J. Phys. Chem. 1987, 91, 1561-1564 the mechanism of this new oscillator. This can be effectively done by using computer simulation techniques if the computing power is available. We have mentioned that the oxidation of thiocyanate by bromate to give bromide (Rl), the conversion of the bromide to give bromine (R2), and the oxidation of thiocyanate by bromine to give bromide (R5) are the major reactions involved in the mechanism. There is no experimental evidence that the reactions are going all the way according to the stoichiometries of reactions R1, R2, and R5. The oscillations may involve different processes than the total behavior of reactions R1, R2, and R5. Intermediates may hold the key to the oscillatory behavior. For example, sulfur goes from the 0 oxidation state (SCN-) to +6 (SO:-). This cannot occur in a single step. The stoichiometry of (R5) has been determined on a bulk system where the reaction was allowed to proceed for hours before the stoichiometric determinations were performed. It is conceivable that lower oxiation states of sulfur (e.g., +2 and +4) could be involved in the mechanism. The other well-known bromine species which are involved in the B-Z system (HBr02, HOBr, BrO,) could prove to be very important in the mechanism. The global behavior of the bromine-thiocyanate oscillator is also very fascinating. The bifurcation sequence obtained has not been observed in any other chemical oscillator. The quasi-periodicity and rampant intermittency observed suggest that the system may be subscribing to a dynamics of higher dimensionality than the one-dimensional dynamics observed in the B-Z.16 There are very few chemical oscillators which show different oscillatory states, and those that do should have their dynamics characterized to probe for any universality in their bifurcations.28 We not only
1561
need more detailed mechanistic studies on this oscillator, but more controlled experimental studies on the bifurcation sequenk as has been done on the B-Z system.I6 Particularly disturbing are recent studies which confirm that, second only to flow rate, stirring has the most profound effect on the behavior of a chemical o s ~ i l l a t o r . ~ ~ Any further dynamical studies should involve higher rpm stirring rates in a reactor with baffles. These studies should be able to confirm whether plots b and c of Figure 5 really show intermittency and quasi-periodic behavior, respectively. In this oscillator, standard techniques like phase diagrams30 and calculation of lyapunov characteristic exponents2' should be used on the chaotic regions of the bifurcation sequence to better understand the dynamics of this fascinating oscillator.
Acknowledgment. I gratefully acknowledge Prof. R. M. Noyes of Oregon University and Prof. I. R. Epstein of Brandeis University for many helpful hints and Dr. Ian Love for help in analyzing the time series plots. I also thank Regina Dururu, who performed some of the batch experiments. This work was supported by Research Grant No. RB 49/83:2543 and 2.901.1:2789 from the University of Zimbabwe Research Board. Registry No. BrOC, 15541-45-4; SCN-, 302-04-5. (28) A number of unrelated physical systems like the nonlinear electrical circuits, the Rayleigh-Benard convection, the Couette-Taylor hydrodynamical system, and the Belousov-Zhabotinskii system as well appear to subscribe to the same dynamics. For a summary, see: Swinney, H. L. Physica D (Amsterdam) 1983, 7 0 , 3-15. (29) Kumpinsky, E.; Epstein, I. R. J . Chem. Phys. 1984, 82, 53-57. (30) Roux, J. C.; Turner, J. S.;McCormick, W. D.; Swinney, H. L. In Nonlinear Problems: Present and Future; Bishop, A. R., Campbell, D. K., Nicolaenko, B., Eds.; North-Holland: Amsterdam, 1982; p 409.
