Ideal glass transitions for hard ellipsoids

TL;DR

This paper develops a comprehensive theoretical phase diagram for ideal glass transitions in hard ellipsoids, revealing how shape and orientation influence glass formation and identifying three distinct transition types.

Contribution

It introduces a unified equations-based framework covering all aspect ratios and packing fractions, highlighting the role of orientational degrees of freedom in glass transitions.

Findings

Three types of glass transition lines identified.

Orientational degrees dominate for high aspect ratios.

Precursor nematic instability influences glass formation.

Abstract

For hard ellipsoids of revolution we calculate the phase diagram for the idealized glass transition. Our equations cover the glass physics in the full phase space, for all packing fractions and all aspect ratios X$_0$. With increasing aspect ratio we find the idealized glass transition to become primarily be driven by orientational degrees of freedom. For needle or plate like systems the transition is strongly influenced by a precursor of a nematic instability. We obtain three types of glass transition lines. The first one ($\phi_c^{(B)}$) corresponds to the conventional glass transition for spherical particles which is driven by the cage effect. At the second one ($\phi_c^{(B')}$) which occurs for rather non-spherical particles a glass phase is formed which consists of domains. Within each domain there is a nematic order where the center of mass motion is quasi--ergodic, whereas the inter--domain orientations build an orientational glass. The third glass transition line ($\phi_c^{(A)}$) occurs for nearly spherical ellipsoids where the orientational degrees of freedom with odd parity, e.g. 180$^o$ flips, freeze independently from the positions.