Sol–gel simulation—I: Scattering response

Scattering of sol–gel structures is investigated computationally. Sol-gels are recreated through an aggregation algorithm incorporating Brownian motion and chemical reactions. Using the fractal character of sol–gels, the concept of recursion is introduced as a tool to perform multi scale computation of the response of sol–gels through the different scales from the molecular level to the macro scale. The concept is illustrated with the prediction of scattering intensity. The relationship between scattering intensity and functionality is investigated, noting that the latter is a function of the Brownian motion and chemical reactivity. Computational simulation tools are developed to predict scattering intensity as a function of density and reactivity, the former represented by the number of particles, or clusters, in the simulation box. Then, the results are correlated to an analytical model that reveals the critical wave number, or critical scale, at which percolation occurs.