Complex Ordering of Soft Spheres in Block Polymer Melts

Hard sphere systems, such as low-z metallic elements and colloids, generally form densely packed crystalline states with BCC, FCC and HCP symmetry. In contrast, a certain self-assembling soft materials including block polymers, surfactants, and dendrimers have the capacity to order into more open crystalline structures. Recently, we have identified five discrete sphere-packing symmetries in poly(styrene-$b$-isoprene-$b$-styrene-$b$-ethylene oxide) (SISO) tetrablock terpolymers: BCC, Frank-Kasper $\sigma $-phase, dodecagonal quasicrystal (DQC), Pm$\bar{3}$n(A15), and non-close-packed hexagonal (sHEX). Some of these packing symmetries have been documented in certain heavy metals and organic dendrimers, and interestingly Landau theory anticipated a similar set of non-close-packed symmetries more than three decades ago. This talk will draw analogies between the ordering of spheres in soft and hard materials.