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Immiscible Polymer Blends
11
Immiscible Polymer Blends
Blends of various polymers have gained a great importance in the field of commercial polymeric materials because special end-use properties can be obtained by a relatively simple mechanical mixing process of different components in the molten state. But only very few polymers are miscible on a molecular scale and that is the reason why one has to deal with special morphological features even in the melt. Thus, in addition to properties of the blend components, interactions between the different phases have to be considered, which may affect rheological properties. As is well known and was widely discussed in the previous chapters, from the linear rheological properties insights into interactions taking place on molecular levels can be obtained. Additionally, the nonlinear rheological behavior can be exploited for the assessment of some aspects of processing. The availability of a wide variety of commercial polymeric materials offers in principle the creation of a great number of polymer blends when it is taken into account that, in addition to specific characteristics of the components, the blend properties obviously depend on the mixing ratios. Moreover, the interactions between the different phases can be changed by the introduction of so-called compatibilizers that affect the interplay between matrix molecules and dispersed phase and, thus, influence material properties. This chapter deals with the rheological behavior of uncompatibilized polymer blends and their elasticity in particular. Like in the previous sections, nonlinear properties that are interesting for processing are discussed separately from linear properties that may be used to elucidate the properties of the polymeric matrix and the dispersed phase.
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11.1 Linear Elastic Behavior In comparison with polymer melts filled with rigid particles, discussed in Chapter 9 and 10, polymer blends are more complex insofar as the dispersed phase is viscoelastic too and may contribute to the overall viscous and elastic properties of a polymer melt. Even in the linear range of deformation two different morphological features have to be distinguished. One may be marked by a constant shape of the dispersed phase during the experiment, the other by a change in shape that is restored after recovery. Studies in which the geometry of the secondary phase can be assumed to remain constant are of special interest, because in this case theoretical descriptions are existent, which become rather complicated when changing particle geometries or morphologies have to be considered.
11.1.1 Dynamic-Mechanical Experiments Dynamic-mechanical experiments at low enough oscillating amplitudes are very suitable for studies in the linear regime, because the morphology can be assumed not to be changed by the acting stresses. For example, the linear range can be determined conveniently by measurements of the storage modulus as a function of the amplitude for given frequencies, as shown for a particle-filled polymethylmethacrylate in Figure 10.3. Linearity can be assumed as long as the modulus is independent of the amplitude. In comparison with polymer melts filled with rigid particles, which are presented in Figures 10.4 to 10.6, the storage modulus as a function of angular frequency exhibits a totally different behavior in the linear regime for an immiscible polymer blend, as demonstrated in Figure 11.1 for polyisobutylene (PIB) as the matrix and polydimethylsiloxane (PDMS) as the dispersed phase [11.1]. The blend components exhibit a distinct terminal regime in the frequency regime chosen, as exof the blend, however, pected due to their relatively small molar masses. The shows a pronounced shoulder in the range of medium frequencies before it further declines with decreasing frequency. The shoulder is characterized by its width (frequency range) and its height (average level of modulus). Their exact determination is a matter of definition. At high frequencies, the modulus of the blend can be described approximately by a simple mixing rule (full line) based on the volume ratios of the components, which is apparently not valid anymore at lower frequencies. For the loss modulus of the blend, it is reported in [11.1] that its frequency dependence is the same as that of the components, within the accuracy of the measurements, and that it is only marginally different from that of the Newtonian PIB matrix. Thus, it may be concluded that the significant effect of the blend com-
11.1 Linear Elastic Behavior
ponent on is due to a change in elastic properties of the polymeric system. Formally, the shoulder of can be interpreted by the assumption of a relaxation process caused by the incompatibility of matrix and dispersed phase. It is clear that the relaxation mechanism results from the interplay of the interfacial tension and the viscoelastic properties of the dispersed phase. Similar effects as presented for PIB/PDMS are reported for blends of polydimethylsiloxane/polyoxyethylene [11.2, 11.3] and by the same group of authors for polystyrene/polymethylmethacrylate and polystyrene/polyethylmethacrylate blends [11.4]. 10
4
G' [Pa] 10
3
10
2
PDMS
PIB/PDMS 70/30 10
1
10
0
PIB
10
-1
10
0
10
1
-1
10
2
[s ]
Figure 11.1 Storage modulus as a function of angular frequency w for a blend of 70 vol % polyisobutylene (PIB) and 30 vol % polydimethylsiloxane (PDMS) and its components at 23 °C. The solid line represents the modulus of the blend according to a mixing rule based on the volume ratios of the components. The blend sample was sheared at a constant shear rate of 0.3 s–1 before the dynamic-mechanical characterization in order to generate a definite morpho logy. Reprinted with permission from [11.1]; copyright 1996 The Society of Rheology
These results were analyzed with Palierne’s theory [11.5], which has been used preferentially over the years to describe dynamic-mechanical experiments on immiscible polymer blends. The model was derived for a secondary phase of spherical shape in the linear range of deformation. Thus, it is particularly suited for the description of the complex modulus as a function of frequency, because dynamic-mechanical experiments can be performed easily under linear conditions and the particle shape can be assumed to remain unchanged when small amplitudes are applied. According to Palierne, the complex modulus of a blend is related to properties of the blend components by
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(11.1) with (11.2) and are the complex moduli of the dispersed phase and the matrix, respectively, is the interfacial tension between matrix and secondary phase, and the volume fraction of the dispersed phase with the radius . This formula in its general feature describes an inhomogeneous distribution with different particle sizes , as it is usually found for real polymer blends. For practical purposes an average particle size is assumed, which simplifies the sums in Equation 11.1 to one term. Some general features of Equation 11.1 and Equation 11.2 are discussed in the following. When the interfacial tension between the two components of a blend and averages of the size of the dispersed phase are known, the modulus of a blend can be calculated from the moduli of the components. Good agreement between numerical descriptions and experimental results of the loss and the storage moduli as functions of the frequency have been found for the measurements on the various samples reported in [11.2], [11.3], and [11.4]. Moreover, the equations above can be used to determine either the interfacial tension or an average radius of the dispersed phase from dynamic-mechanical experiments. From the fit to the may be obtained, and then from either measured modulus curves, the quotient or , known from other methods, the corresponding quantity can be determined. Such an evaluation is described in [11.6] for a blend of 20 vol % PS and 80 vol % = PMMA (PS/PMMA 20/80). The PS had a weight average molar mass of was 64 kg/mol. does exhibit a distinct shoul190 kg/mol and for PMMA and are fitted with Palierneʼs equation. Over der, as Figure 11.2 shows. wide ranges the agreement between experiment and theory is satisfactory and at smaller frethe shoulder is well described. Some discrepancies occur for quencies. the interfacial tension was obtained, making use of From the fit parameter the average diameter of the dispersed polystyrene phase determined from transmission electron micrographs. The surface tension of 2.3 mN/m is in good agreement with values from other methods. The other way around, an average size of the secondary phase of an immiscible blend can be obtained when a known value for the interfacial tension is introduced.
11.1 Linear Elastic Behavior
10 6 10 5 G',G'' [Pa] 10 4 10 3 10 2 G' G'' G'(Palierne) G''(Palierne)
10 1 10 0 -3 10
-2
10
-1
10
0
10
1
-1
[s ]
10
Figure 11.2 Storage modulus and loss modulus as functions of the angular frequency w for PMMA/PS 80/20 at 180 °C. The lines represent the fit with Palierne’s theory. Adapted from [11.6]
From the equations above the influence of various parameters of a blend on the formation of the shoulder in can be discussed. This is done in [11.7] making use of the specific characteristics of the height and the width of the shoulder, which, however, can be assessed only roughly in many cases. An obvious parameter is the concentration of the minor phase. Palierne’s theory predicts an increase in shoulder height and width with growing content of the secondary phase. Measurements on two concentrations of a polyoxyethylene in a polydimethylsiloxane confirm the prediction. Two other parameters are the interfacial tension and the radius of the inclusions, the influence of which is reciprocal to each other (see Equation 11.2). From [11.7] it follows that the shoulder height becomes higher with increasing interfacial tension, while the shoulder width gets narrower. The experimental proof of this prediction is not easy, because the surface tension is one decisive factor for the morphology development and, thus, the interfacial tension and the size of the inclusions are related to each other. However, an indirect confirmation of the prediction of the can be drawn from the experiinfluence of particle size on the shoulder of ments on blends of PDMS and PIB reported in [11.1]. In these investigations, for a definite composition the sizes of the inclusions were altered by shearing the blend at different constant rates before the dynamic-mechanical test. It was found for PIB/PDMS 70/30 that the average size of the secondary PDMS phase became smaller with increasing preshear rate, but it is clear that the interfacial tension remains the same. For the smaller sizes of the inclusions, the heights of the shoulders of increased and their extensions decreased as predicted in [11.7].
