PhD defence: Patterns Beyond Periodicity - Complex Ordering from Quasicrystals to Supraparticles in Soft Matter

My PhD thesis investigates how complex ordered structures emerge in soft-matter systems composed of colloidal particles. Unlike conventional crystals, which exhibit periodic order, many soft-matter systems form more intricate structures such as quasicrystals and hierarchical assemblies whose organisation is governed by entropy, confinement, and particle interactions. The goal of this thesis is to understand the mechanisms that drive the formation and stability of such structures.

First, my collaborators and I study twelve-fold symmetric square-triangle quasicrystals that commonly appear in soft-matter systems. Through Monte Carlo simulations and entropy calculations, we demonstrate that point-like defects can enhance the stability of these quasicrystals by significantly increasing their configurational entropy. This provides a thermodynamic explanation for the high defect concentrations observed in experiments.

Second, we develop computational tools for structural analysis in particle systems. We introduce an adapted solid-angle nearest-neighbor algorithm suitable for systems with low coordination numbers and compare several unsupervised machine-learning methods for identifying local structural motifs in colloidal assemblies.

Finally, we investigate the self-assembly of binary colloidal particles confined within spherical droplets. Simulations reveal that geometric confinement can drive the entropy-driven formation of a polycrystalline AlB₂-type superlattice, illustrating how confinement can guide the formation of complex supraparticles.

Together, these studies provide new insight into how entropy, defects, and confinement govern the formation of complex structures in soft matter, bridging quasicrystals, particle-based simulations, and hierarchical self-assembly.