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

Published online by Cambridge University Press:  21 December 2011

KARL B. GLASNER
KARL B. GLASNER*
Affiliation:
Department of Mathematics and Program in Applied Mathematics, University of Arizona, Tucson, AZ 85721, USA4 email: kglasner@math.arizona.edu
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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.

Keywords

Co-polymerOrder–disorder transitionSelf-replication
Type
Papers
Information
European Journal of Applied Mathematics , Volume 23 , Issue 2 , April 2012 , pp. 315 - 341
Copyright
Copyright © Cambridge University Press 2011

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