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]. [...]