Characterising the disordered state of block copolymers: Bifurcations of localised states and self-replication dynamics

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Abstract

Above the spinodal temperature for micro-phase separation in block co-polymers, asymmetric mixtures can exhibit random heterogeneous structure. This behaviour is similar to the sub-critical regime of many pattern-forming models. In particular, there is a rich set of localised patterns and associated dynamics. This paper clarifies the nature of the bifurcation diagram of localised solutions in a density functional model of A-B diblock mixtures. The existence of saddle-node bifurcations is described, which explains both the threshold for heterogeneous disordered behaviour as well the onset of pattern propagation. A procedure to generate more complex equilibria by attaching individual structures leads to an interwoven set of solution curves. This results in a global description of the bifurcation diagram from which dynamics, in particular self-replication behaviour, can be explained.

Original languageEnglish (US)
Pages (from-to)315-341
Number of pages27
JournalEuropean Journal of Applied Mathematics
Volume23
Issue number2
DOIs
StatePublished - Apr 1 2012

Keywords

  • Co-polymer
  • Order-disorder transition
  • Self-replication

ASJC Scopus subject areas

  • Applied Mathematics

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