Performance evaluation of a novel synchronously interdigitated/winded lithium-ion battery configuration enabled by 3D printing through numerical simulations

Thick electrodes with higher energy density are highly desirable for lithium-ion batteries (LIBs). However, the sluggish transport of Li-ions in thick electrodes is a critical challenge. In this study, a novel synchronously interdigitated/winded battery configuration enabled by 3D printing is proposed. The cathode, separator, and anode are synchronously interdigitated in the core and synchronously winded in the outer-rings to form an integrated full battery. With this novel battery configuration, Li-ions can transport between neighboring cathode and anode, thereby significantly reduce the transport distance of Li-ions, and improve the electrochemical reaction kinetics. To evaluate the electrochemical performance of this battery configuration, this study investigates the effects of various parameters including the electronic conductivity, electrode porosity, electrode line width, separator thickness, and number of winded outer-rings on the electrochemical performance through numerical simulations. Results showed that electronic conductivity is the most crucial factor in determining the electrochemical performance. In combination with multi-material 3D printing, the battery configuration proposed in this study may be utilized to build LIBs with higher energy density.


Introduction
Lithium-ion batteries (LIBs) are regarded as one of the most important energy storage devices and have become the major sources for powering consumer electronics, electric vehicles, and other mobile devices [1][2][3]. Although LIBs technologies have made huge progress over the past decade, the need for LIBs with higher energy density and power density is still urgent. Toward this goal, researchers are devoted to the development of new battery chemistries and materials with higher theoretical capacity such as lithium metal batteries and lithium-sulfur batteries [4][5][6][7][8]. At the same time, some researchers try to improve the energy density by developing thick electrodes [9][10][11].
Commercial LIBs have been following the 'thin tape casted electrodes + stacking/winding' paradigm for several decades [12]. However, this type of battery configuration faces some intrinsic shortcomings. First, the electrode thickness usually cannot exceed 100 µm due to the trade-off between energy density and power density [13]. The transport distance of Li-ions increases proportionally with the increase of electrode thickness, and this will lead to the decay of electrochemical reaction kinetics and power density. Second, thin electrodes require more current collectors and separators, and the existence of large amounts of inactive materials damages the energy density [14].
Although increasing electrode thickness is an effective strategy to improve energy density, the sluggish transport of Li-ions in thick electrodes is a critical challenge. Battery electrodes consisting of active materials, polymer binders, and carbon conductive agents have a tortuous porous microstructure that can be characterized by tortuosity τ , and Li-ions transport tortuously inside the electrodes [15,16]. Usually, the tortuosity is between 3.0-6.0 for most battery electrodes [17,18]. As the electrode thickness increases, the transport distance of Li-ions increases 3.0-6.0 times more. This causes serious degradation of electrochemical reaction kinetics.
Although these new battery configurations can improve the electrochemical reaction kinetics of thick electrodes, there still exists some limitations concerning the mechanical robustness, integration of battery components, and electrochemical performance. In this study, we proposeJ a novel battery configuration with synchronously interdigitated/winded cathode, separator, and anode, that can be fabricated via 3D printing. First, the structure of this battery configuration is introduced and the merits are discussed. Then the electrochemical performance of batteries with this type of configuration is evaluated by numerical simulations. The novel battery configuration proposed in this study may be utilized to achieve higher energy density for LIBs. Figure 2 shows the schematic of the novel synchronously interdigitated/winded battery configuration and its printing process. The full battery consists of an interdigitated core and winded outer rings. In this configuration, the cathode, anode, and separator are synchronously interdigitated and winded into an integrated complete full battery with multi-material 3D printing. This configuration has several advantages. (i) Short Li-ion transport distance. The Li-ions can transport directly between neighboring cathode and anode, thus reduces the ionic transport distance. (ii) Self-supporting. The three battery components including cathode, anode, and separator have a serpentine structure, and active materials do not have to adhere to current collectors, thus makes current collector-free electrodes possible, and further improves the energy density. (iii) Outstanding mechanical properties. The battery components are integrated into a whole structure, and this type of structure has excellent mechanical properties. (iv) Excellent dimensional scalability. By changing the number of interdigitated branches and the number of winded rings, cells with different sizes can be obtained.

