Article pubs.acs.org/Macromolecules
Shear Induced Phase Boundary Shift in the Critical and Off-Critical Regions for a Polybutadiene/Polyisoprene Blend Fasheng Zou,† Xia Dong,*,† Wei Liu,† Jian Yang,† Demiao Lin,† Aimin Liang,‡ Wei Li,‡ and Charles C. Han*,† †
State Key Laboratory of Polymer Physics and Chemistry and CAS Key Laboratory of Engineering Plastics, Joint Laboratory of Polymer Science and Materials, Beijing National Laboratory for Molecular Science, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, China ‡ Yanshan Branch, SINOPEC Beijing Research Institute of Chemical Industry, Beijing 102500, China ABSTRACT: The rheology of near- and off-critical elastomeric blends of polybutadiene (PB)/ low vinyl content polyisoprene (LPI) has been studied as a function of temperature, heating rate, and shear frequency. Depending on the composition, near or far away from the critical point, blends showed different behaviors in several aspects: temperature ramp curves, shift of the apparent binodal and spinodal points under oscillatory shear at the given frequency and strain amplitude. The composition dependent rheological responses are interpreted by the differences in the amplitude of the critical fluctuation near the phase boundary and in the shear induced mixing mechanisms between near- and off-critical blends. For near-critical blends, the critical fluctuation is large enough to induce a considerable extra stress when the blend is still in the miscible state. As a result, a heating rate independent upturn of G′ can be observed and the apparent spinodal point can be greatly shifted through the strong suppression of the large critical fluctuations. In contrast, for off-critical blends, the critical fluctuations in the metastable region are relatively small and there is competition between the phase separation kinetics and the heating rate. Therefore, the blend displayed a heating rate dependent apparent binodal point and a large shift of the apparent binodal point but a moderate shift of the spinodal point under oscillatory shear. By lowering or extrapolating the measured frequency to a very small value (0.1 rad/s in this study) for both binodal and spinodal points, the rheologically determined phase diagram is consistent with the static results obtained by optical microscopy observations.
1. INTRODUCTION The rheology of polymer blends has long been the interests from both fundamental and industrial viewpoints. After some important advancements were obtained in the understanding of the linear and nonlinear rheology of immiscible polymer blends in the past decades,1−7 researchers generally turned their attention toward the miscible or partially miscible polymer blends and on the rheological responses near the boundary of the phase separation. Within the miscible region, research was mainly focused on the concentration dependence of viscosity and linear dynamic properties which can be usually determined by a simple or modified Irving relationship.8−12 Within the phase-separated region, on one hand, the phase-separated structures like the droplet-matrix structure and bicontinuous structure in polymer blends can be reflected by rheological responses which are typically analyzed with the frequency dependence of the storage modulus.13−16 On the other hand, the linear viscoelastic behavior of polymer blends with a droplet-matrix morphology can be described quantitatively by several emulsion models which were developed independently by Palierne, Gramespacher and Meissner, and Bousmina et al.2−4 Besides, these models have been widely used to obtain © 2012 American Chemical Society
either structure information (domain size and distribution) or interfacial tension.17−19 Partially miscible polymer blends in the phase transitional region also exhibit interesting rheologcial behavior. One of the most exciting results is that the rheological responses in this phase transitional region has been studied theoretically and experimentally to obtain the binodal and spinodal points of either lower critical solution temperature (LCST) or upper critical solution temperature (UCST).10,20−25 However, recent developments26−28 showed that rheological determination of the binodal and spinodal points may be more complicated than the traditional experimental descriptions.20,21 Once the measured macroscopic rheological material functions are coupled with the phase separation kinetics, the temperature ramp rate effect on the determination of the binodal and/or spinodal points could occur and must be accounted for in the analysis. Besides, it has been reported that oscillatory shear flow could also affect the thermodynamics and result in shear induced mixing and/or demixing depending on the viscoelastic Received: September 23, 2011 Revised: November 21, 2011 Published: January 23, 2012 1692
