Linking density functional and mode coupling models for supercooled liquids

TL;DR

This paper compares thermodynamic density functional theory and dynamic mode coupling theory models for supercooled liquids, showing that their predictions for particle localization are quantitatively similar.

Contribution

It bridges the gap between thermodynamic and dynamic models of supercooled liquids by relating their mass localization parameters.

Findings

Localization parameters from DFT and MCT are of comparable magnitude.

Both models predict similar particle localization characteristics.

The comparison provides insight into the connection between thermodynamic and dynamic descriptions.

Abstract

We compare predictions from two familiar models of the metastable supercooled liquid respectively constructed with thermodynamic and dynamic approach. In the so called density functional theory (DFT) the free energy $F[\rho]$ of the liquid is a functional of the inhomogeneous density $\rho({\bf r})$. The metastable state is identified as a local minimum of $F[\rho]$. The sharp density profile characterizing $\rho({\bf r})$ is identified as a single particle oscillator, whose frequency is obtained from the parameters of the optimum density function. On the other hand, a dynamic approach to supercooled liquids is taken in the mode coupling theory (MCT) which predict a sharp ergodicity-nonergodicity transition at a critical density. The single particle dynamics in the non-ergodic state, treated approximately, represents a propagating mode whose characteristic frequency is computed from the corresponding memory function of the MCT. The mass localization parameters in the above two models (treated in their simplest forms) are obtained respectively in terms of the corresponding natural frequencies depicted and are shown to have comparable magnitudes.