COMSOL 6.4 - 1D Isothermal Zinc–Silver Oxide Battery

Zinc–Silver oxide (Zn–AgO) batteries are used in different industries due to their high capacity per unit weight. Additionally, they have superior performance characteristics that include long operating life and low self-discharge (long shelf life). Larger size Zn–AgO batteries are used in applications where these performance characteristics are critical, such as in submarine, missile, and aerospace applications. Smaller size button cells are well suited for miniature power sources such as hearing aids, electronic watches and other low power devices. Mathematical models can be very useful for studying the performance of Zn–AgO batteries and for providing insights toward cell design.

In this example, discharge of a Zn–AgO battery (Ref. 1) is simulated using the Battery with Binary Electrolyte interface. The electrochemical reactions in the positive and negative electrodes lead to changes in porosity and species concentration in the electrodes. In this example, model analysis is done to relate the drop in cell voltage at the end of discharge to the concentration of species in the electrode, thereby indicating the limiting electrode in the cell.

Model Definition

A 1D isothermal cell model for Zn–AgO battery is used. The positive electrode is composed of a mixture of AgO and Ag2O, supported by a silver substrate. The negative electrode consists of Zn powder paste on a copper or silver substrate. The substrates act as current collectors. A separator material is used between the electrodes and the unit cell is filled with a solution of concentrated potassium hydroxide (KOH).

Figure 1 shows the 1D model geometry. It consists of three domains, the positive porous electrode, the separator, and the negative porous electrode.

Figure 1: 1D model geometry of a Zn-AgO unit cell.

Electrochemical reactions

During charge and discharge, several electrochemical reactions occur in the porous electrodes. In the positive electrode, the following reactions are considered:

(1)

(2)

The reaction considered in the negative electrode is as follows:

(3)

The kinetic expressions for the electrode reactions are as follows (the subscripts 1, 2, and 3 refer to the above three reactions respectively),

(4)

(5)

(6)

where iloc is the local current density, i0 is the exchange current density, η is the overpotential, αa is the anodic transfer coefficient, and αc is the cathodic transfer coefficient, respectively, of the three electrochemical reactions. ci is the concentration of species i and n is the number of electrons transferred.

The overpotential η for each reaction is calculated from the electric potential (ϕs), the electrolyte potential (ϕl), and the equilibrium potential of the respective reaction (Eeq), as follows:

(7)

Physics setup

The Battery with Binary Electrolyte interface describes the following processes:

•

Electronic current conduction in the porous electrodes

•

Ionic charge transport in the electrolyte present in the porous electrodes and separator

•

Material transport in the electrolyte present in the porous electrodes and separator

•

Electrochemical reaction kinetics in the porous electrodes

Nonintercalating particles, equilibrium potentials calculated using the Nernst equation, and concentration-dependent exchange current densities in the Butler–Volmer electrode kinetics, are used in the Battery with Binary Electrolyte interface. In the porous electrodes and the separator, the Bruggeman correction is used for the effective electrolyte salt diffusivity. The effective electrolyte conductivity is calculated from the following expression:

(8)

where εe is the porosity (of either the porous electrodes or the separator), cl is the electrolyte salt concentration (cOH-), and Di is the diffusion coefficient of species i.

The effective electrical conductivity in the porous electrodes is given as

(9)

where σs,k and mk are the electrical conductivity and the mass fraction, respectively, of species k in the solid phase of the porous electrodes.

The expressions for change in concentration of species (Ag2O, AgO, and Ag) in the positive electrode are

(10)

(11)

(12)

where a is the active specific surface area of the electrode.

(13)

(14)

The reactants and products of the electrochemical reactions in the porous electrodes have different densities, thereby leading to porosity changes in the electrodes. The porosity change in the positive electrode is given by

(15)

where c0,i, MWi, and ρi are the initial concentration, molecular weight, and density of species i, respectively.

(16)

The Dissolving–Depositing Species section of the Porous Electrode node is used for modeling the changes in concentration of species and porosity of the porous electrodes.

Boundary conditions

The negative electrode current collector boundary is set to a potential of 0 V (electric ground condition). At the positive electrode current collector boundary, a discharge current density pulse, as shown in Figure 2, is applied.

Figure 2: The applied discharge current density as a function of time.

A parametric study is done with two initial concentrations of Zn in the negative electrode, to demonstrate the limiting electrode in the cell for each case. The study includes a stop condition with a minimum voltage of 1.25 V.

Results and Discussion

Figure 3 shows the cell voltage profiles for the two initial concentration values of Zn, for the applied discharge current density pulse. The voltage profiles indicate that for the high value of the initial Zn concentration, the cell lasts for a longer time before reaching the minimum cell voltage.

Figure 3: Cell voltage profiles for the applied discharge current density pulse, for the two initial concentration of Zn.

Figure 4 and Figure 5 show the variation of the species concentration in the electrodes during the applied discharge current density pulse, for the low value of the initial Zn concentration. Figure 4 shows the variation of concentration of Ag and AgO with time, across the thickness of the positive electrode. Similarly, Figure 5 shows the variation of concentration of Zn and ZnO with time, across the thickness of the negative electrode. For the low value of the initial Zn concentration in the negative electrode, it can be seen that the concentration of Zn drops close to 0 at the separator/negative electrode edge, at the end of discharge. So, the sharp drop in the cell voltage toward the end of discharge is due to limitation of the negative electrode.

Figure 4: Variation of species concentration in the positive electrode, for the low value of initial concentration of Zn.

Figure 5: Variation of species concentration in the negative electrode, for the low value of initial concentration of Zn.

Figure 6 and Figure 7 similarly show the variation of the species concentration in the electrodes, for the high value of the initial Zn concentration. Figure 6 shows the variation of concentration of Ag and AgO with time, and Figure 7 shows the variation of concentration of Zn and ZnO with time, across the thickness of the positive and negative electrodes, respectively. For the high value of the initial Zn concentration in the negative electrode, it can be seen that the concentration of AgO drops close to 0 at the positive electrode/separator edge, at the end of discharge. In this case, the sharp drop in the cell voltage toward the end of discharge is due to limitation of the positive electrode.