In the Laboratory
Micellar Aggregation Numbers—A Fluorescence Study Jan van Stam, Sigrid Depaemelaere, and Frans C. De Schryver Departement Scheikunde, Division of Photochemistry and Spectroscopy, Katholieke Universiteit Leuven, Celestijnenlaan 200F BE-3001 Heverlee, Belgium Microheterogeneous systems play an important role in nature—for example, in photosynthesis and many other processes in living cells. For applied chemistry such systems are of great importance as well; they are found, for example, in paints, detergents, and pharmaceuticals. The importance of microheterogeneous supramolecular systems (e.g., micellar systems) validates their introduction to chemistry students, as exemplified by some recent contributions (1–3). The picture of the micellar entity presented to the students, however, is often quite obscure. This points to the need for a more consistent introduction before the experimental work can start.1 In this contribution we will show how we present microheterogeneous supramolecular systems, such as micelles, to our students, and how we experimentally unravel the influence of the hydrocarbon chain length and the effect of added salt on the micellar aggregation number for ionic surfactant molecules. We will also discuss the necessity of validating the underlying assumptions when applying a certain model to experimental data, and what the result could be if one or more of the assumptions are not fulfilled. This laboratory experiment was tested with good results by fourth-year students following the chemistry program at the K. U. Leuven 1995/96. Surfactants and Micelles2 Ionic surfactants are amphiphilic molecules with a hydrophilic charged head-group and a hydrophobic hydrocarbon tail (Fig. 1). When dissolved in aqueous media, the salt (i.e., surfactant and counter-ion) dissociates into the bulk. If the tail is not too long, the driving force for solvation of the head-group will be strong enough to dissolve the whole molecule, even though the tail is not soluble in water. Owing to electrostatic repulsion between the head-groups, a homogeneous solution with dissolved surfactant molecules is obtained. Increasing the surfactant concentration results in two different effects. First, the increased surfactant concentration leads to an increased ionic strength of the bulk. This in turn causes a decrease in the electrostatic repulsion between the head-groups due to screening of the charges. Second, an increase in the surfactant concentration is unfavorable for the hydrophobic tails, which on their own do not dissolve in water. The latter effect works against dissolving hydrophilic ionic head-group
hydrophobic hydrocarbon tail Hydrophobic hydrocarbon tail
counterion
Figure 1. Schematic picture of an ionic surfactant molecule and the micelle it forms.
more surfactant molecules. Eventually, the driving force for dissolution will be completely balanced by the forces working against the dissolution of the hydrophobic tails. At this moment, two different scenarios are possible: either, if the hydrocarbon chain-length is long enough, a macroscopic phase separation will appear, or micelles will be formed. In the latter case, this special concentration is a parameter specific for each surfactant and it is called the critical micelle concentration, the cmc. It is worthwhile to stress that micelle formation is not a macroscopic phase separation, but the formation of a thermodynamically stable, microheterogeneous supramolecular system, with surfactant molecules aggregated in micelles dissolved in the aqueous bulk. Another characteristic property of a surfactant is its micellar aggregation number. This value, giving the average number of surfactant molecules in the micelle, depends on the hydrocarbon tail length, the kind of counter-ion, and the ionic strength (as does also the cmc). For the dependence of the micellar aggregation number on the hydrocarbon tail length, both theories and experimental results are available. Nagarajan and Ruckenstein have thoroughly treated the theory of surfactant aggregation from a thermodynamic point of view (4). The molecular volume of the hydrocarbon tail with the number of carbon atoms equal to nC can be calculated as νtail = νCH3 + (nC – 1) νCH2
(1)
At room temperature, the volume of a methyl and a methylene group can be approximated with (4) νCH3 = 54.6 Å3
(2)
νCH2 = 26.9 Å3
Tanford (5) has given an empirical formula for the calculation of the hydrocarbon tail length ltail: ltail = 1.50 + 1.26nC Å
(3)
Assuming the micellar aggregate to be spherical with a radius equal to ltail allows the calculation of the micellar volume: 3
V mic =
4π l tail 3
(4)
From the micellar and molecular hydrocarbon tail volumes, the micellar aggregation number < a > can be approximated as V < a >app = mic (5) νtail or, assuming sufficiently large nC,
< a >app =
4π 1.50 + 1.26n C
3
3 νCH + n C – 1 νCH 3
(6) 2
From eq 6, the aggregation number will evidently have a quadratic dependence on the number of carbon atoms in the hydrocarbon tail, in accordance to experimental results (6).
