Phase behavior of deformable objects in two dimensions

Soft and deformable objects are prevalent in natural and synthetic systems, including micellar domains, microgel particles, foams, and biological cells. Understanding the phase behavior of these soft materials at high concentrations is essential for manipulating their long-range ordered structures. In this study, we employ a vertex dynamic model to explore the two-dimensional self-assembly of such small objects where thermal fluctuations are significant. In our model, interconnected polygons represent the assembly of soft objects, and the total energy of the configuration depends on the deviations in polygon area and perimeter from their preferred values. This simple model exhibits an order-disorder transition: at lower energy penalties for object deformation, the system adopts a disordered configuration, while at higher penalties, the objects organize into a hexagonal crystal lattice. The coarse-grained nature of the model also enables the formation of polycrystalline domains in the assembly thereby facilitating the study of the formation of the grain boundaries. We are also quantifying the effects of polydispersity and shear flow on the phase behavior in such systems.