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Methyl radicals migration in glassy ethanol-1,2d5 at 90 K as studied by hydrogen atom abstraction from the additives
Chemical Physics ELSEVIER
Chemical Physics 2 !6 (1997) 135-145
Methyl radicals migration in glassy ethanol-l,2d5 at 90 K as studied by hydrogen atom abstraction from the additives V l a d i m i r L. V y a z o v k i n *, V l a d i m i r A. T o l k a t c h e v institute of Chemical Kinetics and Combustion, Novosibirsk 630~90, Russian Federation
Received I December 1995; in final form 14 November 1996
Abstract
ESR technique has been used to study the kinetics of methyl radicals decay at 90K in glassy ethanol-l,2d5 with an admixture of diethyl ether and C2HsOH ethyl alcohol. It has been demonstrate(,, that methyl radicals migrate freely throughout the sample. The migration rate strongly depends on sample prehistory. The preliminary annealing at reaction temperature and/or the spontaneous cracking of matrix lead to a decrease in migration rate. The experiments indicate that the mechanism of radical migration in glassy ethanol differs considerably from that in glassy methanol. The probable reasons for this difference have been considered. © 1997 Elsevier Science B.V. All fights reserved.
1. Introdvction
Abstraction of hydrogen atoms from glassy alcohols by alkyi radicals occurs at low temperatures due to quantum tunneling [ 1-3 ]. Whereas the probability of tunneling dramatically depends on potential barrier parameters, the barrier substantially changes with varying relative arrangement of reagents, which complicates the tunneling transfer of atoms. In this case, the motion of atoms in a multi-dimensional potential with regard to the motion dynamics of reagents and products during tunneling is considered [ 4] instead of a simple problem of tunneling in a static double well potential [ 3,5 ]. In solids these motions can occur particularly due to lattice vibrations (for details see e.g. Refs. [6-9] ). However, the question of whether in solids at low temperatures the reagent motions can be treated as the lattice vibrations of a relatively small amplitude calls for additional experimental verification. * Corresponding authoc
If reagents are fixed in the lattice, the tunneling of atoms can proceed with a noticeable rate only from a few neighboring matrix molecules, the reaction must be treated as the in-cage one. This assumption can be verified by studying the radical decay in the mixture of usual and deuterated molecules. Let a fraction of H-molecules be c, and the number of the nearest matrix molecules be N. The probability that a cage contains i H-molecules is given by binomial distribution wi = C]vci (i - c ) N-i, where C]v = N ! / i ! ( N - i ) ! , the binomial coefficient. Particularly, some radicals can be generated in the surrounding of only deuterated molecules. First, the transformation of these radicals will give rise only the products of deuterium atom abstraction. Second, as the tunneling of deuterium is much slower than the hydrogen transfer, the kinetic curves of radical decay in mixed matrices must demonstrate two pronounced regions. First of all, the radicals with at least one H-molecule in a solvent cage, must decay rather rapidly. A slow disappearance of radicals surrounded by deuterated molecules only is to be
0301-0104/97/$17.00 Copyright (~) 1997 Elsevier Science B.V. All fights reserved. Pll S0301-0104(96)00354-0
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observed late in the reaction. The number of radicalaccessible matrix molecules N can be estimated by comparing the experimental values and those assumed for different N: - the ratio between the products of hydrogen and deuterium atoms abstraction; - the transformation depth at which the kinetics of radicals decay in a mixed matrix becomes identical to that in the pure deuterated one. We have studied in detail the kinetics of methyl and ethyl radicals reactions in the solutions of CH3OH, C2H5OH, and CH3CD2OH in methanol-d3 [ 10]. The experimental results are explicitly inconsistent witb the assumption of the in-cage character of the reaction between alkyl radical and matrix molecules. However, the reagent motions in this ma,,-i,: appear to differ much from what is usually called "diffusion". The peculiarities of reaction kinetics can be explained by assuming that the radical can abstract an atom from a rather large but still limited number of matrix molecules. The number of possible partners increases with rising temperature. For the methyl radical at 77 K N ~, 25, and at 90 K N ~, 100. Within an experimental accuracy, the N values for methyl and ethyl radicals coincide. Besides, N sharply decreases with ethanol-ld2 used instead of C2H5OH as the Hadditive when radicals are forced to abstract hydrogen from//-carbon atoms. These peculiarities are thought to indicate the fact that in glassy methanol the tunneling abstraction of H-atoms results from a cooperative fluctuational process [ 10,11]. The question arises of how much in common have the reactions of hydrogen abstraction by alkyl radicals in glassy methanol for glassy alcohols? The aim of the present paper is to determine a feasible mechanism of reagent mobility in ethanol- 1,2d5 at 90 K and to compare the results with the data for methanol.
2. Experimental The deuterated compounds from Isotope Co. (St. Petersburg, Russian Federation) C2DsOH (isotopic purity > 98.5 at. % D) and CD3I ( > 99 at. %) were used. Prior to usage ethanol C2HsOH was dried over anhydrous CaO, distilled, and stored over 3A molecular sieves. CD3I and CH3I (purum grade) were stored in the dark over copper. Dipheny!amine (DPA)
(reagent grade) and 2-chloroethanol (purum grade) were used as supplied. The NMR spectrum of ethanol-l,2d5 showed that the main hydrogen-containing impurity was ether (C2H5)20. Because of this ethanol-l,2d5 was additionally purified. For this purpose alcohol was boiled over CaO in a pyrex flask with a reflux condenser during 10 h. Thereafter upon heating a dry nitrogen flow was fed through the gas-inlet adapter into the bottom of condenser during 4 h. The flow rate was chosen so that ether vapors could be carried away with nitrogen and ethanol had time to condense on the walls of the condenser Dried and purified alcohol was distilled and stored over 3A molecular sieves. NMR spectrum showed that after purification ethanol1,2d5 contained the following impurities: 0.1 mol % (C2H5)20, 0.2 mol% CD3CHDOH, and 0.3 mol% CD2HCD2OH. (The NMR spectra were obtained on an AM-250 NMR spectrometer "Brucker"). The samples consisted of the mixture of ethanol isotopomers with a given composition. Solutions containing about 1 mol % iodomethane or iodomethaned3 and 5 x 10-3 mol % DPA in the solvent ethanol were placed in quartz tubes (3 mm i.d.), degassed by repeated "freeze-pump-thaw" procedure in vacuum line, filled with helium at a pressure about 100 Ton', sealed and cooled rapidly to 77 K by immersion in liquid nitrogen. In some experiments the tubes with detachable vacuum valves were used instead of the sealed ones. Just after cooling the samples formed a transparent matrix without any cracks. Some samples were used after preparation (not later than in 2 minutes). Below these samples will be referred as unannealed. The rest of the samples were kept in liquid oxygen for 37 h (annealed). Some samples, both annealed and unannealed, cracked spontaneously, being, however, still transparent (cracked). A few samples were broken in the tubes (crushed). For this purpose, the vacuum valve was detached from the tube immersed in liquid nitrogen. Liquid air, condensing on cold walls, was expected to fill the tube. Alcohol glass was broken with a sharpened steel rod cooled in liquid nitrogen. As this had taken place, the sample cracked throughout the volume and becmne opaque. During this procedure the sample temperature did not raise above 78 K. Finally, the vacuum valve was attached to the tube. The air was puniped out and the smnple was fi!l~ with helium.
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It is known that at low temperatures ethanol exists not only as a glass but also as the orientationally disordered crystal [12,13]. This raises the question of whether the matrix is completely disordered, glassy ethanol and not a mixture of orientationally disordered crystalline and glassy ethanol. As known, if the glass contains microcrystals, then in a slow cyclic heatingcooling of the sample above glass transition temperature Tg (but below melting point) one may see a matrix devitrification and a gradual growth of microcrystals. In this case, a transparent glass becomes the nontransparent poiycrystailine matrix. If in the case of methanol glass the devitrification of matrix runs rather easily, in the case of ethanol, we have failed to observe any. This is likely to be assigned to a very large viscosity of the supercooled liquid and to a sharp temperature dependence of the ethanol viscosity. According to Ref. [ 14] ethanol crystals could be grown at a temperature very close to the melting point (,,~ 156 K). In our method of sample preparation, the cooling rate was high enough (,,~ 5 K/s) to prevent the formation of the crystalline phase of ethanol. The methyl radicals were generated by UVphotolysis of the samples. The details of sample illumination and kinetics measurements were described in our previous paper [ 10]. The concentration of (~H3 radicals was detected by the side high-field component of their ESR spectrum. The CD3 concentration was detected by the line marked as h in Fig. l a. A distortion of these lines due to overlapping with the spectra of reaction products was negligible.
