Model of nanocrystal formation in solution by burst nucleation and diffusional growth

TL;DR

This paper presents a quantitative model of burst nucleation and diffusional growth in solution, deriving growth laws and validating them with numerical simulations, to better understand nanocrystal formation.

Contribution

It introduces a mathematical model that quantitatively describes burst nucleation and growth, extending LaMer's qualitative explanation with analytical and numerical results.

Findings

Average cluster size grows linearly with time.

Cluster size distribution width grows as the square root of time.

Model results agree with numerical simulations at large times.

Abstract

The phenomenon of burst nucleation in solution, in which a period of apparent chemical inactivity is followed by a sudden and explosive growth of nucleated particles from a solute species, has been given a widely accepted qualitative explanation by LaMer and co-workers. Here, we present a model with the assumptions of instantaneous thermalization below the critical nucleus size and irreversible diffusive growth above the critical size, which for the first time formulates LaMer's explanation of burst nucleation in a manner allowing quantitative calculations. The behavior of the model at large times is derived, with the result that the average cluster size, as measured by the number of atoms, grows linearly with time, while the width of the cluster distribution grows as the square root of time. We develop an effective numerical scheme to integrate the equations of the model and compare the asymptotic expressions to results from numerical simulation. Finally, we discuss the physical effects which cause real nucleation processes in solution to deviate from the behavior of the model.