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Turkevich in New Robes: Key Questions Answered forthe Most Common Gold Nanoparticle Synthesis

Maria Wuithschick, Alexander Birnbaum, Steffen Witte, Michael Sztucki, UllaVainio, Nicola Pinna, Klaus Rademann, Franziska Emmerling, Ralph

Kraehnert, Joerg Polte

To cite this version:Maria Wuithschick, Alexander Birnbaum, Steffen Witte, Michael Sztucki, Ulla Vainio, et al.. Turke-vich in New Robes: Key Questions Answered for the Most Common Gold Nanoparticle Synthesis.ACS Nano, American Chemical Society, 2015, 9 (7), pp.7052-7071. �10.1021/acsnano.5b01579�. �hal-01572852�

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July 06, 2015

C 2015 American Chemical Society

Turkevich in New Robes: KeyQuestions Answered for the MostCommon Gold Nanoparticle SynthesisMaria Wuithschick,† Alexander Birnbaum,† Steffen Witte,† Michael Sztucki,‡ Ulla Vainio,§ Nicola Pinna,†

Klaus Rademann,† Franziska Emmerling, ) Ralph Kraehnert,^ and Jorg Polte*,†

†Department of Chemistry, Humboldt-Universität zu Berlin, Brook-Taylor-Straße 2, 12489 Berlin, Germany, ‡ESRF - The European Synchrotron, 71 Avenue desMartyrs, 38043 Grenoble, France, §Deutsches Elektronen-Synchrotron, Notkestraße 85, 22607 Hamburg, Germany, )BAM Federal Institute of Materials Research andTesting, Richard-Willstätter-Straße 11, 12489 Berlin, Germany, and ^Technische Universität Berlin, Straße des 17. Juni 124, 10623 Berlin, Germany

The applications of gold nanoparticles(AuNP) are diverse due to their uniquecatalytic, biological and optical proper-

ties.1 The most commonly used synthesis ofcolloidal gold in aqueous solution is the reduc-tion of tetrachloroauric acid (HAuCl4) withtrisodiumcitrate (Na3Ct).

2�5 In thepastdecade,the citrate method has increasingly been re-ferred to as “Turkevich synthesis”, named afterJohn Turkevich who described the reaction in1951.6 Although the work of Turkevich and hisco-workers is certainly a landmark for thesynthesis of AuNP, the naming of the synthesisis historically not quite correct if intended tohonor the discoverers. Turkevich et al. referredto the textbook Experiments in Colloid Chem-

istry by Ernst A. Hauser and J. Edward Lynn,already published in 1940, who reported theformation of gold colloids upon reactingHAuCl4 and Na3Ct.

7 Until today, the originalsynthesis protocol was modified numeroustimes allowing the fabrication of AuNP in awide range of sizes.5,6,8�10

Most syntheses of colloidal nanoparticlesolutions are poorly understood in terms of

the growth mechanism. In general, this isattributed to the fact that appropriate dataon the size evolution during particle forma-tion is difficult to obtain.11 In the case of theTurkevichmethod, a surprisingly large num-ber of contributions deal with the particlegrowth process or the molecular reductionmechanism, which emphasizes the generalimportance of this synthetic procedure.However, the multitude of publicationsdoes not lead to a comprehensive under-standing of the growth governing pro-cesses since the published interpretationsare manifold and not consistent. Turkevichand co-workers gave the very first descrip-tion of the growth process. They investi-gated the synthesis astonishingly detailedusing a wide range of analytical methods(slit-ultramicroscopy, nephelometry andelec-tron microscopy).6,12 Turkevich et al. applieda nucleation and growth model similar tothe theory shown by LaMer and Kenyon forthe formation of colloidal sulfur,13 althoughit was pointed out that the observed tem-perature dependence of the nucleation rate

* Address correspondence tojoerg.polte@hu-berlin.de.

Received for review March 12, 2015and accepted July 6, 2015.

Published online10.1021/acsnano.5b01579

ABSTRACT This contribution provides a comprehensive mechanistic picture of

the gold nanoparticle synthesis by citrate reduction of HAuCl4, known as Turkevich

method, by addressing five key questions. The synthesis leads to monodisperse

final particles as a result of a seed-mediated growth mechanism. In the initial

phase of the synthesis, seed particles are formed onto which the residual gold is

distributed during the course of reaction. It is shown that this mechanism is a

fortunate coincidence created by a favorable interplay of several chemical and

physicochemical processes which initiate but also terminate the formation of seed

particles and prevent the formation of further particles at later stages of reaction. Since no further particles are formed after seed particle formation, the

number of seeds defines the final total particle number and therefore the final size. The gained understanding allows illustrating the influence of reaction

conditions on the growth process and thus the final size distribution.

KEYWORDS: Turkevich . gold nanoparticles . growth mechanism . size control . tetrachloroauric acid . SAXS

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This is an open access article published under an ACS AuthorChoice License, which permits copying and redistribution of thearticle or any adaptations for non-commercial purposes.

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was difficult to understand from that perspective. An“organizer model” was established attributing a deci-sive role to the formation of large macromolecules ofgold ions and reducing agent with nucleation eventsbeing induced by dicarboxy acetone (DCA), an oxida-tion product of Na3Ct formed during the synthesis. Thenucleation-diffusional growth mechanism was gener-ally accepted for many decades, also in the highlyrecognized work of Frens.8

In contrast, a contribution published only a fewyears after thework of Turkevich et al. remained almostunnoticed despite its excellent scientific quality.Kazuyoshi Takiyama investigated the citrate methodusing electron microscopy (EM) and UV�vis spectros-copy. From EM in combination with the spray method,the AuNP concentration could be estimated duringthe course of reaction.14 The results revealed that thenumber of particles is determined in the very initialphase of the synthesis and remains constant during thelater course of reaction.Later scientific work on the growth mechanism was

often focused on an observation which is made shortlyafter mixing the reactants. The synthesis solutionappears gray-bluish before turning into purple andthe well-known ruby red color which is characteristicfor spherical AuNP in the size range of r ∼ 5�15 nm.15

In 1994, Chow and Zukoski attributed the gray-bluecolor during the initial stage of the synthesis to thereversible aggregation of primary particles.9 This hy-pothesis has been supported and refined by severalother groups. Pei et al. reported the formation of 2Dgold nanowires networks for low citrate concentra-tions.16 Rodríguez-González and co-workers observeda sudden shift of the redox potential from þ0.75 Vversus Ag/AgCl to þ0.1 V at the end of the reaction,which they correlated to the peptization of aggregatesto form the final monodisperse particles.17 Pong et al.

proposed the formation of linear assemblies fromclusters, adsorption of more Au atoms, defragmenta-tion and aging via Ostwald ripening.18 Ji and co-workers deduced a pH dependent growth mechanismwhich also comprises the formation of aggregates andintraparticle ripening for pH values below 6.5 (refers topH after mixing the reactants).19 Although not consis-tent with their small-angle X-ray scattering (SAXS)experiments, Mikhlin et al.proposed a growthmechan-ism involving the formation of dense liquid domainsenriched with Au clusters and complexes followed bythe formation of AuNP aggregates, which separateduring the course of the reaction.20 The formation ofwire-like aggregates as an intermediate step was alsoreported by Zhao and co-workers.21 All these mechan-isms, which comprise the formation of any kind ofaggregate intermediates during the Turkevich synthe-sis, were derived mainly from UV�vis and TEM data.In this contribution, it will be shown that the origin ofthe gray-bluish color during the initial phase of the

synthesis was misinterpreted: large Au aggregates arenot formed at any time of the Turkevich synthesis.Simultaneously to the establishment of the different

nanowire theories, the nucleation-diffusional growthmodel proposed by Turkevich et al. still remainedwidely accepted.2,3,22 Kumar et al. even developed aquantitative model based on this growth mechanismincluding also Turkevich's organizer model.23 Recently,Georgiev and co-workers suggested a Finke-Watzkygrowth mechanism,24 which consists of a slow, contin-uous nucleation and a fast autocatalytic growth.25 Theirassumption is based on fitting an exponential rateequation to kinetic data (derived from ex situ AFMmeasurements) which shows a sigmoidal-curve shape.Polte et al. developed a synchrotron setup which

allows simultaneous SAXS and X-ray absorption nearedge spectroscopy (XANES) measurements for liquidsamples.26,27 With this setup, time-resolved data onparticle size distribution, relative particle concentra-tion and reduction of Au3þ to Au0 could be obtainedwhich allows tomonitor the particle growth in situ. Thededuced growthmechanism is explained in detail laterin this contribution.In 2010, a molecular mechanism for the reduction of

Au3þ during the Turkevich synthesis was proposed.2

Modeling of this reduction mechanism under differentpH conditions using DFT calculations contributed to abetter description of the underlying Au3þ reductionprocess.28 However, the results remained unrelated tothe particle growth mechanism though the growthobviously depends on the supply of monomers andthus on the reduction process. In general, we are yetfar from understanding the influences of synthesisparameters on the growth process and thus the finalsize. Only the combination of the chemical reductionprocess and the physicochemical particle growthcan deliver a full and comprehensive picture of theTurkevich synthesis.In this contribution, essential key questions of the

Turkevich synthesis are addressed, which lead to aprofound picture of the Turkevich method's growthmechanism:

1. What is the general growth mechanism of theTurkevich synthesis?

2. When is the final particle size determined?3. What determines the final particle size?4. How do synthesis parameters influence the par-

ticle growth and therefore the final size?5. Why does the citrate reduction of silver nitrate

(AgNO3) not result inmonodisperse and uniformparticles as for HAuCl4?

RESULTS AND DISCUSSION

Question #1: What Is the General Growth Mechanism of theTurkevich Synthesis? As mentioned in the introduction,the number of proposed growthmechanisms is almostthe same as the number of publications on the topic

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itself. Therefore, the starting point for a comprehensivestudy on the Turkevich synthesis needs to be a discus-sion of the general growth mechanism.

