Langmuir 1 9 9 S , l l , 3595-3597
3595
Notes Aggregation Numbers of Micelles in Semidilute Solutions Jill M. Biltzt and Michael R. Fisch*J
Department of Chemistry and Department of Physics, John Carroll University, University Heights, Ohio 44118 Received October 11, 1994. I n Final Form: May 30, 1995
Introduction Micelles are self-assembled aggregates of surfactant molecules in solution. Under appropriate surfactant and solution conditions the micelles form one-dimensional rodlike structures, similar to flexible linear polymers, which have been of continuing interest to the scientific community.'-15 Very dilute solutions containing flexible rodlike micelles are considered to be in the dilute solution regime. In this concentrationregime the solution consists of solvent (including monomers and often added electrolytes) and very weakly interacting micelles. However, upon adding more surfactant or changing solvent conditions the micelles can become sufficiently large and/or concentrated that they form transient networks of overlapping micelles. A solution which contains a small volume fraction of surfactant yet consistsof such networks of overlapping micelles is called a semidilute solution. The concentration where the micelles first form these networks, which in practice may be rather low (on the order of a few weight percent), may be obtained experimentally using a variety of techniques.16J7 In recent years there has been increased interest in the study of semidilute micellar solutions and the crossover from dilute to semidilute solution behavior. There have
* Author to whom correspondence should be addressed. Department of Chemistry.
* Department of Physics.
(1)Puwada, S.;Blankschtein, D. J.Chem. Phys. 1990,92,3710, and references therein, especially refs 1-8. (2)Israelachvili, J. N.; Mitchell, D. J.;Ninham, B. W. J.Chem. SOC., Faraday Trans. 2 1976,72, 1525. (3)Israelachvili, J. N.Intermolecular and Surface Forces;Academic: New York, 1985. (4)Young, C. Y.; Missel, P. J.;Mazer, N. A.; Benedek, G. B.; Carey, M. C. J. Phys. Chem. 1978,82,1375. ( 5 ) Missel. P. J.: Mazer. N. A.: Benedek. G. B.; Young, - C. Y.: Carey, M. C. J. Phys. Chem. 1980,84,1044. (6)Missel, P. J.;Mazer, N. A.; Benedek, G. B.; Carey, M. C. J.Phys. Chem. 1983,87,1264. (7)Porte, G.;Appell, J.; Poggi, Y. J. Phys. Chem. 1980,84,3105. (8)Tanford, C. The Hydrophobic Eficect;Wiley: New York, 1980. Also see Mittal, K. L.,Ed.; Micellization,Solubilization, and Microemulsions; Plenum: New York, 1977;Vols. 1 and 2. (9)Van De Sande, W.; Persoons, A. J. Phys. Chem. 1985,89,304. (10)Imae, T.; Ikeda, S. J. Phys. Chem. 1986,90,5216. Imae, T.; Ikeda, S. Colloid Polym. Sci. 1987,265,1090. (11)Nagarajan, R.;Ruckenstein, E. J. Colloid Interface Sci. 1977, 60, 221;1979,71, 580. (12)Missel, P. J.;Mazer, N. A,; Carey, M. C.; Benedek, G. B. J.Phys. Chem. 1989,93,8354. (13)Mukejee, P.J. Phys. Chem. 1972,76, 565. (14)Ben-Shaul, A,; Gelbart, W. M. J. Phys. Chem. 1982,86,316. Also see Gelbart, W.; Ben-Shaul, A.; McMullen, W. E.; Masters, A. J. Phys. Chem. 1984,88,861. (15)Mishic, J. R.; Fisch, M. R. J. Chem. Phys. 1990,92,3222. (16)Cates, M.E.; Candau, S. J. J. Phys.: Condens. Matter 1990,2, 6869,and references therein. Also see Candau, S. J.;Hirsch, E.; Zana, R. In Physics of Complex and Supermolecular Fluids;Safran, S . A., Clark, N. A., Eds.; Wiley: New York, 1987;p 569. (17)Kole, T.M.; Richards, C. J.;Fisch, M. R. J. Phys. Chem. 1994, 98,4949.
