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Langmuir 2001, 17, 7980-7981
On the Significance of the Solubilization Power of Detergents Eurico Melo Instituto de Tecnologia Quı´mica e Biolo´ gicasITQB and Instituto Superior Te´ cnico-IST, R. da Quinta Grande, 6, 2781-901 Oeiras, Portugal
Adilson A. Freitas, Chang Yihwa, and Frank H. Quina* Instituto de Quı´mica, Universidade de Sa˜ o Paulo, CP 26077, Sa˜ o Paulo 05513-970, Brazil Received August 31, 2001 The solubilization power of a detergent, defined as the moles of solute dissolved in the micellar pseudophase at saturation per mole of micellized detergent, is often employed to characterize the affinity of a given detergent micelle for the solute of interest. As shown here, however, the solubilizing power is the product of two equilibrium constants, one of which expresses the intrinsic solute-micelle affinity and the other the saturation solubility of the solute in the intermicellar aqueous phase. Consequently, for relatively water insoluble solutes, the maximum extent of solubilization can be dictated by the saturation of the aqueous phase rather than by saturation of the micellar phase itself, with the result that micellar solutions can saturate even when a substantial fraction of the micelles have no solute dissolved in them (at occupation numbers much less than unity).
The ability of micelles to solubilize very water insoluble organic molecules is a property of fundamental importance in many practical applications of detergents. One common approach for quantification of this property is in terms of the solubilization power of the detergent, PS, defined as the moles of solute dissolved in the micellar pseudophase per mole of micellized detergent at saturation,1,2 usually expressed as
PS ) [Smic]sat/CD
(1)
where [Smic]sat is the analytical concentration of micelleincorporated solute and CD ) CT - cmc is the concentration of micellized detergent, equal to the total detergent concentration (CT) minus the critical micelle concentration (cmc). The value of PS can be conveniently determined by the saturation solubilization method.2,3 In this method, a series of aqueous micellar solutions of increasing total detergent concentration is allowed to come to equilibrium with excess pure liquid or solid solute. After removal of the excess undissolved solute, typically by centrifugation and/or ultrafiltration, the total concentration of solute dissolved in each saturated solution, [ST]sat, is determined by an appropriate analytical method such as absorption spectroscopy. A plot of [ST]sat vs CT (or CD) provides PS as the slope above the cmc
[ST]sat ) [Saq]sat + [Smic]sat ) [Saq]sat + PS(CT - cmc) (2) Alternatively, the saturation solubilization of organic solutes by detergent micelles can be expressed in terms of the micelle-water partitioning coefficient, KS, defined as4,5 * To whom correspondence may be addressed. Fax: 00-55-38155579. E-mail:
[email protected]. (1) Rosen, M. J. Surfactants and Interfacial Phenomena, 2nd ed.; Wiley: New York, 1989; p 170ff. (2) Liu, G. G. H.; Roy, D.; Rosen, M. J. Langmuir 2000, 16, 3595. (3) Kim, J.-H.; Domach, M. M.; Tilton, R. D. Langmuir 2000, 16, 10037. (4) Sepu´lveda, L.; Lissi, E.; Quina, F. H. Adv. Colloid Interface Sci. 1986, 25, 1. (5) Rodrigues, M. A.; Alonso, E. O.; Yihwa, C.; Farah, J. P. S.; Quina, F. H. Langmuir 1999, 15, 6770.
KSsat ) [Smic]sat/([Saq]satCD) ) PS/[Saq]sat
(3)
where [Saq]sat is the limiting solubility of the solute in the aqueous phase at saturation. Combining this expression with the mass balance relationship [ST]sat ) [Saq]sat + [Smic]sat and rearrangement leads to the relationship4,5
[ST]sat/[Saq]sat ) 1 + KSsat CD
(4)
Thus, if [Saq]sat is known, the value of KSsat can also be determined from the slope of plots of the increase in the net solubilization of the solute with increasing CD. Theory indicates that nonionic solutes should ideally distribute between the micelles according to Poisson statistics,6,7 in a manner that depends only on the average number of solutes per micelle, 〈n〉 ) [Smic]/[mic]. In addition to the assumption that the solutes do not interact with each other, Poisson statistics assumes that there is no limit to the number of solutes that can be incorporated into a given micelle. There are a number of experimental studies6 that support the Poisson distribution as the correct one for nonionic solutes at low to moderate 〈n〉. A case in point is pyrene, where self-quenching of pyrene monomer fluorescence in micelles due to excimer formation has been shown by time-resolved fluorescence measurements to fit nicely to the Infelta-Tachiya equation,6 which explicitly assumes a Poisson distribution of the quencher (i.e., ground-state pyrene) among the micelles. The experimental verification of Poisson statistics for pyrene requires that the maximum number of pyrene molecules that can be accommodated in the micelle, nmax, must be much larger than the values of 〈n〉 employed in the experiment8 (typically in the range of 0.2-1.0). One interesting aspect of the results of saturation solubility measurements is that the average number of solutes incorporated per micelle at saturation, 〈n〉sat, not (6) Gehlen, M. H.; DeSchryver, F. C. Chem. Rev. 1993, 93, 199. (7) Barzykin, A. V.; Tachiya, M. Heterogeneous Chem. Rev. 1996, 3, 105. (8) If 〈n〉max were similar to 〈n〉sat, the solute distribution would be binomial rather than Poisson,9 with noticeable deviations from the Infelta-Tachiya equation.7 (9) Hunter, T. F. Chem. Phys. Lett. 1980, 75, 152.
