Investigation on Phase Separation Kinetics of Polyolefin Blends

Jun 10, 2009 - George Mason UniVersity, MS 3E2, Fairfax, Virginia 22030-4444, ... State UniVersity of New York at Binghamton, Binghamton, New York 139...
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J. Phys. Chem. B 2009, 113, 8820–8827

Investigation on Phase Separation Kinetics of Polyolefin Blends through Combination of Viscoelasticity and Morphology Yanhua Niu,† Liang Yang,†,‡ Katsumi Shimizu,§ Jai A. Pathak,| Howard Wang,⊥ and Zhigang Wang*,† CAS Key Laboratory of Engineering Plastics, Beijing National Laboratory for Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, P. R. China., Graduate School, Chinese Academy of Sciences, Beijing 100049, P. R. China., AdVanced Protein Crystallography Research Group, RIKEN SPring-8 Center, Harima Institute, 1-1-1 Kouto, Sayo-cho, Sayo-gun, Hyogo 679-5148, Japan, Chemistry Department, George Mason UniVersity, MS 3E2, Fairfax, Virginia 22030-4444, Department of Mechanical Engineering, State UniVersity of New York at Binghamton, Binghamton, New York 13902 ReceiVed: August 23, 2008; ReVised Manuscript ReceiVed: April 22, 2009

Phase separation kinetics of polyethylene copolymer blends polyethylene-co-hexene (PEH)/polyethylene-cobutene (PEB) at a phase separation temperature of 130 °C have been investigated through the combination of rheological measurements and optical microscope observation. When the blends are located in the unstable region, i.e., PEH/PEB 40/60 blend (H40), 50/50 blend (H50), and 60/40 blend (H60), due to the coeffect of the fast decay of concentration fluctuations and the reduced interfacial area, the stroage modulus, G′, behaves dramatically, decreasing at the early or intermediate stages; while when the blends are located in the metastable region, i.e., PEH/PEB 70/30 blend (H70), G′ decreases slightly and slowly during the whole time sweep process. During the cyclic frequency sweeps, G′ evolutions of H50 and H70 show similar trends. Obviously different from the strong phase segregation systems, the increase of G′ with time in the metastable region has not been observed, possibly due to the entanglement effects and weak interaction between the components of polyethylene blends. The interfacial tension-driven or diffusion-limited morphological evolutions of H50 and H70 during phase separation give direct interpretations to the viscoelastic difference between the two blends, which is dominated by different phase separation kinetics. The relatively low interfacial tensions at the late stage of phase separation for H50 (0.5-0.38 mN/m varying with time) and H70 (1.2 mN/m) can be estimated by using the Gramespacher-Meissner model. Introduction The phase separation behavior of polyolefin blends prepared either by heterogeneous or “single-site” metallocene catalysts has been extensively studied from theoretical1,2 and experimental3-5 viewpoints. Because of the similar chemical structures, and hence the similar refractive indices between the two components of polyolefin blends, oscillatory shear rheology among the several reported experimental measurements6 is well suited to in situ detect the changes of elasticity signal during phase separation, especially at the earlier stages, in which the optical methods show limits.7 Although the interplay between shear flow and thermodynamics in either the homogeneous (pretransitional) or the phase separated regimes might be an inevitable issue for rheological measurements, many linear viscoelastic studies5,8-12 indicate that as long as the applied strain or shear rate is sufficiently small and within the linear viscoelasticity range, this problem can be negligible, which further * To whom correspondence should be addressed. E-mail: Zhi-Gang Wang, [email protected]. Phone: 011-86-10-62558172. Fax: 011-86-1062558172. † CAS Key Laboratory of Engineering Plastics, Beijing National Laboratory for Molecular Sciences, Institute of Chemistry. ‡ Graduate School, Chinese Academy of Sciences. § Advanced Protein Crystallography Research Group, RIKEN SPring-8 Center, Harima Institute. | Chemistry Department, George Mason University. ⊥ Department of Mechanical Engineering, State University of New York at Binghamton.

