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Feb 1, 1996 - and CTA 2-chlorobenzoate, form Newtonian aqueous solutions containing roughly .... describe the micellar dynamics in the semidilute regi...
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Langmuir 1996, 12, 691-698

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Tuning of Micellar Structure and Dynamics in Aqueous Salt-Free Solutions of Cetyltrimethylammonium Mono- and Dichlorobenzoates M. Carver, T. L. Smith, J. C. Gee,† A. Delichere, E. Caponetti,‡ and L. J. Magid* Department of Chemistry, University of Tennessee, Knoxville, Tennessee 37996-1600 Received July 5, 1995. In Final Form: October 23, 1995X Micelle formation and growth in salt-free aqueous solutions have been investigated for five cetyltrimethylammonium (CTA) mono- and dichlorobenzoates using small-angle neutron scattering (SANS) and rheological measurements. Manipulation of the chlorine substitution pattern provides an excellent means of tuning micellar morphology and solution properties. Two of the surfactants, CTA 2,6-dichlorobenzoate and CTA 2-chlorobenzoate, form Newtonian aqueous solutions containing roughly spherical micelles below ca. 70 mM. There follows a region with increasing concentration of significant micellar growth to prolate ellipsoids (or rigid, short cylindrical micelles), micellar overlap, and apparent maximum aggregation numbers, 〈n〉’s, at ca. 200 and 167 mM (φ ) 0.095 and 0.073), respectively. Above these latter concentrations, the SANS Qmax values scale as C1/2, characteristic of an entangled polymer-like micellar network. The three surfactants having chlorine substituents para and/or meta to the counterion’s COO- group (namely CTA35ClBz, CTA4ClBz, and CTA34ClBz) form highly viscoelastic aqueous solutions containing entangled wormlike micelles at mM concentrations. For CTA35ClBz, C* is e2 mM (φ ≈ 0.001), the micelles have a persistence length of 50 nm, and the solutions are Maxwell fluids at C g 20 mM. The mean micellar contour length, assessed from dynamic rheological measurements analyzed using the formalism of Cates and Granek, reaches a maximum of 10 µm at ca. 15-20 mM. The C-dependences of the network correlation lengths, micellar entanglement lengths, and mean contour lengths, are analyzed to explain the recovery of Newtonian fluid behavior at C g 70 mM.

Introduction Understanding the sphere-to-rod transition which occurs in aqueous and oil-based micellar solutions of certain ionic, zwitterionic, and nonionic amphiphiles as a function of surfactant and/or supporting electrolyte concentration has been of interest to colloid scientists for several decades. Since the early 1980’s, it has been recognized that in some micellar systems, the micellar growth is sufficiently rapid to produce highly polydisperse populations of giant, flexible wormlike micelles whose viscoelastic solutions exhibit, by analogy to polymer solutions, a transition from the dilute to semidilute regime at a concentration C* which may correspond to a surfactant volume fraction, φ, of a few percent or less.1 Certain direct micelles formed by cationic surfactants in aqueous solution have been studied most extensively in this regard, beginning with the pioneering work of Hoffmann and co-workers2 on cetyltrimethylammonium salicylate (CTASal) and cetylpyridinium salicylate (CPySal) and of Candau, Zana, and coworkers3 on CTABr/KBr. However, solutions of reverse * Author to whom correspondence should be addressed. E-mail address: [email protected]. † Current addresses: Chevron Chemical Company, Kingwood, TX. ‡ Current address: Universita ` di Palermo, Palermo, Italy. X Abstract published in Advance ACS Abstracts, February 1, 1996. (1) (a) Cates, M. E.; Candau, S. J. J. Phys.: Condens. Matter 1990, 2, 6869 and references therein. (b) Rehage, H.; Hoffmann, H. Mol. Phys. 1991, 74, 933 and references therein. (c) Porte, G. In Micelles, Membranes, Microemulsions and Monolayers; Gelbart, W. M., BenShaul, A., Roux, D.G. Eds.; Springer-Verlag: New York, 1994, Chapter 2. (d) Schurtenberger, P.; Scartazzini, R.; Magid, L. J.; Leser, M. E.; Luisi, P. L. J. Phys. Chem. 1990, 94, 3695. (2) (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. (3) (a) Candau, S. J.; Hirsch, E.; Zana, R. J. Phys. (Paris) 1984, 45, 1263. (b) J. Colloid Interface Sci. 1985, 105, 521.

0743-7463/96/2412-0691$12.00/0

micelles formed in apolar solvents by zwitterionic surfactants such as lecithins are also polymer-like in their behavior.1d,4 With respect to aqueous micellar solutions of RNMe3X and RPyX, it has been known for many years that the introduction of certain neutral aromatic solubilizates or aromatic counterions cause micellar growth and/or generate viscoelastic solutions.5-7 Historically, viscoelasticity was assessed by noting the occurrence of bubble recoil; thus, Gravsholt5 was the first to observe that in the case of CTAX systems, the 4-chlorobenzoate anion (4ClBz) induces viscoelasticity, while the isomeric 2-chlorobenzoate anion (2ClBz) does not. This is the reverse of the situation observed with the 4-hydroxybenzoate and 2-hydroxybenzoate (salicylate) anions. A detailed rationalization on a molecular level concerning the relationship between viscoelasticity and positional substitution is lacking. Heat capacity measurements8 suggest that salicylate anions penetrate the CTA+ micellar interface to a greater extent than 4-hydroxybenzoate, and as a result more extensively lose waters of hydration. Several groups have used proton NMR to assess the orientational details for substituted benzoate counterions bound to RNMe3+ micellar interfaces; whether the substituent(s) are hydroxy,9 chloro,10,11 or methyl,12 substantial penetration of the micellar interface has been inferred for all of the (4) Schurtenberger, P.; Cavaco, C. Langmuir 1994, 10, 100. (5) (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.-A° ; Lindblom, G.; Gravsholt, S. J. Phys. Chem. 1979, 83, 2232. (6) (a) Underwood, A. L.; Anacker, E. W. J. Phys. Chem. 1984, 88, 2390. (b) J. Colloid Interface Sci. 1985, 106, 1985. (7) For examples of CTAB with neutral aromatic solubilizates, see the following and references therein: (a) Shikata, T.; Hirata, H.; Kotaka, T. Langmuir 1989, 5, 398. (b) Lin, Z.; Cai, J. J.; Scriven, L. E.; Davis, H. T. J. Phys. Chem. 1994, 98, 5984. (8) Johnson, I.; Olofsson, G. J. Colloid Interface Sci. 1985, 106, 86. (9) (a) Manohar, C.; Rao, U. R. K.; Valaulikar, B. S.; Iyer, R. M. J. Chem. Soc., Chem. Commun. 1986, 379. (b) Rao, U. R. K.; Manohar, C.; Valaulikar, B. S.; Iyer, R. M. J. Phys. Chem. 1987, 91, 3286. (10) Smith, B. C.; Chou, L. C.; Zakin, J. L. J. Rheol. 1994, 38, 73.

