Impact of state-of-charge and temperature on the cross-plane thermal conductivity of a Li-ion pouch cell

Abstract

A thorough understanding of the thermal transport characteristics of Li-ion batteries is critical for the development of accurate thermal models and the enhancement of thermal management strategies. In this study, the cross-plane thermal conductivity ($k_{\perp }$) of a commercial 20 Ah Li-ion pouch cell was systematically measured across a broad range of state-of-charge (SOC) levels and temperatures (20.6 to 43.3$_{}^{\circ }$C) using a custom-designed guarded hot plate apparatus. The results indicate that at room temperature (27.3$_{}^{\circ }$C), $k_{\perp }$ decreases with increasing SOC, reaching a minimum near $\text{SOC}=80\%$, followed by a marked increase at $\text{SOC}=100\%$. Furthermore, at $\text{SOC}=100\mathrm{\backslash \%}$, $k_{\perp }$ increased by approximately 0.188 ${\text{Wm}}^{-1}$ ${\text{K}}^{-1}$ (80% enhancement) as the temperature rose from 20.6 to 43.3$_{}^{\circ }$C. The observation shows that $k_{\perp }$ consistently increases with temperature across all SOC levels, exhibiting nearly consistent slopes. To elucidate these trends, various contributing factors were systematically examined.

Introduction

The climate crisis and energy scarcity are significant challenges that require the development of advanced energy storage technologies. Lithium-ion batteries (LIBs) have emerged as a key technology for addressing these challenges, owing to their high power and energy density. As a result, they are widely used in electric vehicles, energy storage systems, and portable electronics. However, the thermal safety of LIBs has recently gained attention as a critical concern, as failures can lead to significant human, environmental, and industrial damage^1,2. Electrochemical reactions within batteries are highly sensitive to operating temperature³. In particular, elevated temperatures over 45$_{}^{\circ }$C can accelerate capacity fade and lead to a drastic increase in internal resistance, significantly reducing the performance of LIBs⁴. Furthermore, in large-format lithium-ion (Li-ion) cells, heat generation may be unevenly distributed, leading to internal temperature non-uniformities⁵. These non-uniformities can induce spatial variations in electrochemical reactions, resulting in localized degradation, accelerated aging, and increased thermal instability within the cells^6,7. Therefore, mitigating such temperature non-uniformities is a key challenge in battery thermal management systems, and addressing it requires the development of thermal models capable of resolving temperature fields under various operating conditions⁸.

Thermal modeling of Li-ion cells begins with the accurate characterization of their thermophysical properties, which provides the foundation for thermal analysis. Thermal conductivity represents the intrinsic heat transport capability of a cell, and its low values with directional dependence are a primary cause of temperature non-uniformity⁹. This arises from the fact that these cells are structured as stacks of layers, including the cathode, anode, separator, current collectors, and external casing. Due to this laminated architecture, Li-ion cells inherently exhibit anisotropic thermal conductivity, with cross-plane values being significantly lower than those in the in-plane direction^10,11. Indeed, many studies have shown that cross-plane thermal conductivity could be an order of magnitude smaller than in-plane values¹². Moreover, Xie et al.¹³ demonstrated that uncertainty in cross-plane thermal conductivity has a more pronounced effect on temperature prediction than comparable uncertainty in the in-plane direction. This emphasizes that the accurate determination of cross-plane thermal conductivity is essential for developing reliable and high-fidelity thermal models.

To determine the cross-plane thermal conductivity, many studies have calculated the thermal conductivity of a whole-cell by measuring the thickness and thermal conductivity of each individual layer material^14,15. However, evaluating the thermal conductivity of these layer materials involves considerable uncertainty. This is primarily because lithium intercalation and deintercalation induce structural changes in the active material particles and variations in porosity^16–18. Lithiation of the electrode alters the lattice thermal conductivity of the active material particles^19,20, while microstructural changes affect the heat transport pathways^21,22. Meanwhile, Richter et al.²³ investigated various cell components in both dry and electrolyte-soaked states. Their results showed that the thermal conductivity of a ${\text{LiFePO}}_4$ cathode increased from 0.15 to 0.36 ${\text{Wm}}^{-1}$ ${\text{K}}^{-1}$, while that of the graphite anode increased fourfold from 0.34 to 1.45 ${\text{Wm}}^{-1}$ ${\text{K}}^{-1}$. Despite the dominant influence of the electrolyte on the thermal conductivity of the Li-ion cells, performing measurements in the presence of the liquid electrolyte is challenging due to its tendency to evaporate. In addition, the thermal conductivity of cell materials can vary with temperature, and high-temperature measurements further accelerate electrolyte evaporation. Therefore, measuring the cross-plane thermal conductivity of the whole-cell is considered a more realistic approach^24,25. However, most previous studies either neglected the influence of SOC or temperature¹⁰, or did not consider them simultaneously^17,26,27. This limited scope hinders a comprehensive understanding of the effects of SOC and temperature on the cross-plane thermal conductivity.