strengthens the prominent advantages of rheological measurement to investigate the phase separation behaviors of polymer blends. Up to now, there have been many arguments dealing with the relationship between the resulted phase-separated morphologies and viscoelastic properties of various polymer blend systems.9,13-17 Different observations and explanations were made from temporal evolutions of dynamic moduli in the metastable and unstable regions. With phase separation progressing, dynamic moduli could simply show monotonic increase or decrease essentially depending on the resulted morphologies (droplet in a matrix or cocontinuous). If the time scale of oscillation is small enough, the modulus response during the early stages of phase separation can also be detected. Kapnistos et al.9 and Polios et al.13 indicated that for PS (polystyrene)/PVME (poly vinyl methyl ether) blend system, the modulus first increased with time during the early stages of phase separation, and after passing over a maximum, the modulus gradually decreased and eventually reached equilibrium at the late stages. Mani’s investigation15 on PS/PVME blends revealed that near but below the critical point, the modulus monotonically increased with time, while for the samples heated rapidly to above the critical point, the modulus decreased with time. Vinckier et al.16,17 showed that for PRMSAN (poly-Rmethylstyrene-co-acrylonitrile)/PMMA (polymethyl methacrylate) blends, the storage modulus, G′, monotonically decreased with time during phase separation in the unstable region due to reduced interfacial area, while G′ increased with time in the

10.1021/jp901209b CCC: $40.75  2009 American Chemical Society Published on Web 06/10/2009

Phase Separation Kinetics of Polyolefin Blends metastable region due to increased deformability of phase domains under shear. As clearly judged from the above investigations, there are no consistent agreements on the relationship between phase separation kinetics and rheological responses. However, one standpoint is confirmative at least, that is, the above-mentioned studies all seem to focus on the strong phase segregation systems in which the specific segment-segment interactions as well as the degrees of polymerization for both macromolecules are known to strongly affect the phase separation behaviors.2,18,19 While, for the weak phase segregation systems, i.e., polyethylene blends, the small positive van der Waals-governed interaction parameter and the relatively low degrees of polymerization make their phase separation processes and the eventually formed morphologies quite different from those of the strong phase segregation systems, which further functions to the rheological responses. One direct example is the previously studied PEH (polyethylene-co-hexene)/PEB (polyethylene-co-butene) blend system,7 for which in both the metastable and unstable regions, G′ of the phase-separated blends decreases with time when phase separation progresses. In other words, in the metastable region, the evolution of G′ is contradictory to the results reported by Vinckier et al.16,17 In our previous report,7 we only tentatively considered that the decreased G′ in the metastable region was due to the dominant effect of the reduced interfacial area and the phase domain deformability under small oscillation could be neglected, and we pointed out that further evidence was expected. In this paper, new experimental results will be presented to confirm our previous observations and explanations for this particular weak phase segregation system, the PEH/PEB blends,7 in which the absence of specific interactions makes it a relatively ideal model system for investigating the thermodynamics and kinetics of phase separation. The purpose of this work is to take the advantage of rheological measurement on LLPS of polyethylene blends to obtain the evolutions of rheological parameters under different phase separation kinetics and to elucidate the driving force of phase domain coarsening for this particular PEH/PEB blend system. A fresh insight into the phase separation kinetics of this system will be pursued on the basis of combination of rheological viscoelasticity and morphology. Meanwhile, the variations of interfacial tension under different phase separation kinetics will be quantitatively estimated by using the Gramespacher-Meissner (G-M) model,20 which will be further confirmed by calculations from the thermodynamic viewpoint. The relatively low interfacial tensions in this system may be related to its weak phase separation in nature. Experimental Section Materials and Sample Preparation. The polyethylene copolymers polyethylene-co-hexene (PEH) and polyethyleneco-butene (PEB) were kindly supplied by Exxon-Mobil Chemical Company. They were both synthesized by metallocene catalysis with the mass-average molecular weight, Mw, 112000 for PEH and 70000 for PEB, molecular weight distributions, Mw/Mn ∼ 2, and uniform comonomer distributions. The mass density was about 0.922 g/cm3 for PEH and 0.875 g/cm3 for PEB, and the short branch density was about 9 CH3 per 1000 backbone carbons for PEH and 77 CH3 per 1000 backbone carbons for PEB.7,21 The calculated entanglement molecular weights, Me, for PEH and PEB were 2.13 kg/mol and 2.36 kg/ mol, respectively, on the basis of the Wu’s model,22 and correspondingly the entanglement numbers, Ne, for PEH and PEB were 53 and 30, respectively. The previously obtained Flory-Huggins interaction parameter, χ, between PEH and PEB

