Electrode Reaction
The Electrode Reaction node defines the electrode kinetics for a charge transfer reaction that occurs on an electrolyte-electrode interface boundary.
The node can be added as a subnode to an Electrode Surface node. Add multiple nodes to the same Electrode Surface node to model multiple reactions, for instance in mixed potential problems.
Stoichiometric Coefficients
Specify the Stoichiometric coefficient (vc1, vc2, and so forth) for each of the involved species according to the following generic electrochemical reaction:
(3-2)
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, is computed using the sum of all reacting species charges and accounting for the sign convention of the stoichiometric coefficients:
(3-3)
An easy way to determine the stoichiometric coefficients for a reaction is to write the reaction as a reduction reaction (with the electrons on the left), irrespectively on the expected actual direction of the reaction in the model. The species on the left side then have negative coefficients and the species on the right have positive coefficients.
Equilibrium Potential
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 can 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).
When using Nernst Equation, additional options are available in the Butler–Volmer expression type in the Electrode Kinetics section.
Reference Concentrations
This section is only available, 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
Electrode Kinetics
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), can 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).
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 nonunit stoichiometries. Note that this option is available for Nernst Equation equilibrium potential and Butler–Volmer kinetics with Mass action law.
Butler–Volmer or Linearized Butler–Volmer
The Butler–Volmer kinetics expression is the most common way to define electrochemical kinetics. The Linearized Butler–Volmer option 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 can 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.
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 by Mass action law. For this case, αc is defined automatically, based on the number of participating electrons in the reaction, defined in the stoichiometry section.
Anodic Tafel Equation
This kinetics expression type neglects the cathodic (negative) term in the Butler–Volmer equation. It is only valid for electrode reactions with high anodic overpotentials (>>100 mV).
The Anodic Tafel slope, Αa (SI unit: V), defines the required increase in overpotential to result in a tenfold increase in the current density.
Cathodic Tafel Equation
This kinetics expression type neglects the anodic (positive) term in the Butler–Volmer equation. It is only valid for electrode reactions with significant cathodic overpotentials (<<-100 mV).
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.
Heat of Reaction
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 the case when Temperature derivative is selected. Note that the 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.