Chemistry Reference
In-Depth Information
homopolymer phases. The chemical potential of a copolymer chain at the interface
is calculated using (
107
) as:
A
¼
m
int
¼
@
F
interf
:
film
@
@
@s
þ
@
g
A
g
B
@s
g
A
þ
g
B
þ s
(114)
Q
Therefore, with (
110a
) and (
111a
):
þ
m
int
ln
N
A
sb
2
ln
N
B
sb
2
k
B
T
¼
þ
2
8
<
:
2
=
3
N
A
P
2
=
3
A
N
B
P
2
=
3
B
271
sb
2
(115a)
2
:
ðÞ
þ
ð
wet brush
Þ
þ
N
3
=
2
A
N
3
=
2
B
sb
2
P
1
A
P
1
B
þ
ð
wet mushroom
Þ
The free energy density of a homogeneous mixture of an AB copolymer with a B
homopolymer is [
278
]:
þ
þ wff
A
ð
F
bulk
k
B
T
¼
N
ln
e
1
f
P
B
1
f
e
f
A
fÞ
ln
1
(116)
irrespective of the copolymer architecture. Thus, the chemical potential of a copoly-
mer chain homogeneously distributed within the bulk B homopolymer,
m
bulk
¼
N
½
ð
1
fÞ@
F
bulk
=@f þ
F
bulk
, is:
m
bulk
k
B
T
¼
N
P
B
þ wNf
A
1
2
ln
f f ð
1
fÞ
2
f
A
f þ
f
A
f
(117a)
where
f ¼ f
(
1
) is the copolymer volume fraction in the B-rich homopolymer
phase.
The chemical potential of a copolymer chain in a micelle was evaluated by
Semenov [
278
] for long homopolymer chains (
P
N
), which do not penetrate the
micelles. Depending on the diblock copolymer composition, the micelle morphol-
ogy could be spherical, cylindrical, or lamellar [
278
,
289
]. The chemical potential
of a diblock copolymer chain in a micelle formed within the B phase is then given
by [
55
,
56
,
278
]:
>
h
i
1
=
3
spherical
mic
m
4
=
3
f
4
=
9
A
1
=
3
1
=
3
k
B
T
¼ð
3
=
2
Þ
1
:
74
f
1
ðÞ
wN
A
cylindrical
mic
m
1
=
3
1
1
=
3
k
B
T
¼
1
:
19
wf
A
N
ð
Þ
½
:
64
ln
f
A
m
lamellar
mic
1
=
3
5
1
=
3
k
B
T
¼
0
:
669
wN
ðÞ
ð
:
64
f
A
Þ
(118a)