Most of the deduced Turkevich mechanisms arederived from analytical methods which (i) might notreflect the properties of the colloidal solution (ex situ

methods, e.g. electron microscopy), (ii) cannot deliverdecisive information on the particle concentration (e.g.,UV�vis spectroscopy), or (iii) cannot be applied in asufficient time-resolution (e.g. in situ AFM20). SAXSwas shown to be a versatile tool for the investigationof nanoparticle growth mechanisms since it deliversin situ information on the particle size distribution andthe relative particle concentration.29�31 Combinedwith a free liquid jet, the method offers the benefitsof a container-free measurement (avoiding contami-nation problems) and minimized inducing effects ofthe incident X-ray beam. If the setup is applied at asynchrotron light source, the time-resolution can be inthe range of milliseconds. Coupled with XANES, simul-taneous tracking of the chemical reduction becomesavailable. Therefore, time-resolved SAXS/XANES mea-surements deliver the decisive information necessaryto deduce a comprehensive growth mechanism of theTurkevich synthesis.

A schematic, which can be found in Figure 1,illustrates the mechanism deduced from SAXS/XANESmeasurements by Polte et al.26,27 which was refinedrecently.32 The mechanism comprises four steps. Thefirst step is a partial reduction of the gold precursor andthe formation of small clusters from the Aumonomers.In a second step, these cluster form seed particles withradii >1.5 nm. The remaining gold ions are attractedand attached in the electronic double layer (EDL) of theseed particles as co-ions. The third and fourth stepcomprise the reduction of the ionic gold (first slowly,then fast) whereby the generated gold monomersgrow exclusively on top of the seed particles' surfacesuntil the precursor is fully consumed. Therefore, nofurther particles are formed during the last two steps.It should be mentioned that as early as 1958, Takiyamaalso recognized that the number of particles remainsconstant after a short initial phase. Nevertheless,the time resolution of his applied experimentalprocedure was very limited.14 Although Takiyama

deduced a crucial point of the growth mechanism,his work remained widely unrecognized.

The described mechanism can be referred to asseed-mediated growth mechanism. It can be distin-guished clearly from a so-called nucleation�growthmechanism. The latter is based on the formation of“nuclei”, a term which refers to the first thermodyna-mically stable clusters which in general consist of onlyfew atoms. In contrast, the herein described growthmechanism is based on the formation of seed par-ticles, which already have stable sizes and consistof some hundred atoms (for example, a AuNP withr = 1.5 nm consist of ∼840 atoms).

As mentioned above, several publications claimthe formation and subsequent fragmentation of largegold aggregates in the beginning of the Turkevichsynthesis.9,16�21 This assumption is based on the shiftof the plasmon band maximum from 530 nm toapproximately 520 nm during the early stage of thesynthesis (corresponding to a color change from blue-purple to red), time-resolved DLS measurements andex situ TEM images which show large networks ofparticles. To disprove this hypothesis, ultrasmall angleX-ray scattering (USAXS) measurements at differentreaction times were made at the DORIS III synchrotronlight source using a flow-through capillary. USAXSallows to detect AuNP aggregates since the determi-nation of large objects (r > 25 nm) demands the mea-surement at very small angles (corresponds to lowq values, with scattering vector magnitude definedas q = (4π/λ)sin θ). Figure 2 shows selected scatteringcurves and corresponding fits for a Turkevich synthesiscarried out under same conditions as described inliterature26 (T = 75 �C, final concentrations [HAuCl4] =0.25 mM, [Na3Ct] = 2.5 mM, mixing of equal reactantvolumes). Even at the minimal accessible angle, whichcorresponds to q = 0.04 nm�1, no significant scatteringsignal is detected throughout the synthesis. This con-firms that large structures are not formed at any timeof the Turkevich synthesis. The bluish color of thereaction solution at the early stages is most likelycaused by the attachment of gold ions in the EDLof the seed particles and a change of their electronicproperties.32 Charging effects are known to influencethe optical properties of AuNP significantly.15,33

Figure 1. General growth mechanism of the Turkevich synthesis as deduced by Polte.32 Herein, this growth mechanism isshown to be valid for a wide range of parameter variations.

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Aggregates, which were observed in TEM images ofsamples taken during early stages of the synthesis, aremost likely artifacts formed during the sample pre-paration process (drying) and do not represent theactual properties of the colloidal solution. A detaileddiscussion on the existence or nonexistence of aggre-gates can be found in Supporting Information SI-1.

The proposed growth mechanism was derivedfrom investigations using three different sets of reac-tion conditions (75 and 85 �C, [HAuCl4] = 0.25 mM,[Na3Ct] = 2.5 mM and 75 �C, [HAuCl4] = 0.375 mM,[Na3Ct] = 2.5 mM, both mixing of equal reactantvolumes).25 To investigate the general validity of thededuced growthmechanism, another SAXS study withvarious sets of parameters including a variation ofreactant concentrations, the way of mixing the reac-tants and temperature was carried out at the ESRFsynchrotron light source. The results are shown in theSupporting Information (see SI-2). For all investigatedparameter combinations, the different growth stepsare observed. Only the duration of each particular stepand the corresponding mean particle radii depend onthe reaction conditions. The influence of reactionparameters on the growth process will be discussedin detail later in this contribution. From the parameterstudy, it can be concluded that the deduced growthmechanism is valid for a wide range of reaction condi-tions, at least for sets of parameters commonly used inTurkevich synthesis protocols.

Summary #1. The Turkevich synthesis is character-ized by a seed-mediated growth mechanism. Stableseed particles with sizes of r > 1.5 nm are formed in thebeginning of the synthesis. Remaining gold ions are

attached and reduced in the EDL of the seed particlesand grow exclusively onto the existing particles.Further particles are not formed. Therefore, the totalnumber of particles at the end of the synthesis corre-sponds to the number of seed particles and is deter-mined already in the beginning of the synthesis. Theformation of large aggregates (“nanowires”) during thecourse of the reaction can be excluded.

Question #2: When Is the Final Particle Size Determined?According to the growth mechanism of the Turkevichsynthesis, the final number of particles corresponds tothe number of seed particles formed in step 2. Thenumber of particles determines the final size because itdefines to howmany particles the total amount of gold(defined by initial HAuCl4 concentration) is distributed.Therefore, the final particle size is already determinedby the seed particle formation. Accordingly, step 2 ofthe growth mechanism is investigated in this section.

The end of step 2 corresponds to the point atwhich the relative number of particles remains con-stant. A direct determination of the according reactiontime is difficult. The relative particle number can bederived from SAXS experiments, but a sufficient signal-to-noise ratio is required. In the beginning of theTurkevich synthesis (i.e., during the seed formationstep), the solution contains too few particles for aprecise analysis of the particle concentrationwith SAXS.Nevertheless, the point at which the formation of seedparticles is finished (end of step 2) can be determinedusing an indirect approach as illustrated in Figure 3a. ATurkevich synthesis is carried out under reflux. Aliquotsare extracted from the batch at different reaction timesand immediately cooled down to room temperature.

Figure 2. Selected scattering curves and corresponding mathematical fits of time-resolved USAXS measurements. Thereaction conditionswere in accordance to a previous publication26 (T=75 �C, [HAuCl4] = 0.25mM, [Na3Ct] = 2.5mM,mixing ofequal reactant volumes).

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The aliquots are kept at 20 �C for 4 days during whichthe entire amount of remaining gold slowly grows ontothe preformed seed particles. For colloidal gold, theabsorbance at 400 nm has been shown to be a goodmeasure for the total amount of atomic gold.15 There-fore, the full precursor reduction of the aliquots can bechecked by comparing their absorbance at 400 nm tothe absorbance of the standard synthesis. The com-pleted colloidal solutions (after 4 days) are investigatedwith electron microscopy and SAXS and compared tothe particles of the standard batch. As evident from thegrowthmechanism, the total number of particles in thefinal colloidal solutions should be the same if an aliquotis taken after the seed formation (i.e., after step 2). As aresult, the final particle sizes should be identical. If analiquot is taken before the end of the seed particleformation, step 2 will be disturbed and the number ofseed particles of the aliquot would be different fromthe standard batch. The remaining amount of gold isdistributed tomore or less particles. As a result, the finalparticle size of the aliquot is either smaller or larger

compared to the standard batch. Therefore, the firstreaction time at which the final size of an aliquotmatches the size of the final standard solution is thepoint at the seed formation was completed. Thedescribed experiment (following denoted as quench-ing experiment) was carried out for a typical Turkevichsynthesis. Over the last six decades, a variety of experi-mental protocols have been described. In this publica-tion, the standard synthesis refers to the followingprocedure: 199 mL of a 0.25 mM HAuCl4 solutionare refluxed for 15 min. One milliliter of a 500 mMfreshly prepared Na3Ct solution is added quickly (finalconcentration [Na3Ct] = 2.5 mM). The solution is re-fluxed until ruby red. For the quenching experiment, 9aliquots were taken in the as-described procedure. Inaddition, the reduction progress wasmonitored duringthe course of the synthesis using UV�vis spectroscopy(monitoring the 400 nm absorbance). Figure 3b showsthe absorbance at 400 nm versus time during theperformed standard Turkevich synthesis and displaysthe reaction times at which aliquots were taken fromthe batchmix. Figure 3c displays the finalmean particleradius of the aliquots and the final standard solution asdetermined with SAXS together with exemplarily SEMimages. The final particle sizes determined with SAXSare in accordance to the sizes determined with SEM. Inaddition, selected aliquots were investigated with TEM(see Supporting Information SI-3). The mean particleradius of the final standard solution was 8.7 nm (poly-dispersity 10%). Aliquots 1 and 2 had finalmean radii of10.7 and 9.1 nm (both with high polydispersity of 30%),respectively. Aliquot 3, which corresponds to a reactiontime of 30 s and a reduction progress of approximately1.3% (determined from the absorbance at 400 nm), aswell as the other aliquots showed almost the samemean particle radius as the final standard solution(between 8.5 and 8.8 nm, polydispersity 10%). Thismeans aliquot 3 marks the end of the seed particleformation in the standard synthesis batch. Further-more, the results support the deduced growth me-chanism (see Figure 1) since they prove that thekinetics of the reduction process (some minutes at100 �C, some days at 20 �C) are irrelevant with respectto the final size from a certain point of the synthesis.Steps 1 and 2 of the growth mechanism determine thefinal size, while the exact kinetics and reduction me-chanism of step 3 and 4 have no influence.

