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Langmuir 2007, 23, 5914-5919
Revisiting the Morphology Development of Solvent-Swollen Composite Polymer Particles at Thermodynamic Equilibrium† Naohiko Saito,‡ Yoshimi Kagari,‡ and Masayoshi Okubo*,‡,§ Graduate School of Science and Technology, and Department of Chemical Science and Engineering, Faculty of Engineering, Kobe UniVersity, Kobe 657-8501, Japan ReceiVed December 18, 2006. In Final Form: March 1, 2007 Morphology of polystyrene (PS)/poly(methyl methacrylate) (PMMA)/toluene droplets, in which phase separation proceeds, dispersed in SDS aqueous solution was examined. It changed from ex-centered PS-core/PMMA-shell to hemisphere with increasing SDS concentration. At low polymer weight fraction (wp), PS and PMMA phases contained non-negligible amount of PMMA and PS, respectively. The small amount of PS and PMMA in PMMA and PS phases, respectively, affected significantly the interfacial tension between polymer/toluene and aqueous solutions. Interfacial tension between PS and PMMA phases at low wp was measured by the spinning drop method, showing a quite low value (≈10-2 mN/m). Predicted morphology obtained from calculation of minimum total interfacial free energy of the droplets using the interfacial tensions agreed well with the experimental observation.
Introduction Control of polymer particle morphology has become an increasingly important subject to achieve desirable physical properties for coatings, impact-resistant plastics, and other diverse applications. In general, composite polymer particles were prepared by polymerization of second stage monomer(s) in the presence of seed particles. Numerous kinds of the particle morphology have been reported over the past two decades clarifying the effects of surfactants, initiators, types of polymers, reaction temperature, monomer concentration in the seed particles, cross-linking density of seed polymer, and so on.1-22 It is well †
Part CCXCII of the series “Studies on Suspension and Emulsion”. * To whom correspondence should be addressed. Tel/Fax: +81-78-8036161. E-mail:
[email protected]. ‡ Graduate School of Science and Technology. § Faculty of Engineering. (1) Okubo, M.; Katsuta, Y.; Matsumoto, T. J. Polym. Sci. Polym. Lett. Ed. 1980, 18, 481-486. (2) Okubo, M.; Yamada, A.; Matsumoto, T. J. Polym. Sci. Polym. Chem. Ed. 1980, 16, 3219-3228. (3) Okubo, M.; Ando, M.; Yamada, A.; Katsuta, Y.; Matsumoto, T. J. Polym. Sci. Polym. Lett. Ed. 1981, 19, 143-147. (4) Morgan, L. W. J. Appl. Polym. Sci. 1982, 27, 2033-2042. (5) Okubo, M.; Katsuta, Y.; Matsumoto, T. J. Polym. Sci. Polym. Lett. Ed. 1982, 20, 45-51. (6) Lee, D. I.; Ishikawa, T. J. Polym. Sci. Polym. Chem. Ed. 1983, 21, 147154. (7) Min, T. I.; Klein, A.; El-aasser, M. S.; Vanderhoff, J. W. J. Polym. Sci. Polym. Lett. Ed. 1983, 21, 2845-2861. (8) Dimonie, V.; El-aasser, M. S.; Klein, A.; Vanderhoff, J. W. J. Polym. Sci. Polym. Chem. Ed. 1984, 22, 2197-2215. (9) Muroi, S.; Hashimoto, H.; Hosoi, K. J. Polym. Sci. Polym. Chem. Ed. 1984, 22, 1365-1372. (10) Cho, I.; Lee, K.-W. J. Appl. Polym. Sci. 1985, 30, 1903-1926. (11) Merkel, M. P.; Dimonie, V. L.; El-aasser, M. S.; Vanderhoff, J. W. J. Polym. Sci., Part A: Polym. Chem. 1987, 25, 1755-1767. (12) Okubo, M.; Ikegami, K.; Yamamoto, Y. Colloid Polym. Sci. 1989, 267, 193-200. (13) Lee, S.; Rudin, A. Makromol. Chem., Rapid. Commun. 1989, 10, 655661. (14) Sheu, H. R.; El-aasser, M. S.; Vanderhoff, J. W. J. Polym. Sci., Part A: Polym. Chem. 1990, 28, 629-651. (15) Sheu, H. R.; El-aasser, M. S.; Vanderhoff, J. W. J. Polym. Sci., Part A: Polym. Chem. 1990, 28, 653-667. (16) Okubo, M. Makromol. Chem., Macromol. Symp. 1990, 35/36, 307-325. (17) Shen, S.; El-aasser, M. S.; Dimonie, V. L.; Vanderhoff, J. W.; Sudol, E. D. J. Polym. Sci., Part A: Polym. Chem. 1991, 29, 857-867. (18) Lee, S.; Rudin, A. J. Polym. Sci., Part A: Polym. Chem. 1992, 30, 22112216. (19) Jonsson, J.-E.; Hassander, H.; Tornell, B. Macromolecules 1994, 27, 19321937.
