Three length scales colloidal gels: the clusters of clusters versus the interpenetrating clusters approach

TL;DR

This paper develops two models to describe the structure and rheology of colloidal gels with three length scales, comparing their predictions with experimental data to identify the most accurate structural description.

Contribution

It introduces two novel models for three-scale colloidal gels and validates them against experimental rheo-SAXS data, advancing understanding of gel microstructure.

Findings

Clusters of clusters model fits experimental data well.

Densification occurs as gel length scales increase.

Interpenetrating clusters model is less consistent with experiments.

Abstract

Typically, in quiescent conditions, attractive colloids at low volume fractions form fractal gels structured into two length scales: the colloidal and the fractal cluster scales. However when flow interfere with gelation colloidal fractal gels may display three distinct length scales [Dag\`es, et al., Soft Matter 18, 6645 (2022)]. Following those recent experimental investigations, we derive two models that account for the structure and the rheological properties of such atypical colloidal gels. The gel elasticity is inferred from scaling arguments and the structure is translated into scattering intensities following the global scattering functions approach proposed by Beaucage and typically measured in small angle X-ray scattering (SAXS). In both models, we consider that the colloids condensate into fractal clusters. In the clusters of clusters model, the clusters form superagregates which then build the gel network. In the interpenetrating clusters model, the clusters interpenetrate one-another to form the gel network. Those two models are then utilised to analyse rheo-SAXS experiments carried out on carbon black gels formed through flow cessation. The results of the analysis vouch for the clusters of clusters model with a densification of the structures as the gel characteristic length scales increase.