Effect of Solvent Structure on Electron Reactivity: I-ButanoVWater Mixtures Yadollah Maham and Gordon R. Freeman* Department of Chemistry, University of Alberta, Edmonton, Canada T6G 2G2 (Received: March 26, 1986: In Final Form: October 22, 1986)
The solvent dependence of e; reaction rate constants k2 and their Arrhenius parameters differ for efficient (nitrobenzene, acetone) and inefficient (phenol, toluene) scavengers. The n-butyl group is so large that 1-butanol is not completely miscible with water. The complex changes of physical properties of 1-propanol/water mixtures produced four different zones of e; behavior on going from 0 to 1.00 mole fraction water. Zone c, 0.75-0.97 mole fraction water, which displays StokesSmoluchowski behavior of k2, is inaccessible in 1-butanol/water solvents because it is in the immiscible region. In zone a the viscosity normalized rate constant qk, for inefficient scavengers decreases in spite of the decrease of the electron optical absorption energy E,. Hydrogen-bonded structures, for example H,O(ROH),, apparently make the positive hydrogens on the OH groups less accessible to solvate the electrons and less accessible to protonate S-.
Introduction Rate constants of solvated electron reactions with an efficient scavenger in 1-propanol/water mixed solvents were classified into four zones by their viscosity dependence.' (a) Mole fraction x~~~ < 0.15: Isolated water molecules apparently hydrogen bond with surrounding alcohol molecules and increase the orderliness of the local structure of the liquids2 The rate constant k2 decreases with increasing water concentration,' as the liquid viscosity3 and dielectric relaxation timeM increase; the optical absorption energy (1) Maham, Y.; Freeman, G.R. J . Phys. Chem. 1985, 89, 4347. (2) Leu, A. D.; Jha, K. N.; Freeman, G.R. Can. J . Chem. 1982,60,2342. (3) Timmermans, J. Physicochemical Constants of Binary Mixtures; Interscience: New York, 1960; Vol. 4. (4) Jhon, M. S.;Eyring, H. J . Am. Chem, SOC.1968, 90, 3071. (5) Hassion, F. X.;Cole, R. H. J . Chem. Phys. 1955, 23, 1756. (6) Hasted, J. B. In Water, a Comprehensive Treatise; Franks, F., Ed.; Plenum: New York, 1973; Vol. 2, p 405. (7) Bertolini, D.; Cassettari, M.; Salvetti, G.J . Chem. Phys. 1983, 78, 365.
0022-3654/87/2091-1561$01.50/0
EA,maxof the solvated electrons decreases., (b) 0.15 < x~~~ < 0.75: k2 increases in spite of the increasing viscosity, contrary to the Stokes-Smoluchowski relation.1° (c) 0.75 < xH,05 0.98: k2 a q-I.O as expected from the Stokes-Smoluchowski relation; EA,maxi= constant.2 (d) x~~~> 0.97: The dynamic parameters of the liquid change appreciably (dielectric r e l a ~ a t i o n , nuclear ~-~ relaxation,' diffusionI2), but k2 changes less than expected from the Stokes-Smoluchowski relation;' EA,max changes.,
'
(8) Gestblom, B.; Sjoblum, J. Acta Chem. Scand., Ser. A 1984, A38, 575. (9) Ped, J. P.; Wasan, D. T.; Winsor, P.; Cole, R. H. J . Mol. Liq. 1984, 28, 103. (10) Noggle, J. H. Physical Chemistry; Little and Brown: Toronto, 1985; pp 448, 551. (1 1) (a) Goldammer, E. V.; Zeidler, M. D. Ber. Bunsenges. Phys. Chem. 1969, 73, 4. (b) Goldammer, E. V.; Hertz, H. G.J . Phys. Chem. 1970, 74, 3734. (12) Franks, F.; Ravenhill, Egelstaff, P. A,; Page, D. I. Proc. R . SOC. London, A 1970, 319, 189.