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positional isomers. The most detailed information on differences in hydrocarbon chain packing for CTAX micelles in viscoelastic vs nonviscoelastic solutions is found in our one- and two-dimensional 1H NMR and 13C NMR studies.11 Early investigations of the evolution of micellar size and shape with increasing C, in systems exhibiting a C*, used techniques such as small-angle neutron scattering (SANS) and focused on surfactants in water without supporting electrolyte. The observed scattering patterns are consistent with an evolution from spheres to prolate ellipsoids to (flexible) cylindrical micelles with increasing C. Hoffmann and co-workers2,13 inferred from their SANS data that the C-dependence of the aggregation numbers, 〈n〉, of the growing cylinders exhibited a turnover concentration (Cto ≈ C*) above which the 〈n〉’s decreased monotonically with C at a rate just sufficient to maintain overlap. However, such a turnover in 〈n〉’s and hence micellar contour length is not consistent with the rheological data on such systems. In the case of the doubletailed surfactant C16C8NMe2Br, which has a high C* at ca. 35 mM (φ ) 0.016), Warr, Magid, and co-workers14 were able to demonstrate using dynamic fluorescence quenching that 〈n〉 in fact continues to increase above C*. As far as we have been able to determine, there are only two exceptions to this behavior in solutions of entangled linear micelles: the binary system of ethanediyl-R,ω-bis(dodecyldimethylammonium bromide) (sometimes referred to as the gemini surfactant, 12-2-12) in water, studied by Candau, Zana, and co-workers,15 and the binary system of CTA 3,5-dichlorobenzoate (CTA35ClBz) in water, whose behavior is described in the present work. In both of these cases, as will be seen, the turnover in 〈n〉 occurs far above overlap. Cryo-transmission electron microscopy (cryo-TEM) has provided beautiful direct images of highly entangled, flexible micellar threads in some of these systems, but it is not a useful technique for quantitation of micellar size changes.16 Dynamic rheological measurements and selfdiffusion measurements (NMR, forced-Rayleigh scattering) on binary and especially on ternary (surfactant/salt/ water) viscoelastic direct micellar solutions have revealed a rich spectrum of time scales for micellar motions and for micellar morphology above C* in these systems.17 Under certain circumstances, the rheological data (vide infra) can be used to infer information about the evolution of micellar size with C. During the last several years, Cates and co-workers18 have developed the theoretical framework needed to describe the micellar dynamics in the semidilute regime, dynamics which manifest themselves in the solution’s rheological behavior. The development starts from the (11) Kreke, P. J.; Magid, L. J.; Gee, J. C. Langmuir 1996, 12, 699. Kreke, P. J.; Magid, L. J. Submitted for publication in Langmuir. (12) Bachofer, S. J.; Turbitt, R. M. J. Colloid Interface Sci. 1990, 135, 325. (13) Neubauer, G.; Hoffmann, H.; Kalus, J.; Schwandner, B. Chem. Phys. 1986, 110, 247. (14) Warr, G. G.; Magid, L. J.; Caponetti, E.; Martin, C. A. Langmuir 1988, 4, 813. (15) Kern, F.; Lequeux, F.; Zana, R.; Candau, S. J. Langmuir 1994, 10, 1714. (16) See for example: (a) Vinson, P. K.; Talmon, Y. J. Colloid Interface Sci. 1989, 133, 288. (b) Magid, L. J.; Gee, J. C.; Talmon, Y. Langmuir 1990, 6, 1609. (c) Clausen, T. W.; Vinson, P. K.; Minter, J. R.; Davis, H. T.; Talmon, Y.; Miller, W. G. J. Phys. Chem. 1992, 96, 474. (17) In addition to works referenced in 1a and 1b, useful recent references on light scattering and rheological studies of the CTAB/ NaSal systems in particular may be found in the following: (a) Nemoto, N.; Kuwahara, M.; Yao, M.-L.; Osaki, K. Langmuir 1995, 11, 30. (b) Shikata, T.; Pearson, D. S. Langmuir 1994, 10, 4027. (18) (a) Cates, M. E. Macromolecules 1987, 20, 2289; (b) J. Phys. (Paris) 1988, 49, 1593. (c) J. Phys. Chem. 1990, 94, 371. (d) Granek, R.; Cates, M. E. J. Chem. Phys. 1992, 96, 4758.

