J. CHEM. SOC. FARADAY TRANS., 1994, 90(4), 571-574 57 1 Effect of Preferential Solvation on Reactivity of a Free Radical in Binary Solvent Mixtures Osamu Ito* and Hisanori Watanabe Institute for Chemical Reaction Science, Tohoku University, Katahira ,Aoba-ku, Sendai-980, Japan The absorption maxima of p-NH,C,H,S' and the rate constants and relative equilibrium constants for the reversible addition reaction of p-NH2C6H4S' with a-methylstyrene have been measured by a flash photolysis method in binary solvent mixtures with different compositions. In a polar-non-polar mixture, preferential solva- tion of p-NH,C6H,S' by the polar solvent was observed via the effect on the absorption maximum and the rate parameters. The linear free-energy relationship between the reaction rate constants and the relative equilibrium constants revealed that solvation of the reactant is more important than solvation of the transition state.Preferential solvation of a polar solute by the polar solvent in a polar-non-polar binary solvent mixture has been recog- nized from thermodynamic properties such as solubility and equilibrium constants. '-' Although it has been pointed out that the effect of solvation on the kinetic data is important for an understanding of the reaction process in solution, only a few studies on preferential solvation have been reported for ionic In the case of free-radical reactions, however, the effect of binary solvents on the reaction rates has not been reported, because of the non-polar character of the normal free redical, in addition to the difficulty in obtain- ing the rate parameters of the free-radical elemental reactions.In our previous studies,'-" it was found that flash pho- tolysis was an appropriate method for examining the effect of solvation on the free radical, because the reaction rate con- stant could be determined as an absolute value. In addition, the absorption maximum of the free radical could be observed at the same time by the same We found that the reactivity of the p-NH2C6H,S radical is quite sensitive to the solvent polarity, because of its dipolar ~haracter.','~ In the present study, the effect of binary solvent mixtures on the absorption maxima and reaction rate constants of p- NH,C,H,S' has been determined by flash photolysis in solvent mixtures with different compositions.In this reaction system, the linear free-energy relationship between the rate constants and the relative equilibrium constants, which could be obtained by analysing the reversible addition reaction, would be expected to afford information about the solvation of the transition state of the reaction. Experimental Materials (p-NH,C,H,S), was employed as a source of p-NH,C,H,S'. The disulfide was prepared from air oxidation of the corre- sponding thiol and was purified by recrystallization from ethanol. Commercially available a-methylstyrene (a-MSt) and all other solvents were used after purification. The non-polar solvents used were cyclohexane and carbon disulfide and the polar solvents were pyridine, ethanol and N-methyl pyrrolidin-2-one (NMP). Cyclohexane-pyridine and cyclohexane-NMP are expected to behave as standard polar-non-polar binary mixtures.The cyclohexane-ethanol mixture would be expected to show effects due to hydrogen bonding. CS,-pyridine and CS,-NMP systems were selected because some bituminous coals are quite soluble in the 1:1 (by volume) binary solvents at room temperature." (p-NH,C,H,S), cu. 5 x lo-' mol dmW3 was added to these binary solvent mixtures. This produced a sufficient con- centration Ofp-NH,C,H,S' (ca. 1 x lo-' mol drnp3) with one flash exposure to monitor the decay of the transient absorp- tion band in a cylindrical cell 10 cm long and 1 cm in diam- eter.' The oxygen concentration was controlled by the partial pressure.Apparatus The flash photolysis apparatus was of a standard design with two xenon flash lamps (xenon Corp. N-981C; with a half- duration of 10 ps). The photolysis light of wavelength 310-420 nm was selected by means of filters. The decay kinetics were followed by a photomultiplier detection system. Results and Discussion Absorption Maxima of p-NH,C,H,S' Fig. 1 shows the transient absorption spectra observed on flash photolysis of (p-NH,C,H,S), in cyclohexane, in pyri- dine and in their mixture. The transient absorption band observed in the visible region in each solvent system was attributed to p-NH,C,H,S', because the same absorption bands were observed on flash photolysis of p-NH2C6H,SH.9"3 The absorption peak shifts to longer wave- length with increase in the pyridine content of the mixture.This trend is in agreement with the general bathochromic shifts of the electronic transitions of polar solutes. The dipole moment in the excited state of p-NH,C,H,S' was determined 0.81 0.7 0.3 0.2 0.1 0.0 450 500 550 600 650 700 wavelength/nrn Fig. 1 Transient absorption spectra of p-NH2C,H,S'; (a) in cyclo- hexane, (b) in cyclohexane-pyridine (1 :1) and (c) in pyridine. The absorbance is shown immediately after flash of 1.0 x mol dm-3 @-NH,C,H,S), . 