Nanoclusters, near monodispersed metal particles that are generally less than 10 nm (100 Å) in diame — Organic Chemistry Chemistry Question
Palladium nanoclusters
Nanoclusters, near monodispersed metal particles that are generally less than 10 nm (100 Å) in diameter, have attracted intense interest over the past decade. One reason for this is the belief that nanoclusters will have unique properties, derived in part from the fact that these particles and their properties lie somewhere between those of the bulk and single–particle species. These strange “morsels of matter” have fascinating potential uses; nanoclusters have significant potential especially for catalysis as new types of higher activity and selectivity catalysts.
There are four general synthetic methods for transition metal nanoclusters. These four methods are: (i) transition metal salts reduction (ii) thermal decomposition and photochemical methods (iii) ligand reduction and displacement from organometallics, and (iv) metal vapor synthesis. Furthermore, nanoclusters must be stabilized against aggregation into larger particles. Stabilization can be achieved by electrostatic (charge or “inorganic”) stabilization, steric (“organic”) stabilization or a combination of both. Electrostatic stabilization occurs by the adsorption of ions to the often electrophilic metal surface. This adsorption creates an electrical double (real multi–) layer, which results in a Coulombic repulsion force between individual particles (Fig. 1a). Steric stabilization is achieved by surrounding the metal center by layers of material that are sterically bulky, such as polymers or surfactants. These large adsorbates provide a steric barrier, which prevents close contact of the metal particles centers (Fig. 1b).
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Figure 1. A schematic illustration (a): for an electrostatically stabilized metal (M) particle and (b): a sterically stabilized metal particle.
Metal clusters are constructed by successively packing layers– or shells– of metal atoms around a single metal atom. Metal clusters that have a complete, regular outer geometry are designated full–shell or “magic number” clusters. The total number of metal atoms, y, per nth shell is given by the equation y = 10n2+2 (n = 1, 2, 3, …) (Fig. 2.)
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Figure 2. Idealized representation of hexagonal close–packed full–shell “magic number” clusters. Each metal atom has the maximum number of nearest neighbors, which impart some degree of extra stability to full–shell clusters.
The most widely used technique for characterizing nanoclusters is transmission electron microscopy (TEM) or high resolution TEM (HR–TEM), techniques which provide direct visual information on the size, shape, dispersity, structure and morphology of nanoclusters.
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Figure 3. (a) Transmission electron microscopy image of Pd(0) nanoclusters stabilized by a polymer. (b) Histogram of the Pd(0) nanocluster diameters.
By direct reaction of Pd(II)–polymer complex (1 mM in water solution) with gas H2, Pd(0) nanoclusters are prepared, as following:
n Pd(II) + n H2 Pd(0)n + 2n H +
A transmission electron micrograph of the isolated Pd(0)n nanoclusters shows spherical Pd(0) nanoclusters, protected by the polymer, with an average diameter of 2.05 nm.
Calculate the number (N) of Pd atoms per cluster. Are these nanoclusters full–shell nanoclusters? Calculate the number of shells (n) in the above Pd(0) nanoclusters.
Density of Pd, ρ = 12.02 g cm –3.
Model Answer
To calculate the number of Pd atoms (N) per cluster of average diameter D = 2.05 nm:
1. Calculate the volume of a single spherical Pd(0) nanocluster:
V = (4/3) * π * R^3 = (1/6) * π * D^3
V = (1/6) * π * (2.05 * 10^-7 cm)^3 = 4.51 * 10^-21 cm^3
2. Calculate the mass of one nanocluster:
m = V * ρ = (4.51 * 10^-21 cm^3) * (12.02 g cm^-3) = 5.42 * 10^-20 g
3. Calculate the number of Pd atoms (N) per cluster:
N = (m / M_Pd) * N_A
N = ((5.42 * 10^-20 g) / 106.42 g mol^-1) * (6.022 * 10^23 mol^-1) ≈ 307 atoms
4. Determine if they are full-shell clusters and find the number of shells:
According to the equation y = 10n^2 + 2, full-shell clusters have magic numbers of atoms:
- Shell 0 (central atom): 1 atom
- Shell 1 (n=1): 10(1)^2 + 2 = 12 atoms
- Shell 2 (n=2): 10(2)^2 + 2 = 42 atoms
- Shell 3 (n=3): 10(3)^2 + 2 = 92 atoms
- Shell 4 (n=4): 10(4)^2 + 2 = 162 atoms
Total atoms for a 4-shell cluster (n = 4) is N = 1 + 12 + 42 + 92 + 162 = 309 atoms.
Since the calculated number of atoms (307) is extremely close to 309, these are indeed 4 full-shell nanoclusters (n = 4).
The catalytic activity of the polymer stabilized Pd(0)n nanoclusters is detected by a catalytic olefin hydrogenation reaction, such as the cyclohexene plus H2 reaction:
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In a 400 cm 3 high pressure reactor, an amount of the above polymer–protected Pd(0)n nanoclusters containing a total of 50 mol of Pd(0) was dissolved in 50 cm 3 of acetone, followed by the addition of 5 cm 3 of cyclohexene. The reactor was then sealed, purged several times with prepurified H2 (dry and O2 free) and the H2 pressure was set to the desired value, approximately 4 atm. The solution was stirred continuously during the reaction and the temperature was kept constant at 30 °C. The H2 pressure vs. time until the end of the reaction is presented in Fig. 4.
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Figure 4. Hydrogen uptake curve. Temperature 30 °C, 0.5 mol of Pd(0), 5 cm 3 of cyclohexene.
