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Superlattice Formation on Star Polymer Solutions
JOURNAL OF COLLOID AND INTERFACE SCIENCE ARTICLE NO.
192, 189–193 (1997)
CS974986
Superlattice Formation on Star Polymer Solutions Koji Ishizu, 1 Tomohiro Ono, and Satoshi Uchida Department of Polymer Science, Tokyo Institute of Technology 2-12, Ookayama, Meguro-ku, Tokyo 152, Japan Received February 24, 1997; accepted May 9, 1997
Polyisoprene (PI) stars (arm number f Å 4 Ç 237) were prepared by coupling of PI monoanions with tetrachlorosilane or by cross-linking PI anions with divinylbenzene. The structural ordering of such stars was investigated through small-angle X-ray scattering. PI stars ( f ú ca. 90) formed a body-centered cubic (bcc) structure near the overlap threshold. This structure changed to a mixed lattice of bcc and face-centered cubic structures with increasing polymer concentration. q 1997 Academic Press Key Words: star polymer; SAXS; superlattice.
INTRODUCTION
The star-branched, or radial, polymers have the structure of linked-together linear polymers with a small molecular weight core. Generally, the star polymer has a smaller hydrodynamic dimension than that of a linear polymer with an identical molecular weight. The interest in star polymers arises not only from the fact that they are model branched polymers but also from their enhanced segment densities. Zimm and Stockmayer were the first to study the conformation of star-shaped polymers (1). Recently, Daoud and Cotton (2) have studied the conformation and dimension of star polymer consisting of three regions, a central core, a shell with semidilute density in which the arms have unperturbed chain conformation, and an outer shell in which the arms of the star assume a self-avoiding conformation. Stars with multiarms (the critical number of arms is estimated to be of order 10 2 ) are expected to form a crystalline array near the overlap threshold (C*) (3). Willner et al. (4, 5) investigated the ordering phenomena of stars around the C* by means of small-angle neutron scattering (SANS). They showed that ordering was very weak for 8- and 18-arm polymers but became stronger with increasing arm numbers. On the other hand, de la Cruz and Sanchez (6) have calculated the phase stability criteria and static structure factors in the weak segregation regime for n-arm diblock copolymers [(AB)n star]. According to their results, as the arm number (n) becomes large, the (AB)n star begins to develop a ‘‘core and shell’’ type structure. This self-segregation or 1
To whom correspondence should be addressed.
self-micellization tends to create significant concentration fluctuations at the core–shell interface. We have prepared the (AB)n stars by free radical microgelation in micelles formed by poly[styrene(S)-b-isoprene(I)] diblock macromonomers (7, 8) or cross-linking poly(S-b-I) diblock monoanions with divinylbenzene (DVB) (9). Subsequently, we have studied the self-micellization of (AB)n stars as a parameter of n. As a result, the microphase-separated structures of these star copolymers [n Å 14 Ç 30; polyisoprene (PI) blocks, 16 Ç 19 wt%] were formed with the dimension of a unimolecular micelle even in the strong segregation regime. It was found also from the small-angle X-ray scattering (SAXS) measurements that these stars formed the lattice with a face-centered cubic (fcc) structure in the bulk film (9) and were packed in the lattice with a body-centered cubic (bcc) structure near the C* (10). Moreover, we have investigated the structural ordering of core–shell polymer microspheres through SAXS and transmission electron microscopy (TEM) (11, 12). These microspheres formed the lattice with a BCC structure near the C*. While in the bulk of the film, this structure changed to a fcc lattice. Thus, the transformation of the lattices from a C* threshold into a continuous film for (AB)n stars is very similar to that for the core–shell polymer microspheres. Star polymers with multiarms can be also expected to form such structural ordering in solution. Star polymers are best prepared by coupling of anionic living polymers with multifunctional electrophilic coupling agents. The coupling agents are either multifunctional chloromethylated benzene derivatives or multifunctional chlorosilane compounds. In general, it is difficult to extend the functionality of the stars with these compounds. At present, the most convenient way of preparing star polymers possessing more than 10 arms is by cross-linking monocarbanionic chains with DVB (13–16). More recently, we synthesized PI stars by the free-radical cross-linking of the vinylbenzyl-terminated PI macromonomers with DVB in n-heptane that dissolved PI but precipitated DVB (17). The radical copolymerization of PI macromonomer with DVB led to microgelation in micelles formed by the primary copolymer radicals in the selective solvent (organized polymerization). This idea could be applied to
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TABLE 1 Characteristics of PI Stars Molecular weight
Code
Arma 1004 MV n
Starb 1006 MV w
Arm No. (No./molecule)
RGc (nm)
RHd (nm)
R0e (nm)
C* f (wt%)
(SI33)4 (SI42)43 (SI27)91 (SI42)111 (SI08)237
3.3 4.2 2.7 4.2 0.8
0.12 1.87 2.79 5.00 2.09
4 43 91 111 237
16.0 30.1 29.2 41.3 19.1
10.7 24.7 22.2 33.0 18.1
— 2.7 4.4 4.7 3.9
3.9 4.9 10.1 5.5 14.1
a Determined by gel permeation chromatography (GPC: Tosoh high-speed liquid chromatograph HLC-8020) using PI standard samples with tetrahydrofuran as the eluent at 387C, using a TSK gel GMHXL column and a flow rate of 1.0 ml min01. b Determined by static light scattering (SLS; Photal TMLS-600HL) in cyclohexane with a He–Ne laser (l0 Å 632.8 nm) in the Berry mode. c Radius of gyration (RG) was determined by SLS. d Hydrodynamic radius (RH) was determined by dynamic light scattering (DLS; scattering angle Å 907) in 0.1 wt% cyclohexane (h Å 0.898 cp, nD Å 1.4262) at 237C. e Core radius (R0) was calculated from equation: n Å (4p/3PE)R30rNA, assuming that the core was spherical form. r, density of DVB core (1.01 1 104 mol m03) (19); NA , Avogardo number; PE , the number of monomer units (mixture of DVB and ethylstyrene) at the arm PI terminal end. f Overlap threshold (C*) was calculated from equation C* Å 3MV W/(4pNAR3H).
