Micellar and Columnar Liquid Quasicrystals

Our recent high resolution AFM studies of the dodecagonal liquid quasicrystals formed from self-assembled soft micelles will be presented. The results has enabled us to locate the position of each individual micelle, and to examine in more detail of the tiling rules and 3-d arrangement of micelles in such structures. The implications of the findings for current tiling and structural models will be discussed. We present also the discovery of a new kind of liquid quasicrystals which are 2-dimensional and are formed from self-assembled columns. Previous studies on polyphilic Tand X-shaped molecules have revealed their ability to form complex two dimensional honeycomb-like structures of columns with polygonal cross-sections. The polygons found in those structures so far are triangles, squares, rhombi, pentagons, hexagons and, more recently, giant squares and octagons. The quasicrystalline symmetry of the new phase is clearly shown by the ”forbidden” 12-fold symmetry of the grazing incidence small-angle X-ray scattering pattern obtained from a thin film. The structure of an approximant at the vicinity of the new LQC columnar phase has been solved, suggesting for the LQC phase a tiling pattern consisting of triangles, squares and pentagons.