The non-Arrhenius-type fluids widely exist. The typical cases include the Vogel-
Fulcher-Tamman (VFT) type (Vogel 1921 ; Fulcher 1925 ; Tammann and Hesse 1926 ),
/expðTa
TTVÞ (6.10)
whereTaandTvare the activation temperature and the Vogel temperature, respec-
tively. Often, the temperature dependence of the viscosity can be expressed
according to the mode-coupling theory (MCT) (Go ̈tze 2009 ),
/ðTTcÞg (6.11)wheregis a constant, as illustrated in Fig.6.7.
Angell et al.proposed a demarcation of fluid characteristics between the strong
liquid and the fragile liquid (Angell et al. 1985 ; Angell 1985 ). Glass-formers that
display properties as illustrated by Curve 1 in Fig.6.7are often regarded asthe
strong liquids, which exhibitb~ 1.0. For example, silicone oxide (SiO 2 ) and
germanic oxide (GeO 2 ) are typical strong liquids that have a strong covalently
bonded network structure and often exhibit Debye-like relaxation. In contrast,
glass-formers that display properties as illustrated by Curve 2 are often calledthe
fragile liquids, which exhibitb¼0.3 ~ 0.5. A typical example of those including
o-terphenyl contains a weak-interaction (van der Waals force) network structure.
Polymer fluids lie between these two extremes, and behave slightly more like the
fragile liquids. Often, the ratioTv/Tgprovides a rough estimation on the fragility
of the given liquid. More straightforward, the fragility parameter characterizes
Fig. 6.7 Illustration of the Arrhenius type (curve 1 ), Type A and the non-Arrhenius type (curve 2 ,
including VFT and MCT types) for the change of viscosity with temperature. In a general
experience, especially for small molecules, glass transition occurs when the viscosity reaches as
high as 10^13 Pa·s
6.2 Relaxation of Polymer Deformation 99