Tuning Precursor Reactivity toward Nanometer-Size Control in

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Tuning Precursor Reactivity towards Nanometer-Size Control in Palladium Nanoparticles Studied by in-Situ Small Angle X-ray Scattering Liheng Wu, Huada Lian, Joshua J. Willis, Emmett D. Goodman, Ian Salmon McKay, Jian Qin, Christopher J. Tassone, and Matteo Cargnello Chem. Mater., Just Accepted Manuscript • DOI: 10.1021/acs.chemmater.7b05186 • Publication Date (Web): 03 Jan 2018 Downloaded from http://pubs.acs.org on January 4, 2018

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Chemistry of Materials

Tuning Precursor Reactivity towards Nanometer-Size Control in Palladium Nanoparticles Studied by in-Situ Small Angle X-ray Scattering Liheng Wu,1,2 Huada Lian,2 Joshua J. Willis,2,3 Emmett D. Goodman,2,3 Ian Salmon McKay,2 Jian Qin,2 Christopher J. Tassone,1,* and Matteo Cargnello2,3,* 1

Stanford Synchrotron Radiation Lightsource, SLAC National Accelerator Laboratory, Menlo

Park, CA 94025, USA 2

Department of Chemical Engineering, Stanford University, Stanford, CA 94305, USA

3

SUNCAT Center for Interface Science and Catalysis, Stanford University, Stanford, CA 94305,

USA

*Corresponding authors: [email protected], [email protected]

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Abstract: Synthesis of monodisperse nanoparticles (NPs) with precisely controlled size is critical for understanding their size-dependent properties. Although significant synthetic developments have been achieved, it is still challenging to synthesize well-defined NPs in a predictive way due to a lack of in-depth mechanistic understanding of reaction kinetics. Here we use synchrotron-based small-angle X-ray scattering (SAXS) to monitor in-situ the formation of palladium (Pd) NPs through thermal decomposition of Pd-TOP (TOP: trioctylphosphine) complex via the “heat-up” method. We systematically study the effects of different ligands, including oleylamine, TOP, and oleic acid, on the formation kinetics of Pd NPs. Through quantitative analysis of the real-time SAXS data, we are able to obtain a detailed picture of the size, size distribution, and concentration of Pd NPs during the syntheses, and these results show that different ligands strongly affect the precursor reactivity. We find that oleylamine does not change the reactivity of Pd-TOP complex, but promote the formation of nuclei due to strong ligand-NP binding. On the other hand, TOP and oleic acid substantially change the precursor reactivity over more than an order of magnitude, which controls the nucleation kinetics and determines the final particle size. A theoretical model is used to demonstrate that the nucleation and growth kinetics are dependent on both precursor reactivity and ligand-NP binding affinity, thus providing a framework to explain the synthesis process and the effect of the reaction conditions. Quantitative understanding of the impacts of different ligands enables the successful synthesis of a series of monodisperse Pd NPs in the broad size range from 3 to 11 nm with nanometer-size control, which serve as a model system to study their size-dependent catalytic properties. The in-situ SAXS probing can be readily extended to other functional NPs to greatly advance their synthetic design.


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1. Introduction Rational design and synthesis of well-defined colloidal nanoparticles (NPs) is of utmost importance for fundamentally studying their intrinsic properties and for various technological applications.1-3 Over the past two decades, the synthetic control of colloidal NPs has come to the level that by tuning reaction conditions (e.g., reaction precursors, ligands, reaction temperature, etc.), various sizes, shapes, compositions, and even complex structures of NPs have been achieved.4-8 However, these syntheses are typically developed empirically, using trial-and-error approaches that cause substantial waste of time and resources. Understanding the formation mechanism of these NPs will provide guidelines for greatly accelerating their synthesis with tailored properties. Unfortunately, it is still challenging to study the fast nucleation and growth kinetics due to the lack of proper experimental setups. In past few years, the fast developments of in-situ experimental techniques have enabled the real time probing of NP formation in solution. Direct visualization of NP growth at the atomicresolution has been realized by in-situ transmission electron microscopy (TEM) using liquid environmental cells.9-10 Alternatively, synchrotron based X-ray scattering techniques, due to high penetration of the X-ray and fast data aquisition,11-12 have advanced our understanding of NP nucleation and growth during colloidal synthesis.13-37 Taking Au NPs as an example, using insitu small-angle X-ray scattering (SAXS), the nucleation kinetics of Au NPs synthesized using different ligands were directly monitored.16 The growth mechanism of Au NPs was also studied,18-19 which involves a rapid nucleation followed by NP growth driven by both monomer attachment and particle coalescence. This in-situ technique has also been utilized to experimentally probe NP formation under harsh reaction conditions, such as the formation of CdSe quantum dots at 240 oC in a glass capillary, in which the thermal activation of selenium 3 ACS Paragon Plus Environment


