Modeling of Formation of Gold Nanoparticles by Citrate Method

Abstract

Properties of nanoparticles are size dependent, and a model to predict particle size is of importance. Gold nanoparticles are commonly synthesized by reducing tetrachloroauric acid with trisodium citrate, a method pioneered by Turkevich et al (Discuss. Faraday Soc. 1951, 11, 55). Data from several investigators that used this method show that when the ratio of initial concentrations of citrate to gold is varied from 0.4 to ∼2, the final mean size of the particles formed varies by a factor of 7, while subsequent increases in the ratio hardly have any effect on the size. In this paper, a model is developed to explain this widely varying dependence. The steps that lead to the formation of particles are as follows: reduction of Au 3+ in solution, disproportionation of Au + to gold atoms and their nucleation, growth by disproportionation on particle surface, and coagulation. Oxidation of citrate results in the formation of dicarboxy acetone, which aids nucleation but also decomposes into side products. A detailed kinetic model is developed on the basis of these steps and is combined with population balance to predict particle-size distribution. The model shows that, unlike the usual balance between nucleation and growth that determines the particle size, it is the balance between rate of nucleation and degradation of dicarboxy acetone that determines the particle size in the citrate process. It is this feature that is able to explain the unusual dependence of the mean particle size on the ratio of citrate to gold salt concentration. It is also found that coagulation plays an important role in determining the particle size at high concentrations of citrate.

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

“…After the work by Kumar et al [7], authors such as Ji et al [8], Polte et al [9], and Kettemann et al [10] NPs evolve according to the nucleation-aggregation-growth mechanism described, for instance, by Polte et al [9]. These findings prompted us to investigate the model of Kumar et al [7] for different conditions (including different pH values) and verify whether its predictions are accurate or not.…”

“…These findings prompted us to investigate the model of Kumar et al [7] for different conditions (including different pH values) and verify whether its predictions are accurate or not. The model is complex because it comprises a set of ordinary differential equations that describe the material balances of the fluid components and a population balance that describes the evolution of GNPs size distribution.…”

“…In disagreement with the observation by Turkevich et al [3], Chow and Zukoski [6] reported NPs aggregation along with nucleation and growth. Subsequently, Kumar et al [7] developed a model to explain the synthesis that considers all the previous observations. From a number of possible reactions, they considered only five: citrate reacts with auric chloride to form DCA and aurous chloride; DCA organizes aurous chloride to form the GNP nuclei; DCA decomposes into acetone; unconsumed aurous chloride grows the particles, and acetone can reduce auric chloride if citrate is unavailable.…”

“…We used the experimental findings of these authors to test the model. In this report, we briefly present the model of Kumar et al [7] (in the mathematical form which we implemented in Parsival) and then discuss the results. In particular, Section II illustrates the model, Section III discusses the tests, in which we investigated the effects of temperature and pH, and Section IV reports our conclusions on the validity of the model.…”

Advanced AuNMs as nanomedicine’s central goals capable of active targeting in both imaging and therapy in biomolecules

“…Although this preparation method simply involves controlling the ratios of citrate to Au ions [23], the reaction often needs to be carried out on a relatively large scale at the temperature of boiling water and lacks the reproducible preparation of uniform AuNPs with rather large sizes. After the breakthroughs reported by Schmid [24,25] and Brust et al [26], a variety of methods have been developed to synthesize AuNMs, and many excellent reviews [27] are available now.…”