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The Preparation and Characterization of the Cross-Linked Spherical, Cylindrical, and Vesicular Micelles of Poly(styrene-b-isoprene) Diblock Copolymers Soo-Young Park* and Myeong-Hye Park Department of Polymer Science, Kyungpook National UniVersity, #1370 Sangyuk-dong, Buk-gu, Daegu 702-701, Korea ReceiVed January 13, 2007. In Final Form: March 21, 2007 PI cores of the micelles of poly(styrene-b-isoprene) (PS-b-PI) diblock copolymers, in PS selective solvents, were cross-linked with sulfur monochloride (S2Cl2). The cross-linked micellar structure was maintained after dialysis in THF (neutral solvent) and did not change during heating. Cross-linking brought about the opportunity for TEM images in a solution state; otherwise, the micellar structure would be destroyed (or changed) during the evaporation of the solvent on a carbon-coated copper grid. The Flory interaction parameter, χ, between the PI block and the solvent was controlled by mixing two selective solvents (DMP/toluene, DMP/DEP and DEP/DBP) which have different degrees of selectivity for the PS block, as well as heating the solutions. Two block copolymers, PS(7.2K)-b-PI(7.8K) and PS(5.5K)-b-PI(18.8K), were studied in order to clarify the effects of the relative chain length of each block on the micelle structure in the selective solvents. PS(7.2K)-b-PI(7.8K), which is nearly symmetric, showed only spherical micelles in the DMP/toluene mixture. The basic spherical micellar shape of PS(7.2K)-b-PI(7.8K) did not change with χ, while the size and aggregation number of the micelles increased as χ increased until 2.05 and then were saturated after that. PS(5.5K)-b-PI(18.8K), which is asymmetric, showed a structural change from spherical to cylindrical to vesicular micelles with an increase in the selectivity of the DMP/DEP and DEP/DBP mixtures (which was also confirmed by TEM and SAXS studies). Giant vesicular micelles with a diameter of ∼2.5 µm were observed in high-selectivity solvents. The size of the vesicular micelle seemed to decrease as selectivity decreased. The systematic changes of the micellar structures of PS(5.5K)-b-PI(18.8K), via changes in solvent selectivity, could be demonstrated through TEM images, which were prepared by evaporating the solvent of the cross-linked micellar solution onto the carbon-coated grid after dialysis.

Introduction Block copolymers are one of the most valuable classes of polymeric materials due to their ability to self-assemble, either in the bulk or selective solvents, thus leading to characteristic morphologies in the bulk and to micelle formations in selective solvents.1 In selective solvents, the micelles are made of a core and its surrounding protective corona, which are formed by insoluble and soluble blocks, respectively.2 Insoluble blocks minimize contact with the solvent, and micelle formation is favored. The resulting micelles can access a wide range of morphological shapes such as spheres, rods, vesicles, lamellae, large-compound micelles, nanofibers, and nanotubes.3-9 The morphology of micelles is dependent on several variables, including block copolymer composition and concentration,10 the type and concentration of the added ions,11,12 and the selectivity of the solvent.13,14 A force balance, for example, the stretching * To whom correspondence should be addressed. Tel +82-53-9505630. Fax +82-53-950-6623. E-mail [email protected]. (1) Hadjichristidis, N.; Pispas, S.; Floudas, G. Block Copolymers: Synthetic Strategies, Physical Properties and Applications; Wiley: New York, 2003. (2) Tuzar, Z.; Kratochvil, P. AdV. Colloid Interface Sci. 1978, 6, 201. (3) Liu, G.; Ding, J.; Guo, A.; Herfort, M.; Bazett-Jones, D. Macromolecules 1997, 30, 1851. (4) Yan, X.; Liu, F.; Li, Z.; Liu, G. Macromolecules 2001, 34, 9112. (5) Jenekhe, S. A.; Chen, X. L. Science 1999, 283, 372. (6) Liu, G.; Qiao, L.; Guo, A. Macromolecules 1996, 29, 5508. (7) Zhang, L.; Eisenberg, A. Macromolecules 1996, 29, 8805. (8) Borisov, O. V.; Zhulina, E. B. Macromolecules 2003, 36, 10029. (9) Zhou, Z.; Li, Z.; Ren, Y.; Hillmyer, M. A.; Lodge, T. P. J. Am. Chem. Soc. 2003, 125, 10182. (10) Zhang, L.; Eisenberg, A. Science 1995, 268, 1728. (11) Zhang, L.; Eisenberg, A. Macromolecules 1996, 29, 8805. (12) Van der Maarel, J. R. C.; Groenewegen, W.; Egelhaaf, S. U.; Lapp, A. Langmuir 2000, 16, 7510. (13) Yu, Y.; Eisenberg, A. J. Am. Chem. Soc. 1997, 119, 8383.

