Unwinding Spherical Helices Increases Entropy and Stability of Frank–Kasper and Body-Centered-Cubic Periodic Arrays To Facilitate Discrimination between Self-Organization Mechanisms

Spherical supramolecular dendrimers including helical, self-organize soft Frank-Kasper, other cubic such as body-centered cubic, and quasicrystal periodic and quasiperiodic arrays. When any of these periodic or quasiperiodic arrays forms immediately above a columnar phase, a supramolecular orientational memory effect was found to discriminate between mechanisms of self-organization of supramolecular spheres and generate unprecedented periodic arrays of helical columns which cannot be constructed by any other methodology. Here, we demonstrate that unwinding spherical helices, via their precursor nonhelical columns, increases the entropy and stability of their periodic and quasiperiodic spherical arrays and places the Frank-Kasper and other cubic phases immediately above the columnar phase. This process is not available in biology where spherical viruses self-organize body-centered cubic lattices. However, this concept reengineers, on increasing temperature, the originally expected position of the periodic and quasiperiodic array versus that of the columnar lattice. This process facilitates discrimination between different self-organization mechanisms of supramolecular spheres and also mediates the emergence of unprecedentedly complex and technologically important periodic arrays of nonhelical columns.