Tuning Microstructure of Cationic Micelles on Multiple Length Scales

The differing effects of penetrating (2,6-dichlorobenzoate) and nonpenetrating (chloride) counterions on micellar surface charge density and on the re...
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Langmuir 2000, 16, 149-156

149

Tuning Microstructure of Cationic Micelles on Multiple Length Scales: The Role of Electrostatics and Specific Ion Binding† L. J. Magid,* Z. Han, and Z. Li Department of Chemistry, University of Tennessee, Knoxville, Tennessee 37996-1600

P. D. Butler NCNR, National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8562 Received June 2, 1999. In Final Form: September 20, 1999 Small-angle neutron scattering has been used to obtain detailed information on local structure, including micellar cross-sectional radii, areas per headgroup, and number of surfactant molecules per unit length for mixed micelles of cetyltrimethylammonium 2,6-dichlorobenzoate and cetyltrimethylammonium chloride in water as a function of surfactant and salt concentrations and the relative amounts of the two counterions (the counterion inventory) at the micellar surface. The differing effects of penetrating (2,6-dichlorobenzoate) and nonpenetrating (chloride) counterions on micellar surface charge density and on the relative energies of surfactant monomers in cylindrical vs end-cap micellar environments are elucidated.

Introduction For cationic surfactants such as cetyltrimethylammonium (CTAX) and cetylpyridinium (CPyX) in aqueous solution, it has long been known that counterions which strongly bind to and penetrate the headgroup plane at the micellar surface are strong promoters of micellar growth. Many such counterions are aromatic, such as salicylate (Sal),1-6 mono- and dichlorobenzoates (ClBz’s),7 tosylate,8 and some hydroxynaphthalenecarboxylates,9 but medium-chain alkylsulfonates10 and inorganic anions such as chlorate11 are also effective. For example, CTASal † Part of the Special Issue “Clifford A. Bunton: From Reaction Mechanisms to Association Colloids; Crucial Contributions to Physical Organic Chemistry”.

(1) (a) Kalus, J.; Hoffmann, H.; Reizlein, K.; Ulbricht, W.; Ibel, K. Ber. Bunsen-Ges. Phys. Chem. 1982, 86, 37. (b) Rehage, H.; Hoffmann, H. Faraday Discuss. Chem. Soc. 1983, 76, 363. (c) Hoffmann, H.; Rehage, H.; Reizlein, K. Thurn, H. Proceedings of the ACS Symposium on Macroand Microemulsions; American Chemical Society: Washington, DC, 1985; p 41. (2) (a) Wan, L. S. C. J. Pharm. Sci. 1966, 55, 1395. (b) Gravsholt, S. J. Colloid Interface Sci. 1976, 57, 575. (c) Ulmius, J.; Wennerstro¨m, H.; Johansson, L. B.-Å; Lindblom, G.; Gravsholt, S. J. Phys. Chem. 1979, 83, 2232. (3) Underwood, A. L.; Anacker, E. W. (a) J. Phys. Chem. 1984, 88, 2390. (b) J. Colloid Interface Sci. 1985, 106, 1985. (4) Imae, T.; Kohsaka, T. J. Phys. Chem. 1992, 96, 10030. (5) (a) Shikata, T.; Hirata, H. Langmuir 1987, 3, 1081. (b) Shikata, T.; Hirata, H.; Kotaka, T. Langmuir 1988, 4, 354. (6) Lin, M. Y.; Hanley, H. J. M.; Sinha, S. K.; Straty, G. C.; Peiffer, D. G.; Kim, M. W. Phys. Rev. E. 1996, 53, R4302. (7) (a) Carver, M.; Smith, T. L.; Gee, J. C.; Delichere, A.; Caponetti, E.; Magid, L. J. Langmuir 1996, 12, 691. (b) Kreke, P. J.; Magid, L. J.; Gee, J. C.; Langmuir 1996, 12, 699. (c) Magid, L. J.; Han, Z.; Warr, G. G.; Cassidy, M. A.; Butler, P. D.; Hamilton, W. A. J. Phys. Chem. B 1997, 101, 7917. (8) (a) Soltero, J. F. A.; Puig, J. E. Langmuir 1996, 12, 2654. (b) Kaler, E. W.; Herrington, K. L.; Murthy, A. K.; Zasadzinski, J. A. N. J. Phys. Chem. 1992, 96, 6698. (9) (a) Brown, W.; Johansson, K.; Almgren, M. J. Phys. Chem. 1989, 93, 5888. (b) Hassan, P. A.; Valaulikar, B. S.; Manohar, C.; Kern, F.; Bourdieu, L.; Candau, S. Langmuir 1996, 12, 4350. (c) Mendes, E.; Narayanan, J.; Oda, R.; Kern, F.; Candau, S. J.; Manohar, C. Langmuir 1997, 13, 2256. (d) Narayanan, J.; Manohar, C.; Kern, F.; Lequeux, F.; Candau, S. J. Langmuir 1997, 13, 5235. (e) Hassan, P. A.; Candau, S. J.; Kern, F.; Manohar, C. Langmuir 1997, 14, 6025. (10) Hoffmann, H.; Kalus, J.; Schwandner, B. Ber. Bunsen-Ges. Phys. Chem. 1987, 91, 99.

