Influence of Reduction Kinetics on the Preparation of Well-Defined

Jun 22, 2018 - Jianzhou Wu , Hehe Qian , Linfang Lu , Jie Fan , Yongsheng Guo* , and Wenjun Fang*. Department of Chemistry, Zhejiang University ...
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Cite This: Inorg. Chem. XXXX, XXX, XXX−XXX

Influence of Reduction Kinetics on the Preparation of Well-Defined Cubic Palladium Nanocrystals Jianzhou Wu, Hehe Qian, Linfang Lu, Jie Fan, Yongsheng Guo,* and Wenjun Fang* Department of Chemistry, Zhejiang University, Hangzhou 310058, China

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S Supporting Information *

ABSTRACT: A facile synthesis strategy has been developed to synthesize palladium nanocubes with tunable size and wellcontrolled morphology. Through adjusting the dosages of acetate species (KOAc, NH4OAc, and HOAc), the sizes of well-defined Pd nanocubes are tuned. The reduction of Pd precursors, a first-order reaction, is influenceable by acetate species, and a quantitative relationship between cubic width and apparent reduction rate constant, which has been found to be an effective parameter to describe the growth process of Pd nanocubes, has been uncovered. The effect of apparent reduction rate constant on the growth of Pd nanocubes has been discussed, and the growth kinetics of Pd nanocubes is quantitatively depicted.

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INTRODUCTION Owing to the special electronic density of states at the Fermi level, palladium nanoparticle is an exceptional electrode material for fuel cell and an outstanding candidate catalyst for hydrogenation.1−8 Nanoscale Pd can appear with different shapes, including cubes, octahedra, and rhombic dodecahedra.9−12 The shape and size of Pd nanoparticles are mainly controlled by the growth kinetics,13−15 which is usually affected by certain factors, such as species of precursor, concentration ratio between precursor and reductant, reaction temperature, and reaction time.9,10,16,17 Great progress has been achieved in manipulating the size, morphology, and structure of metallic nanomaterials, and in situ observation technology with liquid cell TEM18−22 has become a feasible approach to monitor the continuous movements of atoms and changes of nanoparticles meticulously. Some decades ago, the generation process of crystalline materials has been studied and many relevant theories have been achieved.23−28 On the basis of the classical nucleation theory (CNT), the generation process of metallic nanocrystals can be divided into three stages, namely, prenucleation, nucleation, and growth, where detailed discussion of different theories has been taking place in fields of chemistry, physics and mathematics.29−38 To handle modern metallic nanoparticle formation phenomena, the Finke and Watzky (FW) 2step nucleation mechanism, which has successfully dealt with many situations of metallic nanoparticle growth, is discovered.39−46 In the FW theory, metallic nanoparticles mainly go through slow, continuous nucleation and autocatalytic surface growth, and the reaction kinetics of nucleation and growth can be facilely separated. As for researchers of chemistry, some physicochemical parameters are options to describe the kinetic phenomena in © XXXX American Chemical Society

nanoscale, and conversely these parameters can be utilized to control the dimension, composition, shape, and architecture of nanoparticles. Practically, the reduction rate of Pd precursors can be used as a knob for selective preparation of Pd nanoparticles with various shapes, via altering the species of Pd precursor47 or reductant.48 By tuning the growth kinetics, concave Pd nanoparticles with high surface energy can be produced.49,50 However, to our knowledge, similar description for size tunable nanostructures is still not well-elucidated. Some typical researches on the formation kinetics of Pd nanoparticles are summarized in Table S1. Theoretical discussion in this area has always been demanded. Up to date, the preparation of Pd nanocubes has been widely investigated, whether with method of seed-mediated growth51,52 or one-pot synthesis,53,54 or with the addition of CTAB55,56 or KBr.57−59 However, the preparation of welldefined Pd nanocubes with small sizes is somehow challengeable, and the relationship between cubic sizes and growth kinetics is still not very clear. In this work, size tunable Pd nanocubes are synthesized by adding acetate species (KOAc, NH4OAc, and HOAc) to maneuver the generation behavior. The apparent reaction rate constant of the reduction of Pd precursors (taking “apparent reduction rate constant” for short) is applied as an indicator to reveal the growth results. Specifically, in a closed reaction system, Pd nanocubes prepared with larger values of reduction rate constant possess smaller mean cubic widths. By varying the concentration of the acetate reagent, kinetic studies were performed to understand how each selected acetate compound affects the reduction of the palladium metal precursor producing possible different size Received: February 8, 2018

