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Growth of Cetyltrimethylammonium Chloride and Acetate Micelles with Counterion Concentration
Journal of Colloid and Interface Science 214, 238 –242 (1999) Article ID jcis.1999.6217, available online at http://www.idealibrary.com on
Growth of Cetyltrimethylammonium Chloride and Acetate Micelles with Counterion Concentration Radha Ranganathan,* ,1 Laura T. Okano,† Chang Yihwa,† and Frank H. Quina† *Department of Physics and Astronomy-MD8268, California State University, Northridge, California 91330; and †Instituto de Quı´mica, Universidade de Sa˜o Paulo, Caixa Postal 26077, Sa˜o Paulo 05599-970, Brazil Received September 30, 1998; accepted March 16, 1998
Time resolved fluorescence quenching measurements with pyrene as probe are employed to determine aggregation numbers for hexadecyltrimethylammonium acetate (CTAOAc) and chloride (CTACl) micelles as a function of the concentration of detergent and added common-counterion salt. The aggregation numbers, N A, of CTACl are roughly twice those of CTAOAc micelles at equivalent concentrations of detergent and salt, consistent with the known relative counterion binding affinity (chloride @ acetate). For both detergents, the increase of N A with the net concentration of counterions in the intermicellar aqueous phase ([Y aq]) follows the relationship found previously for anionic micelles: log N A 5 log N o 1 g log[Y aq], where g and N o are constants. However, compared to anionic micelles, for which g 5 0.2– 0.25, spherical micelles of both CTAOAc and CTACl exhibit less pronounced growth, with g 5 0.1. © 1999 Academic Press Key Words: micelles; cationic surfactants; aggregation number; micellar growth; counterion selectivity.
INTRODUCTION
Micelles of common ionic detergents such as sodium dodecylsulfate (SDS) or hexadecyltrimethylammonium bromide (CTABr) are roughly spherical or globular in aqueous solution at low concentrations of detergent and added salt (1– 6). These spherical micelles grow modestly in size as the detergent and added common-counterion salt concentrations are increased. Above some threshold value of these concentrations, however, many ionic detergents exhibit a marked increase in the aggregation number, becoming rodlike in shape. The onset of this sphere-to-rod transition depends on the nature of the detergent and is facilitated (shifted to lower concentrations) by longer detergent hydrocarbon tails, smaller headgroup size, more strongly bound counterions, and lower temperatures (1–7). The present paper deals with the [detergent]- and [salt]-induced growth of ionic micelles in the concentration region prior to the sphere-to-rod transition, i.e., where they are still roughly spherical or globular in shape. For a number of detergents, it has been shown (5, 8, 9) that 1
To whom correspondence should be addressed. Fax: (818) 677 3234. E-mail: [email protected]. 0021-9797/99 $30.00 Copyright © 1999 by Academic Press All rights of reproduction in any form reserved.
micellar aggregation numbers (N A) at the critical micelle concentration (cmc) increase with the added common-counterion salt concentration ([salt]) according to log N A 5 A log~cmc 1 @salt#! 1 B,
[1]
where A and B are constants. Recently, we demonstrated (10) for SDS micelles below the sphere-to-rod transition, both the [SDS]- and the [NaCl]-induced growth of the micelles could be described by a relationship of analogous form, log N A 5 log N o 1 g log@Y aq#,
[2]
where [Y aq] is the concentration of counterions free in the intermicellar aqueous phase (from salt, unmicellized surfactant, and micellar dissociation) and N o and g are constants. Since [Y aq] 5 cmc 1 [salt] at the cmc, Eq. [2] reduces to Eq. [1] at the cmc, making the latter a particular case of the former. For SDS, experimental values of g and A from a number of studies were shown (10) to fall in the range 0.2– 0.25. Recent experiments with a homologous series of sodium alkylsulfates (octyl, nonyl, decyl, undecyl, and tetradecyl) have confirmed that spherical micelles of these anionic detergents also grow according to Eq. [2] with g values in the range 0.2– 0.25 in all cases (11). The objective of the present work is to verify the applicability of Eq. [2] to cationic micellar systems above the cmc and to examine the influence of detergent charge and counterion binding affinity on the magnitude of g. For this purpose, aggregation numbers of cationic hexadecyltrimethylammonium (CTA) detergent micelles were measured over a range of concentrations of detergent and added common-counterion salt via standard time-resolved fluorescence quenching techniques (12–14). The influence of counterion type was investigated by comparing data for CTA micelles with chloride and acetate counterions (CTACl and CTAOAc, respectively). Several studies (15–19) have shown that the acetate ion is much more weakly bound to CTA micelles than chloride. In addition, both CTACl and CTAOAc are well-studied systems with respect to
