Stephan Förster : Polymer Quasicrystals and Archimedian Tilings

Polymer Quasicrystals and Archimedian Tilings

Stephan Förster

Universität Bayreuth

PhysicalChemistry 1

Bayreuth, Germany

Quasicrystals are a fascinating class of materials. Discovered in 1982 by Dan Shechtman for Al/Mn alloys (Nobel Prize 2011), they have since then been observed in more than 100 different metal alloys. Quasicrystals are ordered structures that lack translational symmetry and periodicity. This can lead to peculiar, crystallographically forbidden 5, 10- or 12-fold rotational symmetries. Interestingly there had also been reports on quasicrystals formed by soft polymeric materials. First considered as a mere lab curiosity they are now thought of being key structures to understand the fundamental principles of quasicrystal formation and stabilization.

In 2009 we discovered quasicrystals formed by a particularly simple polymer system, i.e. block copolymer micelles in concentrated aqueous solutions, and observed quasicrystalline structures of 12-fold and even 18-fold rotational symmetry. We have meanwhile discovered quasicrystals for many different micellar systems. Theory proposes as prerequisites for the formation of soft quasicrystals the existence of two different (incommensurate) characteristic length scales and the existence of three-body interactions. Both features are exhibited by micellar systems. The multitude of ordered structures formed by the self-assembly of such micellar systems can be described by simple two-dimensional Archimedian tilings, but also by much more complex tiling patterns.

Experimental studies require the preparation of single crystals, which is achieved by shear-orientation of multi-domain samples with in-situ monitoring by small-angle neutron (SANS) or X-ray scattering (SAXS). Detailed quasicrystal structure determination by diffraction methods turns out to be challenging, requiring higher-dimensional (5D or 7D) crystallography and the consideration of diffuse scattering features. By developing light-induced chemical cross-linking methods to fix the single crystalline sample structure it has become possible to obtain first images by cryo-scanning electron microscopy. Quasicrystalline structures of 12-fold and higher rotational symmetry exhibit nearly complete optical bandgaps which motivates current investigations into photonic devices and applications.