Rate Constants for Termination and TEMPO Trapping of Some

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8182

J. Phys. Chem. 1995, 99, 8182-8189

Rate Constants for Termination and TEMPO Trapping of Some Resonance Stabilized Hydroaromatic Radicals in the Liquid Phase? I. W. C. E. Arends and P. Mulder* Center for Chemistry and the Environment, Leiden Institute of Chemistry, Gorlaeus Laboratories, Leiden University, P.O.Box 9502, 2300 RA, The Netherlands

K. B. Clark and D. D. M. Wayner* Steacie Institute for Molecular Sciences, National Research Council of Canada, Ottawa, Ontario, Canada KIA OR6 Received: December 2, 1994; In Final Form: March 3, 1995@

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The rate constants for the termination reaction (2k1) of some resonance stabilized carbon centered radicals (SR-) derived from hydroaromatics (SR SR P) have been determined at 294 f 2 K by laser flash photolysis with UV-vis detection. The radicals were generated by hydrogen atom abstraction by t-BuO radicals from the corresponding hydrocarbon (SRH t-BUD SR t-BuOH, k4). The extinction coefficients ( E ) of the SR, essential to calculate 2k1, were obtained using a relative kinetic technique. The change in 2kl for the radicals derived from 1,Ccyclohexadiene, fluorene, 9,1O-dihydroanthracene, diphenylmethane, tetralin, indan, indene, and phenol appeared to be modest; a range of 2k1 = 2-10 x lo9 M-' s-I in mixtures of benzene and di-tert-butyl peroxide was observed. Most of the rate constants are near the diffusion controlled limit. In contrast, quenching the radicals with a persistent radical, 2,2,5,5-tetramethylpiperidin-l-oxyl(TEMPO), resulted in a larger variation of '0.01-23 x lo7 M-' s-I. The strength of the N - 0 bond formed in the latter process may have an important contribution to the observed rate constant.

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Introduction Resonance stabilized carbon centered radicals (SR) are often described as nonreactive species. Benzyl radicals, for example, are known to have a low reactivity toward double bonds and in hydrogen atom abstraction reactions.' In part, this has been rationalized by reaction (activation) enthalpy considerations. Although addition of the benzyl radical to an olefinic bond is exothermic as the result of the formation of a carbon-carbon bond, the intrinsic activation barrier for these reactions can be quite high. Owing to the resonance stabilization in SR., with few exceptions the H-abstraction reactions are endothermic. As a result, at low temperatures the only reaction pathway still available is radical-radical termination:

SR*+ S E - P (1) The rate constant of termination for benzyl radicals2 does not appear to be significantly lower compared with other nonstabilized carbon centered radicals. However, no pertinent data exist concerning the variation in rate constants (2kl) as a function of the size and the degree of stabilization of SR-. Although unreactive, it has been demonstrated that in coal-liquefaction chemistry the 9,lO-dihydroanthracenyl (DHA.) radical plays a key role in the rupture of the strong bonds that results in a breakdown of the coal m a t r i ~ . In ~ addition, SR* species are often associated with the formation of soot. In the gas-phase pyrolysis of toluene, high molecular weight material from benzyl-radical triggered chemistry is obtained. It has been suggested that the combination of benzyl radicals can yield methylenecyclohexadiene-type intermediates; subsequent transformations of these species may be an important pathway in soot formation! Several techniques are available to study the absolute rate constants for reaction 1, including the rotating sector method @

Issued as NRC publication 373 19. Abstract published in Advance ACS Abstrucrs, April 15, 1995.

0022-3654/95/2099-8 182$09.00/0

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with either electronic absorption or electron paramagnetic resonance observation or photolysis techniques with EPR or optical detection5 Although 2k1 for some SR. are already known,2.5we have investigated these reactions under the same experimental conditions. Therefore, in this study the termination rate constants of SR*derived from the hydroaromatics, Le., 1,4cyclohexadiene (CHD), fluorene (F), 9,lO-dihydroanthracene (DHA), diphenylmethane (DPM), tetralin, indan, indene, and the phenoxy1 radical, were determined by laser flash photolysis. For comparison, the reaction rate constants of SR. with a nitroxide radical scavenger were determined.

9.10-Dihydroanthracene (DHA)

Tetralin

1.4-Cyclohexadiene (CHD)

". 0

Fluorene (F)

Indan

Diphenylmethane (DPM)

Indene

Experimental Section Materials. All reagents used in this study were acquired from commercial sources and further purified, except for benzene, diphenylmethane, and 1,4-~yclohexadienewhich were used as received. 9,lO-Dihydroanthracene and fluorene were recrystallized three times from methanol, di-tert-butyl peroxide was passed twice over alumina; tetralin and indan were purified once 0 1995 American Chemical Society