known that morphology can be controlled by competition between thermodynamic and kinetic factors.23 Although the research of kinetic control of morphology has been scant and still has unclear points,24-32 thermodynamic control of morphology is fairly well understood33-42 and is known to be driven by a minimization of the total interfacial free energy of the system. Torza and Mason reported the earliest predictive approach of particle morphology using spreading coefficients and showed that if one knew the various interfacial tensions, the particle morphologies could be readily predicted.43 However, this approach has not been the choice of other investigators due to the inequalities involved in (20) Dimonie, V. L.; Daniels, E. S.; Shaffer, O. L.; El-Aasser, M. S. Emulsion polymerization and emulsion polymers; Lovell, P. A., El-Aasser, M. S., Eds.; Wiley: New York, 1997; Chapter 9, pp 293-326. (21) Rajatapiti, P.; Dimonie, V. L.; El-aasser, M. S.; Vratsanos, M. S. J. Appl. Polym. Sci. 1997, 63, 205-219. (22) Karlsson, O.; Hassander, H.; Wesslen, B. J. Appl. Polym. Sci. 1997, 63, 1543-1555. (23) Sundberg, D. C.; Durant, Y. G. Polym. React. Eng. 2003, 11, 379-432. (24) Cal, J. C. D. L.; Urzay, R.; Zamora, A.; Forcada, J.; Asua, J. M. J. Polym. Sci., Part A: Polym. Chem. 1990, 28, 1011-1031. (25) Gonzalez-Ortiz, L. J.; Asua, J. M. Macromolecules 1995, 28, 31353145. (26) Gonzalez-Ortiz, L. J.; Asua, J. M. Macromolecules 1996, 29, 383-389. (27) Gonzalez-Ortiz, L. J.; Asua, J. M. Macromolecules 1996, 29, 45204527. (28) Stubbs, J.; Karlsson, O.; Jonsson, J.-E.; Sundberg, E. J.; Durant, Y. G.; Sundberg, D. C. Colloids Surf., A 1999, 153, 255-270. (29) Karlsson, l. E.; Karlsson, O. J.; Sundberg, D. C. J. Appl. Polym. Sci. 2003, 90, 905-915. (30) Stubbs, J. M.; Carrier, R.; Karlsson, O. J.; Sundberg, D. C. Progr. Colloid Polym. Sci. 2003, 124, 131-137. (31) Stubbs, J. M.; Sundberg, D. C. J. Appl. Polym. Sci. 2004, 91, 1538-1551. (32) Stubbs, J. M.; Sundberg, D. C. J. Appl. Polym. Sci. 2006, 102, 945-957. (33) Berg, J.; Sundberg, D. C.; Kronberg, B. J. Microencap. 1989, 6, 327337. (34) Sundberg, D. C.; Casassa, A. P.; Pantazopoulos, J.; Muscato, M. R. J. Appl. Polym. Sci. 1990, 41, 1425-1442. (35) Chen, Y.-C.; Dimonie, V.; El-aasser, M. S. Macromolecules 1991, 24, 3779-3787. (36) Chen, Y.-C.; Dimonie, V. L.; El-aasser, M. S. J. Appl. Polym. Sci. 1991, 42, 1049-1063. (37) Jonsson, J.-E. L.; Hassander, H.; Jansson, L. H.; Tornell, B. Macromolecules 1991, 24, 126-131. (38) Chen, Y.-C.; Dimonie, V. L.; El-aasser, M. S. J. Appl. Polym. Sci. 1992, 45, 487-499. (39) Chen, Y.-C.; Dimonie, V. L.; El-aasser, M. S. J. Appl. Polym. Sci. 1992, 46, 691-706. (40) Winzor, C. L.; Sundberg, D. C. Polymer 1992, 33, 3797-3810. (41) Winzor, C. L.; Sundberg, D. C. Polymer 1992, 33, 4269-4279. (42) Durant, Y. G.; Guillot, J. Colloid Polym. Sci. 1993, 271, 607-615. (43) Torza, S.; Mason, S. G. J. Colloid Interface Sci. 1970, 33, 67-83.
