Colloidal gelation with variable attraction energy

TL;DR

This paper develops an analytical approximation for colloidal gelation dynamics incorporating variable attraction energy, predicting key properties like viscosity and gelation time based on cluster fractal dimension and initial conditions.

Contribution

It introduces a novel approximation scheme linking cluster fractal dimension with gelation behavior, extending understanding of nonequilibrium gelation processes in colloids.

Findings

Viscosity, gelation time, and cluster size are analytically predicted as functions of time and parameters.

Fractal dimension modulates the gelation process and transition dynamics.

Homogeneous nucleation and Lifshitz-Slyozov coarsening are recovered under specific conditions.

Abstract

We present an approximation scheme to the master kinetic equations for aggregation and gelation with thermal breakup in colloidal systems with variable attraction energy. With the cluster fractal dimension $d_{f}$ as the only phenomenological parameter, rich physical behavior is predicted. The viscosity, the gelation time and the cluster size are predicted in closed form analytically as a function of time, initial volume fraction and attraction energy by combining the reversible clustering kinetics with an approximate hydrodynamic model. The fractal dimension $d_{f}$ modulates the time evolution of cluster size, lag time and gelation time and of the viscosity. The gelation transition is strongly nonequilibrium and time-dependent in the unstable region of the state diagram of colloids where the association rate is larger than the dissociation rate. Only upon approaching conditions where the initial association and the dissociation rates are comparable for all species (which is a condition for the detailed balance to be satisfied) aggregation can occur with $d_{f}=3$. In this limit, homogeneous nucleation followed by Lifshitz-Slyozov coarsening is recovered. In this limited region of the state diagram the macroscopic gelation process is likely to be driven by large spontaneous fluctuations associated with spinodal decomposition.