A

DOI: 10.1021/acs.inorgchem.8b00368 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry nanocubes. Although palladium nanocubes have been extensively studied, pairing synthetic methods with kinetic concepts is important in understanding the underlying chemistry.

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EXPERIMENTAL SECTION

Materials. Potassium tetrachloropalladate (K2PdCl4, 99.95% metals basis), ascorbic acid (AA, 99.99% metals basis), potassium bromide (KBr, 99.95% metals basis), polyvinylpyrrolidone (PVP, MW = 58 000), and potassium acetate (CH3COOK, AR, 99.0%) were purchased from Aladdin Industrial Co., Shanghai, China. Acetone, ammonium acetate (NH4OAc, AR), acetic acid (HOAc, AR), potassium chloride (KCl, AR), potassium nitrate (KNO3, AR), and potassium sulfate (K2SO4, AR) were acquired from Sinopharm Chemical Reagent Co., Ltd., China. These reagents were adopted without further purification. A water purification system (Direct-Q 3, Millipore, Merck, China) was applied to produce ultrapure water with resistivity above 1.82 × 105 Ω·m at 25 °C. Preparation and Characterization of Pd Nanocubes. The synthetic procedure for Pd nanocubes is improved from the previous work.60 As a typical example, 67 mg of PVP, 36 mg of AA, 360 mg of KBr with a certain volume of 50 mM KOAc (CH3COOK) aqueous solution were dissolved in water to form a 5 mL solution, and preheated at 85 °C for 5 min. Afterward, 1 mL of 120 mM K2PdCl4 aqueous solution was added into the reaction solution. The moles for all of the ingredients are 6.0 × 10−4, 2.0 × 10−4, 3.0 × 10−3, and 1.2 × 10−4 mol for PVP (calculated in monomer), AA, KBr, and K2PdCl4, respectively. The reaction was continued for 3 h before cooled down to room temperature. Products were collected by diluting the resultant solution with acetone and centrifuging at 5000 rpm for 10 min. Then, the black precipitation was washed 5 times with water and acetone to remove excess PVP. The final products were redispersed in water. The sizes and morphologies of all nanoparticles were observed through TEM (transmission electron microscope, HT7700, Hitachi, Japan) with an acceleration voltage of 100 kV and high-resolution TEM (HRTEM, Tecnai G2 F20 S-TWIN, FEI, USA) at 200 kV.

Figure 1. TEM images and corresponding HRTEM images of different Pd nanocubes obtained with (A) 4.17, (B) 8.33, (C) 12.5, and (D) 16.7 mM KOAc, respectively. Numbers in each panel represent the average cubic width. Scale bar: 50 nm (TEM) and 10 nm (HRTEM). [PdCl4]2 − + lOAc− + mBr − + nH 2O F [PdCl4 − l − m − n(OAc)l Brm(H 2O)n ]n − 2 + (m + n + l)Cl− (1)

To obtain deep insight into the effect of KOAc, the reduction kinetics of Pd precursors is studied. A timer was started the moment K2PdCl4 aqueous solution was added into the reaction system. A portion of 200 μL of the reaction liquid was pipetted out and added into a centrifugation tube containing 7.8 mL of acetone at each of 0, 1, 2, 5, 10, 15, 20, 30, 45, 60, and 90 min. Then, the sample was centrifuged at 8000 rpm for 3 min, and UV−vis spectra of the supernatants were recorded from 600 to 375 nm (Figure 2A−D). It has been confirmed that the absorbance peak at around 424 nm caused by the solvent effect of acetone belongs to Pd complex (Figure S5). Consequently, the reduction process of Pd precursors is studied via monitoring the change of absorbance at 424 nm against reaction time, with results presented in Figure 2E−F. Although there are many reagents involved in the generation of Pd atoms, the reduction of Pd precursors is found to be a first-order reaction, whose rate is mainly influenced by the concentration of Pd precursors (detailed description in the Supporting Information). Thus, the kinetic equation under the condition of this work can be derived as follows:

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RESULTS AND DISCUSSION Influence of Acetate Species as Additives toward Pd Nanocubes. Acetate ion, a good organometallic ligand,61,62 was adopted to control the reduction rate of Pd precursor. As shown in Figure 1, when 0.5, 1.0, 1.5, and 2.0 mL of 50 mM KOAc solutions were added into the typical reaction system, namely, concentrations of KOAc was 4.17, 8.33, 12.5, and 16.7 mM, Pd nanocubes were obtained with average widths of 10.5, 8.5, 7.6, and 6.2 nm, respectively. Detailed size distribution diagrams are shown in Figure S3. Subsequently, the influence of acetate species on generation process of Pd nanocubes is investigated and discussed. To begin with, the interaction between KOAc and halogenic palladate complex was studied by monitoring the change of UV−vis spectra. Typically, 0.15 mL of 10 mM K2PdCl4 solution (containing 4.5 mg KBr), x mL of 1.25 mM KOAc solution, and (15 − x) mL of H2O were mixed, and the absorbance curves of the mixtures from 500 to 200 nm were recorded (Figure S4). The volumes of KOAc solutions involved were 0, 0.25, 0.50, 0.75, and 1.00 mL, respectively, and the concentration ratios of all substrates were kept the same as those in preparation procedure. Conspicuously, as the content of acetate ions is increased, the characteristic absorbance peak at 268 nm of halogenic palladate complex60 shrinks, indicating the obvious interaction between acetate ions and halogenic palladate complexes. It can be assumed that acetate ions in reaction system partially coordinate with Pd(II) ions to form the acetate palladate complex:

ln[Pd]t = ln[Pd]0 − kap × t

(2)

where [Pd]t represents the concentration of Pd precursors at a specific time point, [Pd]0 is the initial concentration of Pd precursors, and kap is the apparent reduction rate constant. Herein, [Pd]t was determined based on Figure S6. Accordingly, corresponding values of kap for each reaction are achieved and listed in Table 1. It is apparent that a higher concentration of KOAc in reaction system can lead to a faster B

DOI: 10.1021/acs.inorgchem.8b00368 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

Figure 2. UV−vis spectra for the supernatants of reaction systems at different reaction time in the presence of (A) 4.17, (B) 8.33, (C) 12.5, and (D) 16.7 mM KOAc, respectively. The curves in (E) are specific absorbance at 424 nm of Pd precursors changing against reaction time, with the participant of 4.17, 8.33, 12.5, or 16.7 mM KOAc solution, and panel (F) presents the corresponding relationship between the value of ln[Pd]t and reaction time, t.

additive),60 HOAc scarcely influences the reduction rate of Pd precursors, while NH4OAc greatly increases the rate but is slightly less effective than KOAc. Obviously, these phenomena are related with the interaction of acetate ions with Pd precursors and AA. As previously described, acetate palladate complex (eq 1) would present different reaction kinetics when reduced by reductant compared to halogenic palladate complexes. During the reduction of Pd precursors, large quantities of protons are produced as AA is oxidized and the reaction solution always keeps acidic.60,63 The addition of acetate species into the reaction system is to absorb the produced protons into acetic acid, one kind of weak electrolyte. KOAc, NH4OAc, and HOAc have been chosen because of the basicity, neutrality, and acidity of corresponding aqueous solutions. When the dosages of KOAc and NH4OAc are enhanced, the concentration of acetate ions is increased, leading to the enhancement of consumption rate of proton, thus causing higher consumption rate of AA. Consequently, the reduction rate of Pd precursors is promoted. However, the addition of HOAc can slow down the consumption process of

reaction rate and result in nanocubes with smaller average width, d. The final number of Pd nanocubes produced (Nf) can be calculated from d: Nf =

