第2章：触媒の種類

2.1 金属触媒

貴金属 vs 卑金属

金属触媒は工業化学の主力です。大きく以下のように分類されます：

d-バンド理論

遷移金属の触媒活性は、d-バンド中心の位置に関係しています。サバティエの原理によれば、最適な触媒作用には中程度の結合強度が必要です：

• 結合が弱すぎる：反応物が吸着せず、反応が起こらない
• 結合が強すぎる：生成物が脱離せず、触媒が被毒される
• 最適な結合：最大活性のためのゴルディロックスゾーン

コード例1：水素発生のボルカノプロット

"""
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 金属酸化物触媒

代表的な金属酸化物

コード例2：酸化物の表面積比較

"""
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 ゼオライト：分子ふるい

構造と特性

ゼオライトは、規則的なミクロ多孔質構造を持つ結晶性アルミノケイ酸塩です。主な特徴：

• 規則的な細孔構造：均一な細孔サイズ（3-10 Å）
• 分子ふるい効果：サイズ選択的触媒作用
• 高表面積：300-800 m²/g
• 調整可能な酸性度：Si/Al比で酸点密度を制御
• 形状選択性：反応物、生成物、遷移状態の選択性

代表的なゼオライト骨格構造

コード例3：ゼオライトの形状選択性

"""
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 金属有機構造体（MOF）- 2025年ノーベル賞

MOFの構造

MOFは以下から構成される結晶性材料です：

• 金属ノード（クラスター）：Zn、Cu、Fe、Zr、Alなど
• 有機リンカー：カルボン酸塩、イミダゾール塩、ホスホン酸塩
• 多孔質構造：調整可能な細孔サイズ（5-50 Å）

代表的なMOF

コード例4：MOFの表面積比較

"""
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 単原子触媒（SAC）

SACの利点

• 最大の原子効率：すべての金属原子が潜在的な活性サイト
• 独特の電子構造：ナノ粒子やバルクとは異なる
• 高い選択性：明確に定義された活性サイト
• 均一系と不均一系の橋渡し：両方の利点を組み合わせる

コード例5：SAC効率の計算

"""
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 光触媒と電極触媒

光触媒

光触媒は光エネルギーを使って化学反応を駆動します。最も有名な例は水の分解と汚染物質の分解のためのTiO₂です。

メカニズム：

1. 光吸収：光子エネルギー > バンドギャップ → 電子-正孔対の生成
2. 電荷分離：電子は伝導帯へ、正孔は価電子帯に
3. 表面反応：電子は吸着種を還元、正孔は酸化

電極触媒

電極触媒は電極表面での電気化学反応を促進します。以下に不可欠です：

• 水素発生（HER）：2H⁺ + 2e⁻ → H₂
• 酸素発生（OER）：2H₂O → O₂ + 4H⁺ + 4e⁻
• CO₂還元：CO₂ + 2H⁺ + 2e⁻ → CO + H₂O
• 酸素還元（ORR）：O₂ + 4H⁺ + 4e⁻ → 2H₂O（燃料電池）

コード例6：水分解触媒の比較

"""
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 有機金属触媒

均一系遷移金属触媒

有機金属触媒は金属-炭素結合を含み、反応物と同じ相で作用します。主な例：

2.8 章のまとめ

演習

演習1：ボルカノプロット解析

d-バンド理論を用いて、Pt-Ni合金がある反応において純粋なPtよりも活性が高くなる理由を説明しなさい。

演習2：MOFの設計

CO₂回収のための仮想MOFを設計しなさい。どの金属とリンカーを選びますか？その理由を説明しなさい。

演習3：SAC計算

サイズ1、5、10、50 nmのPtナノ粒子について表面原子の割合を計算しなさい。割合が10%を下回るのは何nmですか？

演習4：電極触媒の選択

費用対効果の高い水電解槽のために、HERとOERにどの非貴金属触媒を組み合わせますか？総過電圧を計算しなさい。

次の章

第3章：主要な触媒反応では、ハーバー・ボッシュ法、フィッシャー・トロプシュ合成、接触分解、水素化、クロスカップリング反応など、現代化学を変革した主要な工業触媒プロセスを探求します。