Langmuir 1996, 12, 3225-3232
3225
Aqueous Solutions of Zwitterionic Surfactants with Varying Carbon Number of the Intercharge Group. 3. Intermicellar Interactions Y. Chevalier* Laboratoire des Mate´ riaux Organiques a` Proprie´ te´ s Spe´ cifiques, LMOPS-CNRS, BP 24, 69390 Vernaison, France
N. Kamenka Laboratoire des Proce´ de´ s et Mate´ riaux Membranaires, UMR9987 CNRS, Universite´ de Montpellier II, place E. Bataillon, 34095 Montpellier Cedex 5, France
M. Chorro Laboratoire des Agre´ gats Mole´ culaires et des Mate´ riaux Inorganiques, URA79 CNRS, Universite´ de Montpellier II, place E. Bataillon, 34095 Montpellier Cedex 5, France
R. Zana Institut Charles Sadron (CRM-EAHP), CNRS-ULP, 6 rue Boussingault, 67000 Strasbourg, France Received December 28, 1995. In Final Form: April 9, 1996X The effect of the presence of salt on the structure of, and interactions between, zwitterionic micelles has been studied using radioactive tracer self-diffusion and elastic and quasi-elastic light scattering. Intermicellar interactions were found to become significantly more repulsive in the presence of salt. Electrostatic interactions calculated from the known micellar charges do not account for the experimental results. The origin of those salt-induced repulsive interactions is discussed with the help of experimental data about a series of zwitterionic surfactants having polymethylene intercharge groups of variable length. An increase of micelle excluded volume by reorientation of the zwitterionic headgroups was found to be consistent with both elastic and quasi-elastic light-scattering data and with their variation with surfactant molecular structure. It is likely that electrostatic screening by salt adsorption at the micellar surface allows more conformational freedom, switching from a zwitterion orientation parallel to the interface to a more radial average orientation in the presence of an increasing NaCl concentration.
Introduction In previous studies reported as parts 1 and 2 in this series,1,2 we have shown that, in spite of the neutral nature of zwitterionic surfactants and their well documented insensitivity to ionic strength,3 electrolytes do bind to zwitterionic micelles. Binding of various ions to micelles which was suggested in earlier reports4-8 was unambiguously established from radioactive tracer self-diffusion and fluorescence-quenching data.1,2,9,10 It was further shown that anions bind more strongly than cations2,9,10 and that ion binding did not induce any variation of micelle aggregation number.1 A mass action law model was used to explain the experimental data, and an electrostatic origin for the binding was proposed.2 The larger binding X
Abstract published in Advance ACS Abstracts, June 1, 1996.
(1) Kamenka, N.; Chevalier, Y.; Zana, R. Langmuir 1995, 11, 3351. (2) Kamenka, N.; Chorro, M.; Chevalier, Y.; Levy, H.; Zana, R. Langmuir 1995, 11, 4234. (3) Bluestein, B. R., Hilton, C. L., Eds. Amphoteric Surfactants; Surfactant Science Series 12; Marcel Dekker: New York, 1982. (4) Bunton, C. A.; Mhala, M. M.; Moffat, J. R. J. Org. Chem. 1987, 52, 3832. (5) Bunton, C. A.; Mhala, M. M.; Moffat, J. R. J. Phys. Chem. 1989, 93, 854. (6) Brochsztain, S.; Berci-Filho, P.; Toscano, V. G.; Chaimovich, H.; Politi, M. J. J. Phys. Chem. 1990, 94, 6781. (7) Baptista, M. S.; Politi, M. J. J. Phys. Chem. 1991, 95, 5936. (8) Hodge, D. J.; Laughlin, R. G.; Ottewill, R. H.; Rennie, A. R. Langmuir 1991, 7, 878. (9) Amin-Alami, A. Thesis, University of Montpellier, 1989. (10) Kamenka, N.; Partyka, S.; Amin-Alami, A.; Chorro, M.; Faucompre´, B.; Zana, R. Colloids Surf., in press.
S0743-7463(95)01571-X CCC: $12.00
of anions with respect to cations results in the appearance of a negative electrical charge at the surface of micelles which are neutral in the absence of electrolytes. The strong intermicellar repulsions, observed by small angle neutron scattering in the presence of salt, were thus ascribed to electrostatic interactions,8 and a surface potential of 32 mV in 0.1 M NaCl medium was found on this basis. Such a surface potential value compares well with those found for micelles of the ionic surfactants dodecyltrimethylammonium bromide (DTAB) in 0.1 M NaBr or hexadecyltrimethylammonium chloride (CTAC) in 0.1 M NaCl.11 This very large and paradoxical effect (addition of salt usually screens electrostatic interactions) may come from this ion-binding process described by an adsorption equilibrium or by the mass action law: the larger the salt concentration, the larger the ion binding, the larger the electrical charge per micelle. The present work reports on a study of the interactions between zwitterionic micelles in the presence of sodium chloride. As the aggregation numbers and degrees of ion binding are known from previous fluorescence quenching1 and tracer self-diffusion2 measurements, electrostatic interactions were calculated and compared to experimental results. Moreover, a systematic study of a series of homologous zwitterionic surfactants of variable intercharge arm length allowed us to discuss more precisely interactions in relation with the surfactant chemical structure, that is at a molecular level.12,13 (11) Hayter, J. B.; Penfold, J. Colloid Polym. Sci. 1983, 261, 1022.