Summary #2. The final size is determined at the endof the seed particle formation (step 2). For the standardsynthesis with a total reaction time of approximately17 min, the formation of seed particles proceedsapproximately within the first 30 s at which approxi-mately 1�2% of the gold precursor is reduced. Conse-quently, the final particle size is already determinedwithin a very short time uponmixing the reactants. Thekinetics of the following growth steps are irrelevant forthe final particle size.

Figure 3. (a) Sketch of the quenching experiment to inves-tigate at which reaction time the final size is determined;(b) UV�vismonitoring of absorbance at 400 nm versus time,corresponds to reduction progress; (c) representativeSEM images and results of SAXS measurements afterAu3þ reduction was completed at 20 �C (polydispersityof samples 1 and 2 = 30%, polydispersity of samples 3 tofinal = 10%).

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Question #3: What Determines the Final Particle Size? Incase of monodispersity, the final particle size is deter-mined by the number of particles to which the totalamount of monomers (atoms) is distributed. The pre-vious sections of this contribution revealed that forthe Turkevich synthesis (which delivers monodisperseparticles) the first two steps of the growth mechanismalready determine the final particle number and there-fore the final size. To understand what determines thefinal size, all decisive influences on this very short initialperiod need to be investigated.

General Considerations Regarding the Number of SeedParticles. As stated, the final size is defined by thetotal number of particles, which corresponds to thenumber of seed particles for the Turkevich synthesis.Figure 4a illustrates the two paths which in generaldetermine the number of seed particles. (Note: Bothcan be relevant at the same time.) The first pathcomprises the amount of Au0 which is available forthe formation of the seed particles. It depends on thereduction chemistry during the process of seed particleformation. A larger amount of Au0 leads to formation of

Figure 4. (a) Sketch to illustrate what determines the final particle size of the Turkevich synthesis. The final size depends onthe total number of particles which corresponds to the number of seed particles. It is determined by the amount of Aumonomers available for seed particle formation (left side) and the seed particle size (right side). Two examples for differentamounts of Au monomers and different seed particle size, respectively, depict their influence on the final particle size. (b,c)Illustration of colloidal stability concept to describe reaction parameter influences on the size of NP. In this contribution, theconcept is used to illustrate the influenceofparameterson the sizeof seedparticles. (b) Schematics of aggregationbarrier versusparticle radius for twodifferent systems. EkT corresponds to the available thermal energy. In area I, particle growth is initiated. Inarea II, stable colloids are obtained. (c) Schematics of influence of temperature change on the colloidal stability of a NP solution.

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more seed particles. The total amount of gold isdistributed to more particles. As a consequence, thefinal size is smaller. This is illustrated on the left side ofFigure 4a.

The second path which influences the number ofseed particles is the seed particle size. Larger seedparticles consist of more Au atoms. Therefore, fewerparticles can be formed from the amount of Au0

available for the seed particle formation and the finalparticle size is larger (illustrated on the right side ofFigure 4a). Recently, a concept to describe nanoparticlegrowth governed by colloidal stability has been intro-duced andwill be usedwithin this discussion.32 In brief,colloidal stability is a result of attractive van der Waalsand repulsive electrostatic forces between two parti-cles. According to a theory by Derjaguin, Landau,Verwey, Overbeek (referred to as DLVO theory), thesum of these opposing forces results in a total interac-tion potential depending on the distance between twoparticles whereby the maximum is referred to asaggregation barrier.34,35 The aggregation barrier canbe interpreted as an energy required for the aggrega-tion of two particles which provides a measure for thecolloidal stability. In general, the aggregation barrier(thus the colloidal stability) between two electrostaticstabilized particles increases with increasing particlesize as illustrated in Figure 4b,c for identical particles.Herein, these curves (aggregation barrier versus parti-cle size) are referred to as “stability curves”. The growthconcept suggests that two particles can overcome theelectrostatic repulsion and aggregate/coalesce as longas the aggregation barrier is lower than the thermalenergy EkT, thus enabling particles to grow (section I).In section II, the aggregation barrier cannot be over-come any longer inhibiting further particle growth.Simplified, the particle radius related to the interceptpoint of EkT and the stability curve defines the mini-mum stable particle size. In the picture of the colloidalstability approach, the final particle size of a colloidalsolution is therefore determined by the stability curvewhich depends on the surface charge and on the

chemical composition of the colloidal solution (e.g.,specific nature of ions, ionic strength etc.) and by theavailable thermal energy EkT. This approach providesan opportunity to describe the influences of reactionparam-eters on the size of particles. The concept was shownto be applicable for different nanoparticle syntheseswhich are based on a fast monomer supply (e.g., reduc-tion of HAuCl4 with NaBH4).

36 Although the Turkevichsynthesis comprises a weak reducing agent, the initialphase of seed particle formation can be describedusing this approach because monomers are providedrelatively fast (see #2).

To summarize Figure 4, the reaction conditions ofthe Turkevich synthesis protocol can influence both,the colloidal stability of the seed particles and thechemistry of reduction during seed formation. Conse-quently, the reaction conditions determine the num-ber of seed particles and therefore the final particlesize. In fact, the final particle size is smaller the moreseed particles are formed and vice versa.

Predominant Path for the Number of Seed Particles. Thenumber of seed particles is determined by their colloi-dal stability and the chemistry of reduction during seedparticle formation. In general, it is difficult to investi-gate these paths independently since most reactionconditions influence both of them at the same time.Therefore, a reproducibility study using only one set ofreaction parameters (standard synthesis) is discussedfirst followed by an ionic strength variation study.Increasing the ionic strength by adding “unreactive”(noninvolved) ions does most likely influence thecolloidal stability but not the reduction chemistry.

Reproducibility Study. For a reproducibility studywith 40 repetitions, the Turkevich synthesis was per-formed by different scientists over a period of one yearusing different reactant solutions always strictly follow-ing the standard synthesis protocol. The final particlesizes were determined with SAXS. Figure 5a showsthe final mean radii versus overall reaction time (timeuntil precursor is reduced completely, determined by

Figure 5. (a) Reproducibility study. Final mean radius versus overall reaction time for repetitions of the Turkevich standardsynthesis (polydispersity = 10%). Repetitions were conducted over a period of one year. The overall reaction time wasdetermined by observing the color change of the reaction solution until it shows a characteristic ruby red color. (b) Influenceof ionic strength on standard Turkevich synthesis. Final mean radii versus total NaClO4 concentration (for 0�30 mM,polydispersity = 10%; for 40 mM, polydispersity = 25%).

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observing the colloidal solution until it has a character-istic ruby red color). The final mean radii vary asmuch as from 6.5 to 10 nm (polydispersity = 10%).For small final radii (correspond to a larger numberof seed particles), a shorter reaction time is observed.This indicates that the total surface area of the seedparticles facilitates the kinetics of growth (steps 3 and 4).In other words, a decreasing final particle size is causedby an increasing number of seed particles, whichin turn increases the kinetics of the steps 3 and 4. Thedeviation of final particle sizes might be surprising sincean often mentioned advantage of the Turkevich syn-thesis is its high reproducibility.3,5,19,37 Nevertheless anextensive study has not been reported yet. In thepresented picture of growth, either the reductionchemistry during seed particle formation, the colloidalstability of the seed particles or both are responsiblefor the lack of reproducibility. Following, it is shownthat the colloidal stability has most likely a minorinfluence.

Influence of Colloidal Stability: Variation of Ionic

Strength. Increasing the ionic strength of the reactionsolution with NaClO4 has no significant influence onthe reduction chemistry since the added ions are“noninvolved” in chemical processes which are linkedto the reduction of the gold precursor. Therefore, onlythe colloidal stability path (illustrated in Figure 4a) willchange with different NaClO4 concentrations. For thecorresponding experiment, NaClO4 was added to theNa3Ct solution prior to mixing with HAuCl4. The finalparticle sizes were determined with SAXS. Figure 5bdisplays the mean particle radius versus total con-centration of NaClO4 (referring to the final colloidalsolution). No significant effect is observed up to 30mM,which corresponds to a 120 times higher concentra-tion compared to Au3þ. Only at concentrations ex-ceeding 30mM larger AuNP are formed; above 50mM,precipitation is observed. Similar observations werereported by Zhao et al. upon addition of NaNO3.

21

The relatively constant particle size for NaClO4

concentrations of up to 30 mM reveals that the colloi-dal stability (and therefore the size of the seedparticles) remains mostly unaffected for a wide rangeof ionic concentrations, in particular in the range ofcommon Turkevich synthesis protocols. Although thecolloidal stability of the seed particles plays an impor-tant role, it appears to be constant. Consequently,the deviations of final particle sizes observed in thereproducibility study are most likely not related tochanges of the colloidal stability. Therefore, the reduc-tion chemistry can be assumed to predominantlycause changes of the seed particle formation stepand the number of particles.

Reduction Chemistry. From the results presented inFigure 5, it could be deduced that the chemistry ofreduction during the first two steps has a considerableeffect on the number of seed particles. Even apparent

small changes during the synthesis can influence thereduction to such a great extent that the final sizediffers significantly. The reaction chemistry of thesolution is extremely complex since the reactants,citrate and gold ions, exist both in different chemicalforms, which can be converted reversibly into eachother. In addition, citrate can be oxidized irreversiblyresulting in a variety of chemical species. This subsec-tion discusses the chemistry of the reactants HAuCl4and Na3Ct followed by an investigation of the decisiveprocesses upon mixing.