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Furthermore, conclusions can be reached from the emulsion theory with respect to the effect of viscoelastic properties of matrix and secondary phase. A declining viscosity of the dispersed phase enhances the height of the shoulder, but its width is not affected much. The influence of the terminal relaxation time of the matrix is predicted in such a way that the shoulder is much more pronounced at shorter relaxation times than at higher ones [11.7]. in combination with Palierne’s This discussion demonstrates in which way emulsion theory can make a contribution to analyze immiscible polymer blends with respect to the size of the inclusions and the interfacial tension acting between , and thus the viscosity, is only weakly matrix and dispersed phase. Because affected by the dispersed phase, it is mainly the elastic property reflected by for comparable viscosities that enables deeper insights into interactions within polymer blends. Dynamic-mechanical measurements on PMMA/PS blends are reported in [11.8], too. The PMMA matrix has a higher molar mass and broader molar mass distri bution than the sample from [11.6] discussed above, resulting in longer terminal and are similar to those presented in relaxation times. The results of for the various concentrations are less disFigure 11.2, but the shoulders of tinct. This observation goes along with the prediction of the emulsion theory that the width of the shoulder decreases with longer terminal relaxation times. Nevertheless, interesting insights into the interactions between matrix and dispersed phase have been obtained from these investigations, using for their interpretation the emulsion model of Choi and Schowalter [11.9] and its specification for the linear behavior [11.10]. From the dynamic-mechanical experiments the weighted relaxation spectra were determined according to [11.11]. An example is given in Figure 11.3 for the blend PMMA/PS 92/8. Besides the two peaks representing the terminal relaxation times of the dispersed and the matrix phase, there occurs a third peak at higher relaxation times at the end of the spectrum. As discussed in [11.8], this peak is related to a relaxation process induced by the interfacial tension . The corresponding relaxation time depends on the volume ratio of the dispersed phase, the viscosity of the matrix, the ratio of the viscosity of the dispersed phase and the , where is the average radius of the inclusions. For a given commatrix, and can be determined from position with known viscosities of the components, the peak relaxation time. Similar to Palierne’s emulsion theory, either or can be obtained when the corresponding quantity is known from other methods. In [11.8] the average size of the PS inclusions is given as 1 μm. The interfacial tension for the blend with 8 vol % PS follows as 2.2 mN/m, which is in very good agreement with the value for the other PMMA/PS blend with 20 vol % PS presented in Figure 11.2. In [11.8] interfacial tensions, very similar within the accuracy of the meas-
11.1 Linear Elastic Behavior
urements, are reported for PMMA/PS blends with higher concentrations of 12 and 16 vol % PS. This result is physically very reasonable, because the interfacial tension is given by the chemical constitution of the components. 5 4
H( ) [10 Pa s] 4
3
2
1
0
10
-4
10
-3
10
-2
10
-1
0
10 10 [s]
1
10
2
10
3
10
4
Figure 11.3 Weighted relaxation spectrum for the PMMA/PS 92/8 blend. is the the relaxation strength. Reprinted with permission from [11.8]; relaxation time and copyright 1992 The Society of Rheology
The dynamic-mechanical behavior of several non-miscible polymer blends and the comparison with the Palierne theory have been presented in [11.12]. The emulsion of PA6/SAN at lower frequencies. The difference model underestimates the was found to be significant for PA6/SAN 10/90 but smaller for PA6/SAN 70/30. For PA6/PS 10/90 a good agreement between measured and calculated curves was observed over the whole frequency range. However, for none of the blends a shoulder was obtained. with respect to interactions between matrix and The obvious sensitivity of polymeric inclusions is interesting from a fundamental point of view, but the contribution to a morphological analysis of the secondary phase is rather limited. Only average diameters of inclusions can be obtained that may belong to different distributions. Thus, dynamic-mechanical experiments, which are easily performed, cannot be used to replace morphology analyses by elaborate microscopic techniques. was found in Section 9.2.5, too, for a completely different hete A shoulder for rogeneous polymer system of a largely Newtonian polyisobutylene with rigid glass beads. Of course, an interfacial tension exists between matrix and filler, but because of the lack of deformability of the glass beads a relaxation process similar to that for polymer blends is not possible. Rather, an interplay between elastic defor-
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mations of the “honey-comb” structure built up by the particles and the viscoelastic matrix molecules has to be envisaged, as discussed in Section 9.2.4. Such a , similarly to interactions between process may formally become visible in inclusions and matrix molecules in a polymer blend, when it occurs at a comparable time scale.
11.1.2 Recoverable Shear As shown in Chapter 10, the recoverable shear, particularly in the linear range, can be used successfully to characterize interactions between nanoparticles and matrix molecules. A very suitable elastic material quantity is the recoverable compliance, defined as (Equation 3.7): with being the recoverable shear strain and s the shear stress applied in the preceding creep experiment. It is preferentially determined by creep recovery measurements, as described in Section 3.1. In Section 4.2.1 it is demonstrated how the linear regime can be determined experimentally. Of particular interest is the time-dependent linear compliance because retardation spectra can be calculated from this material function, as shown in Section 10.3.3 for a melt filled with nanoparticles. In the literature, measurements of recoverable properties in the linear range of polymer blends are very rare. The reason is that investigations of this kind need special experimental care and the few results exhibit features that are difficult to interpret. For example, in [11.13] creep recovery experiments on PS/PMMA blends are presented, which exhibit a phenomenon not completely understood so far. In Figure 11.4(a) the recovery curves for the polystyrene and the polymethylmethacrylate blend components are presented, which both show an increase in the recoverable compliance with time up to an extended plateau, as is well known for polymer melts. The steady-state recoverable compliance of the PMMA is distinctly lower than that of the PS. However, as seen from Figure 11.13(b), for the blend PMMA/PS 84/16, the recoverable compliance after the same preceding creep at a stress of 150 Pa first increases with the recovery time t, but reaches a plateau value only after running through a maximum. The recoverable compliance or the corresponding recoverable shear decreasing with time indicates a reversal of the direction of recovery, which means that the sample creeps again without any external stress before reaching a steady state of deformation. The maximum of the recoverable compliance becomes more pronounced and its position slightly shifts to longer retardation times with increasing PS concentration, as shown in [11.13] for blends with up to 20 wt % PS. The plateau value of PMMA/PS 92/8 is somewhat
11.1 Linear Elastic Behavior
higher than that of the PMMA matrix and is enhanced with growing PS concentration [11.13]. As follows from Figure 11.4, the steady-state recoverable compliance of PMMA/PS 84/16 is larger than that of the pure PS. This result shows that a simple mixing rule is not valid, but indicates a significant contribution of the recoil of the PS inclusions to the total recovery. 3
Jr(t) [10-4 Pa-1]
2
2
1
1
0
a)
3
PS PMMA
Jr(t) [10 -4 Pa-1]
0
500
1000
t [s]
0
1500
b)
0
2000
4000
6000
t [s]
8000
Figure 11.4 Recoverable compliance as a function of recovery time after preceding creep at the shear stress = 150 Pa and 170 °C for a) the PS and PMMA components, and b) the PS/PMMA blend with 16 wt % PS. Reprinted with permission from [11.13]; copyright 1995 The Society of Rheology
Surprisingly, maxima in creep recovery were not found for blends with the PS as the matrix and the PMMA as the dispersed phase [11.13]. For a sample with 16 wt % PMMA, for example, the recoverable compliance steadily increases with time up to a plateau. This behavior is similar to that of unfilled and particle-filled polymer melts described in Section 10.3.2. The steady-state value of the PS/PMMA blend is distinctly higher than those of the matrices, indicating the contribution of the recoil of the deformed secondary PMMA phase. Information on the morpho logy of the blends is not available. The zero-shear viscosity of the PS is higher by about 40 %, and its linear steady-state compliance by a factor of three, than for the PMMA. This means that the maximum relaxation time of the PS is distinctly larger. It is difficult, however, to relate this difference to the phenomena observed. From the literature only very few investigations of the time dependence of the recovery of immiscible polymer blends are available. One example is the measurements on PS/PMMA blends of various compositions with a home-built rheometer [11.14]. For none of the samples, and, in particular, not for those with blend ratios comparable to the PS/PMMA blends in [11.13], a maximum of the recoverable strain as a function of recovery time is reported. Neither rheological or molecular data of the two components nor presentations of the morphology of the blends are given and, thus, a founded comparison of the results on the two blends is not possible.
