  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.
