Electrode Kinetics

Butler-Volmer equation

The Butler-Volmer equation describes the current density j at an electrode as a function of overpotential η = E − E_eq (the departure from equilibrium potential). It captures both the anodic (oxidation) and cathodic (reduction) partial currents.

j = j₀[exp(αFη/RT) − exp(−(1−α)Fη/RT)]

where j₀ is the exchange current density (rate of both forward and reverse reactions at equilibrium), α is the charge transfer coefficient (typically ≈0.5 for simple one-electron transfers), F is Faraday’s constant (96485 C/mol), R is the gas constant, and T is temperature.

Tafel regions

At high |η| (>∼100 mV), one exponential term dominates and log|j| vs η becomes linear (Tafel line). The slope is the Tafel slope b = RT/(αF) for the anodic branch or RT/((1-α)F) for cathodic. Extrapolating both Tafel lines back to η = 0 gives log j₀.

Cyclic voltammetry

In cyclic voltammetry (CV), the potential is swept linearly between two limits at a constant scan rate v (mV/s). The current response as a function of potential reveals oxidation peaks (anodic scan) and reduction peaks (cathodic scan). Peak current i_p = 0.4463 nFAC(nFvD/RT)^½ (Randles-Sevcik equation) scales with √v, confirming diffusion-limited reaction. The peak splitting ΔE_p = 59/n mV at 25°C for an electrochemically reversible couple.

Applications

• Hydrogen evolution and oxygen reduction in electrolyzers and fuel cells
• Corrosion rate measurement (Stern-Geary equation from j₀ and b)
• Battery charge-discharge kinetics and rate capability
• Biosensor design (enzyme electrochemistry, glucose sensors)