Study on Two-Phase Permeation of Oxygen and Electrolyte in Lithium Air Battery Electrode Based on Digital Twin

Abstract

In this paper, the saturation of electrolytes on the mass transfer property of porous electrodes in non-aqueous lithium air batteries has been studied based on digital twin. Herein, we reconstruct the porous cathode based on X-ray micro-computed tomography (μct) and quantitatively analyze the pore size distribution, specific surface area, triple-phase interface area, conductivity and diffusion coefficient of reactants at varying filling degrees of the electrolyte. The results derived from digital twin provide insight into the gas–liquid two-phase mass transfer performance in the porous cathode with various degrees of electrolyte saturation and demonstrate that the optimum electrolyte saturation is 60%.

1. Introduction

The development of advanced energy storage systems plays a crucial role in electric vehicles and renewable energy storage systems [1]. Lithium air batteries are energy conversion devices which show advantages of ultra-high theoretical energy density, low cost, and limited environmental pollution [2,3,4]. Hence, the investigation of lithium air batteries has drawn great attention all over the world in recent years. This novel energy storage device also shows potential application in related military and communication fields [5]. However, the actual performance of lithium air batteries is far from its theoretical calculation, resulting from its fast capacity attenuation during cycling, low cycle numbers, lithium dendrite formation, and the instability of electrolytes [6,7,8]. To solve the above problems, great efforts have been made by researchers to reveal the fundamental mechanism of lithium air batteries.

As the most popular studied lithium air battery, the non-aqueous lithium air battery is composed of a lithium anode, organic electrolytes, a glass fiber membrane, and a porous cathode. One of the crucial components in non-aqueous lithium air batteries, the porous cathode is composed of a gas diffusion layer (GDL) and catalysts loaded on the GDL [9,10]. The porous cathode provides active sites for reaction and space for mass transfer and products agglomeration. Hence, the rational design of porous cathodes plays a crucial role in the performance of lithium air batteries, which require high catalytic activity, high specific area, and reasonable porous structure. As significant parameters of the porous structure, the pore size distribution and porosity determine the transfer performance of reactants and products, which is related with the effective oxygen diffusion coefficient [11,12,13]. Meanwhile, the kinetics of the reaction are also dependent on the specific surface area of the electrode. An electrode with a high specific area is preferred due to the abundant active sites provided. In recent research results, Mn-rich cathodes and porous carbon-based electrode materials for lithium air batteries have been significantly improved [14,15]. Spinel-type transition metal oxides (Zn, Mn, Ni, Mg, etc.) are good candidates for lithium air batteries due to their high theoretical capacity, low price, and environmental friendliness [16,17]. For the mass transfer in a porous cathode, reactants transfer to the surface of the triple-phase interface, where a redox reaction occurs. Therefore, the area of the triple-phase interface, which is related with the distribution of oxygen and electrolytes in the porous electrode, plays a significant role in the performance of lithium air batteries. Hence, it is essential to obtain the actual structure of porous cathodes to analyze the distribution of reactants accurately. Many scholars have studied the properties of porous materials based on μCT. Gao et al. used μCT to scan and reconstruct the GDL and discussed the optimal pitch of the fiber [18]. Subsequently, Ortega-Ramirez et al. checked the soil layer with CT to obtain the cross-sections of materials. They reconstructed the soil layer using GeoDict software and studied the permeability and hydrodynamic coefficient of the soil layer [19]. Soltani et al. used the same method to analyze the sound absorption performance of needled nonwovens [20]. Hui et al. also combined μCT and digital twin methods to study the formation process of the plastic layer in the heating process of coking coal mixture and analyzed the pore size distribution and porosity of the plastic layer [21].

In addition, the electrolyte saturation in a porous cathode is also related to the area of the triple-phase interface [22,23,24]. For electrodes with high saturation, electrolytes drown the electrode and block the channel for oxygen transfer, leading to a small area of the triple-phase interface. Meanwhile, at low saturation, the number of electrolytes is limited, resulting in a small triple-phase interface for reaction. Hence, a reasonable electrolyte saturation is important and has been widely addressed [25,26]. Furthermore, electrolyte saturation also influences the mass transfer property of reactants in lithium air batteries. Esfahanian et al. established a mathematical model to analyze the oxygen transfer in lithium air batteries. They found that the increase in the oxygen diffusion coefficient had a positive impact on the discharge performance of the battery [27]. Zhang et al. confirmed that the filling degree of electrolytes in the positive electrode is related to the oxygen dissolution rate. When the filling degree of electrolytes is low, the oxygen has a longer diffusion distance, leading to a decrease in the oxygen dissolution rate [28]. Xia et al. used carbon materials with high specific surface area as cathode materials and confirmed that the oxygen diffusion in the air cathode was restricted due to the high saturation of electrolytes, resulting in the insufficient utilization of the internal space of the cathode [29]. In addition, the effective conductivity of a cathode is also related to electrolyte saturation. In total, the filling degree of the electrolytes in a porous electrode has a significant role in the area of the triple-phase interface, the mass transfer property of the reactant and the effective conductivity of the porous electrode, resulting in a determining factor of cell performance. Hence, an optimal electrolyte saturation in lithium air battery should be investigated.

