Rheologically Determined Phase Diagram and Dynamically

Moreover, rheology as one of the dynamically measuring techniques is very different ... It is assumed that when an instantaneous and infinitesimal she...
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Macromolecules 2006, 39, 4175-4183

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Rheologically Determined Phase Diagram and Dynamically Investigated Phase Separation Kinetics of Polyolefin Blends Yan-Hua Niu†,‡ and Zhi-Gang Wang*,† CAS Key Laboratory of Engineering Plastics, Joint Laboratory of Polymer Science and Materials, Institute of Chemistry, Chinese Academy of Sciences, Beijing, 100080 P. R. China, and Graduate School, Chinese Academy of Sciences, Beijing, 100049 P. R. China ReceiVed January 16, 2006; ReVised Manuscript ReceiVed March 22, 2006

ABSTRACT: Blends of statistical copolymers ethylene/hexene (PEH) and ethylene/butene (PEB) show the behavior of an upper critical solution temperature (UCST). In this study, the phase diagram of PEH/PEB blends was determined by using rheological measurements, and the kinetics of phase separation was investigated from the viewpoints of polymer viscoelasticity. Based on time-temperature superposition (TTS) principle and mean field theory, rheology methods were used to determine the binodal and spinodal phase separation temperatures. Compared with optical techniques, rheology could sensitively detect phase separation in rather early stages. It was found that in either the metastable or unstable regions, storage moduli of the phase-separated blends decreased when phase separation progressed. The magnitude of G′ decreasing was smaller in the metastable region than in the unstable region because the nucleation and growth process in the metastable region was dominated by diffusion and interfacial tension was much weaker, while in the unstable region, spinodal concentration fluctuations were dominant and interfacial tension was stronger. The decrease of G′ in the unstable region was due to the coupling effects of reduced concentration fluctuations and decreased interfacial tension, whereas the decrease of G′ in the metastable region was determined by competitive effects of the reduced interfacial area and increased deformability.

Introduction Phase separation behaviors of polymer blends have long attracted the interests from both the fundamental and industrial viewpoints, since a lot of physical problems are not well understood yet.1-5 Rheology as a sensitive tool to study the phase behavior of polymer blends has been widely used for several decades. In this field linear rheology has been deeply understood and to some extent nonlinear rheology has been studied for the completely immiscible polymer blends,6-10 but it is still challenging to study the linear rheology in the vicinity of phase separation of the miscible or partially miscible polymer blends. This is because not only the phase separation process but also the interplay between thermodynamics and kinetics and their coupling with rheology during phase separation are rather complex. The physical origin of phase separation is generally regarded as concentration fluctuations, which involves various mechanisms such as nucleation, diffusion, and domain growth and coagulation. Of particular interests about flow effects on phase separation kinetics are the shear-induced morphological changes and the mixing-demixing phenomenon,11-14 which have been successfully described by the concept of an extra stored energy to system during shear. Theoretical and experimental studies on this complex problem basically agree that shear does not affect the critical temperature if strain is small or shear rate is low enough.15-25 In such a case flow is not assumed to interfere with thermodynamics and kinetics of phase separation. In the linear regime of rheology, many fingerprints can be used to qualitatively infer the critical phase separation temperature of polymer blends. The time-temperature superposition (TTS) principle has been very well applied in the homogeneous region * Corresponding author: Tel 011-86-10-62558172; Fax 011-86-1062558172; e-mail [email protected]. † CAS Key Laboratory of Engineering Plastics. ‡ Graduate School.

far away from phase separation as well as far away from the glass transition temperature, but if phase separation occurs or the system enters the pretransitional region, the TTS principle breaks down, and at low frequencies a shoulder of storage modulus, G′, appears, which is an obvious signal of the phase transition behavior for polymer blends. In addition, the ColeCole curve26,27 and Han curve,12,20 which can be straightly obtained by plotting η′′ vs η′ and G′ vs G′′ at different temperatures, are also often used to characterize the lowfrequency thermorheological complexity. It has been suggested that the Cole-Cole curve and Han curve are more sensitive to phase separation behavior than the TTS principle. Although the TTS principle, Cole-Cole curve, and Han curve can be used to effectively distinguish the homogeneous region from the phase-separated region, they cannot quantitatively determine the critical phase separation temperature. The quantitative way to estimate the critical point is using isochrone plot of storage modulus G′ or the tangent of loss angle tan δ with temperature, which shows obvious slope change near the phase separation region due to the enhanced elasticity. By using the mean field theory initially worked out by Fredrickson and Larson for block copolymers28 and later extended to polymer blends by Ajji and Choplin,29 temperature sweep has been successfully employed to obtain spinodal temperature. Madbouly,11 Kapnistos,20 and Sharma25 yielded the spinodal temperatures of the PS/PVME blend system by this method. Bousmina23 applied this mean field theory to the SAN/PMMA blend system and got the critical transition temperatures, and the obtained data agreed very well with that from the other methods, such as optical microscopy and inverse gas chromatography. It is worth noting that this quantitative method is suitable not only for a LCST system but also for a UCST system. By the same way, Vlassopoulos19 obtained the phase diagram of PS/PMPS blends, a model UCST system, which had good accordance with the phase diagram established by turbidity and dynamic light scattering measurements. Therefore, rheological

10.1021/ma060103n CCC: $33.50 © 2006 American Chemical Society Published on Web 05/13/2006

