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Micellar Structures of Poly(styrene-b-4-vinylpyridine)s in THF/Toluene Mixtures and Their Functionalization with Gold Nauman Ali and Soo-Young Park* Department of Polymer Science, Kyungpook National UniVersity, 1370 Sangyuk-dong, Buk-gu, Daegu 702-701, Korea ReceiVed March 19, 2008. ReVised Manuscript ReceiVed May 21, 2008 The effects of the block copolymer composition and the solvent selectivity on the micellar morphologies of poly(styrene-b-4-vinylpyridine)s (PS-b-P4VPs) and their functionalizations with gold were studied in 10 mg/mL solutions using small-angle X-ray scattering and transmission electron microscopy (TEM). The solvent selectivity for the PS block was controlled by toluene/tetrahydrofuran (THF) mixtures in which toluene and THF are selective for PS and nonselective, respectively. The micellar structure was strongly dependent on φ (wt % toluene in toluene/THF mixture) and the composition of the block copolymers. PS(12K)-b-P4VP(11.8K) (symmetric) showed spherical micelles in the entire range of φ except φ ) 0 (THF, nonselective solvent). PS(3.3K)-b-P4VP(18.7K) (asymmetric, longer P4VP) showed multiple morphologies with transitions from spheres to cylinders and finally to vesicles with an increase in φ. PS(19.6K)-b-P4VP(5.1K) (asymmetric, longer PS) showed spherical micelles only at the narrow ranges of 90 wt % e φ e 100 wt % and an isotropic state at the other ranges. The micelles formed a complex with HAuCl4 and were reduced with hydrazine in the solvent mixtures. The morphologies of micelles, hybrid micelles, and gold nanoparticles were investigated by using TEM and UV/vis spectroscopy. The possible mechanisms leading to these morphological changes and the formation of the nanosized gold particles were also discussed.

Introduction Block copolymers have been extensively documented in the scientific literature1–3 due to an increased curiosity about their applications to well-defined surface patterning,4 temperaturesensitive biodegradable hydrogels,5 semicrystalline thermoplastic elastomers,6 and proton exchange membranes.7 Block copolymers are comprised of two or more chemically distinct polymer blocks with different chain lengths joined by covalent bonds. In simple linear diblock copolymers, micelles are formed via self-assembly in a selective solvent. The interactions between the polymer and solvent are characterized by the Flory-Higgins segment-segment interaction parameter, χAB. The micellar shape depends on the composition of the block copolymer and solvent interactions with each block.8 The morphologies that block copolymers can self-assemble into include spheres, cylinders, and vesicles.8 There are three main forces for controlling these morphologies, i.e., the stretching of core blocks, the repulsive interaction among corona chains, and the surface tension of the core/corona interface at the onset of micellization.9,10 Micelles are made up of a core and a surrounding corona; the core of micelles consists of insoluble blocks, which associate together to minimize unfavorable interactions with the solvent, while the surrounding corona consists of dissolved blocks. “Crew-cut” micelles can be formed * To whom correspondence should be addressed. Phone: +82-53-9505630. Fax: +82-53-950-6623. E-mail: [email protected]. (1) Harada, A.; Kataoka, K. Science 1999, 283, 65–67. (2) Cui, H.; Chen, Z.; Zhong, S.; Wooey, L, K.; Pochan, J, D. Science 2007, 317, 647–650. (3) Gindy, M. E.; Panagiotopoulos, A Z.; Prud’homme, R. K. Langmuir 2008, 24, 83–90. (4) Hwang, W.; Ham, M. H.; Sohn, B. H.; Huh, J.; Kang, Y. S.; Jeong, W.; Myoung, J. M.; Park, C. Nanotechnology 2005, 16, 2897–2902. (5) Shim, S. W.; Kim, S. W.; Lee, D. S. Biomacromolecules 2006, 7, 1935– 1941. (6) Schmalz, H.; Abetz, V.; Lange, R. Compos. Sci. Technol. 2003, 63, 1179– 1186. (7) Zhang, X.; Liu, S.; Yin, J. J. Membr. Sci. 2005, 258, 78–84. (8) Bucknall, D. G.; Anderson, H. L. Science 2003, 302, 1904–1905. (9) Zhang, L.; Eisenberg, A. Macromolecules 1996, 29, 8805. (10) Zhang, L.; Yu, K.; Eisenberg, A. Science 1996, 272, 1777–1779.