Various experimental techniques have been proposed to accurately measure the cross-plane thermal conductivity of pouch cells, each offering distinct advantages and limitations in terms of accuracy and experimental complexity. Bazinski and Wang²⁸ employed a modified isothermal calorimeter system to evaluate the thermal conductivity and specific heat of a 14 Ah pouch cell. While this system provides accurate measurements, it is expensive and typically requires complex experimental setups. In contrast, the guarded hot plate (GHP) method is a steady-state method widely used for measuring the thermal conductivity of insulating materials²⁹. Although it requires a complex setup and precise temperature control, it is widely adopted for its accuracy and reliability in thermal conductivity measurements. For this reason, Vertiz et al.³⁰ measured the thermal conductivity of a 14 Ah pouch cell using a standard GHP apparatus as specified in ASTM C177-97, while Tendera et al.²⁵ implemented a modified GHP system incorporating a reference plate to evaluate the cross-plane thermal conductivity. However, according to ASTM C177-97, the minimum sample thickness is limited due to the influence of thermal contact resistance between the sample and the apparatus. As the relative contribution of this contact resistance increases, it may distort the measured heat flux and thus affect the accuracy of the results. Moreover, in the modified GHP system, unlike standard systems that employ a guard heater, lateral heat loss was suppressed solely by means of thermal insulation. Also, the heater consisted of four discrete resistive elements, which may have led to non-uniform heating and compromised the isothermal condition of the heating surface.

This study aims to accurately measure the cross-plane thermal conductivity of a pouch-type lithium iron phosphate (LFP)/graphite cell using a custom-designed GHP apparatus. In our previous work²⁷, this apparatus was developed and validated, and it was used to measure the cross-plane thermal conductivity under various temperature conditions. However, the effect of SOC on the cross-plane thermal conductivity has not yet been systematically investigated. Variations in SOC can significantly alter the intrinsic thermal conductivities of the electrodes¹⁶, thereby affecting the overall cross-plane thermal conductivity^25,30,31. In addition, it still remains unclear whether the effects of SOC and temperature are coupled or mutually independent. Therefore, to gain a more comprehensive understanding of the thermal transport behavior, we investigate the impact of SOC on cross-plane thermal conductivity over a range of temperatures.

Methods

The custom-designed GHP apparatus consists of a hot assembly and a cold assembly, with the test specimen positioned between them in a sandwich configuration, as illustrated in Fig. 1(a). Under ideal steady-state conditions, the temperatures of the two assemblies are kept constant, and heat transfer occurs exclusively through the specimen due to the temperature difference between the assemblies. The hot assembly comprises a main plate and a surrounding guard plate, and the guard plate minimizes lateral heat loss by maintaining the same temperature as the main plate. Both plates were equipped with independently controlled ceramic heaters for precise temperature regulation. During all experiments, the temperature difference between the main and guard plates was maintained within $\pm 0.1^{\circ }$C, ensuring one-dimensional heat conduction within the metering area. The one-dimensional heat transfer in the metering region of the specimen was validated through an axisymmetric thermal simulation performed in our previous study²⁷. The thermal conductivity is calculated over the main plate area, and the heat transfer rate through the specimen is assumed to be equal to the main heater input power, corrected for heat losses. According to Fourier’s law, the thermal conductivity is calculated as

$$\begin{array}{c}\hfill k=\frac{Q_{s}t}{A\mathrm{\Delta }T}\end{array}$$ 1

where $Q_s$ is the heat transfer rate across the specimen, t is the specimen thickness, A is the metering area (i.e., area of the main plate), and $\mathrm{\Delta }T$ is the temperature difference between the hot and cold assemblies.

Fig. 1.

(a) Schematic of the custom-designed GHP apparatus²⁷. All dimensions are in mm. (b) Schematic of the battery tester for charge–discharge cycling.

