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Microscopic Phase Separation and Long-Time Relaxation Behavior in Three-Component Heterogeneous Blend Systems Takayoshi Matsumoto,* Nobuyuki Hori, and Masaoki Takahashi Department of Material Chemistry, Kyoto University, Kyoto 606, Japan Received March 11, 1996. In Final Form: August 5, 1996X Microscopic phase separation and long-time relaxation processes have been studied for the threecomponent polymer blend solutions which are composed of polyethersulfone (PES), polysulfone (PSF), and N-methyl-2-pyrrolidone (NMP) as a solvent for both PES and PSF. The ternary systems of total polymer concentration of 30 wt % change from a clear state to a uniformly turbid state with temperature change. That is, the system has a cloud temperature as a lower critical solution temperature (LCST). The most characteristic behavior of the 30% mixed systems is that the uniformly turbid state is very stable and does not proceed to the macroscopic phase separation for a long time, i.e., more than several months. The mixed systems of PES/PSF ) 3/7 and 5/5 show a long-time relaxation process due to the microscopic phase separation. On the other hand, the system of PES/PSF ) 7/3 does not clearly show the long-time relaxation process in spite of the fact that the microscopic phase separation pattern is very similar to that of the system of 3/7. The long-time relaxation behavior is analyzed using the emulsion model for both the systems, and it revealed that the interfacial tension of the mixed systems is extremely small in comparison with the various blended polymer melts and also that the rheological measurements are very useful to estimate the interfacial tension and the characteristic time for the geometric deformation of the dispersing emulsion particles.
Introduction Rheological properties of heterogeneous systems have been extensively studied from both theoretical and experimental points of view. The most characteristic rheological behavior of heterogeneous systems is an increase in elasticity in the low frequency range, i.e., showing a long-time relaxation mechanism. Taylor extended Einstein’s analysis to include the case of emulsions composed of spherical droplets of Newtonian liquid in another immiscible Newtonian liquid and proposed the following equation.1
5K + 2 φ [ (2K + 2) ]
η ) ηm 1 +
(1)
Here η and ηm are the viscosities of the disperse system and the medium, K is ηi/ηm, where ηi is the viscosity of dispersed particles (inclusion) and φ is the volume fraction of the inclusion. Equation 1 is reduced to Einstein’s equation when K becomes infinite. Schowalter et al. have extended Taylor’s theory and introduced the deformability of the dispersing particles.2,3 When the disperse system undergoes a steady shear flow of shear rate γ˘ , the stress tending to deform the droplet is a viscous drag, ηmγ˘ . On the other hand, the stress R/R, which is due to interfacial tension, R, between two liquids of droplet (radius R) and medium, tends to maintain the droplet in a spherical shape. Consequently, the deformation of the droplet induces the elastic properties of the disperse system. Choi and Schowalter extended this to undiluted disperse systems by taking into account a hydrodynamic interaction between particles.4 Graebling et al. introduced the * To whom all correspondence should be addressed. Telephone: +81(75)753-5616. Fax: +81(75)753-4911. E-mail: matsutk@ rheogate.polym.kyoto-u.ac.jp. X Abstract published in Advance ACS Abstracts, October 15, 1996. (1) Taylor, G. I. Proc. R. Soc. London 1932, A132, 41. (2) Schowalter, W. R.; Chaffey, C. E.; Brenner, H. J. Colloid Interface Sci. 1967, 26, 152. (3) Scholz, P.; Froelich, D.; Muller, R. J. Rheol. 1989, 33, 481. (4) Choi, S. J.; Schowalter, W. R. Phys. Fluids 1975, 18, 420.
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viscoelasticity to the droplet and the medium to be able to describe the viscoelastic behavior over a wide frequency range and proposed as the emulsion model the following expression for the complex modulus of the disperse systems of monodisperse inclusions.5,6
G*(ω) ) G*m(ω)
(
)
1 + 3φF(ω) 1 - 2φF(ω)
(2)
Here
F(ω) ) [4(R/R)(2G*m(ω) + 5G*i(ω)) + (G*i(ω) G*m(ω))(16G*m(ω) + 19G*i(ω))]/[40(R/R)(G*m(ω) + G*i(ω)) + (2G*i(ω) - 3G*m(ω))(16G*m(ω) + 19G*i(ω))] (3) where G*m(ω) and G*i(ω) are complex moduli of the medium and inclusion at an angular frequency ω. Graebling et al. showed that the long-time relaxation mechanism of the polymer blends can be expressed by this emulsion model.5,6 In the present paper, we discuss the microscopic phase separation in three-component systems of polymer blend solutions and the applicability of the emulsion model to these systems. Experimental Section Materials and Characterization. The systems employed are three-component polymer blend solutions composed of polyethersulfone (PES, Sumitomo Chemical 3600G), polysulfone (PSF, Amoco P-1700), and N-methyl-2-pyrrolidone (NMP), shown in Figure 1. NMP is a solvent for both PES and PSF. PES and PSF are dried thoroughly under vacuum at 120 °C prior to preparation of the sample solutions. The weight average molecular weight Mw was measured by means of a low-angle laser light scattering photometer (λ ) 632.8 nm, Chromatix KMX(5) Graebling, D.; Muller, R. J. Rheol. 1990, 34, 193. (6) Graebling, D.; Muller, R.; Palierne, J. E. Macromolecules 1993, 26, 320.
