Percolation in binary and ternary mixtures of patchy colloids

TL;DR

This study explores percolation phenomena in binary and ternary mixtures of patchy colloids through theoretical models and Monte Carlo simulations, revealing multiple percolated states and their stability factors.

Contribution

It introduces a theoretical framework for analyzing percolation in complex colloidal mixtures and identifies eight distinct percolated states in ternary systems.

Findings

Up to eight different percolated states in ternary mixtures.

Strongest gel is a tricontinuous gel with all species percolated.

Theoretical and simulation results agree well, except for temperature thresholds.

Abstract

We investigate percolation in binary and ternary mixtures of patchy colloidal particles theoretically and using Monte Carlo simulations. Each particle has three identical patches, with distinct species having different types of patch. Theoretically we assume tree-like clusters and calculate the bonding probabilities using Wertheim's first-order perturbation theory for association. For ternary mixtures we find up to eight fundamentally different percolated states. The states differ in terms of the species and pairs of species that have percolated. The strongest gel is a trigel or tricontinuous gel, in which each of the three species has percolated. The weakest gel is a mixed gel in which all of the particles have percolated, but none of the species percolates by itself. The competition between entropy of mixing and internal energy of bonding determines the stability of each state. Theoretical and simulation results are in very good agreement. The only significant difference is the temperature at the percolation threshold, which is overestimated by the theory due to the absence of closed loops in the theoretical description.