NPd [Pd]0 VNAa03 = NPd 0 4d3

(3)

where NPd is the total number of moles for Pd, NPd0 is the number of moles for an individual Pd nanocube, V is the volume of the reaction system, NA is the Avogadro constant, and a0 is the unit cell parameter of Pd bulk. As the same procedure, HOAc and NH4OAc were further applied to study the influence of acetate cation species toward the reduction kinetics. The values of kap for each reaction are calculated as shown in Figure 3, and the data are summarized in Table 1. Figure 4 indicates that the sizes of as-synthesized cubes are different from those prepared with KOAc. From the results in Table 1, it can be concluded that higher precursor reduction rate can lead to smaller cubic sizes. Compared with cubes prepared without extra additives (no C

DOI: 10.1021/acs.inorgchem.8b00368 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry Table 1. Apparent Reduction Rate Constants kap, Cubic Widths d, and Number of Pd Nanocubes Nf for Pd Nanocubes with Different Additivesa additive species

KOAc

NH4OAc

HOAc

additive concentration (mM) 4.17 8.33 12.5 16.7 4.17 8.33 12.5 16.7 4.17 8.33 12.5 16.7

no additive

kap (× 103 s−1) 1.93 3.54 6.28 8.50 1.62 3.55 5.76 8.54 0.95 0.86 0.95 0.89 0.94

± ± ± ± ± ± ± ± ± ± ± ± ±

0.02 0.04 0.14 0.50 0.05 0.08 0.20 0.88 0.03 0.02 0.02 0.02 0.02

Nf =

d (nm)

Nf (× 10−14)

± ± ± ± ± ± ± ± ± ± ± ± ±

9.2 17.3 24.2 44.6 5.4 14.6 22.4 38.7 1.5 1.4 1.1 1.1 1.8

10.5 8.5 7.6 6.2 12.5 9.0 7.8 6.5 19.2 19.6 21.0 21.5 18.0

1.8 1.5 1.3 1.6 1.7 1.8 1.8 1.3 1.8 1.8 1.8 1.4 1.2

4d3

=

[Pd]0 VNAa03 4b3

(ln kap − a)3

(5)

Consequently, in current synthetic system, the average cubic width can be quantitatively determined with apparent reduction rate constant of Pd precursors, namely, that the reduction rate constant of Pd precursors can be approximately deduced from cubic width. This empirical expression provides an approach to link the nanoparticle thermodynamic properties (equilibrium cubic width) and kinetic properties of physicochemical reactions (apparent reduction rate constant). Reaction temperature is another key factor that influences the reduction kinetics. Similarly, Pd nanocubes have been prepared at 55, 65, and 75 °C in the presence of 16.7 mM KOAc with measured reduction kinetics (TEM images in Figure S7 and statistical data in Table S3 and Figure 6). The reduction of Pd precursors at different reaction temperatures is still a first-order reaction, and a similar linear relationship between ln kap and 1/d has been found as that in Figure 5B. Thus, based on the Arrhenius equation, the activation energy (Ea) for the reduction of Pd precursors with 16.7 mM KOAc has been calculated as 82.2 kJ·mol−1, with the logarithmic value of pre-exponential factor (ln A) as 22.8. In addition, the influence of other potassium salts on the growth of Pd nanocubes has been studied. As shown in Figure S8, when KOAc is replaced with KCl, KNO3, and K2SO4, the concentration of these salts has little influence of the size of Pd nanocube. In contrast, as shown in Figure 7, KOAc shows the capacity in tuning the sizes of Pd nanocubes. As has been discussed previously, the reduction rate of Pd precursors is critical in determination of the final size of Pd nanocubes. The reduction rate of Pd precursors could be adjusted by the concentration of KOAc due to the interaction between Pd cations and acetate anions as observed from the isosbestic point measurement (Figure S4). Discussion on the Growth Process of Pd Nanocubes. The FW 2-step theory is nowadays a popular model in dealing with the nucleation and growth process of transition metal nanoparticle. With the help of the FW model, the rate constants of nucleation and growth can be facilely separated and calculated. To clarify the generation process of welldefined Pd nanocubes, experimental data are fitted with the theory (details in the Supporting Information). However, due to the fast nucleation process and slow growth of Pd nanocubes, this theory seems to be unsuitable to describe the generation process. Appropriate discussion on the growth