when the corona chains are much shorter than the core chains, and “hairy” micelles can be formed when the relative chain lengths are reversed. A sphere-to-cylinder-to-lamella (or vesicle) transition is sometimes observed from the crew-cut micelles by increasing the solvent selectivity, although usually spherical micelles are observed in the hairy micelles. Crew-cut micelles are more susceptible to the selectivity of the solvent than hairy micelles. A change in the solvent selectivity can give effects on not only the dimensions but also the shape of the micelles. As the solvent selectivity increases, spherical micelles become unfavorable and elongated cylindrical micelles are formed. These cylindrical micelles are particularly attractive in a wide range of applications, such as artificial tissue scaffolds,11 drug delivery,12 and fillers for improving the toughness of polymer resins.13 As the solvent selectivity increases, the core-block stretching will dictate a further morphological transition to a bilayer vesicular form. This vesicular morphology is well documented in the literature from block copolymers,14 and it plays an important role in several biological functions including storage15 and transportation16 of small molecules. The nanometer-sized domains of block copolymers can be utilized as the so-called nanoreactors to synthesize a variety of nanoparticles. Poly(styrene-b-4-vinylpyridine) (PS-b-P4VP) has been studied for the nanoreactor application due to its strong metal-chelating ability in the P4VP core of the micelles in PSselective solvents.17–19 Such micelles may be regarded as a longliving and nanosized reaction vessel, while the growth of colloidal (11) Hartgerink, J. D.; Beniash, E.; Stupp, S. I. Science 2001, 294, 1684–1688. (12) Geng, Yan.; Dalhaimer, P.; Cai, S.; Tsai, R.; Tewari, M.; Minko, T.; Discher, D. E. Nat. Nanotechnol. 2007, 2, 249255> (13) Dean, J. M.; Verghese, N. E.; Pham, H. Q.; Bates, F. S. Macromolecules 2003, 283, 9267–9270. (14) Discher, B. M.; Won, Y. Y.; Ege, D. S.; Lee, J. C. M.; Bates, F. S.; Discher, D. E.; Hammer, D. A. Science 1999, 284, 1143–1146. (15) Petty, H. R. Molecular Biology of Membranes, Structure and Function; Plenum: New York, 1993. (16) Waka, O.; Hiroshi, S.; Masahiro, N.; Itaru, K.; Haruhisa, K.; Yoshiteru, O.; Kohei, H.; Yuzuru, K. FEBS J. 2007, 274, 3392–3404. (17) Liang, H, F.; Yang, T, F.; Huang, C, T.; Chen, M, C.; Sung, H, W. J. Controlled Release 2005, 105, 213–225.

10.1021/la800860q CCC: $40.75  2008 American Chemical Society Published on Web 08/05/2008

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nonselective solvent so that the variation of solvent selectivity through mixing with THF in toluene becomes small as compared with that through the same amount of mixing with ethanol in toluene. HAuCl4 formed a complex with the P4VP core of the micelle and was reduced with hydrazine. The structures of the micelles and gold particles in complex and reduced states were also studied.

Experimental Section

Figure 1. SAXS curves of the 10 mg/mL PS(12K)-b-P4VP(11.8K) solutions as functions of q and φ.