J. Phys. Chem. B, Vol. 113, No. 26, 2009 8821 was expressed as χ(T) ) -0.0011 + 1/T.21 The dried solutionprecipitated PEH and PEB samples exhibited melting point temperatures, Tm, of 119.8 and 48.6 °C, respectively (determined by differential scanning calorimetry at a heating rate of 10 °C/ min). The PEH/PEB blends H40, H50, H60, and H70 (the number denotes the mass percent of PEH in blend) were prepared by coprecipitation from homogeneous hot xylene solutions (ca. 100 °C) into chilled methanol (ca. 0 °C). After being filtered, the obtained floccules were dried in air for 24 h and further dried in a vacuum oven at 60 °C for 72 h until the solvent was completely removed. The dried floccules of blends were compression-molded at 160 °C into disks of about 1 mm in thickness and 25 mm in diameter for rheological measurements. Rheological Measurements. The linear viscoelasticity of the blends was measured by oscillatory shear rheometry on a TA AR-2000 stress-controlled rheometer with 25 mm parallel-plate geometry. The chosen gap for all measurements was approximately 900 µm and could be slightly adjusted with temperature to compensate the sample contraction or expansion. The sample was loaded at 160 °C (well above the phase boundary) and annealed for 20 min to eliminate thermal history and then quenched to the desired temperature of 130 °C in the phase-separated region for the rheological measurements with different modes. First, isothermal strain sweeps at 130 °C for all the blends were carried out from 0.1% to 50% strain (0.01-500 rad/s) to demarcate the linear viscoelastic regime. Second, 8 h dynamic time sweeps at 130 °C with fixed frequency of 0.03 rad/s and strain of 5% for the blends H40, H50, H60, and H70 were carried out to investigate the phase separation kinetics. As references, time sweeps at the same experimental conditions were also performed for pure PEH and PEB samples. Finally, the cyclic frequency sweeps ranged from 0.01 rad/s to 10 rad/s with a given strain of 5% were performed for H50 and H70 at 130 °C, during which seven frequency sweep runs were collected and the global time for each frequency sweep run was 152.9 min and the whole running time for the seven frequency sweep runs was 1070.3 min for each blend. The temperature fluctuation of the rheometer was less than (0.1 °C during isothermal experiments. All experiments were conducted in nitrogen atmosphere in order to exclude any possible oxidative degradation. It should be mentioned here that due to the subtle variations of storage modulus for each blend during phase separation processes, the repeated measurements on fresh specimens were conducted to ensure the reliability of the variations of storage modulus. Optical Microscope Observation. The dried floccules were hot-pressed into films ca. 50 µm between two cover glasses at 160 °C before being quenched to room temperature in air for further use. To avoid thermal degradation of the samples, the pressed films were surrounded with silicone oil and the cover glasses were sealed with epoxy resin. The phase separation processes for H50 and H70 at 130 °C were observed by using a Leitz phase contrast optical microscope coupled with a Sony CCD video camera module (XC-77). The samples were first equilibrated at 160 °C in a hot stage with temperature stability of (0.1 °C for 10 min to remove thermal history and then were rapidly cooled to the target temperature of 130 °C for the in situ optical microscope observation. Results and Discussion Phase Separation Kinetics Measured by Rheology. In Figure 1, we summarize the rheologically determined phase diagram of PEH/PEB blends7 in which φPEH denotes the mass content

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Figure 1. Phase diagram of PEH/PEB blends determined from rheological measurements in which φPEH denotes the mass content of PEH component. The filled circles indicate binodal temperature (solid line is the fitting curve), and the open circles indicate spinodal temperature (dash line is plotted as the spinodal line).