© 1996 American Chemical Society
3226 Langmuir, Vol. 12, No. 13, 1996
Zwitterionic surfactants of the R-(dodecyldimethylammonio)-ω-alkanoate type with the polymethylene intercharge arms being CH2, C3H6, C5H10, or C10H20 have been investigated. They are respectively referred to as C12N1CO2, C12N3CO2, C12N5CO2, and C12N10CO2 in the following. 1-(Dodecyldimethylammonio)-3-propylsulfonate (C12N3SO3) allowed the comparison of carboxylate and sulfonate groups. In pure water, those surfactants aggregate into small spheroidal micelles1,12,13 with different strengths of intermicellar interactions. For example, strong repulsive interactions were found for C12N1CO2 micelles14 while an attraction was found for C12N3SO3 ones, causing a demixion into two isotropic phases upon cooling (upper critical temperature of -2 °C15). The molecular origin of such intermicellar interactions is still not precisely known. Micellar structure and intermicellar interactions were investigated by means of elastic and quasi-elastic lightscattering and self-diffusion measurements. These methods provide complementary information.16 Extrapolations to infinite dilution of micelles give structural data about isolated micelles (at the cmc) while the dependence on surfactant concentration provides different types of thermodynamic functions of the intermicellar interaction potential. Thus, aggregation numbers were measured by elastic light scattering, and micelle hydrodynamic radii related to their translational diffusion coefficient were obtained from dynamic measurements. Systematic measurements were performed for the five surfactants in pure water and in the presence of added NaCl, at mole ratio [surfactant]/[NaCl] ) 1, providing quantitative data about the effect of salt addition in quite a similar way as in our previous studies of this series. Materials and Methods Materials. The surfactants were the same as in parts 1 and 2 in this series.1,2 Their synthesis and purification, together with their basic properties in pure water, were already described.12,13 Methods. Radioactive tracer self-diffusion measurements were described in Part 2 in these series.2 The micelle selfdiffusion coefficients Ds were measured at 25 °C by [14C]decanol labeling of the micelles. The diffusion rates of decanol and micelles are the same because decanol is fully solubilized into the micelles owing to its very low solubility in water. Decanol tracer self-diffusion coefficients are identical to those of decane17 or tetramethylsilane.18 Light-scattering measurements were carried out by means of an experimental device19 composed of a vertically polarized Spectra Physics argon laser operating at 514.5 nm and a Brookhaven-Amtec goniometer. Samples of solution were filtered with a 0.10 µm Millipore membrane into glass tubes of optical quality under a dust-free atmosphere (MV9 type laminar flow hood from ADS Laminaire). For elastic light-scattering, scattered intensities at a 90° scattering angle were expressed as Rayleigh ratios calculated using toluene as a calibration standard (R90° ) 3.20 × 10-5 cm-1). The relative error in scattered intensities (12) Chevalier, Y.; Storet, Y.; Pourchet, S.; LePerchec, P. Langmuir 1991, 7, 848. (13) Chevalier, Y.; Brunel, S.; LePerchec, P. J. Chim. Phys. 1995, 92, 1025. (14) Marignan, J.; Gauthier-Fournet, F.; Appell, J.; Akoum, F.; Lang, J. J. Phys. Chem. 1988, 92, 440. (15) Faulkner, P. G.; Ward, A. J. I.; Osborne, D. W. Langmuir 1989, 5, 924. (16) Candau, S. J. In Surfactant solutions, New methods of investigation; Zana, R., Ed.; Surfactant Science Series; Dekker: New York, 1987; Vol. 22, p 147. (17) Kamenka, N.; Haouche, G.; Faucompre´, B.; Brun, B.; Lindman, B. J. Colloid Interface Sci. 1985, 108, 451. (18) Lindman, B.; Puyal, M. C.; Kamenka, N.; Rymde´n, R.; Stilbs, P. J. Phys. Chem. 1984, 88, 5048. (19) Chevalier, Y.; Me´lis, F.; Dalbiez, J. P. J. Phys. Chem. 1992, 96, 8614.
