WIAS Preprint No. 2649, (2019)

Self-consistent field theory for a polymer brush. Part II: The effective chemical potential


  • Münch, Andreas
  • Wagner, Barbara
    ORCID: 0000-0001-8306-3645

2010 Mathematics Subject Classification

  • 74H10 82B21

2010 Physics and Astronomy Classification Scheme

  • 02.30.Mv, 61.25.H-


  • Self-consistent field theory, asymptotic analysis, chemical potential




The most successful mean-field model to describe the collective behaviour of the large class of macromolecular polymers is the self-consistent field theory (SCFT). Still, even for the simple system of a grafted dry polymer brush, the mean-field equations have to be solved numerically. As one of very few alternatives that offer some analytical tractability the strong-stretching theory (SST) has led to explicit expressions for the effective chemical potential and consequently the free energy to promote an understanding of the underlying physics. Yet, a direct derivation of these analytical results from the SCFT model is still outstanding. In this study we present a systematic asymptotic theory based on matched asymtptotic expansions to obtain the effective chemical potential from the SCFT model for a dry polymer brush for large but finite stretching.

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