UVâVis Study of the Nucleation and

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Simultaneous SAXS/WAXS/UV-Vis Study of the Nucleation and Growth of Nanoparticles – A Test of Classical Nucleation Theory Xuelian Chen, Jan H. Schröder, Stephan Hauschild, Sabine Rosenfeldt, Martin Dulle, and Stephan Förster Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.5b02759 • Publication Date (Web): 22 Sep 2015 Downloaded from http://pubs.acs.org on October 2, 2015

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Simultaneous SAXS/WAXS/UV-Vis Study of the Nucleation and Growth of Nanoparticles – A Test of Classical Nucleation Theory Xuelian Chen, Jan Schröder, Stephan Hauschild, Sabine Rosenfeldt, Martin Dulle, Stephan Förster* Physical Chemistry I, University of Bayreuth, 95447 Bayreuth, Germany

ABSTRACT Despite the increasing interest in the applications of functional nanoparticles, a comprehensive understanding of the formation mechanism starting from the precursor reaction with subsequent nucleation and growth is still a challenge. We for the first time investigated the kinetics of gold nanoparticle formation systematically by means of a lab-based in-situ small-angle X-ray scattering (SAXS) / wide-angle X-ray scattering (WAXS) / UV-vis absorption spectroscopy experiment using a stopped-flow apparatus. We thus could systematically investigate the influence of all major factors such as precursor concentration, temperature, the presence of stabilizing ligands and co-solvents on the temporal evolution of particle size, size distribution and optical properties from the early pre-nucleation state to the late growth phase. We for first time formulated and numerically solved a closed nucleation and growth model including the precursor reaction. We observe that the results can be well described within the framework of classical nucleation and growth theory, including also results of previous studies by other research groups. From the analysis we can quantitatively derive values for the rate constants of precursor reaction and growth together with their activation free enthalpies. We find the growth process to be surface-reaction limited with negligible influence of Ostwald ripening yielding narrow disperse gold nanoparticles.

KEYWORDS Nucleation and growth · gold nanoparticles · SAXS/WAXS/UV-Vis · stopped flow

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Introduction The mechanism of particle nucleation and growth is one of the classical topics in colloid science. It has in recent years attracted increasing attention because of the need to synthesize functional nanoparticles with better control and efficiency. In recent years the study of nucleation and growth has greatly benefitted from the development of new powerful experimental methods that allow one to follow kinetic processes in-situ over a wide range of time scales. In particular third generation synchrotron sources now offer means to monitor particle growth by small- and wide-angle X-ray diffraction (SAXS, WAXS) as well as X-ray- and UV/Vis-spectroscopy to obtain information on the evolution of the particle size distribution and optical properties as a function of time, down to millisecond resolution.1-4 Gold nanoparticles are most intensely investigated in nanoscience and technology, because of their unique optical properties, catalytic reactivity and stability.5-9 The ability to tailor these properties via their size, shape and surface chemistry is a prerequisite for successful applications. Various synthetic methods are known, based on the reduction of Au salt precursors via citrate, borane-complexes, UV- or light irradiation. Because of their importance as nanomaterials, investigations of the nucleation and growth kinetics of gold nanoparticles have motivated several studies by different research groups. In particular the studies by Spalla1-4 and others10-16 demonstrated the use of in-situ X-ray studies to obtain 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 period followed by particle growth to reach the final size when all precursor material has been consumed. Particle aggregation and Ostwald ripening are mechanisms that can decrease the number of particles and change their size distribution during the course of the reaction. Concerning the importance and contributions of these mechanisms there are different, sometimes conflicting reports. In one study the particles were observed to rapidly grow to their final size with the number of particles of this size increasing with increasing reaction time.17 Other reports demonstrate that after nucleation the number of particles is constant, while the size distribution narrows. In a study of NiPt nanoparticle growth only nucleation and growth were observed, without indications for Ostwald-ripening.18 Further studies reported aggregative growth of Au-nanoparticles instead of Ostwald ripening,

19

nearly exclusively Ostwald ripening,

16

or

2

just nucleation and growth without Ostwald ripening . There is also evidence for a nucleation – growth - aggregation mechanism as has been recently proposed.14 Theoretical models to capture different periods of nanoparticle structural evolution have historically focused on the interplay of particle growth and Ostwald-ripening. Lifshitz, Slyozov20 and Wagner21 gave an analytical solution for the particle size distribution in the case of diffusion-limited and reaction2 Environment ACS Paragon Plus

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limited growth, known as the LSW-theory. Their analytical solution made use of a Taylor expansion of the Gibbs-Thompson term. The full expression, adequate for treating small nanoparticles, has been treated numerically by Talapin et al. to elucidate conditions of particle size focusing.22 Numerical algorithms were later refined by Mantzaris to identify suitable control parameters for the synthesis of gold nanoparticles to tailor the size distribution.23 Spalla used a numerical algorithm similar to Talapin and demonstrated 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- and reaction-limited growth on the particle size distribution which could be quantitatively compared to LSW-theory and the synthesis of CdSe-nanoparticles. 24 In view of the variety of different mechanisms of Au-nanoparticle formation and because Aunanoparticles are most intensely considered in research and applications, we performed a systematic study on gold nanoparticle nucleation and growth using in-situ time-resolved small- and wide-angle Xray scattering (SAXS, WAXS) and UV/Vis-spectroscopy in conjunction with a stopped-flow microfluidic device. This was for the first time achieved with lab-based equipment without the need of synchrotron X-ray beamlines. It allowed us to study systematically the influence of a variety of parameters such as precursor concentration, temperature, and the addition of stabilizing ligands and cosolvents to determine their influence on the temporal evolution of particle size, polydispersity, volume fraction, number density and optical properties over the complete nucleation and growth period. For the analysis of the kinetic data we for the first time numerically solved the complete set of reaction rate equations comprising precursor reaction, nucleation, growth and Ostwald-ripening to obtain the evolution of the full particle size distribution from the induction period to the late growth stage. We obtained very good agreement between the calculated and experimentally determined evolution of the particle mean size and polydispersity, also including recently published data by other research groups. This study thus for the first time quantifies available experimental data on particle nucleation and growth in terms of rate constants and activation energies and provides a comprehensive scenario of the structural evolution of one of the most intensely studied nanoparticle systems.