In this paper, the filling degree of electrolyte on the performance of lithium air battery using MnO₂ as catalysts was studied. The digital twin method was used to reconstruct the porous electrode based on cross-section images obtained from μCT. All simulations were carried out based on the commercial software of GeoDict. The pore size distribution and porosity of the porous electrode were analyzed. Furthermore, the effective conductivity, the area of the three-phase interface, and the effective diffusion coefficient of oxygen in a porous electrode under varying electrolyte saturations were calculated from the digital twin model. The optimum filling degree of electrolytes in a porous cathode is obtained based on the analysis of simulations and verified by experimental results.

2. Numerical Simulation and Experiment

2.1. Reconstruction of Porous Electrode

μCT offers the capability to non-destructively resolve the 3D structure of porous electrodes. The numerical model of the actual composite electrode comprising of carbon paper as host and manganese dioxide (MnO₂) as catalysts was reconstructed by importing CT images with a voxel of 2 μm. Figure 1 shows the 2D fiber structure obtained from μCT. According to Figure 1, the white parts, which represent carbon fibers in carbon paper, are randomly and densely distributed in the central region of the electrode. On the contrary, the distribution of carbon fibers is loosely distributed at the bottom and upper region of the electrode. It can be speculated that the densely distributed fiber in the central part can provide more active sites for reaction than that at upper and bottom regions since the reaction occurs on the surface of carbon fibers. The obtained 2D images were segmented using a thresholding technique to convert grayscale images to index images. During the reconstruction process, the gray value interval of the pores was set as 0–26.5, and the gray value intervals of carbon fiber and MnO₂ were set as 26.5~105.5 and >105.5, respectively. The reconstructed composite electrode is shown in Figure 2. To save computational time, a Representative Elementary Volume (REV) with the dimensions of 1000 μm × 1000 μm × 300 μm was derived from the reconstructed electrode, as shown in Figure 2.

2.2. Construction of Electrode with Different Electrolyte Saturation

The organic electrolyte was introduced to construct an electrolyte filling model based on the reconstructed composite electrode, as shown in Figure 3. According to the filling degree of the electrolyte in the composite electrode, the electrolyte filling models can be classified into three types, including unfilled, partially filled, and completely filled models. The electrolyte saturations of the different models are 0%, 20%, 40%, 60%, 80%, and 100%, as shown in Figure 4. The models with 0% and 100% saturation correspond to the unfilled and completely filled types, respectively. The physical parameters of the electrolyte, catalysts, and electrodes used in simulation are reported in other literature, and the detailed values are listed in

Table 1. Parameters of catalysts, electrolytes, and electrodes used in this model.

Parameters	Symbol	Value
Conductivity of MnO2	σMnO2	454 S·m−1
Density of MnO2	ρMnO2	5.03 kg·m3
Conductivity of carbon	σcar	30,000 S·m−1 [30]
Density of carbon	ρcar	1800 kg·m3
Conductivity of electrolyte	σele	0.225 S·m−1 [31]
Density of electrolyte	ρele	1009 kg·m3 [32]
Diffusivity of oxygen in electrolyte	DO2	1.6 × 10−7 cm−2·s−1 [33]
Diffusion coefficient of O2 in gas phase	Dsel	1.89 × 10−5 m−2·s−1

.

2.3. Fundamentals of Simulation

PoroDict module was used to determine the porosity and pore size distribution of composite electrodes. This module uses two methods to determine pore size, namely, granulometry and porosimetry [34]. The granulometry method was used in this paper for the calculation of the pore size distribution. A pore radius is determined by fitting spheres into the pore volume. To be more accurate, a point belongs to a pore of a radius larger than r. If a point is inside any sphere of radius r, this point can be fitted into the pore space. However, the through pores, closed pores, closed pores, and blind pores cannot be distinguished based on granulometry.

