Ligand-Mediated Nucleation and Growth of Palladium Metal Nanoparticles

* These authors contributed equally

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The main goal of this work is to elucidate the role of capping agents in regulating the size of palladium nanoparticles by combining in situ small angle x-ray scattering (SAXS) and ligand-based kinetic modeling.

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Mozaffari, S., Li, W., Thompson, C., Ivanov, S., Seifert, S., Lee, B., Kovarik, L., Karim, A. M. Ligand-Mediated Nucleation and Growth of Palladium Metal Nanoparticles. J. Vis. Exp. (136), e57667, doi:10.3791/57667 (2018).


The size, size distribution and stability of colloidal nanoparticles are greatly affected by the presence of capping ligands. Despite the key contribution of capping ligands during the synthesis reaction, their role in regulating the nucleation and growth rates of colloidal nanoparticles is not well understood. In this work, we demonstrate a mechanistic investigation of the role of trioctylphosphine (TOP) in Pd nanoparticles in different solvents (toluene and pyridine) using in situ SAXS and ligand-based kinetic modeling. Our results under different synthetic conditions reveal the overlap of nucleation and growth of Pd nanoparticles during the reaction, which contradicts the LaMer-type nucleation and growth model. The model accounts for the kinetics of Pd-TOP binding for both, the precursor and the particle surface, which is essential to capture the size evolution as well as the concentration of particles in situ. In addition, we illustrate the predictive power of our ligand-based model through designing the synthetic conditions to obtain nanoparticles with desired sizes. The proposed methodology can be applied to other synthesis systems and therefore serves as an effective strategy for predictive synthesis of colloidal nanoparticles.


Controlled synthesis of metallic nanoparticles is of great importance due to the large applications of nanostructured materials in catalysis, photovoltaic, photonics, sensors, and drug delivery1,2,3,4,5. To synthesize the nanoparticles with specific sizes and size distribution, it is vital to understand the underlying mechanism for the particle nucleation and growth. Nevertheless, obtaining nanoparticles with such criteria has challenged the nano-synthesis community due to the slow progress in understanding the synthesis mechanisms and the lack of robust kinetic models available in the literature. In 1950s, LaMer proposed a model for the nucleation and growth of sulfur sols, where there is a burst of nucleation followed by a diffusion-controlled growth of nuclei6,7. In this proposed model, it is postulated that the monomer concentration increases (due to the reduction or decomposition of the precursor) and once the level is above the critical supersaturation, the energy barrier for particle nucleation can be overcome, resulting in a burst nucleation (homogeneous nucleation). Owing to the proposed burst nucleation, the monomer concentration drops and when it falls below the critical supersaturation level, the nucleation stops. Next, the formed nuclei are postulated to grow via the diffusion of monomers towards the nanoparticles surface, while no additional nucleation events occur. This results in effectively separating the nucleation and growth in time and controlling the size distribution during the growth process8. This model was used to describe the formation of different nanoparticles including Ag9, Au10, CdSe11, and Fe3O412. However, several studies illustrated that the classical nucleation theory (CNT) cannot describe the formation of colloidal nanoparticles, in particular for metallic nanoparticles where the overlap of the nucleation and growth is observed1,13,14,15,16,17. In one of those studies, Watzky and Finke established a two-step mechanism for the formation of iridium nanoparticles13, in which a slow continuous nucleation overlaps with a fast nanoparticle surface growth (where growth is autocatalytic). The slow nucleation and fast autocatalytic growth were also observed for different types of metal nanoparticles, such as Pd14,15,18, Pt19,20, and Rh21,22. Despite recent advances in developing nucleation and growth models1,23,24,25, the role of the ligands is often ignored in the proposed models. Nevertheless, ligands are shown to affect the nanoparticles size14,15,26 and morphology19,27 as well as the catalytic activity and selectivity28,29. For example, Yang et al.30 controlled the Pd nanoparticle size ranging from 9.5 and 15 nm by varying the concentration of trioctylphosphine (TOP). In the synthesis of magnetic nanoparticles (Fe3O4), the size noticeably decreased from 11 to 5 nm when the ligand (octadecylamine) to metal precursor ratio increased from 1 to 60. Interestingly, the size of Pt nanoparticles was shown to be sensitive to the chain length of amine ligands (e.g., n-hexylamine and octadecylamine), where smaller nanoparticle size could be obtained using longer chain (i.e., octadecylamine)31.

