Biomedical Engineering Reference
In-Depth Information
2.2 PRINCIPLES OF BLOCK COPOLYMER
SELF-ASSEMBLY
The term block copolymer refers to the copolymers in which the
two different monomer units are arranged in linear blocks. The
simplest example of a block copolymer is an AB diblock copolymer
(Fig. 2.2) [1].
February 8, 2010 17:21
linear homopolymer
diblock copolymer
triblock copolymer
starblock copolymer
Figure 2.2
Simple homopolymer and block copolymer architectures.
Very few pairs of homopolymers are miscible in the melt;
indeed, the tendency of a blend of polymers to macrophase separate
is much greater than that of an equivalent blend of the unconnected
monomers. The thermodynamics of polymer melts is governed by
the competing influence of energetic and entropic terms in the free
energy of mixing. The energy of mixing (Δ
) is proportional to
the number of monomers present, while the entropic contribution
(Δ
U
mix
), which favors homogenous mixing, is proportional to the
number of polymer chains. The entropy of mixing per monomer
is, therefore, decreased by a factor of the degree of polymerization
(
S
mix
) for a polymer blend compared with a blend of the unconnected
monomers. The Flory-Huggins free energy of mixing per monomer
(Δ
N
F
) for a blend of polymers A and B at temperature
T
, with degree
mix
of polymerization
N
and volume fractions
f
and
f
, respectively, is
A
B
given by
Δ
F
= Δ
U
−
T
Δ
S
(2.1)
mix
mix
mix
Δ
F
f
f
mix
A
N
B
N
= ln
f
A
+
ln
f
+
χ f
f
,
(2.2)
k
T
B
A
B
B
where
is the dimensionless Flory interaction parameter
describing the energetic cost per monomer of contacts between A
and B monomers
χ
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