Figure 2. Evolutions of storage modulus, G′ during time sweeps for H40, H50, H60, H70, PEH, and PEB at a constant frequency of 0.03 rad/s and a strain of 5% at 130 °C.

of PEH component in the blends. The filled circle indicates binodal temperature (solid line is the fitting curve), and the open circle indicates spinodal temperature (dash line is plotted as the spinodal line). In this phase diagram, the critical composition is 0.35 with the critical temperature of 145.2 °C. To investigate the phase separation kinetics under different mechanisms, isothermal time sweeps at 130 °C in the two phaseseparation regions were performed with a fixed frequency of 0.03 rad/s and a small strain of 5% for the blends H40, H50, H60, and H70 after the blends had been annealed at 160 °C for 20 min. Figure 2 compares isothermal evolutions of storage modulus, G′, for H40, H50, H60, and H70 at 130 °C, and as references, G′ evolutions for pure PEH and PEB at the same measurement conditions are also presented. Obviously, for the two pure components of PEH and PEB, G′ values almost keep constant during the whole time sweeps, which indicates that the samples show nice thermal stabilities during the long time annealing and, on the other hand, the effects of shear-induced relaxation at the selected strain can be negligible. Compared with the G′ evolutions of pure components, the situations of the PEH/PEB blends look rather different, in other words, G′ of all the blends more or less decreases with time due to undergoing phase separation. According to the phase diagram, H40, H50, and H60 locate in the unstable region, while H70 locates in the metastable region at a temperature of 130 °C. It should be noted here that the spinodal line shown in Figure 1 could just provide an indication of the spinodal region, and phase separation might proceed by the mechanisms of spinodal decomposition (SD) or nucleation

Niu et al. and growth (NG) for the conditions close to the spinodal line. Therefore, the true phase separation mechanisms for the blends should be further judged by actual morphological observation or rheological measurements. Because of the essentially different phase separation mechanisms for these blends, large distinctions of G′ developments can be observed, not only in the magnitude of G′ decrease but also in the temporal evolution of G′ to equilibrium. For H40, H50, and H60, G′ evidently decreases within 150 min; afterward, G′ decreases slowly and moderately and eventually approaches equilibrium, whereas for H70, G′ decreases tardily during the whole phase separation process and does not reach equilibrium even after 500 min. In our previous study,7 we reported that during spinodal decomposition, G′ should initially reach a maximum in a short time due to the drastic concentration fluctuations, and then G′ dramatically decreased due to concentration fluctuation decay and interfacial area reduction with coarsening phase domains. For the nucleation and growth, the change in concentration between a nucleated particle and the matrix approaches the thermodynamically defined limit, which cannot cause obvious enhancement of G′ during the initial stage of phase separation. The almost equal initial G′ values and large difference in G′ decrease magnitude between H60 and H70 are thought to essentially originate from the different phase separation mechanisms. In addition, according to the reports from other researchers,16,17 the G′ decrease during spinodal decomposition is due to the coupled effects of concentration fluctuations and interfacial tension at the earlier stages of phase separation, and the interfacial area may be mainly responsible for the G′ decrease at the late stages, which is consistent with our results for H40, H50, and H60. However, different from their results, the G′ increase with time in the metastable region has not been observed for our studied system. Vinckier et al.17 considered that the interfacial contribution to storage modulus was proportional to droplet sizes, which was more attributed to the deformability of larger droplets under shear. However, our opinion is that the G′ in the metastable region is determined by two competing factors: the total interfacial area and the domaincoarsening related deformability. If the total interfacial area is dominant, G′ decreases with time, whereas if the domaincoarsening related deformability is the leading factor, G′ increases with time.7 For the PEH/PEB blend system, due to the entanglement effects and the relatively small positive Flory-Huggins interaction parameter, χ (χ(T) ) -0.0011 + 1/T),21 which fundamentally defines the weak phase segregation characteristic for the system, the phase separation via NG for H70 is a rather slow process, and accordingly the domain sizes at a relatively long time scale are very small and the well-defined droplet-matrix morphology may not eventually form; this is the reason why the final constant value of G′ for H70 has not been reached within the long time of 500 min as shown in Figure 2. Therefore, the G′ decrease for H70 is mostly induced by the reduced interfacial area, and the phase domain deformability can be basically neglected. To further confirm the above observations and the influences of different phase separation kinetics on the G′ evolutions, cyclic frequency sweeps (seven runs with a total time of 1070.3 min for each blend) were carried out at 130 °C for H50 and H70. Parts a and b of Figure 3 present the frequency dependences of G′ and G′′ at different phase separation times for H50 and H70, respectively. Consistent with the variations of G′ during time sweeps as shown in Figure 2, G′ for both H50 and H70 decreases with progressing phase separation at low frequencies, but the decreasing magnitude of G′ is much larger for H50 than

Phase Separation Kinetics of Polyolefin Blends

Figure 3. Developments of G′ and G′′ during cyclic frequency sweeps ranged from 10 to 0.01 rad/s with a strain of 5% at 130 °C for (a) H50 and (b) H70. (c) Comparison of G′ evolutions with phase separation time for H50 and H70 at the frequency of 0.01 rad/s.