of core blocks, the repulsive interaction among corona chains, and the surface tension of the core/corona interface at the onset of micellization mainly control these morphological types.15,16 The Flory interaction parameter between constituent blocks (χ), the molecular weight, and the composition of each block mostly determine the morphology in the bulk as well as in solution; however, intrinsic properties such as χ and the molecular weight and composition of each block are not readily tunable factors for a given block copolymer system, although solvent quality can be adjusted to balance these force contributions. Pioneering research has been conducted by Eisenberg et al., who investigated poly(styrene-b-acrylic acid) (PS-b-PAA) ionic diblock copolymers in water/dioxane or water/dimethylformamide (DMF) mixtures.17-21 Transitions from spheres to cylinders to vesicles were observed by increasing the amount of water in the mixture, thereby increasing interfacial tension. Recently, Lodge et al. studied the spherical, cylindrical, and vesicular micelles of a 1 vol % asymmetric PS(13K)-b-PI(71K) solution, in a series of solvent mixtures of dibuthyl phthalate (DBP), diethyl phthalate (DEP), and dimethyl phthalate (DMP), in order to adjust the degree of solvent selectivity for styrene.22 With an increase in solvent selectivity, the predominant micellar shape changed from spheres to cylinders to vesicles, thus reflecting (14) Ding, J.; Liu, G. Macromolecules 1999, 32, 8413. (15) Yu, Y.; Eisenberg, A. J. Am. Chem. Soc. 1997, 119, 8383. (16) Zhang, L.; Eisenberg, A. Science 1995, 268, 1728. (17) Shen, H.; Eisenberg, A. J. Phys. Chem. B 1999, 103, 9473. (18) Chen, L.; Shen, H.; Eisenberg, A. J. Phys. Chem. B 1999, 103, 9488. (19) Zhang, L.; Eisenberg, A. Macromolecules 1999, 32, 2239. (20) Shen, H.; Eisenberg, A. Macromolecules 2000, 33, 2561. (21) Choucair, A.; Eisenberg, A. Eur. Phys. J. E 2003, 10, 37. (22) Bang, J.; Jain, S.; Li, Z.; Lodge, T. P.; Pedersen, J. S.; Kesselman, E.; Talmon, Y. Macromolecules 2006, 39, 1199.

10.1021/la070104o CCC: $37.00 © 2007 American Chemical Society Published on Web 05/08/2007

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Figure 2. The TEM images of PS(7.2K)-b-PI(7.8K), after crosslinking in a dilute DMP solution, which were prepared by the evaporation of solutions on the carbon-coated copper grid and stained with (a) OsO4 and (b) RuO4.

Figure 1. (a) The SAXS patterns and (b) the p(r)’s of PS(7.2K)b-PI(7.8K) solutions in DMP, before (solid line) and after (dotted line) cross-linking in DMP, where the p(r)’s (part b) were calculated from the SAXS patterns (part a).