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where ai is the statistical segment length of repeated unit, χs designates the interaction parameter at the spinodal point, and χ is the interaction parameter. It is this expression that has been used to obtain the spinodal points. If further assuming that the interaction parameter χ is given by the form χ = A + B/T, the following expression can be deduced from eq 1
properties of the specific polymer blends.27−29 Currently, it is believed that oscillatory shear does not affect the phase separation kinetics or the shift of the phase boundary if the strain rate or stress is small enough or the frequency is low enough.20−23 However, it is not clear to what extent the coupling between thermodynamic and the applied strains and stresses can be neglected or what kind of extrapolation procedures are needed in order to obtain the real thermodynamic steady state phase boundary and unperturbed phase separation kinetics. In this work, polybutadiene (PB)/low vinyl content polyisoprene (LPI) blends with the LCST type phase diagram are investigated by rheological measurements. There have been some reports on the PB/LPI blends about their microstructure and cross-link effects on miscibility,30,31 phase separation kinetics under a quiescent state,32−34 oscillatory shear,26,35 or steady shear.36,37 A shear induced mixing situation is always the case for PB/LPI blends under both simple shear and oscillatory shear since these are dynamically symmetrical systems we are dealing with. In addition, unlike the PS/PVME blends, no viscoelastic phase separation needs to be considered.38−40 It is believed that PB/LPI blends can serve as a model polymer blend for studying the normal liquid−liquid phase separation (LLPS) effect on a dynamically symmetrical system by rheology. In this study, we discuss how the LLPS influences the viscoelastic properties of a dynamically symmetrical system and emphasize the basic physics of how to eliminate or extrapolate out the shear influence on the phase boundary and the phase separation kinetics.
⎡ G′′2 (ω) ⎤2/3 B⎛ 1 1⎞ ⎥ ⎢ = ⎜ − ⎟ C ⎝ Ts T⎠ ⎣ G′(ω)T ⎦ where C is given by
⎫ ⎛ 30π ⎞2/3⎧ a12 a 22 ⎬ C=⎜ + ⎟ ⎨ 36(1 − φ) ⎭ ⎝ kB ⎠ ⎩ 36φ
⎪
⎪
⎪
(χs − χ)−3/2
⎪
⎪
⎪
(3) 2/3
Thus a linear dependence of {G″ (ω)/[G′(ω)T]} versus 1/T could be expected, which leads to an intercept at 1/T axis denoting the spinodal temperature, Ts. During the temperature ramp tests, the global storage and loss modulus measured generally include more than one kind of contributions.26,27 However, in Ajji and Choplin’s treatment, only the contribution from critical fluctuations is considered. Therefore, it is understandable that the phase separation kinetics will also affect the extrapolated position of the spinodal temperature as long as the contribution from the interfacial tension part is not negligible. 2.2. Shear Induced Mixing under Oscillatory Shear. In the theoretical calculation,43−45 e.g. the kinetics equations, shear rate is normally used but not the shear frequency or the shear amplitude. Therefore, there is still no well-defined theory for the phenomenon of shear induced mixing under oscillatory shear. In this study, we will only use our basic knowledge about phase separation under steady shear and make an analogy between steady shear and oscillatory shear. For near-critical blends, a useful starting point is the mode-coupling renormalization-group (MCRG) theory of the simple binary fluids under shear.43−45 According to MCRG theory, once γ̇τξ > 1, where γ̇ is the shear rate and τξ is the characteristic relaxation time for concentration fluctuation, the concentration fluctuation should be distorted by the shear and shear induced mixing starts to happen. For off-critical blends, the shear induced mixing should affect the nucleation phenomena more.46−48 For nucleation phase separation under shear flow, if the shear is strong enough to suppress the critical droplet size, that is Rc > R*, where Rc is the critical radius of nucleation and R* is the Taylor break-up size, then no nucleation phase separation could happen.49
3. EXPERIMENTAL SECTION 3.1. Materials. Two polymers with statistical distributed microstructures (PB and LPI) used in this study were supplied by Beijing Yanshan Petrochemical Co., Ltd. Both of them were synthesized by anionic polymerization. The number-average molecular weight (Mn), the mass-average molecular weight (Mw), and the polydispersity of the model polymers were determined by gel permeation chromatography (GPC) using polystyrene as standard in our laboratory. The composition of these materials was obtained by 2H nuclear magnetic resonance (NMR). The results of the polymer characterization are summarized in Table 1. In order to make a comparison with our previous results,18,26,27 the PB/LPI blend is labeled as LPIx, where x represents the volume fraction of LPI in the blend. 3.2. Sample Preparation. The PB/LPI blends were prepared by a solution blending method.18 We started with a dilute solution (mass fraction of 2% of the total polymer), which contains the antioxidant