Carver et al.

theory of polymer dynamics19 and recognizes that for entangled polymer solutions in which the polymer chains undergo reptation, a broad spectrum of relaxation times is observed. Since many viscoelastic micellar solutions in fact show monoexponential stress relaxation functions (e.g., can be identified as Maxwell fluids), there must be an additional (or different) process for relaxation available, namely reversible scission of the micellar threads (with a characteristic time constant for breaking of τbr). The micellar solutions are accordingly referred to as being analogous to solutions of “living” polymers. For semidilute solutions, the resulting scaling laws for the zero-shear viscosity η0 reflect the two dynamical regimes, with micelle breaking being either slow or fast relative to reptation (τrep). The general form is η0 ∝ L h aφb. For fairly rigid rods in the slow-breaking limit, the prediction is a ) 6, b ) 3; for flexible micelles, a ) 3, b ) 3.75. For flexible micelles in the fast-breaking limit (τbr/τrep , 1), a ) 1, b ) 3. For ionic micellar solutions with screened electrostatic repulsions (high salt concentrations), the thermodynamics of micellar growth predicts L h ∝ φ1/2, so that the three cases described give overall exponents for the concentration dependence of η0 as 6, 5.25 and 3.5. At low concentrations of supporting electrolyte (large Debye lengths), larger exponents may be observed as the result of a larger φ-dependence for L h.2c,20,21 Exponents lower than 3.5 have also been observed, for example for CTAB at KBr concentrations of 1.5 M or more and for CPyClO3 in aqueous NaClO3; these have been ascribed20,22 to intermicellar branching or even to formation of a multiconnected network (whose topology resembles the L3 phase). A recent elaboration of the theory by Granek and Cates18d takes into account breathing and local Rouse motions of the chains (in addition to reptation and micelle breaking) in the calculation of the overall stress relaxation function. At higher frequencies, where crossover to the breathing regime occurs, there is a deviation from Maxwellian behavior (e.g., from η0 ) G′∞‚TR, which is characterized by a semicircular Cole-Cole plot) which manifests itself as a minimum in G′′(ω) and as a dip in the Cole-Cole plot separating the low- and high-frequency regimes. The key feature of the elaboration is the recognition that the value of the ratio G′′min/G′∞ at the dip can be used to obtain the average number of entanglement lengths le per L h ,23 where le is the micellar contour length between entanglement points. In our experience, a series of CTA mono- and dichlorobenzoates represent a particularly attractive group of surfactants with which to study the evolution of micellar morphology and the occurrence of polymer-like solution behavior. By appropriate choice of counterion and surfactant concentration, micelles may be produced which (19) Doi, M.; Edwards, S. F. The Theory of Polymer Dynamics; Clarendon Press: Oxford, 1986. (20) For a theoretical treatment of micellar growth in poorly screened solutions, see: (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) Candau, S. J.; Khatory, A.; Lequeux, F.; Kern, F. J. Phys. IV 1993, 3, 197. (22) (a) Khatory, A.; Lequeux, F.; Kern, F.; Candau, S. J. Langmuir 1993, 9, 1456. (b) Appell, J.; Porte, G.; Khatory, A.; Kern, F.; Candau, S. J. J. Phys. II 1992, 2, 1045. (c) Khatory, A.; Kern, F.; Lequeux, F.; Appell, J.; Porte, G.; Morie, N.; Ott, A.; Urbach, W. Langmuir 1993, 9, 933. (23) For an elegant application to CTASal micelles in 0.5 M NaCl, see Berret, J.-F.; Appell, J.; Porte, G. Langmuir 1993, 9, 2851. Information on L h in the entangled regime is not available using scattering methods.

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are (a) roughly spherical or (b) short rigid cylinders or prolate ellipsoids or (c) long (up to ca. 10 µm), flexible, and highly entangled threads. We present here SANS and rheological data on five surfactant-water systems: CTA26ClBz and CTA2ClBz, whose aqueous solutions are not viscoelastic, and CTA4ClBz, CTA34ClBz, and CTA35ClBz, whose aqueous solutions are viscoelastic.24 Experimental Section Materials. The CTA chlorobenzoates (CTAxyClBz, where x and y, if needed, refer to chlorine positions on the counterion’s benzoate aromatic ring) were prepared according to the procedure in ref 16b. Critical micelle concentrations (cmc’s) and extents of micellar ionization just above the cmc’s were determined by conductometry. The values found are: CTA26ClBz, 0.56 mM, 0.36; CTA2ClBz, 0.50 mM, 0.32; CTA4ClBz, 0.20 mM, 0.43 and a cmcII at 0.31 mM, 0.18; CTA34ClBz, 0.13 mM, 0.15; CTA35ClBz, 0.10 mM, 0.10. Deuterium oxide (D2O), 99.9 atom % D, was obtained from Aldrich Chemical Company. Small-Angle Neutron Scattering. The SANS measurements were performed on the W. C. Koehler 30m SANS facility25 at Oak Ridge National Laboratory. The Q range employed (Q ) (4π/λ) sin θ, where 2θ is the scattering angle and the incident neutron wavelength λ is 0.475 nm) depended on C, requiring the use of two or three separate sample-to-multidetector distances. Below 10 mM, the lowest Q was typically 0.045 nm-1; the highest Q measured varied from 1.3 to 2.2 nm-1. The samples were contained in quartz spectrophotometric cells of 2 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 and 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 the SANS facility. The scattered intensity observed from a solution of interacting particles of number density Np can be expressed as:26

I(Q) ) Np〈|F(Q)|2〉 + Np[S(Q) - 1]|〈F(Q)〉|2 + B

(1)