Novel synchronously interdigitated/winded battery configuration
Considering the advantages mentioned above, it is worth exploring this type of battery configuration. Thus, in this study, we try to evaluate the effects of various electrode parameters on the electrochemical performance through numerical simulations. Based on the simulation results, the advantages and disadvantages of this battery configuration are concluded. Figure 3 shows the numerical simulation models before and after meshing. Numerical simulations are performed with the Li-ion battery module in COMSOL Multiphysics. LiNi 0.8 Co 0.1 Mn 0.1 O 2 (NCM811) and graphite are selected as the cathode and anode materials respectively due to their wide applications in industry. The major parameters that affect the electrochemical performance include geometrical parameters such as the electrode line width δ e , the separator thickness δ d , the number of winded rings n, and electrode parameters such as the porosity ε, and the electronic conductivity σ e are listed in table 1. Notably, the electric current is collected at the end of electrodes, and electrons must transport a long distance from the end to the core, and this requires that the electrodes have a high electronic conductivity. As a result, three values of 50 S m −1 , 500 S m −1 , and 2000 S m −1 are selected.

The transport mechanism of Li-ions
To reveal the transport mechanism of Li-ions in this new battery configuration, we firstly conduct simulations on the discharge process of a battery with the line width of 100 µm, separator thickness of 30 µm, outer winded ring number of 4, electrode porosity of 65%, and electronic conductivity of 500 S m −1, at the rate of 0.5 C.
At the beginning of discharge, Li-ions are intercalated into the graphite anode with the concentration of 31 507 mol m −3 , while the NCM811 cathode is completely de-intercalated. The initial distribution of Li-ion concentration is shown in figure 4(b). After the discharge process begins, the flow of Li-ions forms the electrolyte current. Figure 4(a) shows the initial electrolyte current density and direction at the beginning of discharge. We can see that electrolyte current in the outermost rings is larger than the electrolyte current in   Figure 4(c) shows the electrolyte current density and direction at the end of discharge. We can see that the electrolyte current in the core is larger than that in the outer rings. These results suggest that the transport of Li-ions is a sequential process during the discharge process, firstly Li-ions in outer rings diffuse from anode to cathode at the beginning of discharge, then Li-ion in the core diffuse from anode to cathode at the end of discharge. The direction of electrolyte current shows that Li-ions transport directly from anode lines to neighboring cathode lines, thereby the transport distance of Li-ions can be significantly reduced. The shortened ionic transport distance can improve the electrochemical reaction kinetics and is a major merit of this battery configuration.
To further illustrate the merits of shortened ionic transport distance, the transport pathways of Li-ions in the new battery configuration and the conventional tape casted battery with the same electrode thickness are compared (as shown in figures 4(e) and (f)). In the synchronously interdigitated/winded battery, the transport distance of Li-ions between cathode and anode can be described by equation (1). The transport distance is in linear proportion to the line width of the cathode, separator, and anode. The line width of the three components is solely determined by the manufacturing process, and is independent of electrode thickness. Therefore, the transport distance of Li-ions can remain constant with the increase of electrode thickness. While, in conventional tape casted batteries, the maximum transport distance of Li-ions is in linear proportion to the electrode thickness. Generally, the transport distance increases at a rate of 3.0-5.0 times of electrode thickness. As a result, in comparison with the conventional tape casted battery, the synchronously interdigitated/winded battery can significantly shorten the transport distance of Li-ions, thereby improve the reaction kinetics in thick electrodes, where L max is the maximum transport distance of Li-ion between cathode and anode; τ c , τ s , and τ a are the tortuosity of cathode, separator, and anode respectively; w c , w s , and w a are the line width of cathode, separator, and anode in the synchronously interdigitated/winded battery; h c , h s , and h a are the thickness of cathode, separator, and anode in the conventional tape casted battery.

Effects of electronic conductivity on electrochemical performance
Since the electric current is collected at the end of electrodes, the transport of electrons faces great challenge due to the long transport distance. Therefore, the electronic conductivity of electrode is a crucial factor. In  Figure 5(d) shows the comparison of rate capacities between three conductivities. Results show that the specific capacity decreases with the increase of discharge rate. When the electronic conductivity is 50 S m −1 , the discharge capacity is below 100 mAh g −1 @ 0.2 C. When the discharge rate increases to 1.0 C and 2.0 C, the battery cannot deliver any capacities due to the large ohmic impedance caused by the low electronic conductivity. When the electronic conductivity increases to 500 S m −1 and 2000 S m −1 , the electrochemical performance is significantly improved. At the low rate of 0.2 C, the battery can deliver a capacity of ∼270 mAh g −1 which is very close to its theoretical value. With the electronic conductivity of 2000 S m −1 , it can deliver a high capacity of over ∼230 mAh g −1 @ 2.0 C. These results indicate that electronic conductivity plays a very crucial role, and highly conductive electrode is the key to obtain excellent performance for this new battery configuration. Figures 5(e) and (f) show the electrolyte current density and direction at the end of discharge @ 2.0 C for the electronic conductivity of 500 S m −1 and 2000 S m −1 , respectively. For the case of 500 S m −1 , the electrolyte current in the core is much smaller than the electrolyte in the outer rings. This indicates that the outer rings make the major contributions to the discharge capacity, while, in the core, only a small portion of Li-ions can transport from anode to cathode. As the electronic conductivity increases from 500 S m −1 to 2000 S m −1 , the electrolyte current in the core also increases significantly. This indicates that more Li-ions in the core are actively involved in the electrochemical reactions.
To conclude, electronic conductivity is crucial to the electrochemical performance. Only when the electrodes are highly conductive, the active materials in the core can make effective contributions to the discharge capacity, otherwise, the active materials are difficult to involve in the electrochemical reactions due to the large ohmic impedance.

