COMSOL Simulation of the Storage Life of Zinc-silver Reserve Battery

We deduced the reaction kinetic equation of negative electrode zinc and oxygen at room temperature, and the solid-state reaction kinetics of AgO and silver, established the corresponding COMSOL model, verified and simulated the storage and discharge model, and predicted that the storage life of zinc-silver reserve battery is about 18-20 years.


Introduction
Storage life is an important indicator of a zinc-silver reserve battery.During storage, the zinc-silver reserve battery will have the following phenomena such as capacity decline, activation time delay, and voltage drop 1 .Therefore, prolonging the storage life of zinc-silver reserve batteries has become one of the key research.
During the storage of the zinc-silver reserve battery, the following reactions mainly occur inside the battery [2][3] .
AgO Ag O O   ( 2 ) 2 Zn+O ZnO  ( 3 ) The first reaction represents the solid-state reaction of AgO and silver since the resistivity of the product Ag 2 O is much higher than that of AgO.This reaction will seriously affect the voltage of the battery and increase the ohmic internal resistance of the electrode.The second reaction represents the decomposition of AgO at the positive electrode, and the oxygen generated by the decomposition will react with the zinc, resulting in a decrease in battery life.The third reaction represents the reaction between zinc and oxygen, and a passivation film is formed on the surface of the zinc, which will also cause a decrease in the storage life of the battery.Studying the kinetics of the above reactions is one of the directions to prolong the storage life of the zinc-silver reserve battery.Some researchers have studied the decomposition kinetics of AgO [4][5][6] , but the oxidation kinetics of zinc, the solid-state reaction kinetic equation, and parameter values have not been studied yet, and no researchers have used simulations to simulate the storage of zinc-silver reserve battery.Given the above problems, this paper mainly studies the reactions that affect the storage life of zinc-silver reserve batteries, deduces the kinetic equations, uses COMSOL software to establish models, uses literature data to verify the correctness of the models, and finally uses the models to deduce the storage life of the zincsilver reserve battery.

Kinetic equations
There are relatively few studies on the oxidation kinetic of zinc at room temperature, and they are concentrated in the high-temperature area because zinc oxide is an N-type semiconductor, which can be used as a protective material to prevent the corrosion of internal materials.The oxidation kinetic is generally a logarithmic equation.This paper starts from the relationship between the metal and the gas to form the corresponding oxide and uses the particle radius of the reactant and the product to derive the chemical reaction rate equation of zinc as: where c Zn 0 is the initial zinc concentration; α Zn is the reaction rate of zinc; k Zn 0 is the reaction coefficient 7 , which is converted to the three-dimensional structure; k Zn 0 is about 4.51×10 -10 min -1 .For the reaction aA g +bB s →cAB s , considering that the reaction cross-sectional area changes with the progress of the reaction, the reaction kinetic equation of the solid particle solid-state reaction is derived according to the steady-state diffusion and Fick's law: where C Ag 0 is the concentration of silver; ρ Ag 2 O is the density of Ag 2 O; R Ag is the radius of silver particles, with an average of 5~30 um; D A is the diffusion coefficient of Ag + in Ag 2 O 8 , which is about 1.2×10 -13 cm 2 /s.For the solid-state reaction on the current collector, like the solid-state reaction in the positive electrode, the current collector is generally a silver wire current collector.It is assumed as a cylinder, and the kinetic equation of the solid-state reaction on the current collector is derived as: where C AgO 0 represents the concentration of AgO on the surface of the current collector; R 0 is the radius of the silver wire; L is the length of the current collector in the positive electrode.

Model
A three-dimensional model of zinc-silver reserve battery was established, and the physical field interface of "the transport of diluted species in porous media interface" of COMSOL software was used to simulate the storage process, and the physical field of "the battery with binary electrolyte interface" was used to simulate the discharge of the battery.The discharge voltage of the battery and the capacity predicts the storage life of the zinc-silver reserve battery.
The physics field of "the transport of diluted species in porous media interface" obeys the following fundamental equation: The first three items correspond to the accumulation of substances in the liquid phase, solid phase, and gas phase respectively, in which represent the amount of the substance adsorbed on the solid surface, is the concentration of substance i in the gas phase, and respectively represent the volume fraction of the transported substance in the porous medium and the gas phase, and is the concentration of substance i.The fourth term describes the convective transfer caused by the velocity field u. describes the mass diffusion flux vector of the substance due to mechanical mixing or diffusion and volatilization into the gas phase for porous media.The first item on the right side of the equation describes the material reaction rate caused by the chemical reaction or desorption phenomenon in the porous medium.The second item represents other input items such as additional material inputs.
The physics field of "the battery with binary electrolyte interface" uses the Butler-Volmer equation and the Nernst equation to describe the electrode reaction kinetics, and uses the Bruggeman equation to correct the effective electrolyte conductivity and electrode effective conductivity [9][10] .The model parameter input summary is shown in Table 1 and Table 2 Exchange current density i (A/cm 2 ) 2×10 -6 Ref. 9

