J . Phys. Chem. 1987, 91, 2123-2128
2123
Effect of Solvent Structure on Electron Reactivity: fert-Butyl AlcohoVWater Mixtures P. C. Senanayake and G. R. Freeman* Department of Chemistry, University of Alberta, Edmonton, Canada T6G 2G2 (Received: June 17, 1986; In Final Form: December 8, 1986) The reactivity of solvated electrons (e;) with scavenger (S) in tert-butyl alcohol/water mixtures is greatly affected by the solvent structure. The variation of the rate constant k2 with solvent composition displays four zones. The two water-rich zones are characterized by a large change in solvent viscosity q and a small change in optical absorption energy E , of the es-; here k2 for all scavengers correlates inversely with 0. In the two alcohol-rich zones the change of 0 is small and that of E, is large; here k2 for efficient scavengers changes slightly in a complex manner with solvent composition, while for the inefficient scavengers k2 correlates inversely with E,. Similar zone behavior occurs in the Arrhenius activation energy E2 and entropy of activation AS2*,as well as in E, for the solvent viscosity; E2 is related to solvent rearrangement about the reaction site.
Introduction The optical absorption energy and reactivity of solvated electrons (e;) are strongly dependent on solvent properties. Alcohol/water mixtures display widely varying physical properties'V2 and can be used to obtain information about e;.3-5 Alcohols have both a hydrogen-bonding -OH group and a hydrophobic alkyl group. The latter affects the water structure. Of the alcohols that are completely miscible with water, the one with the largest alkyl group, tert-butyl alcohol (t-BuOH), causes the greatest changes in physical proper tie^.',"^ This indicates large changes in solvent structure. The present work extends the studies of prima# and secondary alcohol/water5 to tertiary alcohol/water solvents. Rate constants of e; with solutes of varying reactivity are reported as a function of mixture composition and temperature. Experimental Section Materials. t-BuOH, obtained from Aldrich Chemical Co. (99+%) and British Drug House (99+%), was dried for 3 weeks on Davidson 3A molecular sieves and then treated for 1 day under ultrahigh-purity argon (Liquid Carbonic Canada Ltd.) with sodium borohydride (-1 g/L) a t 323 K. The alcohol was then fractionally distilled under argon through an 80- X 2.3-cm column packed with glass helices. The first 20% and last 35% were discarded, and the middle portion was collected and kept in an argon-pressurized siphon system. The water content measured by Karl Fisher titration was 0.03 mol %. The e; half-life after a 100-nspulse of 1.9-MeV electrons (-2 X 10l6 eV/g) at 298 K was 15 ps. The water was purified in a Barnstead Nanopure I1 ion-exchange system. The e; half-life after a 100-ns pulse of radiation was 20 ps. Techniques. Sample preparation and spectrophotometry to measure the concentration are as described in ref 4. Methods of irradiation, dosimetry, and optical measurements were similar to those described in ref 17. Viscosity Measurements. The kinematic viscosities and densities of the pure and mixed solvents were measured as functions of temperature (303-353 K). The methods and data will be published elsewhere. The Arrhenius temperature coefficients of the dypamic viscosities so obtained are displayed in Figure 1 1. (1) (a) Hydrogen Bonded Solvent Systems; Covington, A. K., Jones, P.,
Eds.; Taylor and Francis: London, 1968. (b) Franks, F.; Ives, D. J. G. Q. 1. (2) Leu, A. D.; Jha, K. N.; Freeman, G. R. Can. J. Chem. 1982,60,2342. ( 3 ) Leu, A. D. Ph.D. Thesis, University of Alberta, Canada, 1980. (4) Maham, Y.; Freeman, G. R. J . Phys. Chem. 1985,89, 4347. ( 5 ) Cygler, J.; Freeman, G. R. Can. J . Chem. 1984, 62, 1265. (6) Internattonal Critical Tables; Washburn, E. W., Ed.; McGraw-Hill: New York, 1928; Vol. 3, p 388. (7) Franks, F. In Physicc-chemical Processes in Mixed Aqueous Solvents; Franks, F., Ed.; American Elsevier: New York, 1967; p 50. (8) Franks, F.; Smith, H. T. Trans. Faraday SOC.1968, 64, 2962. (9) (a) Hafez, A. M.; Sadek, H. Acta Chim. Acad. Sci. Hung. 1976,89, 257. (b) Timmermans, J. Physico-chemical Constants of Binary Mixtures; Interscience: New York, 1960; Vol 4.
