Interfaces and Free Boundaries

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Volume 5, Issue 2, 2003, pp. 193–238
DOI: 10.4171/IFB/78

On energy minimizers of the diblock copolymer problem

Xiaofeng Ren[1] and Juncheng Wei[2]

(1) Department of Mathematics and Statistics, Utah State University, UT 84322, Logan, USA
(2) Department of Mathematics, University of British Columbia, BC V6T 1Z2, Vancouver, Canada

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.

Keywords: energy minimizers; diblock copolymer systems; variational problems; micro-phase separation

Ren Xiaofeng, Wei Juncheng: On energy minimizers of the diblock copolymer problem. Interfaces Free Bound. 5 (2003), 193-238. doi: 10.4171/IFB/78