J . Phys. Chem. 1990, 94, 8800-8805
8800
is to examine the effect on the rate coefficient k(t) of the treatment of the radiation boundary condition (eq 2.25a) by putting a sink term and turning off the force in the region a < ro < a + c and making the boundary ro = a reflecting. For convenience, we write S(m(ro) [S,(+o)l as S(ro) [Sp(ro)l. The steady-state form of eqs 2.23-2.25 is
S,(m) = 1
(A6b)
When eqs A5 are solved subject to the boundary conditions A6 and the condition that S,(ro) and aS,(ro)/aroare continuous at ro = a + C, we find S,(ro) = ( a l r o ) - l { ( D s ) - ' / 2cosh a [(DT)-l/z(ro - a)] + sinh [ ( D s ) - 1 / 2 ( r-o a ) ] ) , a Iro Ia e (A7a)
+
= I S(m)
= 1
a2 + -(I
C r
(A2b)
- ~ ' c / ~ Q ) , ro > a
+c
(A7b)
When eq AI is solved subject to the boundary conditions A2, we find
which gives the steady-state rate coefficient (eqs 2.1)
If we put a sink term and turn off the force in the region a < ro < u e and make the boundary ro = a reflecting, the steady-state survival probability, now denoted as S,(ro), is given by
+
I
sinh [ ( D ~ ) - l / ~ e(A9) ] Equations 2.14 then give = 4*~a~e-'~~~(2~~+ ) - (~a{+( D r ) - ' ~ ~ c)-'(DT)-'/'a cosh [ ( D T ) - ' / ~ 4- ~( ]a e)-' sinh [ ( D r ) - I / % ] ] (AlOa)
kp(m)
+
= k ( m ) [1 - Ye
+
(~/12D I/a
(AlOb)
+ r , / 4 a ' ) e ' ~ / -~ ( ~ / l 2 D+ l / a + r , / a 2 )
-1 = -K T
+ O(€*)]
(A 1Oc)
C
Temperature Dependence of the Rate Constants for Reaction of Inorganic Radicals with Organic Reductants Z. B. Alfassi,' R. E. Huie, P. Neta,* and L. C. T. Shoute2 Chemical Kinetics Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899 (Rereiced: April 23, 1990; In Final Form: June 28, 1990)
Rate constants for the reactions of several inorganic radicals with several organic reductants in aqueous solutions have been measured by pulse radiolysis as a function of temperature, generally between 5 and 75 OC. The reactions studied were those of the radicals N3*,NO2', Br2'-, I**-, and (SCN)*'- reacting with several phenols and ascorbate. Rate constants were also measured for the reactions of Cl;- with phenol and of C102' with p-methoxyphenolate. The rate constants measured were in the range of IOs to nearly I O ' O M-I s-I and the calculated Arrhenius activation energies rangzd from 7 to 41 kJ mol-'. The preexponential factors also varied considerably, with log A ranging from 9.2 to 13.9. The temperature dependences of these reactions do not seem to relate to their exothermicities. Variations in rate constants appear to be more strongly dependent on changes in preexponential factors rather than on changes in activation energy.
Introduction Rate constants have been measured at room temperature for a large number of reactions of inorganic free radica1s.j In general, the one-electron redox reactivity of a free radical is associated ( 1 ) Visiting Professor from Ben-Gurion University of the Negev. Beer Sheva, Israel. (2) Visiting scientist from Bhabha Atomic Research Centre, Trombay, Bombay, India. (3) For compilation of rate constants on reactions of inorganic radicals see: Neta. P.: Huie. R. E.; Ross, A. B. J . Phys. Chem. Ref. Data 1988, 17, 1027.
0022-3654/90/2094-8800$02.50/0
with its reduction potential: when reacting as an oxidant, the higher the reduction potential the more reactive the radical is expected to be. Yet, there appear to be several exceptions to this general rule. For example, the rate constants for the oxidation of various organic and inorganic reductants by the N3' radical are higher than the rate constants for oxidation by Br2*-?despite the fact that the reduction potential4 of N3* is lower than that ( 4 ) For review of redox potentials involving inorganic free radicals in aqueous solution see: Stanbury. D. M. Ado. fnorg. Chem. 1989, 33, 69.
