Diversity in liquid supercooling and glass formation phenomena illustrated by a simple model

The opportunity to map condensed-phase inherent structures (potential energy minima) approximately onto the vertices of a high-dimensional hypercube provides simple conceptual and numerical modeling for first-order melting-freezing transitions, as well as for liquid supercooling and glass formation phenomena. That approach is illustrated here by examination of three interaction examples that were selected to demonstrate the diversity of thermodynamic behavior possible within this hypercube modeling technique. Two of the cases behave, respectively, as "strong" and "fragile" glass formers, at least as judged by their heat capacities. The third presents a "degenerate glass," wherein full equilibration of the supercooling liquid (i.e., no kinetic arrest) leads to (a) residual entropy in the limit of absolute zero temperature, and (b) a linear temperature dependence of heat capacity in the same limit. None of the three cases displays a positive-temperature ideal (intrinsic) glass transition.