been several reasons for this interest. First, the concentration at which this change in solution behavior occurs is typically rather low; for this reason solutions may, unbeknownst to the practitioner, be in the semidilute solution regime-this will have profound effects on the concentration dependence of many physical properties. Second, as discussedin some recent work,16this may have an impact on phase transitions because the crossover concentration,from dilute to semidilute solutionbehavior, may be very similar to the "critical" concentration of these solutions. Third, this is of significance because large micelles can form two types of nondilute solutions: the isotropic semidilute solution which occurs in solutions of flexible micelles and the anisotropic nematic liquid crystalline phase which occurs in solutions of sufficiently rigid micelles. These two phases have very different physical properties.lg One physical property ofmicellesthat is ofgreat interest is the mean number of monomers in a micelle, or mean aggregation number. Generally this quantity is obtained from osmoticpressure measurements20*21 and either static or dynamic light scattering measurement^.^^^^^ Osmotic pressure and light scattering techniques can be accurate and useful for determining aggregation numbers only in dilute solutions where the micelles are weakly interacting. Furthermore, because micellar systems are self-aggregating systems, one cannot extrapolate to zero or even low concentration to determine the appropriate aggregation number; one o h n must determine an "effective" aggregation number that has the effects of micellar interactions included in its determination. In fact, these techniques determine different average aggregation numbers, osmotic pressure measurements determine the weight average aggregation number,21while light scattering determines the z-average aggregation number. Dynamic light scattering, with models for the micellar structure, has also been used to determine the mean aggregation number of the micelles. In this technique the mean aggregation number is obtained from the measured mean hydrodynamic radius by comparing the measurement to a theory that predicts mean hydrodynamic radius as a function of aggregation n ~ m b e r . ~ - ~This J ~ Jtechnique ~ is also susceptible to possible misinterpretation due to micellar i n t e r a c t i ~ n s . ~Thus, J ~ the often used techniques are not particularly good choices for the present study in which stronglyinteracting micelles are of interest and the effects of micellar growth and interaction cannot be cleanly separated. The aggregation number of micelles in such systems should be determined using techniques which probe local properties of the micelles. Techniques such as fluorescencespectroscopy24~25 and very recently Fourier (18)Carale, T. R.;Blankschtein, D. J. Phys. Chem. 1992,96,459. (19)Edwards, S. F.;Doi, M. The Theory of Polymer Dynamics; Claredon, Oxford University Press: New York, 1986. (20)See for instance: Attwood, D.; Elworthy, P. H.; Kayne, S. B. J. Phys. Chem. 1970,74, 3529. (21)Puwada, S.;Blankschtein, D. J. Phys. Chem. 1989,93,7753. (22)Mazer, N. A. In Dynamic Light Scattering; Pecora, R., Ed.; Plenum: New York, 1985;p 305. (23)Magid, L.In Dynamic Light Scattering The method and some applications; Brown, W., Ed.; Oxford University Press: Oxford, 1993; p 554. (24)Zana, R.;Weill, C. J. Phys. Lett. 1986,46, L-953. (25)Makhloufi, R.; Hirsch, E.; Candau, S. J.; Binana-Limbele, W.; Zana, R. J. Phys. Chem. 1989,93,8095.
0743-746319512411-3595$09.00/0 0 1995 American Chemical Society
Notes
3596 Langmuir, Vol. 11, No. 9, 1995
transform IR spectroscopyz6which probe local properties have also been used to determine the mean aggregation number of micelles in dilute solutionsof micelles. Because these are local probes, they are not as susceptible to intermicellar interactions as light scattering or osmotic pressure which measure collective properties. However, a possible problem with fluorescent probes is that they may affect the aggregation number; for this reason, this was not the technique of choice in this study. IR spectroscopy of aqueous solutions is difficult because of water's large absorption in the IR region. Hence this technique, while viable, was not explored in the present study; rather we used Raman spectroscopy to elucidate the aggregation number of the micelles. The purpose of this note is to present the results of measurements of Raman line intensities from dilute and semidilute solutions of sodium dodecyl sulfate, SDS, in NaCI-H20 and to show how these data correlate with the mean aggregationnumbers (determinedusing quasielastic light scattering) of the micelles in dilute solutions. Then, using the dilute solutions as a template, the data in the semidilute regime are analyzed. Given this interpretation, the primary result of this study is that the aggregation number in semidilute solutions is substantially greater than that predicted by models that explain the data in the dilute solution regimes and that Fourier transform Raman spectroscopy may be used to determine aggregation numbers in these systems.
Experimental Materials, Measurements, and Methods Materials. The SDS was obtained from Sigma Chemical, electrophoresis grade, and used without further purification. The solutions were prepared using Red Label deionized water and ACS approved grade NaC1. All samples were freshly prepared before the start of an experiment. Experimental Technique and Equipment. The spectrometer, a Perkin-Elmer 1700x near-IR FT-Raman spectrometer uses a YAG laser and is computer controlled. The runs were made using the following instrumental parameters: 1 W laser power, 1200 scans, a resolution of 4 cm-l, and a wavelength range of 1000-4000 cm-'. A near-infrared quartz cuvette was used for all measurements. Measurements were made at the following temperatures and concentrations: 35 and 40 "C, 1.0 M NaC1-H20 solutions. The followingweight concentration of SDS were used: 0.5,1.0,2.0,4.0, and 8.0%. We found that 1200 scans in this range were necessary to obtain satisfactory signal to noise and such a large wavelength range was desirable in a search for Raman peaks which correlated with aggregation number. All spectra are difference spectra; that is the difference between the recorded spectra with SDS in solution and the solvent without SDS. This was done to eliminate the rather large, wide peaks observed near 1650 cm-' and an even larger peak centered near 3300 cm-l. Further details of the experimental technique are available e l s e ~ h e r e . ~ ~
Results The difference spectra were analyzedto determine shifts in peak position and amplitude with temperature and concentration of SDS. There appeared to be a very slight shift in the peak wavelengths of some peaks with concentration of SDS and temperature. However, this shift was neither systematic nor reproducible. Significantly more testing is needed before one can determine if this slight shift can be related to the mean aggregation number of the micelles. However, the intensity of several peaks, in particular those near 1064,1305,and 1440cm-l, (26)This area is reviewed in the followingFourier Transform Infrared Spectroscopy in Colloid a n d Interface Science; Scheuing, D. R., Ed., American Chemical Society: Washington, DC, 1991. (27) Biltz, J., M.S.Thesis John Carroll University, 1994.