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In the Laboratory The aggregation numbers calculated for nC equal to 12, 14, and 16 by eqs 1–5—that is, 55, 75, and 95, respectively— are in very good agreement with experimental findings for the corresponding alkylsulfate surfactants. For alkyltrimethylammonium surfactants, however, this model predicts an aggregation number too low for the longest surfactant. This is due to a combination of the bulkier head-group of this surfactant as well as a change in shape of the aggregate from a spherical to a more prolate micelle. However, the main point is that within a series of surfactants differing in hydrocarbon chain length only, the aggregation number should increase with increasing tail length. The micellar aggregation numbers can be determined by the method proposed by Turro and Yekta (7). According to this model, the aggregation numbers can be calculated by use of eqs 7 and 8:
ln
Qmic I0 = IQ mic
(7)
where I0 is the emission intensity at a certain wavelength in the absence of an added fluorescence quencher, IQ the intensity at the same wavelength at quencher concentration [Qmic], and [mic] the concentration of micelles in solution. The average aggregation number, , is related to the concentration of micelles, the total surfactant concentration [Stot], and the cmc through
=
Stot – cmc mic
(8)
Equation 7 relies on certain assumptions. First, the probes and the quenchers must be stationary in their host micelles during a time longer than the excited state lifetime, which means that migration of probe and quencher must not occur. Second, the quenching must be very effective; that is, the detected emission emanates from micelles without quenchers only. Third, the probes and quenchers have to have a Poissonian distribution among the micelles. The last condition is theoretically shown to be a plausible assumption for systems with small organic molecules dissolved in micelles (8), whereas the first two conditions are not immediately valid for micellar systems (9–11). Nevertheless, we will use eqs 7 and 8 as they stand, keeping the assumptions in mind when evaluating the experimental data. The use of eq 7 relies also on the knowledge of the quencher concentration in the micelles, which might be different from the total quencher concentration. In the case of 1,3-dicyano-benzene (DCB), [Qmic] can be set equal to the total quencher concentration, whereas this does not hold for the alkylpyridinium quenchers. These are surfactants as well as quenchers, which means that they also have a cmc and thus a certain concentration in the aqueous phase. To circumvent this problem, we assume perfect mixing between the quencher and the surfactant (12). In practice, this means that we assume that an equal relative amount of the quencher is present in the aqueous phase as for the surfactant used. The latter can be calculated as the ratio of the cmc and the total surfactant concentration, and this ratio was used as a correction factor, α, for the calculation of [Qmic]:
α=
cmcsurf Stot
[Qmic] = (1 – α) [Qtot] 94
(9)
(10)
The micelles formed by surfactants with a tail of moderate length (approximately C10–C16) are thought to be spherical or nearly spherical—at least close to the cmc. Often their structure is presented as being raspberry-like, with the hydrophilic charged head-groups closely packed to each other and the hydrocarbon chains stretched toward the center of the micelle. This picture is wrong for two reasons. First, owing to the electrostatic repulsion it is not possible to spontaneously pack up to a hundred charged entities close to each other, even if the counter-ion binding is taken into account. Second, the conformation of all tails being stretched straight toward the center would lead to an enormous local pressure. As an example, Cabane showed in an NMR study that the micelles formed by the well-known surfactant sodium dodecylsulfate (SDS) have about 1/3 of their surface covered by the hydrophilic head-groups, and the remaining 2/3 of the surface covered by hydrocarbon tails (13). A more realistic picture of a micelle is given in Figure 1, where it can be seen that the surface is composed of ionic head-groups, hydrophobic hydrocarbon tails, and counterions. As a consequence of the preceding discussion, we can conclude the following: (i) surfactants with longer tails will have a lower cmc and a larger aggregation number than analogues with shorter tails; (ii) adding salt to an ionic micellar solution will decrease the cmc and increase the