Geodesic
Sharp interface limit of an energy modelling nanoparticle-polymer blends
Stan Alama1 ; Lia Bronsard1 orcid ; Ihsan Topaloglu1 orcid
1McMaster University, Hamilton, Canada
Interfaces and free boundaries, Tome 18 (2016) no. 2, pp. 263-290

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DOI

We identify the Γ-limit of a nanoparticle-polymer model as the number of particles goes to infinity and as the size of the particles and the phase transition thickness of the polymer phases approach zero. The limiting energy consists of two terms: the perimeter of the interface separating the phases and a penalization term related to the density distribution of the infinitely many small nanoparticles. We prove that local minimizers of the limiting energy admit regular phase boundaries and derive necessary conditions of local minimality via the first variation. Finally, we discuss possible critical and minimizing patterns in two dimensions and how these patterns vary from global minimizers of the purely local isoperimetric problem.
DOI : 10.4171/ifb/364
Classification : 49-XX, 35-XX
Mots-clés : Nanoparticles, isoperimetric problem, Γ-convergence, block copolymers, self-assembly, phase separation

Stan Alama  1   ; Lia Bronsard  1   ; Ihsan Topaloglu  1

1 McMaster University, Hamilton, Canada 
Stan Alama; Lia Bronsard; Ihsan Topaloglu. Sharp interface limit of an energy modelling nanoparticle-polymer blends. Interfaces and free boundaries, Tome 18 (2016) no. 2, pp. 263-290. doi: 10.4171/ifb/364
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     pages = {263--290},
     year = {2016},
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     doi = {10.4171/ifb/364},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/364/}
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