Chapter 2: Types of Catalysts

2.1 Metal Catalysts

Noble Metals vs. Base Metals

Metal catalysts are the workhorses of industrial chemistry. They are broadly classified into:

The d-Band Theory

Catalytic activity of transition metals is related to their d-band center position. The Sabatier principle states that optimal catalysis requires intermediate binding strength:

• Too weak binding: Reactants don't adsorb, no reaction
• Too strong binding: Products don't desorb, catalyst poisoned
• Optimal binding: Goldilocks zone for maximum activity

Code Example 1: Volcano Plot for Hydrogen Evolution

"""
Create a volcano plot showing the Sabatier principle
Demonstrates the optimal binding energy for catalysis
"""
import numpy as np
import matplotlib.pyplot as plt

# Metal data: (name, d-band center relative to Fermi level, log exchange current density)
# Approximate values for HER
metals = {
    'Pt': (-2.25, -3.0),
    'Pd': (-1.83, -4.0),
    'Rh': (-1.73, -4.2),
    'Ir': (-2.11, -3.5),
    'Ru': (-1.41, -5.0),
    'Ni': (-1.29, -5.5),
    'Co': (-1.17, -6.0),
    'Fe': (-0.92, -6.5),
    'Cu': (-2.67, -7.0),
    'Au': (-3.56, -6.0),
    'Ag': (-4.30, -7.5),
    'W': (0.77, -8.0),
    'Mo': (0.35, -7.0),
}

# Theoretical volcano curve
d_band = np.linspace(-5, 1, 100)
# Simplified volcano model
activity = -0.5 * (d_band + 2)**2 - 3

# Plot
fig, ax = plt.subplots(figsize=(10, 7))

# Volcano curve
ax.plot(d_band, activity, 'k--', linewidth=2, alpha=0.5, label='Volcano trend')

# Scatter plot of metals
colors = plt.cm.viridis(np.linspace(0, 1, len(metals)))
for (name, (d, log_i)), color in zip(metals.items(), colors):
    ax.scatter(d, log_i, s=150, c=[color], edgecolors='black', linewidth=1.5, zorder=5)
    ax.annotate(name, (d, log_i), xytext=(5, 5), textcoords='offset points',
                fontsize=10, fontweight='bold')

# Formatting
ax.set_xlabel('d-band Center (eV relative to Fermi level)', fontsize=12)
ax.set_ylabel('log(Exchange Current Density / A cm⁻²)', fontsize=12)
ax.set_title('Volcano Plot: Hydrogen Evolution Reaction', fontsize=14, fontweight='bold')
ax.set_xlim(-5, 1.5)
ax.set_ylim(-9, -2)
ax.grid(alpha=0.3)

# Add annotations
ax.annotate('Optimal\nBinding', xy=(-2.2, -3.2), fontsize=11, ha='center',
            bbox=dict(boxstyle='round', facecolor='lightgreen', alpha=0.7))
ax.annotate('Too Weak', xy=(-4, -7), fontsize=10, color='red')
ax.annotate('Too Strong', xy=(0.5, -7.5), fontsize=10, color='red')

plt.tight_layout()
plt.show()

print("\nKey Insight: Pt sits near the volcano peak because it has")
print("optimal hydrogen binding energy - not too strong, not too weak.")

2.2 Metal Oxide Catalysts

Common Metal Oxides

Code Example 2: Comparing Oxide Surface Areas

"""
Compare surface areas and catalytic properties of metal oxides
"""
import numpy as np
import matplotlib.pyplot as plt

# Metal oxide data
oxides = {
    'γ-Al₂O₃': {'surface_area': 200, 'pore_size': 8, 'thermal_stability': 1000},
    'TiO₂ (anatase)': {'surface_area': 50, 'pore_size': 10, 'thermal_stability': 600},
    'SiO₂': {'surface_area': 300, 'pore_size': 6, 'thermal_stability': 1200},
    'CeO₂': {'surface_area': 100, 'pore_size': 5, 'thermal_stability': 800},
    'ZrO₂': {'surface_area': 80, 'pore_size': 4, 'thermal_stability': 1100},
    'ZnO': {'surface_area': 30, 'pore_size': 20, 'thermal_stability': 500},
}

names = list(oxides.keys())
surface_areas = [v['surface_area'] for v in oxides.values()]
thermal_stabilities = [v['thermal_stability'] for v in oxides.values()]