aggregation number owing to the screened electrostatic repulsion; (iii) counterions that are more strongly bound to the surfactant will induce a lower cmc and a higher aggregation number; and (iv) owing to the amphiphilic character of the micellar surface, it can interact with both hydrophilic and hydrophobic species dissolved in the aqueous bulk. In this laboratory experiment, only points (i) and (ii) above will be explored. The determination of the cmc’s, however, can be regarded as an optional extension if time and interest permit. There are several suitable ways to determine the cmc of a surfactant—for example, using absorbance measurements (1), fluorescence intensity of a dissolved probe (2), conductometry (14, 15), and pyrene emission vibronic fine structure (16–19). If one wants to determine the different cmc’s, we suggest that a method where either no probe molecule is used (conductometry) or the same fluorescent probe as in the determination of the aggregation numbers (pyrene vibronic fine structure method) is utilized. Materials The following surfactants were examined: SDS (from BDH, specially pure), DoTAB (dodecyltrimethylammonium bromide, from Aldrich), TTAC (tetradecyltrimethylammonium chloride, from TCI), and CTAB (cetyltrimethylammonium bromide, from ACROS Janssen). C AUTION: These products are harmful if inhaled. Pyrene was used as fluorescent probe (from ACROS Janssen, twice recrystallized from absolute ethanol). CAUTION: Pyrene is a potential carcinogen. The following fluorescence quenchers were used: DCB (1,3-dicyanobenzene, from ACROS Janssen), DoPyrCl (dodecylpyridinium chloride, from Aldrich), TPyrCl (tetradecylpyridinium chloride, from Henkel), and CPyrCl (cetylpyridinium chloride, from Merck). NaCl (sodium chloride, from Aldrich, ultra pure) was used as the added salt. Experimental Procedure The solutions for the determinations of the micellar aggregation numbers were prepared as follows. From a
Journal of Chemical Education • Vol. 75 No. 1 January 1998 • JChemEd.chem.wisc.edu
In the Laboratory stock solution of 0.1 mM pyrene in absolute ethanol, a known volume was pipetted into a volumetric flask. The ethanol was evaporated and distilled water added, and the solution was stirred overnight. The final pyrene concentration was 1–2 µM. From the aqueous pyrene solution, the surfactant stock solutions were prepared with surfactant concentrations well above the respective cmc’s. The quenchers were similarly dissolved in absolute ethanol. From these solutions, quencher stock solutions were prepared by pipetting a known volume of the ethanolic quencher solution into a volumetric flask, evaporating the ethanol, and dissolving the quencher in the surfactant/ pyrene stock solution. The quencher concentrations in these solutions were equal to the maximum quencher concentrations measured, which were calculated to give approximately one quencher molecule per micelle for each surfactant system. By mixing the surfactant/pyrene stock without quencher and the surfactant/pyrene stock with quencher in known proportions, five or six solutions varying in quencher concentration from zero to the maximum concentration were prepared. The emission spectra of these solutions were recorded and the logarithm of the intensity ratio I0 /IQ at a specific wavelength within the spectral emission range was plotted against the quencher concentration, according to eq 7. This plot should yield a straight line through the origin with a slope equal to 1/[mic]. Multiplying the slope by the concentration of surfactant molecules participating in micelle formation (i.e., [Stot] – cmc) gives the aggregation number according to eq 8. We have chosen to use the intensity of band III in the pyrene emission spectrum—the emission peak at approximately 383 nm—to avoid scattering problems, which could occur if the intensity of band I (at 372 nm) was used. The emission spectra were recorded in the right-angle signal-to-reference mode on a SPEX Fluorolog 1680 instrument combined with a SPEX Spectroscopy Laboratory Coordinator DM1B. The slits used gave a bandwidth of approximately 2 nm and the excitation wavelength was 320 nm. This excitation wavelength was chosen instead of the absorption maximum of pyrene, around 337 nm, because the latter might lead to disturbing Raman scattering superimposed on the emission spectra. All measurements were performed at room temperature. All graphics and calculations were performed on a Macintosh Performa 5200 PowerPC within the framework of KaleidaGraph 3.0 (©Abelbeck Software).
