H-atom abstraction from alcohols by alkyl radicals. Cooperative effects in the reactions of alkyl radicals in glassy methanol-d3

Chemical Physics ELSEVIER

Chemical Physics 195 (1995) 313-327

H-atom abstraction from alcohols by alkyl radicals. Cooperative effects in the reactions of alkyl radicals in glassy methanol-d 3 Vladimir L. Vyazovkin, Vladimir A. Tolkatchev Institute of Chemical Kinetics and Combustion, Not'osibirsk 630090, Russian Federation

Received 20 July 1994

Abstract The ESR technique has been used to study the kinetics of the reaction of methyl and ethyl radicals with the additives of hydrogen-substituted alcohols CHsOH, CzHsOH , and CH3CD2OH, dissolved in glassy methanol-d3, within the temperature range 77-92 K. It has been demonstrated that the number of radical-accessible matrix molecules increases with temperature reaching N = 100 at 90 K, and is actually independent of radical type and strongly dependent on the type of H-substituted additive. Upon substitution CH3CH2OH by CH3CD2OH at 90 K the number of methyl radical-accessible molecules decreases from N = 100 to N = 5. Using the data obtained it has been concluded that the large number of radical-accessible matrix molecules is not determined by its migration throughout the matrix as well as by the peculiarities of glass structure (the existence of the regions with high molecular mobility and/or with the large free volume). The model has been proposed fi)r the elementary reaction of hydrogen atom abstraction in solids, according to which the atom transfer becomes possible due to the fluctuation rearrangement of molecular radical environment.

1. Introduction The concepts, developed to describe the processes, occurring either in gases or liquids, are usually used in theoretical considerations of solid-phase chemical reactions. It is assumed then, that the initial state of reagents and the final one of products are separated by a barrier that can be overcome by either classical (over-barrier), or quantum (tunneling) ways. The solid matrix, in which the reaction takes place, is considered as both the thermostat from which and to which the energy is given by reacting molecules, and the medium, limiting the mobility of regents and products. A solids, however, can more directly participate in the reaction. Due to a close matrix packing, the reaction can need the displacement from the

equilibrium positions of not only the reacting particles but also of a sufficiently large number of surrounding molecules. In this case, the many-particle system is known to pass a series of minima and maxima on the surface of potential energy (see e.g. Refs. [1-3]). This problem has already been discussed when studying atomic hydrogen abstraction by free radicals from matrix molecules [4-6]. The assumptions of the existence of many potential barriers in the reaction path help one to understand both the anomalously weak dependence of the probability of H-atom tunneling transfer on the distance between reactants and the low kinetic isotopic effects, observed in some systems. In this paper we are going to discuss once again this issue in connection with other phenomena, observed in the reactions of alkyl

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V.L. Vyazot,kin, V.A. Tolkatchec / Chemical Physics 195 (1995) 313-327

radicals with glassy alcohols, i.e. the anomalously large number of matrix molecules that can react with alkyl radicals. The hydrogen atom abstraction by alkyl radicals from alcohols at low temperatures proceeds via tunneling. This is confirmed by the large magnitudes of kinetic isotopic effect upon substitution of the atom abstracted by deuterium as well as by the existence of a low-temperature limit for the rate constant [ 7 14]. The probability of H-atom tunneling sharply decreases with increasing distance between reagents. According to Ref. [14] it must decrease by an order of magnitude when the distance of under-barrier transfer increases by 0.(15-0.1 ,~. It is concluded then that the atom abstraction occurs only upon direct contact of reagents. The number of molecules from which the abstraction is possible must depend, in this case, on matrix structure at the site of radical stabilization. Assuming that the molecular motions in solids are actually frozen out at low temperatures and reduce to lattice vibrations, a free radical seems to react only with few closest matrix molecules. However, the kinetics of alkyl radicals decay in the mixtures of H- and D-substituted alcohols testifies to the fact that the number of potential partners of radical may be as mach as few tens [6,9-11,13]. Such great distinctions between the value of N theoretically assumed for in-cage reaction (a few units) and the experimentally determined one (a few tens) has provoked a number of questions. First, some doubts are cast upon the correctness of the experimental determination of the number of radical-accessible matrix molecules. These are first of all caused by the fact that even in isotopomerically pure matrices a sharp retardation of reaction has been observed. The alkyl radical concentration [R] decays according to [R]/[R]0=exp(kt~),

(1)

where t is time, k and o~ are the constants varying with temperature, type of radical, and alcohol [9-13]. This kinetic behavior has been explained by different theoretical models [9,11-14]. As a rule, these models contain either clear or unclear assumptions and free parameters, the values of which are chosen to fit a theory to the experimental data. Particularly, in such a manner the large values of N have been obtained for the reactions of alkyl radicals with glassy alco-

