Page 180 - Carrahers_Polymer_Chemistry,_Eighth_Edition

Polycondensation Polymers 143

+
1 0.97 1.97
1 r
+
−
DP =+ (1 r ) 2rp = = = 66 (4.105)
+
1 0.97 − 2(0.97) 0.03
The DP of 66 is above the threshold limit of 50 required for nylon-66 fi bers.
Since quenching the reaction or adding a stoichiometric excess of one reactant is seldom eco-
nomical, the commercial practice is to add a specific amount of a monofunctional reactant in the

synthesis of polyesters, nylons, and other similar polymers. In these cases, a functionality factor, f,
is used that is equal to the average number of functional groups present per reactive molecule. While
the value of f in the preceding examples has been 2.0, it may be reduced to lower values and used in

the following modified Carothers’ equation.
A 2
DP = o = (4.106)
f
p
−
A o [1 ( /2)] 2− pf
Thus, if 0.01 mol of monofunctional acetic acid is used with 0.99 mol of two difunctional reac-
tants, the average functionality or functional factor, f, is calculated as follows:

2 0.99 mol ×+
mol of each reactant × functionality 0.99 mol ×+ 2 0.01 mol × 1
f = = = 1.99 (4.107)
total number of moles 1.99 mol
Substitution of f = 1.99 and p = 1.00 in Equation 4.106 gives a DP of 200 representing an upper
limit for chain size often employed commercially for nylon-66. The same calculation but employing
p = .95 gives a DP of only 20, below the lower desired value for nylon-66.
Since the average molecular weight increases with conversion, useful high molecular weight lin-
ear polymers may be obtained by the step-reaction polymerization when the fractional conversion,
p, is high (>.99). The concentration of reactants decreases rapidly in the early stages of polymeriza-
tion, and differing chain lengths will be present in the final product. The requirement for a linear

polymer is a functionality of 2. Network polymers are typically formed when the functionality is
greater than 2.

4.21 SUMMARY
1. Many naturally occurring and some synthetic polymers are produced by condensation reactions
many of which are described kinetically by the term stepwise polymerization. A high-fractional
conversion is required to form linear polymers, such as polyesters, nylons, polysulfides, PUs, PC,

polysulfones, polyimides, PBI, and polyethers. But a high-fractional conversion is not required
for the production of network, cross-linked, products, such as epoxy, phenol, urea, formaldehyde,
and melamine resins. One major exception to the production of condensation polymers through
the stepwise kinetic process is the use of the interfacial reaction system employing reactive reac-
tants that follows a chainwise kinetic process. The interfacial system is employed to produce PC
and some aramids. The remaining condensation polymers are generally produced using the melt
and solution techniques.
2. The rate expressions and values, mechanisms, and the activation energies for the condensation reac-
tions forming polymers are similar to those of small molecule reactions. Reaction rate increases
with temperature in accordance with the Arrhenius equation. Average DP also increases as the
reaction temperature increases to the ceiling temperature, where polymer degradation occurs.
Long chains are only formed at the conclusion of classical polycondensation processes.
3. The DP for formation of linear condensation polymers can be calculated using the Carothers’
n
equation, DP = 1/(1–p).
n

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