H70. To clarify, Figure 3c illustrates the time evolutions of G′ at the frequency of 0.01 rad/s for H50 and H70 (the data were obtained from Figure 3a,b). Obviously, the prominent G′ decrease for H50 and slight G′ decrease for H70 can be clearly observed. The result agrees well with that for the time sweeps shown in Figure 2, although the G′ values in these two figures are different due to different selected frequencies. This agreement indicates the reliability of our previous results and also demonstrates that the difference between H50 and H70 is indeed related to different phase separation mechanisms and morphological evolutions. At the late stage of SD for H50, the cocontinuous domain coarsening is induced by hydrodynamic flow, and the evolution of domain size R can be described by R ∝ t1.23,24 The droplets formed by NG for H70 may further develop by the evaporation-condensation mechanism or the Ostwald ripening through molecular diffusion, so the phase domain slowly increases by following the relation of R ∝ t1/3.25 Therefore, the domain-coarsening rate in H50 should be much

J. Phys. Chem. B, Vol. 113, No. 26, 2009 8823 faster than that in H70, which is the origin of different G′ developments for these two blends. It is worth mentioning that the decreases of G′ for both H50 and H70 are indeed induced by phase separation rather than any chemical changes, such as degradation etc., because the reproducibility of the measurements and the thermal stability of the samples were examined and ensured before and after the rheological measurements. Evolutions of Morphology with Different Phase Separation Kinetics. Figure 4 illustrates the evolutions of morphology for the blends H50 and H70 at 130 °C after the samples are annealed at 160 °C for 10 min to eliminate thermal histories. The inset in each optical micrograph corresponds to the image obtained by two-dimensional fast Fourier transform (2D-FFT).26 It can be seen that for H50 (Figure 4a), at the early or intermediate stages within 145 min, the phase domains can hardly be discerned due to small domain sizes and similar refractive indices between the two components. However, we cannot conclude that the phase separation does not occur within 145 min because the dramatic decrease of G′ in this period (see Figure 2) has been observed. It infers that the initial concentration fluctuations, which are mainly responsible for the decrease of G′, cannot be clearly detected by using phase contrast optical microscope. However, at the late stages, the cocontinuous morphology obviously forms and a self-similarity development can be observed, which is a characteristic of spinodal decomposition.27,28 The emergence and further evolution of the spinodal ring in the corresponding 2D-FFT patterns as another characteristic also depict the phase domain formation and development. With the development of SD, the reduced spinodal ring diameter indicates the interfacial tension-driven phase domain coarsening, which leads to the decrease of interfacial area29 and hence the decrease of G′. For H70, due to the energy barrier for nucleation, the phase separation process is more delayed (see Figure 4b) if compared with H50. It is clearly seen that even after a relatively long time of annealing, such as 1468 min, the spotty phase separated morphology is obscure and as is the corresponding 2D-FFT pattern. Unlike the strong phase segregation system,16,17 the well-defined droplet-matrix morphology cannot be observed for H70, which may be essentially due to the weak interaction between PEH and PEB components. Therefore, the deformability of such small and obscured phase domains of H70 is not sufficient to induce the increase of G′, while the reduced interfacial area still plays a dominant role to lead to the decrease of G′. Figure 5 presents the developments of the characteristic length scale, lm ) 2π/qm, of the phase separated morphologies at 130 °C for H50 and H70, where qm is the scattering vector associated with the maximum scattering intensity value in the radially averaged 2D-FFT spectrum (not shown), which can be obtained from inset of Figure 4.26 For H50, lm evidently increases from about 2 to 8 µm within the time range of 200 to 1200 min. While for H70, lm cannot be measured until 1200 min and lm does not show obvious change thereafter. Such a notable difference of the domain size-related length scale can give a good interpretation to the interfacial area evolutions under different phase separation mechanisms, which determine the remarkable G′ decrease for H50 and the slight G′ decrease for H70. In the long time limit, it seems the evolution of lm deviates the scaling relation R ∝ t1 for H50 and R ∝ t1/3 for H70 as mentioned above. This may be due to the weak segregation character of this PEH/PEB blend system, in which the hydrodynamic flow-required well-defined interface23 may not eventually form, thus the small hydrodynamic driving force functions to the slow growth rate of phase domains of H50. At the very

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Figure 4. Phase-contrast optical micrographs of (a) H50 and (b) H70, which were isothermally phase-separated at 130 °C for various times with the scale bar of 20 µm. The 2D-FFT patterns are shown as insets in the corresponding phase-contrast optical micrographs. The sizes of the 2D-FFT patterns are squares of 15.6 and 14.1 µm-1 for H50 and H70, respectively.