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11 Immiscible Polymer Blends
Another example of immiscible blends is the blends of styrene acrylonitrile (SAN) with polypropylene (PP) [11.15]. In Figure 11.5 the recoverable shear compliance as a function of the recovery time t is presented for the blends SAN/PP 96/04 and SAN/PP 84/16 and their components SAN and PP. The linearity of the measurements at the chosen creep stress of 5 Pa was proven in [11.15]. The recoverable compliance of the PP is higher than that of the SAN. The curve for SAN/PP 84/16 lies distinctly above the curves for the components and only 4 wt % PP increases the compliance by a factor of around 10 compared to SAN, but maxima as for PS/PMMA do not occur, although the minor PP phase has the distinctly higher viscosity and longer relaxation times like the PS in the PMMA matrix. The increased compliances indicate interaction processes that should be related to morphological effects within the blends, because a simple mixing rule for the compliances based on the ratios of the components and their compliances cannot be derived. Indeed, clearly separated PP spheres of a few microns in diameter were found for the SAN/PP 84/16. Their initial dimensions and those just after the end of creep deformation were the same [11.15]. This finding could be explained by the viscosity of the dispersed PP being higher by a factor of about 10 than that of the SAN matrix, with the consequence of a negligible deformation expected for the PP inclusions during creep, according to the results of Grace on immiscible fluids [11.16]. Taking for granted the morphological findings of a geometry unchanged by creep, a recoil of the secondary PP phase cannot be the reason for the increase in recoverable deformation. Rather, interactions between matrix molecules and the surface of the dispersed polymer have to be postulated, similar to those within the particle-filled polymer melts. -1
10
T = 180 °C = 5 Pa
-2
10
-3
Jr [Pa-1]
210
10
-4
10
SAN SAN/PP 96/04 SAN/PP 84/16 PP
-5
10
10
-1
10
0
10
1
10
2
10
3
10
4
10
5
t [s]
Figure 11.5 Recoverable compliance as a function of recovery time t for the blends SAN/PP 96/04 and SAN/PP 84/16 and their components SAN and PP at 180 °C after creep at the stress of 5 Pa [11.15]
11.2 Nonlinear Elastic Behavior
In [11.17], measurements of the recoverable shear strain on an immiscible blend of polyisobutylene (PIB) and polydimethylsiloxane (PDMS) are reported, which offer the advantage of elastic properties of the two blend components being so low that elastic effects of the blends have to be completely related to morphological features. For the blend PDMS/PIB 90/10 the minor phase has a viscosity about half of that of the matrix. The creep recovery curves from preceding creep at various stresses in the linear range between 50 and 100 Pa do not exhibit a maximum, but continuously increase up to extended plateaus, which for a fixed initial morpho logy become higher with a larger preceding creep stress. This feature is qualitatively comparable to the PMMA/PS blends with PMMA as the minor phase of lower viscosity, which do not show a maximum of the recovery curves either. Studies of the morphology of the PIB/PDMS blends are not available, however, due to the obvious experimental difficulties to prepare samples at the different states of the measurements with rotational rheometers. A reversal of recovery has been reported in the literature from investigations of the structure development under shear flow during spinodal decomposition of a blend from polybutadiene and polyisoprene [11.18]. The measurements were performed by using light scattering in parallel to rheological techniques. The authors argue that relaxation processes of polymer phases taking place at different time scales can be the reason for deformations occurring in the opposite direction of the recovery [11.18]. However, besides some vagueness of the interpretation, the polymeric system and the physical processes during deformation are difficult to compare with the PMMA/PS blend. The results from the different polymer blends and their discussion do show how little elastic phenomena of immiscible polymer blends are understood even in the linear range of deformation and that, besides comprehensive rheological characterizations, the blend morphology during creep and creep recovery has to be investigated in detail to come to reliable insights.
11.2 Nonlinear Elastic Behavior Even more complex are nonlinear elastic properties of polymer blends, because they are dependent on acting stresses or deformation rates, respectively. Recover able elongation and extrudate swell are nonlinear elastic quantities of particular interest. Elongation is an experimental mode that allows a relatively easy and reliable access to investigations of the morphology of a sample. Extrudate swell is of interest because it has some importance for processing (see Chapter 12).
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11.2.1 Recoverable Elongation In Figure 11.6 the recoverable stretching ratio
defined as
(11.3) is plotted as a function of recovery time t for blends from the PMMA and PS presented in Figure 11.4. l is the length of the stretched sample and the length after recovery [11.19]. The measurements were performed with a tensile rheometer based on the device reported in [11.20]. With this instrument the recovery after elongation was determined by cutting the sample into pieces and documenting the retractions of single strands by photographs.
15
r PS [wt.%] 0
10
8 12 16 20
5
100
10
1
10
2
10
3
t [s]
10
4
Figure 11.6 Recoverable stretching ratio as a function of the recovery time t for blends from PS and PMMA. Prior to recovery, the samples were elongated at an elongational rate of and 170 °C up to a total stretching ratio of l = 33. Reprinted with permission from [11.19]; copyright 1997 The Society of Rheology
From Figure 11.6 it follows that the recoverable stretching ratios of the blends continuously increase as functions of the recovery time up to plateaus, which lie significantly above those of the two components. For 20 wt % PS, the plateau value of the blend is higher by a factor of nearly 15 in comparison with the PMMA matrix. A maximum of the recoverable stretching ratio as a function of recovery time, as found for the linear recoverable shear compliance in Figure 11.4 for a sample with comparable composition, does not occur. This finding adds another facet to the complexity of the effect of recovery reversal in shear observed for distinct PS/PMMA blends.
11.2 Nonlinear Elastic Behavior
For PMMA/PS 82/18, the morphology development in parallel to recovery has been presented in [11.19]. The results demonstrate the role of the shape recovery due to the interfacial tension for the elastic recoil of the blends. This influence is reflected by the time scale being much longer for recovery than for creep to reach steady states. To further elucidate the role of morphology, recovery experiments after uniaxial elongation on PS/LLDPE blends were performed. They were carried out under definite conditions and the morphology could be determined at any state of deformation by freezing the sample in the rheometer. For the measurements, the MTR tensile rheometer and the method sketched in Section 4.2.6 were used. Elongational properties of the PS matrix and PS/LLDPE 85/15 are presented in Figure 11.7. The experiments were performed at a constant elongation rate of 0.1 s–1 up to different total stretching ratios . The recoverable stretching ratio increases with the recovery time first, and then reaches an equilibrium value after some time. This plateau grows with the previous total elongation chosen.
r
6 5 4
3
4.1 7.4 12.2
2 1 100 a)
r
101
6 5 4
3
4.1 7.4 12.2
2 102
103
t [s]
104
1 100 b)
101
102
103
t [s]
104
Figure 11.7 Recoverable stretching ratio as a function of the recovery time for a) the polystyrene matrix and b) a blend with 15 wt % linear low density polyethylene (PS/LLDPE 85/15). up to three differThe samples were stretched at 170 °C and an elongational rate of ent total stretching ratios . Reprinted from [11.21] with permission from Springer Nature
The PS matrix and the blend PS/LLDPE 85/15 measured under the same experimental conditions show in principle a similar behavior, but the plateau values of the blend are distinctly larger. This result indicates that the morphology generated by the addition of the minor LLDPE phase distinctly enhances the recoverable portion of the elongation beyond that of the PS matrix. Qualitatively the same results were found at other elongational rates for PS/LLDPE 85/15 [11.21]. Figure 11.8(a) shows the morphology of the blend PS/LLDPE 85/15 and demonstrates that for the initial sample spherical LLDPE particles exist within the PS
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matrix. Figure 11.8(b) exhibits the morphology just after elongation of the sample up to a stretching ratio of 12. It is clearly seen how the initial spherical droplets have developed into fibrils under the elongation, the experimental parameters of which are given in the figure caption.
Figure 11.8 Scanning electron micrographs of the blend PS/LLDPE 85/15 a) before deformation, b) just after elongation up to a stretching ratio of = 12 at 170 °C and an elongational , c) after 480 s of recovery at 170 °C. The arrows indicate the direction of rate of elongation. Reprinted from [11.21] with permission from Springer Nature
In contrast to Figure 11.8(b), showing distinct fibrils directly after stretching, droplet-shaped particles are found again after a recovery time of 480 s. In comparison with the initial morphology, a greater number of particles with smaller diameters can be seen, indicating a decay of fibrils during recovery. This process is investigated in [11.22] and discussed in detail in [11.23]. The observations demonstrate how the morphological change of the fibrils of the stretched second phase back to the initial spherical morphology affects the recovery of polymer blends. This effect driven by interfacial tension has to be added to the recovery of the matrix due to the recoil of the elongated molecules. As can be seen from Figure 11.7(a), the viscoelastic PS matrix exhibits some kind of recovery, too, but it is distinctly smaller than that of the blend. From the measurements it becomes obvious how significantly the recoverable elongation of a polymer blend can be increased by adding a small amount of a dispersed phase even with low elasticity like the LLDPE. A theory that perfectly describes the recoverable elongation of immiscible polymer blends does not exist so far. In [11.24], a theory based on an effective medium approximation is presented to describe the part of the recoverable elongation of polymer blends due to the interfacial tension. These data can be obtained by subtract-
11.2 Nonlinear Elastic Behavior
ing the recoverable elongations of the matrix from those of the total recovery. The application of these considerations to the measurements on the PS/LLDPE 85/15 blends at various elongational rates and total elongations presented in [11.21] shows that the increase in the recoverable stretching ratio with recovery time is described qualitatively, but the model predicts too high plateau values for the recovery of the immiscible polymer blend PS/LLDPE 85/15. In [11.25], measurements of the recoverable stretching ratios of PS/PMMA blends are compared with the model based on the effective medium approximation. The ) and conresults show various tendencies. For a low elongational rate ( tents of 85 and 15 wt % PS, the model significantly underestimates the experimental results; for a PS concentration of 65 wt %, it is just the other way around. At a , the agreement between model prediction higher elongational rate of and experiment is better.
