.14-16 We have made trial calculations of the abstraction rate constants with tunneling corrections at low temperatures for the reactions of hydrogen atoms with methane, ethane, propane, and isobutane.2 The results indicate the possibility that hydrogen atoms are able to abstract a hydrogen atom from these alkanes, except methane, even below 77 K. In addition, we have experimentally demonstrated that thermal H atoms trapped in CHI easily abstract H from C&6 at 10-20 K.4J7 The reactivity of H atoms with below 50 K has been further confirmed in Xe matrixes, in which the detrapped H atoms at 35-50 K easily abstract H from C2H6 as well as C2Ds.4J8J9 However, there is the possibility that the reaction of H atoms with ethane below 50 K is an unusual and exceptional reaction under some particular conditions. Therefore, we have extended our experiments on the hydrogen-atom reactions in Xe matrixes to other alkanes such as CH4,C3H8,and i-C4H1@In the present work, it has been demonstrated that H atoms which are unreactive with CH4 are reactive with C3H8ahd i-CJIl0 at 35-50 K. In addition, it has been found that H-atom addition to C2H4 also takes place at 35-50 K in Xe matrixes with an ease similar to that of the H abstraction. These results must give conclusive evidence that H-atom reactions below 77 K are not an exceptional phenomenon but a rather general reaction behavior of hydrogen atoms in the low-temperature solids. (5) Hudson, R. L.; Shiotani, M.; Williams, F. Chem. Phys. Lett. 1977, 48, 193. (6)Le Roy, R. J.; Murai, H.; Williams, F. J. Am. Chem. SOC.1980,102, 2325. (7) Brunton, G.; Gray, J. A.; Griller, D.; Barcloy, L. R. C.; Ingold, K. U. J. Am. Chem. SOC.1978,100,4197. (8) Goldanski, V. I. Nature (London)1979,279,109. Barkalov, I. M.; Goldanski, V. I.; Kiryukhin, D. P.; Zanin, A. M. Chem. Phys. Lett. 1980, 73, 273. (9) Alberding, N.; Austin, R. N.; Beeson, K. W.; Chan, S. S.;Eisenstein, L.; Frauenfelder, H.; Nordlund, T. M . Science 1976, 192,1002. (10) Peters, K.; Applebury, M.L.; Rentzepis, P. M.BOC. Nutl. Acad. Sci. U.S.A. 1977, 74, 3119. (11) Lucas, D.; Pimentel, G. C. J. Phys. Chem. 1979,83,2311. (12) Catalano, E.; Barletta, R. E. J.Phys. Chem. 1980,84, 1686. (13) Iwasaki, M.; Toriyama, K.; Muto,H.; Nunome, K. J. Chern. Phys. 1976, 65, 596. (14) Iwasaki, M.; Toriyama, K.; Nunome, K.; Fukaya, M.; Muto, H. J. Phys. Chem. 1977,81,1410. (15) Iwasaki, M.; Muto, H.; Toriyama, K.; Fukaya, M.; Nunome, K. J . Phys. Chem. 1979,83,1590. (16) Iwasaki, M.; Toriyama, K. J. Phys. Chem. 1979,83, 1596. (17) Toriyama, K.; Iwaaaki, M.; Nunome, K. J . Chem. Phys. 1979, 71, 1698. (18)Toriyama, K.; Nunome, K.; Iwasaki, M. J.Phys. Chem. 1980,84, 2314. (19) Muto, H.; Nunome, K.; Iwasaki, M. J. Phys. Chem. 1980,84,3402.
The Journal of Physical Chemistty, Vol. 85, No. 10, 1981 1327
TABLE I: Initial Fractional Yields of Alkyl Radicals during 4.2 K Photolysis of HI in Xe Matrixes Containing Hydrocarbon Additives yo = [Rl/I[Ht,l -t [RI}
calcd" concn, additives mol % obsd N= 6 N = 14 CH, 0.5 50.03 0.03 0.03 c*H6 0.5 0.07 0.06 0.10 1.0 0.14 0.12 0.20 C,H, 0.5 0.07 0.06 0.10 2'-C,H,, 0.5 0.09 0.06 0.10 C,H, 1.0 0.19 0.12 0.20 (I Estimated from eq 1 by assuming I? = 6. See text. From ref 19.
