Use of Dispersive Kinetic Models for Nucleation and Denucleation to Predict Steady-State Nanoparticle Size Distributions and the Role of Ostwald Ripening

Abstract

Fundamental kinetic understanding of the formation of various particle size distributions (PSDs) and the time evolution of the mean particle size can guide new synthetic approaches, or improvements to existing ones, for obtaining a desired nanoparticle (NP) morphology, size, and monodispersity. Previous modeling efforts have focused largely on classical kinetic descriptions of nucleation, growth, and particle coarsening/Ostwald ripening (OR) mechanisms, employing numerical methods to simulate the temporal evolution of the NP PSDs. In a very different approach, the activation energy distributions corresponding to recently derived dispersive kinetic models for nucleation and denucleation (Skrdla, P. J. J. Phys. Chem. A2011, 115, 6413–6425) are utilized in this work to derive analytic functions for the stationary/steady-state PSDs relevant to each mechanism. Additionally, the same models are used to obtain the time evolution of the mean NP radius. PSDs for these nanometer-scale phase transformation mechanisms have not been predicted previously in the literature using such a direct approach, circumventing the need for stochastic simulation. The predicted PSD shapes, used individually, together, and/or in combination with the known stationary PSD shapes relevant to OR, are used to qualitatively establish the mechanisms giving rise to PSDs reported in the recent literature. Using this approach, the origin of bimodal PSDs and the phenomenon of PSD focusing are explained. Moreover, the time-evolution functions for the mean NP radius predicted by each mechanism are shown to be sufficiently different so as to allow the three mechanisms to be readily distinguished from one another in treating empirical data.