Theories for the x Parameter

There have been recent efforts to predict, or at least rationalize, the x parameters of these and other polyolefin-polyolefin blends. Bates et al. (1992) and Fredrickson et al. (1994) suggest that the x parameter is correlated to a difference in statistical segment length of the polymer molecules, on a volume-normalized basis. The volume normalization is required because the definition of the statistical segment length depends on how the monomer unit 

Graessley et al, (1994,1995) have proposed an alternative scheme that correlates the x values for polyolefin blends with differences in inferred values of the solubility parameters of the pure components [see Eq. (2-31)]. For the series of polyolefins they studied, values of for the pure components can be assigned in such a way that the x parameters of the mixtures computed from Eq. (2-31) are in reasonable qualitative agreement with measured values. Direct estimates of the (5 s can be obtained from the following formula derived from the van der Waals cohesive energy density (Hildebrand and Scott 1950 Krishnamoorti et al. 1996)  

In addition to these irregularities, Winey et al. (1996) have found that in random and alternating copolymers of styrene and methyl methacrylate, the sequence distribution of monomers along the backbone of the polymer strongly affects its miscibility with polystyrene and polymethylmethacrylate homopolymers, even when the overall ratio of styrene/methyl methacrylate in the copolymer chain is held constant. A strictly alternating sequence of monomers in the copolymer was found to be more miscible with the ho-miopolymers than is a copolymer with a random sequence distribution. These results 

In multiphase complex fluids, it is useful to account for van der Waals forces on a continuum, rather than a molecular, basis. Consider, for example, two spherical particles of material A, each of radius a, approaching each other in a medium of substance B. Let r be the distance separating the centers of the spheres and let D = r —2a he the gap between them. Defining a = Dfla, the van der Waals potential of interaction is found to be (Goodwin et al. 1986) 

For parallel, flat surfaces separated by a distance D, the potential per unit area is 

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