Chemistry Reference
In-Depth Information
Whether or not the polymerization proceeds will depend on the size of the
ring that can be formed by intermolecular or intramolecular cyclization. Five-
and six-membered rings are thermodynamically stable and will be produced to
the exclusion of polymer if the spacing between the coreactive functional groups
is appropriate. Smaller all-carbon rings are relatively unstable because of bond
angle distortions while the stability of rings of 8-12 carbons is adversely affected
by crowding of hydrogens or other substituents inside the ring. The potential ring
size increases with the distance between the coreactive ends of a growing poly-
mer. Large rings will be stable if they are formed but the probability of the two
reactive ends meeting is also diminished sharply, particularly if alternative reac-
tions are available with other molecules in the reaction mixture. As an example,
the equilibrium concentration of cyclic trimer in the polymerization of poly(eth-
ylene terephthalate) (
Fig. 7.2a
) is about 1.5%. This material, with molecular
weight 575, can be detected as a small peak in the SEC chromatogram of poly
(ethylene terephthalate). It can affect the dyeing properties of fibers made from
this polymer.
7.4
Polymer Size and Extent of Conversion of Functional
Groups in Equilibrium Step-Growth Polymerizations
This section develops the relation between the number average size of polymers
produced in a step-growth polymerization and the fraction of functional groups
which have been reacted at any point in the process. The basic equation that will
be developed,
Eq. (7-19)
, is called the Carothers equation. It illustrates the funda-
mental principles that underlie the operation of such polymerizations to produce
good yields of polymers with the desired molecular weights.
7.4.1
Basic Assumptions
The basic assumptions involved in deriving the Carothers equation are reviewed
in this section.
(i)
A major assumption is that the reactivity of all functional groups of the
same kind is equivalent and independent of the size of the molecule to
which the functional group is attached. In the last stages of polymerization,
the rate of polymerization will be low because the concentration of reactive
groups is small, but the specific rate constant for reaction of the given group
will remain constant if this assumption is true.
Equal reactivity of functional groups has been demonstrated by
measurements of reaction rates of several series of reactants that differ in
molecular weight. Further evidence is provided by the occurrence of
interchange reactions under appropriate conditions. In these reactions the
terminal functional group of one molecule reacts with the linking unit in
