Theoretical Rationale for a Thermodynamic Glass State

Area of Science:

• Thermodynamics
• Statistical Mechanics
• Materials Science

Background:

• Mean-field models like van der Waals (VDW) fail to accurately describe liquid behavior at low temperatures.
• VDW models predict unrealistic divergences in attractive forces as temperature decreases.
• Understanding low-temperature liquid states is crucial for materials science and thermodynamics.

Purpose of the Study:

• To investigate the behavior of the square-well (SW) fluid model at low temperatures using a quasichemical approximation (QCSW).
• To determine if the QCSW model can predict a stable liquid state and avoid the theoretical "entropy catastrophe" at low temperatures.
• To compare the QCSW model's predictions with those of mean-field VDW models.

Main Methods:

• Solving the square-well (SW) fluid model using a chemical potential route.
• Employing the quasichemical approximation (QCSW) for theoretical calculations.
• Analyzing the behavior of liquid density and entropy as temperature decreases.

Main Results:

• The QCSW model predicts a limiting liquid density at low temperatures, falling between the SW triple point density and the hard sphere transition density.
• Liquid entropy approaches an asymptotic value, thus preventing the "entropy catastrophe".
• Attractive force contributions in the QCSW model asymptote to a fixed value, unlike the 1/T divergence in VDW models.

Conclusions:

• The QCSW model successfully predicts a stable, force-stabilized liquid state at low temperatures, identified as glass states.
• Attractive forces saturate at high densities, leading to a temperature-independent liquid density and fixed thermodynamic properties.
• The QCSW model offers a more accurate description of liquid behavior at low temperatures compared to VDW models.