Are Aqueous Sodium Dodecyl Sulfate Micelles in the Presence of

Langmuir 1997, 13, 1957-1963

1957

Are Aqueous Sodium Dodecyl Sulfate Micelles in the Presence of Added Salt Polydisperse? A Time-Resolved Fluorescence Quenching Study with Global Analysis G. Bhaskar Dutt, J. van Stam, and F. C. De Schryver* Department of Chemistry, Katholieke Universiteit Leuven, Celestijnenlaan 200F, BE-3001 Heverlee, Belgium Received November 1, 1996. In Final Form: January 17, 1997X Aggregation numbers of aqueous sodium dodecyl sulfate (SDS) in the presence of added salt were estimated using the time-resolved fluorescence quenching method. Tris (2,2′-bipyridyl)ruthenium(II) and 1-ethylpyrene were used as probes and 9-methylanthracene, 3,4-dimethylbenzophenone, and 1-dodecylpyridinium chloride were used as quenchers. It was found that aqueous SDS micelles are monodisperse even in the presence of high salt concentrations contrary to what has been reported. Similar studies were carried out using the nonionic surfactant hexaethylene glycol mono-n-dodecyl ether (HEGDE) in water. Aqueous 33.1% (w/w) HEGDE solutions were found to be polydisperse.

1. Introduction It is well established that surfactant solutions form aggregates known as micelles.1 Their size and shape can be determined by static2-4 and dynamic light scattering techniques,5-10 NMR,11-15 and fluorescence quenching techniques.16-23 The time-resolved fluorescence quenching method is the only way to directly measure the aggregation number, as well as the dynamic properties of the aggregates and of solubilized species in the host structure. Ionic surfactants form small spherical micelles at low ionic strengths, and the micellar aggregation number is a function of the surfactant concentration.24 Addition of salt screens the electrostatic head-group repulsion beX

Abstract published in Advance ACS Abstracts, March 15, 1997.

(1) Mysels, K. J.; Princen, L. H. J. Phys. Chem. 1959, 63, 1699. (2) Emerson, M. F.; Holtzer, A. J. Phys. Chem. 1967, 71, 1898. (3) Anacker, E. W. In Solution Chemistry of Surfactants; Mittel, K. L., Ed.; Plenum: New York, 1979; Vol. I. (4) Ikeda, S.; Hayashi, S.; Imac, T. J. Phys. Chem. 1981, 85, 106. (5) Mazer, N. A.; Benedek, G. B.; Carey, M. C. J. Phys. Chem. 1976, 80, 1075. (6) Young, C. Y.; Missel, P. J.; Mazer, N. A.; Benedek, G. B.; Carey, M. C. J. Phys. Chem. 1978, 82, 1375. (7) Missel, P. J.; Mazer, N. A.; Benedek, G. B.; Young, C. Y.; Carey, M. C. J. Phys. Chem. 1980, 84, 1044. (8) Missel, P. J.; Mazer, N. A.; Benedek, G. B.; Carey, M. C. J. Phys.Chem. 1983, 87, 1264. (9) Corti, M.; Degiorgia, V. J. Phys. Chem. 1981, 85, 711. (10) Flamberg, A.; Pecora, R. J. Phys. Chem. 1984, 88, 3026. (11) Lindman, B.; So¨derman, B. O.; Wennerstro¨m, H. In Surfactant Solutions. New Methods of Investigation; Zana, R., Ed.; Marcel Dekker: New York, 1987; p 295. (12) Wa¨rnheim, T.; Henriksson, U.; So¨derman, O. In Organized Solutions; Friberg, S., Lindman, B., Eds.; Marcel Dekker: New York, 1992. (13) Nery, H.; So¨derman, O.; Canet, D.; Walderhaug, H.; Lindman, B. J. Phys. Chem. 1986, 90, 5802. (14) Ginley, M.; Henriksson, U.; Li, P. J. Phys. Chem. 1990, 94, 4644. (15) Sjo¨berg, M.; Henriksson, U.; Wa¨rnheim, T. Langmuir 1990, 6, 1205. (16) Turro, N. J.; Yekta, A. J. Am. Chem. Soc. 1978, 100, 5951. (17) Almgren, M. In Kinetics and Catalysis in Microheterogeneous Systems; Gra¨tzel, M., Kalyanasundaram, K., Eds.; Marcel Dekker: New York, 1991; p 63. (18) Almgren, M. Adv. Colloid Interface Sci. 1992, 41, 9. (19) Grieser, F.; Drummond, C. J. Phys. Chem. 1988, 92, 5580. (20) Van der Auweraer, M.; De Schryver, F. C. In Inverse Micelles, Studies in Physical and Theoretical Chemistry; Pileni, M. P., Ed.; Elsevier: Amsterdam, 1990; p 70. (21) Gehlen, M.; De Schryver, F. C. Chem. Rev. 1993, 93, 199. (22) Zana, R. In Surfactant Solutions. New Methods of Investigation; Zana, R., Ed.; Marcel Dekker: New York, 1987; p 241. (23) Zana, R.; Lang, J. J. Colloids Surf. 1990, 48, 153. (24) Bales, B.; Almgren, M. J. Phys. Chem. 1995, 99, 15153.