0 I990 American Chemical Societv
Rate Constants for Reaction of Inorganic Radicals of Br2'- by 0.3 V.s*6 The N3* radical also reacts more rapiflly with a variety of reductants than does (SCN)2'-, which has a similar redox potential. The reactions of various reductants with C102*also were noted7s8to occur more rapidly than those of NO2' despite the higher reduction potential of the latter radical. These observations, which are in contrast with simple linear free energy correlations, have been rationalized on the basis of higher selfexchange rates for the more reactive specie^.^,^ Self-exchange rates, however, have proven to be difficult to estimate for these small inorganic radicals and the estimates made on the basis of different reactions often were found to vary by many orders of m a g n i t ~ d e . ~Further, the theory upon which the use of selfexchange rates is based assumes that the reactions involve only outer-sphere electron transfer. This is not necessarily the case for the reactions of these small inorganic free radicals with organic reductants. Since essentially all of the rate constant measurements for small inorganic free radicals in aqueous solution have been carried out only at room temperature, we have set out to measure the rate constants for some electron-transfer reactions of these radicals at different temperatures to determine if the temperature dependence for these reactions could shed some light on the underlying causes of the observed reactivity patterns. Measurements of the temperature effects on the rate constants for reactions of small inorganic free radicals in aqueous solutions are relatively rare. Although the rate constants measured at room temperature number in the thousands, only several reactions have been reported at varying temperatures. The activation energies for reactions of eaq-, H, and O H were summarized in the recent compilation of the rate constants for these species.I0 The electron-transfer reactions typically were very fast ( k lolo M-I s-l) and the Arrhenius parameters were similar to those which would be expected for diffusion-controlled reactions. The reactions of OH with HC03- and C 0 3 2 - ,however, have rate constants well below the diffusion-controlled region, but have very similar activation energies (21.2 and 23.6 kJ mol-', respectively). The difference in reactivity between H C 0 3 - and COj2- appears to be due to the pre-exponential factors, which differ by a factor of 100 (6 X 10I2and 6 X 1Olo M-I s-l, respectively). Activation energies have been reported also for electron transfer from hydroxyalkyl radicals to nitrobenzene and to ferricyanide (8-1 6 kJ mol-')" and from nitroaromatic radical anions to other nitroaromatics of higher electron affinity ( 1 2-25 kJ mol-').I2 Rate constants have been measured also as a function of temperature for reactions of SOL with a scrics of anion^.'^ In that study, the variation in the rate constant was found to depend primarily on the preexponential factor for thc reaction and less on the activation energy. Rate constants have been reported8 for the reaction of C102' with C ~ ( t e r p y r i d y l ) over ~ ~ + the temperature range 10-30 "C, which yield an A factor of 3.9 X 1 OIo M-' s-I and an activation energy of 18.6 kJ mol-!. Finally, rate constants have been reported for several reactions of the free-radical reductant SO2'- over a range of temperature^.'^ The absolute values of these rate constants depend on the temperature dependence of the equilibrium S20d22 2S02'-. There has also been a recent report on the temperature dependence of back electron transfer in geminate radical pairs
-
(5) Alfassi, Z. B.; Harriman, A.; Huie, R. E.; Mosseri, S.;Neta, P. J. Phys. Chem. 1987, 91, 2120. (6) Ram. M. S.; Stanbury. D. M. J. Phys. Chem. 1986, 90,3691. (7) Huie, R. E.; Neta, P.J. Phys. Chem. 1986, 90,1193. Alfassi, Z. B.; Huie, R. E.; Neta, P. J. Phys. Chem. 1986, 90,4156. (8) Stanbury, D. M.; Lednicky, L. A. J. Am. Chem. Soc. 1984,106,2847. Wilmarth, W. K.; Stanbury, D. M.; Byrd. J. E.: Po, H. N.; Chua, C. P. Coord. Chem. Rer. 1983, 51. 155. (9) McDowell. M. S.; Espenson, J. H.; Bakac, A. Inorg. Chem. 1984.23, 2232. Neta. P.; Huie, R. E.; Harriman, A. J. Phys. Chem. 1987, 91, 1606. Zahir. K.; Espenson. J. H.; Bakac, A. J. Am. Chem. SOC.1988, 110, S059. Simmons, C. A.; Bakac, A.; Espenson, J . H. Inorg. Chem. 1989, 28, 581. (IO) Buxton, G. V.;Greenstock. C. L.; Helman, W. P.; Ross, A. B. J. Phys. Chem. Ref Data 1988, 17. 513. ( 1 I ) Toffel. P.: Henglein. A. Eer. Bunsen-Ges. Phys. Chem. 1976,80, 525. (12) Meot-Ner (Mautner). M.; Neta, P. J. Phys. Chem. 1986, 90,4648. (13) Huie, R. E.; Clifton, C. L. J. Phys. Chem., in press. (14) Mehrotra. R. N.; Wilkins, R. G. Inorg. Chem. 1980, 19. 2177. Scaife. C. W. J.: Wilkins. R. G.Inorg. Chem. 1980, 19, 3244.
The Journal of Physical Chemistry, Vol. 94, No. 25, 1990 8801 generated by photoinduced electron transfer.IS Temperature dependencies characteristic of both nonadiabatic and adiabatic electron transfer were observed.
