The Electrode Reaction subnode defines the electrode kinetics for a charge transfer reaction that occurs on an electrolyte-electrode interface boundary. Use multiple nodes to model multiple reactions, for instance in mixed potential problems.

The parent node may be either an Internal Electrode Surface or an Electrode Surface.

The Equilibrium potential, Eeq (SI unit: V), is used in the electrode kinetics expressions in the Electrode Kinetics section (via the definition of the overpotential), or for setting up primary current distribution potential constraints.

The equilibrium potential may be defined either in the Materials node (From material), by using the Nernst Equation, or by using a User defined expression.

If the Nernst Equation is used, the concentration dependence is calculated automatically based on the Reference equilibrium potential Eeq, ref (V).

For all interfaces except the Tertiary Current Distribution interface, the concentration dependence is based on the user-defined Reduced species expression CR (unitless) and Oxidized species expression CO (unitless) parameters. CR and CO should be defined so that the quotient between them is 1 for the reference state (for which Eeq=Eeq, ref).

In the Tertiary Current Distribution interface, the concentration dependence of the Nernst Equation is based entirely on the settings in the Stoichiometric Coefficients and the Reference Concentrations sections.

When using Nernst Equation, additional options are available in the Butler-Volmer expression type in the Electrode Kinetics section.

This section is only available in the Tertiary Current Distribution interface, if the equilibrium potential has been selected to be defined by the Nernst Equation.

The reference concentrations define the reference state for which Eeq = Eeq, ref.

The settings of this section will define the local current density, iloc (SI unit: A/m2), at the interface between the electrolyte and the electrode. Note that iloc for all built-in kinetics expression types will depend on the overpotential, which in turn depend on the Equilibrium potential defined in the previous section.

The Local current density expression, iloc, expr (SI unit: A/m2), may be defined either in the Materials node (From material), by using the From kinetics expression, or by using a User defined expression.

For all kinetic expressions the Exchange current density i0 (SI unit: A/m2) is a measure of the kinetic activity. The exchange current density is typically concentration dependent.

Most kinetic expression types feature the Limiting Current Density option in order to impose an upper limit on the local current density magnitude. The feature can be used to model additional mass transport limitations that are not already included in the local current density expression. For Limiting Current Density enter a value for ilim (SI unit: A/m2).

In the Tertiary Current Distribution interface, the Linearize concentration dependence for low concentrations option is used to set a Concentration linearization limit clim (SI unit: mol/m3) for linearizing the concentration dependence of kinetics for low concentrations, in order to improve convergence for non-unit stoichiometries. Note that this option is available for Nernst Equation equilibrium potential and Butler-Volmer kinetics with either Mass action law or Lumped multistep selected as the exchange current density type.

The Butler-Volmer kinetics expression is the most common way to define electrochemical kinetics. The Linearized Butler-Volmer is valid when the overpotentials of the reactions are small (<<25 mV). The linearized version can also be used to troubleshoot a model with convergence problems.

When using the Nernst Equation for defining the equilibrium potential (see above), the concentration dependence of the Exchange current density i0 may be defined in a thermodynamically consistent way in accordance with the Nernst equation, in combination with a Reference exchange current density i0,ref (A/m2), which is the exchange current density when Eeq=Eeq, ref.

For all interfaces except the Tertiary Current Distribution interface, the concentration dependence when using From Nernst Equation will use CR and CO as pre-exponential factors for the anodic and cathodic terms, respectively. In the Tertiary Current Distribution interface, the Lumped multistep option can be used to define i0 by the use of either Generic exponentials, or Anodic or Cathodic reaction orders. The Mass action law will define the reaction orders according to the reaction stoichiometry and the law of mass action.

The Anodic transfer coefficient, αa (dimensionless), and Cathodic transfer coefficient, αc (dimensionless), parameters will impact how much iloc will change upon changes in the overpotential. In order to ensure thermodynamic consistency, αc cannot be user defined when i0 is calculated From Nernst Equation (or by Mass action law in the Tertiary Current Distribution interface). For this case, αc is defined automatically, based on the and the number of participating electrons in the reaction, defined in the stoichiometry section.

The Anodic Tafel slope, Αa (SI unit: V), defines the required increase in overpotential to result in a tenfold increase in the current density.

The Cathodic Tafel slope, Αc (SI unit: V), describes the required decrease in overpotential to result in a tenfold increase in the current density magnitude. Αc should be a negative value.

This expression type is not available if Nernst equation has been selected in the Equilibrium Potential section.

Note that the combination of Nernst equation and the Butler Volmer kinetics type will in most cases render identical kinetics as for the Concentration Dependent Kinetics. It is recommended to always use Nernst Equation + Butler Volmer whenever possible, since this combination is guaranteed to be thermodynamically consistent.

The Concentration Dependent Kinetics expression type may be used in concentration dependent (tertiary) current distribution problems. One or both of the Oxidizing species expression CO (dimensionless) and Reducing species expression CR (dimensionless) parameters may be concentration dependent, and should typically be defined so that CO = CR at equilibrium.

The node will set the Rate limiting species concentration to zero at the boundary, and balance the fluxes of the species participating in the reaction and the current densities according to the Stoichiometric Coefficients settings.

Specify the Number of participating electrons nm in the electrode reaction and the Stoichiometric coefficient (vc1, vc2, and so forth) for each of the involved species according to the following generic electrochemical reaction:

Set νi as positive (νred) for the reduced species and negative (νox) for the oxidized species in an electrochemical reaction. The number of participating electrons, n, should be positive.

The Heat of Reaction section provides two options: Temperature derivative and Thermoneutral voltage to calculate the reversible heat source of the electrode reaction, which in turn can be used for coupling to heat transfer physics.

The Temperature derivative of equilibrium potential parameter, dEeq/dT (SI unit: V/K), can be specified in case of Temperature derivative selection. Note that dEeq/dT parameter value has no impact on the equilibrium potential variable.

The Thermoneutral voltage parameter, Etherm (SI unit: V), can be specified in case of Thermoneutral voltage selection.