Experimental setup The formation of gold nanoparticles was investigated by means of in-situ SAXS/WAXS/UV-Vis experiments in combination with a stopped flow device using for the first time lab-based equipment, without the need of a synchrotron radiation source. This setup, shown schematically in Fig. 1, enables one to follow the structural evolution of the nanoparticles and the evolution of their optical properties 3 Environment ACS Paragon Plus

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simultaneously. For fast mixing of the two reacting solutions (gold salt and reducing agent) they were pumped with a high precision syringe pump through a Y-shaped Teflon mixer at high flow rates into a quartz capillary. After reaching stationary flow conditions the pumps were stopped. The utilization of this stopped flow device allowed us to minimize the dead time from transferring the reaction solution into the analysis cell (capillary), thus acquiring structural and optical information from the very beginning of the nanoparticle formation process. In our case, the Au nanoparticles formed completely within 1-4 hours with a dead time of approximately 1.3s. The unusual position of the XRD-detector very close to the sample is necessary to acquire wide-angle X-ray diffraction with sufficiently high signal-tonoise ratio. Details of the setup are described in the Supporting Information.

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

Nucleation and Growth Model Precursor reaction: We assume that Au+ (chloro gold(I)-triphenylphosphine) reacts with the reducing agent B (t-butylamineborane) to form Au0 Au+ + B Au0 + R


(1)

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with some reaction product R. Assuming simple second order rate kinetics the rate of formation of Au0,

j+ (in mol/l.s), is given by j+ =

d [ Au 0 ] = k1 [ Au + ][ B ] dt +

(2)

with the rate constant k1 . If reaction (1) proceeds, the concentration [ Au 0 ] will continuously increase and eventually exceed the saturation concentration [ Au 0 ] sat , leading to a supersaturation S=

[ Au 0 ] >1. [ Au 0 ] sat

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

τ sat =

S [ Au 0 ] sat k1 [ Au + ] 0 [ Au + ] 0 − S [ Au 0 ] sat

(

)

(3)

This corresponds to an induction time after which nucleation starts. In common cases where [ Au + ]0 < [ B ]0 , the induction time will be shorter such that τ sat as calculated from Eq. (3) can be considered as an upper limit. For a rate constant of k1 ~ 10 −3 l / mol ⋅ s , a saturation concentration of [ Au 0 ] sat ~ 10 −7 mol / l , a supersaturation of S = 500 , and a precursor concentration [ Au + ]0 ~ 0.02 mol / l , the maximum induction time is τ sat ~ 125 seconds, a typical value for our experiments.

Nucleation: Under supersaturation nuclei of Au-nanoparticles will form at a rate given by

d [ Au 0 ] V  ∆Gc (t )  jnuc (t ) = = β [ Au 0 ] exp− dt nuc v0 kT   with the rate constant β * =

(4)

4kT 4πR 3 ( ≈ 1 ⋅ 10 11 s −1 ), V = the volume of the nucleus, and the free 9ηv m 3

enthalpy of activation ∆Gc (t ) =

16πγ 3vm2

3(kT ) 2 (ln S (t ) )

2

with γ the interfacial tension of the gold nanoparticles

M = 1.69 ⋅10−29 m3 the volume of Au0-atoms. Newly formed nuclei will have a radius ρN A Rcap 2γv0 (critical radius) of R = , where Rcap = is the capillary radius. For the typical range of ln S kT supersaturations in our experiments, critical radii have values between 0.24 nm ( S = 1000 ) and 1.0 nm ( S = 5 ). and v0 =


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Growth: The formed nuclei J will subsequently grow at a growth rate

j gr , J (t ) =

d [ Au 0 ] = 4πn J RJ (t ) DN A [ Au 0 ] sat dt gr , J

  R   S (t ) − exp  cap      RJ (t )     D  1 +  R (t )k  J gr  

(5)

where k gr is the surface growth rate constant, D the diffusion coefficient of Au0, nJ is the

 D concentration of J-nuclei, N A is Avogadro’s number, and R the radius of the particle.   Rk  gr

−1

  = Da  

is the Damköhler number Da, which relates reaction rates to the (diffusive) mass transport rates. The growth mechanism is mostly either surface reaction-limited (SR, the addition of Au0 to the growing particle surface) or diffusion-limited. According to Eq. (5) the diffusion-limited case corresponds to

D > 1 ) whereas the surface-reaction limited case corresponds to D >> Rk gr ( Da > 1 Rk gr

( Da S such that  RJ  nanoparticles of radius R J dissolve. With the capillary radius typically being in the range Rcap ~ 1.5 nm, and

with

radii

in

the

range

0 .5 < R J < 5

nm,

the


exponential

term

has

values

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 Rcap  between 20 > exp   > 1.4 . At the beginning of the nucleation period the supersaturation nearly  RJ  instantaneously rises to very large values >100 (see Fig. 2b) such that negative growth rates, i.e. particle dissolution, do not occur. During the very late growth period where the supersaturation decays to values

S < 5 negative growth rates for particle radii R J < 1 nm can occur. However, since the particle size distributions in our experiments are quite narrow ( σ < 0.15 ) the fraction of nanoparticles with radii < 1 nm is negligibly small. Thus for our experiments which cover the induction, nucleation and growth periods to almost complete consumption of precursor, Ostwald ripening involving negative growth rates has negligible influence, which is in line with numerical calculations in ref. 24.

Kinetic model: The kinetic model describing the time dependence of the concentrations of the precursors [ Au + ] , [B ] , of free Au0-atoms [ Au 0 ] , of Au0-atoms incorporated into nanoparticles by 0 nucleation [ Au N0 ] or by growth onto particles J [ Au PJ ] , as well as the particle concentrations [ PJ ]

during the induction, nucleation and growth period corresponds to a set of coupled first order differential equations being

d [ Au + ] = −k1[ Au + ][ B] dt d [ B] = −k1[ Au + ][ B] dt  [ Au 0 ] sat  Rcap   1 − exp    0 t  R [ Au ] ∆ G d [ Au 0 ] V   J  c  = k1[ Au + ][ B] − β exp− − ∫ 4πRJ DN A [ Au 0 ]  h(t J )dt J  dt v0    kT  0 D 1 +   R k  J gr   0 d [ Au N ] V  ∆Gc  = β exp−  dt v0  kT   [ Au 0 ]sat  Rcap   1 − exp    0  0 R [ Au ] d [ Au PJ ] J    = 4πRJ DN A [ PJ ][ Au 0 ] , J = 1,..., N dt   D 1 +   R k  J gr   d [ PJ ]  ∆Gc  = β exp− δ [t − t J ] = h(t J ) dt t =t J  kT 


(6)

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where δ [t − t J ] is the delta function used to describe the concentration of a new nucleated species [ PJ ] which is determined by the amount of [ Au N0 ] produced at t = t J . Solving this set of coupled differential equations yields the concentrations [ PJ ](t ) and radii R J (t ) of all particles J that have been formed during the nucleation process, from which the size distribution h( R , t ) , the mean radius R (t ) , and the relative standard deviation σ R (t ) can be obtained which can be compared to experimental data. The same kinetic model without consideration of the precursor reaction has been employed by Talapin solved using MC-simulations

22

and by Spalla using the Euler forward method.