In the custom-designed GHP apparatus, the main plate of the hot assembly was composed of aluminum, whereas the guard plate and the cold assembly were fabricated from copper to minimize internal temperature gradients. In addition, an air gap and a PEEK were introduced on top, between the main and guard plates of the hot assembly, to thermally insulate them and minimize heat transfer between the plates. The optimal configuration employed a main plate radius of 12 mm and a guard plate radius of 80.5 mm. The K-type thermocouples were embedded 5 mm above the specimen-contact surface of the hot assembly, as shown in Fig. 1. In the hot assembly, the thermocouples were located at the side of the main plate and at the radial midpoint between the inner and outer edges of the guard plate. Similarly, in the cold assembly, a thermocouple was embedded 5 mm beneath the contact surface. To minimize interfacial thermal contact resistance between the sample and the assemblies, thermal paste was uniformly applied to the contact surfaces. A consistent compression pressure of approximately 0.17 MPa was maintained using a torque wrench to securely fix the pouch cell in the setup. Nevertheless, systematic errors, such as parasitic conduction through lead wires and radiative heat transfer across the plate gap, were corrected using a reference material over the considered range of temperatures. The custom-designed GHP apparatus was specifically designed for the measurement of thin specimens such as pouch-type cells and was validated using various materials with an uncertainty within 3%. Further details (i.e., design, validation, and uncertainty analysis) on the custom-designed GHP apparatus can be found in our previous work²⁷.

We investigated a commercial 20 Ah automotive pouch cell consisting of a graphite anode and a ${\text{LiFePO}}_4$ cathode. Detailed specifications of the cell are provided in our previous work²⁷. To examine the effect of SOC on the cross-plane thermal conductivity, measurements were conducted at discrete SOC levels of 0%, 25%, 50%, 79.6%, and 100%. The charge–discharge test was performed using a BaSyTec Cell Test System-Lab (CTS-Lab) battery tester. Fig. 1(b) shows a schematic of the experimental setup used for the charge–discharge tests. The battery tester operated over a voltage range of 2.4 to 3.4 V with a constant current rate of 0.1 C, while data were acquired at 1-second intervals, with voltage and current accuracies of 1 mV and 1 mA, respectively. The tests were carried out in both constant current–constant voltage (CC-CV) mode and constant current (CC) mode. In CC-CV mode, cells were charged at a current rate of 0.1 C until the cell voltage reached 3.4 V. Then, during the constant voltage phase, the current was gradually reduced to complete the remaining charge while preventing overcharging³². The SOC values were quantified using the coulomb counting method. All charge-discharge tests were conducted at a constant temperature of 25$_{}^{\circ }$C because electrochemical processes, such as polarization and diffusion, which are governed by Arrhenius’ law, exhibit a strong temperature dependence³³.

To evaluate the SOC dependence at different temperatures, measurements were conducted over a temperature range of approximately 20 to 43$_{}^{\circ }$C. The cell temperature ($_{}^{\circ }$C) was defined as the arithmetic average of the hot and cold assembly temperatures, as the GHP method requires a maintained temperature difference across the specimen to ensure a constant heat flux. During each test, the temperature difference between the hot and cold assemblies was set to 8$_{}^{\circ }$C. Steady-state was defined as the condition in which the temperature fluctuation remained within $\pm 0.1^{\circ }$C. Once steady-state was achieved, 30-minute averaged data were used for all measurements.

Results and discussion

To examine the effect of SOC on the cross-plane thermal conductivity ($k_{\perp }$), we conducted measurements at room temperature (i.e., 27.3$_{}^{\circ }$C in this work) across various SOC levels. Fig. 2(a) shows the measured $k_{\perp }$ at five discrete SOC levels. The measurements show that $k_{\perp }$ decreases from 0.255 ${\text{Wm}}^{-1}$ ${\text{K}}^{-1}$ at $\text{SOC}=0\%$ to a minimum of 0.137 ${\text{Wm}}^{-1}$ ${\text{K}}^{-1}$ at $\text{SOC}=79.6\%$, followed by a sharp increase to 0.257 ${\text{Wm}}^{-1}$ ${\text{K}}^{-1}$ at $\text{SOC}=100\%$. This dependence on SOC is likely associated with phase transitions in the active material particles of each electrode, induced by lithiation, as explained below. At low SOC levels, lithium ions are mainly stored in the ${\text{LiFePO}}_4$ cathode. During charging, these ions intercalate into the graphite anode while being deintercalated from the cathode; the reverse occurs during discharging. This process is illustrated in Fig. 2(b) and can be described by the following electrochemical reactions:

$$\begin{array}{cc}\hfill {\text{Li}}_x{\text{C}}_6& \underset{\mathit{charge}}{\overset{\mathit{discharge}}{\rightleftharpoons }}x{\text{Li}}^{+}+x{e}^{-}+6\text{C},\hfill \end{array}$$ 2

$$\begin{array}{cc}\hfill {\text{Li}}_y{\text{FePO}}_4& \underset{\mathit{charge}}{\overset{\mathit{discharge}}{\rightleftharpoons }}{\text{Li}}_{y-x}{\text{FePO}}_4+x{\text{Li}}^{+}+x{e}^{-}.\hfill \end{array}$$ 3

In Eqs. (2) and (3), the leftward arrows represent lithium intercalation, and the rightward arrows represent deintercalation.

Fig. 2.

(a) SOC dependence of the cross-plane thermal conductivity of the 20 Ah LFP/graphite pouch cell measured at room temperature (27.3$_{}^{\circ }$C). (b) Schematic illustration of lithium-ion migration within a unit cell during the charge-discharge process.

Under ideal conditions, $k_{\perp }$ can be calculated as the thickness-weighted harmonic mean of the thermal conductivities of the individual layers. However, phase transitions in the electrodes induced by lithiation and delithiation lead to variations in their thermal conductivity. To date, experimental investigations of electrode thermal conductivity at different lithiation states have been limited to cathodes, with reports showing decreased thermal conductivity upon delithiation and increased values upon lithiation for LCO and NMC cathodes^16,34. Although lithiation can significantly alter thermal conductivity through phase transitions, prior investigations of ${\text{LiFePO}}_4$ and graphite have been limited to theoretical studies.

Structural changes in active material particles occur simultaneously in both the cathode and anode during charging and discharging. For the cathode, ${\text{Li}}_y$ ${\text{FePO}}_4$ exists as $y=1$ at full discharge and $y=0$ at full charge, corresponding to the ${\text{LiFePO}}_4$ and ${\text{FePO}}_4$ phases, respectively. At intermediate SOC levels, the cathode contains grains with coexisting ${\text{LiFePO}}_4$ and ${\text{FePO}}_4$ phases³⁵, and the lattice mismatch between these phases induces distortions and internal phase boundaries^36,37. These misfit-dislocation boundaries are reported to hinder thermal transport by acting as phonon scattering centers¹⁹, which likely contributed to the higher thermal conductivity observed at single-phase SOC levels (i.e., 0% and 100%). In addition, Li et al.³⁸ reported that the lattice thermal conductivity of ${\text{FePO}}_4$ is more than an order of magnitude higher than that of partially or fully lithiated ${\text{LiFePO}}_4$, owing to stronger and more uniform Fe–O bonding. This can explain the decreasing and subsequent increasing trend, especially the sharp rise in $k_{\perp }^{}$ at $\text{SOC}=100\%$ observed in Fig. 2(a). Meanwhile, in the anode, graphite forms stage I (${\text{LiC}}_6$) at full charge and transforms into stage II (${\text{LiC}}_{12}$) and stage III (${\text{LiC}}_{18}$) upon discharge. The c-axis (cross-plane) thermal conductivity of graphite is high for both pristine graphite and ${\text{LiC}}_6$, but shows a pronounced minimum at intermediate stages²⁰. This non-monotonic behavior originates from the competition between enhanced phonon transport due to stronger interlayer coupling at high lithium contents³⁹ and increased phonon scattering by lithium ions at intermediate stages⁴⁰. As a result, the graphite anode may also contribute to the elevated $k_{\perp }$ observed at both $\text{SOC}=0\%$ and $\text{SOC}=100\%$, consistent with previous reports^20,39,40.

