Simultaneous SAXS/WAXS/UV−Vis Study of the Nucleation andGrowth of Nanoparticles: A Test of Classical Nucleation TheoryXuelian Chen, Jan Schroder, Stephan Hauschild, Sabine Rosenfeldt, Martin Dulle, and Stephan Forster*

Physical Chemistry I, University of Bayreuth, 95447 Bayreuth, Germany

*S Supporting Information

ABSTRACT: Despite the increasing interest in the applica-tions of functional nanoparticles, a comprehensive under-standing of the formation mechanism starting from theprecursor reaction with subsequent nucleation and growth isstill a challenge. We for the first time investigated the kinetics ofgold nanoparticle formation systematically by means of a lab-based in situ small-angle X-ray scattering (SAXS)/wide-angleX-ray scattering (WAXS)/UV−vis absorption spectroscopyexperiment using a stopped-flow apparatus. We thus couldsystematically investigate the influence of all major factors suchas precursor concentration, temperature, the presence ofstabilizing ligands and cosolvents on the temporal evolutionof particle size, size distribution, and optical properties from theearly prenucleation state to the late growth phase. We for first time formulated and numerically solved a closed nucleation andgrowth model including the precursor reaction. We observe that the results can be well described within the framework ofclassical nucleation and growth theory, including also results of previous studies by other research groups. From the analysis, wecan quantitatively derive values for the rate constants of precursor reaction and growth together with their activation freeenthalpies. We find the growth process to be surface-reaction limited with negligible influence of Ostwald ripening yieldingnarrow disperse gold nanoparticles.

■ INTRODUCTION

The mechanism of particle nucleation and growth is one of theclassical topics in colloid science. It has in recent years attractedincreasing attention because of the need to synthesizefunctional nanoparticles with better control and efficiency. Inrecent years the study of nucleation and growth has greatlybenefitted from the development of new powerful experimentalmethods that allow one to follow kinetic processes in situ over awide range of time scales. In particular, third generationsynchrotron sources now offer means to monitor particlegrowth by small- and wide-angle X-ray diffraction (SAXS,WAXS) as well as X-ray and UV−vis spectroscopy to obtaininformation on the evolution of the particle size distributionand optical properties as a function of time, down tomillisecond resolution.1−4

Gold nanoparticles are most intensely investigated innanoscience and technology, because of their unique opticalproperties, catalytic reactivity, and stability.5−9 The ability totailor these properties via their size, shape, and surfacechemistry is a prerequisite for successful applications. Varioussynthetic methods are known, based on the reduction of Au saltprecursors via citrate, borane complexes, and UV or lightirradiation. Because of their importance as nanomaterials,investigations of the nucleation and growth kinetics of goldnanoparticles have motivated several studies by differentresearch groups. In particular the studies by Spalla1−4 and

others10−16 demonstrated the use of in situ X-ray studies toobtain details on the nucleation and growth process.These experiments clearly revealed different time regimes

during the structural evolution of gold nanoparticles. Typically,after an initial induction time, there is a short nucleation periodfollowed by particle growth to reach the final size when allprecursor material has been consumed. Particle aggregation andOstwald ripening are mechanisms that can decrease the numberof particles and change their size distribution during the courseof the reaction. Concerning the importance and contributionsof these mechanisms, there are different, sometimes conflictingreports. In one study, the particles were observed to rapidlygrow to their final size with the number of particles of this sizeincreasing with increasing reaction time.17 Other reportsdemonstrate that after nucleation the number of particles isconstant, while the size distribution narrows. In a study of NiPtnanoparticle growth, only nucleation and growth wereobserved, without indications for Ostwald-ripening.18 Furtherstudies reported aggregative growth of Au nanoparticles insteadof Ostwald ripening,19 nearly exclusively Ostwald ripening,16 orjust nucleation and growth without Ostwald ripening.2 There is

Received: July 27, 2015Revised: September 22, 2015Published: September 22, 2015

Article

pubs.acs.org/Langmuir

© 2015 American Chemical Society 11678 DOI: 10.1021/acs.langmuir.5b02759Langmuir 2015, 31, 11678−11691

also evidence for a nucleation−growth−aggregation mechanismas has been recently proposed.14

Theoretical models to capture different periods of nano-particle structural evolution have historically focused on theinterplay of particle growth and Ostwald-ripening. Lifshitz,Slyozov,20 and Wagner21 gave an analytical solution for theparticle size distribution in the case of diffusion-limited andreaction-limited growth, known as the LSW theory. Theiranalytical solution made use of a Taylor expansion of theGibbs−Thomson term. The full expression, adequate fortreating small nanoparticles, has been treated numerically byTalapin et al. to elucidate conditions of particle size focusing.22

Numerical algorithms were later refined by Mantzaris toidentify suitable control parameters for the synthesis of goldnanoparticles to tailor the size distribution.23 Spalla used anumerical algorithm similar to that of Talapin and demon-strated good agreement between theory and experiment.2,4

Using a very elaborate numerical scheme, van Embden et al.were able to provide an in-depth analysis of diffusion- andreaction-limited growth on the particle size distribution whichcould be quantitatively compared to LSW theory and thesynthesis of CdSe nanoparticles.24

In view of the variety of different mechanisms of Aunanoparticle formation and because Au nanoparticles are mostintensely considered in research and applications, we performeda systematic study on gold nanoparticle nucleation and growthusing in situ time-resolved small- and wide-angle X-rayscattering (SAXS, WAXS) and UV−vis spectroscopy inconjunction with a stopped-flow microfluidic device. This wasfor the first time achieved with lab-based equipment withoutthe need of synchrotron X-ray beamlines. It allowed us to studysystematically the influence of a variety of parameters such asprecursor concentration, temperature, and the addition ofstabilizing ligands and cosolvents to determine their influenceon the temporal evolution of particle size, polydispersity,volume fraction, number density and optical properties over thecomplete nucleation and growth period. For the analysis of thekinetic data we for the first time numerically solved thecomplete set of reaction rate equations comprising precursorreaction, nucleation, growth, and Ostwald ripening to obtainthe evolution of the full particle size distribution from theinduction period to the late growth stage. We obtained verygood agreement between the calculated and experimentallydetermined evolution of the particle mean size andpolydispersity, also including recently published data by otherresearch groups. This study thus for the first time quantifiesavailable experimental data on particle nucleation and growth interms of rate constants and activation energies and provides acomprehensive scenario of the structural evolution of one ofthe most intensely studied nanoparticle systems.

■ EXPERIMENTAL SETUPThe formation of gold nanoparticles was investigated by means of insitu SAXS/WAXS/UV−vis experiments in combination with astopped flow device using for the first time lab-based equipment,without the need of a synchrotron radiation source. This setup, shownschematically in Figure 1, enables one to follow the structuralevolution of the nanoparticles and the evolution of their opticalproperties simultaneously. For fast mixing of the two reacting solutions(gold salt and reducing agent), they were pumped with a highprecision syringe pump through a Y-shaped Teflon mixer at high flowrates into a quartz capillary. After reaching stationary flow conditionsthe pumps were stopped. The utilization of this stopped flow deviceallowed us to minimize the dead time from transferring the reaction

solution into the analysis cell (capillary), thus acquiring structural andoptical information from the very beginning of the nanoparticleformation process. In our case, the Au nanoparticles formedcompletely within 1−4 h with a dead time of approximately 1.3 s.The unusual position of the XRD detector very close to the sample isnecessary to acquire wide-angle X-ray diffraction with sufficiently highsignal-to-noise ratio. Details of the setup are described in theSupporting Information.

