When an LIB is charged at room temperature, lithium ions move from the cathode through the electrolyte and SEI layer toward the surface of the anode via an electric field before smoothly moving into the anode via diffusion. The detailed process is illustrated in Fig. 1.

However, a problem occurs on the surface of the anode when an LIB is charged at low temperatures. More specifically, lithium ions are injected from the electrolyte to the surface of the anode via an electric field, similar to the charging process at room temperature. Subsequently, the injected lithium ions move into the anode via diffusion according to Fick’s first law (Eq. 1), and they are then intercalated.

where J_x denotes the diffusion flux, D indicates the diffusion coefficient, C refers to the lithium-ion concentration, x corresponds to the distance from the electrode, and ∂C/∂X refers to the concentration gradient. As indicated in Eq. 1, the diffusion flux is proportional to the diffusion coefficient and concentration gradient. D is determined by

where D₀ indicates the diffusivity, Q symbolizes the activation energy, R denotes the universal gas constant, and T indicates the temperature in Kelvin. Accordingly, the diffusion flux of lithium ions significantly decreases at temperatures below 273.15 K (=0^oC). Consequently, lithium ions injected by the charging current gradually accumulate at the surface of the anode instead of smoothly moving into the anode. When the concentration of ions at the surface of the anode exceeds the saturation concentration, lithium plating occurs at the interface between the anod e and SEI layer, or needle-shaped dendrites form owing to the local concentration of lithium generation [35]. Lithium plating forms an additional SEI layer by reacting with the electrolyte. Consequently, the process causes a permanent reduction in the capacity of the LIB owing to a loss of active lithium material; moreover, it degrades performance owing to an increase in the internal resistance. In worst cases, the dendrite may penetrate the separator and rupture the battery owing to an internal short circuit with the cathode, thereby significantly degrading the stability of the LIB [35].

At low temperatures, reverse-pulse charging can maintain the durability of a cell by alleviating the side effects of CC charging in both the high-current and reverse-current parts. Fig. 2 shows the effect of reversepulse charging at low temperatures. In particular, lithium ions are rapidly injected into the anode interface in the high-current part of the charging profile, which is illustrated as a red line in Fig. 2a. Accordingly, a large lithium-ion concentration gradient, shown as a bold red line in Fig. 2b, is evident from the anode interface to the inside. Therefore, diffusion coefficient D, which is reduced at low temperatures, can be compensated by a significant increase in ∂C/∂X of Eq. 1. If the amplitude and duration of the high-current part are excessive, lithium ions may accumulate over the saturation concentration at the anode interface, which would result in lithium plating and the formation of dendrites, similar to conventional CC charging. Therefore, selecting the amplitude and duration of the current is crucial for stable low-temperature reverse-pulse charging. Subsequently, the reverse-current part, illustrated as a blue line in Fig. 2a, shows that a relaxation time is required for the instantaneously injected lithium ions to diffuse into the anode and get intercalated. Unlike CC charging, in which lithium ions are continuously injected into the anode, the reverse-current period alleviates the accumulation of lithium ions at the anode interface, which is indicated as a blue line at the anode side in Fig. 2b.

In addition, the reverse current creates an electric field in the electrolyte in the direction of the cathode, as shown in Fig. 2b. The electric field makes lithium ions move back to the cathode momentarily, lowering the concentration of lithium ions in the SEI layer. In particular, as shown in Fig. 2b, the lithium dendrites and plating generated during low-temperature charging are uneven and needle-shaped; therefore, the electric field is concentrated even at a low reverse current. Thus, the lithium plating and dendrites generated in the high-current section are selectively removed by the subsequent reverse current before forming an additional SEI layer through a chemical reaction with the electrolyte, thereby preventing a decrease in capacity owing to the aforementioned side effect and improving the durability of the cell.

An excessively long and high reverse-current part is advantageous in terms of durability; however, it is also disadvantageous because the lower mean charging current decreases the charging speed. Therefore, it is imperative to set the duration and amplitude of the reverse current to a minimum value to effectively alleviate the accumulation of lithium ions at the anode interface.

As explained in the previous section, it is crucial to select a pulse charging profile to maintain the durability of the cell while maintaining a charging speed comparable to that of CC. For pulse charging at room temperature, which has been previously studied, charging is performed using a profile with a frequency that minimizes the impedance of a cell to realize efficient charging. However, in the case of low-temperature charging, having suitable conditions to alleviate the accumulation of lithium ions at the anode interface is a decisive factor. Therefore, in this study, the movement characteristics of lithium ions at the interface between the anode and SEI are analyzed to select a suitable charging profile.

Considering that the electric field at the anode interface is relatively small, electrical movement can be ignored. If the diffusion layer is sufficiently thin, convection movement can be ignored because of its proximity to the electrode [19]. Thus, Fick’s second law is established as lithium-ion movement is primarily caused by diffusion.

where t denotes the time. Since the diffusion layer is thin, the movement of lithium ions in Eq. 3 may only be considered in the x direction to the surface of the anode [14]. If the initial concentration of lithium ions is C₀, the initial condition is

Once the charging current is applied, the boundary condition at the electrodes can be expressed as

where i indicates the charging current, n indicates the number of electrons generated or removed during the reaction in the anode, and F symbolizes the Faraday constant.

