168
M 1
2209
19 18
2209 1
56100
212 5
=
−
(
)+
×






=
M 8
2213
19 18
2213 8
56100
1682
=
−
(
)+
×






=
For a polyester formulation with trifunctional glycol, it is important to calculate
the gel point of the reaction and avoid the formation of crosslinked polyester in
reactors, which is a difficult and expensive task to clean the reactor. The gel point of
these systems was studied first by Carothers. Two extensions from Carother’s equation, known as extension of the Carother’s equation and Patton’s constant has been
proposed. In the extension of the Carother’s equation, the gel point of the system
can be calculated by Eq. 8.6.
Degree of thereaction F Xp F
= −
×
2
2
(8.6)
where the average functionality of the polymer is F and the degree of polymerization is X p .
F can be calculated using Eq. 8.7.
F=
Total number of effective groups
Total number of molecules s
.
(8.7)
and X p can be calculated according to Eq. 8.8.
X
Number of moles of starting materials
Number of moles at
p =
the degree of reaction P
.
(8.8)
The number of effective groups is equal to the number of dicarboxylic acid groups
because the hydroxyl groups are in excess. The above-mentioned equation then
becomes:
F
eCOOH
mi.
=
×
2
So, for the aforementioned formulation:
F =
× =
2 18
19
1 89
.
M. Akbari and R. Najjar