a changing interfacial curvature. Detailed micellar morphological shapes were characterized by small-angle X-ray scattering (SAXS), with their vesicular form factors and cryogenic transmission electron microscopy (cryo-TEM). The cryo-TEM technique provided direct images because the solvents used, a series of dialkyl phthalates, were readily vitrified via liquid nitrogen. Another way to fix the PS-b-PI micellar structure in the solution is the direct cross-linking of the PI core block of the micelles.23 The cross-linking reactions of the PI spherical domains of these block copolymers can be carried out with a solution of sulfuric monochloride (S2Cl2) in n-hexane. Liu et al. also prepared PS-b-PI block copolymer nanofibers from cylindrical micelles which formed in a PI-sensitive solvent via the direct cross-linking of the core block.24 In this study, the micelles of PS-b-PI were cross-linked in dialkyl phthalates (PS-selective solvents) with S2Cl2 and then dialyzed in a neutral solvent, THF. Two block copolymers, PS(7.2K)-b-PI(7.8K) and PS(5.5K)-b-PI(18.8K), were studied in order to clarify the effects of the relative chain length of each block on the structure of micelles in the selective solvents. In particular, the TEM images of different types of PS(5.5K)-b(23) Ishizu, K.; Onen, A. J. Polym. Sci., Part A: Polym. Chem. 1989, 27, 3721. (24) Yan, X.; Liu, G.; Li, H. Langmuir 2004, 20, 4677.

PI(18.8K) micelles, such as spheres, cylinders, and vesicles, could be obtained from a simple TEM sample preparation method. This is done by dropping a solution on the carbon-coated copper grid. It is difficult to get TEM images without stabilizing the micelles by cross-linking due to the change (or destruction) of the micelle structures during the evaporation process. CryoTEM is usually necessary to get the image of the micelle structure, although it needs a TEM capable to maintain for the icy state of the sample. In this article, we report on the observed micellar structures of the cross-linked PS-b-PI micelles using TEM and small-angle X-ray scattering (SAXS). Experimental Section Samples. PS-b-PI was purchased from Polymer Source, Inc., (Canada) and was synthesized by an anionic polymerization method. PS(7.2K)-b-PI(7.8K) and PS(5.5K)-b-PI(18.8K) were studied for their representation of symmetric and asymmetric diblock copolymers, respectively; the number in parentheses represents the numberaverage molecular weight for each block in 1000 g/mol. Polydispersity was 1.04 for both PS(7.2K)-b-PI(7.8K) and PS(5.5K)-b-PI(18.8K). Dibuthyl phthalate (DBP), diethyl phthalate (DEP), and dimethyl phthalate (DMP) were used as the selective solvents for PS block and toluene as a neutral solvent. Toluene, DBP, DEP, and DMP were purchased from Aldrich and were used without further purification. DBP/DEP and DEP/DMP mixtures were used to control the selectivity of the solvents for PS(5.5K)-b-PI(18.8K), while DMP/ toluene mixtures were used for PS(7.2K)-b-PI(7.8K) during heating the solutions. PS(7.2K)-b-PI(7.8K) was directly dissolved in the solvent, while PS(5.5K)-b-PI(18.8K) solutions were prepared with the aid of methylene chloride as a cosolvent. The cosolvent was stripped under a stream of nitrogen, at room temperature, until a constant weight was achieved. The concentration of all studied solutions was 20 mg/mL. Cross-Linking of Micelles. S2Cl2 was diluted to 10 vol % in DMP (or DEP) in order to control the exact amount of S2Cl2 when added to the solution. 8 µL of the S2Cl2 solution (0.8 µL S2Cl2) was added to 400 µL of the polymer solution (20 mg/mL concentration)

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Figure 3. The SAXS patterns of a PS(7.2K)-b-PI(7.8K) solution, (a) before and (b) after cross-linking in DMP, with an increase in temperature from 25 to 85 °C at 5 °C intervals; temperature increased downward in part a. via stirring at room temperature for 36 h.23,24 The molar ratios between the isoprene unit and S2Cl2 were 11.46% and 12.98% for PS(7.2K)b-PI(7.8K) and PS(5.5K)-b-PI(18.8K), respectively. The solution was dialyzed in THF for 5 days using dialysis tubing cellulose membrane (Sigma-Aldrich, D9277-100FT, 10 mm × 6 mm) which retains >90% of cytochrome C (MW 12 400) in a solution over a 10 h period. The TEM samples (Hitachi H-7600, 100 kV) were also prepared by dropping solutions onto a 200-mesh carbon-coated copper grid; the solvent was absorbed on filter paper and evaporated at room temperature. Grid samples were stained with RuO4 and OsO4 vapors for 25 min and 3 h 30 min, respectively. Small-Angle X-ray Scattering (SAXS). A SAXS experiment was performed at beamline 4C1 (Pohang Light Source, Korea) whereby a W/B4C double-multilayer monochromator delivered monochromatic X-rays that had a wavelength of 0.16 nm, and an in-house SAXSess system (Anton Parr).25,26 The sample holder for (25) Bolze, J.; Kim, J.; Huang, J.-Y.; Rah, S.; Youn, H. S.; Lee, B.; Shin, T. J.; Ree, M. Macromol. Res. 2002, 10, 2. (26) Yu, C.-J.; Kim, J.; Kim, K.-W.; Kim, G.-H.; Lee, H.-S.; Ree, M.; Kim, K.-J. J. Kor. Vac. Soc. 2005, 14, 138.