11.2.2 Extrudate Swell In Sections 6.2.2, 6.3.2, and 6.4.2.3 the influence of the molecular structure on the extrudate swell of homogeneous polymer melts is discussed, and in Section 10.8.1 it is described how significantly the extrudate swell can be reduced by the addition of solid fillers. From the large recoverable elongation of immiscible polymer blends and the importance of the elongational deformation in the entrance region of a die for the flow behavior of a polymer melt in short capillaries as discussed in Section 5.6.2, a significant effect of the minor phase on the extrudate swell of a blend is expected. This is demonstrated on a blend of PS with LLDPE. For the extrudate swell the defiis used, with being the diameter of the strand completely nition annealed in a silicone oil bath and the diameter of the capillary. The samples = 4 at a were extruded through a capillary with the length to diameter ratio shear stress at the capillary wall of 40 kPa. Under these conditions the PS matrix had an extrudate swell of 0.3 and the LLDPE attained a value of 0.1. The addition of only 10 wt % LLDPE increased the extrudate swell to 0.45, which is distinctly higher than that of the matrix. For 20 wt % LLDPE a value of 0.8 was measured, which is more than twice as high as that of the PS. From these results it is evident that a simple blending rule cannot be applied and that the recoil of the minor LLDPE phase deformed in the entrance region of the capillary contributes a great deal to the extrudate swell. This interpretation is evident from the measurements of the recoverable stretching ratio in Figure 11.7, which demonstrate the increase in the recoverable elongation by the addition of LLDPE. Moreover, a short capillary was used to measure the extrudate swell and thus small throughput times are given, during which the elastic deformation exerted in the entrance region may
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recover only weakly and, consequently, it predominates the swell at the capillary exit. Another example of a significant effect of the addition of an immiscible component on the extrudate swell is given by the measurements on SAN/PP blends [11.15]. In Figure 11.9, the development of the extrudate swell as a function of annealing time is presented for various PP contents. 3.0 SAN/PP
S
T = 200 °C
PP [wt.-%] 16 4 30 8 40 12
2.5 2.0 1.5 1.0 0.5 0.0
0
20
40
60
80
100
120
t [min]
Figure 11.9 Extrudate swell, defined as S = d/d0–1, as a function of annealing time t for SAN/PP blends of various compositions. The samples were extruded through a capillary with a length to diameter ratio L/d0 = 4 under a stress at the wall of 50 kPa and a temperature of 200 °C. The annealing temperature was 200 °C [11.15]
As is well known, the extrudate swell increases with annealing time up to a plateau. For the highest concentration of 40 wt % PP, the plateau value of about 1.3 is attained after 40 min. This extrudate swell corresponds to a diameter increase in the extruded strand by the factor 2.3 and shows the enormous elastic effect due to the recoil of the deformed PP phase. Interesting is the observation that, under the conditions chosen, it takes 40 min for the deformations to completely relax. Due to this slow relaxation it is possible to get a real picture of the morphology just after extrusion by electron microscopy, which obviously has to be performed on a solidified strand. The morphology development within a strand of the blend SAN/PP 84/16 after extrusion at a wall shear stress of 50 kPa and T = 210 °C is shown in Figure 11.10. Just after extrusion, designated by t = 0 min in Figure 11.10, a pronounced fibrillation is visible, which has its origin in the elongation in the entrance region. All the fibrils are orientated in the extrusion direction. Due to the small length to
11.3 References
diameter ratio L/d0 = 4 of the capillary, the morphology exerted by extension in the entrance region can be assumed to be approximately unchanged by the passage through the capillary. The micrographs in Figure 11.10 show the retraction of the fibrils to spherical geometries. The result in Figure 11.9, that for SAN/PP 84/16 the plateau of the extrudate swell is reached after 30 min of annealing, goes conform with the predominance of a spherical morphology after recovery in Figure 11.10(c), which has not changed much after further annealing for 120 min (Figure 11.10(d)). The wide distribution of particle diameters indicates the existence of decay processes of the fibrils during retraction.
Figure 11.10 Electron micrographs of the blend SAN/PP 84/16 extruded at a wall shear stress of 50 kPa and T = 210 °C through a capillary with the length to diameter ratio L/d0 = 4 after the annealing times of a) 0 min, b) 10 min, c) 30 min, and d) 120 min [11.15]
11.3 References [11.1]
Vinckier I., Moldenaers P., Mewis J., Relationship between rheology and morphology of model blends in steady shear flow, J. Rheol. 40 (1996), 613–631
[11.2]
Graebling D., Froelich D., Muller R., Viscoelastic properties of polydimethylsiloxane-polyoxy ethylene blends in the melt. Emulsion model, J. Rheol. 33 (1989), 1283–1291
[11.3]
Graebling D., Muller R., Rheological behavior of polydimethylsiloxane/polyoxyethylene blends in the melt. Emulsion model of two viscoelastic liquids, J. Rheol. 34 (1990), 193–205
[11.4]
Graebling D., Benkira A., Gallot Y., Muller R., Dynamic viscoelastic behavior of polymer blends in the melt – Experimental results for PDMS/POE-DO, PS/PMMA and PS/PEMA blends, Eur. Polym. J. 30 (1994), 301–308
217
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[11.5]
Palierne J. F., Linear rheology of viscoelastic emulsions with interfacial tension, Rheol. Acta 29 (1990), 204–214
[11.6]
Okamoto K., Takahashi M., Yamane H., Kashibara H., Masuda T., Droplet phase and dynamic viscoelasticity of PMMA/PS blend melts, Nihon Reoroji Gakkaishi 25 (1997), 199–200
[11.7]
Graebling D., Muller R., Palierne J. F., Linear viscoelastic behavior of some incompatible polymer blends in the melt. Interpretation of data with a model of emulsion of viscoelastic liquids, Macromolecules 26 (1993), 320–329
[11.8]
Gramespacher H., Meissner J., Interfacial tension between polymer melts measured by shear oscillations of their blends, J. Rheol. 36 (1992), 1127–1141
[11.9] Choi S. J., Schowalter W. R., Rheological properties of nondilute suspensions of deformable particles, Phys. Fluids 18 (1975), 420–427 [11.10] Scholz P., Froelich D., Muller R., Viscoelastic properties and morphology of two-phase polypropylene/polyamide 6 blends in the melt. Interpretation of results with an emulsion model, J. Rheol. 33 (1989), 481–499 [11.11] Weese J., Honerkamp J., A non-linear regularization method for the calculation of relaxation spectra, Rheol. Acta 32 (1993), 65–73 [11.12] Sailer C., Blends of polyamide 6 and styrenic polymers: Influence of reactive compatibilization on melt rheology and morphology, Doctoral Thesis, ETH Zürich, Diss. ETH no. 17964 (2008) [11.13] Gramespacher H., Meissner J., Reversal of recovery direction during creep recovery of polymer blends, J. Rheol. 39 (1995), 151–160 [11.14] Thornton B. A., Villasenor R. G., Maxwell B., The melt elasticity of polymer blends: Polystyrene/poly(methyl methacrylate, J. Appl. Polym. Sci. 25 (1980), 653–663 [11.15] Kirchberger A., Morphologische und rheologische Eigenschaften von unverträglichen und teil verträglichen Polymerblends auf der Basis von Styrol-Acrylnitril-Copolymer (Morphological and rheological properties of immiscible and partially miscible polymer blends on the base of styrene-acrylonitrile-copolymer), Doctoral Thesis, University Erlangen-Nuremberg, Verlag Dr. Hut, Munich (2011) [11.16] Grace H. P., Dispersion phenomena in high viscosity immiscible fluid systems and application of static mixers as dispersion devices in such systems, Chem. Eng. Comm. 14 (1982), 225–277 [11.17] Vinckier L., Moldenaers P., Mewis J., Elastic recovery of immiscible blends 1. Analysis after steady state shear flow, Rheol. Acta 38 (1999), 65–72 [11.18] Gronski W., Läuger J., Laubner C., Structure development under shear flow during spinodal decomposition of a polymer blend observed by simultaneous measurement of small angle light scattering and rheological functions, J. Mol. Structure 383 (1996), 23–30 [11.19] Gramespacher H., Meissner J., Melt elongation and recovery of polymer blends, morphology and influence of interfacial tension, J. Rheol. 41 (1997), 27–44 [11.20] Meissner J., Development of a universal extensional rheometer for the uniaxial extension of polymer melts, J. Rheol. 16 (1972), 405–420 [11.21] Handge U. A., Okamoto K, Münstedt H., Recoverable deformation and morphology after uni axial elongation of a polystyrene/linear low density polyethylene blend, Rheol. Acta 46 (2007), 1197–1209 [11.22] Stary Z., Münstedt H., Morphology development in PS/LLDPE blend during and after elongational deformation, J. Polym. Sci. Part B, 46 (2008), 16–27 [11.23] Münstedt H., Rheological and Morphological Properties of Dispersed Polymeric Materials, Hanser, Munich (2016) [11.24] Handge U. A., Modeling recovery of polymer blends after melt elongation, J. Rheol. 47 (2003), 969–978 [11.25] Handge U. A., Pötschke P., Interplay of rheology and morphology in melt elongation and subsequent recovery of polystyrene/poly(methyl methacrylate blends, J. Rheol. 48 (2004), 1103–1128
Immiscible Polymer Blends
Blends of various polymers have gained a great importance in the field of commercial polymeric materials because special end-use properties can be obtained by a relatively simple mechanical mixing process of different components in the molten state. But only very few polymers are miscible on a molecular scale and that is the reason why one has to deal with special morphological features even in the melt. Thus, in addition to properties of the blend components, interactions between the different phases have to be considered, which may affect rheological properties. As is well known and was widely discussed in the previous chapters, from the linear rheological properties insights into interactions taking place on molecular levels can be obtained. Additionally, the nonlinear rheological behavior can be exploited for the assessment of some aspects of processing. The availability of a wide variety of commercial polymeric materials offers in principle the creation of a great number of polymer blends when it is taken into account that, in addition to specific characteristics of the components, the blend properties obviously depend on the mixing ratios. Moreover, the interactions between the different phases can be changed by the introduction of so-called compatibilizers that affect the interplay between matrix molecules and dispersed phase and, thus, influence material properties. This chapter deals with the rheological behavior of uncompatibilized polymer blends and their elasticity in particular. Like in the previous sections, nonlinear properties that are interesting for processing are discussed separately from linear properties that may be used to elucidate the properties of the polymeric matrix and the dispersed phase.