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tween amphiphiles within a micelle, allowing the surface area per molecule to be reduced. This gives rise to a new packing condition for the micelles with a lower surface to volume ratio.25 Hence as the concentration of the counterion is increased, these micelles grow in size and undergo a sphere-to-rod shape transition. The most widely studied system is that of aqueous sodum dodecyl sulfate (SDS) micelles2,4-9,16,26-50 with and without additives. Lianos and Zana26 measured the aggregation numbers at 0.07 M (25) Israelachvili, J. N.; Mitchell, D. J.; Ninham, B. W. J. Chem. Soc., Faraday Trans. 2 1976, 72, 1525. (26) Lianos, P.; Zana, R. J. Phys. Chem. 1980, 84, 3339. (27) Chen, J.-M.; Su, T.-M.; Mou, C. Y. J. Phys. Chem. 1980, 90, 2418. (28) Almgren, M.; Lo¨froth, J.-E. J. Colloid Interface Sci. 1981, 81, 486. (29) Almgren, M.; Lo¨froth, J.-E. J. Chem. Phys. 1982, 76, 2734. (30) Almgren, M.; Swarup, S. J. Phys. Chem. 1983, 87, 876. (31) van Stam, J.; Almgren, M.; Lindblad, C. Prog. Colloid Polym. Sci. 1991, 84, 13. (32) van Stam, J.; Brown, W.; Fundin, J.; Almgren, M.; Lindblad, C. In Colloid- Polymer Interactions; Dubin, P. L., Tong, P., Eds.; ACS Symposium Series 532; American Chemical Society: Washington, DC, 1993; p 194. (33) Croonen, Y.; Gelade´, E.; Van der Zegel, M.; Van der Auweraer, M.; Vandendriessche, H.; De Schryver, F. C.; Almgren, M. J. Phys. Chem. 1983, 87, 1426. (34) Reekmans, S.; Boens, N.; Van der Auweraer, M.; Luo H.; De Schryver, F. C.; Langmuir 1989, 5, 948. (35) Reekmans, S.; Luo, H.; Van der Auweraer, M.; De Schryver, F. C. Langmuir 1990, 6, 628. (36) Gehlen, M.; De Schryver, F. C. J. Phys. Chem. 1993, 97, 11242. (37) van Stam, J.; Wittouck, N.; Almgren, M.; De Schryver, F. C.; Miguel, M. Can. J. Chem. 1995, 73, 1765. (38) Gehlen, M. J. Phys. Chem. 1995, 99, 4181. (39) Gehlen, M.; Ferreira, M.; Neumann, M. J. Photohem. Photobiol. A 1995, 87, 55. (40) Warr, G. G.; Grieser, F.; Evans, D. F. J. Chem. Soc., Faraday Trans. 1 1986, 82, 1829. (41) So¨derman, O.; Jonstro¨mer, M.; van Stam, J. J. Chem. Soc., Faraday Trans. 1993, 89, 1759. (42) Siemiarczuk, A.; Ware, W. R.; Liu, Y. S. J. Phys. Chem. 1993, 97, 8082. (43) Gao, Z.; Wasylishen, R. E.; Kwak, J. C. T. J. Phys. Chem. 1991, 95, 462. (44) Lissi, E. A.; Abuin, E. J. Colloid Interface Sci. 1985, 105, 1. (45) Brown, W.; Fundin, J.; Miguel, M. Macromolecules 1993, 25, 7192. (46) Harrington, K.; Kaler, E.; Miller, D.; Zasadzinski, J.; Chiruvolu, S. J. Phys. Chem. 1993, 97, 13792. (47) Abrahmse´n-Alami, S.; Stilbs, P. J. Phys. Chem. 1994, 98, 6359. (48) Junquera, E.; Pen˜a, L; Aicart, E. J. Solution Chem. 1994, 23, 421. (49) Jobe, D.; Reinsborough, V.; Wetmore, S. Langmuir 1995, 11, 2476. Thuresson, K.; Nystro¨m, B.; Wang, G.; Lindman, B. Langmuir 1995, 11, 3730. (50) Quina, F. H.; Nassar, P. M.; Bonilha, J. B. S.; Bales, B. L. J. Phys. Chem. 1995, 99, 17028.

