Copolymer time-temperature superposition

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. 

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... 

The maximum strain rate (e < Is1) for either extensional rheometer is often very slow compared with those of fabrication. Fortunately, time-temperature superposition approaches work well for SAN copolymers, and permit the elevation of the reduced strain rates kaj to those comparable to fabrication. Typical extensional rheology data for a SAN copolymer (h>an = 0.264, Mw = 7 kg/mol,Mw/Mn = 2.8) are illustrated in Figure 13.5 after time-temperature superposition to a reference temperature of 170°C [63]. The tensile stress growth coefficient rj (k, t) was measured at discrete times t during the startup of uniaxial extensional flow. Data points are marked with individual symbols (o) and terminate at the tensile break point at longest time t. Isothermal data points are connected by solid curves. Data were collected at selected k between 0.0167 and 0.0840 s-1 and at temperatures between 130 and 180 °C. Also illustrated in Figure 13.5 (dashed line) is a shear flow curve from a dynamic experiment displayed in a special format (3 versus or1) as suggested by Trouton [64]. The superposition of the low-strain rate data from two types (shear and extensional flow) of rheometers is an important validation of the reliability of both data sets. 

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... 

Fig. 2. Dependence of peel strength on rate of separation at 20°C for various copolymers (in Table 1). Sample were aged at 60°C-0.2kg/cm before peeling. Some of data for the curves are from time-temperature superposition.

SAN copolymers at the azeotropic polymerization ratio of 76/24 (by wt) are miscible with a-methyl styrene-AN copolymer at it s azeotropic ratio (69/31 (by wt) [747].aMS-AN (32 wt% AN) was shown to be miscible with SAN copolymers with AN contents of 28 to 40 wt% AN, with lest behavior observed [748]. As the a-methyl styrene-AN copolymer has a Tg 25 °C higher than SAN, it is commercially employed in blends with ABS to boost the heat distortion temperature up to 100 °C, required for some appliance applications. SAN copolymers are also miscible with styrene-maleic anyhdride (SMA) co- and terpolymers (e.g., with MMA), and the SMA co-and terpolymers with TgS in the range of 140 °C can also be employed to enhance the heat distortion temperature of ABS [749, 750]. SAN (styrene content = 75wt%) blends with styrene-N-phenyl maleimide copolymers (styrene content = 58 wt%) were found to be miscible and followed time-temperature superposition over the entire composition range [751 ]. N-phenyl maleimide groups can be prepared by reaction of aniline with maleic anhy-... 

Differential scanning calorimetry (DSC), DMA and TG were used by Tabaddor and co-workersl l to investigate the cure kinetics and the development of mechanical properties of a commercial thermoplastic/ thermoset adhesive, which is part of a reinforced tape system for industrial applications. From the results, the authors concluded that thermal studies indicate that the adhesive was composed of a thermoplastic elastomeric copolymer of acrylonitrile and butadiene phase and a phenolic thermosetting resin phase. From the DSC phase transition studies, they were able to determine the composition of the blend. The kinetics of conversion of the thermosetting can be monitored by TG. Dynamic mechanical analysis measurements and time-temperature superposition can be utilized to... 

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... 

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