The size alteration caused by different concentration and different types of the ligands is a clear evidence for the contribution of ligands in the nucleation and growth kinetics. Unfortunately, few studies accounted for the role of ligands, and in these studies, several assumptions were often made for the sake of simplicity, which in turn make these models applicable only for specific conditions32,33. More specifically, Rempel and co-workers developed a kinetic model to describe the formation of quantum dots (CdSe) in the presence of capping ligands. However, in their study, the binding of the ligand with nanoparticle surface is assumed to be at equilibrium at any given time32. This assumption might hold true when the ligands are in large excess. Our group recently developed a new ligand-based model14 which accounted for the binding of capping ligands with both the precursor (metal complex) and the surface of nanoparticle as reversible reactions14. In addition, our ligand-based model could potentially be used in other metal nanoparticle systems, where the synthesis kinetics seem to be affected by the presence of the ligands.

In the current study, we use our newly developed ligand-based model to predict the formation and growth of Pd nanoparticles in different solvents including toluene and pyridine. For our model input, in situ SAXS was utilized to obtain the concentration of nanoparticles and size distribution during the synthesis. Measuring both the size and concentration of particles, complemented by kinetic modeling, allows us to extract more precise information on the nucleation and growth rates. We further demonstrate that our ligand-based model, which explicitly accounts for the ligand-metal binding, is highly predictive and can be used to design the synthesis procedures to obtain nanoparticles with desired sizes.

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1. Pd Acetate Recrystallization

CAUTION: This protocol involves hands-on operations with high temperature glassware and solution. Use personal protective equipment including goggles and heat-resistant gloves. All the operations involving solution handling should be conducted in a fume hood and avoid other heating sources nearby due to the corrosive and flammable properties of anhydrous acetic acid.

  1. Add 40 mL of anhydrous acetic acid into a 50 mL three neck round bottom flask with 0.75 g of Pd acetate and a stir bar. Attach the condenser to the middle neck, cap the other two openings and fix the flask on the stirring hotplate.
  2. Open the condensing water valve slowly and let the water flow through the condenser. Stir the solution for 10-15 min at 300 rpm at room temperature until no more Pd acetate can dissolve.
  3. Set the hotplate temperature at 100 °C. After the temperature reaches 100 °C, wait for around 30 min until the Pd acetate completely dissolves.
  4. During this time, pre-heat two 20 mL glass vials and all the filtration parts at 90 °C in a drying oven. Also, heat some water in a 500 mL beaker until it approaches the boiling point.
  5. Quickly assemble the filtration parts and place the filter flask on a pre-heated hotplate (at 100 °C). Connect the vacuum pump to the filter flask. Quickly remove the three-neck round bottom flask from the hotplate and filter the Pd acetate solution under vacuum.
  6. After the filtration, quickly pour the liquid into two 20 mL vials. Cap the vials and immerse them into the hot water in the beaker.
  7. Put the beaker on a hotplate at 80 °C and slowly decrease the temperature to room temperature by decreasing the hotplate temperature by 20 °C every hour.
  8. Turn off the hotplate after 3 h. Leave the beaker overnight for crystallization.
  9. Pour the acetic acid out of the vials. Leave the Pd acetate trimer crystals in the vial. Wash the crystals for 3 times to remove the acetic acid residual by dispensing 2 mL of hexane evenly onto the crystals and then draining the solution.
  10. Cover the vials with aluminum foil to avoid light. Dry the crystals under N2 flow at room temperature overnight. Store the crystals in inert atmosphere.

2. Preparation for Pd Acetate – TOP Synthesis Solution14

  1. Degas each solvent (pyridine, toluene or 1-hexanol) under N2 flow at 10 mL/min for 30 min.
  2. Weigh 0.0112 g of recrystallized Pd acetate for 2.5 mL of 20 mM solution in a 7 mL vial. Cap the vial, then purge and fill it with N2 through the inlet on the septum with an inserted needle outlet.
  3. Transfer the solvents and the Pd acetate vial into an N2 glovebox. Add 2.5 mL of pyridine or toluene into the Pd acetate vial. Sonicate the vial for 40 min to dissolve all Pd acetate.
  4. For each sample, transfer 1 mL of 20 mM Pd acetate solution into a 7 mL vial with a micro stir bar in the glovebox. Add 8.9 μL of trioctylphosphine (TOP:Pd molar ratio = 2) into the solution. Shake the vial for 30 s with hands to mix the agents well. Then, add 1 mL of 1-hexanol into each sample vial (solvent:hexanol = 50:50 in volume).