Rev. Chem. SOC.1966.20,
0022-3654/87/2091-2123$01.50/0
Results The first-order decay rate constant kOMof e; in a given solvent was measured for several different concentrations of a solute (scavenger) S at a given temperature. Four scavengers of greatly different reactivity were used: nitrobenzene, acetone, phenol, and toluene. The e; reacts as follows: e,-
+ ROH e,- + S
-
RO;
+H
(1)
product (2) The value of the second-order rate constant k2 of reaction 2 was obtained from the slope of a plot of kobd against concentration of the scavenger. The values of k2 for each solvent were measured over a temperature range of 100 K. The following mole fractions of water ip t-BuOH were used for nitrobenzene: O,O.lO, 0.30,0.40,0.56, 0.64, 0.90, 0.92,0.94, 0.97, 0.98, 1.00. For the other scavengers the mole fractions of water were 0, 0.10, 0.64, 0.92, 0.97, and 1.00. Arrhenius plots for nitrobenzene, acetone, phenol, and toluene are given in Figures 1-4. Values of kz at 298 K were usually obtained by interpolation. In pure t-BuOH they were obtained by extrapolation of the values at -320 to 299 K. The Arrhenius plots of k2 for phenol in pure water and 0.97 mole fraction water display a curvature that increases at higher temperatures (Figure 3). This also exists to a lesser extent in 0.92 mole fraction water. By contrast, toluene in pure t-BuOH contained a maximum at 318 K in the Arrhenius plot (Figure 4). This result was verified by repeating the experiment. Arrhenius parameters from
-
k2 (m3/(mol-s)) = A2e-E2/RT
(3)
and AS2* (J/(mol.K)) = 19(log A , - 9.8), at 298 K
(4)
are listed in Table I. Earlier values obtained in pure water and pure t-BuOH solvents at 298 K are included for comparison. Parameters for the curved plots were obtained from a tangent drawn at 298 K. The average values obtained for the curves are also listed.
Discussion Rate constants for inefficient scavengers are more dependent on solvent composition than are those for efficient scavengers (Figure 5 ) . Efficient Scavengers. The rate constants for nitrobenzene are nearly diffusion controlled, with k2 2 lo7 m3/(mol-s). The Smoluchowski equationlo for diffusion-controlled reactions correlates k2 with the diffusion coefficients D of the reactants k2 = 4rNA(D, + Ds)(R, + Rs) (5) (10) Smoluchowski, M. V. Z. Phys. Chem., Stoechiom. Verwandtschaftsl. 1917, 92, 129.
0 1987 American Chemical Society
2124 The Journal of Physical Chemistry, Vol. 91, No. 8, 1987
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can diffuse more flexibly through the fluid than can a rigid sphere; the value of the effective radius for diffusion, re, is therefore smaller m2/s,Iza than a molecular radius. In pure water De= 4.9 X Pa.s6q9 at 298 DHZO= 2.3 X mz/s,Izband 7 = 8.95 X K, which correspond to re = 0.05 nm and rHtO= 0.10 nm. Thus, although e; is spread over a diffuse space that covers several water molecules, it diffuses more easily than a single water molecule and has a correspondingly small effective radius for diffusion. The values of re in alcohols, calculated from mobilitieslztf and viscosities,'zg*hare not constant. For 296 f 3 K one obtains the following values of re (nm): methanol, 0.28; ethanol, 0.28; 2(12) (a) Micic, 0. I.; Cercek, B. J. Phys. Chem. 1977,81,833. (b) Harris, K. R.; Woolf, L. A. J . Chem. SOC.,Faraday Trans. 1 1980, 76, 377. (c) Dodelet, J.-P.; Freeman, G. R. Can. J. Chem. 1972, 50, 2667. (d) Fowles, P. Trans. Faraday SOC.1971, 67, 428. (e) Rudnev, A. V.; Vannikov, A. V.; Bakh, N. A. High Energy Chem. (Engl. Trans\.) 1972,6,416. (0 Vannikov, A. V.; Mal'tzev, E. I.; Zolotarevsky, V. I.; Rudnev, A. V. Int. J. Radiat. Phys. Chem. 1972.4, 135. (g) Gallant, R. W. Physical Properties of Hydrocarbow; Gulf Publishing Co.: Houston, TX, 1968; Vol. 1 (includes alcohols). (h) DAprano, A,; Donato, D. I.; Agrigento, V. J. Solution Chem. 1981, IO. 673.
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2126
Senanayake and Freeman
The Journal of Physical Chemistry, Vol. 91, No. 8, 1987
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E, (W Figure 9. Effect of optical absorption energy E , on encounter efficiency k , / k N for inefficient scavengers in t-BuOH/H,O (open points) and 1PrOH/H20 (closed points, ref 4) at 298 K. Solute: 0, phenol; V, 7 , toluene.
