Chemistry Reference
In-Depth Information
in the same molecule have reacted. This seems to be a valid assumption, by
and large, with some exceptions, perhaps, in diisocyanates.
CH
3
NCO
NCO
7-2
(iii)
The following calculations presuppose a homogeneous, single-phase reaction
mixture. This condition is unlikely to be realized exactly in practical step-
growth polymerizations. The consequences of deviations from this assumption
in syntheses of branched polymers are considered briefly at the end of
Section 7.4.2
.
7.4.2
Number Average Degree of Polymerization in Step-Growth
Reactions
Calculations of the number average degree of polymerization as a function of
extent of reaction are very useful in designing and controlling step-growth poly-
merizations. Some examples of applications of these calculations are given later
in this section.
The reactions we are considering can be summarized as in
Fig. 7.3
where
monomers carrying A-type functional groups react with B-type monomers. To be
completely general, each functional group need not be confined to a single mono-
mer (e.g., a mixture of acids could be used in a polyamidation reaction), the func-
tionalities of the various monomers may differ, and the functional groups of
opposite kinds need not be present in equivalent quantities.
The method we use is that of Carothers. Functionality is defined (p. 7) as the
number of positions in the monomer that are available for reaction under the spec-
ified conditions, and f
i
is the symbol for functionality of monomeric species i.We
now define the average functionality f
av
as the average number of functional
groups per monomer molecule. That is,
P
N
i
f
i
P
N
i
f
av
(7-15)
where N
i
is the number of moles (either per unit volume or in the whole reaction
vessel) of species i.
The definition of
Eq. (7-15)
holds strictly when functional groups of opposite
kinds are present in equal concentrations. If there is an excess of functional
groups of one kind, the monomers carrying these groups will be able to react only
until
the opposite functional groups are consumed. In such nonstoichiometric