© 1996 American Chemical Society
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Figure 1. Chemical formulas of the systems employed. Table 1. Characterization of Polymers Employed polymer
Mw (103)
Mea (103)
dn/dc (mL g-1)
Rg (nm)
PES PSF
29.2 80.7
3.10 2.25
0.1707 0.1334
5.03 5.26
a
Average molecular weight between coupling loci.
Figure 2. Phase diagram for the three-component mixed system at 25 °C; O, clear solution; 0, microscopic phase separation; 4, macroscopic two phases. 6). The specific refractive index increment dn/dc was measured with a differential refractometer (λ ) 632.8 nm, Chromatix KMX16). The radius of gyration Rg was measured with small-angle X-ray scattering (SAXS) at the High Intensity X-ray Laboratory, Kyoto University.7,8 Table 1 shows the characterization of the PES and PSF samples. The receptacle of the blended solutions is hermetically sealed and kept in a desiccator. Measurements. Rheological properties were measured by means of a cone-plate type rheometer (MR500, Rheologi, Kyoto, Japan). The rheometer was devised to protect the sample solution from moisture, because the solution becomes white by absorption of moisture, indicating phase separation. The diameters of the cone used were 4.0 and 2.13 cm, and the angle was 3.98°. If there is no special description, the dynamic strain amplitude employed is 0.1, though the rheological measurements were carried out at strain amplitudes of 0.1 ∼ 0.4.
Results and Discussion Microscopic Phase Separation. Figure 2 shows a phase diagram for the three-component mixed systems of PES/PSF/NMP at 25 °C. PES and PSF make clear solutions respectively with NMP below ca. 50 wt %. The ternary systems can be distinguished into three types. When the total polymer concentration is equal to or below 25 wt %, the mixed systems become clear solutions. When the polymer concentration is higher than 35 wt %, the mixed systems are in a turbid state and separate macroscopically into two phases within a few hours. On the other hand, the ternary systems of total polymer (7) Matsumoto, T.; Inoue, H.; Chiba, J. J. Appl. Phys. 1992, 71, 1020. (8) Matsumoto, T.; Inoue, H. Chem. Phys. 1993, 178, 591.
Figure 3. Cloud temperature at various mixing ratios of PES/ PSF for the 30 wt % ternary systems.
concentration of 30 wt % change from clear states to uniformly turbid states with temperature change. That is, the system has a cloud temperature. The most characteristic behavior of the 30% systems is that the uniformly turbid state is very stable and does not proceed to the macroscopic phase separation for a long time, more than several months, as discussed later. Figure 3 shows the cloud temperatures at various mixing ratios of PES/ PSF for the 30% ternary systems (PES/PSF30). The cloud temperature is determined as the temperature at which the turbidity of the system starts to increase sharply. The system has a lower critical solution temperature (LCST). The system is in a clear state at temperatures lower than the cloud one and is in a uniformly turbid state at higher temperatures than the cloud point. The turbid state is fairly stable. A microscopic separation structure can be observed in the stable and uniformly turbid state, as shown in Figure 4. Figure 4 shows phase-contrast photomicrographs of the microscopic phase separation at 23 and 50 °C for the system of 3/7. Using the hot stage, the temperature of the sample was held at 21 °C for 60 min. The microscopic phase separation already can be observed at this time, and after that the temperature is sharply changed to 23 °C. Picture A was taken within 1 min after this temperature change. Pictures B and C were taken after 20 and 60 min. Again the temperature was sharply raised and held at 50 °C. Pictures D, E, and F were taken at the lapse of 5, 20, and 200 min at 50 °C. It turns out that the system sensitively responds to the temperature change and the phase separation pattern sharply changes corresponding to the temperature change; however, the pattern is insensitive to the lapse of time at constant temperature. The changes in the pattern of the microscopic phase separation with temperature change are reproducible, and there is not temperature hysteresis. Figure 5 shows the situation of the microscopic phase separation at the lapse of 60 min at 50 °C for the mixed systems of PES/PSF ) 3/7, 5/5, and 7/3 with total polymer concentration 30% at 50 °C. The microscopic phase separation with spherical droplets can be observed for the systems of 3/7 and 7/3. On the other hand, the phase separation for the system of 5/5 is rather complex and a multiemulsion structure in which small droplets contained in a large droplet can be observed, besides spherical microphases. These microscopic phase separation states are stable at least for several months. This phenomenon is curious from the thermodynamical point of view. The microscopic phase must be large with time to reduce the interfacial energy and the system separates finally into
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Figure 4. Phase-contrast photomicrographs for the mixed system of 3/7 at 23 and 50 °C. The total polymer concentration is 30 wt %.
