Viscoelastic properties and interfacial tension of polystyrene-polyethylene blends

Viscoelastic Properties and Interfacial Tension of Polystyrene–Polyethylene Blends NAFAA MEKHILEF,* PIERRE J. CARREAU, BASIL D. FAVIS, PHILIPPE MARTIN, ABDELHAK OUHLAL Center for Applied Research on Polymers, CRASP, Chemical Engineering Department, Ecole Polytechnique, P.O. Box 6079, Stn. Centre Ville, Montreal, Quebec, H3C 3A7, Canada

Received 21 June 1999; revised 24 February 2000; accepted 28 February 2000

ABSTRACT: The linear viscoelastic properties of polystyrene polyethylene (PS/PE) blends have been investigated in the molten state. For concentrations of the dispersed phase equal to 30 vol %, the blends exhibited a droplet-matrix morphology with a volume-average diameter of 5.5 ␮m for a 70/30 PS/PE blend at 200 °C and 14.7 ␮m for a 30/70 PS/PE blend at 230 °C. Enhanced elasticity (G⬘) for both blends, in the terminal zone, compared to the modulus of the matrix (PS and PE, respectively) was observed. This is related to the deformation of the droplets in the matrix phase and hence to the interfacial forces between the blend components. The results for these uncompatibilized blends are shown to be in agreement with the predictions of the emulsion model of Palierne. These predictions were used to obtain the interfacial tension between PS and PE, which was found to be between 2 and 5 mN/m at 200 °C and 4 ⫾ 1 mN/m at 230 °C. Independent interfacial tension measurements using the breaking-thread method resulted in a value of 4.7 mN/m and 4.1 mN/m at 200 °C and 230 °C for the respective blends. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1359 –1368, 2000 Keywords: polymer blends; linear viscoelasticity; emulsion model; interfacial tension

INTRODUCTION The viscoelastic properties of polymers are predominant in the end properties of polymer blends. Usually, the morphology depends highly on the viscosity ratio of the components as well as their elastic ratio.1– 6 The linear viscoelastic properties of polymers give a mirror image of their molecular and morphological structures. In the terminal (low-frequency) zone, the storage modulus (G⬘) is typically quadratic with respect to frequency. Similarly, the loss modulus (G⬙) is linearly proportional to the frequency in the terminal zone. In the case of polymer blends exhibiting droplets-

* Present address: Elf Atochem North America Inc., Research and Development Center, 900 First Avenue, P.O. Box 61536, King of Prussia, Pennsylvania 19406-0936 Correspondence to: P. J. Carreau (E-mail: Pierre.Carreau@ courriel.polymtl.ca) Journal of Polymer Science: Part B: Polymer Physics, Vol. 38, 1359 –1368 (2000) © 2000 John Wiley & Sons, Inc.

matrix morphology, the storage modulus is larger than that of the matrix in the terminal zone. The increase in elasticity is only observed when the zero-shear viscosity or the complex modulus of the dispersed phase is significantly lower than that of the matrix. Under these circumstances, the change in the modulus is a direct result of the competition mechanism of the shear forces deforming the sample and the interfacial forces acting against the shear deformation. If the dispersed phase has a higher viscosity than the matrix then, these effects are less pronounced and the rheological behavior of the blends will be similar to that of filled systems. It is possible to use theoretical approaches to predict the rheological behavior of multiphase systems.7–9 Palierne9 has developed a model, which can predict the linear viscoelastic behavior of polymer emulsions, taking into account the size of the viscoelastic droplets dispersed in a viscoelastic matrix and the interfacial tension between the compo1359