Meanwhile, the effective thermal conductivity of porous electrodes can be described as a combination of the solid and fluid phases^21,22. Electrodes are primarily composed of active materials, binders, and conductive additives, and the resulting porosity depends on the proportions of these constituents. Oehler et al.⁴¹ reported that the effective thermal conductivity of porous electrodes is strongly influenced by porosity. As porosity increases, the volume fraction of thermally conductive solid phases decreases, which may reduce the available heat conduction pathways and lead to lower effective thermal conductivity. In this context, lithiation can induce volume changes in active materials, potentially leading to porosity variations through particle expansion and contraction¹⁶. During charging, SOC variations have been reported to decrease anode porosity by $15\sim 25\%$⁴². This reduction in anode porosity could therefore influence its effective thermal conductivity, which may contribute to the increase in $k_{\perp }$ at high SOC levels.

Building on the authors’ previous study of the temperature-dependent $k_{\perp }$ of the pouch cell²⁷, the present work includes additional temperature-dependent measurements under various SOC levels, as shown in Fig. 3. At all SOC levels, the $k_{\perp }$ exhibited a general increasing trend with temperature as shown in Fig. 3(a). For instance, at $\text{SOC}=100\%$, the measurements show the maximum enhancement of 80% from 0.235 ${\text{Wm}}^{-1}$ ${\text{K}}^{-1}$ at 20.6$_{}^{\circ }$C to 0.423 ${\text{Wm}}^{-1}$ ${\text{K}}^{-1}$ at 43.3$_{}^{\circ }$C.

Fig. 3.

Temperature dependence of the cross-plane thermal conductivity of the 20 Ah LFP/graphite pouch cell measured at various SOC levels.

Loges et al.²¹ showed that the thermal conductivity of various electrodes, including LCO, NMC, and graphite, decreases as temperature increases. However, since these experiments were performed under dry conditions, they did not account for the influence of the liquid electrolyte. The effective thermal conductivity of the porous electrodes can differ significantly between the dry state and electrolyte-saturated state^23,43. Although the intrinsic thermal conductivity of pure electrolytes is relatively low (approximately 0.18 to 0.60 ${\text{Wm}}^{-1}$ ${\text{K}}^{-1}$)^23,44–46, it remains significantly higher than that of air (approximately 0.026 ${\text{Wm}}^{-1}$ ${\text{K}}^{-1}$), thereby enhancing heat transport through the fluid phase. Maleki et al.⁴⁷ reported that $k_{\perp }$ in a commercial Sony 18650 LCO/graphite cell increased by approximately 44%, from 2.36 to 3.40 ${\text{Wm}}^{-1}$ ${\text{K}}^{-1}$, after electrolyte saturation. Vertiz et al.³⁰ observed that the thermal conductivity increased by 92%, from 0.219 to 0.421 ${\text{Wm}}^{-1}$ ${\text{K}}^{-1}$, when a ${\text{LiFePO}}_4$/graphite pouch cell was soaked in electrolyte. Therefore, consideration of the electrolyte is necessary in temperature-dependent thermal conductivity measurements of electrodes. However, this requires a complex experimental setup and only Liebig et al.⁴⁸ conducted measurements under electrolyte-saturated conditions. They found that the thermal conductivities of NMC cathode, graphite anode, and separators increase in thermal conductivity with increasing temperature.

On the other hand, thermal contact resistance (TCR) has been reported to significantly influence $k_{\perp }$⁴⁹, accounting for approximately 25% of the total thermal resistance⁵⁰. Liu et al.⁵¹ showed that TCR partially decreases with temperature, which was attributed to enhanced interfacial adhesion at higher temperatures and an increased real contact area caused by asperity compression, while thermal expansion of the cell may further reduce TCR⁵². Consequently, higher temperature promotes thermal transport across porous interfaces and improves $k_{\perp }$²⁴, consistent with the results in Fig. 3(a). However, quantitatively separating the contribution of TCR requires considerable experimental effort. Nevertheless, our whole-cell measurements inherently capture this effect, thereby providing practical significance by directly reflecting the $k_{\perp }$ behavior under realistic operating conditions.

Additionally, the measured $k_{\perp }$ may have been slightly underestimated due to the interfacial TCRs between the specimen and the assemblies. However, under our experimental conditions (i.e., consistent compression pressure, uniform contact, and smooth surface with the application of thermal paste), the measurements showed only a slight discrepancy (less than about 0.002 ${\text{Wm}}^{-1}$ ${\text{K}}^{-1}$). This was verified using a counterfeit battery composed of multilayer insulating materials, which contained more interfaces under the same conditions than a single specimen. The theoretical $k_{\perp }$ of the counterfeit battery was estimated to be 0.225 ${\text{Wm}}^{-1}$ ${\text{K}}^{-1}$, whereas the measured value was 0.223 ${\text{Wm}}^{-1}$ ${\text{K}}^{-1}$, as examined in our previous study²⁷. Therefore, this effect is considered negligible in the present measurements.