2,4

Since the precursor

reaction was not considered, assumption on an initial particle size and supersaturation were made, which were chosen to give best agreement between calculations and experiment. In our case the set of N + 5 coupled first order differential equations (6) is solved numerically by discretization into finite time steps ∆t using a Runge-Kutta 4th order algorithm, which has low computational effort and fulfills two important criteria for the kinetic model, i.e. (1) the calculated concentrations are always non-negative, i.e. [C ](t ) ≥ 0 and (2) it conserves mass, i.e. the requirement N

VJ [ PJ ] J =1 v 0

0 [ Au + ] 0 = [ Au + ] + [ Au N0 ] + [ Au PJ ] = [ Au + ] + ∑

(7)

is fulfilled at all times. As nucleation and growth may occur over very different time scales, we used up to N = 10000 time steps with linearly or logarithmically spaced time intervals ∆t , or adaptive step size control to capture the temporal evolution of the concentrations over as many orders of magnitude 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 all subsequent time steps the particles J can grow by consumption of Au0. The 0 concentration increase of [ Au PJ ] after the i-th time step is converted to the additional new volume of

particles J via

VJ ,new

([ Au =

0 ] − [ Au PJ ]i −1

0 Pj i

[ P] J

)v

0

This then allows to calculated the new radius RJ according to


(8)

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 3(V + VJ ,new )   RJ =  J 4 π  

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(9)

For the ensemble of particles J = 1,..., i after i time steps the size distribution can then be calculated. Known input parameters for the calculations are the initial concentrations [ Au + ]0 and [B]0 , the temperature T , the viscosity of the solvent (toluene) η = 0.55 mPas, the molar mass of gold

M = 197 g/mol, and its (bulk) density ρ Au = 19.3 g/cm3 . Further the calculations require to specify four at the beginning unknown parameters, i.e. the interfacial tension γ of the gold nanoparticle surface in the presence of the solvent, the precursor rate constant k1 , the growth rate constant k gr , and the saturation concentration [ Au 0 ] sat . These values are varied to obtain the best fit between the calculated and experimentally measured mean radii R (t ) .

Comparison to experimental data: The kinetic model provides the mean radius R , the relative standard deviation σ R , the concentrations [Au+] and [Au0], the supersaturation S , and the size distribution h(R) as a function of time.

Figure 2. a) Temporal evolution of mean particle radius and the polydispersity σ R obtained by fitting the measured in situ SAXS curves to a model of polydisperse spheres. The solid lines represent the best fit to Eq. (6). b) Temporal evolution of the concentrations [Au+], [Au0] and particle concentration N (in mM) together with the supersaturation S obtained from the numerical calculations. 9 Environment ACS Paragon Plus

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Figure 2a shows the temporal evolution of the calculated mean radius R and the polydispersity σ R (rel. standard deviation of particle size) as a function of time together with a comparison with measured data for initial concentrations [ Au + ]0 = 0.0125 mol/l, [ B]0 = 0.125 mol/l, and a stabilizer concentration (dodecanethiol, DDT) of [DDT] =0.025 mol/L. We find very good agreement with the experimental data using values of k1 =1.7 × 10-3l/mol·s, kgr =1.4 × 10-6 m/s, [Au0]sat =4 × 10-7 mol/l and γ = 205 mN/m. To provide a measure of the variance of the fitting parameters, we show in the Supporting Information (Fig. S6) comparisons to experimental growth data using fit parameters that deviated by ± 20% from the above values, showing significant deviations from the experimental data. The calculations predict a reasonable induction time after which nucleation begins (120 s). We then observe a steep rise of the mean radius during the nucleation and early growth period (up to 40 min) followed by a slower increase until the percursor has been consumed. The final radius of 3.1 nm is in good agreement with the results from transmission electron microscopy (see Fig. 4a). Also the calculated polydispersity 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 within the first minutes and then decreases to very low values of 0.001 mM during the remaining growth period due to its immediate consumption by particle growth. Also shown is the supersaturation which increases sharply to values of S = 1800 during nucleation and then decreases to values of down to S = 3 during the remaining growth period. Also shown is the number of particles which increases steeply during the nucleation period and then remains constant. This indicates a negligible effect of Ostwald ripening.


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Figure 3. a) Temporal evolution of the size distribution calculated at different time intervals for the same conditions as in Fig. 2. b) Final size distributions (solid lines) calculated using Lifshitz-Slyozov___

theory (

___

Eq. 11), Wagner-theory (

___

Eq. 12) and a Schulz-Zimm-distribution (

Eq. 10) with the

same mean and standard deviation as in the corresponding numerical calculation (, Eq. 6) and as in the size distribution as measured by SAXS ().

Figure 3a shows the temporal evolution of the size distribution as calculated from Eq. (6) with the same parameters used for the calculations in Fig. 2a. We observe after 3 min. a size distribution characterized by a very sharp increase at R = 0.2 nm corresponding to the smallest size particles nucleated at high supersaturation. With time the size distribution develops into a log-normal type distribution whose relative size distribution decreases with time until the precursor has been consumed. Figure 3b shows the calculated final size distribution from Eq. (6) (after 200 min.), which is compared to a Schulz-Zimm (SZ) distribution with the same mean value and relative standard deviation. This distribution function is given by

hSZ

z +1 ( z + 1) R z R  ( R) = exp − ( z + 1)

R z Γ( z + 1)



(10)

R 

with the average radius R and the relative standard deviation σ R = (z + 1)

−1 / 2

. The distribution is

∞

normalized such that

∫h

SZ

( R )dR = 1 . We observe a quite good agreement between the shape of the

0

calculated size distribution and the SZ-distribution. This size distribution also well describes the