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nents. This model reduces to Oldroyd model if the components are Newtonian liquids and the droplets are of a unique size.7,8 The Palierne model has been successfully used to predict interfacial tension between several polymers.10 –16 In some cases, the values of the obtained interfacial tension have been verified using direct techniques to measure interfacial tension. Among them are the breaking thread, the fiber retraction, the spinning drop, and pendent drop techniques.17–23 Each method presents certain advantages and limitations. The breaking-thread technique requires the knowledge of the zero-shear viscosity of the materials used.18 –20 This is possible for many polymers provided that the molecular weight is not very high and therefore the Newtonian plateau is measurable within a reasonable time. In addition, the polymer should not show any yield stress effects. The pendent drop technique requires equilibrium conditions, which are usually time-consuming for polymeric materials, and also requires good thermal stability of the resins. Moreover, one has to know the melt density, which is not trivial to measure.23 Limitations have been reported with the breaking-thread technique when materials exhibiting a yield stress behavior were investigated. For materials such as thermoplastic elastomers (i.e., butadiene-based copolymer, high vinyl acetate EVA copolymers), it is difficult to distinguish between interfacial forces that tend to break a fiber and the yield stress effects, which are reflected by a steep change in viscosity at low frequencies. To date, no comparison between indirect interfacial tension measurements using an emulsion model of Palierne’s type and a direct technique such as the breaking-thread method has yet been reported. The objective of this work is to carry out a direct comparison of two approaches for the measurement of the interfacial tension of PS/PE blends. The interfacial tension as predicted by the Palierne emulsion model is compared to that determined by the breaking-thread technique. In particular, the limitations of the rheological method are stressed in terms of experimental errors in the measurements by both techniques as well as assumptions made on the obtained morphologies.

EXPERIMENTAL Materials A general-purpose polystyrene (PS) and a highdensity polyethylene (PE), both manufactured by

Table I. Key Characteristics of the Materials Used Polystyrene M aw (g/mol) M na (g/mol) Melt index (g/10 min) Density (20 °C)a (g/mL) Density (200 °C)a (g/mL) ␩0 (200 °C)d (Pa 䡠 s) ␩0 (230 °C)d (Pa 䡠 s)

215,000 100,000

Polyethylene 79,000 24,000

8.0b

4.0c

1.040

0.962

0.974

0.754

5630

1780

1220

1420

a

Given by the supplier. 200 °C/15.0 kg (given by the supplier). c 190 °C/2.16 kg (given by the supplier). d Zero-shear viscosity determined using the Carreau–Yasuda model. b

Dow Chemical Company, Canada, were used. A small amount of Irganox 1010 as an antioxidant was added to PE to reduce the thermal oxidation and crosslinking of the material. Key characteristics of these materials are reported in Table I. Two blends having a volume composition of 70/30 and 30/70 PS/PE were prepared using a corotating Leistritz twin screw extruder at 200 °C. An adequate screw design was selected for optimum mixing. The materials were dry-blended before feeding into the hopper. Rheological Characterization A Bohlin CSM constant stress rheometer equipped with a 25-mm parallel plate configuration was used to study the rheological behavior of the raw materials as well as the blends. First, strain sweeps were carried out to determine the linear viscoelasticity region for each material. The rheological measurements were performed at 200 °C and 230 °C under a nitrogen atmosphere in the frequency range of 0.01 to 250 rad/s and a gap range of 1.3 to 1.7 mm. The viscoelastic properties of the PE and the PS were found to be linear for strains smaller than 3% and 1%, respectively. For the blends, the strain response was kept under 5%. To our surprise, bubbles formed in the polystyrene sample during the initial experiments. These bubbles were attributed to processing additives added during the synthesis of PS. Consequently, molding conditions had to be

POLYSTYRENE–POLYETHYLENE BLENDS

changed. Sample preparation was carried out in two steps. First, the sample was heated at 200 °C in a Carver press for about 10 min to allow for the formation of the bubbles. Subsequently pressure was applied to the sample to release progressively the gas bubbles. This technique proved to be successful in eliminating all bubbles present in the sample. Phase Morphology Morphological examination was carried out using a JEOL 840 scanning electron microscope (SEM). The samples were rapidly cooled inside the rheometer by blowing liquid nitrogen and then removed and cryo-fractured. The fractured samples were coated with a gold–palladium alloy prior to examination. The obtained morphologies were quantified by image analysis. The volume and number average diameters (dv and of dn, respectively) of the dispersed phase were measured by digitalization of the images and reported as a function of the experimental conditions using a sigma scan威 software connected to a digitalization table. Several micrographs were used to generate a valid statistical representation of each morphology (400 particles were scanned for each determination). No corrections were made for the determination of the “true” volume-average diameter (dv). Interfacial Tension Measurements The breaking-thread technique was used to measure the interfacial tension between PS and PE at 200 °C and 230 °C. The principle of the technique consists of inserting a thread of PS in a PE sandwich, which, in turn, is inserted between two glass slides. The sample is then placed in a hot stage under a transmission microscope and brought to the desired temperature. Care was taken to avoid the collapsing of the thread in the molten state and to ensure that all initial stresses are relaxed. Once the sample reached the desired temperature, oscillations in the thread developed due to interfacial forces at the interface of the two polymers. Quantitative analysis of this mechanism was done by recording the distortion amplitude with time. The rate of growth of the distortions is theoretically related to the interfacial tension. More details about the theoretical and experimental procedures are reported in refs.18 – 20, 24, and 25. The equipment used for these measurements was built in-house and consists of