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11.1 Linear Elastic Behavior In comparison with polymer melts filled with rigid particles, discussed in Chapter 9 and 10, polymer blends are more complex insofar as the dispersed phase is viscoelastic too and may contribute to the overall viscous and elastic properties of a polymer melt. Even in the linear range of deformation two different morphological features have to be distinguished. One may be marked by a constant shape of the dispersed phase during the experiment, the other by a change in shape that is restored after recovery. Studies in which the geometry of the secondary phase can be assumed to remain constant are of special interest, because in this case theoretical descriptions are existent, which become rather complicated when changing particle geometries or morphologies have to be considered.
11.1.1 Dynamic-Mechanical Experiments Dynamic-mechanical experiments at low enough oscillating amplitudes are very suitable for studies in the linear regime, because the morphology can be assumed not to be changed by the acting stresses. For example, the linear range can be determined conveniently by measurements of the storage modulus as a function of the amplitude for given frequencies, as shown for a particle-filled polymethylmethacrylate in Figure 10.3. Linearity can be assumed as long as the modulus is independent of the amplitude. In comparison with polymer melts filled with rigid particles, which are presented in Figures 10.4 to 10.6, the storage modulus as a function of angular frequency exhibits a totally different behavior in the linear regime for an immiscible polymer blend, as demonstrated in Figure 11.1 for polyisobutylene (PIB) as the matrix and polydimethylsiloxane (PDMS) as the dispersed phase [11.1]. The blend components exhibit a distinct terminal regime in the frequency regime chosen, as exof the blend, however, pected due to their relatively small molar masses. The shows a pronounced shoulder in the range of medium frequencies before it further declines with decreasing frequency. The shoulder is characterized by its width (frequency range) and its height (average level of modulus). Their exact determination is a matter of definition. At high frequencies, the modulus of the blend can be described approximately by a simple mixing rule (full line) based on the volume ratios of the components, which is apparently not valid anymore at lower frequencies. For the loss modulus of the blend, it is reported in [11.1] that its frequency dependence is the same as that of the components, within the accuracy of the measurements, and that it is only marginally different from that of the Newtonian PIB matrix. Thus, it may be concluded that the significant effect of the blend com-
11.1 Linear Elastic Behavior
ponent on is due to a change in elastic properties of the polymeric system. Formally, the shoulder of can be interpreted by the assumption of a relaxation process caused by the incompatibility of matrix and dispersed phase. It is clear that the relaxation mechanism results from the interplay of the interfacial tension and the viscoelastic properties of the dispersed phase. Similar effects as presented for PIB/PDMS are reported for blends of polydimethylsiloxane/polyoxyethylene [11.2, 11.3] and by the same group of authors for polystyrene/polymethylmethacrylate and polystyrene/polyethylmethacrylate blends [11.4]. 10
4
G' [Pa] 10
3
10
2
PDMS
PIB/PDMS 70/30 10
1
10
0
PIB
10
-1
10
0
10
1
-1
10
2
[s ]
Figure 11.1 Storage modulus as a function of angular frequency w for a blend of 70 vol % polyisobutylene (PIB) and 30 vol % polydimethylsiloxane (PDMS) and its components at 23 °C. The solid line represents the modulus of the blend according to a mixing rule based on the volume ratios of the components. The blend sample was sheared at a constant shear rate of 0.3 s–1 before the dynamic-mechanical characterization in order to generate a definite morpho logy. Reprinted with permission from [11.1]; copyright 1996 The Society of Rheology
These results were analyzed with Palierne’s theory [11.5], which has been used preferentially over the years to describe dynamic-mechanical experiments on immiscible polymer blends. The model was derived for a secondary phase of spherical shape in the linear range of deformation. Thus, it is particularly suited for the description of the complex modulus as a function of frequency, because dynamic-mechanical experiments can be performed easily under linear conditions and the particle shape can be assumed to remain unchanged when small amplitudes are applied. According to Palierne, the complex modulus of a blend is related to properties of the blend components by
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11 Immiscible Polymer Blends
(11.1) with (11.2) and are the complex moduli of the dispersed phase and the matrix, respectively, is the interfacial tension between matrix and secondary phase, and the volume fraction of the dispersed phase with the radius . This formula in its general feature describes an inhomogeneous distribution with different particle sizes , as it is usually found for real polymer blends. For practical purposes an average particle size is assumed, which simplifies the sums in Equation 11.1 to one term. Some general features of Equation 11.1 and Equation 11.2 are discussed in the following. When the interfacial tension between the two components of a blend and averages of the size of the dispersed phase are known, the modulus of a blend can be calculated from the moduli of the components. Good agreement between numerical descriptions and experimental results of the loss and the storage moduli as functions of the frequency have been found for the measurements on the various samples reported in [11.2], [11.3], and [11.4]. Moreover, the equations above can be used to determine either the interfacial tension or an average radius of the dispersed phase from dynamic-mechanical experiments. From the fit to the may be obtained, and then from either measured modulus curves, the quotient or , known from other methods, the corresponding quantity can be determined. Such an evaluation is described in [11.6] for a blend of 20 vol % PS and 80 vol % = PMMA (PS/PMMA 20/80). The PS had a weight average molar mass of was 64 kg/mol. does exhibit a distinct shoul190 kg/mol and for PMMA and are fitted with Palierneʼs equation. Over der, as Figure 11.2 shows. wide ranges the agreement between experiment and theory is satisfactory and at smaller frethe shoulder is well described. Some discrepancies occur for quencies. the interfacial tension was obtained, making use of From the fit parameter the average diameter of the dispersed polystyrene phase determined from transmission electron micrographs. The surface tension of 2.3 mN/m is in good agreement with values from other methods. The other way around, an average size of the secondary phase of an immiscible blend can be obtained when a known value for the interfacial tension is introduced.
11.1 Linear Elastic Behavior
10 6 10 5 G',G'' [Pa] 10 4 10 3 10 2 G' G'' G'(Palierne) G''(Palierne)
10 1 10 0 -3 10
-2
10
-1
10
0
10
1
-1
[s ]
10
Figure 11.2 Storage modulus and loss modulus as functions of the angular frequency w for PMMA/PS 80/20 at 180 °C. The lines represent the fit with Palierne’s theory. Adapted from [11.6]
From the equations above the influence of various parameters of a blend on the formation of the shoulder in can be discussed. This is done in [11.7] making use of the specific characteristics of the height and the width of the shoulder, which, however, can be assessed only roughly in many cases. An obvious parameter is the concentration of the minor phase. Palierne’s theory predicts an increase in shoulder height and width with growing content of the secondary phase. Measurements on two concentrations of a polyoxyethylene in a polydimethylsiloxane confirm the prediction. Two other parameters are the interfacial tension and the radius of the inclusions, the influence of which is reciprocal to each other (see Equation 11.2). From [11.7] it follows that the shoulder height becomes higher with increasing interfacial tension, while the shoulder width gets narrower. The experimental proof of this prediction is not easy, because the surface tension is one decisive factor for the morphology development and, thus, the interfacial tension and the size of the inclusions are related to each other. However, an indirect confirmation of the prediction of the can be drawn from the experiinfluence of particle size on the shoulder of ments on blends of PDMS and PIB reported in [11.1]. In these investigations, for a definite composition the sizes of the inclusions were altered by shearing the blend at different constant rates before the dynamic-mechanical test. It was found for PIB/PDMS 70/30 that the average size of the secondary PDMS phase became smaller with increasing preshear rate, but it is clear that the interfacial tension remains the same. For the smaller sizes of the inclusions, the heights of the shoulders of increased and their extensions decreased as predicted in [11.7].
