Article written by V. Cregan, CRM
Nanotechnology is predicted to play a profound role in the future by impacting a variety of fields such as medicine, renewable energy, industrial production, amongst others. Nanoparticles, small units of matter with dimensions in the range 1-100 nm, lie at the interface of bulk materials and atomic structures, and are the fundamental components of nanotechnology. In contrast to bulk materials where physical and chemical properties tend to be independent of size, material properties at the nanoscale are extremely sensitive to particle size. Hence, the ability to produce monodisperse particles that lie within a controlled size distribution is critical.
Scientists have been searching for feasible strategies to attain particles with monodisperse size distributions. Due to its ease of use, precipitation of nanoparticles from solution is currently one of the most popular synthesis methods [1, 2]. Particle nucleation and growth are usually 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 undesirable broadening of the particle size distribution (PSD). The PSD can be refocused by changing the reaction kinetics via the addition of precipitating material, or varying the temperature or pH [3]. The biggest disadvantage of this synthesis method is that the precise relationship between particle growth and system conditions is still not fully understood.
The aim of our research [4] was to predict the evolution of a system of nanoparticles in solution. Initially, we considered a single particle model consisting of a diffusion equation for the solution concentration, a moving boundary condition to track the particle-liquid interface and a time-dependent expression for the bulk concentration obtained via mass conservation. Rescaling the model yielded a small, dimensionless parameter in front of the time derivative term in the diffusion equation. This parameter was the basis of a pseudo-steady state solution for the concentration. The resulting solution was substituted into the Stefan conditions to obtain an ordinary differential equation for the particle radius. The model was then extended to a system of N nanoparticles, which was solved numerically to obtain the evolving PSD from which we measured the average particle radius and standard deviation.
The results for the N-particle simulation were shown to be in good agreement with experimental data for cadmium selenide nanoparticles [3]. The simulation captured the main features of the synthesis method, namely the initial, rapid size focusing stage and the following long Ostwald ripening phase. The model also successfully predicted the narrowing of the PSD due to the introduction of additional material into the solution.
References
[1] N.V. Mantzaris, Liquid-phase synthesis of nanoparticles: particle size distribution dynamics and control, Chemical Engineering Science, 60(17), pp. 4749-4770, 2005.
[2] R. Viswanatha and D.D. Sarma, Growth of nanocrystals in solution. Nanomaterials Chemistry: Recent Developments and New Directions, Wiley Online Library, pp. 138-170, 2007.
[3] X. Peng, J. Wickham and A.P. Alivisatos, Kinetics of II-VI and III-V colloidal semiconductor nanocrystal growth: “focusing” of size distributions, Journal of the American Chemical Society, 120(21), pp. 5343-5344, 1998.
[4] V. Cregan, T.G. Myers, S.L. Mitchell, H. Ribera Ponsa and M. Calvo Schwarzwalder. Nanoparticle evolution via the precipitation method. In preparation.