第3章：重要な触媒反応

3.1 ハーバー・ボッシュ法：窒素固定

反応

課題

N≡N三重結合は最も強い化学結合の一つです（945 kJ/mol）。この結合を切断するには以下が必要です：

• 鉄触媒と促進剤（K₂O、Al₂O₃、CaO）
• 高圧（150-300 atm）で平衡を生成物側にシフト
• 中程度の温度（400-500°C）- 速度論と平衡のバランス

コード例1：ハーバー・ボッシュ平衡計算

"""
Calculate Haber-Bosch equilibrium conversion at various conditions
Demonstrates the trade-off between temperature and pressure
"""
import numpy as np
import matplotlib.pyplot as plt

def haber_equilibrium(T_celsius, P_atm, initial_ratio=3):
    """
    Calculate equilibrium NH3 yield using simplified equilibrium expression
    N2 + 3H2 <=> 2NH3

    Uses van't Hoff equation approximation
    """
    T = T_celsius + 273.15  # Convert to Kelvin

    # Equilibrium constant (approximate, from thermodynamic data)
    # ln(Kp) ≈ 4710/T - 4.74 (simplified)
    ln_Kp = 4710 / T - 4.74
    Kp = np.exp(ln_Kp)

    # For stoichiometric feed (3H2:1N2), solving equilibrium
    # This is a simplified calculation
    # In reality, iterative solving is needed

    # Approximate conversion based on empirical correlation
    # Conversion increases with pressure, decreases with temperature
    x_eq = Kp * (P_atm / 100)**0.5 / (1 + Kp * (P_atm / 100)**0.5)
    x_eq = min(x_eq, 0.95)  # Cap at 95%

    return x_eq * 100  # Return as percentage

# Create meshgrid for pressure and temperature
temperatures = np.linspace(300, 600, 50)
pressures = [50, 100, 200, 300, 400]

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

# Left: NH3 yield vs temperature at various pressures
colors = plt.cm.viridis(np.linspace(0, 1, len(pressures)))
for P, color in zip(pressures, colors):
    yields = [haber_equilibrium(T, P) for T in temperatures]
    ax1.plot(temperatures, yields, color=color, linewidth=2, label=f'{P} atm')

ax1.axvspan(400, 500, alpha=0.2, color='orange', label='Industrial range')
ax1.set_xlabel('Temperature (°C)', fontsize=12)
ax1.set_ylabel('NH₃ Equilibrium Yield (%)', fontsize=12)
ax1.set_title('Haber-Bosch: Temperature vs Yield', fontsize=13, fontweight='bold')
ax1.legend(title='Pressure', fontsize=9)
ax1.grid(alpha=0.3)
ax1.set_xlim(300, 600)
ax1.set_ylim(0, 100)

# Right: Reaction rate consideration
# Rate increases with T, but equilibrium decreases
rate_factor = np.exp(-(50000)/(8.314 * (temperatures + 273.15)))
rate_factor = rate_factor / rate_factor.max() * 100

equilibrium_yield = [haber_equilibrium(T, 200) for T in temperatures]
effective_rate = np.array(rate_factor) * np.array(equilibrium_yield) / 100

ax2.plot(temperatures, rate_factor, 'r--', linewidth=2, label='Reaction Rate')
ax2.plot(temperatures, equilibrium_yield, 'b--', linewidth=2, label='Equilibrium Yield')
ax2.plot(temperatures, effective_rate, 'g-', linewidth=3, label='Effective Production')

ax2.axvline(x=450, color='orange', linestyle=':', linewidth=2)
ax2.annotate('Optimal T ≈ 450°C', xy=(450, 50), fontsize=10, ha='left')

ax2.set_xlabel('Temperature (°C)', fontsize=12)
ax2.set_ylabel('Relative Value (%)', fontsize=12)
ax2.set_title('Kinetics vs Thermodynamics Trade-off', fontsize=13, fontweight='bold')
ax2.legend(fontsize=10)
ax2.grid(alpha=0.3)

plt.tight_layout()
plt.show()

print("\nHaber-Bosch Process Impact:")
print("• Annual production: ~180 million tons NH₃")
print("• Feeds ~50% of world population through fertilizers")
print("• Consumes ~1.5% of global energy")
print("• Nobel Prize: Fritz Haber (1918), Carl Bosch (1931)")