Chemistry of the Gold Precursor. In the gold coordi-nation sphere, four anions are coordinated in squareplanar geometry; at strong acidic conditions, theseare four Cl� ligands. With increasing pH value, theCl� ligands are exchanged successively by OH� (seeFigure 6, right side). At mild acidic, neutral, and mildalkaline conditions, mixtures of two or more gold com-plex species are obtained. Several researchers investi-gated the ratios between the different [AuCl4‑xOHx]

�

species with dependence on the pH value. The domi-nant gold complexes were determined (occasionallywith different results) from quantitative analysis of thefree Cl� ligands using ion chromatography,38 UV�visand Raman spectroscopy,19,39,40 or by calculationsfrom the pK values.28,41 In addition to the pH value,the ratio of the gold species is also known to beinfluenced by temperature.41 UV�vis spectra of a0.25 mM HAuCl4 solution at different temperatures(see Supporting Information SI-4) indicate, as ex-pected, that elevated temperatures promote a shiftof the equilibrium toward a more hydroxylated form.The redox potential of the gold complexes depends onthe species.2,21,22,42 The concentration of species withhigher redox potential ([AuCl4]

�) decreases with in-creasing pH.2,19,38,41,43 In addition to the redox proper-ties, the actual gold species and thus also the pH valuesignificantly influence the optical properties of theionic gold solution. The [AuCl4]

� complex exhibitstwo absorbance bands at ∼226 and 313 nm, whichcan be assigned to the pπ f 5dx2�y2 and pσ f 5dx2�y2

ligand�metal transition, respectively.19,38,40,41 The ab-sorption bands decrease and blue-shift with exchangeof Cl� by OH� ions (see Supporting Information SI-4).Therefore, the absorbance at 313 nm can be used tomonitor the kinetics of the [AuCl4�xOHx]

� equilibrium.To study the temperature dependence of the establish-ment time of the gold complex equilibrium, NaOHwasadded to a 0.25 mM HAuCl4 solution (pH = 3.3) atdifferent temperatures to give a final pH of ∼6.5(equivalent to pH obtained by addition of 2.5 mMNa3Ct), while the absorbance at 313 nm was recordedtime-resolved. Selected data can be found in Support-ing Information SI-4. Figure 6a depicts the time toestablish the complex equilibrium versus tempera-ture. For 95 �C (boiling conditions are not accessibledue to experimental limitations), the equilibrium is

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reached after ∼30 s. The equilibrium time for the goldcomplexes increases significantly with decreasingtemperature.

Chemistry of the Reducing Agent. Similar to the goldcomplex, different citrate species exist in a chemicalequilibrium (see Figure 6, right side). Citrate has threecarboxyl groups, which can be protonated/deproton-ated, leading to an acid�base buffer. The ratio of thedifferent citrate species in dependence of the pH canbe estimated from their pKa values (3.2, 4.8, and6.4).22,28 At low pH values, the fully protonated formis favored. Citrate shows no absorbance in thevisible region (colorless solution) but absorbs lightin the UV range. The optical properties change withprotonation/deprotonation (see Supporting Informa-tion SI-4). Therefore, the absorbance at 200 nm can beused to monitor the kinetics of the protonation

equilibrium upon addition of Hþ. To avoid saturationeffects of the detector, the concentration was de-creased to [Na3Ct] = 1.25 mM (pH 7.6). HCl was addedin an amount equivalent to 0.125 mM HAuCl4 (to keepa molar ratio of 10:1 as in the standard synthesis) todecrease the pH to 6.44. Figure 6b depicts the absor-bance (200 nm) versus time upon addition of HCl at23 �C. The kinetics at elevated temperatures are notaccessible with a standard UV�vis setup. Within ∼2 s,the absorbance decreases to a constant level indicat-ing that the protonation equilibrium is reached rela-tively fast. Similar to the ligand exchange equilibriumof the gold complexes, the protonation equilibrium ofcitrate is temperature-dependent (see Supporting In-formation SI-4). In addition, the irreversible oxidation ofcitrate to dicarboxy acetone (DCA),3,6,22,23,44�46 ace-tone or other products4 upon heating or in the presence

Figure 6. Chemical reactions of the pure reactants and their kinetics. (a) Time until gold complex equilibrium (see right side) isreached in a 0.25mMHAuCl4 solution upon addition of NaOH to give a final pH of∼6.5. The equilibrium timewas determinedat different temperatures. (b) Absorbance at 200 nm for a 1.25mMcitrate solution at 23 �C upon addition of HCl to give a finalpH of∼6.5. The pH value influences the protonation equilibrium of citrate as illustrated on the right side. (c) UV-vis spectrumof 1.25mM citrate solutions recorded as prepared and spectra of the same solution heated to 30 and 60 �C, respectively, andcooled to 23 �C. The latter spectra are identical.

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of metal ions has been described in the literature.The formation of DCA has been assumed to play adecisive role for the mechanism of the Turkevichsynthesis3,6,12,23,46 which will be discussed later in thiscontribution. However, a threshold temperature for theformation of citrate oxidation products has not beenreported so far. Figure 6c shows UV�vis spectra of1.25mMcitrate solutions recorded at 23 �C as preparedand headed to 30 and 60 �C before, respectively. Thedata indicates that the citrate solution is changedirreversibly, most likely attributed to a decompositionpathway, already upon heating to 30 �C.

In summary, both reactants of the Turkevich syn-thesis exist in a variety of different species. Tempera-ture and pH value determine the actual ratios of thespecies. The ligand exchange equilibrium of the goldcomplexes upon increasing the pH value is reachedmuch slower compared to the protonation equilibriumof citrate upon addition of Hþ. Irreversible oxidationproducts of citrate are formed already at temperaturesslightly above room temperature.

Chemistry upon Mixing HAuCl4 and Na3Ct. The in-vestigations of the pure HAuCl4 and Na3Ct show thatthe reactant solutions can contain a variety of chemical

species already before mixing. Upon addition of Na3Ctto HAuCl4, the pH increases and shifts the gold com-plex equilibrium toward more hydrolyzed forms. Inaddition, oxidation products of citrate are formed.All these processes create a continuously changingTurkevich reaction system with a great complexity anda variety of possible pathways for the reduction ofAu3þ. Recently, a molecular reduction mechanism wasproposedwhich comprises at first a ligand exchange ofthe precursor with a citrate ion to form an intermediategold complex, a ring closure step followed by a con-certed decarboxylation, the reduction of the Au3þ-complex to an Auþ-complex and a disproportiona-tion step which finally leads to atomic Au.2 In fact,20 different combinations of gold and citrate speciesare possible (see Figure 7d). Of course, not every com-bination makes sense from a chemical point of view(e.g., co-occurrence of [Au(OH)4]

� and H3Ct) or regard-ing the given reaction conditions (pH values range onlyfrom ∼3.3 to 7 in the standard Turkevich synthesis).Nevertheless, several potential reaction pathways in-volving different chemical species are available for thereduction process. In a recent publication, DFT calcula-tions for three selected combinations of gold and

Figure 7. Chemistry and kinetics upon mixing the reactants HAuCl4 and Na3Ct. Absorbance at 313 nm of a 0.25 mM HauCl4solution upon addition of 2.5 mM Na3Ct or NaOH to reach a final pH of ∼6.5 at (a) 95 �C and (b) 75 �C; (c) sketch of chemicalprocesses during seed particle formation. (d) Theoretically possible combinations of gold complex and citrate species. Theyellow background designates combinations which are most likely to supply Au monomers during the seed particleformation. The gray background designates combinationswhich aremost likely to supply Aumonomers during steps 3 and 4of the growth mechanism. Note that not all listed combinations can co-occur in a Turkevich synthesis.

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citrate species were made.28 The reduction was foundto be facilitated for [AuCl4]

� and highly deprotonatedcitrate ions with the gold species having the majorimpact on the total reaction free energy. The hereindiscussed growth mechanism of the Turkevich synthe-sis demands that at least one process stops the seedparticle formation. Most likely, this process is asso-ciated with the transformation of the reactant speciesin the beginning of the synthesis. A simple analyticalmethod to determine the change of chemical compo-sition during the seed particle formation phase isnot available. Nevertheless, time-resolved monitoringof the 313 nm absorbance upon mixing the reactantscan deliver useful insights since the [AuCl4]

� speciesshows a significant absorbance at this wavelengthwhile the [AuCl3OH ]� species does only slightly absorbat this wavelength. Figures 7a,b show the absorbance(313 nm) versus time for 95 and 75 �C, respectively, formixing HAuCl4 and Na3Ct (standard concentrations)and mixing HAuCl4 and NaOH (to reach the same finalpH of ∼6.5). For both investigated temperatures, thecurve profiles are almost the same in the beginning.For 95 �C, the seed particle formation phase can beassigned approximately to the first 30 s of the syn-thesis (see #2) matching the phase during which thecurve profiles are almost the same. Therefore, it can beexpected that the gold equilibrium is shifted from[AuCl4]

� to [AuCl3‑x(OH)1þx]� during the seed particle

formation phase. More indication comes from anUV�vis study with varied initial concentration of goldprecursor (see #3 and Supporting Information SI-5).Figure 7c illustrates the most probable chemical pro-cesses during the seed formation step. Before mixing,the HAuCl4 solution contains a certain amount of[AuCl4]

� ions (pH 3.3). Upon addition of citrate, thepH value increases almost immediately to ∼6.5, whichshifts the equilibrium to a less reactive gold complex(causing discoloring of the reaction solution). A smallfraction of reactive [AuCl4]

� can be reduced quicklywithin this time supplying Au0 for the seed particleformation. As soon as the equilibrium is reached, thesolution contains mainly or only [AuCl3�x(OH)1þx]

�

species which are not reactive enough to be reducedfast in solution. Instead, these species are attracted bythe seed particles, enriched in their EDL which leads toa reduction at the seed particles' surfaces. The seed-mediated growth mechanism is basically a fortunatecoincidence and the consequence of a favorable inter-action of many circumstances. The chemically inducedtransformation of a reactive precursor species into aless reactive species (which itself is a lucky circum-stance) happens just in appropriate time to trigger thefast generation of a small but sufficient amount ofmonomers to form seed particles. Just as important,the transformation of [AuCl4]

� to [AuCl3�x(OH)1þx]�

blocks a further fast supply of monomers in solu-tion which could form further particles or grow on

existing particles in an uncontrolled way at later reac-tion times.