*
b
The site preference in the H abstraction from the primary, secondary, and tertiary C-H bonds has also been studied for C8H8and i-C4H10. All of the results can be interpreted in terms of the diffusion-controlled reactions of H atoms, in which the tunnel process allows these reactions to proceed during the first encounter with additives. To understand the H-atom reactions in the low-temperature solids, one must take into consideration not only translational diffusion of H atoms but also rotational diffusion of solute molecules in addition to the steric and orientational effects.
Experimental Section The samples of CHI (>99.95%),C& (>99.7%),i-C4Hio (>99.9%), C2H4 (>99.8%), and Xe (>99.9%) obtained from Takachiho Shoji were used without further purification. The samples of HI obtained from Tokyo Kasei Kogyo as aqueous solutions were distilled under vacuum after being treated with phosphorus pentoxide. The concentrations of hydrocarbons and HI in the Xe mixtures are 0.5-1.0 and 0.01-0.06 mol 70,respectively. Gaseous mixtures were prepared by using a vacuum line and then frozen into a Suprasil ESR tube at 4.2 K to ensure a rapid condensation of the gaseous mixtures. The samples containing C3H8or i-C4H10 showed a sign of poor homogenity of the solutes when the gaseous mixtures were frozen at 77 K. To ensure good thermal conduction and equilibrium during the thermal annealing and the subsequent ESR measurements, we filled the sample tubes with helium to -0.5 atm after condensation of the gaseous mixtures.16 To produce hydrogen atoms, photolysis of HI was performed at 2537 A from a low-pressure mercury lamp (a conventional spiral type). After 4.2 K photolysis the frozen samples were annealed at 35-50 K to mobilize the trapped H atoms to encounter the additives. The thermal annealing of the samples below 77 K was performed in a liquid-helium Dewar by pulling the sample tube up above the liquid-helium level. Because of the temperature gradient above the liquid-helium level, the specimen temperature during the annealing has a range of -A3 K. The experimental setup for the low-temperature ESR measuremenh and the data processing by an on-line computer have already been described e l ~ e w h e r e . " ~ ~ ~ Results The frozen mixtures were first photolyzed at 4.2 K for 2-8 min to produce H atoms by decomposition of HI. A part of the H atoms (-10% or less) reacted with additives forming alkyl radicals during the photolysis, but most of them were trapped in the Xe matrixes. The buildup of (20) Nunome, K.; Muto, H.; Toriyama, K.; Iwasaki, M. Chem. Phys. Lett. 1976, 39, 542.
1328
The Journal of Physical Chemistry, Vol. 85, No. 10, 1981
Iwasaki et ai.
a) H
I
T A W S G Figure 1. ESR spectra of the Xe/CH, (0.5 mol %)/HI (0.05 mol %) mixture measured at 4.2 K: (a) immediately after photolysis at 4.2 K (b) after subsequent annealing at 45 K for 1 mln. Microwave power is 0.006 mW.
Figure 2. ESR spectra of the Xe/C3H8(0.5 mol %)/HI (0.05 mol %) mixture measured at 4.2 K (a) Immediately after photolysis at 4.2 K (b) after subsequent annealing at 50 K for 1 min. Microwave power is 0.006 mW.
Figure 3. ESR spectra of the Xe//C4Hlo (0.5 mol %)/HI (0.01 mol %) mixtures measured at 4.2 K (a) immediately after photolysis at 4.2 K (b) after subsequent annealing at 50 K for 1 min. Mlcrowave power is 0.01 mW.
