J. Phys. Chem. 1985, 89, 4166-4169
4166
(pd Figure 2. Fluorescence decay at 620 nm of a furanoxy radical in benzene [the radical was formed by fragmentation of the triplet of 111 (X = H) sensitized by benzophenone (0.1 M) under 337-nm excitation in the presence of 0.04 M I11 (X = H)]. Triangles are experimental points; curve a is a computer simulation of the triplet-triplet mechanism (processes 1-2-4), and curve b is a computer simulation of the triplet-doublet mechanism (processes 1-3-4) for excited radical formation. Both simulated curves were obtained by using the experimental fluorescence lifetime of 16 ns, the triplet lifetime as 400 ns (best fit in T-D mechanism), the second-order rate constants as 1OIo M-I s- ' (2k for T-T mechanism), and low5M for the initial furanone triplet concentration. TIME
transient absorption measurements. The T-D energy-transfer processes were pursued further by generating furanoxy radicals together with triplets of other molecules and monitoring any sensitized radical fluorescence. The 3-benzoyl-substituted furanone (I) was used to produce 2R. directly by laser flash photolysis at 355 nm in a benzene solution. Excited by the same pulse, triplet states were formed from a potential triplet sensitizer that was present in the same cell. If no triplet-doublet energy transfer occurred, one would expect to see only the short-lived fluorescence (prompt) due to 2R. being excited in the pulse. However, if triplet-doublet energy transfer were to occur, then one would expect to see a long-lived fluorescence component that roughly followed the triplet decay. Experiments of this type were done using a series of triplet sensitizers (ET= 179-240 kJ/mol). All of these triplet sensitizers
have triplet energies, ET, below 250 kJ/mol, the expected triplet energy of the parent furanone (I). This prevented excited radicals being formed by the self-sensitization,triplet mechanisms discussed above (processes 1-2 or 1-3). It was found that long-lived components of the fluorescence were observed for all the sensitizers tried that had ET's above 197 kJ/mol (benzo[b]triphenylene, camphorquinone, chrysene, fluoranthene, and fluorenone), but no such fluorescence was seen when the E$s were less than the 0-0 of the radical fluorescence at -620 nm (192 kJ/mol) (anthracene, 4,4'-dimethoxythiobenzophenone,perylene, and pyrene-1-aldehyde). In cases where the long-lived components of fluorescence were detected, the decay of fluorescence roughly followed the decay of the triplet sensitizer. Thus, the radical fluorescence can be sensitized by triplet states under conditions where the triplet of the parent furanone is absent, yet where there is sufficient energy in a sensitizer triplet to reach the first excited doublet of 2R.. Using two lasers in a cleaner experiment of this type was done where the creation of the radical and the triplet sensitization were separated in time. The first pulse at 337 nm generated the radical, and another pulse at 425 nm, delayed by 5 ~ s generated , the triplet state of camphorquinone (CQ), with ETat 214 kJ/mol. In a first experiment of this type, the 337-nm pulse generated the radical, 2R.,from the benzoyl furanone (I), as above. In a second experiment, the 337-nm pulse generated tert-butoxy radicals2*which abstracted the 5-hydrogen from I1 (X = OCH3), forming the methoxy-substituted furanoxy radical (Scheme I). Both experiments showed a long-lived fluorescence (- 1 ks) which was initiated by the delayed, 425-nm pulse. The triplet state of CQ was monitored by transient absorption at both 700 and 330 nm1,31and the fluorescence was seen to follow its decay. No luminescence was seen without the first laser pulse, showing that the long-lived fluorescence was indeed due to the radicals.
Concluding Remarks Although the T-D energy transfer is spin-allowed and of significance in triplet quenching, there have been almost no studies, except for those of Razi Naqvi and co-workers,'6-20of this process using fluorescence of radicals to directly monitor the process. The experiments described above demonstrate that T-D energy transfer occurs readily in all cases examined where the process is exothermic. Finally, the ease with which the furanoxy radicals can be generated by flash photolysis opens up many possibilities for investigation of other energy-transfer processes involving doublet states. These radicals have an added advantage over other fluorescing radicals studied so far in that their excited states do not seem to be as reactive or short-lived as those of benzophenone ketyl radical^^^-^^ and some of the arylalkyl radicals.22 (31) Singh, A.; Scott, A. R.; Sopchyshyn, F. J . Phys. Chem. 1969, 73, 2633-2643.
