From Order to Disorder: Soft Particle Assemblies with Fluctuating Sizes in 2D

Soft and deformable particles are common in micelles, microgels, foams, and biological cells. Understanding their collective behavior at high concentrations is key to controlling structural order. We use a modified Voronoi model to study the packing of deformable particles in two dimensions under thermal fluctuations. Each particle is represented as an interconnected polygon, with energy penalties for deviations in area and perimeter from preferred values. The area and perimeter terms respectively capture dynamic size dispersity—analogous to chain or solvent exchange—and particle line tension that resists shape deformation. The system exhibits an order–disorder transition (ODT): low line tension leads to disordered states, while higher tension stabilizes hexagonal crystals. Increasing dynamic size dispersity shifts the ODT to higher line tensions. Analysis of particle-size distributions, defect barriers, and Voronoi entropy reveals that reduced area penalties facilitate defect formation, explaining this trend. In regimes far from the ODT, displacement fields from normal mode analysis reproduce structural fluctuations, confirming that deviations from the hexagonal lattice primarily arise from thermal motion rather than defects.