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a Mettler hot stage model FP 82 HT connected to a FP 90 central processor and to a Nikon transmission optical microscope.

THEORETICAL ASPECTS Palierne9 extended Oldroyd’s emulsion model7,8 to include the viscoelasticity of the components as well as a droplet size distribution. The Palierne model was successfully used to predict the rheological behavior of a PETG/EVA blend at various temperatures and different blend compositions.16 It was also found to be applicable to PS/PMMA and PDMS/POE blends as described by Graebling et al.12 Good agreement between the predictions of the model and the experimental data was found by Bousmina and Muller11 and Carreau et al.14 for PS/PMMA and PA/PP blends, respectively. The Palierne model with the inclusion of particle size distribution was used with success by Friedrich et al.13 to describe the distribution of droplets in PMMA/PS blends. Brahimi et al.26 reported similar conclusions for a HDPE/HIPS blend. Bousmina et al.15 have compared the emulsion model predictions with experimental results for PS/PE blends. Good agreement was shown for a 70/30 PS/PE blend for an interfacial tension value of 5.2 mN/m, which is the typical value reported in the literature for this pair of polymers.17 The interfacial tension was found to drop to 3.5mN/m when the same blend had its components treated with corona. For a blend modified with 1% of a triblock SEBS copolymer, the interfacial tension fell to 1.5 mN/m. In all cases, the emulsion model description of the data was found to be excellent. Bousmina et al.15 also examined the linear viscoelastic data of the inversed 30/70 PS/PE blend. However, in that case, the viscosity ratio of the matrix to the dispersed phase being equal to 0.017, the droplets could not be deformed and the emulsion model could not be used to verify the interfacial tension value obtained for the first blend (70/30 PS/PE). For a HDPE/HIPS blend, Brahimi et al.26 have shown that in the presence of well-designed diblock styrene– butadiene copolymers, the Oldroyd model failed in predicting the rheological behavior of the blend when 5 wt % copolymer (based on the blend) was added. A similar failure is expected for the Palierne model due to the yield stress effects in this particular system. Another case where the Palierne model failed in predicting the rheological behavior of two phase systems was

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reported by Carreau et al.14 for PS blends containing thermoplastic elastomers. In that case, the rubber droplets were slightly deformable and the enhancement of elasticity at low frequency was attributed to particle–particle interactions, agglomeration of particles, and percolation. The complex shear modulus of the emulsion of viscoelastic polydispersed droplets can be expressed in terms of the complex moduli of each phase, the interfacial tension, and the radii of the droplets:

冘␸ H*共␻兲 G *共 ␻ 兲 ⫽ G * 共 ␻ 兲 1 ⫺ 2 冘 ␸ H *共 ␻ 兲 1⫹3

i

i

i

i

i

b

m

(1)

