Pinch-point Singularities in Stress-Stress Correlations Reveal Rigidity in Colloidal Gels

TL;DR

This paper shows that stress correlations in 2D colloidal gels can be understood through a theory of emergent elasticity, revealing how rigidity influences stress transmission and the presence of pinch-point singularities.

Contribution

It applies a vector charge theory to describe stress correlations in colloidal gels, distinguishing rigid from floppy states and exploring stress transmission mechanisms.

Findings

Stress correlations match theoretical predictions for rigid gels.

Pinch-point singularities indicate the degree of rigidity.

Evidence of a Debye-like screening effect at certain length scales.

Abstract

We demonstrate that the spatial correlations of microscopic stresses in 2D model colloidal gels obtained in computer simulations can be quantitatively described by the predictions of a theory for emergent elasticity of pre-stressed solids (vector charge theory). By combining a rigidity analysis with the characterization provided by the stress correlations, we show that the theoretical predictions are able to distinguish rigid from floppy gels, and quantify that distinction in terms of the size of a pinch-point singularity emerging at large length scales, which, in the theory, directly derives from the constraints imposed by mechanical equilibrium on the internal forces. We also use the theoretical predictions to investigate the coupling between stress-transmission and rigidity, and we explore the possibility of a Debye-like screening mechanism that would modify the theory predictions below a characteristic length scale.