two macroscopic phases. The systems of 7/3 and 5/5 separate into two macroscopic phases after 5 months at 25 °C; however, the system of 3/7 holds the microscopic phase separation more than 7 months. Tanaka reported a similar anomalous phase separation for bicomponent systems.9 However the pattern of the phase separation is held stable only for several days in his systems. Rheological Properties. Effect of Mixing Ratio. Rheological data depend strongly on the time lapse and temperature hysteresis in many polymer blends with structure due to the microscopic phase separation. For our systems, however, it was confirmed that the rheological data are independent of the lapse of time at constant temperature and also that they are independent of the temperature history. In Figure 6 the storage modulus G′ and the loss modulus G′′ are logarithmically plotted against angular frequency ω for the 3/7 mixed system at 50 °C for various routes of the temperature change. The rheological data are independent of the routes. In Figure 7, the storage modulus G′ and the loss modulus G′′ are logarithmically plotted against angular frequency ω for the 30% mixed systems at various mixing ratios at 50 °C. The mixing ratios of PES/PSF are 0/10, 3/7, 5/5, 7/3, and 10/0. The homogeneous systems of 0/10 and 10/0 are in the flow region; i.e., G′ and G′′ are proportional to ω2 and ω, respectively. The G′′ values of the mixed systems are located between the data of each component system and also proportional to ω in the relatively high frequency region. On the other hand, frequency dependence curves of G′ of the mixed systems show a plateau or shoulder due to a long-time relaxation process, especially in the systems of 3/7 and 5/5. The effect of the long-time relaxation process can also slightly be observed in the G′′ values of the systems of 3/7 and 5/5 in the relatively low frequency (9) Tanaka, H. Macromolecules 1992, 25, 6377; J. Chem. Phys. 1994, 100, 5323.
Figure 5. Phase-contrast photomicrographs for the mixed systems of PES/PSF at mixing ratios of 3/7, 5/5, and 7/3 at 50 °C. The temperature is raised from 23 to 50 °C and held for 60 min at 50 °C.
Figure 6. Frequency dependence curves of the storage modulus G′ and the loss modulus G′′ for the system of 3/7 at 50 °C for various routes of temperature change.
region. According to Figure 5, the microscopic phase separation pattern of the system of 7/3 is similar to that of the system of 3/7 at 50 °C. However the long-time relaxation process is marked in the system of 3/7 but is not so clear in the system of 7/3. This point will be discussed in the next section. Figure 8 shows the logarithm of the zero-shear viscosity
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approximately represented by
log η0 )
Figure 7. Storage and loss moduli plotted against angular frequency for the 30 wt % mixed systems at various mixing ratios at 50 °C. PES/PSF ) 0/10 (1), 3/7 (O), 5/5 (4), 7/3 (0), and 10/0 (2).