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measurements can provide an unambiguous determination of critical phase separation temperature as long as the two components of the blends have different viscoelastic properties. The relationship between the resulted phase-separated morphology and viscoelastic properties of polymer blends for LCST and UCST systems has also been extensively investigated. Different observations were made from time evolutions of the dynamic moduli in either the metastable or unstable regions. With phase separation progressing, the dynamic moduli could show monotonic increase or decrease depending on the resulted morphologies (droplet-matrix or cocontinuous).17,21,22 In addition, if the time scale of oscillation is small enough, modulus response during the early stages of phase separation can also be detected. Polios17 and Kapnistos20 proved that moduli increased with time during the early stages of spinodal phase separation due to the formed highly interconnected cocontinuous morphology, whereas moduli gradually decreased during the late stages due to the breaking-up interconnectivity. However, whether the well-defined droplet-matrix morphology can form or the nucleation can really occur during phase separation in the metastable region has not been well understood.4 More specifically, neither has it been clear whether the moduli inevitably increase with time during phase separation in the metastable region. At least, it is not such a case from our study in this work. As a matter of fact, there is a wide open area about phase separation kinetics and viscoelastic properties of polymer blends for further exploration. In this study, polyolefin blends of PEH and PEB were investigated because of the wide potential application and commercial prospect in industry for the polyolefin blends. PEH/ PEB blends have been proven to be a UCST system. The phase diagram has been fundamentally calculated from the FloryHuggins theory by Wang et al.30 Because of the similar refractive indices of the two components in the blends, it is experimentally difficult to in situ detect the signals of phase separation in the melt by optical techniques. The researchers have used indirect methods such as diffuse light scattering to identify the phase boundary by cooling the sample from the melt to crystallization temperature. However, the spinodal line in the phase diagram of PEH/PEB blends came just from theoretical prediction, and there is lack of experimental evidence. Moreover, rheology as one of the dynamically measuring techniques is very different from the static methods, so it is imperative to establish the phase diagram of the blends in dynamic conditions. Overall, for the PEH/PEB blend system, our recently published work has mostly concentrated on the relationship between phase separation and crystallization.31-34 Very little has been focused on and eventually performed on the molecular dynamics, such as molecular entanglements, relaxation behavior, and other viscoelastic properties. Thus, in this report the rheological measurements can offer useful, basic, and supporting information from the molecular dynamic viewpoints to elucidate the phase separation and crystallization behaviors of the blends in future studies. Theoretical Background Near the mixing-demixing temperature of polymer blends or the order-disorder transition of diblock copolymers, it is expected to exhibit anomalous viscoelastic properties. Inspired by the experimental results of Bates,35 Fredrickson and Larson28 derived a theoretical basis to interpret these anomalous viscoelastic phenomena by introducing a single one-component order parameter, ψ(x), which reflects the spatial density fluctuations. Within the mean field approximation, the authors followed a

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free energy approach to obtain the anomalous shear stress arising from long-lived critical fluctuations. It is assumed that when an instantaneous and infinitesimal shear strain is imposed on the system the differential change in free energy is proportional to the product of the stress and the applied differential strain. It is the strain that establishes a new distribution of order parameter fluctuations P[ψ,t;γ] and produces an affine deformation of a given density pattern. Thus, the anomalous or extra stress σ(t) induced by critical fluctuations can be calculated from the total free energy differential change, F(P;γ,t).

σ(t) )

[

]

∂F(P;γ,t) ∂γ

(1)

γ)0

After integration over the whole wave-vector space and using the relation G* ) σ*/γ* , the following expressions can be obtained for the dynamic storage modulus and loss modulus, respectively:

G′ )

G′′ )

kBTω2

k6S 2(k)

k 0 2 ∫0 2 15π ω + 4$2(k) c

2kBTω 15π2

∫0

kc

[ ] [ ] ∂S0-1(k) ∂k2

k6S02(k)$(k) ∂S0-1(k) ω2 + 4$2(k)

∂k2

2

dk

(2)

2

dk

(3)

where $(k) ) k2S0-1(k)λ(k), S0(k) is the static structure factor, λ(k) the Onsager coefficient, and k the wave vector. The above expressions are valid for either block copolymers or binary homopolymer blends. Using the expressions of static structure factor S0(k) originally calculated by de Gennes36 and the Onsager coefficient λ(k) proposed by Binder37 for polymer blends near the phase separation temperature, Ajji and Choplin29 made an extension of the theory of Fredrickson and Larson for block copolymer melts near the order-disorder transition to the case of homopolymer blends.

1 1 1 ) + - 2χ S0(k) φN1g1(k) (1 - φ)N2g2(k)

(4)

with Ni the number of statistical segments, gi(k) the Debye functions, and χ the interaction parameter.

1 1 1 + ) λ(k) φa12W1g1(k) (1 - φ)a22W2g2(k)

(5)

where ai is the statistical segment length for species i and Wi its rate of reorientation, defined by

Wi ) 3πkBT/ζi

(6)

with ζi the monomeric friction coefficient. Using the expansion of Debye functions gi(k) to the first term, S0(k) and λ(k) can be recalculated as follows:

S0-1(k) ) 2(χs - χ) +

λ-1(k) )

1 2

φa1 W1

+

[

2

]

2

Rg2 2 1 Rg1 1 k + φN1 3 (1 - φ)N2 3

1 + (1 - φ)a22W2

[

]

(7)

Rg22 Rg12 + k2 (8) φa1W1 (1 - φ)a2W2

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where χs denotes the interaction parameter at the spinodal point (S0-1(0) ) 0). Replacing above expressions into eqs 2 and 3 and retaining only the leading order terms as χ tends to χs, the expressions of storage modulus and loss modulus in the terminal one-phase region near the critical point can be obtained as follows:

[{ [ [{ [

}]

kBTω2 1 Rg12 Rg22 + 1920π 3 φN1 (1 - φ)N2

G′(ω) )

1/2

]

2

1 1 + [2(χs - χ)]-5/2 (9) φa12W1 (1 - φ)a22W2

G′′(ω) )

}]

-1/2

Rg22 kBTω 1 Rg12 + 240π 3 φN1 (1 - φ)N2 1

+

2

φa1 W1

]

1 [2(χs - χ)]-1/2 (10) (1 - φ)a22W2

where Rgi is the radius of gyration defined as Rgi2 ) Niai2/6. Using the above equations, the ratio G′(ω)/G′′ 2(ω) can be calculated by properly substituting the values of the defined parameters.

G′(ω) 2

G′′ (ω)

)

{

}

2 a22 30π a1 + kBT 36φ 36(1 - φ)

3/2

(χs - χ)-3/2 (11)

It is worth noting that in eq 11 both the monomeric friction coefficient and the frequency dependence are eliminated. Assuming that the interaction parameter is given by χ ) A + B/T, one can obtain a linear dependence of (G′′2/G′T)2/3 vs 1/T, for which the interception with the 1/T axis is denoted as the reciprocal to the spinodal temperature, Ts. By introducing the expression of correlation length of polymer blends

a′ ξ ) {φ(1 - φ)(χs - χ)}-1/2 6

(12)

where a′ is the characteristic length, related to individual segment length, and the relation between a′ and ai 2

2

a1 a2 a′2 ) + φ 1-φ φ(1 - φ)

(13)

the correlation length near the critical region can be derived from eq 11 as follows:

ξ)

[

]

kBT G′ 30π G′′2

Figure 1. Changes of storage modulus, G′, and loss modulus, G′′, during frequency sweeps for PEH and PEB components at 160 °C, respectively.

1/3

(14)

Here it should be pointed out that eq 14 derived from the rheological measurement is an empirical equation for calculating the correlation length and is only valid near the critical region. Experimental Section Materials and Preparation of the Blends. Polyethylene copolymers used in this study were PEH (ethylene/hexene) and PEB (ethylene/butene), kindly supplied by ExxonMobil Chemical Company. Both of them were synthesized by employing metallocene catalysts and had relatively narrow molecular weight distributions (Mw/Mn ∼ 2) and uniform comonomer distributions.30-34 The mass-average molecular weight, Mw, was 112 kg/mol for PEH and 70 kg/mol for PEB determined by high-temperature gel permeation

chromatography (GPC). The mass density was about 0.922 g/cm3 for PEH and 0.875 g/cm3 for PEB, and the branch density was about 9 CH3 per 1000 backbone carbons for PEH and 77 CH3 per 1000 backbone carbons for PEB. The dried solution-precipitated PEH and PEB samples exhibited Tm of 119.8 and 48.6 °C, respectively, by using DSC at a heating rate of 10 °C/min. Blends of various compositions (by mass) were prepared by coprecipitating from a hot xylene solution (ca. 100 °C) into cold methanol (ca. 0 °C). After filtering, the blends were dried in air for a day and further dried in a vacuum oven at 60 °C for 3 days until the solvent was completely removed, as judged by constant weight. The dried blends were compression-molded at 160 °C into disks of about 1 mm in thickness and 25 mm in diameter for the rheological measurements. Rheological Measurements. The viscoelastic properties of the blends were measured by dynamic rheology in different modes on a TA AR2000 stress-controlled rheometer with 25 mm parallel plates. The chosen gap was ∼900 µm for all measurements and was adjusted for different temperatures. Isothermal strain sweeps were carried out from 0.1 to 50% with fixed frequency (0.01-500 rad/s) to determine the linear viscoelastic regime of the blends. Isothermal frequency sweeps covering the range 0.01-500 rad/s with strains of 1-5% falling well within the linear viscoelastic regime and ensuring large enough torques were performed at different temperatures for various compositions of the blends. Effects of temperature on the viscoelastic behaviors of the blends were studied by isochronal temperature sweeps at a given frequency of 0.03 rad/s and a temperature decrement of 1 °C. The temperature range 123-160 °C ((0.1 °C) covered in this study probed the entire region from the homogeneous region to phase-separated region in the phase diagram. To investigate the phase separation kinetics, 8 h dynamic time sweeps were carried out with a fixed frequency of 0.03 rad/s and a given strain of 5% at various temperatures in the phase-separated region for different compositions of the blends. Before the experimental running, the blends were kept at 160 °C for 20 min to eliminate thermal history and then subsequently quenched to the required experimental temperature. All of the experiments were conducted in a nitrogen atmosphere in order to exclude any possible oxidative degradation and chemical crosslinking.

Results and Discussion 1. Determination of Phase Diagram of PEH/PEB Blends by Rheology. TTS Principle. For reference, Figure 1 shows the changes of storage modulus, G′, and loss modulus, G′′, during frequency sweeps at 160 °C for the two pure components, PEH and PEB. In the whole frequency range, G′ and G′′ of PEH are both higher than that of PEB. The corresponding reptation time, τr, determined from the reciprocal of frequency where G′ ) G′′, is also longer for PEH than PEB (as shown in Figure 1, τr,PEH is about 14 ms and τr,PEB is about 3.9 ms). According to Doi-Edwards,38 the reptation time corresponding to the longest relaxation time of polymer chains is directly proportional to the monomeric friction coefficient and somewhat related to the molecular weight. The difference of reptation time

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Figure 2. Master curves of storage modulus, G′, and loss modulus, G′′, as functions of the shifted frequency aTω, with aT as the temperature shift factor. The reference temperature is 160 °C. The two solid lines have slopes of 2 for G′ and 1 for G′′. The frequencies ωR and ωc associate with reptation time and onset of thermorheological complexity, respectively. (a) For PEH/PEB 50/50 blend; (b) for PEH/PEB 70/30 blend.

for the two components indicates that PEH is the slower component while PEB is the faster one in the blends, but upon blending the friction coefficient of the slower chains should slightly decrease while that of the faster chains should increase.39 At low frequencies the curves in Figure 1 show the terminal zone, but the transition curvature from plateau zone to terminal zone of PEH looks smaller than that of PEB, which may be affected by molecular weight distribution or some other molecular structure factors. To detect phase boundary by the TTS principle, dynamically measured mechanical properties of PEH/PEB blends with PEH compositions ranging from 20 to 80% by mass percentage were obtained in a temperature range with different interval, extending from 125 to 160 °C. To clarify, parts a and b of Figure 2 show the master curves of storage modulus, G′, and loss modulus, G′′, as functions of the shifted frequency, aTω, for PEH/PEB 50/50 and 70/30 blends, respectively. The temperature dependence of the frequency scale shift factor aT, in principle, is related to the reference temperature Tref by the WilliamsLandel-Ferry (WLF) equation

log aT )

-c1(T - Tref) c2 + (T - Tref)

(15)

where c1 and c2 are constants obtained by fitting complex modulus G* with the above equation. In this work the values of aT were obtained by the AR2000 data analysis TTS procedure with the selected reference temperature of 160 °C. Ideally, at low frequencies in terminal zone the scaling laws40 G′ ∼ ω2 and G′′ ∼ ω should be observed for homogeneous polymers. When temperature is above 148 °C for the PEH/PEB 50/50 blend and above 140 °C for the 70/30 blend, the slopes of G′ and G′′ at low frequencies are close to 2 and 1, respectively, which indicates that the two blends basically reach their terminal zones. As shown in Figure 2a, the TTS principle works well for both G′ and G′′ from 160 to 148 °C for the PEH/PEB 50/

50 blend, but when the temperature continuously decreases to 145 °C or below, TTS breaks down and an apparent deviation of G′ from the terminal slope is observed. This deviation is undoubtedly a signature of phase separation, and thus the critical temperature can be estimated to be about 145 °C. The breakdown of TTS at low frequencies is due to the additional elastic deformation and relaxation coming from the phaseseparated domains, whose sizes are much larger than the individual chains. If careful enough, one can find that the deviations of TTS at low frequencies in both parts a and b of Figure 2 become more distinct with temperature decreasing. This phenomenon can be explained by the interplay between thermodynamics of phase separation and the resulting interfacial tension.41 For a UCST system like the PEH/PEB blends, the interaction parameter χ(T) ) A + B/T (where A ) -0.0011, B ) 1.0 for the specific PEH/PEB system30) must increase with temperature decreasing to form the phase-separated morphology. Because the interfacial tension varies in the same direction as the interaction parameter does, that is, the interfacial tension increases with the increasing quench depth,15 that the enhanced elasticity at low frequencies increases with temperature decreasing can be easily understood. In other words, below the critical temperature the enhanced elasticity at low frequencies should be related to the additional relaxation of interfacial tension, especially in the late stages of phase separation. It is also seen that G′ is more sensitive than G′′ because near the phase boundary the additional relaxation corresponding to deformation of phase domains and the domain shape recovery has the elastic origin. Kapnistos found that in the phase-separated region a shoulder of G′ appeared at some low frequencies, but the terminal slope would be eventually reached at even lower frequencies.20 This phenomenon was not observed in our measurements on PEH/PEB blends; however, the terminal slope maybe also exist and locate in a much lower frequency range. The critical frequency of ωc corresponding to the onset of thermorheological complexity marked in Figure 2a,b is about 0.1 rad/s, and the related time scale (τc ) 1/ωc) is much longer than the reptation time (τR ) 1/ωR) of the polymer chains. Therefore, some authors pertinently ascribed the additional relaxation at low frequencies to concentration fluctuations and further explained by the “collective” motions of several polymer chains.20,25 In our study, G′ and G′′ at low frequencies correspond to the phase-separated morphology, in which the concentration fluctuations are nearly saturated and the interfacial tension becomes the dominant role, so we conclude that the thermorheological complexity may be mainly due to supplementary relaxation of the interfacial tension. There are many arguments on the TTS principle since it is widely used in the literature. Generally, TTS has been well applied for homogeneous polymers, whereas its failure means that the studied system exhibits heterogeneity. Colby42 found that TTS fails even for the miscible PMMA/PEO blends in the terminal region. Later, Pathak43 concluded that whether TTS works in a single-phase blend or not depends largely on the difference of glass transition temperatures, Tg, between the two pure components. Kapnistos et al.20 argued that for PS/PVME blends TTS worked in homogeneous region far from the phase boundary but failed in the same region near the phase boundary. Bousmina23 reached the conclusion that the validity of the TTS principle in a given system does not necessarily mean that the system is a homogeneous one; conversely, when TTS fails for some classical systems, this does infer that some structural changes occur in the systems. So the TTS principle is not a universal method to determine the critical phase separation

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Figure 3. Changes of storage modulus during dynamic temperature sweeps for PEH/PEB blends at different compositions with fixed frequency of 0.03 rad/s and strain of 5%.