Role of Dicarboxyacetone (DCA). Regarding the re-duction process, some publications deduced a specialrole for DCA. Turkevich and co-workers found DCA tobe a kinetically faster reducing agent for HAuCl4 thancitrate and assigned the origin of the “induction peri-od” (initial phase during which they could not observethe formation of particles) to the formation of DCAfrom citrate.6,12 In their interpretations, DCA organizesthe gold ions into large macromolecules. The largelocal concentration of gold precursor was supposed tofacilitate the reduction of Au3þ. Later, DCA was sup-posed to form a DCA�Auþ complex facilitating selec-tively the disproportionation step of Auþ to Au0.2,3

However, Doyen et al. could not find experimentalsupport for the existence of such an intermediate fromNMR investigations.4 To investigate the influence ofDCA with regard to the growth mechanism, a series ofexperiments were carried out (i) with DCA used as theonly reducing agent instead of Na3Ct, (ii) DCA added toa standard synthesis after seed particle formation, and(iii) DCA added to Na3Ct before mixing with HAuCl4.Experimental details, results and discussion can befound in Supporting Information SI-6. From the experi-mental results, it can be concluded that large concen-trations of DCA (∼40% with respect to citrate concen-tration) if present already during the seed particleformation change the growth mechanism. The con-centration of DCA during the seed particle formationstep is rather low in a standard Turkevich synthesis.Therefore, DCA plays no essential role in the reductionmechanism of the seed particle formation (i.e., steps1 and 2). However, high concentrations of DCA duringsteps 3 and 4 accelerate the autocatalytic growth of theseed particles but do not affect the final particle size.Consequently, DCA has no significant influence on thefinal particle size for common Turkevich synthesisprotocols.

Summary #3. The seed-mediated growth mecha-nism of the Turkevich synthesis ensures the formationof highly uniformAuNP. To understandwhat determinesthe final particle size, the general mechanism (see #1)has to be extended as illustrated in Figure 8. The seed-mediated growth mechanism is a fortunate coin-cidence created by a favorable interplay of differentchemical processes. Upon mixing the reactants,the buffer effect of Na3Ct induces the transforma-tion of reactive [AuCl4]

� species into less reactive[AuCl3�x(OH)1þx]

� species. This process occurs in justappropriate time to trigger the fast generation of asmall but sufficient amount of monomers from[AuCl4]

� to form stable particles, the seed particles.The transformation of the reactive gold complex blocksa further fast supply of monomers in solution whichcould form further particles or grow onto existingparticles in an uncontrolled way. Therefore, the shift

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of the gold complex equilibrium terminates step 1 ofthe growthmechanism. The kinetics of the transforma-tion of [AuCl4]

� to more hydrolyzed forms and thekinetics of the reduction of [AuCl4]

� to Au0 determinethe amount of monomers available for seed particleformation. The size of the seed particles defines howmany particles can be formed from the available Au0

monomers. The resulting number of seed particlescorresponds to the final particle number and deter-mines the final size since residual gold grows exclu-sively onto the seed particles. Certainly, the describedprocesses are even more complex than illustratedin Figure 8. However, the essential points summarizedherein allow an understanding of parameter influenceson the growth mechanism and the final particle size.

Question #4: How Do Synthesis Parameters Influence theParticle Growth and Therefore the Final Size? The influence ofreaction conditions on the final particle size andthe subsequent development of synthesis protocolsare subject of many publications. However, an under-standing of how the parameters influence the final sizeis still missing. In the following section, results ofparameter variations described in literature in combi-nation with further parameter studies are discussedusing the gained knowledge from sections #1�3. Asshown in #3, the synthesis is not as reproducible asoften stated. This is most likely caused by small differ-ences of the reduction process during the seed particleformation which are difficult to control in a typicallaboratory environment. Therefore, all parameterstudies described herein were, as far as possible,carried out within a short period of time.

Variation of Reactant Concentrations. The variation ofreactant concentrations is the common adjustment ofa synthesis recipe. Table 1 summarizes the results of aparameter study following the standard Turkevichprotocol. For two Na3Ct concentrations (2.5 and3.75 mM), the HAuCl4 concentration was varied(0.125, 0.25 and 0.5 mM). Each experiment was re-peated three times. The effect of Na3Ct concentrationis negligible, while the final size decreases significantlyfor higher HAuCl4 concentrations.

Variation of Citrate Concentration. Kumar et al.23

summarized the results of different publications on the

variation of the Na3Ct concentration at a fixed goldconcentration (∼0.25 mM) using the work ofTurkevich,6 Chow and Zukoski,9 Freund,10 Spiro10 andFrens.8 Kumar's overview shows that the final sizeremains almost unaffected for a wide range of Na3Ctconcentrations, which is also congruent with results byTakiyama14 and those presented herin in Table 1. Onlyfor very small (approximately below 0.5 mM) or veryhigh (10 mM) citrate concentrations, the final size aswell as the polydispersity were shown to increase.19,23

The results can be explained by the different rolesof the citrate species, which include reducing agent,stabilizer and pH mediator. As shown in #3, the buffereffect of citrate shifts the gold complex equilibriumtoward less reactive forms upon mixing so that theseed particle formation is stopped. This process isrequired to create the fortunate coincident of theseed-mediated growth mechanism. If citrate is addedin a sufficient concentration, the kinetics of the pro-tonation equilibrium and the final pH of the solutionare approximately the same irrespective of the molarexcess.19 Therefore, the seed particle formation is al-most not affected by an increasing citrate concentra-tion leading to final particles of about the same size. Ifcitrate is added in very low concentration, the molarexcess might still be sufficient to reduce the amountof Au3þ but not to shift the gold complex equilibriumfrom reactive [AuCl4]

� to less reactive hydrolyzedforms. The fortunate coincident vanishes and, in addi-tion to the reduction of Au3þ in the EDL of preformedparticles, reduction can also occur unselectively duringthe entire synthesis. This produces nonuniform poly-disperse final colloids. Furthermore, Na3Ct plays adecisive role in stabilizing the initially formed particles.For very low concentrations, seed particles which stillmight exist have to grow to larger sizes to reach astable size (see Figure 4b, curve A versus B). For veryhigh citrate concentrations (see Chow and Zukoski9),the Turkevich synthesis can be expected to follow theseed-mediated growth mechanism, but the colloidalstability of the seed particles decreases due to the highionic strength. The seed particle size increases leadingto less particles and larger final sizes (similar to theNaClO4 addition experiment in #3).

Figure 8. Summary of growth process and the underlying chemical processes.

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Variation of HAuCl4 Concentration. Kimling et al.

investigated the influence of HAuCl4 concentrationon the final size distribution for up to 1.2 mM.5 How-ever, size trends are difficult to deduce from thepresented data. Li et al. varied the HAuCl4 and Na3Ctat fixedmolar ratios and found themeanparticle radiusto decrease slightly for increasing HAuCl4 concentra-tion (0.25�1.5 mM).47 Takiyama observed a clear de-crease of particle size with increasing HAuCl4 concen-tration (0.1�1 mM).14

For the study presented in Table 1, the citrateconcentration was held constant (2.5 and 3.75 mM,respectively), while the HAuCl4 concentration wasadjusted to 0.125, 0.25, and 0.5 mM. The citrate con-centrations were chosen sufficiently high to create thefortunate coincident and ensure a seed-mediatedgrowth mechanism for all syntheses. The study showsthat the final particle radius is significantly smaller forincreasing precursor concentration. The origin of theobserved trend becomes apparent from comparingthe pH values of the initial HAuCl4 solutions whichdepend on the precursor concentration. The pH valueof HAuCl4 varies between 3.6 (0.125 mM) and 3.0(0.5 mM). Supporting Information Figure SI-4d showsthe absorbance at 313 nm (characteristic maximumfor [AuCl4]

�) versus the pH of a 0.25 mM precursorsolution. The absorbance decreases significantly be-tween pH 2 and 4 which indicates that the ratio of[AuCl4]

� /[AuCl4�x(OH)x]� decreases in less acidic me-

dium. During the seed particle formation step, mainlythe reduction of the reactive [AuCl4]

� species providesAu0 monomers for the seed particle formation. There-fore, if the initial concentration of [AuCl4]

� is higher,more monomers can be provided and more seedparticles are formed resulting in smaller final particles(cf. chemistry of reduction path in Figure 4a). An addi-tional study with time-resolved UV�vis measurementsand a more detailed discussion can be found in Sup-porting Information SI-5. For example, using a 0.5 mM

HAuCl4 solution, which contains more initial [AuCl4]�

than the standard 0.25 mM solution, about 13 timesmore seed particles are formed leading to smallerfinal particles. This results in a larger total surfacearea available for growth steps 3 and 4 (cf. reprodu-cibility study in #3). As a result, the overall reactiontime decreases with increasing HAuCl4 concen-trations.

Summary #4.1. The concentration of citrate has al-most no effect on the final size as long as its buffercapacity ensures a neutral pH after mixing the reac-tants. This provides a shift of the gold complex equi-librium toward less reactive forms to create thefortunate coincident which is required for the seed-mediated growth mechanism. In contrast, the concen-tration of HAuCl4 has a significant influence since itdetermines the initial pH value of the precursor solu-tion and the ratio of [AuCl4]

�/[AuCl4‑x(OH)x]� during

seed particle formation. For higher HAuCl4 concentra-tions, a larger percentage of [AuCl4]

� is availableduring the seed particle formation. More particles areformed. Therefore, smaller particles are obtained forhigher precursor concentrations.

