Faraday Discuss. Chem. SOC., 1982, 74, 21 5-228 Kinetics of Hydrogen-atom Transfer from Phenols to Galvinoxyl in Aprotic Solvents BY EDWARD F. CALDIN, STEPHEN P. DAGNALL,~ MARK K. S. MAK$ AND DAVID N. BROOKE University Chemical Laboratory, University of Kent, Canterbury, Kent CT2 7NH Received 12th May, 1982 The reactions of phenols with the free radical galvinoxyl (which is stable to air and solvents and deeply coloured) constitute a series of H-atom-transfer reactions where the solvent and substituents can conveniently be varied and accurate kinetic measurements can be made. The kinetics for a series of substituted phenols in toluene solution have been studied; we report rate constants (which vary over a range of more than lo4 at 25 "C), activation parameters and some deuterium isotope effects (rate ratio ca.6 at 25 "C). The results can be interpreted in terms of the electronic effects of substituents in stabilising the incipient phenoxy radical in the transition state and the steric effects of o-substituents in reducing the interaction of the phenol with the solvent. The reaction of one of these phenols, 2,4,6-tri-t-butylphenol, has been studied in a series of aprotic solvents of varying polarity and hydrogen-bond-acceptor properties. The rate constant decreases markedly with increasing polarity of the solvent; the isotopic rate ratio also varies appreciably from solvent to solvent. Desolvation of the phenol is apparently involved. Interpretation of the isotope effects may be sought in terms of tunnelling or of transition-state asymmetry. Solvent effects on the kinetics of proton-transfer reactions in solution have often been studied, but there have been fewer investigations of the role of the solvent in hydro- gen-atom-transfer reactions.A convenient reaction of this type for systematic study is hydrogen abstraction from a phenol ArOH by a free radical R' in solution (ArOH + R'+ArO' + RH), where substituents and solvent are easily varied and the radicals can often by characterised by their e.s.r. spectra. Considerable kinetic solvent effects have been observed for the reaction of 2,4,6-tri-t-butylphenol (I) with DPPH,' for the reactions of various substituted phenols with the tri-t-butylphenoxy radical,2 where a " dissection " showed that the changes of rate with solvent were due to changes in the solvation of the reactants and not of the transition state, and for the reactions of sub- stituted phenols with polyvinyl acetate radicals, several of which also showed high iso- topic rate ratios (>20 in some instances) with a marked solvent dependen~e.~ For the study of hydrogen-atom abstraction from phenols, stable free radicals such as DPPH or galvinoxyl (11),4-6 which are deeply coloured and so permit spectro- photometric monitoring of the reaction, have obvious attractions and have been used in a number of kinetic s t u d i e ~ .~ - ' ~ In the present work, we have used galvinoxyl (If), which is stable towards air and has a very high molar absorbance ( E = 154 000 at A,,, = 43 1 nm in benzene) ; also the reactions proceed nearly to completion.We have studied its reactions with a variety of phenols in toluene solution; the most suitable phenols are those with bulky groups in the ortho-positions (which do not dimerise in solution) and with a substituent also in the 4-position (since head-to-tail dimerisation t Present address : Chemical Technology Division, U.K. A.E.A., Harwell, Didcot, Oxfordshire. $ Present address : Department of Chemistry, St Francis Xavier University, Antigonish, Nova Scotia, Canada B2G 1CO.216 HYDROGEN-ATOM-TRANSFER KINETICS I N SOLUI IUN of the phenoxy radical produced is then avoided). For the investigation of solvent effects, we have chosen 2,4,6-tri-t-butylphenol (TBP), since it may be assumed to be monomeric in solution (the closely-related 2,6-di-t-butylphenol shows no dimerisation in solution or even in the pure state)l4*I5 and also the tri-t-butylphenoxy radical Y produced is stable and can be characterised by e.s.r.spectroscopy, and does not di- meri~e.~*'~*'' The corresponding reaction of this phenol with DPPH, studied by Ayscough and Russell,* showed an isotopic rate ratio of at least 12, but there were some complications. The reactions reported here appear to have simple rate laws at low concentrations. We write the overall reaction in a preliminary way as (1) k? ArOH + GO' F ArO' - - - HOG. k 2 EXPERIMENTAL MATERIALS Galvinoxyl from Aldrich was used without further purification ; its molar absorbance in toluene at A,,, (431 nm) was (9.1 & 0.5) x lo4 dm3 mol-' cm-' (lit. 1.5 x lo5 in benzene). The e.s.r. spectrum in toluene agreed in detail with the published spectrum.6 Solutions in toluene were stable for about a week when kept in the dark in a cold room.Solvents were AR or SLR (Fisons); they were dried with CaS04 or sodium metal, distilled in a stream of nitrogen and kept