The Electrodeposition Module Physics Interfaces
The module has a number of physics interfaces, which describe different phenomena in the electrolyte and at the electrodes in electrodeposition cells. A number of examples exemplify the use of these physics interfaces, which are based on the conservation of current, charge, chemical species, and energy. Figure 2 shows the available physics interfaces in the Electrochemistry branch as displayed in the Model Wizard for a 3D model.
Figure 2: The 3D physics interfaces for the Electrodeposition Module, as shown in the Model Wizard, with the Electrochemistry branch fully expanded.
The Current Distribution Interfaces
The Electrochemistry interfaces include the Primary Current Distribution (), Secondary Current Distribution (), and Tertiary Current Distribution, Nernst Planck () interfaces. These are generic physics interfaces that can be used to model most kinds of electrochemical cells.
These interfaces include functionality to model the current distribution in the electrolyte as well as the deposition and thickness evolution of thin layers on the electrode surfaces. However, if the thickness of the deposited layer is of the same order of magnitude (or one order lower) compared to the geometrical details of the electrodes, then one of the Electrodeposition, Deformed Geometry () interfaces may have to be used instead. These interfaces are described in the next section.
The Primary Current Distribution () interface assumes a perfectly mixed electrolyte and neglects the activation losses for the charge transfer reactions. It should only be used for fast kinetics, where the activation losses are substantially smaller than the ohmic losses. The assumption of a perfectly mixed electrolyte implies that the electrolyte conductivity is not affected by the magnitude of the currents.
In the Secondary Current Distribution () interface the activation overpotential for the electrochemical reactions is taken into account.
The Primary and Secondary Current Distribution interfaces may be combined with a Chemical Species Transport interface (described below) in order to incorporate kinetic effects of active species in the electrolyte or adsorbed species on an electrode surface.
The Current Distribution, Boundary Elements () interface can be used for solving primary and secondary current distribution problems on geometries based on edge (beam or wire) and surface elements. The interface uses a boundary element method (BEM) formulation to solve for the charge transfer equation in an electrolyte of constant conductivity, where the electrodes are specified on boundaries or as tubes with a given radius around the edges. You typically use this interface in order to reduce the meshing and solution time for large geometries where a significant part of the geometry can be approximated as tubes along edges.
The Tertiary Current Distribution, Nernst-Planck () interface accounts for the transport of species through diffusion, migration, and convection. It is therefore able to describe the effects of variations in domain composition on the electrochemical processes. The kinetic expressions for the electrochemical reactions account for both activation and concentration overpotential.
The Aqueous Electrolyte Transport () interface computes the potential and species concentration fields in a dilute aqueous electrolyte. The interface targets modeling of aqueous electrolytes featuring weak acids, weak bases, ampholytes, and generic complex species. This includes, but is not limited to, electrochemical systems and phenomena containing multiple homogeneous reactions coupled to electrode kinetics. The transport is defined by the Nernst-Planck equations in combination with electroneutrality and water autoprotolysis.
The Concentrated Electrolyte Transport interface () is a generic interface for defining electrolyte transport. The electrolyte transport model is based on concentrated solution theory and can be applied to any type of electrochemical cell for an arbitrary number of electrolyte species. In contrast to the Tertiary Current Distribution, Nernst-Planck interfaces, the Concentrated Electrolyte Transport interface does not assume the presence of a neutral solvent, or a supporting electrolyte, of constant concentration.
The Electrodeposition, Deformed Geometry Interfaces
The Electrodeposition, Deformed Geometry () interfaces combine primary, secondary, and tertiary current distributions with a Deformed Geometry interface to keep track of the geometrical changes caused by deposition or dissolution reactions on an electrode surface. The interfaces are exemplified in Figure 3. However, in the case where the thickness of the deposited layer at the surface of the cathode is negligible for the current distribution in the cell, a generic current distribution interface may also be used, as described in the previous section.
Figure 3: An example figure from the Copper Deposition in a Trench tutorial. The solid line shows the original shape of the cathode surface and the deformed field shows the shape of the surface after 10 s of deposition. The color table shows the copper ion concentration.
The Electrode Shell Interface
The Electrode, Shell interface () models electric current conduction in the tangential direction on a boundary. The physics interface is suitable to use for thin electrodes where the potential variation in the normal direction to the electrode is negligible. This assumption allows for the thin electrode domain to be replaced by a partial differential equation formulation on the boundary. In this way the problem size can be reduced, and potential problems with mesh anisotropy in the thin layer can be avoided.
The Electroanalysis Interface
The Electroanalysis interface () models mass transport of diluted species in electrolytes using the diffusion-convection equation, solving for electroactive species concentration(s). The physics interface is applicable for electrolyte solutions containing a large quantity of inert “supporting” electrolyte. Ohmic losses are assumed to be negligible. The physics interface includes tailor-made functionality for setting up cyclic voltammetry problems.
The Chemical Species Transport Interfaces
The Surface Reactions interface () found in Chemical Species Transport can be set up to model adsorbed species on an electrode surface.
The Transport of Diluted Species interface () is available under the Chemical Species Transport Branch. In combination with the Secondary Current Distribution interface (), this physics interface can be used to model systems with supporting electrolytes. In these systems, the ions that give the largest contribution to the conduction of current are assumed to be present in uniform concentrations.
The Nernst-Planck-Poisson Equations () interface can be used for investigation of charge and ion distributions within the electrochemical double layer where charge neutrality cannot be assumed. A requisite when using this interface is that the double layer, which typically is in the range of tens nanometers, is fully resolved in the mesh. The equations solved for are identical to the Electrochemistry>Tertiary Current Distribution, Poisson interface.
The Transport of Diluted Species in Porous Media interface () is also available and describes species transport between the fluid, solid, and gas phases in saturated and variably saturated porous media. It applies to one or more species that move primarily within a fluid filling (saturated) or partially filling (unsaturated) the voids in a solid porous medium. The pore space not filled with fluid contains an immobile gas phase. Using these, models including a combination of porous media types can be studied.
The Electrophoretic Transport () interface can be used to investigate the transport of weak acids, bases, and ampholytes in aqueous solvents. The physics interface is typically used to model various electrophoresis modes, such as zone electrophoresis, isotachophoresis, isoelectric focusing, and moving boundary electrophoresis, but is applicable to any aqueous system involving multiple acid-base equilibria.
The Surface Reactions interface () can be used model reactions and translateral transport of surface (adsorbed) species.
The Chemistry interface () can be used to define systems of reacting species, electrode reactions and ordinary chemical reactions. As such, it serves as a reaction kinetics and material property provider to the space dependent transport interfaces, such as the Tertiary Current Distribution, Nernst-Planck interface, or Transport of Diluted Species interface.
Other Physics Interfaces
The Fluid Flow interfaces can be combined with the above interfaces to model free and forced convection in the electrolytic cell.
The Heat Transfer interfaces have ready-made formulations for the contribution of Joule heating, and other electrochemical losses, to the thermal balance in the cell.
The Level Set interface can be used in problems including deforming electrodes, subject to topological changes.
The detailed equations and assumptions that are defined by the physics interfaces are formulated in the Electrodeposition Module User’s Guide and the COMSOL Multiphysics Reference Manual.
Physics Interface Guide by Space Dimension and Study Type
The table lists the physics interfaces available with this module in addition to those included with the COMSOL Multiphysics basic license.
Chemical Species Transport
Reacting Flow
Electrochemistry
Electrodeposition, Deformed Geometry
Fluid Flow
Porous Media and Subsurface Flow
Nonisothermal Flow
Heat Transfer
Mathematics
Moving Interface