3. Results 3. I. Identification o f reaction products
Fig. l a depicts the first derivative ESR spectrum for CD3I solution in ~thanol-1,2d5 just after the photolysis at 77 K. A seven-line signal with a sepmation of 3.5 G at the center of spectrum is attributable to (~D3 radicals. A weak outer signal arises from matrix radicals forming during photolysis in side reactions. The similar ESR spectra have also been obtained just after the photolysis of CD3I solutions in the C2HsOH + C2DsOH mixtures. When the sample temperature is raised to 90 K, the intensity of methyl radical spectra gradually decreases and that of matrix
CD3CDOIi . . . . .
i
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,
,
CH3CHOC2H~ Fig. 1. ESR spectra of iodomethane-d3solution in ethanol-l,2ds: (a) just after UV-photolysisat 77 K; (b) after complete decayof t~D3 radicals at 90K. (c) ESR spectrum of the DPA solution in ethanol-l,2d5 after photolysis at 77 K and subsequent annealing for 72 h at 90 K. radicals increases. The total radical concentration determined by a double digital integration of ESR spectra remains constant in the course of reaction. Fig. i b demonstrates the spectrum obtained after a comple:te decay of (~D3 radicals in ethanol-l,2ds. It consists of a few overlapping spectra. A signal at the center of spectrum actually coincides with the spectrum of the DPA solution in ethanol- 1,2d5 photolyzed at 77 K and annealed during 72 h at 90 K (Fig. l c). It is known that in the latter case the CD3CDOH radicals form [ 15 ]. Four wide outer lines originate from the radicals generated by the reactions of methyl radicals with diethyl ether impurity. This signal is likely to be caused by CH3CHOC2H5 radicals. Their ESR spectrum is known ~o consist of five broad lines with a splitting of 22G [ 16]. The central line of this quintet overlaps the spectrum of CD3(:DOH radicals and the four outer components are well proaounced i~ ~he ESR spectrum. Fig. 2a shows the ESR spectrum obtained after a complete decay of CD3 radicals in the mixed matrix with 1.0 mol % C2H5OH. The similar spectra were also recorded for the larger contents of C2H5OH.
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V.L. Vyazovkin. [fA. Tolkatchev/Chemical Physics 216 (1997) 135-145
hi
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When a fraction of C2H5OH increases, the contribution of CD3CDOH radical signa~ becomes less noticeable and a relative intensity of four outer lines grows. It is assumed then that these lines arise from the CH3~HOH radicals resulting from H-atom abstraction by methyl radicals from C2H5OH. However, comparing four outer components of spectrum 2a with the corresponding lines in the spectrum of the CH3CHOH radicals obtained by photolysis of DPA solution in C2HsOH (Fig. 2b), one can observe considerable differences. Probably, these differences are 0 :e to overlapping of the (~H2CH2OH radicals spectrum. They can be formed by Hatom abstractioa from the methyl groups of ethanol. This assumption was verifi~d by the photolysis of a frozen 1.0 mol % 2-chloroeti~anoi solution in ethanol-1,2d5. A solid line in Fig. '~c depicts the ESR spectrum obtained just afk.r t,hutolysis. In this case, the CH2CH2OI-[ radicals are generated by the reaction of dissociative electron attachment. The side reactions give rise to the matrix CD3CDOH radicals. The spectrum of CH2CH2OH radicals (dashed line in Fig. 2c) was obtained by numerical subtraction
of CD3t~DOH radical spectrum (Fig. lc). It consists of six lines with an intensity ratio approximately equal to 1:3:4:4:3:1, which are brGadened by anisotropic hyperfine interaction (h.f.i.). The spectrum can be explained assuming the existence of h.f.i, with two equivalent a-protons (isotropic h.f.i, constant aa = 24G) and two inequivalent fl-protons (a~ I) = a~2)/2 = 24 G). As expected, the constants of isotropic h.f.i, for (~H2CH2OH radical are very close to the values typical of the alkyl radicals forming from the radiolysis of nalkanes and n-alkylhalides. For instance, the constants of isotropic h.f.i, for the (~H2CH2CH3 radical a,~ = a~!)~ = a~2)/2 = 23G, and for the (~H2(CH2)2CH3 one a,~ = a~I) = a~2)/2 - 21G [17]. It can readily be seen that the side high- and low-field components of the (~H2CH2OH radical spectrum (marked by asterisks in Fig. 2c) do not overlap the lines of the CH3CHOH one (Fig. 2b). However, no lines of the CH2CH2OH radical were observed in the spectrum of the products of methyl radical decay in the mixed matrix. It can be concluded then that no ¢~H2CH2OH radicals form by the reactions of methyl radicals with the C2HsOH + C2DsOH mixtures. Thus, a feasible reaction of H-atom abstraction from alcohol methyl group can be neglected. The difference in the spectra of ethanol radicals sta.. bilized in C2H5OH and C2DsOH seems to be caused by the following. It is known that ethanol in the solid phase contains both the trans and gauche conformers [ 14 ]. It is quite probable that the CH3CHOH radicals in ethanol also exist in different forms. A complex ESR spectrum lineshape is a result of the spatial averaging of anisotropic h.f.i, and the overlapping of slightly different spectra of the radicals existing in various conformations. Besides, in the deuterated matrix the broadening of spectrum lines due to dipole-dipole interaction is much smaller than in the hydrogen-containing one. It seems likely that the complex structure of the CH3(~HOH spectrum, manifesting itself in the deuterated matrix, is simply blurred in C2HsOH ethanol. The ESR spectra of CH3CHOH and CH3CHOC2H5 radicals in frozen ethanol and diethyl ether, respectively, are known to be almost the same [ 16]. Comparing spectra 2b and I b for the ethanol-1,2d5 matrix their differences (if any) are observed to be minor. It is concluded that in "pure" ethanol-l,2d5 matrix, the methyl radicals can abstract hydrogen only from the
VL. Vyazovkin. V.A. Tolkatchev/ Chemical Physics 216 (1997) 135-145
139
a-carbon atoms of ether impurky. The H-atom abstraction from methyl groups of ether can be neglected. The similar results have been obtained for the CH3I solutions in the mixtures of ethanol isotopomers. The only difference is in the fact that initially the wellknown four-line spectrum with a splitting of 23 G was observed instead of the CDa radical spectrum.
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3.2. The results of kinetic measurements
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As follows from the above data, in the C2HsOH + C2DsOH mixtures the methyl radicals decay by the
following reactions: R + C2DsOH
, RD + CD3CDOH,
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R + (C2H5)20 ---* RH + CH3CHOC2Hs,
(3)
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R + CD3CDHOH ---, RH + CD3CDOH,
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where R is either CH3 or CD3. Fig. 3 presents the relations between the concentrations of the H-atom abstraction products (proportional to line hi intensity in spectra lb and 2a) and the (~D3 radicals (proportional to h in the spectrum ! a) in the course of the reaction. For "pure" ethanol- 1,2d5 the product is the C H 3 C H O C 2 H 5 radicals. Since the spectra of CH3CHOC2H5 and CH3CHOH radicals are very close and fully overlap, in mixed matrices the line hi intensity is proportional to the sum of the concentrations of these radicals. The following peculiarities have engaged one's attention: (i) In all cases, the products of H-atom abstraction from the hydrogen-containing admixture accumulate to the point of methyl radicals disappearance. (ii) The relations between hi and h are linear. Thus, in the matrix of a given composition the relation between the probabilities of the abstraction of both the hydrogen atom from H-additive and the deuterium one,,; from C2DsOH remains constant in the course of reaction. (iii) The greater is the concentration of Hsubstituted reagents in the matrix, the larger fraction of methyl radicals abstracts the H-atoms, however when the fraction of C2H5OH t> 4 tool %, almost all methyl radicals react only with the additive.
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h(t)/h(0) Fig. 3. The dependence between intensities of ESR spectra lines of the (~D3 radicals (h) and the radicals of H-atom abstraction (hi) (see Figs. I and 2) in the course of methyl radicals decay in mixed matrices at 90K. The amount of C:,HsOH in mol%: (1,2) 0.0; (3-6) 1.0; (7) 4.0. Sample: (1,3,7) unannealed, non-cracked; (2,4) annealed, cracked at the moment of reaction initiation (t = 0 ) ; (5) unannealed, crushed at t - 0; (6) unannealed, crushed in the course of reaction at t = 2460s.
(iv) The preliminary annealing of matrix and the cracking of samples are manifested in the relation between hi and h only for the low H-additive cont:entrations, whereas the prehistory of samples can readily be observed for all cases in the reaction kinetics (see below). Fig. 4 depicts the kinetic curves of methyl radical decay in glassy ethanol-l,2d5 and Figs. 5-7 show them for the mixed matrices with 1.0 mol % of C2HsOH. The kinetic curves are plotted as l o g ( [ R ( t ) ] / [ R ( 0 ) ] ) vs. t°'5, where [R(t)] is the methyl radical concentration, t is the time. This method is more convenient for representing the experimental results. The matter is that the above reactions first run rather quickly and then sharply slow down. The nonlinear transformation of the time axis can be used to simultaneously plot a short "fast" initial region of the kinetic curve and a long "tail". Comparing the kinetic curves for the samples of the same composition, we see that the reaction rate is
V.L. Vyazovkin, V.A. Tolkatchev/Chemical Physics 216 (1997) 135-145
140
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Fig. 4. The kinetic curves of the (~H3 (1,2) and (~D3 (3,4) radicals decay in glassy ethanol- 1,2d5 at 90 K. Sample: (!,3) unannealed, non-cracked; (2,4) annealed, cracked at t = O.
Fig. 6. The kinetic curves of the (~L~I3radicals decay in unannealed glassy mixtures O.01C2HsOH + 0.99C2DsOH at 9OK. Sample: ( 1 ) cracked at t = O; (2) cracked .;~ the course of reaction (arrow marks the moment of cracking).