Order of Reactant Addition. Recently, it was reportedthat the order of reactant addition influences the finalparticle size.3,46 In the standard synthesis, a Na3Ctsolution is added to a preheated HAuCl4 solution. Incontrast, the inverse method corresponds to the addi-tion of a small volume of highly concentrated HAuCl4solution to a large volume of diluted preheated Na3Ctsolution. The final concentrations of both reactantsare retained. It was found that final particle size andsynthesis time decrease using the inverse method.Ojea-Jiménez et al. assigned this observation to theformation of DCA by thermal oxidation of citrateduring preheating of the reducing agent solution. Theysuggested that the formation of DCA�Auþ complexesfacilitates the disproportionation to Au0 leading to fastnucleation and small particles.3 Sivaraman et al.

TABLE 1. Variation of HAuCl4 Concentration for Two Different Concentrations of Na3Ct (2.5 and 3.75 mM)a

0.125 mM HAuCl4 0.25 mM HAuCl4 0.5 mM HAuCl4

pH = 3.6 pH = 3.3 pH = 3.0

[Na3Ct] = 2.5 mMFinal size 13.8 ( 1.2 nm 9.3 ( 0.4 nm 5.5 ( 0.1 nmMolar Ratio Ct:Au R = 20 R = 10 R = 5Overall reaction time 19:27 ( 1:30 min 15:30 ( 0:55 min 3:00 ( 0:10 minRelative particle number 0.2 1 9.7

[Na3Ct] = 3.75 mMFinal size 14.2 ( 2.1 nm 9.8 ( 0.5 nm 5.3 ( 0.7 nmMolar Ratio Ct:Au R = 30 R = 15 R = 7.5Overall reaction time 17:45 ( 0:25 min 14:30 ( 0:10 min 4:30 ( 0:15 minRelative particle number 0.2 1 12.6

a Average mean radii (polydispersity = 10%) were calculated from three separated experimental runs. The relative particle number was calculated with respect to the 0.25 mMstandard concentration of HAuCl4 (r.n. = Ær1æ3/Ær2æ3 3 [HAuCl4]2/[HAuCl4]1, see also Experimental Section).

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assigned the influence of inverse reactant addition tothe formation of DCA, too. However, they pointed outthat thermal citrate oxidation during preheating isunlikely to produce a sufficient amount of DCA. Itwas concluded that chemical oxidation of citrate byAu3þ is favored in the inverse method producingmoreDCA during the initial phase of the reaction.46

We repeated the inverse experiment three timesand found the final size to be smaller (7.6( 0.1 nm) andthe reaction time (670 ( 20 s) to be shorter for theinverse method compared to the standard method,congruent to the previous reports. It was shown in #3that a Na3Ct solution is changed irreversibly uponheating, most likely due to the formation of oxidationproducts such as DCA. However, it was also shown thatDCA has no significant influence on the growth mech-anisms and thus the final size evenwhen added in highconcentrations (1 mM) prior to the reaction. There-fore, even if DCA is formed during the preheatingstep in the inverse method, it is unlikely that itsconcentration is high enough to influence the growthmechanism and the reaction outcome. Instead, theeffect of the inverse method can be attributed todifferent initial amounts of reactive [AuCl4]

� similarto the variation of HAuCl4 concentration discussed inthe previous subsection. The gold equilibrium wasshown to be shifted to more hydrolyzed forms withincreasing temperature. Preheating of the gold pre-cursor solution (standard method) leads to less initial[AuCl4]

�. In addition, the concentration of HAuCl4 inthe inverse method is very high (50 mM). The corre-sponding low pH value provides the presence of evenmore [AuCl4]

� during seed particle formation. Conse-quently, more Au0 is available for the seed particleformation andmore particles are formed in the inversemethod (cf. chemistry of reduction path in Figure 4a).This leads to smaller final particles as well as to ashorter reaction time since the total surface area ofthe seed particles is higher facilitating, a fast growthduring steps 3 and 4.

Summary #4.2. The inverse method comprises thechange of reactant addition order and leads to theformation of smaller particles. This effect is caused bydifferent initial amounts of [AuCl4]

� available duringseed particle formation rather than by any DCA in-duced processes as assumed previously.

pH Value. The important role of citrate as pH medi-ator which is essential to ensure a seed-mediatedgrowth mechanism was already pointed out. Ob-viously, the pH value has a significant effect on thefinal size. The acidity influences the initial amount of[AuCl4]

�, the buffer capacity of citrate, the colloidalstability of the seed particles and the reducingpower of citrate. Indeed, Patungwasa et al. reportedthat the pH value influences size, polydispersity andmorphology of the final particles.22 Zhao et al. andOjea-Jiménez and Campanera showed that the final

particles are smaller for more acidic conditions.21,28

It was also reported that the total reaction time de-creases significantly at low pH values.19,28 Figure 9shows the results of a parameter study for which theinitial pH value of the 0.25 mMHAuCl4 (unmodified pH= 3.3) solution was adjusted prior to mixing with Na3Ctadding either HCl or NaOH. As suggested above, thepH value can have several influences creating a com-plex interplay of different processes. For a clearerdiscussion of the results, the graph shown in Figure 9is divided into five areas.

For pH < 1.5 (area 1), no reduction of the gold pre-cursor is observed. The high concentration of Hþ

exceeds the buffer capacity of citrate which becomesfully protonated upon mixing with HAuCl4. Pure H3Ctcannot reduce any Au3þ species since the formation ofan intermediate complex with the gold ion (first step ofmolecular reduction mechanism28) requires at leastone deprotonated carboxy group.

In area 2 (pH 1.5�2.3), Au3þ is reduced to Au0, butonly macro sized particles which precipitate at thecontainer walls are formed. The observation can be ex-plained by the effect of ionic strength which is extre-mely high in area 2 due to the addition of HCl in largeamounts. Colloidal solutions are not stable (cf. colloidalstability path in Figure 4a).

Areas 3 and 5 are complex since the seed-mediatedgrowth mechanism is not retained. For a better under-standing, area 4 is discussed first. Area 4 comprises onlyvery slight acidifying/alkalifying of the initial HAuCl4

Figure 9. Influence of the initial pH value of the HAuCl4solution. (a) Final mean particle radii, (b) polydispersities.

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solution (pH 2.7�4) so that the prerequisites for thefortunate coincident are fulfilled facilitating a seed-mediated growthmechanism. First, enough [AuCl4]

� ispresent in the initial precursor solution to trigger theseed particle formation. Second, the buffer capacity ofNa3Ct is sufficient to shift the gold complex equilibriumupon mixing (terminating the seed particle formation).As a result of the retained seed-mediated growthmechanism, the obtained solutions are relatively uni-form (polydispersity 10%). A minimum mean radius ofr= 5.4 nm is obtained at pH= 2.8. The final size increaseswith increasing pH value which is attributed to theinitial ratio [AuCl4]

�/[AuCl4�x(OH)x]� as already dis-

cussed in detail before (see Variation of HAuCl4 Con-centration).

Within areas 3 and 5, the presented seed-mediatedgrowth mechanism is not retained and the final parti-cles are rather polydisperse. The reasons for the chan-ged growth mechanism are different. In area 3, thebuffer capacity of Na3Ct is not sufficient to stop the seedparticle formation. In contrast, in area 5 the initial con-centration of [AuCl4]

� is too low to trigger the fastformation of seed particles. For both areas, the growthmechanism can be expected to be “mixed”. Seed particleformation might still occur but simultaneously uncon-trolled growth of existing and formation of furtherparticles can take place. The growth mechanism is mostlikely “less and less“ seed-mediated. In addition, the ionicstrength increases themore HCl or NaOH is added to theinitial HAuCl4 solution. The colloidal stability of the seedparticles (if present) and the final particles decreaseswhich leads to larger particle sizes (cf. colloidal stabilitypath in Figure 4a).

The variation study with pH-adjustment of theHAuCl4 solution prior to the synthesis illustrates thecomplexity of the processes which determine the finalsize. Another possibility of pH variation is a changesubsequent to the mixing of the reactants. Shiba et al.added NaOH to the reaction solution after differentdelay times.42 They showed that the final size is larger ifNaOH is added very quickly after mixing HAuCl4 andNa3Ct compared to a later addition. This observation

can be explained by accelerating the gold equilibriumshift toward hydrolyzed forms by addition of NaOH.The seed particle formation is stopped earlier thesooner NaOH is added to the mixture. Less seeds canbe formed (cf. chemistry of reduction path in Figure 4a)resulting in larger final particles.

Summary #4.3. The impact of the pH value on theTurkevich synthesis is enormous. The acidity deter-mines whether the seed-mediated growth mecha-nisms can actually occur. The fortunate coincidentvanishes if the gold precursor solution is too acidicand exceeds the buffer capacity of citrate. It alsovanishes for too high pH values since the initial amountof reactive [AuCl4]

� is too low to trigger the fast forma-tion of seedparticles. As a consequence of the changedgrowth mechanism, the reduction of Au3þ can occurunselectively leading to nonuniform particles forvery acidic or neutral reaction conditions. In addition,the pH value influences the initial amount of [AuCl4]

�

available during seed particle formation. More seedparticles are formed in more acidic HAuCl4 solutions.Furthermore, the colloidal stability decreases withaddition of HCl or NaOH (ionic strength increases) lead-ing to a larger final size. It also has to be noted that thereducing power of citrate is lost at extremely acidicconditions. The minimum size for standard conditionsis obtained at pH(HAuCl4) = 2.8 which leads to particleswith a mean radius of r = 5.4 nm.