a

Compared with the preparation of nanocubes without acetate additives, the reduction rates of Pd precursors with the addition of KOAc or NH4OAc are increased, and the sizes of Pd nanocubes are decreased. However, the results for the case of HOAc are similar to those without acetate additives.

AA. Similarly, ammonium ions from NH4OAc can increase the acidity of reaction solution to some degree, while potassium ions from KOAc cannot. As a result, Pd nanocubes prepared with KOAc are always smaller than those with NH4OAc. The measured pH values for the 13 reaction systems before and after reduction (Table 2) supports the hypothesis. The influence of acetate species on the reduction rate of Pd precursors decreases in the sequence of KOAc, NH4OAc, and HOAc. Summarizing all of the measured kinetic data, we can get the relationship between average cubic width d and the apparent reduction rate constant of each reaction kap as well as a linear plot of the logarithmic values of kap against the reciprocal values of d (Figure 5): ln kap = a + b/d

[Pd]0 VNAa03

(4)

where the constants a and b are correlated as the values of −8.10 and 21.6 (Figure 5B). Since the final number of Pd nanocubes (Nf) is related with the size of cubic nanoparticles, the relationship for kap and Nf can be obtained from eqs 3 and 4 (Figure 5C).

Figure 3. (A) The curves for specific absorbance peak at 424 nm of Pd species changing against reaction time, with or without the participant of NH4OAc or HOAc at different concentrations, and (B) the corresponding relationship between ln[Pd]t and reaction time. D

DOI: 10.1021/acs.inorgchem.8b00368 Inorg. Chem. XXXX, XXX, XXX−XXX

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Figure 4. TEM images of Pd nanocubes prepared with (A) 4.17, (B) 8.33, (C) 12.5, and (D) 16.7 mM HOAc and (E) 4.17, (F) 8.33, (G) 12.5, and (H) 16.7 mM NH4OAc. Numbers in each panel represent the average cubic width. Scale bar: 50 nm.

process of Pd nanocubes is needed. Since the reduction of Pd precursors is a first-order reaction, the concentration of Pd precursors in reaction system can be described as eq 6.

Table 2. Measured pH Values of 13 Reaction Systems before and after the Reduction of Pd Precursors with pH Meter at Room Temperaturea additive species

KOAc

NH4OAc

HOAc no additive

additive concentration (mM)

pHb

pHa

ΔpH

4.17 8.33 12.5 16.7 4.17 8.33 12.5 16.7 4.17 8.33 12.5 16.7

3.35 3.65 3.84 3.99 3.33 3.61 3.79 3.95 2.72 2.71 2.71 2.71 2.74

1.38 1.42 1.46 1.53 1.38 1.44 1.52 1.56 1.36 1.37 1.35 1.36 1.39

1.97 2.23 2.38 2.46 1.95 2.17 2.27 2.39 1.36 1.34 1.36 1.35 1.35

[Pd]t = e−kapt [Pd]0

(6)

Hence, the mole number of Pd atoms produced within certain duration Nt can be put as Nt = [Pd0]t V = ([Pd]0 − [Pd]t )V = (1 − e−kapt )[Pd]0 V (7)

where [Pd ]t is the “concentration” of Pd atoms. Assuming that at specific time point t the volume of the nanocubes is V(t), we can gain the following expression as 0

Nt =

4V (t )Nf a03NA

(8)

where V(t) = d3(t). Relating eqs 7 and 8, the relation between V(t) and Nf can be obtained as

a

pH obtained using S210 SevenCompact pH Meter, Mettler Toledo, China. pHb: pH value before reduction; pHa: pH value after reduction; ΔpH: pH difference before and after reduction, ΔpH = pHb − pHa.