© 1997 American Chemical Society

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SDS in water in the presence of 0-0.6 M sodium chloride. They found that the aggregation number increases from 62 at 0 M NaCl to 400 at 0.6 M NaCl. Chen et al.27 determined the aggregation numbers of SDS micelles in water in the presence of sodium chloride as a function of temperature. Their method is based on the increase of self-quenching of the fluorescence of micelle-solubilized pyrene through excimer formation. They observed an increase in the aggregation number from 50 to 240 for 0-0.8 M NaCl at 35 °C. They also determined aggregation numbers in the presence of 0.5 and 0.8 M sodium chloride in the temperature region 30-70 °C and found that the micelle aggregation number decreases as the temperature is increased. The question if a growth of the micellar aggregate is coupled to a pronounced polydispersity is a matter of debate.40,42,51,52 The problem of polydispersity when using time-resolved fluorescence quenching measurements is well understood theoretically,29,52 and size polydispersity has also been reported for some systems.5,40,42,53 Using quasielastic light scattering spectroscopy, Mazer et al.5 concluded a significant degree of polydispersity in SDS micelles above a NaCl concentration of 0.45 M. From time-resolved fluorescence quenching measurements, Warr et al.40 estimated a decrease in the quencher averaged aggregation number with the quencher concentration (the aggregation number is independent of quencher concentration for monodisperse micelles) for aqueous SDS micelles in the presence of 0.475 M sodium bromide. Reekmans et al.53 studied the size distribution of cetyltrimethylammonium chloride (CTAC) in water. They observed that the system exhibits a broad polydispersity in micellar aggregation numbers at low surfactant concentration. They also found that increasing the surfactant concentration leads to a growth of smaller micelles and, thus, to a more narrow size distribution. In a recent theoretical study,51 Nagarajan commented that the need for maintaining thermodynamic consistency was overlooked while interpreting the fluorescence data. From Nagarajan’s study it was concluded that the general thermodynamic principles of self-assembly for nonionic as well as ionic surfactants rule out the possibility that monodispersed micelles could increase in their size as the total surfactant concentration is increased. These principles also rule out the possibility that the weight-average aggregation number could remain unaffected by increasing surfactant concentration when the micelles are polydispersed. Using the lifetime distribution analysis with the maximum entropy method,54,55 Siemiarczuk et al.42 estimated the polydispersity in SDS and CTAC micelles in the presence of added salt. They also claimed that other methods to evaluate time-resolved fluorescence data were unable to determine polydispersity in micellar systems. The purpose of the present investigation is to study the size distribution by time-resolved fluorescence quenching of the aggregates formed by the surfactant SDS in water in the presence of an added salt. The study is performed in a systematic way by using different probes and quenchers to rule out any specific effects due to the choice of chromophores. In this way, an answer to the question whether these aggregates are polydisperse as reported by Warr et al.40 and Siemiarczuk et al.42 or not is found. (51) Nagarajan, R. Langmuir 1994, 10, 2028. (52) Warr, G. G.; Grieser, F. J. Chem. Soc., Faraday Trans. 1 1986, 82, 1813. (53) Reekmans, S.; Bernik, D.; Gehlen, M.; van Stam, J.; Van der Auweraer, M.; De Schryver, F. C. Langmuir 1993, 9, 2289. (54) Skilling, J.; Bryan, R. K. Mon. Not. R. Astron. Soc. 1984, 211, 111. (55) Livesey, A. K.; Brochon, J. C. Biophys. J. 1987, 52, 693.

Dutt et al.

2. Theory The basic model to describe fluorescence quenching in micelles is developed by Infelta et al.56,57 and Tachiya:58-60

f(t) ) A1 exp[-A2t - A3{1 - exp(-A4t)}]

(1)

Equation 1 is valid under the assumptions that the micellar aggregates are of equal size, the probes and quenchers are distributed in a Poissonian way among the micelles, the probe is stationary in its host micelle during its excited-state lifetime, and the quenchers do not interact with each other. The parameters A1-A4 are given by the following expressions:56,57

A1 ) f(0)

(2a)

j k-kq/A4 A2 ) k0 + n

(2b)

j kq2/A42 A3 ) n

(2c)

A4 ) k- + kq

(2d)

where f(0) is the intensity at time t ) 0, k0 is the composite decay rate constant, including all relaxation paths, in the absence of added quencher, kq is the first-order rate constant for quenching by one quencher in a micelle, kis the first-order rate constant for one quencher to exit from a micelle to the bulk, and n j is the average number of quenchers per micelle. When the quenchers are immobile, i.e., kq . k-, eq 1 reduces to a simpler form

j {1 - exp(kqt)}] f(t) ) f(0) exp[-k0t - n

(3)

The aggregation number 〈a〉 is obtained from n j by

〈a〉 ) n j Sm/Qm

(4)

where Sm and Qm are micellized surfactant and micellized quencher concentrations, respectively. If the system is not monodisperse, but shows a broader size distribution, it is shown28 that the fluorescence decay still is well described by an expression like eq 1. Within each subset of the system, differing in aggregation number, the probe and quencher molecules will be distributed in a Poissonian way. The distribution of molecules between different subsets will, however, be weighted by the relative volume of each subset; i.e., for low quencher concentrations, the quencher molecules will be preferentially solubilized in the larger aggregates. The calculated aggregation numbers will in such a case be dependent on the quencher concentration and should be treated as a quencher-averaged aggregation number, 〈a〉q. From 〈a〉q it is possible to estimate a weight-averaged aggregation number, 〈a〉w, which is independent of the quencher concentration, by29,52 (56) Infelta, P. P.; Gra¨tzel, M.; Thomas, J. K. J. Phys. Chem. 1974, 78, 190. (57) Infelta, P. P.; Gra¨tzel, M. J. Chem. Phys. 1983, 78, 5280. (58) Tachiya, M. Chem. Phys. Lett. 1975, 33, 289. (59) Tachiya, M. J. Chem. Phys. 1982, 76, 340. (60) Tachiya, M. J. Chem. Phys. 1983, 78, 5282.

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〈a〉q ) 〈a〉w - 1/2σ2η + 1/6κη2 - ...

(5)

where σ2 is the variance and κ the third cumulant, giving the skewness, of the size distribution. η is given by

η ) Qm/Sm

(6)