3. Colloidal Pd Nanoparticle Synthesis14

  1. Pre-heat the hotplate with a heating insert at 100 °C. Purge the reaction vials with 10 mL/min of N2 flowing above the solution level to create an inert atmosphere and a constant pressure.
  2. Put the reaction vials in the pre-heated hotplate insert under 300 rpm stirring to start the reaction.
  3. To terminate the reaction, remove the vials from the insert and cool the vials down to room temperature.

4. Pd Nanoparticle Characterization- Ex situ Small-angle X-ray Scattering (SAXS)34

  1. Mean size and size distribution characterization
    1. Initialize the SAXS instrument. Click on the commander window in the measurement software and adjust the voltage and current to 50 kV and 1000 µA, respectively.
    2. Load the background solution (1:1 mixture of the solvent (pyridine or toluene) and 1-hexanol) into the capillary holder. Seal the capillary and fix it to the holder parallel to the X direction. Mount the holder inside the instrument chamber.
    3. Start the vacuum pump and wait until the vacuum level in the chamber stabilizes (lower than 0.3 mbar).
    4. Fix the X axis (along the capillary) and scan in the Y direction (across the capillary) to find the middle position as the measurement position, at which the X-ray pathway length through the liquid sample reaches the maximum (the diameter of the capillary).
    5. Setup and run the wizard to conduct steps 4.1.5 – 4.1.8. Set the capillary position and mount the glassy carbon through the X-ray pathway so that the X-ray will go through the glassy carbon first and then the capillary. Take a measurement of 10 s and save the 2D scattering graph.
    6. Move the glassy carbon out of the pathway. Take a measurement of 1800 s on the background solution and save the background scattering graph.
    7. Move the capillary out of the pathway, mount the glassy carbon only and take a 10 s measurement.
    8. Move the glassy carbon out of the pathway. Take a 10 s measurement of the black current (vacuum chamber only).
    9. To measure the nanoparticle solution, load the sample into the capillary and follow the same procedures from 4.1.2 – 4.1.6.
    10. For data analysis, open SAXS analysis software via File | Import from file | Import the background and the sample files.
    11. Choose the 2D pattern of the background. Click Indirect transmission calculation in tool. Input the background with glassy carbon, glassy carbon and blank frame files and click on OK. Do the same operations on the sample pattern. The transmissions will be automatically calculated.
    12. Drag the circle ring cursor from the edge to the center of the 2D scattering pattern to integrate the background and sample 2D graph to 1D scattering curve.
    13. Choose the background curve in the list. Check it as background measurement in SAXS information.
    14. Choose the background and the sample curves together. Right click and choose Background correction to subtract the background from the sample.
    15. Right click on the curve after background correction. Choose SAXS modeling | Directly modeling | Sphere | Schultz | No interaction.
    16. Set the Q range between 0.02 to 0.3. Click on Initial guess to give an estimation on the fitting results. Then click on Fit to fit the 1D SAXS curve with Schultz polydisperse sphere model to obtain the mean diameter Equation 01 and standard deviation Equation 02 (corresponding to the size distribution of the nanoparticles).
  2. Concentration of particles (Equation 03) extraction
    1. Use the absolute intensity (Equation 04), which can be correlated to both the size and concentration of nanoparticles in the solution as follows14,35:
      Equation 05
      where Equation 06 is the scattering vector, Np is the concentration of nanoparticles, Equation 07 is the nanoparticle volume, and Equation 08 is the single-particle form factor. Calculate the Schultz distribution factor36 Equation 09 in the case of polydisperse spherical shape nanoparticles using the following expression:
      Equation 10
      HereEquation 11.
    2. Consider Equation 06 → 0, which is the extrapolation of the SAXS curve to the intercept to Y axis:
      Equation 12
      Equation 13 is the scattering length density difference between metal and solvent and Equation 14 is the average square of the particle volume.
    3. Calculate Equation 14 using equation:
      Equation 15
    4. To obtain Equation 16, use water (as a standard) to calibrate the scattering intensity to absolute scale due to its well-known absolute differential scattering cross-section of 1.632×10-2 cm-1 at room temperature34. Measure the empty capillary and water and subtract the empty capillary as a background for water following the procedures from 4.1.2 to 4.1.14.
    5. The 1D scattering curve for water is a straight line parallel to X-axis. Extrapolate the line to get the intercept intensity Equation 17 (cm-1) on Y-axis. Calculate the calibration factor (CF) as
      Equation 18.
    6. Find the extrapolation intensity Equation 19 for the nanoparticle curves. Calibrate Equation 19 to obtain Equation 16 at absolute scale using the CF:
      Equation 20
    7. Extract the concentration of the particles from the following equation derived from (3):
      Equation 21
  3. Extraction of concentration of atoms in nanoparticles (Equation 22) from in situ and ex situ SAXS
    1. Use both the concentration of nanoparticles (Equation 59) and average value of number of atoms per nanoparticle (Nave) to calculate the total concentration of atoms as discussed below.
    2. Calculate Nave based on the following equation37:
      Equation 24
      where r is the nanoparticle radius, Equation 25 is the Avogadro’s number, ρ is the metal density, and Equation 26 is the metal molecular weight. For palladium, ρ = 12023 kg/m3 and Equation 26 = 0.1064 kg/mol.
    3. To account for the size distribution in estimating the total concentration of atoms in nanoparticles, calculate the Equation 27 using equation (7) along with the Schultz distribution factor:
      Equation 28
    4. Estimate the concentration of atoms (Equation 29) through multiplying Equation 27 by the concentration of nanoparticles (Equation 59) at any given time as follows:
      Equation 30