particles might be limited by the size of the micelle core.20 Noble metal nanoparticles (especially gold nanoparticles) have been of great interest because they have unique electrical,21 optical,22 and magnetic23 properties and a great potential in biosensors,24 biological imaging,25,26 and catalysis27 due to their high surfaceto-volume ratio. Various synthetic methods were developed to control and stabilize the particle size.28,29 In recent years, much attention has been drawn to the attachment of small molecules (such as cobalt dodecylbenzenesulfonate or p-nonadecylphenol) to PS-b-P4VP.30,31 The noncovalent interactions induced micellization even in nonselective solvents of PS-b-P4VP (such as THF) because the interactions between them changed the solubility of the P4VP and the solvent became selective.32 Park et al. recently reported on the structure of the micelles and their ordered structures of PS-b-P4VP in toluene/ethanol mixtures where toluene and ethanol are selective for PS and P4VP, respectively.33,34 In the present study, toluene/THF mixtures were used for more precise control of the micellar structure because THF is a (18) Koh, H. D.; Kang, N. G.; Lee, J. S. Langmuir 2007, 23, 12817–12820. (19) Bronstein, L. M.; Chernyshov, D. M.; Volkov, I. O.; Ezernitskaya, M. G.; Valetsky, P. M.; Matveeva, V. G.; Sulman, E. M. J. Catal. 2000, 196, 302–314. (20) Yoon, J.; Lee, W.; Thomas, E. L. Nano Lett. 2006, 6, 2211–2214. (21) Kotiaho, A.; Lahtinen, R. M.; Tkachenko, N. V.; Efimov, A.; Kira, Aiko.; Imahori, H.; Lemmetyinen, H. Langmuir 200723, 13117. (22) Oeguet, S.; Idrobo, J. C.; Jellinek, J.; Wang, J. J. Cluster Sci. 2006, 17, 609–626. (23) Sun, S.; Murray, C. B.; Weller, D.; Folks, L.; Moser, A. Science 2000, 287, 1989–1992. (24) Yanga, D. H.; Baeb, A. H.; Koumotoa, K.; Lee, S. W.; Sakurai, K.; Shinkai, S. Sens. Actuators, B 2005, 105, 490. (25) Sharma, P.; Brown, S.; Walter, G.; Santra, S.; Moudgil, B. AdV. Colloid Interface Sci. 2006, 471, 123–126. (26) Storhoff, J. J.; Lazarides, A. A.; Mucic, R. C.; Mirkin, C. A.; Letsinger, R. L.; Schatz, G. C. J. Am. Chem. Soc. 2000, 122, 4640–4650. (27) Okitsu, K.; Ashokkumar, M.; Grieser, F. J. Phys. Chem. B 2005, 109, 20673–20675. (28) Carrot, G.; Valmalette, J. C.; Plummer, C. J. G.; Scholz, S. M.; Dutta, J.; Hofmann, H.; Hilborn, J. G. Colloid Polym. Sci. 1998, 276, 853–859. (29) Groehn, F.; Kim, G.; Bauer, B. J.; Amis, E. J. Macromolecules 2001, 34, 2179–2185. (30) Zhu, R.; Wang, Y.; He, W. Eur. Polym. J. 2005, 41, 2088–2096. (31) Lefevre, N.; Fustin, F, C.; Varsheny; K, S.; Gohy, F. J. Polymer 2007, 48, 2306–2311. (32) Peng, H.; Cheng, D.; Jiang, M. Langmuir 2003, 19, 10989–10992. (33) Park, S. Y.; Sul, W. H.; Chang, Y. J. Macromolecules 2007, 40, 3757– 3764. (34) Park, S. Y.; Chang, Y. J.; Farmer, B. L. Langmuir 2006, 22, 11369– 11379.

