J. Phys. Chem. 1981, 85,2363-2366
2363
tions 5, 8, and 9 are possible. One expects k9 to be comparable to k, and k8, but its true magnitude remains unknown at present. However, it seems probable to us that reactions 5 and 8 do occur significantly, especially in aged air in which the [NO]/[N02] ratio is low. The significant levels of HCOzH identified in the aged smog at Riverside, CA,18 may arise in part from the reaction sequences outlined here and from analogous reactions involving O3and the higher 1-alkenes (propene, 17butene, 1-pentene, 2methylpropene, etc.). It seems probable in view of these results that the interesting compound HOCHzOCHO should be formed in
the polluted troposphere. However, its fate in the atmosphere is unclear. Its photodecomposition may be important as well as its reaction with the ubiquitous HO radical. It may accumulate in atmospheric aerosols as Niki et al. ~ u g g e s tor , ~it may lead to (HC0)20and HC02H in heterogeneous processes like those suggested here which involve atmospheric aerosols or surfaces. Thus, we have found that the transient compound HOCH20CH0 does not build up to detectable levels in O3-CZH4 mixtures containing significant concentrations of SO,; here HzS04 aerosol is observed. This is in part the result of the competition of SOz for the CH202 species in reaction 8. However, HC02H formation rates in SOz-CHzO-containing mixtures show that reaction 5 still occurs in accord with the relative rate-constant ratio, k s / k , .= 4. However, following generation of HOCHzOCHO in these systems presumably (HC0)20may form on the H2SO4 aerosol by a reaction such as reaction 7 or 7a followed by the rapid conversion of (HC0)20to HC02H: (HC0)20+ H20(HzS04aerosol) 2HC02H (H2S04aerosol) (10)
(18) E. C. Tuazon, R. A. Graham, A. M. Winer, R. R. Easton, J. N. Pitts, Jr., and P. L. Hanst, Atmos. Enuiron., 12, 865 (1978). (19) L. B. Harding and W. A. Goddard 111,J. Am. Chem. SOC.,100, 7180 (1978).
Acknowledgment. This work was supported by a research grant (R-806479-03) from the Environmental Protection Agency. We are grateful to Dr. Hiromi Niki for a preprint of his work (ref 3) before publication.
ratio is greater than 4.0, then reaction 5 will be favored over reaction 8. However predictions about the fate of CH202 + SO2 (CH202SOZ) CH2O + SOS(H2S04) (8) the CH20zspecies in the polluted atmosphere require a knowledge of one additional rate constant, that for reaction 9, before meaningful estimates about the extent of reacCHzOz + NO (CH202NO) -+ CH2O + NO2 (9) +
-+
+
-
+
Determination of Micelle Aggregation Numbers by Energy Transfer Peter K.
F. Koglin,
Dennis J. Mlller, Jurgen Steinwandel, and Manfred Hauser"
Institut fur physikalische Chemie, Universitat Stungaff, D 7000 Stungaff-80, PfaffenwaMring 55, West Germany (Received: October 29, 1980; In Final Form: March 6, 198 I )
Forster energy transfer systems may be used to find the aggregation numbers of micelles. Criteria for the choice of donor and acceptor are discussed. The system diphenylacetylene/pyrene is shown to give the correct aggregation number for sodium dodecyl sulfate micelles.