the PI star synthesis by anionic cross-linking of PI monoanions with DVB in n-heptane (18). In this article, PI stars (arm number n Å 4 Ç 237) were prepared by coupling of PI monoanions with tetrachlorosilane or by cross-linking PI anions with DVB in the selective solvent such as n-heptane. The structural ordering of such stars in cyclohexane was investigated through the SAXS measurements, varying the polymer concentration and arm numbers.
SAXS Measurements The SAXS intensity distribution was measured with a rotating-anode X-ray generator (Rigaku Denshi Rotaflex RTP 300RC) operated at 40 kV and 100 mA. The X-ray ˚) source was monochromatized to CuKa ( l Å 1.5418 A radiation. In the measurement of the solution sample, a glass capillary ( f Å 2.0 mm, Mark-Ro¨hrchen Ltd.) was used as a holder vessel. RESULTS AND DISCUSSION
MATERIALS AND METHODS
Synthesis and Characterization of Star Polymers PI anions were prepared by living anionic polymerization techniques using the break-seal method. Details concerning the synthesis and purification of such PI anions have been given elsewhere (17, 18). In brief, PI anions were prepared by usual anionic addition using n-butyllithium (n-BuLi) as an initiator in benzene or n-heptane in a sealed glass apparatus under a pressure of 10 06 mm Hg. PI star (n Å 4) was prepared by coupling of PI anions with tetrachlorosilane in benzene. On the other hand, PI stars with multiarms were prepared by cross-linking PI anions with a small amount of DVB (Tokyo Kasei; 65%, m-/pisomer Å 2; 35% ethylstyrene) in n-heptane. Both polymerizations were stopped by introducing the viscous solution into an excess of methanol. The star polymer was fractionated in a benzene–methanol mixture. Details concerning the fractionation procedure and the characterization of PI stars have been given previously (18). Table 1 lists the characteristics of PI stars.
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In anionic polymerization the reactivity of the double bond in DVB is 10 times greater than that of the pendant double bond (20). So, essentially the PI chains possessing terminal vinylbenzyl groups (primary copolymer anion) must be formed in the initiation reaction stage of PI monoanions with DVB. We have prepared PI stars with various arm numbers, varying the concentration ratio of DVB to PI anions ([DVB]/[M]) and the initial concentration of PI anions. For example, the (SI42)43 sample in Table 1, which shows the star structure having arm molecular weight of 4.2 1 10 4 and arm number n Å 43. Gel permeation chromatography (GPC) distributions for all polymerization products were bimodal [RI and UV at 292 nm (characteristic absorption of vinylbenzyl groups) double detectors]. The polymerization product was the mixture of PI star and its precursor. Unreacted PI precursor had no absorption at 292 nm. This fact indicated that all of the feed DVB were consumed in the core formation of star polymers. Moreover, the macrogelation had never been observed during polymerization for all experiments. The arm number could be controlled by varying the initial
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concentration of PI anions or the feed amount of [DVB]/ [M]. PI stars were formed by anionic cross-linking of PI anions with DVB in n-heptane that dissolved PI but precipitated DVB. The anionic copolymerization of PI anions with DVB led to microgelation in micelles formed by the primary copolymer anions in the selective solvent. So, all of the PI stars prepared had apparently narrow molecular weight distribution (MV w /MV n Å 1.03–1.07) from GPC profiles. As explained earlier, all of the feed DVB was consumed in the core formation of star polymers. It was possible to estimate the core radius (R0 ) of PI stars as shown in Table 1, because the yield of the star and the feed amounts of DVB were known. The values of R0 were very small compared to the corresponding the radii of gyration (RG ) for PI stars. For dendrimers used as coupling agents, R0 was estimated to be 2.4–2.5 nm for the generation m Å 3–4 (21). Therefore, the core size of our PI stars seemed to correspond to the size of dendrimer with m somewhat larger than m Å 4. The hydrodynamic radius (RH ) was measured by dynamic light scattering (DLS) at 907 of scattering angles. The values of RH are also listed in Table 1. The value of RG /RH is a sensitive fingerprint of the inner density profile of star and polymer micelle. The observed values of RG /RH approached unity as n became large. Even the stars with