Micellar Reactions of Hydrophilic Ions: A Coulombic Model Clifford A. Bunton* and John R. Moffatt Department of Chemistry, University of California, Santa Barbara, California 931 06 (Received: May 28, 1985) Distribution of hydrophilic ions about a spherical micelle has been estimated by using the Poisson-Boltzmann equation for finite salt and surfactant concentrations. It is consistent with rate-surfactant profiles for reactions of p-nitrophenyl diphenyl phosphate, 2,4-dinitrochloronaphthalene,and N-methyl-4-cyanopyridiniumion. Effects of sulfate ion upon reactions of nucleophilic anions in cationic micelles follow the predicted ion distribution. Ionic micelles speed bimolecular ionic reactions by bringing reactants together at the micellar surface, and inert and reactive
counterions compete for surface The extent of inhibition follows decreasing reagent ion hydrophilicity, suggesting that both
0022-3654/85/2089-4166$01SO/O 0 1985 American Chemical Society
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The Journal of Physical Chemistry, Vol. 89, No. 20, 1985 4167
specific and nonspecific Coulombic interactions are important, and an ion-exchange model describes the effect. Ion exchange is also important in reactions in other colloidal system^.^ If only reactive ions are present, it appears that the micellar surface is saturated with counterions, provided that they are not very hydrophilic, e.g., CN-, Br-, or N C . ~ But for very hydrophilic ions, e.g., OH-, F, or HC02-, ion binding appears to follow eq 1, written for a surfactant, DOH- (DOH = C16H33N+Me30H-, CTAOH in the present work).
where D, is the micellized surfactant and W and M denote aqueous and micellar pseudophases, respectively.6 Equation 1 fits a considerable amount of data, but its physical significance is unclear. These treatments emphasize specific micelle-ion interactions, but another approach is to write ionic distribution in terms of the Poisson-Boltzmann equation (PBE). The main problem with this approach is estimation of the micellar surface potential. It is sometimes estimated from indicator equilibria: but this circular reasoning merely relates micellar effects upon rates and equilibria and is just as empirical as eq 1 or the ion-exchange model. There are problems with the simple concept of ion exchange, especially with ions such as OH- which only weakly displace Brfrom a micellar surface, and exchange constants measured photochemically do not agree with those based on other methods9 Reactions of dianions can be fitted to the rnodel,l0 but it fails for inhibition by sulfate ion.'b99910 The model emphasizes ion binding in the Stern layer and neglects effects of ions in the diffuse layer (cf. ref 11). We calculated the extent of nonspecific ion binding to spherical micelles using the Poisson-Boltzmann equation. Thus, any additional effect should be specific and not accounted for by a point-charge model which considers only Coulombic interactions.
[OR,]. 02
01
1
03
1
I
1
1
1
0.02
0.04
0.06
0.08
0.1
Figure 1. Predicted variations of k, for reaction of DNCN with OH-: ( 0 )no added OH-; (m, +) at 0.05 and 0.1 M OH-T, respectively; (0) in 0.01 M CTAOH and added N a O H (ref 6).
We used the cell model, with minor modifications of the method of Bell and Dunning.12 Each cell, radius R, contains one micelle, radius a, and aggregation number, N, so that
-47rR3 - -
1OOON NA(IDTI - cmc)
(2)
where N A is Avogadro's number and cmc is the critical micelle concentration. In spherical symmetry at finite [salt]
(3)