Experimental Section The rate constants were determined by kinetic spectrophotometric pulse radiolysis. The inorganic radicals were produced by reaction of the corresponding anions with O H radicals in N 2 0 saturated aqueous solutions as described b e f ~ r e . ~The . ~ ionic strength was established mainly by the precursor salt (NaN3, NaBr, NaI, KSCN, N a N 0 2 , NaC102, and NaCI) and was not otherwise adjusted. The pH was adjusted by the addition of KOH or HCIOl or by the use of phosphate buffer. For radicals which exhibit intense absorptions (Br;- at 360 nm, (SCN)2'- at 480 nm, C12'- at 350 nm, 12*- at 380 nm,and C102' at 360 nm), the rate of reaction was determined by following the decay of the inorganic radical as a function of substrate concentration. For radicals having weak absorptions (N3*and NO2') the rates were determined from the buildup of product radicals (phenoxyl at 400 nm, substituted phenoxyl at 420-430 nm, ascorbate at 360 nm). The second-order rate constants were determined from plots of kobs vs concentration by employing three substrate concentrations that differed by a factor of 4. The concentrations of the substrates varied in the range of 10-5-10-' M, depending on their reactivity, and the concentration of radicals was 2-4 pM in most cases. The whole experiment was repeated at five temperatures, generally between 5 and 75 OC. The temperature was achieved by passing the solution through a thin coiled quartz tubing immersed in a thermostated fluid before entering the irradiation cell, which was also in touch with the same fluid on three sides, and the temperature was read by a thermocouple immersed in the solution at the point of its exit from the cell. The materials used and other details of the experimental procedures were as described b e f ~ r e . ~ . ~ Results Rate constants have been determined for the oxidation of ascorbate, phenol, p-methoxyphenol, hydroquinone, and their anions, by various inorganic radicals. Since all of these reactions have been investigated previ~usly,~ in this work we have studied only the temperature dependence of the rate constants. These reactions are known to proceed by an overall one-electron transfer to form the organic radical, e.g. N,'
-
+ PhOH N < + H+ + PhO' Br2'- + PhO2Br- + PhO'
-
(1)
(2) The second-order rate constants determined for the various reactions at the different temperatures are summarized in Table 1. For each reaction, the pH is specified in order to define the acid-base form of the reacting species. The ionic strength is also specified, but no correction to zero ionic strength was made. The second-order rate constants were fit to the Arrhenius expression, k = Ae-€IRT,by a weighted least-squares routine, A R R H , ~and ~ were weighted by the reciprocal of the squares of the standard errors derived from the second-order fits. The Arrhenius parameters are presented in Table 11, along with the calculated value of the rate constant at 298 K. The error limits reported with the activation energy are the standard errors from the least-squares fit. Due to the long extrapolation involved, we have chosen not to report the calculated statistical error limits for the preexponential factors. We estimate that, over the temperature range of these studies, the errors in the rate constants calculated from the Arrhenius expressions to be f20%.
Discussion The results from Table I are plotted in Arrhenius form (log k vs I / T ) in Figures 1 and 2. These figures represent various overlapping sub-sets of the data, chosen to illuminate reactivity patterns. In Figure I , the results for the reactions of each organic ( 1 5 ) Vauthey, E.; Suppan, P. Chem. Phys. 1989, 139, 381. (16) Cvetanovic, R. J.; Singleton, D. L. Inr. J. Chem. Kinef. 1977, 9, 481,
1007.
8802
