Patterns in Tri-Block Copolymers: Droplets, Double-Bubbles and Core-Shells - A New Partitioning Problem

Explore the fascinating world of tri-block copolymer patterns in this 53-minute lecture by Lia Bronsard at the Colloque des sciences mathématiques du Québec. Delve into the Nakazawa-Ohta ternary inhibitory system, which describes domain morphologies in triblock copolymers as a nonlocal isoperimetric problem. Examine the free energy components, including local interface energy and longer-range Coulomb interaction energy. Investigate global minimizers on a two-dimensional torus, focusing on scenarios where two species have vanishingly small mass but high interaction strength. Discover how this limit leads to mass splitting and rescaling to isoperimetric problem minimizers for 2D clusters. Learn about various structures of global minimizers, from isolated simple droplets to double-bubbles and core-shells, depending on interaction term coefficient strengths. Conclude with an introduction to a new type of partitioning problem arising from these findings.