10.1021/la063653n CCC: $37.00 © 2007 American Chemical Society Published on Web 04/19/2007
Morphology DeVelopment of SolVent-Swollen Particles
those coefficients (e.g., effect of volume ratio is neglected in the prediction). After that, some groups have constructed the basic groundwork of morphology prediction of composite polymer particle comparing the total interfacial free energy among various morphologies (core-shell, inverted core-shell, hemisphere, individual particles, etc.) at thermodynamic equilibrium.34-42 A more advanced approach, which all the morphologies are taken into account for the prediction, was reported by Sundberg et al.44 In most cases, minimization of total interfacial energy results in full or partial engulfment of the less polar polymer by the more polar polymer. In a previous study, we prepared artificially polystyrene (PS)/ poly(methyl methacrylate) (PMMA) composite particles without graft and/or block copolymer by release of toluene from toluene droplets dissolving PS and PMMA, which were prepared by solution polymerizations, dispersed in surfactant aqueous solution. When poly(vinyl alcohol) (PVA) was used as a surfactant, nonspherical PS/PMMA composite particles with a single dimple were obtained.45 On the other hand, when sodium dodecyl sulfate (SDS) was used as a surfactant in place of PVA, the shape of the composite particles was changed from the dimple, via acorn, to spherical with increasing SDS concentration.46 The formation of dimple and acorn shapes were caused by the contraction of the PS phase after hardening of the PMMA phase during toluene evaporation in the droplets having ex-centered core-shell and hemispherical morphologies, respectively. These droplet morphologies are not consistent with theoretical predictions based on interfacial free energy considerations. This discrepancy between experiment and theory with regards to morphology might be explained by each polymer phase containing a small amount of the other polymer, and this in turn affects the interfacial tensions. This article will again compare the experimental observations with the calculated one, taking account of the effects illustrated above. The main purpose of the current study is revisiting how to predict the morphology of composite polymer particles under thermodynamic equilibrium. Experimental Materials. Styrene (S) and methyl methacrylate (MMA) were distilled under reduced pressure in a nitrogen atmosphere. Reagent grade 2,2′-azobis(isobutyronitrile) was purified by recrystallization. Reagent grade 1-pyrenylmethyl methacrylate (PM) (Funakoshi, Tokyo, Japan) was used as a fluorescent moiety of PS without further purification. Deionized water with a specific resistance of 5 × 106 Ω·cm was used after distillation. Toluene was purified with an alumina column. The other materials were used as received from Nacalai Tesque, Inc., Kyoto, Japan. PS and PMMA homopolymers, and styrene-pyrenylmethyl methacrylate copolymer [P(S-PM) (S/PM ) 99.5:0.5, w/w)] were prepared under the same conditions depicted in our previous article.46 Observation of P(S-PM)/PMMA/Toluene Droplets with a Confocal Laser Scanning Microscope. A homogeneous solution (0.65 g) of P(S-PM)/PMMA/toluene (1:1:24, w/w/w) was mixed with an SDS aqueous solution (1.16-11.6 mM) (15 g), and the mixtures were stirred vigorously using a NISSEI ABM-2 homogenizer at 2000 rpm for 2 min in a 50-mL glass vial (surface area between dispersion and air is 8 cm2). The toluene was released by evaporation from the dispersion stirred with a magnetic stirrer at room temperature, and the droplets were observed after release of toluene for 6 h with an Olympus LSM-GB 200 confocal laser scanning microscope (CLSM). The amounts of residual toluene in the (44) Durant, Y. G.; Sundberg, D. C. J. Appl. Polym. Sci. 1995, 58, 16071618. (45) Okubo, M.; Saito, N.; Fujibayashi, T. Colloid Polym. Sci. 2005, 283, 691-698. (46) Okubo, M.; Saito, N.; Kagari, Y. Langmuir 2006, 22, 9397-9402.
Langmuir, Vol. 23, No. 11, 2007 5915
Figure 1. Confocal laser scanning micrographs of P(S-PM)/ PMMA/toluene (1:1:24, initial weight ratio) droplets after left standing in an uncovered glass vial for 0 (a, b, c) and 6 h (a′, b′, c′), where wp is 0.08 and 0.17, respectively, dispersed in various concentrations of SDS aqueous solutions (mM): (a, a′) 1.16; (b, b′) 2.31; (c, c′) 11.6. dispersions were measured by gas chromatography. The PM unit was excited by 351 nm UV laser and radiated fluorescence around 400 nm. Polymer Compositions in PS and PMMA Phases. A PS/PMMA/ toluene (1:1:10, w/w/w) solution was poured into a graduated cylinder. Then, the solution was left in the closed cylinder standing for 5 days. After 5 days, the solution clearly separated into PS and PMMA phases. The volume ratio of PS to PMMA phases was measured by visual inspection of the solution in the cylinder. The weight ratio of PS to PMMA in each phase was measured by 1H NMR with a Bruker DPX 250 MHz spectrometer (Karlsruhe, Germany). Interfacial Tension between Polymer/Toluene and Aqueous Solutions. Interfacial tensions between polymer/toluene and aqueous solutions (γP-T/W) were measured by the pendant drop method with a Drop Master 500 (Kyowa Interface Science Co., Ltd., Japan) at room temperature (ca. 20 °C). Pendant drops of the polymer solution were formed at the tip of a stainless steel needle in a glass cell filled with SDS aqueous solution (0.116-23.2 mM) and the diameter was measured. Before the measurements, the glass cell, syringe, and needle were cleaned by tetrahydrofuran and rinsed several times with distilled water to remove residual polymer and surfactant. The densities of PS and PMMA phases for the measurement of interfacial tension were measured with a pycnometer. Interfacial Tension between PS and PMMA Phases. Interfacial tensions between PS and PMMA phases (γPS-T/PMMA-T) were measured by the spinning drop method with a Site100 (Kru¨ss, Germany) at 20 °C. A drop of the PS phase was suspended in the PMMA phase and made to rotate in a horizontal tube, and the diameter of a drop was measured.
