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.