TY - JOUR
T1 - Characterising the disordered state of block copolymers
T2 - Bifurcations of localised states and self-replication dynamics
AU - Glasner, Karl B.
PY - 2012/4
Y1 - 2012/4
N2 - 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.
AB - 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.
KW - Co-polymer
KW - Order-disorder transition
KW - Self-replication
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U2 - 10.1017/S0956792511000398
DO - 10.1017/S0956792511000398
M3 - Article
AN - SCOPUS:84858720222
SN - 0956-7925
VL - 23
SP - 315
EP - 341
JO - European Journal of Applied Mathematics
JF - European Journal of Applied Mathematics
IS - 2
ER -