Double Layer Capacitance
The Tafel and Butler–Volmer expressions can be used to calculate the magnitude of the current due to electrolysis: this is called faradaic current. However, the electrode-electrolyte interface may also draw capacitive current due to the attraction or repulsion of ions creating an oppositely charged layer of ions to form in solution close to the electrode.
The layer of charge on the electrode and layer of opposite charge in the adjacent electrolyte is called the double layer and can be thought of as behaving like a parallel plate capacitor, since the absolute amount of charge it separates varies with the charge density on the electrode, and hence with its voltage. The physics of double layer structure and formation are highly complex and are not yet well understood. One of the simplest empirical methods to account for the observed influence of capacitance on polarization curves is to introduce a constant ideal capacitance across the electrode-electrolyte interface.
This effect can be added to via the Double Layer Capacitance condition. The capacitor stores a surface charge density Q = Cd(ϕs − ϕl), and contributes a dynamic charging current density (nonfaradaic current) equal to iNF = dQ/dt. The total current recorded in a real experiment equals:
Sometimes in electroanalysis a blank scan with no electrolysis is run to subtract nonfaradaic current. If double layer capacitance is ignored in your model, you should make sure that you are comparing it to experimental data recorded under the same conditions.
The ability of COMSOL Multiphysics to model electrostatics and transport of charged species make it tempting to incorporate the double layer explicitly to add more detail to a model. These coupled equations are always extremely nonlinear and convergence is not trivial except in the simplest cases. Although the diffuse double layer can be modeled in isolation (see example), this is not recommended in conjunction with a fuller electrochemical model.
Double-Layer Capacitance