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measured SAXS-curves. In Fig. 3b the final size-distributions are further compared to theoretical predictions of LSW-theory. It predicts for diffusion-limited growth a size distribution (LS-theory) 20  34 e u2 1   exp  −  5/3 7 /3 11/3  2 1 2 / 3 − u hLS (u ) =    ( u + 3 ) (1.5 − u )  0 

if 0 < u < 1.5

(11)

otherwise

with u = R / Rcr , where Rcr is the critical radius for which the rate of dissolution is equal to the growth rate. In the diffusion-controlled case Rcr = R . In surface reaction controlled case Wagner derived 21  7 3u  3u  exp  − 2 hW (u ) =  (2 − u )5  2 − u   0

if 0 < u < 2

(12)

otherwise

where Rcr = 9R / 8 . As shown in Fig. 3b, we observe that LSW theory siginifcantly overestimates the fraction of smaller particles at the low-R side of the size-distribution. This is due to the dynamic dissolution/growth equlibrium of the smaller particles during Ostwald ripening. As discussed above, in our case even at late growth stages where S < 5 Ostwald ripening has little effect, as the particle size distribution has already narrowed such that the fraction of smaller nanoparticles exhibiting 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 radical polymerization kinetics. 25,26 Here, similar to the formation and consumption of free Au0 by particles of different size, a reactive monomer radical M* is formed by initiation, and subsequently consumed by addition to growing polymer chains of different lengths. Thus the kinetic model is very similar, the only difference being the missing termination step in the nanoparticle growth model.


RESULTS AND DISCUSSION Formation of Au nanoparticles

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the structural changes of the nanoparticles during nucleation and growth. Each SAXS-curve was measured for 5 minutes, a compromise between having a sufficiently high signal-to-noise ratio for successful data analysis and a still sufficient temporal resolution to follow the complete nucleation and growth process. Figure 4a shows a TEM-image of the Au nanoparticles obtained after completion of the in-situ measurement at a molar ratio of 2 (DDT:Au+). It indicates that the nanoparticles are spherical 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 an absorbance maximum in the λ = 510 to 530 nm range, which is attributed to the plasmon resonance of the growing gold nanoparticles. During the experiment, a weak peak at around λ =320 nm was detected and then disappeared gradually. This peak was also detected by Tsukuda et al. who attributed this to intraband and interband transitions for clusters Aun formed within a short time after addition of TBAB.

27

In the following a plasmon peak occurred and shifted from 505 to 522 nm along

with an increasing absorption intensity when the reaction proceeded, suggesting the growth of nanoparticles proceeds continuously. Figure 4c presents the corresponding SAXS scattering curves obtained during the same experiment. During the first 30 minutes we observe the development of the Guinier-plateau in the range 0.4 nm-1 < q < 1.0 nm-1 with a strongly decaying scattering intensity at higher q. This indicates the formation of small nanoparticles with radii R < 1.5 nm. For q < 0.4 nm-1 we observe a small low-q upturn indicating the initial presence of some larger aggregates of unknown structure. For larger times we see the evolution of a pronounced form factor oscillation with a minimum 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 sharp plasmon peak in the UV-Vis spectra. With increasing time the Guinier plateau develops a shallow slope, indicating the formation nanoparticle assemblies. 28 The in-situ WAXS experiment provides insight into the crystalline nature of the Au nanoparticles during the formation process. As shown in Fig. 4d we observed the appearance and growth of two strong diffraction peaks with increasing reaction time, accompanied by weak higher order reflections. The two strongest peaks are located at q=26.5 nm-1 and 30.6 nm-1, respectively. These two main peak positions ((111) at 2θ = 20° , (200) at 2θ = 25° ) together with the higher order reflections can be indexed on an FCC lattice (space group Fm3 m ). The maximum of the (111) peak increases with time, whereas the full-width at half-maximum (FWHM) decreases, indicating that the crystalline domain size continuously increases during the growth of the nanoparticles. 14 Environment ACS Paragon Plus

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

For subsequent analysis, selected curves from the in-situ SAXS/WAXS/ UV-Vis measurements along with the corresponding fits are shown in Figure 5a, b, and c, respectively. UV-Vis spectra were fitted to a sum of a Lorentzian-peak (plasmon resonance) and an absorption edge (band gap) function given by

(λ − λ )

n

A(λ ) = a gap

gap

λ

 2 + ap   πσ  p

 4(λ − λ p )2   1 + 2   σ p  

−1

(13)

The first term in this equation describes the 5d 6s-6p interband transition with an exponent n = 1 / 2 in case of an indirect band gap. The second term describes the plasmon resonance with a Lorentzian line shape. The two prefactors a gap , a p should be roughly proportional to the number of gold atoms in gold nanoparticles. Figure 5a shows that this gives an adequate description of the spectra over the whole wavelength range of λ = 300 − 1000 nm including the plasmon resonance at λ = 530 nm and the absorption edge at slightly shorter wavelength. This five parameter fit ( a gap , λ gap , n, a p , λ p ) is sufficiently robust and accurate to determine the plasmon resonance intensity a p as a function of time as shown in the inset of Figure 5a. The peak intensity shows an approximately linear increase with time. We note that also other time dependencies have been observed, such as a slow initial intensity increase followed by a more rapid increase.29, 30 The peak intensity of the plasmon resonance depends on the number of Au-atoms within nanoparticles, but also on the nanoparticle size such that there is no simple relation to derive these properties from the measured absorption spectra.31


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For the data analysis of the SAXS-curves we considered the contribution from the large population of growing single nanoparticles, giving rise to the pronounced form factor oscillation, and the contribution from nanoparticle assemblies or clusters, giving rise to the low-q upturn observed for q < 0.4 nm-1 at the beginning of the reaction, and causing the shallow slope at intermediate q at later reaction times. To capture the relevant features of the measured SAXS-curves over the whole q-range, we distinguished between the contribution from single nanoparticles and nanoparticle clusters by modeling the scattering curves as 32, 33,34

I (q ) = (∆b ) ρ N F (q ) 2

9 [(sin(qR) − qR cos(qR) )]2 (qR) 6

(14)

where (∆b ) is the X-ray contrast difference between particles and solvent, and ρ N is the number density 2

of nanoparticles, and R is the radius of the nanoparticles. K denotes the average of the form factor for homogeneous spheres over the Schulz-Zimm-distribution (Eq. 10) with a weighting factor R 6 to account for the fact that scattering methods determine the weight-averaged scattered intensity. F (q ) describes the contribution from nanoparticle clusters given by 35,36 F (q) =

