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End date: 2022 × Start date: 2020 × Type: Text × Type: report × Subject: asymptotic analysis × Subject: chemical potential ×

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    Self-consistent field theory for a polymer brush. Part II: The effective chemical potential
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2019) Münch, Andreas; Wagner, Barbara
    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.