10.1021/la0155606 CCC: $20.00 © 2001 American Chemical Society Published on Web 11/30/2001
Letters
Langmuir, Vol. 17, No. 26, 2001 7981
only is highly solute dependent but also can be substantially smaller than unity in some cases (Table 1). Thus, for anthracene and perylene, the 〈n〉sat values for micellar sodium dodecyl sulfate (SDS) are only 0.1 and 0.03, respectively.10 Under these conditions, the fraction of micelles unoccupied by the solute (equal to exp[-〈n〉sat] for a Poisson distribution), is 90% for anthracene and 97% for perylene, i.e., the micellar solution saturates when only a minor fraction of the micelles have any solute at all in them! Even in the case of pyrene, an SDS micellar solution saturates at a value of 〈n〉sat of less than unity (Table 1). Clearly, then, in these cases the value of 〈n〉sat must be substantially smaller than 〈n〉max, implying that the saturation of the micellar solution by the solute can be determined by factors unrelated to the maximum solubilization capacity of the micelle itself. The motive for this apparent conundrum, i.e., that saturation of the micellar solution does not necessarily imply saturation of the micellar phase, is straightforward but not generally perceived. Consider the following expression, readily obtained from eq 3
PS ) KSsat [Saq]sat
(5)
and the definition of 〈n〉sat
〈n〉sat ) [Smic]sat/[mic] ) Nag[Smic]sat/CD ) NagPS ) NagKSsat[Saq]sat (6) where Nag is the average aggregation number of the micelle. The germane feature of these equations is the direct dependence of PS and 〈n〉sat on the product KSsat[Saq]sat. The obvious consequence is that although very highly hydrophobic solutes have large values of KSsat, they are also much less soluble in water. Experimentally, it is well-known that very water insoluble organic molecules are often correspondingly more difficult to solubilize in appreciable quantities in micellar solutions.11,12 This trend is clear in the data of Table 1, where [Saq]sat and KSsat exibit inverse behavior and both PS and 〈n〉sat decrease markedly with decreasing water solubility of the organic molecule. An interesting test of this inverse behavior of [Saq]sat and KSsat is provided by the data (see Table 1) for the saturation solubilization of p-diiodobenzene in micellar SDS in the presence and absence of acetonitrile (10 vol %).13 The addition of acetonitrile increases the solubility of p-diiodobenzene in water by a factor of about 3, while reducing the value of KSsat by a factor of about 1.7, with the net result that PS increases ca. 2-fold. In summary, eq 5 has two important implications for the common assumption that PS values are a measure of the “intrinsic” solubilizing power of the detergent. Evidently, if measurements are made on a single solute in a series of detergents, [Saq]sat should be approximately (10) Almgren, M.; Grieser, F.; Thomas, J. K. J. Am. Chem. Soc. 1979, 101, 279. (11) This is one of the reasons that the saturation solubility method is most adequate for molecules that have very low water solubility. These have small values of 〈n〉sat, providing the value of KS at a low extent of solute incorporation into the micelles. In contrast, for more water soluble molecules, 〈n〉sat can be very large, which may affect the value of KS due to the presence of multiple solutes in the micelles. Thus, the value of 〈n〉sat calculated via eq 3 provides a good indication as to whether the KS value determined by saturation solubility is or is not comparable to values of KS determined at low degrees of solute incorporation by other methods. (12) An uncommon counterexample is provided by saturation solubilization data for the homologous n-alkylbenzenes in 1-dodecanesulfonic acid micelles, where 〈n〉sat was found to increase with decreasing water solubility of the solute: Take’uchi, M.; Moroi, Y. Langmuir 1995, 11, 4719.