temperature, and its validity for a given system should be carefully verified. For our studied PEH/PEB blends, the binodal temperature obtained by the TTS principle roughly agrees with that from diffuse light scattering methods,30 which indicates that the TTS principle is valid for the PEH/PEB blend system and the enhanced elasticity of G′ in low-frequency range is considered to be induced by the phase-separated structures. Dynamic Temperature Sweep. Although the TTS principle can be roughly used to detect the phase boundary of PEH/PEB blends, it has nothing to do with the spinodal temperature. To determine the spinodal phase separation temperature, Ts, and quantitatively obtain the binodal temperature for PEH/PEB blends, dynamic temperature sweeps were carried out at a fixed low frequency of 0.03 rad/s and a given strain of 5%. The experimental temperature was decreasing from the homogeneous region to the phase-separated region (from 160 to 123 °C) with a decrement of 1 °C. The selected frequency of 0.03 rad/s is lower than the onset of thermorheological complexity to guarantee that the changes of viscoelastic properties are surely induced only by phase separation rather than any other factors. Figure 3 shows the changes of storage modulus, G′, during dynamic temperature sweeps for the blends at different compositions. It is seen that in the homogeneous region above the critical temperature G′ gradually increases with temperature decreasing, which is due to the slowing down of molecular motion or increasing of intermolecular friction. As temperature further decreases and the phase boundary is approached, G′ dramatically increases and an obvious upturn appears, which is thought to be the coupling effects of the decreased molecular chain motion and enhanced interfacial tension-driven elasticity. This enhanced elasticity has the same origin as the increase of the elasticity at low frequencies as observed in the isothermal frequency sweep. About the origin of elasticity in the vicinity of phase separation, there are still different interpretations. Kapnistos20 ascribed the enhanced elasticity to concentration fluctuations as a result of the coupling between thermodynamics and chain mobility forces. Bousmina23 argued that the interface formed during phase separation introduces a supplementary elasticity into the system due to deformation and shape recovery of the domains on the macroscopic level and confirmed that the interfacial tension is the first cause for the increase of elasticity. On the basis of these arguments and our experimental results, we consider that the interfacial tension should be the dominant role to account for the elasticity enhancement because during the gradual temperature decreasing the concentration fluctuations could become less significant. It is also evident from Figure 3 that not only the magnitude of G′ upturn but also the temperature range, over which the upturn takes place, strongly depends on the composition of the blend. Near the critical composition, the magnitude of G′ upturns seems more obvious,

Figure 4. Changes of storage modulus, G′, loss modulus, G′′, and tangent of loss angle, tan δ, during dynamic temperature sweeps with fixed frequency of 0.03 rad/s and strain of 5%. (a) For PEH/PEB 35/ 65 blend; (b) for PEH/PEB 50/50 blend.

and the corresponding transitional zone is also narrower than that at the other compositions, which is thought to be due to different phase separation mechanisms (spinodal concentration fluctuations or nucleation and growth). Figure 4a,b displays the changes of storage modulus, G′, loss modulus, G′′, and tangent of loss angle, tan δ, during dynamic temperature sweeps with the fixed frequency of 0.03 rad/s and strain of 5% for PEH/PEB 35/65 and 50/50 blends, respectively. Obviously, both G′ and tan δ are more sensitive than G′′ as aforementioned. The upturn for G′ and downturn for tan δ coherently reflect the phase transition behavior in the vicinity of phase separation. To determine binodal temperature, we specifically assign temperature at the inflexion of curve of G′ or tan δ vs temperature, that is, temperature at the minimum of dG′/dT, as binodal temperature. Temperatures of 145.2 °C for the 35/65 blend and 146.2 °C for the 50/50 blend are marked in the figures as the guides to the eye. For the PEH/PEB 50/50 blend, the binodal temperature obtained by this method agrees very well with that from diffuse light scattering and the FloryHuggins theory.30 To obtain the phase separation temperature quantitatively, we can apply the theoretical approach of Ajji and Choplin29 based on the mean field theory to our studied blend system. By using this method, Vlassopoulos et al.19,20 successfully estimated the spinodal temperatures for both LCST and UCST systems. Figure 5a,b shows the linear dependence of (G′′2/G′T)2/3 vs 1/T, in which the reciprocal to intercept with the 1/T axis indicates the spinodal temperature, Ts. The linear range shown in Figure 5 was proven to be in the phase transitional region, and the corresponding lines give estimates of the spinodal temperatures at about 137.8 °C for the PEH/PEB 35/65 blend and 132.3 °C for the 50/50 blend. It should be kept in mind that the selection of the linear range is crucial for determination of Ts, and in the present case, the error of measurement is about (2 °C. In the rational error range, we argue that the composition of 35/65 is at least near the critical phase separation point. Unlike PEH/ PEB 35/65 and 50/50 blends, the transitional regions of phase separation were unable to discern in the temperature range 160-

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Figure 5. Quantitative evaluations of viscoelastic behavior near the phase separation and determination of spinodal temperature: (a) for PEH/PEB 35/65 blend; (b) for PEH/PEB 50/50 blend.

Figure 6. Phase diagram of PEH/PEB blends determined from rheological measurement. The filled circle indicates binodal temperature (solid line is the fitted curve), and the open circle indicates spinodal temperature (dashed line is plotted as the spinodal line).

