Thermorheological complexity

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. 

Calculation of Master Curves from Mechanical Models. The only way to obtain valid master curves for the thermorheologically complex systems (75/25 and 50/50 blends) is to calculate the moduli of the blends as a function of time, using an appropriate mechanical model. This method requires knowledge of the time and temperature dependence of the mechanical properties of the constituent phases. 

Scalco, Huseby, and Blyler (8), Zosel (9), and Bergen and Morris (10). Prest and Porter (23) applied the same principle to homopolymer blends [poly (2,6-dimethylphenylene oxide)-polystyrene]. Recently some papers were published on triblock copolymers of styrene-butadiene-styrene and on their blends with polybutadiene (24, 25). Triblock copolymers can be considered heterophase material as the different constituent blocks are thermodynamically incompatible with each other, and, consequently, polystyrene domains are enclosed in polybutadiene (continuous matrix). The findings indicate that these systems are in general thermorheologically complex, so that the shift factor ar depends not only on temperature but also on time. These conclusions have been extrapolated to other two-phase systems. 

In the first experiments over an extended frequency range, the biaxial viscoelastic as well as uniaxial viscoelastic properties of wet cortical human and bovine femoral bone were measured using both dynamic and stress relaxation techniques over eight decades of frequency (time) [Lakes et al, 1979]. The results of these experiments showed that bone was both nonlinear and thermorheologically complex, that is, time-temperature superposition could not be used to extend the range of viscoelastic measurements. A nonlinear constitutive equation was developed based on these measurements [Lakes and Katz, 1979a]. 

Glass Transition-Related Thermorheological Complexity in Polystyrene Melts... 

Thus, s values at different temperatures can be uniquely obtained by fitting the calculated Jp t) curves closely to the measured ones as shown in Figs. 14.1 and 14.2 with Aq and (3 well determined by the small-compliance region. In other words, the whole thermorheological complexity in Jp t) of the polystyrene samples is reduced to the simple temperatme dependence of the obtained s values as shown in Fig. 14.4. This reduction is of particular... 

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