238
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GROWTH OF HEXADECYLTRIMETHYLAMMONIUM MICELLES
micellar properties such as cmc and apparent degree of counterion dissociation (7, 20 –23). MATERIALS AND METHODS
Materials Pyrene (Aldrich) was purified by the method of Geiger and Turro (24). Hexadecyltrimethylammonium chloride (CTACl) and acetate (CTAOAc) were prepared from the corresponding bromide (CTAB, Aldrich) by the xanthate counterion exchange technique (25) and purified by recrystallization from acetone (CTACl) or acetone-ethyl ether (CTAOAc). N-Hexadecylpyridinium chloride (HPCl, Aldrich) was purified by several recrystallizations from acetone (26). Analytical reagent grade sodium chloride (Merck, p.a.) and sodium acetate (NaOAc, Merck, p.a.) were used as received. All solutions were prepared in ultrapure (Millipore Milli-Q) water. Methods All experiments were performed at 30°C. Pyrene (5 3 10 26 M) was added to air-equilibrated aqueous micellar solutions of CTACl, with or without added NaCl, or of CTAOAc, with or without added NaOAc. Aliquots of a concentrated aqueous stock solution of the quencher (HPCl) were added with the aid of a Hamilton microliter syringe. The concentration of HPCl stock solutions was verified by absorption spectroscopy at 260 nm (« 5 4200 M 21 cm 21) (27). Absorption spectra were recorded on a Hewlett–Packard 8452A Diode Array Spectrometer. Pyrene fluorescence decay curves were collected by the single photon counting technique (12–14, 27–29) on an Edinburgh Analytical Instruments Model FL-900 Lifetime Spectrometer (H 2 flashlamp gas, 310 nm excitation, 390 nm emission). Fluorescence decays in the absence of quencher were analyzed utilizing the standard single exponential decay routines of the FL-900 operating software. The corresponding decay curves in the presence of the quencher HPCl were fit to the Infelta–Tachiya equation (13),
is the average number of bound quenchers per micelle and [HPCl] and [M] are the total concentrations of quenchers and micelles, respectively. Measurements were made at values of ^n& less than one in all cases to ensure that the quencher occupation could safely be assumed to obey a Poisson distribution (13). Micelle aggregation numbers (N A) were calculated from the relationship N A 5 ^n&C D/@HPCl#,
[5]
where C D 5 [Det tot ] 2 [m aq ] is the analytical concentration of micellized detergent. The values of the free monomer concentration, [m aq ], at each concentration of detergent and added salt, [Y ad ], were estimated from the equation (10, 30, 31) log@m aq# 5 K 1 2 K 2 log@Y aq#,
[6]
@Y aq# 5 a C D 1 @m aq# 1 @Y ad#
[7]
where
is the concentration of counterions in the intermicellar aqueous phase. For CTACl, the values K 1 5 25.00, K 2 5 0.75, and a 5 0.25 were employed throughout (20). For CTAOAc, the values K 1 5 24.14 and K 2 5 0.46, which reproduce the data of Toullec and Couderc (23) for the acetate concentration dependence of the cmc of CTAOAc, were employed in Eq. [6]. The values of a reported by Toullec and Couderc (23) for CTOAc micelles were found to follow the empirical relationship
a 5 $0.51 1 0.26~@OAc 2 aq#/cmc0 !%/ ~0.51 1 ~@OAc 2 aq#/cmc0 !!,
[8]
where cmc 0 in the absence of added salt is 1.4 mM (23). RESULTS
F~t! 5 F~0!exp$2A 2 t 2 A 3 @1 2 exp~2A 4 t!#%,
[3]
using the micelle quenching module of Edinburgh Analytical Instruments Level 2 analysis software (Version 1.60). In all cases, the observed fits were consistent with the expected behavior for a nonmobile quencher (k q @ k 2 ). Thus, at fixed concentrations of detergent and salt, the values of A 2 and A 4 were independent of quencher concentration, with 1/A 2 5 t o, the pyrene fluorescence lifetime in the absence of the quencher, and A 4 5 k q. Under these conditions, the value of A 3 5 ^n&, where ^n& 5 @HPCl#/@M#
[4]
The aggregation numbers (N A ) of CTAOAc and CTACl micelles determined in this work are collected in Tables 1 and 2, together with the calculated values of [m aq ] (Eq. [6]), [Y aq ] (Eq. [7]), and, in the case of CTAOAc, a (Eq. [8]). For both detergents, the values of N A in the absence of added electrolyte are consistent with the approximate relationship (7) for spherical CTA micelles of N A 5 20/a used by Toullec and Couderc (23) to estimate aggregation numbers of CTAOAc micelles. The N A values of CTACl are in reasonable agreement with other data in the literature (7, 13, 22, 32). The dominant role of the counterion in determining N A was confirmed by measuring the micellar aggregation number of 0.018 M CTAOAc before (N A 5
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RANGANATHAN ET AL.