Table 1. Saturation Solubilization of a Series of Aromatic Hydrocarbons and Derivatives in Micellar Sodium Dodecyl Sulfate (SDS) solutea
[Saq]sat, M
PS (eq 1)
perylene
1.6 × 10-9
4 × 10-4
anthracene
2.2 ×
pyrene
6×
p-diiodobenzened p-diiodobenzene (10% CH3CN)d,e o-diiodobenzened m-diiodobenzened biphenyl 1-methylnaphthalene toluene p-xylene benzene
KSsat, M-1 (eq 3)
〈n〉sat (eq 6)
5.6 × 10-6 1.7 × 10-5
1.5 × (1.0 × 10-3)b 1.6 × 10-2 (6.8 × 10-3)c (9.0 × 10-3)b 7.2 × 10-3 1.3 × 10-2
2.7 × 105 (2.2 × 105)b 6.5 × 103 (3.3 × 103)b 2.7 × 104 (1.1 × 104)c (1.5 × 104)b 1.3 × 103 740
0.46 0.56
6.1 × 10-5 3.1 × 10-5 4.1 × 10-5 2.1 × 10-4
1.8 × 10-2 7.0 × 10-2 4.8 × 10-2 0.25
290 2.3 × 103 1.2 × 103 1.2 × 103
1.1 4.5 3.1 16
6.8 × 10-3 1.84 × 10-3 2.3 × 10-2
0.58 0.47 0.60
85 260 26
37 30 38
10-7
10-7
10-3
0.03 0.1 1.0 (0.5)c
a From data of ref 10 at 21 °C in water assuming N ) 64, except ag as noted. b Reference 2, at 25 °C. c Reference 3, at 25 °C. d This work, at 30 °C; see ref 13. e 10% acetonitrile (by volume) added.
constant and the PS values will in fact be directly proportional to the relative affinities of the solute for each micellar pseudophase, i.e., to KSsat. In contrast, if measurements are made for a series of different solutes in a single detergent (e.g., the values for SDS in Table 1), the PS values depend not only on KSsat but also on [Saq]sat, i.e., on the maximum extent to which the solute dissolves in the intermicellar aqueous phase. Thus, in this latter case, PS does not itself provide a simple measure of the intrinsic affinity of the solutes for the micelle. Furthermore, in both cases, the solubilization can be limited by saturation of the aqueous phase (by the value of [Saq]sat) rather than by saturation of the micellar phase itself. This is undoubtedly the case when saturation of the micellar solution occurs at 〈n〉sat values less than unity, i.e., when a substantial fraction of the micelles are still unoccupied by solute. Acknowledgment. This work was supported by an ICCTI/CAPES grant for international collaborative research and project PRAXIS/2/2.1/QUI/317/94 to E.M. F.H.Q. thanks the Conselho Nacional de Desenvolvimento Cientı´fico e Tecnolo´gico (CNPq) for fellowship support. A.A.F. and C.Y. acknowledge doctoral fellowship support from the Fundac¸ a˜o de Amparo a` Pesquisa do Estado de Sa˜o Paulo (FAPESP). LA0155606 (13) Ultrapure water (Millipore Milli-Q) with or without 10% acetonitrile (Mallinckrodt, spectroquality) by volume was employed to prepare a series of solutions with varying concentrations (0, 0.06, 0.08, 0.10, and 0.12 M) of SDS (Baker ultrapure bioreagent grade SDS). The solutions were equilibrated at 30 °C with liquid o-diiodobenzene or solid m- or p-diiodobenzene (Aldrich, 98-99%) and centrifuged for 10 min at 2000g in a Fisher Marathon 21k centrifuge. An aliquot of the supernatant was diluted in acetonitrile, and [ST]sat values were determined by absorption spectroscopy employing the experimentally determined molar extinction coefficients (analysis wavelength) of 29600 (216), 19200 (226), and 22000 M-1 cm-1 (244 nm) for o-, m-, and p-diiodobenzene. The values of [Saq]sat for o-, m-, and p-diiodobenzene in water at 30° C (Table 1) agree well with those reported at 25° C (5.1 × 10-5, 2.8 × 10-5, and 4.9 × 10-6, respectively).14 The cmc values in the presence (0.0106 M) and absence (0.0074 M) of 10% acetonitrile were determined by conductivity in the usual manner and a micellar aggregation number of 44 in the presence of 10% acetonitrile was determined by time-resolved fluorescence quenching6 with pyrene as probe and the N-hexadecylpyridinium ion as the immobile quencher, following the procedure described elsewhere.15 (14) Yalkowsky, S. H. Aqueous Solubility: Methods of Estimation for Organic Compounds; Marcel Dekker: New York, 1992. (15) Ranganathan, R.; Okano, L. T.; Yihwa, C.; Quina, F. H. J. Colloid Interface Sci. 1999, 214, 238.
