Direct AFM observation of individual micelles, tile decorations and tiling rules of a dodecagonal liquid quasicrystal

Abstract

We performed an atomic force microscopy study of the dendron-based dodecagonal quasicrystal, the material that had been reported in 2004 as the first soft quasicrystal. We succeeded in orienting the 12-fold axis perpendicular to the substrate, which allowed the imaging of the quasiperiodic xy plane. Thus for the first time we have been able to obtain direct real-space information not only on the arrangement of the tiles, but also on their ‘decorations’ by the individual spherical micelles or ‘nanoatoms’. The high-resolution patterns recorded confirm the square-triangle tiling, but the abundance of different nodes corresponds closely to random tiling rather than to any inflation rule. The previously proposed model of three types of decorated tiles, two triangular and one square, has been confirmed; the basic Frank–Kasper mode of alternating dense-sparse-dense-sparse layer stacking along z is confirmed too, each of the four sublayers being 2 nm thick. The consecutive dense layers are seen to be rotated by 90°, as expected. The 2 nm steps on the surface correspond to one layer of spheres, nonetheless with a dense layer always remaining on top, which implies a layer slip underneath and possibly the existence of screw dislocations.

Breaking Parallel Orientation of Rods via a Dendritic Architecture toward Diverse Supramolecular Structures

“…In the two‐dimensional ab plane, the DQC only possesses 3‐fold, 4‐fold, and 6‐fold rotational symmetry and without translational operations . From the BF TEM image along the [00001] direction (Figure B (vi)), representative tiling patterns (3 6 , 4 4 , 3 3 .4 2 and 3 2 .4.3.4) with similar abundance corresponding to DQC phase as reported before can be identified, further confirming the formation of the DQC phase …”

Expanding quasiperiodicity in soft matter: Supramolecular decagonal quasicrystals by binary giant molecule blends

“…4 F , Middle ). This redistribution on a submesoatomic level further change the packings on the mesoatomic level, affording the characteristic “triangle square” tiling elements for DDQC and FK σ structures ( 23 ). Inherited from the random tiling in DQC-SLs, the random distribution of these “triangle square” tiling elements leads to a metastable DDQC-SL ( 20 , 43 ).…”

“…in 1984 ( 2 ), various QC alloys have been successively identified ( 3 , 4 ), and among them are three-dimensional (3D) icosahedral QCs (IQC) ( 5 – 10 ), 10-fold two-dimensional (2D) decagonal QCs (DQC) ( 11 – 14 ), and 12-fold 2D dodecagonal QCs (DDQC) ( 15 , 16 ). Recently, various condensed soft matters [e.g., block copolymers ( 17 – 21 ), dendrimers ( 22 , 23 ), and giant molecules ( 24 – 26 )] were also reported to form supramolecular DDQCs by a hierarchical assembling procedure. In these cases, the submesoatomic (molecular) units first aggregate into mesoatoms (i.e., the supramolecular spherical motifs compared to “atoms” in the metal alloy crystals), and then, the mesoatoms further assemble into the quasicrystalline superlattices (QC-SLs).…”

Molecular ejection transition in liquid crystal columns self-assembled from wedge-shaped minidendrons

“…In many fan-shaped molecules the 2d-ordered columnar phase that appears at lower temperatures transforms on heating to one or a series of 3d spherical micellar phases. These have their counterparts in metals and are either cubic such as Pm3n (A15) 5 and body-centered cubic (BCC) 6 , or tetragonal (α-phase) 7 or even quasicrystalline 8,9 . Interestingly, all phases observed so far in these series of compounds can be seen in the simplest of them, known as 'minidendrons' [10][11][12] (see e.g.…”