TABLE 1 Aggregation Numbers of CTAOAc Micelles Measured at 30°C [CTAOAc] (mM)
[NaOAc] (mM)
a
[m aq] (mM)
2 [OAc aq ] (mM)
NA
3.9 8.7 17.1 17.4 87.2 8.7 17.1 87.2
0 0 0 14 0 49.0 87.5 95.0
0.43 0.38 0.34 0.29 0.28 0.27 0.27 0.26
1.17 0.94 0.75 0.44 0.40 0.28 0.22 0.19
2.4 3.9 6.2 19.3 24.8 51.6 92.2 118
44 6 4 47 6 4 51 6 4 57 6 5 60 6 5 63 6 5 67 6 5 68 6 6
57 6 5) and after (N A 5 118 6 10) addition of 0.10 M NaCl to the solution. In all cases, the aggregation numbers are consistent with spherical or, at most, only slightly globular micelles, as assumed by the analysis outlined in the Discussion.
FIG. 1. Aqueous counterion concentration dependence of the micellar aggregation numbers of CTACl (, this work, 30°C; ■, Ref. (24), 24°C) and CTAOAc (F, this work, 30°C).
DISCUSSION
The aggregation numbers of CTAOAc micelles are roughly a factor of two smaller than those of CTACl micelles under comparable conditions. In this context, specific counterion effects on micellar aggregation numbers are known to accompany trends in counterion binding selectivities (1, 2, 5–7), and the acetate ion is known to be more weakly bound to cationic micelle surfaces than the chloride ion (15–19). Many of the properties of CTAOAc solutions, in particular the variation of a with detergent concentration (23), are reminiscent of those of CTA micelles with highly hydrated counterions such as fluoride (33, 34) and hydroxide (33–35). The aggregation numbers of CTAOAc micelles are indeed quite similar to those reported for CTAOH micelles (7, 35). Figure 1 shows log–log plots of the N A values in Tables 1 and 2 as a function of the aqueous counterion concentration ([Y aq], Eq. [7]). Also included in this figure are data for the aggregation numbers of CTACl micelles determined at 24°C by Malliaris et al. (32) on the basis of intramicellar pyrene TABLE 2 Aggregation Numbers of CTACl Micelles Measured at 30°C [CTACl] (mM)
[NaCl] (mM)
[m aq] (mM)
2 [Cl aq ] (mM)
NA
21 43 86 86 86 86 86
0 0 0 10 20 40 80
0.47 0.29 0.18 0.13 0.11 0.08 0.06
5.87 11.1 21.8 74.6 41.6 61.6 102
94 6 9 99 6 10 110 6 11 133 6 11 115 6 11 119 6 12 121 6 12
excimer formation. As predicted by Eq. [1], log N A is a linear function of log[Y aq] for both detergents. Standard linear regression analysis provides the relationships log N A 5 ~1.94 6 0.01! 1 ~0.11 6 0.01! 3 ~log@OAc 2 aq#!
CTAOAc ~308C!
[9]
log N A 5 ~2.19 6 0.01! 1 ~0.096 6 0.009! 3 ~log@Cl 2 aq#!
CTACl ~308C!
[10]
log N A 5 ~2.23 6 0.01! 1 ~0.11 6 0.01! 3 ~log@Cl 2 aq#!
CTACl ~248C!.
[11]
For all three data sets, the value of g, given by the slopes of the correlations, is 0.1 within experimental error. Values of A (Eq. [1]) of the same magnitude (0.09 6 0.03) have been found for the salt-induced growth of alkyltrimethylammonium bromides and chlorides at the cmc (5). At present, Eqs. [1] and [2] have no firm theoretical basis. For SDS (10), combination of an empirical relationship between the micellar aggregation number and the cmc with the known dependence of the cmc on the aqueous counterion concentration was shown to lead to Eqs. [1] and [2] with A 5 g 5 0.33*(1 2 a ). If general, this expression would predict g values in the range 0.19 – 0.26 for most detergents, given the fact that a values of ionic detergents are typically 0.2– 0.4 (6). Although g values of this magnitude were found for SDS (10) and several of its homologues (11), those of CTACl and CTAOAc are much smaller than expected from this approach. For salt-induced
GROWTH OF HEXADECYLTRIMETHYLAMMONIUM MICELLES
growth of spherical micelles at the cmc, Ikeda (5) proposed a model that leads to Eq. [1] with an A value given by the relationship A 5 N Aa ~e 2 /DkT!/~8b! 2 1.