Rate Constants for Termination of Resonance Stabilized Radicals over alumina. Prior to use, indene was eluted over silica. TEMPO (2,2,5,5-tetramethylpiperidin-l-oxyl) was purified by sublimation. Laser Flash Photolysis. The instrument used has been described elsewhere: In this study three lasers, depending on the absorption properties of the radicals, were utilized for excitation: an eximer laser at A = 308 nm, a nitrogen laser at A = 337, and a Nd:YAG laser at A = 355. The standard solution composition in the sample cells varied with the laser wavelength; thus the ratio (v/v) di-tert-butyl peroxide:benzene was 1:16 (at 308 nm), 1:2 (at 337 nm), and 3:l (at 355 nm) so as to ensure that the peroxide absorption at the excitation wavelength was identical (ca. 0.3). The photolytic cells had a path length of 0.7 cm. Growth and decay traces from an average of three to five laser flashes were used to determine the rate constants. In all cases the effect of the laser dose was investigated using neutral density filters. All experiments were carried out at 294 f 2 K. Extinction Coefficients. In addition to the relative kinetic technique described below, the extinction coefficient (c) for the 9,lO-dihydroanthracenyl radical (DHA-) was determined using Aberchrome-540 as an a~tinometer.~ This compound has an absorption maximum at 344 nm, and upon W irradiation it interconverts to a ring-closed form (fulgide B) with a quantum yield (4Aber-540) of 0.20 in toluene at room temperature. This reaction can be used as an actinometer for short-lived intermediates as has been done for benzophenone ketyl radical^.^ Measurements were performed at several laser doses by placing neutral density filters in the laser beam. For the Aberchrome-540 solution, the variation in optical density, AOD, of B at the absorption maximum at 494 nm was found in the range 0.0007-0.0249, while for DHA. at 350 nm AOD values of 0.005 to 0.097 were obtained. The extinction coefficient for DHA. was calculated using the slopes, s, obtained from the linear correlations of the responses (AOD) with respect to laser dose, according to:

with ~ O O = B O M 8 (the quantum yield for photodissociation of di-tert-butyl peroxide in benzene; the factor of 2 takes into consideration that every photon produces two t-BuD radicals). In these calculations the intercept of the linear correlation lines was forced to be zero. Computations according to an alternative m e t h ~ d calculating ,~ the product EDHA.~BOOBfor each pair of data points and then extrapolating this function to zero light dose, proved to be less accurate.

Results

1. Rate Constants of Termination Reactions (21). With the laser flash photolysis (LFP) method, the rate constants of termination of SR. can easily be measured by following the decay of the radical species. The radicals were photolytically generated in mixtures of di-tert-butyl peroxide (Me3COOCMe3) and the parent hydroaromatic (SRH) according to reactions 3 and 4. Me,COOCMe3

S R H + t-BuO

-

kv

2t-BuO

(3)

+

(4)

SR* t-BuOH

The experimentally determined second-order rate constant obeys 2 k 1 / 4with 6 the extinction coefficient of the radical species at a given absorption wavelength (Amax) and 1 the path length of the photolysis cell.

J. Phys. Chem., Vol. 99, No. 20, 1995 8183

Experiments were carried out under carefully deoxygenated conditions by purging with ultrapure nitrogen and repeated in triplicate. The curve-fitting procedure according to second-order kinetics of the decay trace resulted in the 2kllc1 values with a correlation coefficient (9) better than 0.999. Typically, within a time window of (200 ps, more than 90% of the radicals disappeared. The overall variation in results for a given substrate did not exceed f 1 5 % . For 9,lO-dihydroanthracene (DHA) it was demonstrated that experiments performed in sealed tubes with mixtures prepared by degassing with three thaw-freeze cycles gave the same results. In general, the radical concentrations, recorded at the maximum optical density, were in the order of 5-7 x M. The species in the reaction mixture most likely to interfere with the termination process is oxygen. The SR radicals can be trapped by oxygen usually with a rate constant (ca. 5 x lo9 M-' s-l) comparable9 with those for the self-reaction of SR. SR-