The Journal of Physical Chemistry, Vol. 94, No. 25, 1990
Alfassi et al.
TABLE I: Rate Constants for Various Oxidation Reactions at Different Temperatures reaction
pH
N3* + phcnol N3* p-methoxyphenol N,' hydroquinone N,' + ascorbate Br2'- + phenol Br*- + phenolate Br,*- p-methoxyphenol Br2'- p-methoxyphenolate Br2*- hydroquinone Br2'ascorbate 1,'- + phenolate 12*' + p-methoxyphenolate
5.6 5.6 5.6 5.8 5.6 11.8 5.6 I 1.5 6.0 6.0 11.6 I 1.6
12'- + ascorbate (SCN),'phenol (SCN),'- + phenolate (SCN),'- + p-methoxyphenol (SCN),'ascorbate NO,' + phenolate NO2' p-methoxyphenolate NO2' + ascorbate CIO,' + p-methoxyphenolate Clz'- + phenol
6.0 6.0 11.6 5.8 6.0 11.3 11.6 6.7 11.7 2.5
+ +
+ + + +
+ +
+
M 0.1
p,
0.1 0.1 0.1 0.1 0.1 0.1 0.1
0.1 0.1 0.1 0. I 0.1 0.8 0.1 0.1 0.1 0.1 0.02
0.02 0.02 0.1
k. k, k, k, k, T , "C M-I s-' T, O C M-' s-I T, "C M-l S-I T, "C M-I s-I T , O C M-l s-I IO 3.0 x 107 22 3.2 x 107 37 4.6 x 107 59 6.9 y: 107 72 7.6 x 107 11 2.9 X IO9 22 4.0 X IO9 36 5.0 X IO9 58 6.6 X IO9 75 8.8 X IO9 II 3.8 x 109 22 4.3 x 109 36 5.9 x 109 59 7.3 x 109 75 8.4 x 109 7 7 3 7 I
IO IO I 1 3 8 1
IO 3
I 4 I 1 6 1 1
1.9 x 109 3.8 X IO6 3.5 X IOs 5.8 x 107 7.1~108 6.0 X IO7 8.3X1OS 9.3 x 106 3.5 X IO7 4.9 X IO7 4.6 X IO7 1.0 X IOs 3.8 X IO5 1.6 X IO8 2.3 X IO7 4.2 X IOs 3.5 x 106 9.9 X IO7 1.3 X IO7 5.8 X IOs 2.5 X IOs
22 18 16 28 18 21 21 16 12 17
2.7 x 109 37 5.3 X IO6 35 4.8 X IO8 37 7.4 x 107 1 . 1 ~ 1 0 9 38 7.7 X IO' 36 I . 0 X 1 0 9 36 1.6 x 107 37 6.7 X IO7 29 1.1 X IOs 38
16 21 16 16 16 16 16 16 16 16
1.3 5.9 3.0 4.0 5.5
X X X X X
IO8 IO5 IO8 IO7 IO8
1.0 x 107 1.5 3.2 7.7 2.7
X X X X
10' IO7 IO8 IO8
35 37 37 37 35 37 37 37 37 37
3.3 x 109 8.6 X IO6 5.8 X IO8
57 53 56 54 1 . 4 ~ 1 0 9 57 8.3 X IO7 55 1 . 3 X 1 0 9 56 3.6 x 107 57 1.4 X IO8 57 1.5 X IO8 67 1.7 X 1.2 X 3.9 X 7.4 X 7.9 X 2.9 x 3.9 X 1.2 X 1.9 X 3.4 X
10'
IO6 10'
IO7 IOs 107 10'
IO8 IO9 10'
55 53 57 58 55 57 56 56 56 57
6.1 x 109 69 1.1 X IO7 80 7.6 X IOs 76 9.2 X IO7 72 1 . 3 ~ 1 0 9 77 9.9 X IO7 68 1.6X109 69 7.0 x 107 77 1.8 X IOs 77 2.2 X IOs 95 2.1 3.8 5.9 1.1 9.2 7.7 5.6 1.3 2.7 4.3
X X X X
10' IO6 10'
IO8
X IO8 x 107 X X X X
IOs IOs IO9 IOs
75 81 75 77 75 78 76 75 75 76
7.1 x 109 1.6 X IO7 8.8 X IO8 1.1 X IOs 1.8~109 1.1 X IO8 1.8X109 9.3 x 107 1.8 X IO8 2.6 X IO8 2.7 1.1 8.4 1.4 1.2 1.2 1.4 3.3 3.8 3.8
X 10' X IO7 X 10' X IO8 X IO9
x 10s X X X X
IO9 IO8 IO9 IO8
TABLE 11: Arrhenius Parameters and Room Temperature Rate Constants for the Reactions of Small Inorganic Radicals with Organic Reductants reaction (R' + S ) N,' phenol N,' + p-methoxyphenol N,' + hydroquinone N,' + ascorbate Br2'phenol Br2*- + phenolate Br2'- + p-methoxyphenol Br2'- + p-methoxyphenolate Br2'hydroquinone Br2'- + ascorbate 1,-' + phenolate 1,'- + p-methoxyphenolate (low r ) 1,'p-methoxyphenolate (high r ) 1,'- + ascorbate (SCN),'- + phenol (SCN),'- + phenolate (SCN),'- + p-methoxyphenol (SCN),'- + ascorbate NO,' phenolate NO,' p-methoxyphenolate NO,' + ascorbate CIO,' + p-methoxyphenolate C1,'- + phenol
+
+ +
+
+ +
PH 5.6 5.6 5.6 5.8 5.6
EoR - E's, V 0.36 0.61 0.87
11.8 5.6 11.5 6.0 6.0 11.6 11.6
1 .oo 0.69 0.87 0.94 1.12 1.20 1.33 0.24 0.49
6.0 6.0 11.6 5.8 6.0 11.3 11.6 6.7 11.7 2.5
0.70 0.36 0.54 0.6 I 1 .oo 0.25 0.50 0.7 I 0.40 1.12
