Electrode Surface
Use the Electrode Surface node to model an electrochemical electrode-electrolyte interface between an electrolyte domain and an electrode boundary where the electrode is not included explicitly as a domain in the model geometry. Set the electric potential of the electrode or specify a current condition that the potential of the electrode shall fulfill, and use subnodes to specify the Electrode Reaction and the Double-Layer Capacitance at the interface.
This node can only be applied on outer boundaries to electrolyte domains. For interior boundaries between electrolyte and electrode domains, use the Internal Electrode Surface node. For interior boundaries to electrolyte domains, use the Perforated Electrode Surface node.
Dissolving-Depositing Species
Use the settings of this section to define species that participate in dissolution-deposition electrode reactions, for instance metal deposition/dissolution or oxide formation.
Use the Add () and Delete () buttons as needed in the table to control the number of species.
The Density and Molar mass, in conjunction with the reaction rates and stoichiometry, defined in the Electrode Reaction subnodes, determine the normal electrode growth rate. The growth rate can be used in conjunction with the Deforming Electrode Surface and Nondeforming Boundary multiphysics couplings to model geometry deformations.
When the Solve for species concentrations variables check box is checked, dependent variables for the molar surface concentration of the dissolving-depositing species are added. These can be used to model the thickness of a dissolving/depositing layer in a time-dependent simulation where the resulting deformation in the model geometry is small and will have negligible impact on the current distribution. In stationary studies, the molar surface concentration variables will be defined but not solved for by default.
When solving for the species concentration variables, corresponding thickness variables are defined that you for instance can use to couple to the Film Resistance (see below).
Deposition-Dissolution Rates, Growth Velocities, and Thicknesses on an Electrode Surface
Species Conservation on Deforming Geometry
In Deforming Geometry simulations, the Compensate for Boundary Stretching adds a tangential convection term, based on the movement of the mesh, to the mass balance equations of the dissolving-depositing species surface concentrations.
Adsorbing-Desorbing Species
Use the settings of this section to define species that may adsorb or desorb on the electrode surface during charge transfer, or nonfaradaic, reactions.
The Density of sites parameter will be used to set up the local surface mass balance equations for the fractional surface coverages.
Use the Add () and Delete () buttons as needed in the table to control the number of species. The name of each adsorbing-desorbing Species may be edited in the first column of the table. Use a Site occupancy number larger than unity for species that occupy more than one site at the electrode surface.
According to the settings of the table, the fractional surface coverage variable names will be defined according to xxx.theta_yyy_zzz where xxx is the interface name, yyy the tag of the electrode surface node, and zzz the species name. The variable xxx.thetafree_yyy represents the fraction of free surface sites. These variable names may be used when defining kinetics parameters in Electrode Reaction subnodes.
Use The Surface Reactions Interface to model surface diffusion.
Film Resistance
Use a film resistance if you want to include an additional potential drop due to an ohmic resistance at the interface between the electrode and the electrolyte, for instance due to build-up of insulating deposits.
Specify either a Surface resistance Rfilm (SI unit: Ω·m2) directly or choose the Thickness and conductivity option to calculate the surface resistivity based on a depositing film thickness.
Harmonic Perturbation
Use this section in conjunction with AC Impedance study types to control the perturbation amplitude in the frequency domain.
The perturbation parameter is either Electric potential, Electrode potential, Total current, or Average current density, based on the Boundary condition selected in the next section.
The frequency spectrum is specified in the study node.
Electrode phase potential Condition
This section specifies the potential in the electrode phase of the electrolyte-electrode interface. The electrode potential is used (via the overpotential) by the Electrode Reaction subnodes.
Use the Electric potential option to set the value of the potential explicitly with respect to ground whereas the Electrode potential will set the potential value with respect to a reference potential. Total current, Average current density, and External short all add an extra global degree of freedom for the potential in the electrode phase, set to comply with the chosen condition.
When using the Total current option in 1D or 2D, the boundary area is based either on the Cross-sectional area (1D), or the Out-of-Plane thickness (2D) properties, set on the physics interface top node.
See also the documentation for the Electrode Potential and External Short nodes for further information about these boundary condition.
Cyclic Voltammetry
The Cyclic voltammetry setting varies the electric potential linearly in time as follows when used in conjunction with a Cyclic Voltammetry study step:
Figure 3-1: Electric potential vs time generated by the cyclic voltammogram boundary condition. The linear sweep rate is 100 mV/s, the number of cycles is 2. Potentials levels are also shown.
More advanced waveforms can be obtained using the Electric potential option with a parameter setting based on Functions found in the Definitions menu.
Counter Electrode (Electroanalysis Only)
This boundary condition is only available for the Electroanalysis charge conservation model in the Tertiary Current Distribution, Nernst-Planck (tcd) interface.
The Counter electrode option will set a potential to ensure an overall charge balance of the cell so that the integral of all electrode reaction currents of all electrode surface node sums up to zero.
See also Counter Electrodes and Overall Charge Balance
Advanced Cyclic Voltammetry Settings
To display this section, click the Show More Options button () and select Advanced Physics Options in the Show More Options dialog box.
If Cyclic voltammetry is selected as the Boundary condition, the check boxes Add events at vertex potentials in cyclic voltammetry and Smoothing of cyclic voltammetry wave functions are both selected by default.
When Smoothing of cyclic voltammetry wave functions is enabled, smoothing is applied on the triangular wave around the vertex potentials. The Smoothing factor defaults to 1·10-3. The smoothing zone corresponds to the product of the smoothing factor with half the duration of one period of the triangular wave.
When Add events at vertex potentials in cyclic voltammetry is enabled, solver events are added at the vertex potentials for the cyclic voltammogram. When the vertex potentials are reached, these events cause the solver to stop, reinitialize some variables, and then continue. This typically improves solver convergence. In addition, by forcing the time-dependent solver to resolve the time steps when the vertex potentials are reached, the solution accuracy is improved, especially if the solver is set to output solutions before and after events.
Equilibrium Potential Handling (Primary Condition)
This setting only has an effect if there are multiple Electrode Reaction subnodes present and if either a Current Distribution Initialization study step (using a Primary Current distribution type) or the Primary Current Distribution interface is used.
The setting determines which equilibrium potential value will be used for defining the primary current distribution constraint. When the First reaction has been selected, the first electrode reaction subnode must be active in the model.
To display this section, click the Show More Options button () and select Advanced Physics Options in the Show More Options dialog box.
Constraint Settings
For primary current distributions, the use of weak constraints will in some cases give a more accurate value of the local current density during the solver process. This may in turn render more accurate results when coupling to the local current density variable to describe other phenomena in the model, for instance when modeling geometry deformation due to electrode dissolution/deposition.
The section is available in the Primary Current Distribution and Secondary Current Distribution interfaces when the Current Distribution Model property has been set to Primary.
This section is only available in the Primary Current Distribution and Secondary Current Distribution interfaces when the Current Distribution Model property has been set to Primary. To display this section, click the Show More Options button () and select Advanced Physics Options in the Show More Options dialog box.
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Electrode Reactions Theory
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Film Resistance