Unwinding Spherical\nHelices Increases Entropy and\nStability of Frank–Kasper and Body-Centered-Cubic Periodic\nArrays To Facilitate Discrimination between Self-Organization Mechanisms

Spherical supramolecular dendrimers including helical,\nself-organize\nsoft Frank–Kasper, other cubic such as body-centered cubic,\nand quasicrystal periodic and quasiperiodic arrays. When any of these\nperiodic or quasiperiodic arrays forms immediately above a columnar\nphase, a supramolecular orientational memory effect was found to discriminate\nbetween mechanisms of self-organization of supramolecular spheres\nand generate unprecedented periodic arrays of helical columns which\ncannot be constructed by any other methodology. Here, we demonstrate\nthat unwinding spherical helices, via their precursor nonhelical columns,\nincreases the entropy and stability of their periodic and quasiperiodic\nspherical arrays and places the Frank–Kasper and other cubic\nphases immediately above the columnar phase. This process is not available\nin biology where spherical viruses self-organize body-centered cubic\nlattices. However, this concept reengineers, on increasing temperature,\nthe originally expected position of the periodic and quasiperiodic\narray versus that of the columnar lattice. This process facilitates\ndiscrimination between different self-organization mechanisms of supramolecular\nspheres and also mediates the emergence of unprecedentedly complex\nand technologically important periodic arrays of nonhelical columns.