Nf =

a03NANt 1 − e−kapt = a03NA[Pd]0 V × 4V (t ) 4V (t )

(9)

Assuming that the number of Pd nanoparticles through the growth period merely changes and is equal to the number of

Figure 5. (A) Relationship between apparent reduction rate constant kap and cubic width d, (B) linear plot between ln kap and 1/d, and (C) linear plot for ln kap and Nf1/3. E

DOI: 10.1021/acs.inorgchem.8b00368 Inorg. Chem. XXXX, XXX, XXX−XXX

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Figure 6. (A) Relationship between ln[Pd]t and t for Pd nanocubes prepared at 55, 65, 75, and 85 °C. (B) Relationship of ln kap and 1/d for Pd nanocubes prepared at 55, 65, 75, and 85 °C. (C) Relationship between ln kap and 1/T for the preparation process of Pd nanocubes with 16.7 mM KOAc at 55, 65, 75, and 85 °C. Combining (C) with the Arrhenius equation, the activation energy for the reduction of Pd precursors with 16.7 mM KOAc is calculated as 82.2 kJ·mol−1, and the logarithmic value of pre-exponential factor is 22.8.

Table 3. Measured and Fitted Cubic Width of Pd Nanoparticles Prepared without Further Additives at Specific Reaction Time Point Based on Figure S9 and Equation 10 t (s) 300 600 900 1200 1800 2700 3600 5400 7200 9000 10800 25200 36000

Figure 7. Influence of 4 kinds of potassium salts on the sizes of Pd nanocubes. KOAc is a better option in controlling the sizes of Pd nanocubes.

measured d(t) (nm)

fitted d(t) (nm)

± ± ± ± ± ± ± ± ± ± ± ± ±

11.3 13.6 14.9 15.8 16.8 17.5 17.8 18.0 18.0 18.0 18.0 18.0 18.0

4.0 7.1 9.6 9.9 11.7 13.9 15.8 16.6 16.7 17.4 18.0 18.1 18.0

0.8 1.3 1.5 1.8 1.7 2.2 1.6 2.2 2.1 2.1 1.2 2.6 1.9

final products, d(t) can be described as a function of d, the final size of Pd nanocubes, from eqs 3 and 9. d (t ) = =

3

3

V (t ) =

3

[Pd]0 − [Pd]t ×d [Pd]0

1 − e−kapt × d

(10)

Equation 10 is necessarily the same as the expression of transition metal nanocluster size against formation time in the FW theory.43 According to previous work,60 the change of cubic widths against reaction time for Pd nanocubes prepared without further additives is recorded in Table 3 (detailed data in Figure S9). With corresponding kinetic data in Table 1, the values of d(t) at different reaction times are calculated from eq 10 and listed in Table 3. Obviously, the average width of Pd nanocubes enhances as the reduction proceeding before equilibrium (Figure 8). To gain an empirical equation for d(t) against t, the values of V(t) are related with t, with results exhibited in Figure 9. Interestingly, in the empirical equation (eq 11a), the final average cubic width is included, and two constants A and B are introduced to make the equation a derivative from eq 10 (eq 11b).

Figure 8. Changes for plots of measured d(t) and fitted d(t) with eq 10 against reaction time. −4

V (t ) = d3(t ) = 5926.2 − 6555.7 × e−2.73 × 10 = (18.10 × d (t ) = F

3

3

t

−4

1 − 1.106 × e−0.291 × 9.37 × 10 t )3

1 − A e−Bkapt × d

(11a) (11b)

