Chemistry Reference
In-Depth Information
and (2) the copolymer chains have a certain tendency to localize to the interface. In
the case of nearly miscible species (near the consolute point), the first mechanism
dominates whereas, for the highly incompatible case, the second dominates. Thus,
for nearly miscible systems, the mechanism involved is quite different from that
invoked for highly immiscible species. The dominant effect is the presence of
copolymer chains in both the A-monomer-rich and B-monomer-rich phases: in
consequence, when the copolymer amount increases, the difference between the
total volume fractions of monomer A in the B-rich phase and B-rich phase
decreases. The interfacial tension was found to consist of two parts:
g ¼ g
0
g
1
(102)
The first term,
g
0
, represents the interfacial energy due to the inhomogeneity of
the overall concentration of B monomer:
g
0
¼ g
0
ð
0
Þ
R
ðfÞ
(103)
where:
2
1
=
2
k
B
TN
1
=
2
6
b
2
3
=
2
g
0
ð
Þ¼
ð
wN
Þ
0
2
(104)
and:
3
=
2
3
=
2
R
ðfÞ¼
ð
f
Þ wN
1
½
ð
f
Þ
ð
wN
Þ
1
2
2
1
=
2
2
N
2
1
w
f
1
ð
f
Þ=
8
(105)
Here
wN
is the degree of incompatibility of the species,
k
B
is the Boltzmann
constant,
T
is the absolute temperature,
f
is the average copolymer volume fraction,
and
b
is the Kuhn statistical segment length. Formally, the same expression for
g
0
would be obtained if there were no copolymer chains in the system.
The second contribution,
g
1
, expresses a decrease in the interfacial tension due to
the effect of the preferential localization of the copolymers at the interface. Near the
critical region,
g
1
may be approximated by:
3
2
fg
0
g
1
(106)
Calculations showed that, near the critical point, the contribution of
g
1
to the
interfacial tension was almost negligible. However, for higher incompatibility
degrees, i.e., higher values of
wN
,theterm
g
1
could be comparable with
g
0
.
Therefore, it is the localization of the copolymer at the interface that is important.
To summarize, the mechanisms involved in the two different cases of highly
immiscible systems and nearly compatible blends are quite different. In the first
case, it is the surfactant activity of the block copolymer chains that cause the
interfacial tension reduction whereas, in the second case, it is the presence of
copolymer molecules in the bulk homopolymer phases that causes the compatibi-
lizing behavior.
