The lyotropic liquid crystals formed by amphiphiles include lamellar and cylindrical phases with smectic A and columnar order, respectively, representing both 2D and 1D layered liquids. Bicontinuous networks form at intermediate compositions and consist of liquid-like interfaces, combining both layer and cylindrical geometries, that percolate all three dimensions. Of the bicontinuous networks, the predominant structures are based on gyroid, diamond, and primitive minimal surfaces, all of which have cubic crystal symmetries. While possessing a rigidity and 3D elasticity description of conventional solids, mass transport along interfaces lead to complex, non-affine relaxation modes. We consider a liquid network model that is able to capture the non-affine deformations observed in bicontinuous networks formed by block copolymers. We additionally identify topology-preserving transformation pathways between different network phases enabled by mass transport along interfaces, uncovering conditions under which the bicontinuous double diamond is a transition state between stable double gyroid and a metastable tetragonal network phase. Finally, we consider a new model of the general structure and free energy of inhomogeneous deformations and defects in bicontinuous networks.
https://indico.ijs.si/event/4010/