Steady state compliance experimental results

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. 

The introductory considerations of the previous section were induced by interesting experimental results obtained by Daum (32), who investigated the best way of extrapolating results to zero concentration. From this work and some recent results of Wales (59) on polymer melts, Fig. 4.4 is constructed. This figure shows the concentration dependence of reduced steady-state compliance JeR for a series of anionic polystyrenes. The molecular weights of these polymers are given in Table 4.1. For a specification of the solutions see the caption to Fig. 4.4. 

Many amorphous homopolymers and random copolymers show thermorheologically simple behavior within the usual experimental accuracy. Plazek (23,24), however, found that the steady-state viscosity and steady-state compliance of polystyrene cannot be described by the same WLF equation. The effect of temperature on entanglement couplings can also result in thermorheologically complex behavior. This has been shown on certain polymethacrylate polymers and their solutions (22, 23, 26, 31). The time-temperature superposition of thermorheologically simple materials is clearly not applicable to polymers with multiple transitions. The classical study in this area is that by Ferry and co-workers (5, 8) on polymethacrylates with relatively long side chains. In these the complex compliance is the sum of two contributions with different sets of relaxation mechanisms the compliance of the chain backbone and that of the side chains, respectively. 

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... 

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.

That the steady-state compliance is independent of the molecular weight is in agreement with experimental results (Fig. 7.S). On the other hand, the experimental exponent in the molecular weight dependence of Tmax and Vo is slightly larger than 3, ranging from 3 to 3.7. An example of the viscosity in melts is ven in Fig. 7.6. The reason for die discrepancy will be disrassed later. 

The results of eqns (7.263) and (7.264) are in qualitative agreement with experimental results the viscosity increases steeply because of the exponential factor, and the steady state compliance is pri rtional to M. However, the quantitative agreement is not satisfactory. The observed viscosity is smaller than the calculated one, and the best fit with experiments is obtained only when the numerical coefficient in the exponential of eqn (7.263) is replaced by a smaller number (about 1/2) instead of lS/8. This suggests that relaxation mechanisms other than the contour length fluctuations are important for star polymers. Indeed it has been pointed out that in the case of star polymers the constraint release, and perhaps other tube reorganization processes, are as important as the contour length fluctuation. 

The steady-state compliance has a minimum at p = p f2 and then increases again by the pretransitional effect. This has indeed been observed by Berry and coworkers. On the other hand the viscosity is unaffected by the pretransitional effect. (This is a result of the cancellation of the effect on the relaxation time t and on the rigidity modulus Gg.) Experimental results on the viscodastidty of the isotropic solution have been reviewed by Baird. ... 

Fig. 23. Normalized reciprocal steady-state recoverable compliance Je,max/Je for three polymers, poly(dimethyl siloxane), PIB, and PS, versus the reduced temperature T/Tg Tg is the glass temperature and the normalized compliance

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