Theoretical investigations into the nucleation of silica growth in basic solution part II – derivation and benchmarking of a first principles kinetic model of solution chemistry

Abstract

A kinetic model of silicate oligomerization in water, up to and including tetramer formation, has been compiled exclusively from rate constants derived from transition state theory based on either quantum chemical data (derived under a hybrid solvation framework) for all bond breaking–forming reactions, or using empirically-based approximated pK_a's and diffusion coefficients for rate constants of pH-based and bimolecular steps. The rate constants, based on an exhaustive search of all relevant elementary steps, form the basis of our kinetic model; numerical solution of the resulting rate equations allows the simulation of the reaction system, given a set of initial conditions and with almost no restriction on concentrations, pH, or reaction time, in a matter of only minutes. The model, which we believe contains all possible isomers of both neutral and singly anionic clusters, has been extensively benchmarked and reproduces a number of important experimental observations in the range pH ≈ 4–10. In particular, it provides a good description of the dominant products; product yields and reaction times (also as a function of pH) are in agreement with experiment; the linear relationship between the log of the rate of silica dissolution and pH is well reproduced; the origin of silica scaling naturally arises; and we can also simulate the observed fourth order dependence of the rate of monomer consumption on H₄SiO₄ concentration. This should be a general approach to exploring solution phase chemistry, and could be a useful complement to more conventional molecular dynamics and Monte Carlo modelling approaches in understanding complex reaction networks in solution.