123 °C for PEH/PEB 80/20 and 20/80 blends. As a result, the spinodal temperatures for PEH/PEB 80/20 and 20/80 blends have not been experimentally obtained. Figure 6 summarizes the phase diagram of PEH/PEB blends determined by the rheological measurements in this study. Except the binodal temperatures of PEH/PEB 20/80 and 80/20 blends determined by the TTS principle, all other data points including the binodal and spinodal temperatures were derived from the data of dynamic temperature sweeps. Compared with the phase diagram established by Wang et al.,30 the binodal temperatures of PEH/PEB 40/60, 50/50, and 60/40 blends determined by the rheological measurements in this work show good accordance with that from the diffuse light scattering measurement. We notice here that these methods in detecting phase boundary are much different at the time and spatial scales. The rheological measurement is sensitive to polymer chain reptation, diffusion, and interfacial tension, and thus it is particularly great for detecting concentration fluctuations and interfacial tension in the early stages of phase separation, compared with the other optical techniques such as phase contrast optical microscopy. From this viewpoint, we argue that the time scale as well as the spatial scale from rheology is smaller than that from the indirect methods that Wang et al. have introduced. Comparatively, the spinodal temperatures extrapolated by rheological data seem more dispersed than the

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binodal temperatures; however, the shape of spinodal line can still be roughly obtained, which indicates that the critical composition of the blends is approximately close to 35/65. Actually, this spinodal line can sufficiently provide us an informatory temperature range to distinguish the metastable region (for nucleation and growth mechanism) from the unstable region (for spinodal concentration fluctuations mechanism). In an ideal condition, the binodal line and spinodal line should overlap at a critical composition, but for the phase diagram of PEH/PEB blends shown in Figure 6 there is a temperature gap of about 7 °C at the critical composition close to 35/65. Except for the error produced by selection of the linear range when Ts was determined, several shortcomings of the theory itself should be taken into account to explain this existing temperature gap. First, the theory considers only the time scale larger than reptation time while the short chain or segment motions are all ignored, which contradicts the preliminary assumption on elastic response in the case of the applied instantaneous and infinitesimal strain. Second, the absence of interaction parameter in the Onsager coefficient equation (eq 5) also introduces an error to the scaling relation, since variation of the interaction parameter with temperature can consequently induce a variation of (G′′2/G′T)2/3 with temperature.23 Third, the intermolecular entanglement ignored in theory is another factor responsible for the resulted error because the molecular weights of PEH and PEB are obviously far beyond the thresholds for the chain entanglements of polyolefins. Nevertheless, the spinodal line determined by the rheological measurement can still provide us sufficiently useful experimental evidence for the further investigations on the phase separation kinetics of the blends. 2. Rheologically Investigated Phase Separation Kinetics. To probe phase separation kinetics of PEH/PEB blends, 8 h time sweeps with the fixed frequency of 0.03 rad/s and strain of 5% were carried out for PEH/PEB 50/50 and 70/30 blends at different temperatures. Figure 7a presents the evolutions of storage moduli G′ of the PEH/PEB 50/50 blend during phase separation at 130, 135, and 140 °C. Clearly, the storage moduli at these three temperatures all decrease with time, but the decreasing magnitude becomes small as the quench depth decreases because the quench depth affects the strength of the initial concentration fluctuations for spinodal phase separation in the unstable region and nucleation and growth in the metastable region.22 At 130 and 135 °C, G′ dramatically decreases in the early stages and then keeps about constant for the remaining time, which is related to the decreased concentration fluctuations and reduced interfacial area due to interfacial tension-driven phase domain coarsening and coalescence. In more detail, the drastic decrease of G′ in the early stages should be caused by the coupling effects of concentration fluctuations and interfacial tension. In the late stages, when the concentration fluctuations become nearly saturated and the compositions of both phases remain about constant, the interfacial tension becomes dominant; however, it continuously decreases because of the phase domain coarsening or coalescence and/or breaking up of the highly interconnected bicontinuous structures. In terms of phase diagram in Figure 6, the PEH/PEB 50/50 blend at 140 °C locates in the metastable region. At this temperature the phase separation process is slower and weaker than that at 130 and 135 °C because the nucleation and growth of phase separation are mainly controlled by chain diffusions rather than by spinodal concentration fluctuations, which occur at 130 and 135 °C. At 140 °C the variation of G′ with time largely depends on the evolution of interfacial tension. Thus, the decreasing of G′ with time is moderate as can be seen from

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Figure 7. Evolutions of storage modulus, G′, during time sweeps at different phase separation temperatures with fixed frequency of 0.03 rad/s and strain of 5%: (a) for PEH/PEB 50/50 blend; (b) for PEH/PEB 70/30 blend; (c) for both PEH/PEB 50/50 and PEH/PEB 70/30 blends at 130 °C; (d) temperature dependence of correlation length for PEH/PEB 50/50 and 70/30 blends.

Figure 7a. To further verify the result, Figure 7b illustrates the evolutions of G′ of the PEH/PEB 70/30 blend during time sweeps at 127, 130, and 133 °C, which all locate in the metastable region. Similar to the PEH/PEB 50/50 blend at 140 °C, the storage moduli of the PEH/PEB 70/30 blend gradually decrease with time and the decreasing magnitude of G′ becomes small with quench depth decreasing. In addition, at temperature of 133 °C (with the smallest quench depth), the decreasing of G′ can hardly be detected. Unlike other investigations,21,22 the increasing of G′ with time in the metastable region has not been observed for our studied system. In terms of Palierne’s emulsion model,44 at very low frequencies the elastic contribution of the two components to G′ is negligible, and the development of G′ is only related to the interfacial tension, which in turn largely depends on the shape deformation and variation of interfacial area of the droplets formed during phase separation. Vinckier21 argued that the interfacial contribution to storage modulus is proportional to the droplet sizes, which attributes to more deformability of larger droplets. In fact, the interfacial tension is determined by two competitive factors: the total interfacial area and deformability of the droplets. If total interfacial area is dominant, G′ will decrease with time, whereas if droplet deformability is the leading factor, G′ will increase with time. Although Palierne’s model has been successfully used to explain the morphological evolution for immiscible and some partially miscible polymer blends, for the PEH/PEB blend system, the particularity, of which are the similar chain structures of the two consisting components, should be carefully taken into account because the well-defined droplet-matrix morphology may not really form during phase separation in the metastable region.34 From the above understanding, it does not seem so reasonable to describe G′ decreasing of PEH/PEB blends in the metastable region by using this model, for which it was first derived from the immiscible polymer blends. According to Kapnistos et al.,20 the enhanced concentration fluctuations in the early stages of phase separation could lead to an increasing of G′. However, such an increasing of G′ during phase separation has not been obviously observed so far for the PEH/PEB blend system in our experiments possibly because of the frequency limit. Actually, if we extrapolate the data of