DOI: 10.1021/acs.inorgchem.8b00368 Inorg. Chem. XXXX, XXX, XXX−XXX

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calculated from the apparent reduction rate, the growth process could be deduced theoretically. Generally, during the formation process of Pd nanocubes, different from the slow and continuous nucleation in FW theory, there should be a so-called “burst nucleation” period,29,32 within which large quantities of Pd nucleus are produced, and the growth begins ever since. In the growth process of Pd nanocubes, there should be no more nucleation. The addition of KOAc, NH4OAc, or HOAc has apparent influence on the reduction kinetics of Pd precursors, and the average cubic width is quantitatively related with the reaction rate constant. A larger value of kap means a higher initial generation rate of Pd atoms, and within the burst nucleation period, there would be more Pd nucleus produced. Consequently, there would be more particles with smaller sizes produced. Thus, in a closed preparation system where no extra Pd supply is introduced during the whole generation process, the apparent reduction rate constant, kap, can be applied as an indicator to reveal the growth process of Pd nanocubes.

Figure 9. Relationship between the volume of Pd nanocubes V(t) and reaction time t.

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where the values of constants A and B are 1.106 and 0.291. To this point, combining eqs 4 and 11b, when the final width of as-synthesized Pd nanocubes is known, the apparent reduction rate is able to be determined, and the size of nanoparticles at specific time point is accessible. Furthermore, the growth rate of Pd nanocubes, vg(t), could be denoted as follows from eq 11b.

CONCLUSION Well-defined palladium nanocubes with tunable sizes have been prepared with the participant of acetate species, which are found to influence significantly the reduction rate of Pd precursors. The apparent rate constant of a first-order reaction to describe the reduction kinetics of Pd precursors can be applied as an indicator for the growth process of Pd nanocubes. By associating the average cubic width and the apparent reduction rate constant under various circumstances, a quantitative curve, which is further used to describe the growth stage of Pd nanocubes, has appeared. On the basis of the reduction rate constant, the change in cubic sizes can be determined along reaction time, and the growth kinetics can be deduced accordingly. This research has investigated and discussed the growth process of Pd nanocubes with controllable sizes, and thus builds an empirical bridge over thermodynamic properties of nanoparticles and kinetic parameters of the growth process.

1

ABkapd e−Bkapt d d (t ) 3 vg(t ) = = dt (1 − A e−Bkapt )2/3

(12)

To verify the rationality of the discussion on the growth process of Pd nanocubes, an extra experiment is proceeded with 2.08 mM KOAc while all other conditions are kept the same. The change of cubic widths along reaction time is recorded in Figure S10 and Table S4. Similarly, the data are treated with same approaches as above, and the results are presented in Figure 10. As shown in the figure, we can obtain a reasonable final cubic width as 16.2 nm for Pd nanocubes prepared with 2.08 mM KOAc, with apparent reduction rate constant as 1.15 × 10−3 s−1. Under this circumstance, the values of A and B are close to those without further additives. Thus, it is acceptable to declaim that the empirical eq 11b is rational, and the change of cubic width can be express with constants a, b, A, and B. Conclusively, by obtaining the final thermodynamic Pd cubic width, which can be empirically

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.8b00368.

Figure 10. (A) Relationship between the volume of Pd nanocubes V(t) and reaction time t for Pd nanocubes prepared with 2.08 mM KOAc, and (B) change of corresponding cubic width along reaction time. G

DOI: 10.1021/acs.inorgchem.8b00368 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

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Detailed deduction for the stoichiometry of the reduction of Pd precursors and corresponding kinetic proof, literature comparison on formation kinetics of Pd nanoparticles, relevant size distribution diagrams, detailed UV−vis spectra, and relevant TEM images (PDF)

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. Tel.: +86-571-88981416. Fax: +86571-88981416. ORCID

Jie Fan: 0000-0002-8380-6338 Yongsheng Guo: 0000-0001-7609-1891 Wenjun Fang: 0000-0002-5610-1623 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China (Nos. 21773209, 91441109, and J1210042).

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REFERENCES

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DOI: 10.1021/acs.inorgchem.8b00368 Inorg. Chem. XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.inorgchem.8b00368 Inorg. Chem. XXXX, XXX, XXX−XXX