Chemistry Reference
In-Depth Information
Organic Solvents/Block Copolymers
This is a further kind of system that cannot be modeled by means of the simple (
32
),
referring to typical homopolymer solutions. Like with aqueous solutions of poly-
saccharides, the reason lies in special interactions between the segments of the
different polymer chains. With block copolymers, the interactions are due to the
high preference of contacts between like monomeric units over disparate contacts in
cases where the homopolymers are incompatible. There is, however, a fundamental
difference, namely in the number of segments that are involved in the formation of
the energetically preferred structures. Two units are required for the polysacchar-
ides (two segments are involved in the formation of a hydrogen bond), but with
block copolymers of this type the interaction of at least three like monomeric units is
on the average indispensable to form a microphase. This is another consequence of
chain connectivity. For low molecular weight compounds, the number of nearest
neighbor molecules is approximately six in the condensed state. The corresponding
number of contacting polymer segments on the other hand is only about half
this value, because of the chemical bonds connecting these segments to a chain
molecule.
Based on these considerations, postulating the simultaneous interaction of three
like segments for the establishment of a microphase, we can formulate the follow-
ing relation for the integral interaction parameter
g
, by analogy to (
42
), increasing
the power of the composition dependence of the third term from two to three:
a
3
g
¼
Þ
z 1
ð
þ
ð
1
l
Þ'
Þ þ
t
'
(44)
ð
1
n
Þ
ð
1
n
'
The system-specific parameter t accounts for the degree of incompatibility of
homopolymer A and homopolymer B.
Equation (
44
) yields, by means of (
9
), the following expression for the experi-
mentally accessible Flory Huggins interaction parameter w:
a
2
4
w
¼
2
zl
ð
þ
21
ð
l
Þ'
Þ þ
t
'
ð
'
3
Þ
(45)
ð
'
Þ
1
n
Like with normal polymer solutions, it is also possible to merge z and l for
solutions of block copolymers, i.e., to eliminate one adjustable parameter.
2.1.2 Polymer Blends
For mixtures of two types of linear chain molecules, A and B, the segment molar
Gibbs energy of mixing is usually formulated as:
D
G
AB
RT
¼
ð
1
'
B
Þ
Þ
'
B
ln 1
ð
'
B
N
B
ln
'
B
þ
g
AB
'
B
1
ð
'
B
Þ
(46)
N
A
