6.2 Langmuir-Hinshelwood and Eley-Rideal Mechanisms

Surface reactions are key to understanding catalysis. Langmuir-Hinshelwood and Eley-Rideal mechanisms explain how molecules interact on surfaces to form products. These models help us predict reaction rates and design better catalysts.

Understanding these mechanisms is crucial for optimizing industrial processes. By knowing how reactants adsorb and react on surfaces, we can improve catalysts for cleaner energy, more efficient chemical production, and environmental remediation.

Langmuir-Hinshelwood vs Eley-Rideal Mechanisms

Key Principles and Surface Coverage

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• Langmuir-Hinshelwood mechanism
  • Adsorption of both reactants onto the surface
  • Reaction on the surface
  • Desorption of products
• Eley-Rideal mechanism
  • Direct reaction between an adsorbed reactant and a gas-phase reactant
  • Desorption of the product
• Surface coverage and fraction of available active sites determine reaction rates in both mechanisms
• Rate-limiting step in Langmuir-Hinshelwood mechanism can be surface reaction or product desorption (depending on the system)
• Rate-limiting step in Eley-Rideal mechanism is typically the direct reaction between adsorbed and gas-phase reactants

Roles and Implications

• Surface coverage plays a crucial role in determining reaction rates
  • Higher surface coverage leads to increased probability of reactant interaction and reaction
  • Limited surface coverage can hinder reaction progress
• Fraction of available active sites affects reaction kinetics
  • More active sites allow for higher reaction rates (catalyst optimization)
  • Deactivation of active sites can slow down the reaction (catalyst poisoning)
• Rate-limiting step determines the overall reaction rate
  • Identifies the slowest step in the reaction mechanism
  • Optimizing the rate-limiting step can enhance overall reaction efficiency (catalyst design)

Rate Equations for Surface Reactions

Derivation and Steady-State Approximation

• Derivation of rate equations involves applying steady-state approximation and rate-limiting step concept
• Langmuir-Hinshelwood mechanism rate equation
  • Depends on surface coverages of adsorbed reactants
  • Depends on rate constant of the surface reaction
• Eley-Rideal mechanism rate equation
  • Proportional to surface coverage of adsorbed reactant
  • Proportional to partial pressure or concentration of gas-phase reactant
• Langmuir adsorption isotherm expresses surface coverages in terms of reactant partial pressures or concentrations

Simplification and Assumptions

• Rate equations can be simplified based on assumptions
  • Rate-limiting step assumption (slowest step determines overall rate)
  • Relative magnitudes of adsorption and desorption rate constants
• Common simplifications
  • Quasi-equilibrium assumption (fast adsorption/desorption compared to surface reaction)
  • Irreversible surface reaction assumption (negligible reverse reaction rate)
• Simplified rate equations provide insights into reaction kinetics and mechanism
  • Dependence on reactant concentrations or partial pressures
  • Apparent reaction orders and rate constants

Determining Dominant Reaction Mechanisms

Experimental Data Analysis

• Reaction rates, surface coverages, and activation energies help distinguish between mechanisms
• Reaction rate dependence on reactant pressures or concentrations provides insights
  • Langmuir-Hinshelwood: non-linear dependence due to surface site saturation
  • Eley-Rideal: linear dependence on gas-phase reactant pressure
• Surface coverage measurements
  • Langmuir-Hinshelwood: coverage of both reactants important
  • Eley-Rideal: coverage of adsorbed reactant crucial
• Activation energy measurements
  • Eley-Rideal generally has lower activation energy than Langmuir-Hinshelwood

Kinetic Modeling and Fitting

• Kinetic modeling helps validate proposed reaction mechanisms
  • Fit experimental data to rate equations derived from mechanisms
  • Estimate kinetic parameters (rate constants, activation energies)
• Goodness of fit and statistical analysis assess the validity of the model
  • Residual analysis and error minimization
  • Comparison of different mechanistic models (model discrimination)
• Sensitivity analysis identifies the most influential parameters on reaction kinetics
  • Guides further experimental design and mechanism refinement

Limitations of Mechanistic Models

Assumptions and Simplifications

• Langmuir-Hinshelwood and Eley-Rideal models make several assumptions
  • Homogeneous surface with identical active sites (not always true in real systems)
  • Neglect surface reconstructions, adsorbate-adsorbate interactions, multiple active site types
  • Single rate-limiting step assumption (may not hold in complex reaction networks)
  • Overlook the role of surface defects, step edges, or other structural features
• Simplified models may not capture the full complexity of real catalytic systems
  • Actual mechanism may involve a combination of Langmuir-Hinshelwood and Eley-Rideal steps
  • More sophisticated models may be required for accurate kinetic description

Extension and Refinement

• Incorporation of surface heterogeneity and site-specific reactivity
  • Dual-site models (different types of active sites with distinct reactivities)
  • Microkinetic modeling (elementary step-based approach)
• Consideration of adsorbate-adsorbate interactions and lateral effects
  • Inclusion of coverage-dependent activation energies and pre-exponential factors
  • Mean-field approximation or kinetic Monte Carlo simulations
• Integration of computational methods (density functional theory, molecular dynamics) for mechanistic insights
  • Prediction of adsorption energies, activation barriers, and reaction pathways
  • Elucidation of the role of surface structure and composition on reactivity