2 ⎫3/2 a 22 30π ⎧ a1 ⎨ ⎬ = + kBT ⎩ 36φ 36(1 − φ) ⎭ G′′2 (ω) ⎪
⎪
2
2. THEORETICAL BACKGROUND 2.1. Rheological Determination of the Binodal and Spinodal Points. For a multicomponent polymer blend, its viscoelastic properties such as storage modulus G′ and loss modulus G″ are generally related to three kinds of contributions:27 the bulk part from the polymer chain dynamics and entanglements, G′bulk or G″ bulk, the concentration fluctuations from thermal noise, G′fluctuation or G″fluctuation, and the interfacial contribution due to the phase-separated domains, G′interface or G″interface. In temperature ramp rheological measurements, when the blend is in the miscible region far from the spinodal point, its viscoelastic properties are mainly determined by the contribution from the bulk part. As the temperature approaches the spinodal point, G′fluctuation (or G″fluctuation) becomes larger and larger and may cause the global storage modulus (or loss modulus) to display an observable increase. Besides, once the blend is in the two-phase region, either in the metastable region or in the unstable region, the phase-separated domains can contribute to the complex modulus as well. Thus, it is believed that a quantitative extracting of the “real” binodal point is a doable but challenging task in a temperature ramp rheological measurement. In contrast, the determination of a spinodal point is normally based on the theoretical work of Fredrickson and Larson41 as well as Ajji and Choplin.42 An important expression that can be drawn from the above theories is the ratio of G′(ω)/G′′2(ω),
G′(ω)
(2)
(1) 1693
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Table 1. Characterization Results of Polymers microstructure, mol % sample code
Mn (g/mol)
Mw/Mn
density (g/cm3)
Tg (°C)
1,4
1,2
3,4
PB LPI
55 000 34 000
1.10 1.50
0.877 0.895
−97 −63
89 88
11 0
0 12
butylated hydroxytoluene (BHT) with mass fraction 0.02% of the solution in a solvent of methylene chloride. Then the solution was filtered through a 0.45 μm Millipore filter, and the solvent was evaporated at 35 °C with stirring. Samples were further dried in a vacuum oven at 35 °C for a week in order to remove the residual methylene chloride. 3.3. Experiments. 3.3.1. Rheologcial Measurements. All the rheological measurements were performed by an Advanced Rheometric Expansion System (ARES, Rheometric Scientific, Piscataway, NJ), which is a strain-controlled rheometer with a parallel plate−plate fixture (25 mm diameter), and a testing gap value of 0.5 mm between two plates was used. Temperature control in the rheometer is carried out by hot nitrogen gas with an accuracy of ±0.1 °C. Before measurements all blends were kept at 4 °C in a refrigerator and then put into a vacuum oven at 35 °C for 2 days to remove air bubbles and to ensure the same thermal history. The following oscillatory shear experiments were carried out in the steady state region of the blends,26 as was verified by preliminary amplitude sweep tests: (i) Dynamic temperature ramp tests were carried out by measuring storage and loss modulus at a fixed frequency and different heating rates (0.2 and 1.0 °C/min) from miscible region to the two-phase region at a constant strain (10%). (ii) Shear quench experiments were performed at a series of temperatures which included the single-phase and two-phase regions at a fixed frequency and a given strain of 10%. The detailed procedure of the shear quench experiments is as follows: first the dynamic temperature ramp tests at a frequency of 25 rad/s and strain amplitude of 10% were conducted to reach a certain temperature, and at this temperature there was no apparent phase separation at 25 rad/s. Then the temperature was held at the specified value, and the test mode was switched to a time sweep mode at a constant but lower frequency and strain amplitude of 10%. All the measurements started from 40 °C, where all blends are in the single-phase region under quiescent conditions. 3.3.2. Optical Microscopy (OM). An Olympus (BX51) phase contrast optical microscope (PCOM) was applied, and the results were recorded with an Olympus (C-5050ZOOM) camera. The experimental temperature was controlled by a Linkam (LTS 350) hot stage, and fresh nitrogen gas was circulated in the hot stage to avoid possible thermal degradation. Samples were sandwiched between a clean microscope slide and cover glass with a spacer about 30 μm in thickness. In order to obtain the static phase diagram of this polymer blend, the prepared blend was heated in 5 K increments and then annealed for a sufficient time to form observable domains, and typically the annealing time was from 2 to 24 h. Near the transitional temperature, the intervals were reduced to 2 K for better accuracy.