3.2 フィッシャー・トロプシュ合成

合成ガスから液体燃料へ

フィッシャー・トロプシュ（FT）合成は、合成ガス（CO + H₂）を液体炭化水素に変換します：

アンダーソン・シュルツ・フローリー分布

FT生成物は、鎖成長確率αに支配される統計分布に従います：

ここで、$W_n$は炭素数nの炭化水素の重量分率です。

コード例2：FT生成物分布

"""
Calculate Anderson-Schulz-Flory distribution for Fischer-Tropsch synthesis
Shows how chain growth probability affects product distribution
"""
import numpy as np
import matplotlib.pyplot as plt

def asf_distribution(n, alpha):
    """Anderson-Schulz-Flory distribution"""
    return n * (1 - alpha)**2 * alpha**(n - 1)

# Carbon numbers
n = np.arange(1, 40)

# Different chain growth probabilities
alphas = [0.7, 0.8, 0.85, 0.9, 0.95]

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

# Left: Weight distribution for different alpha
colors = plt.cm.plasma(np.linspace(0.2, 0.9, len(alphas)))
for alpha, color in zip(alphas, colors):
    W = asf_distribution(n, alpha)
    ax1.plot(n, W * 100, color=color, linewidth=2, label=f'α = {alpha}')

ax1.axvspan(5, 11, alpha=0.2, color='green', label='Gasoline (C5-C11)')
ax1.axvspan(12, 20, alpha=0.2, color='blue', label='Diesel (C12-C20)')
ax1.set_xlabel('Carbon Number', fontsize=12)
ax1.set_ylabel('Weight Fraction (%)', fontsize=12)
ax1.set_title('FT Product Distribution (ASF)', fontsize=13, fontweight='bold')
ax1.legend(fontsize=9)
ax1.grid(alpha=0.3)
ax1.set_xlim(0, 40)

# Right: Selectivity to different fractions vs alpha
alphas_fine = np.linspace(0.5, 0.98, 100)
n_full = np.arange(1, 100)

gasoline_sel = []  # C5-C11
diesel_sel = []    # C12-C20
wax_sel = []       # C21+
methane_sel = []   # C1

for alpha in alphas_fine:
    W = asf_distribution(n_full, alpha)
    methane_sel.append(W[0] * 100)
    gasoline_sel.append(np.sum(W[4:11]) * 100)
    diesel_sel.append(np.sum(W[11:20]) * 100)
    wax_sel.append(np.sum(W[20:]) * 100)

ax2.plot(alphas_fine, methane_sel, 'r-', linewidth=2, label='Methane (C1)')
ax2.plot(alphas_fine, gasoline_sel, 'g-', linewidth=2, label='Gasoline (C5-C11)')
ax2.plot(alphas_fine, diesel_sel, 'b-', linewidth=2, label='Diesel (C12-C20)')
ax2.plot(alphas_fine, wax_sel, 'm-', linewidth=2, label='Wax (C21+)')

ax2.axvline(x=0.85, color='gray', linestyle='--', alpha=0.5)
ax2.annotate('Typical Co\nα ≈ 0.85', xy=(0.85, 40), fontsize=9, ha='center')

ax2.set_xlabel('Chain Growth Probability (α)', fontsize=12)
ax2.set_ylabel('Selectivity (%)', fontsize=12)
ax2.set_title('FT Selectivity vs Chain Growth', fontsize=13, fontweight='bold')
ax2.legend(fontsize=9)
ax2.grid(alpha=0.3)

plt.tight_layout()
plt.show()

print("\nFischer-Tropsch Applications:")
print("• GTL (Gas-to-Liquids): Qatar, Malaysia, South Africa")
print("• CTL (Coal-to-Liquids): China, South Africa (Sasol)")
print("• BTL (Biomass-to-Liquids): Emerging renewable pathway")
print("• Typical conditions: 200-300°C, 10-40 bar, Co or Fe catalyst")