G′ in the homogeneous region (Figure 3) to the temperatures used in time sweep experiments, that is, to eliminate the enhanced elasticity induced by phase separation, the ideal values of G′ for time of zero denoting as G′0 can be obtained. For the PEH/PEB 50/50 blend, G′0 of 11.8, 10.5, and 9.3 Pa at 130, 135, and 140 °C, respectively, were obtained. These values are much lower than the first data points that we have detected at the three temperatures. Thus, such an increasing of G′ may truly exist, and it should go through a maximum in the very early stages of phase separation. Figure 7c compares the evolutions of G′ for PEH/PEB 50/ 50 and 70/30 blends at 130 °C. Obviously, the magnitude of G′ decreasing and the time for G′ reaching to the equilibrium for these two blends are obviously different because of different phase separation mechanisms. For the 70/30 blend the nucleation and growth process should undergo at this temperature, whereas for the 50/50 blend the bicontinuous morphology should form through the spinodal concentration fluctuations mechanism. Therefore, phase separation is much slower and the magnitude of G′ decreasing is smaller for the former, for which the nucleation and growth process is dominated by diffusion and the interfacial tension is much weaker than that due to the spinodal concentration fluctuations of the latter. Figure 7d illustrates the temperature dependence of correlation length ξ calculated from eq 14 for PEH/PEB 50/50 and 70/30 blends. The correlation length has important physical significance and is related to concentration fluctuations. As shown in Figure 7d, the estimated correlation lengths for the two blends are on the order of 17-22 Å, which are in small scales and indicate the similar structures of the two consisting components. In the phase transition region, correlation length dramatically changes with temperature, reflecting the changes of the degree of local ordering during phase separation. For the 50/50 blend, the correlation length sharply increases with temperature decreasing near the phase boundary and keeps about constant below 140 °C, while for the 70/30 blend the change of correlation length is not only delayed but also moderate. This means that the progress of phase separation for the 50/50 blend is faster than that for the 70/30 blend because the former is much closer to critical composition and has much stronger

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fluctuations and decreased interfacial tension, whereas the decreasing of G′ in the metastable region is determined by competitive effects of the reduced interfacial area and the increased deformability. Acknowledgment. The authors acknowledge the financial support from the “One Hundred Talents” Program of the Chinese Academy of Sciences and the National Science Foundation of China with Grants NSFC 10590355 and NSFC 50573088. The authors would like to give thanks to Dr. Pathak at NIST for his helpful suggestions. Figure 8. Comparison between evolutions of storage modulus, G′, during time sweeps for PEH/PEB 50/50 and PEH/PEB 70/30 blends at 140 and 130 °C, respectively.

References and Notes (1) (2) (3) (4)

spinodal concentration fluctuations than the latter. The correlation lengths estimated from the rheological method are proven to agree reasonably with that obtained from SANS.25,29 To further indicate dynamics of phase separation in the metastable region, the evolutions of G′ for PEH/PEB 50/50 and 70/30 blends at 140 and 130 °C are shown in Figure 8. Interestingly, the trends of G′ decreasing are similar for these two blends, although G′ of the PEH/PEB 70/30 blend is higher than that of the PEH/PEB 50/50 blend because of the higher volume fraction of PEH in the former. We consider that the PEH/PEB 50/50 blend at 140 °C should undergo nucleation and growth process during phase separation as the PEH/PEB 70/30 blend does. The experimental evidence from our previous publication33 confirms this finding, in which time evolutions of the characteristic lengths from the optical techniques for various blends at different temperatures were presented. Surprisingly, time evolutions of the characteristic lengths for the PEH/ PEB 50/50 blend at 140 °C and the PEH/PEB 70/30 blend at 130 °C were similar and both developed slowly,33 which agree very well with our current results shown in Figure 8. The above accordance provides strong support to the judgment that the PEH/PEB 50/50 blend at 140 °C locates in the metastable region, which in turn confirms that the spinodal line in the phase diagram determined by the rheological measurement is relatively reliable.

(21) (22)

Conclusions

(23)

In this work, we have systematically studied the viscoelastic properties of PEH/PEB blends during phase separation. The phase diagram of the blends has been experimentally established by rheological measurement, in which the binodal line was obtained by the TTS principle and dynamic temperature sweeps and the spinodal temperatures were quantitatively estimated on the basis of mean field theory. The measured binodal temperature agrees very well with that from other methods. The obtained spinodal temperature is proven to be relatively reliable by the rheological experimental evidence. The phase separation kinetics from polymer viscoelasticity viewpoints was further investigated on the basis of the obtained phase diagram. Rheological measurement can sensitively detect the rather early stages of phase separation compared with the optical techniques. It is found that in either the metastable or unstable regions the storage moduli G′ of the phase-separated blends decrease when phase separation progresses. The magnitude of G′ decreasing is smaller in the metastable region than the unstable region because the nucleation and growth in the metastable region are dominated by diffusion and the interfacial tension is much weaker, while for the latter, spinodal concentration fluctuations are dominant. The decrease of G′ in the unstable region is due to the coupling effects of the reduced concentration

(24)

(5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) (19) (20)

(25) (26) (27) (28) (29) (30) (31) (32) (33) (34) (35) (36) (37) (38) (39)