5. Obtaining Kinetic Data from in situ SAXS on Colloidal Pd Nanoparticle Synthesis at Synchrotron

  1. Before starting the reaction, take SAXS measurements on the empty capillary, capillary filled with water, and capillary filled with solvent:hexanol at 50:50.
  2. Consider that the agent preparation procedures for in situ SAXS are the same with steps 1 and 2, except that the total reaction solution volume is 6 mL (10 mM Pd(OAc)2 in 3 mL of pyridine or toluene mixed with 3 mL of 1-hexanol, with TOP:Pd molar ratio = 2).
  3. In the glovebox, transfer the reaction solution into a 25 mL round bottom flask with a stir bar inside. Purge the space above the solution with N2 (10 mL/min).
  4. Set the stirring rate at 300 rpm. Put the flask in the pre-heated hotplate insert to trigger the reaction.
  5. Take 300 μL of reaction solution into the capillary mounted through the X-ray beam path every 8 s using a programmed syringe pump. Collect the scattering data by the detector.
    Note: The transmission of the sample is directly measured by an ionized chamber (without glassy carbon). After each measurement, the solution is pumped back to the bulk reactor.
  6. Consider that the data can be automatically converted to 1D curve with the beamline program. The mean diameter and standard deviation are obtained by fitting the data with Schultz polydisperse sphere model. The extraction of concentration of particles follows the same procedures in step 4.2 using the synchrotron X-rays.