Nucleation and Growth Model. Precursor Reaction. We assumethat Au+ (chloro gold(I)-triphenylphosphine) reacts with the reducingagent B (t-butylamineborane) to form Au0

+ → ++Au B Au R0 (1)

with some reaction product R. Assuming simple second-order ratekinetics the rate of formation of Au0, j+ (in mol/L·s), is given by

= =++

+jt

k Bd[Au ]

d[Au ][ ]

0

1(2)

with the rate constant k1. If reaction 1 proceeds, the concentration[Au0] will continuously increase and eventually exceed the saturationconcentration [Au0]sat, leading to a supersaturation S = [Au0]/[Au0]sat> 1.

For the special case of equal initial concentrations [Au+]0 = [B]0,one can analytically calculate the time, until a supersaturation S[Au0]satto induce nucleation has been reached as

τ =−+ +

Sk S

[Au ][Au ] ([Au ] [Au ] )sat

0sat

1 0 00

sat (3)

This corresponds to an induction time after which nucleation starts. Incommon cases where [Au+]0 < [B]0, the induction time will be shortersuch that τsat as calculated from eq 3 can be considered as an upperlimit. For a rate constant of k1 ∼ 10−3 L/mol·s, a saturationconcentration of [Au0]sat ∼ 10−7 mol/L, a supersaturation of S = 500,and a precursor concentration [Au+]0 ∼ 0.02 mol/L, the maximuminduction time is τsat ∼ 125 s, a typical value for our experiments.

Nucleation. Under supersaturation, nuclei of Au nanoparticles willform at a rate given by

β= = −Δ⎡

⎣⎢⎤⎦⎥j t

tVv

G tkT

( )d[Au ]

d[Au ] exp

( )nuc

0

nuc

0

0

c

(4)

with the rate constant β* = (4kT/9ηvm) (≈1 × 1011 s−1), V = (4πR3/3) is the volume of the nucleus, and the free enthalpy of activationΔGc(t) = (16πγ3vm

2)/3(kT)2(ln S(t))2 with γ being the interfacialtension of the gold nanoparticles and v0 = M/ρNA = 1.69 × 10−29 m3

being the volume of Au0 atoms. Newly formed nuclei will have a radius(critical radius) of R = Rcap/ln S, where Rcap = 2γv0/kT is the capillaryradius. For the typical range of supersaturations in our experiments,

Figure 1. Schematic presentation of in situ setup employed for real-time SAXS/WAXS/UV−vis measurements during the formation of Aunanoparticles. The setup measures SAXS, WAXS, and the UV−visspectra simultaneously in the same sample volume. A photograph ofthe setup can be found in the Supporting Information (Figure S5).

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critical radii have values between 0.24 nm (S = 1000) and 1.0 nm (S =5).Growth. The formed nuclei J will subsequently grow at a growth

rate

π

=

=−

+⎜ ⎟

⎛⎝⎜

⎡⎣⎢

⎤⎦⎥⎞⎠⎟

⎛⎝

⎞⎠

j tt

n R t DNS t

( )d[Au ]

d

4 ( ) [Au ]( ) exp

1

JJ

J J

R

R t

DR t k

gr,

0

gr,

A0

sat

( )

( )

J

J

cap

gr (5)

where kgr is the surface growth rate constant, D is the diffusioncoefficient of Au0, nJ is the concentration of J nuclei, NA is Avogadro’snumber, and R is the radius of the particle. (D/Rkgr)

−1 = Da is theDamkohler number Da, which relates reaction rates to the (diffusive)mass transport rates. The growth mechanism is mostly either surfacereaction-limited (SR, the addition of Au0 to the growing particlesurface) or diffusion-limited. According to eq 5, the diffusion-limitedcase corresponds to D ≪ Rkgr (Da ≫ 1) whereas the surface-reactionlimited case corresponds to D ≫ Rkgr (Da ≪ 1). For smallnanoparticles with radii R ∼ 1 nm with a growth rate of kgr ∼ 10−6 m/sas in our experiments, and diffusion coefficients of D ∼ 10−10 m2/s, theratio (D/Rkgr) ∼ 105 ≫ 1 (Da ≪ 1) such that nanoparticle growth isclearly surface reaction limited, as was previously also noted bySpalla.2,4

The final particle radius should be proportional to the ratio ofgrowth rate to the nucleation rate, and thus according to eqs 4 and 5proportional to ∼kgr exp[γ3/ln2 S]. Thus, one would expect anincreasing growth rate constant kgr and an increasing interfacial tensionγ to lead to larger final particle sizes.Ostwald Ripening. The term (S − exp[Rcap/RJ]) in eq 5 describes

the Ostwald ripening process. The exponential term reduces thegrowth rate, which can become negative if exp[Rcap/RJ] > S such thatnanoparticles of radius RJ dissolve. With the capillary radius typicallybeing in the range Rcap ∼ 1.5 nm, and with radii in the range 0.5 < RJ <5 nm, the exponential term has values between 20 > exp[Rcap/RJ] >1.4. At the beginning of the nucleation period, the supersaturationnearly instantaneously rises to very large values > 100 (see Figure 2b)such that negative growth rates, that is, particle dissolution, do notoccur. During the very late growth period where the supersaturationdecays to values S < 5, negative growth rates for particle radii RJ < 1nm can occur. However, since the particle size distributions in ourexperiments are quite narrow (σ < 0.15), the fraction of nanoparticleswith radii < 1 nm is negligibly small. Thus, for our experiments whichcover the induction, nucleation and growth periods to almost completeconsumption of precursor, Ostwald ripening involving negative growthrates has negligible influence, which is in line with numericalcalculations in ref 24.

Kinetic Model. The kinetic model describing the time dependenceof the concentrations of the precursors [Au+], [B], of free Au0 atoms[Au0], of Au0 atoms incorporated into nanoparticles by nucleation[AuN

0 ] or by growth onto particles J [AuPJ0 ], as well as the particle

concentrations [PJ] during the induction, nucleation, and growthperiod corresponds to a set of coupled first order differential equationsbeing

∫

β

π

β

π

β δ

= −

= −

= − −Δ

−−

+

= −Δ

=−

+

=

= −Δ

− =

++

+

+

=

⎜ ⎟

⎜ ⎟

⎡⎣⎢

⎤⎦⎥

⎛⎝⎜

⎡⎣⎢

⎤⎦⎥⎞⎠⎟

⎛⎝

⎞⎠

⎡⎣⎢

⎤⎦⎥

⎛⎝⎜

⎡⎣⎢

⎤⎦⎥⎞⎠⎟

⎛⎝

⎞⎠

⎡⎣⎢

⎤⎦⎥

tk B

Bt

k B

tk B

Vv

GkT

R DN h t t

tVv

GkT

tR DN P

J N

P

tG

kTt t h t

d[Au ]d

[Au ][ ]

d[ ]d

[Au ][ ]

d[Au ]d

[Au ][ ] exp

4 [Au ]1 exp

1( )d

d[Au ]d

exp

d[Au ]

d4 [ ][Au ]

1 exp

1,

1, ...,

d[ ]

dexp [ ] ( )

t

J

R

R

DR k

J J

JJ J

R

R

DR k

J

t tJ J

1

1

0

10

c

0A

0

[Au ]

[Au ]

N0

0

c

P0

A0

[Au ]

[Au ]

c

J

J

J

J gr

J

0sat

0cap

gr

0sat

0cap

(6)

where δ[t − tJ] is the delta function used to describe the concentrationof a new nucleated species [PJ] which is determined by the amount of[AuN

0 ] produced at t = tJ.Solving this set of coupled differential equations yields the

concentrations [PJ](t) and radii RJ(t) of all particles J that havebeen formed during the nucleation process, from which the sizedistribution h(R,t), the mean radius R(t), and the relative standarddeviation σR(t) can be obtained which can be compared toexperimental data.

The same kinetic model without consideration of the precursorreaction has been employed by Talapin solved using MC simulations22

and by Spalla using the Euler forward method.2,4 Since the precursorreaction was not considered, assumption on an initial particle size andsupersaturation were made, which were chosen to give best agreementbetween calculations and experiment.

Figure 2. (a) Temporal evolution of mean particle radius and the polydispersity σR obtained by fitting the measured in situ SAXS curves to a modelof polydisperse spheres. Solid lines represent the best fit to eq 6. (b) Temporal evolution of the concentrations [Au+], [Au0], and particleconcentration N (in mM) together with the supersaturation S obtained from the numerical calculations.

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In our case, the set of N + 5 coupled first order differential eq 6 issolved numerically by discretization into finite time steps Δt using aRunge−Kutta fourth order algorithm, which has low computationaleffort and fulfills two important criteria for the kinetic model, that is,(1) the calculated concentrations are always non-negative, that is,[C](t) ≥ 0, and (2) it conserves mass, that is, the requirement

∑= + + = ++ + +

=

V

vP[Au ] [Au ] [Au ] [Au ] [Au ] [ ]J

J

NJ

J0 N0

P0

1 0

(7)

is fulfilled at all times.As nucleation and growth may occur over very different time scales,

we used up to N = 10 000 time steps with linearly or logarithmicallyspaced time intervals Δt, or adaptive step size control to capture thetemporal evolution of the concentrations over as many orders ofmagnitude in time as needed with a relative accuracy of ε < 10−10.Each time step generates a new particle species, such that after i

time steps i particle species J = 1,...,i have emerged. During allsubsequent time steps, the particles J can grow by consumption of Au0.The concentration increase of [AuPJ

0 ] after the ith time step isconverted to the additional new volume of particles J via

=− −V

Pv

([Au ] [Au ] )

[ ]Jj i J i

J,new

P0

P0

10

(8)

This then allows to calculated the new radius RJ according to

π=

+⎛⎝⎜

⎞⎠⎟R

V V3( )

4JJ J ,new

1/3

(9)

For the ensemble of particles J = 1,...,i after i time steps, the sizedistribution can then be calculated.Known input parameters for the calculations are the initial

concentrations [Au+]0 and [B]0, the temperature T, the viscosity ofthe solvent (toluene) η = 0.55 mPa s, the molar mass of gold M = 197g/mol, and its (bulk) density ρAu = 19.3 g/cm3. Further, thecalculations require to specify four at the beginning unknownparameters, that is, the interfacial tension γ of the gold nanoparticlesurface in the presence of the solvent, the precursor rate constant k1,the growth rate constant kgr, and the saturation concentration [Au0]sat.These values are varied to obtain the best fit between the calculatedand experimentally measured mean radii R(t).Comparison to Experimental Data. The kinetic model provides

the mean radius R, the relative standard deviation σR, theconcentrations [Au+] and [Au0], the supersaturation S, and the sizedistribution h(R) as a function of time.

Figure 2a shows the temporal evolution of the calculated meanradius R and the polydispersity σR (rel. standard deviation of particlesize) as a function of time together with a comparison with measureddata for initial concentrations [Au+]0 = 0.0125 mol/L, [B]0 = 0.125mol/L, and a stabilizer concentration (dodecanethiol, DDT) of[DDT] = 0.025 mol/L. We find very good agreement with theexperimental data using values of k1 = 1.7 × 10−3 L/mol·s, kgr = 1.4 ×10−6 m/s, [Au0]sat = 4 × 10−7 mol/L, and γ = 205 mN/m. To providea measure of the variance of the fitting parameters, we show in theSupporting Information (Figure S6) comparisons to experimentalgrowth data using fit parameters that deviated by ±20%from the abovevalues, showing significant deviations from the experimental data. Thecalculations predict a reasonable induction time after which nucleationbegins (120 s). We then observe a steep rise of the mean radius duringthe nucleation and early growth period (up to 40 min) followed by aslower increase until the percursor has been consumed. The finalradius of 3.1 nm is in good agreement with the results fromtransmission electron microscopy (see Figure 4a). Also the calculatedpolydispersity is in good agreement with the experimental data.

Figure 2b shows the temporal evolution of the concentrations [Au+]and [Au0] together with the supersaturation S. We observe that [Au+]decreases exponentially, whereas [Au0] first increases sharply withinthe first minutes and then decreases to very low values of 0.001 mMduring the remaining growth period due to its immediate consumptionby particle growth. Also shown is the supersaturation which increasessharply to values of S = 1800 during nucleation and then decreases tovalues of down to S = 3 during the remaining growth period. Alsoshown is the number of particles which increases steeply during thenucleation period and then remains constant. This indicates anegligible effect of Ostwald ripening.

Figure 3a shows the temporal evolution of the size distribution ascalculated from eq 6 with the same parameters used for thecalculations in Figure 2a. We observe after 3 min a size distributioncharacterized by a very sharp increase at R = 0.2 nm corresponding tothe smallest size particles nucleated at high supersaturation. With timethe size distribution develops into a log-normal type distributionwhose relative size distribution decreases with time until the precursorhas been consumed. Figure 3b shows the calculated final sizedistribution from eq 6 (after 200 min), which is compared to aSchulz−Zimm (SZ) distribution with the same mean value and relativestandard deviation. This distribution function is given by

= + Γ +

− +

+ ⎡⎣⎢

⎤⎦⎥h R

z RR z

zRR

( )( 1)

( 1)exp ( 1)

z z

zSZ

1

(10)

with the average radius R and the relative standard deviation σR = (z +1)−1/2. The distribution is normalized such that ∫ 0

∞hSZ(R) dR = 1. Weobserve a quite good agreement between the shape of the calculatedsize distribution and the SZ distribution. This size distribution also

Figure 3. (a) Temporal evolution of the size distribution calculated at different time intervals for the same conditions as in Figure 2. (b) Final sizedistributions (solid lines) calculated using Lifshitz−Slyozov theory (red line, eq 11), Wagner theory (black line, eq 12) and a Schulz−Zimmdistribution (green line, eq 10) with the same mean and standard deviation as in the corresponding numerical calculation (blue circle, eq 6) and as inthe size distribution as measured by SAXS (black/white circle).

