A rigorous derivation of mean-field models for diblock copolymer melts

We study the free boundary problem describing the micro phase separation of diblock copolymer melts in the regime that one component has small volume fraction such that micro phase separation results in an ensemble of small spheres of one component. Mean-field models for the evolution of a large ensemble of such spheres have been formally derived in [6, 11]. It turns out that on a time scale of the order of the average volume of the spheres, the evolution is dominated by coarsening and subsequent stabilization of the radii of the spheres, whereas migration becomes only relevant on a larger time scale. We present here a rigorous derivation of the meanfield equations in the early time regime. Our analysis is based on passing to the homogenization limit in the variational framework of a gradient flow.