Brownian Dynamics Simulation of the Growth of Metal Nanocrystal Ensembles on Electrode Surfaces from Solution. I. Instantaneous Nucleation and Diffusion-Controlled Growth

The diffusion-controlled growth of ensembles of metal nanoparticles on a planar surface from solution is modeled using Brownian Dynamics (BD) simulation method. Both random and hexagonal 2D ensembles were considered with coverages ranging from 5 × 109 to 2 × 1011 cm-2. Attention is focused on the evolution of particle size dispersion as a function of the experimental variables. Three temporal regimes in the growth of these nanoparticle ensembles are distinguished from the simulation data: At short times (t < 20 ns), the standard deviation of the particle radius, σR, rapidly increases to 0.05−0.1 nm. At intermediate times in the interval from 20 to 200 ns, σR peaks and begins to declinenearly to zero in some simulations. This “convergent” growth segment continues until overlap of the diffusion layers of adjacent nanoparticles on the surface is nearly complete. We derive an analytical expression for σR in this time regime which is based on the stochastic nature of the deposition process, and excellent agreement with the simulation data is obtained. Finally, at yet longer times (at which diffusion to the surface is planar), the behavior of random and hexagonal ensembles diverge: Random ensembles again transition into a divergent growth regime in which σR increases monotonically with time; the size dispersion of hexagonal arrays, however, continues to decrease with deposition time. In this time regime, the data support the conclusion that size dispersion is caused by an inhomogeneous distribution of interparticle distances which translates into an inhomogeneity in the diffusion-limited flux at each particle.