A Kinetic Monte Carlo Simulation Study of Synthesis Variables and Diffusion Coefficients in Early Stages of Silicate Oligomerization

A kinetic Monte Carlo (kMC) approach combined with density functional theory (DFT) calculations is used to examine the effects of molecular diffusion and synthesis parameters (pH 7–12) as well as initial monomer concentration (0.01–1 mol L^–1) for a silicate oligomerization model. To implement this approach, we have adapted the open source kMC SPPARKS software in order to simulate the early stages involved in zeolite formation and more generally kinetically driven reactional systems, using a variety of lattice models (fcc/octahedral/tetrahedral, i.e., fcc/oct/tet). First, these adaptations were validated with kinetically driven reactional systems of the “Lodka” model, providing an excellent match with the analytical solution of the reactive system. The calculations reveal that both the lattice complexity and the diffusion coefficients of species have an impact on the steady state concentration (ssc) of oligomers in solution. Second, the approach is further applied to the early stages of silicate oligomerization using chemical pathways (activation barriers and associated prefactors) taken from the literature. Besides the expected impact of key input parameters (amplitudes of energy barriers, influence of water molecules in reaction pathways, pH, etc.), we demonstrate the impact of diffusion (viscosity of the clear solution) on the ssc of silicate oligomers. Considering that the kMC model is limited by the frequencies of reactional rare events, we find that when diffusional frequencies are much larger than reactional ones, the system diffuses instead of reacting. In that respect our calculations suggest that the magnitude of the diffusion coefficient determines the relative ssc of cyclic vs linear oligomers with a transition regime around of 10^–14 m² s^–1 under the reaction conditions studied here (pH 9, 350 K, and initial concentration of 1 mol L^–1)