[12]
In the present case, however, upon substitution of the relationship N A 5 20/a for spherical CTA micelles (7) and the appropriate values of the Bjerrum length (e 2 /DkT 5 0.71 nm) (36) and the micellar radius (b 5 2.6 nm) (4) into Eq. [12], one obtains a value of A 5 20.07. Thus, unless a is treated as a purely disposable fitting parameter (5), this model incorrectly predicts that the aggregation number of spherical CTACl and CTAOAc micelles should decrease with increasing added salt concentration. The present results, together with those from previous work (10, 11), show that the [detergent]- and [salt]-induced growth of spherical or globular ionic micelles below the onset of the sphere-to-rod transition can be conveniently described by Eq. [2]. In developing any detailed model for the growth in this region, several experimental trends should be taken into consideration. For a given headgroup, the value of g (Eq. [2]) or A (Eq. [1]) is relatively insensitive to detergent chain length. This was verified for g in previous work (10, 11) with anionic detergents and for A with homologous alkyltrimethylammonium chloride and bromide micelles (5). Although the affinity of the counterion for the micelle surface has a pronounced influence on micellar aggregation numbers themselves, no corresponding specific counterion effect is evident in either g or A. Thus, we find similar g values for CTACl and CTAOAc, and A values for the chloride and bromide salts of alkyltrimethylammonium (5), dodecyldimethylammonium (5), and dodecylpyridinium (8, 9) detergents appear to be counterion insensitive as well. In contrast, the nature of the detergent headgroup does appear to be a significant factor in determining the values of g or A. Thus, g values of anionic sodium alkylsulfate micelles (g 5 0.2– 0.25) (10, 11) are significantly larger than those of cationic CTA micelles (g 5 0.1). The A values of spherical dodecyltrimethylammonium, dodecyldimethylammonium, and dodecylammonium chloride micelles (5) are, respectively, 0.11, 0.16, and 0.42. These last results, in particular, suggest that smaller headgroups enhance the susceptibility of spherical micelles to [detergent]- and [salt]induced growth in the concentration region below the sphere-to-rod transition. CONCLUSIONS
Aggregation numbers of spherical CTACl and CTAOAc micelles, determined by time-resolved fluorescence quenching, increase with increasing concentration of counterions free in the intermicellar aqueous phase according to Eq. [2],
241
with g values on the order of 0.1. Although the rate of growth is insensitive to the nature of the counterion, the relative micelle sizes, determined by the constant N o , are strongly influenced by the counterion type. The present results for cationic CTA micelles confirm that Eq. [2] is a convenient general expression for describing the detergentand common-counterion salt-induced growth of ionic micelles in the concentration region below the sphere-to-rod transition. ACKNOWLEDGMENTS This work was supported by grants from the Fundac¸a˜o de Amparo a` Pesquisa do Estado de Sa˜o Paulo—FAPESP (Thematic Project 1994/ 3505-3) and PADCT-FINEP (Project 65-92-0063-00). L.T.O. and C.Y. acknowledge graduate and undergraduate fellowship support, respectively, from CAPES (Coordenac¸a˜o de Aperfeic¸oamento de Pessoal de Nı´vel Superior) and the CNPq (Conselho Nacional de Desenvolvimento Cientı´fico e Tecnolo´gico). F.H.Q. acknowledges the CNPq for research fellowship support. During her stay at the IQ-USP as a visiting research professor, R.R. was supported by a grant from FAPESP (Project 1998/ 3674-0).
REFERENCES 1. Porte, G., and Appell, J., in “Surfactants in Solution” (K. L. Mittal and B. Lindman, Eds.), Vol. 2, p. 805. Plenum, New York, 1984. 2. Ikeda, S., in “Surfactants in Solution” (K. L. Mittal and B. Lindman, Eds.), Vol. 2, p. 805. Plenum, New York, 1984. 3. Birdi, K. S., Acta Chem. Scand. A40, 319 (1986). 4. Quirion, F., and Magid, L. J., J. Phys. Chem. 90, 5435 (1986). 5. Ikeda, S., Colloid Polymer Sci. 269, 49 (1991). 6. Pramauro, E., and Pelizzetti, E., “Surfactants in Analytical Chemistry, Applications of Organized Amphiphilic Media,” Chap. 1, p. 1. Elsevier, Amsterdam, 1996. 7. Berr, S., Jones, R. R. M., and Johnson, J. S., Jr., J. Phys. Chem. 96, 5611 (1992). 8. Fujio, K., and Ikeda, S., Langmuir 7, 2899 (1991). 9. Fujio, K., and Ikeda, S., Bull. Chem. Soc. Jpn. 65, 1406 (1991). 10. Quina, F. H., Bales, B. L., Nassar, P. M., and Bonilha, J. B. S., J. Phys. Chem. 99, 17028 (1995). 11. Ranganathan, R., Peric, M., and Bales, B. L., J. Phys. Chem. B 102, 8436 (1999). 12. Kalyanasundaram, K., “Photochemistry in Microheterogeneous Systems.” Academic Press, Orlando, 1987. 13. Malliaris, A., Int. Rev. Phys. Chem. 7, 95 (1988). 14. Gehlen, M. H., and De Schryver, F. C., Chem. Rev. 93, 199 (1993). 15. Bartet, D., Gamboa, C., and Sepu´lveda, L., J. Phys. Chem. 84, 272 (1980). 16. Broxton, T. J., Aust. J. Chem. 34, 2313 (1981). 17. Abuin, E. B., Lissi, E., Araujo, P. S., Aleixo, R. M. V., Chaimovich, H., Bianchi, N., Miola, L., and Quina, F. H., J. Colloid Interface Sci. 96, 293 (1983). 18. Lissi, E., Abuin, E., Ribot, G., Valenzuela, E., Chaimovich, H., Araujo, P. S., Aleixo, R. M. V., and Cuccovia, I. M., J. Colloid Interface Sci. 103, 139 (1985). 19. Nascimento, M. G., Miranda, S. A. F., and Nome, F., J. Phys. Chem. 90, 3366 (1986). 20. Bonilha, J. B. S., Chiericato, G., Jr., Martins-Franchetti, S. M., Ribaldo, E. J., and Quina, F. H., J. Phys. Chem. 86, 4941 (1982). 21. Grieser, F., and Drummond, C. J., J. Phys. Chem. 92, 5580 (1988). 22. Nagarajan, R., Langmuir 10, 2028 (1994).