and CTA35ClBz micellar solutions contain giant flexible wormlike micelles and are already semidilute at volume fractions, φ, below 0.1%. These micelles are often called equilibrium, rather than quenched, polyelectrolytes because their aggregation numbers (e.g., degree of polymerization) are concentration-dependent.12 In the case of the almost complete counterion binding exhibited by surfactants such as CTAC8SO3 and CTAHNC (HNC ) 3-hydroxy-2-naphthalenecarboxylate), vesicles instead of micelles are found. This can be understood in terms of geometry, e.g., the surfactant packing parameter,13 v/al, where v is the volume per surfactant, a is the effective area per molecule at the surfactant/water interface, and l is the extended length of the surfactant chain. Surfactant aggregate morphology follows v/al as spheres (∼1/3), cylinders (∼1/2), and bilayers (∼1). Strong counterion binding screens electrostatic repulsions, allowing a to decrease, just as adding salt does; penetrating counterions also increase v and may decrease l as well. Penetrating counterions are thus in some respects similar to cosurfactants. Average counterion loci at micellar surfaces can be assessed via measurement of surface potentials, zeta potentials and counterion-induced chemical shift changes for NMR resonances of surfactant headgroups. Surface potentials report on the extent of counterion penetration into the headgroup region: the closer to zero they are, the more extensive the penetration and the higher the counterion concentration in the micelles’ Stern layer. Zeta potentials are sensitive to the counterion distribution in the diffuse double layer as well. For tetradecyltrimethylammonium micellar surfaces, surface potentials remain positive when NaSal is added to the solution, but the micelles’ zeta potential reverses sign.14 For highly hydrated counterions such as chloride, which bind more weakly and do not penetrate the micelle surface, (11) Appell, J.; Marignan, J. J. Phys. II 1991, 1, 1447. (12) Magid, L. J. J. Phys. Chem. B 1998, 102, 4064. (13) Israelachvili, J. N.; Mitchell, D. J.; Ninham, B. W. J. Chem. Soc., Faraday Trans. 2 1976, 72, 1525. (14) Cassidy, M. A.; Warr, G. G. J. Phys. Chem. 1996, 100, 3237.

10.1021/la990686c CCC: $19.00 © 2000 American Chemical Society Published on Web 11/12/1999

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the micelles are small and globular over a wide range of surfactant and salt concentrations. The salt-induced sphere-to-rod micellar transition for CTACl is assessed by light scattering15 to occur at 1.2 M NaCl. The Debye screening length (κ-1) for these solutions is ca. 0.3 nm, much smaller than the mean micellar radius of ca. 2.5 nm, so that intermicellar electrostatic repulsions are wellscreened long before micellar growth starts for CTACl. Intermediate cases include counterions such as bromide and 2,6-dichlorobenzoate (26ClBz-). In prior work, we established that for CTABr16 and CTA26ClBz7a micelles in water the onset of growth occurs above surfactant concentrations, c, of 150 and 70 mM, respectively; at 10 mM surfactant, salt-induced growth begins at 0.07 M KBr (κ-1 ) 1.2 nm) and 0.04 M Na26ClBz (κ-1 ) 1.5 nm). In a salted mixed micellar system of CTA26ClBz/CTACl with Na26ClBz/NaCl, we established that at total salt concentrations, cs, below 0.1 M, increasing the mole fraction of 26ClBz increases the value of κ-1 at which growth begins.7c At constant ionic strength, produced by holding cs/c constant at five, growth begins at κ-1 ) 1.05 nm for a molar ratio of 2:8 but at 1.5 nm for 6:4, clearly showing the role of counterion specificity. Counterion selectivity coefficients7c for the CTA+ micellar surface, measured via the ion flotation technique or by 1H NMR, are ca. 2-3 for KBr/Cl and 16-20 for K26ClBz/Cl, consistent with the observed effects of differential counterion binding on micellar growth. In the present study, we explore fully the morphological consequences of counterion inventory for CTA26ClBz/ CTACl mixed micellar systems. The progression from globular micelles through short rigid rods to semiflexible wormlike micelles and back to globular micelles is tuned by varying the counterion molar ratio as well as the overall cs. In this work, analysis of small-angle neutron scattering (SANS) data allows us to obtain detailed information on local structure, including micellar cross-sectional radii, areas per headgroup, and number of surfactant molecules per unit length. Qualitative information on overall micellar size (length) and flexibility is presented, but quantitative analysis of the SANS data to obtain overall micellar contour lengths and persistence lengths will be addressed in a later paper.17

growth.20 The effect of the electrostatics depends on the screening length. In dilute, salt-free solution where the average micellar length is less than the mesh size for the cylinders (L h < r/φ1/2, r being the micellar radius), there is a well-defined minimum in the free energy per surfactant as a function of n, and L h depends only weakly on φ:

L h = lBv*2(Ec + log(φ/n))

Factors affecting micellar growth. Figure 112,18 summarizes micellar growth regimes for neutral micelles (nonionic surfactants or ionic surfactants in the presence of high concentrations of salt) and for charged micelles at a range of ionic strengths. For neutral micelles undergoing unidimensional growth, the mean micellar length (or equivalently aggregation number, n) at volume fraction φ is given by:19

(1)

where Ec is the end-cap energy, the energy required to create two (hemispherical) end caps as a result of rod scission. High end-cap energies favor the formation of large micelles. For charged micelles, there is an electrostatic contribution to the energy of scission, arising from the repulsion of micellar surface charges, which opposes micellar (15) Imae, T.; Ikeda, S. Colloid Polym. Sci. 1987, 265, 1090. (16) Quirion, F.; Magid, L. J. J. Phys. Chem. 1986, 90, 5435. (17) Manuscript submitted to J. Phys. Chem. B. (18) Faetibold, E.; Waton, G. Langmuir 1995, 11, 1972. (19) Cates, M. W.; Candau, S. J. J. Phys.: Condens. Matter 1990, 2, 6869.

