Page 386 - Elements of Chemical Reaction Engineering Ebook

Sec. 7.3 Polymerization 357

By usiing diols and diacids we can form polymers with two different structural
units which together become the repeating unit. An example of an ARIA plus
BR,B reaction is that used to make Coca-cola@ bottles, i.e. terephthalic acid
plus ethylene glycol to form poly (ethylene glycol terephthalate).
When discussing the progress of step polymerization it is not meaningful
to use conversion of monomer as a measure because the reaction will still pro-
ceed even though all the monomer has been consumed. For example, if the
monomer A-R-B has been consumed. The polymerization is still continu-
ing with
A--R,-B + A-R,-B A-RS-B + AB
A-MR5-B + A-R,-B + A-R1o-B + AB

because there are both A and B functional groups that can react. Consequently,
we measure the progress by the parameter p which is the fraction of functional
groups, A, B, that have reacted. We shall only consider reaction with equal
molar feed of functional groups. In this case

M, - - fraction of functional groups of either A or B that
p=--- have reacted
M,

A4 = concentration of either A or B functional groups (mol/dm3)
As an example of step polymerization, consider the polyester reaction in which
sulfuric acid is used as a catalyst in a batch reactor. Assuming the rate of dis-
appearance is first order in A, B, and catalyst concentration (which is constant
for an externally added catalyst). The balance on A is

-- -d'A1 - k[AI[Bl (7-22)
dt
For equal molar feed we have
[A] = [B] = M

d'- -_ -kM2
dt

M= (7-23)
1 + M,kt
In terms of the fxactional conversion of functional groups, p,

-- - M,kt+ 1 (7-24)
1-P
,
The number average degree of polymerization, x,, is the average number of
structural units per chain
Degree Elipi -
x,
of Polymerization = (7-.25)