The quantity σ/〈a〉w can be used as a polydispersity index, showing trends in size distribution. Recently, the influence of the added quencher on the estimation of the micellar aggregation numbers was discussed by Almgren et al.61 The relation between the surfactant concentration and the aggregation number estimate was discussed by Bales and Almgren.24 As in this contribution several different probe/quencher pairs were used and all SDS systems were of the same surfactant concentration, the above mentioned effect must not be taken into account. 3. Experimental Section Materials and Methods. The probes, 1-ethylpyrene (Etpy) (Molecular Probes) and tris(2,2′-bipyridyl)ruthenium(II) chloride (Ru(bpy)32+) (Fluka) were of highest available purity and were used as such. The surfactants, sodium dodecyl sulfate (SDS) (BDH, 99% purity) and hexaethylene glycol mono-n-dodecyl ether (HEGDE) (Nikko Chemicals, Tokyo, Japan) were used without further purification. The quenchers 1-dodecylpyridinium chloride (DoPyrCl) (Aldrich) and 3,4-dimethylbenzophenone (DMBP) (Acros) were recrystallized from ethanol, while 9-MeA (Kodak) was used as such. The salts NaBr (Fluka 99%) and NaCl (Aldrich 99.99%, optical grade) were also used without further purification. All samples were prepared with deionized water of Milli-Q quality. The solutions containing SDS were degassed by repeated freezepump-thaw cycles while the viscous HEGDE solutions were deoxygenated by bubbling argon gas. The probe concentration was kept low enough to avoid multiple occupancy over the micelles. All measurements were performed in a constant temperature room at 21 °C. The solutions were allowed to equilibrate for at least several hours. For measurements at elevated temperature (the system 60 mM SDS-500 mM NaCl with Etpy as probe and DoPyrCl as quencher was measured at 33 °C for solubility reasons), a standard waterbath thermostate was coupled to the cell holder of the single-photon counting equipment. Samples containing Etpy were excited at 325 nm using the frequency-doubled output of a kiton red dye laser which is synchronously pumped by an argon-ion laser. The decays were collected at 390 nm using the single-photon counting method. A repetition rate of 400 kHz was used to excite the sample. The details of the setup were described previously.62,63 Samples with the probe Ru(bpy)32+ were excited at 410 nm using the frequencydoubled output of a mode-locked titanium-sapphire laser (Spectra Physics Model 3960) which is synchronously pumped by a continuous beam-locked argon-ion laser (Spectra Physics, Model 2080). In the titanium-sapphire laser the titanium-doped sapphire crystal is pumped with the 488 nm line of the argon-ion laser and produces wavelengths 720-980 nm. The emission was monitored at 610 nm. A repetition rate of 80 kHz was used to excite the sample. All fluorescence decays were measured at magic angle (54.7°) orientation of the emission polarizer to eliminate the effects of fluorescence depolarization. All decays contained 104 peak counts and were collected in 512 channels of the multichannel analyzer. Appropriate time increments were chosen so that less than 2% of the peak counts were present in the end channels. A degassed sample of 9-cyanoanthracene in methanol (τf ) 17.3 ns) and fluoranthene in ethanol (τf ) 30.1 ns) were used as references for the deconvolution of the (61) Almgren, M.; Hansson, P.; Wang, K. Langmuir 1996, 12, 3855. (62) Boens, N.; Van den Zegel, M.; De Schryver, F. C.; Desie, G. In From Photophysics to Photobiology; Favre, A., Tyrell, R., Cadet, J., Eds.; Elsevier: Amsterdam, 1987; p 93. (63) Khalil, M. M. H.; Boens, N.; Van der Auweraer, M.; Ameloot, M.; Andriessen, R.; Hofkens, J.; De Schryver, F. C. J. Phys. Chem. 1991, 95, 9375.

fluorescence decays.64 For the HEGDE sample, a Nikon optical microscope with cross polarizers was used to examine the hexagonal, H1, and lamellar, L1, phases for birefringence. Data Analysis. Global, i.e., when several decay curves are analyzed simultaneously and with one or more parameters held common, and single curve analyses with reference convolution64 were used, and eq 3 was used to fit the experimentally measured decay curves. The goodness of the fit was judged by numerical statistical tests which include the calculation of the global reduced chi-square, χg2 and its normal deviate, Zχg2. All the global analyses were performed on an IBM RISC 6000 computer with the programs developed by Boens et al.34,65

4. Results and Discussion From a previous study,66 it is clear that the estimated aggregation numbers seem to depend to some extent on the choice of the probe/quencher combination used. Warr and Grieser66 measured the aggregation numbers of SDS micelles using Ru(bpy)32+ and modifying the probe by attaching one or two alkyl chains of varying chain lengths to one bipyridyl ligand. They obtained aggregation numbers of 57-75 for SDS micelles in water depending on the choice of the probe. The popularity of Ru(bpy)32+9-MeA probe/quencher pair is due chiefly to the long excited state lifetime of the probe. However, the association of Ru(bpy)32+ with a micelle is mainly electrostatic, which makes it only useful as probe for anionic micelles with reasonably high charge densities, such as SDS.30 Lianos and Zana26 expressed that Ru(bpy)32+-9-MeA may not be the right choice in the presence of added salt. Another probe that is most widely used is pyrene and its 1-alkyl derivatives. The reasons being its long lifetime and limited solubility in water which makes it exclusively solubilized in the micellar phase. In view of these different opinions, we have carried out the present investigation using Ru(bpy)32+-9-MeA as well as Etpy in combination with different quenchers. For the quenching of Etpy, DoPyrCl and DMBP were employed. DoPyrCl, itself being a surfactant, could in principle have an impact on the estimated micellar aggregation numbers, as well on the determination of the size distribution. The impact on the aggregation numbers, however, is negligible at low quencher concentrations. For quencher occupation numbers up to 3, only 18% of the micelles will carry five or more quenchers. At low quencher concentrations, this effect will be even lower, e.g., for n j ) 2, only 5% will have occupation numbers higher than or equal to 5. As the aggregation number of SDS micelles at high salt concentrations is in the range of 150-200, there is no need to compensate for this effect. For the determination of polydispersity, the same argumentation holds. The effect of polydispersity is most pronounced at very low quencher concentrations, and for n j e 1, virtually no micelles will carry more than two quencher molecules. Concerning the use of DMBP as fluorescence quencher, another problem has to be discussed. DMBP is known to distribute between the micelles and the aqueous bulk.31,37 This leads to, if not corrected for, an underestimation of the micellar aggregation numbers. It is, however, possible to determine the distribution constant KD and to correct the quencher concentration in the micelles, Qm, according to37 (64) Boens, N.; Ameloot, M.; Yamazaki, I.; De Schryver, F. C. Chem. Phys. 1988, 121, 73. (65) Boens, N.; Malliaris, A.; Van der Auweraer, M.; Luo, H.; De Schryver, F. C. Chem. Phys. 1988, 121, 199. (66) Warr, G. G.; Grieser, F. Chem. Phys. Lett. 1985, 116, 505.