over molecular sieve under nitrogen. Chloro- benzene and dichloromethane were shaken with aqueous sodium bicarbonate or carbonate to remove HCl and washed with water before drying with CaSO,. Chlorobenzene was not distilled, since HCI would be produced. The boiling points agreed with literature values. The water content of the dried toluene samples was Phenols (ArOH) were purified either by vacuum sublimation or by fractional crystal- lisation from 40-60 "C petrdeum ether, and kept in the dark in a vacuum desiccator over Pz05.Purity was checked by m.p. Deuterated phenols (ArOD) were prepared as follows : the purified phenol (ArOH) was shaken with NaOD in D20 and the solution neutralised by addition of D2S04; the deuterated phenol was extracted with AR chloroform saturated with D20 and the solvent removed by evaporation on a vacuum line. (The use of D20 alone gave a product containing at most 95% of ROD.) D2O (>99.7%) and D2S04 (>99%) were from Mekck, Sharpe and Dohme; NaOD (>98%) was from BOC Prochem. niol dm-', by g.1.c. SOLUTIONS No special precautions were needed in the preparation of solutions of the proto-phenols. Experiments on the reaction with 2,4,6-tri-t-butylphenol (TBP) in toluene at 25 "C showed that the rate constant was altered <loyo by addition of water up to saturation (0.016 mol dm-3) and in DMSO the addition of 2% of water increased it by no more than 207;.Removal of atmospheric oxygen by bubbling nitrogen through the solution had no effect. In some experiments in dichlorobenzene, the addition of a drop of concentrated aqueous HCI or NH40H made no difference to the rate. For the deutero-phenols, solutions were made up from the carefully dried materials in a glove-box. Separate experiments showed that solutions contained least water when theE . F . CALDIN, s. P . DAGNALL, M. K . s. MAK AND D . N . BROOKE 217 glove-box contained a static atmosphere of air dried by molecular sieve. The water con- centration was then in the region of 4-12 ppm (v/v). It was determined by a Shaw " hygro- meter " calibrated by a series of toluene solutions containing known amounts of water; a value for the water content of toluene dried by molecular sieve was assumed.18 Galvinoxyl solutions were made up fresh each day.Reaction solutions of the deutero-phenols were made up by volume from a known stock solution (kept for not more than two days), trans- ferred in the glove-box to stoppered 1 cm cells and placed in the spectrophotometer to come to the required temperature. A drop of a solution of galvinoxyl was then added quickly from a microsyringe. Solutions were exposed to the atmosphere only during this operation, which took a few seconds. The run was then started immediately. Considerable practice was required to obtain reproducible results. For rate measurements in the strongly hydrogen-bonding solvents ethyl acetate, THF and DMSO, further precautions were taken to exclude atmospheric moisture. The cell and syringe were filled inside the glove-box, and the syringe was mounted directly above the cell; then the whole unit was transferred to the spectrophotometer, and the run was started without opening it.This arrangement worked well for H-atom-transfer, but reproducible results could not be obtained for D-atom-transfer. KINETIC MEASUREMENTS The course of the reaction was monitored spectrophotometrically, either in a 1 cm cell in a Pye-Unicam SP 8000 or a Hitachi 139 spectrophotometer, thermostatted to 50.1 IS, or (for some of the faster H-transfer reactions) in a small-volume stopped-flow apparatus of the type devised by Robinson and Treg10an.l~ The output was taken to a transient recorder, which permits rate constants to be determined by a curve-matching (analog) technique.20 For times above 200 s, an external time-base built in the laboratory was used; this arrange- ment extends the time range up to ca. 5 h.The reactions were studied under first-order conditions, the concentration of galvinoxyl being ca. 5 x mol dm-3 and that of the phenol 102-104 times larger. The experimental traces were accurately exponential (except where noted) and reproducible to 1-2%. They were replicated typically 10 times in stopped-flow work, 3 or 4 times when a spectro- photometer was used. Linear plots of the first-order rate constants against concentration of phenol were obtained, except in the cases noted below.In the determination of rates of D transfer, it is essential to keep the phenol fully deu- terated. We assume that if ArOH and ArOD are both present the H-transfer and D- transfer reactions proceed independentjy, so that if the mole fraction of D is xD the observed rate constant (assuming that the back reaction is negligible) will be k = xDkf + (1 - xD)kfH. Thus, for example, if 1% of the phenol remains undeuterated and the isotopic rate ratio kF/ky is 10, the observed rate constant will be higher by 976 than for pure