Correlated rigidity percolation and colloidal gels

TL;DR

This paper demonstrates that structural correlations significantly influence rigidity percolation in colloidal gels, lowering the transition point and aligning theoretical models with experimental observations of gelation.

Contribution

It introduces a lattice model and molecular dynamics simulations to show how attractive interactions induce correlations that shift the rigidity percolation threshold.

Findings

Structural correlations lower the RP transition volume fraction.

Attractive interactions increase correlations in colloidal systems.

Experimental data agrees with the model's predictions.

Abstract

Rigidity percolation (RP) occurs when mechanical stability emerges in disordered networks as constraints or components are added. Here we discuss RP with structural correlations, an effect ignored in classical theories albeit relevant to many liquid-to-amorphous-solid transitions, such as colloidal gelation, which are due to attractive interactions and aggregation. Using a lattice model, we show that structural correlations shift RP to lower volume fractions. Through molecular dynamics simulations, we show that increasing attraction in colloidal gelation increases structural correlation and thus lowers the RP transition, agreeing with experiments. Hence colloidal gelation can be understood as a RP transition, but occurs at volume fractions far below values predicted by the classical RP, due to attractive interactions which induce structural correlation.