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Table 1. Aggregation Numbers of SDS Micelles in Water Determined by Fluorescence Quenching Measurements Using the Probe/Quencher Sysem Etpy-DoPyrCl in the Presence of 0.500 M NaCla

Table 3. Aggregation Numbers of SDS Micelles in Water Determined by Fluorescence Quenching Measurements Using the Probe/Quencher System Etpy-DMBP in Presence of 0.475 M NaBra

[Q], mM

[Q]/[S]

〈a〉b

〈a〉c

〈a〉d

〈a〉e

n j

[Q], mM

[Q]/[S]

〈a〉b

〈a〉c

〈a〉d

〈a〉e

n j

0.0604 0.1804 0.3011 0.4554 0.6029 0.9047

0.0010 0.0030 0.0050 0.0076 0.0101 0.0151

144 147 154 160 158 169

160 152 157 172 166 174

154 150 154 159 159 165

148 148 157 174 165 174

0.16 0.46 0.79 1.31 1.67 2.62

0.1005 0.2031 0.2998 0.3985 0.4966 0.5989 0.6939 0.7965

0.0020 0.0041 0.0060 0.0080 0.0099 0.0120 0.0139 0.0159

139 142 141 154 150 152 167 161

144 148 148 162 155 156 170 163

141 142 139 155 151 153 166 154

142 149 149 162 154 155 170 164

0.29 0.60 0.89 1.29 1.54 1.87 2.35 2.60

a The measurements were performed at 33 °C, λ ) 325 nm, λ ex em ) 400 nm, [SDS] ) 60.0 mM, [Etpy] ) 5.5 µM. 9-Cyanoanthracene in methanol is used as reference. For the discussions and the further evaluation, the results obtained by global analysis with A2 as common parameter (in bold) were used. The quencher occupation numbers, n j , refer to this analysis. b Single curve analysis: A2 is freely adjustable and τref fixed during the analysis. c Global analysis: A2 treated as common parameter and τref fixed during the analysis. τ0 ) 217.1 ns, χg2 ) 1.29, Zχ2 ) 11.6. d Global analysis: A2 treated as common parameter and τref fixed during the analysis. kq ) 19.92 × 106 s-1, χg2 ) 1.15, Zχ2 ) 6.1. e Global analysis: A2 and A4 treated as common parameters and τref fixed during the analysis. τ0 ) 217.5 ns, kq ) 17.78 × 106 s-1, χg2 ) 1.34, Zχ2 ) 13.5.

Table 2. Aggregation Numbers of SDS Micelles in Water Determined by Fluorescence Quenching Measurements Using the Probe/Quencher System Etpy-DoPyrCl in the Presence of 0.475 M NaBra [Q], mM

[Q]/[S]

〈a〉b

〈a〉c

〈a〉d

〈a〉e

n j

0.1033 0.2019 0.3032 0.4017 0.5025 0.6010 0.7034 0.8019

0.0021 0.0040 0.0061 0.0080 0.0100 0.0120 0.0140 0.0160

160 157 162 164 162 161 163 166

164 165 168 168 167 165 165 166

154 155 160 162 162 162 164 166

163 165 169 168 167 164 164 165

0.34 0.67 1.02 1.35 1.68 1.98 2.31 2.65


Qm )

QtSmKD SmKD + 1

(7)

where Qt is the total quencher concentration. The distribution constant KD for 50 mM SDS and 500 mM NaCl was determined67 to be 3850 M-1, which means that 99.6% of the DMBP molecules will be present in the micellar aggregates under the present conditions. Thus, for the systems studied in this contribution, no correction for the DMBP distribution has to be made. The probe Ru(bpy)32+ is hydrophobically and electrostatically bound to the anionic SDS micelles. At high salt concentrations, the screening of the charges could lead to a distribution of the probe between the micelles and the bulk. In such a case, the fluorescence decay from a sample without any added quencher would most probably be biexponential, unless the relaxation kinetics is equal for the two possible distributions. Furthermore, a situation where the decay kinetics is equal would lead an under(67) van Stam, J.; So¨derholm, H. Unpublished results.


