Dynamics of wire frame glasses in two dimensions

TL;DR

This study models the dynamics of wire frame particles in 2D suspensions, revealing distinct behaviors from rods, including a critical concentration leading to immobilization and differences in stress response.

Contribution

It introduces a 2D model for wire frame particles, deriving their mean squared displacement and rheological properties, highlighting unique dynamical and stress behaviors compared to rods.

Findings

Wire frames become frozen above a critical concentration.

Wire frames exhibit larger initial elastic stress than rods.

Stress in wire frames persists indefinitely above the critical concentration.

Abstract

The dynamics of wire frame particles in concentrated suspension are studied by means of a 2D model and compared to those of rod-like particles. The wire frames have bent or branched structures constructed from infinitely thin rigid rods. In the model, a particle is surrounded by diffusing points that it cannot cross. We derive a formal expression for the mean squared displacement (MSD) and, by using a self-consistent approximation, we find markedly different dynamics for wire frames and rods. For wire frames, there exists a critical concentration of points above which they become frozen with the long time MSD reaching a plateau. Rods, on the other hand, always diffuse by reptation. We also study the rheology through the elastic stress, and more striking differences are found; the initial magnitude of the stress for wire frames is much larger than for rods, scaling like the square of the point concentration, and above the critical concentration, the stress for wire frames appears to persist indefinitely while for rods it always decays.