multiarm behaved not as neat hard spheres ( RG /RH Å 0.775) but as soft spheres that were penetratable near the outer edge in a good solvent. We studied structural ordering of PI stars in cyclohexane. According to the theoretical results of Witten et al. (3), a crystalline structure of the stars should appear near the C*. The calculated C* for each PI star is also listed in Table 1. Below C*, the star polymers remain isolated, as any arrangement of stars in solution is expected near or above C*. We measured first the SAXS intensity profiles of the (SI42)43 star at 6 and 13 wt% of cyclohexane polymer solutions. Both polymer concentrations were higher than the C* (4.9 wt%). However, no regular scattering peaks appeared at these concentrations due to disordering. As a matter of course, the structural ordering had never been observed in the (SI33)4 star. Figure 1 shows typical SAXS intensity profiles for the (SI08)237 star in the small-angle region, where q [ Å (4p / l )sin u] is the magnitude of the scattering vector. The values shown in Fig. 1 indicate the q. The arrows show the scattering maxima and the values in parentheses indicate the interplaner spacings (dl /dn ) calculated from Bragg reflections. Below 8 wt% of polymer concentration (C* Å 14.1 wt%), no regular scattering peaks appeared due to disordering. At 11 wt% of polymer concentration (Fig. 1a), the first four peaks appear closely at the relative q positions of q q 1: 2: 3:2 as shown in parentheses. The interplaner spacing (dl /di ) at the scattering angles is relative to the angle of the first maximum according to Bragg’s equation: 2d sin u Å
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FIG. 1. The SAXS intensity profiles for cyclohexane solutions of (SI08)237 star: (a) 11 wt%; (b) 33 wt%; (c) 67 wt%; (d) bulk film.
n l (where u is one-half the scattering angle, l Å 1.5418 ˚ ). In general, this packing pattern appears in the lattice of A not only simple cubic but also bcc structures. As mentioned in the introduction, the (AB)n stars with multiarm were packed in the lattice of a bcc structure near C* (10). The conformation of stars can be regarded as similar to one of (AB)n stars in solution. It is reasonable that these values correspond to the packing pattern of (110), (200), (211), and (220) planes in a bcc structure. This result was well in agreement with the theoretical one predicted by Witten et al. (3). In the SAXS intensity profile at 33 wt% of polymer con-
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centration, the complicated scattering peaks appear as shown in Fig. 1b.qThe first appear at the relative q posiq qfive peaks q tions of 1: q4/3: q2: 8/3: 3. In general, the relative q positions of 1: 4/3: 8/3 correspond to a packing pattern of (111), (200), and (220) planes in a fcc structure. Therefore, it is concluded that the stars are packed in the mixed lattice of bcc and fcc structures at this polymer concentration. Similar mixed lattice patterns are also observed in the SAXS profile at 67 wt% of polymer concentration (Fig. 1c). It is noticed that the first peak shifts to the side of high q position in the order of the increment of polymer concentrations. This fact means that the Bragg spacing dl became shorter with increasing the polymer concentration. It is also noticed q that the scattering intensity at the relative q position of 4/3 based on a fcc lattice increases with increasing the polymer concentration. This means that the fcc lattice fraction in the mixed lattices increases during the concentration of polymer solutions. Figure 1d shows the SAXS intensity profile for the (SI08)237 star film. In this measurement, the scattering peaks seem to originate from the DVB core of PI star. It is found that q the qfirst q four peaks appear at the relative q positions of 1: 4/3: 2: 8/3: as shown in parentheses. The star is packed in the mixed lattice of a bcc and fcc structure even in the bulk. However, the film specimen of PI star did not take the state of thermal equilibrium, because the measurement temperature was 257C. Precise lattice structure of the stars in the bulk could not be determined from the measurement method in this work. The results of SAXS data obtained for (SI27)91 and (SI42)111 stars were almost the same as those for the (SI08)237 star. That is to say, the polymer solution below C* showed disordering. The structural ordering such as a bcc lattice appeared near C* and this structure changed to the mixed lattice of bcc and fcc with increasing polymer concentration.
