Rheology of immiscible blends

With the knowledge of the flow behavior of simpler systems, viz. suspensions, emulsions, block copolymers, as well as that of the mumal interactions between the rheology and thermodynamics near the phase separation, one may consider the flow of more complex systems where all these elements may play a role. Evidently, any constitutive equation that may attempt to describe flow of immiscible polymer blends should combine three elements the stress-induced effects on the concentration gradient an orientation function and the stress-strain description of the systems, including the flow-generated morphology. Such a comprehensive description stiU remains to be formulated. 

The first steps toward such a theory of blend flow behavior were proposed by Helfand and Fredrickson [1989], then by Doi and Onuki [1992]. A greatly simplified constitutive equation for immiscible 1 1 mixture of two Newtonian fluids having the same viscosity and density was also derived [Doi and Ohta, 1991]. The derivation considered time evolution of the area and orientation of the interface in flow, as well as the interfacial tension effects. The relation predicted scaling behavior for the stress and the velocity gradient tensors  

Doi-Ohta s theory was also compared to the experimental data of semi-concentrated mixtures of PIB in PDMS [Vinckier et ai, 1997]. The theory described reasonably well the transient effects at the startup of steady state shearing. The scaling laws were also obeyed by these slightly viscoelastic blends. 

Following Doi and Ohta s work, a more general theory was derived for immiscible polymer blends by Lee and Park [1994]. A constitutive equation for immiscible blends was proposed. The model and the implied blending laws were verified by comparison with dynamic shear data of PS/LLDPE blends in oscillatory shear flow. 

Experimental verification of Eqs 7.94 indicated that the scaling relationships are valid, but the shape of experimental transient stress curves, after step-change of shear rate, did not agree with Doi-Ohta s theory [Takahashi et al., 1994]. Similar conclusions were reported for PA-66 blends with 25 wt% PET [Guenther and Baird, 1996]. For steady shear flow the agreement was poor, even when the strain-rate dependence of the component viscosities was incorporated. Similarly, the 

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Rheology of Immiscible Blends 7.5.1 Rheological Equation of State... 

Thareja, P. and Velankar, S. (2008) Rheology of immiscible blends with particle-induced drop clusters. Rheol. Acta, 47 (2), 189-200. 

Grmela M, Bousmina M, Palierne JF. On the rheology of immiscible blends. Rheol Acta 2001 40(6) 560-569. 

Ruckdaschel H, Rausch J, Sandler JKW, Altstadt V, Schmalz H, Muller AHE (2008) Correlation of the melt rheological properties with the foaming behavior of immiscible blends of poly(2,6-dimethyl-l,4-phenylene ether) and poly (styrene-co-acrylonitrile). Polym Eng Sci 48 2111-2125... 

The rheology of polymer blends is discussed in Chapter 7. Here only an outline will be given. Since the flow of blends is complex, it is useful to refer to simpler system, e.g., for miscible blends to solutions or a mixture of polymer fractions for immiscible blends to suspensions or emulsions. 

Elias, L., Fenouillot, R, Majeste, J. C., and Cassagnau, P. 2007. Morphology and rheology of immiscible polymer blends filled with silica nanoparticles. Polymer 48 6029-6040. 

As another approach to predict the rheological behavior of immiscible blends, Almusallam et al. (2003) and Zkiek et al. (2004) constructed hybrid models based... 

Bar sky and Robbins performed NEMD simulations of the interfacial structiue and rheology of binary blends of symmetric polymers which were made immiscible to various degrees by adjusting the cross-interaction parameters. A liquid film was sheared by sliding boundaries. They found that there was a difference in velocity of the two species at the interface, suggesting a partial slip boundary condition. They attributed this to a difference in the positions of the centres of mass of the species on opposite sides of the interface. The viscosity in the interfacial region was lower than the bulk viscosity. 

Blends are classified as either thermodynamically miscible or immiscible, with the latter dominating. However, imposition of a flow affects the thermodynamic equilibrium and it may enhance the miscibiUty of immiscible blends or vice-versa - there is an interrelation between rheology and thermodynamics. Similarly, flow affects the degree of deformation of the dispersed phase, thus in immiscible blends there are other interrelations between rheology and morphology, which affect the blend performance. To the complexity of polymer alloys and blends (PAB) behavior one must add the incorporation of soUds, either in the form of filler and nanofiller particles or by simple factofblendingtwocomponents with widely differenttransitiontemperatures. 

As a conclusion to the aforementioned observations, it can be asserted that the rheological features of complex partially miscible polymer blends are only partially elucidated in terms of their thermodynamics, based on the behavior of immiscible blends and if their phase state is well known. 

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