ArOD and the apparent value of kfH/kP will be lower than the true value by the same amount. RESULTS SPECTRA OF PHENOLS I N SOLUTION 1.r. spectra of 2,4,6-tri-t-butylphenol in the solvents used show a single absorption, which in donor solvents is appreciably shifted from its position in a weakly interacting solvent such as cyclohexane (table 1).The shape varies, and in some solvents is complex, but we do not observe two distinct peaks, which would indicate the presence of dimers as well as monomers, or of free and H-bonded phenol molecules (as reported by Simonyi for solutions in vinyl acetate 21). We can therefore treat the molecules of the phenol as being all monomeric and all subject to similar solvent interactions. The absorption is attributable to the OH-stretching frequency (v). The shifts (Av) in theTABLE 1 .-KINETIC RESULTS FOR THE REACTION OF 2,4,6-TRI,T,BUTYLPHENOL AND ITS DEUTERATED ANALOGUE WITH GALVINOXYL IN VARIOUS SOLVENTS, AND SOME SPECTROSCOPIC DATA ~~~~~ ~ ~~ temp. phenol conc.solvent -Avl 102A6 1031r* 103P D, no. range no. range at25 "C Ea - A S kH/kD 1.r. n.m.r. H, (-A-, (-h-, kH, kD, kD* /dm3 mol-I s-I /kcal mol-I /cal K-' mol-l at 25 "C mol dm-3 /cm- (PPm) D* /"C 0 8-44 25 7-47 15-50 3-50 3-49 5-5 1 2.50 2-48 25 2-49 6-52 6-52 6-5 1 6-52 6-54 16-52 '50-49 6-44 5-52 2-50 5-32 16-44 12-46 25-39 25 25 25 25 25 6 6 5 5 5 5 6 6 7 6 6 5-6 0.5-5 0.6-2 1-50 2-30 1-50 1-10 2-50 1-10 2-20 4-18 20- loo 5-50 3-30 20- 100 5-50 20-90 0.1-4 3-30 2-50 10-100 7-30 2-40 10-100 10-100 10-100 1-8 1-8 5-13 0.6-5 0.7-5 62 f 3 25 f 4 Z9 41.2 f 1 18.4 f 1.3 256 36.9 f 0.3 254 26.2 f 4 5.11 f 0 . 2 2.21 f O . l 14.1 f 0 . 2 1.23 f 0.5 12.6 f 0.1 1.95 f 0.04 1.20 f 0.2 15.3 f 0.1 1.10 f 0.2 15.0 f 0.2 2.42 f 0.03 1.49 & 0.05 5.45 f 0.3 3.0 f 0.1 0.70 f 0.02 5.4 -I 0.1 60.7 0.31 f O.Old 6.3 & 0.1 3.5 f O .l 2.3 f 0.1 4.25 f 0.07 4.5 f 0.2 5.5 f 0.4 7.6 f 0.2 5.6 f 0.3 4.4 f 0.1 5.3 f 0.2 5.6 f 0.2 6.5 f 0.3 6.0 f 0.1 6.4 f 0.1 6.15 f 0.1 6.3 4 0.2 5.1 fO.1 - - - 38.0 f 0.2 41 f 1 34.6 f 1.2 29.0 f 0.6 38 f 1 38.6 f 0.1 40 $1 1 35.3 f 0.5 - - 1, cyclohexane 0 - H 4 D 1 D * 7 " I H 5 D 6 D * 7 " H 6 D * 7 " - H 2 " D 1 D * 7 " - H 6 D * 6 71 H 6 D 1 D * 6 100 H 6 D * 5 D 1 D * 5 310 H 6 D 1 D * 7 " - H 4 D 1 D * 4 446 H 5 550 H 2 764 H 1 - 112 H 12 - 2.5 f 0.3 2.3 f 0.4 2, n-heptane -2 0.3 - 80 3, cyclohexene 4, cc14 10 -12 0.4 3.4 294 5.2 f 0.3 37 & 1 35.3 f 0.2 38.8 f 0.1 34.8 f 0.4 13 18.5 -1 7 703 6 6 5 5 5 4-7 6 6 6 4 3 6 6 5 5 5 3 6.5 f 0.2 - 39.1 & 0.1 38.1 f 0.4 36.9 f 0.3 39.9 f 0.1 36.5 f 0.7 34.7 f 0.4 37.0 f 1 33.1 & 0.6 - - - 20 16 21 16 588 535 7, benzene 8, toluene 6.1 0.1 5.35 f 0.1 6.3 f 0.3 1.8 f 0.2 2 8 - - - - 6.9 f 0.2 6.7 f 0.1 7.2 &0.4 7.2 f 0.2 7.7 f 0.1 5.7 f 0.8 - - 9, CH3CN 80 38.5 71 3 10, CHzClp 1 36 802 37.2 f 0.1 40 f 10 68 102 184 545 576 1000 1 1, EtOAc 12, THF 13, DMSO U 0 Z 1.r.results: v = observed frequency, Av relative to cyclohexane value (3630 cm-'), A v relative to gas value (3645 cm-I). N.m.r, results: 6 = chemical shift (reference dioxan), Ad relative to cyclohexane (1.24 ppm). Solvent parameters: n* = polarity-polarisability parameter [ref. (33)J; = hydrogen- bond acceptor (basicity) parameter [ref. (33)]. Kinetic results: In column 6, H refers to the H-atom-transfer reaction in dry solvent; D to the D-atom- transfer reaction in dry solvent ; and D* to the D-atom-transfer reaction in solvent saturated with DzO.The corresponding forward second-order rate constants are represented by kH, kD and kD* in column 11. " Values of k were determined at the 2 extreme temperatures from plots of k(obs.) against concentration over range stated in column 10, and also at 5 other temps from k(obs.) at a single concentration with an estimate (from the preceding re- sults) of the small intercept on the plot of k(obs.) against concentration. * Different observer and equipment gave 18.3 f 0.2. = kD From 3 lowest points (at 0.01 - 0.04 mol dm-3) < 0.7 dm3 mol-' s-', higher than least-squares value for all 6 points (0.47 d= 0.02). An independent determination (at 0.007-0.02 mol dm-3) gave k < 0.5 dm3 mol-' s-', in reasonable agreement.Errors are standard deviations from best lines by least squares, usually rounded to nearest integer. Provisional values determined by D. N. Brooke. 