Boltzmann equation for the modelling of formation of silver nanoparticles using trisodium citrate as the reducing agent

Abstract

The kinetics of formation of silver nanoparticles using trisodium citrate as the reducing agent was studied in order to evaluate the rate constants and the rate expression. The inability to measure the concentration of the reactant (precursor silver salt) at millimolar concentrations using conventional spectrophotometric techniques renders the studies of kinetics cumbersome. An attempt was made to study the kinetics of this reaction by measuring the concentration of silver nanoparticles instead of the silver ions as a function of time. The initial concentration of the reducing agent (trisodium citrate) was taken to be nearly 20 times that of the initial concentration of the silver ions. Hence, the reaction could be modelled as pseudo-first-order kinetics, considering the bimolecular nature of the reaction. The final second-order rate constant was evaluated using integral method of analysis as 0.254 l (g min)^–1. The key steps in the formation of silver nanoparticles (i.e., reduction, nucleation, growth and saturation) were modelled as a sigmoidal plot using Boltzmann equation. A very good fit of experimental data (R² ≈ 0.99) was observed with the model.