Quantitative investigation of the mean-field scenario for the structural glass transition from a schematic mode-coupling analysis of experimental data

Abstract

A quantitative application to real supercooled liquids of the mean-field scenario for the glass transition ($T_g$) is proposed. This scenario, based on an analogy with spin-glass models, suggests a unified picture of the mode-coupling dynamical singularity ($T_c$) and of the entropy crisis at the Kauzmann temperature ($T_K$), with $T_c>T_g>T_K$. Fitting a simple set of mode-coupling equations to experimental light-scattering spectra of two fragile liquids and deriving the equivalent spin-glass model, we can estimate not only $T_c$, but also the static transition temperature $T_s$ corresponding supposedly to $T_K$. For the models and systems considered here, $T_s$ is always found above $T_g$, in the fluid phase. A comparison with recent theoretical calculations shows that this overestimation of the ability of a liquid to form a glass seems to be a generic feature of the mean-field approach.