J . Phys. Chem. 1984, 88, 1231-1236 ined. One such indicator might be the magnitudes of the moments of a specific dimer in several solvents. It is expected that the equilibrium constant for an acyclic-cyclic dimer mixture would vary drastically with the particular solvent due to differences in solutesolvent interactions, giving largely differing average dimer moments. This would be especially noticeable if some solvents were capable of hydrogen bonding while others were not. A cyclic dimer should exhibit relatively small changes in its dipole moment upon changing solvents due to the lesser importance of solutesolvent interactions. However, care must be taken in interpreting the data as even simple monomeric molecules are subject to solvent effects. Another indicator of the presence or absence of an acyclic-cyclic equilibrium might be the temperature dependence of the dimer moment. If the acyclic species becomes more prevalent as the temperature increases, as one would expect, the observed average dipole moment will increase with increasing temperature (the acyclic n-mer will usually have a larger permanent dipole moment than a cyclic species). If only a cyclic dimer whose apparent moment arises from atomic polarization is present, this moment will be temperature independent because the atomic polarization is a temperature-independent quantity. The apparent moments of (t-C4H9)zP(0)OHin benzene and dioxane are very similar, indicative of the existence of only the cyclic dimer. This is in accord with the infrared spectra. On the basis of all the evidence presented herein, it is concluded that the origin of the apparent moment in this molecule is the atomic polarization. The different solution behavior of PhzP(0)OH compared to that of (t-C4H9),P(0)OH is undoubtedly another manifestation
1231
of the forces which cause their solid-state structures to differ greatly. In dioxane, the formation of a monomer-dioxane complex and no self-associated species is the same as the behavior of 2-pyrrolidinone' and 7-azaindole3 in this solvent. Thus, the self-association is much stronger in (t-C4H9)2P(0)OHthan in Ph,P(O)OH. In benzene, the single self-associated Ph,P(O)OH species present could be cyclic, acyclic or, in this case, a mixture of the two for a given n-mer. Since PhzP(0)OH forms a hydrogen-bonded spiral in the crystalline state, acyclic self-associates seem to be likely species in solution. However, the magnitude of the observed moment in benzene seems too small for an acyclic species to be the only one present. Calculations reveal that the dipole moment of an extended dimer will be in the range 4.4-8.6 D depending on its conformation. If an acyclic species does exist in these solutions, there is the possibility that the free O H end is weakly hydrogen bonded to the n-electron system of benzene. Unfortunately, the solubility of PhzP(0)OH in other nonpolar solvents is even smaller than in benzene and dioxane. This precludes the measurement of its moment in other solvents to compare with the moment in benzene. Acknowledgment. I thank ZZ for a grant-in-aid in partial support of this research. Registry No. [(CH,),C],P(O)OH, 677-76-9; (C,H5),P(0)OH, 1707-03-5; benzene, 71-43-2; 1,4-dioxane, 123-91-1.
Supplementary Material Available: A table of dielectric constants and refractive indices as a function of concentration (2 pages). Ordering information is given on any current masthead page.
Pyrene Triplet-State Lifetimes in Micellar Solutions. Tetradecyltrimethylammonium Bromide and Sodium Dodecyl Sulfate Tom F. Hunter* and Adam J. Szczepanski School of Chemical Sciences, University of East Anglia, Norwich h'R4 7TJ. U.K. (Received: March 18, 1983: In Final Form: August 1, 1983)
Triplet-state lifetimes are reported for pyrene in tetradecyltrimethylammonium bromide (C,,TAB) and sodium dodecyl sulfate (SDS) micellar solutions. The lifetimes depend on both pyrene and micellar concentrations and vary with the distribution of pyrene among the micelles. A model is developed for the overall triplet-state decay, and values for the intrinsic lifetime in both the micellar and aqueous phases and rate constants for exit from and entry into the micelles are given.
In contrast to fluorescence measurements, relatively little work has been done on the details of triplet-state lifetimes in micellar solutions. Much of the work that does exist has been on the quenching of the triplet state of some solubilizate by an added ion. Thus, in C16TAB (hexadecyltrimethylammonium bromide)-anthracene systems Thomas et al.' studied the shortening lifetime induced by added Cuz+ ions. In the absence of Cu2+the anthracene triplet lifetime was measured as 1.5 ms.' Further studies were carried outZon energy transfer between triplet states of benzophenone and biphenyl and on I- quenching in these solutions. Fendler et aL3 looked at triplet-state naphthalene as it transferred energy to terbium chloride, and found the naphthalene s in SDS (sodium dodecyl sulfate) triplet lifetime to be 21.1 X solution. Triplet-state pyrene has been produced, as above, by (1) P. P. Infelta, M. Gratzel, and J. K. Thomas, J . Phys. Chem., 78, 190 (1974). ( 2 ) S. C. Wallace and J. K. Thomas, Radial. Res., 54, 49 (1973). (3) J. R. Escabi-Perez, F. Nome, and J. H. Fendler, J. Am. Chem. SOC., 99, 7749 (1977).
