Nonaffinity of Liquid Networks and Bicontinuous Mesophases

Amphiphiles self-assemble into a variety of bicontinuous mesophases whose equilibrium structures take the form of high-symmetry cubic networks. Here, we show that the symmetry-breaking distortions in these systems give rise to anomalously large, nonaffine collective deformations, which we argue to be a generic consequence of ``mass equilibration'' within deformed networks. We propose and study a minimal ``liquid network'' model of bicontinuous networks, in which acubic distortions are modeled by the relaxation of residually stressed mechanical networks with constant-tension bonds. We show that nonaffinity is strongly dependent on the valency of the network as well as the degree of strain-softening or strain-stiffening tension in the bonds. Taking diblock copolymer melts as a model system, liquid network theory captures quantitative features of two bicontinuous phases based on comparison with self-consistent field theory predictions and direct experimental characterization of acubic distortions, which are likely to be pronounced in soft amphiphilic systems more generally.