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Inefficient scavengers. Rate constants for inefficient scavengers when plotted against 7 (Fighre 8) display behavior similar to that for efficient scavengers in zones c and d only (Figure 6). In these water-rich zones, characterized by the large change of 7 (Figure 7), kz is inversely correlated to 7. The alcohol-rich zones a and b display behavior quite different from that of the efficient scavengers. For the efficient scavengers kz decreased slightly in zone a and increased slightly in zone b, whereas for inefficient scavengers there is a sharp decrease that extends throughout zones a and b. Viscosity in these two zones changes only slightly. Therefore, another effect must be involved. Low rate constants for inefficient scavengers are due to the low probability of reaction of an (e; + S ) encounter pair. When the electron affinity of the scavenger is low, a larger solvation energy of the electron decreases the probability that the electron would transfer from the solvent trap to the s ~ l u t e . ' ~ - Therefore, '~ for the inefficient scavengers, the solvation energy of the electron (the electron trap depth) is more important. The electron trap depth in the solvent is related to the optical absorption energyeZ0The absorption band is very broad, and there is not universal agreement about the Whatever the cause, the electrons that have the lowest excitation energies have the greatest reactivity with inefficient ~ c a v e n g e r s . ' ~ For ~ - l ~kinetic purposes E, has been chosen as an indicator of trap depthl7sZ5
= )
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IL '7 (mPa.s) Figure 8. Plot of k , against 7 for inefficient scavengers in 1-BuOHlwater mixtures at 298 K. Solute: 0 , phenol; V, toluene.
are approximately the same. The boundary of the zone is approximately 0.97 mole fraction water for both types of alcohol/water mixtures. This composition for t-BuOHlwater is characterized by the maximum structure enhancement of liquid water, by the hydrophobic t-Bu group occupying its cavities.l3-l6 (13) Nakanishi, K.; Ikari, K.; Okazaki, S.; Touhara, H. J . Chem. Phys. 1984, 80, 1956. (14) Huidt, .4.; Moss, R.; Neilsen, G. Acta Chem. Scand., Ser. B 1978, 32, 274.
EA,,,
- wr
(8)
where EA,, is the energy a t maximum absorption and W, is the width of the band on the low-energy side at half-height. Zones a and b correspond to a large change in E , (Figure 7). (1 5) Roux, G.; Roberts, D.; Peron, G.; Desnoyers, J. E. J . Solution Chem. 1980, 9, 629. (16) (a) Tanaka, H.; Nakanishi, K.; Touhara, H. J . Chem. Phys. 1984, 81, 4065. (b) Nakanishi, K.; Ikari, K.; Okazaki, S.; Touhara, H. J. Chem. Phys. 1984, 81, 890. (17) Jou, F. Y . ;Freeman, G. R.(a) Can. J . Chem. 1976,54, 693; (b) J . Phys. Chem. 1977,81,909; (c) J. Phys. Chem. 1979,83, 1979. (d) Okazaki, K.; Freeman, G. R. Can. J . Chem. 1978,56, 2313. (18) Bolton, G. L.; Freeman, G. R.J. Am. Chem. SOC.1976, 98, 6825. (19) Afannasiev, A. M.; Okazaki, K.; Freeman, G. R. J . Phys. Chem. 1979, 83, 1244. (20) Jortner, J.; Noyes, R. M. J . Phys. Chem. 1966, 70, 770. (21) Webster, B. C.; Carmichael, I. C. J . Chem. Phys. 1978, 68, 4086. (22) Brodsky, A. M.; Tsarevsky, A. V. J . Phys. Chem. 1984, 88, 3790. (23) Stupak, C. M.; Tuttle, T. R.; Golden, S . J . Phys. Chem. 1984, 88, 3804. (24) (a) Jou, F.-Y.; Freeman, G. R.J . Phys. Chem. 1984,88, 3900. (b) Baird, J. K.; Morales, C. H. J . Phys. Chem. 1985,89, 774. (c) Baird, J. K.; Lee, L. K.; Meehan, E. J. J . Chem. Phys. 1985,83, 3710. (25) Leu, A. D.; Jha, K. N.; Freeman, G. R.Can. J. Chem. 1983,61, 1115.
The Journal of Physical Chemistry, Vol. 91, No. 8. 1987 2121
Effect of Solvent Structure on Electron Reactivity
1
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Figure 10. Viscosity normalized rate constant vkz at 298 K as a function of t-BuOHlwater composition. Solute: 0, nitrobenzene;0,acetone; 0 , phenol; V, toluene.
