Theoretical Rationale for a Thermodynamic Glass State

Using a chemical potential route, the square-well (SW) fluid model is solved in a quasichemical approximation (QCSW). At low temperatures, the liquid reaches a limiting density greater than the triple point density of a SW fluid but less than the equilibrium liquid-to-solid transition density for hard spheres. As this unique density is approached with decreasing temperature, the liquid entropy also approaches an asymptotic value, thus averting the "entropy catastrophe". Mean-field models in the van der Waals (VDW) genre fail to predict this type of behavior. In VDW models, attractive force contributions to the equation of state incorrectly diverge with decreasing temperature as 1/T, whereas those for the QCSW model asymptote to a fixed value. The QCSW model posits the intuitively pleasing idea that, at high densities, attractive contributions to the configurational energy begin to saturate well before zero temperature is reached. As a consequence, the force balance between repulsive and attractive forces stabilizes the liquid density, which thereafter becomes effectively independent of temperature. This fixed density in turn fixes all other density-dependent thermodynamic properties. These low-temperature, force-stabilized states are identified as glass states.