6. Modeling Approach and Simulation Procedures for Nucleation and Growth of Palladium (Pd) Metal Nanoparticles

  1. Consider the reduction and nucleation as one first-order pseudo-elementary reactions (equation (10)).
    Note: A pseudo-elementary reaction is defined as the sum of one (or more) slow elementary reactions followed by fast elementary reactions (non-rate determining reactions). Herein, the pseudo-elementary reaction represents the kinetics of the slow reaction(s), but have reaction orders equal to the stoichiometry of the sum reaction (hence, the term pseudo-elementary)38. For example, the corresponding reactions for Pd(OAc)2 reduction and nucleation (TOP:Pd molar ratio=1) in the excess of 1-hexanol are presented below15:
    (i) Pd(TOP)(OAc)2(Solv) + R'CH2OH→Pd0 + TOP + R'CHO + 2AcOH + Solv (overall ligand dissociation and reduction), which can be split into steps (ii) and (iii):
    (ii) Pd(TOP)(OAc)2(Solv) + Solv → Pd(OAc)2(Solv)2 + TOP (Ligand dissociation)
    (iii) Pd(OAc)2(Solv)2 + R'CH2OH→Pd0 + R'CHO + 2AcOH + (Solv)2 (reduction)
    (iv) n Pd0 →Pd0n (nucleation)
    The reduction (iii) and nucleation (iv) reactions are combined and shown as one pseudo-elementary reduction-nucleation step (A→B). Note that A represents the kinetically active precursor, and while it is written as Pd(OAc)2(Solv)2 in reaction (iii), other Pd complexes could be present.
  2. Consider the surface growth of nanoparticles to be autocatalytic. Autocatalytic growth is one mode of growth which occurs through the reduction of precursor on the nanoparticle surface (equation (11))37.
  3. Account for the binding of capping ligands (TOP) with the precursor (which alter the precursor reactivity) as well as the surface of the particle.
    Note: The dissociation of the ligands (reverse reaction 12) was shown to be important for the nucleation of Ir nanoparticles39. Additionally, other studies have shown that the ligands affect the precursor reactivity (reaction 12) as well as the growth rate of colloidal nanoparticles14,15,16. Include these reactions in the model (equations (12) and (13)) as two reversible reactions (neither is assumed to be equilibrated during the reaction)14. Note that our expansion of the FW mechanism13 (reactions 10 and 11) accounted for the first time for the reversible binding of the ligands with both the precursor (reaction 12) and the surface of the nanoparticles (reaction 13).14
  4. Assume the following reactions are pseudo-elementary.
    Equation 31
    Equation 32
    Equation 34
    Equation 35
    Here, Equation 36 is the reduction/nucleation rate constant, Equation 37 the surface growth rate constant, Equation 38 the forward reaction rate constant for reaction (12), Equation 39 the equilibrium constant for ligand-metal precursor binding (i.e. reaction 12), Equation 40 the forward reaction rate constant for reaction (13), and Equation 41 the equilibrium constant for the binding of ligand with the nanoparticle surface (i.e. reaction 13).
    Note: In addition, A is representative of the kinetically active precursor, L the capping ligand (here TOP), AL the ligand–metal complex (here Pd(II)–TOP) which can be coordinated with different ligands (such as acetate, 1-hexanol or pyridine), B the uncapped Pd surface atom, and BL the Pd atom bound with ligand, Pd0 –TOP. In addition, see the complete list for model description and assumptions in previous publication14.
  5. Calculate the concentration of Pd atoms (Equation 29) from the kinetic model based on the following equation.
    Equation 42
  6. Calculate the concentration of nanoparticles (Equation 59) from the model (if no evidence of agglomeration exists) as follows:
    Equation 43
    Here, Equation 44 is reaction time, Equation 45 the active precursor concentration, Equation 46 Avogadro’s number (6.022 x 1023) and Equation 48 the nucleus size (atoms/nucleus). Equation 48 is selected to be “4” based on the smallest size detected during the reaction.
  7. Use the following differential equations and initial conditions (in MATLAB) to obtain the concentration profile of different species.
    Differential Equations:
    Equation 49
    Equation 50
    Equation 51
    Equation 52
    Equation 53
    In addition, for the metal precursor and ligand concentrations (equations 21 and 22) at any given time “t”, the following relationships can be written as follows:
    Equation 54
    Equation 55
    Equation 56
    Note: Reaction Equation 57 is considered to be at equilibrium at time=0. After the reaction proceeds, the reaction is no longer constrained to be at equilibrium.
    Equation 58
  8. Minimize the SR (i.e., sum of normalized squared errors) between the experiments and model for Equation 59 and Equation 62 using the MATLAB function fminsearch to extract the fitting parameters (rate constants shown in equations 10-13).
    Equation 60
    Here Equation 61 is number of experimental data points.
  9. Select similar distribution of the number of data points along the reaction time and Y-axis (Equation 59 or Equation 62) to make sure the minimization function is not weighted toward data points at early or later reaction times.

7. Obtaining Nucleation and Growth Rates from Both the Experimental Data and Model

  1. Calculate the nucleation and growth rates from the model using the followings equations.
    Equation 63
    Equation 64
    Here, [Equation 65] represents the concentration of atoms that contributed only to the particle growth.
    Note: To make the unit of nucleation and growth rates the same (i.e., mol.L-1.s-1), it is required to multiply equation (26) by [Equation 66]. This allows us to make a comparison between the rates.
  2. Estimate the nucleation rate from the experimentally measured number of particles using short time intervals.
    Equation 67
  3. Estimate the growth rate by subtracting the contribution of nucleation from the total concentration of atoms (Equation 68) or metal precursor consumption. “Equation 68” quantifies both the formation of particles (nucleus) and particle growth.
    Equation 69

