Spinodal curve of some supercooled liquids

There exist two possible limits to the extent to which a liquid can be supercooled: the Kauzmann temperature and the spinodal curve. The virial theorem imposes severe constraints on the type of interactions that can give rise to loss of mechanical stability upon supercooling and therefore to a supercooled liquid spinodal. Systems composed of particles interacting via pair potentials whose repulsive core has a positive curvature (such as the Lennard-Jones potential) cannot become mechanically unstable upon supercooling. Systems composed of particles interacting via potentials whose repulsive core is softened by a curvature change are capable of losing stability upon supercooling, and of contracting when heated isobarically. This is consistent with the idea that loss of stability upon supercooling can only occur for liquids capable of contracting when heated. Microscopically, this occurs via the formation of open structures which can be collapsed into denser arrangements through the input of thermal and mechanical energy. In the quasichemical approximation, a very simple model of a core-softened fluid the lattice gas with attractive nearest-neighbor and repulsive next-nearest-neighbor interactions, exhibits density anomalies in one, two, and three dimensions, and a reentrant, continuous spinodal bounding the superheated, supercooled, and subtriple liquid states in three dimensions.