Random energy model for dynamics in supercooled liquids: N dependence

Area of Science:

• Condensed Matter Physics
• Statistical Mechanics
• Computational Chemistry

Background:

• Thermodynamic properties of liquids are derived from unconditional state distributions.
• Liquid dynamics necessitate understanding the distribution of energies between connected states.
• Previous uncorrelated random energy models (REM) exhibit limitations in the thermodynamic limit.

Purpose of the Study:

• To develop an improved random energy model (REM) for analyzing critical points in liquid potential energy landscapes.
• To derive a more accurate distribution function G(c)(E';E) for connected state energies.
• To investigate the implications for liquid dynamics, configuration entropy, and supercooled liquid behavior.

Main Methods:

• Development of a new, simple expression for the connected energy distribution G(c)(E';E).
• Calculation of key properties: fraction of imaginary-frequency instantaneous normal modes (f(u)), configuration entropy (S(c)), critical point distributions, and escape rates (R).
• Fitting simulation data for Lennard-Jones and CS2 liquids to determine model parameters and validate the theory.

Main Results:

• The refined REM yields reasonable dependencies on system size (N).
• A universal scaling form for f(u) is established, enabling consistent calculation of mode-coupling temperatures (T(c)).
• The self-diffusion constant (D) is shown to be proportional to f(u) in deeply supercooled states.

Conclusions:

• The enhanced REM provides a robust framework for understanding liquid dynamics and critical phenomena.
• The model successfully interprets the phenomenology of fragile supercooled liquids.
• The random energy model (REM) does not necessitate a Kauzmann transition above the glass transition temperature.