∑wi log ηi0
(4)
Here wi is the weight fraction of each component polymer in the mixed system and ηi0 is the zero-shear viscosity of the 30% solution of each component polymer. Effect of Phase Separation. Figure 9 shows the frequency dependence curves of G′ and G′′ for the mixed systems of 3/7, 5/5, and 7/3 at various temperatures from -20 to 50 °C. These are master curves which are obtained by applying the time-temperature superposition principle to the data in the relatively high frequency region. A long-time relaxation process can be observed clearly in the low frequency region of G′ at temperatures beyond ca. 20 °C for the systems of 3/7 and 5/5. It is likely that the relaxation process is attributed to the heterogeneity due to the phase separation of the systems, as shown in Figure 5. It should be noted that the system of 7/3 does not clearly show a plateau region due to the heterogeneity in spite of the fact that the system shows the microscopic phase separation as shown in Figure 5. This point will be discussed in relation to the emulsion model in the next section. Figure 10 shows the shift factor aT in the timetemperature superposition on the above systems. The value of aT at each temperature is almost independent of the mixing ratio of PES/PSF. The temperature dependence of the shift factor can be represented by the WLF relation,10 which is shown by the solid line in Figure 10. The parameters in the WLF equation are C1 ) 4.63 and C2 ) 194.6 °C at the reference temperature 23 °C. Figure 11 shows the frequency dependence of G′ and G′′ for the system of 3/7 at various strain amplitudes. The strain dependence can be observed rather slightly at the plateau region of G′ and cannot be observed in high- and low-frequency regions where G′ is proportional to ω2. This result is congruent with our previous results for the disperse systems of solid particles.11 Although the effect of strain must also appear in G′′ corresponding to G′, it is difficult to detect that effect. That is, G′ is more sensitive to the strain than G′′. Figure 12 shows the relaxation spectrum, H(τ), for the system of 3/7 which was calculated from G′ and G′′ at the strain of 20% using Tschoegl’s second-order approximation.12 The spectrum calculated from G′ coincides well with that from G′′ within an incidental error in the approximation. This indicates that the nonlinearity of the system is not so marked and that the G′ and G′′ shown in Figure 11 are measured with enough accuracy. A characteristic relaxation time τw can be calculated from the relaxation spectrum by the equation
∫-∞∞τ2H(τ) d ln τ τw ) ∞ ∫-∞τH(τ) d ln τ
(5)
The value of τw can be obtained as ca. 1.1 s, as shown by the arrow in Figure 12. The shift factor aT in Figure 10 is 0.36 at 50 °C for the reference temperature 23 °C; i.e., τ50/τ23 ) 0.36. That is, the characteristic relaxation time τw corresponds to ca. 3.1 s at 23 °C. This relaxation time must be related to the deformability of the microscopic phase. Analysis Using the Emulsion Model. The emulsion model was derived for a simple disperse system of spherical particles. Using eq 2, the plateau modulus Gp and a Figure 8. Logarithm of zero-shear viscosity plotted against the weight fraction of PSF in the systems of PES/PSF 30.
η0 of the mixed solutions plotted against the weight fraction of PSF in the system of PES/PSF 30. The relationship is
(10) Ferry, J. D. Viscoelastic Properties of Polymers, 3rd ed.; John Wiley & Sons: New York, 1980; Chapter 11. (11) Matsumoto, T.; Hitomi, C.; Onogi, S. Trans. Soc. Rheol. 1975, 19, 541. (12) Tschoegl, N. W. Rheol. Acta 1971, 10, 583.
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Figure 10. Temperature dependence of the shift factor aT for the time-temperature superposition.
Figure 11. Effect of strain amplitude on the frequency dependence of G′ and G′′ for the system of 3/7.
Figure 9. Frequency dependence curves of G′ and G′′ for the mixed systems of 3/7 (a), 5/5 (b), and 7/3 (c) at various temperatures.
Figure 12. Relaxation spectra for the system of 3/7 which are calculated from G′ (O) and calculated from G′′ (4) at the strain amplitude 20% in Figure 11.