hols in Refs. [10,13,14]. In this case, the N values can be considered not as the evidence for possible reactions between radical and distant partners, but rather as the evidence for the inadequacy of the proposed theoretical models to experimental results. Therefore the primary aim of this study is to determine the number of matrix molecules accessible for methyl and ethyl radicals in glassy methanol without recourse to any additional theoretical assumptions. As will be shown below, this number is large indeed and sometimes amounts to 100. The next aim of the paper is to experimentally choose between the different possible mechanisms that allow radical to react with distant partners. There are data in the literature that testify both to and against each following mechanism. The most simple explanation is that even at low temperatures the radical migrates over matrix successively changing the possible partners. The atom transfers in the "radical-molecule" pair by tunneling. Particularly, the same mechanism has been proposed in Refs. [10,13,14] in attempting to bring into agreement the developed theory with experimental results. The following can be the possible reason for high molecule mobility in glassy alcohols. The glass is assumed to consist of fairly large areas that substantially differ in their medium density and the molecular mobility. These concepts are widely used for describing relaxation phenomena and the diffusion of small molecules in glasses [15-17]. Since radicals result from the decay of precursors, it is quite probable that their stabilization mainly occurs in the zones with excess free volume a n d / o r high molecular mobility, in which the fragments of precursors become widely separated. It is concluded then that the reaction proceeds in these " p o r o u s " zones. If the zone size is small enough, it can determine the number of possible radical partners. One can propose another mechanism of H-atom abstraction from matrix molecules in solids. Assume that the radical does not migrate from the site of its generation until it decays. The probability of atom transfer from matrix molecules to radical, while the reagents occupy the equilibrium sites in the lattice, is negligibly small. Since the glass is a thermodynamically nonequilibrium system, in a small volume, surrounding the radical, the excess energy, stored in

V.L. Vyazovkin, V.A. Tolkatchec / Chemical Physics 195 (1995) 313-327

the matrix during either vitrification or radical formation, can be set free. While the matrix is in the " h o t " state, the reagents quickly approach each other and the atom is transferred to the radical. In this case, the reaction radius will depend on the mean volume of the zone into which the energy is released, on the rate of reagent movement in the zone and the life-time of the zone in the " h o t " state. The next mechanism is actually the combination of the above two. Let either the radicals be generated in the zones with high molecular mobility, or their formation cause such a local change in matrix structure that, initially, at the site of radical location the molecular mobility is high. Further the glass structure relaxes and the molecular motions slow down with time. In this case, the number of radical-accessible molecules will be determined by the distance, covered by radical upon the relaxation of matrix structure. In some papers [5,6] the authors have considered the following mechanism of the tunneling reaction of hydrogen atom abstraction in solids. The reaction act involves not only the reactants, but also a large number of the surrounding matrix molecules. The reason is that any motions of molecules in solids have of necessity a cooperative character because of a close matrix packing. The potential energy of such a molecular cluster, as mentioned above, must have many local minima. Each minimum corresponds to a definite cluster configuration, including a radical and a number of matrix molecules. There is a global minimum, corresponding to the equilibrium position of the radical and its molecular surrounding. (The existence of many configurations of radical environment with a minor difference in their structure, but with a major one in their energy, has been experimentally verified by, e.g. studying the realignments of the radical pairs in the ",/-irradiated potassium malonate monohydrate single crystals [18].) Due to fluctuations, the reaction cluster can pass from the initial state, where molecules occupy the equilibrium positions in the lattice, to the more energetic one. In this case, a fairly long-living state of the radicalmolecule pair can be obtained, in which the partners have the optimal mutual arrangement, and are in the energy state required for the quantum atom tunneling. While the molecular cluster is in the nonequilibrium state, the atom transfer is fast enough. When

315

the molecular system reverts to the equilibrium state, the matrix structure recovers, the exchange of atoms between reagents actually comes to a halt. Within the frame of this mechanism, the large value of reaction radius is caused by substantial fluctuative displacements of reagents with the appearance of the excited state of a molecular cluster. In this case, no bulk migration of reagents is observed because most time they occupy the almost same matrix sites as at the moment of radical generation. Reagent diffusion appears at higher temperatures when the fluctuative displacements of the molecules are so large that the system is able to pass to a new equilibrium state. In order to determine the mechanism realized during hydrogen atom abstraction by alkyl radicals from glassy alcohols a series of questions should experimentally be answered. (1) Whether the observed reaction peculiarities are related to glass structure inhomogeneities or, kinetically, the matrix is homogeneous enough? (2) Whether the large values of reaction radius are caused by usual reagent diffusion over the homogeneous matrix, by diffusion within the zone with high molecular mobility, or by the migration of reagents with a gradually slowing down rate, or neither of these mechanisms is realized in practice? We have tried to answer these questions studying the hydrogen atom abstraction by alkyl radicals from methanol and ethanol additives, dissolved in glassy methanol-d 3.

2. Experimental 2.1. Compounds The deuterated alcohols from Isotope Co. (St. Petersburg, Russian Federation) CD3OH (isotopic purity > 9 9 . 5 at% D), C2DsOH ( > 9 8 . 5 % ) and CH3CD2OH ( > 98.5%) were used. Deuterated alcohols were dried over molecular sieves 3A. Before usage, CH3OH and C 2 H s O H were distilled and dried over molecular sieves 3A. Alkylhalides CH3I and C2HsBr (both purum grade) were distilled before usage. CD3I ( > 99%) from Isotope Co. was used without further purification. CH3I and CD3I were stabilized with copper and stored in the dark. Diphenylamine (DPA) (reagent grade) was used as received.

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2.2. Preparation of samples The samples consisted of the mixture of alcohols with a given composition, involving 1-1.5 mol% of alkylhalides and 5 × 10 3 mol% of DPA. To freeze them to glass, 2.0 vol% of H 2 0 were added. The samples for UV-photolysis were prepared in quartz tubes 4 mm i.d. The samples for "y-radiolysis were prepared in the tubes of SK-4B glass giving no ESR signal after irradiation. The samples were degassed by repeated " f r e e z e - p u m p - t h a w " procedure in vacuum line, filled with helium at pressure 5 0 - 1 0 0 Torr and sealed.

