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, UNITED STATES
(2) Department of Mathematics, The Chinese University of Hong Kong, Shatin, HONG KONG, CHINA

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