Chemistry Reference
In-Depth Information
The glass transition temperature of miscible polymer mixtures can be calcu-
lated from
1
T
g
C
w
A
T
g
A
1
w
B
T
g
B
(4-5)
where
T
g
i
and
w
i
are the glass temperature (in K) and weight fraction of compo-
nent
i
of the compound. This equation is useful with plasticizers (Section 5.3.2)
which are materials that enhance the flexibility of the polymer with which they
are mixed. The
T
g
values of plasticizers themselves are most effectively esti-
mated by using
Eq. (4-5)
with two plasticized mixtures of known compositions
and measured
T
g
's. The foregoing equation cannot be applied to polymer blends
in which the components are not mutually soluble, because each ingredient will
exhibit its characteristic
T
g
in such mixtures. The existence of a single glass
temperature is in fact a widely used criterion for miscibility in such materials
(Section 5.1).
Equation (4-5)
is also a useful guide to the glass transition temperatures of
statistical copolymers. In that case
T
g
A
and
T
g
B
refer to the glass temperatures
of the corresponding homopolymers. It will not apply, however, to block and
graft copolymers in which a separate
T
g
will be observed for each component
polymer if the blocks or branches are long enough to permit each homopolymer
type to segregate into its own region. This separation into different domains is
necessary for the use of styrene
butadiene block polymers as thermoplastic
rubbers.
4.4.3
Correlations between T
m
and T
g
A rough correlation exists between
T
g
and
T
m
for crystallizable polymers,
although the molecular mechanisms that underlie both transitions differ. Any
structural feature that enhances chain stiffness will raise
T
g
, since this is the tem-
perature needed for the onset of large-scale segmental motion. Stronger intermo-
lecular forces will also produce higher
T
g
's. These same factors increase
T
m
,as
described in Section 4.3, in connection with
Eq. (4-1)
.
Statistical copolymers of the types described in Chapter 10 tend to have broad-
er glass transition regions than homopolymers. The two comonomers usually do
not fit into a common crystal lattice and the melting points of copolymers will be
lower and their melting ranges will be broader, if they crystallize at all. Branched
and linear polyethylene provide a case in point since the branched polymer can
be regarded as a copolymer of ethylene and higher 1-olefins.
4.4.4
Measurement of T
g
Glass transition temperatures can be measured by many techniques. Not all meth-
ods will yield the same value because this transition is rate dependent. Polymer
segments will respond to an applied stress by flowing past each other if the
