Laboratoire Matière et Systèmes Complexes

Thermally driven order-disorder transition in 2D soft cellular systems

Marc Durand

Foams, emulsions, and confluent biological tissues are examples of Soft Cellular Systems : they are constituted of highly deformable — yet almost incompressible — units (bubbles, drops, cells,...), interacting through attractive adhesive interactions and soft steric repulsions. At two dimensions, these systems offer natural tesselations of plane, in which transitions from ordered to disordered patterns are often observed, in both directions. In confluent tissues in particular, there is growing indication that order-disorder transitions play a role during various biological processes.

Over the last years, special attention has been given to the glass transition in soft cellular systems, i.e. in the transition from a disordered, solid phase to a disordered, liquid phase. In contrast, order-disorder transitions received little attention from a theoretical point of view. Due to their unique high deformability–low compressibility feature, interactions between the cellular units are not pairwise additive. Many-body interactions are known to affect the mechanical properties of cellular systems; they also make the phase transition scenario uncertain.

In this talk, I will present a numerical exploration of the order-disorder transition in two-dimensional cellular systems driven by thermal agitation. For this purpose, we used a modified Cellular Potts Model algorithm that captures contour fluctuations at the cellular scale, and allows rapid thermalization of large systems. We compare our findings with the standard defect-mediated theories for melting of two-dimensional solids, including the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) theory.