Synthesis Temperature. The synthesis temperature hasbeen investigated only occasionally yet. Turkevich et al.reported that the final size decreases for a synthesistemperature of 80 �C.6 In addition, the overall synthesistime was found to be longer at lower temperatures.6,47

Takiyama conducted an elaborated temperature studyfor which he also varied the initial HAuCl4 concentra-tion at each investigated temperature. He observed adecreasing final size for changing the synthesis tem-perature from 100 to 80, 70, and 60 �C. In Figure 10,the results of a temperature study following the stan-dard synthesis are displayed. The HAuCl4 solution washeated to the according synthesis temperature for15 min before adding the citrate solution. Particles

Figure 10. Results of temperature variation study. (a) Mean radii (polydispersity = 25% at 20 �C, 20% at 30 �C, rest 10%). (b)Overall synthesis time versus temperature determined by observing the color change of the reaction solution.

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synthesized at room temperature are rather poly-disperse and large (r = 12.6 nm, polydispersity = 25%).The particle size decreases with increasing synthe-sis temperature and reaches a minimum at 60 �C(r = 6.1 nm, polydispersity = 10%). Further tempera-ture increase results in larger particles. The synthesisaccelerates significantly with increasing temperature(see Figure 10b).

Similar to the pH value, the temperature influenceon the final size is very complex. The kinetics of thechemical processes which determine the amount ofAu0 during seed particle formation are temperature-dependent. The gold complex equilibrium is also influ-encedby temperaturewhich changes the initial amountof reactive [AuCl4]

� (cf. chemistry of reduction path inFigure 4a). In addition, the seed particle size depends ontemperature (cf. colloidal stability path in Figure 4a).

As discussed in #3, two chemical processes influ-ence the amount of Au0 available for seed particleformation. The transformation kinetics of [AuCl4]

� f

[AuCl3�xOH1þx]� determine the time frame during

which Au0 can be produced for seed particle formation.The kinetics of the reduction [AuCl4]

�fAu0 determinewhich amount of monomers is supplied during thistime frame. Both processes become faster with increas-ing temperature. In other words, the time frame of theseed particle formation step becomes shorter withincreasing temperature, but [AuCl4]

� is also reducedfaster during the available time. Due to these opposingtendencies, the amount of Au0 available for seedparticle formation will vary with temperature. As stat-ed, another temperature influence that needs to beconsidered is the shift of the gold equilibrium. Theinitial ratio of reactive [AuCl4]

� decreases at highertemperatures (see Supporting Information SI-4) whichcontributes to a decreasing amount of available Au0 forseed particle formation. The temperature also influ-ences the seed particle size. The concept to describenanoparticle growth via colloidal stability as presentedin #3 can be used to illustrate this influence. Highertemperatures increase the thermal energy EkT of thereaction system. The intersection of EkT and stabilitycurve, which is associated with the minimal stableparticle radius, is obtained for larger particle sizes(see Figure 4c). This temperature effect on particlesize has been shown previously for AuNP obtainedby NaBH4 reduction.36 Therefore, for a defined Au0

amount, an increasing temperature leads to the for-mation of larger and fewer seed particles. At last, it hasto be noted that the principle growth mechanismmight change for low temperatures (around roomtemperature). At these temperatures, too few Au0

monomers might be formed in the initial phase to forma sufficient amount of seed particles. Other pathwayswhich can comprise the reduction of [AuCl3�xOH1þx]

�

species in solution might also occur. The result isa nonuniform polydisperse solution as obtained for

20 and 30 �C. The combination and interplay of thedifferent described tendencies leads to a nonlinearcurve shape for final size versus synthesis temperature.

Summary #4.4. The significant temperature influenceon the final size is derived from a combination ofprocesses. For increasing temperatures, the timeframe for the seed particle formation becomes shorter.The reduction of [AuCl4]

� during the available time isaccelerated at higher temperatures which enhancesthe supply of Au monomers. Since the gold complexequilibrium is temperature-dependent, the ratio ofinitial [AuCl4]

� decreases at higher temperatures facil-itating the formation of less Au0 and less particles. Inaddition, the seed particle size is larger for highertemperatures, also resulting in the formation of lessseed particles. The interplay of all described processesleads to the measured nonlinear temperature depen-dence with a size minimum at 60 �C (r = 6.1 nm).

Question #5: Why Does the Citrate Reduction of Silver Nitrate(AgNO3) Not Result in Monodisperse and Uniform Particles as forHAuCl4? Inspired by the Turkevich synthesis, Lee andMeisel used Na3Ct to prepare silver nanoparticles(AgNP) by the chemical reduction of aqueous AgNO3.

48

In contrast to the Turkevich synthesis, the AgNP ob-tained by Lee�Meisel aremuch larger (r = 30�100 nm)with a high polydispersity and with different mor-phologies.49 Spherical particles can only be obtainedusing a stepwise reduction method.50 The Lee�Meiselmethod was investigated by recording UV�vis spectraat different reaction times.50�52 In the beginning, noabsorbance is detectable. After approximately 1/3 ofthe total reaction time, a plasmon band is observedwhich increases during the course of the reactionindicating the growth of AgNP. Gorup et al. quenchedthe particle growth by addition of ammonia after firstappearance of a plasmon absorbance (the residual Agþ

forms a stable [Ag(NH3)2]þ complex). They detected

AgNP with average radius of 1.1 nm as apparent fromSEM imaging.51 Nevertheless, it cannot be excludedthat these small particles were formed from unreactedprecursor residues on the substrate reduced by theelectron beam. In general, the growth mechanism ofthe Lee�Meisel synthesis is rather unclear.

To investigate the Lee�Meisel synthesis, time-resolvedSAXS measurements using a free-liquid jet setup wereconducted at beamline ID02 (ESRF). The synthesis wascarried out with concentrations of [AgNO3] = 0.25 mMand [Na3Ct] = 2.5 mM at 85 �C (total reaction time∼70 min). The SAXS experiment was conducted twiceusing different sample to detector distances to mea-sure the scattering in the lower and larger q-scale. Thetwo separated SAXS measurements were necessary toinvestigate the formation of smaller particles (demandshigherq values, see Figure 11a) and the growthof largerparticles (demands very small q values, see Figure 11b).In the first 25 min of the reaction, no particle scatteringcould be detected. The origin of this induction period

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remains unclear. The first evaluable scattering intensitywas detected at about 30 min. The scattering corre-sponds to relatively large particles. Assuming a sphericalparticle shape, the mean radius is ∼13 nm at a poly-dispersity of ∼30% (see Supporting Information SI-7).In the course of the reaction, the scattering intensityincreases only in the low q range which correspondseither to the growth of the already existing particles orthe formation of further large particles. The relativenumber of particles and volume fraction cannot bedetermined from the SAXS curves because the AgNP atall reaction times are too large, polydisperse and mostlikely also nonuniformly shaped. It is also not possibleto determine the point of full precursor reduction.Although the growth mechanism of the Lee-Meiselsynthesis cannot be deduced from theses experiments,it is clearly not similar to the Turkevich seed-mediatedgrowth mechanism. The processes which create thefortunate coincident in the first seconds of the Turkevichreaction do not appear for the Lee�Meisel synthesis.This might be due to the fact that, although the silver ioncould exist in different species (e.g., different aquacomplexes), no chemical process which transforms areactive into a less reactive silver precursor species isavailable which triggers the formation of seed particles.As a result, the final AgNPs are nonuniformly shaped,polydisperse and large (size range of 30 nm in radius).

Summary #5. The growthmechanism of the reductionof AgNO3 with Na3Ct (known as Lee-Meisel synthesis) isnot similar to the Turkevich synthesis. The chemicalprocesses occurringduring the Lee-Meisel synthesis doesnot ensure a certain phase in which a defined amount ofAg monomers for the formation of seed particles isdelivered. Therefore, the synthesis leads to relatively largeparticles at high polydispersities and is not reproduciblewith respect to size, polydispersity and morphology.

CONCLUSIONS

This contribution provides a comprehensive pictureof the Turkevich synthesis which includes the relevantunderlying physicochemical processes. The gained

knowledge enables more than a growth characteriza-tion by a detailed growth mechanism. It allows under-standing what determines the final particle size andillustrating the influence of reaction conditions on thegrowth process and thus the final size.In question #1 it is shown that the previously

described32 four-step growth mechanism is valid fora wide range of reaction conditions. The first step is apartial reduction of the gold precursor and the forma-tion of small clusters from the Au monomers. In asecond step, these clusters form seed particles withradii >1.5 nm. The third and fourth steps comprise thereduction of the residual ionic gold (first slowly, thenfast) whereby the generated gold monomers growexclusively on top of the seeds until the precursor isfully consumed. Therefore, no further particles areformed during the last two steps. The described 4-stepgrowth mechanism can be referred as seed-mediatedgrowth mechanism.The mechanism leads to monodisperse AuNP since

only a slight amount of the ionic gold is reduced duringthe seed particle formation (see question #2). The fewformed seed particles are polydisperse26,53 but growinto monodisperse AuNP due to a continuous mono-mer supply during growth steps 3 and 4 which couldbe described by a size focusing effect.54

The seed-mediated growth mechanism is actually afortunate coincidence created by a favorable interplayof different chemical and physicochemical processesas shown in question #3 and illustrated in Figure 8. Thefirst important aspect of the fortunate coincidence isthe initiation of seed particle formation in the initialphase of the synthesis. Au monomers are supplied bythe fast reduction of reactive [AuCl4]

�. Moreover, thestandard reaction conditions are moderate enoughto allow the formation of colloidally stable small seedparticles from these monomers. The second aspect ofthe fortunate coincidence is the termination of seedparticle formation just within an appropriate timeframe so that only “very few” seed particles (still inthe scale of trillions) are formed. This aspect is a result of

Figure 11. Time-resolved SAXS investigations of the Lee�Meisel synthesis. Scattering curves for (a) large q and (b) small qvalues. The results shown were obtained from two separated experiments.