i

where G*b, G*m are the complex modulus of the blend and the matrix, respectively; ␸i is the volume fraction of the dispersed phase corresponding to the particles of di and Hi(␻) is given by: H *i共 ␻ 兲 ⫽ 8共 ␣ Ⲑd i兲关2G *m共 ␻ 兲 ⫹ 5G *d共 ␻ 兲兴 ⫹ 关G *d共 ␻ 兲 ⫺ G *m共 ␻ 兲兴关16G *m共 ␻ 兲 ⫹ 19G *d共 ␻ 兲兴 80共 ␣ Ⲑd i兲关G *m共 ␻ 兲 ⫹ G *d共 ␻ 兲兴 ⫹ 关2G *d共 ␻ 兲 ⫺ 3G *m共 ␻ 兲兴关16G *m共 ␻ 兲 ⫹ 19G *d共 ␻ 兲兴 (2) where ␣ is the interfacial tension between the two polymer components and G*d is the complex modulus of the minor phase (droplets). For a monodisperse emulsion at low frequency, the Palierne and Oldroyd models are equivalent. In this work, the Palierne model is used to obtain the interfacial tension between polystyrene and polyethylene. Knowing the storage and loss moduli (G⬘ and G⬙) of both components and those of the blends, the droplet size distribution of the dispersed phase (PE at 200 °C and PS at 230 °C), it is possible to determine the interfacial tension ␣ using eqs 1 and 2. Since the volume-average diameter, dv, is known to take most of droplet size distribution effects into account11,12,15, the model can be simplified using dv. Graebling et al.12 and Bousmina et al.11,15 have shown that using an average diameter, dv, instead of a distribution of particle size has little consequence on the model predictions, when the volume-average diameter is not larger than 2 times the numberaverage diameter of the droplets. The storage and

loss moduli (G⬘ and G⬙) can then be calculated using simple algebraic equations given in refs. 15, 16, and 27. Knowing the average particle size of the dispersed phase, the interfacial tension between components of immiscible blends has been determined from dynamic data. In addition, the sensitivity of the model parameters has been examined. The rheological measurements have to be carried out with care, since the sensitivity of the model is significant in the low-frequency region where measurements are very long to carry out. The stabilized polymer components and blends were found to be thermally stable and morphological changes during the measurements were observed to be minor. The rheological measurements have been carried in the linear viscoelasticity regime for both components as well as for the blends.

RESULTS AND DISCUSSION The poor thermal stability of the initial (as received) PE did not allow rheological measurements even for short times. It was necessary to add 0.2% of Irganox威 to improve the stability of the material. Avoiding bubble formation in the polystyrene samples during preparation, rheological time sweep experiments showed a good thermal behavior of this resin even for long times. The results of the thermal behavior of the base resins were published in a previous article.24 For the blends, the concern is in relation with possible morphological changes through annealing in the rheometer. Indeed, the blend samples were tested for over 30 min and one needed to verify that no structural changes (coalescence) occurred especially at low frequencies. This has also been verified and reported elsewhere.24 The complex viscosity of the PS, PE, and the 70/30/PS/PE blend at 200 °C is shown in Figure 1. The viscosity of PS is higher than that of PE in the low-frequency region. For the base resins, the viscosity curves were fitted with the four-parameter Carreau–Yasuda model27 to obtain the zero-shear viscosity values at 200 °C and 230 °C, reported in Table I. The viscosity ratio of the matrix-droplet (PS/PE) is found to be 3.2 at 200° C. Blending the PE with the PS at 70/30 PS/PE resulted in a slight increase in the viscosity, in the low-frequency region, compared to both phases (PS and PE). Note, however, that the zero-shear plateau for the blend is not attained at the lowest frequency used. At

POLYSTYRENE–POLYETHYLENE BLENDS

Figure 1. Complex viscosity versus frequency of PS, PE, and 70/30 PS/PE blend at 200 °C.

high frequencies, the viscosity of the blend is comparable to that of the matrix. The complex viscosity at 230 °C for the base resins and the 30/70 PS/PE blend are reported in Figure 2. Because of the difference in thermal sensitivity (shift factor aT), the zero-shear viscosity of the pure resins is comparable (1220 Pa.s and 1420 Pa.s for the PS and the PE, respectively) and are reported in Table I. The zero-shear viscosity ratio of the matrix-droplet (PE/PS) is now equal to 1.2. This change in the viscosity ratio of PS/PE (⬎ 1 at 200 °C and ⬍ 1 at 230 °C) will allow us to test the Palierne model for the complementary blend composition. The viscosity of the 30/70 PS/PE blend is much larger at low frequencies compared to both phases (PE and PS). This is due to the contribution of the deformation of the droplets, which is significant at low frequencies only. Again we note the absence of a zero-shear plateau

Figure 2. Complex viscosity versus frequency of PS, PE, and 30/70 PS/PE blend at 230 °C.