Introduction Photophysical processes provide an increasingly important tool for the investigation of detergent solutions.' Because the lifetime of singlet excited states is shorter than the time scale of solubilizate exchange, each micelle acts as a cage. In excimer kinetics, for example, this leads to both qualitative and quantitative differences between micellar and homogeneous s o l ~ t i o n . ~ Long-range ~~ (Forster-type) energy transfer, which occurs over distances comparable with micelle dimensions, also shows a number of interesting effects in detergent solution^.^-^^ (1) N. J. Turro, M. Gratzel, and A. M. Braun, Angew. Chem., 92,712 (1980). (2) (a) M. Hauser and U. K. A. Klein, Acta Phys. Chem., 19, 363 (1973); (b) D. J. Miller, U. K. A. Klein, and M. Hauser, Z . Naturjorsch. A , 32,1030 (1977); (c) D. J. Miller, U. K. A. Klein, and M. Hauser, Ber. Bunsenges. Phys. Chem., 84, 1135 (1980); (d) M. Hauser and U. K. A. Klein, Z. Phys. Chem. (Frankfurt am Main), 7 8 , 32 (1972). (3) D. J. Miller, Ber. Bunsenges. Phys. Chem., 85, 337 (1981). (4) N. Roessler and G. von Bunau, J. Photochem., 9, 307 (1978). (5) N. J. Turro and A. Yekta, J. Am. Chem. SOC.,100, 5951 (1978). (6) G. A. Kenney-Wallace, J. H. Flint, and S. C. Wallace, Chem. Phys. Lett., 32, 71 (1975). (7) Y. Usui and A. Gotou, Photochem. Photobiol., 29, 165 (1975).
The overall efficiency of energy transfer depends on two factors:" (a) occupation statistics, i.e., the probability that n acceptor molecules share a micelle with an arbitrary donor, and (b) intramicellar energy transfer efficiency, which depends on the size of the micelle and the Forster radius. If the micelle diameter is less than the Forster radius, energy transfer is very efficient. The overall efficiency is then governed by the occupation statistics alone, and problems concerned with the solubilization site, the orientation factor, or diffusion do not arise. Photostationary measurements enable the fraction of acceptor-occupied micelles and hence the aggregation number to be found. Although many pairs of substance show energy transfer, the choice of system requires careful consideration if spurious results are to be avoided.
Experimental Section Sodium dodecyl sulfate (SDS) (Merck) was purified by extracting with petroleum ether. Pyrene (FLUKA) was zone refined. Diphenylacetylene (DPA) from EGA-Chemie was used without further purification. Fluoroscence spectra were measured with a Perkin-Elmer MPF-3L
(8)J. R. Escabi-Perez, F. Nome, and J. H. Fendler, J.Am. Chem. Soc.,
99. 7747 (1979). '(9) T. Matsuo, Y. Aso, and K. Kano, Ber. Bunsenges. Phys. Chem.,84, 146 11980). (IO) Y.'Kusumoto and H. Sato, Chem. Phys. Lett., 68, 13 (1979).
(11) D. J. Miller, P. K. F. Koglin, and M. Hauser, "Proceedings of NATO-AS1 on Time-Resolved Fluorescence Spectroscopy", Plenum Press, London, in press.
0022-3654/81/2085-2363$01.25/0 0 1981 American Chemical Society
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The Journal of Physical Chemistty, Vol. 85, No. 16, 1981
Koglln et ai.
spectrophotometer. A correction curve was determined by comparing the spectra of several substances with the corrected spectra given by Berlman.12J3 The quantum yield of DPA was measured relative to 1-naphthol (v = 0.21)12and aniline (7= 0.08).” Decay-time measurements enabled the quantum yield of pyrene in air-saturated SDS solutions to be compared with that in degassed SDS solution (7 = 0.60).14
Energy Transfer in Micelles If donor fluorescence and acceptor absorption overlap, Forster-type energy transfer occurs. The rate of transfer for an isolated donor-acceptor pair is a function of the distance RDA between them and the Forster radius Ro as shown in eq 1. The Forster radius Ro is related to the IZD-A
= (~/~o)(Ro/RD-A)‘
(1)
-
0
2
RDP, /%re
Figure 1. Distribution of donor-acceptor distances In a sphere.