Figure 1. The static phase diagram of PB/LPI blend obtained by PCOM observations and rheological measurements. The solid and dash curves are the least-squares fit for a polynomial equation through the experimental data and are only used to guide the eye.
been focused on the compositions of the right half of the phase diagram, namely the LPI50, LPI60, LPI70, and PI80. 4.2. Temperature Ramp Experiments. Among the rheological measurements, the temperature sweep or ramp test at a fixed frequency is most widely used to investigate the binodal phase separation temperatures. There have been some papers that reported21−24 a single shear rheological temperature ramping measurement is sufficient to determine both the binodal and spinodal curves. However, in this study, we shall demonstrate that distinguished discrepancies in temperature ramp curves can be observed between near- and off-critical blends. This indicated that the rheological determination of the binodal and spinodal points may be more complicated than the traditional experimental procedures used.20,21 Figure 2 showed the typical temperature ramp curves of two near-critical blends (LPI50 and LPI60) and two off-critical blends (LPI70 and LPI80) at a fixed frequency of 0.25 rad/s and different heating rates of 1.0 and 0.2 °C/min. As shown in Figure 2, two nearcritical blends displayed the heating rate independent initial upturn of G′, while two off-critical blends displayed that the slower the heating rate the lower the temperature at which G′ started to increase. By closely examining the temperatures at which G′ started to increase, four temperature values (59.0 ± 1, 63.0 ± 1, 78.5 ± 1, and 95.0 ± 1 °C) were obtained for LPI50, LPI60, LPI70, and LPI80 (from the lowest heating rate), respectively. Then the first qualitative discrepancy in temperature ramp curves between near- and off-critical blends is as follows: the static binodal temperatures are higher than the apparent turning points in the rheological measurements for near-critical blends and lower than the rheological measured apparent turning points for off-critical blends. And this can be interpreted as follows. For two near-critical blends, it is believed that the initial upturn of G′ is attributed to the large critical fluctuations near the critical region. Such an analysis can be proved by comparing the temperature at which G′ starts to increase with its corresponding static cloud point, Tb(0), which was determined by optical microscopy. It is obvious that, for either LPI50 or LPI60 blend, the static cloud point is above the temperature at which G′ has encountered the fluctuation contribution and starts to increase. When the composition of G′ measurements is far away from the critical composition, the critical fluctuations near the binodal phase boundary become weaker and weaker. Therefore, for off-critical blends, the initial
4. RESULTS AND DISCUSSION 4.1. Phase Diagram under Static State. Before the rheological measurements, PCOM observations have been performed to investigate the miscibility of the PB/LPI blends under the static state. As is shown in Figure 1, the PB/LPI system displayed an LCST type phase diagram with the critical temperature at about 64.0 ± 1 °C. The critical composition of LPI is about 0.5 by volume fraction, which agrees with the calculated value, 0.485, from the Flory−Huggins theory. In our studies, we simply separate our blends into two categories: offcritical blends (LPI20, LPI30, LPI70, and LPI80) and nearcritical blends (LPI40, LPI50, and LPI60). As the phase diagram is rather symmetrical, more systematic studies have 1694
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Figure 2. Temperature ramp results of G′ at the fixed frequency of 0.25 rad/s and different heating rates of 1.0 and 0.2 °C/min for (a) LPI50, (b) LPI60, (c) LPI70, and (d) LPI80. Tb(0) as shown in Figure 2a−d are the static cloud points which were obtained by PCOM.