1 cal = 4.184 J.E. F . CALDIN, s. P . DAGNALL, M. K . s. MAK AND D. N . BROOKE 219 absorption maximum do not correlate with the n.m.r. shifts (see below) nor with other solvent properties (table 1). This is not altogether surprising; although some degree of correlation between Av and AH* has been noted for various systems,22 it appears that the integrated intensity of the band is a more reliable indication of the interaction energy.23 -25 The lH n.m.r. spectra of 2,4,6-tri-t-butylphenol in various solvents showed the expected lines and the chemical shift of the hydroxy proton could be determined.In a given solvent at room temperature, variation of the concentration from 0.01 to 0.3 mol dm-3 produced no change in the chemical shift, such as would be produced either by dimerisation of the phenol or by variation of the proportions of solvated and un- solvated molecules. Like the i.r. spectra, these results confirm the view that in these aprotic solvents the phenol consists of single molecules all of which interact similarly with the solvent. (Similar results were obtained with 2,4,6-trimethylphenol in toluene up to 0.1 mol dm-3.) The chemical shift 6 varied considerably with solvent (table l), in the general order that might be expected for increasing interaction. THE PRODUCT OF REACTION Galvinoxyl in toluene solution mol dm-3) gave an e.s.r.spectrum agreeing with the published spectrum.6 After reaction with 2,4,6-tri-t-butylphenol (0.1 mol dm-3) under nitrogen, the e.s.r. spectrum agreed in detail with that for the corres- ponding phenoxy radical and there were no indications of the presence of any other radical. With 2,6-di-t-butylphenol and 2,4,6-trimethylphenol no e.s.r. spectrum could be observed, presumably because of dimerisation of the radical. KINETICS SOLVENT EFFECTS ON RATES OF H-ATOM TRANSFER FROM TBP TO GALVINOXYL The experimental traces were accurately exponential in all 13 solvents, and plots of the observed first-order rate constants k(obs.) against the concentration of TBP were satisfactorily linear (some of them down to mol dm-3). Results obtained by stopped-flow and spectrophotometer measurements agree well with each other.The plots mostly show small positive intercepts on the vertical axis. Such plots are in accordance with a reaction of the type A + B C , as in eqn (l), and we assume that the slope gives the value of k? and the intercept the value of k f in eqn (1). The ratio slope/intercept then gives values of KH in the region of 103-104, but the intercepts are too small to be reliable and are not recorded. Since the values of kH(obs.) are too numerous to record in detail, we give in table 1 the concentration ranges and the values of kp at 25 "C. The Arrhenius plots were linear within experimental error, and the activation parameters are given in table 1, with their standard deviations.Reproduci- bility is represented by two values obtained by different observers at different times, using different equipment, for the rate constant at 25 "C in toluene: 18.3 & 0.2 and 15.0 & 0.2 dm3 mol-I s-l. SOLVENT EFFECTS ON RATES OF D-ATOM TRANSFER FROM TBP TO GALVINOXYL Rates have been measured in seven carefully dried solvents, mostly at 25 "C only; they are surnmarised in table 1. The traces were again accurately exponential. The plots of k(obs.) against phenol concentration at 25 "C are satisfactorily linear in the concentration ranges cited, with small intercepts; at higher concentrations the slope220 HYDROGEN-ATOM-TRANSFER KINETICS IN SOLUTION decreases. (In cyclohexane, exceptionally, the plot is scattered and the value of k: given is a lower limit.) As regards reproducibility, in toluene at 25 "C k: was deter- mined in two sets of runs in different spectrophotometers, and the values obtained, with their standard deviations, were 2.62 & 0.13 and 2.42 & 0.03 dm3 mol-l s-l.(As noted above, we have not been able to obtain reproducible values in DMSO, THF or EtOAc, possibly because of adventitious H20.) A kinetic investigation of the D-atom-transfer reaction in solvents saturated with D20 was also carried out. The rate constants, represented by kF*, in these " wet " solvents are markedly lower than in the dry solvents, and the values of kF/kF* are considerably higher than the isotopic rate ratios kr/kp given in table 1 (last column), rising to 18 for CH2C12. It is not clear why the effect of added D20 on kp is larger than that of added H20 on k7, but the result shows the importance of using carefully-dried solvents.Reproducible results were obtained. EFFECT ON SUBSTITUENTS O N RATES FOR VARIOUS PHENOLS I N TOLUENE Rates and Arrhenius parameters have been determined for H-atom transfer in toluene solution to galvinoxyl from various 2,6-di-t-butylphenols and 2,6-dimethyl- phenols in which the p-substituent is varied; the results are summarised in table 2. For some of these phenols, rates were also determined for D-atom transfer in toluene saturated with D,O, and these results also are summarised in table 2. Rates of H- atom transfer at 25 "C have been determined for various other halogenated phenols and the results are shown in table 2. Data are given only for those systems which yielded experimental traces that were accurately exponential over their entire duration, corresponding to ca.7 half-lives. (Non-exponential traces were observed for the D- atom-transfer reactions of deuterated 2,6-dimethylphenol, 2,4,6-trimethylphenol, 2,6-di-t-butylphenol and 2,6-dimethyl-4-nitrophenol in toluene; these systems were not examined further.) DISCUSSION THE REACTION SCHEME The type of reaction under investigation can be represented by eqn (I), in which ArOH represents a phenol and GO' represents the galvinoxyl radical. The evidence for this is the clean second-order kinetics for the disappearance of galvinoxyl and (in the case of 2,4,6-tri-t-butylphenol) the e.s.r. spectra showing the disappearance of GO' and the appearance of ArO'. That the rate-limiting step is the H-atom transfer is shown by the isotope effects.The variation of rate with solvent indicates that the solvent is also involved. The values of the Arrhenius A-factor are strikingly low (104-106 dm3 mol-1 s-l), as for other reactions of free radicals with phenol^.