Results and Discussion Figure 1 shows confocal laser scanning micrographs of P(SPM)/PMMA/toluene droplets before and after partial release of toluene for 6 h, where the weight fraction of the polymers (wp) was approximately 0.08 and 0.17, respectively. The small amount of PM units in the P(S-PM) (PM/S ) 0.17:99.83 mol/mol) would not affect the droplets morphology. As expected, no differences in morphology of particles prepared from PS/PMMA/ toluene and P(S-PM)/PMMA/toluene droplets at the same SDS concentration were observed by optical microscopy. Before toluene evaporation, all the droplets were homogeneous, indicating that phase separation had not occurred. After 6 h, a heterogeneous structure consisting of a P(S-PM)-rich phase (light region) and a PMMA-rich phase (dark region) was observed in all the droplets. The morphology of the droplets changed from ex-centered PS-core/PMMA-shell to hemispherical with increasing SDS concentration. In all the CLSM photographs, the PMMA rich phase contained a small amount of P(S-PM) molecules. After further release of toluene, P(S-PM)/PMMA composite particles had dimplelike, acornlike, and hemisphere shapes
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Saito et al.
Figure 2. Cross-sectional image of PS/PMMA/toluene droplet before and after phase separation.
depending on the SDS concentration (data not shown). The formation mechanism of these nonspherical particles was discussed in a previous article.46 The difference in the morphologies of PS/PMMA/toluene droplets at each SDS concentration after 6-h release of toluene can be explained from the viewpoint of total interfacial free energy change. When predicting the thermodynamic equilibrium morphology of a composite polymer particle, the Gibbs free energy change (∆G) for structural development of the particle during phase separation is expressed only in terms of the total interfacial free energy changes.33-38,40-44 The enthalpic and entropic energy changes among the various shapes can be neglected due to the fact that the droplets are macroscopic compared to the size of molecules. Accordingly, the total free energy change for various shapes can be expressed as
Figure 3. Geometrical map of morphologies of composite polymer particles.
A simple geometric relationship also exists in Figure 2, which can be expressed as
r12 - (h - r1)2 ) r22 - [(H - h) - r2]2 ) R2 - (R - a)2 (6)
Assuming that the total volume of droplets (Vt) does not change after phase separation yields
If all the interfacial tensions (γPS-T/PMMA-T, γPS-T/W, γPMMA-T/W, γPSPMMA-T/W), the volume ratio of VPS to VPMMA, and the radius before phase separation (R0) are determined, it is possible to calculate ∆G as a function of h and H by combining eqs 2-6. The last term on the right-hand side in eq 2, which represents the total interfacial free energy of the droplet before phase separation, does not affect the equilibrium morphology (h and H at minimum ∆G) after phase separation (although the absolute value of ∆G is influenced). Various combinations of h and H yield a continuous array of two-dimensional morphologies (Figure 3). It should be noted that the geometrical map does not consist of three straight lines, but two curves (slanting lines from individual to core-shell and inverted core-shell) and one straight line (core-shell to inverted core-shell). The volume ratio of PS to PMMA layers (VPS/VPMMA) phaseseparated in PS/PMMA/toluene (1:1:10, w/w/w) solution was ca. 1.5 after leaving the solution for 5 days. The volume ratio of 1.5, which was consistent with that obtained in our previous study,45 indicates that toluene partitioned more into PS phase than into PMMA phase. This volume ratio hardly changed even after 3 months, thus revealing near equilibrium of the phase separation after 5 days. The reason that toluene partitioned more into PS phase than into PMMA phase could be explained from viewpoint of the difference of the solubility parameters (δ), which correlate to the enthalpy of mixing. The difference of δPS and δtoluene is smaller than that of δPMMA and δtoluene; [δPS ) 18.6; δPMMA ) 19.4; δtoluene ) 18.2 (MPa1/2)].47 Molar ratios of PS to PMMA (nPS/nPMMA) in the phase-separated PS and PMMA layers in the PS/PMMA/toluene (1:1:10, w/w/w) solution (wp ) 0.17) after 5 days were, respectively, measured to be 1:0.294 and 0.185:1 by 1H NMR. It is noteworthy that both the PS and PMMA layers, respectively, contained non-negligible amounts of PMMA and PS. It is likely that presence of small amount of PMMA (or PS) molecules in the PS (or PMMA) phase affect the γPS-T/W (or γPMMA-T/W). To our knowledge, the effect of such small amounts of polymers on the morphology prediction has not been discussed quantitatively and interfacial tension value of homopolymer/monomer (solvent) solutions and
Vt ) 4πR03/3 ) VPS + VPMMA
(47) Brandrup, J.; Immergut, E. H.; Grulke, E. A. Polymer Handbook, 4th ed.; Wiley: New York, 1999; Chapter VII, pp 675-714.
