Entangled fractal clusters forming the lattice animals in irreversible DLCA binary systems

Irreversible DLCA of binary spheres was simulated by modifying the Brownian Cluster Dynamics. Volume fraction of randomly distributed $N$ spheres in a box of size $L$ is given by ${\Phi_{tot}=\frac{\pi}{6} N_{tot}/L^3}$. ${N_{A}}$ and ${N_{B}}$ number of spheres of same size are defined as species $A$ and $B$. Intra-species form irreversible bonds, while inter-species interaction is through hard core repulsions. We kept ${N_{B}}$ $\geq$ ${N_{A}}$, and observed bigel for certain fraction of $A$ species. By tuning the $\Phi_{tot}$ and fraction of $A$ and $B$ species we were able to regulate the size of the cage and designed clusters of a specific size. We found that the accessible volume of the system increases when compared to the monomeric case, which means that species $A$ is aggregating inside the cage created by $B$. Unlike monomeric DLCA we observe that for moderate ${\Phi_{tot}}$ both the species undergo a transition from lattice animal(fractal dimension,$d_f=2.0$) to the percolation region($d_f=2.5$). We found that $A$ clusters are stuck inside the $B$ percolating cluster and always have a fractal dimension of $2$, thus having $2$ characteristic length scale for binary system. Also, diffusion of one species are hindered by the presence of the other species forming cages.