Self-Consistent Field Theory and Its Applications by M. W. Matsen

5
[
H
C
H
Polyethylene (PE)
Polyisoprene (PI)
[
H
C
H
H
H
C
C H
H
Polypropylene (PP)
H
[ C
H
C
H
C
H
H
C
H
Polybutadiene (PB)
H
H
[ O C C Polyethyleneoxide (PEO)
H H
H
C
H
H
[ Polyvinylchloride (PVC)
C
Cl
Figure 1.2: Chemical structure of some common monomers used to form polymer molecules.
proximations. In most applications, the theory employs the simple coarse-grained Gaussian
model for polymer chains, and treats their interactions by mean-field theory. Section 1.1 begins
by justifying the applicability of the Gaussian model, and then Section 1.2 develops the
necessary statistical mechanics for a single chain subjected to an external field, w(r). Following
that, a number of useful approximations are introduced for handling special cases such as
when w(r) is either weak or strong. This provides the necessary background for discussing
SCFT.
As with most theories, the framework of SCFT is best described by demonstrating its
application on a representative sample of systems. To this end, we focus on the three examples
depicted in Fig. 1.3: polymer brushes, homopolymer interfaces, and block copolymer
microstructures. Not only do they represent a varied range of applications, but they are also
important systems in their own right. A polymeric brush is formed when chains are grafted to
a substrate in such high concentration that they create a dense coating with highly extended
configurations. Brushes are simple to prepare and provide a convenient way of modifying
the properties of a surface, and can, for example, greatly reduce friction, change the wetting
behavior, and affect adhesion properties. Polymeric alloys (or blends) provide an economical