Phase Separation Kinetics of Polyolefin Blends

J. Phys. Chem. B, Vol. 113, No. 26, 2009 8825 of the ratio R/σ, where R is the average domain size of the dispersed phase and σ is the interfacial tension. Thus the storage modulus and loss modulus can be described as follows:

G′blend ) G′components + G′interface ) (φAG′A + φBG′B) +

ω2η(τ1 - τ2) 1+

G″blend ) G″components + G″interface ωη(τ1 - τ2) ) (φAG″A + φBG″B) + τ1(1 + ω2τ21)

Figure 5. Time evolutions of the characteristic length scale for H50 and H70, which were isothermally phase separated at 130 °C.

late stages of SD, the bicontinuous spinodal microstructures tend to break up into discrete droplets, which coarsen more slowly due to the enthalpy barrier-retarded mass transport of the large chain-like molecules. Therefore the transition from percolation to cluster may further lead to the pinning or slowing down of the domain growth.30,31 For H70, due to the slow phase separation process, even at the time longer than 1060 min, the phase domains are still quite small (about 3 µm), which are almost close to the resolution of our optical measurements. Therefore, only a few data points can be obtained within the time limit of 1468 min, which seems to deviate from the scaling behavior, however, the scaling behavior may appear more clearly if judged from the runs with even longer time. Evolutions of Interfacial Tension with Different Phase Separation Kinetics. During the late stage of SD, the driving force for phase domain coarsening is generally regarded as interfacial tension, which leads to the reduced interfacial area for H50. While for H70, the phase separation progress may be diffusion-limited. Although the phase separation kinetics for these two blends are different, Gramespacher and Meissner,20 Palierne,32 and Graebling33 directly considered that the enhanced elasticity at low frequencies was due to interfacial energy for simplification. According to the comparison made by Jeon et al. on several models,34 it is regarded that the GramespacherMeissner (G-M) model and the Palierne model are more suitable for polybutadiene/polyisoprene (PB/PI) blends and the related fitting results agree well with each other. Considering the expressions for these two models, there are no essential differences between them, so in this study we just selected the G-M model to fit our experimental data and quantitatively evaluated the changes of interfacial tension during different phase separation processes on the basis of cyclic frequency sweep data for H50 and H70. To apply this model to our blend system, it is necessary to ascertain that the phase domains have attained their equilibrium concentration profile, for which it is expected that the interfacial tension or G′ should initially increase. The initial increase has been presented and discussed in our previous publication35 and the initial stage of phase separation is proven to be shorter than 15 min. Therefore, during the cyclic frequency sweeps, even for the first run of 152.9 min the blend should have gone into the late stage of phase separation and the phase domains attain their equilibrium concentration profile. In terms of the G-M model, any deviation of the complex modulus of the blend from a simple linear addition of individual components is attributed to the change

(1)

ω2τ21

(2)

τ1 ) τ0 1 + φA

[

5(19λ + 16) 4(λ + 1)(2λ + 3)

]

(3)

[

3(19λ + 16) 4(λ + 1)(2λ + 3)

]

(4)

τ2 ) τ0 1 + φA

τ0 )

ηmR (19λ + 16)(2λ + 3) σ 40(λ + 1)

(5)

ηd ηm

(6)

λ)