Chevalier et al. was then 5%. Specific refractive index increments dn/dC (Table 1) were measured with a 2% accuracy using a BP-2000-V BricePhoenix differential refractometer equipped with a green light source. The overall accuracy of processed elastic scattering data (micelle aggregation numbers) was estimated to be 10%. The temperature was regulated at 25 ( 1 °C in both the lightscattering goniometer and the differential refractometer. In quasi-elastic light-scattering measurements, fluctuations of the scattered intensity were measured for sample times ranging from 0.1 to 3000 µs by logarithmic increments and the light autocorrelation functions were calculated with a digital correlator. Each measurement took from 10 to 30 min for obtaining a large enough signal-to-noise ratio. Surfactant molecular volumes were obtained from density measurements of aqueous solutions. Densities were measured with a PAAR DMA 602 density meter as a function of surfactant concentration above the cmc and converted into partial molecular volumes (Table 1) according to usual procedures.20,21
Theory Elastic Light Scattering. The intensity scattered by a micellar solution of surfactant concentration C (and micellized surfactant concentration C - cmc) is expressed as the excess Rayleigh ratio, R90° ) R90°,C - R90°,cmc. For a simple binary mixture of surfactant and solvent, it is related to the micelle aggregation number N and intermicellar interactions through
R90° )
4π2n2 dn 2 (C - cmc)NMmolS(0) ) NAvλ4 dC K0N(C - cmc)S(0) (1)
( )
where all symbols have their usual meaning16,22 and Mmol is the molar weight of the surfactant. As no angular dependence of scattered intensity was observed because of the small size of micelles,1 the form factor P(θ) was omitted in eq 1. The structure factor S(0) describes the intermicellar interactions. The aggregation number is obtained at infinite dilution of particles (at the cmc) when intermicellar interactions vanish (S(0) ) 1). This is carried out by means of an extrapolation of K0(C - cmc)/R90° to (C - cmc) ) 0 (Debye plot). Interactions between micelles of radius R and volume V ) NVmol ) 4πR3/3 are revealed by the second virial coefficient B defined in the following expansion in powers of the surfactant volume fraction Φ (eq 2) and related to the pairwise interaction potential U(r) by eq 3
K0(C - cmc)/R90° ) (1/N)(1 + BΦ + ...) B)
∫0∞(1 - e-U(r)/kT)r2 dr
4π V
(2) (3)
For pure hard spheres of radius Rhs, B ) 8(Rhs/R)3. If the interaction potential is split into two parts, a hard sphere core and a U(r) tail for r > Rhs, then
( )
B)8
Rhs R
3
+
∫2R∞
3 R3
hs
(1 - e-U(r)/kT)r2 dr
(4)
For multicomponent mixtures such as those containing surfactant, salt (Na+ and Cl- ions), and solvent, the situation is much more complex if the exact thermody(20) Guggenheim, E. A. Thermodynamics, 5th ed.; North-Holland: Amsterdam, 1967. (21) Desnoyers, J. E.; DeLisi, R.; Ostiguy, C.; Perron, G. In Solution Chemistry of Surfactants; Mittal, K. L., Ed.; Plenum Press: New York, 1979; Vol. 1, p 221. (22) Kerker, M. The scattering of light and other electromagnetic radiation; Academic Press: New York, 1969.
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Langmuir, Vol. 12, No. 13, 1996 3227
namic theory of Zernike23 is applied. The multicomponent system can be treated as a binary one consisting of scattering species immersed in a nonscattering medium, but the dn/dC term is then the partial derivative of the refractive index relative to the scattering species concentrations under the conditions of constant chemical potential of all other species.24 As sodium and chloride ions bind to micelles with fractions of bound ions βNa+ and βCl-, the scattering species are aggregates of concentration (C - cmc)/N composed of N surfactant molecules, NβNa+ sodium ions, and NβCl- chloride ions. The nonscattering medium contains the water solvent and sodium and chloride ions of respective concentrations (Csalt - βNa+C) and (Csalt - βCl-C) and free surfactant molecules of concentration equal to the cmc. Light-scattering and dn/ dC measurements upon independent concentration variations of each component and under osmotic equilibrium with the other ones are extremely difficult, and some concentrations cannot be varied independently because of the overall electroneutrality requirement. An accepted approximation then consists in lumping all species whose concentrations are varying concomitantly into a unique pseudocomponent. Thus, the solute pseudocomponent was defined as the surfactant + salt mixture at a constant [salt]/[surfactant] ratio and the solvent was pure water. The same approximation level has been extensively used in studies of micellar solutions of ionic surfactants in pure water for which the surfactant ion and its counterion are considered as a single