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Fig, 5. The kinetic curves of the (~D3 (1,2) and CH3 (3-6) radicals decay in glassy mixtures O.OIC2HsOH 4-0.99C2DsOH at 90K. Sample: (1,3) unannealed, non-cracked; (2,6) annealed, cracked at t = 0; (4) annealed, non-cracked; (5) unannealed, cracked at t = O.
the highest in the unannealed and non-cracked samples (Figs. 4-6). Note that the reaction kinetics in such samples demonstrates a poor reproducibility. Repeating experiments for both (~H3 and CD3 radicals, we have established that the reaction rate accidentally varies within rather wide limits. Curves 1 and 3 in Figs. 4 and 5 are given as the boundaries of a nonreproducibility region. Both the preliminary annealing and spontaneous cracking of samples slow down the reaction. Of interest also is a lower degree of kinetics nonreproducibility in the annealed and/or cracked samples compared to the unannealed ones (Figs. 4 and 5). When the ma-
-1.5 -20
Fig. 7. The kinetic curves of the (~H3 radicals decay in unannealed glassy mixtures 0.01C2HsOH + 0.99C2DsOH at 90K. Sample: ( I ) non-crocked; (2) crushed at t = 0; (3) crushed in the course of reaction (arrow marks the moment of crushing); (4) cracked at t = O .
trix cracks during reaction, its rate (to within experimental accuracy) becomes the same as in the matrix, cracked at the instant of (or just after) methyl radical generation (Fig. 6). A mechanical crushing of matrix both before the photolysis and during the reaction has no effect on the kinetics of methyl radical decay (Fig. 7). In both cases the reaction runs to within experimental accuracy so as in the unannealed and noncracked samples.
V.L. Vyazovkin, VA. Tolkatchev/Chemicai Physics 216 (1997) 135-145
141
4. Discussion
4.2. Matrix relaxation
4.1. The number of radical-accessible matrix molecules
It is common knowledge that a fast freezing of liquid gives rise to the inhomogeneous stressed glass, either the long-term annealing or slow freezing result in the formation of a more homogeneous glass with a higher specific density. In these glasses the rate of molecular motions is less than in the unannealed ones. A decrease in molecular mobility in glasses during at.~aealing below Tg was recorded e.g. by the decrease in the ionic conductivity of alkali-silicate glasses [ 19,20], by the changes in the spectrum of dielectric losses [ 13 ], by the changes in the rate of phenanthrene phosphorescence quenching by oxygen in methanol [21]. The relaxation of matrix is manifested in the kinetics of diffusion-controlled reactions. In Ref. [22] the influence of preliminary matrix annealing on the kinetics of ethyl radical oxidation by molecular oxygen in methanol-d4, ethanol-d6, and n-butanol-dl0 is described in detail. In all cases the oxidation rate is decreased upon preannealing. The preannealing was observed to retard also the oxidation of methanol radicals in glassy CH3OD [21 ] and of tert-butyi radicals in squalane [23]. As in the present paper, the rate of radical decay in 3-methylpentane-dl4 (3MP-d14) at 77 K noticeably decreases after the preannealing of glass [24]. Unfortunately, the mechanism of methyl radical decay in 3MP-dl4 has not been established unambiguously. It can be assumed that one of the substantial channels is the H-atom abstraction from the residual C-H bonds in 3MP-dl4. This is confirmed by a large CH4 methane yield upon CH3I radiolysis in 3MP-dl4 [ 25 ]. Due to annealing the matrix structure changes rather slowly. Experimentally, however, the fast relaxation of glass structure accompanied by its cracking is also possible. In kinetics as in preannealing, this results in reaction retardation. In this case, the fractures can be recorded on the kinetic curves (see e.g. Fig. 6). Earlier, the influence of matrix cracking has already been observed both in studying the decay of methyl radicals in 3MP-d~4 [ 24 ] and in the oxidation of tert-butyl radicals in squalane [23]. However, there are some differences from our case. When 3MP-dl4 cracks, not only the rate of methyl radical decay decreases but also the kinetic law changes. In unrelaxed 3MP-dl4 the kinetics of radical decay is nonexponential. In the relaxed matrix the variations in their concentration with
The above data show that, in ethanol at 90K the methyl radical quite rapidly migrates throughout the matrix. In this case, it can either abstract an H-atom at random encounter with H-additive or slowly react with the surrounding ethanol-1,2d5 molecules abstracting a deuterium atom from one of them. The migration rate is high enough to provide a fairly high probability of radical encounter with H-molecule even if its concentration in the matrix is about 0.1 moi %. This is verified by the linear dependences in Fig. 3. If the mobility of methyl radicals was limited, then the accumulation of H-atom abstraction products from the additive would te~xninate at any degree of their conversion. The probability that among N encountering molecules there are no H-substituted ones is w0 = (1 - c ) ~¢. For example, when the number of accessible molecules N = 100, with c -- 10 -3 only 10% of the initial amount of methyl radicals could react with H-molecules. During the decay of the remaining 90% of radicals no accumulation of the products of H-atom abstraction could occur. Such a situation is exemplified in Fig. 3 (dashed line). The dala in Fig. 3 can be used to estimate the number of matrix molecules, N, with which the radical can react during its lifetime. Experimentally, not less than 95% of the initial amount of methyl radicals can meet at least one impurity diethyl ether molecule during its lifetime in ethanol- 1,2d5. Thus, w0 ~< 0.05 with c ~ 10 -3. As a result, N ) 3 x 103. This number is approximately 100 times as much as that of matrix molecules accessible for methyl radicals in glassy methanol-d3 at 90 K [ 10]. It is assumed that at 90 K in ethanol- 1,2d5 the methyl radicals migrate rather freely whereas in methanol-d3 their movements are limited to a small region near formation site. A significant distinction between radicals mobilitles in glassy ethanol and methanol is of interest, because the glass transition temperatures for these matrices are close. According to the data in Refs. [ 13,18 ] for methanol Tg - 103 K and for ethanol Tg = 97 K. To this we can add, that the recombination of alkoxy radicals in these matrices take place in the same temperature ranges T = 95100K.
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V.L. Vyazovkin, V.A. Tolkatchev/Chemical Physics 216 (1997) 135-145
time are described in terms of the normal first-order law. In our case, the relaxation has almost no effect on the kinetic law. Concerning the oxidation of ten-butyl radicals in squalane, the reaction retards not only due to annealing or spontaneous cracking, but also due to the mechanical crushing of samples [23]. In the artificially cracked ethanol glass the abstraction reaction runs so as in the non-cracked unannealed matrix (Fig. 7). The influence of matrix relaxation on the kinetics of methyl radicals reaction with the mixtures of isotopesubstituted ethanols can be considered as an argument in favor of the diffusion mechanism of reagent approach in this matrix. In glassy methanol the annealing has actually no effect on the kinetics of H-atom abstraction [ 10] whereas the kinetics of the diffusioncontrolled oxidation is subjected to a noticeable action of annealing.
where [R] is the methyl radical concentration ( [ R] << c); [ PH] and [ PD ] are the concentrations of the products of H and D-atom abstraction, respectively; Wo(t,p) is the time-dependent rate constant of deuterium abstraction from matrix molecules; W(t,p) is the radical diffusion rate; t is the elapsed time from the reaction initiation; p is the set of parameters determining the matrix properties that can also vary with time (matrix relaxation). A number of mechanisms can cause WD and W to vary with time. As an example one can refer to the random walk of particles in the energetically disordered and lowdimensional media (fractals). Both of these models present a way to obtain a rate constant of diffusion controlled reaction which varies with time (see e.g. reviews [ 27-29] and references cited therein). The time dependence of WD will be discussed below. Dividing (6) by (5), we obtain: d[PH] / d[R] =-cW( t, p ) / ( W o ( t , p ) +cW( t,p) ).
4.3. Reaction kinetics
(8) Thus, both the results obtained and the low magnitudes of isotopic effects in the yield of methane isotopomers [26] allow the conclusion that in the mixture of ethanol isotopomers at sufficiently low content of H-molecules the rate of H-atom abstraction reaction is limited by the diffusion approach of reagents. The rate of methyl radical migration is high as compared to the radical decay rate due to deuterium atom abstraction from the nearest matrix molecules. However one major complication exists. The reaction proceedts with time nonexponentially. As it has been shown earlier, the reaction of hydrogen atom abstraction by alkyl radicals in the glassy mixtures of alcohol isotopomers and diffusion-controlled reactions of radical oxidation in glassy alcohols could be explained in terms of a time~lependent reaction rate "constant" [ 26,22]. Probably, in our case (c << 1) the decay of methyl radicals and the accumulation of the products of deuterium and hydrogen atoms abstraction can be described by the following set of equations:
dIR]/dt---(WD(t,p) +cW(t,p))[Rl,
(5)
d[PH]/dt = cW(t,p)[R],
(6)
dtPDl/dt = WD(t,p)[R],
(7)
If c is large enough, so that WD(t,p) < cW(t,p), then d[PH]/d[R] ,~ 1. It is suggested that at a sufficiently high H-additive concentration the relation between the concentration of methyl radicals and H-atom abstraction products will be independent of matrix relaxation. As follows from Fig. 3 c = 0.01 can be assumed high enough. Its further 4-time increase leads to only a 30-40% increase in the fraction of methyl radicals reacting with the H-additive. No wonder that already with c .>i 0.01 for all kinds of the samples the same relation has been observed between the concentrations of CD3radicals and H-abstraction products in the course of reaction, although the preliminary annealing and cracking of samples are manifested in kinetics (Figs. 5-7). Another limiting case is realized, probably, for the decay of methyl radicals in "pure" ethanol- 1,2d5: d[PH]/d[R] ~ - - c W ( t , p ) / W D ( t , p ) .