Park and Park

Figure 4. The FT-IR spectra of PS(7.2K)-b-PI(7.8K), before (solid line) and after (dotted line) cross-linking; the sample for FT-IR was prepared by dropping a solution on KBr, then drying in a vacuum oven at room temperature. the synchrotron experiment had a mica window and a hole for the injection of the solution. The hole of the sample holder was sealed with epoxy after the solution was injected. This was done in order to prevent the solvent from evaporating during SAXS measurements. 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 SAXS data to be obtained in a q range between 0.06 and 1.11 nm-1. The sdd was calibrated using SEBS (polystyreneblock-poly(ethylene-ran-butylene)-block-polystyrene). The SAXSess system is a laboratory-based small-angle diffractometer that provides a monochromatic X-ray beam with a wavelength of 1.54 Å and a fixed camera length of 26.7 cm.27 The dimensions of the X-ray beam from this system were 20 mm horizontal and 0.25 mm vertical. The samples were exposed in a horizontal alignment with as much of the sample exposed to the beam as possible. X-ray diffraction patterns were collected using an image plate detector of 6.5 cm × 5.5 cm with a 50 µm pixel size. The SAXSess camera tube evacuated during (27) Round, A. R.; Wilkinson, S. J.; Hall, C. J.; Rogers, K. D.; Glatter, O.; Wess, T.; Ellis, I. O. Phys. Med. Biol. 2005, 50, 4159-4168.

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Figure 5. (a) The SAXS patterns and (b) the p(r)’s of a PS(7.2K)b-PI(7.8K) solution in DMP without cross-linking, as functions of temperature and q; temperature increases downward in part b. Table 1. Solubility Parameters (δ) and Molar Volumes (Vs) of PS, PI, DMP, DEP, DBP, and Toluene PS PI DMP DEP DBP toluene

Vs (cm3/mol)a

δ (J1/2/cm3/2)b

163.0 198.8 266.9 105.9

19.07 16.68 22.06 20.55 20.19 18.16

a Polymer Data Handbook; Mark, J. E., Ed.; Oxford University Press: New York, 1999. b Hansen Solubility Parameters, A User’s Hand book; Hansen, C. M.; CRC Press: Boca Raton, 1999.

data collection in order to minimize scattering and attenuation from air. Samples were held in a vacuum dividable cylindrical holder approximately 10 cm in length and 1 cm in diameter. The internal dimensions to accommodate the sample were 2.5 cm in length, 1 mm in height, and 1 mm in depth. The exposure time for all samples was 20 min. Data Analysis. Raw synchrotron 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 2D X-ray scattering patterns from the SAXSess system were reduced to 1D plots using a proprietary SAXSquant software package (Anton Paar). A region of interest (ROI) was applied to each scattered image. The width of the ROI was equal to 1 cm, and the ROI length corresponded to the limits