+ 0, - S R O O

As a result, small amounts of residual oxygen can have a large impact on the measured rate constant. Kinetic modelling (see Appendix 1) shows that with a constant [ 0 2 ] of 6 x lop8 M and an initial [SR]. of 6 x lop6M, the computed 2k1 for DHA increases from 4.8 to 5.7 x lo9 M-' s-l, while still giving excellent second-order fits to the data. However, in a realistic situation the oxygen concentration is not constant and small amounts will be consumed in the course of the experiment (depending on the number of laser shots) which makes a detailed kinetic analysis too complex. It suffices to note that the perturbation of the pure second-order behavior of SR. may lead to an over-estimation of 2kl. For this reason, the influence of laser power was also studied to ensure that the initial [SR.] was high enough to avoid this problem. The apparent second-order rate constant was shown to be independent of the laser power. Only at very low energy levels was an increase of 30% observed, which was ascribed to the interference by, e.g., 0 2 . The hydroaromatics used in this study, although well purified, contained the polycyclic aromatic analogues either as an impurity, e.g., naphthalene in tetralin or anthracene in 9,lOdihydroanthracene, or as a reaction product during the photolysis. To avoid any interference from light absorption by these aromatics, the majority of the experiments are performed in Me3COOCMe3henzene mixture of (v/v) 3:l as the solvent and at a photolysis wavelength of 355 nm. Some rate constants were determined at other photolysis wavelengths (337 and 308 nm) using mixtures containing more benzene. Results are presented in Table 1. With indene two transients absorptions were observed at Amax at 330 and 450 nm, respectively. The tentative assignment of these absorptions is as follows. t-BuO. can both abstract a benzylic hydrogen and add to the double bond. The absorption at 450 nm is probably the indenyl radical by comparison with a similar type species: the fluorenyl radical which has a ,ImaX of 500 nm. Addition to the double bond is expected to occur primarily at the ,&position. This benzylic product-radical resembles, e.g., the 1-tetralinyl. Addition to the a-position is less likely on thermodynamic grounds and results in the formation of a secondary alkyl radical which is invisible in the W - v i s region. In the case of the diphenylmethyl radical (DPM) self-reaction, an additional precursor has been employed. Photolysis of tetraphenylacetone (TPA) in benzenelo is known to be a clean source for DPM-: (Ph,)CH(CO)CH(Ph),

hv

2(Ph),CW

+ CO

(6)

8184 J. Phys. Chem., Vol. 99, No. 20, 1995

TABLE 1: Rate Constantsn for SR. A,,

SRH

1,4-c yclohe~adiene~ 9,lO-dihydroanthracene fluorene diphenylmethane toluene tetralin indan indene indene phenolk

nm 31 1 350 500 335 316 330 335 450 330 400

Arends et al.

+ SR- - (21) and SR*+ TEMPO - ( k ~ dat 294 f 2 K 2kll~1,

s-'

M-I cm-'

2.8 0.31f 2.3 0.21

5 350" 22 000 3 6009 27 000 8 800' 2 200 1 200 500 1 600 2 100'

1.3 4.2 15 5.1 2.4

2k1,~

M-' s-] 10 4.8 5.8 4.0 5.2' 2.0 3.5 5.3 5.7 3.5

lo-' M-' s-'

kl2,b

kcal mol-'

23 1.1 3.1 2.1(4.6)* 1& (49)h 14 22 0.73

-34 -34 -39 -39 -47 -43 -40 -37

'0.01'

-23"

a Determined using the 355 nm laser system in Me3COOCMe3henzene mixture of (v/v) 3: 1. Error limits (a): E , & 16%; 2k1, &22%; and klz, &lo%. Reaction enthalpy for combination of SR. TEMPO; see Appendix 2. Determined using the 337 nm laser system in Me3COOCMe3/ benzene mixture of (v/v) 1:2. e See ref 5. f With the 308 nm laser system in Me3COOCMeJbenzene mixture of (v/v) 1:16: 2k&l = 2.2 x 105.gSee ref 13. See ref 14, solvent isooctane. See ref 2, solvent toluene. See ref 15a, solvent benzene. Photolysis of Me3COOCMe3/triphenylphosphite 3:l. 'Estimated upper limit rate constant. Estimated based on the observed trend between k12 and AH12; see text.

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TABLE 2: Termination Rate Constants: 2 1 , for Diphenylmethyl in Various Solvents at 294 ?C 2 K solvent

ratio

Me3COOCMe3/benzenec Me3COOCMe3henzene benzene isooctane/benzened isooctane/benzened isooctane/benzened

3: 1 1:16 3: 1 1:l 1:16

2kl,b

produced in an intermolecular competition. Therefore, a relative internal kinetic method was applied to measure the extinction coefficients for the SR. radicals. The only spectroscopic criterion is that the two species do not have extensively overlapping electronic absorption spectra. In a mixture containing two hydroaromatic compounds [(e.g., diphenylmethane (DPM), fluorene (F), and Me3COOCMe3), the two radicals (DHA. and F.) are simultaneously generated after photolysis:

M-' s-' 4.0 2.1 1.4 4.2 2.5 1.3

With the 308 laser system. Using E = 27 000 M-I cm-I. See Table 1, footnote a. With tetraphenylacetone (ca. M) as the precursor for DPM..

To explore the possible solvent effect on reaction 1, mixtures containing TPA and various amounts of isooctane and benzene were prepared. In these experiments the initial DPM* radical concentrations were approximately the same, as was shown by the maximum optical absorption. It is important to note that the same results were obtained with isooctanehenzene (3:1) using TPA and Me3COOCMe3henzene (3:l)using DPM (see Table 2). Another stabilized radical investigated in this study is the phenoxyl radical (PhD). Although at first hand this radical species does not appear to be a carbon centered radical, product studies demonstrate that this radical can be regarded as a stabilized carbon centered species." A documented source for phenoxyl radicalsI2 in the liquid phase is the photolysis of Me3COOCMe3 in the presence of triphenyl phosphite: (PhO),P

+ t-BuO. - (t-BuO)(PhO),P + P h O

(7)

