Exact treatment of interface fluctuations in a two-dimensional emulsion

Summary

We present a model for a polydisperse ensemble of two-dimensional droplets wich accounts for the effects of arbitrarily large distortions of the droplet shape. Interactions within a droplet include bending rigidity and spontaneous curvature. Interactions between droplets are omitted. Even at high temperatures, the effects of the shape fluctuations on the droplet size distribution remain small, as they are dominated by the contributions from the mixing entropy. In contrast, shape fluctuations lead to a pronounced peak in thermodynamic quantities like specific heat. This peak occurs at temperatures where thermal excitations become of the order of the bending energies of the droplet surface. The fluctuation-dominated regime extends to temperatures far lower than expected from a mean-field calculation.