quencher concentrations (Fig. 2). Good fits of eq 7 and consistent aggregation numbers were obtained in all cases (Fig. 3 and Table 2). Adding NaCl caused an increase in micelle volume, as expected. This is due to the higher ionic strength of the system, screening the electrostatic interactions. With a decreased electrostatic repulsion between the charged head-groups of SDS, it is possible to pack the surfactant head-groups closer to each other, with a subsequent increase in aggregation number. The same could be obtained by simply increasing the SDS concentration. The latter, however, is much less pronounced and will only be observed at rather high SDS concentrations.
Table 1. Values of CMC for Systems Investigated System
CMC Concentration (mM) This Report a
Literature
SDS
7.6
8
2
SDS + 220 mM NaCl
0.9
⬇1
18
DoTAB
Ref
16.6
15.5
22
TTAC
4.0
4.3
20
CTAB
0.7
0.8
22
a Values
in this column are cmc’s determined by students using the pyrene emission vibronic fine structure method (16–19 ).
Results and Discussion
Critical Micelle Concentration The cmc’s of the different systems investigated were determined with the pyrene emission vibronic fine structure method (16-19). The results are summarized in Table 1 together with literature values. If one chooses not to perform this part of the laboratory experiment, the literature values can be given as a priori information to the students. The results show that adding a salt to the SDS system lowers the cmc substantially. Furthermore, the cmc determinations of the different alkyltrimethylammonium surfactants show that an increasing hydrocarbon tail length indeed lowers the cmc for surfactants of the same kind. Micellar Aggregation Numbers SDS with and without Added NaCl Two quenchers were used in the salt-free system, DCB and DoPyrCl, whereas only DoPyrCl was employed for the system with added NaCl. Spectra were recorded at several
Figure 2. Steady-state emission spectra of pyrene in SDS micelles at different DoPyrCl concentrations (see inserted legend), in the absence of added NaCl (top) and with 220 mM NaCl added (bottom).
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ln ( I0 / IQ)
ln ( I0 / IQ)
In the Laboratory
CQ (mM)
Figure 3. Plot according to eq 7 for the SDS system. 䊏: SDS with DCB as quencher; 䉱: SDS with DoPyrCl as quencher; 䉬: SDS + 220 mM NaCl with DoPyrCl as quencher.
CQ (mM)
Figure 4. Plot according to eq 7 for the DoTAB system. 䊏: DoTAB with DCB as quencher; 䉬: DoTAB with DoPyrCl as quencher.