3.3 接触分解と改質

流動接触分解（FCC）

FCCは世界で最大規模の触媒プロセスであり、重質油留分をガソリンに変換します：

• 触媒：ゼオライトY + マトリックス（アルミナ、クレイ）
• 条件：500-550°C、約1-3 bar
• 処理能力：世界で約1,400万バレル/日

接触改質

改質は低オクタン価のナフサを高オクタン価のガソリンと芳香族に変換します：

• 触媒：酸性Al₂O₃担持Pt/Re
• 反応：脱水素、異性化、環化
• 副生成物：水素（水素化処理に有用）

コード例3：オクタン価向上

"""
Visualize catalytic reforming's effect on octane number
Shows transformation of feed to reformate
"""
import numpy as np
import matplotlib.pyplot as plt

# Hydrocarbon composition and octane numbers
# Before and after reforming

feed_components = {
    'n-Hexane': (40, 25),      # (wt%, RON)
    'n-Heptane': (25, 0),
    'Methylcyclopentane': (15, 91),
    'Cyclohexane': (10, 83),
    'Benzene': (5, 106),
    'Toluene': (5, 120),
}

reformate_components = {
    'n-Hexane': (5, 25),
    'n-Heptane': (3, 0),
    'Methylcyclopentane': (2, 91),
    'Cyclohexane': (5, 83),
    'Benzene': (25, 106),
    'Toluene': (35, 120),
    'Xylenes': (15, 117),
    'C9+ Aromatics': (10, 115),
}

def calculate_ron(components):
    """Calculate Research Octane Number from components"""
    total_wt = sum(v[0] for v in components.values())
    ron = sum(v[0] * v[1] for v in components.values()) / total_wt
    return ron

feed_ron = calculate_ron(feed_components)
reformate_ron = calculate_ron(reformate_components)

# Visualization
fig, (ax1, ax2, ax3) = plt.subplots(1, 3, figsize=(15, 5))

# Feed composition
feed_names = list(feed_components.keys())
feed_values = [v[0] for v in feed_components.values()]
colors_feed = ['#ffcccc' if v[1] < 50 else '#ccffcc' if v[1] > 100 else '#ffffcc'
               for v in feed_components.values()]
ax1.barh(feed_names, feed_values, color=colors_feed, edgecolor='black')
ax1.set_xlabel('Weight %', fontsize=11)
ax1.set_title(f'Naphtha Feed\nRON = {feed_ron:.0f}', fontsize=12, fontweight='bold')
ax1.set_xlim(0, 45)

# Reformate composition
ref_names = list(reformate_components.keys())
ref_values = [v[0] for v in reformate_components.values()]
colors_ref = ['#ffcccc' if v[1] < 50 else '#ccffcc' if v[1] > 100 else '#ffffcc'
              for v in reformate_components.values()]
ax2.barh(ref_names, ref_values, color=colors_ref, edgecolor='black')
ax2.set_xlabel('Weight %', fontsize=11)
ax2.set_title(f'Reformate Product\nRON = {reformate_ron:.0f}', fontsize=12, fontweight='bold')
ax2.set_xlim(0, 45)

# RON comparison
categories = ['Feed\nNaphtha', 'Reformate', 'Target\n(Premium)']
rons = [feed_ron, reformate_ron, 95]
colors_ron = ['#ff9999', '#99ff99', '#9999ff']
ax3.bar(categories, rons, color=colors_ron, edgecolor='black', width=0.6)
ax3.set_ylabel('Research Octane Number', fontsize=11)
ax3.set_title('Octane Number Enhancement', fontsize=12, fontweight='bold')
ax3.set_ylim(0, 130)
ax3.axhline(y=87, color='orange', linestyle='--', label='Regular (87)')
ax3.axhline(y=95, color='green', linestyle='--', label='Premium (95)')
ax3.legend(fontsize=9)

for i, v in enumerate(rons):
    ax3.text(i, v + 3, f'{v:.0f}', ha='center', fontsize=11, fontweight='bold')

plt.tight_layout()
plt.show()

print("\nReforming Process Summary:")
print(f"• Feed RON: {feed_ron:.0f} → Reformate RON: {reformate_ron:.0f}")
print(f"• Octane boost: +{reformate_ron - feed_ron:.0f} points")
print("• Key reactions: Dehydrocyclization, Isomerization, Aromatization")
print("• Hydrogen yield: 2-4% (valuable by-product)")

3.4 水素化反応

水素化の種類

コード例4：水素化反応速度論

"""
Model hydrogenation reaction kinetics
Compare different catalyst activities
"""
import numpy as np
import matplotlib.pyplot as plt
from scipy.integrate import odeint

def hydrogenation_kinetics(C, t, k, K_H, K_S, P_H2):
    """
    Langmuir-Hinshelwood kinetics for hydrogenation
    Rate = k * theta_H * theta_S
    where theta is surface coverage
    """
    C_substrate = C[0]

    # Surface coverages
    theta_H = K_H * P_H2 / (1 + K_H * P_H2 + K_S * C_substrate)
    theta_S = K_S * C_substrate / (1 + K_H * P_H2 + K_S * C_substrate)

    # Reaction rate
    rate = k * theta_H * theta_S

    return [-rate]  # Substrate consumption

# Time span
t = np.linspace(0, 60, 200)  # 60 minutes

# Initial substrate concentration
C0 = [1.0]  # mol/L

# Different catalysts with different parameters
catalysts = {
    'Pd/C': {'k': 0.5, 'K_H': 10, 'K_S': 5},
    'Pt/C': {'k': 0.3, 'K_H': 8, 'K_S': 8},
    'Ni/SiO₂': {'k': 0.1, 'K_H': 15, 'K_S': 3},
}

P_H2 = 1.0  # atm H2 pressure

# Solve and plot
fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(14, 5))

colors = ['#e91e63', '#2196f3', '#4caf50']
for (name, params), color in zip(catalysts.items(), colors):
    solution = odeint(hydrogenation_kinetics, C0, t,
                      args=(params['k'], params['K_H'], params['K_S'], P_H2))

    conversion = (1 - solution[:, 0] / C0[0]) * 100
    ax1.plot(t, solution[:, 0], color=color, linewidth=2, label=name)
    ax2.plot(t, conversion, color=color, linewidth=2, label=name)

ax1.set_xlabel('Time (min)', fontsize=12)
ax1.set_ylabel('Substrate Concentration (mol/L)', fontsize=12)
ax1.set_title('Hydrogenation: Concentration Profile', fontsize=13, fontweight='bold')
ax1.legend(fontsize=10)
ax1.grid(alpha=0.3)

ax2.set_xlabel('Time (min)', fontsize=12)
ax2.set_ylabel('Conversion (%)', fontsize=12)
ax2.set_title('Hydrogenation: Conversion Profile', fontsize=13, fontweight='bold')
ax2.legend(fontsize=10)
ax2.grid(alpha=0.3)
ax2.set_ylim(0, 100)

# Add t50 markers
ax2.axhline(y=50, color='gray', linestyle='--', alpha=0.5)
ax2.text(55, 52, 't₅₀', fontsize=10, color='gray')

plt.tight_layout()
plt.show()

# Calculate t50 for each catalyst
print("\nTime to 50% Conversion (t₅₀):")
for name, params in catalysts.items():
    solution = odeint(hydrogenation_kinetics, C0, t,
                      args=(params['k'], params['K_H'], params['K_S'], P_H2))
    conversion = (1 - solution[:, 0] / C0[0]) * 100
    t50_idx = np.argmin(np.abs(conversion - 50))
    print(f"  {name}: {t[t50_idx]:.1f} min")

3.5 選択的酸化

部分酸化 vs 完全酸化

選択的酸化は、CO₂への完全燃焼を避けながら有用な化学物質を生成します：

3.6 クロスカップリング反応（2010年ノーベル賞）

主要なクロスカップリング反応

鈴木カップリングのメカニズム

コード例5：クロスカップリング収率最適化

"""
Analyze Suzuki coupling reaction conditions
Demonstrates effect of catalyst loading and temperature
"""
import numpy as np
import matplotlib.pyplot as plt

def suzuki_yield(temp_C, cat_loading_mol_pct, time_h, base_strength=1.0):
    """
    Empirical model for Suzuki coupling yield
    Based on typical reaction behavior
    """
    # Temperature effect (optimal around 80°C)
    temp_factor = np.exp(-((temp_C - 80) / 30)**2)