Materials. PS-b-P4VPs which were synthesized by an anionic polymerization method were purchased from Polymer Source, Inc. (Canada). Toluene/THF mixtures were used for control of solvent selectivity for the PS block where toluene and THF are selective for PS and nonselective solvents, respectively. The number-average molecular weights of PS-b-P4VP used in this investigation were 12000/11800 (PS/P4VP) (PS(12K)-b-P4VP(11.8K)), 3300/18700 (PS(3.3K)-b-P4VP(18.7K)), and 19600/5100 (PS(19.6K)-b-P4VP(5.1K)). The polydispersity data were less than 1.1 for all block copolymers. Chloroauric acid (HAuCl4; 99.9%, Sigma-Aldrich) and hydrazine (N2H2 · H2O; 98%, Aldrich) were used as gold-complexing and reducing agents, respectively, and used as received. The solutions were dialyzed for one day using a dialysis-tubing cellulose membrane (Sigma-Aldrich, D9277-100FT, 10 mm × 6 mm) which retains >90% of cytochrome c (MW 12400) in a solution over a 10 h period. Sample Preparation. The copolymers were dissolved in the solvent mixtures with a fixed concentration of 10 mg/mL. The toluene content in the toluene/THF mixture was denoted as φ (wt %). The solutions were heated under the boiling point for 1 h and then cooled to room temperature to make standard solutions. The metallization was performed by adding a stoichiometric amount (4.2 × 10-7 mol) of HAuCl4 per pyridine unit to the solution and then stirring for 24 h. The HAuCl4 complex solutions were reduced with 10 times more than the stoichiometric amount (i.e., 4.2 × 10-6 mol) of N2H2 · H2O35 and then dialyzed for 24 h. Analysis. The samples for transmission electron microscopy (TEM; Hitachi H-7600, 100 kV) were prepared by dropping the solutions onto a 200-mesh carbon-coated copper grid, absorbing the solvent on filter paper, and evaporating the solvent at room temperature. The samples on the grid were stained with I2 vapors for 10 min, while the complex and reduced samples were used without staining. UV/vis spectra were recorded using a Shimadzu UV-2401PC spectrophotometer with 1 cm quartz cells. Samples were diluted to 1 mg/mL for UV/vis spectra. Small-Angle X-ray Scattering (SAXS). The sample holder for SAXS has a mica window and a hole for the injection of the solution. Experiments were performed at beamline 4C1 (Pohang Light Source, Korea), where a W/B4C double-multilayer monochromator delivered monochromatic X-rays that had a wavelength of 0.16 nm. A flat Au mirror was used to reject higher harmonics from the beam. A MarCCD camera (Mar USA, Inc., CCD165) was used to collect the scattered X-rays. The sample-to-detector distance (sdd) was 3 m, which allowed the SAXS data to be obtained in a q (scattering vector) range between 0.06 and 1.11 nm-1. The sdd was calibrated using SEBS (polystyreneb-poly(ethylene-ran-butylene)-b-polystyrene). Data Analysis. The raw spectra were corrected for the background of the solvent and sample cell and detector efficiency by conventional procedures. Two-dimensional scattering spectra were azimuthally averaged. The measured intensity (I(q)) can be expressed as the product of form (F(q)) and structure (S(q)) factors, although S(q) is negligible for the dilute solution. We used dilute solutions (10 mg/mL) in this study so that I(q) represented only a form factor, although little contribution of S(q) to I(q) might be expected, if any. SAXS data were analyzed with GIFT software, which was developed by Glatter.36–42 Fourier transformation of I(q) yields the pair distance (35) Antonietti, M.; Wenz, E.; Bronstein, L.; Seregina, M. AdV. Mater. 1995, 7, 1000–1005. (36) Glatter, O.; Krathy, O. Small-Angle X-ray Scattering; Academic Press: London, 1982; p 126. (37) Glatter, O. J. Appl. Crystallogr. 1997, 10, 415–401. (38) Glatter, O. Appl. Crystallogr. 1980, 13, 577–584.

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Figure 2. (a) p(r), (b) Dmax (9) and Rg (2), and (c) I(0) (9) and I(0)/V (b) (V ) (3/4)π(Dmax/2)3) of the 10 mg/mL PS(12K)-b-P4VP(11.8K) solutions with respect to φ. p(r) was calculated from Figure 1, and Dmax, Rg, and I(0) were calculated from p(r).

distribution function (p(r)) of a particle, which is a histogram of distances inside the particle weighted with electron density differences. The shape of p(r) allowed the determination of basic geometrical shapes (spheres, cylinders, or vesicles), even for inhomogeneous particles. This methodology, using an indirect Fourier transformation, has been described elsewhere.36–42 Dmax was determined at an r value at p(r) ) 0. The radius of gyration (Rg) can be calculated by the following equation:

∫r2p(r) Rg ) 2∫p(r)

(1)

Results and Discussion Symmetric PS(12K)-b-P4VP(11.8K). Figure 1 shows the SAXS curves of PS(12K)-b-P4VP(11.8K) as functions of q and φ. The SAXS curves showed a deep groove with a small hill, (39) Glatter, O. J. Appl. Crystallogr. 1981, 14, 101–108. (40) Brunner-Popela, J.; Glatter, O. J. Appl. Crystallogr. 1997, 30, 431–442. (41) Bergmann, A.; Fritz, G.; Glatter, O. J. Appl. Crystallogr. 2000, 33, 1212– 1216. (42) Eyerich, B.; Brunner-Popela, J.; Glatter, O. J. Appl. Crystallogr. 1999, 32, 197–153.

