2D lattice animal formation in the irreversible aggregation of patchy particles

Abstract

With the self-assembly of patchy colloids, we can engineer many complex structures. In the present work, we are modeling spherical particles with 2 diagonally opposite patches using the Kern-Frenkel potential coupled with isotropic square well potential having different interaction ranges. The isotropic square well potential formed reversible bonds while the patches were irreversibly bonded. A state diagram is calculated where we observed a range of structures from a 1D chain, 2D planar cluster, and 3D random clusters depending on the width of the patch. These structures are controlled by the number of bonds each patch can form for a given patch angle. The range of the patch width can be analytically calculated using geometric arguments to identify different types of clusters, which agree with our simulations. The aggregation process was diffusion-limited, forming clusters with fractal dimension 2 in the low volume fraction limit, otherwise known as flocculation region, and 2.5 in the high volume fraction limit or percolation region, irrespective of the type of clusters formed. In the flocculation limit of the DLCA aggregation model, we expect a fractal dimension of 1.8, contrary to that, we observed the formation of lattice animals having a fractal dimension of 2. The presence of lattice animals is confirmed using the scaling laws of size distribution and chemical length of the clusters formed in the flocculation limit.