∆G )
∑ γiAi - γ0A0
(1)
where γi is the interfacial tension of the ith interface and Ai is the corresponding interfacial area. In order to calculate the total interfacial energy change, we applied the similar geometry to that used by Sundberg et al.44 as shown in Figure 2. In their model, the geometry is divided into three regions as a function of four angles and the volume ratio of polymer phases is estimated from the chemical potentials of the monomer. Our geometry, however, consists of one region as a function of the two variables (H and h) described below, and the volume ratio is measured experimentally and inserted into the following equation. Figure 2 allows rewriting eq 1 as
∆G ) γPS-T/W2πr1h + γPMMA-T/W2πr2(H - h) + γPS-T/PMMA-T2πRa - γPS,PMMA-T/W4πR02 (2) where γPS-T/PMMA-T, γPS-T/W, γPMMA-T/W, and γPS,PMMA-T/W are, respectively, the interfacial tensions between the toluene phases of PS and PMMA, the PS/toluene phase and water, the PMMA/ toluene phase and water, and the PS/PMMA/toluene solution (before phase separation) and water. The parameters r1, r2, and R are defined in the cross-sectional image after phase separation in Figure 2. R0 is the radius of droplets before phase separation. The morphology having minimum ∆G is the thermodynamically most stable structure. The volumes of PS and PMMA phases are, respectively, expressed as
VPS ) π(r1h2 - h3/3) + π(Ra2 - a3/3)
(3)
VPMMA ) π[r2(H - h)2 - (H - h)3/3] - π(Ra2 - a3/3) (4)
(5)
Morphology DeVelopment of SolVent-Swollen Particles
Langmuir, Vol. 23, No. 11, 2007 5917
water has been used for the morphology prediction.36,38 In order to clarify this point, two different PS and PMMA phases were ready for the interfacial tension measurement. (i) PS/toluene (1:6, w/w) and PMMA/toluene (1:4, w/w) solutions were separately prepared. (ii) A PS/PMMA/toluene (1:1:10, w/w/w) solution, which was somewhat turbid, was poured into a graduated cylinder, left standing in the closed cylinder for 5 days, and resulted in transparent PS and PMMA layers, which, respectively, contained small amount of PMMA and PS, and referred to PS* and PMMA* in the latter case. Pure PS and PMMA phase referred to PS° and PMMA°. Parts of the PS* and PMMA* layers were removed by syringe before the interfacial tension measurements. Figure 4 shows γP-T/W as a function of SDS concentration in aqueous solution. Both γPS-T/W and γPMMA-T/W decreased with increasing SDS concentration up to the CMC (ca. 8 mM). γPS*/W were significantly lower than γPS°/W, indicating the adsorption of PMMA in PS* at the interface. On the other hand, γPMMA*/W was a little higher than γPMMA°/W by the incorporation of small amount of PS in PMMA phase. By fitting these graphs, empirical equations of relationship between γP-T/W and SDS concentration were obtained. From Figure 4a, γPS°/W and γPMMA°/W below the CMC are expressed as
γPS°/W ) 34.1 e-0.3732Cs
(7)
γPMMA°/W ) 18.5 e-0.2507Cs
(8)
where Cs is the SDS concentration (mM). From Figure 4b, γPS*/W and γPMMA*/W below the CMC are expressed as
γPS*/W ) 20.0 e-0.2515Cs
(9)
γPMMA*/W ) 19.9 e-0.2499Cs
(10)
Increasing the SDS concentration beyond the CMC (Cs > 8 mM) did not lead to any further decreases in γPS-T/W and γPMMA-T/W, but the values reached a constant level at 4 mN/m. This indicates that the entire surface area of the droplets would be saturated by SDS above CMC. The above equations (7-10) are only applicable to the PS/PMMA/toluene system at low wp. If toluene is replaced by another solvent, then eqs 7-10 are still applicable if the solvent is more hydrophobic than PMMA, although slight modification of the equations is required. If the solvent is less hydrophobic than PMMA, the equations cannot be used. When changing the solvent from toluene to a more hydrophilic one, the situation is entirely different because adsorption of PMMA at the interface (to decrease the interfacial tension between polymer/solvent and the aqueous solution) may not occur. However, as long as the solvent is more hydrophobic than PMMA, the same relationships would be obtained, as shown in Figure 4. According to theory40,48 and experimental observation,49 the interfacial tensions between the polymer phase and the aqueous solution would be expected to increase with increasing wp, though the increase is quite small for wp < 0.3. Thus, the above equations might be applied below wp ) 0.3. As phase separation between PS and PMMA in the droplets tends to be dominated by kinetic factors when wp > 0.3,46 the above equations are sufficient for consideration of equilibrium morphology of PS/PMMA/toluene droplets. Although extensive quantitative data about interfacial tension between different polymers without solvent were reported by (48) Siow, K. S.; Patterson, D. J. Phys. Chem. 1973, 77, 356. (49) Sundberg, D. C.; Durant, Y. G. Macromol. Symp 1995, 92, 43-51.
