Theoretical Treatment of Polymer Blends

The theoretical treatment of two-phase flow has been reviewed by several authors [168-170]. As indicated before, dispersions of one Newtonian liquid in another result in systems that are characterized by elasticity and relaxation times, for example, see Eq. (2.18). 

In 1990, Honerkamp and Weese published a seminal paper on the use of Tikhonov s regularization for the determination of material functions [171]. The developed method of data treatment was found to be particularly useful for computation of the relaxation and retardation spectra [172, 173]. It has also been used to compute the sphere-size distribution of the dispersed phase in binary blends [174], as well as the ratio of the dispersed drop diameter divided by the interfacial tension coefficient, d/t 12 [175]. Friedrich ctak [176] modified Eq. (2.23) to read  

For infinitely diluted viscoelastic emulsions the shear dependence of inherent 

Semi-concentrated emulsions were examined theoretically and experimentally only within the linear viscoelastic region [178-181]. Recognizing that the interphase has a final thickness (sometimes the total volume of interphase exceeds that of the dispersed phase) the authors postulated that it might have two interfacial coefficients, / and facing the two principal polymer domains. Next, two models of the interphase were evaluated (i) a two-dimensional viscoelastic film and (ii) the interphase of final thickness. Both led to at least two relaxation times [181]  

The dynamic test data in the kHz region of ionic emulsions could be described using either model. The emulsion elasticity originates in the interphase deformation. For non-ionic emulsions, only one relaxation time was observed. The data were interpreted in terms of the second Oldroyd model in which the interfacial tension is more important than the viscoelasticity of the interphase. The steady state viscosities of both ionic and non-ionic systems at the volume fraction 0.2 were found to follow Simha s equation (Eq. (2.8)). 

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Theoretical and thermodynamic approaches to describing the nature of polymer blends are generally based on the efforts of investigations many decades ago (Prigogine, Guggenheim, Hory, Huggins). Additional concepts are under current development initially applied to small molecule systems but extended to polymeric systems as well. More recent papers discussing newer theoretical treatments of polymer blends include Dudowicz et al. [1990] and Yethiraj and Sch-weizer [1992]. 

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