How to calculate a Tafel slope and exchange current density
The Tafel slope describes how quickly the reaction rate rises with overpotential, and the exchange current density tells you the rate at equilibrium. Both come from a straight-line fit on the right part of a polarization curve. The method is simple, and most errors come from the data you feed it.
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Step by step
Start from a steady, well-defined polarization curve
Use potential and current data recorded slowly enough that the cell is near steady state at each point. Convert current to current density by dividing by the electrode area.
Correct for iR drop first
Remove the ohmic drop, which is the current density multiplied by the area-specific ohmic (high-frequency) resistance: add it back to the measured voltage for a fuel cell, subtract it for an electrolyzer. Without this the curve bends at higher current and the slope comes out too large. See the guide on high-frequency resistance for how to measure that resistance.
Convert to overpotential
Overpotential is the iR-corrected potential minus the equilibrium (or reference) potential for the reaction, taken with the sign that makes it positive for the process you study.
Plot overpotential against log10 of current density
Put log10 of current density (not the natural log) on the x-axis and overpotential on the y-axis. In the kinetic region the points fall on a straight line.
Fit only the kinetic (activation) region
Choose the range where the plot is linear. Exclude the lowest currents, where background or crossover currents distort the data, and the highest currents, where mass transport and residual resistance bend the curve. Fit a straight line over that range.
Read the slope and the exchange current density
The slope of overpotential against log10(j) is the Tafel slope, usually quoted in mV per decade. Extrapolate the fitted line back to zero overpotential: the current density there is the exchange current density, j0.
Doing it in Vizalyze
Vizalyze has a function called Tafel slope and exchange current density. It fits log10 of current density against potential over a range you choose, reports the slope in mV per decade and the extrapolated j0, and returns the data with the fitted line so you can check it by eye.
Because j0 is read where the x-axis variable is zero, give the function an iR-corrected overpotential channel if you want a meaningful exchange current density. The function is part of the Scientific & Simulation and Lab & Instruments packs, and the 14-day trial includes every feature and format with no credit card needed.
To look at a curve first, the free online polarization curve analyzer at /tools/polarization-curve-analyzer needs no installation.
Common pitfalls
Fitting into the mass transport region: at high current the curve bends away from the line. Include those points and the slope is inflated.
Not correcting for iR: uncorrected data bends upward at high current, which looks like a larger Tafel slope than the true kinetics.
A fit range that is too narrow: a range of much less than a decade makes the slope very sensitive to noise. Aim for the widest range that is still clearly linear, and report the range you used.
Wrong log base: Tafel slopes are defined with log10. A fit on ln(j) gives a number that is about 2.3 times smaller, so state which you used.
Extrapolating j0 from a short line: the exchange current density is an extrapolation across a long gap, so small slope errors turn into large j0 errors. Treat it as an estimate and compare it only between measurements analysed the same way.
Frequently asked questions
What units does a Tafel slope have?
Usually millivolts per decade of current density, written mV/dec.
How do I get the exchange current density from a Tafel plot?
Extend the fitted straight line to zero overpotential. The current density at that point is j0. This needs the x-axis to be overpotential, not raw potential.
Should I use natural log or log10?
Use log10 for the conventional mV per decade. If you fit with the natural log, convert before comparing with published values.
Do I always have to iR-correct?
For reliable kinetics, yes, unless the ohmic drop is negligible over your fit range. Report whether your data were corrected.