# Create figure with two subplots
fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(14, 5))

# Surface area comparison
colors = plt.cm.Purples(np.linspace(0.4, 0.9, len(names)))
bars1 = ax1.barh(names, surface_areas, color=colors, edgecolor='black')
ax1.set_xlabel('BET Surface Area (m²/g)', fontsize=12)
ax1.set_title('Surface Area Comparison', fontsize=13, fontweight='bold')
ax1.grid(axis='x', alpha=0.3)

# Add values on bars
for bar, val in zip(bars1, surface_areas):
    ax1.text(val + 5, bar.get_y() + bar.get_height()/2,
             f'{val}', va='center', fontsize=10)

# Thermal stability comparison
colors2 = plt.cm.Oranges(np.linspace(0.4, 0.9, len(names)))
bars2 = ax2.barh(names, thermal_stabilities, color=colors2, edgecolor='black')
ax2.set_xlabel('Thermal Stability (°C)', fontsize=12)
ax2.set_title('Thermal Stability Comparison', fontsize=13, fontweight='bold')
ax2.grid(axis='x', alpha=0.3)

for bar, val in zip(bars2, thermal_stabilities):
    ax2.text(val + 20, bar.get_y() + bar.get_height()/2,
             f'{val}°C', va='center', fontsize=10)

plt.tight_layout()
plt.show()

print("\nKey Points:")
print("• SiO₂ and γ-Al₂O₃ have highest surface areas - excellent supports")
print("• SiO₂ and ZrO₂ have best thermal stability")
print("• Trade-off: high surface area oxides often less thermally stable")

2.3 Zeolites: Molecular Sieves

Structure and Properties

Zeolites are crystalline aluminosilicates with ordered microporous structures. Their key features:

• Ordered pore structure: Uniform pore sizes (3-10 Å)
• Molecular sieve effect: Size-selective catalysis
• High surface area: 300-800 m²/g
• Tunable acidity: Si/Al ratio controls acid site density
• Shape selectivity: Reactant, product, and transition state selectivity

Common Zeolite Frameworks

Code Example 3: Zeolite Shape Selectivity

"""
Demonstrate zeolite shape selectivity through molecular size filtering
"""
import numpy as np
import matplotlib.pyplot as plt

# Molecular kinetic diameters (Å) and zeolite pore sizes
molecules = {
    'H₂': 2.89,
    'N₂': 3.64,
    'O₂': 3.46,
    'CO₂': 3.30,
    'CH₄': 3.80,
    'C₂H₆': 4.44,
    'n-Hexane': 4.30,
    'Benzene': 5.85,
    'Cyclohexane': 6.00,
    'p-Xylene': 5.85,
    'o-Xylene': 6.80,
    'm-Xylene': 6.80,
}

zeolites = {
    'Zeolite A (LTA)': 4.1,
    'ZSM-5 (MFI)': 5.5,
    'Zeolite Y (FAU)': 7.4,
    'Zeolite Beta (BEA)': 7.0,
}

# Create visualization
fig, ax = plt.subplots(figsize=(12, 8))

# Plot molecular sizes as horizontal bars
y_pos = np.arange(len(molecules))
mol_names = list(molecules.keys())
mol_sizes = list(molecules.values())

colors = ['#4CAF50' if s < 5.5 else '#FF9800' if s < 7.0 else '#f44336'
          for s in mol_sizes]
bars = ax.barh(y_pos, mol_sizes, color=colors, alpha=0.7, edgecolor='black')

# Add zeolite pore size lines
for zeolite, pore_size in zeolites.items():
    ax.axvline(x=pore_size, linestyle='--', linewidth=2, alpha=0.8,
               label=f'{zeolite}: {pore_size} Å')

ax.set_yticks(y_pos)
ax.set_yticklabels(mol_names, fontsize=10)
ax.set_xlabel('Kinetic Diameter (Å)', fontsize=12)
ax.set_title('Zeolite Shape Selectivity: Molecular Sieve Effect', fontsize=14, fontweight='bold')
ax.legend(loc='upper right', fontsize=9)
ax.set_xlim(0, 9)
ax.grid(axis='x', alpha=0.3)

# Add annotations
ax.text(2.5, 11.5, '✓ Can enter ZSM-5', color='green', fontsize=10)
ax.text(6.5, 11.5, '✗ Cannot enter ZSM-5', color='red', fontsize=10)

plt.tight_layout()
plt.show()

# Explain selectivity
print("\nXylene Isomer Separation with ZSM-5:")
print("• p-Xylene (5.85 Å): Can diffuse through ZSM-5 pores (5.5 Å)")
print("• o-Xylene (6.80 Å): Too large, blocked at pore entrance")
print("• m-Xylene (6.80 Å): Too large, blocked at pore entrance")
print("\nThis enables selective production of p-xylene (polymer feedstock)!")