2.3. Radical generation Alkyl radicals were generated by the dissociative electron attachment to alkylhalides subsequent to two-quantum photoionization of DPA. Photolysis was carried out using the focused light of a 1 kW DRSh1000 high-pressure arc mercury lamp, filtered through a 10 cm water layer and a glass UFS-5 filter band-pass 220-400 rim. At 87 K, irradiation was performed in the ESR-cavity. In this case, its duration was less than 1 rain. In other cases, photolysis

~

_

was performed for 2 min outside the cavity at 77 K. In some experiments, radicals were generated by ",/-rays of ~°Co at 77 K.

2.4. Kinetic measurements Kinetic measurements at 77, 87, and 90 K were provided using boiling nitrogen, argon, and oxygen, respectively. At 92 K reaction was performed in a thermostabilized flow of nitrogen vapors passed through a quartz Dewar tube. Temperature was controlled with a silicon diode to within 0.1 K. Temperature inhomogeneity in the sample in this case was less than 0.2 K. ESR spectra were recorded in a 110 kHz modulation X-band " E S R - 3 Siberia" spectrometer with a cylindrical cavity. The microwave power fed in the cavity was 40 ~xW. The ESR spectrum intensity was measured by comparing it with the signal from a CuC1 z × 2 H 2 0 single crystal mounted in the cavity. In all cases the ESR signal was far from saturation. In the case of kinetic experiments provided at 87 K the spectra were recorded at the same temperature. In all other cases, the spectra were obtained at 77 K. When the reaction temperatures were 77 and 87 K

( tls )o.s 1000

I

I

2000

I

A

"1-0.5 1

0 _...I -1,0

Fig. 1. The kinetic curves of the decay of methyl radicals in glassy CD3OH with the additions of H-containing alcohol at 77 K. Amount in mole fractions and the type of the additive: (1) without additive; (2) 0.01 of CH3OH; (3) 0.02 of C2HsOH; (4) 0.02 of CH3OH. Hereafter the filled and empty circles on the kinetic curves correspond to the data on the different samples.

V.L. Vyazockin, V.A. Tolkatchet: / Chemical Physics 195 (1995) 313-327

(t/s)~5 0

3. Experimental results 500

250

317

750 i

Figs. 1 - 4 show the kinetic curves of methyl radicals decay in the mixtures of normal and deuterated methanols at different temperatures by the following reactions:

o o-, - 0 . 5 "lt_)

CH 3 + CH3OH ~ CH 4 + CH2OH , CH 3 + CD3OH + CH3D + CD2OH.

cn o -1.o _._l

(2)

0.o~82" ~ - " t ~ ' ~

-1.5

Fig. 2. The kinetics curves of the methyl radicals decay in glassy CD.~OH with CH3OH additives at 87 K. The numbers near the curves denote the mole fraction of CH 3OH.

the moment of the irradiation ceasing was set to be time zero. In other cases the time was counted from the moment when sample placed in liquid oxygen or in thermostabilized flow of nitrogen vapors. In kinetic measurements performed at 90 and 92 K we stopped to count time during spectrum recording when the sample was cooled to 77 K.

Here and further log([R]/[R]0) is plotted versus t °5. These coordinates have been chosen just for better representation of the kinetic curves. It is not the attempt to fit (1) with o~ = 0.5 to the data. The obtained results remain intact despite changes in the graphical displays of experimental data. The methyl radical concentration was detected by the high-field line of their ESR spectrum the distortion of which due to overlap with the spectra of CH2OH and CD2OH radicals was negligible. It is seen that the initial rate of methyl radicals decay increases with increasing CH3OH fraction in the matrix. For high degrees of radical conversion, the curves become parallel so that the CH 3 radicals decay with the same rate as in pure CD3OH.

(t/s) 250

500

750

-0.5

-~-

-1.0

Q

-1.5

"t"

- 5

Fig. 3. The kinetic curves of the methyl radicals decay in glassy CD3OH with the additions of isotope-substitutedalcohols at 90 K. The amount in mole fractions and the type of the additive: (1) without additive;(2) 0.005 CH3OH; (3) 0.01 CzHsOH; (4) 0.005 CzHsOH; (5) 0.05 C2DsOH.

V.L. Vyazoukin, V.A. Tolkatchel, / Chemical Physics 195 (1995) 313-327

318

The rates of alkyl radical decay in H- and D-substituted alcohols differ by a few orders of magnitude [7-13]. It is quite natural to assume that in the mixtures of isotope-substituted alcohols at the initial reaction stage the decay of the same part of alkyl radicals is observed, in the nearest environment of which there is at least one hydrogen-containing molecule. At the final stage the radicals decay in the environment, containing deuterated molecules only. This assumption can be verified by following the growth of the products of H and D atoms abstraction upon alkyl radicals decay. When using CH3OH as the H-substituted additive this is difficult due to a strong overlap of the ESR spectra of the CH 3, CH2OH, and CD2OH radicals. However, this becomes possible if C2HsOH is used instead of CH3OH. Figs. 1 and 3 show the kinetic curves of the decay of methyl radicals in the CD3OH + C2HsOH mixtures at 77 K and 90 K by the reactions CH 3 + C2HsOH ~ CH 4 + CH3CHOH, CH 3 + CD3OH ~ CH3D + CD2OH.

(3)

The ESR spectrum of products testifies to the fact that only reactions (3) run in the samples (Fig. 5). The spectrum consists of two signals, i.e. the five-line spectra with the splitting of = 22 G belonging to the CH3CHOH radical and the central single line with the width of ~ 10 G with a poorly resolved hyperfine structure ( = 3 G), belonging to CD2OH.