(9)
First, experimentally, due to matrix relaxation the diffusion rate changes more dramatically than that of deuterium abstraction. Second, the linearity of the relation between [ Pa] and [ R] (Fig. 3) requires that the time-dependence of the rate "constants" of WD and W must be rather close. The nonexponential kinetics of the tunneling atom abstraction from matrix
V.L. Vyazovkin, V.A. Tolkatchev/Chemical Physics 216 (1997) 135-145
molecules was explained by the different theoretical models [6,30]. As a rule, in these models the analysis starts with the following assumptions: - the reaction rate is controlled by the rate of hydrogen or deuterium atom transfer; - atom tunneling probability vary sharply with the distance between reagents; - the disorder of glass structure causes a broad distribution of a distance between the radical and the nearest matrix molecules thus leading to the dispersion in reactivity. In our case this approach is inadequate. If radical diffusion brings matrix molecules close to the radical than they would be in the static structure, then the radical will decay more rapidly. So the distribution of reactivity will be more narrow than in static case and the decay kinetics will be more closer to the regular exponential one expected for the first-order reactions. It is clear that the shape of decay curve would be determined by the relationship between the rates of atom tunneling and of radical migration. One would expect that the kinetics of radicals decay in the deuterated matrix must be less nonexponentia~ than in the normal one due to more complete dynamical averaging of reactivity dispersion. It is easy to see that this conclusion is inconsistent with the experimental results [ 10,26,30]. It is quite possible that the rate of deuterium atom abstraction is controlled not only by atomic tunneling, but also by the processes of methyl radical approach to matrix molecule and their mutual orientation to reach the arrangement which is more suitable for atomic transfer (for details see Refs. [10,26]).
4.4. Radicals mobility and structure of a glassy alcohol A considerable difference in the kinetic behavior of the reactions of H-atom abstraction by methyl radicals from H-molecules in glassy methanol-d3 and ethanol1,2d5 is likely to be due to the difference in the structures of t~ese glasses. According to Ref. [ 31 ], the lineshape of the ESR spectra of methyl radicais in glassy CH3OD and CHD2OH can be explained assuming that the local structure of glassy methanol resembles the structure of a high-temperature fl-phase of crystalline methanol. According to Ref. [ 32], the orthorhombic lattice of the methanol fl-phase exhibits infinite, flat, zig-zag chains of hydrogen-bonded
143
Fig. 8. Projection of a unit cell of ethanol along the crystalline axis a (according to data of Ref. | 141 ).
methanol molecules. In this case, the structure of methanol-water glass can be represented as the short (5-10 molecules) portions of such chains joined via water molecules into a sufficiently rigid random thl'eedimensional network. The crystal lattice of ethanol is an array of infinite chains of hydrogen-bonded molecules too [ 14]. The hydrogen-bonds form almost flat units containing the alternating gauche and trans conformers (Fig. 8). Probably, the glassy ethanol structure consists of the molecular chains of various lengths, the local structure of which is close to the crystalline one. (It is obvious that some ef these cl~ains can form the ring-like structures.) It is of first importance that these chains remain non-linked due to absence of water molecules which are able to form more than two H-bonds per molecule and to serve as the junction of hydrogen-bonded network. The different hydrogen-bonds spatial structures can cause a higher methyl radical mobility in glassy ethanol compared to that in methanol as well as a greater influence of the preliminary annealing. A probable reason can be the following. Due to the close packing of molecules in solids, a molecule can move only when a sufficiently large number of the surrounding molecules are displaced from their normal fattice positions. For example, the computer modellag of oxygen diffusion in glassy poly (iso-butylene) shows that a penetrant moves from a cavity to the
14~
VL. Vyazovkin. V.A. Tolkatchev/Chemical Physics 216 (1997) 135-145
neighboring one in a very shot time compared to the residence time. Infrequent jumps between the cells result from the formation of fairly wide passages between the neighboring cells, arising from random cooperative shifts of a large number of molecules [ 33 ]. A rigid structure of methanol-water glass requires that in such cooperative shifts the hydrogen-bond network be distorted and may be some of the bonds be ruptured. It is clear that at low temperatures such energetically expensive motions of matrix molecules must become unduly infrequent. In ethanol, compared to methanol, the diffusion of small particles, such as methyl radical, is likely to need no strong distortions of the hydrogen-bonds, i.e. substantial free energy losses. For example, as it is seen from Fig. 8, a passage for methyl radicals to move from one cell to another can result from the torsional displacements of the ethyl groups of alcohol molecules about the C-O bonds. Evidently, the relaxation of nonequilibrium glass structure due to annealing will be different in ethanol and methanol. A rigid network of hydrogen bonds must prevent substantial shifts of molecules in glassy methanol. In ethanol, the non-linked molecular chains can move more freely relative to each other. In addition, in ethanol the matrix structure can relax due to the torsional movements of ethyl groups around the C.-O bonds. In this case, a free volume in glassy ethanol is expected to decrease upon a sufficien0y long annealing and the probability of I~,~ctua6onal formation of a free volume near the radical d.ecreases. According to the concept of free volume relaxation [341, the rate of radical diffusion must drop. The relaxation of glass structure due to the tension release upon matrix cracking can be considered in a similar way. However, unclear is the absence of the influence of artificial matrix cracking. More likely, this testifies to the fact that the development of cracks leads to the structural changes just near the cracks rather than in the bulk. Below the glass transition temperature the response of an electrical or mechanical stress known as a secondary or/~-relaxation occurs in the amorphous solids. This type of relaxation is determined by the increased local molecular mobility in media. As it is known, the height of the loss peak for the secondary relaxation decreases on physical ageing (annealing) of a glass. It is quite probable that the molecular motions associated with fl-relaxaticn determine the molecu-
lar diffusion in a glass. It may be of interest to study the correlation between the influence of any variable and procedure (annealing, glass composition and the like) on the secondary relaxation and on the reaction kinetics in the glassy alcohols. Unfortunately our attempts to lind the data on the ,8-relaxation in glassy methanol and ethanol in the literature have failed. The data on the glass transition processes in more complex monohydroxy alcohols [35] are in agreement with our interpretation. In all alcohols (2-propanol, land 2-butanol, 2-methyl- l-propanoi and 3-methyl- lbutanol) the two glass transition temperatures are detected and attributed to the freezing of H-bonded network and free molecules, respectively. Below Tg, all liquids show two processes, one of which (with activation energy 4.5-7 kcai/mol) was attributed to the free molecules (or segmental) motion and the other ( " 2.5 kcal/mol) to the OH group motion. It is believed that in glassy ethanol the same sub-Tg processes take place with the close values of activation energy and loss-peak frequency.
5. Conclusion The kinetics of methyl radical decay at 90K in glassy ethanol-l,2d5 with dissolved H-substituted compounds favors the actually frec bulk migration of radicals. The migration rate is subjected to the influence of sample relaxation both during the annealing and due to spontaneous cracking. On the other hand, as reported earlier [ 10], in glassy methanol the motions of reagents occur in the bounded regions of matrix, and the matrix relaxation during annealing or due to cracking does not practically manifest itself in reaction kinetics. This testifies to the substantial differences in the mechanisms of methyl radical migration in these apparently similar matrices. Most probably, this difference is related to that in the molecular structure of glassy methanol and ethanol.
Acknowledgement The authors are grateful to Dr. A.I. Kruppa for his assistance in NMR analysis of ethanol-1,2d5.
V.L. Vyazovkin, V.A. Tolkatchev/Chemical Physics 216 (1997) 135-.145 References Ill A. Campion and E Williams, J. Am. Chem. Soc. 94 (1972) 7633. 121 R.L. Hudson, M. Shiotani and E Williams, Chem. Phys Lett. 48 ( ! 977) 193. 131 R.J. LeRoy, H. Murai and E Williams, J. Am. Chem. Soc. 102 (1980) 2325. 141 M. Ya. Ovchinnikova, Chem. Phys. 36 (1979) 85. 151 W. Siebrand, T.A. Wildman and M.Z. Zgierski, J. Am. Chem. Soc. 106 (1984) 4083. 161 V.I. Goldanskii, L.I. Trakhtenberg and V.N. Flerov, Tunneling phenomena in chemical physics (Gordon and Breach, New York, ! 989). 171 V.A. Benderskii, D.E. Makarov and C.A. Weight, Tunneling dynamics at low temperatures (Wiley, New York, 1994). 181 L.I. Trakhtenberg, V.L. Klochkhin and S.Ya. Pshezhetsky, Chem. Phys. 59 ( 198 ! ) 19 i. 191 V.A. Benderskii, P.G. Philippov, Yu.l. Dakhnovskii and A.A. Ovchinnikov, Chem. Phys. 67 (1982) 301. II01 V.L. Vyazovkin and V.A. Tolkatchev, Chem. Phys. 195 (1995) 313. I I I i V.A. Tolkatchev, V.M. Syutkin and V.L. Vyazovkin, Chem. Phys. 170 (1993) 427. 1121 G.P. Johari, Phil. Mag. B 41 (1980) 41. 1131 G.E Johari, J. Chim. Phys. 82 (1985) 283. ~' ' " ' ~ 232. il41 P.-G. J6nsson, Acta Crystallogt. B 32 ~,~,~j 1151 H.S. Bagdasaryan, Two-quantum photochemistry (Nauka, Moscow, 1976) p. 72. ll6l V.S. Chervonenko, V.A. Roginskii and S.Ya. Pshezhetskii, Khim. Vys. Energ. 4 (1970) 450. 1171 RB. Ayscough and C. Thomson, Trans. Faraday Soc. 58 ( i 962) ! 477. 1181 C.A. Angell and D.L. Smith, J. Phys. Chem. 86 (1982) 3845.