Results and Discussion The PBE has been solved in spherical symmetry for finite [surfactant] and [electrolyte],I2*l3 and Gunnarsson et al. have used this treatment to estimate counterion concentrations at a micellar surface.14 They showed that the fractional counterion binding, p, within a 3-A shell was essentially independent of [counterion], even in the absence of specific effects. (1) (a) Romsted, L. S. In 'Micellization, Solubilization and Microemulsions"; Mittal, K.L., Ed.; Plenum Press, New York, 1977; p 509 (b) Romsted, L. S. In "Surfactants in Solution"; Mittal, K.L., Lindman, B., Us.; Plenum Press: New York, 1984; Vol. 2, p 1015. (2) Chaimovich, H.;Bonilha, J. B. S.; Politi, M. J.; Quina, F. H. J. Phys. Chem. 1979,83, 1851. (3) Bunton, C. A. Cutul. Rev.-Sci. Eng. 1979, 20, 1. (4) (a) Fendler, J. H.; Fendler, E. J. "Crystals in Micellar and Macromolecular Systems"; Academic Press: New York, 1975. (b) Fendler, J. H. "Membrane Mimetic Chemistry"; Wiley-Interscience: New York, 1982. (c) Mackay, R. A. J. Phys. Chem. 1982,86,4756. (5) Bunton, C. A,; Romsted, L. S.; Savelli, G. J. Am. Chem. Soc. 1979, 101, 1253. Bunton, C. A.; Romsted, L. S.;Thamavit, C. Ibid. 1980, 102, 3900. (6) Bunton, C. A.; Gan, L.-H.; Moffatt, J. R.; Romsted, L. S.; Savelli, G. J . Phys. Chem. 1981,85, 41 18. (7) Stigter, D. Prog. Colloid Polym. Sci. 1978, 65, 45. (8) (a) Fernandez, M. S.;Fromherz, P. J. Phys. Chem. 1977, 81, 1755. (b) Frahm, J.; Diekmann, S.J. Colloid Interface Sci. 1979, 70,440; ref Ib, p 897. (9) (a) Abuin, E. B.; Lissi, E.; Araujo, P. S.; Aleixo, R. M. V.; Chaimovich, H.; Bianchi, N.; Miola, L.; Quina, F. H. J. Colloid Interface Sci. 1983, 96, 293. (b) Lissi, E. A.; Abuin, E. B.; Sepulveda, L.; Quina, F. H. J. Phys. Chem. 1984, 88, 8 1. (10) Cuccovia, I. M.; Aleixo, R. M. V.; Erismann, N. E.; Van der Zee, N. T. E.; Scbreier, S.;Chaimovich, H.J . Am. Chem. SOC.1982, 104, 4544. (1 1) Stadler, E.; Zanette, D.; Rezende, M. C.; Nome, F. J . Phys. Chem. 1984,88, 1892. (12) Bell, G. M.; Dunning, A. J. Truns. Furuduy SOC.1970, 66, 500. ( 13) (a) Mille, M.; Vanderkooi, G. J. Colloid Interfuce Sci. 1977, 59,2 11. (b) Mille, M. Thesis, University of Wisconsin, Madison WI, 1976. (14) Gunnarsson, G.; Jonsson, B.; Wennerstrom, H. J. Phys. Chem. 1980, 84, 3114.
J
[CTAOH], M
where B is the reduced potential, B = e#/kT, # the potential, t the dielectric constant (78.54 a t 25 "C), T the absolute temperature, e the electrostatic charge (esu), and k Boltzmann's constant. For a colloidal cation Z+ and Z- are the valencies of co- and counterion and n+R and n-R are the respective number concentrations (ions cm-') at the cell wall. The boundary conditions are B = dO/dr = 0 at r = R
(4)
dO/dr = Ne2/ta2kT at r = a
(5)
The average concentrations and those at the cell wall are related by n+R
=
n+avV lRexp(-Z+O)4.ar2 d r
n-avv
; KR=
lRexp(Z-B)47rr2 d r
(6) with V = 4r(R3 - u3)/3
(7)
These equations were solved with the boundary conditions, eq 4 and 5 , by calculating the values of the integrals in eq 6 by reiteration with a judicious choice of first-order relaxation factors. Convergence was assumed when the calculated and prescribed boundary conditions differed by less than 0.01%. Test runs of the algorithm agreed to within 0.5% of literature v a 1 ~ e s . I ~ ~ Counterion binding and surface potentials have also been estimated for [surfactant] just above the cmc, with a curvature correction and by assuming infinitely dilute micel1es.l5 Our (15) (a) Mitchell, D. J.; Ninham, B. W. J . Phys. Chem. 1983, 87, 2996. (b) Evans, D. F.; Ninham, B. W. Ibid. 1983, 87, 5025.
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The Journal of Physical Chemistry, Vol. 89, No. 20, 1985
calculated values of fi agreed with those given by this simpler, but less general, method. Kinetic Analysis. We apply our treatment to attack of OHin CTAOH at 25.0 'C with p-nitrophenyl diphenyl phosphate (p-NPDPP), 2,4-dinitrochloronaphthalene (DNCN),6 and N methyl-4-cyanopyridinium ion (MCP).I6
[CTAOH], M
002
1
'
'
,
004
'
'
0.06
008
"
"
0 10
'
A I
4 M
5
I
p-NPDPP
0-
CI
I
1
2 3 i03[CTAOH].