2.4 Metal-Organic Frameworks (MOFs) - 2025 Nobel Prize

MOF Structure

MOFs are crystalline materials composed of:

• Metal nodes (clusters): Zn, Cu, Fe, Zr, Al, etc.
• Organic linkers: Carboxylates, imidazolates, phosphonates
• Porous structure: Tunable pore sizes (5-50 Å)

Representative MOFs

Code Example 4: MOF Surface Area Comparison

"""
Compare surface areas of MOFs, zeolites, and other materials
Demonstrates the extraordinary porosity of MOFs
"""
import numpy as np
import matplotlib.pyplot as plt

# Material data: (name, surface_area in m²/g, material_class)
materials = [
    ('Activated Carbon', 1000, 'Traditional'),
    ('Silica Gel', 500, 'Traditional'),
    ('Zeolite Y', 700, 'Zeolite'),
    ('ZSM-5', 400, 'Zeolite'),
    ('HKUST-1', 1500, 'MOF'),
    ('UiO-66', 1200, 'MOF'),
    ('MOF-5', 3800, 'MOF'),
    ('NU-110', 7140, 'MOF'),
]

# Separate by class
classes = {'Traditional': [], 'Zeolite': [], 'MOF': []}
for name, sa, cls in materials:
    classes[cls].append((name, sa))

# Colors
class_colors = {'Traditional': '#78909c', 'Zeolite': '#42a5f5', 'MOF': '#ab47bc'}

# Create figure
fig, ax = plt.subplots(figsize=(12, 6))

# Plot bars
x_pos = 0
x_ticks = []
x_labels = []
bar_width = 0.8

for cls, data in classes.items():
    for name, sa in data:
        color = class_colors[cls]
        bar = ax.bar(x_pos, sa, bar_width, color=color, edgecolor='black', alpha=0.8)
        x_ticks.append(x_pos)
        x_labels.append(name)
        x_pos += 1

    x_pos += 0.5  # Gap between classes

# Formatting
ax.set_xticks(x_ticks)
ax.set_xticklabels(x_labels, rotation=45, ha='right', fontsize=10)
ax.set_ylabel('BET Surface Area (m²/g)', fontsize=12)
ax.set_title('Surface Area Comparison: MOFs vs Traditional Materials', fontsize=14, fontweight='bold')
ax.grid(axis='y', alpha=0.3)

# Add legend
from matplotlib.patches import Patch
legend_elements = [Patch(facecolor=c, edgecolor='black', label=cls, alpha=0.8)
                   for cls, c in class_colors.items()]
ax.legend(handles=legend_elements, loc='upper left', fontsize=10)

# Add reference lines
ax.axhline(y=1000, color='gray', linestyle='--', alpha=0.5)
ax.text(7.5, 1100, 'Activated Carbon baseline', fontsize=9, color='gray')

# Annotate record
ax.annotate('World Record!\n7,140 m²/g', xy=(7, 7140), xytext=(5.5, 6500),
            fontsize=10, fontweight='bold', color='purple',
            arrowprops=dict(arrowstyle='->', color='purple'))

plt.tight_layout()
plt.show()

# Calculate comparison
print("\nMOF Surface Area Perspective:")
print(f"• NU-110: 7,140 m²/g = 0.714 hectares per gram!")
print(f"• 1 gram of NU-110 has the surface area of a tennis court")
print(f"• MOFs have 5-10x more surface area than activated carbon")

2.5 Single-Atom Catalysts (SACs)

SAC Advantages

• Maximum atom efficiency: Every metal atom is a potential active site
• Unique electronic structure: Different from nanoparticles and bulk
• High selectivity: Well-defined active sites
• Bridging homogeneous and heterogeneous: Combines benefits of both

