Dynamic Overlap Concentration Scale of Active Colloids

TL;DR

This paper introduces a dynamic overlap concentration scale for active colloids, revealing universal features of their mechanical properties and providing a new framework to understand their behavior through simulations and theoretical analysis.

Contribution

The paper defines a new run-length dependent concentration scale, $^*$, for active colloids, unifying their mechanical behavior and revealing previously unreported features.

Findings

$^*$ delineates distinct concentration regimes affecting particle trajectories.

Simulation results confirm $^*$'s role in collapsing the equation-of-state.

Inclusion of $^*$ alters predictions of colloidal stability and spinodal behavior.

Abstract

By introducing the notion of a dynamic overlap concentration scale, we identify universal and previously unreported features of the mechanical properties of active colloids. These features are codified by recognizing that the characteristic length scale of an active particle's trajectory, the run-length, introduces a new concentration scale $\phi^*$. Large-scale simulations of repulsive active Brownian particles (ABPs) confirm that this new run-length dependent concentration, which is the trajectory-space analogue of the overlap concentration in polymer solutions, delineates distinct concentration regimes in which interparticle collisions alter particle trajectories. Using $\phi^*$ and concentration scales associated with colloidal jamming, the mechanical equation-of-state for ABPs can be collapsed onto a set of principal curves that contain a number of previously overlooked features. The inclusion of these features qualitatively alters previous predictions of the behavior for active colloids as we demonstrate by computing the spinodal for a suspension of purely-repulsive ABPs. Our findings suggest that dynamic overlap concentration scales should be of great utility in unraveling the behavior of active and driven systems.