Quantifying The Mechanical Energy Landscape of Two-Dimensional Cellular Matter*

The local mechanical equilibrium states of cellular materials - consisting of space-filling domains with dominant interfacial energy - are characterized by a spectrum of metastable-state energies on a generally complex landscape. Recent theoretical work quantifies these energies in dramatically simpler ways exploiting geometric and topological statistical information from the structure of the system only, independent of the specific energy functional [1]. We elaborate on and test these theories by analyzing cellular matter samples, particularly in foam monolayer systems, where energies can be directly and independently determined. Two approaches to inferring energies are tested using (i) measured lengths of select boundaries between domains; (ii) the probability distribution of domain sizes and topologies. The experimental results support both theories and elucidate advantages and disadvantages of either approach. It is thus practically demonstrated that the mechanical state of cellular matter is quantifiable by its morphology only, suggesting simple and general diagnostic tools in the study of systems as diverse as biological tissues, foams, or superlattice materials.

[1] S. Kim. Y. Wang, and S. Hilgenfeldt, Phys. Rev. Lett. 120, 24801 (2018).