^^-^' They are comparable with those for proton-transfer and other ion-forming reactions in the same which are attributed to electrostriction of solvent molecules around the polar activated complex. For the analogous reactions of phenols with the tri-t-butylphenoxy radical, it has been shown by a " dissection " method that the transition state is less solvated than the initial state; it is also less solvated in CCI, + acetonitrile mixtures than in CC14 and is evidently not highly polar.Another indication is that the activation volume for the analogous reaction of 2,4,6-tri-t-butylphenol with DPPH suggests that electrostriction is sma11.12 We adopt the explanation put forward to account for low values of A and E, for the reactions of phenols with other radicals by Mahoney and DaRooge l2 and by Howard Such an explanation is unlikely for the present reaction.TABLE 2.-KINETIC RESULTS FOR THE REACTIONS OF SUBSTITUTED PHENOLS WITH GALVINOXYL IN TOLUENE ~ ~~~~ ~ ~ ~ ~ ~~ ~ ~ ~ ~~~ ~~~ ~ ~~~~~~~ A S kH/kD phenol Ea phenol I H, temperature concentrations kH, Dk, kD * ' D, r-~-, r--, at25 "C /kcalmol-l logl,A /calK-'mol-' at25 "C su bst i tuent s Abbn. (--A-, D* no. range no. range /dm3mol-'s-l 4 2,6 3 5 1°C mol dm-3 (1) DMP Me (2)TMP Me Me (3) - C1 Me (4) - Br Me ( 5 ) - NOz Me (6) DBP Bu (7) - Me Bu (8) TBP Bu Bu (9) - Me Bz (10) 4-NP NO2 (11) 4-FP F (12) 4-CP c1 (1 3)3,4-DCP "C1 (14) 3,5-DCP (15) - Br H 6 6-51 H 6 6-37 H 10 6-51 D * 5 16-51 H 6 6-51 D * 5 15-51 H 6 7-51 H 13 -30-49 H 5 6-44 D * 5 6-44 H 12 -50-49 D 1 25 H 1 25 H 1 25 H 1 25 D * 5 6-44 H 6 7-49 D 6 7-49 c1 H 7' 1-49 D 6 ' 8-49 CI C1 H 1 25 H 1 25 8 5 6-8 5 7-8 5 5-8 7-8 5 4-7 6 6 5 3 3 5 3 5 5-80 8.55 f 0.06 6.85 f 0.2 5-50 151 f 2.5 4.8 f 0.2 2-40 12.9 f 0.2 6.7 f 0.3 20-100 1.47 f 0.03 6.9 f 0.25 -5-50 9.65 f 0.1 7.35 f 0.2 20-100 1.29 f 0.02 7.3 f 0.2 0.18 f 0.01 7.25 f 0.4 15-100 2.58 f 0.03 6.6 f 0.2 4-30 24.2 f 0.2 4.5 f 0.1 25-120 2.08 f 0.06 5.1 f 0.25 0.1-4 15.0 f 0.2 5.35 f 0.1 3-30 2.42 f 0.03 - 2-50 1.49 f 0.05 6.9 f 0.2 5-50 25.6 f 5 , - - 0.01 - -0.7 - 0.01-0.04 0.60 f 0.04 9.8 f 0.2 0.005-0.05 0.106 f 0.002 11.5 f 0.6 0.01-0.2 0.147 0.01 11.7 f 0.1 0.008-0.1 0.0265 f 0.001 12.55 f 0.3 -0.015 - 0.005-0.05 -0.025 - 6.0 f 0.2 33.3 f 0.6 5.7 f 0.15 34.5 & 0.6 6.0 f 0.2 33.0 f 1.0 5.25 f 0.2 36.3 f 0.5 6.4 f 0.15 31.4 4 0.6 5.45 f 0.15 35.5 f 0.4 4.6 & 0.3 39.6 f 1.2 5.3 f 0.2 36.4 f 0.7 4.65 f 0.04 39.2 f 0.2 4.07 f 0.2 41.8 f 0.5 5.3 f 0.1 36.9 f 0.3 5.24 f 0.15 36.5 f 0.7 - - - - - - - - 6.95 f 0.12 28.7 f 0.5 7.5 f 0.04 26.3 f 2 7.75 f 0.04 25.0 f 0.3 7.65 f 0.2 25.6 1.0 - - - - 6.3 k 0.3 - - - 5.6 f 0.5 5.6 f 0.6 - - Symbols as in Table 1.Bz = benzyl. Abbn = abbreviation. Uncorrected for rate of back reaction. " For 3,CDCP at 25 "C, in heptane kH w 1.1 dm3 mol-I s-' and in dichloromethane kH x 0.13 dm3 mol-' s-'.Values of kH for 4-chlorophenol in toluene were determined at 33.7 and 49.0 "C from plots of kH (obs.) against concentration over range of concentrations stated in table (these plots were not linear at concentrations >0.1 rnol dm-3); also at 4 other temps in the range 7-40 "C from kH (obs.) at a single concentration along with estimates (from the previous results) of the small intercepts on the plots of k (obs.) against concentration. Values of kD for 4-chlorophenol in toluene were determined (a) at 35 and 50 "C from linear parts of plots of kD (obs.) against concentration (using 3 concentrations, 0.005-0.05 rnol dm-3) and (6) at 6 temperatures (7-49 "C) at a single concentration (0.05 mol dm-3) along with estimates of the intercepts. Methods (a) and (6) gave, respectively, kD (at 25 "C) = 0.110 f 0.007 and 0.106 f 0.002 dm3 mo1-' s-', E," = 11.5 f 0.6 and 12.4 f 0.15 kcal mol-' and A S n = -26.3 f 2 and -23.2 f 0.5 kcal K-' mol-'.The values given in the table are those from method (a). Those from method (b) would give values of E," - Eq and of log AD/AH much higher than the others in this work (2.6 f 0.4 kcal mol-I and 1.2 f 0.2, respectively). Method as in note d; plots of k (obs.) against concentration were linear up to 0.2 rnol dmb3. Method as in note d; plots linear to 0.1 mol dm-3. a From initial rates; traces non-exponential.222 HYDROGEN-ATOM-TRANSFER KINETICS I N SOLUTION and Furim~ky,~' namely that the H-atom transfer is preceded by a fast equilibrium step in which the reactants produce a hydrogen-bonded complex within which the atom transfer occurs: ArOH + 'OG% ArOH - *OH kZ' ArO' - * H OG-ArO'.