Figure 3. Temperature ramp results of G′ at the fixed frequency of 1.0 rad/s and different heating rates of 1.0 and 0.2 °C/min for (a) LPI50 and (b) LPI80.
upturn of G′ can come only when the nucleation phase separation process started which happens after the temperature has increased to a value higher than the binodal temperature. From Figure 2c,d, it seems that the detection of the phaseseparated domains needed a rather large quench depth into the metastable region. However, what we should keep in mind is the competition between the nucleation phase separation kinetics and the heating rate. Figure 2c,d showed that a slower heating rate results in a lower apparent binodal point although they are all above the real binodal temperatures of Tb(0). Another important effect we should keep in mind is that shear induced mixing can raise the apparent binodal points also. As
either the two near-critical blends or the two off-critical blends should have similar rheological responses, in the next section, we mainly focus on LPI50 and LPI80. In Figure 3 we showed the temperature ramp curves of LPI50 and LPI80 at a fixed frequency of 1.0 rad/s, which is 4 times that used for the data shown in Figure 2. Again different heating rates of 1.0 and 0.2 °C/min were used. Compared with Figure 2a and d, a heating rate independent initial upturn of G′ for LPI50 and a heating rate dependent apparent binodal point for LPI80 still exist at the higher frequency of 1.0 rad/s. And the rise in temperature at which G′ started to increase for either LPI50 or LPI80 with higher frequency is generally believed to be the shear induced 1695
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Figure 4. Time evolution of G′ at the frequency of 1.0 rad/s after the shear quench from the frequency of 25 rad/s at different temperatures for (a) LPI50 and (b)LPI80. Data points are shifted vertically to avoid crossover. The experimental data for 67 and 96 °C are original data, and the shift values for each higher temperature for LPI50 and LPI80 are 40 and 30 dyn/cm2, respectively.
mixing effect.18,26−28 In fact, since the main contributions to the initial upturns of G′ in temperature ramp curves are quite different between near- and off-critical blends, the determination of the apparent binodal points should also be treated differently. Up to now, it is believed that the apparent binodal point for near-critical blends should be higher than the temperature at which G′ starts to increase in their temperature ramp curves. However, it is still not clear which point of the temperature ramp curve is more suitable for assignment as the apparent binodal point. Although the inflection point of the temperature ramp curves had been used as the apparent binodal point by several research groups,20−22,38 they also stated that such a method had no significant physical base. Besides, as shown in Figure 3a, the LPI50 blend displayed different inflection points at different heating rates, which causes the determination of the apparent binodal point to become more confusing. For off-critical blends, although the temperature where G′ starts to increase in the temperature ramp curve can be assigned as the apparent binodal point, the “real” binodal point should be obtained by extrapolating the heating rate to 0 °C/min. Since the heating rate effects on the apparent binodal point are usually very complex,28 the heating rate extrapolation for the apparent binodal point was rarely reported. Thus, in the next section we will use the shear quench experiments to detect the phase separation temperature. 4.3. Shear Quench Experiments. Earlier studies from our group26,27,36 and the above results of LPI50 and LPI80, both demonstrated that shear induced mixing could take place for either near- or off-critical blends. From the early work of Zhang et al.,27 shear quench experiment can be used as an adequate technique to investigate the phase separation temperature and the phase separation kinetics of polymer blends. The details of these shear quench experiments have been described in the “Experimental Section”. The basic theoretical foundation for this treatment is the assumption that the higher shear rate could shift the binodal temperature more than the lower shear rate. Figure 4 showed the time evolution of G′ of LPI50 and LPI80 at the frequency of 1.0 rad/s after the shear quench from 25 rad/s at various temperatures which cover the apparent onephase (homogeneous) and two-phase regions. It showed that both blends displayed one or two transformation temperatures below and above some temperature where the curves of G′ versus scan time t are quite different. As the LPI50 blend is rather close to the critical composition, the metastable region is
