A mathematical investigation of the Turkevich organizer theory in the citrate method for the synthesis of gold nanoparticles

•The model based on the “Turkevich organizer theory” was investigated.•We tested its predictions against experimental data reported in the literature.•The model does not yield satisfactory predictions in various cases.•A novel model, with a more accurate mechanistic description, is required.

Gold nanoparticles are commonly manufactured by the citrate reduction method, a synthesis method pioneered by Turkevich et al. (1951). Based on their experimental evidence, Turkevich et al. (1951) advanced the organizer theory, a nucleation-growth synthesis mechanism. Subsequently, Kumar et al. (2007) developed a mathematical model for the description of the synthesis, basing it on such a theory. However, this model has not been thoroughly tested. Recently, contrary to the evidence provided by Turkevich et al. (1951), other mechanistic descriptions of the synthesis, which emphasize the role of the pH of the solution, have been advanced in the literature. In this paper, we investigated the model of Kumar et al. (2007) for different conditions of pH, temperature and initial reactant concentrations. To solve the model, we used the numerical code Parsival, which is used for solving population balance equations. We tested the model for different synthesis conditions studied experimentally by various researchers, for which results are available in the literature. The model poorly predicted the experimental data because the Turkevich organizer theory does not account for the acid-base properties of chloroauric acid and sodium citrate. A new model, with a more accurate mechanistic description of the synthesis and of the chemistry involved, is therefore required.