Figure 4. ESR spectra of the Xe/C2H4 (1 mol %)/HI (0.05 mol %) mixture measured at 4.2 K (a) Immediately after photolysls at 4.2 K; (b) after subsequent annealing at 50 K for 1 min. Microwave power Is 0.006 mW.
the trapped H atoms (Hb) and the alkyl radicals (R.) with illumination time showed a trend of saturation for prolonged illumination longer than 2 min. Since the extent of the saturation is slightly higher for Hk, the fractional [R-I),showed a trend of slight yield, Y = [R.]/([H,] increase with illumination time. Therefore, the initial fractional yield Yoobtained from the extrapolation to zero time is tabulated in Table I. Typical examples of the ESR spectra of H, and alkyl radicals are shown in Figures 1-4. The outer slgnals with a well-resolved superhyperfine structure are due to Htr trapped in the octahedral interstitial site of the fccub lattice of XeaZ1 The central spectra are due to the alkyl radicals, as will be described in the following sections. After the photolysis the samples were annealed at each elevated temperature for 1-2 min, and the ESR spectra were remeasured at 4.2 K. The decay of H* started at 35 K and became very rapid at -50 K in every sample, including the sample without hydrocarbon additives. The Hb signal decayed within 1-2 min at 50-55 K. The signal from alkyl radicals concomitantly increased with the decay of He as shown in Figures 1-4. These spectral changes are quite analogous to those previously observed for Xe/ CzH6/HI mixture^.^*^^^'^ It is clear that Ht, species detrapped at 35-50 K are mobilized to encounter the dilute additives to form alkyl radicals. As is previously reported:8Je He also reacts competitively with the remaining HI, which is known to be a good scavenger of thermal H atoms
at ordinary temperature, so that the efficienty of the reaction with these hydrocarbons decreases with increasing concentration of HI remaining after the photolysis. Xe/CH4/HI. Shown in Figure l a is the ESR spectrum obtained from the Xe/CH4 (0.5 mol %)/HI (0.05 mol %) mixture immediately after photolysis at 4.2 K for 8 min. The central four-line spectrum arises from CH,. The deviation of the intensity ratio from k 3 3 1 to 1:l:l:lis due to an onset of the tunneling rotation of CH3 about the CSu axis.143z The initial fractional yield of CH, was estimated to be 50.03. Upon annealing at 35-50 K the Hb signal disappeared, whereas the CH, signal remained nearly unchanged, as shown in Figure lb. The slight change in the spectral line shape of CH3 is due to the overlap of the spectra of CzHs-formed from a trace impurity of CzH6in the sample. From the decomposition of the overlapping spectra by the computer the amount of CHs was estimated to be nearly constant during the decay of Hw The results indicate that the detrapped H atoms cannot abstract H from CHI at 35-50 K in Xe matrixes. Most of the detrapped H atoms are supposed to be scavenged by the remaining HI, as is reasonably expected from our previous studies on the competitive reaction of CzHe and HI.lD The reactivity of thermal H atoms with CH4 has been further examined by the 4.2 K photolysis of frozen mixtures of CH4/HI (0.5 mol %). It was found that most of the H atoms produced by decomposition of HI were trapped and that CH3 formed by the H abstraction from CH, during the photolysis of 4.2 K was only a few percent
(21) Morton, J. R.; Preston, K. F.; Strach, S. nAbrian, F. J.; Jette, A. N. J. Chem. Phys. 1979, 70,2889.
(22) Freed, J. H. J. Chem. Phys. 1966,43,1710. Clough, S.; Poldy, F. Ibid. 1969,51, 2076.