reactant with a series of radicals are presented. In several of these plots, it appears that the dihalide radicals, Br;- and lz'-, roughly parallel each other; i.e., the logarithms of their rate constants for reaction with the same substrate increase at roughly the same rate with temperature. In its reaction with ascorbate, it appears that the reactivity of the dithiocyanate radical also parallels that of the dihalide radicals. Also, the relative reactivities of the dihalide radicals and (SCN)2'- with several reactants at room temperature increase in line with their relative reduction potentials. This simple relationship between the dithiocyanate radical and the dihalide radicals is not continued in the temperature dependence studies for the reactions of these radicals with phenol and p-methoxyphenol. As the temperature is raised, the rate constant for (SCN),'- (E" = 1.33 V) approaches, and even surpasses, that for Br2'- (E" = 1.66 V). The temperature dependence of the reactions of Iz'- and NOz' also provides some interesting information about the behavior of these radicals. These two radicals have almost the same reduction potentials (1.03 and 1.04 V). At low temperature, we find that 12*- reacts with ascorbate and phenolate (Figure la,c) faster than does NOz'. i z s the temperature is raised, the reactivity of NOz'
Ea,
kJ mol-' 12.9 14.5 9.6 18.4 17.3 9.3 7.2 9.4 8.4 10.4 24.1 29.5 8.9 10.3 41.3 19.8 17.3 9.7 34.3 26.1 35.6 23.0 7.3
f 1.1
f 1.2 f 0.8 f 0.9 f 1.1 f 1.7 f 1.7 f 1.5 f 0.5 f 0.5 f 0.1 f 4.1 f 1.2 f 0.3 f 1.3 f 2.3 f 1.2 f 1.0 f 1.6 f 2.3 f 2.3 f 1.2 f 0.6
log A 9.8 12.1 11.4 12.7 9.8 10.3 9.1 10.7 9.3 10.9 11.6 10.3 9.7 10.0 13.2 12.0 10.8 10.5 13.2 12.9 13.8 13.1 9.8
k298
3.7 x 3.9 x 4.9 x 3.0 x 6.1 X 5.1 X 7.2 x 1.0 x 7.3 x 1.1 x 2.2 x 1.3 X 1.3 X 1.5 X 9.0 x 3.1 X 5.2 X 6.5 X 1.5 x 2.1 x 3.5 x 1.0 x 3.2 X
107 109 109
109
IO6 IO8 107 109 107 109
IO7 IO8 IO8 IO8 105
IO8 IO7 IOs 107 108 107 109
IO8
increases more rapidly than the reactivity of Iz'- so that NO2' reacts faster at our highest temperatures. The behavior of l2'in its reaction with p-methoxyphenolate (Figure le) is anomalous. Above 17 OC, the rate constant for NOz' increases more rapidly than for 12'-, as it does with ascorbate and phenolate. The line extrapolated from the higher temperature data suggests that the rate constants for NOz' and Iz'- should be the same at low temperature. Instead, the rate constant for the Iz'- reaction drops rapidly as the temperature is decreased below 17 "C. The higher temperature points for lz'- also roughly parallel the results for Br2-, as observed for the ascorbate reaction. We have also studied the reaction of C102' with p-methoxyphenolate (Figure le). The rate constant for this reaction increases more rapidly than the rate constants for the dihalide radicals. Indeed, its high-temperature rate constants are higher than those for BrZ-, which has a 0.7-V higher reduction potential. Even though N,' only has a moderately high reduction potential (1.33 V), it is more reactive toward various reductants than any other of the radicals studied except CI2'- (E" = 2.09 V). Several of the reactions of N,' studied are sufficiently fast that they are likely to be at least partly limited by the rate at which the reactants
The Journal of Physical Chemistry, Vol. 94, No. 25, 1990 8803
Rate Constants for Reaction of Inorganic Radicals
I
Ti*
10'0:
c
I
I n
Y
a 1
,
I
,
A
, I 1081
c
*
-* ' lo8l I - 1071
,
I
Y
C
t c
t
, I
l--
I
* io9
I
I
I
9 ~
*
Ti
,
10
4
1081
- lo8
Y
e 2 .7
t I
2.9
3.1
1000/T,
3.3
3.5
3.7
K-'
2.7
i
I
2.9
3.1
1000/T,
3.3
3.5
3.7
K-'
Figure 2. Arrhenius plots for the reactions of several inorganic radicals with organic reductants: (a) N3'; (b) Br2*-; (c) I*'-; (d) (SCN),'-; (e) NO,'; reacting with phenol (0). phenolate (W), p-methoxyphenol (0).
Figure I . Arrhenius plots for the reactions of several inorganic radicals with organic reductants: (a) ascorbate, (b) phenol, (c) phenolate, (d)
p-methoxyphenol. (e) p-methoxyphenolate: reacting with N; (0); Br2*(W); (SCN),'- (0); 1,'- (e):NO,' (A):CIO,' (A);and CI1'- (*).
p-methoxyphenolate (e),hydroquinone (A),and ascorbate (*). In 2a the solid lines are for the measured rate constants and the dotted lines are for results corrected for diffusion rate: the results for phenol are not shown here.
