Monomeric friction coefficient transition zone

The most striking feature which varies among polymers is therefore the position of the transition zone on the time or frequency scale, when different systems are examined either all at the same temperature or at suitable corresponding temperatures. This comparison will first be undertaken, both in terms of directly measured quantities and in terms of the monomeric friction coefficient fo whose magnitude sets the time scale according to theory. Subsequently, detailed differences in the shapes of all the spectra will be scrutinized. 

The values for the methacrylate series show the effect of side chain length already observed. The other polymers do not fit irtto any comparative series. They show that a low Tg is generally associated with a high frequency for the transition zone, but this is not the only controlling parameter as evidenced by a comparison of polyisobutylene and unvulcanized Hevea rubber at 298°K. Although Tg is nearly the same for these two, the transition lies at higher frequencies by nearly three logarithmic decades in the rubber. Such differences will be discussed in more detail in terms of the monomeric friction coefficient in Section B below. 

If is chosen as a corresponding temperature at which different polymers are to be compared, the calculation of fo involves reduction of the time scale by extrapolation, since experimental measurements in the transition zone cannot easily be made at Tg directly. In most cases the extrapolation can be made by the WLF equation and the coefficients of Table 11-11. The results are included in Table 12-111, and show that even when compared each at its own Tg polymers can still have different monomeric friction coefficients. In particular, Cog decreases with increasing side chain length in the polymethacrylate series, although it appears to be approaching a limiting value. (Recent work casts doubt on some of the Tg values used in this Table, especially for poly(methyl acrylate) and poly(methyl methacrylate), and the values for Co at Tg will require future revision. 

Comparison of Monomeric Friction Coefficients from Relaxation Spectrum in Transition Zone and from Viscosity at Low Molecular... 

From the low-frequency region of the transition zone where the corresponding relaxation spectrum has a slope of — on the logarithmic scales, as in Fig. 12-4, the monomeric friction coefficient fb can be calculated by equation 1 of Chapter 12. If the cross-linking process is not accompanied by side reactions which significantly alter the chemical nature of the polymer, the effects on fo and the position... 

As an example of assignments of mechanisms for a specific polymer, the temperature-frequency loci shown in Fig. 15-11 for polystyrene have been attributed to the following motions " a, segmental motions of the main chain governed by the monomeric friction coefficient (i.e., the transition zone of viscoelastic behavior) j(3, local mode torsional oscillations of the main chain y, rotation of the phenyl group around the bond joining it to the main chain 5 (observed in dielectric measurements only, and nearly absent in isotactic polymer), relaxations of resultant... 

With increasing proportion of diluent, the monomeric friction coefficient fo is normally diminished, as evidenced by displacement of logarithmic plots of viscoelastic functions in the transition zone to higher frequencies or shorter times with relatively little change in shape. Examples are shown in Fig. 17-2 for the relaxation spectrum of poly( -bulyl methacrylate), and in Fig. 17-3 for the creep compliance of poly(vinyl acetate), both diluted to varying extents with diethyl phthalate. (In the latter figure, we focus attention now on the transition zone, where log J t) < -6.5 the other zones will be discussed later.) Introduction of diluent displaces the time scale by many orders of magnitude. Similar results were obtained in an ex-... 

In the range of time or frequency where the mecheinical response of an amorphous polymer varies from that of a soft rubber to that of a hard glass, the relaxation spectrum (which determines time or frequency dependence) has been obtained experimentally for about two dozen polymers Its form depends somewhat on chemical structure, but these relations are still not well understood. At the low frequency or long time end, it can be approximated by the Rouse spectrum and a match here can furnish values of the monomeric friction coefficient, a measure of the location of the transition zone on the time or frequency scale. 

---