+
N
-
Reactions of Thermal Hydrogen Atoms below 77
The Journal of Physical Chemistry, Vol. 85, No. 10, 1981 1329
K
TABLE 11: Relative Yields of Primary and Secondary (Tertiary) Alkyl Radicals from C3H, (i.C,H,,) and Reactivity Ratios in H Abstraction Reactions at 50 K relative yields of radicals and reactivity ratios during 50 K after -50 K during 4 K annealing additives radicals expecteda photolysis annealing
-
-
0.75 f 0.1 0.25 f 0.1 1 0.90 0.90 f 0.05 cH2CH(CH31 2 CH(CH3)3 C(CH,), 0.10 0.10 f 0.05 k( tert)/k(prim) 1 Expected from the numbers of the C-H bonds assuming the same reactivity. CH,CH,CH, k( sec)/k(prim)
CH,CH,CH, CH,CHCH3
0.75 0.25
50G
Figure 5. ESR spectra of C3H, radlcals In the Xe/C3H, (0.5 mol %)/HI (0.05 mol % ) mixture measured at 4.2 K and the decomposition into the spectra arising from CH2CH2CH3and CH36HCH$ (a) immediately after photolysis at 4.2 K; (b) after subsequent annealing at 45 K for 1 min. The two lower spectra in a and b are the decomposed spectra. The stick diagrams indicate the theoretically expected llne positions and intensities. Microwave power is 0.006 mW.
of the trapped H atoms. This means that most of H atoms are thermalized without reacting with CHI. The thermal annealing experiments after the photolysis showed that H, was detrapped and disappeared at 10-20 K during remained unchanged, although which the amount of (%.!H3 a small amount of C2H6.was formed from a trace impurity of C2H6in the sample. Most of the detrapped H atoms are supposed to be scavenged by the remaining HI. These results are quite analogous to those observed in the Xe/ CH4/HI mixtures. As is reported,4J7Ht, in CH4produced by radiolysis at 4.2 K also behaves in a similar manner. On the other hand, the trapped H atoms were not observed in the 4.2 K photolysis of HI in other alkanes such as ethane, cyclohexane,neopentane, and decane, although trapped alkyl radicals were observed. The results can be explained if the thermalized H atoms are reactive with these alkanes during photolysis at 4.2 K, as is expected from the results described in the following sections. Xe/C&/HI. Shown in Figure 2 are the spectra obtained from the Xe/C3H8 (0.5 mol %)/HI (0.05 mol %) mixture. The initial yield of C3H7radicals was estimated to be 0.07. Upon successive annealings at 35-50 K, C3H7* increased with the decrease of Hb, as shown in Figure 2. The conversion efficiency was -30%. Shown in Figure 5 are the computer-assisted decompositions of the observed spectra. The spectra of C3H7*can be interpreted by a As shown by the mixture of cH2CH2CH3and CH3(%.!HCH3. stick diagrams in Figure 5, CH2CH2CH3gives a six-line spectrum arising from the two inequivalent &proton
0.47 f 0.1 0.53 f 0.1 0.65 f 0.06 0.35 f 0.05
0.35 f 0.64 f 6 0.39 f 0.61 f 14
0.1 0.1 0.07 0.07
Flgure 6. ESR spectra of the C4H,radicals in the Xe/lC4Hlo (0.5 mol %)/HI (0.01 mol %) mixture measured at 4.2 K and the decomposition into the spectra arising from 6H2CH(CH& and C(CH&: (a) lmmedlately after photolysis at 4.2 K; (b) after subsequent annealing at 50 K for 1 min. The two lower spectra in a and b are the decomposed spectra. The stick diagrams indicate the theoretically expected line positions and Intensitles. Microwave power Is 0.01 mW.