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Figure 3. Storage and loss moduli versus frequency of PS, PE, and 70/30 PS/PE blend at 200 °C. The solid lines are descriptions of the moduli for the unblended components using the generalized Maxwell model.

for the blend, in the experimental frequency window. At high frequencies, the viscosity of the blend is slightly lower than that of the matrix, due to the bulk contribution of the dispersed phase, which is considerably less viscous. The storage and loss moduli of PS and PE as well as the 70/30/PS/PE blends at 200 °C are shown in Figure 3. In the low-frequency region, G⬘ and G⬙ of the PS are larger than those of the polyethylene, for which the terminal zone (slope of ⫺2 on a log–log plot) is not reached. Additional data obtained separately28 and going to lower frequencies have also been added to the present data. Both sets of data, obtained by two different investigators, show very good agreement, within the reproducibility of rheological measurements (⫾10%). For the 70/30/PS/PE blend, the storage modulus is considerably larger in the terminal zone compared to that of the matrix (PS). By coincidence the G⬘ data for the blend superposes the matrix G⬙ data. The large enhancement of the blend storage modulus is attributed to the deformation of the PE droplets dispersed in the PS matrix. The loss modulus for the blend is comparable to that of the matrix, except at very high frequencies where the blend becomes more viscous due to the bulk contribution of the dispersed phase (see Fig. 1). The moduli for the base materials and the 30/ 70/PS/PE blend measured at a higher temperature (230 °C) are reported in Figure 4. In the low-frequency region, PE shows a higher storage modulus than PS, while the loss modulus of both materials is comparable. The behavior of the 30/70 PS/PE blend is similar to that of the 70/30

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Figure 4. Storage and loss moduli versus frequency of PS, PE, 30/70 PS/PE, and 30/70/20 PS/PE/SEBS blends at 230 °C. The solid lines are descriptions of the moduli for the unblended components using the generalized Maxwell model.

PS/PE blend observed at 200 °C, that is, a strong increase in elasticity (G⬘) of the blend is observed compared to the matrix in the low-frequency range. For this blend, the loss modulus is only slightly enhanced by the drop deformation at low frequencies, but becomes lower than that of the matrix (PE), due to the bulk contribution of the less viscous, dispersed phase at high frequencies. The solid lines in Figures 3 and 4 are the description of the storage and loss moduli of both pure components at the different temperatures, using the generalized Maxwell model.27,29 A nonlinear regression method was used to determine the discrete relaxation and retardation time spectra.30,31 Excellent fits have been obtained with the use of five relaxation times for the PS and six relaxation times for the PE. The terminal zones at low frequencies are indicated by the extrapolated lines of slope 2 (log–log scale) and 1 for G⬘ and G⬙, respectively. The terminal behavior was reached for the PS at higher frequencies, compared to the PE. This is particularly visible in Figure 4, where the G⬘ data for the PE at 230 °C does not reach the limiting behavior. The rheological properties of both components are quite similar, the PE being slightly more elastic at low frequencies and more viscous at high frequencies. The generalized Maxwell model was used to calculate the component properties for the use in the predictions with the Palierne model. The morphology of the 70/30 and 30/70 PS/PE blends, cooled rapidly in the rheometer from the initial temperatures of 200 °C and 230 °C, respectively, were examined using SEM and typical mi-

crographs are presented in Figure 5(a,b). In both cases, the blends had a droplet-matrix morphology with a volume average particle diameter of 5.5 and 14.7 ␮m for the 70/30 and the 30/70 PS/PE blends, respectively. The obtained values for the average diameter on quenched samples are believed to be representative of the real morphology of the blend. These values were slightly larger (less than 10% for the volume-average diameter) for samples examined after rheometry than for initial samples. Coalescence during measurements was hence believed not to affect significantly the determined rheological data, as reported in our previous work.24 The coarser morphology of the 30/70 PS/PE blend was due to coalescence effects overcoming the droplet breakup during melt-blending at 200 °C. Comparison Between the Experimental Results and the Model Predictions Figure 6 compares the linear viscoelastic data of the 70/30 PS/PE blend at 200 °C and the theoret-

Figure 5. SEM micrographs: (A) 70/30 PS/PE blend at 200 °C, (B) 30/70 PS/PE blend at 230 °C.

