Polymer, thermorheological simplicity

Generally, the rheology of polymer melts depends strongly on the temperature at which the measurement is carried out. It is well known that for thermorheological simplicity, isotherms of storage modulus (G (co)), loss modulus (G"(complex viscosity (r (co)) can be superimposed by horizontal shifts along the frequency axis ... 

For low molecular weight fractions, the variation in the values of the compliance function increases as either the chain length or the temperature increases. The changes observed in the compliance with temperature for very low molecular weight fractions are illustrated in Figure 8.17 (16). This lack of thermorheological simplicity was also observed for other amorphous polymers, specifically poly(ethyl methacrylate) (21), poly( -butyl methacrylate) (22), poly( -hexyl methacrylate) (23), and low molecular weight poly(methylphenyl siloxane) (24). 

Breakdown of Thermorheological Simplicity of Low Molecular Weight Polymer... 

The most common means to extend the frequency scale is to invoke time-temperature superpositioning (Ferry, 1980). If all motions of a polymer contributing to a particular viscoelastic response are affected the same by temperature, then changes in temperature only alter the overall time scale such a material is thermorheologically simple. Thermorheological simplicity means conformance to the time-temperature superposition principle, whereby lower and higher strain rate data can be obtained from measurements at higher and lower temperatures, respectively. 

Viscoelastic functions depend on both temperature and time. For many polymers, the logarithmic plot of a viscoelastic function at the temperature T may be obtained from that at the temperature Tq by shifting the curve along the logarithmic time axis by the amount of log (T)- This procedure is called time-temperature superposition. The ability to superpose viscoelastic data is known as thermorheological simplicity. Thermorheological simplicity demands that all the molecular mechanisms involved in the relaxation process have the same temperature dependencies. 

The WLF equation was developed empirically to describe the change in viscoelastic properties of polymers above the glass transition.Starting from the principle of thermorheological simplicity, Le, that the spectrum of relaxation (or retardation times) changes with temperature by a simple shift along the time axis, it was found that the shift factor for the viscosity could be written as ... 

Another example of the thermorheological complexity is found for multicomponent polymer systems. If the motion of different component chains contributes to the viscoelastic moduli of the system, the thermorheological complexity prevails even for the case that respective components exhibit the simplicity but have different shift factors. In more general cases, each component exhibits the complexity, thereby providing the systems with very strong complexity. This strong complexity of multicomponent systems (miscible blends) is explained in Section 3.5.2.S. 

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