Sharp interface limit of an energy modelling nanoparticle-polymer blends

  • Stan Alama

    McMaster University, Hamilton, Canada
  • Lia Bronsard

    McMaster University, Hamilton, Canada
  • Ihsan Topaloglu

    McMaster University, Hamilton, Canada


We identify the  -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.

Cite this article

Stan Alama, Lia Bronsard, Ihsan Topaloglu, Sharp interface limit of an energy modelling nanoparticle-polymer blends. Interfaces Free Bound. 18 (2016), no. 2, pp. 263–290

DOI 10.4171/IFB/364