Lecture on Butler-Volmer Equation in Electrochemical Kinetics

Introduction to Butler-Volmer Equation

• Central equation of electrochemical kinetics.
• Approach relates to experimental chemical kinetics.
• Quantified mathematically; important parameters obtained from experiments.

Electrochemical Reactions and Potential

• Two scenarios: changing potential
  • Anodic direction: Oxygen evolution.
  • Cathodic direction: Hydrogen evolution.
• Measure rate of evolution via current.
• Direction of current changes with potential.
• Region with negligible/no current exists.
• Analogy to chemical kinetics
  • Variable: temperature vs. electrochemical potential.
  • Rate increases exponentially with potential (similar to temperature in chemical kinetics).

Electrode Potential and Overpotential

• Overpotential: Applied potential above the equilibrium potential.
• Exponential change in rates with increasing overpotential.
• Experimental observation across various electrochemical systems.

Approaches to Butler-Volmer Equation

• Phenomenological Chemical Kinetics Approach
  • Quantifiable but requires experimental parameters.
• Potential Energy Surface Approach
  • Greater mechanistic insight but less clear.

Single Electron Transfer Reaction

• Simplified case for analysis.
• Reduced species loses an electron (oxidized species in metal/electrolyte).
• Example systems: ionic species with single electron transfer.

Modeling Challenges

• Chemical kinetics often non-equilibrium systems.
• Theories for equilibrium (chemical/statistical thermodynamics) are well developed.
• Non-equilibrium systems:
  • Rates in non-equilibrium are less understood.
  • Continuum theories (macroscopic) vs. molecular systems.
• Transition from equilibrium to non-equilibrium description.

Deriving Butler-Volmer Equation

• Net Reaction: Forward rate - Backward rate. -Empirical observation: Rate function of potential, exhibiting linear or exponential dependence.
• Use equilibrium principles to model non-equilibrium.
• Forward and backward reaction rates
  • Proportional to species’ concentrations.
  • Associated rate constants vary with potential.

Nernst Equation & Null Potential

• Null Potential: No net reaction rate.
• Nernst equation describes equilibrium potential.
• Chemical Potentials: Equilibrium condition linked to chemical potential of species.
• General form applicable for any concentration.

Formal and Standard Potentials

• Formal Potential: Null potential at 1M concentration of species.
• Standard potential refers to activities.
• Exchange current density: Reference point for rates.

Symmetry Factors

• Alpha and 1-Alpha: Symmetry factors / charge transfer coefficients.
• Experimentally measurable.

Current-Potential Relationship

• Adapt forward/backward reaction rates into current expression.
• Results in Butler-Volmer Equation.
• Segregation of variables for analysis.
  • Blue: Control (E) & measured (I) variables.
  • Green: Surface concentrations (often experimentally inaccessible).
  • Red: Constants specific to experimental setup.

Rewriting Butler-Volmer Equation

• Utilize activity of electrons as a chemical species.
• Similar to chemical kinetics expressions.

Summary and Connection to Arrhenius Equation

• Need for Butler-Volmer due to non-equilibrium nature of electrochemical reactions.
• Approach parallels chemical kinetics (activity of electrons analogous to chemical species).
• Utilized Nernst equation.
• Derived expression analogous to Arrhenius equation.

Next Steps

• Further discussions on Butler-Volmer equation and its connections to Arrhenius equation in subsequent lectures.
• Explore different approaches to the Butler-Volmer equation in future sessions.

Thank you!