where F(Q) is the single-particle scattering amplitude, S(Q) is the interparticle structure factor, and B is a Q-independent term to account for residual incoherent scattering. For monodisperse spheres, eq 1 reduces to I(Q) ) NpS(Q)‚〈|F(Q)|2〉 + B. The number particle density Np (micelles/cm3) is given by (C - cmc)NA/(〈n〉‚ 106) for C in mM. When modeling the micellar structure by prolate ellipsoids, the appropriate orientational averages for 〈|F(Q)|2〉 and |〈F(Q)〉|2 were computed (see for example refs 26b and 26c). For polydisperse spheres and ellipsoidal micelles, we assumed the decoupling approximation to be valid.2 To calculate the structure factors, we used the analytical solution for the one-component Ornstein-Zernike equation by Hayter and Penfold,27 on the basis of the RMSA closure relation. For prolate ellipsoidal micelles (axes a, b, b), the micellar diameter used was that of the equivalent sphere. (24) (a) A preliminary report on SANS of CTA2ClBz and CTA4ClBz appeared in the following: Magid, L. J. in Ordering and Organization in Ionic Solutions; Ise, N., Sogami, I., Eds.; World Scientific Publishing Co.: Singapore, 1988; pp 288-301. (b) For a determination of the persistence length of the CTA35ClBz micelles, see: Butler, P. D.; Magid, L. J. In Structure and Flow in Surfactant Solutions; Herb, C. A., Prud’homme, R. K., Eds.; ACS Symposium Series 578; American Chemical Society: Washington, DC; 1994; p 250. (c) For an example of the spectacular ability of CTA35ClBz/CTAB mixed micellar systems to align under shear, see: Hamilton, W. A.; Butler, P. D.; Baker, S. M.; Smith, G. S.; Hayter, J. B.; Magid, L. J.; Pynn, R. Phys. Rev. Lett. 1994, 72, 2219. (d) For an example of the kinetics of alignment for CTA35ClBz under Couette shear, see: Butler, P. D.; Magid, L. J.; Kreke, P. J.; Hayter, J. B.; Hamilton, W. A.; Hammouda, B. In Neutron Scattering in Materials Science II; Neumann, D. A., Russell, T. P., Wuensch, B. J., Eds.; MRS Symposium Proceedings Vol. 376; 1994. (25) Koehler, W. C. Physica (Utrecht) 1986, 137B, 320. (26) (a) Hayter, J. B.; Penfold, J. Colloid Polym. Sci. 1983, 261, 1022. (b) Magid, L. J. Colloids Surf. 1986, 19, 129. (c) Kotlarchyk, M.; Chen, S.-H. J. Chem. Phys. 1983, 79, 2461. (27) (a) Hayter, J. B.; Penfold, J. Mol. Phys. 1981, 42, 109. (b) Hansen, J. P.; Hayter, J. B. Mol. Phys. 1982, 46, 651.

A weighted (by the reciprocal of the square of the statistical error of the individual points) nonlinear least-squares fitting routine was used. In addition to B, the adjustable parameters were the aggregation number, 〈n〉, the apparent micellar charge, Z, the micelles’ aspect ratio, a/b, in the case of prolate ellipsoids, and a scale factor (typically found to be 1.0 ( 0.2) to account for variations in the absolute scaling. In the present work we are interested mainly in the very different micellar sizes found for CTA26ClBz and CTA2ClBz micelles vs CTA4ClBz, CTA34ClBz, and CTA35ClBz micelles. Accordingly, we have not used fitting of the SANS data to test the most physically reasonable model for the detailed organization of surfactant moieties within the micelles nor to provide detailed information on the distribution of micellar sizes. In particular, incorporating polydispersity into the fits for either spherical or ellipsoidal micelles does not provide measurable improvement in the fits. Kaler and co-workers recently came to the same conclusion in their study of mixed micelles of DTAB and DDAB.28 For completeness, we note that whether fitting the observed I(Q)’s to a model of spherical or prolate ellipsoidal micelles, a core plus shell micellar model was used. For spherical micelles the core radius Rc was set at 2.17 nm, the extended length of a C16 chain. For prolate ellipsoidal micelles, the core dimensions were set to accommodate 80% of the hydrocarbon chain’s volume, and a single aspect ratio (atot/ btot ) acore/bcore) was used as an adjustable parameter. The micellar shell is comprised of whatever fraction of the surfactant tails cannot be accommodated in the core, plus headgroups, bound counterions, and their associated waters of hydration (taken as 1.5 and 4, respectively). Thus for the spherical micelles of core radius Rc and overall radius Rtot, the form factor is given by:

〈|F(Q)|2〉 ) {(Fc - Fsh)Vc[3J1(QRc)/QRc] + (Fsh - Fsolv)Vtot[3J1(QRtot)/QRtot]}2 (2) J1(x) is the first-order Bessel function. The scattering length densities Fc and Fsh are computed by summing values for the constituent groups in the respective regions of the micelle. Rheological Measurements. Steady shear and dynamic shear measurements for CTA35ClBz micellar solutions were made on a Rheometrics Fluids rheometer (model 7800) equipped with a 10 g‚cm torque transducer and a 10 g full scale normal force transducer. All runs were performed in Couette geometry, with the solutions thermostated at 25.0 ( 0.2 °C. In dynamic shear, a frequency range (ω) of 0.01-32 rad/s was covered; for steady shear measurements, an ωmin ) 0.001 rad/s was used. The frequency-dependent magnitude of the complex viscosity is related to the storage and loss moduli, G′(ω) and G′′(ω), respectively, according to

|η*(ω)| ) (G′(ω) + G′′(ω))1/2/ω

(3)

For those surfactant solutions which behave as Maxwell fluids, the following relationships hold, with τ ) TR, the terminal relaxation time:

G′(ω) ) G′∞ω2τ2/(1 + ω2τ2)

(4)

G′′(ω) - ηsolvω ) G′∞ωτ/(1 + ω2τ2)

(5)

|η*(ω)| ) η0/(1 + ω2τ2)

(6)

Capillary viscometry using Cannon-Fenske viscometers was performed on CTA26ClBz solutions. The viscometer constants were determined from calibration runs using distilled water or glycerol/water mixtures; all measurements on standards and sample solutions were performed at 25.0 ( 0.1 °C.

Results Figure 1, which presents SANS data for 20 mM solutions (φ ) 0.0095) in D2O of CTA26ClBz and CTA35ClBz, is a convenient starting point for our categorization of micellar (28) Lusvardi, K. M.; Full, A. P.; Kaler, E. W. Langmuir 1995, 11, 487.

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Carver et al. Table 1. Fitted and Derived Parameters for Micelles of CTA26ClBz and CTA2ClBz

Figure 1. SANS data for (0) 20 mM CTA26ClBz, which contains spherical micelles, and for (O) 20 mM CTA35ClBz, which contains entangled wormlike micelles.