(2)

Here the Bjerrum length is denoted by lB, and v* is an effective charge per unit length. The electrostatic contribution and the size distribution in the semidilute regime are given by:

Ee = kBTlBrv*2φ-1/2

(3)

L h = φ1/2 exp[(Ec - Ee)/2kBT]

(4)

As Figure 1 shows, the predicted onset of strong micellar growth for the salt-free case occurs at the overlap volume fraction, φ*, for the micellar cylinders, which marks the transition from dilute to semidilute solution:

φ* = (kBTlBrv*2/Ec)2

Theoretical Background

L h = φ1/2 exp[Ec/2kBT]

Figure 1. Micellar growth upon increasing surfactant volume fraction. The curves for the salt-free micelles and the neutral micelles were calculated with Ec ) 20kBT. The curve for systems at moderate ionic strength is schematic. The dashed straight line represents the overlap concentration. Reprinted with permission from ref 12.

(5)

Equation 5 predicts that values of φ* for CTAX micelles can vary greatly, as observed experimentally, because of the dependence of v* and Ec on the identity of X-. In the presence of salt, micellar growth can occur already in the dilute regime. This is understood by replacing the surfactant volume fraction by an effective volume fraction which includes both surfactant and salt concentrations and is directly related to the screening length of the electrostatic interactions: φ ) φ + 8πlbr2cs. When c , cs, the second term dominates and eq 3 becomes:

Ee = kBTlBv*2/κ

(6)

given that κ equals (8πlBcs)1/2, with cs expressed as molecules per unit volume. Many rheological investigations,21-23 of CTAX and CPyX micellar solutions for which φ* is small have been (20) (a) Safran, S.; Pincus, P.; Cates, M. E.; Mackintosh, F. J. Phys. (Paris) 1990, 51, 503. (b) Mackintosh, F.; Safran, S.; Pincus, P. Europhys. Lett. 1990, 12, 697. (21) Kern, F.; Lequeux, F.; Zana, R.; Candau, S. J. Langmuir 1994, 10, 1714. (22) Khatory, A.; Kern, F. Lequeux, F.; Appell, J.; Porte, G.; Morie, N. Ott, A.; Urbach, W. Langmuir 1993, 9, 933.

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interpreted in terms of the occurrence of intermicellar connections (branching), equivalent to a decrease in average micellar length, as either or both c and cs increase. Branching has also been observed directly in cryo-TEM images.24 The formation of connections is inferred to occur when the scission energy, Ec - Ee, becomes larger than the energy of formation of a 3-fold branch. A high end-cap energy results when the difference in free energy per surfactant molecule in the two local packing environments of the (hemispherical) end-cap and cylindrical body of the micelle, fcap - fcyl, is large. The nonelectrostatic components of these free energies include:25

f ) fhg + fint + fch

(7)

where fhg refers to steric interactions between headgroups, fint to the surface energy associated with the hydrocarbonwater interface, and fch to the chain (hydrocarbon tail) contribution to the free energy. All three terms depend on the local geometry, e.g., on a and on the local radii of curvature. Use of Bending Rod Plots in Assessing Micellar Radii of Gyration and Flexibility. In static scattering, the excess scattered intensity due to the micelles, neglecting intermicellar interactions, is given by:26

I(Q,c) ) KcMw〈P(Q,c)〉

(8)

where Q ) (4π/λ) sin θ, with 2θ denoting the scattering angle and λ the incident neutron wavelength; K is the usual collection of constants appropriate for light, X-rays or neutrons. S(Q,c) is the time-averaged structure factor. 〈P(Q,c)〉 is the form factor averaged over the micellar molecular weight distribution; for rigid cylindrical or flexible wormlike micelles, it can be split into two factors, written here for the case of the wormlike object:27

〈P(Q,c)〉 ) Pcs(Q,rcs)〈Pwc(Q,L(c),lp(c))〉

(9)

Pcs corresponds to the structure of the particle’s cross section, whose radius is rcs, while Pwc, the form factor for the infinitely thin wormlike chain, depends on micellar length, L, and persistence length, lp, and is proportional to Q-1. Figure 2 presents a typical bending rod (BR) plot,28 Q I(Q) vs Q, which is a useful device29,30 for highlighting the Q ranges sensitive to the various micellar length scales of interest. Provided the average contour length, 〈L(c)〉 , is greater than 2lp, a maximum appears in the BR plot. The micellar radius of gyration, Rg, can be obtained from (23) (a) Kadoma, I. A.; Ylitalo, C.; van Egmond, J. W. Rheol. Acta 1997, 36, 1. (b) Kadoma, I. A.; van Egmond, J. W. Langmuir 1997, 13, 4551. (24) (a) Danino, D.; Talmon, Y.; Levy, H.; Beinert, G.; Zana, R. Science 1995, 269, 1420. (b) Lin, Z. Langmuir 1996, 12, 1729. (25) May, S.; Bohbot, Y.; Ben-Shaul, A. J. Phys. Chem. B 1997, 101, 8648. (26) When interactions are included (see ref 17 for details), eq 8 becomes instead I(Q,c) ) KcMwSRPA(Q, c). See Jerke, G.; Pedersen, J. S.; Egelhaaf, S. U.; Schurtenberger, P. Phys. Rev. E 1997, 56, 5772, for application of a phenomenological derivative of the original RPA expression, namely: SRPA(Q,c) ) 〈P(Q,c)〉/[1 + ((1 - S(0))/S(0))fDebye(Q2Rg2)]. (27) (a) Pedersen, J. S.; Laso, M.; Schurtenberger, P. Phys. Rev. E 1996, 54, R5917. (b) Pedersen, J. S.; Schurtenberger, P. Macromolecules 1996, 29, 7602. (28) (a) Casassa, E. F. J. Chem. Phys. 1955, 23, 596. (b) Holtzer, A. J. Polym. Sci. 1955, 17, 433. (29) Schmidt, M.; Paradossi, G.; Burchard, W. Makromol. Chem. Rapid Commun. 1985, 6, 767. (30) Denkinger, P.; Burchard, W. J. Polym. Sci. B: Polym. Phys. 1991, 29, 589.

