Chemistry Reference
In-Depth Information
Fig. 11 Copolymer chain with different segment types
whereas
m
a
is the number of
segments in the copolymer (according to Table
2
,
each polymer unit could consist of more than one segment). In addition, bond
fractions
B
ab
are used to describe, at least to certain extent, the arrangement of the
segments in the polymer chain. Here, a bond fraction
B
ab
is the fraction of all bonds
within the copolymer, which is a bond between a segment
a
. The
bond fractions are estimated on the basis of the molecular structure of the copoly-
mer. In the case of block copolymers, the values of the respective bond fractions are
clearly defined. Out of (
m
a
and a segment
b
1) bonds, there is only one bond of type
a b
, i.e.,
z
a
ð
m
2
Þ
1
m
1
B
ab
¼
(the
same for
B
bb
)[
52
]. In the case of an alternating copolymer, there exist only one
bond type
. The bond fraction of type
a a
is simply given by
B
aa
¼
ð
Þ
ð
m
1
Þ
, i.e.,
B
ab
=1.
The bond fractions in a random copolymer are usually not exactly known and
can only be estimated. One possibility is to assume that if segment type
ab
a
is in the
majority, there exist no bonds between two
b
-segments. Hence, the bond fractions
for such a copolymer are [
53
]:
2
z
a
m
m
B
bb
¼
0
;
B
ab
¼
Þ
;
B
aa
¼
1
B
ab
(23)
ð
1
Taking this into account, the expression for the hard-chain contribution can be
extended to copolymer systems [
52
]:
(24)
X
X
X
A
hc
NkT
¼
m
A
hs
d
iaib
NkT
x
i
m
i
ð
1
Þ
B
iaib
ln
g
iaib
i
a
b
whereas the segment number
m
i
of a copolymer is determined by:
X
M
i
X
a
m
M
m
i
¼
m
ia
¼
w
ia
(25)
ia
a
with
w
ia
being the weight fraction of
a
-segments within the copolymer. All other
expressions [(
8
) (
18
)] are used as for the homopolymer system considering the
copolymer/solvent system consisting of three types of segments (the solvent seg-
ments and (at least) two different types of polymer segments). The concentration
x
ia
of copolymer segments of type
a
is given by the product of the copolymer
concentration x
i
and the segment fraction
z
ai
:
