Make Simulation a Part of Your Workflow
As with all chemical processes, you can study many of the effects of your electrodeposition processes at different scales, depending on your purpose. On the microscale level, this could mean investigating the electrochemical kinetics of the participating reactions and the influence of different levelers or striking conditions on the kinetics of electrodeposition. At the counter electrodes, a careful selection of electrocatalyst and electrode micro structure may be required, especially for electrowinning where you need to minimize losses. Simulating these processes and comparing them to experiments or data from your process will allow you to understand the charge transfer reaction mechanism at the electrode surfaces, and derive the electrochemical kinetics parameters, like the exchange current densities and the charge transfer coefficients for each reaction. By knowing these mechanisms and parameters, you can simulate the rate and distribution of deposition or etching at a larger scale. Simultaneously, you will be accounting for the operating conditions of the system, such as cell and electrode geometry, cell voltage or imposed current, masking and shielding, electrolyte composition and flow, gas evolution, and temperature.
The standardized COMSOL Desktop® user interface, which is the basis for the Electrodeposition Module, is also used for all the other add-on products in the COMSOL Product Suite. This enables you to couple the physics describing your electrodeposition or etching process to other modules, such as the Heat Transfer Module for studying thermal effects, or the CFD Module for understanding the effects of two-phase flow. Moreover, other physical characteristics, like structural integrity for example, can be modeled sharing the same model files that you used to model your electrochemical cell. This unified modeling platform is the perfect tool for collaborating with engineers working on the same process across different fields.
Easy-to-use Tools for Modeling Electrodeposition and Electroplating cells
The Electrodeposition Module comes with a number of easy-to-use tools for many of the characteristics associated with electrodeposition and electroplating cells. These include the following:
Electrochemical Reaction Kinetics
You can define electrochemical charge transfer reactions where the kinetics expressions can be arbitrary functions of the modeled variables. Examples of these include chemical species concentration, local electrode and electrolyte potential at the electrode-electrolyte interface, and temperature. In the Secondary and Tertiary Current Distribution interfaces, you can also enter parameters for the electrode kinetics, such as exchange current density, anodic and cathodic charge transfer coefficients, stoichiometry, and equilibrium potential for the electrode reactions in your system. Predefined expressions are also available for Butler-Volmer and Tafel expressions. Moreover, you may add several competing reactions on a single electrode surface, for instance add hydrogen evolution at the plating electrode. In the case of tertiary current distribution, you can couple the electrode reactions to the local concentration of the electroactive species in the electrode kinetics expressions by using the variables for the concentration. Concentration overpotential may also be estimated by using Nernst equations for the contribution of the concentration overpotential.
Interfaces for modeling laminar and porous media flow are also available in the Electrodeposition Module, through Navier-Stokes, Darcy's Law, and the Brinkman equations. Turbulent and two-phase flow may be considered by coupling appropriate physics interfaces from the CFD Module to your simulations.
The Electrodeposition Module is further equipped with support for including the effects of geometric changes to the electrochemical process by modeling moving boundaries as the deposited layer grows in thickness at the cathode. Receding or growing surfaces can significantly affect the operation of your cell, and the Electrodeposition Module dynamically considers these changes as part of your simulation. In addition, for the cases where the deposited metal layer or anode thickness variations are small, you can also select a physics interface that keeps track of the plated layer thickness, and how this may influence ohmic effects in the electrode, without actually changing the geometry. Instead, a variable for the thickness is introduced that also affects the local electrical conductance of the electrode. The changes in thickness of the electrode can be automatically calculated from the electrode kinetic expressions by defining the stoichiometry coefficients, the molar mass, and the density of the deposited or consumed metal for the electrode reactions.
Current Balances in the Electrolyte and Electrodes
The descriptions of ion transport in the electrolyte and the electron conduction in the electrodes, in combination with the conservation of current and charge, form the backbone of the Electrodeposition Module. In the Primary and Secondary Current Distribution interfaces, ion transport in the electrolyte is assumed to take place through migration of ions, neglecting the influence of diffusion. This is useful when mixing in the electrolyte is good enough to nearly eliminate concentration gradients. Secondary current distribution formulations may also be used when you only have concentration gradients close to the electrode surface, by using analytical expressions for the concentration variations across the boundary layer at the electrode surface. In the Tertiary Current Distribution interfaces, the transport of ions in the electrolyte is described using diffusion, convection, and migration (Nernst-Planck equations). The current density is automatically evaluated by the module through adding all contributions from the transport of ions to the current density. Thus, the current density is described by diffusion and migration of ions, which is required when substantial concentration variations are present in the electrolyte. The current balance in the electrodes is fully coupled to the current balance in the electrolyte at the electrode surfaces through the electrode reaction kinetics. Ohm's law describes the conduction of current in the electrodes. The Electrodeposition Module also contains an interface for modeling current transfer through thin metallic structures or shells, for example to model the strike in the beginning of the plating process. This allows you to model thin electrodeposited layers on non-conductive structures together with current balances in the electrolyte accounting for ohmic losses in the electrodes.