145
1191 L.E Boehm and C.A. Angeli, J. Non-Cryst. Solids 40 (1980) 83. 1201 L.E Boesh and C.T. Moynihan, J. Non-Cryst. Solids 17 (1975) 44. 1211 E.L. Zapadinsky, V.V. Korolev, N.E Gfitsan, NM. Bazhin, and V.A. Tolkatchev, Chem. Phys. 108 (1986) 373. 1221 V.M. Zaskul'nikov and V.A. Tolkatchev, Kinet. Catai. (USSR) 23 (|982) 1063. 1231 S.V. Vasenkov, V.A. Bagryansky, V.V. Korolev and V.A. Tolkatchev, Radiat. Phys. Chem. 38 (1991) 191. 1241 M.A. Neiss and J.E. Willard, J. Phys. Chem. 79 (1975) ~ 3 . 1251 M.A. Neiss, E.D. Sprague and .I.E. Willard, j. :i~aem. Phys. 63 (1975) I ! 18. 1261 V.L. Vyazovkin, B.V. Bok'shakov and V.A. Tolkatchev, Chem. Phys. 95 (1985) 93. I271 J.-E Bouchaud and A. Georges, Phys. Rep. 195 (1990) 128. 1281 A. Plonka, Annu. Rep. Prog. Chem. Sect. C. Phys. Chem. 91 (1994) 107. 1291 G. Zumofen, J. Klafier and A. Blumen, in: Disoder effects on relaxational processes, eds. R. Richert and A. Blumen (Springer, Berlin, 1994) pp. 251-278. 1301 T. Doba, K.U. lngold, J. Lusztyk and W. Siebrand, J. Chem. Phys. 98 (1993) 2962. 1311 T. Doba, K.U. Ingold, A.H. Reddoch, W. Siebrand and T.A. Wildmano J. Chem. Phys. 86 (1987) 6622. 1321 K.J. Tauer and W.N. Lipscomb, Acta Crystallogr. 5 (1952) 606. 1331 E Miiller-Piathe, L. Laaksonen and W.E Van Gunsteren, J. Mol. Graphics !1 (1993) 118. 1341 M.H. Cohen and G.S. Grest, Phys. Rev. B 20 (1979) 1077. 1351 S.S.N. Murthy and S.K. Nayak, .I. Chem. Phys. 99 (1993) 5362.
Chemical Physics 2 !6 (1997) 135-145
Methyl radicals migration in glassy ethanol-l,2d5 at 90 K as studied by hydrogen atom abstraction from the additives V l a d i m i r L. V y a z o v k i n *, V l a d i m i r A. T o l k a t c h e v institute of Chemical Kinetics and Combustion, Novosibirsk 630~90, Russian Federation
Received I December 1995; in final form 14 November 1996
Abstract
ESR technique has been used to study the kinetics of methyl radicals decay at 90K in glassy ethanol-l,2d5 with an admixture of diethyl ether and C2HsOH ethyl alcohol. It has been demonstrate(,, that methyl radicals migrate freely throughout the sample. The migration rate strongly depends on sample prehistory. The preliminary annealing at reaction temperature and/or the spontaneous cracking of matrix lead to a decrease in migration rate. The experiments indicate that the mechanism of radical migration in glassy ethanol differs considerably from that in glassy methanol. The probable reasons for this difference have been considered. © 1997 Elsevier Science B.V. All fights reserved.
1. Introdvction
Abstraction of hydrogen atoms from glassy alcohols by alkyi radicals occurs at low temperatures due to quantum tunneling [ 1-3 ]. Whereas the probability of tunneling dramatically depends on potential barrier parameters, the barrier substantially changes with varying relative arrangement of reagents, which complicates the tunneling transfer of atoms. In this case, the motion of atoms in a multi-dimensional potential with regard to the motion dynamics of reagents and products during tunneling is considered [ 4] instead of a simple problem of tunneling in a static double well potential [ 3,5 ]. In solids these motions can occur particularly due to lattice vibrations (for details see e.g. Refs. [6-9] ). However, the question of whether in solids at low temperatures the reagent motions can be treated as the lattice vibrations of a relatively small amplitude calls for additional experimental verification. * Corresponding authoc
If reagents are fixed in the lattice, the tunneling of atoms can proceed with a noticeable rate only from a few neighboring matrix molecules, the reaction must be treated as the in-cage one. This assumption can be verified by studying the radical decay in the mixture of usual and deuterated molecules. Let a fraction of H-molecules be c, and the number of the nearest matrix molecules be N. The probability that a cage contains i H-molecules is given by binomial distribution wi = C]vci (i - c ) N-i, where C]v = N ! / i ! ( N - i ) ! , the binomial coefficient. Particularly, some radicals can be generated in the surrounding of only deuterated molecules. First, the transformation of these radicals will give rise only the products of deuterium atom abstraction. Second, as the tunneling of deuterium is much slower than the hydrogen transfer, the kinetic curves of radical decay in mixed matrices must demonstrate two pronounced regions. First of all, the radicals with at least one H-molecule in a solvent cage, must decay rather rapidly. A slow disappearance of radicals surrounded by deuterated molecules only is to be
0301-0104/97/$17.00 Copyright (~) 1997 Elsevier Science B.V. All fights reserved. Pll S0301-0104(96)00354-0
136
V.L. Vyazovkin. V.A. Tolkatchev/Chemical Physics 216 (1997) 135-145
observed late in the reaction. The number of radicalaccessible matrix molecules N can be estimated by comparing the experimental values and those assumed for different N: - the ratio between the products of hydrogen and deuterium atoms abstraction; - the transformation depth at which the kinetics of radicals decay in a mixed matrix becomes identical to that in the pure deuterated one. We have studied in detail the kinetics of methyl and ethyl radicals reactions in the solutions of CH3OH, C2H5OH, and CH3CD2OH in methanol-d3 [ 10]. The experimental results are explicitly inconsistent witb the assumption of the in-cage character of the reaction between alkyl radical and matrix molecules. However, the reagent motions in this ma,,-i,: appear to differ much from what is usually called "diffusion". The peculiarities of reaction kinetics can be explained by assuming that the radical can abstract an atom from a rather large but still limited number of matrix molecules. The number of possible partners increases with rising temperature. For the methyl radical at 77 K N ~, 25, and at 90 K N ~, 100. Within an experimental accuracy, the N values for methyl and ethyl radicals coincide. Besides, N sharply decreases with ethanol-ld2 used instead of C2H5OH as the Hadditive when radicals are forced to abstract hydrogen from//-carbon atoms. These peculiarities are thought to indicate the fact that in glassy methanol the tunneling abstraction of H-atoms results from a cooperative fluctuational process [ 10,11]. The question arises of how much in common have the reactions of hydrogen abstraction by alkyl radicals in glassy methanol for glassy alcohols? The aim of the present paper is to determine a feasible mechanism of reagent mobility in ethanol- 1,2d5 at 90 K and to compare the results with the data for methanol.
2. Experimental The deuterated compounds from Isotope Co. (St. Petersburg, Russian Federation) C2DsOH (isotopic purity > 98.5 at. % D) and CD3I ( > 99 at. %) were used. Prior to usage ethanol C2HsOH was dried over anhydrous CaO, distilled, and stored over 3A molecular sieves. CD3I and CH3I (purum grade) were stored in the dark over copper. Dipheny!amine (DPA)
(reagent grade) and 2-chloroethanol (purum grade) were used as supplied. The NMR spectrum of ethanol-l,2d5 showed that the main hydrogen-containing impurity was ether (C2H5)20. Because of this ethanol-l,2d5 was additionally purified. For this purpose alcohol was boiled over CaO in a pyrex flask with a reflux condenser during 10 h. Thereafter upon heating a dry nitrogen flow was fed through the gas-inlet adapter into the bottom of condenser during 4 h. The flow rate was chosen so that ether vapors could be carried away with nitrogen and ethanol had time to condense on the walls of the condenser Dried and purified alcohol was distilled and stored over 3A molecular sieves. NMR spectrum showed that after purification ethanol1,2d5 contained the following impurities: 0.1 mol % (C2H5)20, 0.2 mol% CD3CHDOH, and 0.3 mol% CD2HCD2OH. (The NMR spectra were obtained on an AM-250 NMR spectrometer "Brucker"). The samples consisted of the mixture of ethanol isotopomers with a given composition. Solutions containing about 1 mol % iodomethane or iodomethaned3 and 5 x 10-3 mol % DPA in the solvent ethanol were placed in quartz tubes (3 mm i.d.), degassed by repeated "freeze-pump-thaw" procedure in vacuum line, filled with helium at a pressure about 100 Ton', sealed and cooled rapidly to 77 K by immersion in liquid nitrogen. In some experiments the tubes with detachable vacuum valves were used instead of the sealed ones. Just after cooling the samples formed a transparent matrix without any cracks. Some samples were used after preparation (not later than in 2 minutes). Below these samples will be referred as unannealed. The rest of the samples were kept in liquid oxygen for 37 h (annealed). Some samples, both annealed and unannealed, cracked spontaneously, being, however, still transparent (cracked). A few samples were broken in the tubes (crushed). For this purpose, the vacuum valve was detached from the tube immersed in liquid nitrogen. Liquid air, condensing on cold walls, was expected to fill the tube. Alcohol glass was broken with a sharpened steel rod cooled in liquid nitrogen. As this had taken place, the sample cracked throughout the volume and becmne opaque. During this procedure the sample temperature did not raise above 78 K. Finally, the vacuum valve was attached to the tube. The air was puniped out and the smnple was fi!l~ with helium.
137
V.L. Vyazovkin, VA. Tolkatchev/ChemicalPhysics 216 t1997) 135-145
It is known that at low temperatures ethanol exists not only as a glass but also as the orientationally disordered crystal [12,13]. This raises the question of whether the matrix is completely disordered, glassy ethanol and not a mixture of orientationally disordered crystalline and glassy ethanol. As known, if the glass contains microcrystals, then in a slow cyclic heatingcooling of the sample above glass transition temperature Tg (but below melting point) one may see a matrix devitrification and a gradual growth of microcrystals. In this case, a transparent glass becomes the nontransparent poiycrystailine matrix. If in the case of methanol glass the devitrification of matrix runs rather easily, in the case of ethanol, we have failed to observe any. This is likely to be assigned to a very large viscosity of the supercooled liquid and to a sharp temperature dependence of the ethanol viscosity. According to Ref. [ 14] ethanol crystals could be grown at a temperature very close to the melting point (,,~ 156 K). In our method of sample preparation, the cooling rate was high enough (,,~ 5 K/s) to prevent the formation of the crystalline phase of ethanol. The methyl radicals were generated by UVphotolysis of the samples. The details of sample illumination and kinetics measurements were described in our previous paper [ 10]. The concentration of (~H3 radicals was detected by the side high-field component of their ESR spectrum. The CD3 concentration was detected by the line marked as h in Fig. l a. A distortion of these lines due to overlapping with the spectra of reaction products was negligible.