and their intensity continuously decreased as φ decreased. The deep groove in the solution SAXS pattern indicates that the micelles were present in the solution with a regular size. The intensity at φ ) 0 (THF) became low and flat as compared to those of other solutions, indicating that the solution in THF was isotropic. Toluene and THF are known to be selective for PS and nonselective solvents, respectively,43,44 and the solvent selectivity for the PS block rises as φ increases. Thus, the micelles formed would have P4VP in their cores and PS in their coronas in their toluene/THF mixture solutions. Figure 2 shows p(r), Dmax, Rg, and I(0) in which p(r) was calculated from Figure 1 and Dmax, Rg, and I(0) were calculated from p(r). All p(r) functions (Figure 2a) were typical of spherical micelles. Figure 2b shows the plots of Dmax and Rg versus φ. The ratio Dmax/Rg was ∼3.06, which was larger than that of the theoretical homogeneous sphere (2.58), and this discrepancy might be due to a nonuniform core/shell structure in the micelle. Dmax (and Rg) continuously decreased from 45 to 26 nm as φ decreased (43) Brandrup, J.; Immergut, E. H.; Grulke, E. A. Polymer Handbook, 4th ed.; John Wiley and Sons: Hoboken, NJ, 1999; Chapter VII. (44) Zhao, H.; Douglas, P. E.; Harrison, H. B.; Schanze, S. K. Langmuir 2001, 17, 8428.

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Figure 3. TEM images of the micelles of PS(12K)-b-P4VP(11.8K) before (a, b) and after (c, d) complexing and after reducing (e, f) at φ ) 20 wt % (a, c, e) and 100 wt % (b, d, f). The samples were evaporated on the carbon-coated copper grid from the 5 mg/mL solutions and stained with I2 for 10 min, and the complexed and reduced samples were analyzed without staining. The inset shows a micelle with gold nanoparticles in raspberry (e) and cherry (f) morphologies, and the rectangular box represents the enlarged part in the inset.

Figure 4. UV/vis absorption spectra of 1 mg/mL PS(12K)-bP4VP(11.8K)/HAuCl4 solutions in the reduced state.

from 100 to 10 wt %. Figure 2c shows I(0) and I(0)/V ()(3/ 4)π(Dmax/2)3) with respect to φ. I(0) was calculated from the integration of p(r) and is proportional to the aggregation number of micelles (Z) (i.e., the total electrons in one micelle). I(0)/V represents the density of the block copolymer in the micelle. I(0) decreased from 2820 to 229 as φ decreased from 100 to 10 wt %. However, V decreased less than I(0) with respect to φ, so that the ratio of I(0)/V decreased from 2820/((3/4)π(45/2)3) ()0.104) to 229/((3/4)π(26/2)3) ()0.044) as φ decreased from 100 to 10 wt %. This result indicates that the micelles formed at high selectivity were harder than those formed at low selectivity. The “hard” and “soft” micelles are for describing the relative hardness of the micelles; more chains are in the hard micelle than the soft one per unit volume because the relative hardness of the micelle was studied with the aggregation number divided

by the volume of the core of the micelle (I(0)/V ()(3/4)π(Dmax/ 2)3) in this study. Figure 3 shows the TEM images of micelles at φ ) 20 and 100 wt % before and after complexing and after reducing. The choice of φ ) 20 and 100 wt % is for soft and hard micelles, respectively. The TEM samples were prepared by the evaporation of 5 mg/mL solutions on a carbon-coated grid and staining with I2, which made the P4VP part visible. This sample preparation method for TEM cannot control the concentration of the solution because it becomes concentrated during evaporation, and the equilibrium structures cannot be observed due to the difference in the evaporation speeds of toluene and THF. Information about the kinds of micelles present in the solution, however, could be obtained because the TEM samples were prepared with very diluted solutions (5 mg/mL), which might have little effect on the already-formed micelle during its drying on the grid. Spherical micelles were observed at all φ values before complexing (Figure 3a,b), and the diameter of the micelle increased as φ increased from 28 nm (φ ) 20 wt %) to 40 nm (φ ) 100 wt %), which was consistent with the SAXS data. TEM micrographs of the complex-state micelles (Figure 3c,d) show that the basic shape of the spherical micelles remained. Reduction with hydrazine led to nanosized spherical Au particles inside the core (Figure 3e,f). A “raspberry” morphology of Au particles was observed at φ ) 20 wt % with a diameter of ∼3 nm, whereas a “cherry” morphology was obtained at φ ) 100 wt % with an increased diameter of ∼8 nm (Figure 3f).35 This result suggests that hydrazine had difficulty penetrating into the micelle core for the hard micelles (at φ ) 100 wt %), which caused a slow reduction, leading to the cherry morphology, while easy penetration of hydrazine in the soft micelles led to a rapid reduction, resulting in the raspberry morphology.45 Figure 4 shows UV/vis absorption spectra of the 1 mg/mL solutions in their reduced states at different φ values. The solutions before reduction did not show any absorbance in the visible (45) Mayer, A. B. R. Polym. AdV. Technol. 2001, 12, 96–106.