POLYSTYRENE–POLYETHYLENE BLENDS

Figure 6. Comparison of the Palierne model predictions with the data of the 70/30 PS/PE blend at 200 °C, using different values of the interfacial tension; (a) storage modulus, (b) loss modulus.

ical predictions of the Palierne emulsion model. In this case, the volume-average diameter was 5.5 ␮m. The linear viscoelastic properties of the base components, as described by the generalized Maxwell model were used. The interfacial tension between the blend components was varied between 0.5 mN/m and 20 mN/m. The resulting calculations of the storage and loss moduli were compared to the experimental data. The value of 5.0 mN/m reported in the literature 15,17,18,32 gives satisfactory fits of both G⬘ [Fig. 6(a)] and G⬙ [Fig. 6(b)] data at low frequencies. Note that the loss modulus is not very sensitive to the value of the interfacial tension and no effects on both moduli are detected at high frequencies. The Palierne model slightly underestimates the high-frequency data. This was also observed by Lacroix et al.33 for a different 20/80 PE/PS blend. A better fit of the linear viscoelastic data was obtained for that particular blend, using the more empirical Lee and Park model.34 However, the model can no longer

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be used to predict the interfacial tension. For the data examined here, in the restricted experimental window, a slightly better fit is obtained using a value of ␣ equal to 2.0 mN/m (the average deviation between predicted and G⬘ data drops from 24% to 20% when ␣ is decreased from 5 to 2 mN/m, but the fit for G⬙ data is slightly better when using ␣ equal 5 mN/m, 10% compared to 11 %). The figure stresses the need for accurate lower-frequency data (⬍10⫺2 rad/s) if one hopes to determine the interfacial tension using rheometry. The experimental data are not accurate enough to allow a precise determination of the interfacial tension. At best, the value of ␣, from this first set of data, is between 2 and 5 mN/m. The lack of fit of the Palierne model may be attributed to particle–particle interactions, not accounted for in the model, but expected for such a high concentration of droplets (30 vol %). In previous works (see refs. 14, 15, and 33) the Palierne model has been shown to be valid for blends at that high concentration of the dispersed phase. The same lack of fit discussed below for a lower concentration blend of the same polymers suggests that interaction between the droplets are not responsible for the lack of fit. Figure 7 presents the same comparison between the model predictions and data obtained for a lower concentration emulsion, a 80/20 (wt %) PS/PE blend, for which the data were extended to lower frequencies.28 The experimentally determined volume-average diameter for the droplets equal to 7.82 ␮m and ␾ equal to 0.244 were used for the Palierne model predictions. The best fit for G⬘ [Fig. 7(a)] is now obtained for ␣ equal 5 mN/m, but the differences between fits using other values for ␣ are marginal (the average deviation for the G⬘ data is 22.7% and 22.8% for ␣ equal 5.0 and 4.0 mN/m, respectively). Considering the terminal zone only, the best fit is obtained for ␣ equal 2 mN/m. For this lower concentration blend, the fit with the model predictions is not much better than that obtained for the higher concentration blend. For a similar 80/20 PS/PE blend, Lacroix et al.33 have reported a similar lack of fit using the Palierne model. For the 30/70 PS/PE blend at 230 °C, dv was found to be equal to 14.7 ␮m. The deformation of the larger droplets at low frequencies affects more the viscoelastic properties of the blend and for this complementary blend we could obtain an excellent fit of the data using the Palierne model, as shown in Figure 8. The best agreement is obtained for an interfacial tension