3. Results 3. I. Identification o f reaction products
Fig. l a depicts the first derivative ESR spectrum for CD3I solution in ~thanol-1,2d5 just after the photolysis at 77 K. A seven-line signal with a sepmation of 3.5 G at the center of spectrum is attributable to (~D3 radicals. A weak outer signal arises from matrix radicals forming during photolysis in side reactions. The similar ESR spectra have also been obtained just after the photolysis of CD3I solutions in the C2HsOH + C2DsOH mixtures. When the sample temperature is raised to 90 K, the intensity of methyl radical spectra gradually decreases and that of matrix
CD3CDOIi . . . . .
i
I
,
,
CH3CHOC2H~ Fig. 1. ESR spectra of iodomethane-d3solution in ethanol-l,2ds: (a) just after UV-photolysisat 77 K; (b) after complete decayof t~D3 radicals at 90K. (c) ESR spectrum of the DPA solution in ethanol-l,2d5 after photolysis at 77 K and subsequent annealing for 72 h at 90 K. radicals increases. The total radical concentration determined by a double digital integration of ESR spectra remains constant in the course of reaction. Fig. i b demonstrates the spectrum obtained after a comple:te decay of (~D3 radicals in ethanol-l,2ds. It consists of a few overlapping spectra. A signal at the center of spectrum actually coincides with the spectrum of the DPA solution in ethanol- 1,2d5 photolyzed at 77 K and annealed during 72 h at 90 K (Fig. l c). It is known that in the latter case the CD3CDOH radicals form [ 15 ]. Four wide outer lines originate from the radicals generated by the reactions of methyl radicals with diethyl ether impurity. This signal is likely to be caused by CH3CHOC2H5 radicals. Their ESR spectrum is known ~o consist of five broad lines with a splitting of 22G [ 16]. The central line of this quintet overlaps the spectrum of CD3(:DOH radicals and the four outer components are well proaounced i~ ~he ESR spectrum. Fig. 2a shows the ESR spectrum obtained after a complete decay of CD3 radicals in the mixed matrix with 1.0 mol % C2H5OH. The similar spectra were also recorded for the larger contents of C2H5OH.
138
V.L. Vyazovkin. [fA. Tolkatchev/Chemical Physics 216 (1997) 135-145
hi
a
3H
,,.
CD~CDOH ,
I
i
I
,
CH3CHOH
L
I
I
I
m
,
CH2CH2OH Fig. 2. (a) ESR spectrum of CH31 solution in the mixture 0,01C2HsCH + 0.99C2DsOH after complete decay of the methyl radicals. (b) Spectrum of DPA solution in C2HsOH after photolysis at 77K and annealing for 48 h at 90K. (c) Spectrum of 2-chloroethanol solution in ethanol-l,2d5 just after photolysis at 77 K. The dashed line depicts a result of numerical subtraction of CD~t~DOH radical spectrum (Fig. Ic).
When a fraction of C2H5OH increases, the contribution of CD3CDOH radical signa~ becomes less noticeable and a relative intensity of four outer lines grows. It is assumed then that these lines arise from the CH3~HOH radicals resulting from H-atom abstraction by methyl radicals from C2H5OH. However, comparing four outer components of spectrum 2a with the corresponding lines in the spectrum of the CH3CHOH radicals obtained by photolysis of DPA solution in C2HsOH (Fig. 2b), one can observe considerable differences. Probably, these differences are 0 :e to overlapping of the (~H2CH2OH radicals spectrum. They can be formed by Hatom abstractioa from the methyl groups of ethanol. This assumption was verifi~d by the photolysis of a frozen 1.0 mol % 2-chloroeti~anoi solution in ethanol-1,2d5. A solid line in Fig. '~c depicts the ESR spectrum obtained just afk.r t,hutolysis. In this case, the CH2CH2OI-[ radicals are generated by the reaction of dissociative electron attachment. The side reactions give rise to the matrix CD3CDOH radicals. The spectrum of CH2CH2OH radicals (dashed line in Fig. 2c) was obtained by numerical subtraction
of CD3t~DOH radical spectrum (Fig. lc). It consists of six lines with an intensity ratio approximately equal to 1:3:4:4:3:1, which are brGadened by anisotropic hyperfine interaction (h.f.i.). The spectrum can be explained assuming the existence of h.f.i, with two equivalent a-protons (isotropic h.f.i, constant aa = 24G) and two inequivalent fl-protons (a~ I) = a~2)/2 = 24 G). As expected, the constants of isotropic h.f.i, for (~H2CH2OH radical are very close to the values typical of the alkyl radicals forming from the radiolysis of nalkanes and n-alkylhalides. For instance, the constants of isotropic h.f.i, for the (~H2CH2CH3 radical a,~ = a~!)~ = a~2)/2 = 23G, and for the (~H2(CH2)2CH3 one a,~ = a~I) = a~2)/2 - 21G [17]. It can readily be seen that the side high- and low-field components of the (~H2CH2OH radical spectrum (marked by asterisks in Fig. 2c) do not overlap the lines of the CH3CHOH one (Fig. 2b). However, no lines of the CH2CH2OH radical were observed in the spectrum of the products of methyl radical decay in the mixed matrix. It can be concluded then that no ¢~H2CH2OH radicals form by the reactions of methyl radicals with the C2HsOH + C2DsOH mixtures. Thus, a feasible reaction of H-atom abstraction from alcohol methyl group can be neglected. The difference in the spectra of ethanol radicals sta.. bilized in C2H5OH and C2DsOH seems to be caused by the following. It is known that ethanol in the solid phase contains both the trans and gauche conformers [ 14 ]. It is quite probable that the CH3CHOH radicals in ethanol also exist in different forms. A complex ESR spectrum lineshape is a result of the spatial averaging of anisotropic h.f.i, and the overlapping of slightly different spectra of the radicals existing in various conformations. Besides, in the deuterated matrix the broadening of spectrum lines due to dipole-dipole interaction is much smaller than in the hydrogen-containing one. It seems likely that the complex structure of the CH3(~HOH spectrum, manifesting itself in the deuterated matrix, is simply blurred in C2HsOH ethanol. The ESR spectra of CH3CHOH and CH3CHOC2H5 radicals in frozen ethanol and diethyl ether, respectively, are known to be almost the same [ 16]. Comparing spectra 2b and I b for the ethanol-1,2d5 matrix their differences (if any) are observed to be minor. It is concluded that in "pure" ethanol-l,2d5 matrix, the methyl radicals can abstract hydrogen only from the
VL. Vyazovkin. V.A. Tolkatchev/ Chemical Physics 216 (1997) 135-145
139
a-carbon atoms of ether impurky. The H-atom abstraction from methyl groups of ether can be neglected. The similar results have been obtained for the CH3I solutions in the mixtures of ethanol isotopomers. The only difference is in the fact that initially the wellknown four-line spectrum with a splitting of 23 G was observed instead of the CDa radical spectrum.
O'
c "
~,6
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3.2. The results of kinetic measurements
~
[] - 7
As follows from the above data, in the C2HsOH + C2DsOH mixtures the methyl radicals decay by the
following reactions: R + C2DsOH
, RD + CD3CDOH,
e2
( 1) (2)
R + (C2H5)20 ---* RH + CH3CHOC2Hs,
(3)
, RH + CH3CHOH,
-2 -3
03
v-
R + CD3CDHOH ---, RH + CD3CDOH,
R + C2HsOH
8
(4)
where R is either CH3 or CD3. Fig. 3 presents the relations between the concentrations of the H-atom abstraction products (proportional to line hi intensity in spectra lb and 2a) and the (~D3 radicals (proportional to h in the spectrum ! a) in the course of the reaction. For "pure" ethanol- 1,2d5 the product is the C H 3 C H O C 2 H 5 radicals. Since the spectra of CH3CHOC2H5 and CH3CHOH radicals are very close and fully overlap, in mixed matrices the line hi intensity is proportional to the sum of the concentrations of these radicals. The following peculiarities have engaged one's attention: (i) In all cases, the products of H-atom abstraction from the hydrogen-containing admixture accumulate to the point of methyl radicals disappearance. (ii) The relations between hi and h are linear. Thus, in the matrix of a given composition the relation between the probabilities of the abstraction of both the hydrogen atom from H-additive and the deuterium one,,; from C2DsOH remains constant in the course of reaction. (iii) The greater is the concentration of Hsubstituted reagents in the matrix, the larger fraction of methyl radicals abstracts the H-atoms, however when the fraction of C2H5OH t> 4 tool %, almost all methyl radicals react only with the additive.
0.0
0.2
0.4
0.6
0.8
1.0
h(t)/h(0) Fig. 3. The dependence between intensities of ESR spectra lines of the (~D3 radicals (h) and the radicals of H-atom abstraction (hi) (see Figs. I and 2) in the course of methyl radicals decay in mixed matrices at 90K. The amount of C:,HsOH in mol%: (1,2) 0.0; (3-6) 1.0; (7) 4.0. Sample: (1,3,7) unannealed, non-cracked; (2,4) annealed, cracked at the moment of reaction initiation (t = 0 ) ; (5) unannealed, crushed at t - 0; (6) unannealed, crushed in the course of reaction at t = 2460s.