0 1987 American Chemical Society
Maham and Freeman
1562 The Journal of Physical Chemistry, Vol. 91, No. 6. 1987 TABLE I: e: Reaction Rate Parameters in 1-BuOH/Water
nitrobenzene" 9"
XH20
kzb
2.60 2.63 2.66 2.77 2.98 1.09 0.89
0 0.05 0.10 0.30 0.50 0.99 1 .oo
860 880 920 1050 1150 3500 3800
E2C 18 18 18 18 18 18 17
acetoneg
log Azd
Ass2*
k,b
E2c
10.05 10.31 10.06 10.10 10.29 10.63 10.61
+5 +6 +5 +6 +9 +16 +16
270 270 260 330 380 770 770
18 16 15 17 16 14 13
phenolh kZb 9.8 5.2 3.3 1.5 0.84 2.6 2.7
xH20
0 0.05 0.10 0.30 0.50 0.99 1 .oo
23 23 21 18 23 20 19
A s 2 *e -5
-10 -1 5 -6 -8 -10 -1 4
toluene' As2'
log A2d 8.97 8.66 8.22 7.26 7.97 8.00 7.83
E2=
log A2d 9.53 9.27 9.00 9.46 9.40 9.29 9.08
-16 -22 -30 -48 -35 -34 -37
e
k2b
E2c
1.1 1.o 0.92 0.54 0.34 1.2 1.3
34 28 26 19 17 14 19
log 10.06 8.88 8.47 7.13 6.57 6.57 7.43
A s 2 *e +5 -17 -25 -5 1 -6 1 -6 1 -45
IO4 m3/(mol.s) at 298 K. CInkJ/mol. d A 2in m3/(mol.s). eIn J/(mol.K). fConcentrations "Viscosity at 298 K, mPa-s (cP). Present results. 1-11 (lo-* mol/m3). f0.03-0.27 mol/m3. 1-11 mol/m3. '2-10 mol/m3.
1
10
5
t
--'
\ \
1
0.5
0.1
0.05 L
0.2
2.6
\
'
I
'
' 30
I
I
I
'
' 3.5
I
'
01
A
005 27
I
4.0
1000/T (K) Figure 1. Arrhenius plots of k,(nitrobenzene) in I-BuOH/water mixed solvents. xH20: 0, 0; 0, 0.10; 0,0.30; v 0.50; I,' 0.99; 0 , 1.00 (+,data of C. Senanayake).
Increasing the size of the alkyl group on the alcohol increases its influence on the water structure. The present article reports electron reaction rates in 1-butanol/water mixed solvents as a function of temperature.
Experimental Section Materials. 1-Butanol (1-BuOH) was obtained from Aldrich Chemical Co. (99+%, spectrophotometric grade, Gold Label). Nitrobenzene (99+%) and phenol (99+%) were also from Aldrich. Acetone (99.9%) and toluene (99.8+%) were from Burdick and Jackson Labs. 1-BuOH was stored over freshly activated (200 "C) Molecular Sieves 3A for 1 week and then fractionally distilled under ultrahigh-purity argon (Liquid Carbonic Co.) from sodium borohydride (2 g/L). The middle 50%fraction was collected and stored in an argon-pressurized siphon flask. The UV spectrum of the purified alcohol was structureless down to 220 nm. The water content was 5 X lo-" mole fraction (Karl Fischer titration). The half-life of e; after a 100-ns pulse of 1.9-MeV electrons (-2 X l o i 6 eV/g) at 298 K was 10-12 ps.
30
35
40
05
1000/T (K) Figure 2. Arrhenius plots of k2(acetone)in I-BuOH/water mixed solvents. x ~ o,~0; 0~, 0.10; : 0 , 0.30; V, 0.50; 'I,0.99; . , 1.00 (+, data of C. Senanayake).
The water was passed through a Nanopure I1 Barnstead ion exchanger. The half-life of e; after a 100-ns pulse at 298 K was -25 ps. In the mixed pure solvents the half-lives were as follows (mole fraction H 2 0 , ps): 0.05, 12 f 1; 0.10, 17 f 1; 0.30, 23 f 1; 0.50, 33 f 2; 0.99, 25 f 3. Techniques. The method of sample preparation' and irradiawere essentially the same as in the indicated references.