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Interfacial Tension Results Using the Breaking-Thread Method The breaking-thread technique has been successfully used by other authors for PS/HDPE and PS/LDPE blends.18 This technique requires the knowledge of the zero- shear viscosity of the components. The experiments were carried out at 200 °C and at 230 °C and details of the experiments can be found in our earlier work.24 Table II compares the values of the interfacial tension obtained using both techniques. At 200 °C the obtained value via the breaking-thread technique is 4.7 mN/m. This in agreement with literature data17,18 and comparable to a value ranging from 2 to 5.0 mN/m obtained by rheometry. At 230 °C, the breaking-thread method yielded a value of 4.1 mN/m, which is identical to that determined using the emulsion model (4 ⫾ 1 mN/m). The slight decrease of the interfacial tension with increasing temperature is expected from thermodynamics

Figure 7. Comparison of the Palierne model predictions with the data of the 80/20 (wt %) PS/PE blend at 200 °C, using different values of the interfacial tension; (a) storage modulus, (b) loss modulus.

value of 4.0 ⫾ 0.5 mN/m. The average deviation between the predicted and experimental values of G⬘ [Fig. 8(a)] for ␣ equal 4.0 is 14.6% compared to 15.6% for ␣ equal 3.0 or 5.0 mN/m. The best fit of the G⬙ data [Fig. 8(b)] is for ␣ equal 5.0 mN/m, but the difference is marginal compared to the fit with ␣ equal 4.0 mN/m (6.0% vs. 6.4%). These results are in good agreement with those of other authors.15,17,18 Both the 70/30 and 30/70 PS/PE blends at 200 °C and 230 °C are characterized by an increase in the storage modulus and also by a significant shift of the terminal zone to lower frequencies. This suggests a longer relaxation time process of the blends compared to that of the pure components. The results presented here are unique since, so far, the increase in elasticity at low frequency was observed only on one side of the composition range.11–16,26

Figure 8. Comparison of the Palierne model predictions with the data of the 70/30 PE/PS blend at 230 °C, using different values of the interfacial tension; (a) storage modulus, (b) loss modulus.

POLYSTYRENE–POLYETHYLENE BLENDS

Table II. Interfacial Tension Results of the PS/PE Blends at 200 °C and 230 °C

Blend PS/PE 70/30 PS/PE 30/70

Temperature (°C)

Breaking Thread (mN/m)

Emulsion Model (mN/m)

200

4.7 ⫾ 0.5

2–5

230

4.1 ⫾ 0.5

4⫾1

principle and it is in good agreement with the results obtained for the same system and for PA/PP blends.18

CONCLUSIONS The rheological behavior of PS/PE blends and components has been investigated in the linear viscoelastic region at two temperatures (200 °C and 230 °C). This particular blend system is shown to exhibit an uncommon behavior in terms of the zero-shear viscosity ratio of the components with temperature. The viscosity ratio of the matrix to that of the dispersed phase was found to be higher than unity at both temperatures. It was therefore possible to investigate the effect of droplet deformation on the viscoelastic properties of this system for two opposite concentrations (70/30 PS/PE and 30/70 PS/PE), both as emulsions. In both cases, an increase in the storage modulus, compared to the individual matrices, was observed in the low-frequency region due to the deformation of the droplets of the minor phase. The viscoelastic properties of the blends were correctly described by the Palierne emulsion model. At low frequencies, the model was used to obtain the interfacial tension of the PS/PE pairs at both temperatures. Best agreement between the model predictions and the rheological data was obtained for values ranging between 2 and 5 mN/m and 4 ⫾ 1 mN/m at 200 °C and 230 °C, respectively. The best fit of the Palierne model was for the data obtained for the 30/70 PS/PE blend at 230 °C. This polymer blend system was, however, not as well described by the Palierne model as we have shown for many other polymer blends.14,16,33 The breaking-thread technique was also used to measure the interfacial tension between PS and PE. The data obtained were 4.7 mN/m and 4.1 mN/m at 200 °C and 230 °C, respectively,

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values in agreement with those determined by rheometry. For this polymer pair, the breakingthread technique is much more accurate for the determination of the interfacial tension. The authors would like to thank Ms. Dale E. Bristow at Dow Chemical Canada for providing raw materials and technical support. Thanks are also due to Environmental Science and Technology Alliance Canada (ESTAC) and the Natural Sciences and Engineering Research Council of Canada (NSERC) for financial support.

