Aperiodic tilings in self-assembled soft-matter quasicrystals

Aperiodic (quasicrystalline) tilings, such as Penrose's tiling, can be built up from (for example) kites and darts, squares and triangles, rhombi or shield-shaped tiles and can have a variety of different symmetries. However, almost all quasicrystals occurring in soft matter are of the dodecagonal (12-fold rotation symmetry) type, and many can be described in terms of square and equilateral triangular tiles. Here, we explore what contributes to the thermodynamic stability of soft-matter quasicrystals, both in two dimensions and in three, and how the details of how soft-matter particles interact leads to different kinds of aperiodic tilings. Although dodecagonal quasicrystals are the most common, this work points to how more general (beyond dodecagonal) quasicrystals can be designed in soft matter.

Alastair Rucklidge Brief bio:

After an education in engineering and theoretical physics and a PhD from Cambridge in Applied Mathematics in 1992, Alastair Rucklidge has made his career in the School of Mathematics at the University of Leeds. The overall aim of his research is to understand why different patterns are found in different circumstances: what are the mechanisms that are responsible for stabilising complex or disordered patterns in physical and chemical systems? At the simplest level, the question is "why do zebras have stripes and leopards have spots?" but there are more complex versions of this question in (for example) fluid dynamics, soft matter crystalisation and reaction-diffusion systems. In recent years he has focussed on understanding properties of quasicrystals, so named because they have symmetries (e.g., 12-fold rotation symmetry) that were, until the 1980s, thought to be forbidden.