absorption and fluorescence spectra by eq 2.15 7D = donor ”OO\
quantum yield; K~ = orientation factor;16 F(e) = donor fluorescence; t(8) = acceptor absorption; n, = refractive index. A suitable energy transfer system must fulfill several criteria. Obviously the size of the Forster radius in relation to the micellar size is important. If efficient intramicellar energy transfer is desired, it should not be much smaller than the micelle diameter. If time-resolved fluorescence from micelles containing an acceptor is to be studied, Ro must not be too large compared to the micelle, otherwise the energy transfer will be too fast to be measurable. The absorption spectra should be such that the donor can be excited without exciting the acceptor. If the extinction coefficients are t D and CA at the exciting wavelength, the fraction of light absorbed by acceptor is
X
=
CACA/(~ACA
+ ~DCD)
(3)
This effect is readily corrected for. More difficult is the question of reabsorption. Forster-type energy transfer occurs when donor fluorescence and acceptor absorption overlap. This overlap also enables fluorescence to excite acceptor molecules which in turn fluoresce, resulting in a spurious contribution to the energy transfer. The effect can be obviated by ensuring that the donor fluorescence travels only a very short distance through the solution, for example, by observing fluorescence from the front of a very thin cuvette. If the optical density is high at the excitation wavelength, the light penetrates only a short distance beyond the front window and a thin cuvette is not necessary. Even when these precautions are taken, it is desirable to estimate the extent of trivial reabsorption. Using Beer’s law, one can obtain readily the intensity of exciting light as a function of penetration depth. The amount of donor fluorescence absorbed by the solution for a fluorescing volume element at a given distance from the window also follows from Beer’s law. By integrating over all distances and using an empirical factor to describe the effects of the optical system, one can obtain a correction for the (12) I. Berlman, “Handbook of Fluorescence Spectra of Aromatic Compounds”, Academic Press, New York, 1971. (13)P. Koglin, Diplomarbeit, Stuttgart, 1979. (14)U. K. A. Klein, Doktorarbeit, Stuttgart, 1974. (15) Th. Farater, in “Comprehensive Biochemistry”, Elsevier, Amsterdam, 1967,p 61. (16)R. E. Dale and J. Eisinger, Biopolymers, 13, 1573 (1974);L. Stryer, Annu. Reo. Biochem., 47,819 (1978).
5
10 R,orJR.a
15
20
25
30
Figure 2. Intramicellar energy transfer efficiency, qT, as a function of micelle core radius/Forster radius. Donor and acceptor taken to be randomly distributed within the core.
trivial effect. Details are provided in the supplementary material. (See paragraph a t end of text regarding supplementary material.) A further important point is the solubility of the donor and the acceptor in the micellar solution. Problems may arise because the donor or the acceptor is not sufficiently soluble, or is distributed between the micelles and the bulk solution, as in the case of naphthalene.“ The solubilization site is also of interest. Ionic substances are solubilized in the ionic layer while nonpolar molecules reside in the hydrocarbon core. Also, the solubilized substances should not alter the micelles. There is evidence for this in a number of cases. For example, the excimer method yields reasonable aggregation numbers for SDS micelles assuming the aggregation number to be independent of the concentration of solubilized pyrene.2~~ Moreover, the solubilized pyrene has little effect on the critical micellar concentration.” If the donor-acceptor distance of any given pair is R D A , it follows from eq 1 that the efficiency of energy transfer is In a real system, the distribution of donor-acceptor distances must be taken into account.1s We have made quantitative calculations for donor and acceptor randomly distributed in a spherical micelle (radius Rmm). The VT for a finite system (of any shape) can be found by averaging (17) R. Hautala and N. J. Turro, Mol. Photochem., 4, 545 (1972). (18)(a) C.R.Cantor and P. Pechukas, h o c . Natl. Acad. Sci. U.S.A., 68,2099(1971); (b) A. Grinvald, E. Haas, and I. 2.Steinberg, h o c . Natl. Acad. Sci. U.S.A., 69,2273 (1972).
The Journal of Physical Chemistry, Vol. 85, No. 16, 1981 2365
Determination of Micelle Aggregation Numbers
t
40 000
-20 000
1 n
I
I\
1.51
1.0.
\\
0.5 .