* .HOG. (3) Assuming that the fraction of the 'OG radicals that are H-bonded to ArOH is small, the observed rate constant and other kinetic parameters for the forward reaction will be (dropping the subscript f and writing Ea for the Arrhenius activation energy) k = K1k2; AHf = AH? +- AH;; ASt = AS? +- AS;; Since AS? will be ca. -30 cal K-' mol-', while AS$ will be small, this scheme predicts a large negative value for AS: and a low value for A , as observed. Also, since AH? will be negative, the experimental value of AHf will be lower than AH;. There is direct support for this scheme in the case of the analogous reaction of TBP with the corresponding phenoxy radical (ArOH + 'OAr+ArO' + HOAr) in carbon tetra~hloride.~~ N.m.r.line-broadening measurements show that (a) there is a pre- liminary complex formation without hydrogen transfer, (b) this is fast compared with H-atom transfer, (c) the concentration of complex is low ( K z dm3 mol-' at 27 "C) and its lifetime short (ca. lo-' s) and (d) AH: is small and negative (-2.3 rf 1 kcal mol-l) while AS? is large and negative (-35 rf 3 cal K-l mol-I), as expected. Since the solvent effects (see below) suggest that in solvating solvents the formation of the activated complex involves the desolvation of the phenol, we may elaborate the reaction scheme of eqn (3) as follows (S = solvent) ArOH - . S + *OG--L ArOH ArO' 9 - * HOG + S.(5) We now apply this reaction scheme [eqn (5)] to the interpretation of the solvent and substituent effects on the rates, Arrhenius parameters and isotope effects. Ea = Ea2 + AH?; In A = In A2 + (ASr/R). (4) Kt 'OGkZ- ArO - * - H * OG + S ---t SOLVENT EFFECTS The rate constant kH for H-atom transfer from TBP to galvinoxyl at 25 "C varies ca. 30-fold in the range of solvents used, kD for the D-atom transfer varies ca. 30-fold, and the isotopic rate ratio kH/kD ca. 4-fold (table 1). These are large variations for so limited a range of solvents. Interpretations may be sought in terms of the several types of solute-solvent interactions due to polarity, polarisability, x--7t interaction and hydrogen bonding. It is reasonable to suppose that the solvation of the phenol, not of the transition state, is the prime consideration, by analogy with the reactions of the phenol with its radical.2 Correlations may be attempted (a) within the kinetic data, (b) with the spectroscopic data on the same system (table 1) and (c) with solvent para- meters such as Taft's H-bond-acceptor basicity parameter @, or his polarity-polarisa- bility parameter x* which is intended to reflect all non-specific contributions to the free energy of solute-solvent interactions 33-36 (see table 1).COMPARISON OF RATES AND ACTIVATION ENERGIES Plots of log kH and log kD against E," (not shown) give clear trends, but are scat- tered; the plot of log (kH/kD) against E," is a fairly good straight line for five of the solvents, while acetonitrile (9) and n-heptane (2) show relatively low values.E .F . CALDJN, s. P . DAGNALL, M . K . s. MAK AND D . N . BROOKE 223 THE INFRARED 0 -H STRETCHING FREQUENCY From the data in table 1, it is evident that there is no clear correlation between Av This is not entirely surprising; see the Results and the values of kH, kD or kH/kD. section. THE N . M . R . CHEMICAL SHIFT The values of 6 for the phenolic proton correlate quite well with the rate data, as is shown in fig. 1 (a), (b) and ( c ) (the correlation need not be linear). Acetonitrile is again an exception. The shift should depend on the interactions of all types that affect the shielding of the OH proton,37 including hydrogen bonding (especially with the aromatic 7c-electron system and the C=N triple bond) as well as non-specific inter- actions.SOLVENT PARAMETERS The plot of log kH against n* [fig. l(d), (e) and cf)] shows that solvents which do not accept hydrogen bonds give points lying fairly close to a straight line, while the points for hydrogen-bond acceptors lie below. The plot of log kH against the H-bond basicity /3 shows a fair correlation for the seven solvents concerned [fig. l(g)]. The plots of log kD and log kH/kD also show moderate correlations. (Acetonitrile is peculiar in lying high on the plot of log kD and therefore low on the plot of log kH/kD.) The results indicate that hydrogen bonding and non-specific interactions are both important. This suggests that the desolvation in eqn (5) need not always be the breaking of a directional bond. ELECTROSTATIC INTERACTIONS The Kirkwood function ( e - 1)/(2~ + 1) gives scattered plots, indicating that a purely electrostatic treatment would be inadequate.The