Tanaka, H. Phys. ReV. Lett. 1996, 76, 787-790. Taniguchi, T.; Onuki, A. Phys. ReV. Lett. 1996, 77, 4910-4913. Tanaka, H. J. Phys.: Condens. Matter 2000, 12, R207-R264. Balsara, N. P.; Rappl, T. J.; Lefebvre, A. A. J. Polym. Sci., Part B: Polym. Phys. 2004, 42, 1793-1809. Clerke, N.; McLeish, T. C. B.; Pavawongsak, S.; Higgins, J. S. Macromolecules 1997, 30, 4459-4463. Doi, M.; Ohta, T. J. Chem. Phys. 1991, 95, 1242-1248. Vinckier, I.; Moldenaers, P.; Mewis, J. J. Rheol. 1996, 40, 613-631. Takahashi, Y.; Kato, T. Korea-Australia Rheol. J. 2005, 17, 125130. Bousmina, M. Rheol. Acta 1999, 38, 73-83. Chopara, D.; Vlassopoulos, D.; Hatzikiriakos, S. G. J. Rheol. 2000, 44, 27-45. Madbouly, S. A.; Ougizawa, T. Macromol. Chem. Phys. 2004, 205, 1222-1230. Kim J. K.; Son, H. W. Polymer 1999, 40, 6789-6801. Kim J. K.; Son, H. W.; Lee, Y.; Kim, J. J. Polym. Sci., Part B: Polym. Phys. 1999, 37, 889-906. Takahashi, Y.; Suzuki, H.; Nakagawa, Y.; Noda, I. Macromolecules 1994, 27, 6476-6481. Jeon, H. S.; Nakatani, A. I.; Han, C. C.; Colby, R. H. Macromolecules 2000, 33, 9732-9739. Nesarikar, A. R. Macromolecules 1995, 28, 7202-7207. Polios, I. S.; Soliman, M.; Lee, C.; Gido, S. P.; Schmidt-Rohr, K.; Winter, H. H. Macromolecules 1997, 30, 4470-4480. Mani, S.; Malone, M. F.; Winter, H. H. J. Rheol. 1992, 36, 16251649. Vlassopoulos, D.; Koumoutsakos, A.; Anastasiadis, S. H. J. Rheol. 1997, 41, 739-755. Kapnistos, M.; Vlassopoulos, D.; Anastasiadis, S. H.; Stammer, A.; Wolf, B. A. Macromolecules 1996, 29, 7155-7163. Vinckier, I.; Laun, H. M. Rheol. Acta 1999, 38, 274-286. Zhang, Z. L.; Zhang, H. D.; Yang, Y. L.; Vinckier, I.; Laun, H. M. Macromolecules 2001, 34, 1416-1429. Bousmina, M.; Lavoie, A.; Riedl, B. Macromolecules 2002, 35, 62746283. Steinmann, S.; Gronski, W.; Friedrich, C. Rheol. Acta 2002, 41, 7786. Sharma, J.; Clarke, N. J. Phys. Chem. B 2004, 108, 13220-13230. Ajji, A.; Choplin, L.; Prud’homme, R. E. J. Polym. Sci., Part B: Polym. Phys. 1988, 26, 2279-2289. Zheng, Q.; Du, M.; Yang, B. B.; Wu, G. Polymer 2001, 42, 57435747. Fredrickson, G. H.; Larson, R. G. J. Chem. Phys. 1987, 86, 15531560. Ajji, A.; Choplin, L. Macromolecules 1991, 24, 5221-5223. Wang, H.; Shimizu, K.; Hobbie, E. K.; Wang, Z. G.; Meredith, J. C.; Karim, A.; Amis, E. J.; Hsiao, B. S.; Hsieh, E. T.; Han, C. C. Macromolecules 2002, 35, 1072-1078. Wang, H.; Shimizu, K.; Kim, H.; Hobbie, E. K.; Wang, Z. G.; Han, C. C. J. Chem. Phys. 2002, 116, 7311-7315. Wang, Z. G.; Wang, H.; Shimizu, K.; Dong, J. Y.; Hsiao, B. S.; Han, C. C. Polymer 2005, 46, 2675-2684. Shimizu, K.; Wang, H.; Wang, Z. G.; Matsuba, G.; Kim, H.; Han, C. C. Polymer 2004, 45, 7061-7069. Zhang, X. H.; Wang, Z. G.; Muthukumar, M.; Han, C. C. Macromol. Rapid Commun. 2005, 26, 1285-1288. Bates, F. S. Macromolecules 1984, 17, 2607-2613. De Gennes, P. G. J. Chem. Phys. 1980, 72, 4756; Scaling Concepts in Polymer Physics; Cornell University Press: Ithaca, NY, 1979. Binder, K. J. Chem. Phys. 1983, 79, 6387-6409. Doi, M.; Edward, S. F. The Theory of Polymer Dynamics; Oxford Press: New York, 1986. Pathak, J. A.; Kumar, S. K.; Colby, R. H. Macromolecules 2004, 37, 6994-7000.

Macromolecules, Vol. 39, No. 12, 2006 (40) Ferry, J. D. Viscoelastic Properties of Polymers, 3rd ed.; Wiley: New York, 1980. (41) Vinckier, I.; Schweizer, T.; Laun, H. M. J. Polym. Sci., Part B: Polym. Phys. 2002, 40, 679-690. (42) Colby, R. H. Polymer 1989, 30, 1275-1278.

Polyolefin Blends 4183 (43) Pathak, J. A.; Colby, R. H.; Kamath, S. Y.; Kumar, S. K.; Stadler, R. Macromolecules 1998, 31, 8988-8997. (44) Palierne, J. F. Rheol. Acta 1990, 29, 204-214.

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