Unlike the other SR. termination processes in this study, the decay of the phenoxyl radical was insensitive to oxygen. After purging the reaction solution with oxygen instead of nitrogen, no change in the second-order rate constant was observed. The 2kl values can be calculated when the extinction coefficients of the radical species (see sections 2 and 3) are known. The overall relative error (a)in the 2kl values can be assessed following a statistical error analysis. Thus, with a(2kll EZ) = 15%, a(2kl) = [a2(€) a2(2kl/d)]o~5 = 22% (see also section 2), consequently 2kl(DHA*)becomes 4.8 f 1.1 x lo9 M-1 s-l 2. Determination of Extinction Coefficients, E. With the actinometer method, E values are obtained by comparing in separate experiments the effect of varying the laser dose on the optical densities (see Experimental Section). One of the main difficulties in this approach is to ensure that the same number of radicals is produced from one experiment to the next. On the other hand, given precise kinetic data for the formation of radicals, one can easily determine the molar ratio of two radicals

+

+ t-BuO. - DPM. + t-BuOH F + t-BuO - F*+ t-BuOH

DPM

(4b)

With the known rate constants kDPM and kF for hydrogen abstraction for reactions 4a and 4b, the final concentration of the radicals DPM. and F. will be dictated by:

provided that the (cross) termination reactions do not play a significant role within the timeframe of the experiment (ca. 2 ps). The actual measured parameters are the plateau values of the optical densities (OD) of the two radical species. By varying the concentration ratio (DPM/F), a linear correlation between the ratios of the OD's and the relative substrate concentration was obtained: OD,pM/ODF. = Al[DPM]/[F]

+ A2

(9)

where A2 represents the residual absorption without any DPM. Combining eq 8 and 9 yields:

With the known value of EF. = 3600 M-' s-I,l3 the separately determined rate constants (see section 3)and the experimentally obtained slope A I , the appropriate extinction coefficient can be calculated according to eq 10 (see Figure 1). The extinction coefficient for the diphenylmethyl radical, EDPM., was found to be 27 000 M-' cm-'. The relative error in the derived extinction coefficients, a(€), was estimated as follows. According to a statistical error analysis and following eq 10, ~ ( E D P M . ) = [u*(~F) a 2 ( k o p ~ ) o~(EF.) AI)]^.^, using a&) = a ( k ~ p = ~ ) 10% and U(EF.)= &AI) = 5%, the overall error in U(EDPM.) is 16%; consequently E D P M becomes 27 000 f 4200 M-' cm-I. According to the literature there seems to be a discrepancy with regard to the value of EDPM., for which a range from 40 000 to 140 000 M-' cm-l I 6 - l 8 has been reported. For example, our value is at variance with the 80 000 M-' cm-I reported by

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J. Phys. Chem., Vol. 99, No. 20, 1995 8185

Rate Constants for Termination of Resonance Stabilized Radicals

I

61

t

A

I

TABLE 3: Rate Constants, k4, for SRH t-BuOH at 294 f 2 K SRH

M-' s-'

no. H"

k,,, per H

9,lO-dihydroanthracene 1,4-~yclohexadiene tetralin diphen ylmethane to1uene ethylbenzene cumene fluorene c yclopentadiene c yclopentene indene indan phenol

38 33 7.9d 0.91 0.2Y 1.1s 0.87f 3.1 2.8' 5.9' 2.8' 5.7d 330

4 4 4 2 3 2 1 2 2 4 2 4 1

1.00 0.88 0.21 0.05 0.006 0.06 0.09 0.16 0.14 0.15 0.14 0.14 8.7

k4,a

-

0

0.5

1 1.5 Concentration ratio D P M P

2

Figure 1. Determination of the extinction coefficient using the relative kinetic method of diphenylmethyl radical (DPM.) relative to the fluorenyl radical (F.).

Scaiano et a1.I6 In this study, using a value for EDPM. of 27 000 M-' cm-', a range for 2k1 (depending of the solvent) of 1.3-4 x lo9 M-' s-I is obtained which is similar to the value reported in acetonitrile (2 x lo9 M-I s-') using an electrochemical method.Ig A higher value of E would lead to inexplicably high rate constant for the diphenylmethyl radical self-reaction of > 1O'O M-' s-l. Analogously, an EDHA. of 23 000 M-' cm-' was obtained using fluorene as a reference. Following the same relative approach but now using 1,Ccyclohexadiene (CHD) as the reference compound (ECHD. = 5350 M-' s-' and EDHA. of 22 000 M-I cm-' was found, confirming that the applied method is consistent. For comparison, with the actinometer method a value of E D H A . = 23 200 k 5500 M-' cm-' was obtained, in good agreement with the relative kinetic method. An overview of the results is presented in Table 1. A more simplified way to determine the relative E values for the radical species would be to monitor the specific maximum OD's in separate experiments but under the same experimental conditions, e.g., with the same peroxide concentration and reaction vessel. Since the number of carbon centered radicals produced after the laser flash is relatively constant under conditions in which more than 90% of the tert-butoxyl radicals react with the substrate, the relative E is reflected by the ratio of the maximum optical densities. Thus, comparison of the OD's for 1-tetralinyl and 1-indanyl, at concentrations of the precursors of ca. 0.5 M, yields a ratio Of ~l-tetralinyl/El-indanylOf ca. 2 (according to Table 1, 1.8). However, in this approach any residual UV absorption in the reaction mixture is ignored and may generate grossly inaccurate extinction coefficients. 3. Rate Constants for t-BuO. SRH, k4. The rate constants for H-abstraction, k4, were measured by monitoring the growth of the radical (SR.) which was generated according to (3) and (4). Under pseudo-first-order conditions and by variation of the substrate concentration, the relation between the experimental rate (constant) (/qexp) and k4 is given by:

