Polymer Physics

a deviation from the linear temperature dependence (Arrhenius type) of logarithmic
relaxation time (or viscosity) at the glass transition temperature, as

m

dlog 10 t

dðTg=TÞ

(^) T¼Tg (6.12)
The fragility parameter is normally large for liquids that exhibit the non-
Arrhenius-type temperature dependence of the relaxation time. One extreme exam-
ple is glycerin. Its fragility parameter is as high as 200 (Boehmer et al. 1993 ;
Richert and Angell 1998 ).

6.2.2 Boltzmann Superposition Principle

The experiment we introduced at the beginning of the previous subsection is also
called thecreepexperiment. A small stress ofs 0 is imposed on a solid sample for a
time period oft 0 at a constant temperature; after the stop of stress, the strain ofe
changing with the time period oftmonitors the relaxation curve. There are four
typical responses separately corresponding to viscous, elastic, anelastic and visco-
elastic responses, as illustrated in Fig. 6.8. The creep curve of polymer
viscoelasticity exhibits both instant and retarded elastic responses upon imposing
and removal of the stress, and eventually reaches the permanent deformation.
We define thecreep complianceas given by

JðtÞ

eðtÞ

s 0

(6.13)

Fig. 6.8 Illustration of four
typical strain responses upon
imposing the stress for a
time period of t 0. 1 The
viscous response, 2 the elastic
response, 3 the
anelastic response, 4 the
viscoelastic response

100 6 Polymer Deformation