Molecular Frustration and Formation of Lyotropic Liquid Crystalline Frank-Kasper Phases

Minimally hydrated amphiphiles self assemble into lyotropic liquid crystals (LLCs), which exhibit periodic aqueous and hydrophobic nanodomains. Commonly observed lyotropic mesophases include 1D lamellae, 2D columnar phases, 3D bicontinuous networks, and high symmetry 3D sphere packings. Based on hard sphere packings, spherical micelles are intuitively expected to form high symmetry body-centered cubic, face-centered cubic, and hexagonally close-packed structures. However, we recently discovered ionic surfactant micelles can spontaneously produce a low symmetry, tetrahedrally close-packed Frank-Kasper (FK) sigma phase with exceptional long-range translational order. The LLC sigma phase comprises micelles of five different and discrete sizes, which are arranged into a large tetragonal unit cell containing 30 particles. This and other new, low symmetry FK phases arise from a frustrated non-covalent force balance that minimizes local variations in amphiphile solvation, while maximizing global micelle cohesion within the ensemble. We will focus on how surfactant structure dictates lyotropic sphere packing symmetry selection and the thermodynamic stabilities of these complex assemblies. This work may inform new methods for harnessing frustration in self-assembled systems to access complex periodic and aperiodic structures derived from various building blocks.