variation in rates is com- parable with that for ion-producing reactions in these solvent^,^^*^* but in the opposite direction. In terms of electrostatic theory, this would imply a large decrease in dipole moment on forming the transition state: this is unlikely. It appears that as a measure of non-specific interactions the Kirkwood function is, for this reaction, inferior to z*. VARIATION OF THE ISOTOPIC RATE RATIO WITH SOLVENT The values of kH/kD show a variation with solvent, which even after all account is taken of experimental difficulties appears to be genuine. The zero-point-energy difference between 0-H and 0-D bonds will not by itself account for this solvent- dependence.Possibilities to be considered are (i) asymmetry of the transition state and (ii) the role of tunnelling. Noting that for the two-step reaction k = K,k, [eqn (3) and (4j], we assume that the observed values of kH/kD represent those of kF/k,D, since the isotopic difference between K': and K y is not likely to be important, if analogy with other hydrogen-bonding equilibria is to be t r ~ s t e d . ~ ' ~ ~ ' We are thus considering the transfer of an H or D atom within an OH - * * 0 hydrogen bond. Change of solvent might affect the asym- metry of the transition state, by producing different changes in the various force constants. The analysis due to Westheimer 40-42 then shows that on classical grounds we can expect that kH/kD will vary with AG" and will pass through a maximum at AG" = 0, i.e.K2 = 1. The treatment was originally developed for substituent effects but has more recently been applied to solvent effect^.^^-^^ We do not possess quan- (i) Asymmetry of the transition state.224 HYDROGEN-ATOM-TRANSFER KINETICS IN SOLUTION 8 log kH log kD L d iiE . F . CALDIN, s. P . DAGNALL, M. K . s. MAK AND D. N . BROOKE 225 titative data on K2 with which to test this hypothesis, but note that the overall equili- brium constant K shows no sign of wide variations. According to the Marcus theory, however, the variation of kH/kD with K will be steeper the lower the intrinsic free- energy barrier [cf. eqn (2.28) of ref. (42)], and for H-atom transfer within an OH - * * 0 hydrogen bond this barrier might be fairly low, so the wide variation of kH/kD is not necessarily incompatible with relatively small changes of K.The largest value of kH/kD (ca. 8, for dichloromethane) is below the maximum attributable to the zero- point-energy difference of ArOH and ArOD, which for an 0-H stretching frequency of 3600 cm-' is ca. 12. It would be interesting to determine kD in a wider range of solvents, but the difficulty of excluding water is considerable. (ii) T ~ n r t e l l i n g . ~ ~ - ~ ~ An alternative explanation of the variations in kH/kD with solvent is that tunnelling is important. If we consider first a simple 3-centre model (OH - - - O-tO - - HO), the tunnelling factor QH/QD by which the actual value of kH/kD exceeds the value attributable to the zero-point-energy difference will increase with the height and curvature of the energy barrier, especially when the barrier is sharply curved, according to calculations based on Bell's equation for a parabolic barrier [see the table on p. 38 of ref.(42)) If desolvation, or partial desolvation, precedes or accompanies the H-atom transfer, the energy required will contribute to the barrier height and an increase in this energy will increase QH/QD and hence kH/kD. In this case the effect will be reduced if the solvent reorganisation involves coupled motion of heavy atoms, since this will increase the effective mass and will therefore reduce QH below the value it would have for the simple 3-centre model. With these considerations in mind, we might attribute the increase of kH/kD with E,H, Ad and n* in the series of solvents (with the notable exception of acetonitrile) to an increase in QH/QD due to an increase in the barrier height, as manifested by the in- crease in EF (which will be correlated with the barrier height, although smaller).The correlations with Ad, j? and n* show that the barrier height increases with these indexes of phenol-solvent interaction; this would imply that the energy required to desolvate the OH group contributes to the barrier height. A rough calculation suggests that the range of values of kH/kD is not too large to be explained by the range of values of E,H. The barrier height EH will be not less than (EF - AH?), and if we take AH? x -2.3 kcal mol-l (as for the analogous system ArOH + ArO.) 32 the minimum range of EH will be from ca.7 to 10 kcal mol-'. The barrier width may be taken as equal to the distance apart of the oxygen atoms in the OH * - - 0 hydrogen bond, which on average is ca. 270 pm,54 minus the length of the two OH bonds (ca. 100 pm each); this gives the width 2b as ca. 70 pm. If we assume a symmetrical parabolic barrier, the above value corresponds to an imaginary