pseudocomponent or when salt was added at a constant concentration, the solvent component being the salt solution (brine).24-29 As concentrations C are weights of surfactant + salt mixture per unit volume, the extrapolation to infinite dilution in the Debye plot gives the weight of micelles including surfactant and salt in the same ratio as for the overall solution composition. On the other hand, if C is defined as the surfactant weight per unit volume in both light-scattering and dn/dC measurements, the weight of the micelles which comes out of a Debye plot is that of their surfactant content only. We have used this later definition in the following because it allows a direct comparison with the salt-free measurements. The aggregation number is the micellar weight divided by the surfactant molecular weight in both cases. Quasi-Elastic Light Scattering. For a translational diffusion motion of monodispersed scattering particles, the exponential decay of the autocorrelation function g(1)(τ) is related to the collective (mutual) diffusion coefficient Dm by16,30 2
g(1)(τ) ) e-Dmq τ, with q ) (4πn/λ) sin(θ/2)
(5)
Dm depends on both direct and hydrodynamic intermicellar interactions.16,31 Because of these two contributions, the dependence of Dm on the micelle volume fraction Φ is linear in a larger concentration range than in a Debye plot for elastic light scattering. Intermicellar interactions are described by the same structure factor S(0) as for elastic scattering, giving a (1 + BΦ ) S(0)-1) linear dependence. Hydrodynamic interactions appear in the friction coef-
ficient as the (1 + H(0)) term, which gives a (1 - kfΦ) dependence
1 + H(0) Dm ) Dm0 ) Dm0(1 + kmΦ) ) S(0) Dm0(1 + (B - kf)Φ) (6) Thus, an extrapolation of the experimental data to Φ ) Φcmc gives the diffusion coefficient of an isolated micelle Dm0. For a hard sphere potential and a U(r) tail, an approximate expression of kf is16,27,32-34
kf ) 6.44 +
3 Rhs2
∫2R∞
hs
(1 - e-U(r)/kT)r dr
Radioactive Tracer Self-Diffusion. The micelle volume fraction dependence of the self-diffusion coefficient Ds reads
Ds ) Ds0(1 + ksΦ)
(8)
For hard spheres with hydrodynamic interactions, ks values ranging between 0 and -2.5 were found.35,36 The values ks ) -1.8330 or -1.7331 were shown to compare quite well with experiments,37 but the linear variation of Ds with Φ was found to hold over a volume fraction range larger than the limit of validity of theoretical approximations.37,38 This has already been observed with zwitterionic micelles.17,18,39,40 Interactions between Micelles. As chloride ions bind more strongly to zwitterionic micelles than sodium ions,2 the micelles get charged when sodium chloride is added. The interaction potential between micelles should then contain an electrostatic contribution Uel(r) arising from this electrical charge. The nonelectrostatic intermicellar potential is approximated as a hard sphere one, used as an effective potential which includes all short range interactions. Different approximate expressions of the surface electrostatic potential ψ0 and of the interaction potential U(r) have been given, their validity depending on the value of the micelle radius to Debye length (κ-1) ratio, κR. According to the charging by ion binding, the charge per micelle Z is
Z ) N(βNa+ - βCl-)
(9)
The inverse Debye length is related to the ionic concentrations in water as
κ2 )
103e2NAv 0kT
∑Cizi2
(10)
For NaCl, zi2 ) 1 and the Ci’s are the concentrations of Na+ and Cl- ions in water expressed in mol/L. Thus
∑Cizi2 ) 2Csalt - (βNa
+
(23) Zernike, F. Arch. Neerl. Sci. Exactes Nat. 1918, 4, 74. (24) Huisman, H. F. Proc. K. Ned. Akad. Wet., Ser. B: Phys. Sci. 1964, 67, 367, 376, 388, and 407. (25) Ikeda, S.; Tsunoda, M.; Maeda, H. J. Colloid Interface Sci. 1979, 70, 448. (26) Hayashi, S.; Ikeda, S. J. Phys. Chem. 1980, 84, 744. (27) Corti, M.; Degiorgio, V. J. Phys. Chem. 1981, 85, 711. (28) Imae, T.; Kamiya, R.; Ikeda, S. J. Colloid Interface Sci. 1985, 108, 215. (29) Imae, T.; Ikeda, S. Colloid Polym. Sci. 1985, 263, 756. (30) Berne, B. J.; Pecora, R. Dynamic Light Scattering; Wiley: New York, 1976. (31) Ackerson, B. J. J. Chem. Phys. 1978, 69, 684.
(7)
+ βCl-)C
(11)
(32) Batchelor, G. K. J. Fluid Mech. 1976, 74, 1. (33) Felderhof, B. U. J. Phys. A: Math. Gen. 1978, 11, 929. (34) Anderson, J. L.; Rauh, F.; Morales, A. J. Phys. Chem. 1978, 82, 608. (35) Jones, R. B.; Pusey, P. N. Annu. Rev. Phys. Chem. 1991, 42, 137. (36) Evans, G. T.; James, C. P. J. Chem. Phys. 1983, 79, 5553. (37) Pusey, P. N.; van Megen, W. J. Phys. 1983, 44, 285. (38) Walrand, S.; Belloni, L.; Drifford, M. J. Phys. 1986, 47, 1565. (39) Faucompre´, B.; Lindman, B. J. Phys. Chem. 1987, 91, 383. (40) Brun, B.; Haouche, G.; Kamenka, N. Tenside Deterg. 1984, 21, 307.
3228 Langmuir, Vol. 12, No. 13, 1996
Chevalier et al.