The Electrodeposition Module models the transport of chemical species through diffusion, convection, and migration in dilute and concentrated solutions. The module includes a predefined Nernst-Planck Equations interface, but migration is also added by the module to the Chemical Species Transport interfaces in dilute and concentrated solution, as well as in porous media.
Convection, conduction, and Joule heating can all be modeled when you have the Electrodeposition Module, which contains a specific physics interface for heat transfer through porous media. The module adds contributions from electrochemical processes to the heat balance. For example, it adds the losses due to activation overpotential as heat sources at the electrode boundaries.
- Primary, Secondary, and Tertiary Current Distribution interfaces for current balances in the electrolyte
- Formulations for electroneutrality, supporting electrolyte, or Poisson equation for the charge balance equations
- Nernst-Planck equations in dilute and concentrated solutions
- Nernst-Einstein equation for relating mobility and diffusivity in electrolytes
- Ohm's law and conservation of current in the electrodes
- Nernst equation for equilibrium potential and concentration overpotential
- Automatically coupled stoichiometry and Faraday's law for automatic coupling of material and current balances to electrode reactions
- Electrode kinetics accounting for activation and concentration overpotential
- Electrocatalysis for counter electrodes, for example oxygen evolution
- Butler-Volmer and Tafel equations for predefined kinetics
- Electrode thickness variable at electrode surfaces that affects local conductance for small changes in electrode geometry during deposition
- Nernst-Planck-Poisson Equations
- Electrophoretic Transport
- Current distribution based on the boundary element method
- Moving boundaries for deposited layers on electrodes and electrochemical etching for large changes in electrode geometry
- Joule heating due to ohmic losses in the electrodes and in the electrolyte
- Heating due to activation losses
- Throwing power estimates
- Wagner Number estimates
- Bipolar effect estimation in metal cells
- Chrome plating
- Electrodeposition for mining applications
- Electrodeposition for PCB manufacturing
- Flush layer plating
- Functional electroplating
- Hull cells
- Striking methods
- Surface finishing
- Wear resistance coatings
- Electrochemical manufacturing
- Electrochemical polishing
- Electrochemical machining
- Shielding and masking
Copper Deposition in a Trench
This model demonstrates the use of moving meshes in the application of copper electrodeposition on circuit boards. In these environments, the presence of cavities or 'trenches' are apparent. The model makes use of the Tertiary, Nernst-Planck interface for electrodeposition to keep track of the deformation of the mesh. Furthermore, ...
Tutorial model of electroplating. The model uses secondary current distribution with full Butler-Volmer kinetics for both anode and cathode. The thickness of the deposited layer at the cathode is computed as well as the pattern caused by dissolution of the anode surface.
Electrodeposition of a Microconnector Bump in 2D
This model demonstrates the impact of convection and diffusion on the transport-limited electrodeposition of a copper microconnector bump (metal post). Microconnector bumps are used in various types of electronic applications for interconnecting components, for instance liquid crystal displays (LCDs) and driver chips. The location of the bumps ...
Rotating Cylinder Hull Cell
Rotating cylinder Hull cells are an important experimental tool in electroplating and electrodeposition and are used for the measurement of nonuniform current distribution, mass transport, and throwing power of plating baths. The model reproduces the results for a commercially available cell (RotaHull(R)) as published in paper . In particular, ...
Secondary Current Distribution in a Zinc Electrowinning Cell
This is a model of the secondary current distribution in a zinc electrowinning cell. The model investigates the impact on the current distribution when changing the electrode alignment in a parametric study. The geometry is in 2D.
Cyclic Voltammetry at a Macroelectrode in 1D
The purpose of the app is to demonstrate and simulate the use of cyclic voltammetry. You can vary the bulk concentration of both species, transport properties, kinetic parameters, as well as the cycling voltage window and scan rate. Cyclic voltammetry is a common analytical technique for investigating electrochemical systems. In this method, the ...
Electrochemical Impedance Spectroscopy
The purpose of this app is to understand EIS, Nyquist, and Bode plots. The app lets you vary the bulk concentration, diffusion coefficient, exchange current density, double layer capacitance, and the maximum and minimum frequency. Electrochemical impedance spectroscopy (EIS) is a common technique in electroanalysis used to study the harmonic ...
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