In the above equations, φA and φB are volume fractions of two components with the subscript “A” denoting the dispersed phase, ηd and ηm the Newtonian viscosities of the dispersed phase and matrix phase of the blend, respectively, λ the viscosity ratio, and τ the interfacial tension relaxation time scale. According to the lever rule, the volume fractions of the dispersed phase φA and matrix phase φB can be expressed as φA ) (φB - φ0)/(φB-φA) and φB ) (φ0 - φA)/(φB-φA), in which φA and φB are the equilibrium values of the order parameter at coexistence at the phase separation temperature and φ0 is the order parameter in the one-phase region.36 Specifically speaking for this study, φ0-H50 is 0.487 and φ0-H70 is 0.689, respectively. In terms of the phase diagram shown in Figure 1, at 130 °C, the blends near the equilibrium state should phase separate into the PEB-rich phase with φA ) 0.160 and the PEH-rich phase with φB ) 0.748. That is to say, for both H50 and H70, the PEH-rich phase with φB ) 0.748 is the matrix, and accordingly the PEB-rich phase with φA ) 0.160 is the dispersed phase. Therefore, according to the lever rule, φA-H50 and φB-H50 are equal to 0.444 and 0.556, respectively, and φA-H70 and φB-H70 are equal to 0.100 and 0.900, respectively. ηd and ηm can be estimated by using the log additive mixing rule based on viscosities of PEH (29350 Pa · s) and PEB (6260 Pa · s) at 130 °C. By calculation, ηd and ηm are 9954 Pa · s and 23531 Pa · s, respectively. Correspondingly, the values of λ, τ0 and the expressions of τ1 and τ2 can be obtained. In eqs 1 and 2, the values of η are experimentally measured values of the blends, more specifically, ηH50 is 13750 Pa · s and ηH70 is 18720 Pa · s. By fitting the experimental data corresponding to different runs during cyclic frequency sweeps for H50 and H70 through using eqs 1 and 2, the parameter of R/σ (with unit of m2/N) can be obtained. Two assumptions were made in the fitting process: one was that the concentration fluctuations had decayed and the equilibrium concentrations were almost reached for both H50 and H70 at the late stage of phase separation, so the concentration evolutions during the cyclic frequency sweep were neglected for simplification; the

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Figure 6. Developments of G′ and G′′ during cyclic frequency sweeps ranged from 10 to 0.01 rad/s with a strain of 5% at 130 °C for H50 with the symbols representing the experimental data and the lines the fitting curves for different runs.

other one was that the domain size R kept almost invariant during each frequency run due to the slow phase separation process for each blend. Figure 6 shows the fitting curves in the whole frequency range for H50, which agree well with the experimental data for both the storage modulus G′ and loss modulus G′′. At low frequencies, the fitting curves agree well with the experimental data, indicating that the phase separation-induced interfacial tension has relatively long relaxation time. In other words, the change of total interfacial energy is the origin of G′ variation, while at high frequencies the interfacial energy portion is negligible compared with the elastic energy portion coming from the polymer components.20 Therefore, we considered that the G-M model could be well applied to estimate the change of interfacial tension during phase separation for the PEH/PEB blends because only the long time relaxation at low frequencies is meaningful to the calculation. For clarity, the low frequency data of G′ and the fitting curves for H50 and H70 during different frequency sweep runs are shown in parts a and b of Figure 7, respectively. In Figure 7a, it can be obviously found that with increasing phase separation time, the parameter R/σ for H50 remarkably increases from 0.004 to 0.021 m2/N, while in Figure 7b, with increasing phase separation time, R/σ for H70 slightly increases from 0.0018 to 0.0025 m2/N. Compared with H50, both the absolute values and increasing magnitude of R/σ for H70 during phase separation are much smaller, which is directly related to the different phase separation kinetics and morphologies. To calculate the evolutions of interfacial tension σ for these two blends, we can simply regard the characteristic length scale lm in Figure 5 as the domain size R. According to Figure 5, the domain size of H50 during the whole cyclic frequency sweep (from 152.9 to 1070.3 min) changes approximately from 2 to 8 µm, and accordingly the interfacial tension σ decreases from 0.5 to 0.38 mN/m, which are quantitatively very close to that of the PI/PB blend system.34 If taking into account of the curvature or domain size dependence, the interfacial tension can be expressed as σ(R) ) σ0 + (2k/R2) in which the first term signifies the stretching contribution, which can be viewed as the interfacial tension of a flat interface, the second term represents the bending contribution, which is dependent on the curvature and thus on the size of the local curvature of the phase domains, and the parameter k is the bending rigidity.24 As judged from the above equation, interfacial tension should decrease with phase domain coarsening, which is consistent with our fitting results. Therefore, we conclude that the decrease of G′ for H50 during phase separation at low frequencies is due to the combined effects of phase domain size increase and interfacial

