Preface

As well-known quasicrystals with 12-fold symmetry observed since 2004 in liquid crystals, colloids, polymers and nanoparticles have been received a great deal of attention. In particular, 18-fold symmetry quasicrystals in colloids were discovered in 2011. More recently the quasicrystals with 12-fold symmetry were also found in giant surfactants. The formation mechanisms of these kinds of quasicrystals are connected closely with self-assembly of spherical building blocks by supramolecules, compounds, block copolymers and so on and are quite different from that of the metallic alloy quasicrystals. They can be identified as soft-matter quasicrystals exhibiting natures of quasicrystals with soft-matter characters. Soft matter lies in the behaviour of intermediate phase between solid and simple fluid, while the nature of quasicrystals exhibits importance of symmetry as they are highly ordered phase. These features are very complex yet extremely interesting and attractive. Hence, they have raised a great deal of attention of researchers in physics, chemistry and materials science. All the observed soft-matter quasicrystals so far are two-dimensional quasicrystals. It is well known that two-dimensional quasicrystals consist of only two distinct types from the angle of symmetry theory, one being 5-, 8-, 10and 12-fold symmetries, the other being 7-, 9-, 14and 18-fold according to the symmetry theory. Therefore, two terminological phrases can be defined such as the first and second kinds of two-dimensional quasicrystals respectively. The two-dimensional solid quasicrystals observed so far belong to the first kind ones only, while soft-matter quasicrystals discovered up to now can be in both kinds. This may imply that many new types of soft-matter quasicrystals in addition to those with 12and 18-fold symmetries may be observed in the near future. Hence, the interdisciplinary studies on soft-matter quasicrystals present great potential and hopeful research topics. However, some difficulties exist in studying those new phases due to the complexity of their structures and lack of fundamental experimental data including the material constants to date. Furthermore, the theoretical studies are also difficult. For example, the symmetry groups of soft-matter quasicrystals observed or possibly to be observed have not yet been well investigated although there are some work