Polymer Physics

permanent. However, both the generation and the recovery of deformation need
certain time periods to reach their stationary states. The mobility of polymers
determines the lengths of these periods.
If a small deformationDx 0 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 asthe
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 timet, as given by

Dx¼Dx 0 expð

t

t

Þ (6.7)

Here,tisthe 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

Dx¼Dx 0 expð

t

t

Þb (6.8)

wherebis the stretching exponent. For relaxation processes of polymer materials
near glass transition temperatures, we normally haveb0.5.
Besides the relaxation time, the steady-state shear viscosityis 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 asthe Arrhenius type(Arrhenius 1889 ),

/expð

DE

kT

Þ (6.9)

whereDEis the activation energy of relaxation.

Fig. 6.6 Illustration of the
exponential decay of
deformationDxwith timet

98 6 Polymer Deformation