Corresponding States of Structural Glass Formers. II

TL;DR

This paper extends the application of a parabolic relaxation time formula for fragile glass formers, showing it captures effects of attractive forces and suggests certain parameters are intrinsic material properties, unlike other fitting models.

Contribution

It demonstrates the universality of the parabolic relaxation formula and identifies key parameters as material-specific, contrasting with other models whose parameters depend on data range.

Findings

The parabolic formula accurately describes relaxation times below the onset temperature.

Material properties can be inferred from parameters J and T_o.

Other fitting formulas' parameters depend on data range and are less universal.

Abstract

The earlier paper of this same title demonstrated a collapse of relaxation data of fragile supercooled glass forming liquids [\textit{J. Phys. Chem. B} \textbf{113}, 5563-5567 (2009)]. For temperature $T$ below that of the onset to supercooled behavior, $T_{\mathrm{o}}$, the logarithm of structural relaxation time, $\log \tau$, is given by the parabolic form $\log (\tau/\tau_{\mathrm{o}}) \, =\, J^2(1/T - 1/T_{\mathrm{o}})^{2}$, where $J$ and $\tau_{\mathrm{o}}$ are temperature independent. This paper presents further applications of this formula. In particular, it is shown that the effects of attractive forces in numerical simulation of glass forming liquids can be logically organized in terms of $J$ and $T_{\mathrm{o}}$. Further, analysis of experimental data for several systems suggests that $J$ and $T_{\mathrm{o}}$ are material properties. In contrast, values of similar parameters for other fitting formulas are shown to depend not only upon the material but also upon the range of data used in fitting these formulas. Expressions demonstrated to fail in this way include the Vogel-Fulcher-Tammann formula, a double-exponential formula, and a fractional exponential formula.