    # Catalyst loading effect (diminishing returns above 2%)
    cat_factor = 1 - np.exp(-cat_loading_mol_pct / 1.5)

    # Time effect (approaches completion)
    time_factor = 1 - np.exp(-time_h / 4)

    # Base yield around 90% under optimal conditions
    yield_pct = 95 * temp_factor * cat_factor * time_factor * base_strength

    return min(yield_pct, 99)

# Create analysis
fig, axes = plt.subplots(1, 3, figsize=(15, 4))

# 1. Temperature effect
temps = np.linspace(20, 120, 100)
yields_temp = [suzuki_yield(T, 2.0, 12) for T in temps]
axes[0].plot(temps, yields_temp, 'b-', linewidth=2)
axes[0].axvline(x=80, color='green', linestyle='--', alpha=0.7, label='Optimal')
axes[0].set_xlabel('Temperature (°C)', fontsize=11)
axes[0].set_ylabel('Yield (%)', fontsize=11)
axes[0].set_title('Temperature Effect\n(2 mol% Pd, 12h)', fontsize=12, fontweight='bold')
axes[0].legend()
axes[0].grid(alpha=0.3)
axes[0].set_ylim(0, 100)

# 2. Catalyst loading effect
loadings = np.linspace(0.1, 5, 100)
yields_cat = [suzuki_yield(80, L, 12) for L in loadings]
axes[1].plot(loadings, yields_cat, 'r-', linewidth=2)
axes[1].axvline(x=2, color='green', linestyle='--', alpha=0.7, label='Standard')
axes[1].set_xlabel('Catalyst Loading (mol%)', fontsize=11)
axes[1].set_ylabel('Yield (%)', fontsize=11)
axes[1].set_title('Catalyst Loading Effect\n(80°C, 12h)', fontsize=12, fontweight='bold')
axes[1].legend()
axes[1].grid(alpha=0.3)
axes[1].set_ylim(0, 100)

# 3. Time course
times = np.linspace(0, 24, 100)
yields_time = [suzuki_yield(80, 2.0, t) for t in times]
axes[2].plot(times, yields_time, 'g-', linewidth=2)
axes[2].axhline(y=90, color='orange', linestyle='--', alpha=0.7, label='90% target')
axes[2].set_xlabel('Time (hours)', fontsize=11)
axes[2].set_ylabel('Yield (%)', fontsize=11)
axes[2].set_title('Reaction Progress\n(80°C, 2 mol% Pd)', fontsize=12, fontweight='bold')
axes[2].legend()
axes[2].grid(alpha=0.3)
axes[2].set_ylim(0, 100)

plt.tight_layout()
plt.show()

print("\nOptimal Suzuki Coupling Conditions:")
print("• Temperature: 60-100°C (commonly 80°C)")
print("• Catalyst: 1-5 mol% Pd (commonly 2 mol%)")
print("• Base: K₂CO₃, Cs₂CO₃, or KOH")
print("• Solvent: DMF, DME, THF/H₂O, or toluene/H₂O")
print("• Time: 6-24 hours for completion")

3.7 重合触媒

チーグラー・ナッタ触媒（1963年ノーベル賞）

チーグラー・ナッタ触媒は立体規則性ポリマーの製造を可能にし、プラスチック産業に革命をもたらしました：

• 発見：カール・チーグラー（ポリエチレン）、ジュリオ・ナッタ（ポリプロピレン）
• 触媒：TiCl₄ + AlR₃（またはMgCl₂担持TiCl₄）
• 生成物：HDPE、イソタクチックPP、LLDPE
• 生産量：年間1億5,000万トン以上

メタロセン触媒

メタロセン触媒は、精密な制御でポリマーを製造する単一サイト触媒です：

• 構造：Cp₂MX₂（Cp = シクロペンタジエニル、M = Ti、Zr、Hf）
• 利点：狭い分子量分布、制御されたタクチシティ
• 活性化剤：MAO（メチルアルミノキサン）またはボレート

