Steady-state compliance values

Fig. 15.1 Comparison of the s (AT)/sq values (with Sq = 1,500) of polystyrene samples A(o), B(0) and C(D obtained by analyzing the J(t) line shapes A by matching the calculated and experimental steady-state compliance values) with the diffusion enhancement factors /r(AT) of OTP ( isothermal desorption A NMR) as a function of AT = T — Tg. The solid line is calculated from the modified VTF equation (Elq. (14.13)) which best fits the s (AT)/sq results of the three polystyrene samples collectively. The dashed line represents the curve calculated from the modified VTF equation best fitting the fj, AT) data of OTP.

The greater melt viscosities observed for some branched polymers, as compared with linear ones of the same MW, are not accounted for by current theories, as indicated in Section 5. The greater values of the steady state compliance mentioned above is also unexpected theory (128) would suggest a difference in the opposite sense. 

Values of the Reduced Steady-State Compliance. Validity of... 

Once, viscosity or shear stress are determined, the remaining steady-state flow properties in shear are governed by the value of the reduced steady-state compliance JeR, as has been shown in the previous section. Carrying out the appropriate summations, as indicated by eq. (3.40) one obtains for the free-draining case ... 

It is observed that the reduced steady-state compliance is more sensitive to chain branching than the intrinsic viscosity. Whereas the intrinsic viscosity decreases with increasing degree of branching due to the fact that the values of the longest relaxation times are decreasing, the reduced steady-state compliance decreases as a consequence of the fact that the lines of the spectrum of relaxation times come closer together [cf. Ham]. 

From the results of Section 3.7 it becomes obvious that extremely sharp fractions are needed for a check of eqs. (3.41a) or (3.42). Only in this case a quantative agreement of the experimental values of the steady-state compliance JeR with the theoretical ones, as given by the eqs. (3.61), (3.62a) or (3.62b), can be expected. Otherwise, the polydisper-sity factor p will play a significant role. 

Possible other reasons for a too high value of the reduced steady-state compliance, when compared with the expected non-draining value, are given by the facts that bromo-benzene is a very good solvent and that even the anionic polystyrenes have no completely uniform molecular weight. The second point will be treated in Section 3.8.3. As to the first point, it can be shown by experiment that the excluded volume... 

The linear viscoelastic properties of all samples were characterized by dynamic shear measurements in the parallel-plate geometry. Experimental details have been previously published [9]. Using time-temperature equivalence, master curves for the storage and loss moduli were obtained. Fig. 1 shows the master curves at 140°C for the relaxation spectra and Table 3 gives the values of zero-shear viscosities, steady-state compliances and weight-average relaxation times at the same temperature. 

The steady-state compliance shows a strong dependence on the molecular heterodispersity. Thus the value of for a mixture of two fractions of the same polymer, one of low and the other of high molecular weight, may be up to 10 times as high as that of each component. This behavior can be explained by taking into account that 4 is the total recoverable deformation per unit of shear stress. The chains of high molecular weight have a very... 

The strong effect of molecular chains on the viscoelastic behavior of polymeric solutions, even in the most dilute ones, is shown in Figure 8.24 (37). Here the recoverable compliance of a very dilute solution of polystyrene of weight-average molecular weight 860,000 in tri-m-tolyl phosphate is compared with that of the solvent. It is noteworthy that the value of the steady-state compliance for the solvent is 10 cm /dyn while that of the very dilute solution (Wpoi = 0.001) is nearly 10 cm /dyn. In other words, a very small fraction of the molecular chains are responsible for the fact that the steady-state compliance of the solution is more than 10 times that of the solvent. 

Though theory predicts the molecular weight independence of Jg for M3 > Mg( 6Mg), the theoretical values of are somewhat lower than the experimental ones. It should be pointed out that a certain degree of poly-dispersity may enhance the experimental values of the steady-state compliance of even so-called monodisperse systems. Finally, the theoretical... 

Diluents and plasticizers in polymeric systems increase the steady-state compliance and decrease the zero shear rate viscosity. These two combined opposing effects give rise to a diminution in the value of Hence the critical value of the shear rate in dilute systems is shifted to higher values as the dilution increases (see Fig. 13.28). 

Fig. 4.11(b)) is produced, which is in general measured with respect to t = 0 as the reference time — i.e. A(0 ) = 0. After a sufficiently long time, the deformation of the fluid reaches a steady state namely, the deformation proceeds with a constant rate-of-strain, Ao . The strain value Aq, obtained by extrapolating the strain in the steady-state region to the time t = 0, is a viscoelastic quantity of special meaning. We define the steady-state compliance as the ratio of Aq to the apphed constant stress [Pg.66]

As the steady-state compliance J° is sensitive to the molecular-weight distribution, the experimental results of the nearly monodisperse samples are higher than the theoretical values for ideal monodispersity. Shown in Fig. 10.11 is the comparison of the experimental data of (the experimental results shown in Fig. 10.11 are consistent with those shown in Fig. 4.12) with four theoretical curves curve 1 is calculated from Eq. (9.25) curves 2 and 3 are numerically calculated from the substitution of Eq. (9.19) into... 

The value of the steady-state compliance due to the entanglement network depends on the polymer and the concentration. For bulk liqitid polymer, there exists a limiting molecular weight below which the liquid does not display a rubberlike compliance, M. The corresponding compliance for the solution can be expressed as ... 

Fig. 13. Steady state compliance oflinear and branched polyisoprenes in tetradecane (0.33 g/ml) at 25°. Symbols as in Fig. 8, Ref. Eteshed lines are values calculated from Rouseflam Theory...

Slant value ao analogous to in Fig. 1 -11, plus a viscous flow contribution (Tot/t]o- Here 7 is the steady-state compliance, a measure of the elastic deformation during steady flow. After a sufficiently long time (but before the stress is removed... 

Table 9-1 also includes values of the reduced intrinsic steady-state compliance, J%, which is defined as... 

The low-frequency limiting viscoelastic behavior is thus governed by the sums S1 and 82- Values of these, together with 1S2/5 and the first two relaxation time ratios, are given in Table 9-II for several choices of h and other parameters. The greatest differences are seen in the ratio 82/8 to which the steady-state compliance Je is proportional. The table also includes some data for branched polymers which will be discussed in Section 8. 

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