(iv) The preliminary annealing of matrix and the cracking of samples are manifested in the relation between hi and h only for the low H-additive cont:entrations, whereas the prehistory of samples can readily be observed for all cases in the reaction kinetics (see below). Fig. 4 depicts the kinetic curves of methyl radical decay in glassy ethanol-l,2d5 and Figs. 5-7 show them for the mixed matrices with 1.0 mol % of C2HsOH. The kinetic curves are plotted as l o g ( [ R ( t ) ] / [ R ( 0 ) ] ) vs. t°'5, where [R(t)] is the methyl radical concentration, t is the time. This method is more convenient for representing the experimental results. The matter is that the above reactions first run rather quickly and then sharply slow down. The nonlinear transformation of the time axis can be used to simultaneously plot a short "fast" initial region of the kinetic curve and a long "tail". Comparing the kinetic curves for the samples of the same composition, we see that the reaction rate is
V.L. Vyazovkin, V.A. Tolkatchev/Chemical Physics 216 (1997) 135-145
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O "~" tw -0.5
,----a
A
-1.0
•
"I
o
,,~I
m
-3
-1.0 ,,_._.a
7
.00 -I,5
o -1.5
-2.0
-2.0
Fig. 4. The kinetic curves of the (~H3 (1,2) and (~D3 (3,4) radicals decay in glassy ethanol- 1,2d5 at 90 K. Sample: (!,3) unannealed, non-cracked; (2,4) annealed, cracked at t = O.
Fig. 6. The kinetic curves of the (~L~I3radicals decay in unannealed glassy mixtures O.01C2HsOH + 0.99C2DsOH at 9OK. Sample: ( 1 ) cracked at t = O; (2) cracked .;~ the course of reaction (arrow marks the moment of cracking).
(seconds) °.5 50 .
.
.
.
I
100 .
.
.
.
I
150 .
.
.
.
!
'
'
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(seconds) °.s
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50 .
.
.
.
!
100 .
.
.
.
I
150 .
.
.
.
1
'
o -2
m -3 ~-1.5
^
-4
~'-05
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-1,0 -20
--
Fig, 5. The kinetic curves of the (~D3 (1,2) and CH3 (3-6) radicals decay in glassy mixtures O.OIC2HsOH 4-0.99C2DsOH at 90K. Sample: (1,3) unannealed, non-cracked; (2,6) annealed, cracked at t = 0; (4) annealed, non-cracked; (5) unannealed, cracked at t = O.
the highest in the unannealed and non-cracked samples (Figs. 4-6). Note that the reaction kinetics in such samples demonstrates a poor reproducibility. Repeating experiments for both (~H3 and CD3 radicals, we have established that the reaction rate accidentally varies within rather wide limits. Curves 1 and 3 in Figs. 4 and 5 are given as the boundaries of a nonreproducibility region. Both the preliminary annealing and spontaneous cracking of samples slow down the reaction. Of interest also is a lower degree of kinetics nonreproducibility in the annealed and/or cracked samples compared to the unannealed ones (Figs. 4 and 5). When the ma-
-1.5 -20
Fig. 7. The kinetic curves of the (~H3 radicals decay in unannealed glassy mixtures 0.01C2HsOH + 0.99C2DsOH at 90K. Sample: ( I ) non-crocked; (2) crushed at t = 0; (3) crushed in the course of reaction (arrow marks the moment of crushing); (4) cracked at t = O .
trix cracks during reaction, its rate (to within experimental accuracy) becomes the same as in the matrix, cracked at the instant of (or just after) methyl radical generation (Fig. 6). A mechanical crushing of matrix both before the photolysis and during the reaction has no effect on the kinetics of methyl radical decay (Fig. 7). In both cases the reaction runs to within experimental accuracy so as in the unannealed and noncracked samples.
V.L. Vyazovkin, VA. Tolkatchev/Chemicai Physics 216 (1997) 135-145
141
4. Discussion
4.2. Matrix relaxation
4.1. The number of radical-accessible matrix molecules
It is common knowledge that a fast freezing of liquid gives rise to the inhomogeneous stressed glass, either the long-term annealing or slow freezing result in the formation of a more homogeneous glass with a higher specific density. In these glasses the rate of molecular motions is less than in the unannealed ones. A decrease in molecular mobility in glasses during at.~aealing below Tg was recorded e.g. by the decrease in the ionic conductivity of alkali-silicate glasses [ 19,20], by the changes in the spectrum of dielectric losses [ 13 ], by the changes in the rate of phenanthrene phosphorescence quenching by oxygen in methanol [21]. The relaxation of matrix is manifested in the kinetics of diffusion-controlled reactions. In Ref. [22] the influence of preliminary matrix annealing on the kinetics of ethyl radical oxidation by molecular oxygen in methanol-d4, ethanol-d6, and n-butanol-dl0 is described in detail. In all cases the oxidation rate is decreased upon preannealing. The preannealing was observed to retard also the oxidation of methanol radicals in glassy CH3OD [21 ] and of tert-butyi radicals in squalane [23]. As in the present paper, the rate of radical decay in 3-methylpentane-dl4 (3MP-d14) at 77 K noticeably decreases after the preannealing of glass [24]. Unfortunately, the mechanism of methyl radical decay in 3MP-dl4 has not been established unambiguously. It can be assumed that one of the substantial channels is the H-atom abstraction from the residual C-H bonds in 3MP-dl4. This is confirmed by a large CH4 methane yield upon CH3I radiolysis in 3MP-dl4 [ 25 ]. Due to annealing the matrix structure changes rather slowly. Experimentally, however, the fast relaxation of glass structure accompanied by its cracking is also possible. In kinetics as in preannealing, this results in reaction retardation. In this case, the fractures can be recorded on the kinetic curves (see e.g. Fig. 6). Earlier, the influence of matrix cracking has already been observed both in studying the decay of methyl radicals in 3MP-d~4 [ 24 ] and in the oxidation of tert-butyl radicals in squalane [23]. However, there are some differences from our case. When 3MP-dl4 cracks, not only the rate of methyl radical decay decreases but also the kinetic law changes. In unrelaxed 3MP-dl4 the kinetics of radical decay is nonexponential. In the relaxed matrix the variations in their concentration with
The above data show that, in ethanol at 90K the methyl radical quite rapidly migrates throughout the matrix. In this case, it can either abstract an H-atom at random encounter with H-additive or slowly react with the surrounding ethanol-1,2d5 molecules abstracting a deuterium atom from one of them. The migration rate is high enough to provide a fairly high probability of radical encounter with H-molecule even if its concentration in the matrix is about 0.1 moi %. This is verified by the linear dependences in Fig. 3. If the mobility of methyl radicals was limited, then the accumulation of H-atom abstraction products from the additive would te~xninate at any degree of their conversion. The probability that among N encountering molecules there are no H-substituted ones is w0 = (1 - c ) ~¢. For example, when the number of accessible molecules N = 100, with c -- 10 -3 only 10% of the initial amount of methyl radicals could react with H-molecules. During the decay of the remaining 90% of radicals no accumulation of the products of H-atom abstraction could occur. Such a situation is exemplified in Fig. 3 (dashed line). The dala in Fig. 3 can be used to estimate the number of matrix molecules, N, with which the radical can react during its lifetime. Experimentally, not less than 95% of the initial amount of methyl radicals can meet at least one impurity diethyl ether molecule during its lifetime in ethanol- 1,2d5. Thus, w0 ~< 0.05 with c ~ 10 -3. As a result, N ) 3 x 103. This number is approximately 100 times as much as that of matrix molecules accessible for methyl radicals in glassy methanol-d3 at 90 K [ 10]. It is assumed that at 90 K in ethanol- 1,2d5 the methyl radicals migrate rather freely whereas in methanol-d3 their movements are limited to a small region near formation site. A significant distinction between radicals mobilitles in glassy ethanol and methanol is of interest, because the glass transition temperatures for these matrices are close. According to the data in Refs. [ 13,18 ] for methanol Tg - 103 K and for ethanol Tg = 97 K. To this we can add, that the recombination of alkoxy radicals in these matrices take place in the same temperature ranges T = 95100K.
142
V.L. Vyazovkin, V.A. Tolkatchev/Chemical Physics 216 (1997) 135-145
time are described in terms of the normal first-order law. In our case, the relaxation has almost no effect on the kinetic law. Concerning the oxidation of ten-butyl radicals in squalane, the reaction retards not only due to annealing or spontaneous cracking, but also due to the mechanical crushing of samples [23]. In the artificially cracked ethanol glass the abstraction reaction runs so as in the non-cracked unannealed matrix (Fig. 7). The influence of matrix relaxation on the kinetics of methyl radicals reaction with the mixtures of isotopesubstituted ethanols can be considered as an argument in favor of the diffusion mechanism of reagent approach in this matrix. In glassy methanol the annealing has actually no effect on the kinetics of H-atom abstraction [ 10] whereas the kinetics of the diffusioncontrolled oxidation is subjected to a noticeable action of annealing.
where [R] is the methyl radical concentration ( [ R] << c); [ PH] and [ PD ] are the concentrations of the products of H and D-atom abstraction, respectively; Wo(t,p) is the time-dependent rate constant of deuterium abstraction from matrix molecules; W(t,p) is the radical diffusion rate; t is the elapsed time from the reaction initiation; p is the set of parameters determining the matrix properties that can also vary with time (matrix relaxation). A number of mechanisms can cause WD and W to vary with time. As an example one can refer to the random walk of particles in the energetically disordered and lowdimensional media (fractals). Both of these models present a way to obtain a rate constant of diffusion controlled reaction which varies with time (see e.g. reviews [ 27-29] and references cited therein). The time dependence of WD will be discussed below. Dividing (6) by (5), we obtain: d[PH] / d[R] =-cW( t, p ) / ( W o ( t , p ) +cW( t,p) ).
