Modified kinetic rate equation model for cooling crystallization

Modeling of Nucleation and Growth in the Synthesis of PbS Colloidal Quantum Dots Under Variable Temperatures

Lead sulfur colloidal quantum dots (PbS CQDs) are a kind of IV-VI semiconductor nanocrystals which have attracted enormous interest in recent years because of their unique physicochemical properties. Controlling size, size distribution, and yield of PbS CQDs plays key priorities in order to improve their properties when they are applied in the photovoltaics and energy storage applications. Despite many systematical studies in PbS CQD syntheses with various perspectives, details of the formation mechanism impacted on the size, concentration, and size distribution of PbS CQDs in complicated reaction conditions remain poorly understood. In this work, an improved kinetic rate equation (IKRE) model is employed to describe PbS CQD formation under variable solution temperatures. After establishing the necessary discretized equations and reviewing the link between model parameters and experimental information, a parametric study is performed to explore the model's feature. In addition, a set of experimental data has been compared with the result of IKRE model fits, which would be used to obtain corresponding thermodynamic and kinetic parameters that can further affect the CQD growth over longer timescales. This method builds up the relationship between the nucleation and Ostwald ripening stage that would provide the possibility for future large-scale manufacturing of CQDs.