0.1
--IO000
\
1 I
I,
10000
\
50000
30000
\
I
I /
A[ nm] Figure 3. Absorption spectra of pyrene (-) of diphenylacetylene (- - -).
-
and fluorescence spectra
over 15000 pairs of randomly distributed donors and acceptors. The result of this Monte-Carlo calculation is shown in Figures 1 and 2. There are essentially three regions: For Rcore/Ro< 0.5 the energy transfer is very from ca. 0.5 to 2.0 the transfer efficient. For Rcore/Ro efficiency depends strongly on the micelle diameter; this could be used to investigate micellar size and shape. For Rcore/Rogreater than 2.5 there is hardly any energy transfer. If the donor has a long lifetime, diffusion increases the efficiency of energy transfer. This effect has been treated quantitatively for homogeneous solution.19 The overall efficiency of energy transfer may be related to the aggregation number, the acceptor concentration, and the intramicellar transfer efficiency. If the number of acceptor molecules per micelle is small, we need only consider micelles with zero and one acceptor molecule. The fraction of micelles containing an acceptor molecule is given by CA g
cDet - cmc
1 -
-
CA
.-- -- - .
/
+
1
(5)
where cDet is the detergent concentration, g is the aggregation number, and cmc is the critical micellar concentration. The ratio of intensities of donor and acceptor fluorescence is then given by
Energy transfer can be observed both from decrease in donor fluorescence intensity on adding acceptor5 or by observing the donor/acceptor ratio. We prefer the latter method as it is less sensitive to the effects of light scattering.
Results and Discussion The energy transfer system used for photostationary work was diphenylacetylene (donor)/pyrene (acceptor). From the Strickler-Berg equationz0the fluorescence life(19)U.Gosele, M.Hauser, U. K. A. Klein, and R. Frey, Chem. Phys. Lett., 34,519 (1976). (20)S. J. Strickler and R. A. Berg, J. Chem. Phys., 37,814 (1962).
Figure 4. Quantum ratio of donor/acceptor fluorescence vs. reciprocal acceptor concentration in L mol-’: (X) 0.1 M SDS in water (-): ( 0 ) 0.1 M SDS in 0.2 M aqueous Na,SO, (---).
time of diphenylacetylene was estimated to be 6 ps. This is too short to be of use for time-resolved studies. On the other hand, the system chosen shows several advantages. No diffusion takes place within the lifetime of the excited state. In micellar systems the effects of diffusion are difficult to deal with because of uncertainties in the microviscosity. Further advantages of the DPA-pyrene system are that both substances are very insoluble in water and that both reabsorption and direct excitation of acceptor molecules can be virtually eliminated. In Figure 3 the spectra are shown. The quantum yields in air-saturated 0.1 M SDS were ?A = 0.31 for pyrene and ?lD = 0.0043 for DPA. These experimental data yield a Forster radius of 15 A using eq 1 and taking the refractive index inside the micelle to be that of dodecane. The Forster radius was also determined experimentally. In homogeneous solution the ratio of donor fluorescence with and without acceptor is given by eq 7,21where c is the VD/1Do
= 1- &tc/co)
exp(c/co)z[l - erf(c/co)l 3000 1
c0=--
(7)
2 6 3 NRO3
acceptor concentration. The ratio of acceptor to donor fluorescence is related to this by eq 8: The donor con~D/VD’
+ VA/VA’
=1
(8)
centration, which according to eq 7 does not affect the results, was mol/L. Using both types of measurements, we found Ro = 26 A in dodecane and Ro = 28 A in cyclohexanol. This is about twice that calculated, a large discrepancy in view of the dependence of the transfer rate on the inverse sixth power of Ro. The reason is by no means obvious, and experimental work on the topic is in progress. We emphasize the importance of checking Forster radii experimentally.22 The ratio of donor to acceptor fluorescence was measured for various acceptor concentrations as shown in Figure 4. The intensity ratios were corrected for direct excitation (