As E, increases, k2 decreases. The effect is magnified for inefficient scavengers since trap depth is more important for those. In zones c and d the change of E, is very small, but the change in q is large and k2 correlates with q. The rate of reaction for inefficient scavengers is controlled by both the diffusion rate and other factors such as the e; trap depth. Dividing k2 by the nearly diffusion controlled rate constant kN of nitrobenzene displays the effect due to other factors. The ratio k 2 / k Nis approximately equal to the encounter efficiency of the reaction, taking that with nitrobenzene to be approximately unity. (It is probably -0.3; see previous section.) The encounter efficiency k2/kNis plotted against E, in Figure 9. There is an inverse correlation between log ( k 2 / k N and ) E,, for both phenol and toluene. Rate constants for inefficient scavengers decrease due to the increase of electron trap depths. Values for 1-propanol/water mixtures also agree with the correlation, except in zone a. In the primary alcohol/water mixtures a mole fraction of 0.10 of water corresponds to a water-nucleated hydrogen-bonded structure.25 This makes the protons of the -OH'S less available to the electron. Therefore E, decreases. These protons are also needed to protonate the S-: S-
e,- + S S+ R O H SH + RO;
-.
(9) (10)
The hydrogen-bonded structure makes the protons of the -OH'S less accessible to the S-, thus slowing reaction 10. Therefore, in zone a the encounter efficiency of inefficient scavengers for primary alcohol/water mixtures decreases even though the trap depth decreases. Deviation from Stokes-Smoluchowski behavior is displayed for all four scavengers in Figure 10 by plotting qk2 against the mole fraction of water. For all four scavengers qk, decreases in zone a. It is more intense for inefficient scavengers due to trap depth dependence. This decrease continues up t o x,,- for inefficient scavengers, while that for efficient scavengers increases slightly. The value of qk2 in zone c does not change significantly except in the case of acetone, in which experimental scatter is greater because of concentration measurement problems. Zone d displays a decrease in qk, for all scavengers because in this zone k2 has a smaller viscosity dependence than that in zone c. Changes for All Alcohols. The alkyl group attached to the -OH in tertiary alcohol is the bulkiest of all three types of alcohols.
Figure 11. Activation energy for reaction 2, E2,and activation energy for viscosity, E, (X), of the t-BuOHlwater mixtures against water composition. Solute: 0,nitrobenzene; 0,acetone; 0 , phenol; V, toluene.
It is more difficult to orient the molecule around the electron site because a greater disruption of liquid structure is needed. Therefore, tertiary alcohols produce the lowest solvation energies of the three types of alcohols. As the mole fraction of water in alcohol increases, the solvation energies in the mixed solvents become more equal. Thus, the range of solvation energies in tertiary alcohol/water mixtures is greatest, and the change of k2 in the alcohol-rich zones a and b is largest for t-BuOHlwater mixtures. On the water-rich side, the change of k2 values is largest for t-BuOH because the viscosity change is largest. In addition, k2 values are slightly higher in t-BuOH, probably due to a larger reaction radius. Energies and Entropies of Activation. Activation energies E2 of the reaction between e; and scavengers decrease sharply in zone a, stay constant in zone b, and then decrease gradually in zones c and d (Figure 11). The activation energy for viscous flow E,, displays the same zone behavior (Figure 11). The present values are consistent with earlier, more limited data.26-27 There is a correlation between E2 and E,,. It would be of interest to compare the E2 values with that for dielectric relaxation E,, because dipole rotation must occur simultaneously with charge migration. Measurements of the dielectric relaxation time T at different temperatures for alcohol/water mixtures are needed. Activation energies for the e; reaction with different scavengers (Figure 11) display a slight shift against each other in zones b, c, and d. They are in the order toluene > nitrobenzene > phenol > acetone. The solubility of scavengers in water is in the order acetone > phenol > nitrobenzene > toluene. Less soluble scavengers have higher activation energies. This indicates a tendency for the electron to be preferentially solvated by water and the organic solute to be preferentially solvated by the alcohol, creating a small energy barrier for the close approach of the reactants. The entropy of activation AS2* also displays zone behavior similar to E2 and E,, (Figure 12). Entropies of activation are more negative for less efficient scavengers. The ASz*values for reaction between e; and inefficient scavengers are about 45 J/(mol.K) more negative than that for nitrobenzene. The E2 for the reactions of inefficient scavengers are within f 2 kJ/mol of that for nitrobenzene. Therefore, differences of reactivity between efficient (26) Nosova, T.A.; Zelvenskii, M. Ya.; Aleksandryuk, P. V. Depasited Document (VINITI), 1982, 3031-3082. (27) Afanassiev, A. M.;Okazaki, K.; Freeman, G . R. Can. J. Chem. 1979, 57, 839.
2128 The Journal of Physical Chemistry, Vol. 91, No. 8, 1987
Senanayake and Freeman Reaction 12 is probably first-order; one of the ROH's in the solvent shell of CH3C6HS,;protonates the anion. The net rate of decay of the solvated electron is
4
The reversal of direction of change in the rate constant with increasing temperature can be explained as follows. At lower temperatures k12>> kIland koM = kll. At higher temperatures k I 2