F%gure2. Predicted variations of 4 for reaction of p-NPDPP in CTAOH (0). Insert: (0, 0,0) reactions with added 0.02, 0.04 and 0.1 M NaOH, respectively (ref 6 ) . CONI;!
I
t ,/
l
I
r
II ,'
0
r
. 000-
jl
,!'
,.
;,'
,'
Me
MC P
I
Me
The two nonionic substrates are hydrophobic and bind in the micelles according to a simple distribution equation,6.'' but MCP stays wholly in the water.* We first consider reactions of p N P D P P and DNCN.6 Initially we assumed a constant N a n d calculated ion concentrations within 2.4-and 3-A shells. These values are similar to those used earlier to describe a Stern or kinetic and our qualitative conclusions are unaffected by the precise value. If we assume constant micellar size and only nonspecific Coulombic interactions, the calculated concentration of OH- within these shells is independent of [CTAOH] (cf. ref 14),and this calculation does not fit ratesurfactant profiles for CTAOH or similar surfactants.'b*6 We can postulate various sources of ion specificity, e.g., binding of polarizable ions could be described by an additional potential term or by a mass action equation;19 but polarizability effects should be small with OH-. Therefore, we postulate that N changes with [surfactant] or [electrolyte] according to
N = No
+ ANK,[X-]/(l + K,[X-])
+ 26.9nc)
+
(8)
where No and No + U are minimum and maximum aggregation numbers and X-is total counterion. The micellar volume (A3), and hence radius a, is given by Tanford's equation:20 Vmic = N ( 2 7 . 4
The problem is then that of estimating concentrations of both reactants at the micellar surfaces. The distribution of substrate is written in terms of a binding constant, Ks,lbs2Iand that of OHis calculated from the PBE. The values of No = 30 and No AN = 120 (eq 8) are reasonable in view of other noting that bound hydrophobic solutes should stabilize small micelles, and there are limits to the size of spherical micelles.20 Under the conditions discussed N varied between 50 and 80,with K , = 9 . The first-order rate constants are given by
(9)
n, = 16 for CTAOH. We also examined an alternative and essentially equivalent approach which related charge density to
[x-I.
The rate constants for reactions of DNCN and p-NPDPP are in Figures 1 and 2 and are so much larger than those in water that we consider only reactions in the micelles in fitting the data. (16) Chaimovich, H.; Cuccovia, I, M.; Bunton, C. A,; Moffatt, J. R. J . Phys. Chcm. 1983,87, 3584. (17) Menger, F. M.;Portnoy, C. E. J . Am. Chem. SOC.1967,89, 4968. (18) Stigter, D. J . Phys. Chem. 1975, 79, 1008. (!9) Davies, J. T.;Rideal, E. K. "Interfacial Phenomena", 2nd 4.;Academic Press: New York, 1963; Chapter 2.
where [OH-],,A is the average concentration within a 2.4-A shell. The second-order rate constants, kzm,are 0.0175 and 0.12 M-' s-l for DNCN and p-NPDPP, respectively. These rate constants are similar to those estimated from eq 1.6 The rate constants in water are 0.0064 and 0.48 M-' s-l for DNCN and p-NPDPP, respectively,6 and as is common, micelles have relatively small (20) (a) Tanford, C. "The Hydrophobic Effect"; Wiley: New York,1973. (b) Liebner, J. E.; Jacobus, J. J. Phys. Chem. 1977, 81, 130. (21) Micellar binding of substrate, S, is given by [S,] = k,[$]/(l + KJD] cmc)) with K, = 1600 and 1.6 X 10' M-l for DNCN and p-NPDPP, respectively. (22) (a) Hashimoto, S.; Thoma8, J . K.;Evans, D. F.; Muhkerjce, S.; Ninham, B. W. J. Colloid Interfnce Sci. 1983,594. (b) Lianos, P.; Zana, R. J . Phys. Chem. 1983,87, 1289. (c) Athanassakis, V.;Moffatt, J. R.; Bunton, C. A.; Dorshow, R. B.; Savelli, G.; Nicoli, D. F. Chem. Phys. Lerr. 1985,115, 467.
