Geometry of Empty Space is the Key to Near-Arrest Dynamics

TL;DR

This paper investigates kinetically constrained lattice models, identifying two regimes of dynamical slowing through accessible volume metrics, and explores their relation to self-diffusion and scaling near dynamical arrest.

Contribution

It introduces a new response function based on dynamically accessible volume to distinguish regimes and analyzes the connection between hole density and self-diffusion in these models.

Findings

Two distinct dynamical regimes with a sharp transition.

A new response function effectively characterizes dynamical slowing.

Evidence of scaling behavior near dynamical arrest.

Abstract

We study several examples of kinetically constrained lattice models using dynamically accessible volume as an order parameter. Thereby we identify two distinct regimes exhibiting dynamical slowing, with a sharp threshold between them. These regimes are identified both by a new response function in dynamically available volume, as well as directly in the dynamics. Results for the selfdiffusion constant in terms of the connected hole density are presented, and some evidence is given for scaling in the limit of dynamical arrest.