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The Tafel Equation Calculator determines the activation overpotential for an electrochemical reaction using the empirical Tafel equation, one of the most important relationships in electrode kinetics. Developed by Julius Tafel in 1905, this equation describes the logarithmic relationship between current density and overpotential at an electrode. The Tafel equation is the high-overpotential limit of the more general Butler-Volmer equation and applies when the overpotential exceeds about 50–100 mV. This calculator computes the overpotential from the Tafel slope (b), exchange current density (i₀), and the actual current density (i). It also extracts the transfer coefficient (α) — a key kinetic parameter. Tafel analysis is fundamental in corrosion science, fuel cell R&D, electrocatalysis, and battery research.
The Tafel equation relates overpotential to current density:
$$\eta = a + b \cdot \log_{10}\left(\frac{i}{i_0}\right)$$
where a is the Tafel constant (equals b × log(i₀) in some formulations), b is the Tafel slope (V/decade), i is the current density, and i₀ is the exchange current density. In its most common form:
$$\eta = b \cdot \log_{10}\left(\frac{i}{i_0}\right)$$
The Tafel slope is related to the transfer coefficient by:
$$b = \frac{2.303 \cdot RT}{\alpha F}$$
Therefore the transfer coefficient can be extracted from the slope:
$$\alpha = \frac{2.303 \cdot RT}{bF}$$
At 25°C, b = 0.1183/α V/decade. For a single-electron transfer with α = 0.5, b ≈ 0.118 V/decade (≈120 mV/decade). A Tafel slope of 60 mV/decade suggests α ≈ 1, potentially indicating a 2-electron process with α = 0.5 per electron.
The Tafel slope reveals the reaction mechanism. A slope of ~120 mV/decade at 25°C indicates a single-electron rate-determining step with α ≈ 0.5. A slope of ~60 mV/decade suggests either a two-electron transfer or a chemical step following a fast electron transfer. The exchange current density indicates inherent reaction speed — higher i₀ means lower overpotential for a given current. A Tafel plot (η vs. log i) should show a linear region; deviations at low η indicate proximity to equilibrium (Butler-Volmer regime) and at high η indicate mass transport limitations.
Inputs
Results
η = 0.030 × log₁₀(0.01/0.001) = 0.030 × 1 = 30 mV. The low Tafel slope (30 mV/decade) on Pt suggests a fast multi-step mechanism. α ≈ 2 indicates the Volmer-Tafel mechanism with chemical recombination as the rate-determining step.
Inputs
Results
η = 0.120 × log₁₀(0.01/10⁻⁶) = 0.120 × 4 = 480 mV. The 120 mV/decade slope with α ≈ 0.5 indicates a single-electron rate-determining step. The very low i₀ shows OER is kinetically sluggish, requiring large overpotential.
The Tafel equation (η = b × log(i/i₀)) is an empirical relationship between overpotential and current density at an electrode. It applies at sufficiently high overpotentials where the reverse reaction is negligible, typically |η| > 50–100 mV.
The Tafel slope (b, in V/decade or mV/decade) is the change in overpotential per tenfold increase in current density. It depends on the transfer coefficient and temperature: b = 2.303RT/(αF). At 25°C with α = 0.5, b ≈ 118 mV/decade.
The exchange current density (i₀) is the equal forward and reverse current density at equilibrium (η = 0). It reflects the intrinsic rate of the electrode reaction. Higher i₀ means faster kinetics and lower overpotential for a given net current.
The transfer coefficient (α) characterizes the symmetry of the activation energy barrier for the electron transfer step. For a symmetric barrier, α = 0.5. Values typically range from 0.3 to 0.7 for elementary steps. α is extracted from the Tafel slope.
Plot overpotential (η) on the y-axis vs. log₁₀(i) on the x-axis. The linear region (Tafel region) gives the slope b and the x-intercept gives log(i₀). The plot is obtained from potentiodynamic or steady-state current-voltage measurements.
At low overpotentials (|η| < 50 mV), both forward and reverse reactions are significant, and the full Butler-Volmer equation is needed. At very high overpotentials, mass transport limitations cause deviation from linearity on the Tafel plot.
The Butler-Volmer equation i = i₀[exp(αFη/RT) − exp(−(1−α)Fη/RT)] is the complete kinetic expression valid at all overpotentials. The Tafel equation is its high-η approximation where one exponential term dominates.
Tafel extrapolation of anodic and cathodic polarization curves gives the corrosion potential (E_corr) and corrosion current density (i_corr). From i_corr, the corrosion rate in mm/year can be calculated using Faraday's law.
At 25°C, b = 40 mV/decade gives α = 118/40 ≈ 1.5. This can indicate a mechanism where the rate-determining step involves a species formed by a preceding fast electron transfer, effectively increasing the apparent transfer coefficient.
A better electrocatalyst shifts the Tafel line to the right (higher i₀, lower η for the same current) and/or changes the slope (different mechanism with lower b). The ideal catalyst has both high i₀ and low Tafel slope.
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