Nanocrystal growth via the precipitation method

Abstract

A mathematical model to describe the growth of an arbitrarily large number of nanocrystals from solution is presented. First, the model for a single particle is developed. By non-dimensionalising the system we are able to determine the dominant terms and reduce it to the standard pseudo-steady approximation. The range of applicability and further reductions are discussed. An approximate analytical solution is also presented. The one particle model is then generalised to N well dispersed particles. By setting N = 2 we are able to investigate in detail the process of Ostwald ripening. The various models, the N particle, single particle and the analytical solution are compared against experimental data, all showing excellent agreement. By allowing N to increase we show that the single particle model may be considered as representing the average radius of a system with a large number of particles. Following a similar argument the N = 2 model could describe an initially bimodal distribution. The mathematical solution clearly shows the effect of problem parameters on the growth process and, significantly, that there is a single controlling group. The model provides a simple way to understand nanocrystal growth and hence to guide and optimise the process.

Diffusion processes and nanoparticle growth

“…The N = 2 model can equally well represent the average radii for an initially bimodal distribution of nanocrystals while an N > 2 model can represent a much larger distribution of particles. This work has been already accepted and is pending printing [29].…”