(15e) Self-Assembly of Deformable Particles in Two Dimensions

Soft and deformable objects are common in both natural and synthetic systems, such as micellar domains, microgel particles, foams, and biological cells. Understanding the phase behavior of these soft materials at high concentrations is crucial for controlling their long-range ordered structures. In this study, we use a vertex model to investigate the self-assembly of deformable particles in two dimensions, where thermal fluctuations play a significant role. In our model, interconnected polygons represent the assembly of particles. The total energy of the system is expressed in terms of two energy penalty components: the deviations in polygon area and polygon perimeter from their preferred values. This simple model displays an order-disorder transition (ODT): when energy penalties on polygon perimeters are low, the system adopts a disordered configuration, whereas at higher penalties, the particles arrange into a hexagonal crystal lattice. When we introduce a large dynamic particle size dispersity into the assembly, we find that the minimum energy penalty on perimeters required for the occurrence of the ODT is larger. We explain this phenomenon by comparing particle shapes and energy barriers for defect formation in the cases studied.