(i) Calculate the % conversion of the cyclohexene.
(ii) Taking under consideration that only the surface Pd(0) atoms of the nanoclusters are catalytically active, calculate the turnover number, TON, where TON = moles H2 consumed / moles of catalytically active Pd(0) and the turnover frequency, TOF, where TOF = moles H2 consumed / moles of catalytically active Pd(0)/ time (min) of the consumption. Density of cyclohexene, ρ = 0.81 g cm –3.
Model Answer
(i) Calculation of % conversion:
- From Fig. 4, the initial pressure of H2 is 4.15 atm, and the final pressure of H2 at the end of the reaction (after 184 min) is 2.05 atm.
- Therefore, the pressure drop of H2 is Δp = 4.15 - 2.05 = 2.10 atm.
- Using the ideal gas law: n(H2) = (Δp * V_gas) / (R * T)
- V_gas = V_reactor - V_solution = 400 cm^3 - 55 cm^3 = 345 cm^3 = 0.345 dm^3
- T = 30 °C = 303.15 K
- R = 0.08206 dm^3 atm mol^-1 K^-1
- n(H2) = (2.10 * 0.345) / (0.08206 * 303.15) ≈ 0.029 mol
- Calculate initial moles of cyclohexene (C6H10):
- Mass of cyclohexene = 5 cm^3 * 0.81 g/cm^3 = 4.05 g
- M_C6H10 = 82.15 g/mol
- n_C6H10 = 4.05 / 82.15 ≈ 0.048 mol
- Since 1 mole of H2 reacts with 1 mole of cyclohexene:
- % Conversion = (reacted moles / initial moles) * 100% = (0.029 / 0.048) * 100% = 60%
(ii) Calculation of TON and TOF:
- For a 4 full-shell cluster (n = 4), only the atoms in the outermost (4th) shell are on the surface.
- Surface atoms (outermost shell) = 162 atoms.
- Total atoms in a 4-shell cluster = 309 atoms.
- Fraction of catalytically active Pd(0) = 162 / 309 = 0.524.
- Active moles of Pd(0) = 0.524 * 50 * 10^-6 mol = 2.62 * 10^-5 mol.
- Turnover Number (TON):
- TON = moles H2 consumed / moles of active Pd(0)
- TON = 0.029 mol / (0.524 * 50 * 10^-6 mol) ≈ 1106
- Turnover Frequency (TOF):
- TOF = TON / reaction time
- TOF = 1106 / 184 min = 6.0 min^-1
The polymer–protected Pd(0)n nanocluster catalyst are also used for the catalytic hydrogenation of hex–1–ene by H2. The experiment was performed under the conditions cited above, exept that the solvent was chloroform. It was found that Pd(0)n nanoclusters are an efficient catalyst for the hydrogenation of hex–1–ene.
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The 1 H–NMR spectra of the hex-1-ene and the reaction mixture after 30 min of reaction and after the removal of the catalyst are shown in the Fig. 5.
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Figure 5. 300 MHz 1 H–NMR spectra of (a) hex-1-ene and (b) the solution of the reaction after 30 min of reaction and after the elimination of the catalyst and the solvent.
The relative integrals of the 1 H–NMR spectra are given in the table below:
[VISUAL]
Calculate the % conversion of hex-1-ene to hexane after 30 min.
Model Answer
1. Analyze the 1H-NMR of the reactant hex-1-ene (CH3-CH2-CH2-CH2-CH=CH2):
- δ = 0.88 - 0.96 ppm (relative integral 3): -CH3 protons (3H)
- δ = 1.15 - 1.32 ppm (relative integral 4): -(CH2)2- protons (4H)
- δ = 1.99 - 2.08 ppm (relative integral 2): allylic -CH2- protons (2H)
- δ = 4.85 - 4.98 ppm (relative integral 2): terminal vinylic =CH2 protons (2H)
- δ = 5.65 - 5.79 ppm (relative integral 1): internal vinylic =CH- proton (1H)
2. Analyze the 1H-NMR of the product mixture after 30 min:
- The vinylic and allylic peaks of hex-1-ene are still present with relative integrals:
- δ = 5.65 - 5.79 ppm: 1 unit
- δ = 4.85 - 4.98 ppm: 2 units
- δ = 1.99 - 2.08 ppm: 2 units
This represents 1 equivalent of unreacted hex-1-ene.
- The aliphatic peaks in the product mixture have increased due to the formation of hexane (CH3-CH2-CH2-CH2-CH2-CH3):
- δ = 0.88 - 0.96 ppm: total relative integral of 9
- δ = 1.12 - 1.37 ppm: total relative integral of 12
3. Determine the amount of hexane formed:
- Since 1 equivalent of unreacted hex-1-ene contributes 3 units to the methyl region (δ = 0.88 - 0.96 ppm), the remaining 9 - 3 = 6 units in this region must come from hexane.
- Since a hexane molecule has two methyl groups (6 protons), a relative integral of 6 represents exactly 1 equivalent of hexane.
- (This is verified by the methylene region: 1 equivalent of hex-1-ene contributes 4 units, leaving 12 - 4 = 8 units, which matches exactly the 8 methylene protons of 1 equivalent of hexane).
4. Calculate the conversion:
- Ratio of remaining hex-1-ene to hexane is 1 : 1.
- % Conversion = (moles of hexane / (moles of hex-1-ene + moles of hexane)) * 100% = (1 / (1 + 1)) * 100% = 50%.