+

+ t-BuO. - SR. + BDE(SR-H), kcal mol-] 76b 76' 85' 81b 899 85h 83h 81b 79 82k 79" 82" 87"

"Error limit (a) in k4 f 1 0 8 ; no. H: number of abstractable (benzylic) hydrogens. See ref 21. See ref 22. Tetralin contains four a-(benzylic) hydrogens and four P-hydrogens. The global rate constant, 8.3 x IO6 M-' s-l, contains both reaction modes. The contribution of the /3-abstractions can be estimated as follows. The rate constant, k4, for cyclohexane is 1 x lo6 M-' s-' (taken equal to the rate constant for H-abstraction by cumyloxyl radicals, ref 23) when assuming that the 12 hydrogens are kinetically identical; then the rate constant for a-H-abstraction in tetralin becomes (8.3-1 x 4/12) x lo6 = 7.9 x lo6 M-' s-l. For indan the global rate constant is 5.9 x lo6 M-' s-I; following the same analogy, and using cyclopentane with k4 = 8.6 x lo5 M-' s-I (ref 24) leads to k4 for the a-hydrogens in indane of 5.7 x lo6 M-] S - I . 'BDE is assumed to be equal to the C-H BDE in ethylbenzene. f See ref 20; rate constants determined applying the laser flash photolysis probe method (diphenylmethanol). See ref 25. See ref 26. 'See ref 24 and ref 27; rate constants are corrected for the contribution of addition by tert-butoxyl, cyclopentene, 10%; cyclopentadiene, 6 0 8 . 'See ref 28. See ref 29. Overall rate constant for addition and abstraction is 5.4 x lo6 M-' s-I; see text. " See ref 30. BDE is assumed to be equal to the C-H BDE in cyclopentene. See ref 11.

'

From Table 3, it is observed that the relative abstraction rate constant per hydrogen, krel, in the series of compounds with a five-membered ring remains virtually constant. This fact can be used to disentangle the global rate constant for indene of 5.4 x lo6 M-' s-I. Since there are two reaction pathways, Le., H-abstraction (k4) and addition to the /3-position (kadd) in indene (see section l), both rate constants can be estimated. The molecule contains two abstractable hydrogens; thus for k4 = 2.8 X lo6 M-] S-' and kadd = 2.4 X lo6 M-' S-', ca. 50% of the t-BuO. radicals add to indene. This reaction selectivity is similar to that with cyclopentadiene (see Table 3) in which 60% of the t-BuO. add to the double bonds,24 the reaction enthalpies for cyclopentadiene and indene also are likely to be similar. The H-abstractions reactions are all exothermic. The reaction enthalpy, depending on the degree of resonance stabilization, ranges from - 16 (toluene) to -29 kcal mol-] (9,lO-dihydroanthracene) (see Table 3). Since in this series the transition states are likely to be similar, the rate constants may reflect the strengths of the C-H bond only. In Figure 2 a plot is given for In k4 versus the BDE(SR-H). A reasonable correlation (excluding the data for tetralin and diphenylmethane) is obtained; according to an Evans-Polanyi treatment (E, = aAH, /3), the activation energy for abstraction of a benzylic hydrogen, taking a constant value for the pre-exponential factor of M-I s-'(per H), becomes Ea,4 = 0.21~!df4 7.9 (or, altematively, Ea,4 = 0.21BDE(SR-H) - 14.1). These correlations are utilized to predict the reactivity within homologous series of substrates. In general, the magnitude of a decreases with increasing reaction exothermicity. For a series of alkanes consisting of CH3-H, CH&H;?-H, (CH&CH-H, and (CH3)3C-H rate measurements at 298 K in the gas phase yield

+

In eq 11 includes all other (pseudo-) first-order processes of t-BuO.. When t is lower than lo7 M-' s-l, the pseudo-firstorder growth of SR. becomes distorted by the competing secondorder recombination of ~-BuO*.~O Therefore, by gradually reducing the laser power and hence the initial concentration of t-BuO., the reaches a plateau value independent of the photolysis conditions. The results, together with some k4 literature values of other relevant compounds and the strength of the SR-H bonds, BDE(SR-H), are presented in Table 3.