According to the concentration range of the present study, the values of κR range between 0.5 and 10. For κR > 0.5, the following analytical equation relating the micellar charge eZ to the surface potential ψ0 was shown to compare with exact numerical calculations within 5%41,42
eZ )
(
4π0kTκR2 2 sinh(eψ0/2kT) +
4 tanh(eψ0/4kT) κR (12)
)
This equation can be solved for ψ0, giving
(
)
cos-1(P/Q3) - a1 3 3 with P ) (1 - 3a1a2 - 2a1 )/2, Q ) (a12 + a2)1/2, a1 ) (1 + 4/κR - A)/3, a2 ) (1 + 4/κR + A)/3, eZ and A ) (13) 4π0kTκR2
eeψ0/2kT ) 2Q cos
For κR , 1 and small surface potential (eψ0/kT , 1), the DLVO interaction potential energy at constant electrical surface potential43,44 can be used. It is valid up to κR ) 1 at any interparticle separation and is shown by
e-κ(r-2R) U(r) ) 4π0ψ02R2 r
(14)
For κR > 3, a modified version of the expression given by Derjaguin43,45 introduced by Sader, Carnie, and Chan46 has been used
ln(1 + e-κ(r-2R)) U(r) ) 4π0Y2(r)R2 with Y(r) ) r (4kT/e)eκ(r/2-R) tanh-1(e-κ(r/2-R) tanh(eψ0/4kT)) (15) For 1 < κR < 3, there is no satisfactory analytical expression of U(r) and both equations 14 and 15 were used for comparison with the experimental data. The exact result is expected to lie in between those two. Results and Discussion Micelles at Infinite Dilution: Aggregation Number, Hydrodynamic Radius, and Hydration. From elastic and quasi-elastic light scattering, the aggregation number N and the mutual diffusion coefficient Dm0 at infinite dilution were obtained by extrapolation at the cmc. The autocorrelation functions were all single exponential (Figure 1) and the q2-dependence of the decay rate Γ was observed, showing that Dm is a mutual translational diffusion coefficient. Since the autocorrelation function is a single exponential, the micelles are quite monodisperse.47 A similar conclusion was reached1 on the basis of the constancy of the micelle aggregation number upon increasing the surfactant concentration. (41) Loeb, A. L.; Overbeek, J. Th. G.; Wiersema, P. H. The Electrical Double-Layer Around a Spherical Colloid Particle; MIT Press: Cambridge, MA, 1961. (42) Ohshima, H.; Healy, T. W.; White, L. R. J. Colloid Interface Sci. 1982, 90, 17. (43) Derjaguim, B. Trans. Faraday Soc. 1940, 36, 203. (44) Verwey, E. J. W.; Overbeek, J. Th. G. The Theory of the Stability of Lyophobic Colloids; Elsevier: Amsterdam, 1948. (45) Hogg, R.; Healy, T. W.; Fuerstenau, D. W. Trans. Faraday Soc. 1966, 62, 1638. (46) Sader, J. E.; Carnie, S. L.; Chan, D. Y. C. J. Colloid Interface Sci. 1995, 171, 46. (47) Pusey, P. N.; Fijnaut, H. M.; Vrij, A. J. Chem. Phys. 1982, 77, 4270.
Figure 1. Autocorrelation function for a 0.15 mol/L solution of C12N3SO3 with 1 equiv of NaCl.
At infinite dilution, Dm0 is the translational diffusion coefficient of an isolated micelle; it is thus identical to the self-diffusion coefficient Ds0. Also, as the [salt]/[surfactant] concentration ratio was equal to 1 throughout the measurements, both surfactant and salt were diluted concomitantly. Data extrapolated to infinite dilution of surfactant micelles were also extrapolated to [NaCl] ) cmc. The cmc values are small as compared to the concentration range used and can be neglected. Thus, Dm and Ds data with and without salt all tend to the same value at C ) cmc (Figure 2). For the same reason, elastic light-scattering data obtained both with and without salt extrapolated in a Debye plot to the inverse aggregation number of micelles at the cmc in pure water (Figure 3). Aggregation Numbers. The N values as obtained from elastic light scattering are collected in Table 1. They agree to within 20% with our previous determinations by means of time-resolved fluorescence quenching1 and with values reported in the literature from light scattering,48,49 selfdiffusion coefficients,17,40 and fluorescence.14,50,51 The larger discrepancy with out previous study1 is for C12N10CO2, which forms the smallest micelles. The aggregation numbers decrease as the length of the intercharge group increases because of the increasing bulkiness of the headgroup, as already discussed in previous papers.1,12,13,18 Hydrodynamic Radii. Assuming spherical micelles, their hydrodynamic radius Rh was calculated from their translational diffusion coefficient D0 by the StokesEinstein relationship
D0 )
kT 6πηRh
(16)
where η is the viscosity of the surfactant solution at the cmc (η ) 0.89 mPa s). The Rh values listed in Table 1 correlate with the values of the micelle aggregation number N. The hydrodynamic volume (4πRh3/3) exceeds that of the surfactant content of the micelles (V ) NVmol ) 4πR3/3). If this excess volume is ascribed to hydration water, an hydration number nh defined as the number of water molecules per surfactant can be estimated (Table 1) as
nh )
4π (R 3 - R3) 3NVwater h
(17)
where Vwater is the molecular volume of water (30 Å3). (48) Herrmann, K. W. J. Colloid Interface Sci. 1966, 22, 352. (49) Bathia, A.; Qutubuddin, S. Colloids Surf. 1993, 69, 277. (50) Lianos, P.; Zana, R., J. Colloid Interface Sci. 1981, 84, 100. (51) Malliaris, A.; LeMoigne, J.; Sturm, J.; Zana, R. J. Phys. Chem. 1985, 89, 2709.
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Langmuir, Vol. 12, No. 13, 1996 3229
Table 1. Aggregation Number and Hydrodynamic Radius at the cmc
surfactant
dn/dC (cm3/g) for surfactants in pure water
dn/dCa (cm3/g) for surfactants + 1 equiv NaCl
surfactant molecular volume, Vmol (nm3)
aggregation number, N
hydrodynamic radius, Rh (nm)
hydration number, nh
C12N1CO2 C12N3CO2 C12N5CO2 C12N10CO2 C12N3SO3
0.156 0.162 0.169 0.163 0.151
0.179 0.189 0.189 0.177 0.161
0.465 0.506 0.556 0.693 0.531
72 47 34 32 67
2.50 2.33 2.33 2.23 2.60
15 21 34 25 19
a C is the surfactant concentration expressed in g/cm3, but NaCl was diluted in the same way as the surfactant so as to retain the 1/1 stoichiometry.