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23. Toullec, J., and Couderc, S., Langmuir 13, 1918 (1997). 24. Geiger, M. W., and Turro, N. J., Photochem. Photobiol. 22, 273 (1975). 25. Sepu´lveda, L., Cabrera, W., Gamboa, C., and Meyer, M., J. Colloid Interface Sci. 117, 460 (1987). 26. Miola, L., Abakerli, R. B., Ginani, M. F., Berci Filho, P., Toscano, V. G., and Quina, F. H., J. Phys. Chem. 87, 4417 (1983). 27. Alonso, E. O., and Quina, F. H., Langmuir 11, 2459 (1995). 28. Alonso, E. O., and Quina, F. H., J. Braz. Chem. Soc. 6, 155 (1995). 29. Okano, L. T., Alonso, E. O., Waissbluth, O. L., and Quina, F. H., Photochem. Photobiol. 63, 746 (1996).
30. Cutler, S. G., Meares, P., and Hall, D. G., J. Chem. Soc. Faraday Trans. 1 74, 1758 (1978). 31. Hall, D. G., J. Chem. Soc. Faraday Trans. 1 77, 1121 (1981). 32. Malliaris, A., Lang, J., and Zana, R., J. Chem. Soc. Faraday Trans. 1 82, 109 (1986). 33. Bunton, C. A., Nome, F. J., Quina, F. H., and Romsted, L. S., Acc. Chem. Res. 24, 357 (1991). 34. Neves, M. F. S., Zanette, D., Quina, F. H., Moretti, M. T., and Nome, F., J. Phys. Chem. 93, 1502 (1989). 35. Lianos, P., and Zana, R., J. Phys. Chem. 87, 1289 (1983). 36. Weisbuch, G., and Gue´ron, M., J. Phys. Chem. 85, 517 (1981).
Growth of Cetyltrimethylammonium Chloride and Acetate Micelles with Counterion Concentration Radha Ranganathan,* ,1 Laura T. Okano,† Chang Yihwa,† and Frank H. Quina† *Department of Physics and Astronomy-MD8268, California State University, Northridge, California 91330; and †Instituto de Quı´mica, Universidade de Sa˜o Paulo, Caixa Postal 26077, Sa˜o Paulo 05599-970, Brazil Received September 30, 1998; accepted March 16, 1998
Time resolved fluorescence quenching measurements with pyrene as probe are employed to determine aggregation numbers for hexadecyltrimethylammonium acetate (CTAOAc) and chloride (CTACl) micelles as a function of the concentration of detergent and added common-counterion salt. The aggregation numbers, N A, of CTACl are roughly twice those of CTAOAc micelles at equivalent concentrations of detergent and salt, consistent with the known relative counterion binding affinity (chloride @ acetate). For both detergents, the increase of N A with the net concentration of counterions in the intermicellar aqueous phase ([Y aq]) follows the relationship found previously for anionic micelles: log N A 5 log N o 1 g log[Y aq], where g and N o are constants. However, compared to anionic micelles, for which g 5 0.2– 0.25, spherical micelles of both CTAOAc and CTACl exhibit less pronounced growth, with g 5 0.1. © 1999 Academic Press Key Words: micelles; cationic surfactants; aggregation number; micellar growth; counterion selectivity.
INTRODUCTION
Micelles of common ionic detergents such as sodium dodecylsulfate (SDS) or hexadecyltrimethylammonium bromide (CTABr) are roughly spherical or globular in aqueous solution at low concentrations of detergent and added salt (1– 6). These spherical micelles grow modestly in size as the detergent and added common-counterion salt concentrations are increased. Above some threshold value of these concentrations, however, many ionic detergents exhibit a marked increase in the aggregation number, becoming rodlike in shape. The onset of this sphere-to-rod transition depends on the nature of the detergent and is facilitated (shifted to lower concentrations) by longer detergent hydrocarbon tails, smaller headgroup size, more strongly bound counterions, and lower temperatures (1–7). The present paper deals with the [detergent]- and [salt]-induced growth of ionic micelles in the concentration region prior to the sphere-to-rod transition, i.e., where they are still roughly spherical or globular in shape. For a number of detergents, it has been shown (5, 8, 9) that 1
To whom correspondence should be addressed. Fax: (818) 677 3234. E-mail: [email protected]. 0021-9797/99 $30.00 Copyright © 1999 by Academic Press All rights of reproduction in any form reserved.