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precursor was found to be the growth rate determining step.24 Despite this success, important questions still unanswered are whether the measured nucleation and growth kinetics is valid in the lab-scale batch synthesis and how the kinetics can be utilized for designing better synthetic strategies towards well-defined NPs for desired applications. Here we report the in-situ SAXS probing of the synthesis of Pd NPs through thermal decomposition of Pd-TOP complex in 1-octadecene solution using a “heat-up” method.38-40 We use a custom-made flask reactor to mimic typical laboratory reaction conditions (e.g., high temperature, inert atmosphere) for solution-phase colloidal synthesis.41 We chose to study the synthesis of Pd NPs because of their widespread catalytic applications in many important chemical reactions, including methane combustion reaction,42 methane steam reforming reaction,43 and electrochemical oxidation of formic acid.44-45 Understanding the size-activity relationship is critical for designing better catalysts for those reactions. Although different synthetic approaches have allowed for the preparation of different-sized Pd NPs with narrow size distributions,38, 46-52 currently, there is still no general guideline for precisely controlling their size due to the lack of insights into the formation kinetics. By systematically studying the roles of different ligands (i.e., trioctylphosphine (TOP), oleylamine, and oleic acid) via in-situ SAXS, we are able to quantitatively explore the reaction kinetics. We find that the Pd-TOP precursor reactivity is strongly affected by the type and amount of ligands used, which controls the nucleation kinetics and allows for the fine control of the final particle size. Theoretical models suggest that the growth of Pd NPs is limited by surface reaction between monomers and NPs or by thermal activation of Pd-precursor depending on the precursor reactivity. The mechanistic understanding of the effects of different ligands enables the synthesis of Pd NPs in the size range of 3 to 11 nm with nanometer-size control. We believe that the in-situ SAXS characterization 4 ACS Paragon Plus Environment

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coupled with the versatile reactor geometry described here can be extended to accelerate the synthetic developments of various functional NPs. 2. Experimental Section 2.1. Chemicals and Materials Pd(acac)2 (acac = acetylacetonate, 35% Pd) was purchased from Acros Organics. Oleic acid (90%), oleylamine (70%), and 1-octadecene (90%) were purchased from Sigma-Aldrich and degassed under vacuum at 100 oC for 1 h before use. TOP (97%) was purchased from SigmaAldrich and used without further purification. Hexanes and isopropanol were purchased from Fisher Scientific. 2.2. Syntheses of Pd NPs The syntheses were performed in a custom-made flask reactor under inert Ar gas. Pd NPs were synthesized via thermal decomposition of Pd-TOP complex modified from previously reported procedures.38-39 In a typical procedure, 1-octadecene (10 mL) and Pd(acac)2 (0.25 mmol) were mixed via magnetic stirring under a gentle flow of Ar for 15 min. Then TOP was injected, immediately forming a light yellow Pd-TOP complex,53 followed by the addition of oleylamine or oleic acid depending on experimental choices (Table 1). The mixture was kept at 60 oC for 30 min under the Ar flow to remove air and moisture and then heated to 280 oC using a heating rate of ~15 oC min-1 (the heating rates for all the reactions are very similar) and kept at the final temperature for up to 30 min. After the reaction, the flask was cooled down to room temperature by removing the heating tape. The obtained Pd NPs were isolated by precipitation with 20 mL of 2-propanol followed by centrifugation at 8000 rpm for 3 min. The precipitated Pd NPs were



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further purified by another 2 cycles of precipitation (5 mL of hexanes as the solvent and 20 mL of 2-propanol as the anti-solvent). After purification, the Pd NPs were re-dispersed in 5 mL of hexanes for further characterizations. Different combinations of ligands were studied to systematically evaluate their effect on reaction kinetics, and are summarized in Table 1. For reaction E-G, due to large volume of oleic acid used, the amount of 1-octadecene used was tuned such that the total volume of 1-octadecene and oleic acid was 10 mL to maintain similar precursor concentration for these reactions. Table 1. Different combinations of ligands for the synthesis of Pd NPs in this work. The amount of Pd(acac)2 used in each synthesis is 0.25 mmol. Reaction A B C D E F G