572 as 7.3 D, while that of the ground state was 4.3 D.13 A slight decrease in the absorption intensity was also observed; this is attributed not only to the hypsochromic effect but also to a decrease in the yield of the radical.For other binary solvent mixtures, similar tendencies in the absorption maximum and absorption intensity were observed. In Fig. 2 the variations of the absorption maxima of p-NH,C,H,S* are plotted against the mole fraction of the polar-non-polar binary solvent mixtures with cyclohexane as non-polar solvent. The line in each system shows the ideal case without specific solvation such as preferential solvation. For all binary solvents in this study, the absorption maxima move to a longer wavelength on addition of a small amount of polar solvent. This suggests that the polar solvent prefer- entially solvates p-NH,C,H,S' even though the content of polar solvent is less than that of the non-polar solvent.Fig. 2 shows that the extent of the preferential solvation is in the order NMP > ethanol > pyridine. The same tendency was observed when CS2 was used as non-polar solvent, although the absorption maximum in CS, was at a longer wavelength than that in cyclohexane. This suggests that CS, polarizes p-NH,C,H,S' more than cyclohexane; the polarizability also plays an important role. The extent of the preferential solva- tion in CS, on addition of a polar solvent was less than that in cyclohexane. Reaction Rate Constants Fig. 3 shows the first-order plots of the decay of p-NH2C,H,S' in the absence and in the presence of a-MSt in the binary solvent mixture of cyclohexane and pyridine.In the absence of a-MSt, p-NH,C6H4S' decays with second- order kinetics, thus, a deviation from the linearity of the first- order plot was seen [Fig. 3(a)]. This indicates that p-NH,C6H4S' decays predominantly by recombination to the disulfide. The low reactivity of p-NH,C,H,S* to oxygen was confirmed, since the decay did not change appreciably on the addition of oxygen to the ~olution.~ Since the arylthiyl radicals add reversibly to the alkene double bond, the decay rate of p-NH,C,H,S' was not accel- erated even in the presence of a-MSt in the degassed solution as shown in Fig. 3(b). In order to shift the fast equilibrium between the thiyl radical and the carbon-centred radical, it is necessary to add a radical trapping reagent which reacts selectively with the carbon-centred radical.Because oxygen has low reactivity to the thiyl radical and high reactivity to the carbon-centred radicals, oxygen may be appropriate for 18.5 1 1 18.1 r I 6 17.7 z ---2 I*E" 17.3 16.9 t I16.5 1 I 0.0 0.2 0.4 0.6 0.8 1.0 mole fraction Fig. 2 Spectral shift of the absorption maxima (imaX)of p-NH2C,H,S' in binary solvent mixtures of cyclohexane with (a)pyri-dine, (b) ethanol and (c) NMP J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 -2*o * -2.5 -3.0 :-3.5-this role. As shown in Fig. 3(c) and (4, the decay rate of p-NH2C,H4S' increases when oxygen and a-MSt are present in solution. The whole reaction scheme is represented by Scheme l.'*14 k' k'li +IOd 1k2 proxy radical Scheme 1 The decay rates of p-NH,C,H,S' depend on the concen- trations of a-MSt and oxygen.The rate constants in reaction Scheme 1 can be expressed as143's where [a-MSt] and kfirs,-ordcrrefer to the concentration of a-MSt and the first-order rate constant, respectively. The kfirst-ordervalue can be evaluated from the slope of Fig. 3(c) and (4.When the first-order plots are not linear, the contri- bution of the second-order decay due to the recombination of the thiyl radical can be eliminated by a graphic or computer simulation ' In Fig. 4, the plots of eqn. (1) are shown for cyclohexane- pyridine systems with five different ratios of pyridine to cyclo- hexane. The addition reaction rate constant (k,) can be evaluated from the intercept of Fig.4; the slope gives the value of Kk,[O,], where K = k,/k_, and [O2Isrefers to the oxygen concentration in the oxygen-saturated solution. The results for all the binary solvent systems studied are sum- marized in Table 1. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 7.0I r( 1 6.01 n/"Id 5.0 X 4.0 ? In &c 3.0--.