Figure 2. SANS data for 6.2 mM CTA26ClBz/Cl (4:96) in 1 M Na26ClBz/Cl (4:96) in D2O, represented in a bending rod (BR) plot.

the Q position of the plot’s maximum, using the relationship u ) QmaxRg. The numerical value of u depends on polydispersity; it is 1.41 for monodisperse chains and 1.78 when Mw/Mn ) 2. At higher Q, a plateau (or inflection) in the BR plot is observed, whose extent in Q depends on rcs. The ratio of the height of the maximum to the height of the plateau is a measure of the number of lp’s per chain.29 Thus simple visual comparison of two scattering curves in BR format allows an assessment of flexibility. Because 〈P(Q,c)〉 takes a different functional form for scattering from spherical or ellipsoidal micelles rather than wormlike chains, BR plots of their scattering curves lack this clear separation of length scales, but the position of Qmax is still a useful indicator of micelle size. Evaluation of Local Micellar Structure. The intermediate Q range in a BR plot can be analyzed to obtain the cross-sectional radius of gyration, Rg,cs, of the cylinders or worms, by employing a Guinier approximation for Pcs:

Q I(Q) ) KBR exp(-Q2Rg,cs2/2)

(10)

For a circular cross section, the micellar radius, rcs ) x2Rg,cs. The value of KBR is given by:

KBR ) πc〈N/L〉w(bm - VmFsolv)2

(11)

where bm and Vm are respectively the sum of the neutron scattering lengths and the volume per surfactant monomer in the micelle; Fsolv is the scattering length density of the solvent. In what follows, the weight-average aggregation number per unit length will simply be denoted as N/L. The value of N/L is derived from KBR, given a value for the contrast term, (bm - VmFsolv)2, and the area per surfactant headgroup, Ahg, equals 2πrcsL/N. Ahg’s can also be determined by analyzing the high Q portion of the scattering curves, e.g., the Porod limit,31 which is proportional to the total micellar surface area per unit volume, Σ. For particles (micelles) with a sharp interface, the limit is equal to:

lim{Q4 I(Q)} ) 2πVm-2(bm - VmFsolv)2Σ

(12)

Ahg can be calculated according to Ahg ) Σ/nsurf, where nsurf is the number density of micellized surfactant. As described in more detail below, the fitting protocol used (31) Porod, G. Kolloid Z. 1951, 124, 83; 1952, 125, 51; 1952, 125, 109.

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to obtain the Porod limit also provides an independent determination of the micellar radii for both spherical and cylindrical micelles. The contrast factor needed can be calculated for an assumed average micellar content which includes the number and identity of counterions per surfactant ion or it can be obtained from the measured scattering curves by computing the Porod invariant, Q*:

Q* )

∫Q2I(Q) dQ ) 2π2Vm-2(bm - VmFsolv)2φ(1 - φ)

(13)

Materials and Methods Materials. The synthesis of CTA26ClBz from CTABr and sodium 2,6-dichlorobenzoate (Na26ClBz) has been described previously.7a Elemental analysis provided the following results, expressed as mass percents. CTA26ClBz: C, 65.88%; H, 9.61%; Cl, 14.84% (Theoretical C, 65.79; H, 9.61; Cl, 14.94). Na26ClBz: C, 39.74%; H, 1.37%; Cl, 33.32% (Theoretical C, 39.5; H, 1.42; Cl, 33.29). A bromide ion selective electrode was used to confirm the absence of Br- ions. CTACl from Fluka Chemicals was used as received. Deionized water was obtained from a Millipore-Q apparatus; D2O, with an atom fraction of 99.9% D, was obtained from Aldrich or Isotec. Na26ClBz was prepared by titration of 2,6-dichlorobenzoic acid (from TCI America) with 3 N NaOH. AR grade NaCl was used as received. Small-Angle Neutron Scattering. SANS measurements were performed on the NG-3 and NG-7 SANS spectrometers32 at the Cold Neutron Research Facility, National Institute of Standards and Technology, Gaithersburg, MD, and at the W. C. Koehler 30 m SANS facility33 at Oak Ridge National Laboratory, Oak Ridge, TN. The range of scattering vector used was 0.018 nm-1 < Q < 4.2 nm-1, requiring three separate settings of the sample-to-detector distance. Some samples were measured at only two of the three settings. The incident neutron wavelengths used were 0.5 or 1.0 nm at NIST and 0.475 nm at ORNL; ∆λ/λ values were respectively 0.1 and 0.05. The samples were contained in quartz spectrophotometric cells of 2 mm or 5 mm path length, mounted in a thermostated cell holder held at 25.0 ( 0.1 °C. Each two-dimensional set of raw scattering data was corrected for detector background and sensitivity, for scattering from the empty cell, and then radially averaged. The resulting I(Q)’s were converted to absolute intensities (in cm-1) using precalibrated secondary standards provided by NIST and ORNL. Porod Analysis. A single background correction, B, containing contributions from incoherent scattering by surfactant and coherent and incoherent scattering by solvent, was applied to each scattering curve. Before the invariant was computed according to eq 13, the experimental curves were synthetically extended to Q ) 0 (Guinier approximation) and to Q ) 10 nm-1 (Porod). Contrast factors derived from Q* in general agreed well with those calculated from solution composition. The Porod limit was obtained from a weighted (by the reciprocal of the square of the statistical error of the individual points) nonlinear leastsquares fit of the experimental scattering curves recast in the form CQ4[I(Q) - B], in the range 0.6 nm-1 < Q < 4.2 nm-1. In this Q range, oscillations are observed that reflect the form factor of the local micellar structure, either spherical or cylindrical:

I(Q) ∼ [3.0(sin x - cos x)x-3]2 I(Q) ∼ Q-1[2J1(x)/x]2,

x ) Q‚rcs

(14) (15)

The Q positions of the successive maxima and minima obviously provide information about micellar size; the depth and height of the minima and the second maximum onward depend on the polydispersity of rcs. Accordingly, a Gaussian distribution of radii was used, with rjcs and 〈(rcs - rjcs)2〉1/2 as fitting parameters. Values for Σ and hence Ahg can then be determined directly from the high Q limit of the fitted curve, which equals QΣ/πφ(1 - φ). (32) Details of the instruments may be found at http://rrdjazz.nist.gov/ chrnsans.html. (33) Koehler, W. C. Physica (Utrecht) 1986, 137B, 320.

Figure 3. SANS data for CTA26ClBz/Cl micelles at various molar ratios in 1 M Na26ClBz/Cl in D2O. The surfactant concentration is 7.5 mM, with the exception of the 1:99 molar ratio solution, 12.5 mM scaled to 7.5 mM. The molar ratios are given in the legend.

Results and Discussion The Impact of Counterion Inventory and Salt Content on Overall Micellar Size. Figure 3 presents BR plots for CTA26ClBz/Cl micellar solutions in 1 M salt that clearly demonstrate dramatic unidimensional micellar growth and increase in number of lp’s per wormlike chain as the mole fraction of 26ClBz- increases. The CTACl micelles in 1 M NaCl are globular, with 〈n〉w ) 156 (fit not shown). The Q value of the maximum in Q I(Q) then moves progressively to lower Q; by a mole fraction of 2.5% 26ClBza plateau has developed in the BR plot, characteristic of substantial separation of three main micellar length scales: contour, persistence, and cross-sectional radius. Figure 4 shows the effect on micellar growth of increasing cs for three molar ratios of 26ClBz-/Cl-: 10:0; 6:4; 2:8. The surfactant concentration is 20 mM in most cases and for the larger micelles therefore some of the solutions are in the semidilute regime.34 However, in no case is c/c* much larger than 1, and as a result, the upturn and maximum in Q I(Q) at low Q can still be qualitatively interpreted in terms of significant micellar elongation and flexibility. When 26ClBz- is the only counterion present (Figure 4a), the micelles never become sufficiently elongated and/ or flexible for the well-defined low-Q maximum to appear in the BR plot. After increasing at low [Na26ClBz], the apparent micelle size starts to decrease between 0.2 and 0.5 M Na26ClBz; at 1 M Na26ClBz, the micelles are spherical, with 〈n〉w ) 100 (fit not shown). At a 6:4 molar ratio (Figure 4b), data are unfortunately not available for low Q values, but the trend in micellar size is clear enough: the upturn at Q < 0.12 nm-1 for both 0.2 and 0.5 M salt is sufficient to infer the presence of a maximum in those BR plots. Furthermore, the micelles at 0.5 M salt may be slightly smaller than those at 0.2 M salt. At still higher cs the apparent micellar size is much smaller at 1 M and smaller still at 2 M salt, where the scattering curve is superimposable on the curve in Figure 4a for 1 M Na26ClBz, suggesting spheres. At 2:8 (Figure 4c) the turnover in size is displaced to still higher cs, occurring (34) In the semidilute regime, the characteristic length which dominates the low-Q scattering is no longer identified with the micelles’ Rg values, but rather with the mesh size of the entangled worms. The mesh size decreases with increasing c, so the values of Qmax in the BR plots, after monotonically decreasing with increasing c below c* now increase above c*.

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Figure 5. Evolution of micelle size as a function of cs and mole fraction of 26ClBz-, taking the Qmax-1 values derived from BR plots as proportional to the micellar Rg values.