assumed to be quite narrow. Therefore, its time evolution curves of G′ display two types which defines the critical temperature (68.0 ± 1 °C) below which G′ is almost constant with scan time t. At a temperature higher than the critical temperature, a monotonous decrease of G′ versus scan time t is observed, which is generally related to the structure evolutions of spinodal decomposition.16,50,51 The simple intuitive physical explanation is that once the system is shear quenched back into the spinodal region, the spontaneous phase separation is very fast. The contribution of the growing domains (or structures) to G′ becomes negative (when size is over 1 μm for this kind of system26) in a very short time. All the time scan observations in Figure 4a for 71 and 69 °C are due to the continuous growth of phase separating structures. In contrast, G′ of the LPI80 blend displayed three types of time evolution behaviors. Except for the nearly constant G′ at low temperatures and the monotonous decrease of G′ at high temperatures versus scan time t, which is similar to the near-critical blend LPI50, an obvious initial increase of G′ versus scan time t is observed at the intermediate temperature region. The increase of G′ versus scan time t is generally related to the nucleation phase separation process.16,27,50,51 Thus, through the above shear quench experiments, we obtained the critical temperature (namely 68.0 ± 1 °C) for LPI50 and the apparent binodal and spinodal points (namely 97.0 ± 1 and 121 ± 1 °C, respectively) for LPI80 at the given frequency of 1.0 rad/s. Compared with the results shown in Figure 3a,b, we find that these two apparent binodal points (68.0 ± 1 and 97.0 ± 1 °C) basically correspond to the temperature at which G′ has increased and the temperature at which G′ starts to increase in their temperature ramp curves. In other words, our shear quench experiment results are consistent with the temperature ramp results and our interpretation. 4.4. The Shift of Apparent Binodal and Spinodal Point under Oscillatory Shear. Figure 5 showed the apparent binodal points for LPI50 and LPI80 as a function of the final frequency of the shear quench experiments. Both blends displayed a relatively larger shift of the apparent binodal point in the low frequency region (from 0.1 to 1.0 rad/s) and a trend of saturation of shear induced mixing in the high frequency region (from 1.0 to 2.5 rad/s). Besides, at the frequency of 0.1 rad/s (the lowest frequency which we have used), the apparent binodal point for LPI50 has reached its static value (66.0 ± 1 °C), while the apparent binodal point for LPI80 is already well 1696
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temperature, T is the experimental temperature, and ν is the Ising exponent, τξ becomes smaller and smaller as the temperature moves away from Tc. Therefore, it is more difficult to suppress the concentration fluctuation by increasing the temperature quench depth. The maximum strain rates under an oscillatory shear of 0.1 and 2.5 rad/s are not too big, and the corresponding values are 0.01 and 0.25 s−1, respectively. Consequently, we observed that the shift of the apparent binodal point is relatively small for LPI50 within our experimental conditions. For off-critical blends, the shift of the apparent binodal point under oscillatory shear should be even smaller if suppression of the concentration fluctuation effect is the main mechanism for the apparent shift of the binodal points. However, we observed a larger shift of the apparent binodal point as a function of the final frequency or shear rate. Therefore, we believe that this large shift of the apparent binodal point is due to the shear effect on the nucleation phenomena.46−48 Generally, there exist two characteristic sizes for nucleation phase separation under shear,49 Rc and R*, where Rc is the critical radius of nucleation due to free energy barriers and R* is the Taylor break-up size due to the rupture of droplets by shear flow. The observation of appreciable droplets of the new phase requires the critical droplet not to be suppressed by shear, which means Rc < R* must be satisfied. Since the critical size of nucleation, Rc, increases with deceasing quench depth and tends to infinity as the binodal point (or coexistence curve) is approached, the critical droplet can be easily suppressed by shear near the binodal phase boundary. Therefore, the oscillatory shear with low frequency may greatly shift the binodal point as shown in Figure 5. The rheological investigation of spinodal point also showed distinct differences between near- and off-critical blends. Technically, each temperature ramp curve can be analyzed by the plot of (G″2/G′T)2/3 vs 1/T to acquire its corresponding spinodal point. In Ajji and Choplin’s theory,42 only the contribution from critical fluctuations is considered in their analysis and the shear suppression (or distortion) of critical fluctuations has been neglected. However, the global storage and loss modulus measured generally also included the contribution from the nucleation phase separation as displayed in off-critical blends. Besides, once we apply Ajji and Choplin’s theory to off-critical blends, the assumption that the critical fluctuations at off-critical region are similar to that at the critical
Figure 5. Shear quench experiments determined apparent binodal temperature as a function of the final frequency for LPI50 and LPI80. As a reference, the static cloud points of LPI50 and LPI80 are shown as open symbols.
