Spatially Localized Quasicrystals

We investigate quasicrystal-forming soft matter such as dendrimers and star block copolymers, using a two-scale phase field crystal model. At state points near thermodynamic coexistence between bulk quasicrystals and the liquid phase, we find multiple metastable spatially localized quasicrystals embedded in a background of liquid. We use the terminology of spatially localized quasicrystals to refer to structures that turn into an extended quasicrystal in a continuous manner when a system parameter is varied. In two dimensions, we compute several families of spatially localized quasicrystals with dodecagonal structure and investigate their properties as a function of the system parameters. In three dimensions we obtain spatially localized icosahedral quasicrystals. In both 2D and 3D the localized quasicrystals are metastable, and so correspond to energetically locally favored structures. The presence of such structures is expected to crucially affect the dynamics of the crystallization process.