N sin [(D − 1) arctan(qξ ]

(15)

(D − 1)qξ (1 + q 2ξ 2 )( D−1) / 2

where D the fractal dimension and N the number of particles of the cluster. ξ =

2 R g2

D (D − 1)

where R g is

the radius of gyration of the clusters. Using Eq. (14) it is possible to nearly quantitatively describe the measured scattering curves over the whole q-range, as shown in Fig. S7 in the Supporting Information. We found that in all cases the contribution of single growing nanoparticles by far dominates the measured scattering intensity, in particular in the q-range of q > 0.8 nm-1, where we obtain information on the radius and polydispersity of the growing nanoparticles. As shown in Fig. 5b we could well analyze this region of the measured SAXS-curves by fitting to a model of polydisperse homogeneous spheres using F (q ) = 1 . The fitted curves are indicated by the red solid lines showing good agreement with the experimentally determined scattering curves. From the fits we obtain the scattered intensity I(0), the mean radius of the particles R , and the relative polydispersity σ. The contribution from clustered nanoparticles giving rise to the low-q features of the scattering curves can be separately considered and are discussed further below. We also considered whether the measured scattering curves could be described by a bimodal size distribution of 16 Environment ACS Paragon Plus

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spherical particles (Eq. S14 in the Supporting Information), but found less agreement with the measured data, which supports the view that nanoparticles tend to form correlated assemblies. The WAXS-curves in Figure 5c were similarly analyzed by fitting the measured diffraction curves to a model of FCC-packed spherical particles. 32, 33,34 I (q) = (b1 − b2 ) ρ N P( q, R) S ( q) 2

(16)

where S (q ) is the structure factor and P(q, R) is the averaged form factor as in Eq. (14). The fits are indicated by the red solid lines in Figure 5c. From the fits we obtain the unit cell size a and the crystalline domain size D which is directly related to the peak width. With the described analysis of the simultaneously measured SAXS-, WAXS- und UV/Vis-data we can obtain the particle radius R , the polydispersity σ, the crystalline domain size D, the unit cell size a, the scattered intensity I(0) and the relative number of Au0 as a function of time. From the latter two parameters we can calculate the relative number and volume fraction of nanoparticles. The unit cell size a = 0.7 nm is in good agreement with literature data (0.70 nm) and does not change with time or particle size. The temporal evolution of radius, polydispersity and number of nanoparticles can then be compared to model calcuations of nucleation and growth as outlined above.

Crystallinity

Figure 6. WAXS patterns of gold nanoparticles measured during nanoparticle formation and growth at different reaction times. The diffraction cones have hyperbolic shape due to the horizontal positioning of the detector above the sample. 17 Environment ACS Paragon Plus

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Table 1. Unit cell dimension a, crystalline domain size D, deviation from ideal lattice point ∆ (DebyeWaller factor), lattice type, and diameter 2R of the nanoparticles as determined from fits to the measured WAXS- and SAXS-curves. Time (min)

a [nm]

D [nm]

∆[nm]

lattice

2R [nm]

30

0.41

1.6

0.01

FCC

3.9

50

0.41

2.1

0.01

FCC

4.7

70

0.41

2.4

0.01

FCC

5.2

100

0.41

3.1

0.01

FCC

5.4

150

0.41

3.6

0.01

FCC

5.8

190

0.41

3.9

0.01

FCC

6.0

With the WAXS-detector positioned very close (~ 1 cm) to the sample, we were able to detect wideangle X-ray diffraction from the growing nanoparticles in dilute solution. Selected WAXS patterns at different reaction times are presented in Fig. 6 for a molar ratio of DDT/Au+ as 2:1. Only during the first 10 minutes, i.e. during the induction period, the WAXS-signal was very weak and structureless. At subsequent times we observe well-defined WAXS-signals indicating a crystalline structure from the very beginning of particle formation indicating that nanoparticles during nucleation and growth are crystalline at all times.

The measured diffraction curves can be quantitatively described by Eq. (16) to obtain more detailed structural information. From the analysis we directly obtain the unit cell dimension a, the mean displacement of atoms from lattice point ∆ (Debye-Waller factor), as well as the mean size D of crystalline 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 ∆ are ± 10% except for the very first measured WAXS-curves with low signal-to-noise ratios, where the relative error of ∆ is much larger. For this case we assumed a fixed value of ∆ = 0.01 which describes the WAXS-curves at later times very well. Table I shows that the crystalline domain sizes, which would correspond to the nanoparticle diameters in case of single crystals, increases with increasing reaction time whereas all other parameter values stay constant. The increasing crystalline domain size can be compared to the 18 Environment ACS Paragon Plus

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diameter of the nanoparticles as obtained from the SAXS-curves. We observe that generally 2 R > D such that the nanoparticles are multi-domain particles, which is also evident from the TEM-images (Fig. S4), where different domains within the nanoparticles can be distinguished by their grey-scale which differs due to different orientation and the corresponding different diffraction contrast.

The unusual role of Au+ concentration on kinetics.

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 of the 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 of Au+ precursor concentrations on the evolution of the size polydispersity. (d) Effect of Au+ precursor concentrations on the number density of nanoparticles.


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Table 2. Results for the fits of the radius at different Au+ precursor concentration Concentration of Au+

12.5

10

7.5

5

k1 (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

As a first parameter we investigated the effect of the gold precursor concentration on the kinetics and final size of the nanoparticles. This effect had not been studied in any of the previously published investigations on the growth kinetics of gold nanoparticles, although it has a decisive influence on the nucleation and growth kinetics. We systematically decreased the initial concentration of gold precursor from 12.5 to 5 mM, whereas the molar ratio of the reducing agent to the gold precursor TBAB:Au+ remained unchanged at 10:1. The temporal evolution of the measured SAXS scattering curves at a low Au+ concentration of 7.5 mM is shown as a representative example in Figure 7a. The presence of a Guinier plateau at low q (q < 0.7 nm-1) and a shift of the form factor oscillations at high q are clearly observable, demonstrating a sufficiently high signal-to-noise ratio to allow data analysis even at low concentrations. From the measured SAXS curves we determined the mean radius R , polydispersity σ , and particle concentration N as a function of time at varying concentration of Au+ precursor solutions (12.5, 10, 7.5 and 5mM) from Eq. (14). The time dependence of these parameters is shown in Fig. 7b-d.

