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J . Phys. Chem. 1984,88, 6348-6350
In evaluating this expression, it is necessary to remember that R varies with a, being related through geometry by a a 1/R. The difference between this expression and that used previously lies in neglect of that connection. This makes little difference to values
of quantities computed earlier. Last, the surface free energy per micelle is given by Ng,= N(gel + ~ ~ aFor) .cylindrical geometry, eq A.11, A. 14, and A. 15 remain the same, except that R is replaced by 2R everywhere.
Solvent Isotope Effect on the Reactivity of Photoproduced Cations Embedded in Micelles Andrzej Plonkat and Larry Kevan* Department of Chemistry, University of Houston, Houston, Texas 77004 (Received: May 7 , 1984; In Final Form: August 3, 1984)
Lifetime distributions of photoproduced N,N,N',N'-tetramethylbenzidinecation radicals in micelles of sodium decyl sulfate and of sodium dodecyl sulfate in HzO and DzO were determined from inverse Laplace transforms of the experimental decay at room temperature. The decay curves are adequately approximated by [TMB'] = [TMBCJoexp[-(t/~~)"].The constant a,determining the lifetime distribution width for a given value of T ~changes , from 0.6 to 0.4 upon substitution of D 2 0 for H 2 0 . Thus the lifetime distribution is broader in DzO as compared to H 2 0 . Also, 70 increases in D 2 0 compared to H 2 0 which means the maximum of the lifetime distribution shifts toward larger lifetimes for this solvent change. Such kinetics and solvent isotope effects are discussed in terms of cooperative processes.
Introduction Recently the reactivity of species embedded in micelles has been satisfactorily interpreted in terms of a time-dependent rate constant.' Here we use this kinetic interpretation to examine a solvent isotope effect caused by changing the medium from light to heavy water. The perturbation of hydrophobic interactions in micelles,2 vesicle^,^ and microemulsions4~5due to a solvent change from H 2 0 to DzOis substantially greater than expected from the small differences in surfactant solubility or in critical micelle concentration in H 2 0 and D 2 0 observed nearly two decades ago.6s For species embedded in micelles, as we demonstrate below for photoproduced N,N,N',N'-tetramethylbenzidine cation radical (TMB') in micelles of sodium decyl sulfate (SlOS) and of sodium dodecyl sulfate (S12S), the increase of the hydrophobic interaction due to substitution of D,O for H 2 0 results in significant broadening of the lifetime distri bution accompanied by an increase in the effective lifetime. The lifetime broadening effect is similar in both kinds of micelles. In a given solvent an increase of the hydrocarbon chain length increases the effective lifetime of TMB+ cation radicals in agreement with previous finding^.^ Experimental Section SlOS, S12S, and T M B (Eastman Kodak Co.) were used as received to prepare H 2 0 and D 2 0 (Aldrich, Inc.) deoxygenated solutions of micelles with solubilized T M B according to the procedure described previo~sly.~ Solutions of 0.1 m M TMB in 0.1 M SlOS or S12S were used for which there is less on average than one T M B molecule per micelle. The micellar solutions in 77-pL micropiets were irradiated in the cavity of a Varian E-4 spectrometer with a 900-W high-pressure mercury lamp. The lamp output passed through a Corning band-pass filter No. 760 (350 30 nm) to give an intensity of lo2 W m-2. The concentration of photoproduced TMB+ was monitored by recording overmodulated ESR spectra.
*
Results To illustrate the solvent isotope effect on the reactivity of species embedded into micelles, Figure 1 shows the multiexponential decay patterns of photoproduced TMB+ cation radicals in aged1° micelles On leave from the Institute of Applied Radiation Chemistry, Technical University of Lodz, 93-590 Lodz, Poland.
0022-3654/84/2088-6348$01.50/0
TABLE I: Numerical Values of Constants a and T,,, Eq 1, for Decay of Photoproduced TMB' in Micelles of SlOS and S12S in H 2 0 and
Dz0 kinetic
parameters a ~ O - ' T ~ ,s
SlOS micelles H20 D20 0.6 0.8
0.4 2.2
S12S micelles
H,O 0.6
D,O
1.8
4.4
0.4
of S12S in light and heavy water. These multiexponential decay patterns, as we have shown previously,' can be adequately described by a first-order kinetic equation with a time-dependent rate constant: with 0