above its static value (85.0 ± 2 °C). Consistent results have been obtained from other composition blends, as will be shown in Figure 8. These observed phenomena with different apparent phase boundary shifts may be rationalized by two different theories on the shear induced shift of the phase boundary between near- and off-critical blends. For near-critical blends, a useful starting point is the mode-coupling renormalizationgroup (MCRG) theory of the simple binary fluids under shear.43−45 Since all the rheological measurements in this study were carried out under oscillatory shear, the maximum strain rate (for a given frequency and strain amplitude) instead of the shear rate is used, although it is understandable that the shear rate is the correct quantity which can be expressed in a kinetic equation for a theoretic analysis. However, in order to make a good comparison with many studies published on binary systems with oscillatory measurements, and also to make possible temperature and time (kinetics) dependent measurements of the system, the oscillatory measurement was selected in this study. According to MCRG theory, once γ̇τξ > 1, where γ̇ is the shear rate and τξ is the characteristic relaxation time of concentration fluctuation, the concentration fluctuation should be distorted and shear induced mixing starts to happen. However, since τξ ∝ |T/Tc − 1|−3ν if we assume the symmetry in fluctuations in a two-phase region,52,53 where Tc is the critical
Figure 6. Plots of {G″2/(G′T)}2/3 and {G″2(ω,0)/[G′(ω,0)T]}2/3 versus 1/T in temperature ramp tests at a fixed frequency of 1.0 rad/s and different heating rates of 1.0 and 0.2 °C/min for (a) LPI50 and (b) LPI80. 1697
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region is needed. Figure 6 showed the plots of (G″2/G′T)2/3 vs 1/T for blends LPI50 and LPI80 at the frequency of 1.0 rad/s and different heating rates of 1.0 and 0.2 °C/min. In order to eliminate the influence of the contribution from nucleation phase separation on the extrapolated position of the spinodal point,27 the shear quench experiment result {G″2(ω,0)/ [G′(ω,0)T]}2/3, where G′(ω,0)3 and G′′(ω,0) are the initial storage and loss modulus values during the dynamic time sweep after the shear quench from 25 rad/s to 1.0 rad/s at a given temperature, is also included. The essence of such a shear quench method is to measure the contribution only from critical fluctuations to the storage and loss modulus in the metastable region. For example, after the shear quench from 25 rad/s to 1 rad/s at 98 °C, the LPI80 blend will take a nucleation phase separation as shown in Figure 4b since it is in the metastable region at 1 rad/s.” However, because of the slow kinetics of the nucleation phase separation, G″(ω,0) and G′(ω,0) have minimum contribution from the nucleation phase separation and are mainly affected by the critical fluctuations. From Figure 6 we observed that, for the LPI50 blend, since G′ values in the linear part of the curve (G″2/G′T)2/3 vs 1/T basically come from the critical fluctuations near the critical region as shown in Figure 3a, the heating rate hardly changes the extrapolated position of the spinodal point and the shear quench method gives the same spinodal point (82.8 ± 2 °C) as shown in Figure 6a. In contrast, for LPI80 blend, both critical fluctuation and nucleation phase separation contributed to G′ in the linear part of the curve (G″2/G′T)2/3 vs 1/T. Furthermore, G′ values which were used to estimate the spinodal point have their main contribution coming from the nucleation phase separation processes as have been discussed in Figure 3b; therefore, there is a strong heating rate (or time) dependence for the extrapolated spinodal point, and the shear quench method gives the highest spinodal point, 120.4 ± 2 °C. In fact, this value is in good agreement with the second transformation temperature (121 ± 1 °C) shown in Figure 4b. Again, it is found that the extrapolation was done mainly to the data from the temperature region between the binodal and spinodal point, which probably means that, for off-critical blends, by only going through into the metastable region and in the vicinity of the spinodal point the blend may be able to achieve a large enough concentration fluctuation. Figure 7 showed the extrapolated spinodal points from shear quench experiments as a function of
the quenched final frequency for LPI50 and LPI80. The spinodal points obtained for both blends increase with frequency. Quantitatively, in the low frequency region (from 0.1 to1.0 rad/s) the shift of the spinodal point of LPI50 is more distinguished than that of LPI80, which probably means that the suppression of critical fluctuation is more serious for LPI50 than that for LPI80. For near-critical blend LPI50, the critical fluctuation near the phase boundary is rather strong so that it is more easily suppressed by the applied oscillatory shear. In contrast, for off-critical blend LPI80, the critical fluctuation in the metastable region is relatively weak; therefore, only under high frequency, e.g. 2.5 rad/s, the shift of the spinodal point is distinguishable. The composition discrepancy in the shift of the apparent binodal and spinodal points with frequency is more obvious as illustrated in Figure 8. All the data are obtained from shear quench experiments as described above. From Figure 8
Figure 8. Shear quench experiments determined apparent binodal points (Tb) and spinodal points (Ts) at the final frequency of 0.1 and 1.0 rad/s. The dash and solid curves are the least-squares fit for polynomial equation through the experiment data and are only used to guide the eye.