TABLE 3 Physical Values on Spatial Packing of Cubic Lattices for (SI08)237 Star in Cyclohexane Solution Polymer concentration (wt %)
q1a (nm01)
d1b (nm)
D0c (nm)
4 11 14 19 25 33 38 56 67 100
— 0.281 0.341 0.370 0.398 0.469 0.491 0.533 0.533 0.583
— 22.37 18.40 16.99 15.78 15.39 12.80 11.78 11.78 10.77
— 27.40 22.54 20.80 19.32 16.40 15.68 14.42 14.42 13.20
a
Calculated by q Å 4p sin u/l. Calculated by d1 Å 2pq/q1 . c Determined by D0 Å ( 3/2)d1 . b
We consider spacial packing of the cubic lattice in solution. The measured Bragg spacing dl is related to the cell edge ac of the cubic lattice and the nearest-neighbor distance of the spheres D0 : q
q
D0 Å ( 3/2)ac Å ( 3/2)dl q
for bcc
[1]
for fcc.
[2]
q
D0 Å (1/ 2)ac Å ( 3/2)dl
Tables 2 and 3 list the physical values on spatial packing of the cubic lattices for (SI27)91 and (SI08)237 stars, respectively. It is found that D0 for (SI27)91 stars (MV w Å 2.79 1 10 6 ) shows higher values than that for (SI08)237 stars (MV w Å 2.09 1 10 6 ) at the same polymer concentration, due to high total molecular weight. Figure 2 shows the relationship
TABLE 2 Physical Values on Spatial Packing of Cubic Lattices for (SI27)91 Star in Cyclohexane Solution Polymer concentration (wt%)
q1a (nm01)
d1b (nm)
D0c (nm)
4 8 12 16 44 50 60 100
— 0.249 0.281 0.284 0.370 0.405 0.413 0.420
— 25.24 22.37 22.09 16.99 15.50 15.23 14.97
— 30.92 27.40 27.04 20.80 18.92 18.66 18.34
a
Calculated by q Å 4p sin u/l. Calculated by d1 Å 2pq/q1 . c Determined by D0 Å ( 3/2)d1 . b
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FIG. 2. Relationship between d1 or D0 and polymer concentration for (SI08)237 star.
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to hierarchical structure transformation of the cubic lattices observed on the core–shell microspheres and the (AB)n stars. Such ordering depends strongly on the polymer concentration and the arm number. ACKNOWLEDGMENT This work was supported in part by a Grant-in-Aid for Scientific Research (Priority Areas of ‘‘New Polymers and Their Nano-Organized Systems’’ (No. 277/08246218) from Ministry of Education, Science, Sports, and Cultures, Japan.
REFERENCES
FIG. 3. Double-logarithmic plot of D0 as a function of polymer concentration for (SI08)237 star.
between d1 or D0 and polymer concentration for the (SI08)237 star. PI star takes the disordered state below ca. C* (14.1 wt%). Near the C*, the star forms the lattice with a bcc structure. Beyond ca. 19 wt% of polymer concentration, this structure changes into a mixed lattice of bcc and fcc and leads to shrinkage of the spherical particles. A fcc lattice is the most efficient way of packing spheres. It is also found that both values of d1 and D0 decrease continuously with an exponential function increasing the polymer concentration. Then, we carried out the double-logarithmic plot of D0 as a function of polymer concentration (Fig. 3). It is found that the measured D0 is proportional to the 00.32th power of the polymer concentration and fits well with the 013 power expected for a homogeneous system. This fact means that the spherical particles of (SI08)237 stars lead to isotropic shrinkage increasing the polymer concentration around high polymer concentration. The structural ordering of star polymers is very similar
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1. Zimm, B. H., and Stockmayer, W. H., J. Chem. Phys. 17, 1301 (1949). 2. Daoud, M., and Cotton, J. P., J. Phys. (Les Ulis, Fr.) 43, 531 (1982). 3. Witten, T. A., Pincus, P. A., and Cates, M. E., Europhys. Lett. 2, 137 (1986). 4. Willner, L., Jucknischeke, O., Richter, D., Farago, B., Fetters, L. J., and Huang, J. S., Europhys. Lett. 19, 297 (1992). 5. Willner, L., Jucknischeke, O., Richter, D., Roovers, J., Zhou, L.-L., Toporowski, P. M., Fetters, L. J., Huang, J. S., Lin, M. Y., and Hadjichristidis, N., Macromolecules 27, 3821 (1994). 6. de la Cruz, M. O., and Sanchez, I. C., Macromolecules 19, 2501 (1986). 7. Ishizu, K., Yukimasa, S., and Saito, R., J. Polym. Sci. Polym. Chem. Ed. 31, 3073 (1993). 8. Ishizu, K., and Yukimasa, S., Polym. Commun. 34, 3753 (1993). 9. Ishizu, K., and Uchida, S., Polymer 35, 4712 (1994). 10. Ishizu, K., and Uchida, S., J. Colloid Interface Sci. 175, 293 (1995). 11. Saito, R., Kotsubo, H., and Ishizu, K., Polymer 35, 1580 (1994). 12. Ishizu, K., Sugita, M., Kotsubo, H., and Saito, R., J. Colloid Interface Sci. 169, 456 (1995). 13. Bi, L. K., and Fetters, L. J., Macromolecules 8, 90 (1975). 14. Bi, L. K., and Fetters, L. J., Macromolecules 9, 732 (1976). 15. Alward, D. B., Kinning, D. J., Thomas, E. L., and Fetters, L. J., Macromolecules 19, 215 (1986). 16. Young, R. N., and Fetters, L. J., Macromolecules 8, 899 (1978). 17. Ishizu, K., and Sunahara, K., Polymer 36, 4155 (1995). 18. Ishizu, K., Ono, T., and Uchida, S., Macromol. Chem., in press. 19. Hashimoto, T., Nakamura, N., Shibayama, M., Izumi, A., and Kawai, H., J. Macromol. Sci. Phys. B17, 389 (1980). 20. Worsfold, D. J., Macromolecules 3, 514 (1970). 21. Lascanec, R. L., and Muthukumar, M., Macromolecules 23, 2280 (1990).
