On energy minimizers of the diblock copolymer problem

Abstract

We view the free energy of a diblock copolymer system as a variational problem, in which the integrand of the functional contains an interesting nonlocal term, and a small parameter $ϵ$. We prove that as $ϵ$ approaches $0$, the energy minimizers develop a growing number, of the order ${ϵ}^{-1/3}$, of periodic oscillations, explaining the micro-phase separation phenomenon.