Table 4. Aggregation Numbers of SDS Micelles in Water Determined by Fluorescence Quenching Measurements Using the Probe/Quencher System Ru(bpy)32+-9-MeA in Presence of 0.545 M NaBra [Q], mM

[Q]/[S]

〈a〉b

〈a〉c

〈a〉d

〈a〉e

n j

0.1076 0.2127 0.3186 0.4137 0.5114 0.6024 0.7107 0.8040

0.0022 0.0043 0.0064 0.0083 0.0102 0.0121 0.0142 0.0161

163 152 173 172 170 174 161 156

169 164 176 177 169 172 158 155

148 147

168 167

165 170 170 165

178 167 171 152

0.37 0.70 1.13 1.46 1.73 2.08 2.25 2.49

a The measurements were performed at 21 °C, λ ) 410 nm, λ ex em ) 610 nm, [SDS] ) 50.0 mM, [Ru(bPy)32+] ) 47 µM. Fluoranthene in ethanol is used as reference. For the discussions and the further evaluation, the results obtained by global analysis with A2 as common parameter (in bold) were used. The quencher occupation numbers, n j , refer to this analysis. b Single curve analysis: A2 is freely adjustable and τref fixed during the analysis. c Global analysis: A2 treated as common parameter and τref fixed during the analysis. τ0 ) 748.3 ns, χg2 ) 1.14, Zχ2 ) 6.2. d Global analysis: A4 treated as common parameter and τref fixed during the analysis. kq ) 5.00 × 106 s-1, χg2 ) 1.28, Zχ2 ) 11.3. e Global analysis: A2 and A4 treated as common parameters and τref fixed during the analysis. τ0 ) 738.5 ns, kq ) 4.88 × 106 s-1, χg2 ) 1.83, Zχ2 ) 33.3.

estimation of the quencher occupancy number n j and, consequently, to an overestimation of the micellar aggregation. Comparing the results obtained with Ru(bpy)32+ as probe with those when Etpy was used as probe, would immediately reveal such an effect. As this is not the case (vide infra), it can be concluded that Ru(bpy)32+ is bound to the SDS micelles under the present experimental conditions. 4.1. SDS-Salt-Water System. Fluorescence decays were measured using different probe-quencher combinations in SDS-salt-water systems, and the results are summarized in Tables 1-4. The concentration of SDS is 50.0 mM in all the systems involving NaBr, and unless specified, the [NaBr] is 0.475 M. Four different kinds of analyses, based on eq 1, were performed for each system. First, single curve analysis was performed with the parameters A1-A4 freely adjustable. This was done to establish, in a first approximation, if there occurred any quencher migration in the system. From eq 2b, it is clear that a detectable quencher migration leads to increasing

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Langmuir, Vol. 13, No. 7, 1997 1961

Figure 1. Fluorescence decays from the different systems investigated: (a) Etpy/DoPyrCl in SDS micelles in presence of [NaCl] ) 0.500 M; (b) Etpy/DoPyrCl in SDS micelles in presence of [NaBr] ) 0.475 M; (c) Etpy/DMBP in SDS micelles in presence of [NaBr] ) 0.475 M; (d) Ru(bpy)32+/9-MeA in SDS micelles in presence of [NaBr] ) 0.545 M; (e) Etpy/DMBP in HEGDE micelles. For each system, the decay curves have an increasing amount of quencher from the top curve to the bottom curve. The top curve is measured in the absence of an added quencher, while the others have the quencher concentrations given in Tables 1-5, respectively.

values of A2 with increasing quencher concentration. One must remember, however, that a single curve analysis in most cases is insufficient to precisely estimate the kinetics. Second, a global analysis with A2 held common for the whole decay surface was executed. This analysis, yielding the same values of A2 as in the preceding step and with good statistics, proves that there is indeed no quencher migration in the studied systems. Third, global analysis with A4 as common parameter was performed. In polydisperse systems, with stationary quenchers, A4 will be a function of the quencher concentration, due to the higher probability of dissolving a quencher molecule in a larger micelle at low quencher concentrations. For stationary quenchers, A4 equals the quenching rate kq. kq is roughly proportional to 1/〈a〉, so keeping A4 common in the evaluation of a polydisperse micellar system will lead to unacceptable values of the statistical parameters. Another consequence is that an averaged value on kq will be estimated, leading to that no polydispersity in the aggregation numbers will be detected, even if present. Also

this analysis yielded good statistics for all the SDS/salt/ water systems studied. Finally an analysis with both A2 and A4 was performed, also yielding results in full accordance with the results obtained with the other evaluation methods. 4.1.1. 1-Ethylpyrene/1-Dodecylpyridinium Chloride/NaCl. Figure 1a gives the fluorescence decays of Etpy quenched by DoPyrCl in SDS micelles in the presence of 500 mM NaCl. For this system, the SDS concentration was 60.0 mM and the temperature 33 °C. The results are shown in Table 1. The measurements were performed at six different quencher concentrations to cover a wide range of η, i.e., the values of η are in the range of 0.001-0.015. The quencher-averaged aggregation number did not decrease with increasing quencher concentration, thereby indicating that there is no polydispersity in the system and the average aggregation number is found to be 164 ( 9. This aggregation number agrees well with that determined by Warr et al. for a similar system, i.e., 162 for 50 mM SDS and 0.424 M NaCl.40 On the contrary,