TOP 1.25 mmol 1.25 mmol 1.25 mmol 2.50 mmol 1.25 mmol 1.25 mmol 1.25 mmol

Oleylamine -0.63 mmol 2.50 mmol 2.50 mmol ----

Oleic acid ----3.75 mmol 9.40 mmol 15.60 mmol

2.3. In-situ SAXS Characterization In-situ SAXS measurements were performed at Beamline 1-5 of Stanford Synchrotron Radiation Lightsource (SSRL) using our custom-made setup (Figure S1).41 The X-ray path length within the reactor was 5 mm. The X-ray energy was 15.5 keV and the beam spot size was 500 µm × 500 µm. The sample-to-detector distance was calibrated to be 741.6 mm using a silver behenate standard. For each data acquisition, an exposure time of 5 s was applied. A Rayonix SX165 CCD area detector was used to collect the two-dimensional (2D) scattering patterns. The 2D SAXS patterns were reduced to 1D data, calibrated to absolute scale using a glassy carbon standard (Figure S2a)54 and were further analyzed using the Irena package (available at 6 ACS Paragon Plus Environment

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usaxs.xray.aps.anl.gov/staff/ilavsky/irena.html from the APS).12 The size, size distribution, and concentration, and volume fraction of the Pd NPs were modeled in Irena package using a spherical form factor (see details in the Supporting Information (SI)). The yield (Y) of Pd NPs was obtained based on the equation Y = φ/φmax, where φ is the volume fraction of total Pd NPs at a specific reaction time, φmax is the maximum volume fraction of Pd NPs in the solution at 100% conversion of Pd-precursor to Pd nanoparticles. 2.4. Ex-Situ Characterization The purified Pd NPs were characterized by TEM. TEM samples were prepared by drop-casting a dilute NP dispersion in hexane onto carbon-coated 300 mesh Cu grids. TEM images were collected on a FEI Tecnai transmission electron microscope operated with an accelerating voltage of 200 kV. The obtained superlattices of Pd NPs with the oleic acid ligand were imaged using a FEI Magellan 400 XHR scanning electron microscopy operating at 5 kV. Fourier transform infrared spectra of the NPs were recorded on a Nicolet iS50 spectrometer. 3. Results and Discussion Pd NPs were synthesized through thermal decomposition of Pd-TOP complex in 1-octadecene (see Experimental Section for details). The synthesis procedure using only TOP as surfactant (reaction A in Table 1) is taken as standard. The Pd-TOP complex solution was heated up from 60 oC to 280 oC and kept at 280 oC for up to 30 min. During the reaction, SAXS patterns were consecutively acquired at an exposure time of 5 s for each pattern. The obtained 2D SAXS data were integrated into 1D data and the background signal from the reactor and solvent were subtracted. As reaction temperature increases up to 230 oC, the scattering from nuclei with diameter larger than 1 nm appears. This temperature, defined as the nucleation temperature, is 7 ACS Paragon Plus Environment


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taken as t = 0 s. Representative background-subtracted SAXS patterns are shown in Figure 1a and S2b. As the reaction proceeds, the scattering intensity at low scattering vector q increases quickly, indicating increased particle size. Obvious oscillation peaks appear as well, suggesting the narrowing of the NP size distribution. To obtain more information about size, size distribution, and concentration of the Pd NPs, the SAXS data were fitted using a spherical NP model in the Irena package (see SI for details). Figure 1b-d show the quantitative analysis of the mean diameter, polydispersity and concentration of Pd NPs as a function of reaction time. Based on the analysis of particle concentration, burst nucleation occurs in the first 50 s, during which the NP concentration increases with a constant nucleation rate of 1.22 × 1014 mL-1 s-1 in the case of the standard reaction A (Table 1). Meanwhile, the polydispersity of the formed nuclei dropped significantly to ~14 %. The narrow size distribution of the nuclei is critical for their further simultaneous growth into uniform NPs. During this nucleation stage ~27 % of the Pd atoms in the precursor are incorporated into Pd NPs (Figure 3c). Between 50 to 115 s, the Pd NPs continue to slowly grow in size from 2.8 to 3.7 nm. Although a small concentration of new nuclei is formed during this period, the much slower nucleation rate (2.4 × 1013 mL-1 s-1) guarantees that the fraction of newly formed nuclei is relatively small and the overall polydispersity was not increased, but instead dropped to ~ 10%. Between 115 s and 160 s Pd NPs slowly grow to 3.9 nm at nearly constant particle concentration due to much decreased monomer concentration. After 160 s, there is a slight decrease in particle concentration (Figure 1b), suggesting the existence of NP-NP coalescence or Ostwald ripening, which is common in the colloidal synthesis of NPs.18, 24, 55-56 After 5 min, Pd NPs with the final size of 4.0 ± 0.4 nm are obtained and their size and concentration do not change during further aging process. The final Pd NPs were also characterized by TEM, as shown in Figure 3d. The size based on TEM