Effects of electrode porosity on the electrochemical performance
Electrode porosity ε is also an important parameter in affecting the electrochemical performance. According to the Bruggemann constitutive relation, the electrode tortuosity τ = A ε −B , where A and B are coefficients [61,62]. This indicates that tortuosity is inversely proportional to the porosity, and the tortuosity decreases with the increase of electrode porosity. Meanwhile, the effective ionic conductivity σ eff Li+ = ε τ σ bulk Li+ , where σ bulk Li+ is the bulk ionic conductivity in the electrolyte [63]. This indicates that with larger porosity and smaller tortuosity, a higher effective ionic conductivity can be achieved, which is beneficial to the transport of Li-ions in the electrodes.
To evaluate the effects of electrode porosity on the electrochemical performance for this new battery configuration, three electrode porosities of 45%, 55%, and 65% are selected to perform the numerical simulations. In these simulations, electronic conductivity is 2000 S m −1 , the electrode line width is 100 µm, separator thickness is 30 µm, and the number of winded outer-rings is 4. Figures 6(a)-(c) show the discharge curves with the porosity of 45%, 55%, and 65%, respectively, and figure 6(d) shows the comparison of the rate capacities. As the porosity increases from 45% to 55% and 65%, there is a slight increase in discharge capacities. This indicates that increasing porosity can improve the rate performance, however, the effect seems to be marginal.
Figures 6(e)-(g) show the electrolyte current density and direction at the end of discharge @ 2.0 C with porosity of 45%, 55%, and 65%, respectively. The results also confirm that the electrolyte current densities in the core of the battery are very similar for different porosities. Therefore, we can conclude that electrode porosity has little effects on the electrochemical performance for this battery configuration. This is because that, in the synchronously interdigitated/winded battery, the Li-ions transport between neighboring cathode lines and anode lines, the shortened transport distance of Li-ions can ensure the fast diffusion of Li-ions in the electrodes, and reducing tortuosity is not necessarily required to further promote the transport of Li-ions.

Effects of electrode line width on electrochemical performance
Electrode line width is an important geometrical parameter, and three electrode line width of 100 µm, 150 µm, and 200 µm are selected to evaluate effects of electrode line width on the electrochemical performance. In these simulations, the electronic conductivity is 2000 S m −1 , separator thickness is 30 µm, the number of winded outer-rings is 4, and the electrode porosity is 65%. Figures 7(a)-(c) show the discharge curves with the electrode line width of 100 µm, 150 µm, and 200 µm, respectively. Figure 7(d) shows the comparison of the rate capacities between three electrode line widths. Results show that the discharge capacities decrease with the increase of electrode line width. As the width increases from 100 µm to 200 µm, the discharge capacity exhibits a significant decrease of specific capacity from ∼230 mAh g −1 @ 2.0 C to ∼180 mAh g −1 @ 2.0 C. Meanwhile, the increase of line width seems to have little effects on the discharge capacities at the rates of below 0.5 C. To be noted, in this new battery configuration, the transport distance of Li-ions is in linear proportion with the electrode line width. This proportional increase of ionic transport distance leads to the decline of discharge capacity at high rates. Figures 7(e)-(g) show the electrolyte current density and direction at the end of discharge @ 2.0 C for the electrode line width of 100 µm, 150 µm, and 200 µm, respectively. The electrolyte current density in the core of the battery decreases with the increase of electrode line width. This indicates that it is more difficult for active materials in the core to get involved in the electrochemical reactions. Therefore, it is desirable to minimize the electrode line width to obtain better performance.