micellar aggregation numbers (N A) at the critical micelle concentration (cmc) increase with the added common-counterion salt concentration ([salt]) according to log N A 5 A log~cmc 1 @salt#! 1 B,
[1]
where A and B are constants. Recently, we demonstrated (10) for SDS micelles below the sphere-to-rod transition, both the [SDS]- and the [NaCl]-induced growth of the micelles could be described by a relationship of analogous form, log N A 5 log N o 1 g log@Y aq#,
[2]
where [Y aq] is the concentration of counterions free in the intermicellar aqueous phase (from salt, unmicellized surfactant, and micellar dissociation) and N o and g are constants. Since [Y aq] 5 cmc 1 [salt] at the cmc, Eq. [2] reduces to Eq. [1] at the cmc, making the latter a particular case of the former. For SDS, experimental values of g and A from a number of studies were shown (10) to fall in the range 0.2– 0.25. Recent experiments with a homologous series of sodium alkylsulfates (octyl, nonyl, decyl, undecyl, and tetradecyl) have confirmed that spherical micelles of these anionic detergents also grow according to Eq. [2] with g values in the range 0.2– 0.25 in all cases (11). The objective of the present work is to verify the applicability of Eq. [2] to cationic micellar systems above the cmc and to examine the influence of detergent charge and counterion binding affinity on the magnitude of g. For this purpose, aggregation numbers of cationic hexadecyltrimethylammonium (CTA) detergent micelles were measured over a range of concentrations of detergent and added common-counterion salt via standard time-resolved fluorescence quenching techniques (12–14). The influence of counterion type was investigated by comparing data for CTA micelles with chloride and acetate counterions (CTACl and CTAOAc, respectively). Several studies (15–19) have shown that the acetate ion is much more weakly bound to CTA micelles than chloride. In addition, both CTACl and CTAOAc are well-studied systems with respect to
238
239
GROWTH OF HEXADECYLTRIMETHYLAMMONIUM MICELLES
micellar properties such as cmc and apparent degree of counterion dissociation (7, 20 –23). MATERIALS AND METHODS
Materials Pyrene (Aldrich) was purified by the method of Geiger and Turro (24). Hexadecyltrimethylammonium chloride (CTACl) and acetate (CTAOAc) were prepared from the corresponding bromide (CTAB, Aldrich) by the xanthate counterion exchange technique (25) and purified by recrystallization from acetone (CTACl) or acetone-ethyl ether (CTAOAc). N-Hexadecylpyridinium chloride (HPCl, Aldrich) was purified by several recrystallizations from acetone (26). Analytical reagent grade sodium chloride (Merck, p.a.) and sodium acetate (NaOAc, Merck, p.a.) were used as received. All solutions were prepared in ultrapure (Millipore Milli-Q) water. Methods All experiments were performed at 30°C. Pyrene (5 3 10 26 M) was added to air-equilibrated aqueous micellar solutions of CTACl, with or without added NaCl, or of CTAOAc, with or without added NaOAc. Aliquots of a concentrated aqueous stock solution of the quencher (HPCl) were added with the aid of a Hamilton microliter syringe. The concentration of HPCl stock solutions was verified by absorption spectroscopy at 260 nm (« 5 4200 M 21 cm 21) (27). Absorption spectra were recorded on a Hewlett–Packard 8452A Diode Array Spectrometer. Pyrene fluorescence decay curves were collected by the single photon counting technique (12–14, 27–29) on an Edinburgh Analytical Instruments Model FL-900 Lifetime Spectrometer (H 2 flashlamp gas, 310 nm excitation, 390 nm emission). Fluorescence decays in the absence of quencher were analyzed utilizing the standard single exponential decay routines of the FL-900 operating software. The corresponding decay curves in the presence of the quencher HPCl were fit to the Infelta–Tachiya equation (13),
is the average number of bound quenchers per micelle and [HPCl] and [M] are the total concentrations of quenchers and micelles, respectively. Measurements were made at values of ^n& less than one in all cases to ensure that the quencher occupation could safely be assumed to obey a Poisson distribution (13). Micelle aggregation numbers (N A) were calculated from the relationship N A 5 ^n&C D/@HPCl#,
[5]
where C D 5 [Det tot ] 2 [m aq ] is the analytical concentration of micellized detergent. The values of the free monomer concentration, [m aq ], at each concentration of detergent and added salt, [Y ad ], were estimated from the equation (10, 30, 31) log@m aq# 5 K 1 2 K 2 log@Y aq#,