Results and Discussion Four scavengers, with rate constants ranging from lo7 to lo4 m3/(mol.s), were studied as a function of temperature in 1BuOH/water mixtures. First-order decay constants k l were measured at four or five different scavenger concentrations in a given solvent. Second-order rate constants k2 were obtained from the slopes of plots of k , against concentration.' Arrhenius plots of k2 for nitrobenzene, acetone, phenol, and toluene are given in Figures 1-4, respectively. (13) Okazaki, K.; Freeman, G. R. Can. J . Chem. 1978,56, 2313. 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. (14) Jou,
The Journal of Physical Chemistry, Vol. 91 No. 6, 1987 1563
Solvent Structure Effects: Solvated Electrons
~
TABLE 11: e: Reaction Rate Parameters in 1-PrOH/Water nitrobenzene ~~
xH20
va
E,b
0 0.97 0.98 0.99 1.00
1.96 1.33 1.19 1.05 0.89
1.43 1.40 1.38 1.37
k2c 120 290 320 340 380
qk2d 390 380 360 340
E2' 16 19 17 18 17
log A / 9.87 10.72 10.69 10.77 10.61
phenol kzC
qkZd
E2'
log A ]
AS2*g
0.23
0.31
18
7.53
-43
0.26 0.27
0.27 0.24
20 19
7.95 7.83
-35 -37
AS2'9
+I +18 +I7 +I8 +I6
lo5 m3/(mol.s) at 298
"Viscosity at 298 K, mPa-s (cP), ref 3. boptical absorption energy of e[ halfway up low-energy side of band, eV, ref 2.
K. " I O 2 Pam3/mol. 'kJ/mol. / A 2 in m3/(mol.s). g I n J/(mol.K).
2.6
3.0
3.5
1000/T (K) Figure 3. Arrhenius plots of k2(phenol) in I-BuOH/water mixed solvents. X H ~ O : 0, o; A, 0.05; o, 0.10; 0, 0.30; V, 0.50; V, 0.99; 0 , 1.00 (+, data of C. Senanayake).
The Arrhenius parameters A , (m3/(mol-s)) and E , (kJ/mol) are listed in Table I, along with the entropy of activation AS* (J/ (mol-K)) .
k2 = A2 exp(-E2/RT)
(1)
AS' = 19(log A2 - 9.8) (at 298 K)
(2)
0.2 I
1
,
I
2.6
l
I
1
I
3.0
I
I
I
l
3.5
1000/T (K) Figure 4. Arrhenius plots of k2(toluene) in I-BuOH/water mixed solvents. XH~O: 0, 0; 0, 0.10; 0,0.30;V, 0.50; V, 0.99; 0 , 1.00 (+, data of C. Senanayake). I
500
1
ZONE
1
(a) (
I
(b) I
~
I
~
j
(c) I
k(d) I
I
I
1-Butanol and water are not miscible in the range 52-98.5 mol % water. The variation of k, in the miscible ranges was similar to that in the 1-propanol/water mixed solvents (Figure 5). As a result of the comparison, several points in the 1-propanol/water system were doubly remeasured, and the slightly modified results are recorded in Table 11. The Stokes-Smoluchowski equation for the rate constant of the diffusion-controlled reaction is15 (3)
E In
5
v
N
where kBis Boltzmann's constant, NA is Avogadro's constant, 9 is the solvent viscosity, re and rs are the effective radii of the solvated electron and scavenger for diffusion, and R, and Rs are the reaction radii. The reaction radii are probably not equal to the diffusion radii. For example, the highly polarizable charge distribution of e; might cause it to have a relatively small value of reI5and a larger Re. The value of Re is probably related to the size of the charge distribution of e;, which is linked to the binding energy of the electron in its solvent potential well and the optical absorption energy of e;.16 The optical absorption energies EA,max of solvated electrons in primary alcohols and water at 298 K are all in the range 1.85 f 0.13 eV;17 the mean radii of the
Figure 5. Dependence of k2 at 298 K on I-BuOH/water solvent composition. Solute: A, nitrobenzene; 0, acetone; 0, phenol; 0, toluene. (- - 0 - -) I-PrOH/water solvent.'
