Chapter 2. Self-Consistent Field Theory and Its Applications

  1. Prof. Dr. Gerhard Gompper2 and
  2. Prof. Dr. Michael Schick3
  1. Prof. Mark W. Matsen

Published Online: 15 OCT 2007

DOI: 10.1002/9783527617050.ch2

Soft Matter, Volume 1: Polymer Melts and Mixtures

Soft Matter, Volume 1: Polymer Melts and Mixtures

How to Cite

Matsen, M. W. (2005) Self-Consistent Field Theory and Its Applications, in Soft Matter, Volume 1: Polymer Melts and Mixtures (eds G. Gompper and M. Schick), Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, Germany. doi: 10.1002/9783527617050.ch2

Editor Information

  1. 2

    Institut für Festkörperforschung, Forschungszentrum Jülich, 52425 Jülich, Germany

  2. 3

    Department of Physics, University of Washington, Seattle, WA 98195-1560, USA

Author Information

  1. Department of Physics, University of Reading, Reading, RG6 6AF, United Kingdom

Publication History

  1. Published Online: 15 OCT 2007
  2. Published Print: 16 DEC 2005

Book Series:

  1. Soft Matter

ISBN Information

Print ISBN: 9783527305001

Online ISBN: 9783527617050

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Keywords:

  • polymer melts;
  • polymer mixtures;
  • self-consistent field theory;
  • Gaussian chain;
  • strong-stretching theory (SST);
  • classical mechanics;
  • mathematical techniques;
  • approximations;
  • polymer brushes;
  • polymer blends

Summary

This chapter contains sections titled:

  • Introduction

  • Gaussian Chain

  • Gaussian Chain in an External Field

  • Strong-Stretching Theory (SST): the Classical Path

  • Analogy with Quantum/Classical Mechanics

  • Mathematical Techniques and Approximations

    • Spectral Method

    • Ground-State Dominance

    • Fourier Representation

    • Random-Phase Approximation

  • Polymer Brushes

    • SST for a Brush: the Parabolic Potential

    • Path-Integral Formalism for a Parabolic Potential

    • Diffusion Equation for a Parabolic Potential

    • Self-Consistent Field Theory (SCFT) for a Brush

    • Boundary Conditions

    • Spectral Solution to SCFT

  • Polymer Blends

    • SCFT for a Polymer Blend

    • Homogeneous Phases and Macrophase Separation

    • Scattering Function for a Homogeneous Blend

    • SCFT for a Homopolymer Interface

    • Interface in a Strongly Segregated Blend

    • Grand-Canonical Ensemble

  • Block Copolymer Melts

    • SCFT for a Diblock Copolymer Melt

    • Scattering Function for the Disordered Phase

    • Spectral Method for the Ordered Phases

    • SST for the Ordered Phases

  • Current Track Record and Future Outlook for SCFT

  • Beyond SCFT: Fluctuation Corrections

  • Appendix: The Calculus of Functionals