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Modeling of Formation of Gold Nanoparticles by Citrate Method† Sanjeev Kumar,* K. S. Gandhi,* and R. Kumar
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Department of Chemical Engineering, Indian Institute of Science, Bangalore 560012, India
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 Au3+ 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. 1. Introduction Nanoparticles have potential for many applications, and their synthesis has assumed importance. Size obviously is their most important property, and many applications depend on it. Polydispersity in size is often an undesirable feature in these applications. Thus, prediction of both size and dispersity for a given system is of concern in systematizing the manufacture of nanoparticles. A variety of methods to synthesize nanoparticles are reported in the literature. A detailed account of these methods is provided by Cushing et al.2 and Schmid.3 Broadly, these methods can be classified into gas-phase and liquid-phase-based methods. In gas-phase-based methods, bulk material is evaporated using high-energy sources such as resistive heating and lasers to obtain a supersaturated gas phase, which, under controlled conditions, produces nuclei that grow to become nanoparticles. In liquid-phase methods, also known as wet methods, precursors react to form a supersaturated solution, which nucleates and gives rise to particles ranging from 1 to 100 nm in size with stability ranging from a couple of hours to years. Wetsynthesis methods are attractive at least for two reasons: they are more energy efficient and they can be used to produce nanoparticles using the standard apparatus available in a laboratory. So far, two strategies have been followed for wet synthesis. In the first strategy, two reactants, usually both of them in (reverse) micellized form, are mixed and nanoparticles form inside them by precipitation. The size of particles is controlled by the rates of nucleation and growth, and stabilization is provided by adsorption of surfactant. Nucleation is correlated to the size of micelles, and growth is determined by the rate of * To whom correspondence should be addressed. E-mail: sanjeev@ chemeng.iisc.ernet.in (Tel., +91-080-22933110), gandhi@ chemeng.iisc.ernet.in (Tel., +91-080-22932320). Fax: +91-080-2360 8121. † The authors are happy to contribute this investigation to the special issue honoring Prof. M. M. Sharma. A part of this work formed the basis for a paper presented at CHEMCON04 held in Mumbai in December 2004.
exchange of material between micelles. Both these features can be altered through chemical nature and concentration of surfactant. This strategy offers scope for good control over particle size and has been modeled by several investigators. Results have been obtained by kinetic Monte Carlo simulations using the method of interval of quiescence in several articles.4-6 Equivalently, mean-field population balance models have been developed for nanoparticle synthesis7-9 and to study the effect of mixing on the synthesis process.10 A large amount of surfactant is, however, used in this method, which makes it expensive. Recovery of surfactant, e.g., by using nanofiltration, has been proposed as a remedy, but it needs to be evaluated rigorously for determining the economics. In the second strategy, precipitation is carried out in bulk in the presence of stabilizers that adsorb on nanoparticles and prevent coagulation of particles. Most of these methods were first demonstrated for their ability to make gold nanoparticles and then extended to the synthesis of other types of particles, including those of semiconductors. Three widely used bulkprecipitation-based techniques for the synthesis of gold nanoparticles are as follows: (i) citrate method of Turkevich et al.,1 (ii) citrate-tannic acid method of Muhlpfordt,11 and (iii) BrustSchiffrin method of Brust et al.12 The first two methods yield particles which are stable against coagulation, whereas the last one produces particles which are also capped and cannot be grown bigger. Additionally, only the product of the BrustSchiffrin method can be dried and redispersed. In the simplest procedure for preparation of gold particles (Turkevich method), tetrachloroauric acid is reduced with trisodium citrate. Here, citrate is both the reducing agent and the stabilizer. Similarly, in the Brust-Schiffrin method, alkane thiols that provide long-term stability also take part in reduction of gold along with sodium borohydride, which is the main reducing agent. In all these methods, it is expected that the relative amounts of gold salt to reducing agent influence the particle size. The rate of adsorption of stabilizer also plays a role in controlling particle size. Thus, a single reagent can play
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Figure 1. Variation of particle size with ratio of initial concentrations of citrate to gold salt.
