Viscoelastic frequency dependence above glass transition temperature

The curves showing the frequency dependence of loss functions [tan 5, G"(g)), or / (to)] permit the detection in the frequency domain, at temperatures just slightly above the glass transition temperature, of a prominent absorption or a process. The unavailability of experimental devices to measure mechanical viscoelastic functions at high frequencies impedes the detection of a fast process or P relaxation in the high frequency region. This latter process is usually detected in the glassy state at low frequencies. 

Spin-spin relaxation times (T2) in polymer systems range from about 10-5 s for the rigid lattice (glassy polymers) to a value greater than 10-3 s for the rubbery or viscoelastic state. In the temperature region below the glass transition, T2 is temperature independent and not sensitive to the motional processes, because of the static dipolar interactions. The temperature dependence of T2 above Tg and its sensitivity to low-frequency motions, which are strongly affected by the network formation, make spin-spin relaxation studies suitable for polymer network studies. 

Although the Cole-Cole plot was first introduced in the context of a dielectric relaxation spectrum, it helped discover that the molecular mechanism underlying both dielectric relaxation and stress relaxation are substantially identical (44). Figure 8.13 provides an illustration, with temperature instead of frequency. Specifically, the same molecular motions that generate a frequency dependence for the dielectric spectrum are also responsible for the relaxation of orientation in polymers above Tg. Subsequently the Cole-Cole type of plot has been applied to the linear viscoelastic mechanical properties of polymers, especially in the vicinity of the glass transition, including the dynamic compliance and dynamic viscosity functions. 

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