Monte Carlo simulations of the nucleation and growth process of colloidal particles

We have examined the effect of the total initial monomer concentration and that of the monomer-monomer attraction energy on the nucleation and growth process of colloidal particles using a reversible aggregation model (Shih-Aksay-Kikuchi model) with the Monte Carlo method. We showed that the equilibrium monomer concentration c(e) exhibited a peak with respect to the total initial monomer concentration c(t). Furthermore, the solution may be divided into three regimes with respect to c(t). In the first regime where the initial monomer concentration was low, all monomers remained as individual monomers in the solution and c(e) increased linearly with c(t). In the second regime where small clusters of monomers began to form, c(e) underwent a peak with respect to c(t). In the third regime where large particles form, c(e) slowly decreased with c(t). Moreover, with increasing monomer-monomer attraction energy, the peak in c(e) moved to a lower c(t) and became sharper. The equilibrium monomer concentration surrounding a particle with respect to particle size was shown to agree with the Kelvin equation, indicating that the model can indeed capture the equilibrium solution physics involving colloidal particles. The peak exhibited in c(e) versus c(t) was manifested as a peak in the monomer concentration versus time under conditions where monomers were gradually fed to the solution. The present simulation is a simulation model for illustrating a peaked solute concentration with respect to time first proposed by LaMer and Dinegar. We further showed that the supersaturation peak in the monomer concentration versus time depended on the feeding rate. The peak height increased with an increasing feeding rate.