A complex network approach for the growth of aerogels

The formation of the gel structure of a finite set of inorganic particles interacting via long range potentials is studied via Monte Carlo simulations for different conditions of temperature and concentration. We found that there are certain specific conditions wherein gelation can occur. Moreover, the integrated network of connected particles is investigated. A divergence of an order parameter was observed and indicates the transition from random Erdös-Rényi to scale-free networks. The effects of a reaction limited process are also investigated and indicate that the dissociation of particles favors the formation of random networks.