[6]
@Y aq# 5 a C D 1 @m aq# 1 @Y ad#
[7]
where
is the concentration of counterions in the intermicellar aqueous phase. For CTACl, the values K 1 5 25.00, K 2 5 0.75, and a 5 0.25 were employed throughout (20). For CTAOAc, the values K 1 5 24.14 and K 2 5 0.46, which reproduce the data of Toullec and Couderc (23) for the acetate concentration dependence of the cmc of CTAOAc, were employed in Eq. [6]. The values of a reported by Toullec and Couderc (23) for CTOAc micelles were found to follow the empirical relationship
a 5 $0.51 1 0.26~@OAc 2 aq#/cmc0 !%/ ~0.51 1 ~@OAc 2 aq#/cmc0 !!,
[8]
where cmc 0 in the absence of added salt is 1.4 mM (23). RESULTS
F~t! 5 F~0!exp$2A 2 t 2 A 3 @1 2 exp~2A 4 t!#%,
[3]
using the micelle quenching module of Edinburgh Analytical Instruments Level 2 analysis software (Version 1.60). In all cases, the observed fits were consistent with the expected behavior for a nonmobile quencher (k q @ k 2 ). Thus, at fixed concentrations of detergent and salt, the values of A 2 and A 4 were independent of quencher concentration, with 1/A 2 5 t o, the pyrene fluorescence lifetime in the absence of the quencher, and A 4 5 k q. Under these conditions, the value of A 3 5 ^n&, where ^n& 5 @HPCl#/@M#
[4]
The aggregation numbers (N A ) of CTAOAc and CTACl micelles determined in this work are collected in Tables 1 and 2, together with the calculated values of [m aq ] (Eq. [6]), [Y aq ] (Eq. [7]), and, in the case of CTAOAc, a (Eq. [8]). For both detergents, the values of N A in the absence of added electrolyte are consistent with the approximate relationship (7) for spherical CTA micelles of N A 5 20/a used by Toullec and Couderc (23) to estimate aggregation numbers of CTAOAc micelles. The N A values of CTACl are in reasonable agreement with other data in the literature (7, 13, 22, 32). The dominant role of the counterion in determining N A was confirmed by measuring the micellar aggregation number of 0.018 M CTAOAc before (N A 5
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TABLE 1 Aggregation Numbers of CTAOAc Micelles Measured at 30°C [CTAOAc] (mM)
[NaOAc] (mM)
a
[m aq] (mM)
2 [OAc aq ] (mM)
NA
3.9 8.7 17.1 17.4 87.2 8.7 17.1 87.2
0 0 0 14 0 49.0 87.5 95.0
0.43 0.38 0.34 0.29 0.28 0.27 0.27 0.26
1.17 0.94 0.75 0.44 0.40 0.28 0.22 0.19
2.4 3.9 6.2 19.3 24.8 51.6 92.2 118
44 6 4 47 6 4 51 6 4 57 6 5 60 6 5 63 6 5 67 6 5 68 6 6
57 6 5) and after (N A 5 118 6 10) addition of 0.10 M NaCl to the solution. In all cases, the aggregation numbers are consistent with spherical or, at most, only slightly globular micelles, as assumed by the analysis outlined in the Discussion.
FIG. 1. Aqueous counterion concentration dependence of the micellar aggregation numbers of CTACl (, this work, 30°C; ■, Ref. (24), 24°C) and CTAOAc (F, this work, 30°C).
DISCUSSION
The aggregation numbers of CTAOAc micelles are roughly a factor of two smaller than those of CTACl micelles under comparable conditions. In this context, specific counterion effects on micellar aggregation numbers are known to accompany trends in counterion binding selectivities (1, 2, 5–7), and the acetate ion is known to be more weakly bound to cationic micelle surfaces than the chloride ion (15–19). Many of the properties of CTAOAc solutions, in particular the variation of a with detergent concentration (23), are reminiscent of those of CTA micelles with highly hydrated counterions such as fluoride (33, 34) and hydroxide (33–35). The aggregation numbers of CTAOAc micelles are indeed quite similar to those reported for CTAOH micelles (7, 35). Figure 1 shows log–log plots of the N A values in Tables 1 and 2 as a function of the aqueous counterion concentration ([Y aq], Eq. [7]). Also included in this figure are data for the aggregation numbers of CTACl micelles determined at 24°C by Malliaris et al. (32) on the basis of intramicellar pyrene TABLE 2 Aggregation Numbers of CTACl Micelles Measured at 30°C [CTACl] (mM)
[NaCl] (mM)
[m aq] (mM)
2 [Cl aq ] (mM)
NA
21 43 86 86 86 86 86
0 0 0 10 20 40 80
0.47 0.29 0.18 0.13 0.11 0.08 0.06
5.87 11.1 21.8 74.6 41.6 61.6 102
94 6 9 99 6 10 110 6 11 133 6 11 115 6 11 119 6 12 121 6 12
excimer formation. As predicted by Eq. [1], log N A is a linear function of log[Y aq] for both detergents. Standard linear regression analysis provides the relationships log N A 5 ~1.94 6 0.01! 1 ~0.11 6 0.01! 3 ~log@OAc 2 aq#!
CTAOAc ~308C!