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well describes the measured SAXS curves. In Figure 3b, the final sizedistributions are further compared to theoretical predictions of LSWtheory. It predicts for diffusion-limited growth a size distribution (LStheory)20

=+ −

× −−

< <⎧

⎨⎪⎪⎪

⎩⎪⎪⎪

⎡⎣⎢

⎤⎦⎥

h u

e uu u

u

u

( )

32 ( 3) (1.5 )

exp1

1 2 /3

if 0 1.5

0 otherwise

LS

4

5/3

2

7/3 11/3

(11)

with u = R/Rcr, where Rcr is the critical radius for which the rate ofdissolution is equal to the growth rate. In the diffusion-controlled case,Rcr = R. In surface reaction controlled case, Wagner derived21

= −−

−< <

⎧⎨⎪⎩⎪

⎡⎣⎢

⎤⎦⎥h u

uu

uu

u( )

23

(2 )exp

32

if 0 2

0 otherwiseW

75

(12)

where Rcr = 9R/8. As shown in Figure 3b, we observe that LSW theorysiginifcantly overestimates the fraction of smaller particles at the low-Rside of the size distribution. This is due to the dynamic dissolution/growth equilibrium of the smaller particles during Ostwald ripening.As discussed above, in our case even at late growth stages where S < 5Ostwald ripening has little effect, as the particle size distribution hasalready narrowed such that the fraction of smaller nanoparticlesexhibiting negative growth rates eq 5 is very small.The good agreement with the Schulz−Zimm distribution is not

accidental. This distribution function has been derived for radicalpolymerization kinetics.25,26 Here, similar to the formation andconsumption of free Au0 by particles of different size, a reactivemonomer radical M* is formed by initiation, and subsequentlyconsumed by addition to growing polymer chains of different lengths.

Thus, the kinetic model is very similar, with the only difference beingthe missing termination step in the nanoparticle growth model.

■ RESULTS AND DISCUSSION

Formation of Au Nanoparticles. The Au nanoparticleswere prepared through the reduction of a gold(I) salt (chlorogold(I)-triphenylphosphine) with a borane complex (t-butylamineborane, TBAB) in toluene in the presence ofdodecanethiol (DDT) as a stabilizer. The kinetics of thenanoparticle formation process was investigated via in situSAXS/WAXS/UV−vis in conjunction with a stopped-flowmicrofluidic device. Figure 4 illustrates the temporal evolutionof the measured diffraction curves and absorbance spectrareflecting the structural changes of the nanoparticles duringnucleation and growth. Each SAXS curve was measured for 5min, a compromise between having a sufficiently high signal-to-noise ratio for successful data analysis and a still sufficienttemporal resolution to follow the complete nucleation andgrowth process.Figure 4a shows a TEM-image of the Au nanoparticles

obtained after completion of the in situ measurement at a molarratio of 2 (DDT:Au+). It indicates that the nanoparticles arespherical in shape and almost uniformly sized (10%polydispersity) with a mean diameter of 5.9 nm.Figure 4b displays the UV−vis spectra recorded during the

course of the reaction. They show the evolution of anabsorbance maximum in the λ = 510−530 nm range, whichis attributed to the plasmon resonance of the growing goldnanoparticles. During the experiment, a weak peak at around λ= 320 nm was detected and then disappeared gradually. Thispeak was also detected by Tsukuda et al., who attributed this to

Figure 4. (a) TEM image of collected Au NPs from an in situ measurement and corresponding size distribution. Formation of Au NPs by in situUV−vis/SAXS/WAXS: (b) UV−vis spectrum as a function of time. (c) Time resolved SAXS curves. (d) Time-dependent WAXS curves. The twopeaks (111) and (200) are clearly visible, and their intensity increases with time. The experiments were performed at an Au+ concentration of 12.5mM.

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intraband and interband transitions for clusters Aun formedwithin a short time after addition of TBAB.27 In the following aplasmon peak occurred and shifted from 505 to 522 nm alongwith an increasing absorption intensity when the reactionproceeded, suggesting the growth of nanoparticles proceedscontinuously.Figure 4c presents the corresponding SAXS scattering curves

obtained during the same experiment. During the first 30 minwe observe the development of the Guinier plateau in the range0.4 < q < 1.0 nm−1 with a strongly decaying scattering intensityat higher q. This indicates the formation of small nanoparticleswith radii R < 1.5 nm. For q < 0.4 nm−1, we observe a smalllow-q upturn indicating the initial presence of some largeraggregates of unknown structure. For larger times, we see theevolution of a pronounced form factor oscillation with aminimum shifting from q = 3 nm−1 to q = 2 nm−1

corresponding to the growth of monodisperse nanoparticles,as also evidenced by the emergence and red-shift of the sharpplasmon peak in the UV−vis spectra. With increasing time theGuinier plateau develops a shallow slope, indicating theformation nanoparticle assemblies.28

The in situ WAXS experiment provides insight into thecrystalline nature of the Au nanoparticles during the formationprocess. As shown in Figure 4d, we observed the appearanceand growth of two strong diffraction peaks with increasingreaction time, accompanied by weak higher order reflections.The two strongest peaks are located at q = 26.5 and 30.6 nm−1,respectively. These two main peak positions ((111) at 2θ = 20°,(200) at 2θ = 25°) together with the higher order reflectionscan be indexed on an fcc lattice (space group Fm3m). Themaximum of the (111) peak increases with time, whereas thefull-width at half-maximum (fwhm) decreases, indicating thatthe crystalline domain size continuously increases during thegrowth of the nanoparticles.For subsequent analysis, selected curves from the in situ

SAXS/WAXS/UV−vis measurements along with the corre-sponding fits are shown in Figure 5. UV−vis spectra were fittedto a sum of a Lorentzian peak (plasmon resonance) and anabsorption edge (band gap) function given by

λλ λ

λ πσ

λ λ

σ=

−+ +

−−⎛

⎝⎜⎜

⎞⎠⎟⎟⎛⎝⎜⎜

⎞⎠⎟⎟A a a( )

( ) 21

4( )gap

gapn

pp

p

p

2

2

1

(13)

The first term in this equation describes the 5d → 6s-6pinterband transition with an exponent n = 1/2 in case of anindirect band gap. The second term describes the plasmon

resonance with a Lorentzian line shape. The two prefactors agap,ap should be roughly proportional to the number of gold atomsin gold nanoparticles.Figure 5a shows that this gives an adequate description of the

spectra over the whole wavelength range of λ = 300−1000 nmincluding the plasmon resonance at λ = 530 nm and theabsorption edge at slightly shorter wavelength. This fiveparameter fit (agap, λgap, n, ap, λp) is sufficiently robust andaccurate to determine the plasmon resonance intensity ap as afunction of time as shown in the inset of Figure 5a. The peakintensity shows an approximately linear increase with time. Wenote that also other time dependencies have been observed,such as a slow initial intensity increase followed by a more rapidincrease.29,30 The peak intensity of the plasmon resonancedepends on the number of Au atoms within nanoparticles, butalso on the nanoparticle size such that there is no simplerelation to derive these properties from the measuredabsorption spectra.31

For the data analysis of the SAXS curves, we considered thecontribution from the large population of growing singlenanoparticles, giving rise to the pronounced form factoroscillation, and the contribution from nanoparticle assembliesor clusters, giving rise to the low-q upturn observed for q < 0.4nm−1 at the beginning of the reaction, and causing the shallowslope at intermediate q at later reaction times.To capture the relevant features of the measured SAXS urves

over the whole q-range, we distinguished between thecontribution from single nanoparticles and nanoparticle clustersby modeling the scattering curves as32−34

ρ= Δ −I q b F qqR

qR qR qR( ) ( ) ( )9

( )[(sin( ) cos( ))]2

N 62

(14)

where (Δb)2 is the X-ray contrast difference between particlesand solvent, ρN is the number density of nanoparticles, and R isthe radius of the nanoparticles. ⟨...⟩ denotes the average of theform factor for homogeneous spheres over the Schulz−Zimmdistribution eq 10 with a weighting factor R6 to account for thefact that scattering methods determine the weight-averagedscattered intensity. F(q) describes the contribution fromnanoparticle clusters given by35,36

ξξ ξ

=−

− + −F qN D q

D q q( )

sin[( 1)arctan( ]

( 1) (1 ) D2 2 ( 1)/2(15)

Figure 5. (a) Characteristic UV−vis spectra, (b) SAXS curves, and (c) WAXS curves measured at different times during the nucleation and growthof the gold nanoparticles together with the corresponding fits (solid lines) for quantitative analysis. The inset in (a) is the intensity of plasmonresonance band versus reaction time.

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where D is the fractal dimension and N is the number ofparticles of the cluster. ξ = 2Rg

2/(D(D − 1)), where Rg is theradius of gyration of the clusters.Using eq 14, it is possible to nearly quantitatively describe

the measured scattering curves over the whole q-range, asshown in Figure S7 in the Supporting Information. We foundthat in all cases the contribution of single growing nanoparticlesby far dominates the measured scattering intensity, in particularin the q-range of q > 0.8 nm−1, where we obtain information onthe radius and polydispersity of the growing nanoparticles. Asshown in Figure 5b we could well analyze this region of themeasured SAXS curves by fitting to a model of polydispersehomogeneous spheres using F(q) = 1. The fitted curves areindicated by the red solid lines showing good agreement withthe experimentally determined scattering curves. From the fits,we obtain the scattered intensity I(0), the mean radius of theparticles R, and the relative polydispersity σ. The contributionfrom clustered nanoparticles giving rise to the low-q features ofthe scattering curves can be separately considered and arediscussed further below. We also considered whether themeasured scattering curves could be described by a bimodalsize distribution of spherical particles (eq S14 in the SupportingInformation), but found less agreement with the measured data,which supports the view that nanoparticles tend to formcorrelated assemblies.The WAXS curves in Figure 5c were similarly analyzed by

fitting the measured diffraction curves to a model of fcc-packedspherical particles.32−34

ρ= − ⟨ ⟩I q b b P q R S q( ) ( ) ( , ) ( )N1 22

(16)

where S(q) is the structure factor and ⟨P(q,R)⟩ is the averagedform factor as in eq 14. The fits are indicated by the red solidlines in Figure 5c. From the fits, we obtain the unit cell size aand the crystalline domain size D which is directly related to thepeak width.With the described analysis of the simultaneously measured

SAXS, WAXS, and UV/vis data we can obtain the particleradius R, the polydispersity σ, the crystalline domain size D, theunit cell size a, the scattered intensity I(0), and the relativenumber of Au0 as a function of time. From the latter twoparameters, we can calculate the relative number and volumefraction of nanoparticles. The unit cell size a = 0.7 nm is ingood agreement with literature data (0.70 nm) and does notchange with time or particle size. The temporal evolution ofradius, polydispersity and number of nanoparticles can then becompared to model calcuations of nucleation and growth asoutlined above.Crystallinity. With the WAXS detector positioned very

close (∼1 cm) to the sample, we were able to detect wide-angleX-ray diffraction from the growing nanoparticles in dilutesolution. Selected WAXS patterns at different reaction times arepresented in Figure 6 for a molar ratio of DDT/Au+ as 2:1.Only during the first 10 min, that is, during the inductionperiod, the WAXS signal was very weak and structureless. Atsubsequent times we observe well-defined WAXS signalsindicating a crystalline structure from the very beginning ofparticle formation indicating that nanoparticles duringnucleation and growth are crystalline at all times.The measured diffraction curves can be quantitatively

described by eq 16 to obtain more detailed structuralinformation. From the analysis, we directly obtain the unitcell dimension a, the mean displacement of atoms from lattice

point Δ (Debye−Waller factor), as well as the mean size D ofcrystalline domains. All values are summarized in Table 1. The

unit cell dimension could be determined with a precision of±1%. The variance of the fitted values of D and Δ are ±10%except for the very first measured WAXS curves with lowsignal-to-noise ratios, where the relative error of Δ is muchlarger. For this case, we assumed a fixed value of Δ = 0.01which describes the WAXS curves at later times very well. Table1 shows that the crystalline domain sizes, which wouldcorrespond to the nanoparticle diameters in case of singlecrystals, increases with increasing reaction time whereas allother parameter values stay constant. The increasing crystallinedomain size can be compared to the diameter of thenanoparticles as obtained from the SAXS curves. We observethat generally 2R > D such that the nanoparticles aremultidomain particles, which is also evident from the TEMimages (Figure S4), where different domains within thenanoparticles can be distinguished by their gray scale whichdiffers due to different orientation and the correspondingdifferent diffraction contrast.

The Unusual Role of Au+ Concentration on Kinetics.As a first parameter, we investigated the effect of the goldprecursor concentration on the kinetics and final size of thenanoparticles. This effect had not been studied in any of thepreviously published investigations on the growth kinetics ofgold nanoparticles, although it has a decisive influence on thenucleation and growth kinetics. We systematically decreasedthe initial concentration of gold precursor from 12.5 to 5 mM,whereas the molar ratio of the reducing agent to the goldprecursor TBAB:Au+ remained unchanged at 10:1. Thetemporal evolution of the measured SAXS scattering curvesat a low Au+ concentration of 7.5 mM is shown as a

Figure 6. WAXS patterns of gold nanoparticles measured duringnanoparticle formation and growth at different reaction times. Thediffraction cones have hyperbolic shape due to the horizontalpositioning of the detector above the sample.

Table 1. Unit Cell Dimension a, Crystalline Domain Size D,Deviation from Ideal Lattice Point Δ (Debye−WallerFactor), Lattice Type, and Diameter 2R of the NanoparticlesAs Determined from Fits to the Measured WAXS and SAXSCurves

t (min) a [nm] D [nm] Δ [nm] lattice 2R [nm]

30 0.41 1.6 0.01 fcc 3.950 0.41 2.1 0.01 fcc 4.770 0.41 2.4 0.01 fcc 5.2100 0.41 3.1 0.01 fcc 5.4150 0.41 3.6 0.01 fcc 5.8190 0.41 3.9 0.01 fcc 6.0

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representative example in Figure 7a. The presence of a Guinierplateau at low q (q < 0.7 nm−1) and a shift of the form factoroscillations at high q are clearly observable, demonstrating asufficiently high signal-to-noise ratio to allow data analysis evenat low concentrations. From the measured SAXS curves, wedetermined the mean radius R, polydispersity σ, and particleconcentration N as a function of time at varying concentrationof Au+ precursor solutions (12.5, 10, 7.5, and 5 mM) from eq14. The time dependence of these parameters is shown inFigure 7b−d.We observe that the time dependences of all three

parameters give a consistent picture of the nanoparticlenucleation and growth process: (1) a rapid formation ofsmall nanoparticles within the first 20 min, (2) a subsequentslow growth, and (3) finally the cessation of growth afterconsumption of the precursor after ca. 200 min. Duringformation of Au nanoparticles, the polydispersity decreasesdown to 10−14% gradually within 50 min and then staysconstant until completion of the reaction for all concentrations.The initial rapid increase of the number of particles with amean radius of around 1.2 nm during the first 15 min signalsthe occurrence of a fast nucleation that was captured by theSAXS measurements. It is evidenced by the consumption of asmall amount of Au0 monomers as shown in Figure S3 of theSupporting Information.To obtain a quantitative description of the formation

mechanism of Au nanoparticles, we used eq 6 and adjustedthe kinetic parameters k1, kgr, γ, and [Au0]sat to calculate thedevelopment of the three parameters R, σ, and N as a functionof time from the induction period to the late growth stage. The

parameters used for the calculated growth curves aresummarized in Table 2. The calculated growth curves are

displayed as solid lines in Figure 7b showing very goodagreement between calculated and experimentally determinedmean particle radii. We observe a clear increase of the precursorreaction rate constant k1 from 1.7 × 10−3 to 6.7 × 10−3 L/mol·swith an Au+ precursor concentration decreasing from 12.5 to 5mM, whereas the growth rate constant remains almostunchanged (kgr ∼ 1.0−1.4 × 10−6 m/s). Generally, as theparticle size should be roughly proportional to the ratio ofgrowth rate to nucleation rate, that is, ∼kgr exp[γ3/ln2 S], onewould assume that higher Au+ precursor concentrations yieldfaster reduction rates, higher supersaturation S, increasednucleation rates and thus smaller nanoparticles. This wouldbe consistent with reports from bulk Au nanoparticle synthesis,where an increase in the final size of the nanoparticles isobserved with decreasing initial metal ions concentration insolution caused by slower reduction rate of Au3+.14 Yet, weclearly observe larger nanoparticles and a smaller number ofparticles in our kinetic experiment (Figure 7b, d). The fact thatk1 depends on [Au+] indicates the existence of a concurrent

Figure 7. (a) SAXS intensity versus reaction time at an Au+ concentration of 7.5 mM. (b) Effect of Au+ precursor concentrations on the evolution ofthe particle radius. The lines are the best fits obtained from the model described in the paper eq 6 with the parameters given in Table 2. (c) Effect ofAu+ precursor concentrations on the evolution of the size polydispersity. (d) Effect of Au+ precursor concentrations on the number density ofnanoparticles.

Table 2. Results for the Fits of the Radius at Different Au+

Precursor Concentration

Au+ concn 12.5 10 7.5 5k1 (l/mol·s) 1.7 × 10−3 2.2 × 10−3 3.5 × 10−3 6.7 × 10−3

[Au0]sat 4 × 10−7 4 × 10−7 4 × 10−7 4 × 10−7

kgr (m/s) 1.4 × 10−6 1.2 × 10−6 1.1 × 10−6 1.0 × 10−6

γ (mN/m) 205 205 205 205

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reaction, which is inhibiting the reduction of free Au+ toproduce Au0 and which promotes growth rather thannucleation. In a kinetic study of the Au3+ reduction with asimilar reducing agent (dimethylborane), it was similarly foundthat k1 decreases with increasing Au3+ concentration. Here thereaction rate constant increased by a factor of 5, when theconcentration was decreased by a factor of 3, similar to ourobservations (see Table 2). They suggested that Au3+ absorbsto the gold nanoparticle surfaces which are less accessible to theborane reducing agent, thus reducing electron transfer andreduction rate.32 This would indicate that in fact Au+ iselectrochemically reduced at the particle surface, and not insolution.Nanoparticle Aggregation and Clustering. As seen in

Figure 7d, we observe a reduction of the number density of theparticles during the growth period. This could, in principle, beeither due to nanoparticle aggregation or due to Ostwaldripening.4 As outlined above, Ostwald ripening should benegligible under our experimental conditions. Nanoparticleaggregation could occur in a form that nanoparticles come intocontact, form an aggregate and then fuse into a largernanoparticle. In order to suppress this form of aggregation, alarge excess of stabilizing ligand (dodecanethiol, DDT) is usedin all experiments. The measured SAXS curves rather indicate,that nanoparticles arrange into regular assemblies, similar as hasbeen observed for Au nanoparticles by Spalla et al,3 wherehighly ordered fcc arrangements or nanoparticles were formed.As seen in Figure S7 in the Supporting Information, there issome increased scattering intensity at q = 1.0 nm−1,corresponding to a length scale of 6.3 nm, which is of theorder of the center-to-center distance of the nanoparticlesincluding the ligand layer. To support this further, we haveincluded in Figure S8 in the Supporting Information a set ofSAXS-curves measured for a more weakly stabilized Au-nanoparticle system, where a pronounced peak develops,indicating the formation of such ordered assemblies duringthe growth period. Also the development and shift of the formfactor oscillation indicates that nanoparticles do not fuse intolarger aggregates. Notably, the position and width of theoscillations indicate also that nanoparticles that have assembledinto clusters further grow, similar to the free single nano-particles.We also investigated the influence of added stabilizing ligand

dodecanethiol (DDT) on the nucleation and growth kinetics ofthe nanoparticles. The time dependence of the mean radius R,polydispersity σ, and particle concentration N at differentDDT/Au+ ratios (2:1, 5:1, and 8:1) are shown in Figure 8.Again, we observe the three characteristic stages of the

nucleation and growth process: a rapid increase in particleradius and a simultaneous rise in number density during thefirst 15 min, a subsequent region with slower particles growthand a plateau in particle number density, and finally cessation ofparticle growth at the longest reaction times. We observe thatgrowth is completed earlier at higher ligand concentration (110min) as compared to experiments with lower ligandconcentration (190 min). The kinetic parameters that gavethe best agreement between calculation and experimental dataare summarized in Table 3.

From the analysis, we observe that the ligand ratio primarilyaffects the precursor reaction rate constant k1, which increasesfor higher ligand ratios. This relates to the observation of aslight decrease of the induction period and smaller particles forhigher ratios. The growth rate constant is not affected by theligand ratio. The increase in k1 is a consequence of the betterstabilization of Au0 (product, see eq 1) compared to Au+ byDDT, which also stabilize the transition state to increase k1.The effect of the ligand ratio is also apparent from the lowerconversion of Au+ to nanoparticles as deduced from the overallvolume fraction of Au0 in nanoparticles (see Figure S3 in theSupporting Information). From Figure 8b, it can be clearly seenthat the evolution of the size distribution is essentiallyunaffected by the variation of the ligand concentration, whichis similar as in the investigation of the concentration effect.

The Effect of Cosolvent on the Kinetics. To determinethe key parameters of the nucleation and growth mechanism,we also systematically investigated the kinetics of Au nano-particle formation in the presence of two polar cosolvents(THF, ethanol (EtOH)) during the synthesis. Their influenceon the temporal evolution of the particle radius are shown inFigure 9. We find that the two solvents exhibit very differentbehavior.The addition of THF decreased the precursor reaction rate

constant k1 from 1.7 × 10−3 to 1.0 × 10−3 L/mol·s and similarlythe growth rate constant kgr from 1.4 × 10−6 to 8.2 × 10−7 m/swith increasing fraction of THF from 0 to 25% in toluene.When THF is introduced into the reaction, the growth processbecame much slower and the final plateau was absent since data

Figure 8. Particle radius (a), particle polydispersity (b), and number density (c) obtained from fitting the measured SAXS curves as a function ofreaction time at different molar ratios of R-SH/Au+. The experiments were performed at an Au+ concentration of 12.5 mM.

