Chemistry Reference
In-Depth Information
Figure 11.14.
Arrhenius representation of characteristic relaxation times (
mol
) for amorphous
sucrose-water samples, as derived from various techniques: * and
~
,
relaxation in DMTA (99
and 93% sucrose);
, complex viscosity (80% sucrose);
&
, viscosity (65% sucrose); + and x,
relaxation in DS (99% sucrose).
All the
relaxation and viscosity data could be fitted to the WLF expression with the coefficients
C
g1
¼
-19.8 and C
g2
¼
51.6 K (i.e. the fragility did not vary significantly with water content). The
continuous lines correspond to WLF with these coefficients (but with the different T
g
varying
with water content) (Champion et al., 1997b). The activation energy for the
relaxation near T
g
was
375 kJ/mol and
60 kJ/mol for the
relaxation (Champion et al., 2003).
200-400 kJ/mol near T
g
(Figure 11.14). This strong influence of temperature
on viscosity is due to the fact that molecules no longer move individually, as
they do above T
m
, but in a coordinated manner, e.g. due to physical entangle-
ments, which are not able to relax during experiments with too short a
timescale. Above T
g
, the variation of viscosity is satisfactorily described by
the so-called Vogel, Tamman and Fulcher expression (VTF)
B
T
T
0
Z
T
¼
Z
0
exp
(18)
or by the Williams, Landel and Ferry expression (WLF; Williams et al., 1955):
log
Z
T
Z
T
g
¼
C
1g
ð
T
T
g
Þ
C
2g
þ
T
T
g
(19)
