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

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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
6 1 Self-consistent field theory and its applications (a) Polymeric Brush Substrate (b) Homopolymer Interface (c) Diblock Copolymer Lamellar Phase D Figure 1.3: (a) Polymeric brush consisting of polymer chains end-grafted to a flat substrate. (b) Polymer interface separating an A-rich phase (blue domain) from a B-rich phase (red domain). (c) Lamellar diblock copolymer microstructure consisting of alternating thin A- and B-rich domains with a repeat period of D. method of designing new materials with tailored properties. Because large macromolecules possess relatively little translational entropy, the unlike polymers in an alloy tend to segregate while they are being processed in the melt state, leaving the solid material with a domain
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Bibliography Almdal, K., Rosedale,
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BIBLIOGRAPHY 81 Matsen, M. W. and G
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Index action 17 binodal point 46 bl
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Self-Consistent Field Theory and Its Applications by M. W. Matsen

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