Figure 7. Developments of G′ during cyclic frequency sweeps at 130 °C in the frequency range from 0.1 to 0.01 rad/s with the symbols representing the experimental data and the lines the fitting curves during different runs for (a) H50 and (b) H70.

tension decrease, especially the interfacial area decrease. However, at the very late stage of phase separation, the domains are much larger than the critical dimension Rc ) 2k/σ0, which is the crossover length scale where the stretching and bending terms are equal. Therefore, in the situation of R . Rc near the asymptotic limit, the interface can be approximately regarded as a flat interface, where σ ≈ σ0. According to Broseta and Helfand,37,38 for asymmetric polymers, the simple expression relating the interfacial tension σ0 to the interaction parameter χ is:

σ0 )

kT (χ/6)1/2 a2

(7)

in which k is the Boltzmann constant, T the absolute temperature, and a the statistical segment length. For the specific PEH/PEB blends, χ is 0.00138 at 130 °C according to the equation χ ) -0.0011 + 1/T. The statistical segment length can be expressed as a ) (aPEHaPEB)1/2 in which aPEH and aPEB are both 5.0 Å.38 Therefore, the estimated value of σ0 from eq 7 is about 0.34 mN/m, which is close to the value of 0.38 mN/m at 1070.3 min obtained from the G-M model fitting. The nice consistency between the estimated interfacial tensions of H50 at the very late stage of phase separation determined by the two different methods further strengthens that the variations of rheological parameters are directly related to the morphological evolutions. For H70, the domain size cannot be well estimated from the 2D-FFT patterns before 1200 min because of the slow phase separation process and obscure phase domains, and the domain sizes are less than 3 µm even at the very late stages as judged from Figure 5. Therefore, the exact interfacial tension variation for H70 during the whole cyclic frequency sweeps cannot be

Phase Separation Kinetics of Polyolefin Blends well determined, but if we approximately consider that the phase domain of H70 at 1070.3 min is about 3 µm, the interfacial tension should be 1.2 mN/m. It is obvious that the absolute interfacial tension values for both H50 and H70 are rather low, which may be related to the weak phase separation of the blends in nature. Nevertheless, the interfacial tension of H70 at the phase separation time of 1070.3 min is relatively high, which is considered to be ascribed to the slowly reduced interfacial area and the spotty-like morphology. The interfacial tension or interfacial area of H70 decreases slightly and slowly due to the diffusion-limited process, which directly leads to the slight decrease rather than the increase of G′. Meanwhile, due to the small phase domain sizes and the small strain, the domaincoarsening related deformability for H70 can be neglected. In other words, the phase domain area change is dominant for the decrease of G′ with phase separation progressing. Conclusions The phase separation kinetics of PEH/PEB blends in the unstable and metastable regions have been studied through combination of rheological measurements and optical microscope observation. Rheological time sweeps and cyclic frequency sweeps coherently show that for both blends with SD or NG mechanisms, the storage modulus G′ decreases with phase separation time, while due to the different phase separation kinetics and hence the different morphological evolutions, the decreasing magnitudes of G′ are rather different. Different from the strong phase segregation systems, the increase of G′ with time in the metastable region has not been observed, which may be essentially due to the entanglement effects and weak interaction between the two components of PEH/PEB blends. By fitting with the Gramespacher-Meissner model, the changes of interfacial tension during cyclic frequency sweeps can be estimated, which can be further confirmed through calculations from the thermodynamic viewpoint. The relatively low interfacial tension at the late stage of phase separation for H50 (0.5-0.38 mN/m varying with time) and H70 (1.2 mN/m) were observed. The decrease of storage modulus at low frequencies for H50 is due to the coupled effects of the increased phase domain sizes and decreased interfacial tension or interfacial area, while for H70, the development of storage modulus depends mainly on the interfacial area rather than the domain-coarsening related deformability. Acknowledgment. Y. H. Niu and Z. G. Wang acknowledge financial support from the National Science Foundation of China with grant number 20674092. Z. G. Wang acknowledges financial support from the National Science Foundation of China with grant number 10590355 for the Key Project on Evolution of Structure and Morphology during Polymer Processing. H. Wang acknowledges the support from the National Science Foundation of USA under grant DMR-0711013.

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