Lattice animals in diffusion limited binary colloidal system

TL;DR

This paper models irreversible diffusion-limited aggregation in binary colloids, revealing the presence of lattice animals with a fractal dimension of 2 and proposing a universal parameter for such systems.

Contribution

It introduces the concept of lattice animals in binary colloids, predicts bigel formation, and proposes a universal scaling parameter for these systems.

Findings

Presence of lattice animals with fractal dimension 2 in binary colloids

Cluster growth follows Smoluchowski's kinetic equations

Universal scaling law for irreversible binary colloidal systems

Abstract

In soft matter system controlling the structure of the amorphous materials have been a key challenge. In this work we have modeled irreversible diffusion limited cluster aggregation of binary colloids, which serves as a model for chemical gels. Irreversible aggregation of binary colloidal particles lead to the formation of percolating cluster of one species or both species also called bigels. Before the formation of the percolating cluster the system form self similar structure defined by a fractal dimension. For a one component system when the volume fraction is very small the clusters are far apart from each other and the system has a fractal dimension of $1.8$. Contrary to this we will show that for the binary system we observe the presence of lattice animals which has a fractal dimension of $2$ irrespective of the volume fraction. When the clusters start inter penetrating we observe a fractal dimension of $2.5$ same as in the case of one component system. We were also able to predict the formation of bigels using a simple inequality relation. We have also shown that the growth of clusters follows the kinetic equations introduced by Smoluchowski for diffusion limited cluster aggregation. Further more we are also proposing a universal parameter for irreversible binary colloidal system, which follows the scaling laws proposed by percolation theory.