Table 3. Results for the Fits of the Radius

molar ratio R-SH:Au+ 2:1 5:1 8:1k1 (L/mol·s) 1.7 × 10−3 2.3 × 10−3 2.3 × 10−3

[Au0]sat 4 × 10−7 4 × 10−7 4 × 10−7

kgr (m/s) 1.4 × 10−6 1.4 × 10−6 1.5 × 10−6

γ (mN/m) 205 205 205

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collection was terminated at 4 h. THF as a polar solventstabilizes charged states and thus the precursor Au+ more thanAu0, which reduces the rate constant k1. It also increases theinterfacial energy of the nanoparticles which are coated withhydrophobic ligands. As growth is surface-reaction limited, thiswill negatively affect the growth rate.In contrast, the addition of ethanol considerably increased

the precursor reaction rate constant k1 from 1.7 × 10−3 to 6.7 ×10−3 L/mol·s and also the growth rate constant kgr from 1.4 ×10−6 to 2.2 × 10−6 m/s with increasing the fraction of ethanolfrom 0 to 15%. The reason is that ethanol acts also as areducing agent and thus increases the rate of Au0 formation.The effect on the growth rate might be due to stabilizing effectsof the reaction products, but that is not yet clear at themoment.Both solvents affect both the precursor reaction rate and the

growth rate in a way that their ratio increases, such that smallernanoparticles (2 nm size) are formed upon their addition, but

for THF at a much slower rate, in line with reports fromliterature for ethanol.37,38

Temperature-Dependent Kinetics. The temperaturedependence of the nucleation and growth kinetics is explicitlygiven in eq 6, but in addition there may be an implicittemperature dependence of the rate constants k1 and kgr. Wemeasured the growth kinetics at three different temperatures of22, 33, and 45 °C where the kinetics could be followed withinthe time resolution of our experiment.The temperature dependent particle size changes as a

function of time and the corresponding calculations from themodel eq 6 is presented in Figure 10a. The fitting parametersare summarized in Table 5. We observe that the kinetics andthe final particle size are strongly influenced by the reactiontemperature. The reaction proceeds significantly faster at thehigher temperatures, leading to completion of the reactionwithin 1 h at 45 °C as compared to room temperature where ittakes for 3 h. In addition, the increase in temperature leads to alarger final size of the nanoparticles, which is similar to the

Figure 9. Evolution of the particle radii as a function of reaction time in the presence of THF (a) and ethanol (EtOH) as cosolvent (b). The lines arethe best fits obtained from the model described in the paper eq 6 with the parameters summarized in Table 4.

Table 4. Results for the Fits of the Radius for Different Cosolvents

fraction in toluene 0% 10% THF 25% THF 5% EtOH 15% EtOHk1 (L/mol·s) 1.7 × 10−3 1.1 × 10−3 1 × 10−3 4.3 × 10−3 6.7 × 10−3

[Au0]sat 4 × 10−7 4 × 10−7 4 × 10−7 4 × 10−7 4 × 10−7

kgr (m/s) 1.4 × 10−6 9.2 × 10−7 8.2 × 10−7 1.8 × 10−6 2.2 × 10−6

γ (mN/m) 205 205 205 205 205

Figure 10. (a) Effect of temperature on the evolution of the particle radius obtained from in situ SAXS. The lines are the best fits obtained from themodel eq 6 described in the paper using the parameters given in Table 5. (b) Measured growth rate constants k1 (red square) and kgr (blue traingle)versus temperature in an Arrhenius representation.

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observation in the synthesis of gold nanoparticles at thetoluene−water interface by varying the temperature (14).39

We observe an increase in reduction rate constant k1 from1.7 × 10−3 to 6.7 × 10−3 L/mol·s and a drastic change of thegrowth rate kgr from 1.4 × 10−6 to 1.7 × 10−5 m/s whenincreasing the temperature from 295 to 318 K. Both processesare thermally activated where the rate constants are expected tofollow an Arrhenius dependence

= −Δ *k k e G RT0

/(16)

We obtained the value of ΔG1* = 47 kJ/mol for reductionrate constant k1 (lit. 52 kJ/mol) and a value of ΔGgr* = 85 kJ/mol for the growth rate constant kgr from linear fits of −ln(k)against 1/T (Arrhenius plot) as shown in Figure 10b. The valueof ΔG1* = 47 kJ/mol for the reduction of Au+ is somewhatlarger, but of similar magnitude compared to values publishedin literature for the reduction of Au3+ using a borohydride BH4

−

complex (52 kJ/mol),4 dimethylamine borane (39.8 kJ/mol),40

or NaHSO3 (31−38 kJ/mol).41 An estimate of the growth rateactivation energy can be given from the consideration of thesurface energy that an Au0-atom has to overcome to pass theligand layer to merge with the nanoparticle. It can be estimatedas ΔGgr* ∼ γANL, where NL is Avogradros constant. From thevalue of the interfacial tension of γ = 205 mN/m (see Table 5)and the measured activation energy of ΔGgr* = 85 kJ/mol, wecan estimate the related surface area A = d2 which is involved inthe transition and reduction of a single Au0 atom. Thecorresponding lateral dimension is d = 0.83 nm whichreasonably is about twice the diameter (0.32 nm) of a goldatom. The value of the activation energy is in very goodagreement with a value of 85.3 kJ/mol determined for bindingof long-chain thiols to gold nanoparticles.42 The lateraldimension calculated from the critical surface coverage of theexperiments of ref 42 (1.8 × 1014/cm2) is 0.75 nm, which is notvery different from the value of d = 0.83 nm estimated in our

study. The measured free activation enthalpy is also of similarmagnitude as the activation free enthalpy of nucleation, whichfor T = 300 K and S = 70 (a typical value during growth) isequal to ΔGc = 88 kJ/mol (eq 4).

Comparison with Published Data on Gold Nano-particle Nucleation and Growth. To demonstrate the moregeneral validity of developed model for the description ofnucleation and growth of nanoparticles, we applied this modelto gold nanoparticle systems prepared via various othersynthesis routes where the growth curves have all beenmeasured and published in literature. The data together withthe model descriptions are shown in Figure 11. The reactionconditions and fitting parameters are summarized in Table 6.We observe that the formation processes of gold nanoparticlesvia different approaches can be well described with thedeveloped model (eq 6). The parameters, especially k1 andkgr are strongly dependent on the reaction conditions andreagents. k1- and kgr-values for fast reduction routes are both 3orders of magnitude faster than values measured for slowreaction routes. It should be pointed out that our model is onlyable to describe the first growth process for data from ref 14because of the occurrence of unusual faster growth processafterward. For all other data, the above consideration ofnucleation and growth (eq 6) gives very good agreement withthe experimental results.The underlying kinetic model that describes our observations

is visualized in the scheme in Figure 12. First, Au atoms aregenerated by the reduction of Au+ with a reducing agent(TBAB). The reduction rate is influenced by the followingfactors (symbols (+) or (−) indicate increasing or decreasingeffect on reaction rate)

• Ligand concentration (DDT): (+) due to bettersolvation of Au0,

• Addition of cosolvent ethanol: (+) due to acting as anadditional reducing agent,

• Addition of cosolvent THF: (−) due to better solvationof Au+ compared to Au0,

• Strength of reducing agent: (+) due to faster reduction,• Au+ concentration: (−) due to self-inhibition (possibly

absorption to nanoparticle surface),• Temperature: (+) due to decreasing the free enthalpy of

activation

Table 5. Results for the Fits of the Radius at DifferentTemperatures

T [K] 295 306 318k1 (L/mol·s) 1.7 × 10−3 3 × 10−3 6.7 × 10−3

[Au0]sat 4 × 10−7 4 × 10−7 4 × 10−7

kgr (m/s) 1.4 × 10−6 4.2 × 10−6 17 × 10−6

γ (mN/m) 205 205 205

Figure 11. Evolution of the particle radii as measured by other groups and us for slow growth conditions (a) and fast growth conditions (b). Solidlines denote the best fit from to the kinetic model (eq 6).