couplings (22.3 and 46.6 G) and the two equivalent aproton couplings (22.3 G), while CH&HCH3 gives a 15-line spectrum arising from one a-proton coupling (23.2 G ) and the six equivalent /+proton couplings (23.2 G ) in the two methyl groups which undergo tunneling rotation at 4.2 K.= The abundance ratio of the secondary to the primary radicals was estimated to be 0.250.75 before the annealing. From this the ratio of the abstraction rate constants (per bond) from the secondary to the primary C-H bonds was estimated to be k(sec)/k(prim) = 1. The abundance ratio of the secondary to the primary radicals increased to 0.53:0.47 after the annealing at 35-50 K. This clearly indicates that the H atoms detrapped at 35-50 K abstract from the secondary C-H bond more favorably, giving k(sec)/k(prim) = 6, as shown in Table 11. Xe/i-Cfilo/HI. Similar results were also obtained from the frozen mixture containing 0.5 mol % of i-C4HlP1as shown in Figure 3. It is clearly seen that CIHBradicals increased with the decrease of Htr. The conversion efficiency was -30%. In this m e , the C4HDradicals initially formed consist of (%.!(CH3), and CH2CH(CH3)2with the abundance ratio of 0.1:O.g (see Figure 6). This leads to k(tert)/k(prim) = 1for the abstraction during photolysis at 4.2 K. As shown by the stick diagrams in Figure 6, cH2CH(CH3)2gives five-line structures arising from the two equivalent a-proton couplings (23 G) and the one @-protoncoupling (42 G), whereas C(CH3)sgives 19-line structures arising from the nine equivalent &proton couplings (22.5 G) in the three methyl groups which undergo tunneling rotation.l4S The abundance ratio of the teritary to the primary radicals after the annealing at 35-50 K was estimated to be 0.35:0.65 from the spectral decomposition
1330
The Journal of Physical Chemistry, Vol. 85, No. 10, 1981
shown in Figure 6. The increase of this ratio indicates that the H atoms detrapped at 35-50 K abstract from the tertiary C-H bond more favorably, leading to k(tert)/k(prim) = 14. Xe/C2H4/HI. As shown in Figure 4, analogous results were obtained from the mixtures containing 1mol % of C2H4, although the reaction involved is H addition to the C=C bond formjng CZHp The six-line spectrum a t the center is due to CzH5, in which the CH3 group undergoes classical hopping rotation at 4.2 K. Both the initial yield (0.19) of CzHs after 4.2 K photolysis and the efficiency (60%)of the reaction of H atoms detrapped at 35-50 K were found to be comparable with 0.14 and 96%, respectively, obtained from the Xe/C2& (1mol %)/HI (0.05 mol %) mixtures in our previous work.lg It is to be mentioned here that the CH3 group in C2H6 formed from H abstraction from CZ& undergoes tunneling rotation giving a different hyperfine structure from that shown in Figure 4b. From the ENDOR measurements of the tunneling frequency, the barrier height of the internal rotation was found to be considerably higher in C2H5 formed from the abstraction reaction. The difference may be ascribable to. the interaction with the Hz molecule trapped close to C2H5 after the abstraction reaction. The details will be given elsewhere.23
Discussion Initial Yield of Alkyl Radicals. The initial yield of alkyl radicals expected from a simple statistical consideration is approximately given by the following equation for low concentrations of additives and HIi6J8J9
YO= [R*I/(IHtrl + IR*l)= (n + N ) f
(1)
where f is the fraction of additives and it is assumed that (1) H atoms are thermalized after n collisions, (2) if the H atoms encounter the additives before being thermalized, radicals are formed from the additives by hot processes, (3) the thermalized H atoms become trapped H atoms if they do not find any additives in the cage wall consisting of N neighbors, and (4) otherwise the thermal H atoms react with the additives. In the above approximation the concentration of HI is assumed to be very small as compared with that of the additives. The first and the second terms in the right side of eq 1correspond to the hot and thermal contributions, respectively. Since thermal H atoms do not react with CH4,all of the initial amounts of CH, are ascribable to the hot contribution giving n 6 6. Since the excess kinetic energy of H atoms is mainly moderated by collisions with Xe atoms, the value of n may not be largely affected by the kind of dilute additives. Therefore, larger initial yields of alkyl radicals in other mixtures (Table I) may suggest that thermalized H atoms contribute to the initial yield of alkyl radicals during photolysis at 4 K for other additives. If H, in the octahedral interstitial site reacts only with the first neighbors, N is 6, and, if the second neighbors are involved, N becomes 14. The initial yields statistically expected from this model with N = 6 or 14 are in reasonable agreement with the observed values, as shown in Table I. Since the rate constant of the tunneling-dominated reactions becomes nearly temperature independent below 50 K,’@ the reactions of Htr with the cage wall can be expected even at 4 K. Very recently Willard et al.24have (23) Toriyama, K.; Iwasaki, M.; Nunome, K.; Muto, H. “The 19th ESR Symposium”; Yokohama, Japan, Oct 1980,p 68.