(15) See: Senanayake, P. C.; Freeman, G. R.J . Phys. Chem., in press. Carmichael, I. J . Phys. Chem. 1980.84, 1076 and references therein. (17) Leu,A.-D.; Jha,K.N.;Freeman,G.R. C m J . Chem. 1983,61,1115.
charge distributions are similar, rrm = 0.23 0.02 nm calculated by the same modeli6 The values of EA,maxfor the I-BuOH/water mixtures were also in this relatively narrow range,2 so the size
(16)
Y YN\[5
1
0.5
-. --- .
I
0
02
04
06
08
I
10
'H20
1564 The Journal of Physical Chemistry, Vol. 91, No. 6, 1987
Maham and Freeman
ZONE I
I
---.--
70
5
0
"
"
02
1
'
04
1
1
06
'
08
t
IO
'H20
lo4
Figure 6. Viscosity-normalized rate constant ~ kat, 298 K, as a function of I-BuOH/water composition. Solute: A, nitrobenzene; 0 ,acetone; 0,phenol; 0,toluene. Pa.m3/mol = 10 P.m3/(mol.s). ( - - e - - ) 1PrOH/water solvent.'
of e; can be assumed to be relatively constant as a function of composition. Equation 3 therefore reduces to
qk, = constant
(4)
A plot of qk, against solvent composition shows deviation from eq 4, especially for the inefficient scavengers (Figure 6). The region of zone c in 1-propanol/water' is not accessible in l-butanol/water due to immiscibility. The reactivity of inefficient scavengers such as phenol and toluene tends to decrease with increasing solvation energy (trap depth) of the electron^.^*-^^ An appropriate indicator of trap depth for this purpose is the optical absorption energy E,? halfway up the low-energy side of the band.I8-l9 To remove the effect of diffusion as much as possible, the ratio of ks for an inefficient scavenger to kN for nitrobenzene is plotted against E, in Figure 7 . The ratio ks/kN is approximately the encounter efficiency of the reaction of e; with S, taking that with nitrobenzene to be near unity. Zones a-d are all visible. In zone a the encounter efficiency decreases in spite of the decrease in E, (Figure 7 ) . The inverse correlation between encounter efficiency and E, exists only in zones b and c for phenol and toluene. The addition of xHIO= 0.10 to an alcohol apparently produces hydrogen-bonded structures that make the hydrogens of the -OH'S (18) Afanassiev, A. M.; Okazaki, K.; Freeman, G. R. Can. J . Chem. 1979, 57, 839. (19) Afanassiev, A. M.; Okazaki, K.; Freeman, G. R. J . Phys. Chem. 1979, 83, 1244.
L 125
130
135
140
145
E, (W
.;
+
Figure 7. Variation of (S e;) reaction encounter efficiency, k s / k N , with e[ optical absorption energy E,. N = nitrobenzene, T = 298 K. S: phenol A, A; toluene 0,H. Solvent: 1-butanol/water A, 0; 1propanol/water A, water 0, V. E, values from ref 2. The numbers labeling the points indicate mol % water.
somewhat less accessible to the electron.* This causes E, to decrease. Hydrogens of the -OH'S are also needed to stabilize electron capture by phenol and toluene, by protonation of the anions: S-
e,- + S S+ R O H SH + ROC
(5)
(6) The hydrogen-bonded structure makes the hydrogens of the -OH'S less accessible to S-, thereby slowing reaction 6. This reaction is not required to stabilize electron capture by nitrobenzene, so ks/kN decreases in zone a. Addition of 1-3 mol 7% alcohol to water decreases the fluidity of the liquid*O but has relatively small effect on k s / k N (zone d, Figure 7). The diffusion rate which affects kN and the rotational relaxation rate which affects k6 and therefore ks are changed by similar amounts. --+
Acknowledgment. We thank the Natural Sciences and Engineering Research Council of Canada for financial assistance and the staff of the Radiation Research Center for technical assistance. Registry No. Nitrobenzene, 98-95-3; acetone, 67-64- 1; phenol, 10895-2; toluene, 108-88-3. (20) Hafez, A. M.; Sadek, H. Acta Chim. Hung. 1976, 89, 257.