Figure 4. SANS data at various total cs given in the legends for (a) pure CTA26ClBz, (b) 6:4 CTA26ClBz/Cl, and (c) 2:8 CTA26ClBz/Cl. Surfactant concentration is 20 mM, except in 2 M salt, where it is 10 mM. The salt in each case contains the same molar ratio of chlorobenzoate to chloride anions as the surfactant does.

now between 1 and 2 M salt; the micelles in 2 M salt at 2:8 are still significantly larger than those in the 6:4 system at the same cs. Figure 4 also confirms the earlier results from static LS experiments that the micelles grow faster in the low-cs regime (0.04 and 0.08 M salt) the higher the mole fraction of 26ClBz- present: 10:0 > 6:4 > 2:8. At low ionic strength, Ee (eq 6) cannot be neglected relative to Ec, and the values

of v* and the micellar surface potential are important: 26ClBz- lowers them much more effectively than Cl-, and the order for micellar growth reflects this. Once cs reaches 0.2-0.5 M, this trend is reversed; the impact of the counterions on Ec is now dominant, and Ec is decreasing. Recall that this decrease results in an increase in φ* according to eq 5. Figure 5 summarizes the effects of counterion mole fraction and cs on overall micellar size for the samples in Figures 3 and 4 and for many additional samples which show the same general trends. At the higher ionic strengths, chloride ions alone do not initiate micellar shrinkage; the higher cs is, the smaller the mole fraction of 26ClBz- needed to cause it. To help understand the origin of the penetrating aromatic anions effect on micellar morphology, their role in changing local micellar structure is considered next. The Impact of Counterion Inventory and Salt Content on Local Micellar Structure. Figure 6a shows the scattering curve for 35 mM CTA26ClBz in 2 M NaCl, plotted as ln[Q I(Q)] vs Q2 and fitted in the region 0.13 nm-2 < Q2 < 0.8 nm-2 according to eq 10. From the slope of this Guinier-like plot a value of Rg,cs of 1.57 nm is obtained, which corresponds to rcs ) 2.22 nm. From the intercept a value of 2.42 nm-1 cm-1 is obtained for KBR; to extract a value for N/L, a value for (bm - VmFsolv)2 is needed. The contrast factor was calculated from the composition of the dry micelle, assuming7c that K26ClBz/Cl ) 20, that the total fraction of counterions bound is 90%,35 and that the nonpenetrating Cl- ions retain their hydration and do not contribute to the dry micellar volume. Table 1 tabulates the scattering length and volume increments used in the calculation. The calculated contrast factor is 1.50 × 10-21 cm2; a similar value, 1.537 × 10-21 cm2, was determined experimentally from the Porod invariant, Q*, found to be 1.05 × 10-7 nm-4 for 35 mM CTA26ClBz in 2 M NaCl. The derived N/L is 25.5 monomers per nanometer of wormlike micelle and the derived Ahg is 0.55 nm2. Table 2 contains for 35 mM CTA26ClBz in 2 M NaCl and many other samples the calculated contrast factors, the fraction of the bound counterions that are 26ClBz-, R26ClBz, and values of rcs and N/L obtained from the Guinier (35) The total counterion binding is not experimentally accessible at high salt concentration. Ninety percent is a reasonable assumption, given the effect of these two counterions on the micelles surface and zeta potentials.7c

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Figure 6. For 35 mM CTA26ClBz in 2 M NaCl in D2O: (a) Guinier-like plot of the SANS data in the intermediate-Q region, fitted according to eqs 10 and 11; (b) Porod region, fitted using eqs 12, 13, and 15. Table 1. Scattering Lengths and Volume Increments for Surfactant and Counterion Moieties, Solvent, and Salta species

b/10-12 cm

V/nm3

CH3(CH2)15-+N(CH3)3 C7H3Cl2O2Na+,ClD2O

-1.707 -0.446 6.608 1.321 1.915

0.458 0.102 0.201 b 0.302

a Based on the following individual b values: 0.66484 (C); -0.3741 (H); 0.6674 (D); 0.926 (N); 0.5805 (O); 0.363 (Na); 0.9579 (Cl). b Actual solution densities were used to compute the scattering length densities of the solvent.

plots. Since scattering was not measured at high Q for many of the samples, calculated contrast factors were used in all cases to obtain N/L values from the fitted intercepts. Figure 6b shows the experimental and fitted (using eq 15 for the form factor) Porod plots for 35 mM CTA26ClBz in 2 M NaCl. The fitted value of rjcs is 1.97 ( 0.08 nm, with 〈(rcs - rjcs)2〉1/2 ) 0.30 ( 0.01 nm; as Appell et al.36 have also observed, the cross-sectional radius determined from the Porod regime is generally a few percent smaller than the value obtained using eq 10. The fitted Porod limit is 3.5 × 10-8 nm-5; combined with the experimental Q*, the value of Ahg is determined to be 0.62 nm2. The results tabulated in Table 2 indicate that Ahg values determined (36) Appell, J.; Bassereau, P.; Marignan, J.; Porte, G. Prog. Colloid Polym. Sci. 1990, 81, 13.

Figure 7. Impact of increasing R26ClBz on the micelle crosssectional radii, with the calculated values of R26ClBz and the fitted values of Rg,cs presented in the legend. (a) Guinier-like plots for 20 mM surfactant: (*) CTA26ClBz in 1 M NaCl; (3) 4:96 CTA26ClBz/Cl in 1 M 4:96 Na26ClBz/Cl; (0) 2:8 CTA26ClBz/Cl in 1 M 2:8 Na26ClBz/Cl; (O) CTA26ClBz in 0.2 M Na26ClBz. (b) summary of cross-sectional Rg values for CTA26ClBz/Cl solutions.