Figure 4. Interfacial tensions between the polymer phase and water, measured by the pendant drop method after 30 min, as a function of the SDS concentration. Polymer phases: O, PS° (PS/toluene ) 1:6, w/w); 0, PMMA° (PMMA/toluene ) 1:4, w/w); b, PS* [PS phase removed from PS/PMMA/toluene (1:1:10, w/w/w) solution]; 9, PMMA* [PMMA phase removed from PS/PMMA/toluene (1: 1:10, w/w/w) solution].
Wu et al.,50 only a few reports on the direct measurement of interfacial tension between polymers in the presence of solvent (γPA-T/PB-T) have been published.51,52 Furthermore, all measurements of γPA-T/PB-T were confined to dilute polymer solutions because of the experimental difficulties associated with measurements at high wp. Broseta et al. proposed a theoretical model for the prediction of γPA-T/PB-T taking into account the excluded volume effect.53 In their study, they measured the interfacial tensions of demixed PS, poly(dimethylsiloxane) (PDMS), and toluene mixtures as functions of the molecular weight of polymers and the polymer concentration, and very good agreement between the experimental results and the theoretical predictions was reported. Thus, their model has been applied by a number of the references to the morphology prediction.36,38,40,41 In this study, the theoretical estimation of γPS-T/PMMA-T with toluene was carried out on the basis of Broseta’s approach and compared with experimental results. The following equations were used for the estimation of γPS-T/PMMA-T.
(
1.64 - 1.67u ω
γ0 )
kT u 1/2 ξ2 6
γ ) γ0 1 -
)
(11)
where
()
(12)
(50) Wu, S. J. Macromol. Sci., Part C, ReV. Macromol. Chem. 1974, 10, 1. (51) Gaillard, P.; Ossenbach-Sauter, M.; Riess, G. Mackromol. Chem., Rapid. Commun. 1980, 1, 771-774. (52) Shinozaki, K.; Saito, Y.; Nose, T. Polymer 1982, 23, 1937-1943. (53) Broseta, D.; Leibler, L.; Kaddour, L. O.; Strazielle, C. J. Chem. Phys. 1987, 87, 7248-7256.
5918 Langmuir, Vol. 23, No. 11, 2007
Saito et al. Table 1. Parameters of Weight Average Molecular Weight (Mw), Radius of Gyration (Rg), Critical Concentration of Demixing (ck) for the Calculation of Interfacial Tension between PS and PMMA Phases a
PS PMMAa average
Figure 5. Graphic displays of morphology calculation of the PS/ PMMA/toluene droplets using interfacial tensions of PS° and PMMA° and the predicted morphologies. SDS concentrations (mM): (a) 1.16; (b) 2.31; (c) 11.6.
k, T, and u are Boltzmann’s constant (1.38 × 10-23 J/K), temperature (300 K), and interaction parameter between “blobs”,54 which can be estimated from the knowledge of the critical concentration of demixing, ck, in the semidilute regime, respectively.
()
u(c) ) u0
c ck
0.3
(13)
Interaction parameter at critical concentration is given as55
2ckξk3NAV u0 ) Mw
(14)
In the symmetric solvent case each “blob” occupying a correlation volume, ξ3, and being composed of A (or B) monomers. ξ is the correlation length of semidilute polymer solutions, which depends on the concentration of polymer56
ξ(c) c -3/4 ) 0.43 Rg c*
( )
(15)
where c and c* are, respectively, polymer concentration and the overlap concentration, which can be expressed as
c* )
3Mw 4πRg3NAV
(16)
Mw and NAV are the weight-average molecular weight of both polymers and Avogadro’s number (6.02 × 1023 mol-1). The incompatibility degree, ω, is expressed as
ω ) uNb
(17)
Here,
Nb )
Mw cξ3NAV
(18)
represents the number of blobs per chain. By using eqs 11-18, the interfacial tension can be estimated in terms of measurable quantities such as Mw, radius of gyration of chains in the dilute solution, Rg, and critical concentration of demixing, ck. The relationships between Rg and Mw in the bulk and in Flory θ-solvents were extensively studied by using small-angle neutron scattering and light scattering. For PS and PMMA, (Rg2/Mw)1/2 (54) Gennes, P. G. D. Scaling Concepts in Polymer Physics; Cornell University Press: Ithaca, NY, 1979. (55) Broseta, D.; Leibler, L.; Joanny, J.-F. Macromolecules 1987, 20, 19351943. (56) Lapp, A.; Picot, C.; Strazielle, C. J. Phys. Lett. 1985, 46, L1031.