( i ls )0.5 100

~

200

300

-0,5

0.0041 -1.0

Fig. 4. The kinetic curves of the methyl radicals decay in glassy CD3OH with the additions of CH3OH at 92 K. The numbers on the curves denote the mole fraction of CH3OH.

30G I =

Ho Fig. 5. ESR spectrum obtained after the decay of 90% of the initial amount of methyl radicals in the matrix, 0.02 C~ HsOH + 0.98 CD3OH at 77 K. Filled circles: lines from CH~ radicals; asterisks: lines from CH3CHOH radicals.

Substituting CH3OH by C2HsOH has actually no effect on the kinetics of methyl radical decay. Besides, as will be seen from Fig. 3, the addition of 5 mol% of ethanol-l,2d 5 to methanol-d 3 has, within experimental accuracy, no effect on the decay of methyl radicals. These results indicate that, first, the addition of small quantities of ethanol to the methanol has no effect on the kinetics of deuterium abstraction from CD3OH. Second, the kinetics of H-atom abstraction from hydrogen-substituted molecules remains practically the same upon substitution of CH3OH by C2HsOH. In this case, one can follow the accumulation of the product of H-atom abstraction from matrix molecules during the decay of methyl radicals because one of the lines of the ESR spectrum of CH3CHOH radicals (hi in Fig. 5) is not overlapped by the CD2OH spectrum. Its distortion due to overlap with the wing of the side high-field component of methyl radical spectrum can readily be taken into account by the method proposed in Ref. [19]. Fig. 6 depicts the dependence of h~ on the line intensity of methyl radicals and the concentration of CH3CHOH radicals as a function of methyl radicals concentration in the sample. First, the appearance of CH3CHOH during CH 3 radical decay has been observed. However, since an almost 60% transformation of methyl radicals, there is no gain in the product of their reaction with ethanol. Thus, at the final stage the radicals react so as if their environment involves the deuterated molecules only.

V.L. Vyazovkin, V.A. Tolkatchev / Chemical Physics 195 (1995) 313-327

[C H3CHOH] ,orb. un. I i

t

o

2

,

r

~

I

,

'

1

1.0

0.5

I

I

i

1

h,

2

I

Fig. 6. The dependence between h 1 and h (see Fig. 5) and between the concentration of CH3GHOH and GH 3 radicals during the methyl radicals decay at 77 K in the matrix 0.02 GzH5OH+

0.98 CD3OH.

The data obtained allow one to estimate the number of matrix molecules accessible for the methyl radical, i.e. the molecules from which the radical can

319

abstract the H or D atoms during its lifetime. Let this number be N. Then the probability that the radical will be generated in the environment, consisting of deuterated molecules only, WD = (1 - C ) N, where C is the mole fraction of H-substituted molecules in the matrix. As soon as the concentration of methyl radicals in the sample decreases approximately to W o × [CH3]0, the gain of H-atom abstraction product is terminated which is experimentally verified. As follows from the data in Fig. 6, W o = 0.4 + 0.1 with C = 0.02. Hence, at 77 K N = 25 + 6. The gap between the kinetic curves of radical conversion in deuterated and mixed matrices at large transformation depth (a in Figs. 1-4) is related to N via the following expression N = - a / l o g ( 1 - C). The N values determined from the kinetic data are depicted in Fig. 8. It is seen that the values of N for the reaction of methyl radicals with methanol and ethanol at 77 K, estimated from the kinetic data and from the data on accumulation of the H-atom abstraction products coincide within experimental accuracy. Of interest is the fact that N rapidly increases with temperature and in all the cases it substantially exceeds the presumed number of the matrix molecules, involved in the nearest environment of the methyl radical [14,20].

( t Is )o.s 250

500

750 ,

~

-0.5

2 - 1.0

-J o,e-unanneoled

o.oos

- 1.5

Fig. 7. The kinetic curves of the methyl radicals decay in annealed and unannealedglassy CD3OH with CH3OH additives at 90 K. The numbers on the curves denote the mole fractionof CH3OH.

V.L. Vyazockin, V.A. Tolkatcheu / Chemical Physics 195 (1995) 313-327

320

We have studied the influence of the method of matrix preparation on the value of N. It is well known that glassy material obtained by slow cooling as well as by long-term annealing has a higher density than that obtained by rapid cooling. Fig. 7 shows the kinetic curves of the decay of methyl radicals in annealed and unannealed samples. Unannealed samples were prepared by rapid cooling in liquid nitrogen 5 - 1 0 min before reaction. In the center of sample temperature had been dropping with the rate = 5 K / s . Annealed samples were prepared by aging quickly cooled ones at reaction temperature (T = 90 K) during 60 h before radical generation. It will readily be seen that the difference of the kinetic curves for annealed and unannealed samples is rather small. The N values coincide for two types of samples to within experimental accuracy (Fig. 8). Thus the preliminary annealing of glassy matrix has little or no effect on the reaction kinetics. Using the following experiment we have tried to elucidate the influence of alkyl radical size on the value of N substituting the methyl radical by the ethyl one. Fig. 9 shows the kinetic curves of the

(t/s)0.~ 0

500

1000

1500

A o ~I~ - 0 . 5

u~ "IN 0.009

CTI 0

- 1.0

Fig. 9. The kinetic curves of the ethyl radicals decay in glassy CD3OH with CH3OH additives at 90 K. The numbers on the curves denote the mole fraction of CH3OH.

decay of ethyl radicals at 90 K in the mixtures of isotope-substituted methanols due to the reactions C z H 5 + CH3OH ~ C2H 6 + C H z O H , C~H 5 + CD3OH ~ C 2 H s D + CD2OH.