+

8186 J. Phys. Chem., Vol. 99, No. 20, 1995 17 l6

Arends et al.

I

1

I

were investigated.

+

DHA

SR* TEMPO

CHD

- SRT

(12)

The pseudo-first-order rate constants (kl 2,exp) were obtained from the transient decay at different TEMPO concentrations. The rate constant for the quenching, k12, of the SR. radicals is given by

t

t l2 I

11

74

TOL 0 "

'

"

76

"

78

'

'

80

'

"

"

'

~

82 84 86 BDE SR-H (kcal.moT')

90

88

+

-

Figure 2. In k4 (per H) for the H-abstraction reaction: t-BuO. SRH t-BuOH + SR. plotted against the bond dissociation energy (BDE) SR-H. CHD, 1,Ccyclohexadiene;CP, cyclopentene; CPD, cyclopentadiene; CUM, cumene; DHA, 9,lO-dihydroanthracene;DPM, diphenylmethane; ETB, ethylbenzene;F, fluorene; IND, indan; TET, tetralin;

TOL, toluene.

a = 0.4 for O H radicals.31 Hydrogen abstraction by the CH3D or t-BuQ are less exothermic, and hence a increases to ca. 0.6 in the gas p h a ~ e . ~ IInterestingly, -~~ the rate constants on a per hydrogen basis for t-BuO. with cyclohexane and propene in the gas phase at ca. 400 K32 and cyclohexane and toluene in the liquid phase at 294 K (see Table 3, footnote 6) are almost identical, while the difference in reaction enthalpies in both systems is ca. -9 kcal mol-', implying that for alkoxyl radicals the Evans-Polanyi correlation using hydroaromatics should yield a lower a compared with a series of alkanes. From Figure 2, a deviation is noticed for tetralin. In order to fit this point to the correlation, the benzylic C-H BDE in tetralin would have to be changed from 85 to 81 kcal/mol. However, such an adjustment is not supported by experimental evidence. The activation energies and hence the BDE(C-C) for benzylic carbon-carbon bond cleavage in ethylbenzene and tetralin are almost identical.34 The enhanced reactivity relative to ethylbenzene has been demonstrated; in the liquid phase the rates for benzylic hydrogen (per H) abstraction by C&', ROD, CHy, B r are higher,35while in the gas phase at 298 K NO3 reacts at least 20 times faster.31 Since the rate constants are determined by enthalpic and entropic changes along the reaction coordinate, a variation in activation entropy may explain the observed deviation. Examination of the entropy changes (AS) between product and reactant shows that S(SR*) - S(SRH) is in most cases negative since the internal rotation around the C-Cphenyl bond in SRH is changed into a torsional motion in SR.. Using group additivity rules, AS values are calculated to be -1.4 eu (toluene), -2.8 eu (ethylenebenzene), -1 eu (tetralin), and -3.1 eu (cumene), while for 1,4-~yclohexadieneand 9,lO-dihydroanthracene AS is around -6 eu.25 On the other hand, AS is positive for DPM DPM. (+2.8 e ~ ~ If~ the ) .differences in activation entropy are proportionally related to the differences in reaction entropy, then a substantial variation in the preexponential factors is expected for the H transfer reaction to t-BUD, and as a consequence the Evans-Polanyi relationship (in which the pre-exponential factor is assumed to be constant) would no longer be valid. Thus, a more detailed investigation is necessary to disentangle enthalpy and entropy considerations for hydrogen abstraction rate constants by alkoxyl radicals.37 4. Rate Constants for SR. TEMPO, k12. In order to correlate the termination rate constant with another radicalradical process (other than the addition of oxygen, reaction s), the dynamics of SR., under the same experimental conditions, with a nitroxide, 2,2,5,5-tetramethylpiperidin1-oxy1 (TEMPO),

-

+

where represents all other uni- and bimolecular reactions and is supposed to be c o n ~ t a n t ' ~(see * ' ~ Appendix 1). Results are given in Table 1. Interestingly, the phenoxyl was completely unreactive with TEMPO; even with TEMPO concentrations as high as 0.1 M, the phenoxyl decay remained a second-order reaction. The measured k12,exp for the hydroaromatic radicals in the presence of sufficient amounts of TEMPO all displayed a firstorder behavior. The TEMPO concentration range was dependent on the reactivity of the SR- studied; with the slow reacting DHA., concentrations of 2 to 10 mM TEMPO were used. In general, high concentrations of TEMPO should be avoided because this persistent radical is known to absorb UV laser light, and on photoexcitation hydrogen abstraction from hydroaromatics may also O C C U T . ' ~

