A path integral approach for the colloidal glass transition based on an analogy with the $\lambda$-transition in liquid helium

TL;DR

This paper introduces a novel model for the colloidal glass transition inspired by Feynman's theory of the lambda transition in liquid helium, focusing on configuration counting of dynamic heterogeneities.

Contribution

It applies a path integral approach to colloidal glasses, linking the transition to configuration distributions of loops, strings, and clusters, and incorporates confinement effects.

Findings

Predicts the glass transition volume fraction from heterogeneity distributions

Provides a framework to calculate confinement effects on $\,\,\,\,\,\,\,\,\,\,",

Abstract

We describe a model for the colloidal glass transition that is based on Feynman's theory for the $\lambda$-transition in liquid helium. Our model essentially counts the number of configurations of dynamic loops, strings or clusters of different sizes, and determines the glass transition volume fraction $\phi_{g}$ from the distribution of these heterogeneities. Since confinement restricts the available number of configurations for these loops, strings and clusters, its effect on $\phi_{g}$ can also be calculated in a relatively straightforward manner.