Figure 6. (a) Rg and (b) I(0) (which were calculated from the p(r)’s in Figure 5), with respect to temperature at different toluene/DMP mixtures: DT1000 (b), DT9010 (3), DT8020 (9), DT7030 (]), and DT6040 (2) [DTXXYY where D and T represent DMP and toluene, respectively, and XX and YY represent the vol % of DMP and toluene, respectively]. of the q-space of interest. The data in the ROI were integrated to produce a one-dimensional data set of intensity versus q ) (4π/λ) sin(θ/2). A semitransparent beam stop was employed to allow measurements of direct beam intensity and to correct for transmission. 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 a dilute solution. SAXS data were analyzed with GIFT software, which was developed by Glatter.28-34 The Fourier transformation of the F(q) yields a pair distance distribution function (p(r)) of a particle, which is a histogram of distances inside a particle weighted with electron density differences. The shape of the p(r) allowed for (28) Bosse´, F.; Schreiber, H. P.; Eisenberg, A. Macromolecules 1993, 26, 6447. (29) Park, S.-Y.; Chang, Y. J.; Farmer, B. L. Langmuir 2006, 22, 11369. (30) Coleman, M. M.; Graf, J. F.; Painter, P. C. Specific interactions and the miscibility of polymer blends; Technomic Publishing: Lancaster, PA, 1991. (31) Mangaraj, D.; Bhatnagar, S. K.; Rath, S. B. Makromol. Chem. 1963, 67, 75. (32) Kuo, S. W.; Lin, C. L.; Chang, F. C. Polymer 2002, 43, 3943. (33) Watzlawek, M.; Likos, C. N.; Lo¨wen, H. Phys. ReV. Lett. 1999, 82, 5289. (34) McConnell, G. A.; Lin, M. Y.; Gast, A. P. Macromolecules 1995, 28, 6754.

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Figure 7. I(0) (a,b) and Rg (c,d) with respect to χ, which was calculated by eq 2 in which B was constant at 0.34 for (a,c) and was adjusted to get a linear curve for (b,d); the B values in part b were 0.34, 0.32, 0.36, 0.40, and 0.49, and those in part c were 0.34, 0.25, 0.34, 0.34, and 0.45 for DT1000 (b), DT9010 (3), DT8020 (9), DT7030 (]), and DT6040 (2), respectively. the determination of basic geometrical shapes (spherical, cylindrical, or planar), even for inhomogeneous particles. This methodology, using an indirect Fourier transformation, has been described elsewhere.28-37 Dmax was determined by an r value of 0 in p(r). The radius of the gyration (Rg) could be calculated by eq 1.

∫r p(r) ) 2 ∫p(r) 2

Rg

(1)

Results and Discussion Figure 1 shows the SAXS patterns and the p(r)’s of PS(7.4K)b-PI(7.1K) solutions in DMP, before and after cross-linking where p(r)’s (Figure 1b) were calculated from the SAXS patterns (Figure 1a). The scattering patterns and p(r)’s were almost identical before and after cross-linking, indicating that the basic micellar structure did not change by cross-linking with S2Cl2. The p(r) was typical of the spherical micelle with a Dmax of 26 nm. The SAXS pattern and p(r) barely changed for other mixture solutions after crosslinking. Figure 2 shows the TEM images of PS(7.2K)-b-PI(7.8K), after cross-linking in a DMP solution, which were prepared by the (35) Hamley, I. W.; Pople, J. A.; Fairclough, J. P. A.; Ryan, A. J.; Booth, C.; Yang, Y.-W. Macromolecules 1998, 31, 3906. (36) Hamley, I. W.; Pople, J. A.; Diat, O. Colloid Polym. Sci. 1998, 276, 446. (37) Ackerson, B. J. J. Rheol. 1990, 34, 553.

evaporation of solutions on the carbon-coated copper grid and stained with OsO4 and RuO4. OsO4 selectively stains PI, and RuO4 stains both PS and PI. Figure 2a shows the sample stained with OsO4, in which the darker core part was PI and the diameter (DOsO4) was 25.2 nm, which is similar to Dmax (26 nm) of SAXS. The micelles were packed in a two-dimensional unit cell with an a dimension of 28.5 nm, which is the closest distance between micelles, and the core and corona parts are included. Figure 2b shows the sample stained with RuO4, in which the whole micelle was stained and the diameter (DRuO4) was 33.8 nm, which was a little larger than DOsO4 due to the corona. DOsO4 and DRuO4 represent the averages of over 30 micelles. The overall micelle size in the solution would be larger than DOsO4 because the corona chains collapsed during drying on the TEM grid. These results strongly suggest that the SAXS results reflected mostly the core part (similar to those of Lodge’s data).22 Figure 3 shows the SAXS patterns of a PS(7.2K)-b-PI(7.8K) solution before (Figure 3a) and after (Figure 3b) cross-linking in DMP with an increase in temperature from 25 to 85 °C. The intensity of the SAXS patterns continuously decreased with an increase in temperature before cross-linking, indicating that the size and aggregation number of the micelles were a function of temperature. The solvent selectivity decreased as temperature increased, because the Flory interaction parameter between the core chains and solvent (χ) decreased as shown in eq 2 (will be discussed later); however, the intensity of the SAXS patterns