frequency of ca. 1 130-1 360 cm- I. Calculations based on the first two terms of Bell's equations 46*49 indicate that the corresponding values of QH/QD are ca. 3 for the lowest barrier and ca. 8 for the highest; these are to be com- pared with the observed range of kH/kD from ca. 2 to 8. Tunnelling thus offers a plausible interpretation of the isotope effect; but values of kD in a wider range of solvents are needed to decide whether kH/kD has reached a maximum at ca.8, or whether in strongly hydrogen-bonding solvents it would be larger. The calculations illustrate, incidentally, the striking increase of QH/ QD with barrier height when the barrier is relatively narrow. Some further calculated values indicate that for H-atom-transfer along an OH 0 hydrogen bond, with kH/kD z 10 QH/QD at 25 "C, one might expect to find values of kH/kD in the range 20-100 at 25 "C for moderate barrier heights, if concerted solvent motions do not reduce the value. Large isotope effects, up to 100, have in fact been observed in some intramolecular H-atom- transfer reaction^,^^-^^ where the solvent would be expected to play little part.226 HYDROGEN-ATOM-TRANSFER KINETICS I N SOLUTION SUBSTITUENT EFFECTS EFFECT OF VARYING THE p-SUBSTITUENTS When the p-substituent is varied in the series of 2,4-dimethylphenols (table 2, nos.2-5) the rate constant kH at 25 "C varies by nearly three powers of ten, in the order Me 9 C1, Br 9 NOz; kH is markedly reduced by electron-withdrawing substituents and increased by electron-donating substituents, as has been found for related reac- t i o n ~ . ~ ~ ~ * ~ ~ ~ The Hammett plot of log kH is linear, with slope -3.1. In the absence of o-alkyl groups, introduction of halogens or NO, into the 4, 3 or 5 positions (nos. 10-14) reduces the rate constant still further, and the overall variation is ca. 25 000- fold. According to our reaction scheme [eqn (5)], substituents might influence the ob- served kinetics by their effect either on step 1 (hydrogen-bonding between phenol and radical) or on step 2 (H-atom transfer within the hydrogen-bonded complex).If the data on stable systems may be assumed to provide a suitable analogue,39 the major effect will be on k f . Electron-donating substituents will stabilise the electron- deficient radical product ArO*, and to a lesser extent the transition state, relative to ArOH, thus increasing ky ; electron-withdrawing substituents will have the opposite effect. This interpretation agrees with the order of the observed rate constants and is in accord with the linear Hammett plot and its large p-value. The activation para- meters are less easy to understand. In the 2,6-dimethyl series, the low rate constant for the 4-nitro compound is due to a low A-factor, while the high rate constant for the 4-methyl compound is due to a low activation energy.The relatively low rate con- stants for the 3,4- and 33- chlorophenols (nos. 13 and 14) are due to larger values of E,, partly compensated by larger values of A . EFFECTS OF VARYING THE 0-SUBSTITUENTS The effect of replacing the two o-methyl groups in 2,4,6-trimethylphenoI by the more bulky t-butyl groups is to decrease kH by a factor of ca. 8 (table 2, nos. 6 and 7). There is a reduction of the A-factor by a factor of ca. 12, as would be expected if the effect is due to steric hindrance. There is no accompanying increase in EF, presumably be- cause the effect of electron donation from the t-butyl groups in stabilising the transition state is greater than that of their bulk in increasing repulsion.The same is presumably true for replacement of the o-methyl groups by benzyl groups, which results in an increase of rate constant despite the effects of bulk (table 2, no. 9). The effect of replacing o-methyl groups by bromine atoms is to reduce the rate by a factor of 300, presumably mainly by reason of electron-withdrawal. Thus both steric and electronic effects are concerned. CONCLUSION Our results are in general agreement with the mechanism involving preliminary formation of a hydrogen-bonded complex, within which the rate-limiting H-atom transfer occurs, and with the view that the decrease of rate with increasing " polarity " of the solvent is attributable to increasing interaction with the phenol in the initial state.The variation in the deuterium kinetic isotope effect with solvent is consider- able, but not enough to show whether it is atttributable to assymetry of the transition state or to tunnelling. Note added in proof. In a recent paper by Malatesta and IngoldS5 on the kinetics of H- atom abstraction from toluene by the radical (CF3)N02', the deuterium isotope effects areE . F . CALDIN, s. P . DAGNALL, M . K . s. MAK AND D . N . BROOKE 227 reported to be considerable (kH/kD x 10 at 25 "C, E y - EF M 1.6 kcal mol-I) and are tentatively attributed by the authors to tunnelling. 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