100

• - 1

N

0-3

The ethyl radicals are observed to react much slower than the methyl ones. However, the shape of the kinetic curves and the character of their change with increasing fraction of hydrogen-substituted component in the matrix for both of the radical types are actually the same. The N values also coincide to within experimental accuracy (Fig. 8). It is known that at 77 K the decay of methyl radicals in glassy CH3CD2OH runs 150 times slower than in CEH5OH [10], but more than 60 times faster than in methanol-d 3. It is interesting to compare the N values for the reactions of alkyl radicals with the different H-substituted additives having different rates. The two channels are possible in the reaction of methyl radicals with ethanol-1 d2:

z~-4

5O

0

1

so

I

T/K

(4)

9o

Fig. 8. The dependence of the number of alkyl radical-accessible matrix molecules, N, in glassy CD3OH on temperature and the type of H-substituted additive. Type of alkyl radical: (1-4) CH 3, (5) C2H 5. Type of additive: (1, 2, 5) CH3OH, (3) C2HsOH, (4) CHsCD2OH. Method of sample vitrification: (1, 3-5) freezing in liquid nitrogen directly before usage; (2) freezing in liquid nitrogen and subsequent annealing at 90 K for 60 h.

CH 3 + CH3CD2OH ---) CH 4 + CHECD2OH, CH 3 + CH3CD2OH ----)CH3D + CH3CDOH.

(5)

We have tried to ascertain which of these is predominant. The ESR spectrum obtained after the decay of methyl radicals in e t h a n o l - l d 2 at 90 K (Fig. 10a) is rather complex. It is the sum of the overlapping

V.L. Vyazot,kin, V.A. Tolkatchec / Chemical Physics 195 (1995) 313-327

a

hl

,,,

II[

[I

,,,

CH3CDOH

30G

Ho

,llfl

"~-

l l I I, CH2CD20H

Fig. 10. (a) ESR spectrum of CH31 solution in ethanol-ld 2 after photolysis at 77 K and annealing for 48 h at 90 K. (b) ESR spectrum of '),-irradiated at 77 K ethanol-ld 2 after photobleaching with visible light and annealing at 90 K. (c) The difference spectrum, the result of the subtraction of spectrum (b) from spectrum (a).

signals induced by several types of paramagnetic species. Fig. 10b shows the ESR spectrum of ethanol-ld 2 ~-irradiated at 77 K (absorbed dose being 0.25 Mrad). The samples were photobleached by visible light (A >~ 450 rim) and annealed at 90 K for 48 h until the ESR spectrum shape stopped to change. The well-resolved four-line spectrum with the splitting of = 23 G is observed. Each line is a poorly resolved triplet with the splitting of 3.7 G. The number of lines in the spectrum, a fairly small broadening due to hyperfine interaction (hfi) anisotropy, as well as the values of splitting unambiguously testify to the fact that the ESR spectrum of ~/-irradiated ethanol-ld 2 is mainly caused by CH3CDOH radicals. A hyperfine structure of the ESR spectrum is related to the hfi of an unpaired electron with one a-deuton and three [3protons. Using the data available for CH3CHOH

321

radical [21] one can obtain the assumed values for the isotropic hfi constants for CH3CDOH (a~ = a~/6.51 = 3.4 G, aft = 22 G) well coinciding with the values of splitting observed in the ESR spectrum. Comparing the spectra given in Figs. 10a and 10b it is seen that the sensibilized DPA photolysis of the mixture of ethanol-ld 2 with CH3I and the following reaction give rise to the radical products involving the CH3CDOH radicals. However, the radicals of another structure have also been observed. Fig. 10c shows the difference spectrum obtained by subtracting the spectrum in Fig. 10b from that in Fig. 10a. In this case the spectra were normalized so that the h 1 and h 2 line intensities were the same. (We have assumed that the side high-field line of CH3CDOH radicals in the spectrum on Fig. 10a is least distorted.) The structure of the difference spectrum can well be explained assuming it to be caused by CHzCDzOH radicals. Indeed, the spectrum is the triplet with the splitting of = 21.5 G the side components of which are strongly broadened due to anisotropic hfi which is typical of the radicals with two c~-protons. Each of the lines is a quintet with the splitting of = 5.4 G that most vividly manifests itself at the spectrum center which can be determined by hfi with two equivalent [3-deutons. The values of splittings observed can be compared with the well-known constants of isotropic hfi for the alkyl radicals forming from the radiolysis of n-alkanes and n-alkylhalides. This comparison is quite reasonable because the hydroxyl group of alcohol is far apart from the atom with free valence and slightly affects the hfi constant. For instance, the constants of isotropic hfi of n-propyl radicals, generated by radiolysis of liquid propane are a,~ n = 22.08 G, aft = 33.2 G [22], and by the radiolysis of n-C3HvC1 at 77 K a,~n 24 G, aft(~) --- 24 G, aft (2) = 48 G [23]. The values of splittings observed in the difference spectrum are in fair agreement with the data obtained for alkyl radicals, taking into account that a n / a D = 6.51. Fig. 11 gives the ESR spectrum of CD3I solution in ethanol-1 d 2 obtained just after sample photolysis at 77 K. The kinetics of CD 3 radicals decay at 90 K coincides with that of the CH 3 ones. The ESR spectra of the products, forming from complete conversion of both types of the radicals also coincide. Kinetically, these radicals are absolutely equivalent. The photolysis gives rise not only to the CD 3 radi-

V.L. Vyazovkin, V.A. Tolkatchec / Chemical Physics 195 (1995) 313-327

322

',

* x20

30G

alcohol methyl groups. The radicals of deuterium abstraction are generated not by reaction (5) but due to the DPA sensibilized photolysis of the matrix. Fig. 12 shows the kinetic curves of methyl radical decay in the CH3CD2OH + CD3OH mixtures at 90 K due to the reactions

I=

Ho

CH 3 + CH3CD2OH ~ CH 3 + CH2CD2OH, CH 3 + CD3OH --) CH3D + CD2OH.