yields aggregation numbers in excellent agreement with the literature. Even without knowing the literature values, one can use eqs 1–5 to judge the results. For DCB, the discrepThe part treating the CnTA+ halides (n = 12, 14, 16) is ancy between experimental data (34) and model (55) is ala good example of the need to take both photochemical feamost 40%. If we conclude that something is wrong with the tures and model requirements into account when employformer value, we also have to answer the following quesing a given model. tion: why does DCB not work well in the DoTAB system, To begin with, the same quenchers used for the SDS whereas it could be used in the SDS system? systems were employed to determine the aggregation numThe explanation is that DCB acts as an electron accepber of DoTAB. From the quality of the fits of eq 7 to data tor, causing a subsequent attraction between the DCB an(Fig. 4), one would conclude that both quenchers result in a ionic radical and the cationic surfactant head-groups. When fluorescence quenching according to the Turro–Yekta model performing time-resolved fluorescence quenching measure(7). Comparing the calculated aggregation numbers, howments, this is not a problem, and DCB can be used as ever, shows that DCB yields a much lower < a > than quencher (20, 21), as the electron captured by the DCB molDoPyrCl. Evidently, there is a discrepancy between the agecule will return to the donor (pyrene) before the next excitagregation number obtained from the measurements with tion event. Under continuous excitation, however, the DCB and the literature values (Table 3), whereas DoPyrCl charge transfer has a disastrous impact, as it creates a constant amount of negatively charged DCB radicals. First, the effective quencher concentration will be lowered, because Table 2. Aggregation Numbers of Systems with SDS as Surfactant part of the quenchers will be “bound” to System Aggregation Number < a > the surfactant head-groups instead of Ref [SDS] [NaCl] being able to freely diffuse in the micelle. Quencher This Report Literature Theory a (mM) (mM) Second, even those DCB molecules that are not so strongly attracted by the cat63 0 DCB 58 60–65 55 7 ionic ammonium groups will diffuse more 61 0 DoPyrCl 65 60–65 55 7 slowly owing to electrostatic attraction. 60 220 DoPyrCl 103 – 18 ⬇ 100 This violates one of the assumptions neca Values in this column were calculated by the semi-empirical model leading essary for the use of eq 7, namely, that to eqs 1–6. the quenching must be very fast and efficient. None of this would be a problem if the plots according to eq 7 clearly showed that the model is invalid in Table 3. Aggregation Numbers of Systems with Alkyltrimethylammonium Salts these systems, but this is not the case. as Surfactants The plot according to eq 7 when using System Aggregation Number < a > DCB as a quencher in the DoTAB-sysSurfactant Ref tem yields a straight line through the Quencher This Report Literature Theory a Compound Conc. (mM) origin, but with a slope giving a much too low aggregation number when used DoTAB 75 DCB 34 55–65 55 22 in eq 8. DoTAB 72 DoPyrCl 64 55–65 55 22 Using alkylpyridinium salts as TTAC 101 DoPyrCl 51 70 75 20 quenchers offers an alternative, but with some difficulties. First, the effective TTAC 37 TPyrCl 58 60–65 75 20 quencher concentration in the micelles, CTAB 101 DoPyrCl 61 140 95 22 [Qmic], has to be calculated from the toCTAB 35 CPyrCl 41 100 95 20 tal quencher concentration, [Qtot], by eqs a Values in this column were calculated by the semi-empirical model leading to eqs 1–6. 9 and 10. As can be seen from Figure 4 Alkyltrimethylammonium Halides with Different Hydrocarbon Tail Lengths
96
Journal of Chemical Education • Vol. 75 No. 1 January 1998 • JChemEd.chem.wisc.edu
ln ( I0 / IQ)
ln ( I0 / IQ)
In the Laboratory
CQ (mM)
CQ (mM)
Figure 5. Plot according to eq 7 for the TTAC system. 䊏: TTAC with DoPyrCl as quencher; 䉬: TTAC with TPyrCl as quencher.
Figure 6. Plot according to eq 7 for the CTAB system. 䊏: CTAB with DoPyrCl as quencher; 䉬: CTAB with CPyrCl as quencher.