Mwa (g/mol)
Rgb,c (cm)
ckd (g/cm3)
100 000 100 000 100 000
8.70 × 10 9.49 × 10-7 9.09 × 10-7
0.117
-7
a Prepared by solution polymerizations (M ) ca. 100 000). b (R 2/ w g Mw)1/2 ) 0.0275 nm‚mol1/2/g1/2. c (Rg2/Mw)1/2 ) 0.03 nm‚mol1/2/g1/2. d c ) 221.37M -0.6556. k w
) 0.0275 and 0.03 nm‚mol1/2/g1/2, respectively.57,58 In order to obtain the critical concentration of demixing, ck, of PS/PMMA/ toluene, turbid points, which indicate the starting point of the phase separation of PS/PMMA/toluene solutions at various molecular weights of the polymers, were examined. By fitting the experimental relation of turbid points and Mw, we obtained ck ) 221.37Mw-0.6556. γPS-T/PMMA-T was calculated on the basis of the data in Table 1, using averaged values of Rg and Mw. The value obtained for u0 at 27 °C on the basis of eq 14 is 0.0141, resulting in χ ) 0.0277, which is somewhat lower than that predicted from the temperature dependence of χ ()0.028 + 3.9/ T) for PS-block-PMMA reported by Russell et al.59 In order to obtain χ ) 0.041 at 27 °C, a revised u0 (0.0208) was used for the calculation of γPS-T/PMMA-T in the same way as Winzor et al.40 Experimental results of γPS°/PMMA° and γPS*/PMMA* by the spinning drop method were, respectively, 0.025 and 0.015 mN/m at wp ) 0.17, while calculated γPS-T/PMMA-T at wp ) 0.17 is 0.073 mN/m. The reproducibility of the experimental results was within 0.01 mN/m. According to the Broseta’s model, the interfacial tension between polymers containing solvent is affected by the ck, which strongly depends on the kind of solvent, and wp. Thus, these values (γPS°/PMMA° ) 0.025, γPS*/PMMA* ) 0.015 mN/m) are only applicable for PS/PMMA/toluene system at wp ) 0.17. Because the spinning drop method cannot be applicable at high wp due to the high viscosity, the measurement of γPS-T/PMMA-T was only performed at low wp. Both experimental results obtained by the spinning drop method did not agree with the theoretical result. The extent of the disagreement between experimental and theoretical results of γPS-T/PMMA-T increased with decreasing molecular weight of the polymers (data not shown). This might be due to the PS/PMMA/toluene system having low incompatibility to apply the above model in comparison to the PS/PDMS/toluene system. Broseta et al. mentioned that the above model neglects some theoretical limitations.53 First, it cannot be simply generalized to describe the crossover of composition profile of demixed polymer A/polymer B/solvent at the interface using the Chan-Hilliard model.60 Such a crossover situation may occur for relatively short incompatible chains. Second, the blob model used here neglects chain ends effects and is valid in the limit of very long chains. Therefore, the experimental results are used for the calculation of equilibrium morphology prediction. Figures 5 and 6, respectively, show the partial expanded graphic displays of the morphology calculation using γPS°/W and γPMMA°/W, and using γPS*/W and γPMMA*/W at thermodynamic equilibrium for a PS/PMMA/toluene droplet at wp ) 0.17 dispersed in SDS (57) Cotton, J. P.; Decker, D.; Benoit, H.; Farnoux, B.; Higgins, J.; Jannink, G.; Ober, R.; Picot, C.; desCloizeaux, J. Macromolecules 1974, 7, 863. (58) Kirste, R. G.; Kruse, W. A.; Ibel, K. Polymer 1975, 16, 120. (59) Russel, T. P.; Hjelm, R. P.; Seeger, P. A. Macromolecules 1990, 23, 890-893. (60) Cahn, J. W.; Hilliard, J. E. J. Chem. Phys. 1958, 28, 258-267.
Morphology DeVelopment of SolVent-Swollen Particles
Figure 6. Graphic displays of morphology calculation of the PS/ PMMA/toluene droplets using interfacial tensions of PS* and PMMA* and the predicted morphologies. SDS concentrations (mM): (a) 1.16; (b) 2.31; (c) 11.6.
