Kinetic Monte Carlo Modelling of The Initial Stages of Zeolite Synthesis

Abstract

The very early stages of solid-state formation from solution can be crucial in determining the properties of the resulting solids. Thus, higher levels of control over nucleation cannot be achieved without understanding the fundamentals of the elementary steps of zeolite synthesis. The mechanisms governing the transformation of small silicate molecules into clusters are still far from being understood. In this thesis the silicate oligomerization is studied using our newly developed method, their aggregation and the subsequent gelation are also discussed. A form of kMC simulations, which we call continuum kMC, that is useful to simulate reactions in solution is presented. In this method, the rate constants of the reactions can be determined prior to the simulation, so that the simulation itself takes little computer time, or can be done on large systems. We have derived the method from the master equation that described the evolution of the system as hops from one minimum of the potential-energy surface to a neighboring one. This master equation is coarse-grained by using an analytical approach to the diffusion of the particles. This leads to a new master equation that describes only the chemical reactions, and no other processes. The diffusion is incorporated in the expression for the rate constants. Solvent molecules need not be included explicitly in the simulations. Their effect can be incorporated in the rate constants as well. An important aspect of zeolite synthesis is the effect of template molecules, other cations, pH, and temperature. All this can easily be included in our method. We think that continuum kMC will be useful for many other systems. This may open the way to study many other important problems occurring in solutions on the atomic length and macroscopic time scale. We report an investigation of oligomerization reactions of large scale silicate-solution systems. The calculated results demonstrate that the continuum kMC theory is able to provide detailed information regarding the early stage of zeolite formation. Comparing continuum kMC and mean field approximations on the silica-solution system, we conclude that the mean field approximation is rate-limited by intermediate species. We demonstrate that pH and temperature greatly influence the oligomerization rate and pathway. Therefore, silicate oligomerization can be controlled by varying the pH and temperature of the solution. A significant finding is that near neutral pH favors linear growth, because the linear growth is mainly driven by an anionic mechanism in which there is one neutral and one anionic reactant, while a higher pH makes the silicate species anionic, which facilitates ring closure. In the case of pH 7, the species oligomerize first to linear tetramers and then close to form 4-rings, while at high pH the linear growth and ring closure occurs simultaneously. The total growth rate is a interplay between linear growth and ring closure. pH 8 is found to be the optimum value that takes care of both linear growth and ring closure, and hence the silicate oligomerization is the fastest at pH 8. The decrease of cluster size with pH is due to the fact that the double-anionic mechanism operable is very slow. The rate-determining steps are ring closure, at very low pH, and linear growth, at very high pH. Preferred conditions necessary for effective oligomerization that can accelerate the initial stage of silicate oligomerization and as a result avoid the formation of undesired species have been obtained. The silicate oligomerization with presence of counterions is investigate. A comparison of the results in the presence of counter ions (Li+ and NH4 +) with those obtained without a counterion is presented. The dominant species depends sensitively on the counterions. Extending our research to a larger scale would be valuable. However the continuum kinetic Monte Carlo method could not probe the formation mechanism of larger species, due to that the silicate oligomers are regarded as pointlike particles. We also present a lattice kinetic Monte Carlo study of the silicate oligomerization and gelatio. The lattice kinetic Monte Carlo results reveal that the linear species tend to close to form rings. 3-rings are metastable, the formed 3-rings reopen to support formation of larger species. 4-rings dominant the ring population. The aggregation of silicate oligomers is followed by aging that leads to more condensed silicate clusters. The gelation proceeds from 4-ring containing structures. 6-rings are mainly formed during aging of the silicate clusters. These findings are in good agreement with experimental results. We believe that our research have provided valuable insight into the mechanism of the initial stages of zeolite synthesis.