8804
The Journal of Physical Chemistry, Vol. 94, No. 25, 1990
can diffuse toward each other. This is particularly true for the reactions of N3' with ascorbate, p-methoxyphenol, and hydroquinone. An approximate value for the diffusion-controlled rate constant can be calculated by using the equation"
kdiff= 1 /4(2
+ rl/r2 + r2/rl)8kT/3v
(3)
We have assumed that rl = rz in our calculations and have taken values of the viscosity, 9,from Lange's Handbook.I8 If the radii are not equal, the rate constants will be somewhat greater, so that this assumption should underestimate the diffusion-controlled rate constant. We can correct for diffusion control by use of the equation
/ kcor,
=
/ kobs
-
/ kdiff
(4)
In Figure 2a, we present the kinetic data on the three fast N3' reactions with and without correction for diffusion. The corrected rate constants are higher than the experimental values and the slopes for p-methoxyphenol and ascorbate remain almost unchanged (calculated activation energies of 1 1.5 and 18.7 kJ mol-' as compared to 14.5 and 18.4 kJ mol-I). The hydroquinone reaction shows no temperature dependence after correcting for diffusion, as compared to a value of 9.6 kJ mol-' before correction. There are significant errors associated with these corrections for diffusion, although to some extent these errors will be the same for all three reactions. in the discussion above, the reactions were compared according to how a specific organic reductant reacts with a series of oxidizing radicals. I n Figure 2. the results from Table I are compared for the radicals reacting with series of organic reductants. As expected from its relatively high reduction p ~ t e n t i a l(0.97 ' ~ V), phenol is the least reactive reductant. Its reactions also tend to have a greater temperature dependence. p-Methoxyphenol (0.72 V) and hydroquinone (0.46 V ) follow in reactivity, and both are less reactive than phenolate (0.79 V). After phenolate in reactivity are methoxyphenolate (0.54 V) and ascorbate (0.33 V), in order of their reduction potentials. For NO,', however (Figure 2e). the order of the latter two is reversed. This may be due to a contribution from an addition of NO2' to the aromatic ring. Although hydroquinone and p-methoxyphenol have significantly different reduction potentials, they show identical rate constants, over the temperature range studied, in their reactions with Br2+ (Figure 2b). Hydroquinone reacts somewhat more rapidly with N,' than does p-methoxyphenol (Figure 2a). They are both slightly more reactive than ascorbate toward N,', but I O times less reactivc than ascorbate toward Br2*-. The observation that phenolate is more reactive than either hydroquinone or p-methoxyphenol (Figure 2, b and d) confirms previous observations20 that the nonionized phenols are less reactive than would be expected based on their reduction potentials and the reactivity of the ionized phenols. This difference does not appear to arise from a stronger temperature dependence for the reactions of the neutral species, although the reaction of phenol has a relatively strong temperature dependence. Stanbury and co-workers6*8,2' have discussed the reactivity of several of these small inorganic free radicals in terms of the classical model of Marcus-Hush theory. They start with the basic assumption that the rate constant for a self-exchange reaction can be expressed a5 k = Z exp(-AC*/RT)
(5)
and that AG*, the activation barrier, can be expressed as the sum of a solvent reorganization barrier, AGO*, and a molecular re(17) Debye, P. Trans. Elecrrochem. SOC.1942, 82, 268. (18) Dean. J . A., Ed. Lange's Handbook of Chemistry, 12th ed.: McGraw-Hill: New York, 1979. (19) For a review see: Wardman, P. J . Phys. Chem. Ref. Dura 1989, 18, 1637. The redox potentials for the phenols and phenolates were taken from the more recent publication: Lind, J.; Shen, X.; Eriksen, T. E.; MerEnyi, G. J . Am. Chem. SOC.1990, 112. 479. (20) Stecnken, S.; Neta, P. J . Phys. Chem. 1982, 86, 3661. (21) Stanbury. D. M . Inorg. Chem. 1984. 23. 2914.
Alfassi et al. organization barrier, AC,*. Values of AGO*were estimated to be -40 kJ mol-] for these radicals. The differences in the self-exchange rates for N3*,C102', and NO2' were ascribed to differences in the values of AG,*, which they calculate to be roughly 0, 13, and 34 kJ mol-', respectively. They also predict I C , * to be about 26-29 kJ mol-' for I,'-, 25 kJ mol-' for Br2'-, and 22 kJ mol-' for CI2'-. These differences in the values of AG,* correlate well with the relative reactivitites at room temperature, but they do not correlate at all with the temperature dependences observed for the reactions of these radicals. For example, ClO,' dnd NO2' have essentially the same temperature dependence in their reactions with p-methoxyphenolate, in spite of the large difference in the calculated AG,* between the two. The dihalide radicals, which have calculated values of AC,*intermediate between those for CIO,' and NO2', have a lower temperature dependence for reaction with p-methoxyphenolate than either ClO,' or NO2'. Since SG = AH - T U , these observations can be interpreted to suggest that the entropy term contributes more to the activation barrier, AG*, than does enthalpy. Of the radicals we have chosen for study, N3' is the