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 $\e$. We prove that as $\e$ approaches $0$, the energy minimizers develop a growing number, of the order $\e^{-1/3}$, of periodic oscillations, explaining the micro-phase separation phenomenon.