Cross-Linked PS-b-PI Diblock Copolymers

Figure 8. (a) SAXS patterns of PS(5.5K)-b-PI(18.8K) solutions (20 mg/mL) as functions of q and DMP/DEP/DBP mixing ratios, where 100, 0, and -100 represent pure DMP, DEP, and DBP, respectively, and 100 to 0 is for the DMP vol % in a DMP/DEP mixture, and the absolute value of 0 to -100 is for the DBP vol % in a DEP/DBP mixture; (b) the slope in the log-log plot between q ) 0.0652 nm-1 to 0.0848 nm-1 in part a.

barely changed with an increase in temperature after cross-linking. This indicates that the structure of the micelle was fixed after cross-linking and became stable during heating of the solution. Figure 4 shows the FT-IR spectra of PS(7.2K)-b-PI(7.8K), before (solid line) and after (dotted line) cross-linking. The peaks at 760, 690, and 1600 cm-1 came from the PS block. These peaks are due to a CH out-of-plane vibration, a ring out-of-plane deformation of the monosubstituted aromatic group, and the aromatic ring stretching vibration, respectively.38 The peaks at 840, 890, and 1665 cm-1 came from the PI block, which are the characteristics of 1,4-trans, 3,4-trans, and 1,4-cis additions of the isoprene unit, respectively.39,40 The intensity of the peaks at 840, 890, and 1665 cm-1 decreased significantly as compared to those at 760, 690, and 1600 cm-1, indicating that cross-linking occurred. (38) Socrates, G. Infrared and Raman Characteristic Group Frequencies Table and Charts, 3rd ed.; John Wiley & Sons Inc.: New York, 2000. (39) Liu, G.; Li, Z.; Yan, X. Polymer 2003, 44, 7721. (40) Miyaki, Y.; Nagamatsu, H.; Iwata, M.; Ohkoshi, K.; Se, K.; Fujimoto, T. Macromolecules 1984, 17, 2231.

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Figure 5 shows the SAXS patterns and p(r)’s of a PS(7.2K)b-PI(7.8K) solution in DMP without cross-linking, as functions of temperature and q. The p(r)’s were typical of spherical micelles for all temperatures, indicating that the spherical shape of the micelles did not change by an increase in temperature. The intensity of SAXS and p(r) decreased as the temperature increased. Similar results were observed for other solvent mixtures. The SAXS data of PS(7.2K)-b-PI(7.8K) solutions in DMP/toluene mixtures and at different temperatures could be analyzed with two parameters such as Rg and I(0), where Rg and I(0) represent the size and the aggregation number of the spherical micelles, respectively. Figure 6a shows Rg (which was calculated from the p(r) in Figure 5 using eq 1), with respect to temperature at different toluene/DMP mixtures; the solvent mixture was coded DTXXYY where D and T represent DMP and toluene, respectively, and XX and YY represent the vol % of DMP and toluene, respectively. The Dmax (26 nm) was approximately 2.71 times higher than the Rg (9.6 nm) at 25 °C. If the micelle was a homogeneous sphere, the ratio between the Dmax and the Rg would be 2.58 (2 × x5/3). The fact that the observed Dmax/Rg (2.71) was larger than that of the theoretical homogeneous sphere (2.58) might be due to a core/shell structure in the micelle. Rg decreased as temperature increased except for the DT1000 (pure DMP) solution, where Rg linearly deceased after a small increase until 60 °C. Rg decreased as the amount of toluene in the DMP/ toluene mixture (φ) increased, due to a decrease in the solvent selectivity. I(0) is known to be in proportion to the aggregation number (Z). Figure 6b shows I(0) (and Z) with respect to temperature, at different φ values. Rg decreased by ∼25% from 9.6 nm (DT1000) to 7.3 nm (DT6040) at 25 °C, although I(0) decreased by ∼95% from 4000 (DT1000) to 200 (DT6040); the volume would decrease by ∼56%. The much larger decrease in I(0) (than Rg) indicated that the micelles contained far fewer block copolymers and became softer as the temperature and φ increased. The selectivity of the solvent and solution temperature can be expressed as one parameter, χ. Figure 7 shows the I(0) and Rg with respect to χ. The χ value was calculated by eq 2.