(6)

The number of matrix molecules accessible for the radical determined from these data is N = 5 + 1. Thus, the substitution of C2H5OH by CH3CD2OH causes an almost twenty-fold decrease in N. t Fig. 11. ESR spectrum of CD31 solution in ethanol-ld 2 recorded just after photolysis at 77 K. Arrows: lines of CD 3 radicals; asterisks: lines of CH3CDOH radicals.

cals but also to the radicals, the shape and position of lines in ESR spectrum of which coincide with the shape and position of the side components of the ESR spectrum of CH3CDOH radicals. Since these lines do not overlap the C D 3 spectrum, one can follow the change in the concentration of CH3CDOH during the conversion of methyl radicals. It appears that the amplitude of the CH3CDOH spectrum line (h in Fig. 11) is constant during reaction. It is concluded then that the decay of methyl radicals in ethanol-ld 2 results from H-atom abstraction from (t/s) °'5 J

A

250

500

750

-0.5 o

"--A •"r-

-1.0

c) ...3 -L5

Fig. 12. The kinetic curves of the methyl radicals decay in the mixtures CD3OH+CH3CD2OH at 90 K. The numbers near the curves denote the mole fraction of CH3CD2OH.

4. Discussion Consider now the agreement between the data obtained and the different reaction models. 4.1. Diffusion in a homogeneous medium The data given allow the conclusion that a large number of radical-accessible matrix molecules is not due to usual radical migration throughout homogeneous medium. First, in the case of usual reagent diffusion in deuterated matrices with the addition of an H-substituted reagent the decay of radicals would have always been faster than in the pure deuterated matrix. The products of H-atom abstraction would have been accumulated until complete decay of alkyl radicals which contradicts the data given in Fig. 6. Second, it is difficult to explain the coincidence of the number of molecules accessible for methyl and ethyl radicals in terms of usual diffusion. Finally, another argument against this is the actual insensitivity of radical decay kinetics to the preliminary annealing of glass. Such annealing is known often slow down the diffusion processes. For instance, the annealing leads to the decrease in the ionic conductivity of alkali-silicate glasses [24,25]. In Ref. [26] it is shown that the preliminary annealing of methanol glass at 90 K for 100 min leads to a more than two-fold decrease of the diffusion coefficient of dissolved oxygen. If the large value of N is determined by reactant diffusion, the preliminary annealing should have had an effect on both the reaction kinetics and the measured number of radical-accessi-

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ble matrix molecules. However, no effect of annealing have experimentally been observed.

4.2. Reaction in "porous" zones The data given contradict the assumption that the reaction runs in the zones with high molecular mobility the size of which determines the number of radical-accessible molecules. This hypothesis can be used to explain the limited number of radical-accessible molecules and, accordingly, the fact that in the matrix with hydrogen-containing additives no growth of H-atom abstraction products has been observed at the sufficiently large transformation depth. It allows one to account for the large values of N and their coincidence for the CH 3 and C z H 5 radicals. However, in the frame of this hypothesis it is difficult to account for the increase of N with temperature. One should expect the influence of preliminary annealing on the reaction kinetics and the number of radical-accessible molecules because the sample thermal history must influence the glass structure which can be confirmed by the following. The annealing of alkali-silicate glasses causes a noticeable increase of the refraction coefficient which can probably be related to the increase in the mean medium density [24]. Upon annealing of glassy squalane, the decrease in the values of the reaction radius of the diffusion-controlled t-butyl radical oxidation by molecular oxygen from 12 to 4 A [27] was observed. The decrease of the reaction radius was attributed to the fact that the t-butyl radicals in squalane are generated in the "liquid-like" regions in which oxygen can diffuse much faster than in the bulk. Due to annealing the molecular structure of the "liquid-like" regions changes and becomes the same as that of most of the matrix. The hypothesis that the reaction runs in the regions with high molecular mobility fails to explain the sharp decrease of N upon substitution of CzHsOH by CH3CD2OH. It is hardly probable that substitution of the molecules with similar characteristics causes significant changes in the matrix structure. As has been experimentally verified the substitution of CH3OH by substantially differing CzHsOH has practically no effect on the reaction kinetics (Figs. 1, 3).

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4.3. Diffusion in inhomogeneous medium Assume that the radical mobility constantly decreases with distance from the site of radical generation, e.g. due to the packing of molecular matrix structure and the corresponding increase of diffusion energy barriers. Actually, this is the extended model of "porous" zones that takes into account the structural inhomogeneity of the zone with high molecular mobility. In this case, at high temperature the radical can penetrate into the periphery of the "porous" zone whereas at fairly low temperatures it migrates near the site of its formation. Thus, one can readily explain the increase of the reaction radius with temperature. When the time the radical spends at the periphery of the zone exceeds the time necessary for H-atom transfer from additive molecule to radical, the number of N will be large. When the rate of H-atom tunneling decreases, e.g. due to substitution of C2HsOH by CH3CD2OH, the proportion can be reverse so that the H-atom abstraction will be effective only from the molecules situated near the site of radical formation. Thus, the model can be used to explain the variations of the number of radical-accessible molecules with H-substituted additives. However, the model faces the same difficulties as the previous one when interpreting the experimental results on the influence of preliminary matrix annealing on reaction kinetics. It is also difficult to account for the coincidence of N for methyl and ethyl radicals. For larger particles, the diffusion barriers must be higher. Accordingly, the reaction zone size seems to be smaller.

