590
13 Chemical Reaction Mechanisms II: Catalysis and Miscellaneous Topics
Synthetic polymers are also classified by the type of reaction that forms them. Two
major classes are condensation polymers and addition polymers. When a monomer
unit is added to a condensation polymer chain there is a small molecule (often water)
produced in addition to the lengthened chain. In an addition polymer there is no other
product besides the chain. The monomer of an addition polymer generally has a carbon–
carbon double bond that opens up to bond with other monomers and form a chain of
covalently bonded carbon atoms. Two common examples of condensation polymers are
nylon and polyester and two common examples of addition polymers are polyethylene
and polystyrene.
Polymerization Kinetics
We discuss the reaction kinetics of condensation polymerization, but addition polymerization can be discussed in much the same way. 23 Consider the formation of a polyester
from a monomer diacid, HOOC–X–COOH, and a monomer dialcohol, HO–Y–OH,
where X and Y represent two hydrocarbon chains. The first step in the polymerization is
HOOC−X−COOH+HO−Y−OH − → HOOC−X−COO−Y−OH+H 2 O
(13.4-1)
The principal product is an ester, but it also has one carboxyl group and one hydroxyl
group, so it can react with a second diacid at one end and with a second dialcohol at the
other end, and so on to form a chain. Two chains of any length can also bond together
to form a longer chain. A long chain with the repeating unit –OOC–X–COO–Y– is
eventually formed. This chain is terminated by adding a hydroxyl group at the Y– end
and a hydrogen atom at the –OOC end so that it has a hydroxyl group at one end and
a carboxyl group at the other.
To proceed with the solution of the rate differential equations for the polymerization
reactions, we make some simplifying assumptions. We first assume that the rate coefficients for all condensation reactions have the same value, irrespective of the length
of the chain involved. This approximation is commonly justified by the assertion that
the behavior of a functional group in a “cage” of neighboring molecules or groups is
nearly independent of the length of the chain to which the functional group is attached
since the functional group is nearly immobilized in any event. We begin with a stoichiometric mixture that has equal concentrations of diacid and dialcohol and a small
concentration of a catalyst. We let c represent the sum of the concentrations of all types
of molecules other than catalyst or solvent molecules. At t 0, when the polymerization reaction begins, c c 0 and the diacid concentration and dialcohol concentration
are both equal to c 0 /2. There are two carboxyl groups on each diacid molecule, so that
the initial concentration of carboxyl groups is equal to c 0 and the initial concentration
of hydroxyl groups is also equal to c 0 . We assume that the reaction occurs in a nonpolar solvent so that the water that is formed is insoluble in the reaction solution and
is removed as it is formed. Each time a condensation reaction occurs, one free carboxyl group disappears and one free hydroxyl group disappears, and the number of
molecules decreases by unity. As c changes it remains equal to the concentration of free
(unesterified) carboxyl groups, and also to the concentration of free hydroxyl groups.
23 See H. R. Allcock and F. W. Lampe, Contemporary Polymer Chemistry, Prentice-Hall, Englewood
Cliffs, NJ, 1981, p. 245ff, or C. Tanford, Physical Chemistry of Macromolecules, Wiley, New York, 1961,
p. 588ff for the standard treatments of both types of polymerization.
13 Chemical Reaction Mechanisms II: Catalysis and Miscellaneous Topics
Synthetic polymers are also classified by the type of reaction that forms them. Two
major classes are condensation polymers and addition polymers. When a monomer
unit is added to a condensation polymer chain there is a small molecule (often water)
produced in addition to the lengthened chain. In an addition polymer there is no other
product besides the chain. The monomer of an addition polymer generally has a carbon–
carbon double bond that opens up to bond with other monomers and form a chain of
covalently bonded carbon atoms. Two common examples of condensation polymers are
nylon and polyester and two common examples of addition polymers are polyethylene
and polystyrene.
Polymerization Kinetics
We discuss the reaction kinetics of condensation polymerization, but addition polymerization can be discussed in much the same way. 23 Consider the formation of a polyester
from a monomer diacid, HOOC–X–COOH, and a monomer dialcohol, HO–Y–OH,
where X and Y represent two hydrocarbon chains. The first step in the polymerization is
HOOC−X−COOH+HO−Y−OH − → HOOC−X−COO−Y−OH+H 2 O
(13.4-1)
The principal product is an ester, but it also has one carboxyl group and one hydroxyl
group, so it can react with a second diacid at one end and with a second dialcohol at the
other end, and so on to form a chain. Two chains of any length can also bond together
to form a longer chain. A long chain with the repeating unit –OOC–X–COO–Y– is
eventually formed. This chain is terminated by adding a hydroxyl group at the Y– end
and a hydrogen atom at the –OOC end so that it has a hydroxyl group at one end and
a carboxyl group at the other.
To proceed with the solution of the rate differential equations for the polymerization
reactions, we make some simplifying assumptions. We first assume that the rate coefficients for all condensation reactions have the same value, irrespective of the length
of the chain involved. This approximation is commonly justified by the assertion that
the behavior of a functional group in a “cage” of neighboring molecules or groups is
nearly independent of the length of the chain to which the functional group is attached
since the functional group is nearly immobilized in any event. We begin with a stoichiometric mixture that has equal concentrations of diacid and dialcohol and a small
concentration of a catalyst. We let c represent the sum of the concentrations of all types
of molecules other than catalyst or solvent molecules. At t 0, when the polymerization reaction begins, c c 0 and the diacid concentration and dialcohol concentration
are both equal to c 0 /2. There are two carboxyl groups on each diacid molecule, so that
the initial concentration of carboxyl groups is equal to c 0 and the initial concentration
of hydroxyl groups is also equal to c 0 . We assume that the reaction occurs in a nonpolar solvent so that the water that is formed is insoluble in the reaction solution and
is removed as it is formed. Each time a condensation reaction occurs, one free carboxyl group disappears and one free hydroxyl group disappears, and the number of
molecules decreases by unity. As c changes it remains equal to the concentration of free
(unesterified) carboxyl groups, and also to the concentration of free hydroxyl groups.
23 See H. R. Allcock and F. W. Lampe, Contemporary Polymer Chemistry, Prentice-Hall, Englewood
Cliffs, NJ, 1981, p. 245ff, or C. Tanford, Physical Chemistry of Macromolecules, Wiley, New York, 1961,
p. 588ff for the standard treatments of both types of polymerization.