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CS974986
Superlattice Formation on Star Polymer Solutions Koji Ishizu, 1 Tomohiro Ono, and Satoshi Uchida Department of Polymer Science, Tokyo Institute of Technology 2-12, Ookayama, Meguro-ku, Tokyo 152, Japan Received February 24, 1997; accepted May 9, 1997
Polyisoprene (PI) stars (arm number f Å 4 Ç 237) were prepared by coupling of PI monoanions with tetrachlorosilane or by cross-linking PI anions with divinylbenzene. The structural ordering of such stars was investigated through small-angle X-ray scattering. PI stars ( f ú ca. 90) formed a body-centered cubic (bcc) structure near the overlap threshold. This structure changed to a mixed lattice of bcc and face-centered cubic structures with increasing polymer concentration. q 1997 Academic Press Key Words: star polymer; SAXS; superlattice.
INTRODUCTION
The star-branched, or radial, polymers have the structure of linked-together linear polymers with a small molecular weight core. Generally, the star polymer has a smaller hydrodynamic dimension than that of a linear polymer with an identical molecular weight. The interest in star polymers arises not only from the fact that they are model branched polymers but also from their enhanced segment densities. Zimm and Stockmayer were the first to study the conformation of star-shaped polymers (1). Recently, Daoud and Cotton (2) have studied the conformation and dimension of star polymer consisting of three regions, a central core, a shell with semidilute density in which the arms have unperturbed chain conformation, and an outer shell in which the arms of the star assume a self-avoiding conformation. Stars with multiarms (the critical number of arms is estimated to be of order 10 2 ) are expected to form a crystalline array near the overlap threshold (C*) (3). Willner et al. (4, 5) investigated the ordering phenomena of stars around the C* by means of small-angle neutron scattering (SANS). They showed that ordering was very weak for 8- and 18-arm polymers but became stronger with increasing arm numbers. On the other hand, de la Cruz and Sanchez (6) have calculated the phase stability criteria and static structure factors in the weak segregation regime for n-arm diblock copolymers [(AB)n star]. According to their results, as the arm number (n) becomes large, the (AB)n star begins to develop a ‘‘core and shell’’ type structure. This self-segregation or 1
To whom correspondence should be addressed.
