(631c) Ordering of Sphere-Forming Block Polymers

Face-centered cubic (FCC) and hexagonally-packed spheres (HEX) are well-established as the most dense arrangements and lowest energy states of order for hard spheres, yet these structures rarely have been observed in block polymers. We recently have identified five different states of ordering in in poly(styrene-b-1,4-isoprene-b-styrene-b-ethylene oxide) (SISO) tetrablock terpolymers that form spherical domains: body-centered cubic (BCC), Frank-Kasper σ-phase, dodecagonal quasicrystals (DQC), Pm-3n (A15), and simple hexagonally packing (sHEX). Some of these sphere-packing symmetries have been documented in dendrimers, another form of soft material that is structurally distinct from linear block polymers, and the σ-phase has been reported in the heavy metal elements uranium and tantalum. Classically, the packing of hard spheres on a crystalline lattice has been modeled using simple pair-potentials such as the Lennard-Jones function. This lecture will consider how surrounding a spherical domain with a corona of polymer blocks modifies interparticle interactions leading to the remarkable compliment of ordered states.