1962 Langmuir, Vol. 13, No. 7, 1997

Warr et al. observed polydispersity effects, σ/〈a〉 ) 0.6 in their study, while no polydispersity at all is observed in the present system. The probable explanation for this discrepancy will be discussed below. 4.1.2. 1-Ethylpyrene/1-Dodecylpyridinium Chloride/NaBr. In the preceding studies NaCl was used and no polydispersity was observed. Since NaBr is known to interact stronger than NaCl with micelles,40 we carried out the remainder of this investigation using NaBr. It was also possible to perform the measurements at a lower temperature, i.e., 21 °C. Figure 1b gives the fluorescence decays of Etpy quenched by DoPyrCl in SDS micelles in the presence of NaBr. The results of this study are shown in Table 2. The η range was from η ) 0 to η ) 0.016. The exchange of added salt from NaCl to NaBr does not lead to any polydispersity. The estimated aggregation numbers remain constant over the whole η range with an average of 166 ( 2. This result, an unaffected aggregation number when NaCl is replaced by NaBr, is in contrast with the reults of Warr et al.40 First they found a polydispersity of the same magnitude as when NaCl was added, i.e., σ/〈a〉w ) 0.6, and second, they estimated the weightaveraged aggregation number to be 241. 4.1.3. 1-Ethylpyrene/3,4-Dimethylbenzophenone/ NaBr. In order to rule out the possibility of a specific effect due to the choice of probe and quencher, measurements were also performed with other probes and/or quenchers. Figure 1c gives the fluorescence decays of Etpy quenched by DMBP in SDS micelles in the presence of NaBr. The use of DMBP as quencher of Etpy instead of DoPyrCl yielded more or less identical results, Table 3, and the average aggregation number was estimated to be 156 ( 9. 4.1.4. Ruthenium Tris(bipyridyl) Chloride/9-Methylanthracene/NaBr. Changing the probe from Etpy to Ru(bpy)32+ also changes the time-scale studied. The very long excited-state lifetime of Ru(bpy)32+, approximately 720 ns, allows a better study of larger aggregates. As fluorescence quenching in micelles is a diffusioncontrolled process, a long excited-state lifetime allows a large volume to be probed. The quencher 9-MeA is known to be a very efficient fluorescence quencher.28,40 Furthermore, this probe/quencher pair is the same that Warr et al. used in their study of micellar polydispersity.40 Figure 1d gives the fluorescence decays of Ru(bpy)32+ quenched by 9-MeA in SDS micelles in the presence of 0.545 M NaBr. The results are compiled in Table 4. Even if the quality of the fits are slightly lower than those for the preceding, due to the very high ionic strength, it can be concluded that also this system is monodisperse and with micellar aggregates of approximately the same size, i.e., 〈a〉 ) 168 ( 8. The aggregation numbers of the four systems are given as a function of η in Figure 2a with the inserted lines indicating their algebraic average. 4.1.5. Comparison with Literature Data. The present results are not in agreement with the results of Warr et al.40 and Siemiarczuk et al.,42 who claim that these systems are polydisperse. Some of the plausible reasons for this discrepancies have to be highlighted. Warr et al.40 used Ru(bpy)32+ which has a very long excitedstate lifetime (τ0 ) 725 ns), but no information is given about the choice of the time increment, ∆t, used in the multichannel analyzer, MCA; hence no information on the total time-window for the decay is given. A biexponential decay function was used, and the unquenched part of the decays, obtained at long times, was extrapolated back to t ) 0 to determine n j . If the total time-window is too narrow, the measured decays are not complete and the unquenched part will not develop. In this case, the n j values at higher Qm are underestimated, leading to a

Dutt et al.

Figure 2. (a) q vs η for SDS micelles in water at different ionic strengths, as determined from time-resolved fluorescence quenching data when different probe/quenchers pairs were employed: b, Etpy-DoPyrCl/[NaCl] ) 0.500 M; 2, EtpyDoPyrCl/[NaBr] ) 0.475 M; 1, Etpy-DMBP/[NaBr] ) 0.475 M; 9, Ru(bpy)32+-9-MeA/[NaBr] ) 0.545 M. Inserted lines give the algebraic means for each system. (b) Plot of q vs η for 33.1% (w/w) HEGDE in water. The inserted line shows the result of a fit of eq 5 to data. The estimated weight averaged aggregation number, w, is 503 and σ ) 200. See text for further details.

pseudo-polydispersity. At low quencher concentrations there is very little quenching, which can lead to large errors in the calculation of n j by this method, and hence, the estimated aggregation numbers will be very uncertain. In the present measurements we used a time-window of 3 µs when measuring the decays of Ru(bpy)32+ and the unquenched decay was well developed; see Figure 1d. In the present analysis, eq 1 was used to fit the data and no extrapolation was done. The use of global instead of single curve analysis increases the certainty of the determined aggregation numbers at very low Qm. 4.2. Hexaethylene Glycol Dodecyl Ether (HEGDE)/ Water System. In order to claim that a nonobservation of a certain event is real, one must also show the ability to observe this event when it occurs. In other words, to prove that the evaluation in the present study shows that SDS forms monodisperse micelles even at high ionic strengths, we must also show that it is possible to determine a real polydisperse system. For this purpose, the aqueous HEGDE system was investigated. This surfactant, with a well-studied phase diagram,68 also offers another option: to verify that eq 1 can be used for polydisperse micellar systems, in spite of the doubts expressed by Siemiarczuk et al.42 From the phase diagram (68) Mitchell, D. J.; Tiddy, G. J. T.; Waring, L.; Bostock, T.; McDonald, M. P. J. Chem. Soc., Faraday Trans. 1 1983, 79, 975.