205
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11 Immiscible Polymer Blends
Furthermore, conclusions can be reached from the emulsion theory with respect to the effect of viscoelastic properties of matrix and secondary phase. A declining viscosity of the dispersed phase enhances the height of the shoulder, but its width is not affected much. The influence of the terminal relaxation time of the matrix is predicted in such a way that the shoulder is much more pronounced at shorter relaxation times than at higher ones [11.7]. in combination with Palierne’s This discussion demonstrates in which way emulsion theory can make a contribution to analyze immiscible polymer blends with respect to the size of the inclusions and the interfacial tension acting between , and thus the viscosity, is only weakly matrix and dispersed phase. Because affected by the dispersed phase, it is mainly the elastic property reflected by for comparable viscosities that enables deeper insights into interactions within polymer blends. Dynamic-mechanical measurements on PMMA/PS blends are reported in [11.8], too. The PMMA matrix has a higher molar mass and broader molar mass distri bution than the sample from [11.6] discussed above, resulting in longer terminal and are similar to those presented in relaxation times. The results of for the various concentrations are less disFigure 11.2, but the shoulders of tinct. This observation goes along with the prediction of the emulsion theory that the width of the shoulder decreases with longer terminal relaxation times. Nevertheless, interesting insights into the interactions between matrix and dispersed phase have been obtained from these investigations, using for their interpretation the emulsion model of Choi and Schowalter [11.9] and its specification for the linear behavior [11.10]. From the dynamic-mechanical experiments the weighted relaxation spectra were determined according to [11.11]. An example is given in Figure 11.3 for the blend PMMA/PS 92/8. Besides the two peaks representing the terminal relaxation times of the dispersed and the matrix phase, there occurs a third peak at higher relaxation times at the end of the spectrum. As discussed in [11.8], this peak is related to a relaxation process induced by the interfacial tension . The corresponding relaxation time depends on the volume ratio of the dispersed phase, the viscosity of the matrix, the ratio of the viscosity of the dispersed phase and the , where is the average radius of the inclusions. For a given commatrix, and can be determined from position with known viscosities of the components, the peak relaxation time. Similar to Palierne’s emulsion theory, either or can be obtained when the corresponding quantity is known from other methods. In [11.8] the average size of the PS inclusions is given as 1 μm. The interfacial tension for the blend with 8 vol % PS follows as 2.2 mN/m, which is in very good agreement with the value for the other PMMA/PS blend with 20 vol % PS presented in Figure 11.2. In [11.8] interfacial tensions, very similar within the accuracy of the meas-
11.1 Linear Elastic Behavior
urements, are reported for PMMA/PS blends with higher concentrations of 12 and 16 vol % PS. This result is physically very reasonable, because the interfacial tension is given by the chemical constitution of the components. 5 4
H( ) [10 Pa s] 4
3
2
1
0
10
-4
10
-3
10
-2
10
-1
0
10 10 [s]
1
10
2
10
3
10
4
Figure 11.3 Weighted relaxation spectrum for the PMMA/PS 92/8 blend. is the the relaxation strength. Reprinted with permission from [11.8]; relaxation time and copyright 1992 The Society of Rheology
The dynamic-mechanical behavior of several non-miscible polymer blends and the comparison with the Palierne theory have been presented in [11.12]. The emulsion of PA6/SAN at lower frequencies. The difference model underestimates the was found to be significant for PA6/SAN 10/90 but smaller for PA6/SAN 70/30. For PA6/PS 10/90 a good agreement between measured and calculated curves was observed over the whole frequency range. However, for none of the blends a shoulder was obtained. with respect to interactions between matrix and The obvious sensitivity of polymeric inclusions is interesting from a fundamental point of view, but the contribution to a morphological analysis of the secondary phase is rather limited. Only average diameters of inclusions can be obtained that may belong to different distributions. Thus, dynamic-mechanical experiments, which are easily performed, cannot be used to replace morphology analyses by elaborate microscopic techniques. was found in Section 9.2.5, too, for a completely different hete A shoulder for rogeneous polymer system of a largely Newtonian polyisobutylene with rigid glass beads. Of course, an interfacial tension exists between matrix and filler, but because of the lack of deformability of the glass beads a relaxation process similar to that for polymer blends is not possible. Rather, an interplay between elastic defor-
207
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11 Immiscible Polymer Blends
mations of the “honey-comb” structure built up by the particles and the viscoelastic matrix molecules has to be envisaged, as discussed in Section 9.2.4. Such a , similarly to interactions between process may formally become visible in inclusions and matrix molecules in a polymer blend, when it occurs at a comparable time scale.
11.1.2 Recoverable Shear As shown in Chapter 10, the recoverable shear, particularly in the linear range, can be used successfully to characterize interactions between nanoparticles and matrix molecules. A very suitable elastic material quantity is the recoverable compliance, defined as (Equation 3.7): with being the recoverable shear strain and s the shear stress applied in the preceding creep experiment. It is preferentially determined by creep recovery measurements, as described in Section 3.1. In Section 4.2.1 it is demonstrated how the linear regime can be determined experimentally. Of particular interest is the time-dependent linear compliance because retardation spectra can be calculated from this material function, as shown in Section 10.3.3 for a melt filled with nanoparticles. In the literature, measurements of recoverable properties in the linear range of polymer blends are very rare. The reason is that investigations of this kind need special experimental care and the few results exhibit features that are difficult to interpret. For example, in [11.13] creep recovery experiments on PS/PMMA blends are presented, which exhibit a phenomenon not completely understood so far. In Figure 11.4(a) the recovery curves for the polystyrene and the polymethylmethacrylate blend components are presented, which both show an increase in the recoverable compliance with time up to an extended plateau, as is well known for polymer melts. The steady-state recoverable compliance of the PMMA is distinctly lower than that of the PS. However, as seen from Figure 11.13(b), for the blend PMMA/PS 84/16, the recoverable compliance after the same preceding creep at a stress of 150 Pa first increases with the recovery time t, but reaches a plateau value only after running through a maximum. The recoverable compliance or the corresponding recoverable shear decreasing with time indicates a reversal of the direction of recovery, which means that the sample creeps again without any external stress before reaching a steady state of deformation. The maximum of the recoverable compliance becomes more pronounced and its position slightly shifts to longer retardation times with increasing PS concentration, as shown in [11.13] for blends with up to 20 wt % PS. The plateau value of PMMA/PS 92/8 is somewhat
11.1 Linear Elastic Behavior
higher than that of the PMMA matrix and is enhanced with growing PS concentration [11.13]. As follows from Figure 11.4, the steady-state recoverable compliance of PMMA/PS 84/16 is larger than that of the pure PS. This result shows that a simple mixing rule is not valid, but indicates a significant contribution of the recoil of the PS inclusions to the total recovery. 3
Jr(t) [10-4 Pa-1]
2
2
1
1
0
a)
3
PS PMMA
Jr(t) [10 -4 Pa-1]
0
500
1000
t [s]
0
1500
b)
0
2000
4000
6000
t [s]
8000
Figure 11.4 Recoverable compliance as a function of recovery time after preceding creep at the shear stress = 150 Pa and 170 °C for a) the PS and PMMA components, and b) the PS/PMMA blend with 16 wt % PS. Reprinted with permission from [11.13]; copyright 1995 The Society of Rheology
Surprisingly, maxima in creep recovery were not found for blends with the PS as the matrix and the PMMA as the dispersed phase [11.13]. For a sample with 16 wt % PMMA, for example, the recoverable compliance steadily increases with time up to a plateau. This behavior is similar to that of unfilled and particle-filled polymer melts described in Section 10.3.2. The steady-state value of the PS/PMMA blend is distinctly higher than those of the matrices, indicating the contribution of the recoil of the deformed secondary PMMA phase. Information on the morpho logy of the blends is not available. The zero-shear viscosity of the PS is higher by about 40 %, and its linear steady-state compliance by a factor of three, than for the PMMA. This means that the maximum relaxation time of the PS is distinctly larger. It is difficult, however, to relate this difference to the phenomena observed. From the literature only very few investigations of the time dependence of the recovery of immiscible polymer blends are available. One example is the measurements on PS/PMMA blends of various compositions with a home-built rheometer [11.14]. For none of the samples, and, in particular, not for those with blend ratios comparable to the PS/PMMA blends in [11.13], a maximum of the recoverable strain as a function of recovery time is reported. Neither rheological or molecular data of the two components nor presentations of the morphology of the blends are given and, thus, a founded comparison of the results on the two blends is not possible.