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characterization was measured to be 3.7 ± 0.3 nm, which is in good agreement with the SAXS measurement (Figure 3e,f, and Table 2).

Figure 1. (a) Representative SAXS data (colored plots) and the corresponding fits (black plots) of Pd NPs at different reaction times during the synthesis using only TOP as surfactant (reaction A, Pd:TOP molar ratio = 1:5). The scattering intensities are offset for clarity. Time t = 0 s is set when nucleation starts. (b) Quantitative analysis of the concentration of Pd NPs as a function of reaction time. (c) Size (dots) and size distribution (bars) of Pd NPs as measured by in-situ SAXS. (d) Reaction temperature profile during the synthesis.



b

a 429 s

423 s

290 s

285 s

239 s

218 s

220 s

202 s

193 s

176 s Intensity (a.u.)

149 s Intensity (a.u.)

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134 s 115 s 97 s

158 s 138 s 119 s 92 s 78 s

81 s

64 s

63 s

43 s 42 s

28 s

0.04

16 s

14 s

0s

0s 0.1 q (Å-1)

0.6

0.04

0.1 q (Å-1)

0.6

Figure 2. Representative SAXS patterns (colored plots) and the corresponding fits (black plots) of Pd NPs at different reaction times in the presence of (a) TOP 1.25 mmol + oleylamine 0.65 mmol (reaction B); (b) TOP 1.25 mmol + oleylamine 2.50 mmol (reaction C). The scattering intensities are offset for clarity. Time t = 0 s is set when nucleation starts and the nucleation temperature is at ~230 oC for both reactions.


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Figure 3. (a-c). Quantitative analysis of (a) size, (b) concentration, and (c) yield of Pd NPs with different amounts of oleylamine as measured via in-situ SAXS. (d) TEM images of the final Pd NPs synthesized with different ligands. (e) SAXS patterns (colored plots) and the corresponding fits (black plots) of the as-synthesized Pd NPs. (f) Size and size distribution measured from TEM (histogram) and SAXS (dotted plots, normalized to the maximum of the histogram). Results from reaction A, B, C are shown in red, blue and purple, respectively.

Table 2. Average Pd NP sizes measured from TEM and SAXS. Reaction

A

B

C

D

E

F

G

SAXS (nm)

4.0 ± 0.4

3.8 ± 0.4

3.4 ± 0.4

5.5 ± 0.6

7.5 ± 0.5

9.2 ± 0.6

11.0 ± 0.9

TEM (nm)

3.7 ± 0.3

3.5 ± 0.3

3.3 ± 0.3

5.2 ± 0.7

7.3 ± 0.3

8.7 ± 0.6

10.5 ± 0.9

To study the effect of different ligands on the synthesis of Pd NPs, we started by comparing the standard reaction condition (reaction A) with those where oleylamine, a widely used stabilizing ligand for metallic NPs,57 is present. Real-time SAXS patterns using different amounts of oleylamine are shown in Figure 2. We observed similar nucleation temperature at ~230 oC, indicating that oleylamine does not affect the formation of monomer species or the 11 ACS Paragon Plus Environment