Micelle Studies

Langmuir, Vol. 13, No. 7, 1997 1963

Table 5. Aggregation Numbers of 33 wt % HEGDE Micelles in Water Determined by Fluorescence Quenching Measurements Using the Probe/Quencher System Etpy-DMBPa [Q], mM

[Q]/[S]

〈a〉b

〈a〉c

〈a〉d

〈a〉e

n j

1.1242 2.1915 3.2821 4.1202 5.0114 6.1078 7.1173

0.0010 0.0020 0.0030 0.0038 0.0046 0.0056 0.0065

488 450 444 431 438 395 396

488 460 444 434 440 397 399

121 140 146 160 153 156 156

389 404 405 412 440 418 422

0.50 0.92 1.33 1.63 2.00 2.21 2.58

a The measurements were performed at 21 °C, λ ) 325 nm, λ ex em ) 400 nm, [HEGDE] ) 33.1% (w/w), [Etpy] ) 6.2 µM. 9-Cyanoanthracene in methanol is used as reference. For the discussions and the further evaluation, the results obtained by global analysis with A2 as common parameter (in bold) were used. The quencher occupation numbers, n j , refer to this analysis. b Single curve analysis: A2 and τref fixed during the analysis. c Global analysis: A2 treated as common parameter and τref fixed during the analysis. τ0 ) 212 ns, χg2 ) 1.21, Zχ2 ) 9.1. d Global analysis: A4 treated as common parameter and τref fixed during the analysis. kq ) 6.7 × 106 s-1, χg2 ) 1.10, Zχ2 ) 4.3. e Global analysis: A2 and A4 treated as common parameters and τref fixed during the analysis. τ0 ) 211.1 ns, kq ) 2.86 × 106 s-1, χg2 ) 1.29, Zχ2 ) 12.8.

of aqueous HEGDE,68 it has been established that a transition from a lamellar, L1, to a hexagonal, H1, phase occurs at around 33% (w/w) of HEGDE at room temperature. Different compositions around 33% (w/w) of HEGDE in aqueous solutions were examined for birefringence with an optical microscope equipped with cross polarizers. The phase transition from the birefringent H1 to the isotropic L1 phase was determined at 33.1% (w/w). At this concentration, there is a narrow region where the two phases coexist, leading to a highly polydisperse system. Figure 1e gives the fluorescence decays of Etpy quenched by DMBP in HEGDE aggregates. As we are in a phase-transition region, several different kinds of aggregates are present, of which the relative contribution depending on temperature. The decays in Figure 1e are characteristic for a system of rodlike micelles, from which it can be concluded that they are dominant in the present case. It has been shown that eq 1 is not applicable to fluorescence quenching in one-dimensional systems.69 If applying eq 1 to a polydisperse system of rodlike micelles, the effects will be a highly underestimated weightaveraged aggregation number, 〈a〉w, and a highly underestimated width, σ, of the size distribution. Nevertheless, this procedure will show that the micelles are large and polydisperse. As the purpose of this study is to investigate aqueous SDS micelles in the presence of salt, and the aqueous HEGDE system is only used in order to prove the capability of determining the polydispersity when present, eq 1 was used for the evaluation of the decays of Figure 1e. Keeping in mind the short-comings of this method, (69) Almgren, M.; Alsins, J.; Mukhtar, E.; van Stam, J. J. Phys. Chem. 1988, 92, 4479.

the results are underestimated. Nevertheless, the results, compiled in Table 5, clearly show that this system is polydisperse. A plot of 〈a〉q vs η, Figure 2b, and applying eq 5, yields the weight averaged aggregation number 〈a〉w ) 503 and the variance, σ ) 200. These results prove that the use of eq 1 will reveal micellar size polydispersity if present and justify the conclusion that the aqueous SDS-salt systems discussed above are not polydisperse to a significant extent. 4.3. Thermodynamics of Ionic Micellar Systems. In a careful thermodynamic treatment, Nagarajan showed that (i) monodispersed micelles remain monodispersed and with the same aggregation number when increasing the surfactant concentration and (ii) polydispersed micelles will grow in size upon increasing the surfactant concentration. Our results seem virtually to contradict Nagarajan’s thermodynamic treatment. For initially small spherical micelles with low size polydispersity, however, it is likely that the polydispersity remains more or less unchanged upon increasing 〈a〉w, at least as long as the micelles stay spherical or nearly spherical. Evidently, this is the case for the SDS systems investigated, and the present results can be regarded as thermodynamically consistent. 5. Conclusions From time-resolved fluorescence quenching measurements of aqueous SDS micelles, with Ru(bpy)32+ and Etpy as probes and 9-MeA, DMBP, and DoPyrCl as quenchers, the micellar aggregation numbers were determined. For all the systems studied, higher aggregation numbers were obtained for the micelles as compared to what is found for the corresponding system without added salt. Furthermore, the micelles are virtually monodisperse, even at high ionic strengths, in contradiction to what is reported by others.5,40,42 With the same methods, also aqueous 33.1% (w/w) HEGDE was investigated. For this system, a pronounced polydispersity was observed, and it was shown that the model proposed by Infelta et al.56,57 and Tachiya58-60 is suitable for the evaluation of time-resolved fluorescence quenching data from polydisperse systems of spherical micelles, in spite of the doubts expressed by Siemiarczuk et al.42 Acknowledgment. The authors wish to thank Steven De Backer, Wouter Verbouwe, Herman Faes, and Anton De Gezelle for their assistance with single-photon counting measurements. Professor M. Van der Auweraer is thanked for a fruitful discussion. G.B.D. and J.v.S. thank KUL for postdoctoral fellowships. The continuing support of the Belgian National Fund for Scientific Research (FWO) and the Ministry of Scientific Programming (DWTC) through IUAP-III-040 and IUAP-II-16 is gratefully acknowledged. LA9610617

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