Chemistry Reference
In-Depth Information
Figure 1.2.
Free energy
-
temperature
diagram for a single-component system
(reproduced with permission from
Ref. 3. Copyright 2001, Elsevier).
crystal as the temperature of the sample is increased until we reach the melting
temperature
T
m
where the crystal undergoes a spontaneous
first-order conversion to
the liquid form, with the liquid now in a lower free energy state. If the liquid is slowly
cooled to below
T
m
, and there is suf
cient time for nucleation and crystal growth to
occur, the system will revert to the equilibrium state of the crystal. If, however, as seen in
Figure 1.2, the liquid sample is cooled rapidly through
T
m
so as to kinetically avoid
crystallization, the system will show no discontinuities at
T
m
and maintain the equili-
brium properties of the liquid as a supercooled liquid that is metastable relative to the
crystal. Upon further cooling and as the viscosity of the supercooled liquid increases and
diffusive motions of the molecules decrease, equilibrium can no longer be maintained
and a distinct discontinuity in the free energy
temperature diagram occurs with the
formation of the unstable glassy state. This occurs at a distinct temperature, designated
the glass transition temperature
T
g
, the value of which for a particular molecule under the
same processing conditions is determined by the molecular weight, degree of polarity,
and the effect of molecular shape on the closeness of molecular packing. For example,
the more polar the solid or the higher the molecular weight, the greater the value of
T
g
,
while the bulkier the shape of the molecule and poorer the packing, the lower the
T
g
. The
value of
T
g
is experimentally determined most conveniently by using differential
scanning calorimetry, where the heat capacity can be measured as the sample temperature
is continuously changed at a constant rate from low temperatures to the melting
temperature. Because of structural changes that bring about changes in the rate of
molecular motions, the heat capacity generally undergoes a distinctly abrupt change at
T
g
, as illustrated in Figure 1.3. In general, it has been shown that the viscosity of an
organic liquid at
T
m
is on the order of 10
2
Pas, while at
T
g
this value has increased to
about 10
12
Pas, a 14 order of magnitude change! Since this point of discontinuity is
associated with such a signi
-
cant change in viscosity as cooling occurs, experimental
values of
T
g
will depend to a small extent on the rate of cooling: the faster the rate of