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Representative Results

To systematically examine whether the capping ligands alter the kinetics of nucleation and growth, we took the two following approaches: (i) the binding of the ligand with the metal was not considered in the kinetic model similar to previous studies (i.e., the nucleation and autocatalytic growth) (ii) the reversible binding of capping ligand with the precursor and surface of the nanoparticle was taken into account in the model (i.e., ligand-based model described in Protocol). Regarding the Pd synthesis in toluene, as shown in Figure 1, without accounting for the ligand-metal binding, the model failed to capture the time evolution of the nanoparticles concentration (Equation 72) and concentration of Pd atoms (Equation 73). As an alternative, we implemented our newly developed kinetic model (Figure 2) and as depicted in Figure 3, the model accurately predicts our in situ data (both Equation 72 and Equation 73 during reaction).This further indicates that the capping ligands indeed affect the nucleation and growth kinetics of Pd nanoparticles.

Estimating the rate constants (Table 1) from the model further enables us to obtain useful information on the kinetics of the nanoparticle formation. In this regard, Figure 4A shows the comparison between the nucleation and growth rates (as estimated from the model) and the results clearly reveal that nucleation is slow while the growth is fast, which agrees well with previous studies1,14. Both modeling and experimental results demonstrate that the metal precursor/monomer does not undergo burst nucleation. This is illustrated by the in situ SAXS and modeling results where the nucleation continues till the end of synthesis (Figure 3B and Figure 4A). The continuous formation of nuclei, therefore, contradicts the LaMer burst nucleation and growth model but supports the continuous nucleation reaction in the Finke-Watzky two step mechanism. In addition, the nucleation can be fitted by pseudo-first order; however, we cannot exclude the possibility that the nucleation could be higher in order. Herein, as shown in Figure 4B, the ligand plays a central role in the continuity of nucleation by further binding to the nanoparticle surface and reducing the concentration of active sites (i.e., [B]). This drastically decreases the particle growth rate and expands the time window for the nucleation throughout the synthesis. In addition, our current results presented in this work in combination with our previous study14 (where the synthesis was conducted under different experimental conditions) indicate that the ligand and precursor concentrations do not have a significant effect on the rate and equilibrium constants, which shows the chemical fidelity between the model and the real system.

Next, we probed the applicability of our ligand-based model to a different solvent system, where pyridine was used as a solvent instead of toluene. We can see that despite the significant difference observed for the nucleation and growth kinetics in pyridine compared to toluene (Figure 5 and Table 1), the model accurately captures the in situ data, Equation 72 and Equation 73, and allows for more accurate estimation of rate constants (Table 1). One of the important features that makes a kinetic model robust is that it should be able to predict synthetic conditions for achieving nanoparticles with desired sizes. Therefore, we implemented our ligand-based model (using the same rate constants reported in Table 1) to predict the size under different concentrations of metal precursor, Pd(OAc)2, in pyridine. Figure 6 shows that the model can provide a very accurate estimation of the nanoparticle size under different concentrations of the metal precursor. The modeling as well as the experimental results demonstrate that the nanoparticles become larger in size at higher precursor concentration. This is because the growth is second order kinetics while the nucleation is first order which makes the growth faster at higher precursor concentration14.

Figure 1
Figure 1. Experimental and two-step modeling results for the synthesis of Pd nanoparticles in toluene: (A) concentration of Pd atoms and (B) concentration of nanoparticles. The rate constants are Equation 36= Equation 74s-1 and Equation 75= Equation 76 L.mol-1.s-1. Experimental condition: [Pd(OAc)2]=25 mM , TOP:Pd molar ratio= 2, and T (°C) = 100. Please click here to view a larger version of this figure.

Figure 2
Figure 2. The schematic of ligand-mediated nucleation and growth model. In this proposed model, the capping ligands can associate and dissociate from both the metal precursor and nanoparticle surface, thereby, affecting the nucleation and growth kinetics (through altering the concentration of kinetically active precursor and the number of free surface sites, respectively). Please click here to view a larger version of this figure.

Figure 3
Figure 3. Experimental and ligand-based modeling results for the synthesis of Pd nanoparticles in toluene: (A) concentration of Pd atoms and (B) concentration of nanoparticles. The rate constants are summarized in Table 1. Experimental condition: [Pd(OAc)2]=25 mM , TOP:Pd molar ratio= 2, and T (°C) = 100. Please click here to view a larger version of this figure.