Iwasakl et al.
reported that the decay of H, (DJin 3-methylpentane-d14 and other deuterated glasses in the temperature region of 5-30 K can be explained by the tunneling abstraction from the C-D bond in the cage wall. The abstraction from the C-H bond must be easier in our case. Reactions of Detrapped H Atoms. The drastic difference in the ease of abstraction from CHI and from other alkanes may be expected in the tunnelingdominated reactions, as is previously reported.’ The relative ease of abstraction from C3H8or i-C4H10was not very much different from that from CzH6 although large differences are expected from the previous calculations.’ One of the reasons might be the neglect of the zero-point energy and the assumption of the continuous energy levels in the conventional method. The discrete energy model with the zero-point energy might reduce the large difference arising from the difference in potential barrier heights.6 In addition, the requirement for the level matching in the discrete model also affects the relative ease of the tunneling reactions. In spite of these possibilities, the extremely small kH/kD ratio of 1-2 at 35 K reported in our previous paper18 cannot be expected from the calculation of the tunneling-dominated reaction rates.2*6 The concept of diffusion-controlled reaction must be required to interpret k H / k , = 1-2 at 35 K and 60 at 50 K, as is discussed in our previous paper.18 Ht, is mobilized at the temperature at which the rigidity of the matrix cage is softened. Then, jumping of H atoms from trap to trap becomes possible at this temperature. If the jumping rate is sufficiently slow, the H atoms abstract from the C-H bond during the first encounter with a rateaimply proportional to the encounter probability. The H addition reaction to CzH4 at ordinary temperature has a lower activation energy (4 kcal/mol) than that of the abstraction reactions from C2H6 (8 kcal/mol). Nevertheless, a large difference was not observed between the addition and the abstraction. This can also be understood from the reactions which are strongly diffusion controlled. In comparing the relative ease of the addition and abstraction reactions, one may have to take into further consideration the orientational effect in the addition reaction. The competitive abstractions from CzHBand HI have also indicated that the reaction is strongly diffusion controlled, giving k(HI)/k(CzH6) = 1-2 at 35-50 K.le Intramolecular Site Preference in H Abstraction. The abstraction reactions from C3H8or i-C4H10 during photolysis at 4.2 K did not show a site preference, as is tabulated in Table 11. This is partly due to the contribution from, the hot abstraction. However, as is discussed in the foregoing section, the thermalized H atoms also contribute to the abstraction during the photolysis. Since the rotational diffusion of the additives must be frozen at 4.2 K, the H atom in a cage is allowed to react only with a particular C-H bond having a favorable orientation. If any C-H bond has the same probability to make a favorable reaction angle with an €4 atom in a cage, abstraction must take place with a probability statistically expected from the number of C-H bonds. This may be why the thermalized H atoms also show the same abstraction rate constants per bond for the primary and the secondary (tertiary) C-H bonds. On the other hand, the abstraction by the H atoms detrapped at 35-50 K showed a considerable preference for the secondary or tertiary C-H bond, as shown in Table 11. In the case of diffusion-controlled reactions of H atoms in low-temperaturesolids, the preferential abstraction may (24) Aditya, S.; Wilky, D. D.; Wang,H. Y.; Willard, J. E. J. Phys. Chern. 1979,83, 599. Wang, H.Y.; Willard, J. E. Ibid. 1979, 83, 2585.