simplest; there is no significant structural difference between the ion and the radical.6 There is probably also little structural difference between the organic reductants and their one-electron-oxidized forms. Therefore, there should be little contribution to the temperature dependence of the reaction from inner-sphere reorganization. The reactions of N3' with hydroquinone, p-methoxyphenol, and ascorbate, which have reduction potentials of 0.46, 0.72, and 0.33 V respectively, have activation energies of 9.6, 14.5, and 18.4 (or, after correcting for diffusion, 0, 1 1.5, and 18.7) kJ mo1-I Therefore, there appears to be no correlation between the exothermicity of the reaction and the temperature dependence. The reactions of NO,' with phenolate, ascorbate, and p methoxyphenolate have considerably higher activation energies than the N,' reactions, with an average value of about 32 kJ mol-'. (There does seem to be an increase in activation energy as the rate constant decreases, but not as the exothermicity increases.) NO,' undergoes a considerable change in geometry when it is reduced to NOT, leading to an inner-sphere reorganization barrier to electron-transfer reactions8 CI02*is closer in geometry to C102-, so that less of an inner-sphere reorganization barrier expected. Yet we find that the temperature dependence for the reaction of ClO,' with p-methoxyphenolate is about the same as for the NO; reaction. (Correcting the ClO,' reaction for diffusion increases the activation energy to 24.1 kJ mol-', closer to the NO; value.) This suggests that it is not the inner-sphere reorganization barrier which causes the higher temperature dependence in the reactions of the bent triatomics. The reactions of Br2'- have a considerably lower temperature dependence than the reactions of either N3*or NO,', with an average value of about 9 kJ mol-'. This low-temperature dependence is coupled with a low preexponential factor. We suggest that the reaction may occur by an inner-sphere mechanism in which the dibromide radical adds to the organic reductant to form a complex, which subsequently dissociates.22 'Br2-
+ PhO-
-
[-BrBrPhO-]
'BrPhO-
-
Br-
-
Br-
+ PhO'
+ 'BrPhO-
(6) (7)
For most of the reactions studied here, rate constants have been reported a t room temperatures3 Our k298values (Table 11) typically agree with these previous results to within &50%. Some results from this on the reactions of Iz'- and NOz' with ascorbate are higher by a factor of 2, probably due to the higher pH employed in the previous work which would allow some contribution from the ascorbate dianion. The lower rate constant reported by us7 for the phenolate reaction with NO2' may be due (22) Such an oxidation mechanism, involving addition of Br on the oxygen atom of phenol, has been suggested recently for the reactions of other Br atom complexes (RBPBr) in organic solvents (Shoute. L. C. T.; Neta, P. J . Phys. Chem. 1990, 94, 2447). (23) Alfassi. 2. B.; Huie, R . E.; Mosseri, S.;Neta. P. J . Phys. Chem. 1987, 91. 3888.
J . Phys. Chem. 1990, 94, 8805-881 1 to the use of a lower temperature than 298 K in that study. I n conclusion, we find that, although the rate constant of free-radical electron-transfer reactions can be related to the exothermicity of the reaction, the temperature dependence of the rate constant is not. This is in contrast to hydrogen-abstraction reactions where a clear relation between the strength of the C-H bond and the activation energy is typically observed. For these electron-transfer reactions, the rate constant variations among a series of reactions appear to be dependent on both the activation energy and the preexponential factor, the latter being the predominant factor in most cases and appearing to be the factor most
8805
strongly tied to the energetics of the reaction. Acknowledgment. This research was supported by the Office of Basic Energy Sciences of the U.S. Deparment of Energy. L.C.T.S. was partly supported by the Indo-US collaborative program in material science. Registry No. N3', 12596-60-0; Br2'-, 12595-70-9;12*-, 12190-71-5; (SCN),'-, 34504-17-1; NO,', 10102-44-0; C102', 10049-04-4; Clz*-, 1 2595-89-0; phenol, 108-95-2; phenolate, 3229-70-7; p-methoxyphenol, 150-76-5; p-methoxyphenolate, 29368-59-0; hydroquinone, 123-3 1-9; ascorbate, 299-36-5.
Free-Volume Effect of Organic Dye Monomers in the Adsorbed State Klaus Kemnitz*.+ and Keitaro Yoshihara* Institute f o r Molecular Science, Myodaiji, Okazaki 444, Japan (Received: December 27, 1989; In Final Form: May 21, 1990)
The temperature dependence ranging from 298 to 4 K of the monomer fluorescence lifetimes of a thiacarbocyanine, pseudoisocyanine, and malachite green adsorbed on silica gel and on quartz has been examined. The fluorescence lifetimes at 298 K are about 20 times longer than the corresponding lifetimes in low-viscosity solvents. Weakly activated or completely activationless behavior of the rate constants of internal conversion has been observed. Asymmetric potential surfaces, induced by unidirectional forces exerted by the surface, are proposed that can expla.in the observed temperature dependences. The fluorescence lifetimes at 4 K are substantially shorter than the corresponding ones in rigid matrix and are attributed to a large free-volume effect in the adsorbed state.