Figure 4
Figure 4. (A) The rates of the nucleation and growth extracted from the ligand-based model for the synthesis of Pd nanoparticles in toluene and (B) Equation 77 ratio. Experimental condition: [Pd(OAc)2]=25 mM , TOP:Pd molar ratio= 2, and T (°C) = 100. Please click here to view a larger version of this figure.

Figure 5
Figure 5. Experimental and ligand-based modeling results for the synthesis of Pd nanoparticles in pyridine: (A) concentration of Pd atoms and (B) concentration of nanoparticles. The rate constants are summarized in Table 1. Experimental condition: [Pd(OAc)2]=2.5 mM , TOP:Pd molar ratio= 2, and T (°C) = 100. Please click here to view a larger version of this figure.

Figure 6
Figure 6. Model prediction of final nanoparticle size as a function of precursor concentration in pyridine solution (experimental data from Mozaffari et al.14). The error bars represent the standard deviation of the particle size distribution. Experimental condition: TOP:Pd molar ratio= 2, and T (°C) = 100. Please click here to view a larger version of this figure.

k1-nuc k2-growth k3-f  (A+L) k4-f  (B+L) K5-eq  (A+L) K6-eq  (B+L)
Units s-1   L.mol-1.s-1 L.mol-1.s-1 L.mol-1.s-1 L.mol-1 L.mol-1
25 mM Pd in Toluene 1.8×10-5 10×10-1 4.7×10-3 3×10-1 1.5×101 1×103
2.5 mM Pd in Pyridine 1.74×10-5 2.34×101 1.7×10-1 2.13×10-2 3.54×102 1.44×102

Table 1. The extracted rate constants for Pd nanoparticle synthesis in different solvents (toluene and pyridine). Experimental condition: TOP:Pd molar ratio= 2, and T (°C) = 100.

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In this study, we presented a powerful methodology to examine the effect of capping ligands on the nucleation and growth of metal nanoparticles. We synthesized Pd nanoparticles in different solvents (toluene and pyridine) using Pd acetate as the metal precursor and TOP as the ligand.We used in situ SAXS to extract the concentration of reduced atoms (nucleation and growth events) as well as the concentration of nanoparticles (nucleation event), where both experimental observables were used as the model inputs. In addition, by considering the slope of the concentration of the nanoparticles and concentration of the atoms at the early reaction time, our methodology (the use of in situ SAXS and kinetic modeling), allowed us to estimate the upper and lower bonds for the nucleation and growth rate constants (more details can be found in ref. 14, which was the first study to decouple the contributions of nucleation and growth to the total metal reduction).

There are three critical steps in systematically examining the effects of ligand-metal binding on the nucleation and growth of colloidal nanoparticles: (i) measuring the evolution of size as well as the concentration of nanoparticles (steps 4.1-4.3). This is an important step as it can provide more detailed information on both the nucleation and growth events, (ii) developing a robust kinetic model, which explicitly accounts for the reactions of capping ligands with the metal and also includes the most relevant reactions during the formation and growth of nanoparticles (step 6.4), and (iii) constructing an appropriate link between the experimental observables and those extracted from the model (e.g., size measured experimentally versus size extracted from the model).

It is important to note that due to the small size of the particles (< 10 nm in diameter), and the fast nucleation and growth rates in the beginning of the reaction, a high energy and high flux X-ray beam is needed for obtaining in situ data, which can be only realized at the synchrotron. Even with synchrotron beams, it is difficult to capture any size below 0.5 nm unless the concentration of the particle is high enough. A rule of thumb principle is that SAXS intensity reduces with 6th power of the particle size but it is only linearly proportional to the concentration of the nanoparticles. In addition, for smaller nanoparticles, data acquisition up to much higher wave vector q (wider angle) is required, where the background scattering from solvents become more significantly detrimental to signal to noise ratio. This limits the size and concentration of small nanoparticles that can be detected in the early stages of the reaction, especially when the nucleation is slow and continuous as shown in this work. However, while the high energy/flux allows the acquisition of in situ data, the beam can also cause damage to the sample (agglomeration of nanoparticles and/or deposition on the cell walls). Therefore, in step 5.1, the beam energy and X-ray exposure time need to be tested and adjusted to the level that provides the best data quality (signal to noise ratio) for the detection of small nanoparticles in the early stages of the reaction without causing damage to the sample. The troubleshooting has to be done at the synchrotron during the in situ SAXS measurement, i.e., to monitor the SAXS spectra and ensure that no agglomeration/precipitation occurs during the synthesis. Through a few tests, the beam energy was finally set at 18 keV with an appropriate exposure time (0.1 s) to capture enough signal, and hence, the small Pd nanoparticle size in the early stage of reaction. We also note that while the current kinetic model does not account for agglomeration, if such growth mechanism is dominant, the model can be modified to include agglomeration steps (for example, B + B → C and B + C → 1.5C, where B and C represent the small and larger nanoparticles, respectively)1. However, agglomeration as well as other modes of growth (i.e., Ostwald and digestive ripening)40 would be best described by population based models24,25,32,33.

