Hydrodynamic interaction parameter

The viscoelastic properties of solutions of linear and 4-armed star polybutadienes were studied by Osaki and co-workers (117), who compared the storage and loss shear moduli extrapolated to zero concentration with theoretical values. The results for the branched polymer could be accounted for well in terms of the Zimm and Kilb theory (34) a lower value of the hydrodynamic interaction parameter was indicated for the branched polymer than for the linear one, which may be associated with the higher density of polymer segments in the former. 

The non-dimensional hydrodynamic interaction parameter appears here... 

Fig. 2.5. Flory constant 0 from Zimm theory evaluated by various methods of calculation plotted against hydrodynamic interaction parameter h Circles from eigenvalues of difference equation (2.18) thin lines from Eq. (2.41) thick line result of Tschoegl from Eq. (2.20). Values of h are shown, and cross mark indicates N = 104 for a given value of h = hN 112 (72)...

Some Remarks on Theories. We have seen that several versions of the Zimm theory can be applied to the intrinsic complex modulus. Now we will examine the merits and defects of each version and speculate on the nature of the hydrodynamic interaction parameter. 

Tg transition at all composition, but the authors regard this as inconclusive with regard to miscibility due to the proximity of the Tg values of the pure constituents. From the results the authors conclude that the hydrodynamic interaction parameter a is a more sensitive indicator of miscibility than p or y, although in our view, such an interpretation would be more definitive if independent evidence of a miscibility gap had been presented. 

Raj et al. °" have compared the efficiency of microwave and e-beam irradiations to stabilize the interface of various partially miscible or nonmiscible blends polystyrene (PS)/polymethyl methacrylate (PMMA), polyvinyl chloride (PVC)/ethylene vinyl acetate (EVA), PP/acrylonitrile butadiene rubber (NBR), and polyvinyl chloride (PVC)/poly(styrene acrylonitrile) (SAN). For this purpose, they used positron annihilation lifetime measurements, and they considered particularly a hydrodynamic interaction parameter a. This... 

In Eq. (27.24), a is the hydrodynamic interaction parameter. The parameter m accounts for the effects of collective motion it increases the term (a + tti) in the square bracket (correction for nonideal intermolecular friction) in the limit of infinitely dilute solution (Q —> 0 nondraining coils). Substituting the above equations into Eq. (27.22) and simplification leads to ... 

The final expression employed for the determination of hydrodynamic interaction parameter a is... 

The hydrodynamic interaction parameter is then plotted as a function of composition, as shown in Figure 27.14 for these blends. It was very clear that, for the miscible blend SAN/PMMA, a was highest (—63.4) at 20% PMMA in the blend and about -12.4 at 50/50 cocontinuous phase. This inferred that an 80/20 composition would be optimal for the SAN/PMMA blend, producing the highest... 

Figure 27.14 Hydrodynamic interaction parameter (a) as a function of PMMA, PVC and PS contents in SAN/PMMA, PVC/PMMA and PS/PVC blends. Reproduced with permission from Ref [63].

Equation (57) shows the same degenerate form of relaxation times as Eq. (30). The characteristic relaxation times are derived from the exact Zimm-Kilb eigenvalues [11,81]. The matching of the experimental and theoretical dependence of the moduli on frequency has only one adjustable parameter, i.e., die hydrodynamic interaction parameter, h. The free-draining case was evaluated by Ham [79]. 

An example of the moduli-frequency dependence for the case of a nine-arm star polystyrene is shown in Figure 16. For comparison coXoj has been multiplied by Si to realize identical values of [G"]r for linear and star polymers at low frequency. It can be seen that star polymers have relatively higher values of [GHj and [G jj than linear polymers at high frequency. Also, the transition from low to high frequency occurs over a narrower frequency range. The low value of [G ] of the star at low frequency compared to the linear polymer is to be noted. Unfortunately, in order to fit the 0-temperature data an unrealistically high hydrodynamic interaction parameter h — 0.40 had to be used. This problem does not occur in good solvents. 

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