self-micellization tends to create significant concentration fluctuations at the core–shell interface. We have prepared the (AB)n stars by free radical microgelation in micelles formed by poly[styrene(S)-b-isoprene(I)] diblock macromonomers (7, 8) or cross-linking poly(S-b-I) diblock monoanions with divinylbenzene (DVB) (9). Subsequently, we have studied the self-micellization of (AB)n stars as a parameter of n. As a result, the microphase-separated structures of these star copolymers [n Å 14 Ç 30; polyisoprene (PI) blocks, 16 Ç 19 wt%] were formed with the dimension of a unimolecular micelle even in the strong segregation regime. It was found also from the small-angle X-ray scattering (SAXS) measurements that these stars formed the lattice with a face-centered cubic (fcc) structure in the bulk film (9) and were packed in the lattice with a body-centered cubic (bcc) structure near the C* (10). Moreover, we have investigated the structural ordering of core–shell polymer microspheres through SAXS and transmission electron microscopy (TEM) (11, 12). These microspheres formed the lattice with a BCC structure near the C*. While in the bulk of the film, this structure changed to a fcc lattice. Thus, the transformation of the lattices from a C* threshold into a continuous film for (AB)n stars is very similar to that for the core–shell polymer microspheres. Star polymers with multiarms can be also expected to form such structural ordering in solution. Star polymers are best prepared by coupling of anionic living polymers with multifunctional electrophilic coupling agents. The coupling agents are either multifunctional chloromethylated benzene derivatives or multifunctional chlorosilane compounds. In general, it is difficult to extend the functionality of the stars with these compounds. At present, the most convenient way of preparing star polymers possessing more than 10 arms is by cross-linking monocarbanionic chains with DVB (13–16). More recently, we synthesized PI stars by the free-radical cross-linking of the vinylbenzyl-terminated PI macromonomers with DVB in n-heptane that dissolved PI but precipitated DVB (17). The radical copolymerization of PI macromonomer with DVB led to microgelation in micelles formed by the primary copolymer radicals in the selective solvent (organized polymerization). This idea could be applied to
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TABLE 1 Characteristics of PI Stars Molecular weight
Code
Arma 1004 MV n
Starb 1006 MV w
Arm No. (No./molecule)
RGc (nm)
RHd (nm)
R0e (nm)
C* f (wt%)
(SI33)4 (SI42)43 (SI27)91 (SI42)111 (SI08)237
3.3 4.2 2.7 4.2 0.8
0.12 1.87 2.79 5.00 2.09
4 43 91 111 237
16.0 30.1 29.2 41.3 19.1
10.7 24.7 22.2 33.0 18.1
— 2.7 4.4 4.7 3.9
3.9 4.9 10.1 5.5 14.1
a Determined by gel permeation chromatography (GPC: Tosoh high-speed liquid chromatograph HLC-8020) using PI standard samples with tetrahydrofuran as the eluent at 387C, using a TSK gel GMHXL column and a flow rate of 1.0 ml min01. b Determined by static light scattering (SLS; Photal TMLS-600HL) in cyclohexane with a He–Ne laser (l0 Å 632.8 nm) in the Berry mode. c Radius of gyration (RG) was determined by SLS. d Hydrodynamic radius (RH) was determined by dynamic light scattering (DLS; scattering angle Å 907) in 0.1 wt% cyclohexane (h Å 0.898 cp, nD Å 1.4262) at 237C. e Core radius (R0) was calculated from equation: n Å (4p/3PE)R30rNA, assuming that the core was spherical form. r, density of DVB core (1.01 1 104 mol m03) (19); NA , Avogardo number; PE , the number of monomer units (mixture of DVB and ethylstyrene) at the arm PI terminal end. f Overlap threshold (C*) was calculated from equation C* Å 3MV W/(4pNAR3H).
the PI star synthesis by anionic cross-linking of PI monoanions with DVB in n-heptane (18). In this article, PI stars (arm number n Å 4 Ç 237) were prepared by coupling of PI monoanions with tetrachlorosilane or by cross-linking PI anions with DVB in the selective solvent such as n-heptane. The structural ordering of such stars in cyclohexane was investigated through the SAXS measurements, varying the polymer concentration and arm numbers.
SAXS Measurements The SAXS intensity distribution was measured with a rotating-anode X-ray generator (Rigaku Denshi Rotaflex RTP 300RC) operated at 40 kV and 100 mA. The X-ray ˚) source was monochromatized to CuKa ( l Å 1.5418 A radiation. In the measurement of the solution sample, a glass capillary ( f Å 2.0 mm, Mark-Ro¨hrchen Ltd.) was used as a holder vessel. RESULTS AND DISCUSSION
MATERIALS AND METHODS
Synthesis and Characterization of Star Polymers PI anions were prepared by living anionic polymerization techniques using the break-seal method. Details concerning the synthesis and purification of such PI anions have been given elsewhere (17, 18). In brief, PI anions were prepared by usual anionic addition using n-butyllithium (n-BuLi) as an initiator in benzene or n-heptane in a sealed glass apparatus under a pressure of 10 06 mm Hg. PI star (n Å 4) was prepared by coupling of PI anions with tetrachlorosilane in benzene. On the other hand, PI stars with multiarms were prepared by cross-linking PI anions with a small amount of DVB (Tokyo Kasei; 65%, m-/pisomer Å 2; 35% ethylstyrene) in n-heptane. Both polymerizations were stopped by introducing the viscous solution into an excess of methanol. The star polymer was fractionated in a benzene–methanol mixture. Details concerning the fractionation procedure and the characterization of PI stars have been given previously (18). Table 1 lists the characteristics of PI stars.
