Relaxation Via Molecular Motions

Large-scale deformation of polymers is realized by the integration of monomer motions that is driven by the external forces. After the external force has been removed, part of the deformation recovers quickly, while the rest may remain 

If a small deformation Axo is generated on a piece of polymer materials by employing a small external force for a time period, after the force has been removed, a spontaneous recovery process of deformation can be regarded as the relaxation process. The most common style of such a relaxation process is the Debye relaxation process (Debye 1913), as demonstrated in Fig. 6.6, which exhibits an exponential decay of deformation with time t, as given by 

x is the relaxation time, which reflects the mobility of polymers, like in the previous chapter. 

In practice, there exist many non-Debye relaxation processes, which can be described by a stretched exponential function, namely the Kohlrausch-Williams-Watts (KWW) equation (Kohlrausch 1854 Williams and Watts 1970), as given by 

Besides the relaxation time, the steady-state shear viscosity p is often used to characterize the mobility of polymers in the fluid phase as well. The change of shear viscosity with temperature reflects the viscous feature of the fluid. The most common fluids appear as the Arrhenius type (Arrhenius 1889), 

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