multiple roles, which creates more complexity. This feature combined with the fact that reactions that usually occur in these systems are fast makes the particle size more sensitively dependent on the concentrations of precursors, rate of addition of precursors, state of mixing in the reactor, and other variables. While this sensitivity requires strict adherence to protocols that work, it also permits particle size and polydispersity to be changed substantially merely by changing the concentrations of the precursors. All the three synthesis protocols listed above have been subsequently modified by changing the ratio of common precursor tetrachloroauric acid to other reagents to synthesize nanoparticles of significantly different sizes.13,14 Although direct precipitation using the citrate method is in wide use because it produces uncapped but stable particles, a quantitative model to predict particle size and the associated distribution is not available. The objective of this paper is to develop a quantitative model for the citrate method of Turkevich et al.1 Because the chemistry involved and the processes of nucleation and growth of particles are different from one another in the three methods, the model developed here is for the experimental method of Turkevich et al.1 only. 2. Features of the Citrate Process We consider the formation of gold nanoparticles by reduction of tetrachloroauric acid by trisodium citrate. The method has been pioneered by Turkevich et al.,1 and variants of it are still widely used15 to produce gold nanoparticles. Because of its simplicity, various facets of the process have been investigated by Frens,13 Freund and Spiro,16 Chow and Zukoski,17 Abid,18 and others. In this process, an aqueous solution of tetrachloroauric acid is brought up to boiling and a small volume of trisodium citrate is then added to it. In ∼10 s, bluish color appears, indicating formation of gold nuclei. In a few minutes or less, the solution turns brilliant red because of the formation of nanoparticles. The completion of reaction may take tens of minutes depending upon the amount of citrate taken. A plot of mean particle size against the ratio of initial concentrations of citrate to gold species is presented in Figure 1. It summarizes data from Turkevich et al.,1 Ferns,13 Freund and Spiro,16 Chow and Zukoski,17 and Abid.18 All the data shown in this figure, except those of Chow and Zukoski,17 are obtained for approximately the same concentration of auric chloride and by varying concentration of sodium citrate. It is interesting to note that the data spanning a 50-year period show a good correlated trend. Figure 1 reveals several interesting features. First is the widely varying dependence of particle size on the ratio of citrate to gold. When this ratio increases by a factor of 5, from ∼0.4 to ∼2, the particle size decreases by a factor of 7, which
Figure 2. Illustration of complex of aurous species and dicarboxy acetone.
corresponds to a change of nearly 3 orders of magnitude in volume. Yet, when the ratio increases from about 2 to 7, there is very little change in the particle size. On the other hand, when the concentration of sodium citrate is kept fixed and that of auric chloride is varied, Chow and Zukoski17 found that the particle size varies sensitively over a wide range of auric chloride concentrations investigated. With a decrease in initial concentration of auric chloride, particle size first decreases, passes through a minimum, and then increases (the experimental data are shown in Figure 5). Another interesting feature is that complete conversion of auric chloride has been reported at all the ratios of citrate to gold. Data with small ratios of citrate to gold were reported by Frens,13 and the least of them corresponds to a ratio of ∼0.43. A model is presented below that attempts to explain these unusual features quantitatively. 3. Model 3.1. Chemical Reactions. Gold nanoparticles have been synthesized using the citrate method for a long time now, and although most reactions occurring in the method and the intermediates formed in the process are known, some of the steps are still not fully understood. In the following discussion, we point out these and state how they are modeled in this work. The initial step of this multiple-step process, with reactions occurring in series and parallel, is the oxidation of citrate, which yields dicarboxy acetone:
The second step is the reduction of auric salt to aurous salt:
AuCl3 + 2e- f AuCl + 2Cl-
(2)
The next step is the disproportionation of aurous species to gold atoms:
3AuCl f 2Auo + AuCl3
(3)
The disproportionation step requires three aurous chloride molecules to combine. This is facilitated by dicarboxy acetone, which, according to Turkevich et al.1 and Abid,18 plays the role of organizer through the formation of a complex. An illustration of the complex as visualized in this work is presented in Figure 2. In the chain-like structure pictured here, three Au+ can be tethered by a minimum of two dicarboxy acetone molecules.
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Once gold particles are formed, disproportionation can occur19 on the particle surface, too. The overall stoichiometry of the reduction reaction can then be represented as
If these were the only reactions that led to the formation of gold atoms, the overall stoichiometry would require three citrate molecules to reduce two auric chloride molecules. Since at high temperatures dicarboxy acetone is lost in side reactions1 to form acetone,
the stoichiometric ratio of citrate to gold required for complete conversion of auric chloride should be even larger than 1.5. In contrast, Frens13 reports complete conversion of auric chloride at a stoichiometric ratio as low as 0.43. He, however, does not discuss the chemistry involved. It appears reasonable to conclude that some products of degradation of dicarboxy acetone reduce trivalent gold, though the chemistry leading to the formation of gold is not clear. Turkevich et al.1 and Davies20 have shown that acetone can reduce auric chloride to produce gold particles, though the conditions in the two experiments are different. In view of the foregoing, we assume that it is acetone formed by degradation of dicarboxy acetone that additionally reduces auric chloride for its complete conversion. To explain the observations of Frens,13 we assign a stoichiometric ratio of 4 for this reaction.
(CH3)2CdO + 4AuCl3 f 4AuCl + products
(6)
This allows for complete reduction of ∼3 mol of auric chloride by 1 mol of citrate. This assumption influences the model results only for ratios of citrate to gold