As already discussed in the manuscript, the underlying mechanism governing the nanoparticle nucleation and growth is poorly understood, particularly in the presence of coordinating ligands. For example, recent studies showed that TOP-Pd binding lowers the nucleation and growth rate of Pd nanoparticles14,15,16,30. Therefore, we accounted explicitly for the ligand-metal binding in our kinetic model. What distinguishes our method from other relevant studies is that our ligand-based model considers the ligand binding with both the precursor and surface of metal nanoparticle as reversible reactions and no priori assumptions are made on whether the ligands are in equilibrium with either of them. In addition, unlike previous studies where only one experimental observable (either size33 or concentration of atoms23, etc.) was used for model verification, our ligand-based model uses both the particle size and concentration of nanoparticles as model inputs. Therefore, it allows us to obtain more accurate estimates for the reaction rate and equilibrium constants.

Using our proposed methodology, we demonstrated the predictive power of our ligand-based model. In this regard, we showed that the model can predict the synthesis conditions to obtain nanoparticles with various sizes, which as a result minimizes the need for trial and error. Furthermore, with this simple "heat-up" synthesis method, the nanoparticle size can be tuned by changing the type of solvent or the metal concentration. These different sized Pd nanoparticles can have potential applications in catalysis, drug delivery, and sensors15,41. The presented synthesis strategy along with the kinetic modeling can be potentially used to provide insights on the role of capping ligands in the nucleation and growth of different types of nanoparticles to guide their controlled synthesis.

For future work, we direct our research toward developing kinetic models with the ability of predicting the size distribution during the synthesis. In addition, we will further investigate the validity of our ligand-based model under different experimental conditions, including different temperature ranges and different types of ligands and metals.

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There is no conflict of interest to report.


The work was primarily funded by the National Science Foundation (NSF), Chemistry Division (award number CHE-1507370) is acknowledged. Ayman M. Karim and Wenhui Li acknowledge partial financial support by 3M Non-Tenured Faculty Award. This research used resources of the Advanced Photon Source (beamline 12-ID-C, user proposal GUP-45774), a U.S. Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under Contract No. DE-AC02-06CH11357. The authors would like to thank Yubing Lu, a Ph.D. candidate in the Chemical Engineering Department at Virginia Tech for his kind help with the SAXS measurements. The presented work was partly executed at the Center for Integrated Nanotechnologies, an Office of Science User Facility operated for the U.S. Department of Energy (DOE) Office of Science. Los Alamos National Laboratory, an affirmative action equal opportunity employer, is operated by Los Alamos National Security, LLC, for the National Nuclear Security Administration of the U.S. Department of Energy under contract DE-AC52-06NA25396.


Name Company Catalog Number Comments
palladium acetate (Pd(OAc)2) ALDRICH 520764
anhydrous acetic acid SIAL 338826
trioctylphosphine ALDRICH 718165
pyridine MilliporeSigma PX2012-7
toluene SIAL 244511
1-hexanol SIAL 471402
N8 Horizon SAXS Bruker A32-X1
glovebox Vaccum Atmospheres Co. 109035
MR HEI-TEC 115V Hotplate Heidolph 5053000000
hotplate Monoblock insert Heidolph 5058000800
heat-On 25-ml insert Heidolph 5058006200
7 mL vials SUPELCO 27518
micro stir bar PTFE  VWR 58948-353
egg-Shaped Bars  Fisherbrand™  14-512-121
25 mL round bottom flasks ALDRICH Z167495
quartz capillary Hampton Research HR6-148
MATLAB R2016b MathWorks
Bruker SAXS 1.0v Bruker
Diffrac Measurement Center 4.0v Bruker



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