REFERENCES AND NOTES 1. Paul, D. R.; Newman, S. Polymer Blends; Academic Press: New York, 1978; Vols. 1, 2. 2. Favis, B. D.; Chalifoux, J. P. Polym Eng Sci 1987, 27, 1591. 3. Chu, L. H.; Guo, S. H.; Chiu, W. Y.; Tseng, H. C. J Appl Polym Sci 1993, 49, 1791. 4. Forteiny, I.; Kovar, J. Eur Polym J 1992, 28, 85. 5. Hietaoja, P. T.; Hoisti-Miettinen, R. M.; Seppala, J. V.;. Lkkala, Q. T. J Appl Polym Sci 1994, 54, 1613. 6. Serpe, G.; Jarrin, J.; Dawans, F. Polym Eng Sci 1990, 30, 553. 7. Oldroyd, J. G. Proc R Soc London Ser A 1953, 218, 122. 8. Oldroyd, J. G. Proc R Soc London Ser A 1955, 232, 567. 9. (a) Palierne, J. F. Rheol Acta 1990, 29, 204; (b) Palierne, J. F. Rheol Acta 1991, 30, 497. 10. Gramespacher, H.; Meissner, J. J Rheol 1992, 36, 1127. 11. Bousmina, M.; Muller, R.; J Rheol 1993, 37, 663. 12. Graebling, D.; Benkira, A.; Gallot, Y.; Muller, R. Eur Polym J 1994, 30, 301. 13. Friedrich, C.; Gleinser, W.; Korat, E.; Maier, D.; Weese, J. J Rheol 1995, 36, 1411. 14. Carreau, P. J.; Bousmina, M.; Ajji, A. In Progress in Pacific Polymer Science; Springer-Verlag: New York, 1994; Vol. 3, p 25. 15. Bousmina, M.; Bataille, P.; Sapieha S.; Schreiber, H. P. J Rheol 1995, 39(3), 499. 16. Lacroix, C.; Bousmina, M.; Carreau, P. J.; Favis, B. D.; Michel, A. Polymer 1996, 37, 2939. 17. Wu, S. Polymer Interface and Science; Marcel Dekker: New York, 1982. 18. Elemans, P. H. M.; Janssen, J. M. H.; Meijer, H. E. H. J Rheol 1990, 34, 1311. 19. Elmendorp, J. J.; de Vos, G. Polym Eng Sci 1986, 26, 415. 20. Elmendorp, J. J. Ph.D. Thesis, Delft University of Technology, The Netherlands, 1986. 21. Carriere, C. J.; Cohen, A.; Ardens, C. B. J Rheol 1989, 33, 681.

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22. Cohen, A.; Carriere, C. J. Rheol Acta 1989, 28, 223. 23. Demarquette, N. R.; Kernel, M. R. Polym Eng Sci 1994, 34, 1823, 1834. 24. Mekhilef, N.; Favis, B. D.; Carreau, P. J. J Polym Sci Polym Phys Ed 1997, 35, 293. 25. Tomotika, S. Proc R Soc London Ser A 1935, 150, 322. 26. Brahimi, B.; Ait Kadi, A.; Ajji, A.; Jerome, R.; Fayt, R. J Rheol 1991, 35(6), 1069. 27. Carreau, P. J.; De Kee, D.; Chhabra, R. P. Rheology of Polymeric Systems: Principles and Applications; Hanser: Munich, 1997.

28. Martin, P.; Carreau, P. J.; Favis, B. D.; Je´roˆme, R. J Rheol, in press, 2000. 29. Ferry, J. D. Viscoelastic Properties of Polymers, 3rd ed.; Wiley Interscience: New York, 1980. 30. Baumgaertel, M.; Winter, H. H. Rheol Acta 1989, 28, 511. 31. Baumgaertel, M.; De Rosa, M. E.; Machado, J.; Masse, M.; Winter, H. H. Rheol Acta 1992, 31, 75. 32. Chen, C. C.; White, J. L. Polym Eng Sci 1993, 33, 923. 33. Lacroix, C.; Aressy, M.; Carreau, P. J. Rheol Acta 1997, 36, 416. 34. Lee, H. M.; Park, O. O. J Rheol 1994, 38, 1405.