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the buffer effect of Na3Ct and the pH-dependent ligandexchange equilibrium of gold complexes. Upon mixingthe reactants, Na3Ct increases the pH level of the goldprecursor solution inducing the transformation of thereactive [AuCl4]

� into less reactive [AuCl3�x(OH)1þx]�

species. This transformation quenches the fast mono-mer supply in solution and constitutes the end of step 2of the growth mechanism. The third aspect of thefortunate coincidence is the exclusive growth of resi-dual gold onto the seed particles during growth steps 3and 4. The reduction of [AuCl3�x(OH)1þx]

� species atthe surface of the particles is favored over the reduc-tion “in solution”. DCA is formed as chemical product ofthe reduction of Au3þ by citrate. It accelerates thereduction process but has no effect on the final particlesize in the standard Turkevich synthesis.The understanding of the origin of the seed-

mediated growth mechanism reveals how the finalparticle size is determined. The final size is alreadydetermined at a very early stage of the synthesis�afterthe end of seed particle formation (after step 2 of thegrowth mechanism). Since no further particles areformed during growth steps 3 and 4, the final totalnumber of AuNP is equivalent to the number of seedparticles and determines to how many particles thetotal amount of Au (depends on initial HAuCl4concentration) is distributed. The number of seedparticles is determined by two factors as illustrated inFigure 4 in question #3: (i) the amount of Aumonomerswhich is available during the seed particle formation; ifmore monomers are available, more seed particles canbe formed and the total amount of gold is distributedto more particles leading to a smaller final size; and (ii)

the minimum size of the seed particles determined bythe colloidal stability; if seed particles are stable atlarger sizes, less particles can be formed from theavailablemonomers leading to larger final AuNP. Thesefactors are determined by the reaction conditions sincethey influence either the reduction chemistry duringseed particle formation, the colloidal stability of theseed particles or both.Taking these two pathways into consideration, it is

possible to understand and illustrate the influencesof reaction conditions on the final NP size. In question#4, the influences of parameters such as concentration,pH value, order of reactant addition and synthesistemperature are discussed in detail. Furthermore, theboundaries of the seed-mediated growth mechanismare identified. For extreme reaction conditions (strongdeviation from standard synthesis protocol), thefortunate coincidence vanishes as soon as one of itsconditions is no longer fulfilled. This leads to thesynthesis of polydisperse and large particles up to goldprecipitates.Any seed-mediated growthmechanismdemands an

interplay of processes that start and terminate a seedparticle formation step. For the citrate reduction ofAgNO3, known as Lee-Meisel synthesis, the absenceof conditions which create a seed-mediated growthmechanism results in large and polydisperse AgNP(see #5).In principle, the picture of parameter influences on

the final particle size presented for the Turkevichsynthesis might be representative for other colloidalsyntheses which comprise a seed-mediated growthmechanism.

EXPERIMENTAL SECTION

Colloidal Syntheses. Chemicals. HAuCl4 (99.999%), AgNO3

(99.9999%), Na3Ct 3 2H2O (g99%), NaClO4 3 2H2O (98%) and1,3-dicarboxyacetone (technical grade) were purchased fromSigma-Aldrich. All solution were prepared using Milli-Q water.The labware was cleaned after each synthesis using aqua regiaand Milli-Q water.

Standard Turkevich Synthesis. A volume of 199 mL of a0.25 mM HAuCl4 solution was refluxed in a round-bottomedflask equipped with a condenser for 15 min. One milliliter of afreshly prepared 500 mM Na3Ct solution was added quickly(final concentration [Na3Ct] = 2.5mM). Themixturewas refluxeduntil the precursor was completely reduced. The overall reac-tion time can be determined by observing the solution until acharacteristic ruby red color is obtained.

Lee�Meisel Synthesis. One liter of a 0.5 mM AgNO3 solution(freshly prepared) and one liter of a 0.5 mMNa3Ct solution wereheated to 85 �C. The reducing agent was added quickly to themetal precursor (final concentrations [AgNO3] = 0.25 mM,[Na3Ct] = 2.5 mM). The obtained mixture was kept at 85 �C.

Comments on Parameter Variation Studies. The standardprotocol wasmaintained in all points which were not addressedby a certain parameter variation. For the variation of ionicstrength, NaClO4 was added in different amounts to the Na3Ctsolution prior to mixing with HAuCl4. For the pH variation, theinitial pH of the HAuCl4 solution was varied by addition of HClor NaOH. Note that the kinetics of the complex equilibrium is at

room temperature in the range of several minutes. Therefore,the pH value of the HAuCl4 solution cannot be determineddirectly after addition of HCl or NaOH. For the inverse method,199 mL of a 2.5 mM Na3Ct solution was refluxed and 1 mL of a50 mM HAuCl4 solution was added.

Ex Situ Characterization. For SEM imaging, a sample dropletwas deposited on a Si/TiO2 wafer and removed immediatelywith an Eppendorf pipet. Measurements were performed on aJEOL JSM-7401F (Hitachi Ltd., Tokyo, Japan) with an accelera-tion voltage of 10 kV at a working distance of 8 mm. For TEMimaging, a sample droplet was deposited on a copper grid andremoved immediately with an Eppendorf pipet. Measurementswere performed on a FEI Tecnai G2 20 S-TWIN instrumentoperated at 200 kV (images displayed in Figure 2 and Support-ing Information SI-3) and on a Philips CM200 LaB6 operated atan acceleration voltage of 200 kV, respectively (images dis-played in Supporting Information SI-2).

UV�Vis Spectroscopy. UV�vis spectra were recorded on anEvolution 220 (Thermo Fischer Scientific). For time-resolvedmeasurements, an external cuvette holder with heating andtemperature control function was connected to the spectro-meter via fiber optical cables. Measurements were carried out ina quartz cuvette.

Small Angle X-ray Scattering (SAXS) and Ultrasmall Angle X-rayScattering (USAXS) Experiments. Synchrotron SAXS Investigations.The synchrotron SAXS investigations were performed at theID02 beamline (ESRF) using a free-liquid jet setup. Details are

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describe elsewhere.27 The distance between reaction vessel andjet wasminimized to achieve a low dead time (approximately 5 s)and to avoid agglomeration of the particles inside the tubings.The technique offers the possibility to follow the nanoparticlegrowth in situ with a time-resolution that is limited just by thephoton flux and the acquisition time of the detector. In addition,X-ray induced effects are minimized, and contamination pro-blems (contamination of capillary walls) are eliminated.

Synchrotron USAXS Investigations. USAXS measurementswere performed at the B1 beamline (DORIS III) using a flow-through capillary.

Lab-Scale SAXS Investigations of Final Colloidal Solutions.The scattering curves of the final colloidal solutions wererecorded on a SAXS instrument (SAXSess, Anton Paar GmbH)using a quartz flow cell.

SAXS Evaluation. The scattering curves of the colloidalsolution were analyzed assuming spherical shape, a homoge-neous electron density, and a Schulz-Zimm size distribution.The Schulz-Zimm distribution is given by

f (r) ¼ (zþ1)zþ1x2exp[ �(zþ 1)x]RavgΓ(zþ 1)

(1)

where Ravg is the mean radius, x = r/Ravg, z is related tothe polydispersity p (p = σ/Ravg) by z = 1/p2 � 1, and σ2 is thevariance of the distribution. The scattering intensity of nonag-gregated particles can be assumed to be proportional to theform factor of a single particle P(q). Thus, the scattering intensityof N monodisperse spheres with homogeneous electron den-sity and volume Vpart is given by

I(q) ¼ NIpart(q) ¼ NV2partP(q)

¼ NV2part ΔF

3(sin(qR) � qRcos(qR))qR

� �2(2)

In case of polydisperse spherical particles, one has to sumthe scattering intensities over all particle sizes weighted by theirfrequency as given by the size distribution function. It iscommon to use the Schulz-Zimm distribution for polydisperseparticles. Hence, the scattering intensity is given by

I(q) ¼ N

Z ¥

0f (r)V2

partP(q) dr (3)

An analytical solution of the integral can be found inKotlarchyk et al.55 To analyze the growth mechanism of nano-particles, the number of particles is important. This informationcan be obtained by using the general relation of I(q = 0) =(ΔF)2Vpart2 for a single particle. Thus, the scattered intensityI(q = 0) of polydisperse particles can be written as

I(q ¼ 0) ¼ NÆV2æ(ΔF)2 (4)

where N is the number of particles and ÆV2æ is the mean valueof Vpart

2 . Due to the overlapping of the scattering intensity withthe primary beam, I(q = 0) cannot be measured directly, but isaccessible via the extrapolation of I(q) for q f 0. Selectedscattering curves and mathematical fits can be found in Sup-porting Information SI-7.

The equation to calculate the relative number of particles inTable 1 is derived from the average volume:

ÆVæ ¼ 4π3

ÆR3æ ¼ 4π3

ÆRavgæ3(zþ 3)(zþ 2)

(zþ1)2(5)

Since the polydispersities of the colloidal solutions investi-gated in Table 1 are the same (10%), it follows that ÆV1æ/ÆV2æ =ÆRavg,1æ3/ÆRavg,2æ3).

Conflict of Interest: The authors declare no competingfinancial interest.

Supporting Information Available: Scheme of the generalgrowth mechanisms, SAXS, SEM, TEM, UV�vis data of AuNPsyntheses and precursor investigations. The Supporting Infor-mation is available free of charge on the ACS Publicationswebsite at DOI: 10.1021/acsnano.5b01579.

Acknowledgment. J.P. acknowledges generous fundingby the Deutsche Forschungsgemeinschaft within the projectPO 1744/1-1. M.W. acknowledges financial support by theFonds der Chemischen Industrie. R.K. thanks in particularEinstein Foundation Berlin for generous support provided byan Einstein-Junior-Fellowship (EJF-2011-95). R.K. also acknowl-edges funding from BMBF (FKZ 03EK3009). The authors ac-knowledge the European Synchrotron Radiation Facility forprovision of synchrotron radiation facilities and would like tothank Dr. T. Narayanan for assistance in using beamline ID02 forSAXS measurements. USAXS measurements were conducted atbeamline B1 at light source DORIS III at DESY, a member of theHelmholtz Association (HGF).

REFERENCES AND NOTES1. Zhao, P.; Li, N.; Astruc, D. State of the Art in Gold

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