Interestingly, Fig. 3(a) shows that the $k_{\perp }$ curves exhibit similar slopes with increasing temperature across different SOC levels. Similarly, Fig. 3(b) presents consistent SOC-dependent trends in $k_{\perp }$ regardless of temperature. To verify this observation, we conducted an analysis of covariance (ANCOVA) including the interaction term between temperature and SOC. For the ANCOVA, the relationship between $k_{\perp }$ and temperature was treated as linear, with an $R^2=0.94$. The interaction term was not statistically significant in either model, with $F=2.11$ ($p=0.130$, adjusted $R^2=0.94$) for ordinary least squares (OLS) and $F=1.18$ ($p=0.358$, adjusted $R^2=0.93$) for weighted least squares (WLS). These results support the conclusion that no meaningful slope differences across SOC levels exist within the studied temperature range, indicating that SOC and temperature independently influence $k_{\perp }$. In this analysis, the homoscedasticity of residuals was confirmed using the Breusch–Pagan test ($p=0.396$), showing that the assumption of constant variance was not violated. In addition, the Durbin–Watson statistic was 1.96, which is close to 2 and indicates the independence of errors. The independence of SOC and temperature effects is likely due to the investigated temperature range (20.6 to 43.3$_{}^{\circ }$C), which induces negligible structural changes in the electrodes. Nevertheless, since Li-ion cells inherently undergo temperature fluctuations during charging and discharging, both effects must be considered simultaneously in practical thermal modeling.

Since $k_{\perp }$ is influenced by intrinsic cell characteristics such as chemistry, capacity, layer thickness, and electrode composition, its direct generalization to other cells is limited. Indeed, previous studies have reported inconsistent SOC- and temperature-dependent trends in $k_{\perp }$ for LFP/graphite cells^24,28,30,31. Such discrepancies primarily arise from differences in geometry, individual layer thicknesses, applied compression pressure, and material composition, all of which affect both the intrinsic thermal conductivity and the thermal contact resistance (TCR)⁵³. Accordingly, while SOC and temperature variations are known to influence $k_{\perp }$, the specific trend may differ among cells. This underlines the practical advantage of whole-cell measurements, as efficiently enabled by the custom-designed GHP method used in this study.

Conclusion

In this study, we accurately measured the cross-plane thermal conductivity ($k_{\perp }$) of a 20 Ah LFP/graphite pouch cell using a custom-designed GHP apparatus. At room temperature (27.3$_{}^{\circ }$C), the results show that $k_{\perp }$ decreases with increasing SOC, reaching a minimum of 0.137 ${\text{Wm}}^{-1}$ ${\text{K}}^{-1}$ at $\text{SOC}=79.6\%$, followed by a sharp increase to 0.257 ${\text{Wm}}^{-1}$ ${\text{K}}^{-1}$ at $\text{SOC}=100\%$. This trend was consistently observed across the entire temperature range of 20.6 to 43.3$_{}^{\circ }$C. At a given SOC level (i.e., $\text{SOC}=0\mathrm{\%}$), $k_{\perp }$ increased from approximately 0.235 to 0.423 ${\text{Wm}}^{-1}$ ${\text{K}}^{-1}$ as the temperature increased from 20.6 to 43.3$_{}^{\circ }$C, corresponding to a relative increase of about 80%. Although this trend may not be consistent with that observed in other LFP/graphite cells, we demonstrate that both SOC and temperature influence $k_{\perp }$. Moreover, their effects are independent, and the variation of $k_{\perp }$ with temperature exhibits consistent trends across different SOC levels. These findings provide valuable insights into the $k_{\perp }$ behavior of Li-ion cells and underscore the importance of accounting for both SOC and temperature dependence, which independently affect $k_{\perp }$.

Author contributions

M.K. and J.K. performed the majority of work. S.K. contributed to battery experiments. Y.K. and B.L. supervised and conceptualized the study. All authors reviewed and commented the manuscript.

Funding

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. RS-2024-00442068).

Data availability

The datasets generated and/or analyzed during the current study are available from the corresponding author upon reasonable request.

Declarations

Competing interests

The authors declare no competing interests.