χ≈B+

Vs (δ - δs)2 RT p

(2)

where B is close to 0.34 and δp and δs are the Hansen solubility parameters for the core polymer (PI) and the mixture solvent, respectively. The δs of the mixture solvent was calculated from the mixing rule in vol %. The solubility parameters and molar volumes of PS, PI, DMP, DEP, DBP, and toluene are listed in Table 1. B represents the entropic effect in χ. B would not be the same for the different solutions which have different mixing ratios and, thus, different selectivity. The differences in B among the solutions would increase as the difference in selectivity increases; the less-selective solvent might give more degrees of freedom in the core chains than the more-selective solvent. Figures 7a,c show the results when B was fixed at 0.34, and Figures 7b,d represent when B was adjusted to get a linear curve. The B values in Figure 7b were 0.34, 0.32, 0.36, 0.40, and 0.49 and those in Figure 7d were 0.34, 0.25, 0.34, 0.34, and 0.45 for DT1000, DT9010, DT8020, DT7030, and DT6040, respectively. This graph is similar to a master curve, which can be adjusted by using a sift factor of B with a reference value of 0.34 at DT1000. I(0) and Rg linearly increased as χ increased until 2.05. An increase in χ means more phase separation between the solvent and the core polymer. Thus, a high aggregation number could be expected as χ increases; however, the aggregation number was saturated

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Figure 9. The TEM images of PS(5.5K)-b-PI(18.8K) in DMP/DEP/DBP solutions, which were cross-linked with S2Cl2 in mixture solvents and dialyzed in THF. The TEM images were prepared by the evaporation of dilute solutions onto a carbon-coated copper grid and the evaporated solutions stained with OsO4; the numbers in each part represent the DMP/DEP/DBP mixing ratios, φ; scale bars from φ ) 90 to -30 are 500 nm and those from φ ) -40 to -90 are 100 nm.

at χ ) 2.05, and a further increase of χ above 2.05 did not affect the aggregation number. If the core is densely filled with chains in that the density of the core reaches a solid state, no further increase of the aggregation number or size of the micelle would be possible by an increase in solvent selectivity. Figure 8a shows the SAXS patterns of PS(5.5K)-b-PI(18.8K) solutions, as functions of q and DMP/DEP/DBP mixing ratios (φ’s), where 100, 0, and -100 represent DMP, DEP, and DBP, respectively, and 100 to 0 represents the DMP vol % in a DMP/ DEP mixture, and the absolute value of 0 to -100 is for the DBP vol % in a DEP/DBP mixture. DMP, DEP, and DBP represent the selective solvents for PS, and the selectivity of the solvents increases in the order of DMP, DEP, and DBP. Thus, the selectivity of the mixture solvents increases when φ increases from -100 to 100. PS(5.5K)-b-PI(18.8K) would be a crew-cut micelle in the mixture solvent, because a short PS block is soluble in the solvent mixture. The SAXS patterns of PS(5.5K)-b-PI(18.8K) showed a deeper decrease in intensity as q increased in the initial q range, as compared to that of PS(7.2K)-b-PI(7.8K) (see Figure 1). Figure 8b shows the slope in a log-log plot between q ) 0.0652 nm-1 and q ) 0.0848 nm-1. The slope was calculated by a linear curve-fitting method using Origin software. The slope at the small angle region for a sphere is close to zero because it approaches the Guinier region, although those for the cylinder and plate are close to 1 and 2, respectively. The slope continuously increased until φ ) -30 and was saturated above 1.4. This 1.4 value indicated that the micelles would be twodimensional, because a slope of 2 for a plate is for the theoretical one at an extremely small angle region. Other reasons for the slope being smaller than 2 could be a curved, two-dimensional sheet-like vesicle and/or the size distribution of micelle size. The