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In anionic polymerization the reactivity of the double bond in DVB is 10 times greater than that of the pendant double bond (20). So, essentially the PI chains possessing terminal vinylbenzyl groups (primary copolymer anion) must be formed in the initiation reaction stage of PI monoanions with DVB. We have prepared PI stars with various arm numbers, varying the concentration ratio of DVB to PI anions ([DVB]/[M]) and the initial concentration of PI anions. For example, the (SI42)43 sample in Table 1, which shows the star structure having arm molecular weight of 4.2 1 10 4 and arm number n Å 43. Gel permeation chromatography (GPC) distributions for all polymerization products were bimodal [RI and UV at 292 nm (characteristic absorption of vinylbenzyl groups) double detectors]. The polymerization product was the mixture of PI star and its precursor. Unreacted PI precursor had no absorption at 292 nm. This fact indicated that all of the feed DVB were consumed in the core formation of star polymers. Moreover, the macrogelation had never been observed during polymerization for all experiments. The arm number could be controlled by varying the initial
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concentration of PI anions or the feed amount of [DVB]/ [M]. PI stars were formed by anionic cross-linking of PI anions with DVB in n-heptane that dissolved PI but precipitated DVB. The anionic copolymerization of PI anions with DVB led to microgelation in micelles formed by the primary copolymer anions in the selective solvent. So, all of the PI stars prepared had apparently narrow molecular weight distribution (MV w /MV n Å 1.03–1.07) from GPC profiles. As explained earlier, all of the feed DVB was consumed in the core formation of star polymers. It was possible to estimate the core radius (R0 ) of PI stars as shown in Table 1, because the yield of the star and the feed amounts of DVB were known. The values of R0 were very small compared to the corresponding the radii of gyration (RG ) for PI stars. For dendrimers used as coupling agents, R0 was estimated to be 2.4–2.5 nm for the generation m Å 3–4 (21). Therefore, the core size of our PI stars seemed to correspond to the size of dendrimer with m somewhat larger than m Å 4. The hydrodynamic radius (RH ) was measured by dynamic light scattering (DLS) at 907 of scattering angles. The values of RH are also listed in Table 1. The value of RG /RH is a sensitive fingerprint of the inner density profile of star and polymer micelle. The observed values of RG /RH approached unity as n became large. Even the stars with multiarm behaved not as neat hard spheres ( RG /RH Å 0.775) but as soft spheres that were penetratable near the outer edge in a good solvent. We studied structural ordering of PI stars in cyclohexane. According to the theoretical results of Witten et al. (3), a crystalline structure of the stars should appear near the C*. The calculated C* for each PI star is also listed in Table 1. Below C*, the star polymers remain isolated, as any arrangement of stars in solution is expected near or above C*. We measured first the SAXS intensity profiles of the (SI42)43 star at 6 and 13 wt% of cyclohexane polymer solutions. Both polymer concentrations were higher than the C* (4.9 wt%). However, no regular scattering peaks appeared at these concentrations due to disordering. As a matter of course, the structural ordering had never been observed in the (SI33)4 star. Figure 1 shows typical SAXS intensity profiles for the (SI08)237 star in the small-angle region, where q [ Å (4p / l )sin u] is the magnitude of the scattering vector. The values shown in Fig. 1 indicate the q. The arrows show the scattering maxima and the values in parentheses indicate the interplaner spacings (dl /dn ) calculated from Bragg reflections. Below 8 wt% of polymer concentration (C* Å 14.1 wt%), no regular scattering peaks appeared due to disordering. At 11 wt% of polymer concentration (Fig. 1a), the first four peaks appear closely at the relative q positions of q q 1: 2: 3:2 as shown in parentheses. The interplaner spacing (dl /di ) at the scattering angles is relative to the angle of the first maximum according to Bragg’s equation: 2d sin u Å
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FIG. 1. The SAXS intensity profiles for cyclohexane solutions of (SI08)237 star: (a) 11 wt%; (b) 33 wt%; (c) 67 wt%; (d) bulk film.
n l (where u is one-half the scattering angle, l Å 1.5418 ˚ ). In general, this packing pattern appears in the lattice of A not only simple cubic but also bcc structures. As mentioned in the introduction, the (AB)n stars with multiarm were packed in the lattice of a bcc structure near C* (10). The conformation of stars can be regarded as similar to one of (AB)n stars in solution. It is reasonable that these values correspond to the packing pattern of (110), (200), (211), and (220) planes in a bcc structure. This result was well in agreement with the theoretical one predicted by Witten et al. (3). In the SAXS intensity profile at 33 wt% of polymer con-
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centration, the complicated scattering peaks appear as shown in Fig. 1b.qThe first appear at the relative q posiq qfive peaks q tions of 1: q4/3: q2: 8/3: 3. In general, the relative q positions of 1: 4/3: 8/3 correspond to a packing pattern of (111), (200), and (220) planes in a fcc structure. Therefore, it is concluded that the stars are packed in the mixed lattice of bcc and fcc structures at this polymer concentration. Similar mixed lattice patterns are also observed in the SAXS profile at 67 wt% of polymer concentration (Fig. 1c). It is noticed that the first peak shifts to the side of high q position in the order of the increment of polymer concentrations. This fact means that the Bragg spacing dl became shorter with increasing the polymer concentration. It is also noticed q that the scattering intensity at the relative q position of 4/3 based on a fcc lattice increases with increasing the polymer concentration. This means that the fcc lattice fraction in the mixed lattices increases during the concentration of polymer solutions. Figure 1d shows the SAXS intensity profile for the (SI08)237 star film. In this measurement, the scattering peaks seem to originate from the DVB core of PI star. It is found that q the qfirst q four peaks appear at the relative q positions of 1: 4/3: 2: 8/3: as shown in parentheses. The star is packed in the mixed lattice of a bcc and fcc structure even in the bulk. However, the film specimen of PI star did not take the state of thermal equilibrium, because the measurement temperature was 257C. Precise lattice structure of the stars in the bulk could not be determined from the measurement method in this work. The results of SAXS data obtained for (SI27)91 and (SI42)111 stars were almost the same as those for the (SI08)237 star. That is to say, the polymer solution below C* showed disordering. The structural ordering such as a bcc lattice appeared near C* and this structure changed to the mixed lattice of bcc and fcc with increasing polymer concentration.