C, mM

〈n〉

7 10 20 35 58 90 140 200 300

117 ( 6 118 ( 3 115 ( 1 117 ( 1 115 ( 1 159 ( 1 153 ( 1 206 ( 3 195 ( 3

CTA26ClBz 16 ( 2 13 ( 1 16 ( 1 12 ( 1 14 ( 1 20 ( 1 14 ( 1 3.0 ( 0.3 25 ( 1 4.0 ( 0.1 28 ( 2 3.6 ( 0.1

20 35 50 70 100 130 167 200 234

122 ( 4 126 ( 2 128 ( 1 137 ( 12 193 ( 3 221 ( 2 290 ( 3 260 ( 3 236 ( 4

CTA2ClBz 16 ( 1 17 ( 1 17 ( 1 20 ( 6 15 ( 1 3.1 ( 0.3 18 ( 1 4.2 ( 0.1 22 ( 1 5.6 ( 0.1 29 ( 1 4.7 ( 0.1 29 ( 2 4.2 ( 0.1

Z

a/b

b, nma

Rtot, nma

χb

2.92 2.93 2.89 2.92 2.90 3.23

1.4 1.1 1.3 2.3 3.6 4.5 4.7 5.3 7.1

2.89 2.92 2.94 3.01

1.7 1.4 1.5 3.5 2.7 3.8 3.0 6.8 7.5

2.22 2.22 2.24

2.34 2.22 2.22 2.26 2.27

a Derived from 〈n〉, Z, and a/b using standard volumes for the surfactant tails, headgroups, bound counterions, and waters of hydration. b The fits to experiment were by weighted nonlinear least squares, with the weighting factors for the intensities being the reciprocal of their variances, v. For n points per curve and p parameters being varied, χ is given by {∑i[(obsdi - calcdi)2/vi]/(n p + 1)}1/2.

Figure 2. Evolution of SANS curves with C for micelles of CTA26ClBz. Solid lines present the fitted I(Q)’s, using a model of interacting spherical micelles for 7, 10, 20, 35, 58, and 90 mM and of prolate ellipsoids for 140, 200, and 300 mM.

growth in the aqueous micellar solutions of various CTAClBz’s. The similar Q-dependence of the I(Q)’s at intermediate Q values make it obvious that the short dimensions of the micelles Rsph or the cross-sectional radii Rcs (of a cylinder or prolate ellipsoid), respectively, are similar.29 The different values for QImax ≈ QSmax indicate that the mean nearest-neighbor spacing (2π/Qmax; denoted 〈r〉 if between discrete micellar centers of mass or 〈k〉 if between micellar segments in an entangled micellar mesh) is quite different for the two solutions. If both solutions are at C < C*, then the 20 mM CTA35ClBz solution must contain fewer, larger micelles and have a lower Np than does 20 mM CTA26ClBz. Are both of these solutions in fact in the dilute regime? It will become clear in what follows that 20 mM CTA35ClBz is at ca. 10C*, while 20 mM CTA26ClBz is dilute. This section is organized as follows: (1) derivation of 〈n〉’s from SANS data for the five CTAClBz’s assuming that the observed scattering is characteristic in all cases of discrete interacting micelles; (2) determination of the scaling exponent x in Qmax ∝ Cx; (3) results from rheological (29) For three of the chlorobenzoates, namely CTA35ClBz, CTA4ClBz, and CTA34ClBz, SANS curves for the surfactants in aqueous NaCl follow at intermediate Q’s the functional form I(Q) Q ∝ exp(-Rc2Q2/2), from which Rcs values ()x2Rc) of 2.15-2.3 nm are obtained.

Figure 3. Evolution of SANS-derived 〈n〉’s with C for CTA26ClBz and CTA2ClBz.

measurements for CTA35ClBz and CTA26ClBz, including in the case of CTA35ClBz determination of correlation lengths (≡ distance between entanglement points, ξ’s), h from dynamic rheological measurements; (4) le’s and L comments on micellar morphology for micellar solutions of CTA26ClBz and CTA35ClBz as determined by cryoTEM. SANS Data for CTA26ClBz and CTA2ClBz: Micelles of Low Aspect Ratio. Figure 2 shows the evolution of I(Q) with increasing concentration for CTA26ClBz and the results of fitting the data as described in the Experimental Section. Table 1 tabulates fitted and derived parameters for CTA26ClBz and CTA2ClBz micelles, and Figure 3 shows the evolution of 〈n〉 with C for the two surfactants. Above an 〈n〉 of ca. 150-160, a model of interacting prolate ellipsoids gives a better fit than a model of spherical micelles. The micelles cannot be modeled successfully as disks. At a given concentration, micelles of CTA2ClBz are slightly larger than those of CTA26ClBz; the onset of significant micellar growth and of an apparent turnover of 〈n〉 both occur at lower

Micellar Structure and Dynamics

Figure 4. Evolution of SANS curves with C for micelles of CTA35ClBz. Solid lines present the fitted I(Q)’s, assuming the scattering arises from interacting prolate ellipsoidal micelles.

Figure 5. Evolution of SANS-derived 〈n〉’s with C for CTA35ClBz, CTA4ClBz, and CTA34ClBz. Solid line represents 〈n〉app ∝ C-1/2.

concentrations for CTA2ClBz. At Cto, where the SANSderived 〈n〉max is reached, 2a is equal to 1.6 and 1.8 times 2π/Qmax, respectively, for CTA26ClBz and CTA2ClBz. SANS Data for CTA35ClBz, CTA34ClBz, and CTA4ClBz: Micelles of High Aspect Ratio. Figure 4 shows scattering curves at several concentrations of CTA35ClBz, together with fits which assume that the observed scattering can still be treated as characteristic of discrete interacting micelles, which are again modeled as prolate ellipsoids. As is the case when fitting scattering curves from strongly interacting particles, the position of QImax ≈ QSmax is an important determinant of the 〈n〉’s obtained, while the Q-dependence at Q’s greater than Qmax is sensitive to the ellipsoids semiminor axes. SANS data were also collected at concentrations low enough to place Qmax below the Qmin of the SANS instrument used; fits are not presented for those scattering curves. Figure 5 presents the concentration dependence of the fitted 〈n〉’s, from which it can be seen that the apparent 〈n〉’s are monotonically decreasing with increasing C. Hence at the lowest concentration for which a fit was made, 5.5 mM, already the condition C > Cto is satisfied. This model of discrete interacting micelles, although now known to be physically incorrect, is employed for two reasons. The first is to remind the reader of the limitations inherent in relying on SANS data to the exclusion of other techniques, and the second is to point out that in early