Introduction The mechanism of internal conversion in organic dye molecules often involves the twisting of molecular constituents around single or double bonds in the excited state. In cyanine dyes in lowviscosity solvents, this twisting is thought to occur around one of the partial double bonds of the polymethine bridge,' and in triphenylmethane (TPM) dyes a synchronous rotation around the three carbon-phenyl bonds seems to be the established mechaThe issue of internal conversion seems far from being settled, however, in the case of xanthene dyes such as rhodamine B, where several new mechanisms have been proposed in recent years. Drexhage first pointed to the importance of the flexibility of diethylamino and carboxyphenyl groups and learnt from molecular modifications, such as the rigidification of the diethylamino groups in rhodamine 101, and from viscosity-dependence studies that enhanced rigidity decreased the rate of internal con~ersion.~ Later, Snare et al. refined Drexhage's mechanism by exploring the importance of the energy gap between the ground and excited state^,^ and recently Rettig et al. suggested the involvement of a twisted intramolecular charge-transfer (TICT) state.s Most recently, a two-state model with an excited-state equilibrium between planar and twisted form has been proposed by Casey and Quitevk6 This paper examines the internal conversion of dye molecules in the adsorbed state and reports the presence of altered potential surfaces in the adsorbed state and a possible involvement of additional, surface-induced decay channels. I n our initial studies of internal conversion of xanthene dyes adsorbed on quartz and other substrates, we proposed the presence of an activationless downhill excited-state potential surface for molecules adsorbed at distorted sites and invoked the participation of a butterfly-like motion in oxygen-bridged, TPM-analogue dyes such as rhodamine B and rhodamine 101.' The present study describes the close analogy of the temperature behavior of the rate constant of internal conversion of both T P M dye malachite green and the previously
'
Present address: Micro-Photoconversion Project, ERATO Program, JRDC, I5 Morimoto-cho. Shimogamo, Sakyo-ku, Kyoto 606, Japan.
studied T P M analogue rhodamine B. The study of the nonradiative behavior of cyanine dyes such as pseudoisocyanineand thiacarbocyanines possibly helps to answer the interesting question whether isomerization, involving largeamplitude motions, can occur in the adsorbed state.
Experimental Section The time-correlated single-photon-counting system and the method of data analysis employed have been described in detail e l ~ e w h e r e . ~The fluorescence decays were independent of the polarization of the collected fluorescence. All fluorescence decays could be analyzed by two or three exponentials. An attempt to discriminate between the present sum-of-exponential decay law and alternatives, such as a distribution of lifetimes, had not been undertaken in regard to the submonolayer samples of inherently weak fluorescence. Such discrimination requires 1los counts/peak channel and is not attainable with the present dye/adsorbate ( 1 ) (a) Tredwell, C. J.; Keary, C. M. Chem. Phys. 1979, 43, 307. (b) Velsko, S. P.; Fleming, G.R. Chem. Phys. 1982, 65, 59. (c) Sundstrom, V.; Gillbro, T. J . Chem. Phys. 1985,83, 2733. (d) Akesson, E.; Bergstrom, H.; Sundstrom, V.; Gillbro, T. Chem. Phys. Left. 1986, 126, 385. (e) Akesson, E.; Sundstrom, V.; Gillbro, T. Chem. Phys. Lett. 1985, 121, 513. (2) (a) Sundstrom, V.; Gillbro, T.; Bergstrom, H. Chem. Phys. 1982, 73, 439. (b) Doust, T. Chem. Phys. Lett. 1983, 96, 522. (c) Bagchi, B. Chem. Phys. Letf. 1987,135, 558. (d) Trebino, R.; Siegman, A. E. J . Chem. Phys. 1983, 79, 3621. (e) Sundstroem, R.; Gillbro, T. J . Chem. Phys. 1984, 81, 3463. (f) Mokhtari, A.; Fini, L.;Chesnoy, J. J . Chem. Phys. 1987.87, 3429. (8) Ben-Amotz, D.; Jeanloz, R.; Harris, C. B. J . Chem. Phys. 1987,86,6119. (3) Drexhage, K.-H. Dye Lasers; Schaefer, F. P., Ed.; Springer: Berlin, 1978. (4) Snare, M. J.; Treloar, F. E.; Ghiggino, K. P.; Thistlethwaite, P. J. J . Photochem. 1982, 18, 335. (5) (a) Rettig, W. Angew. Chem., Int. Ed. Engl. 1986,25,971. (b) Vogel, M.; Rettig, W.; Sens, R.; Drexhage, K.-H. Chem. Phys. Leu. 1988, 147,461. (c) AI-Hassan, K. A,; Azumi, T. Chem. Phys. Left. 1988, 146, 121. (6) Casey, K. G.; Quitevis, E. L. J . Phys. Chem. 1988, 92, 6590. (7) Kemnitz, K.; Tamai, N.; Yamazaki, 1.; Nakashima, N.; Yoshihara, K. J . Phys. Chem. 1987, 91, 1423. (8) 5,5'-Dichloro-3,3'-disulfopropyl-9-ethylthiacar~yanine. (9) Kemnitz, K.; Nakashima, N.; Yoshihara, K.J . Phys. Chem. 1988, 92, 3915.
0022-3654/90/2094-8805$02.50/00 1990 American Chemical Society