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The Journal of Physical Chemistry, Vol. 89, No. 20, 1985 4169
we take NO= 15, because MCP does not bind and stabilize small micelles,2 but the fit is only slightly impaired taking No = 30, in eq 8. The value of the cmc is taken as 3 X M.6 The fit (Figure 3) is similar to that based on eq 1, and the discrepancies at high [CTAOH] are probably due to neglect of specific electrolyte and medium effects (cf. ref 2). We next consider interionic competition for micelles, in particular the role of ion valency, ignoring specific interactions. cannot be fitted to Inhibition by an inert dianion, e.g., so42-,23 an ion-exchange e q ~ a t i o n , ~and ~ * although '~ dilute S042- is as effective an inhibitor as C1- or Br-, the inhibition levels off at high [SOq2-].23324
\
I
20
.- - - _ _ lb
I
I
40
60
1-439*10
Figure 4. Distribution of OH- (0.005 M) around a cationic micelle ([D'] = 0.05 M): broken lines (l), 0.05 M X-;solid lines (2), 0.025 M SO:-. a and be denote X- or SO4*- and OH-, respectively.
effects on the rate constant^.'^^ The fits between observed and calculated rate-surfactant profiles in Figures 1 and 2 are reasonably good in view of the approximations of the treatment which assumes that p-NPDPP and D N C N do not affect micellar structure. This is a general ptoblem in reactivity studies and in estimations of micellar size based on photochemical probes because apolar solutes may promote micellar growth.*%Sbespecially with very dilute surfactant. Another assumption, made in common with other treatments, is that there is a uniform micellar reaction environment.'" This assumption neglects ionic distribution within the shell around the micelle and probable differences in location of various substrates. Despite these uncertainties, the treatment satisfactorily describes rate-surfactant profiles, and the predicted profiles are similar to those based on eq 1, despite its lack of theoretical underpinnings. The first-order rate constant for reaction of MCP is given by R
k+ = kwC [OH-rIxr a
Figure 4 illustrates the difference between uni- and divalent ions in competing nonspecifically with a reactive ion. The dianion could be S042-and the reactive ion OH- for example, and X-is a nonspecifically binding anion. For simplicity we take constant values of N = 78 and a = 23 A and neglect the cmc. Anionic distribution toward the micelle is skewed sharply in favor of a divalent ion,14 and [OH-] a t the micellar surface is much lower when the inert ion is divalent. These differences are consistent with micellar surface potentials (relative to the cell wall) of 177 and 107 mV for uni- and divalent ions, respectively (cf. ref 12 and 13). Figure 4 (insert) shows that for nonspecifically binding ions an inert divalent ion is very effective at excluding a reactive univalent ion from the micellar surface. Comparison with experiment suggests that ions such as C1-, Br-, and NO3- compete both specifically and Coulombically with OH-, for example. Reaction of 0.01 M OH- with p-nitrophenyl benzoate (p-NPB) is much slower in 0.005 M (CTA),S04 than in 0.01 M CTACl (k+ = 0.284 and 0.614 s-l, respectively), but the situation is reversed with high [salt], e.g., with added 0.1 M Na2S04and 0.05 M NaCl k+ = 0.48 and 0.023 s-l, re~pectively.~~ Other evidence bearing on this question is cited in ref lb, 9, and 10, and differences in the Coulombic binding of mono- and divalent ions are discussed in ref 14. Analysis of experimental data suggests that effects of such hydrophilic ions at OH- and SO:- upon micellar-assisted reactions are governed largely by Coulombic interactions but that less hydrophilic anions also interact specifically. Despite their empirical and that based nature both the pseudophase ion-exchange on eq l6 fit the kinetic data and provide reasonable values of rate constants at micellar surfaces. Although eq 1 is written in a mass action form, it probably reflects increasing N , and therefore increasing and increased binding of OH-. We note that for the CI4 surfactant N increases modestly with added NaOH.228
(11)
where [OH;] is the local concentration and xrthe fractional local concentration of MCP at distance r. The value of the second-order rate constant in water, k,, is 2.7 M-' s-l.16 In fitting the data,
+,
Acknowledgment. Support of this work by the National Science Foundation (Chemical Dynamics Program) and the U S . Army Office of Research (DAA9 29-83-9-0098 and DAAG 29-85-K001 6) is gratefully acknowledged. (23) Cordes, E. H.; Gitler, C. Prog. Bioorg. Chem. 1973, 2, 1 . Bunton, C. A.; Robinson, L. J. Org. Chem. 1969, 34, 773. (24) Biresaw, G., unpublished results.