-6 2.0L 1 .o 0.0 0 1 2 3 4 5 6 1/[O,I, Fig. 4 Plot of eqn. (1) for the reaction of p-NH,C,H,S' with a-MSt in pyridine-cyclohexane binary solvent mixture; ratio = (a) 1 :0, (b) 3 :1, (c) 1 : 1, (d)1 :3 and (e)O:1 The log k, values are plotted against the mole fraction of each solvent for mixtures with cyclohexane, in Fig. 5. The values decrease with the increase in the mole fraction of polar solvent in each mixture.Preferential solvation by the polar Table 1 Rate parameters for Scheme 1 in binary solvent mixtures binary mixture f k'l mol-' dm3s-' (k-i/kz[Oz]s)/ mol-'dm3 Kk 2 ro2 I,/10-4mol-1 dm3 s-' cyclohexane- 0.00 23 0.14 170 pyridine 0.13 3.5 0.15 41 0.25 2.1 0.17 12 0.31 2.3 0.25 9.0 0.57 1.2 0.30 2.0 0.80 0.9 0.67 1.6 1 .00 0.8 0.85 0.9 cyclohexane- 0.00 23 0.14 170 ethanol 0.02 10 0.11 90 0.10 3.4 0.15 22 0.17 2.2 0.20 11 0.29 1.3 0.26 5.0 0.38 1 .o 0.22 4.5 0.64 0.7 0.21 3.2 0.85 0.7 0.20 3.3 1.00 0.8 0.26 3.5 cyclohexane- 0.00 23 0.14 170 NMP 0.01 4.2 0.18 24 0.03 1.7 0.25 6.9 0.05 0.71 0.17 4.2 0.11 0.45 0.26 1.7 0.22 0.38 0.32 1.2 0.27 0.35 0.38 0.93 0.53 0.25 0.40 0.63 0.77 0.22 0.44 0.50 1 .00 0.20 0.67 0.30 cs,- 0.00 9.2 0.46 20 pyridine 0.16 1.7 0.47 3.6 0.21 1.6 0.64 2.5 0.43 1.4 0.70 2.0 0.67 1.1 0.85 1.3 1 .00 0.80 0.89 0.9 CSZ-NM P 0.00 9.2 0.46 20 0.06 0.59 0.32 1.8 0.17 0.37 0.63 0.6 0.38 0.25 0.50 0.5 0.65 0.20 0.50 0.4 0.93 0.13 0.43 0.3 1.oo 0.10 0.50 0.2 x represents the mole fraction of the polar component, i.e.pyridine, ethanol or NMP. 573 5.0 ,-4.5 0 -4.0 3.5 3.0 0 0.2 0.4 0.6 0.8 1 mole fraction Fig. 5 Plot of log k, us. mole fraction of the binary solvent mixture of cyclohexane with (a)pyridine, (b)ethanol and (c) NMP solvent was observed in all solvent systems.In the case of the cyclohexane-NMP mixture, only 0.2 mole fraction of the polar solvent is needed to decrease the log k, value by 80-90%. The extent of preferential solvation by the polar solvent in cyclohexane increases in the same order as indicated by the absorption maxima in Fig. 2. In the addition reaction of p-NH,C,H,S' to a-MSt, it is assumed that the transition state has a dipole moment intermediate between the reactant and product which is the carbon-centred radical whose dipole moment may be negligibly small. This leads to a small reac- tion rate constant in polar media, because stabilization of the transition state by the polar solvent is less than that of the rea~tant.'O*'~~~ In Table 1, the k-,/k,[O,], values do not vary consider- ably on changing the concentration of the polar solvent. The k, values for the carbon-centred radicals with small dipole moment may not vary much on changing the solvent polarity.Thus, the variation of k-, between cyclohexane, pyridine, ethanol and NMP may be small. On putting k, = lo9 dm3 mol-' s-l and [O,],= lo-' mol dm-3, k-, can be calculated as ca. 3 x lo6 s-' which is large enough to estab- lish the fast equilibrium in Scheme 1 during a flash-lamp exposure of 10 ps duration. The small change in log k-,with solvent polarity can be understood from the less polar carbon-centred radical and the transition state of the reac- tion.On the other hand, the variation of Kk,[O,], with chang- ing solvent polarity is large. With an increase in the mole fraction of the polar solvent, the Kk,[O,], value tends to decrease. The decrease in log K implies an increase in the endo t hermici ty . In Fig. 6, the log k, values are plotted against log Kk,[O,], values to examine the linear free-energy relation- ship. A good linear relationship with slope of 0.75 can be seen; k,[O,],can be thought to be constant. A(1og k,) = aA(1og K) (2) In the equation above, o! = 0.75, which implies that the stabil- ization by solvation is one quarter of that of the reactant. In this study, we found a specific interaction within the binary mixture or with the solute. In the preferential solva- tion observed from the absorption maxima, a small amount of ethanol has a stronger effect than a small amount of pyri-dine in the mixture with cyclohexane (Fig.2), while a pro- nounced deviation cannot be found in log k, (Fig. 5). From Table 1 a specific interaction could not be deduced for CS,-pyridine and CS,-NMP. It was noticed that the rate 6.0 - 5.5 5.0 - c 0 4.5 - - 4.0 - - 3.5 - 3.0 2.5I 1 I I I I I I 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 ~og(~~,ro,l,) Fig. 6 Linear free-energy relationship (log k, vs. log Kk,[O,],) for the reaction of p-NH,C,H,S' with a-MSt in the binary solvent mix- tures shown in Table 1 constants and absorption maxima in the solvent mixtures with CS, tend to change gradually with time after mixing.Our data were determined immediately after mixing. Summary Preferential solvation by the polar solvent in a binary solvent mixture with a non-polar solvent was observed from its effect on the absorption maximum of p-NH,C6H,S' and its effect on the rate of the addition reaction with a-MSt. By compari- son of the reaction rate constants and absorption maxima, it is seen that preferential solvation of the reactant by polar solvent has a marked effect on the reactivity. From the linear free-energy relationship between the rate parameters evalu- ated from the reversible reaction, the preferential solvation of J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 the transition state was also evaluated to be one-quarter of that of the reactant p-NH,C,H,S'.The authors would like to express thanks to Prof. M. Matsuda and M. Iino and Ass. Prof. A. Watanabe of Tohoku University for useful discussions. References 1 Y. Marcus, Ion Solvation, Wiley, Chichester, 1985, ch. 7, pp. 185-217. 2 C. 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