Chemistry Reference
In-Depth Information
evolution, by which the material is approaching closer to the metastable
equilibrium, by reduction of the excess volume, enthalpy and entropy,
which had been ''frozen-in'' at the glass transition (Figure 11.8). Since the
timescale for equilibrium becomes very long as the storage temperature is
reduced, this evolution can be observed only in a narrow temperature interval
below T
g
(Hutchinson, 1995). In the field of material science, physical ageing
is well known for its technological significance, as it manifests itself as an
increase in rigidity and brittleness and a decrease in dimensions and perme-
ability. It is expected to be of importance for the stability of low-moisture
food and pharmaceutical products and is currently receiving a lot of atten-
tion. The extent of structure relaxation is generally characterized by the
amplitude of the enthalpy recovery (commonly denoted as ''relaxation
enthalpy'') as a function of storage time. To characterize the kinetics of
enthalpy relaxation, several models can be used, the most popular being the
Cowie-Ferguson semi-empirical model (Cameron et al., 2001), which is based
on the stretched exponential (KWW) expression:
ð
t
Þ¼
exp
½ð
t
=Þ
(22)
where is the property studied as a function of time (t), e.g. the proportion of
glass that has not yet relaxed at time t and that is calculated as (t)
¼
1-DH
t
/
DH
1
, DH
t
being the enthalpy recovery measured with DSC. The parameter
is close to 1 for strong liquids (nearly exponential relaxation). For
fragile liquids, it changes from near 1 at high temperature to a value close
to 0.3-0.5 near T
g
. It must be remembered, however, that the KWW and
Cowie-Ferguson expressions are only phenomenological models, whose
parameters lack real physical meaning. In particular, the Cowie-Ferguson
expression is an oversimplified model because the characteristic relaxation
time varies with ageing time (non-linearity) (Hodge, 1994).
Since the rate of structure relaxation depends on the molecular mobi-
lity, it may be expected to increase with the water content and to be higher in
glasses of lower molecular weight. The rate of enthalpy relaxation of gelatine
was indeed found to increase with water content (7-14%). The effect of water
could be fully explained in terms of decreasing T
g
(Badii et al., 2005). To
judge the specific influence of the constituents, enthalpy relaxation must be
measured for a same increment (T
a
-T
g
) of the ageing temperature from T
g
.
The rate of enthalpy relaxation was reduced, as expected, upon addition of a
substance with a higher T
g
, for instance dextran in sucrose (Blond, 1994;
Shamblin et al., 1998). In contrast, increasing the weight fraction of fructose
in glucose-fructose mixtures resulted in a decrease in the ageing rate,
although T
g
was depressed (Wungtanagorn and Schmidt, 2001a,b). In