Figure 2. Diffusion coefficient data for micelles of C12N3CO2, C12N5CO2, C12N10CO2, and C12N3SO3 in salt-free solution and with a stoichiometric amount of NaCl: (+) Dm in pure water; (*) Dm with NaCl; (O) Ds with NaCl.
Figure 3. Debye plots for C12N10CO2 and C12N3SO3 in pure water (+) and in the presence of a stoichiometric amount of NaCl (*). The vertical scale is such that the extrapolated values are in units of 1/N.
These hydration numbers may be different from those measured by other techniques because the definition of hydration water is related to the measurement method.52 (52) Chevalier, Y.; Zemb, T. Rep. Prog. Phys. 1990, 53, 279.
The hydration number of C12N1CO2 agrees with that determined by water self-diffusion.17,40 Also, as the aggregation numbers determined by light scattering (Table 1) and by dynamic fluorescence quenching1 are slightly different, hydration numbers may differ by ∼20% according to the choice of N. For the carboxylate surfactants having between 1 and 5 intercharge methylene numbers, the hydration numbers increase as the intercharge carbon number increases, that is as the carboxylate group gets more freedom to orient in a radial direction toward water. Conversely, the lesser hydration of C12N10CO2 is consistent with the folding of the hydrophobic intercharge group into the micelle core, which has been previously observed at the air-water interface.12,13 Interactions between Salt-free Micelles. The values of the second virial coefficient B and the interaction parameter km (Table 2) are quite sensitive to the molecular structure of the surfactants. In particular, the value of B decreases from 13.7 to -4.8, upon increasing the spacer carbon number. Recall that the results reported in Part 1 also suggested the existence of attractive interactions between C12N10CO2 micelles. The comparison of C12N3CO2 and C12N3SO3 shows that the nature of the headgroup has a very strong effect on the intermicellar interactions.
3230 Langmuir, Vol. 12, No. 13, 1996
Chevalier et al.
Table 2. Second Virial Coefficient B, km, and ks Values for the Salt-free Micelles and in the Presence of a Stoichiometric Amount of NaCl salt-free values
with added NaCl (1/1)
surfactant
B
km
B
km
ks
C12N1CO2 C12N3CO2 C12N5CO2 C12N10CO2 C12N3SO3
13.7 13.0 11.6 4.0 -4.8
1.81 1.46 0.97 -2.05 -4.03
19.2 20.9 27.5 10.7 7.6
2.83 3.68 3.48 0.85 2.52
-3.10 -3.18 -3.36 -3.50 -3.05
In the absence of salt, the micelles are expected to be electrically neutral. For pure hard sphere interactions, B ) 8Φhs/Φ ) 8(Rhs/R)3 and km ) 1.56Φhs/Φ ) 1.56(Rhs/ R)3. Thus, B or km values exceeding the limiting respective values of 8 or 1.56 are still consistent with pure hard sphere intermicellar interactions if Φhs g Φ. This is the case of surfactants with intercharge carbon numbers 1, 3, or 5 (Table 2). Then, if it is assumed that the hard sphere volume is filled with the surfactant and the hydration water, the values of B and km can be used to evaluate the hydration number nh as
nh )
Vmol B -1 Vwater 8
(
)
(18)
and a similar equation holds when replacing B/8 by km/ 1.56. Hydration numbers of 14, 11, and 8 can be calculated for the C12N1CO2, C12N3CO2, and C12N5CO2 surfactants, respectively, when using the B values given in Table 2. Clearly, the variation in these nh values is very different from that of the more directly calculated values of Table 1. Also, when considering km, only the value for C12N1CO2 is larger than 1.56 and the calculated hydration number of 2.5 is much lower than those calculated from B or from D0. Those discrepancies reveal that intermicellar interactions other than of the hard sphere type are operative in the system. The values of km for all surfactants but C12N1CO2 and of both B and km for C12N10CO2 and C12N3SO3 indicate that these interactions must be attractive. Such attractive interactions have been observed by direct force measurements between monolayers of the same surfactants adsorbed on mica.53 A phase separation upon cooling (upper consolute boundary) has been reported below a critical temperature of -2 °C15 with C12N3SO3, which shows the larger attractive intermicellar interactions (see values of B and km in Table 2). The hard sphere model has been successfully applied to zwitterionic micelles made with surfactants of the phenylphosphinate type, yielding a reasonable hydration number of 5.19 In light of the present study, this may result from a near complete compensation of attractive interactions by shorter range repulsive ones. A strong intermicellar attraction was observed for the surfactant with a decanediyl intercharge group, which led to phase separation upon heating.19 Table 2 also shows that strong attractive interactions are associated with long intercharge groups. Intermicellar Interactions in the Presence of Salt. The results listed in Table 2 clearly show that both B and km increase in going from salt-free systems to systems at [NaCl]/[surfactant] ) 1. The ks value for C12N1CO2 is also slightly more negative in the presence of NaCl than in pure water.17 Besides, in the course of the time-resolved fluorescence quenching studies of the same systems, we observed a slowing down of intermicellar exchange in (53) Chapel, J. P.; Perez, E.; Chevalier, Y. Colloids Surf., A 1993, 76, 59.
