Parasitic Reactions in an Electrochemical Capacitor

This model demonstrates how to set up side reactions in an electrochemical supercapacitor using the Tertiary Current Distribution, Nernst–Planck (tcd) interface.

The 1D isothermal model includes the following processes:

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Electronic current conduction in the electrodes

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Ionic charge transport in the porous electrodes and separator

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Double layer capacitance in the porous electrodes

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Side reactions involving hydrogen evolution reaction (HER) and oxygen evolution reaction (OER) for an aqueous electrolyte

The model is based on the theoretical framework of Newman (Ref. 1) and White (Ref. 2). In the model presented, the effect of the parasitic reactions in an aqueous electrolyte-based supercapacitor on the performance during charge discharge behavior is studied.

See also the Electrochemical Capacitor with Porous Electrodes tutorial for an introduction to electrochemical capacitor modeling using the Tertiary Current Distribution interface.

Model Definition

This example models the electrochemical capacitor cross section in 1D, which implies that edge effects in the length and height of the capacitor cell are neglected. The example uses the following domains:

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Two porous electrode (right and left): 50 μm

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Separator (flooded with electrolyte): 25 μm

Domain Conditions

The model solves for the potentials in the electrode and aqueous electrolyte phases, in combination with four concentration dependent variables for the cation, the anion and the dissolved concentrations of hydrogen and oxygen.

Due to the aqueous electrolyte, proton and hydroxide transport are also included in the model. Using two algebraic equations: electroneutrality and the water-autoprotolysis to be in equilibrium, the proton and hydroxide concentrations do not need to be solved for as dependent variables.

The electric potential in the electron conducting phase,

, is calculated using a charge balance based on Ohm’s law. The migrative and diffusive charge and species transport in the electrolyte is modeled using the Nernst–Planck equations.

The double layer charging is defined as a source term in the porous electrodes based on the time derivative of the potential jump over the double layer according to

(1)

where av,dl (m2/m3) is the active specific surface area for double layer charging, and Cdl is the double layer capacitance (F/m2).

Due to the aqueous electrolyte, oxygen and hydrogen may start evolving in the electrodes. In the positive porous electrode, oxygen evolution, or reduction, occurs according to

(2)

In the negative porous electrode, hydrogen evolution, or oxidation, occurs according to

(3)

The porous electrode reactions are modeled using concentration-dependent Butler–Volmer reactions.

Boundary Conditions

For the electronic current balance, a potential of 0 V is set on the left electrode’s current collector/feeder boundary.

At the right electrode current collector/feeder, an event-based charge-discharge condition is used. First the capacitor is charged at 100 A until a voltage of 2 V is reached, then the capacitor rests for 1 h, followed by a discharge at 100 A until a voltage of 0.5 V is reached. The cycle is then repeated.

At the separator-negative electrode boundary, it is assumed that the electrode potential is so low that oxygen, produced at the positive electrode and diffusing over the separator, will be immediately reduced at this point. Similarly, at the separator-positive electrode boundary, it is assumed that any hydrogen reaching this point will be immediately reduced.

The above conditions are modeled by setting the respective hydrogen or oxygen concentration to 0 at the electrode-separator boundaries, and by adding the corresponding electrode current density (based on the species flux and Faraday’s law) to the charge balance equations. This is achieved using an Internal Electrode Surface boundary node.

Results and Discussion

Figure 1 shows the current-voltage response versus time for a 5000 simulation. Each charge pulse is followed by a 1 h during which the voltage relaxes due to the parasitic oxygen reduction and hydrogen oxidation at the electrode-separator boundaries.

Figure 1: Voltage and current profiles for the capacitor.

Figure 2 shows the maximum activities (the concentration divided by the respective solubility limit) in the cell for the oxygen and hydrogen species versus time. The activities increase during the charge pulses, and relax linearly vs time during the rest period.

Figure 2: Maximum cell activity for O2 and H2 vs. time.

Figure 3, finally, shows oxygen and hydrogen concentrations in the cell at the end of a charge period. The maximum values are found at the separator-current collector boundaries.