Result & discussion
We verify the correctness of the simulation model.Compared the simulation results with the actual storage data, as shown in Figure 1 (b) and (c), the AgO decomposition kinetics and the oxidation kinetic equations of zinc are compared with the AgO decomposition rate.The change of the oxidation rate of zinc with storage time is in good agreement.The maximum deviation of the AgO decomposition rate is 11.16% when the storage time is 8.3 years, and the decomposition rate is 13.8%.The maximum deviation of the oxidation rate of zinc is also at the storage time of 13 years, the oxidation rate of zinc is 10.8%, and the deviation is 6.82% currently.All the deviations come from the calculation deviation of the model precision, the systematic deviation of the model, and the deviation of data iteration by COSMOL software, etc.Within the allowable range of deviation, the zinc-silver reserve battery model and the physical field of "the transport of diluted species in porous media interface" can simulate the storage process of the zinc-silver reserve battery.As shown in Figure 1 (d)~(i), with the increase in storage time, the decomposition rate of AgO in the positive electrode is significantly higher than that of zinc.A relatively dense zinc oxide film is formed on the surface, which will hinder further oxidation reaction, so the reaction rate gradually decreases.However, the self-decomposition reaction of AgO and the positive active material have no such limitation.At the same time, the positive active material is the oxide of the noble metal silver, and the amount of the negative active material is more than that of the positive active material.In summary, the decrease in the zinc-silver reserve battery is mainly caused by the reduction of the positive active material.This conclusion can be verified by simulating the discharge of a zinc-silver battery.
The simulation of the discharge process of a zinc-silver reserve battery is conducted.Firstly, we verify the correctness of the discharge model, as shown in Figures 2 (a) and (b), and simulate the discharge of batteries under different discharge current densities (50 mA/cm 2 , 100 mA/cm 2 ), two of which the voltage deviations under the discharge current density are 5.44% and 7.75%.As the constant current discharge proceeds, the discharge voltage of the simulation drops more slowly.Because the simulation model is ideal, the discharge of the actual battery may be affected by other factors, resulting in a greater voltage drop.Within the allowable range of deviation, the electrode discharge kinetic model of the zinc-silver reserve battery has a good fit with the experimental data.It can be considered that the physical field of "the battery with binary electrolyte interface" can simulate the discharge process of the zinc-silver reserve battery.   2 (d) and (e), before and after 17 years of storage, the battery voltage drops about 0.7 V, and the ohmic internal resistance of the battery after the storage is about 0.26 Ω.From Figure 2 (f), the battery capacity drops rapidly at the initial time of storage, because the reaction rate of AgO inside the battery is fast, and then the decomposition rate slows down, and the battery capacity drops slowly.When the battery capacity drops by 20%, it is considered that the battery can no longer be used.The zinc-silver reserve battery can be stored for 18-20 years at most.

Conclusion
Zinc and oxygen at room temperature, as well as the solid-state reaction kinetics of AgO and silver, were deduced , the established COSMOL simulation model and discharge model were verified, and the kinetic equation was applied to the storage model of the zinc-silver reserve battery.The battery storage and discharge processes were simulated, and the storage life of the zinc-silver reserve battery is about 18-20 years according to the simulations.

Figure 1 .
Figure 1.The simulation of storage.(a): 3D model of zinc-silver battery with current collector; (b) and (c): Comparison of simulation and experimental data; (d), (e), and (f): The molar distribution of AgO with storage time (0 a, 10 a, and 17 a); (g), (h), and (i): The molar distribution of zinc with storage time (0 a, 10 a, and 17 a).

Figure 2 .
Figure 2. Discharge simulation of zinc-silver battery.(a): 3D model of battery; (b): Comparison of simulation and experiment; (c): 3D model of storage and discharge; (d): The discharge voltage of the battery at a current density of 50 mA/cm 2 before and after storage; (e): Ohmic resistance of the battery after 17 years of storage; (f): Changes of battery capacity and SOH.

Figure 2 (
Figure 2 (c)~(f) shows the changes in battery discharge voltage, ohmic internal resistance, and battery capacity before and after 17 years of battery pack storage.It can be obtained from Figures 2(d) and (e), before and after 17 years of storage, the battery voltage drops about 0.7 V, and the ohmic internal resistance of the battery after the storage is about 0.26 Ω.From Figure2(f), the battery capacity drops rapidly at the initial time of storage, because the reaction rate of AgO inside the battery is fast, and then the decomposition rate slows down, and the battery capacity drops slowly.When the battery capacity drops by 20%, it is considered that the battery can no longer be used.The zinc-silver reserve battery can be stored for 18-20 years at most.