The Journal of Physical Chemistry, Vol. 85, No. 10, 1981 1931
Reactions of Thermal Hydrogen Atoms below 77 K become possible if onset of rotational diffusion of the additives allows the choice of the C-H bond during the first encounter. In other words, the detrapped H atom abstracts H from the additive molecule during the first encounter with a probability close to unity. However, which C-H hydrogen atom is abstracted is affected by the rate of rotational diffusion of the additives. A t -50 K the probability of abstraction from the primary C-H bond during the first encounter in the sense of rotational motion may become less than unity, resulting in the preferential abstraction from the secondary or tertiary C-H bond. The observed rate-constant ratios at -50 K are comparable with those at ordinary temperature2sand are not as large as expected from our previous calculations.2 Although the discrete model with the zero-point energy might reduce the large difference in the tunneling reaction rate constants: it may be suggested that the abstraction reactions at -50 K in Xe matrixes might be still intermediately controlled by rotational diffusion of additives while they are strongly controlled by translational diffusion of H atoms. Diffusion Rate. The rate constant for the diffusioncontrolled reactions is given by eq 2,26 where D is the
k = 12~p~DN/[1000(3p + a)]
(2)
diffusion constant, p the encounter diameter, u the rootmean-square displacement distance for diffusive motion, and N Avogadro’s number. Although the diffusion constant of H atoms in Xe matrixes is not known, it is wellknown that an impurity atom in the interstitial site in the bccub lattice shows unusually fast diffusion in metals.27 Interstitial H atoms in the bccub metals exhibit a considerable mobility at low temperature with an activation energy of -1 kcal/mo1.27 Since D(H) = 10-11-10-15cm2/s in a-Fe(bccub) at 50-60 K,2’ D(C0) = 2 X cm2/s in Ar at 30 K,28 and D(Cu) = 4 X lo-’’ cm2/s in Ar at 35 K,%the assumption of D(H) 2 lo-“ cm2/s in Xe at -50 K may not be unrealistic. If the distance from the interstitial site to the first neighbor is taken as an encounter diameter, p is 3.07 A. For the jump to the nearest interstitial site u = a o / d 2 = 4.33 A, and thus k is estimated to be 21.6 L/(mol s). If one assumes a pseudo-first-order reaction, a half-life of detrapped H atoms at 50 K is estimated to be 71/2 5 2.1 s for 1 mol 70additives Since the decay rate of H atoms is determined by the detrapping process,lg it was not possible to measure the abstraction rate itself of the jumping hydrogen atoms. However, the reactions must be completed within an experimental time scale of 30 s. The half-life estimated from the diffusion constant is thus consistent with our experiments. The crude jumping rate of the H-atom diffusion is estimated to be 2321s from the relation D = vu2/6.26Thus, the H atoms spend 50.03 s in a cage. Without the tunnel process, it may not be expected that the abstraction reaction takes place during this short period. In our previous calculations, the half-lives of H atoms at 50 K in C2H6, CsHs, and i-C4H10are estimated to be 50.001 s for the potential thickness parameter a 5 0.52 A for the nondiffusion-controlled reactions. Therefore, abstraction during the first encounter may be possible, allowing the
(c&).
(25)Russell, G.A. “Free Radicals”; Kochi, J. K., Ed.; Wiley: New York, 1973;p 285. (26) Noyes, R. M. J. Am. Chem. SOC.1956, 78, 5486. J.; Alefeld, G. “Diffusion in Solids”; Nowick, A. S., S.,Burton, (27)Volkl, J.; J. J., Eds.; Academic Press: New York, 1975; J. 1975;.p p 231. (28)Moskovita, M.; Ozin, G. A. “Cryochemistry”;Wiley: New York, 1976;p 335.
diffusion-controlled reactions. It may be worthwhile to comment here on the tunneling contribution to the H-atom diffusion. If the activation energy of H-atom diffusion in Xe matrixes is sufficiently low (