Effects of separator thickness on the electrochemical performance
Another geometrical parameter that may affect the electrochemical performance is the separator thickness. Serpentine separator is placed between cathode and anode as they are synchronously interdigitated and winded. Therefore, with the increase of separator thickness, the transport distance of Li-ions also increases. This might cause the deterioration of electrochemical reaction kinetics and the decline of discharge capacity. Three separator thickness of 30 µm, 60 µm, and 90 µm are selected to evaluate the effects of separator thickness on electrochemical performance. In these simulations, the electronic conductivity is 2000 S m −1 , electrode line width is 30 µm, the number of winded outer-rings is 4, and the electrode porosity is 65%.  show the electrolyte current density and direction at the end of discharge @ 2.0 C for the separator thickness of 30 µm, 60 µm, and 90 µm, respectively. A slight decrease of discharge specific capacity at the rate of 2.0 C is observed as the separator thickness increases from 30 µm to 90 µm. Separator thickness affects the electrochemical performance in the same way as the electrode line width. The transport distance of Li-ions also increases proportionally with the increase of separator thickness. But, since the separator thickness is much smaller than the electrode line width, it seems to have less impacts on the electrochemical performance, as evidenced in figures 8(e)-(g), the electrolyte current densities are quite similar for different separator thickness.

Effects of number of winded outer-rings on the electrochemical performance
The number of winded outer-rings is a critical geometrical parameter. The transport distance of electrons increases as the number of winded outer-rings increases, since the electric current is collected at the end of the electrodes. To evaluate the effects of the number of winded outer-rings on battery performance, battery configurations with 2 winded outer-rings and 4 winded outer-rings are investigated. For other simulation parameters, electronic conductivity is 2000 S m −1 , the electrode porosity is 65%, electrode line width is 200 µm, and separator thickness is 30 µm. Figures 9(a) and (b) show the discharge curves of batteries with 2 winded outer-rings and 4 winded outer-rings, respectively. Figure 9(c) shows the comparison of rate capacities. Figures 9(d) and (e) show the electrolyte current density and direction at the end of discharge @ 2.0 C. As the number of winded outer-rings increases from 2 to 4, there is a significant decrease of specific capacity @ 2.0 C, while the specific  capacities at low discharge rates only decrease slightly. The electrolyte current densities in the core of battery with 4 winded outer-rings are lower than battery with 2 winded outer-rings, indicating that the electrochemical performance deteriorates with the increase of the number of winded outer-rings. This is due to the larger electric resistance resulted from longer total extension length of electrodes as the number of winded outer-rings increases.

Conclusions
In this study, a novel synchronously interdigitated/winded LIB configuration enabled by 3D printing is proposed. This configuration has some advantages over traditional tape-casted batteries and other 3D LIBs, such as short transport distance of Li-ions, excellent mechanical strength and self-supporting capability, and excellent geometrical scalability. Numerical simulations are conducted to reveal the transport mechanism of Li-ions, and Li-ions are found to transport between neighboring cathode and anode, enabling the short transport distance of Li-ions, which is crucial to battery performance.
The effects of various parameters on the electrochemical performance, including the electrode electronic conductivity, electrode porosity, electrode line width, separator thickness, and the number of winded outer-rings, are evaluated. It is found that electronic conductivity has the most significant effects on the battery performance. In the synchronously interdigitated/winded battery configuration, the electrons must transport a long distance to reach the reaction sites in the core of the battery, thereby, it is essential that the electrodes have high electronic conductivity. Thus, in this study, an electronic conductivity of 2000 S m −1 is selected.
In addition, the electrode line width and separator thickness affect the battery performance in a similar way. The transport distance of Li-ions increases proportionally with the increase of electrode line width and separator thickness, thereby degrades the electrochemical performance. Notably, the electrode line width has greater impacts than separator thickness. Moreover, the electrochemical performance deteriorates with the increase of number of winded outer-rings due to a longer transport distance of electrons and larger electric resistance.
To push the synchronously interdigitated/winded battery configuration further, there are some critical challenges to be addressed. The most important one is to develop highly conductive electrodes that can overcome the transport limitations of electrons. Otherwise, this battery configuration cannot fully make use of its advantages such as the short transport distance of Li-ions. In addition, multi-material 3D printing process needs to be developed and optimized to fabricate this type of integrated battery. We anticipate that the battery configuration proposed in this study may provide a new solution to the construction of LIBs with high energy density.

Data availability statement
All data that support the findings of this study are included within the article (and any supplementary files).