4.4. Diffusion in relaxing matrix According to the data on the binding energies of carbon-halide bonds and the electron affinities to the Br and I atoms [28,29] upon formation of methyl and ethyl radicals the energy of 0.57 and 0.46 eV results from the dissociative electron attachment to the corresponding alkylhalides. It is assumed then that the release of a sufficient amount of energy causes the local change in matrix structure so that the molecular mobility is initially high at the site of radical formation. Further, the structure relaxes and the mobility gradually decreases. In this case, the radical migration throughout the matrix will be the following:

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first, fast diffusion displacement from the generation site, and then, when the process of matrix relaxation is over, almost complete stopping. Thus, the two regions can be distinguished on the kinetic curves of the decay of alkyl radicals in the mixtures of isotope-substituted alcohols. In the first region a comparatively fast conversion of radicals will be observed due to occasional encounters with H-substituted molecules and the following hydrogen atom abstraction. In the second one, a slow in-cage D-atom abstraction reaction from the nearest matrix molecules can be recorded. In terms of the model, the number of radical-accessible matrix molecules will formally be determined by the fraction of radicals, decaying before the end of matrix relaxation process. In the framework of the model under study one can readily obtain the increase of N with temperature. The absence of the influence of preliminary matrix annealing on reaction kinetics can be explained quite naturally. Indeed, the minor differences in the structures of annealed and unannealed glasses can be negligibly small compared to the local changes in matrix structure caused by radical generation. One can explain the decrease observed in N upon substitution of C2HsOH by CH3CD2OH. In this case, not each encounter with the H-substituted molecule is sure to lead to radical decay, and the probability of its stabilization by the time the matrix relaxation is over, will be higher. However, this model fails to account for the coincidence of N for methyl and ethyl radicals. The larger particle must move throughout the matrix with a lower rate. The relaxation rate of matrix structure can hardly change upon substitution of only one molecule when the C 2 H 5 radical takes the place of the C H 3 one. In any case, it is seen that the substitution of CH3OH by C2HsOH has actually no effect on the decay kinetics of methyl radicals. Thus, before the end of migration the ethyl radical must come into contact with a smaller number of molecules than the methyl one. Accordingly, the number of molecules accessible for the ethyl radical must be less which contradicts the experiment. 4.5. Fluctuation model

As follows from the above, using the hypothesis on the diffusion migration of radicals and even the

additional assumptions (diffusion throughout inhomogeneous medium, diffusion in relaxing matrix) it is difficult to unambiguously interpret all experimental facts. We guess that the movement of reagents to obtain the optimal relative positions and the transfer of the atom from matrix molecule to radical take place during one and the same process, which involves not only the reacting molecules but also a great number of the surrounding matrix molecules. The larger is the distance between the radical and the molecule, the greater number of particles must participate in the process of the creation of the reactive radical state with this concrete molecule. It is evident that the probability of atom abstraction must decrease with increasing distance between reactants. In the matrix, containing a small fraction of Hsubstituted molecules the competing processes of H and D atoms abstraction occur. Let the probability of H-atom abstraction from the molecules, located beyond the limits of the sphere of radius R with its center at the place radical location, be rather low compared with that of deuterium abstraction from the matrix molecules, situated within the sphere. Then the reaction with the H-substituted molecules placed at the distance of r > R from the radical will not manifest itself in the kinetics. In the mixed matrices, once all the radicals involving in their environment if only one hydrogen-substituted molecule at the distance r ~
WNH+I< ~ WjD,

(7)

j-I

where WNH+t is the probability of H-atom abstraction from the molecule that is not included in the number N of the closest ones; WjD is the probability of deuterium abstraction from one of the N nearest matrix molecules. Consider now the effect of changing the H-substituted additive on the value of N. The binding energy of the broken bond in CzHsOH is by 4 kJ/mol smaller than in methanol [28]. In line with

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theory, this is sure to lead to the decrease of the reaction energy barrier and to the increase of the probability of H-atom tunneling. However, no reaction acceleration has been observed. This is possible if atomic hydrogen tunneling is fast enough and has no effect on the reaction rate, i.e. the rate of atom abstraction is limited by the process of the organization of the corresponding reactive state of the radical-molecule pair. The same conclusion has been drawn in Ref. [9] when analyzing the isotopic composition of methanes in the products of the reactions (2). The concentration of H-substituted additive is small. To make the additive molecule accessible for the radical, a large number of matrix molecules must be displaced. Since upon substitution of CH3OH by C2H5OH only one of these changes, namely the H-substituted one, the rate of reactive state formation should not undergo detectable changes. Hence, the probabilities of atomic hydrogen abstraction, WjH, will remain actually the same. According to experiment, upon such a substitution the number of radical-accessible matrix molecules, N, determined from the kinetics, will also be the same. When CH3CD2OH is used as the H-substituted additive, the binding energy of the broken bond increases. (We have failed to find any data on the C - H bond in ethanol methyl group in the literature. We think that the binding energy of this bond must be close to the energy of the abstraction of the end hydrogen atom from the ethyl group of ethylmethylketone equal to 411 kJ/mol [29]). The increase of the binding energy by 15-25 kJ/mol must substantially slow down H-atom tunneling which is experimentally verified. However, since the matrix substance, i.e. methanol-d3, does not change, the difference between WjH and W/D decreases. Thus condition (7) can be fulfilled for smaller N. Kinetically, this will be observed as the decrease in the number of radical-accessible molecules. The radical sizes increase upon substitution of the CH 3 radicals by the C 2 H 5 o n e s . The transport of the radical needs greater shifts of matrix molecules from equilibrium positions. It is only natural to assume that the probability of the formation of the reactive radical state with an isolated molecule must decrease. As a result, at the given temperature and isotope composition of matrix the decay of ethyl radicals will be slower than that of the methyl ones.

