Using the method of routes for the modelling of the kinetics of the growth of silver nanoparticles in aqueous solution

Among the large references of literature, which considers the methods of synthesis, properties and applications of metal nanoparticles, it is necessary to separately note the works devoted to the study of the mechanisms of formation of nanosystems, in particular under the conditions of their homogeneous nucleation. Mostly, the mechanisms of the formation of metal nanoparticles are studied using the example of noble metals, in particular gold, silver, platinum, palladium or iridium. This is due to the high values of the redox potential of noble metals, which allows the use of a wide range of reducing agents to obtain the corresponding nanoparticles, as well as to the high stability of the obtained noble metal nanoparticles. At the same time, despite the fact that the processes of formation of colloidal (or nano) metal particles have been studied for a long time, at present there is no unanimous opinion among researchers regarding the mechanisms of formation of such nanosystems in general, as well as the mechanisms of individual stages of the process. Based on the analysis of the kinetics of the formation of silver nanoparticles (AgNPs) by the reduction reaction of Ag+ with hydrazine in alkaline solutions, a particle growth scheme is proposed, which includes the stages of adsorption of the silver ion on the surface of growing nanoparticle; adsorption of a molecule of hydrazine and the formation of a surface complex [Ag(N 2 H 4 )] + ; decomposition of the formed complex in an alkaline medium. Using the basic principles of the theory of graphs and the method of routes, a kinetic equation to describe the growth of AgNPs has been proposed and the rate constants of the elementary stages have been calculated. It is shown that the limiting stage of the autocatalytic growth of AgNPs is the reduction of the [Ag(N 2 H 4 )] + complex on the surface of the particle in the presence of hydroxide ions. Using the example of AgNPs, it is shown that the use of such an approach allows us to establish the mechanism of the multi-stage heterogeneous growth process of metal nanoparticles, namely: to determine the chemistry and calculate the rate constants of elementary reactions, and, accordingly, to establish the limiting stages of the process. Keywords: method of routes, theory of graphs, kinetics, silver nanoparticles.