Morphological Phase Diagrams for Self-Assembly

While self-assembly has been harnessed to achieve materials with long-range order and emergent properties for decades, approaches to predicting the resulting structures have long been limited to heuristic models. These models are often best suited for specific particle geometries or solvent conditions and cannot describe competition between multiple structures. This highlights the need for a general theory, rooted in thermodynamics, that can predict the morphological phase diagram for any molecular structure. We use statistical mechanics and coarse-grained simulations to highlight driving forces for amphiphile self-assembly and develop a theory that predicts the assembly of a variety of structures, including spherical micelles, fibers, and planar sheets. Our theory describes how the fraction and size of each aggregate changes as a function of tunable parameters such as system concentration, temperature, and molecular topology. We predict the transition between mesoscopic and macroscopic structures as a function of these molecular parameters. Our theory is able to qualitatively reproduce trends observed in silico as well as in experiments of a model polymer prodrug. This theoretical framework offers intriguing rational design strategies for controlling the size and morphology of self-assembling systems.