solutions of C12N10CO2 in going from water to 0.2 M NaCl aqueous solutions.1 All these results reveal an overall increase of intermicellar repulsions which can arise from an enhancement of intermicellar repulsions and/or a weakening of intermicellar attractions. The first possible cause of increasing intermicellar repulsions, upon addition of NaCl, lies in the larger binding to the micelles of Cl- with respect to Na+.2 The micelles thus become negatively charged and an intermicellar electrostatic repulsion should arise.8 Since the bound fractions of Na+ and Cl- ions are known from ref 2, the increases of B and km due to this micelle charging can be calculated from the values of the micellar charge Z (eq 9) and ionic strength (eqs 10 and 11), as explained in the theoretical section. B and km are experimentally obtained as the slopes of the linear variations of K0(C - cmc)/R90° and Dm with the surfactant volume fraction Φ. Under the present experimental conditions, the electrostatic intermicellar potential varies with the surfactant concentration because βNa+ and βCl- (thus Z and κ) depend on the salt and surfactant concentrations according to the salt-binding equilibrium.2 B and km are then experimental effective values. Therefore, theoretical effective B and km values were calculated as follows. The concentration-dependent electrostatic contributions to B and km, Bel(Φ) and kmel(Φ), were calculated as a function of Φ from the varying values of Z and κ-1. This allows the calculation of the theoretical variations of K0(C - cmc)/R90° and Dm with Φ as
NK0(C - cmc)/R90° ) 1 + B(salt-free)Φ + Bel(Φ)Φ ) 1 + BtheoΦ (19) Dm/Dm0 ) 1 + km(salt-free)Φ + kmel(Φ)Φ ) 1 + kmtheoΦ (20) The theoretical effective values Btheo and kmtheo were then determined from the slopes by a least square linear regression of the calculated data for surfactant concentrations below 0.05 g/cm3, where a quasi-linear variation is observed in the experimental data. The experimental and theoretical increases of B and km, ∆B ) B(with salt) - B(salt-free), and ∆km can in this manner be compared without any assumption about the type of interactions between salt-free micelles. Because surfactant and salt were diluted concomitantly under the experimental conditions, the Debye length varies in a large domain, resulting in values of κR between 0.5 and 10. The choice of equations permitting the calculations of B and km depends on whether κR is smaller or larger than 1. The calculations were thus carried out in the two limiting situations where κR . 1 and κR , 1, the exact result being expected to lie in between these two limits. The results listed in Table 3 clearly indicate that the increase of intermicellar repulsions upon NaCl addition cannot be due to the charging of the micelles, the calculated values being 5 to 20 times smaller than the experimental ones. The charge per micelle indeed remains moderate because both Cl- and Na+ bind to micelles, but the main reason for the weakness of electrostatic repulsions lies in the high ionic strength. Large micellar electrical charges require high concentrations of salt, resulting in high ionic strengths, which screen quite efficiently electrostatic interactions. Thus, some mechanism(s), other than electrostatic repulsions arising from micelle charging, must be operative in solutions of zwitterionic micelles and is (are) difficult to identify among the large number of interaction mech-
Aqueous Solutions of Zwitterionic Surfactants
Langmuir, Vol. 12, No. 13, 1996 3231
Table 3. Comparison of Experimental and Theoretical (Electrostatic) Salt-Induced Increases of B and km exp values
calc values for κR , 1
calc values for κR . 1
surfactant
∆B
∆km
∆B
∆km
∆B
∆km
C12N1CO2 C12N3CO2 C12N5CO2 C12N10CO2 C12N3SO3
5.5 7.9 15.9 6.7 12.4
1.02 2.22 2.51 2.90 6.55
0.24 0.26 0.41 0.43 0.08
0.16 0.14 0.21 0.23 0.05
0.20 0.22 0.34 0.36 0.06
0.14 0.12 0.17 0.19 0.04
anisms between colloidal particles.54 The physical origins of interactions between salt-free zwitterionic micelles are not known. Direct force measurements between monolayers of these zwitterionic surfactants53 have shown a very short range steep repulsive force and a longer range attractive one. The same behavior has been reported with zwitterionic phospholipids.55 The short range repulsion, referred to as ‘hydration force’, may be due to water structuring at the interface56 and/or steric repulsion associated with surfactant protrusion or undulations on a molecular scale.57-60 Discrete jumps of 0.27 nm (diameter of a water molecule) were observed upon both compression and decompression for separations (water layer thickness) below 1 nm.53 The exact origin of the total attractive force, often ascribed to dispersion forces only, is still obscure. The virial coefficients measured on micellar solutions of long intercharge group zwitterionic surfactants are stronger than those calculated for classical dispersion forces according to the accepted range of Hamaker constants.19 Since the short range repulsive ‘hydration’ and long range attractive forces are poorly understood, it is difficult to know in a definite manner whether the changes of B and km are due to a decrease of the attractive forces or an increase of the repulsive ones. The following discussion rests on interaction mechanisms that are still a subject of controversy.61 Ion binding should influence the short-range repulsive forces between micelles. Indeed, electrolytes modify the water structure at its vicinity and screen the electrostatic attractions between the opposite charges of the zwitterions, giving more conformational freedom to the headgroups. In particular, a larger protrusion of the hydrophilic carboxylate groups toward water may increase the range of this repulsive potential. On the other hand, low-frequency electrokinetic attractions between micelles can be screened by the presence of electrolyte in intermicellar water. Thus, London-van der Waals interactions are partly reduced62 and the attractive electrostatic interaction between micellar surfaces covered with orientable dipoles63-66 should vanish in high ionic strength media.