4.3. Reaction kinetics
(8) Thus, both the results obtained and the low magnitudes of isotopic effects in the yield of methane isotopomers [26] allow the conclusion that in the mixture of ethanol isotopomers at sufficiently low content of H-molecules the rate of H-atom abstraction reaction is limited by the diffusion approach of reagents. The rate of methyl radical migration is high as compared to the radical decay rate due to deuterium atom abstraction from the nearest matrix molecules. However one major complication exists. The reaction proceedts with time nonexponentially. As it has been shown earlier, the reaction of hydrogen atom abstraction by alkyl radicals in the glassy mixtures of alcohol isotopomers and diffusion-controlled reactions of radical oxidation in glassy alcohols could be explained in terms of a time~lependent reaction rate "constant" [ 26,22]. Probably, in our case (c << 1) the decay of methyl radicals and the accumulation of the products of deuterium and hydrogen atoms abstraction can be described by the following set of equations:
dIR]/dt---(WD(t,p) +cW(t,p))[Rl,
(5)
d[PH]/dt = cW(t,p)[R],
(6)
dtPDl/dt = WD(t,p)[R],
(7)
If c is large enough, so that WD(t,p) < cW(t,p), then d[PH]/d[R] ,~ 1. It is suggested that at a sufficiently high H-additive concentration the relation between the concentration of methyl radicals and H-atom abstraction products will be independent of matrix relaxation. As follows from Fig. 3 c = 0.01 can be assumed high enough. Its further 4-time increase leads to only a 30-40% increase in the fraction of methyl radicals reacting with the H-additive. No wonder that already with c .>i 0.01 for all kinds of the samples the same relation has been observed between the concentrations of CD3radicals and H-abstraction products in the course of reaction, although the preliminary annealing and cracking of samples are manifested in kinetics (Figs. 5-7). Another limiting case is realized, probably, for the decay of methyl radicals in "pure" ethanol- 1,2d5: d[PH]/d[R] ~ - - c W ( t , p ) / W D ( t , p ) .
(9)
First, experimentally, due to matrix relaxation the diffusion rate changes more dramatically than that of deuterium abstraction. Second, the linearity of the relation between [ Pa] and [ R] (Fig. 3) requires that the time-dependence of the rate "constants" of WD and W must be rather close. The nonexponential kinetics of the tunneling atom abstraction from matrix
V.L. Vyazovkin, V.A. Tolkatchev/Chemical Physics 216 (1997) 135-145
molecules was explained by the different theoretical models [6,30]. As a rule, in these models the analysis starts with the following assumptions: - the reaction rate is controlled by the rate of hydrogen or deuterium atom transfer; - atom tunneling probability vary sharply with the distance between reagents; - the disorder of glass structure causes a broad distribution of a distance between the radical and the nearest matrix molecules thus leading to the dispersion in reactivity. In our case this approach is inadequate. If radical diffusion brings matrix molecules close to the radical than they would be in the static structure, then the radical will decay more rapidly. So the distribution of reactivity will be more narrow than in static case and the decay kinetics will be more closer to the regular exponential one expected for the first-order reactions. It is clear that the shape of decay curve would be determined by the relationship between the rates of atom tunneling and of radical migration. One would expect that the kinetics of radicals decay in the deuterated matrix must be less nonexponentia~ than in the normal one due to more complete dynamical averaging of reactivity dispersion. It is easy to see that this conclusion is inconsistent with the experimental results [ 10,26,30]. It is quite possible that the rate of deuterium atom abstraction is controlled not only by atomic tunneling, but also by the processes of methyl radical approach to matrix molecule and their mutual orientation to reach the arrangement which is more suitable for atomic transfer (for details see Refs. [10,26]).
4.4. Radicals mobility and structure of a glassy alcohol A considerable difference in the kinetic behavior of the reactions of H-atom abstraction by methyl radicals from H-molecules in glassy methanol-d3 and ethanol1,2d5 is likely to be due to the difference in the structures of t~ese glasses. According to Ref. [ 31 ], the lineshape of the ESR spectra of methyl radicais in glassy CH3OD and CHD2OH can be explained assuming that the local structure of glassy methanol resembles the structure of a high-temperature fl-phase of crystalline methanol. According to Ref. [ 32], the orthorhombic lattice of the methanol fl-phase exhibits infinite, flat, zig-zag chains of hydrogen-bonded
143
Fig. 8. Projection of a unit cell of ethanol along the crystalline axis a (according to data of Ref. | 141 ).
methanol molecules. In this case, the structure of methanol-water glass can be represented as the short (5-10 molecules) portions of such chains joined via water molecules into a sufficiently rigid random thl'eedimensional network. The crystal lattice of ethanol is an array of infinite chains of hydrogen-bonded molecules too [ 14]. The hydrogen-bonds form almost flat units containing the alternating gauche and trans conformers (Fig. 8). Probably, the glassy ethanol structure consists of the molecular chains of various lengths, the local structure of which is close to the crystalline one. (It is obvious that some ef these cl~ains can form the ring-like structures.) It is of first importance that these chains remain non-linked due to absence of water molecules which are able to form more than two H-bonds per molecule and to serve as the junction of hydrogen-bonded network. The different hydrogen-bonds spatial structures can cause a higher methyl radical mobility in glassy ethanol compared to that in methanol as well as a greater influence of the preliminary annealing. A probable reason can be the following. Due to the close packing of molecules in solids, a molecule can move only when a sufficiently large number of the surrounding molecules are displaced from their normal fattice positions. For example, the computer modellag of oxygen diffusion in glassy poly (iso-butylene) shows that a penetrant moves from a cavity to the
14~
VL. Vyazovkin. V.A. Tolkatchev/Chemical Physics 216 (1997) 135-145
neighboring one in a very shot time compared to the residence time. Infrequent jumps between the cells result from the formation of fairly wide passages between the neighboring cells, arising from random cooperative shifts of a large number of molecules [ 33 ]. A rigid structure of methanol-water glass requires that in such cooperative shifts the hydrogen-bond network be distorted and may be some of the bonds be ruptured. It is clear that at low temperatures such energetically expensive motions of matrix molecules must become unduly infrequent. In ethanol, compared to methanol, the diffusion of small particles, such as methyl radical, is likely to need no strong distortions of the hydrogen-bonds, i.e. substantial free energy losses. For example, as it is seen from Fig. 8, a passage for methyl radicals to move from one cell to another can result from the torsional displacements of the ethyl groups of alcohol molecules about the C-O bonds. Evidently, the relaxation of nonequilibrium glass structure due to annealing will be different in ethanol and methanol. A rigid network of hydrogen bonds must prevent substantial shifts of molecules in glassy methanol. In ethanol, the non-linked molecular chains can move more freely relative to each other. In addition, in ethanol the matrix structure can relax due to the torsional movements of ethyl groups around the C.-O bonds. In this case, a free volume in glassy ethanol is expected to decrease upon a sufficien0y long annealing and the probability of I~,~ctua6onal formation of a free volume near the radical d.ecreases. According to the concept of free volume relaxation [341, the rate of radical diffusion must drop. The relaxation of glass structure due to the tension release upon matrix cracking can be considered in a similar way. However, unclear is the absence of the influence of artificial matrix cracking. More likely, this testifies to the fact that the development of cracks leads to the structural changes just near the cracks rather than in the bulk. Below the glass transition temperature the response of an electrical or mechanical stress known as a secondary or/~-relaxation occurs in the amorphous solids. This type of relaxation is determined by the increased local molecular mobility in media. As it is known, the height of the loss peak for the secondary relaxation decreases on physical ageing (annealing) of a glass. It is quite probable that the molecular motions associated with fl-relaxaticn determine the molecu-
lar diffusion in a glass. It may be of interest to study the correlation between the influence of any variable and procedure (annealing, glass composition and the like) on the secondary relaxation and on the reaction kinetics in the glassy alcohols. Unfortunately our attempts to lind the data on the ,8-relaxation in glassy methanol and ethanol in the literature have failed. The data on the glass transition processes in more complex monohydroxy alcohols [35] are in agreement with our interpretation. In all alcohols (2-propanol, land 2-butanol, 2-methyl- l-propanoi and 3-methyl- lbutanol) the two glass transition temperatures are detected and attributed to the freezing of H-bonded network and free molecules, respectively. Below Tg, all liquids show two processes, one of which (with activation energy 4.5-7 kcai/mol) was attributed to the free molecules (or segmental) motion and the other ( " 2.5 kcal/mol) to the OH group motion. It is believed that in glassy ethanol the same sub-Tg processes take place with the close values of activation energy and loss-peak frequency.
5. Conclusion The kinetics of methyl radical decay at 90K in glassy ethanol-l,2d5 with dissolved H-substituted compounds favors the actually frec bulk migration of radicals. The migration rate is subjected to the influence of sample relaxation both during the annealing and due to spontaneous cracking. On the other hand, as reported earlier [ 10], in glassy methanol the motions of reagents occur in the bounded regions of matrix, and the matrix relaxation during annealing or due to cracking does not practically manifest itself in reaction kinetics. This testifies to the substantial differences in the mechanisms of methyl radical migration in these apparently similar matrices. Most probably, this difference is related to that in the molecular structure of glassy methanol and ethanol.
Acknowledgement The authors are grateful to Dr. A.I. Kruppa for his assistance in NMR analysis of ethanol-1,2d5.
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