Time-temperature superposition block copolymers

Time-temperature superposition in materials with multiple transitions can be studied advantageously in block copolymers. Although exceptions have been noted (25), random copolymerization of monomers... 

Since the relaxation mechanisms characteristic of the constituent blocks will be associated with separate distributions of relaxation times, the simple time-temperature (or frequency-temperature) superposition applicable to most amorphous homopolymers and random copolymers cannot apply to block copolymers, even if each block separately shows thermorheologically simple behavior. Block copolymers, in contrast to the polymethacrylates studied by Ferry and co-workers, are not singlephase systems. They form, however, felicitous models for studying materials with multiple transitions because their molecular architecture can be shaped with considerable freedom. We report here on a study of time—temperature superposition in a commercially available triblock copolymer rubber determined in tensile relaxation and creep. 

In an earlier section, we have shown that the viscoelastic behavior of homogeneous block copolymers can be treated by the modified Rouse-Bueche-Zimm model. In addition, the Time-Temperature Superposition Principle has also been found to be valid for these systems. However, if the block copolymer shows microphase separation, these conclusions no longer apply. The basic tenet of the Time-Temperature Superposition Principle is valid only if all of the relaxation mechanisms are affected by temperature in the same manner. Materials obeying this Principle are said to be thermorheologically simple. In other words, relaxation times at one temperature are related to the corresponding relaxation times at a reference temperature by a constant ratio (the shift factor). For... 

Because this observation was obtained independently from three structurally different types of micelles, it was concluded that the broad relaxation is an inherent property of block copolymer micelles. Consistent with these findings is the almost linear dependence of R t) on a log-time scale of PS-PEP micelles in squalane presented by Choi et al. [63]. They used TR-SANS to study two pairs of PS-PEP micelles, d-PS-h-PEP-l/h-PS-h-PEP-1 and d-PS-h-PEP-2/h-PS-h-PEP-2 with different PS degrees of polymerization pair 1, Aps 255 and pair 2, Aps 412. Each specimen was measured at three different temperatures. Individual master curves for R(f) were obtained by time-temperature superposition principles. A comparison of R f) of the two PS-PEP samples was done at a reference temperature of 125°C and... 

Elastic (G ] and loss (G") moduli and their ratio (G"/G = tan delta) versus frequency at 25°C for a styrenic block copolymer-based adhesive. Constructed via time-temperature superposition... 

Tan delta vs. temperature at lOx frequency intervals from 0.1 rad/s(B)to 100 rad/s (A) via time-temperature superposition for a general purpose tape adhesive based on styrenic block copolymers... 

The time-temperature superposition principle has been applied to the loss and storage moduli. For the homogeneous blend (one phase at temperature equal to 115 C), the superposition method works very well. Typical low frequency behaviours of G and G are shown by the lines in Figure 10. For temperatures close to (125, 135 and 140 C), a shoulder develops in the low frequency region for the storage modulus and becomes more important as the temperature is closer to T. This behaviour is similar to that observed by Bates et al. [19] for block copolymers near in the homogeneous region (disordered zone). In fact, these temperatures are well below as determined... 

A summary of Macosko s results is given in Table 11, adapted from Reference 213, while Figure 18, also taken from Reference 213, shows the adiabatic temperature rise data for the block copolymer formation and the excellent agreement with Malkin s model. The additional temperature rise at longer times is due to polymer crystallization, underlining that the two phenomena, polymerization and crystallization, can be kept well separated by choosing proper experimental setup, thus, avoiding any superposition effect. 

---