by Porod analysis of the high-Q regime and by Guinier analysis of the intermediate-Q regime generally agree rather well. Examination of the counterion inventories represented by the tabulated R26ClBz values in Table 2 shows that in the mixed 26ClBz-/Cl- systems, the mole fraction of aromatic counterion at the micelle surface is 8-10 times the overall mole fraction in solution. The increasing presence of counterions penetrating the plane of the surfactant headgroups increases the effective volume per surfactant monomer, lowers v*, and has three main consequences for the local micellar structure. First, as Figure 7a demonstrates, increases in R26ClBz result in decreases in Rg,cs. Figure 7b summarizes the dependence on c of Rg,cs values for several different surfactant/salt series. The decrease suggests that the C16 alkyl chains on average are less extended in the cylindrical portion of the micelles; gauche conformations and other chain constraints increase fcyl,ch relative to fcap,ch, making the environment of the hemispherical end-caps, where the chains are more extended, relatively less unfavorable. For the globular micelles found in 20-50 mM CTA26ClBz solutions in water or in 1 M Na26ClBz, the Ahg values are typically 0.90 nm2; the 〈n〉w values are typically 115. If these micelles were spheres, their radii would be 2.7 nm, a little longer than an all-trans C16NMe3 surfactant ion (ca. 2.5 nm). The corresponding minimum-sphere

Microstructure of Cationic Micelles

Langmuir, Vol. 16, No. 1, 2000 155

Table 2. The Dependence of Local Micellar Structure on Counterion Inventory systema

26ClBz/Cl

R26ClBzb

Vmon, nm3

(bm - VmFsolv)2, (10-21 cm2)

N/L, nm-1

rcs, nm

Ahg, nm2

CTA26/Cl in 1 M salt

0:100 1:99 2.5:97.5 4:96 8:92 12:88 16:84 2:8 2:8

0.0 0.14 0.31 0.44 0.62 0.72 0.78 0.83 0.83

0.560c 0.585 0.616 0.639 0.672 0.690 0.701 0.710 0.710

1.41 1.46 1.53 1.62 1.70 1.75 1.77 1.75 1.83

24.3e 23.3 22.4 20.1 19.2 18.6 17.6 17.7

2.25 2.19 2.19 2.15 2.15 2.09 2.11 2.09

0.58 0.59 0.62 0.67 0.70 0.71 0.74 0.74

6:4

0.27 0.33 0.38 0.49 0.90

0.609 0.620 0.629 0.649 0.734

CTA26/Cl in 2 M salt CTA26/Cl in 1 M salt in 10 mM salt in 25 mM salt in 40 mM salt in 80 mM salt CTA26/Cl in 1 M salt 7.5 mM 10 20 35 in 10 mM salt in 25 mM salt in 40 mM salt in 80 mM salt CTA26ClBz in 1 M NaCl 7.5 mM 10 12.5 20 35 CTA26ClBz in 2 M NaCl 7.5 mM 12.5 20 35 CTA26ClBz 20 mM 50 mM CTA26ClBz/ 0.08 M Na26ClBz 0.2 M Na26 0.5 M Na26 1M Na26

Ahg (Porod) 0.62

0.76f 0.75 0.75 0.77 1.79 17.4 18.2 18.5 18.7

1.77 1.85 1.94 2.09

0.64 0.64 0.66 0.70

0.76 0.88 0.94 0.94

0.697 0.719 0.730 0.730

0.88 0.86 0.79 0.77

0.12 0.16 0.18 0.24 0.30

0.582 0.588 0.592 0.604 0.615

1.47 1.49 1.50 1.53 1.57

24.1 24.9 24.6 22.9 24.0

2.12 2.19 2.25 2.18 2.21

0.55 0.55 0.57 0.60 0.59

0.07 0.11 0.16 0.23 1.0

0.572 0.579 0.588 0.601 0.730d

1.43 1.45 1.47 1.50

25.1 25.4 25.2 25.5

2.29 2.28 2.32 2.22

0.57 0.56 0.57 0.55

0.55 0.59 0.58 0.62 0.93 0.88 0.79

1.0

0.740

1.86

16.0

1.99

0.79

1.0 1.0 1.0

0.740 0.740 0.740

1.85

15.2

1.92

0.80

0.59 0.62 0.65

0.78 0.86 0.99

a The molar ratio of 26ClBz- to Cl- in the salt is the same as that in the surfactant. b The fraction of bound counterions that are 26ClBz-. The selectivity coefficient, K26ClBz/Cl ) ([26ClBz-]/[Cl-])mic([Cl-]/[26ClBz-])free and the additional assumption that [26ClBz-]mic + [Cl-]mic ) 0.9c, ref 35, allow computation of R26ClBz, which is defined as [26ClBz-]mic/0.9c. c Vmon ) 0.560 + (0.9R)0.201. d Total counterion binding is 85% here (ref 7c). e Error bars for N/L and rcs are (3%. f Error bars for Ahg determined from the Porod region are (6%.

micelle with a radius of 2.5 nm and an 〈n〉w of 90 has a v/al of 1/3 when Ahg is 0.90 nm2. To achieve cylindrical packing (v/al ) 1/2) at the same area per headgroup would require an rcs of 1.66 nm. The smallest rcs observed for short cylindrical micelles of CTA26ClBz is ca. 1.8 nm, suggesting that fcyl,ch may become larger than fcap,ch before rcs reaches 1.8 nm. The other consequences of an increase in R26ClBz are the increase in Ahg and the decreases in N/L, Table 2. For a nonpenetrating counterion, an increase in Ahg creates an additional aliphatic hydrocarbon-water surface, which is energetically unfavorable. The increase is larger for fcap,int, leading to an increase in fcap,int - fcyl,int. The penetrating counterions are in contact with portions of the C16 alkyl tails, shielding them in part from water, and the additional surface created primarily involves contact of water with aromatic moieties, which involves a lower surface energy than aliphatic/water contact. This contribution acts to moderate to some extent the increase in fcap,int - fcyl,int. Steric repulsions between headgroups favor the formation of end caps, decreasing fcap,hg - fcyl,hg as Ahg increases.

