Biomedical Engineering Reference
In-Depth Information
Fig. 11.1
Two simple condensation polymerization reactions
namely the synthesis of a polyester using a diacid (a molecule with two COOH
groups) and a diol (a molecule with two OH groups) and the synthesis of a polyester
using an hydroxy-alcohol: the symbols R1 and R2 that appear in the scheme
are functional groups. One of the simplest cases is when both are methylenes
(R1
D
CH
2
and R2
D
CH
2
). Polycarbonates are condensation polymers. The
polymer called Nylon 6 belongs to the group of Polyamides. It is obtained industri-
ally by a “ring opening” synthetic route [
1
-
3
]. In the following, we shall describe
a series of different polymerization reaction conditions and, for each different reac-
tion, we will derive a prediction for the sequence of the reaction products. This will
be followed by a section on experimental methods to measure the sequence.
11.2
Sequence Prediction
In order to define the quantities of interest, it is necessary to recall some concepts
from the previous chapter. A polymerization reaction is a chemical reaction in which
reactants are transformed into reaction products. The reactants are called the feed.
The feed contains monomers at a concentration of
z
tot
. In binary copolymers the feed
contains A and B at a concentration of
z
A
and
z
B
and thus the sum of the molar ratio
of A and B units in the feed,
f
A
C f
B
, equals one. In a similar manner, the sum of
the molar ratio of A and B units in the reaction products (i.e., in copolymer chains),
c
A
C c
B
, equals one indeed. A sequence made of three repeat units is called triad.
Tetrads, pentads, hexads, and heptads are sequences made of four, five, six, and
seven repeat units, respectively. Some polymers possess a high oligomeric content.
In oligomers, the chain is short (by definition). The dimer contains two repeat units,
whereas the trimer, tetramer and the pentamer contain three, four, and five repeat
units, respectively. The Molar Mass Distribution (MMD) measures the abundances
of chains of length
and
Q
w
are important. The Schulz-Zimm
MMD function is given by the product of a power law and a decreasing exponential:
Q
n
s
. MMD averages
.s/ D a
nofa
.s/
˛
exp
MMD
.s=/;
(11.1)
where
˛
and
are two adjustable parameters and
a
nofa
is a suitable normalization
Q
w
factor. When
˛ D 0
, the distribution is a decreasing exponential and thus
dou-
Q
n
bles
:
N
Y
w
D 2
N
Y
(11.2)
n
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