Nanoparticle Growth via the Precipitation Method

Abstract

Nanoparticles are small units of matter with dimensions in the range 1-100 nmthat lie at the interface of bulk materials and atomic structures. Whilst the physical and chemical properties of bulk materials tend to be independent of size, at the nanoscale, size strongly dictates material properties. Consequently , nanoparticles exhibit many advantageous size-dependent magnetic, electrical, chemical and optical properties. These properties are extremely sensitive to the particle size, and thus the ability to produce monodisperse particles that lie within a controlled size distribution is critical. Due to its ease of use, precipitation of nanoparticles from solution is currently one of the most widely employed synthesis methods [1, 2]. Typically, the nucleation and growth processes are separated, where the former is used to generate seeds for the latter. The resulting two-phase system is not in its lowest possible energy state due to the presence of small particles. Thermodynamic equilibrium is achieved by Ostwald ripening, whereby large particles grow at the expense of the more soluble small particles. This leads to the unwanted defocusing of the particle size distribution (PSD), caused by growth and dissolution of bigger and smaller particles, respectively. The PSD can be refocused by changing the reaction kinetics by the addition of precipitating material, or varying the temperature or pH [4, 5]. However, the main disadvantage of this process is that the precise relationship between particle growth and system conditions is still not fully understood [3]. We consider the evolution of a system of nanoparticles in solution via size focusing and Ostwald ripening. The model consists of a diffusion equation for the concentration of the solution, Stefan-type conditions to track the particle-liquid interfaces and a time-dependent expression for the bulk concentration obtained via mass conservation. Rescaling the model leads to a small, dimensionless parameter in front of the time derivative term in the diffusion equation, which is the basis of a pseudo-steady state solution for the concentration. This solution is substituted into the Stefan conditions to yield a system of ordinary differential equations for the particle radii. The model is solved numerically to give the evolving PSD from which we measure the average particle radius and standard deviation. The results are shown to be in good agreement with experimental data for cadmium selenide nanoparticles [5].