Electrochemical polarization

Displacement of electrode or cell voltage from equilibrium under current flow. Kinetic, transport and resistive contributions should be separated.

A kinetic model for the net electrode current near and away from equilibrium. For a single effective reaction with consistent activities and ${\alpha }_a+{\alpha }_c=1$, $j=j_0[\exp ({\alpha }_{a}nF\eta /RT)-\exp (-{\alpha }_{c}nF\eta /RT)]$. Near equilibrium it gives $j\simeq j_{0}nF\eta /(RT)$; at sufficiently large overpotential one exponential gives the Tafel equation. Multistep reactions can require a different kinetic interpretation.

A limiting rate of charge transfer per area imposed by reactant transport or another bottleneck. In a simple diffusion film, $j_L=nFD{c}_b/\delta$ and a consuming electrode has $c_s/c_b=1-j/j_L$. Increasing internal roughness does not necessarily increase external mass-transfer flux proportionately.

The equal magnitudes of the opposing partial electrode-reaction current densities at equilibrium. Their net current is zero. The area convention, activities and temperature must be specified; an exchange current density alone does not specify a nonlinear current-potential curve.

An activation-controlled large-overpotential relation $|\eta |=b{\log }_{10}(|j|/j_0)$. The Tafel slope $b$ uses volts per decade when the logarithm is base ten. Exchange current density and operating current density must use the same area convention.

The change in overpotential per decade of current density in the activation-controlled regime of a Tafel equation. In a single-step Butler-Volmer equation with constant transfer coefficient, the anodic slope is $b_a=RT\ln 10/({\alpha }_{a}nF)$, where $T$ is temperature, $R$ is the molar gas constant, $n$ is the number of transferred electrons and $F$ is the Faraday constant. The magnitude of the cathodic slope is $b_c=RT\ln 10/({\alpha }_{c}nF)$. Inferring one from the other requires the model's relation between the two coefficients; the equality ${\alpha }_a+{\alpha }_c=1$ applies to this effective single-step model and need not describe a multistep reaction.

Additional voltage needed to nucleate or grow a new phase, or overcome a phase-transformation barrier. It can cause an initial voltage dip and voltage hysteresis.

A voltage loss from ionic and electronic resistance, ideally $IR$.

A voltage loss from differences between interfacial and bulk reactant or product activities caused by finite mass transport.

A voltage loss associated with finite charge-transfer reaction kinetics.