We observe that the time-dependences of all three parameters give a consistent picture of the nanoparticle nucleation and growth process: (1) a rapid formation of small nanoparticles within the first 20 minutes, (2) a subsequent slow growth, and (3) finally the cessation of growth after consumption of the precursor after ca. 200 minutes. During formation of Au-nanoparticles, the polydispersity decreases down to 10-14 % gradually within 50 min and then stays constant until completion of the reaction for all concentrations. The initial rapid increase of the number of particles with a mean radius of around 1.2 nm during the first 15 minutes signals the occurrence of a fast nucleation that was captured by the SAXS measurements. It is evidenced by the consumption of a small amount of Au0 monomers as shown in Figure S3 of the Supporting Information.


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To obtain a quantitative description of the formation mechanism of Au nanoparticles, we used Eq. (6) and adjusted the kinetic parameters k1 , k gr , γ ,[ Au 0 ]sat to calculate the development of the three parameters R , σ , and N as a function of time from the induction period to the late growth stage. The parameters used for the calculated growth curves are summarized in Table 2. The calculated growth curves are displayed as solid lines in Figure 7b showing very good agreement between calculated and experimentally determined mean particle radii. We observe a clear increase of the precursor reaction rate constant k1 from 1.7 × 10-3 to 6.7 × 10-3 l/mol.s with an Au+ precursor concentration decreasing from 12.5 mM to 5 mM, whereas the growth rate constant remains almost unchanged ( k gr ~ 1.0-1.4 × 10-6 m/s). Generally, as the particle size should be roughly proportional to the ratio of growth rate to

[

]

3 2 nucleation rate, i.e. ~ k gr exp γ / ln S , one would assume that higher Au+ precursor concentrations

yield faster reduction rates, higher supersaturation S, increased nucleation rates and thus smaller nanoparticles. This would be consistent with reports from bulk Au-nanoparticle synthesis, where an increase in the final size of the nanoparticles is observed with decreasing initial metal ions concentration in solution caused by slower reduction rate of Au3+. 14 Yet, we clearly observe larger nanoparticles and a smaller number of particles in our kinetic experiment (Figs. 7b, d). The fact that k1 depends on [Au+] indicates the existence of a concurrent reaction, which is inhibiting the reduction of free Au+ to produce Au0 and which promotes growth rather than nucleation. In a kinetic study of the Au3+-reduction with a similar reducing agent (dimethylborane) it was similarly found that k1 decreases with increasing Au3+concentration. Here the reaction rate constant increased by a factor of 5, when the concentration was decreased by a factor of 3, similar to our observations (see Table 2). They suggested that Au3+ absorbs to the gold nanoparticle surfaces which are less accessible to the borane reducing agent, thus reducing electron transfer and reduction rate.32 This would indicate that in fact Au+ is electrochemically reduced at the particle surface, and not in solution.

Nanoparticle aggregation and clustering As seen in Fig. 7d, we observe a reduction of the number density of the particles during the growth period. This could, in principle, be either due to nanoparticle aggregation, or due to Ostwald ripening.4 As outlined above, Ostwald ripening should be negligible under our experimental conditions. Nanoparticle aggregation could occur in a form that nanoparticles come into contact, form an aggregate and then fuse into a larger nanoparticle. In order to suppress this form of aggregation, a large excess of stabilizing ligand (dodecanethiol, DDT) is used in all experiments. The measured SAXS-curves rather 21 Environment ACS Paragon Plus

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indicate, that nanoparticles arrange into regular assemblies, similar as has been observed for Aunanoparticles by Spalla 3, where highly ordered FCC-arrangements or nanoparticles were formed. As seen in Fig. S7 in the Supporting Information, there is some increased scattering intensity at q = 1.0 nm1

, corresponding to a length scale of 6.3 nm, which is of the order of the center-to-center distance of the

nanoparticles including the ligand layer. To support this further, we have included in Fig. S8 in the Supporting Information a set of SAXS-curves measured for a more weakly stabilized Au-nanoparticle system, where a pronounced peak develops, indicating the formation of such ordered assemblies during the growth period. Also the development and shift of the form factor oscillation indicates that nanoparticles do not fuse into larger aggregates. Notably, the position and width of the oscillations indicate also that nanoparticles that have assembled into clusters further grow, similar to the free single nanoparticles.

Figure 8. Particle radius (a), particle polydispersity (b), and number density (c) obtained from fitting the measured SAXS-curves as a function of reaction 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

8:1

k1 (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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We also investigated the influence of added stabilizing ligand dodecanethiol (DDT) on the nucleation and growth kinetics of the nanoparticles. The time dependence of the mean radius R , polydispersity σ , and particle concentration N at different DDT/Au+ ratios (2:1, 5:1, and 8:1) are shown in Figure 8a-c. Again, we observe the three characteristic stages of the nucleation and growth process: a rapid increase in particle radius and a simultaneous rise in number density during the first 15 min, a subsequent region with slower particles growth and a plateau in particle number density, and finally cessation of particle growth at the longest reaction times. We observe that growth is completed earlier at higher ligand concentration (110 min) as compared to experiments with lower ligand concentration (190 min). The kinetic parameters that gave the best agreement between calculation and experimental data are summarized in Table 3.

From the analysis we observe that the ligand ratio primarily affects the precursor reaction rate constant

k1 , which increases for higher ligand ratios. This relates to the observation of a slight decrease of the induction period and smaller particles for higher ratios. The growth rate constant is not affected by the ligand ratio. The increase in k1 is a consequence of the better stabilization of Au0 (product, see Eq. 1) compared to Au+ by DDT, which also stabilize the transition state to increase k1 . The effect of the ligand ratio is also apparent from the lower conversion of Au+ to nanoparticles as deduced from the overall volume fraction of Au0 in nanoparticles (see Fig. S3 in the Supporting Information). From Figure 8b, it can be clearly seen that the evolution of the size distribution is essentially unaffected by the variation of the ligand concentration, which is similar as in the investigation of the concentration effect.


