Revisiting packing frustration and strong-segregation stability of double-gyroid in block copolymer melts

Formation of double gyroid(DG) in self-assembled block copolymer(BCP) melts, along with understanding molecular-scale mechanisms behind its equilibrium selection, has been a topic of longstanding interest in polymer physics. In this talk, we will revisit equilibrium DG in strong segregation limit(SSL) using parabolic brush theory for computing entropic cost of stretching BCP chains. We introduce a new variational method based on tessellations using medial set construction to compute space filling optimal chain packing within SSL and show that our approach results in a lower free energy chain packing relative to previous studies in SSL which included a constraint that chains within tubular domains have to stretch till 1D skeletal graphs. Critically, we show that reduced entropic cost of medial vs. skeletal packing qualitatively alters the equilibrium phase diagram based on the SSL, with DG only showing a stable composition window when stretching is not confined to 1D skeleton. Our medial model can also be extended to morphologies beyond networks and is easily adaptable to study packing frustration using simulation or experimental data thereby providing valuable insights to engineer molecular design to target yet unrealized novel self-assembled BCP morphologies.