Quasicrystal Formation in Two-Dimensional Assemblies of Deformable Particles

Since their discovery in 1982, quasicrystals (QCs) have been observed in soft matter systems such as block copolymers, giant surfactants, and star polymers, with potential applications in photonics, coatings, and membranes. Despite these advances, the thermodynamic mechanisms underlying QC formation remain poorly understood. Here, we study the 2D assembly of bidisperse deformable particles using a modified vertex model. System configuration is represented as interconnected polygons, with energy penalties for deviations in area and perimeter capturing dynamic size dispersity and resistance to shape deformation, respectively. We map the phase boundary between the dodecagonal QC approximant sigma phase and the disordered phase. Near this boundary, particles rearrange into distinct local environments, whose coexistence acts as a precursor to QC formation. By implementing quenching protocols, we tune the relative fractions of these environments to probe their role in nucleation, growth, and defect formation. Analysis of local configurations, particle rearrangements, and energy landscapes provides insight into how deformability and thermal fluctuations facilitate QC assembly, offering a route to controlling the formation of aperiodic order in soft matter.