Discussion Termination Rate Constants. From Table 1 it can be seen that the range in 2k1 values for the termination reactions of SRis less than a factor of 3 with the exception of cyclohexadienyl radical. The rate constants are obtained from two independently determined parameters: 2klld and E . The extinction coefficients are measured relative to fluorenyl, so any deviation in the absolute EF. value may alter the absolute but not the relative 2kl's. The magnitude reveals that in the liquid phase for highly resonance stabilized radicals the termination rate constants are compatible with those for other carbon centered species (2kl = 1-10 x lo9 M-' s-').~* The termination reactions for, e.g., alkyl radical are classified as diffusion controlled processes. Hence, this study reveals that the self-reaction of hydroaromatic radicals still is diffusion controlled, substantiatingthat resonance stabilization has no retarding effect on the overall kinetics. From the relative small range in rate constants it is obvious that structural and electronic effects are limited. A direct comparison with literature data is hampered by the fact that reported rate constants are measured in various solvent systems (vide infra). In principle, the delocalization of the free electron in the n-system of the aromatic ring(s) should result in a number of reactive sites; the spin density in the benzyl radical, as measured by EPR,39is located at the ortho, para positions and the benzylic carbon. Although ca. 40% of the spin is localized in the aromatic nucleus, product studies show that combination yields bibenzyl (>go%), Le., coupling of two benzylic moieties. This observation can be rationalized since other products (e.g., orthoortho combination) are already thermally unstable at 294 K.40,41 Therefore, the observed rate comprises exclusively the coupling at the benzylic positions. As a consequence, it seems more likely that soot formation in toluene pyrolysis (see Introduction) at elevated temperatures starts with, e.g., bibenzyl as the precursor. With the more stabilized species SR- with respect to benzyl (see SR-H BDE, Table 3), the contribution of these side reactions can be ignored as well since the formed carboncarbon bonds are even weaker. Accordingly, for the 9,lOdihydroanthracenyl radical only one productive site can be

Rate Constants for Termination of Resonance Stabilized Radic:als allocated, which leads to the 9,9'-bi(dihydroanthraceny1) as the combination product. The termination rate constant, provided that &hydrogens are available, consists of two modes: disproportionation (kd) and recombination (kc). It has been demonstrated that, based on product studies, for S R radicals the degree of disproportionation can be related to the reaction enthalpy (A&). Thus, with A H d for CHD. and DHA. of -54 and -31 kcal mol-', respectively, the larger contribution of the disproportionation for the former species is r a t i ~ n a l i z e d . ~ ~ , ~ ~ The 2kl for CHD. is found to be significantly higher when compared with other SR. species, so based on thermochemical consideration this effect stems from a relative increase of kd. However, for a diffusion controlled process the transport phenomena of the medium dictate the encounter rate of two radical species and hence the observed 2k1. In this model the rate of decomposition of nonproductive coupling products followed by reorientation inside the solvent cage is supposed to be fast relative to the escape rate.'''' Since in CHD. three equivalent reactive and productive sites for both recombination and disproportionation are available, the re-orientation constraints in the encounter complex become less important. In sum, the self-reaction rate constant of CHD. is very close to the diffusion controlled limit, and the other investigated species are slightly slower due to a possible minor contribution of backdiffusion. Solvent Influence. It is well established that the solvent and solvent composition play an important role in the termination of radicals. In general, the influence of the solvent viscosity on radical-radical interaction can be described by combination of the von Smoluchow~ki~~ equation (eq 14) and the approximation for the diffusion coefficient (D) of the radical through the medium as given by the Stokes-Einstein relation (eq 15), to yield the Debye formula'"' (eq 16):

2k, = 08nDeNL(1000)

(14)

D = kT16nrq

(15)

2k, = RTl15q

J. Phys. Chem., Vol. 99, No. 20, 1995 8187 of 3. A similar observation has been made for the quenching rates of triplet P-phenylpropiophenone in various solvents.50 Since these rates are believed to be at the diffusion controlled limit, this implies that there is a difference of almost a factor of 2 in the diffusion limited rate constant in benzene and isooctane. A possible explanation might be that diffusion of an aromatic species (radical or triplet) in a aromatic solvent is retarded due to additional solvent-solute or solvent-solvent interactions. Therefore, eq 16 gives only an estimate of 2kl since no structural, entropy, and enthalpy effects andor solvent dependent interactions are included. Comparison with Termination Rate Constants in the Gas Phase. It is of interest to compare termination in the gas and the liquid phase in order to disentangle solvent properties and interactions. Surprisingly, the 2kl for the benzyl radical in the gas phase3' and in the liquid phase2 (toluene, 0.21 cP) at 294 K are almost identical with ca. 5.1 x lo9 M-I s-l, while for allyl some difference can be noticed in 2kl: 3.2 x 1Olo in the gas phase3I and in liquid propene42(0.16 cP) 1.6 x lolo M-' s-l. In the gas phase the rate constants are near the collision frequency combined with a correction factor for orientational requirement. According to collision or transition state theory:' the 2kl decreases with increasing molecular weight and size. In the liquid phase, however, the solvent acts as a shell around the encounter pair. So even though collision rates in the liquid phase are lower than in the gas phase, encounter times will be considerably longer and as a result the rate constants for bulky radicals like 9,lO-dihydroanthracenyl can be even larger than in the gas phase. Radical Recombination with TEMPO. In contrast to the self-reaction of SR., large variations in the rate constants for reaction with TEMPO are observed (about a factor of 3 for the termination versus a factor of 30 for the TEMPO reaction). It is known that the rate constants for combination of carbon centered radicals with TEMPO is below the diffusion limit, and a significant solvent dependence is n 0 t i ~ e d . IThe ~ ~ suggested mechanism for these slow radical-radical reactions involves the formation of a loose encounter complex followed by a solvent dependent rearrangement:

+

SR* TEMPO With (T = spin statistical factor (I/& only one-fourth of the encounters of the radicals with spin l/2 leads to an electronic singlet product and has been confirmed i n d e ~ e n d e n t l ye; ~= ~ reaction distance; r = diffusion radius; v = the viscosity (cP); and R (WL)= 8.3 x lo7 erg mol-' K-I. According to eq 16 in a particular solvent, the 2kl's for all the radicals terminations are predicted to be equal; typically in benzene with T,J = 0.64 C P ? ~a 2kl of 2.5 x lo9 M-I s-I at 294 K is calculated47(see Table 1). However, with experimentally determined diffusion coefficients (D), small experimental differences can be explained2 by eq 14 like 2kl for benzyl radicals in toluene (5.2 x lo9) and cyclohexane (4.1 x lo9). In this study the most 2kl values were measured in mixtures containing 75% Me3COOCMe3 and 25% benzene of which the exact composite viscosity is not known. For instance, our 2k1 for the cyclohexadienyl radical is considerably highefi9 when compared with an aqueous solution (2kl = 2.5 x lo9 M-' s-l 1 and cannot be explained by viscosity differences (qwater= 1.0 cp6). In the case of diphenylmethyl radical (DPM.), a clear solvent dependence was noticed. When replacing the peroxide by isooctane, a molecule with a similar shape and presumably comparable viscosity, an identical rate constant was obtained. However, by increasing the amount of benzene and consequently increasing slightly the overall viscosity of the solution ( V i s m t a n J vknzene= 0.84 at 294 K49, the rate constant dropped by a factor

'

- [C]

SRT

(17)

As a result, the overall rate constant has an activation energy and a preexponential factor lower than for a diffusion controlled process.I4 Combination of hindered phenoxyl radicals (2,6-ditert-butyl phenoxyl and 2,4,6-tri-tert-butyl phenoxyl) display a similar type of activated recombination with an overall negative temperature c o e f f i ~ i e n t . ~The ~ solvent dependence can be rationalized if the free energy gap between the (solvated) radicals and the (solvated) transition state for [C] SRT is a key factor in the dynamics of this type of recombination. If one accepts the suggestion that a complex is formed between TEMPO and SR. at the diffusion controlled rate,15athe product forming step must be an activated process and subject to variations as a result of changes in the overall enthalpy (Le., Hammond postulate) as well as entropic and steric effects. A plot of In kl2 versus the overall reaction enthalpy for cross combination, A H 1 2 , shows a clear trend in which the reactivity decreases as the bond in the coupling product becomes weaker (see Table 1 and Appendix 2). For example, there is a factor of 10 difference in kl2 in the reaction benzyl versus 9,lO-dihydroanthracenylradical, together with a difference in the reaction enthalpy of ca. 13 kcal mol-'. Even in the case of fluorenyl and 9,lO-dihydroanthracenyl radical, where steric factors are expected to be about the same, a difference in kl2 of a factor of 3 is observed. However, a factor of 10 is noticed between the radicals fluorenyl

-

8188 J. Phys. Chem., Vol. 99, No. 20, 1995

Arends et al.

and 1-indanyl. These results imply that both steric and enthalpic factors will influence the overall kinetics. The high k12 value for cyclohexadienyl radical can be partially explained by considering that an additional reaction route, namely the disproportionation with TEMPO to form benzene and the hydroxylamine, (TEMPO-H), occurs. CHD.

+ TEMPO - C6H6+ TEMPO-H

(18)

competition between TEMPO (eq 12) and the self-reaction (eq 1) can be disentangled as follows. In the presence of TEMPO, the overall rate of disappearance of SR. is given by: d[SR*]/dt = -k12[TEMPO][SR*] - 2kl[SRl2

(19)

The exact solution of this differential equation results in: ln([SR*]J(l

+ a[SR-],)) = -K,2t + ln([SR*]d(l + a[SR*],))

The heat of reaction for the disproportionation (eq 18) is around -48 kcal mol-' (note that in the case of DHA., A H d is only -27 kcal mol-'). Analogously to the self-reaction of SR- where disproportionation rates have been found to be enthalpy dependent,42 for the cross termination of CHD- with TEMPO a relatively large contribution of the disproportionation route can be expected. Product studies are needed to confirm the contribution of reaction 18. No reaction could be observed between phenoxyl and TEMPO. The incipient C - 0 bond (no reactivity can be expected from coupling of TEMPO to the oxygen site of the phenoxyl radical) is relatively weak so that even on the time scale of the experiment reaction 12 is too slow (upper limit