Langmuir, Vol. 23, No. 11, 2007 5919
polymer phases.62-64 Therefore, even if a small amount of PSPMMA block copolymer were present in the current PS/PMMA/ toluene system, the decrease of γPS-T/PMMA-T might cause the morphology to change from hemispherical to PS-core/PMMAshell (unless the block copolymer affects both γPS-T/W and γPMMA-T/W). To date, there are only very few papers dealing with the effect of compatibilizer on morphology of composite polymer particles,21,61,65-68 and no quantitative data have been published on the equilibrium morphology to the best of our knowledge. More work is required to reach a full quantitative understanding of the equilibrium morphology of two-component polymer colloid system, and efforts to this end are currently underway in our laboratory.
Conclusions aqueous solution and cross sections of the predicted morphologies. When γPS°/W and γPMMA°/W were estimated from eqs 7 and 8 and γPS°/PMMA° ) 0.025 mN/m were used for the calculation, the predicted morphology (having minimum ∆G) of the PS/PMMA/ toluene droplets is PS-core/PMMA-shell structure at SDS concentration of 1.16-11.6 mM, as shown in Figure 5. Even if the tolerance of the interfacial tensions is taken into account for the prediction, the conclusion remains the same (only PScore/PMMA-shell structure is predicted). This result is inconsistent with the experimental observations in Figure 1b′,c′. On the other hand, γPS*/W and γPMMA*/W estimated from eqs 9 and 10 and γPS*/PMMA* ) 0.015 mN/m were used for the calculation, the predicted morphologies are changed from PScore/PMMA-shell, via ex-centered PS-core/PMMA-shell, to hemisphere structures with increasing SDS concentration of 1.16-11.6 mM, in good agreement with the morphologies in Figure 1a′-c′. These results indicate that the fact that each polymer phase contains a small amount of the other polymer cannot be neglected when considering the interfacial tension between the polymer phase and aqueous solution for accurate morphology prediction. Composite polymer particles are normally prepared by seeded emulsion polymerization using a water-soluble initiator (e.g., KPS), thus generating a polymer having polar end groups. These polar end groups would decrease the interfacial tension between the polymer phase and water, and this in turn affects the morphology at thermodynamic equilibrium.36 Furthermore, a small amount of graft and/or block copolymer are sometimes formed during the polymerization, which would affect the morphology of composite polymer particles,21,61 because it is well known that the block copolymer would operate as a compatibilizer decreasing the interfacial tension between (61) Nelliappan, V.; El-aasser, M. S.; Klein, A.; Daniels, E. S.; Roberts, J. E. J. Polym. Sci., Part A: Polym. Chem. 1996, 34, 3183-3190.
This paper deals with the prediction of particle morphology of phase-separated polymers at thermodynamic equilibrium from the viewpoint of interfacial energy. The morphologies of PS/ PMMA/toluene droplets at wp ) 0.17 dispersed in various concentrations of SDS aqueous solutions were examined. The interfacial tension between the polymer/toluene and the aqueous solutions was significantly affected by even a small amount of PS (15.6 mol %) and PMMA (22.7 mol %) incorporated in the PMMA and PS phases, respectively. The droplet morphology could be quantitatively predicted on the basis of the experimentally obtained interfacial tensions. However, neglecting the small amount of PS and PMMA in PMMA and PS (which is common practice) resulted in erroneous morphology predictions. No report has been published about the effect of the small amount of another polymer incorporated in each phase on the interfacial tension and resulting morphology of composite polymer particles at thermodynamic equilibrium. Thus, the present results demonstrate the importance of accounting for the actual polymer composition in each phase. Acknowledgment. This work was supported by Creation and Support Program for Start-ups from Universities (No. 1509) from the Japan Science and Technology Agency (JST), and by Research Fellowships of the Japan Society for the Promotion of Science (JSPS) for Young Scientists (given to N.S.). LA063653N (62) Retsos, H.; Anastasiadis, S. H.; Pispas, S.; Mays, J. W.; Hadjichristidis, N. Macromolecules 2004, 37, 524-537. (63) Jorzik, U.; Wolf, B. A. Macromolecules 1997, 30, 4713-4718. (64) Liang, H.; Favis, B. D.; Yu, Y. S.; Eisenberg, A. Macromolecules 1999, 32, 1637-1642. (65) Ding, J.; Liu, G. Macromolecules 1999, 32, 8413-8420. (66) Okubo, M.; Saito, N.; Takekoh, R.; Kobayashi, H. Polymer 2005, 46, 1151-1156. (67) Yabu, H.; Higuchi, T.; Shimomura, M. AdV. Mater 2005, 17, 2062-2065. (68) Herrera, V.; Pirri, R.; Leiza, J. R.; Asua, J. M. Macromolecules 2006, 39, 6969-6974.
