Behavior in the Terminal Zone

In the terminal zone where G and G are proportional to co and co respectively, the viscoelastic properties are dominated by the longest relaxation times and these are determined by long-range motions in which a molecule of high molecular weight 

Since for M Me, Vo is observed experimentally to be proportional to M, - this behavior can be reproduced by setting 

The calculation of 7° is unaltered by the introduction of Qe, which cancels out in equation 11, so 

Logarithmic plot of J° against molecular weight for polystyrenes of narrow molecular weight distribution. (Plazek and O Rourke. ) 

It may be concluded that when entanglements are present the molecular motions do not correspond to the normal modes of the Rouse theory. Indeed, the topological restraints must necessitate very different motions to achieve configurational rearrangements, and other models have been proposed to describe them. 

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Other features of the viscoelastic behavior in the terminal zone are represented by the constants rjo and Rearrangement of equations 7 and 9, together in the equation 51 of Chapter 9 with omission of r)s as appropriate for undiluted polymer, gives for these quantities... 

The dependence of the non-Newtonian viscosity jj on shear rate at relatively low shear rates is a property which can be classed with viscoelastic behavior in the terminal zone, since it reflects long-range conHgurational motions which are influenced by entanglements to the maximum degree. As pointed out in Chapter 10, the characteristic time r, which specifies the onset of non-Newtonian, behavior with increasing shear rate is closely related to the terminal viscoelastic relaxation time. (In this discussion of shear viscosity, the subscript 21 will be omitted from stress [Pg.380]

The different aspects of behavior in the terminal zone will be reviewed in the same order as the preceding sections ijo, J , t, and... 

Isothermal measurements of the dynamic mechanical behavior as a function of frequency were carried out on the five materials listed in Table I. Numerous isotherms were obtained in order to describe the behavior in the rubbery plateau and in the terminal zone of the viscoelastic response curves. An example of such data is shown in Figure 6 where the storage shear modulus for copolymer 2148 (1/2) is plotted against frequency at 10 different temperatures. 

The question as to whether the same ot reduction factors can be applicable in both the transition and terminal zones depends on whether parameters such as Qe or Me vary with temperature. On the basis of the entanglement concept or the tube model, such temperature dependence would be expected to be very slight. In a number of cases, the same reduction factors have been found to be applicable in both zones to a close approximation. However, in polyisobutylene anc especially in very precise investigations of polystyrene >2 and poly(vinyl acetate) the absolute values of log aj in the transition zone were found to be somewhat greater than those calculated from equation 13. On the other hand, for certain methacrylate polymers and their concentrated solutions, the absolute values of log ar are found to be smaller in the transition zone than in the terminal zone. This behavior, formally attributable to a temperature-dependent Qe or Me, does not prevent successful use of the method of reduced variables within a single zone of the time scale, but in the plateau zone a complicated transition takes place (Section F below). 

Some practical aspects of viscoelastic behavior in dilute solutions (Chapter 9, Section G) and in the terminal zone (Chapter 10, Section C5) have already been mentioned others are inherent in Chapters 16 and 17. We now call attention to some additional applications. 

An interesting special case is a= 0, which is equivalent to the behavior of a single Maxwell element for which the Cole-Cole plot is a perfect semi-circle. It is important to note that except in this special case, Eqs. 5.67 do not give a correct fit to data in the terminal zone, where r should be proportional to the frequency, and vf should approach a constant and thus become independent of frequency and of r[. And in the high frequency Hmit, both components approach zero. 

Garcia-Franco and Mead [142] proposed the use of the parameters of Eq. 5.65 to describe the behavior of polyethylenes prepared by means of anionic polymerization, gas-phase metallocene catalysis, and Ziegler-Natta catalysis. They reported that Eqs. 5.67 gave a good fit of their data and suggested that it is valid for all linear, flexible polymers with monomodal molecular weight distributions except in the terminal zone. They found that except in the terminal zone it provides a representation of the data that is similar to that given by the double-reptation model. They... 

In close analogy to the PCL based nanocomposites, the terminal zone dependence of G and G" for the 2 and 5 weight % samples, show non-terminal behavior with power-law dependencies for G and G" much smaller than the expected 2 and 1 respectively. Furthermore, like the PCL based nanocomposites, there also appears to be a gradual decrease in the power-law dependence of G and G" with increasing silicate loading. 

In a typical test the wire mesh basket is initially in an upper, cooled portion of the reactor in which a downward, inert gas flow is maintained. During this time the desired temperature and pressure conditions are established in a lower, heated portion of the reactor in the presence of a flowing gas. A test is initiated by lowering the basket into the heated reaction zone, a procedure which takes 5-6 sec. Theoretical computation shows that about 2 min are needed for the sample to achieve reactor temperature as measured by several thermocouples surrounding the basket in the reaction zone. This computation is reasonably corroborated by various kinetic indications and by the behavior of the thermocouples in re-attaining their preset temperatures. The sample is kept in the heated portion of the reactor for the specified time while its weight is continuously recorded. The test is terminated by raising the basket back to the upper, cooled portion of the reactor. 

It was observed that the addition of crosslinker (2-4% DVB) to styrene considerably affected the homogeneity profile behavior [116]. The distribution became practically homogenous across the whole width of the film and the homogeneity increased at 4% DVB [116,139]. That behavior was attributed to the decreased rate of diffusion in the grafted zone near the surface, an increase in the rate of termination of growing chains, and a decrease in the concentration of styrene in surface layers [116]. The observations for the TFS-... 

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