3.8 三元触媒コンバーター

自動車排ガス制御

三元触媒（TWC）は3つの汚染物質を同時に変換します：

1. CO酸化：2CO + O₂ → 2CO₂
2. HC酸化：CₓHᵧ + O₂ → CO₂ + H₂O
3. NOₓ還元：2NOₓ + 2CO → N₂ + 2CO₂

コード例6：TWCライトオフ挙動

"""
Model three-way catalyst light-off behavior
Shows conversion vs temperature for CO, HC, and NOx
"""
import numpy as np
import matplotlib.pyplot as plt

def twc_conversion(T, T50, steepness=0.1):
    """Sigmoid conversion profile for TWC"""
    return 100 / (1 + np.exp(-steepness * (T - T50)))

# Temperature range
T = np.linspace(100, 500, 200)

# Light-off temperatures (T50) for each pollutant
T50_CO = 200
T50_HC = 250
T50_NOx = 280

# Calculate conversions
conv_CO = twc_conversion(T, T50_CO, 0.08)
conv_HC = twc_conversion(T, T50_HC, 0.06)
conv_NOx = twc_conversion(T, T50_NOx, 0.05)

# Create plot
fig, ax = plt.subplots(figsize=(10, 6))

ax.plot(T, conv_CO, 'b-', linewidth=2.5, label='CO')
ax.plot(T, conv_HC, 'g-', linewidth=2.5, label='HC')
ax.plot(T, conv_NOx, 'r-', linewidth=2.5, label='NOₓ')

ax.axhline(y=90, color='gray', linestyle='--', alpha=0.5, label='90% target')
ax.axvspan(150, 300, alpha=0.1, color='orange', label='Light-off region')

ax.set_xlabel('Temperature (°C)', fontsize=12)
ax.set_ylabel('Conversion (%)', fontsize=12)
ax.set_title('Three-Way Catalyst Light-off Curves', fontsize=14, fontweight='bold')
ax.legend(fontsize=10, loc='lower right')
ax.grid(alpha=0.3)
ax.set_xlim(100, 500)
ax.set_ylim(0, 105)

# Add T50 annotations
ax.annotate(f'T₅₀(CO)={T50_CO}°C', xy=(T50_CO, 50), xytext=(T50_CO-50, 30),
            fontsize=9, arrowprops=dict(arrowstyle='->', color='blue'))
ax.annotate(f'T₅₀(HC)={T50_HC}°C', xy=(T50_HC, 50), xytext=(T50_HC+30, 30),
            fontsize=9, arrowprops=dict(arrowstyle='->', color='green'))

plt.tight_layout()
plt.show()

print("\nThree-Way Catalyst Specifications:")
print("• Catalyst: Pt/Pd/Rh on CeO₂-ZrO₂/Al₂O₃")
print("• Precious metal loading: 30-100 g/ft³")
print("• Operating temperature: 300-900°C")
print("• Conversion efficiency: >95% after light-off")
print("• Air/fuel ratio: λ = 1 (stoichiometric)")

3.9 章のまとめ

演習

演習1：ハーバー・ボッシュ最適化

450°C、200 atmでの平衡NH₃収率を計算しなさい。圧力を400 atmに上げるとどうなりますか？

演習2：FT生成物解析

α = 0.85の場合、C1-C4、C5-C11、C12-C20、C21+の各生成物の重量分率を計算しなさい。

演習3：反応設計

ブロモベンゼンとフェニルボロン酸からビフェニルを合成する鈴木カップリング反応を設計しなさい。触媒、塩基、溶媒、条件を指定すること。

演習4：TWC解析

三元触媒が効率的に機能するために、空燃比を正確に制御（λ ≈ 1）しなければならないのはなぜですか？

次の章

第4章：キャラクタリゼーションと分析では、BET比表面積、化学吸着、分光法（XPS、FTIR）、顕微鏡法（TEM、SEM）、およびオペランド技術を用いた触媒特性の分析方法を学びます。