Code Example 5: SAC Efficiency Calculation

"""
Calculate and compare atom efficiency of different catalyst types
Demonstrates the advantage of single-atom catalysts
"""
import numpy as np
import matplotlib.pyplot as plt

def calculate_surface_atoms(particle_size_nm, atom_diameter_nm=0.28):
    """
    Estimate fraction of surface atoms for a spherical nanoparticle

    For spherical particles, surface atoms ≈ 6 * (atom_diameter / particle_diameter)
    """
    if particle_size_nm <= atom_diameter_nm:
        return 1.0  # Single atom
    return min(1.0, 6 * atom_diameter_nm / particle_size_nm)

# Particle sizes to analyze
sizes = np.logspace(-0.5, 2, 100)  # 0.3 nm to 100 nm

# Calculate surface atom fractions
surface_fractions = [calculate_surface_atoms(s) for s in sizes]

# Create figure
fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(14, 5))

# Left: Surface atom fraction vs size
ax1.plot(sizes, np.array(surface_fractions) * 100, 'b-', linewidth=2)
ax1.axhline(y=100, color='green', linestyle='--', label='Single Atom (100%)')
ax1.axhline(y=50, color='orange', linestyle='--', alpha=0.5)
ax1.axhline(y=10, color='red', linestyle='--', alpha=0.5)

ax1.set_xscale('log')
ax1.set_xlabel('Particle Size (nm)', fontsize=12)
ax1.set_ylabel('Surface Atoms (%)', fontsize=12)
ax1.set_title('Atom Utilization vs Particle Size', fontsize=13, fontweight='bold')
ax1.grid(alpha=0.3)
ax1.set_ylim(0, 110)

# Add annotations
ax1.annotate('Single Atom\nCatalyst', xy=(0.5, 100), fontsize=10, color='green',
             fontweight='bold', ha='center')
ax1.annotate('Nanoclusters\n(1-2 nm)', xy=(1.5, 70), fontsize=9)
ax1.annotate('Nanoparticles\n(5-50 nm)', xy=(20, 25), fontsize=9)
ax1.annotate('Bulk\n(>100 nm)', xy=(70, 8), fontsize=9, color='red')

# Right: Cost comparison
categories = ['Bulk Pt\n(wasteful)', 'Pt Nanoparticles\n(5 nm)', 'Pt Nanoclusters\n(1 nm)', 'Pt SAC']
efficiency = [3, 30, 60, 100]
relative_cost = [100, 33, 17, 10]  # Relative to bulk for same activity

x = np.arange(len(categories))
width = 0.35

bars1 = ax2.bar(x - width/2, efficiency, width, label='Atom Efficiency (%)',
                color='#4CAF50', alpha=0.8)
bars2 = ax2.bar(x + width/2, relative_cost, width, label='Relative Cost (%)',
                color='#f44336', alpha=0.8)

ax2.set_ylabel('Percentage', fontsize=12)
ax2.set_title('SAC Economic Advantage', fontsize=13, fontweight='bold')
ax2.set_xticks(x)
ax2.set_xticklabels(categories, fontsize=9)
ax2.legend(fontsize=10)
ax2.grid(axis='y', alpha=0.3)

plt.tight_layout()
plt.show()

print("\nSAC Economic Impact:")
print("• 100% atom efficiency vs 3% for bulk Pt")
print("• 10x cost reduction for equivalent catalytic activity")
print("• Critical for precious metal sustainability")

2.6 Photocatalysts and Electrocatalysts

Photocatalysis

Photocatalysts use light energy to drive chemical reactions. The most famous example is TiO₂ for water splitting and pollution degradation.

Mechanism:

1. Light absorption: Photon energy > bandgap → electron-hole pair
2. Charge separation: Electrons to conduction band, holes in valence band
3. Surface reactions: Electrons reduce, holes oxidize adsorbates

Electrocatalysis

Electrocatalysts facilitate electrochemical reactions at electrode surfaces. Critical for:

• Hydrogen Evolution (HER): 2H⁺ + 2e⁻ → H₂
• Oxygen Evolution (OER): 2H₂O → O₂ + 4H⁺ + 4e⁻
• CO₂ Reduction: CO₂ + 2H⁺ + 2e⁻ → CO + H₂O
• Oxygen Reduction (ORR): O₂ + 4H⁺ + 4e⁻ → 2H₂O (fuel cells)