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Figure 6. Log Qmax vs log C for all five CTA chlorobenzoates. Qmax ∝ C0.25 (- - -) below C* for CTA26ClBz and CTA2ClBz; Qmax ∝ C0.5 (s) above C*.

investigations of related systems (e.g., CTASal and CPySal) by SANS, the use of this model was fairly effectively advocated and accepted. Concentration Dependence of the SANS Qmax. Figure 6 presents the concentration dependence of Qmax for the five CTAClBz’s studied. Data for CTA26ClBz and CTA2ClBz at concentrations below 90 mM, where the micelles are roughly spherical and 〈n〉 increases modestly with C, follows Qmax ∝ C0.25. The result expected when the added surfactant ions self-assemble into additional micelles of the same C-independent 〈n〉 is Qmax ∝ C1/3, since Qmax/2π ≈ 〈r〉-1 ≈ Np1/3, and Np ∝ C/〈n〉, giving Qmax ∝ (C/〈n〉)1/3, or simply Qmax ∝ C1/3 for a C-independent 〈n〉. For CTA2ClBz from 20 to 70 mM, 〈n〉 ∝ C0.1 is found, and hence Qmax ∝ C0.27 is predicted, in reasonable agreement with the observed exponent of 0.25. In contrast, for CTA35ClBz, CTA4ClBz and CTA34ClBz in the same concentration regime, the exponent is 1/2, consistent with 2π/Qmax representing 〈k〉, the network’s mesh size, where 〈k〉 ) Rcyl(π/φ)1/2. Table 2 tabulates the experimental and calculated values for 〈k〉. As Figure 6 demonstrates, for the higher concentrations of CTA26ClBz and CTA2ClBz, the observed Qmax values also follow C1/2. Dynamic Rheological Measurements for CTA35ClBz. These micellar solutions are shear-thinning and strongly viscoelastic, with bubble recoil easily visible already at 2 mM. At C g 20 mM, they behave as Maxwell fluids, having stress relaxation behavior characterized by a single terminal relaxation time, TR. Figure 7 provides representative rheological data, fit using eqs 4-6. Concentration dependences of the viscosities, the G′∞ values, of G′′min/G′∞ and of TR are presented in Figure 8. A turnover in η0 with increasing concentration can be inferred from the C-dependence of the complex and steady-shear viscosities and from the η0’s obtained from fitting G′, G′′, and η* as described above. Such behavior was observed first by Hoffmann and co-workers in CPyCl/NaSal systems. To our knowledge, the only other aqueous binary surfactant system (e.g., no supporting electrolyte) showing this behavior is the gemini cationic surfactant, 12-2-12, studied by Candau, Zana, and co-workers. At C e 15 mM where the stress relaxation is characterized by a distribution of relaxation times, there is no ω-invariant regime for G′(ω). However, from 8 to 15 mM, there is above the crossover frequency a region of low slope from which G′∞ can be estimated. G′∞ scales as C2.29, close to the exponent 9/4 as expected for an entangled system of linear (rather

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Table 2. Calculated and SANS-derived Values for 〈k〉 for Micelles of CTA35ClBz, CTA4ClBz, and CTA34ClBz φ

2π/Qmax, nm

Rcyl‚(π/φ)1/2, nma

0.00261 0.00380 0.00475 0.00664 0.00949 0.0142 0.0237

CTA35ClBz 77.1 62.8 56.1 47.6 39.5 33.4 27.8

76.4 63.3 56.6 47.8 40.0 32.7 25.3

0.00242 0.00440 0.00616 0.00880 0.0132 0.0176 0.0220 0.0264 0.0352 0.0660

CTA4ClBz 86.3 57.4 51.1 42.7 33.6 29.0 26.8 24.2 21.2 17.3

79.3 58.8 49.7 41.6 33.9 29.4 26.3 24.0 20.8 15.2

0.00332 0.00380 0.00664 0.00949 0.0166 0.0237 0.0285 0.0380

CTA34ClBz 69.5 65.1 60.4 44.3 32.1 25.8 25.0 22.4

70.8 66.2 50.0 41.8 31.7 26.4 24.2 20.9

a R cyl ) 2.2 nm for CTA35ClBz and CTA4ClBz; 2.3 nm for CTA34ClBz.

than branched) wormlike micelles;18 from them, the correlation lengths can be obtained from the relation G′∞ ) kBT/ξ3. From Figure 8c we see that there is a concentration range having G′′min/G′∞ on the order of 0.1. Accordingly, the formalism of Granek and Cates, in which G′′min/G′∞ ≈ h , can be applied to extract values for micellar enle/L tanglement lengths [le ) ξ5/3·lp-2/3] and mean micellar contour lengths. The micellar persistence length (lp) needed in the calculations is taken as 50 nm, the value obtained by light scattering and SANS measurements on salted CTA35ClBz systems.24b The results are tabulated in Table 3, along with the ξ values derived from G′∞. Capillary Viscometry for CTA26ClBz. Aqueous micellar solutions of CTA26ClBz are Newtonian. From 10 to 100 mM, ηsoln obeys the relationship η ∝ φ0.12, with η reaching 0.0014 Pa‚s at 100 mM. Starting at ca. 170 mM and continuing beyond the volume fraction corresponding to Cto, the exponent is 7.4. The respective η’s at 200 and 300 mM, which bracket Cto, are 0.045 and 0.088 Pa‚s. Results from Cryo-TEM. In previous work,16b,30 we imaged successfully CTA35ClBz solutions having concentrations ranging from 2.1 to 10.5 mM; each of the solutions produced images showing highly entangled wormlike micelles. In contrast, images obtained for CTA26ClBz solutions below 40 mM showed spherical micelles only, of a diameter similar to those found in 55 mM CTAB. At 40 mM, coexisting spherical and (short) cylindrical micelles were observed, and at 80 mM CTA26ClBz, entangled wormlike micelles were observed and their presence was ascribed to a shear-induced transition of spherical micelles into cylinders. Neither the SANS-determined 〈n〉 nor the low viscosity at 80 mM are consistent with highly elongated micelles. Discussion The five CTA mono- and dichlorobenzoate binary surfactant/water systems reported on in this work fall

