Polymer coils, dimensions

In 1955, major questions concerning the flow laws for polymer q tems still remained unanswered, however. Conclusive evidence that a is unity for short chains at constant f was lacking. The importance of polymer coil dimensions in addition to (or instead o chain length per se in the dependence of rj on molecular parameters was unknown. Similarly, the relation of Zg for different pol5miers to characteristic molecular dimensions was unknown. The usefulness of the WLF relation over a wide temperature range and the universality of the parameters in the WLF relation for a wide variety of materials 220) had not been demonstrated. 

Excluded volume effects (2) in polymers are defined as those effects which come about through the steric interaction of monomer units which are remotely positioned along the chain contour. Each Individual interaction has only a small effect, but, because there can be many such interactions in a long polymer, excluded volume effects become very large. One consequence of excluded volume is to expand the polymer coil dimensions over that predicted from simple random walk models. The "unperturbed values of the... 

Fig. 5.5 Temperature dependence on polymer coil dimensions for major VI improver chemistries (a) PMA, (b) OCP and (c) HSD [50]...

The smooth change in the polymer coil dimension passing through the 6-temperature is exemplified by the data of Pritchard and Caroline (1981) shown in Fig. 6.4. Here the hydrodynamic expansion factor is plotted as a fimction of the temperature. Contrary to the predictions of the blob theory, da /dr is clearly non-zero at the 0i -temperature, irrespective of the molecular weight. Its positive value is consonant with the predictions of the cluster series... 

Determination of the Polymer Coil Dimensions from the Intrinsic Viscosity... 

Nevertheless, even the critical concentration obtained from absolute polymer coil dimensions, is only a relative value since the radii measured with scattering experiments are not equal to the hydrodynamic radii of the same polymer coils in solution. A detailed discussion on how to calculate a hydrodynamic radius is given in The critical concentration of a real coil in Chap. 8. 

The assumption in Determination of the polymer coil dimensions from the intrinsic viscosity in Chap. 7 that the polymer coils in solution behave like hard spheres with a constant density inside the coil and a fixed boundary to the solvent is only a simple approximation. In reality, a polymer chain shows a dynamic behavior with fast and statistically changing conformations. 

Figure 6 The effect of solvent quality on polymer coil dimensions. Figure The effect of electrolyte on the coil dimensions...

This is reasonable since the polymer coil dimension in a 0-solvent is significantly smaller than that in a good solvent. The value of < in dilute solution is higher in the 0-solvent than that in DCE, which also reflects a higher spatial segment density of the coil in a 0-... 

A theoretical model has been proposed to treat the concentration dependence of the flexible polymer coil dimension in semidilute solutions by a perfectly reflecting spherical wall around each segment of the coil, which influences the random walk conformation. In a 0-solution the intersegmental interaction is expressed by a potential... 

The radius of the spherical reflecting wall around each segment of the coil in solution should be connected to the concentration of the solution. At least it is reasonable to assume a relation c in the semidilute region. The function ft2e(c)/h as a function is shown in Fig. 7, which should simulate the concentration dependence of the flexible polymer coil dimension in a 0-solution. It is interesting to note that the normalized coil dimension, A20(c)/h o decreases with increasing concentration to a minimum value of 0.69 at = 1 and then it will increase with further increase in concentration in a concentrated solution. The function h Q c)/ o given by (Eq. 4) approaches unity when t 0, i.e., c - < , in accord with the experimental fact that in an amorphous solid film the coil dimension is the same as that in a dilute 0-solution. 

The light-scattering data of Nose and Chu on a PS sample of = 190kD in trans-decal in at 20.0 C) seem to fit fairly well to the curve of Fig. 7, if one fits the first data point (c = 0.21 g/dl) to the theoretical curve at = 0.91 to fix the concentration scale of the figure. However, another publication in literature, using a mixture of randomly substituted p-iodostyrene and a PS sample of M = 110 kD in trans-decalin at T9 = 21.2 C, showed by SAXS that the polymer coil dimension remained constant independent of concentration up to a volume fraction of 0.4 within the experimental error of 5%. More experimental studies are certainly needed before a reliable conclusion could be drawn, especially when results obtained by independent methods are avail-... 

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