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Figure 5. (a) SAXS curves and (b) p(r) functions of the 10 mg/mL PS(3.3K)-b-P4VP(18.7K) solutions as functions of q and φ.

Figure 6. TEM images of the micelles of PS(3.3K)-b-P4VP(18.7K) before (a, b) and after (c, d) complexation and after reducing (e, f) at φ ) 50 wt % (a, c, e) and 80 wt % (b, d, f). The samples were evaporated on the carbon-coated copper grid from 5 mg/mL solutions and stained with I2 for 10 min, and the complexed and reduced samples were analyzed without staining. The insets in (e) and (f) show gold nanoparticles inside the cylinder and vesicle, respectively, and the rectangular box represents the enlarged part in the inset.

region. After reduction, the solutions changed from light yellow to red, and a peak in the visible region appeared at 525 nm as shown in Figure 4. The peak at 525 nm was due to the surface plasmon resonance of the conduction electrons of the gold nanoparticles with a diameter of less than 10 nm.46,47 THF (φ ) 0 in Figure 4) was a nonselective solvent, so the mechanism for Au nanoparticle formation may be different from that for the other selective solvents. However, the difference in wavelength maxima was small, so the size difference may be negligible. The size of the Au nanoparticles was polydispersed, maybe due to the inhomogeneous reduction speed in the core of the micelle, (46) Park, J. H.; Lim, Y. T.; Park, O. O.; Kim, Y. C. Macromol. Rapid Commun. 2003, 24, 331–334. (47) Zhang, L.; Li, P.; Dan, Li,.; Guo, S.; Wang, E. Langmuir 2008, 24, 3407– 3411.

although the size distribution was still narrow compared to that of other chemical methods, where gold nanoparticles were stabilized with different ligands48–52 and reducing agents such as sodium citrate,48 tetraheptylammonium bromide,49 NaBH4,50 lithium triethylborohydride,51 and tetraoctylammonium bromide.52 The other block copolymers in their reduced states also showed similar results. (48) Bogatyrev, V. A.; Dykman, L. A.; Khlebtsov, B. N.; Khlebtsov, N. G. Opt. Spectrosc. 2004, 96, 128–135. (49) Dai, X.; Tan, Y.; Xu, J. Langmuir 2002, 18, 9010–9016. (50) Zhang, L.; Li, P.; Li, D.; Guo, S.; Wang, E. Langmuir 2008, 24, 3407– 3411. (51) Corbierre, M. K.; Cameron, N. S.; Lennox, R. B. Langmuir 2004, 20, 2867–2873. (52) Walker, C, H.; John, J.; V, S.; Neilson, P. W. J. Am. Chem. Soc. 2001, 123, 3846–3847.

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Figure 7. (a) SAXS curves and (b) p(r) functions of the 10 mg/mL PS(5.1K)-b-P4VP(19.6K) solutions as functions of q and φ.

Figure 8. TEM images of the micelles of PS(19.6K)-b-P4VP(5.1K) before (a) and after (b) complexation and after reduction (c) at φ ) 100 wt %. The samples were evaporated on the carbon-coated copper grid from 5 mg/mL solutions and stained with I2 for 10 min, and the complexed and reduced samples were analyzed without staining. The box in (c) represents the inset, which shows the raspberry morphology of the gold nanoparticles in the micelle.

Asymmetric PS(3.3K)-b-P4VP(18.7K). Figure 5a shows the SAXS patterns of the 10 mg/mL PS(3.3K)-b-P4VP(18.7K) solutions as functions of q and φ. The solutions at φ ) 100 and 90 wt % were insoluble (in a milky state) due to the short length of the soluble PS chain. The SAXS intensities of the solutions at φ ) 0 and 10 wt % were significantly low, indicating that those solutions were isotropic. Thus, the range of φ in which micelles were formed was narrowed. The SAXS curves show a deep increase in intensity at a low angle (