Chemistry Reference
In-Depth Information
Figure 1.9.
A plot representing the reciprocal of relaxation time versus temperature for
propylene carbonate (reproduced with permission from Ref. 17. Copyright 1993, American
Physical Society).
τ
nity or zero molecular mobility. For small organic
molecules,
T
0
generally falls between 40 and 70 K below
T
g
. Figure 1.9 provides an
example of a plot of 1/
(
T
) eventually would reach in
versus
T
for amorphous propylene carbonate, in the supercooled
equilibrium state, having a
T
g
of 150 K; decreases in the parameter represented on the
y
-axis re
τ
ect an increase in relaxation time or increase in viscosity [17]. Here, we can see
that at temperatures above 225 K, or
1.5
T
g
, relaxation times appear to follow Arrhenius
kinetics (Equation 1.6) as expected for an equilibrium liquid with a single mode of
relaxation. At a temperature labeled
T
A
, equal to the
∼
T
c
,
previously discussed, however, we can observe in Figure 1.9 that there is a marked
discontinuity, where the increase in relaxation time now follows the VTF equation
(Equation 1.8) with much higher values of relaxation time than predicted by Equation 1.6.
Note also in Figure 1.9 the extrapolation of relaxation times to a value of
T
0
, as presented
in Equation 1.8. The data presented in Figure 1.9 show that at temperatures above
T
A
(
T
c
),
the supercooled liquid is structurally similar to the equilibrium liquid. However, as the
system is cooled to below
T
c
, but above
T
g
, the supercooled liquid appears to exhibit
structural changes and spatial heterogeneity that give rise to multiple modes of relaxation
and a very rapid increase in the average
“
crossover temperature
”
τ
as the temperature approaches
T
g
[15]. An