l ~ ' " ' ' " ' " " " " ' ' ' ~
1100
1300
1500
1700
1900
2100
2300
Number Average Aggregation Number
Figure 1. Peak height of three Raman lines versus aggregation number in the dilute solution regime: 0, 1065 cm-l; 0,1305 cm-1; 0, 1441 cm-l. The peak height is in arbitrary units. showed a systematic increase in amplitude that in dilute solutions could be well correlated with mean aggregation numbers predicted by the theory of Missel et aL5v6 We
believe that this amplitude effect is not simply the result of increased concentration of surfactant for two reasons. First, the peak heights scale linearly with the square root of the concentration rather than as the concentration. Second, linear fits of peak height versus aggregation number were quite good straight lines (the correlation R obtained values 20.97)for these three spectral lines. While a value of R near 1 is indicative of strong correlation, it should be noted that it does not indicate causality and as such the followinginterpretation is provisional. A representative set of data showing the peak height dependenceon the predicted aggregation number is shown in Figure 1. The data are limited to two temperatures and the relatively small number of concentrationsbecause these temperatures are above the critical micelle temperature; hence the micellar phase is stable, and both the concentrations and the temperature are in ranges where there is sufficient micellar growth to study the desired effect. In the dilute solution regime, when the surfactant concentration is much greater than the critical micelle concentration, the theory of Missel et al.5,6predicts the number average aggregation number, n, = xm, where x is the mole fractionof SDS. The proportionality coefficient in the above expression depends on temperature and electrolyte concentration and was calculated from the data in these papers. We assume that the same linear relationships, between peak height and mean aggregation number, are valid in the semidilute regime. The alternate assumption that this is not the case led to several inconsistentinterpretations of these results. For example, under this alternate assumption different Raman lines predicted substantially different aggregation numbers in both the dilute and semidilute solutionregimes. Further, the quality of fit, as indicated by R values, and predictive value of the fits were substantially reduced in both solution regimes under this assumption. The raw data are summarized in Table 1. Under the assumption that there is a linear relationship between the peak height of the Raman lines and the number average aggregation number of the micelles, we determined that the mean number average aggregation number in the semidilute solution regime, at 35 "C and a SDS concentration of 4%, is 3300 f 400,while at a concentration of 8% it is 6500 f 1100. At 40 "C the correspondingnumbers are 3500 f500 and 6400 f 1000. (28)See for instance, Baird, D. C. Experimentation; F'rentice Hall: Englewood Cliffs, NJ, 1988.
Notes
Langmuir, Vol. 11, No. 9, 1995 3597 Table 1. Raw Data from This Experiment"
conc of SDS (g of SDS/100 g of solution)
1064 cm-'
0.5 1 2 4 8 a
8000
6
7000
.-6
6000
e
5000 c1 0.
=z
4000
a, 0.
?
2 i
1440 cm-'
1064 cm-l
T=40"C 1305 cm-'
1440 cm-1
1.52 2.94 4.10 6.38 13.52
2.58 3.19 5.45 9.77 21.01
2.32 4.44 6.12 14.32 28.36
1.21 2.18 2.10 7.11 13.89
1.91 3.78 4.11 11.07 20.82
1.42 4.0 7.4 13.32 27.83
The entries in the table are normalized intensities in arbitrary (normalized) units. * Raman line,
5
z
T=35"C 1305 cm-l
3000
I i F
2000
.a
$
tions. The second is that by using a theory that describes dilute solutions, we found a linear relationship between the mean aggregation number and the peak height in this solution regime. Using this analysis, we found that in the semidilute solution regime the number average aggregation number, n,, is independent of temperature, at least for the two temperatures studied, but still a strong function of concentration. Furthermore, the aggregation number thus determined is higher than that predicted based on extrapolations of the theory that fits the data in the dilute solution regime. Such an increase in n, is predicted for the transition from isotropic to nematic micellar liquid crystal t r a n ~ i t i o n However, .~~ we know of no predictions of a similar increase in aggregationnumber in semidilute isotropic solutions.
1000
Z
0
1
2
3
4
5
6
7
8
Consnetration (MassZ)
Figure 2. Number average aggregation number versus concentration: 0, T = 35 "C; 0,T = 40 "C.
The aggregationnumbers determined using the present are shown in Figure 2,which is a graph Of the number average aggregationnumber versus concentration of SDS for the two temperatures studied. The lines in this figure are the predictions of the theoretical form that is valid for dilute solutions.
Conclusions There are two conclusions from this studv. The first is aggregation number of SDS micelles in Nac
Acknowledgment. This work was supported by NSF Grant NSF DMR-9321924. We also thank fiofessors William Weaver and Nick Baumgartner for their interest in this project. LA9407931