[9]
log N A 5 ~2.19 6 0.01! 1 ~0.096 6 0.009! 3 ~log@Cl 2 aq#!
CTACl ~308C!
[10]
log N A 5 ~2.23 6 0.01! 1 ~0.11 6 0.01! 3 ~log@Cl 2 aq#!
CTACl ~248C!.
[11]
For all three data sets, the value of g, given by the slopes of the correlations, is 0.1 within experimental error. Values of A (Eq. [1]) of the same magnitude (0.09 6 0.03) have been found for the salt-induced growth of alkyltrimethylammonium bromides and chlorides at the cmc (5). At present, Eqs. [1] and [2] have no firm theoretical basis. For SDS (10), combination of an empirical relationship between the micellar aggregation number and the cmc with the known dependence of the cmc on the aqueous counterion concentration was shown to lead to Eqs. [1] and [2] with A 5 g 5 0.33*(1 2 a ). If general, this expression would predict g values in the range 0.19 – 0.26 for most detergents, given the fact that a values of ionic detergents are typically 0.2– 0.4 (6). Although g values of this magnitude were found for SDS (10) and several of its homologues (11), those of CTACl and CTAOAc are much smaller than expected from this approach. For salt-induced
GROWTH OF HEXADECYLTRIMETHYLAMMONIUM MICELLES
growth of spherical micelles at the cmc, Ikeda (5) proposed a model that leads to Eq. [1] with an A value given by the relationship A 5 N Aa ~e 2 /DkT!/~8b! 2 1.
[12]
In the present case, however, upon substitution of the relationship N A 5 20/a for spherical CTA micelles (7) and the appropriate values of the Bjerrum length (e 2 /DkT 5 0.71 nm) (36) and the micellar radius (b 5 2.6 nm) (4) into Eq. [12], one obtains a value of A 5 20.07. Thus, unless a is treated as a purely disposable fitting parameter (5), this model incorrectly predicts that the aggregation number of spherical CTACl and CTAOAc micelles should decrease with increasing added salt concentration. The present results, together with those from previous work (10, 11), show that the [detergent]- and [salt]-induced growth of spherical or globular ionic micelles below the onset of the sphere-to-rod transition can be conveniently described by Eq. [2]. In developing any detailed model for the growth in this region, several experimental trends should be taken into consideration. For a given headgroup, the value of g (Eq. [2]) or A (Eq. [1]) is relatively insensitive to detergent chain length. This was verified for g in previous work (10, 11) with anionic detergents and for A with homologous alkyltrimethylammonium chloride and bromide micelles (5). Although the affinity of the counterion for the micelle surface has a pronounced influence on micellar aggregation numbers themselves, no corresponding specific counterion effect is evident in either g or A. Thus, we find similar g values for CTACl and CTAOAc, and A values for the chloride and bromide salts of alkyltrimethylammonium (5), dodecyldimethylammonium (5), and dodecylpyridinium (8, 9) detergents appear to be counterion insensitive as well. In contrast, the nature of the detergent headgroup does appear to be a significant factor in determining the values of g or A. Thus, g values of anionic sodium alkylsulfate micelles (g 5 0.2– 0.25) (10, 11) are significantly larger than those of cationic CTA micelles (g 5 0.1). The A values of spherical dodecyltrimethylammonium, dodecyldimethylammonium, and dodecylammonium chloride micelles (5) are, respectively, 0.11, 0.16, and 0.42. These last results, in particular, suggest that smaller headgroups enhance the susceptibility of spherical micelles to [detergent]- and [salt]induced growth in the concentration region below the sphere-to-rod transition. CONCLUSIONS
Aggregation numbers of spherical CTACl and CTAOAc micelles, determined by time-resolved fluorescence quenching, increase with increasing concentration of counterions free in the intermicellar aqueous phase according to Eq. [2],
241
with g values on the order of 0.1. Although the rate of growth is insensitive to the nature of the counterion, the relative micelle sizes, determined by the constant N o , are strongly influenced by the counterion type. The present results for cationic CTA micelles confirm that Eq. [2] is a convenient general expression for describing the detergentand common-counterion salt-induced growth of ionic micelles in the concentration region below the sphere-to-rod transition. ACKNOWLEDGMENTS This work was supported by grants from the Fundac¸a˜o de Amparo a` Pesquisa do Estado de Sa˜o Paulo—FAPESP (Thematic Project 1994/ 3505-3) and PADCT-FINEP (Project 65-92-0063-00). L.T.O. and C.Y. acknowledge graduate and undergraduate fellowship support, respectively, from CAPES (Coordenac¸a˜o de Aperfeic¸oamento de Pessoal de Nı´vel Superior) and the CNPq (Conselho Nacional de Desenvolvimento Cientı´fico e Tecnolo´gico). F.H.Q. acknowledges the CNPq for research fellowship support. During her stay at the IQ-USP as a visiting research professor, R.R. was supported by a grant from FAPESP (Project 1998/ 3674-0).
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