Statistical thermodynamic foundation for mesoscale aggregation in ternary mixtures

Ternary solvent mixtures with two mutually miscible and one immiscible solvent pairings often exhibit persistent scattering profiles corresponding to mesoscale structure formation. Despite the morphological information on such mesostructures via extensive scattering measurements and simulation, the origin of these mesostructures, why they persist over a wide composition range, and why they appear around the plait point have remained a mystery. Here we answer all these questions through constructing a fundamental molecular thermodynamic theory, synthetizing thermodynamic stability, scattering and the fluctuation solution theory. The plait point condition, when interpreted via differential geometry, is shown to be the origin of the large structure factor persistent over a wide composition range.