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

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...

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Bibliographic Details
Published in:European journal of applied mathematics 2012-04, Vol.23 (2), p.315-341
Main Author: GLASNER, KARL B.
Format: Article
Language:English
Subjects:
Applied mathematics
Asymmetry
Bifurcations
Blocking
Copolymers
Density
Dynamics
Heterogeneous structure
Mathematical models
Polymers
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Summary: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.
ISSN:0956-7925
1469-4425
DOI:10.1017/S0956792511000398