"Liquid network" theory of supramolecular soft matter networks

Macromolecules can self-assemble into a variety of ordered nanostructures, including the triply-periodic double-gyroid and double-diamond network phases. These phases consist of complex, intercatenated, labyrinthine domains, yet are supramolecular soft crystals with long-range order. Interruptions to their crystal symmetries, e.g. due to defects or composition gradients, result in collective changes in domain morphology as a result of thermodynamic forces and constraints on molecular packing. Motivated by experiments and self-consistent field calculations of block copolymer melts, we propose a "liquid network" theory that coarse-grains the collective behavior of such supramolecular networks into an effective mechanical network model. Unlike canonical models of mechanical networks, our theory describes networks whose struts possess a length-independent line tension, and is thus characterized by the mathematics of so-called Steiner networks. We show that our model reproduces key observations of experiments and simulations, namely significant non-affinity of node displacements and highly correlated bond angles. Finally, we discuss structural transformations under shear and deformation pathways that facilitate transitions between different network phases.