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The effect of co-solvent on the kinetics

Figure 9. Evolution of the particle radii as a function of reaction time in the presence of THF (a) and ethanol (EtOH) as co-solvent (b). The lines are the 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 co-solvents Fraction in toluene

0%

10% THF

25% THF

5% EtOH

15% EtOH

k1 (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

To determine the key parameters of the nucleation and growth mechanism, we also systematically investigated the kinetics of Au nanoparticle formation in the presence of two polar co-solvents (THF, ethanol (EtOH)) during the synthesis. Their influence on the temporal evolution of the particle radius are shown in Figure 9. We find that the two solvents exhibit very different behavior. 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 similarly the growth rate constant k gr from 1.4 ×10−6 to 8.2 ⋅ 10 −7 m/s with increasing fraction of THF from 0 to 25% in toluene. When THF is introduced into the reaction, the growth process became 24 Environment ACS Paragon Plus

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much slower and the final plateau was absent since data collection was terminated at 4hs. THF as a polar solvent stabilizes charged states and thus the precursor Au+ more than Au0, which reduces the rate constant k1 . It also increases the interfacial energy of the nanoparticles which are coated with hydrophobic ligands. As growth is surface-reaction limited, this will 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 k gr from 1.4 ×10−6 to 2.2 ×10−6 m/s with increasing the fraction of ethanol from 0 to 15%. The reason is that ethanol acts also as a reducing agent and thus increases the rate of Au0-formation. The effect on the growth rate might be due to stabilizing effects of the reaction products, but that is not yet clear at the moment.

Both solvents effect both the precursor reaction rate and the growth rate in a way that their ratio increases, such that smaller nanoparticles (2 nm size) are formed upon their addition, but for THF at a much slower rate, in line with reports from literature for ethanol .37,38

Temperature-dependent kinetics

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 the model (Eq. 6) described in the paper using the parameters given in Table 5. (b) Measured growth rate constants k1 (red square) and k gr (blue traingle) versus temperature in an Arrhenius representation.


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Table 5. Results for the fits of the radius at different temperatures T [K]

295

306

318

k1 (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

The temperature dependence of the nucleation and growth kinetics is explicitly given in Eq. (6), but in addition there may be an implicit temperature dependence of the rate constants k1 and k gr . We measured the growth kinetics at three different temperatures of 22, 33, and 45 °C where the kinetics could be followed within the time-resolution of our experiment.

The temperature dependent particle size changes as a function of time and the corresponding calculations from the model (Eq. 6) is presented in Figure 10a. The fitting parameters are summarized in Table 5. We observe that the kinetics and the final particle size are strongly influenced by the reaction temperature. The reaction proceeds significantly faster at the higher temperatures, leading to completion of the reaction within 1 hour at 45°C as compared to room temperature where it takes for 3 hours. In addition, the increase in temperature leads to a larger final size of the nanoparticles, which is similar to the observation in the synthesis of gold nanoparticles at the toluene-water interface by varying the temperature (14).39 We observe an increase in reduction rate constant k1 from 1.7 ×10−3 to 6.7 ×10−3 l/mol.s and a drastic change of the growth rate k gr from 1.4 ×10−6 to 1.7 ×10−5 m/s when increasing the temperature from 295 to 318 K. Both processes are thermally activated where the rate constants are expected to follow an Arrhenius dependence

k = k0e−∆G*/ RT


(16)

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We obtained the value of ∆G1 * = 47 kJ/mol for reduction rate constant k1 (Lit. 52 kJ/mol) and a value of ∆Ggr * = 85 kJ/mol for the growth rate constant k gr from linear fits of –ln(k) against 1/T (Arrhenius plot) as shown in Fig. 10b. The value of ∆G1 * = 47 kJ/mol for the reduction of Au+ is somewhat larger, but of similar magnitude compared to values published in literature for the reduction of Au3+ using a boro hydride 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 rate activation energy can be given from the consideration of the surface energy that an Au0-atom has to overcome to pass the ligand layer to merge with the nanoparticle. It can be estimated as ∆Ggr * ~ γAN L , where N L is Avogradros constant. From the value of the interfacial tension of γ = 205 mN/m (see Table 5) and the measured activation energy of ∆Ggr * = 85 kJ/mol we can estimate the related surface area A = d 2 which is involved in the transition and reduction of a single Au0-atom. The corresponding lateral dimension is d = 0.83 nm which reasonably is about twice the diameter (0.32 nm) of a gold atom. The value of the activation energy is in very good agreement with a value of 85.3 kJ/mol determined for binding of long-chain thiols to gold nanoparticles. 42

The lateral dimension calculated from the critical surface coverage of the experiments of ref.

42

(1.8.1014 / cm2) is 0.75 nm, which is not very different from the value of d = 0.83 nm estimated in our study. The measured free activation enthalpy is also of similar magnitude as the activation free enthalpy of nucleation, which for T=300 K and S=70 (a typical value during growth) is equal to ∆Gc = 88 kJ/mol (Eq. 4).


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Comparison with published data on gold nanoparticle nucleation and growth

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

Table 6. Reaction conditions and fitting results from recently published data present

Vaia’s data

Polte’s data

Spallaacid ligand

Spallaamine ligand

data

Ref. 16

Ref. 14

Ref. 4

Ref. 4

Au+/Au3+

12.5 mM

40 mM

0.25 mM

3.5 mM

3.5 mM

B

125 mM

120 mM

2.5 mM

10 mM

10 mM

Reaction time

190 min

150 min

60 min

16 s

2s

k1 (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

To demonstrate the more general validity of developed model for the description of nucleation and growth of nanoparticles, we applied this model to gold nanoparticle systems prepared via various other synthesis routes where the growth curves have all been measured and published in literature. The data together with the model descriptions are shown in Fig. 11. The reaction conditions and fitting 28 Environment ACS Paragon Plus

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parameters are summarized in Table 6. We observe that the formation processes of gold nanoparticles via different approaches can be well described with the developed model (Eq. 6). The parameters, especially k1 and k gr are strongly dependent on the reaction conditions and reagents. k1 - and k gr -values for fast reduction routes are both three orders of magnitude faster than values measured for slow reaction routes. It should be pointed out that our model is only able to describe the first growth process for data from ref. 14 because of the occurrence of unusual faster growth process afterwards. For all other data the above consideration of nucleation and growth (Eq. 6) gives very good agreement with the experimental results.