Figure 7. Dynamic rheological data for (a) 25 mM and (b) 35 mM CTA35ClBz, fit using eqs 4-6.

into two distinct categories. CTA26ClBz and CTA2ClBz produce Newtonian aqueous solutions of modest viscosities containing small micelles and having large C*’s. In contrast, CTA4ClBz, CTA34ClBz, and CTA35ClBz produce strongly non-Newtonian, viscoelastic micellar solutions at C’s as low as 2 mM (φ ) 0.001). At 20 mM, CTA26ClBz micelles are characterized by 〈n〉 ) 115 and j〉 ) η0 ) 0.0011 Pa‚s, while CTA35ClBz micelles have 〈n h ) 10 µm and a SANS2 × 105 (as determined from L derived value of 2 × 1010 monomers/m) and η0 ) 1200 Pa‚s. Micellar Morphology. Micellar solutions of CTA26ClBz and of CTA2ClBz first form roughly spherical micelles at low volume fractions, which then grow (above 70-100 mM, φ ) 0.033-0.047) to prolate ellipsoidal micelles of modest aspect ratio. The observed φ-dependence of the solution viscosities for CTA26ClBz (η ∝ φ7.4) is consistent with fairly rigid elongated objects in the slowbreaking regime. As expected, at a given C these micelles further elongate when a supporting electrolyte such as NaCl is added; for CTA26ClBz, it has been inferred from low-Q SANS data31 that the resulting rodlike micelles are quite rigid at least up to [NaCl] ) 1 M. In contrast, micellar solutions of CTA4ClBz, CTA34ClBz, and CTA35ClBz form wormlike micelles already at very low φ’s (certainly below (30) Gee, J. C. Ph.D. Dissertation, 1991. (31) Butler, P. D.; Magid, L. J.; Hamilton, W. A.; Kreke, P. J.; Hayter, J. B. In Neutron Scattering in Materials Science II, Neumann, D. A., Russell, T. P., Wuensch, B. J., Eds.; MRS Symposium Proceedings Vol. 376; 1994.

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Figure 8. C dependence for aqueous CTA35ClBz of (a) various viscosities: |η*(ω)| at 0.01 s-1; η from steady shear at 0.001 s-1; η0 from fits of dynamic rheological data; (b) G′∞, scaling as C2.29; (c) G′′min/G′∞; (d) terminal relaxation time, TR. Table 3. Network Dimensions and L h ’s Derived from Rheological Measurements on CTA35ClBz Solutions C, mM

G′∞, Pa

ξ, nm

8.0b 10.0b 15.0 20.0 25.0 30.0 35.0 40.0

0.35 0.40 0.57 2.4 3.7 5.1 7.6 9.7

228 218 197 118 104 93.2 81.6 75.2

le, G′min/ nm G′∞ 630 580 490 210 170 140 110 99

L h, µm

0.26 2.4 0.12 4.7 0.049 10 0.024 8.7 0.027 6.3 0.051 2.8 0.11 1.1 0.13 0.73

η* (0.01 s-1), η0(fit), Pa‚s Pa‚sa 13.7 21.9 37.8 187 288 105 34.5 11.1

690 1200 440 100 34 11

TR, sa

[1200] 500 120 20 4.5 1.1

a Fitting the dynamic shear results for the Maxwell fluids to eqs 4-6; η0 ) G′∞‚TR. b For CTA35ClBz at 8 and 10 mM the solutions are not simple Maxwell fluids, as the behavior of G′′(ω) vs G′(ω) makes evident (the Cole-Cole plot deviates strongly from the characteristic semicircle). The reported G′∞ for these two solutions is an inflection point rather than a plateau; curve fitting to obtain TR and η0 is not successful.

5 mM, or φ ) 0.0024) in all three cases. Cryo-TEM16b,30 images for all three surfactants as well as low-Q SANS data24b and our rheological data for CTA35ClBz indicate substantial flexibility (lp’s ≈ 50 nm) of the micelles. Details of the C-Dependence of the Micellar Sizes: CTA26ClBz and CTA2ClBz. The SANS-derived 〈n〉’s locate the onset of the transition to prolate ellipsoidal micelles at C ≈ 60-80 mM. By 150-200 mM (φ ) 0.0710.095), the turnover in SANS-derived 〈n〉’s has occurred. If we estimate C* as the C at which twice the prolate ellipsoids’ semimajor axis a just equals 〈r〉, as derived from SANS, then for CTA26ClBz C* is ca. 140 mM and for

CTA2ClBz, 100-130 mM. By this criterion, C* is somewhat less than Cto. Alternatively, the master curve in Figure 6 for Qmax vs C indicates that 200 and 170 mM, respectively (≡Cto), may be taken as operational C*’s. These are the concentrations at which Qmax for the two surfactants join the line described by Qmax ∝ C1/2. The rheological data for CTA26ClBz suggests that 〈n〉 at Cto may be underestimated by SANS. In that narrow window of concentrations between 80 and 150 mM, the values of x in 〈n〉 ∝ Cx are roughly 0.7 and 1.5, respectively, for CTA26ClBz and CTA2ClBz. For CTA26ClBz, the exponent is thus only moderately above the exponent of 0.5 expected for solutions having well-screened electrostatic repulsions. Since the extent of micellar ionization is substantial, for these two surfactants, the Debye lengths in this C regime are already small. The large Cdependence of the viscosities for CTA26ClBz make it clear that micellar growth continues above C*, so that the SANSderived Cto is detecting the transition from scattering characteristic of separate micellar entities to scattering characteristic of the micellar network. Details of the C-Dependence of the Micellar Sizes: CTA35ClBz. Analysis of the SANS data for the three rod-forming CTA chlorobenzoates under the (incorrect) assumption that the scattering can be treated at every C studied as arising from discrete interacting micelles produces (Figure 5) a single master curve following 〈n〉 ∝ C-1/2. If those 〈n〉’s were correct, twice the micelle’s semimajor axis (2a) would be slightly larger than 2π/Qmax, signifying that the C-dependence of the 〈n〉’s corresponded to micellar overlap just being maintained.13