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The isotope composition of the resulting ethane [9] testifies to the fact that the atom tunneling is slow enough so that the rate of H-atom abstraction by ethyl radical from methanol is probably unlimited by the rate of the formation of the reactive state of radical-molecular pair. For the same matrix composition and temperature, the isotope effect in the formation of the products of H and D atoms abstraction by ethyl radicals is by an order of magnitude larger than by the methyl ones. Thus, it is concluded that the difference in the rate of H and D atoms abstraction increases upon substitution of the methyl radical by the ethyl one. The energy estimations are also in agreement with this conclusion. According to Ref. [28], the binding energy in ethane is by 19 kJ/mol smaller than in methane. Accordingly, the energy barrier for the reaction of ethyl radicals with methanol is higher than for the methyl ones. In this case, the probability of atom tunneling from matrix molecule to radical sharply decreases whereas the difference in the rates of H and D atoms tunneling increases. As a result, (7) can be fulfilled for large N. When the rate constants decrease the number of radical-accessible matrix molecules can be the same or even increase upon transition from methyl to ethyl radicals. Explain now the increase in N with increasing temperature in the framework of the model under discussion. As has been mentioned above, the H-atom abstraction from the additives CH3OH and C2H5OH in methanol-d 3 is limited by the process of the organization of the reactive radical-molecule pair. The higher is the temperature, the higher are the rates of the generation and decay of the nonequilibrium state of the molecular radical environment. The temperature dependence of the rate of atom tunneling from matrix molecule to radical is weak enough [14]. (For our case, when the studied temperature range is rather narrow, this dependence can be neglected). Therefore, when the temperature rises, the rate of H-atom abstraction can become unlimited by the processes of reactive state formation. This is sure to lead to the fact that the difference in the rates of H- and D-atom abstraction will increase with increasing temperature thus approaching the limiting value determined by the isotope effect magnitude in tunneling. This is confirmed by the fact that in the temperature range under study the fraction of the product of hydrogen atoms abstraction increases in

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the reactions of methyl radicals with the CH3OH and CD3OH mixtures [9]. In this case, when the temperature increases, condition (7) will be fulfilled for the large values of N, i.e. the number of radical-accessible matrix molecules, determined from kinetics will increase. Thus, the fluctuation model is observed to qualitatively agree with the available experimental data.

5. Conclusion The alkyl radicals in glassy alcohols can abstract the hydrogen atoms from the molecules that are not their nearest neighbors. The number of accessible molecules can be as great as a few tens. However, the large value cannot be attributed to radical migration throughout the matrix. We guess that one should not identify the reaction zone size with the characteristic sizes of structural inhomogeneities, that are likely in glassy solids, i.e. with the sizes of the regions with high molecular mobility. The observed kinetic peculiarities of the tunneling reactions of alkyl radicals in glassy alcohols can be explained assuming the atom transfer to be realized upon fluctuative rearrangement of matrix structure in a small volume, including the radical. In this case, one can observe the considerable displacements from equilibrium positions. A series of questions should be answered to quantitatively develop the theory and to compare it with experiment. First of all, the necessary experimental and theoretical studies should be performed to evaluate the mechanism that allows the reagents to move from the equilibrium positions occupied by them in the matrix. From the general considerations it is clear that the character of these movements must depend on the molecular structure of the nearest environment of the radical. If the structure is such that allows a lot of close in energy molecular configurations, the transitions from which are divided by minor energy barriers, then the shifts of reagents for large distances become quite probable. If the matrix structure in radical surrounding permits a small number of possible configurations, strongly differing in energy, the motions of reagents can take place only within an elementary unit of solids. However, in the last case as well, the character of the motions, deter-

mining the reaction kinetics, can be far from simple lattice vibrations. It is quite probable, that the possibility of substantial shifts of reagents depends on the nonequilibrium of glass structure at the place of radical location. The latter can result from active particle generation because in this case: (i) the energy evolves, (ii) the fragments, resulting from the decay of precursors, can locate in the matrix only in some excess, compared to equilibrium, free volume. It is not inconceivable that the process of matrix structure relaxation to a new equilibrium manifests itself in the kinetics as the gradual reaction retardation. Below glass transition temperature the response of an electrical or mechanical stress known as a secondary or 13-relaxation occurs in amorphous solids. This type of relaxation is determined by increased local molecular mobility in glasses [16]. In the context of obtained results it may be of interest to study correlation between influence of any variable and procedure (temperature, glass composition, annealing, irradiation and the like) on the kinetics and on the [3-relaxation in the glassy alcohols. Experiments along this lines may provide answers to the questions mentioned above.

Acknowledgement This work was supported by the Russian Foundation for Fundamental Studies. We are also grateful to V.A. Kotchetkov for the performance of some kinetic measurements, to V.M. Syutkin and B.V. Bol'shakov for their fruitful participation in discussion of results.

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