Thermorheological simple systems

A fundamental characteristic of the so-called thermorheologically simple systems is that consecutive isotherms have similar habits, so they overlie each other when they are shifted horizontally along the log t axis. In other words, the time-temperature correspondence principle holds. This property in creep experiments can be expressed by the relation (2,3)... 

In thermorheological simple systems, the time-temperature correspondence principle holds. Chapter 8 gives examples of isotherms for compliance functions and relaxation moduli. The shift factors are expressed in terms of terminal viscoelastic parameters, and the temperature dependence of the shift factors is interpreted in terms of the free volume and the WLF equation. The chapter outlines methods for determining the molecular weight between entanglements, and analyzes the influence of diluents and plasticizers on the viscoelastic functions. 

The Eqs. (2.1a) and (2.1b) apply thus actually to a rate scale and, in the frequait case of cyclic exposure, to a frequency scale co. If a thermorheologically simple system is considei ed the fr juency scale can be replaced by a temperature sale 1/T. Steps A that satisfy Eqs. (2.1a) and (2.1b) appear then in the response-functions for systmis of this nature that are measured as a function of temperatiue at pven, fixed paturbation rate. The temperature at whidi the steps occur depends, however, on the rate of external i rturbution. The temperature-dependent thawing of conformational isomers in thermorheologically complicated systems can be similariy observed in the response-functions, but the steps no longer satisfy Eqs. (2.1 a) and (2.1 b). These two equations lose, in addition, their validity with rrapect to the rate scale if, as is the case of polymers, several mutually independent, internal variables are required in order to uniquely define the conformational isomerism. In this case. Eqs. (2.1a) and (2.1b) become inequalities... 

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... 

In addition, the partially miscible polymer blends are thermorheologically simple, so that all considerations available for homogeneous systems can be applied in their case as well (Utracki 1990). The composition of the two phases from the vicinity of phase separation is not the same as in the case of immiscible mixtures where it is supposed that, if droplets are present in their corresponding morphology, they are composed from one of the mixture components and that their total volume is equal to that of the blend composition. This theory is not applicable to partially... 

Thus, the shifting of the data demonstrated in Fig. 7.3 should be represented by Eq. 7.4. The term thermorheologically simple refers to the key caveat that all relaxation times of the polymer must be affected by temperature in the same way. This assumption has been found to hold for a vast array of homogeneous polymer systems. Typically shift factors are found experimentally or by the WLF equation discussed in the next section. 

Few examples of the homogeneous diblock-incompatible homo-polymer behavior have been reported. One that has received considerable attention is the system polystyrene-poly-a-methylstyrene (2). Block copolymers of styrene and a-methylstyrene exhibit a single loss peak in dynamic experiments (2,3) and have been shown to be thermorheologi-cally simple (4) hence they are considered to be homogeneous. Mechanical properties data on these copolymers also has been used to validate interesting extensions of the molecular theories of polymer viscoelasticity (2,3,4). 

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