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chemistry of the Pd-TOP complex. The Pd NP size and concentration are derived from the fits of the SAXS results and their quantitative comparisons are shown in Figure 3a-c. Similar to the case without oleylamine, a rapid nucleation occurred in the first ~50 s, followed by a slow growth of NP from ~2.8 nm in size. The similar yield of Pd NPs over reaction times suggests that oleylamine does not affect precursor reactivity (Figure 3c). However, slightly higher nucleation rate (1.37 × 1014 mL-1 s-1) was observed when 0.63 mmol of oleylamine was used (reaction B), generating more nuclei. Since the precursor amount is constant, the more nuclei are formed, the smaller the final Pd NPs, as confirmed by the smaller size measured from SAXS (3.8 ± 0.4 nm) and TEM (3.5 ± 0.3 nm) (Figure 3d-f and Table 2). The difference in the nucleation rate in the presence of oleylamine is likely due to stronger binding between oleylamine and the Pd0 nuclei, which facilitates the formation of nuclei by stabilizing them with reduced nuclei-solvent interfacial tension. This observations is also supported by the fact that the TOP ligand on the Pd surface can be easily exchanged with oleylamine (Figure S3), and further corroborated by previous studies involving NMR.53 Further increasing the amount of oleylamine from 0.63 mmol to 2.50 mmol correspondingly increases the nucleation rate to 1.86 × 1014 mL-1 s-1 (Figure 3), leading to even smaller Pd NPs with an average diameter of 3.4 ± 0.4 nm from SAXS (Figure 3d-f). Although oleylamine changes the nucleation rate, the change is small which leads to limited tunability of final particle size. We also tested the effect of final reaction temperature on the formation of Pd NPs and found that it has minimal or no effect on particle size and size distribution, as long as it is above the critical nucleation temperature that enables burst nucleation. For example, there is no obvious difference in the final size of Pd NPs ex situ synthesized using the same ligand mixture from reaction C but at different final reaction temperature of 240 oC and 290 oC (Figure S4).


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In contrast to oleylamine, TOP substantially changes the reactivity of Pd precursor. It has been demonstrated that Pd(II) forms a stable PdII-(TOP)4 complex and a large excess of TOP retards the thermal decomposition of the Pd-TOP complex.53 Taking advantage of the in-situ SAXS, we quantitatively studied the effect of TOP by doubling its amount (molar ratio of Pd:TOP increases from 1:5 to 1:10, reaction D). We observed the formation of Pd NPs at 255 oC rather than 230 oC due to the shift in the reaction equilibrium of the decomposition of Pd-TOP complex into Pd NPs, which requires higher energy to activate it. Quantitative analysis of the SAXS data (Figure S5) shows that the formation rate of Pd NPs is reduced by a factor of 5 (Figure 4c). Due to a depressed precursor reactivity in the presence of large excess of TOP which cannot support a large amount of monomer, the nucleation rate (1.01 × 1013 mL-1 s-1) is more than an order of magnitude smaller compared to that for reaction C (1.86 × 1014 mL-1 s-1), and the nucleation process lasts much longer (~290 s) compared to the rapid nucleation (~50 s) for reaction C (Figure 4a,b). As a result, fewer nuclei are formed (1.9 × 1015 mL-1 vs. 8.5 × 1015 mL-1), and the final Pd NPs are larger in diameter (5.5 ± 0.6 nm for reaction D vs. 3.4 ± 0.4 nm for reaction C) from SAXS, Figure 4e,f), which are also confirmed by ex-situ TEM (Figure 4d). It is worth mentioning that due to much longer nucleation process in reaction D, particle size distribution is wider (Figure 4d), thus highlighting the importance of controlling precursor reactivity for burst nucleation in order to obtain narrow size distribution.



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Figure 4. Quantitative analysis of (a) size, (b) concentration, and (c) yield of Pd NPs as measured via in-situ SAXS during the syntheses with different amounts of TOP. (d) Representative TEM image of the final Pd NPs. (e) SAXS pattern (colored plot) and the corresponding fit (black plot) of the as-synthesized Pd NPs. (f) Size and size distribution measured from TEM (histogram) and SAXS (dotted plots, normalized to the maximum of the histogram).