Figure 12. Schematic presentation of Au NP growth

The underlying kinetic model that describes our observations is visualized in the scheme in Fig. 12. First, Au atoms are generated by the reduction of Au+ with a reducing agent (TBAB). The reduction rate is influenced by the following factors ((+) or (-) indicate increasing or decreasing effect on reaction rate) -

Ligand concentration (DDT): (+) due to better solvation of Au0,

-

Addition of co-solvent ethanol: (+) due to acting as an additional reducing agent,

-

Addition of co-solvent THF: (-) due to better solvation of 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

Second, nuclei or clusters containing several atoms are simultaneously formed by fast nucleation (LaMer mechanism) 43 within a short time. With the time increasing, nuclei or clusters grow via surface reaction limited addition of Au atoms to the growing nanoparticle surface. We observe that also under surface reaction limit growth there is a size focusing of the nanoparticles, in agreement with the results of van Embden et al. 24

The growth kinetics is mainly influenced by -

Addtion of co-solvent ethanol: (+) due to increasing solubility of DDT-coated nanoparticles, 29 Environment ACS Paragon Plus

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-

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Temperature: (+) due to decreasing the free enthalpy of activation

From our experiments together with the results published in literature on other reduction reactions we conclude that at least the formation of gold nanoparticles can be very well described within the framework of classical nucleation theory.

Conclusion In this paper we demonstrate for the first time the use of in-situ microfluidic SAXS/WAXS/UV-Vis experiments to study the nucleation and growth kinetics of gold nanoparticles by using a lab-based equipment. It allowed us to study the kinetics as a function of the most relevant parameters such as concentration, temperature, ligand ratio and the addition of polar co-solvents. The temporal evolution of particle size, polydispersity and particle number has been compared to a theoretical model formulated within the framework of classical nucleation and growth theory. By quantitative comparison of calculated and measured growth curves we could identify the influence of each of the parameters on different steps during nucleation and growth. We observe a fast formation of small nuclei and subsequent surface-reaction limited slow growth until the precursor has been fully consumed. The methodology developed here can directly applied to the study of also other nanoparticle formation reactions.

Methods Nanocrystal synthesis. Gold nanoparticles were synthesized according to the procedure described by Vaia et al.16 and Stucky et al.17 In a standard experiment, an Au precursor solution containing 6.2 mg of chloro gold-triphenylphosphine AuPPh3Cl and 6 µL of dodecanethiol (DDT) were prepared in 1mL of toluene by sonication and added into 10.87 mg of t-butylamine borane complex (TBAB) dissolved in 1mL of toluene to obtain gold nanoparticles at room temperature. Additional experiments were conducted by the variation of concentration of Au+ precursor, reaction temperature, the addition of ligand and solvents upon standard experiment. For in-situ SAXS/WAXS/UV-vis measurements, two freshly prepared precursors were mixed together in the capillary by using stopped flow device as shown in Figure 1.

In-situ Cell To monitor the real-time formation process of Au NPs by means of SAXS/WAXS/UVvis techniques, temperature controlled in-situ cell was designed combining with stopped-flow device as illustrated in Figure 1. 3D printed In-situ cell integrated with heating copper tube enables us to follow kinetics of nano-materials during the formation at elevated temperature. We chose 1mm quartz capillary 30 Environment ACS Paragon Plus

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with wall thickness of 10 µm as analysis cell, which was connected to Y-shaped teflon micro-mixer via PE tubing to achieve fast mixing of the precursor solutions at a flow rate of 10 mL/h using pump. The other end was designed to connect with PE tubing for product collection.

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

UV-visible absorbance Spectroscopy and analysis. UV absorbance spectra were recorded on a USB 2000+XR1-ES detector equipped with Deuterium-Halogen light source (DH-2000-BAL, Ocean Optics, Germany), connected to in situ cell via fiber optical cables. The acquisition time was set at 1 min for each data point. UV/Vis-spectroscopy detects the formation of gold nanoparticles via the onset of the plasmon absorption at a wavelength λ p = 520 nm. To analyze the UV/Vis-spectra quantitatively, we considered contributions both from the plasmon resonance and the d-interband transition with the corresponding band gap at the wavelength λ gap = 608 nm, which is observed at wavelengths below 400 nm. The absorbance as a function of the wavelength is then given by Eq. 13.

SAXS instrument and data analysis. In-situ SAXS experiments were performed with a ‘‘Double Ganesha AIR’’ system (SAXSLAB, Denmark). The X-ray source of this laboratory-based system is a rotating anode (copper, MicroMax 007HF, Rigaku Corporation, Japan) providing a micro-focused beam at λ = 0.154 nm. The scattering data were recorded by a position sensitive detector (PILATUS 300 K, Dectris). The sample to detector distance was set to be 35 cm, thus leading to q-range from 0.28 nm-1 to 5 nm-1. Here q is the magnitude of the scattering wave vector defined as, q = (4π / λ ) sin(θ / 2) , where

θ is the scattering angle and λ is the wavelength of X-ray. Silver behenate with a d-spacing of 58.38 Å was used as a standard to calibrate. The X-ray path is evacuated, except at the position where the sample cell was set. The 2D patterns were acquired at an interval of 300 seconds for the first 10 patterns and 600 s for the rest data during reaction. 1 min time interval was used when experiments were performed at higher temperature (33 and 45 0C). The obtained 1D SAXS profiles were corrected by toluene solvent as background.

WAXS data evaluation. For the analysis of the WAXS data of the Au nanoparticles we used the complete expression in Eq. S1 with an expression for the lattice factor corresponding to an FCC lattice.


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Z (q, R ) =

(2π )3 nv

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∞

∑f

2 hkl

Lhkl ( q, g hkl )

h ,k ,l =−∞ ( hkl ) ≠( 000 )

Where n is the number of particles per unit cell, f hkl the structure factor of the unit cell, v is the volume of the unit cell, and Lhkl (q, g ) a normalized peak shape function, for which in our case a normalized Gaussian is used, and g hkl is the reciprocal lattice vector. This expression is fitted to the WAXS-curves to obtain the unit cell size, the Debye-Waller factor, and the crystalline domain size from the peak width of the Bragg reflections. Further details can be found in ref. 32 and 33.

Acknowledgements X. C., J. S., and S. F. acknowledge financial support by an ERC Advanced Grant (STREAM, No. 291211).

Supporting Information The Supporting Information is available free of charge via the Internet at http://pubs.acs.org/. Additional information on SAXS-, WAXS-, UV/Vis-data and kinetic analysis, and description of experimental setup.

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Simultaneous SAXS/WAXS/UV-Vis Study of the Nucleation and Growth of Nanoparticles – A Test of Classical Nucleation Theory Xuelian Chen, Jan Schröder, Stephan Hauschild, Sabine Rosenfeldt, Martin Dulle, Stephan Förster*


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