Chemistry Reference
In-Depth Information
a cross-linking system turns into a single infinite network. At this point, the system
loses its ability flow. Theoretically [
6
], gelation occurs at a certain extent of cure
that depends only on the functionality of the monomers. It was mentioned earlier
that an epoxy-amine system would form a network when DGEBA is reacted with
a diamine. The functionality of DGEBA is two because it has two reactive epoxy
groups, and that of diamine is four because it has four reactive hydrogens. The theo-
retical value of the extent of cure at gelation,
ʱ
gel
, is [
6
]:
12
/
12
/
1
1
1
4121
α
gel
=
=
−−
=
0 577
.
,
(4.26)
(
f
−
)(
f
−
1
)
(
)(
)
A
E
where
f
A
and
f
E
are the respective functionalities of the amine and epoxy.
As discussed in Sect. 4.2.1, vitrification occurs when the glass transition tem-
perature of the forming product (i.e., network in the present case) reached the tem-
perature of the reaction system. In accord with the TTT diagram (Fig.
4.11
), the
phenomena of gelation and vitrification are independent from each other. If curing
is performed at a temperature above
T
g,0
(the glass transition temperature of the
epoxy monomer) but below
gel
T
g
(temperature at which gelation and vitrification
occur simultaneously), the system would turn from liquid to glass without gelation.
However, if curing is conducted above
gel
T
g
but below
T
g,∞
(the glass transition tem-
perature of the fully cured epoxy), the liquid system would first transform into a gel
and then into a glass. Finally, if a curing system is maintained above
T
g,∞
, it will gel
without vitrification.
The TTT diagram can be recast in simpler temperature versus conversion form
similar to that shown in Fig.
4.2
. To do this, one needs to track the evolution of the
glass transition temperature of a curing system as a function of conversion. This can
be done by means of the modified DiBenedetto equation [
38
,
39
]:
=+
−
−−
λα
(
TT
)
g
,
∞
g
,0
TT
,
(4.27)
g
g,0
11
(
λα
)
where
ʻ
is a fit parameter. The actually measured [
40
] values of
T
g
at different val-
ues of
ʱ
for an epoxy-amine curing system are shown in Fig.
4.12
. It is seen that the
glass transition temperature rises quickly with the progress of cross-linking and that
the trend is well described by Eq. 4.27.
The
T
g
line from Eq. 4.27 limits the region of vitrification in the temperature
versus conversion diagram (Fig.
4.13
). Relative to the diagram for regular linear
polymerization (Fig.
4.2
), the diagram for cross-linking reveals the presence of a
new phase, gel. The latter exists at conversions above
ʱ
gel
(Eq. 4.26) and tempera-
tures above
T
g
(Eq. 4.27).
Unlike the progress of linear polymerization, the progress of curing is difficult to
characterize straightforwardly in terms of the average molecular weight and steady-
state viscosity. As soon as a curing system gels, the steady-state viscosity turns
Search WWH ::
Custom Search