TABLE 3 Physical Values on Spatial Packing of Cubic Lattices for (SI08)237 Star in Cyclohexane Solution Polymer concentration (wt %)
q1a (nm01)
d1b (nm)
D0c (nm)
4 11 14 19 25 33 38 56 67 100
— 0.281 0.341 0.370 0.398 0.469 0.491 0.533 0.533 0.583
— 22.37 18.40 16.99 15.78 15.39 12.80 11.78 11.78 10.77
— 27.40 22.54 20.80 19.32 16.40 15.68 14.42 14.42 13.20
a
Calculated by q Å 4p sin u/l. Calculated by d1 Å 2pq/q1 . c Determined by D0 Å ( 3/2)d1 . b
We consider spacial packing of the cubic lattice in solution. The measured Bragg spacing dl is related to the cell edge ac of the cubic lattice and the nearest-neighbor distance of the spheres D0 : q
q
D0 Å ( 3/2)ac Å ( 3/2)dl q
for bcc
[1]
for fcc.
[2]
q
D0 Å (1/ 2)ac Å ( 3/2)dl
Tables 2 and 3 list the physical values on spatial packing of the cubic lattices for (SI27)91 and (SI08)237 stars, respectively. It is found that D0 for (SI27)91 stars (MV w Å 2.79 1 10 6 ) shows higher values than that for (SI08)237 stars (MV w Å 2.09 1 10 6 ) at the same polymer concentration, due to high total molecular weight. Figure 2 shows the relationship
TABLE 2 Physical Values on Spatial Packing of Cubic Lattices for (SI27)91 Star in Cyclohexane Solution Polymer concentration (wt%)
q1a (nm01)
d1b (nm)
D0c (nm)
4 8 12 16 44 50 60 100
— 0.249 0.281 0.284 0.370 0.405 0.413 0.420
— 25.24 22.37 22.09 16.99 15.50 15.23 14.97
— 30.92 27.40 27.04 20.80 18.92 18.66 18.34
a
Calculated by q Å 4p sin u/l. Calculated by d1 Å 2pq/q1 . c Determined by D0 Å ( 3/2)d1 . b
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FIG. 2. Relationship between d1 or D0 and polymer concentration for (SI08)237 star.
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to hierarchical structure transformation of the cubic lattices observed on the core–shell microspheres and the (AB)n stars. Such ordering depends strongly on the polymer concentration and the arm number. ACKNOWLEDGMENT This work was supported in part by a Grant-in-Aid for Scientific Research (Priority Areas of ‘‘New Polymers and Their Nano-Organized Systems’’ (No. 277/08246218) from Ministry of Education, Science, Sports, and Cultures, Japan.
REFERENCES
FIG. 3. Double-logarithmic plot of D0 as a function of polymer concentration for (SI08)237 star.
between d1 or D0 and polymer concentration for the (SI08)237 star. PI star takes the disordered state below ca. C* (14.1 wt%). Near the C*, the star forms the lattice with a bcc structure. Beyond ca. 19 wt% of polymer concentration, this structure changes into a mixed lattice of bcc and fcc and leads to shrinkage of the spherical particles. A fcc lattice is the most efficient way of packing spheres. It is also found that both values of d1 and D0 decrease continuously with an exponential function increasing the polymer concentration. Then, we carried out the double-logarithmic plot of D0 as a function of polymer concentration (Fig. 3). It is found that the measured D0 is proportional to the 00.32th power of the polymer concentration and fits well with the 013 power expected for a homogeneous system. This fact means that the spherical particles of (SI08)237 stars lead to isotropic shrinkage increasing the polymer concentration around high polymer concentration. The structural ordering of star polymers is very similar
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