we can observe that the slight shift of binodal points with frequency is accompanied by a large shift of spinodal points for three near-critical blends (LPI40, LPI50, and LPI60). In contrast, for four off-critical blends (LPI20, LPI30, LPI70, and LPI80), the shift of the binodal point with frequency is only a little larger than that of the spinodal point. Since the oscillatory shear induced shifts of the binodal point and spinodal point are quite different, especially for near-critical blends, it is found that there is no critical point at which the binodal curve contacts the spinodal curve at the frequency of 1.0 rad/s as shown in Figure 8. However, it is noteworthy to state that the rheologically determined phase boundary under the oscillatory shear frequency of 1.0 rad/s is the “apparent” value which included the coupling between the thermodynamics and the oscillatory shear flow. Due to the obvious shift of both binodal and spinodal points under oscillatory shear, we can conclude that, in order to acquire a phase diagram that can be compared with its static phase diagram of polymer blends by rheological measurements, extrapolations of both the binodal and spinodal point measurements to 0 rad/s are necessary. However, since there is no measurement if the frequency is set at 0 rad/s and there is no theory regarding the frequency extrapolation scheme of either the binodal or spinodal point, we are using the lowest frequency (0.1 rad/s) data for binodal and spinodal
Figure 7. Frequency dependence on the extrapolated spinodal point for LPI50 and LPI80. All data are acquired by shear quench experiments. 1698
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points to compare with the static binodal points. Nevertheless, it is found from Figure 1 that the shifts of both the binodal and spinodal points are rather small, especially for near-critical blends, which confirms the statement that the rheologically determined phase boundary can eventually coincide with the static phase boundary determined by PCOM observations if the applied frequency is lowered.
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CONCLUSION The rheology of the elastomeric blend of PB/LPI in the miscible and immiscible region has been investigated as a function of temperature, composition, and oscillatory frequency. Our studies revealed that near- and off-critical blends displayed quite different viscoelastic properties in several aspects, such as temperature ramp curves, time evolution of storage modulus, and the shift of the apparent binodal and spinodal points under oscillatory shear. In the temperature ramp experiments, because the initial upturns of G′ between near- and off-critical blends originate from different kinds of contributions, the temperature ramp curves displayed varying heating rate dependence. For near-critical blends, the basis of the upturn of G′ is attributed to the increasingly large critical fluctuations near the critical region. Therefore, the heating rate independent upturn of G′ can be observed. For off-critical blends, although the growing concentration fluctuations in the metastable region may elevate G′ too, the main contribution to G′ is the nucleation phase separation process. As a result, a slower heating rate gives a lower apparent binodal point. In the shear quench experiments, the time evolution of G′ curves of near-critical blend LPI50 displayed two kinds of behaviors, which are believed to happen in the miscible and unstable region, respectively. For off-critical blend LPI80, the time evolution curves of G′ displayed three different behaviors, which are believed to happen in the miscible, metastable, and unstable region, respectively. As for the shift of apparent binodal and spinodal points under the oscillatory shear, the differences in the shear induced mixing mechanism and the critical fluctuation amplitude near the binodal phase boundary should be considered. For near-critical blends, the metastable region is rather narrow and the critical fluctuation is relatively large. Therefore, the slight shift of the binodal point and large shift of the spinodal point may be interpreted by MCRG theory and by the shear induced distortion of critical fluctuations, respectively. For off-critical blends, its large shift of the binodal point and moderate shift of the spinodal point can be explained by the theory regarding nucleation under shear and by the relatively weak suppression of critical fluctuations in the metastable region, respectively. Finally, by lowering the measured frequency to a very small value (0.1 rad/s in this study) for the spinodal point, then the rheologically determined phase diagram is well consistent with the results obtained by optical microscopy observations.
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ACKNOWLEDGMENTS The authors are thankful for the funding support of NSFC Projects 50930002 and 51173195. 1699
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