Penetrating aromatic counterions may introduce another contribution to fcap - fcyl, which is not included in eq 7, one that acts to decrease fcyl more than fcap. As Bunton and co-workers noted 25 years ago, the interaction between both neutral and charged aromatic species and quaternary ammonium cations are known to be energetically favorable, occurring also in nonmicellar solutions.37 The influence of this interaction on counterion orientation at the micellar surface, and hence on Ahg, is not known, but it can be supposed that the more favorable the interaction is, the more strictly the counterion is oriented on average perpendicular to the surface. With very large penetrating counterions such as HNCfor which vesicles are obtained with CTA+, Manohar, Candau, and co-workers38 have proposed that the coun(37) (a) Bacaloglu, R.; Bunton, C. A.; Cerichelli, G.; Ortega, F. J. Phys. Chem. 1989, 93, 1490. (b) Bunton, C. A.; Minch, M. J. J. Phys. Chem. 1973, 78, 1490 and references therein. (38) (a) Hassan, P. A.; Narayanan, J.; Menon, S. V. G.; Salkar, R. A.; Samant, S. D.; Manohar, C. Colloid Surf., A 1996, 117, 89. (b) Oda, R.; Narayanan, J.; Hassan, P. A.; Manohar, C.; Salkar, R. A.; Kern, F.; Candau, S. J. Langmuir 1998, 14, 4364.

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terions produce a small effective Ahg that allows the bilayerlike packing. This behavior is in marked contrast to that of pure CTA26ClBz, where the minimum Ahg observed is 0.79 nm2. Estimating the volume of HNC- as 0.40 nm3, double the volume of 26ClBz-, leads to a volume of 0.96 nm3 for the CTA+HNC- pair. To maintain an effective alkyl tail length no smaller than 1.8 nm in the bilayers would require Ahg ) 0.53 nm2. This suggests a natural direction for further SANS investigations on CTA+ micelles with aromatic counterions. One can speculate that the strength of the aromatic/alkylammonium interaction for a large species such as HNC- promotes the aforementioned orientation of the counterion in which the plane of the aromatic ring is on average perpendicular to the micelle/bilayer surface and Ahg is accordingly minimized. Conclusions The interplay among the various factors that determine the micellar morphology of cationic surfactants have been manipulated for CTA26ClBz/CTACl mixed micellar solutions by changing the counterion molar ratio as well as the concentration of supporting electrolyte. SANS provides a powerful technique for the determination of the multiple length scales present in these systems. At low ionic strength, electrostatics is dominant: counterions that strongly bind to and penetrate the micellar surface are most effective at lowering v* and promoting growth (eqs 4 and 5). Thus for CTA26ClBz/CTACl at low ionic strength, micellar growth with increasing surfactant and salt concentration is more rapid at a mole fraction of 60% 26ClBz- than at 20%. For nonpenetrating and highly hydrated counterions such as chloride, the charge density in the headgroup plane remains high even in 1 M NaCl, resulting in an electrostatic repulsion between headgroups that favors globular micelles. As 26ClBz- is progressively introduced at 1 M salt, rapid micellar growth results at low mole fraction of 26ClBz-: v* rapidly decreases, an energetically favorable interaction between the positively charged headgroup nitrogen and

Magid et al.

the delocalized π-electrons occurs, other nonelectrostatic contributions (eq 7) come into play, and the impact of counterion identity on Ec (equivalently fcap - fcyl) can be seen. Adding 26ClBz- increases the difference in the interfacial free energy (fcap,int - fcyl,int) for surfactant in an end-cap environment relative to the micellar cylindrical body. However, successive additions of 26ClBz- decreases the free energy difference for surfactant chains and for headgroups between the two environments (fcap,ch - fcyl,ch and fcap,hg - fcyl,hg both get smaller), with end-caps becoming progressively more favorable. The net effect of all three nonelectrostatic contributions taken together is to decrease Ec; this eventually shows up in significant decreases in micelle size. The changes in fcap - fcyl thus produce several consequences for micellar structure: increasing areas per headgroup, a decreasing number of surfactant monomers per unit length of the micelles, and decreases in the radius of the micellar cross section. Beyond a mole fraction of 12% 26ClBz-, the micelle size starts decreasing; for the pure CTA26ClBz micelles in 1 M Na26ClBz, the micelles have reverted to spherical morphology. The maximum in micelle size is displaced to still lower mole fraction of 26ClBz- as the salt concentration increases beyond 1 M. Acknowledgment. Support of this work by the National Science Foundation (CHE-9729433) is gratefully acknowledged. The SANS measurements were performed on the NIST NG3 and NG7 SANS instruments, supported by NSF under Agreement No. DMR-9423101. Identification of certain equipment or materials does not imply recommendation by NIST. Our interest in the impact of aromatic counterions and neutral solubilizates on the size and shape of cationic micelles began many years ago. A 1973 paper by C. A. Bunton and his co-worker, M. J. Minch, taught us how to think about interactions between cationic headgroups and aromatic π-electron systems. It is therefore a pleasure to congratulate Professor Bunton on the occasion of this commemorative issue. LA990686C