Code Example 6: Water Splitting Catalyst Comparison

"""
Compare electrocatalysts for water splitting (HER and OER)
Shows overpotential requirements for different materials
"""
import numpy as np
import matplotlib.pyplot as plt

# Catalyst data: overpotential at 10 mA/cm² (mV)
her_catalysts = {
    'Pt/C': 20,
    'MoS₂': 150,
    'Ni-Mo': 80,
    'CoP': 90,
    'WC': 120,
    'Fe₃P': 160,
}

oer_catalysts = {
    'IrO₂': 250,
    'RuO₂': 280,
    'NiFe-LDH': 230,
    'CoFe₂O₄': 350,
    'Ni₃S₂': 300,
    'Co₃O₄': 380,
}

# Create figure
fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(14, 5))

# HER catalysts
colors_her = ['#4CAF50' if v < 50 else '#FFC107' if v < 100 else '#FF5722'
              for v in her_catalysts.values()]
bars1 = ax1.barh(list(her_catalysts.keys()), list(her_catalysts.values()),
                  color=colors_her, edgecolor='black')
ax1.set_xlabel('Overpotential at 10 mA/cm² (mV)', fontsize=11)
ax1.set_title('Hydrogen Evolution (HER) Catalysts', fontsize=13, fontweight='bold')
ax1.axvline(x=50, color='green', linestyle='--', alpha=0.5, label='Excellent (<50 mV)')
ax1.axvline(x=100, color='orange', linestyle='--', alpha=0.5, label='Good (<100 mV)')
ax1.legend(fontsize=9)
ax1.grid(axis='x', alpha=0.3)
ax1.set_xlim(0, 200)

# OER catalysts
colors_oer = ['#4CAF50' if v < 250 else '#FFC107' if v < 300 else '#FF5722'
              for v in oer_catalysts.values()]
bars2 = ax2.barh(list(oer_catalysts.keys()), list(oer_catalysts.values()),
                  color=colors_oer, edgecolor='black')
ax2.set_xlabel('Overpotential at 10 mA/cm² (mV)', fontsize=11)
ax2.set_title('Oxygen Evolution (OER) Catalysts', fontsize=13, fontweight='bold')
ax2.axvline(x=250, color='green', linestyle='--', alpha=0.5, label='Excellent (<250 mV)')
ax2.axvline(x=300, color='orange', linestyle='--', alpha=0.5, label='Good (<300 mV)')
ax2.legend(fontsize=9)
ax2.grid(axis='x', alpha=0.3)
ax2.set_xlim(0, 450)

plt.tight_layout()
plt.show()

print("\nWater Splitting Efficiency:")
print("Theoretical: E = 1.23 V")
print(f"With Pt/C + IrO₂: E = 1.23 + 0.02 + 0.25 = 1.50 V")
print(f"Efficiency = 1.23/1.50 = {1.23/1.50*100:.1f}%")
print("\nNon-precious metal alternatives (NiFe-LDH + Ni-Mo):")
print(f"E = 1.23 + 0.08 + 0.23 = 1.54 V, Efficiency = {1.23/1.54*100:.1f}%")

2.7 Organometallic Catalysts

Homogeneous Transition Metal Catalysis

Organometallic catalysts contain metal-carbon bonds and operate in the same phase as reactants. Key examples:

2.8 Chapter Summary

Exercises

Exercise 1: Volcano Plot Analysis

Using the d-band theory, explain why Pt-Ni alloys can be more active than pure Pt for some reactions.

Exercise 2: MOF Design

Design a hypothetical MOF for CO₂ capture. What metal and linker would you choose? Justify your answer.

Exercise 3: SAC Calculation

Calculate the surface atom fraction for Pt nanoparticles of sizes 1, 5, 10, and 50 nm. At what size does the fraction drop below 10%?

Exercise 4: Electrocatalyst Selection

For a cost-effective water electrolyzer, which non-precious metal catalysts would you combine for HER and OER? Calculate the total overpotential.

Next Chapter

In Chapter 3: Key Catalytic Reactions, we will explore major industrial catalytic processes including the Haber-Bosch process, Fischer-Tropsch synthesis, catalytic cracking, hydrogenation, and cross-coupling reactions that have transformed modern chemistry.