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Second, nuclei or clusters containing several atoms aresimultaneously formed by fast nucleation (LaMer mecha-nism)43 within a short time. With the time increasing, nuclei orclusters grow via surface reaction limited addition of Au atomsto the growing nanoparticle surface. We observe that also undersurface reaction limit growth there is a size focusing of thenanoparticles, in agreement with the results of van Embden etal.24

The growth kinetics is mainly influenced by

• Addtion of cosolvent ethanol: (+) due to increasingsolubility of DDT-coated nanoparticles,

• Temperature: (+) due to decreasing the free enthalpy ofactivation

From our experiments together with the results published inliterature on other reduction reactions, we conclude that at leastthe formation of gold nanoparticles can be very well describedwithin the framework of classical nucleation theory.

■ CONCLUSIONIn this paper, we demonstrate for the first time the use of in situmicrofluidic SAXS/WAXS/UV−vis experiments to study thenucleation and growth kinetics of gold nanoparticles by using alab-based equipment. It allowed us to study the kinetics as afunction of the most relevant parameters such as concentration,temperature, ligand ratio, and the addition of polar cosolvents.The temporal evolution of particle size, polydispersity, andparticle number has been compared to a theoretical modelformulated within the framework of classical nucleation andgrowth theory. By quantitative comparison of calculated andmeasured growth curves we could identify the influence of eachof the parameters on different steps during nucleation andgrowth. We observe a fast formation of small nuclei andsubsequent surface-reaction limited slow growth until theprecursor has been fully consumed. The methodologydeveloped here can directly applied to the study of also othernanoparticle formation reactions.

■ METHODSNanocrystal Synthesis. Gold nanoparticles were synthesized

according to the procedure described by Vaia et al.16 and Stucky etal.17 In a standard experiment, an Au precursor solution containing 6.2mg of chloro gold-triphenylphosphine AuPPh3Cl and 6 μL of

dodecanethiol (DDT) were prepared in 1 mL of toluene by sonicationand added into 10.87 mg of t-butylamine borane complex (TBAB)dissolved in 1 mL of toluene to obtain gold nanoparticles at roomtemperature. Additional experiments were conducted by the variationof concentration of Au+ precursor, reaction temperature, the additionof ligand, and solvents upon standard experiment. For in situ SAXS/WAXS/UV−vis measurements, two freshly prepared precursors weremixed together in the capillary by using stopped flow device as shownin Figure 1.

In Situ Cell. To monitor the real-time formation process of Au NPsby means of SAXS/WAXS/UV−vis techniques, a temperaturecontrolled in situ cell was designed combining with stopped-flowdevice as illustrated in Figure 1. A three-dimenstional printed in situcell integrated with heating copper tube enables us to follow kinetics ofnanomaterials during the formation at elevated temperature. We chose1 mm quartz capillary with wall thickness of 10 μm as analysis cell,which was connected to Y-shaped Teflon micromixer via PE tubing toachieve fast mixing of the precursor solutions at a flow rate of 10 mL/husing a pump. The other end was designed to connect with PE tubingfor product collection.

Transmission Electron Microscopy (TEM). To analyze colloidalsample with TEM, Au NPs products were collected at the outlet ofcapillary using a vial, washed several times with ethanol, and thendispersed in toluene. TEM grids of final products were prepared bydrop-casting a 3 μL aliquot of the washed nanoparticle solution onto acarbon film-coated Cu grid and allowing the solvent to evaporate.TEM images were obtained on a Zeiss 922 Omega microscope.

UV−Vis Absorbance Spectroscopy and Analysis. UVabsorbance spectra were recorded on a USB 2000+XR1-ES detectorequipped with deuterium-halogen light source (DH-2000-BAL, OceanOptics, Germany), connected to in situ cell via fiber optical cables. Theacquisition time was set at 1 min for each data point.

UV−vis spectroscopy detects the formation of gold nanoparticlesvia the onset of the plasmon absorption at a wavelength λp = 520 nm.To analyze the UV−vis spectra quantitatively, we consideredcontributions both from the plasmon resonance and the d-interbandtransition with the corresponding band gap at the wavelength λgap =608 nm, which is observed at wavelengths below 400 nm. Theabsorbance as a function of the wavelength is then given by eq 13.

SAXS Instrument and Data Analysis. In situ SAXS experimentswere performed with a ‘“Double Ganesha AIR”’ system (SAXSLAB,Denmark). The X-ray source of this laboratory-based system is arotating anode (copper, MicroMax 007HF, Rigaku Corporation,Japan) providing a microfocused beam at λ = 0.154 nm. The scatteringdata were recorded by a position sensitive detector (PILATUS 300 K,Dectris). The sample to detector distance was set to be 35 cm, thusleading to a q-range from 0.28 to 5 nm−1. Here q is the magnitude ofthe scattering wave vector defined as q = (4π/λ)sin(θ/2), where θ isthe scattering angle and λ is the wavelength of the X-ray. Silverbehenate with a d-spacing of 58.38 Å was used as a standard tocalibrate. The X-ray path is evacuated, except at the position where thesample cell was set. The two-dimensional patterns were acquired at aninterval of 300 s for the first 10 patterns and 600 s for the rest dataduring reaction. One min time interval was used when experimentswere performed at higher temperature (33 and 45 °C). The obtained1D SAXS profiles were corrected by toluene solvent as background.

Table 6. Reaction Conditions and Fitting Results from Recently Published Data

Spalla et al.4

present data Vaia et al.16 Polte et al.14 acid ligand amine ligand

Au+/Au3+ 12.5 mM 40 mM 0.25 mM 3.5 mM 3.5 mMB 125 mM 120 mM 2.5 mM 10 mM 10 mMreaction time 190 min 150 min 60 min 16 s 2 sk1 (l/mol·s) 1.7 × 10−3 0.83 × 10−3 0.25 × 10−3 1.6 × 101 7.2 × 101

[Au0]sat 4 × 10−7 4 × 10−7 4 × 10−7 0.6 × 10−7 0.6 × 10−7

kgr (m/s) 1.4 × 10−6 0.87 × 10−6 0.63 × 10−6 1.1 × 10−3 3.6 × 10−3

γ (mN/m) 205 205 205 235 210

Figure 12. Schematic presentation of Au NP growth.

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WAXS Data Evaluation. For the analysis of the WAXS data of theAu nanoparticles, we used the complete expression in eq S1 with anexpression for the lattice factor corresponding to an fcc lattice.

∑π==−∞

∞

≠

Z q Rnv

f L q g( , )(2 )

( , )h k l

hkl hkl hkl

3

, ,

2

hkl( ) (000)

where n is the number of particles per unit cell, f hkl is the structurefactor of the unit cell, v is the volume of the unit cell, Lhkl(q,g) is anormalized peak shape function, for which in our case a normalizedGaussian is used, and ghkl is the reciprocal lattice vector. Thisexpression is fitted to the WAXS curves to obtain the unit cell size, theDebye−Waller factor, and the crystalline domain size from the peakwidth of the Bragg reflections. Further details can be found in refs 32and 33.

■ ASSOCIATED CONTENT*S Supporting InformationThe Supporting Information is available free of charge on theACS Publications website at DOI: 10.1021/acs.lang-muir.5b02759.

Additional information on SAXS, WAXS, and UV/visdata and kinetic analysis, and description of experimentalsetup (PDF)

■ AUTHOR INFORMATIONNotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSX.C., J.S., and S.F. acknowledge financial support by an ERCAdvanced Grant (STREAM, No. 291211).

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