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Table 2. Various Parameters for Application of the Emulsion Model PES/ PSF
ηi (Pa s)
ηm (Pa s)
τi (10-3 s)
τm (10-3 s)
φ
R (µm)
7/3 3/7
35.5 (PSF) 5.4 (PES)
5.70 32.0
5.63 0.741
0.829 5.26
0.285 0.165
6.17 4.15
characteristic relaxation time τd are represented by the equations6
20R 1 φ R [2K + 3 - 2φ(K - 1)]2
(6)
R ηm(19K + 16)[2K + 3 - 2φ(K - 1)] 4R 10(K + 1) - 2φ(5K + 2)
(7)
Gp )
τd )
Here τd corresponds to the geometric relaxation time in the shape change of the deformed particle. The phase separation pattern is spherical in the systems of 3/7 and 7/3, but it is relatively complex in the system of 5/5. Consequently, the emulsion model will be applied to the systems of 3/7 and 7/3. The microscopic phase separation of these systems is so stable that the phase separation pattern does not change with centrifugation for more than 60 min at ca. 104g. According to the estimation by the photographs of Figure 5, the volume fraction φ and the average radius R of the inclusion droplets are φ ) 0.165 and R ) 4.15 µm for the system of 3/7 and 0.285 and 6.17 µm for the system of 7/3 at 23 °C, respectively. The system of 7/3 separated into two macroscopic phases after more than 5 months. The volume fractions of the upper and the lower phases were 0.11 and 0.89. It is reasonable to consider that the upper phase corresponds basically to the inclusion droplets and the lower phase corresponds to the matrix of the system of 7/3. These volume fractions respectively coincide well with the values of 0.10 and 0.90 calculated from the fraction of the length of tie line at 23 °C, x/y ) 7/3 in Figure 3. On the other hand, the system of 3/7 has held the microscopic phase separation for more than 7 months. Consequently it is impossible to know separately the viscosity values of the inclusion and the matrix at the time when the viscoelasticity was measured. Considering these facts, it is reasonable to use the values estimated from the photographs as the volume fraction of the inclusion, i.e. 0.285 for the system of 7/3 and 0.165 for the system of 3/7. Table 2 shows various parameters employed for applying of the emulsion model for the systems of 3/7 and 7/3. The following approximation is assumed to estimate the viscosity values of the inclusion ηi and the matrix ηm when the systems exist in the stable microscopic phase separation states. It is basically assumed that the major component forms the matrix and the minor component forms the inclusion.12 However the volume fraction of the inclusion φ is smaller than 0.3 in both the systems of 7/3 and 3/7. That is, the values of φ are 0.285 for the system of 7/3 and 0.165 for the system of 3/7. So, it was assumed that the difference between 0.3 and the volume fraction of each system dissolved from the inclusion to the matrix. According to this assumption, we can employ the viscosity values of PSF and PES for the viscosities of inclusions of the systems of 7/3 and 3/7, respectively. And the viscosity of the matrix ηm can be estimated from Figure 8. Maxwell relaxation is sufficiently applicable to the inclusion and the matrix. τi and τm are the Maxwell relaxation times of the inclusion and the matrix. Figure 13 shows the comparison between the experimental data and theoretical results by the emulsion model for the systems of 3/7 and 7/3. The best fitting curves can be obtained by fitting the plateau modulus Gp in eq 6 to
Figure 13. Comparison between the experimental data and theoretical results by the emulsion model for the systems of 3/7 (a) and 7/3 (b).
Figure 14. Comparison between the experimental data and theoretical results by the emulsion model for the systems of 3/7, assuming that the inclusion and matrix are composed of PES and PSF and that φ ) 0.3.
the height of the plateau region of G′ using various values of interfacial tension R. The value of R by which the best fitting curves can be obtained is 0.018 mN/m. The value of R is much smaller than the value for the blends of
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polymer melts, e.g. 5 mN/m.12,13 This point must be a reason why the microscopic phase separation can be held stably for such a long time in the systems employed in this experiment. The values of Gp and τd are 1.1 Pa and 11.9 s for the system of 3/7 and 0.11 Pa and 15.3 s for the system of 7/3. It is reasonable to consider that the plateau modulus is so small that it is difficult to observe the plateau region in the system of 7/3. As described in the previous section, the characteristic relaxation time τw is ca. 3.1 s at 23 °C and this value is different from τd, 11.9 s for the system of 3/7. The cause of this difference is not clear at the present time. The above comparison method is rather complex. It might be useful to show the result by a more simple comparison method. Figure 14 shows the comparison between experimental data and the theoretical curves for (13) Bousmina, M. M.; Bataille, P.; Sapieha, S.; Schreiber, H. P. J. Rheol. 1995, 39, 499. (14) Utracki, L. A. Polymer Alloys and Blends; Carl Hanser Verlag: Munich, 1978; p 147.
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the system of 3/7, assuming that the inclusion and matrix are composed of PES and PSF solutions, respectively, and the volume fraction of the inclusion is 0.3. Two theoretical curves are shown. One is the curve for R ) 0.018 mN/m, and the other is for R ) 0.010 mN/m, which is the best fitting curve under these conditions. The fitting between the data and the theoretical curve is not so good in comparison with the result shown in Figure 13a, and also it should be noticed that the value of R is smaller than the value in Figure 13a. From these considerations of the viscoelastic data, it is suggested that it might be possible to get information for the heterogeneous systems such as the interfacial tension between the two phases and also the geometric relaxation time of the deformed particle. Acknowledgment. The authors thank Prof. Toshiro Masuda, Department of Material Chemistry, Kyoto University, for his invaluable discussion. LA9602269