Figure 4. Schematic representation of the effect of salt adsorption on the micellar surface. The shaded region represents the micellar core.
The hard sphere potential can be used as a reference for describing zwitterionic micelles in the presence of salt. This is an effective potential characterized by the ratio Φhs/Φ. If only short range interactions were present, the hard sphere model should hold, and Φhs/Φ values calculated from B and km (after correcting for the small electrostatic contribution calculated above) should agree. This is obviously not the case, showing that long range interactions are operative, even at high salt concentrations. In cases where strong attractive interactions occur in salt-free solutions, at least part of them remain operative in the presence of NaCl, as indicated by the B value below 8 for C12N3SO3 and the km value below 1.56 for C12N10CO2. Thus the presence of electrolyte does not suppress totally intermicellar attractive interactions. The dependence of ∆B and ∆km on the surfactant chemical structure can help in a further discussion about the origin of the salt-enhanced intermicellar repulsions. The largest effects of the presence of NaCl were found for C12N5CO2 and C12N10CO2, which have the most flexible intercharge group. This suggests that the unpairing of the two opposite charges of the zwitterionic headgroup by bound ions sets the carboxylate group free into water. This provides a stronger short range intermicellar repulsion owing to excluded volume effects between those protruding groups, as shown in Figure 4. Unfolding of the zwitterionic intercharge groups in the presence of salt has been reported for lecithin bilayers.67 Also, molecular dynamics simulation of lecithin monolayers revealed that a reduction of the zwitterion electrical charge leads to a reorientation of the dipoles, which tend to become perpendicular to the interface.68 As reducing the charges is equivalent to adding salt, the conformation of the zwitterionic headgroup thus depends closely on electrostatic interactions at the interface. Therefore, the representation of the effect of salt in Figure 4 is in agreement with experimental data and simulations. Conclusions
(54) vanOss, C. J. J. Dispersion Sci. Technol. 1991, 12, 201. (55) Marra, J.; Israelachvili, J. Biochemistry 1985, 24, 4608. (56) Marcelja, S.; Radic, N. Chem. Phys. Lett. 1976, 42, 129. (57) Israelachvili, J. N.; Wennerstro¨m, H. Langmuir 1990, 6, 873. (58) Nilsson, U.; Jo¨nsson, B.; Wennerstro¨m, H. Faraday Discuss. Chem. Soc. 1990, 90, 107. (59) Granfeldt, M. K.; Miklavic, S. J. J. Phys. Chem. 1991, 95, 6351. (60) Miklavic, S. J. Chem. Phys. Lett. 1993, 210, 25. (61) Leikin, S.; Parsegian, V. A.; Rau, D. C.; Rand, R. P. Annu. Rev. Phys. Chem. 1993, 44, 369. (62) Mahanty, J.; Ninham, B. W. Dispersion Forces; Academic Press: London, 1976. (63) Granfeldt, M.; Jo¨nsson, B.; Wennerstro¨m, H. Mol. Phys. 1988, 64, 129. (64) Attard, P.; Mitchell, D. J. J. Chem. Phys. 1988, 88, 4391. (65) Jo¨nsson, B.; Attard, P.; Mitchell, D. J. J. Phys. Chem. 1988, 92, 5001. (66) Attard, P.; Mitchell, D. J.; Ninham, B. W. Biophys. J. 1988, 53, 457.
Intermicellar interactions between zwitterionic micelles in pure water and in the presence of NaCl have been studied by complementary techniques. Thus, elastic and quasi-elastic light scattering yielded the second virial coefficient B and the interaction parameter km, which depend in a different way on intermicellar interactions. Enhanced intermicellar repulsions occurred in the presence of added NaCl. Although micelles become charged in the presence of salt because of the different binding constants for Na+ and Cl-, electrostatic interactions between micelles remain negligibly small, owing to the (67) So¨derman, O.; Arvidson, G.; Lindblom, G.; Fontell, K. Eur. J. Biochem. 1983, 134, 309. (68) Ahlstro¨m, P.; Berendsen, H. J. C. J. Phys. Chem. 1993, 97, 1391.
3232 Langmuir, Vol. 12, No. 13, 1996
high ionic strengths required to obtain significant micellar charges. This result is at variance with the interpretation of small angle neutron-scattering data on a similar zwitterionic surfactant where salt-induced repulsions were assigned to electrostatics only.8 The elastic and quasielastic light-scattering data show that rather long range intermicellar interactions occur, even at high salt concentration. An electrostatic screening of attractions between opposite charges of the zwitterionic headgroups which leads to an unfolding of the zwitterion intercharge group at the micellar surface is a possible origin for the enhanced intermicellar repulsions in the presence of salt.
Chevalier et al.
By this mechanism, a larger protrusion of the carboxylate groups in water gives rise to an additional repulsive intermicellar interaction in qualitative agreement with the experimental data, especially with their dependence on the surfactant molecular structure. However, the results do not allow us to give a definite conclusion because of the low spatial resolution of light scattering. Future small angle neutron-scattering studies should provide higher resolution structural data about the micellar interfacial structure. LA951571L