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11 Immiscible Polymer Blends
Another example of immiscible blends is the blends of styrene acrylonitrile (SAN) with polypropylene (PP) [11.15]. In Figure 11.5 the recoverable shear compliance as a function of the recovery time t is presented for the blends SAN/PP 96/04 and SAN/PP 84/16 and their components SAN and PP. The linearity of the measurements at the chosen creep stress of 5 Pa was proven in [11.15]. The recoverable compliance of the PP is higher than that of the SAN. The curve for SAN/PP 84/16 lies distinctly above the curves for the components and only 4 wt % PP increases the compliance by a factor of around 10 compared to SAN, but maxima as for PS/PMMA do not occur, although the minor PP phase has the distinctly higher viscosity and longer relaxation times like the PS in the PMMA matrix. The increased compliances indicate interaction processes that should be related to morphological effects within the blends, because a simple mixing rule for the compliances based on the ratios of the components and their compliances cannot be derived. Indeed, clearly separated PP spheres of a few microns in diameter were found for the SAN/PP 84/16. Their initial dimensions and those just after the end of creep deformation were the same [11.15]. This finding could be explained by the viscosity of the dispersed PP being higher by a factor of about 10 than that of the SAN matrix, with the consequence of a negligible deformation expected for the PP inclusions during creep, according to the results of Grace on immiscible fluids [11.16]. Taking for granted the morphological findings of a geometry unchanged by creep, a recoil of the secondary PP phase cannot be the reason for the increase in recoverable deformation. Rather, interactions between matrix molecules and the surface of the dispersed polymer have to be postulated, similar to those within the particle-filled polymer melts. -1
10
T = 180 °C = 5 Pa
-2
10
-3
Jr [Pa-1]
210
10
-4
10
SAN SAN/PP 96/04 SAN/PP 84/16 PP
-5
10
10
-1
10
0
10
1
10
2
10
3
10
4
10
5
t [s]
Figure 11.5 Recoverable compliance as a function of recovery time t for the blends SAN/PP 96/04 and SAN/PP 84/16 and their components SAN and PP at 180 °C after creep at the stress of 5 Pa [11.15]
11.2 Nonlinear Elastic Behavior
In [11.17], measurements of the recoverable shear strain on an immiscible blend of polyisobutylene (PIB) and polydimethylsiloxane (PDMS) are reported, which offer the advantage of elastic properties of the two blend components being so low that elastic effects of the blends have to be completely related to morphological features. For the blend PDMS/PIB 90/10 the minor phase has a viscosity about half of that of the matrix. The creep recovery curves from preceding creep at various stresses in the linear range between 50 and 100 Pa do not exhibit a maximum, but continuously increase up to extended plateaus, which for a fixed initial morpho logy become higher with a larger preceding creep stress. This feature is qualitatively comparable to the PMMA/PS blends with PMMA as the minor phase of lower viscosity, which do not show a maximum of the recovery curves either. Studies of the morphology of the PIB/PDMS blends are not available, however, due to the obvious experimental difficulties to prepare samples at the different states of the measurements with rotational rheometers. A reversal of recovery has been reported in the literature from investigations of the structure development under shear flow during spinodal decomposition of a blend from polybutadiene and polyisoprene [11.18]. The measurements were performed by using light scattering in parallel to rheological techniques. The authors argue that relaxation processes of polymer phases taking place at different time scales can be the reason for deformations occurring in the opposite direction of the recovery [11.18]. However, besides some vagueness of the interpretation, the polymeric system and the physical processes during deformation are difficult to compare with the PMMA/PS blend. The results from the different polymer blends and their discussion do show how little elastic phenomena of immiscible polymer blends are understood even in the linear range of deformation and that, besides comprehensive rheological characterizations, the blend morphology during creep and creep recovery has to be investigated in detail to come to reliable insights.
11.2 Nonlinear Elastic Behavior Even more complex are nonlinear elastic properties of polymer blends, because they are dependent on acting stresses or deformation rates, respectively. Recover able elongation and extrudate swell are nonlinear elastic quantities of particular interest. Elongation is an experimental mode that allows a relatively easy and reliable access to investigations of the morphology of a sample. Extrudate swell is of interest because it has some importance for processing (see Chapter 12).
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11 Immiscible Polymer Blends
11.2.1 Recoverable Elongation In Figure 11.6 the recoverable stretching ratio
defined as
(11.3) is plotted as a function of recovery time t for blends from the PMMA and PS presented in Figure 11.4. l is the length of the stretched sample and the length after recovery [11.19]. The measurements were performed with a tensile rheometer based on the device reported in [11.20]. With this instrument the recovery after elongation was determined by cutting the sample into pieces and documenting the retractions of single strands by photographs.
15
r PS [wt.%] 0
10
8 12 16 20
5
100
10
1
10
2
10
3
t [s]
10
4
Figure 11.6 Recoverable stretching ratio as a function of the recovery time t for blends from PS and PMMA. Prior to recovery, the samples were elongated at an elongational rate of and 170 °C up to a total stretching ratio of l = 33. Reprinted with permission from [11.19]; copyright 1997 The Society of Rheology
From Figure 11.6 it follows that the recoverable stretching ratios of the blends continuously increase as functions of the recovery time up to plateaus, which lie significantly above those of the two components. For 20 wt % PS, the plateau value of the blend is higher by a factor of nearly 15 in comparison with the PMMA matrix. A maximum of the recoverable stretching ratio as a function of recovery time, as found for the linear recoverable shear compliance in Figure 11.4 for a sample with comparable composition, does not occur. This finding adds another facet to the complexity of the effect of recovery reversal in shear observed for distinct PS/PMMA blends.
11.2 Nonlinear Elastic Behavior
For PMMA/PS 82/18, the morphology development in parallel to recovery has been presented in [11.19]. The results demonstrate the role of the shape recovery due to the interfacial tension for the elastic recoil of the blends. This influence is reflected by the time scale being much longer for recovery than for creep to reach steady states. To further elucidate the role of morphology, recovery experiments after uniaxial elongation on PS/LLDPE blends were performed. They were carried out under definite conditions and the morphology could be determined at any state of deformation by freezing the sample in the rheometer. For the measurements, the MTR tensile rheometer and the method sketched in Section 4.2.6 were used. Elongational properties of the PS matrix and PS/LLDPE 85/15 are presented in Figure 11.7. The experiments were performed at a constant elongation rate of 0.1 s–1 up to different total stretching ratios . The recoverable stretching ratio increases with the recovery time first, and then reaches an equilibrium value after some time. This plateau grows with the previous total elongation chosen.
r
6 5 4
3
4.1 7.4 12.2
2 1 100 a)
r
101
6 5 4
3
4.1 7.4 12.2
2 102
103
t [s]
104
1 100 b)
101
102
103
t [s]
104
Figure 11.7 Recoverable stretching ratio as a function of the recovery time for a) the polystyrene matrix and b) a blend with 15 wt % linear low density polyethylene (PS/LLDPE 85/15). up to three differThe samples were stretched at 170 °C and an elongational rate of ent total stretching ratios . Reprinted from [11.21] with permission from Springer Nature
The PS matrix and the blend PS/LLDPE 85/15 measured under the same experimental conditions show in principle a similar behavior, but the plateau values of the blend are distinctly larger. This result indicates that the morphology generated by the addition of the minor LLDPE phase distinctly enhances the recoverable portion of the elongation beyond that of the PS matrix. Qualitatively the same results were found at other elongational rates for PS/LLDPE 85/15 [11.21]. Figure 11.8(a) shows the morphology of the blend PS/LLDPE 85/15 and demonstrates that for the initial sample spherical LLDPE particles exist within the PS
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matrix. Figure 11.8(b) exhibits the morphology just after elongation of the sample up to a stretching ratio of 12. It is clearly seen how the initial spherical droplets have developed into fibrils under the elongation, the experimental parameters of which are given in the figure caption.
Figure 11.8 Scanning electron micrographs of the blend PS/LLDPE 85/15 a) before deformation, b) just after elongation up to a stretching ratio of = 12 at 170 °C and an elongational , c) after 480 s of recovery at 170 °C. The arrows indicate the direction of rate of elongation. Reprinted from [11.21] with permission from Springer Nature
In contrast to Figure 11.8(b), showing distinct fibrils directly after stretching, droplet-shaped particles are found again after a recovery time of 480 s. In comparison with the initial morphology, a greater number of particles with smaller diameters can be seen, indicating a decay of fibrils during recovery. This process is investigated in [11.22] and discussed in detail in [11.23]. The observations demonstrate how the morphological change of the fibrils of the stretched second phase back to the initial spherical morphology affects the recovery of polymer blends. This effect driven by interfacial tension has to be added to the recovery of the matrix due to the recoil of the elongated molecules. As can be seen from Figure 11.7(a), the viscoelastic PS matrix exhibits some kind of recovery, too, but it is distinctly smaller than that of the blend. From the measurements it becomes obvious how significantly the recoverable elongation of a polymer blend can be increased by adding a small amount of a dispersed phase even with low elasticity like the LLDPE. A theory that perfectly describes the recoverable elongation of immiscible polymer blends does not exist so far. In [11.24], a theory based on an effective medium approximation is presented to describe the part of the recoverable elongation of polymer blends due to the interfacial tension. These data can be obtained by subtract-
11.2 Nonlinear Elastic Behavior
ing the recoverable elongations of the matrix from those of the total recovery. The application of these considerations to the measurements on the PS/LLDPE 85/15 blends at various elongational rates and total elongations presented in [11.21] shows that the increase in the recoverable stretching ratio with recovery time is described qualitatively, but the model predicts too high plateau values for the recovery of the immiscible polymer blend PS/LLDPE 85/15. In [11.25], measurements of the recoverable stretching ratios of PS/PMMA blends are compared with the model based on the effective medium approximation. The ) and conresults show various tendencies. For a low elongational rate ( tents of 85 and 15 wt % PS, the model significantly underestimates the experimental results; for a PS concentration of 65 wt %, it is just the other way around. At a , the agreement between model prediction higher elongational rate of and experiment is better.
