Cylinder↔GyroidEpitaxial Transitions in Complex Polymeric Liquids

The topography of the Landau free energy surface of a diblock copolymer melt is found to exhibit a low-energy pathway connecting the local minima of the cylinder (C) and gyroid (G) mesophases. Energy barriers and stability limits are accurately evaluated for experimentally relevant conditions, and they imply that the $\mathrm{C}\leftrightarrow \mathrm{G}$ transitions proceed epitaxially by a nucleation and growth mechanism. Furthermore, we predict the detailed polymorphism by which one phase transforms into the other.