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However, the occurrence of such short micelles is completely inconsistent with the cryo-TEM images and with the results of the rheological measurements. Rather, the relationship Qmax ∝ C-1/2 from at least 5.5 mM on (Figure 6) can be regarded as tracking the distance between adjacent micellar threads in a network of entangled micelles, which decreases with increasing C. The scaling behavior discussed above means that aqueous micellar solutions of the three rod formers are already above C* at 5.5 mM, which is also consistent with the cryo-TEM data. To quantitate the various length scales existing in these solutions, we therefore turned to dynamic rheological measurements on one of them, the CTA35ClBz system. Considering first the results (Table 3) obtained for L h at 8, 10, and 15 mM, we find L h ∝ φ2.2. Given that the extent of micellar ionization is low, the Debye lengths in these solutions will be large, and micellar growth with increasing C is therefore expected to be rapid. Considering that no supporting electrolyte is present, the CTA35ClBz micellar solutions contain remarkably large micelles at remarkably low C’s. To estimate C*, we note h (in m), compute Np and hence 〈r〉 from that 〈n j 〉 ) 2 × 1010L 〈n j 〉, and then take 〈r〉 ≈ L h (since the short rodlike micelles are expected to be rather rigid) as the criterion for overlap. The observed C-dependence of L h produces an estimate of 2.1 mM for C* by this means. However, η0 for 2 mM CTA35ClBz is already 0.02 Pa‚s, and there is a G′/G′′ crossover at ω ) 3 rad/s, suggesting that C* may be somewhat lower than 2 mM. The cryo-TEM imaging,16b,30 although subject to concerns about changes in C and/or the generation of shear-induced structures during preparation of the vitrified thin films, also supports C* < 2 mM for CTA35ClBz.32 Consistent with the large φ-dependence of the micelle size, η0 also shows a large φ dependence, with an exponent of 5-5.5 below 10 mM. However, since the 8, 10, and 15 mM solutions are not Maxwell fluids, being rather in the regime where reptation is an important mode of stress relaxation, the exponent observed is in fact considerably below the theoretical value for φ’s exponent of ca. 9 (for stiff unbreakable rods) to 10 (from η ∝ L h 3φ15/4, for flexible micelles in the slow-breaking limit). Zana, Candau, and co-workers observed the same lower-than-expected value

of the exponent just above C* for the 12-2-12 gemini surfactant. Furthermore, the observed exponent is consistent with an entangled network of linear micelles, rather than with intermicellar branching or the formation of a multiconnected network, indicating that the formation of micellar end caps is not yet energetically prohibitive. By the time the concentration of CTA35ClBz reaches 20 mM, the mean micellar length is beginning to decline. However, the scaling law (derived from that for G′∞ vs φ) for ξ, the distance between entanglement points in the network, from 8 to 40 mM is that expected of a fullyentangled micellar network. Indeed, as the tabulated values in Table 2 make clear, the various length scales follow the order L h > le > ξ > 〈k〉. The fact that the contour entanglement lengths remain greater than the correlation lengths over the concentration range investigated indicates that the networks remain unsaturated over that range. In the more restricted range of concentrations from 20 to 40 mM CTA35ClBz, where the solutions are Maxwell fluids and G′′min(ω) is in the experimentally accessible range of frequencies, the terminal relaxation time decreases by 3 orders of magnitude, from 1200 to 1.1 s. Recently, Shikata and Pearson17b have identified in the CTAB/NaSal system a transition to the normal hexagonal mesophase at the C where ξ ≈ le and these two lengths become roughly the Kuhn length (2lp), as suggested on theoretical grounds. These were Maxwell fluids; the NaSal content of their solutions was adjusted to keep TR at 2-3 s; G′∞ followed C2.2 up to the concentration at which the phase transition occurred. Hence their system shows h with C. For the no turnover in η0 nor presumably in L CTA35ClBz system, we observe the scaling laws ξ ∝ C-0.65 and le ∝ C-1.1; at 73 mM, ξ ) le ) 51 nm. However, our system does not display the phase transition to an LC state. In fact, 70 mM CTA35ClBz is Newtonian over the frequency range 0.01-32 rad/s, with η ) 1.7Pa‚s. An estimate of L h at 70 mM, using the data from Table 3 for lower concentrations, yields a value of 27 nm, suggesting that the CTA35ClBz system is below overlap. Finally, we note that the analysis above of the value for le of 51 nm, characteristic of a saturated network, suggests a value of lp which is roughly 1/2 the value we determined by light scattering.24b

(32) The source of the small differences in C*’s determined by different experimental techniques is most likely not an isotope effect. Scattering measurements (light scattering and/or SANS) for aqueous solutions of cationic surfactants such as CTAB or anionic surfactants such as SDS show only modest isotope effects on micellar aggregation numbers (on the order of 10%). See for example: Berr, S. S.; Caponetti, E.; Johnson, J. S.; Jones, R. R. M.; Magid, L. J. J. Phys. Chem. 1986, 90, 5766. Chang, N. J.; Kaler, E. W. J. Phys. Chem. 1985, 89, 2996.

Acknowledgment. Financial support from the National Science Foundation (CHE90-08589 and CHE8611586) is gratefully acknowledged. Initial financial suppport for M.C. and A.D. was provided by Dow Chemical. LA950965+