The effective diffusion coefficient is defined as the diffusion rate in porous media, which is proportional to the diffusion coefficient in open space [35]. The diffusion coefficient of oxygen in porous media is described by Fick’s first law [36,37], as in Equation (1):

$$J=-D\frac{\Delta c}{L}$$

(1)

where J is the diffusion flux (mol·m⁻²·s⁻¹), $\Delta c$ is the concentration difference, $L$ is the diffusion distance, and D is the effective diffusion coefficient. For the diffusion in porous materials, the effective diffusion coefficient is related to the intrinsic diffusion coefficient of reactants and the structure of porous electrode. The effective diffusion coefficient follows Equation (2):

$$D=D_0·\frac{\eta }{\tau }$$

(2)

where D₀ is the intrinsic diffusion coefficient, η is the porosity of porous electrode, and τ is the tortuosity of porous electrode.

In a 3D reconstructed porous structure model, the distribution of concentrations can be solved based on Equation (3) at steady-state conditions:

$$\mathrm{div}\left(D\left(x\right)\nabla c\right)=0$$

(3)

where D(x) is the function of local effective diffusion coefficient, $\nabla$c is the concentration gradient.

For the calculation of O₂ effective diffusion coefficient, only the diffusion coefficient along the Z direction, which is perpendicular to carbon paper, was calculated. To ensure a constant concentration of O₂ at the boundary, a symmetric boundary condition is applied in this paper. The diffusion of a reactant is driven by the concentration gradient. The inlet of O₂ is located at the upside of the electrode, and the outlet of O₂ is set at the bottom of the electrode. The initial concentrations of O₂ at the inlet and outlet are set as 9.69 mol·m⁻³ and 0 mol·m⁻³, respectively. The iterative method was used until the tolerance of effective diffusion rate is smaller than 0.001.

Electrical conductivity σ is calculated based on Ohm’s Law. Ohm’s Law relates the electric potential φ and the magnitude of current density j:

$$j=-\sigma \nabla \varphi$$

(4)

where φ represents the electric potential between two points. The work conducted by the electric field force is EL, where E is the strength of the electric field. When the distance between the two points is small enough, it is approximated by EL = −φ. When L tends to 0, it is denoted as EdL = −dφ; thus: $E=-\mathrm{d}\varphi /\mathrm{d}L=-\nabla \varphi$. The current density can be obtained by the product of electrical conductivity and electric field strength.

The conductivity of the composite electrode along the Z direction was calculated. Considering the accuracy and efficiency of computation, periodic boundary condition was used. To calculate the conductivity of samples, the standard potential of 2.96 V for Li air battery is applied on the boundary of electrode. The tolerance is also set as 0.001, and the iterative method is conducted.

2.4. Experimental Section

To validate the reliability of the simulation results, the performance of a cell with a composite electrode was evaluated in this paper. The influence of electrolyte filling degree on the performance of lithium air batteries was analyzed based on charge–discharge tests.

All reagents used here were analytical grade and used without further purification. Multi-walled carbon nanotubes (MWCNTs) were purchased from Beijing Deke Daojin Science and Technology Co., Ltd. (Beijing, China). Manganese dioxide (MnO₂) as catalyst was purchased from Aladdin Reagent Co., Ltd. (Shanghai, China). N-methyl-2-pyrrolidone (NMP) and Polytetrafluoroethylene (PTFE) were bought from Shenzhen Kejing Zhida Technology Co., Ltd. (Shenzhen, China). Carbon paper (battery level) was purchased from Shanghai Hesen Electric Co., Ltd. (Shanghai, China). Tetraethylene glycol dimethyl ether/bis trifluoromethanesulfonimide lithium salt (TEGDME/LITFSI) was purchased from Shanghai Monils Chemical Co., Ltd. (Shanghai, China). Diaphragm (battery level) was purchased from Tianjin Yongda Chemical Reagent Co., Ltd. (Tianjin, China).

Firstly, 0.45 g of MnO₂, 0.45 g of MWCNTs, and 0.1 g of PTFE were uniformly mixed, then an appropriate amount of NMP was dropped into the mixture. Finally, the mixture was placed in a magnetic stirrer and stirred continuously for 12 h. The obtained mixture in a sticky paste state was uniformly coated on carbon paper. Then, the obtained sample with the coating thickness of 300 μm was transferred to a vacuum drying oven and kept at 80 °C for 8 h. Finally, the carbon paper loaded with catalysts was cut into circular slices with diameters of 16 mm.

Lithium air battery performance tests were carried out based on CR2632 coin cells. Lithium air batteries were assembled in an argon-filled glove box (O₂ < 0.1 ppm and H₂O < 0.1 ppm). The electrolyte used in this paper was 1 M LiTFSI/TEGDME. To investigate the filling degrees of electrolyte on lithium air battery performance, batteries containing different contents of electrolyte were assembled. The battery with 60 µL electrolyte reaches the state of 100% filling degree. Then, 0 µL, 12 µL, 22 µL, 31 µL, 42 µL, and 50 µL of the electrolytes were dropped during the assembling process, corresponding to the filling degrees of 0%, 20%, 40%, 60%, and 80%, respectively. To evaluate the durability of the lithium air batteries, charge–discharge tests were performed at a constant current density of 100 mA·g⁻¹ by LAND test system with cut-off voltage ranging from 2 V to 4.5 V.

3. Results and Discussion

Based on the restructured porous electrode, the porosity and pore size distribution were calculated. In addition, the influence of electrolyte filling degree on effective oxygen diffusion coefficient and effective conductivity in the composite electrode were studied.

3.1. Pore size Distribution

The pore size distribution of the composite electrode is shown in Figure 5a. It is obvious that the inhomogeneous distribution of pore size is found in the composite electrode. The major pore size is in the range of 10–40 μm, which can provide space for mass transfer and product deposition. The morphology of the pores in the 3D reconstructed electrode is shown in Figure 5b. It is qualitatively observed that large pores are distributed on the upper side and underneath of the composite electrode. The average porosity of the integral electrode is 0.792. To further analyze the pore structure, the reconstructed electrode was uniformly divided into five parts along the Z direction. The corresponding porosity of each part was calculated. The porosity of each part along the direction from the bottom toward the upper side is 0.959, 0.731, 0.730, 0.724, and 0.816, indicating the nonuniform distribution of porosity in the electrode along the Z direction. It is clear the largest porosity is located at the bottom part of the electrode, and the inferior porosity is located on the upper side. These results imply that relatively large pore sizes and porosities exist in the underside and upper side of the composite electrode, which may have significant influence on battery performance.

3.2. Specific Surface Area and Triple-Phase Interface Area

The average specific surface of the porous electrode is 6.485 × 10¹⁰ m²·cm⁻³. As shown in Figure 6a, the calculated specific surfaces of the different parts of the composite electrode from, bottom to top, are 1.079 × 10¹⁰, 7.765 × 10¹⁰, 8.559 × 10¹⁰, 8.751 × 10¹⁰, and 6.110 × 10¹⁰ m²·cm⁻³, respectively. It can be seen that the specific areas of the bottom part and upper part are lower than the other parts, which is in accordance with the results of the porosity distribution, as larger porosity results in a lower specific area.

Since the reaction in the lithium air battery mainly takes place at the triple-phase interface, the area of the triple-phase interface was calculated for electrodes with different saturations. According to Figure 6b, the area of the triple-phase interface increases with the saturation of the electrolyte, increasing until a saturation of 60% is reached. Then, the triple-phase interface area decreases sharply with an increase in electrolyte saturation. The highest triple-phase interface area is obtained for the electrode with 60% saturation, while the electrode with 40% saturation shows a similar value. It can be clarified that the pore size and porosity are large at the upper side and underneath of the composite electrode, resulting in the low interface between carbon fiber, oxygen, and electrolyte. However, the carbon fibers in the central part are compactly interconnected, resulting in low porosity and a smaller pore size distribution. Hence, the area of the triple-phase interface is high in the central part of the electrode.

3.3. Oxygen Effective Diffusion Coefficient

Figure 7 shows the distribution of the oxygen concentration distribution in different electrolyte filling models. It can be seen that the oxygen concentration in gas phase is significantly higher than that in liquid phase due to the low solubility of oxygen in electrolytes. Therefore, the concentration of oxygen decreases significantly after passing through the interface between the electrolyte and oxygen. Furthermore, the concentration of oxygen in a composite electrode decreases with the increasing saturation of. For the electrode with 100% saturation, the insufficient oxygen supply in the electrode may lead to poor electrochemical performance.

The effective oxygen diffusion coefficient in electrodes with different saturations is shown in Figure 8. Compared with the electrode without electrolyte filling, the effective oxygen diffusion coefficient in the electrode with 20% saturation decreases significantly, decreasing from 8.1 × 10⁻⁶ to 1.7 × 10⁻¹¹ m²·s⁻¹. The is owed to the fact that electrolytes have a significantly higher resistance toward oxygen transfer, leading to a lower diffusion rate in electrolytes than in the gas phase. With a further increase in the electrolyte filling degree, the effective oxygen diffusion coefficient gradually decreases to 6.7 × 10⁻¹² m²·s⁻¹ due to the increasing transfer resistance of oxygen with the increased amount of electrolytes.

3.4. Effective Electrical Conductivity

Effective conductivity is another critical parameter which determines the performance of a composite electrode. Figure 9 shows the potential distribution in models with different electrolyte saturations. It can be seen that the potential on the upside of the electrode is higher than that at the underside. The nonuniform distribution of potential is found due to the heterogeneous porous structure.

Electrodes with high effective conductivity are conductive to the decrease in ohmic resistance, resulting in superior lithium air battery performance, especially during operation at high current density. Figure 10 shows the effective conductivity of composite electrodes with different electrolyte filling degrees. Since oxygen is an insulator, the conductivity is approximate to 0. When the electrolyte filling degree is 0%, it can be inferred that the pores in the composite electrode are filled with oxygen, resulting in the lowest effective conductivity of 56.0 S·m⁻¹. With the electrolyte filling degree increasing to 20%, the oxygen at the bottom region of the electrode is occupied by electrolytes. Since the conductivity of the electrolyte is higher than that of oxygen, the overall effective conductivity of the composite electrode increases significantly. The conductivity increases slowly when the electrolyte filling degree ranges from 20% to 80%. The reason for this is mainly due to the fact that the pore size and porosity are relatively low in the central part of the electrode and the amount of electrolytes filling in the pore slowly increases with the increasing filling degree. It should be noted that the effective conductivity of an electrode with 100% saturation significantly increases compared to that with a filling degree in the range of 20–80%. Since the pore size and porosity in the upper side of the electrode is large, this indicates that a relatively large amount of electrolyte can be reserved. Therefore, the effective conductivity reaches 108.1 S·m⁻¹ for an electrode with 100% saturation.

The rational design of a porous cathode requires abundant active sites derived from high triple-phase interface area and fast electron and reactant transfer rates coming from highly effective conductivity and an effective diffusion coefficient. However, the filling degree of electrolytes has the opposite effect on the effective oxygen diffusion coefficient and the effective conductivity. In addition, there exists an optimal range of filling degree when considering the triple-phase interface area. Therefore, it is important to consider the balance between these parameters related with reaction sites and mass transfer. According to the simulation results, it can be speculated that the composite electrode with the electrolyte filling degree in range of 40–60% is preferred.

3.5. Electrochemical Performance Analysis

To verify the speculation that the optimal electrolyte saturation ranges from 40% to 60%, charge–discharge tests were carried out. Figure 11 shows the specific capacity of the battery under different electrolyte filling degrees. The curves shown in Figure 11 are based on the experimental data obtained from the actual experiment. As expected, when the electrolyte filling degree is 0% and 100%, the limited reaction sites and insufficient oxygen supply result in the low discharge capacity of 1955 mAh·g⁻¹ and 2288 mAh·g⁻¹, respectively. When the electrolyte filling degree increases to 20% and 40%, the specific capacity was significantly improved to 4320 mAh·g⁻¹ and 4434 mAh·g⁻¹, respectively. The reason is the increased area of the triple-phase interface available for reaction and the enhanced conductivity for charge transfer. Furthermore, the proper pore size and oxygen diffusion rate also contribute to the improved performance. As the electrolyte filling degree increases to 60%, a balance between the effective conductivity, diffusion rate of oxygen, and triple-phase interface area is achieved, resulting in the highest discharge capacity of 5034 mAh·g⁻¹. When the saturation is further increased to 80%, the specific area of triple-phase interface significantly decreases. Furthermore, the effective diffusion coefficient of oxygen decreases, leading to a decrease in the discharge capacity (3982 mAh·g⁻¹). Hence, the battery with an electrolyte saturation of 60% shows the best performance due to the optimal balance between the mass transfer and electrochemical reaction kinetics, indicating the significance of simulation prediction based on digital twin.

4. Conclusions

In this paper, digital twin technology based on μCT is used to reconstruct the numerical model of porous cathode in lithium air battery. The results demonstrate that relatively smaller pore size distribution and lower porosity exist in the center part of the composite electrode, corresponding to the higher specific area and specific triple-phase interface area. The heterogeneous distribution of these intrinsic parameters results in a significant difference in the mass transfer property and cell performance when the electrode is at different saturations. At the saturation of 60%, the oxygen diffusion coefficient, specific triple-phase interface area, and effective conductivity are optimized, resulting in the highest discharge capacity of the lithium air battery. The μCT-based digital twin technology provides a fast and accurate method to reveal the mass transfer and critical parameters in composite electrode. Furthermore, this method also provides a valuable forecast for cell performance and is expected to play an important role in the design of porous electrodes in energy storage systems.