and Table 3, DoPyrCl works out very well as a quencher in the DoTAB system. The results are in good accord with the literature values, and students can judge the obtained results as satisfactory by eqs 1–5. When DoPyrCl is applied as quencher in the TTAC system, however, it yields too low an aggregation number. In this case, the conflict is due to our assumption that the mixing of the surfactant and the quencher is ideal. Such an assumption will hold only if the values of the cmc’s of the quencher and the surfactant are similar and, consequently, it does not hold if the lengths of the quencher and surfactant hydrophobic tails differ. In the present case, the real [Qmic] is much lower than the one calculated from eqs 9 and 10. Again, the plot of eq 7 does not reveal this anomaly because a straight line through the origin is obtained (Fig. 5), but the obtained aggregation number again is much lower than what could be predicted from eqs 1–5, and the students should be able to disregard this result. The use of the quencher TPyrCl should solve this problem, because it can be assumed that TPyrCl mixes ideally with TTAC. Indeed, TPyrCl yields a good aggregation number for TTAC (Table 3), illustrating the necessity of knowing the real [Qmic]. Finally, applying DoPyrCl in the CTAB systems results in too low an aggregation number for the same reason that it failed in the TTAC system. Trying to circumvent the problem with nonideal mixing by using the quencher CPyrCl, however, does not work (see Table 3), even though the fit of eq 7 is good (Fig. 6). This is because CTAB micelles do not conform to one of the assumptions for eq 7: that the quenching process is very effective. For such a bulky quencher in large CTAB micelles, the diffusion toward an excited probe molecule is too slow to assure complete quenching in all micelles containing both an excited probe and a quencher molecule. The plots of eq 7 yield straight lines through the origin both for DoPyrCl and CPyrCl (Fig. 6), but with aggregation numbers much lower than would be expected from eqs 1–5.
gregation numbers will result in a severe underestimation of these numbers in several cases—for example, when the underlying assumptions for the equations used are violated. Such an unfavorable situation can, however, be used pedagogically in discussing the results and helps to explain to the students that they have to be aware of both chemical and physical aspects of a system under investigation. It is possible for students to use a semi-empirical model to judge their results and the discrepancies between experimental data and model can be rationalized if taking the underlying physical assumptions of the model into account.
Conclusions The use of fluorescence techniques to determine critical micelle concentrations and aggregation numbers for surfactant micelles offers the possibility to introduce photophysics, spectroscopy, and microheterogeneous supramolecular systems to chemistry students. The methodology works well in the systems investigated, but must be applied with care. Using fluorescence quenching uncritically to determine ag-
Acknowledgments We thank the fourth-year students who performed most of the measurements presented here: Joris Baele, Davy Briers, Joke Creuwels, and Jan De Rudder. Notes 1. We would stress the need of a thorough introduction to photophysics before students start the practical work. It is, however, beyond the scope of this contribution to treat that part. Interested readers will find sufficient information in the literature (9, 23–26). 2. Surfactants and micelles have been extensively discussed in the literature. Only the major concepts related to the micellar aggregation number are discussed in this paper. Readers interested in a more thorough discussion and presentation of the micellar aggregation phenomenon can consult some excellent articles and books (5, 27–32).
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22. Almgren, M.; Hansson, P.; Mukhtar, E.; van Stam, J. Langmuir 1992, 8, 2405. 23. Lakowicz, J. Principles of Fluorescence Spectroscopy; Plenum: New York, 1983. 24. Reekmans, S.; De Schryver, F. C. In Frontiers in Supramolecular Chemistry; Schneider, H. J.; Dürr, H., Ed.; VCH: Weinheim, 1991; p 287. 25. Almgren, M. Adv. Coll. Int. Sci. 1992, 41, 9. 26. Winnik, F. Chem. Rev. 1993, 93, 587. 27. Israelachvili, J. N.; Mitchell, D. J.; Ninham, B. W. J. Chem. Soc., Faraday Trans. 1 1976, 72, 1525. 28. Wennerström, H.; Lindman, B. Phys. Rep. 1979, 52, 1. 29. Lindman, B.; Wennerström, H. Top. Curr. Chem. 1980, 87, 1. 30. Israelachvili, J. N. Intermolecular and Surface Forces. With Applications to Colloidal and Biological Systems; Academic: London, 1985. 31. Moroi, Y. Micelles: Theoretical and Applied Aspects; Plenum: New York, 1992. 32. Shaw, D. J. Introduction to Colloid and Surface Chemistry; Butterworth-Heinemann: Oxford, 1992.
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