The block copolymer and its related problems and mathematical models

Abstract

By competing short and long-range interactions, there exists some energies have been introduced and studied in the mathematics. These energies are relevance to the diblock copolymer microphase separation model. The diblock copolymer is a linear-chain molecule with two sub-chains. These two sub-chains are covalently linked to each other. One of the sub-chains is NA monomers of typed A and the other one is NB monomers of types B. The problem of diblock copolymers was introduced by Ohta and Kawasaki [1] in 1986 at first based on a density-functional theory. Nowadays, this problem has rekindled the interest of mathematicians. The following research of the diblock copolymers is about the droplet regime. Furthermore, a continuous study of the sharp interface of the diblock copolymers is addressed as a study of small volume-fraction asymptotic properties of a nonlocal isoperimetric functional with a confinement term. This functional is the sharp interface limit with a large number static nanoparticles as a confinement term and penalize the energy outside of a fixed region [2]. [...]