Recently we reported that, in stark contrast to conventional colloidal synthesis, the Pd NPs rapidly crystallize into three-dimensional superlattices in the presence of oleic acid rather than dispersed NPs, and weak binding between oleic acid and Pd NPs plays a critical role in the crystallization.41 We found that in the presence of oleic acid (1:1 molar ratio of oleic acid:TOP), Pd NPs start to form at 200 oC, which is ~30 oC lower than the standard reaction A with only TOP. Oleic acid acts like a “catalyst” for the thermal decomposition of Pd-TOP complex, which is probably due to either the active involvement of oleic acid in the thermal decomposition of PdTOP complex or the formation of a Pd(oleate)x(TOP)y complex that decompose at lower temperatures compared to pure Pd-TOP complex.58-60 The reduced reaction temperature resulted 14 ACS Paragon Plus Environment

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in a smaller nucleation rate, and consequently, larger particles of 6.8 ± 0.4 nm, which is ~ 2.8 nm larger than the Pd NPs synthesized without oleic acid (reaction A).41 By increasing the amount of oleic acid, we observed similar in-situ assembly of Pd NPs into face-centered cubic superlattices, followed by post-growth of Pd NPs inside the superlattices as described before41 (Figure S6-9). The mean diameter and the yield of Pd NPs as a function of reaction time derived from SAXS are shown in Figure 5a,b. Interestingly, increasing the molar ratio of oleic acid:TOP results in even larger Pd NPs with narrow size distributions. Pd NPs of 7.5 ± 0.5 nm, 9.2 ± 0.6 nm, and 11.0 ± 0.9 nm average diameters from SAXS were synthesized using 3:1, 7.5:1 and 12.5:1 molar ratio of oleic acid:TOP, respectively (Figure 5c-e). We ascribe the large tunability of size to different nucleation rates caused by different binding affinity of oleic acid/TOP on Pd NPs.

Figure 5. (a,b) Quantitative analysis of (a) size and (b) yield of Pd NPs measured via in-situ SAXS at varying molar ratios of oleic acid:TOP (reactions E-G). (c) Represenative TEM images of the dispersed Pd NPs synthesized from reaction E (upper), reaction F (middle), and reaction G (lower). Scale bars are 20 nm. (d) SAXS patterns (colored plots) and corresponding fits (black line) of the as-synthesized Pd NPs. (e) Size and size distribution measured from TEM (histogram) and SAXS (dotted plots, normalized to the maximum of the histogram). Results from reaction E, F, G are shown in red, blue, and purple, respectively.



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Figure 6. Classical modelling of the formation kinetics of Pd NPs using different ligands. (a) Only TOP (reaction A). (b) A mixture of TOP and oleylamine (reaction C). (c) A large excess of TOP (reaction D). (d) A mixture of oleic acid and TOP (reaction F). The red lines are from the classical model, and the size and size distribution are experimental results from SAXS. Table 3. Fitting parameters used for modelling the nucleation and growth kinetics.

Reaction

A

B

C

D

E

F

G

(J m-2)

1.155

1.150

1.142

1.245

1.160

1.175

1.192

100000

115000

135000

80000

56700

50000

40000

/T (nm s-1 K-1)

0.407

0.355

0.305

0.566

0.714

0.799

0.985

To gain more insights on the formation of Pd NPs with different ligands, we modelled the nucleation and growth kinetics using classical models61 in which three steps are involved: i) decomposition of Pd precursor into monomers; ii) reaction of monomers to form nuclei; and iii) growth of nuclei with addition of monomers (See details in SI). Fitting the experimental results


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to these models provides useful insights on the nucleation kinetics and the growth-limiting mechanism of Pd NPs in the presence of different ligands. The nucleation rate is dependent on the degree of supersaturation, reaction temperature, and interfacial tension between NP and the

solvent. The growth rate can be expressed by the equation: =

/

, where D is

the diffusion coefficient of Pd monomers, Vm is the molar volume of Pd NPs, C0 is monomer solubility, S is the dimensionless parameter describing the supersaturation of Pd monomer in the solution, r is the radius of Pd NPs, γ is interfacial tension between Pd NP and the solvent, R is gas constant (8.314 J K−1 mol−1), and T is the reaction temperature.62-64 This equation is converted into dimensionless form

∗ !

=

"#/ ∗ $ ∗ %

with three dimensionless parameters: the

'(

reduced radius & ∗ = & , the reduced kinetic length + = )*

,=

'(

)*

'(

)*

, and the reduced time

)

"-. /0 $12. By adjusting the parameters, we obtained a good fit to experimental

results in both nucleation and growth regimes of reaction A with γ = 1.155 J m-2, kr/T = 4.07 × 10−1 nm s-1 K-1, and + = 1.0 × 105 (Figure 6a). The large + >> 1 indicates that 3

Tuning Precursor Reactivity toward Nanometer-Size Control in

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