0022-3654/84/2088-1231$01.50/0
flash photolysis and used to examine the subsequent production of 'A oxygen4 or in reaction with Br2-.5 The long triplet lifetimes involved are shown by the roomtemperature observation of solution phosphorescence6-*for solubilizates such as pyrene, naphthalene, and their brominated derivatives. Gratzel et aL7 showed that the silver surfactant, silver decyl sulfate, enhanced the phosphorescence; and Turro et a1.,8 using 1,4-dibromonaphthalene, measured a lifetime of 1 ms and showed that in the micellar solutions some protection from oxygen quenching was afforded. This latter observation had also been noted by Dorrance and Hunterg using anthracene as solubilizate.
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(4) N. Miyoshi and G. Tomita, Z . Naturforsch. B, 33, 622 (1978). (5) A. J. Frank, M. Gratzel, A. Hsnglein, and E. Janata, Znt. J . Chem.
Kinet., 8, 817 (1976). ( 6 ) K . Kalyanasundaram, F. Grieser, and J. K. Thomas, Chem. Phys. Lett., 51, 501 (1977). ( 7 ) R. Humphry-Baker, Y . Moroi, and M. Gratzel, Chem. Phys. Lett., 58, 207 (1978). (8) N. J. Turro, K. C. Lia, M. F. Chow, and P. Lee, Photochem. Phorobiol., 27 523 (1978).
0 1984 American Chemical Society
1232 The Journal of Physical Chemistry, Vol. 88, No. 6,1984
Analysis of the movement between aqueous and micellar phases for quenchers and energy-transfer acceptor molecules has been made in a number of studies.'&13 The solubilizate, pyrene, used in the present work has yielded various values for k, the inverse of the triplet lifetimes, each at 298 K: SDS with added TlN0,: lo, then the effect of micelles containing two or more pyrene molecules must become apparent; but such solutions are not stable.) The presence of variation in the plots in Figures 1 and 2 with A, and thus with the distribution, is also a strong indication of the
-d (18)
510
-d[Twl/dt =
( k + k+[MI)[T,l
- k-[TiI
(19)
These lead to the following expression for kT:
+
kT = (k,(ki + k- k+S,) + k+[M] X [ k , + k+S, + k-(l - ~o)Il/lk, + k- + k+[MIJ (201
which is similar to eq 9 but with the terms in Po and in S, added. It is these terms which give the differences shown in Figures 1 and 2. The physical process represented by the presence of Po is that a triplet pyrene molecule entering a micelle containing no pyrene molecules lasts a long time whereas it is quickly deactivated as soon as it enters a micelle containing one or more pyrene molecules. At high [MI, S, is likely to be very low (for a molecule like pyrene) but k+S, is included since both k l and k- are also likely to be small. The value taken for S, depends on the assumed distribution law, and it can be shown that, for Poisson statistics S, = k S / ( k -
+ k+[M])
(21)
where S is the total concentration of solubilizate. At high [MI, then S, = kS/(k+[M]) giving
k+S, = k-ii
(22)
For non-Poisson statistics S, = PokS/(Pok-
+ k+[M])
(23)
giving at high [MI
k+S, = kPoti
(24)
It is, of course, likely that the two distribution laws represented in the above equations are limiting laws, not only with respect to the k+ term23with limitations on the number of solubilizate molecules, but also with respect to the k- term where the exit rate may be intermediate between the two limiting cases expressed in Poisson and non-Poisson statistics. If one takes the high-[MI points, as given in Figures 1 and 2, it is possible to graphically estimate values for k, and k-, but it was found much more accurate to computer fit all the high-[MI points by using eq 20 with either eq 22 or 24. The results of this are given in Table 11. Both Poisson and non-Poisson statistics give reasonable fits and it was not possible to say that one distribution law was suggested by fitting these results. The results in Table I which are not shown in Figures 1 and 2 were not fitted well by eq 20. These points all have low values of [MI; Le., the detergent concentration is approaching the cmc, and the reason for the lack of fit is that S, is now important. In the derivation of eq 20 it was assumed that all absorption is to pyrene solubilized in the micelles; for these low-[MI points a significant fraction of the absorption is taking place to aqueous-phase pyrene, S,. Allowance for this has been made in the more complex models previously referred to and details of which will be given elsewhere; the fit with these models is good and does not significantly alter the values of the parameters given inTable 11.
1236 The Journal of Physical Chemistry, Vol. 88, No. 6,1984 The point here is the use of the high-[M] values to establish the parameters and merely to indicate that agreement on the low-[MI points can be achieved by proper allowance for aqueous pyrene. Two points of interest are worth noting, however. (a) At low [MI the concentration of aqueous pyrene is greater than the solubility of pyrene in water; this strongly suggests that aqueous pyrene is present in association with a small number of detergent monomer units. This tends to back up the “clumps” suggested in previous ~ o r k . * ~ , ~ ~ (b) At low [MI, the use of fi in the Poisson and non-Poisson statistics has to be carefully handled. With the Poisson example, it is readily shown23that
P, = Xne-x/n! The x in this relationship is normally taken as fi or S / M where S and M are the total concentrations of solubilizate and micelles, respectively. However, x is really S,/M with S, the concentration of solubilizate in the micelles. The formula for P, should be Pn = (n!)-’I(S/W[l
+ ( k - / ( k + W ) I - ’ Y exp(-[(S/M)
X
[1 + ( k - / ( k + W ) l - ’ l l ( 2 5 ) which only reduces to the normal
P,, = ii”e-”n! when M is fairly high, i.e. k-/(k+M)