continuous decrease in slopes below φ ) -30 indicates that the micellar shape would change from two-dimensional shapes to a less-dimensional ones such as that of a cylinder or a sphere (or a mixture). Additional experiments were conducted with the TEM images of cross-linked micelles. Figure 9 shows the TEM images of PS(5.5K)-b-PI(18.8K) in DMP/DEP/DBP solutions, which were crosslinked with S2Cl2 in mixture solvents and dialyzed in THF. We were successful in acquiring the images of the micelle structures in a solution after cross-linking, but it was difficult to get TEM images due to changes (or destruction) of the micelle structures during the evaporation process without cross-linking. Cross-linking enabled us to get TEM images of micelles by fixing the micelle structure in the solution. Cryo-TEM is usually necessary to get the micelle structure of PS-b-PI; however, it needs TEM capability for the icy state of the sample. PS(5.5K)-b-PI(18.8K) was not soluble at φ ) 100 due to the short PS chain. The solution at φ ) 90 shows big vesicular micelles (diameter ∼2.5 µm). These giant vesicular micelles were due to the high selectivity of the solvent. The size of the vesicular micelles became smaller as the selectivity of the solvent decreased, although size distribution was present. A small fluctuation in solvent selectivity might influence the curvature of vesicle, and a small curvature change led to the large size distribution, especially for the giant vesicular micelle. The solutions at φ ) -40 and -50 showed a combination of cylindrical and vesicular micelles. The solutions at φ ) -60 and -70 showed a combination of spherical and cylindrical micelles. The solutions at φ ) -80 and -90 showed only spherical micelles. The solution at φ ) -100 became the nonselective solvent. We could confirm the transitions from two-dimensional vesicular to cylindrical to spherical micelles by a decrease in the core

Cross-Linked PS-b-PI Diblock Copolymers

solvent selectivity in the case of PS(5.5K)-b-PI(18.8K). The universality of the shape sequence (sphere/cylinder/vesicle), which was well-established for aqueous solutions of surfactants and block copolymers, could be confirmed from the TEM images of the cross-linked micelles.

Conclusions The PI core chains of the spherical, cylindrical, and vesicular PS-b-PI micelles, in PS selective solvents such as DMP/toluene, DMP/DEP, and DEP/DBP mixtures, could be cross-linked with S2Cl2. The dialyzed micelles were stable in THF (neutral solvent), and the shape of the micelles did not change during heating. The micellar structures were studied using SAXS and TEM. PS(7.2K)-b-PI(7.8K) showed spherical micelles in DMP/toluene mixtures, while the size and aggregation number of the micelles increased as χ increased until 2.05 and then was saturated after that. PS(5.5K)-b-PI(18.8K) showed a structural changes in the micelles from spherical to cylindrical to vesicular ones with an

Langmuir, Vol. 23, No. 12, 2007 6795

increase in the selectivity of the solvent mixtures of DMP/DEP and DMP/DBP. Giant vesicular micelles (diameter ∼2.5 µm) were observed at high selectivity solvents, and their size seemed to decrease as selectivity decreased. We were able to demonstrate the systematic changes of the micellar structures of PS(5.5K)b-PI(18.8K) from TEM images by changing the solvent selectivity, which was obtained from samples prepared by evaporation of the solvent of cross-linked micellar solutions after dialysis. Acknowledgment. This work was supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD, Basic Research Promotion Fund) (KRF-2006-311D00426). Synchrotron work was supported in part by the Ministry of Science & Technology (MOST), by POSCO, by the Center for Integrated Molecular System (Korea Science & Engineering Foundation), and by the KISTEP (Basic Research Grant of Nuclear Energy, MOST). LA070104O