11.2.2 Extrudate Swell In Sections 6.2.2, 6.3.2, and 6.4.2.3 the influence of the molecular structure on the extrudate swell of homogeneous polymer melts is discussed, and in Section 10.8.1 it is described how significantly the extrudate swell can be reduced by the addition of solid fillers. From the large recoverable elongation of immiscible polymer blends and the importance of the elongational deformation in the entrance region of a die for the flow behavior of a polymer melt in short capillaries as discussed in Section 5.6.2, a significant effect of the minor phase on the extrudate swell of a blend is expected. This is demonstrated on a blend of PS with LLDPE. For the extrudate swell the defiis used, with being the diameter of the strand completely nition annealed in a silicone oil bath and the diameter of the capillary. The samples = 4 at a were extruded through a capillary with the length to diameter ratio shear stress at the capillary wall of 40 kPa. Under these conditions the PS matrix had an extrudate swell of 0.3 and the LLDPE attained a value of 0.1. The addition of only 10 wt % LLDPE increased the extrudate swell to 0.45, which is distinctly higher than that of the matrix. For 20 wt % LLDPE a value of 0.8 was measured, which is more than twice as high as that of the PS. From these results it is evident that a simple blending rule cannot be applied and that the recoil of the minor LLDPE phase deformed in the entrance region of the capillary contributes a great deal to the extrudate swell. This interpretation is evident from the measurements of the recoverable stretching ratio in Figure 11.7, which demonstrate the increase in the recoverable elongation by the addition of LLDPE. Moreover, a short capillary was used to measure the extrudate swell and thus small throughput times are given, during which the elastic deformation exerted in the entrance region may
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recover only weakly and, consequently, it predominates the swell at the capillary exit. Another example of a significant effect of the addition of an immiscible component on the extrudate swell is given by the measurements on SAN/PP blends [11.15]. In Figure 11.9, the development of the extrudate swell as a function of annealing time is presented for various PP contents. 3.0 SAN/PP
S
T = 200 °C
PP [wt.-%] 16 4 30 8 40 12
2.5 2.0 1.5 1.0 0.5 0.0
0
20
40
60
80
100
120
t [min]
Figure 11.9 Extrudate swell, defined as S = d/d0–1, as a function of annealing time t for SAN/PP blends of various compositions. The samples were extruded through a capillary with a length to diameter ratio L/d0 = 4 under a stress at the wall of 50 kPa and a temperature of 200 °C. The annealing temperature was 200 °C [11.15]
As is well known, the extrudate swell increases with annealing time up to a plateau. For the highest concentration of 40 wt % PP, the plateau value of about 1.3 is attained after 40 min. This extrudate swell corresponds to a diameter increase in the extruded strand by the factor 2.3 and shows the enormous elastic effect due to the recoil of the deformed PP phase. Interesting is the observation that, under the conditions chosen, it takes 40 min for the deformations to completely relax. Due to this slow relaxation it is possible to get a real picture of the morphology just after extrusion by electron microscopy, which obviously has to be performed on a solidified strand. The morphology development within a strand of the blend SAN/PP 84/16 after extrusion at a wall shear stress of 50 kPa and T = 210 °C is shown in Figure 11.10. Just after extrusion, designated by t = 0 min in Figure 11.10, a pronounced fibrillation is visible, which has its origin in the elongation in the entrance region. All the fibrils are orientated in the extrusion direction. Due to the small length to
11.3 References
diameter ratio L/d0 = 4 of the capillary, the morphology exerted by extension in the entrance region can be assumed to be approximately unchanged by the passage through the capillary. The micrographs in Figure 11.10 show the retraction of the fibrils to spherical geometries. The result in Figure 11.9, that for SAN/PP 84/16 the plateau of the extrudate swell is reached after 30 min of annealing, goes conform with the predominance of a spherical morphology after recovery in Figure 11.10(c), which has not changed much after further annealing for 120 min (Figure 11.10(d)). The wide distribution of particle diameters indicates the existence of decay processes of the fibrils during retraction.
Figure 11.10 Electron micrographs of the blend SAN/PP 84/16 extruded at a wall shear stress of 50 kPa and T = 210 °C through a capillary with the length to diameter ratio L/d0 = 4 after the annealing times of a) 0 min, b) 10 min, c) 30 min, and d) 120 min [11.15]
11.3 References [11.1]
Vinckier I., Moldenaers P., Mewis J., Relationship between rheology and morphology of model blends in steady shear flow, J. Rheol. 40 (1996), 613–631
[11.2]
Graebling D., Froelich D., Muller R., Viscoelastic properties of polydimethylsiloxane-polyoxy ethylene blends in the melt. Emulsion model, J. Rheol. 33 (1989), 1283–1291
[11.3]
Graebling D., Muller R., Rheological behavior of polydimethylsiloxane/polyoxyethylene blends in the melt. Emulsion model of two viscoelastic liquids, J. Rheol. 34 (1990), 193–205
[11.4]
Graebling D., Benkira A., Gallot Y., Muller R., Dynamic viscoelastic behavior of polymer blends in the melt – Experimental results for PDMS/POE-DO, PS/PMMA and PS/PEMA blends, Eur. Polym. J. 30 (1994), 301–308
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[11.5]
Palierne J. F., Linear rheology of viscoelastic emulsions with interfacial tension, Rheol. Acta 29 (1990), 204–214
[11.6]
Okamoto K., Takahashi M., Yamane H., Kashibara H., Masuda T., Droplet phase and dynamic viscoelasticity of PMMA/PS blend melts, Nihon Reoroji Gakkaishi 25 (1997), 199–200
[11.7]
Graebling D., Muller R., Palierne J. F., Linear viscoelastic behavior of some incompatible polymer blends in the melt. Interpretation of data with a model of emulsion of viscoelastic liquids, Macromolecules 26 (1993), 320–329
[11.8]
Gramespacher H., Meissner J., Interfacial tension between polymer melts measured by shear oscillations of their blends, J. Rheol. 36 (1992), 1127–1141
[11.9] Choi S. J., Schowalter W. R., Rheological properties of nondilute suspensions of deformable particles, Phys. Fluids 18 (1975), 420–427 [11.10] Scholz P., Froelich D., Muller R., Viscoelastic properties and morphology of two-phase polypropylene/polyamide 6 blends in the melt. Interpretation of results with an emulsion model, J. Rheol. 33 (1989), 481–499 [11.11] Weese J., Honerkamp J., A non-linear regularization method for the calculation of relaxation spectra, Rheol. Acta 32 (1993), 65–73 [11.12] Sailer C., Blends of polyamide 6 and styrenic polymers: Influence of reactive compatibilization on melt rheology and morphology, Doctoral Thesis, ETH Zürich, Diss. ETH no. 17964 (2008) [11.13] Gramespacher H., Meissner J., Reversal of recovery direction during creep recovery of polymer blends, J. Rheol. 39 (1995), 151–160 [11.14] Thornton B. A., Villasenor R. G., Maxwell B., The melt elasticity of polymer blends: Polystyrene/poly(methyl methacrylate, J. Appl. Polym. Sci. 25 (1980), 653–663 [11.15] Kirchberger A., Morphologische und rheologische Eigenschaften von unverträglichen und teil verträglichen Polymerblends auf der Basis von Styrol-Acrylnitril-Copolymer (Morphological and rheological properties of immiscible and partially miscible polymer blends on the base of styrene-acrylonitrile-copolymer), Doctoral Thesis, University Erlangen-Nuremberg, Verlag Dr. Hut, Munich (2011) [11.16] Grace H. P., Dispersion phenomena in high viscosity immiscible fluid systems and application of static mixers as dispersion devices in such systems, Chem. Eng. Comm. 14 (1982), 225–277 [11.17] Vinckier L., Moldenaers P., Mewis J., Elastic recovery of immiscible blends 1. Analysis after steady state shear flow, Rheol. Acta 38 (1999), 65–72 [11.18] Gronski W., Läuger J., Laubner C., Structure development under shear flow during spinodal decomposition of a polymer blend observed by simultaneous measurement of small angle light scattering and rheological functions, J. Mol. Structure 383 (1996), 23–30 [11.19] Gramespacher H., Meissner J., Melt elongation and recovery of polymer blends, morphology and influence of interfacial tension, J. Rheol. 41 (1997), 27–44 [11.20] Meissner J., Development of a universal extensional rheometer for the uniaxial extension of polymer melts, J. Rheol. 16 (1972), 405–420 [11.21] Handge U. A., Okamoto K, Münstedt H., Recoverable deformation and morphology after uni axial elongation of a polystyrene/linear low density polyethylene blend, Rheol. Acta 46 (2007), 1197–1209 [11.22] Stary Z., Münstedt H., Morphology development in PS/LLDPE blend during and after elongational deformation, J. Polym. Sci. Part B, 46 (2008), 16–27 [11.23] Münstedt H., Rheological and Morphological Properties of Dispersed Polymeric Materials, Hanser, Munich (2016) [11.24] Handge U. A., Modeling recovery of polymer blends after melt elongation, J. Rheol. 47 (2003), 969–978 [11.25] Handge U. A., Pötschke P., Interplay of rheology and morphology in melt elongation and subsequent recovery of polystyrene/poly(methyl methacrylate blends, J. Rheol. 48 (2004), 1103–1128