Chemistry Reference
In-Depth Information
where
T
and
Tg
are viscosities at T and T
g
, respectively, and
0
,B,T
0
,C
1g
and C
2g
are constants. Both expressions (VTF and WLF) can be intercon-
verted. They were originally phenomenological expressions, although theo-
retical interpretations have been given.
In the glass, long-range cooperative motions are restricted. Motions
(vibrations of atoms, reorientation of small groups of atoms) are mainly
local, not involving the surrounding atoms or molecules. The temperature
dependence of dynamic properties in glasses is generally considered to obey
Arrhenius law, with an apparent activation energy that is lower than at T
>
T
g
but still rather high (Perez, 1994). Mobility in the glass will be described more
extensively in the next section.
The most popular method used to determine T
g
isbasedonthechange
in heat capacity monitored by DSC (Figure 11.7). For the study of food
systems where the glass transition is smeared out over a broad temperature
range, the method may not be sensitive enough; the glass transition range is
then determined from the
relaxation, monitored by mechanical or dielec-
tric spectroscopy (Figure 11.9). The points that are chosen on the curves to
define T
g
(onset, midpoint) or T
(maximum of the loss moduli E
00
or G
00
,
maximum of the loss factor tan
or drop in E
0
or G
0
) must be specified, as
well as the measurement conditions (cooling/heating rates, frequency, ther-
mal history).
Equations (18) and (19) can be written with viscosity replaced by a
relaxation time (
). Significantly different values of
may be obtained with
different techniques because of varying response of the material to the
imposed perturbations (Angell et al., 1991). The relaxation time most char-
acteristic of glass transition is considered the relaxation time of the system at
the calorimetric T
g
, i.e.
200 s (Angell et al., 1991).
Parameters C
1g
and C
2g
are frequently considered as universal
constants (17.4 and 51.6, respectively). This should be true for C
1g
(Angell
et al., 1994). On the contrary, C
2g
is now recognized to show large
variations. The variations in C
2g
and B are related to the classification
scheme for glass-forming liquids that has been proposed based on the
dependence of
or
on temperature (Angell, 1985; Angell et al., 1994).
''Strong'' liquids are those with Arrhenius or almost-Arrhenius behaviour
(above T
g
) and show only a small change in heat capacity at T
g
.Theseare
liquids with a three-dimensional network of bonds, such as SiO
2
.Incon-
trast, ''fragile'' liquids show VTF/WLF behaviour and a large change in
heat capacity at T
g
. Various approaches have been taken to quantify the
fragility (Angell et al., 1994; Simatos et al., 1995b; Angell 2002). One of
them is the m fragility parameter, defined as the slope at T
g
in an Arrhenius
plot of viscosity or relaxation time, where the abscissa is scaled to T
g
;mis
then given by