When a constant current is applied, the solution of Eq. 3 with the initial and boundary conditions is obtained using the Laplace transformation [19].

The concentration of lithium ions accumulated in the anode interface during one cycle of a pulse profile comprising charge and discharge (or rest) can be calculated using Eq. 6. Using the principle of superposition, the concentration of lithium ions accumulated during a cycle is given as

where i_c and i_d denote the charge and discharge currents, respectively, and t_c and t_d denote the charge and discharge times, respectively.

To prevent lithium plating and the formation of dendrites, the lithium-ion concentration accumulated at the anode interface can be maintained below the saturation concentration until full charging is achieved under the following condition:

where f denotes the frequency of the pulse profile, Q_t denotes the capacity of the LIB, C_sat corresponds to the saturation concentration, and i_m denotes the mean charge current of the pulse profile, which is expressed as

Fig. 3 illustrates the three charging profiles for low-temperature charging. In the case of CC charging, a constant current i_c is used to charge the LIB. In the case of pulse current (PC) or reverse-pulse current (RPC) charging, current i_c for charging during t_c and a reverse-current period for discharging with current i_d during t_d are repeatedly performed. Parameters i_c, i_d, t_c, and t_d were selected to satisfy Eq. 8, and their corresponding values are listed in Table 1.

Simulations were performed to confirm the effectiveness of the selected profiles using the simulator PyBaMM [36]. Fig. 4 shows the change in the concentration of lithium ions accumulated at the anode interface with respect to the charging time. In the case of CC charging at –10^oC, the concentration of lithium ions at 1000 s increased by 61% compared to CC charging at 25^oC. As discussed previously, such an increase in the concentration of lithium ions causes lithium plating and dendrite formation, which degrade the performance and durability of an LIB. Meanwhile, in the case of PC and RPC charging at –10^oC, the concentration of lithium ions at 1000 s increased by 39% and 33% for the PC and RPC, respectively, compared to CC charging at 25^oC, which significantly decreased the increase in the concentration, compared to CC charging. Based on these results, it is evident that the PC or RPC can improve the durability of LIBs during low-temperature charging, and this was further confirmed through experiments, as discussed in Section 3.

Three test cells with a capacity of 5 mAh were manufactured in the form depicted in Fig. 5 for use in the experiment on the three charging profiles: CC, PC, and RPC. The cathode was NCM622, the electrolyte was 1 M LiPF₆ in EC/DMC, and the anode was composed of graphite. A spring was used to apply pressure inside the cell, a nickel disk was used as a current collector, and a gasket was utilized to seal the cell.

The experiments include a capacity verification experiment and impedance analysis to compare the performance of the test cells at 25^oC, and a cycle experiment to compare the effect of the charging profiles during low-temperature charging. The experimental platform for the test cells was set up as shown in Fig. 6. The experimental platform comprises a temperature chamber, oscilloscope, battery tester, and host computer. A battery tester (VSP, Biologics) was employed to perform the cycle experiment and analyze cell performance and impedance.

The sequence of experiments is as follows.

1. After soaking the test cells at 25^oC for more than 8 h, the test cells were charged and discharged five times between 2.7 V and 4.2 V. This step is identified as “Pre-conditioning”.

2. Following the pre-conditioning, all cells were fully charged with CC (0.2 C, until 4.2 V)–CV (4.2 V, under 0.02 C). Subsequently, the cells were discharged to 2.7 V at 0.2 C to verify the cell capacity.

3. The impedance of the cells was measured using electrochemical impedance spectroscopy (EIS) under the conditions of the Potentiostatic mode, voltage of 10 mV, and frequency from 100 mHz to 1 MHz in a fully discharged state. Steps 2 through 3 are identified as “Cell analysis”.

4. Cell analysis was performed before the test, after 10 and 20 cycles.

5. After soaking the test cells at –10^oC for more than 8 h, each cell was charged to 4.2 V at –10^oC using the three profiles, namely, CC, PC, and RPC, as introduced in the previous section.

6. A rest period of 5 min was allowed to stabilize the voltage.

7. The cell was discharged to 2.7 V with a current of 0.2 C.

8. A rest period of 5 min was allowed to stabilize the voltage.

9. Steps 5–8 were repeated 10 times. These processes are identified as the “Cycle experiment”.

10. In total, 20 cycle experiments and three cell analyses were performed for each test cell, and the experiment was terminated.

Fig. 7 shows the flowchart indicating the sequence of experiments. The proceeding section presents detailed explanations and results of each experiment.

Prior to the cycle experiment, a capacity verification experiment was performed on each test cell after 10 and 20 cycles to quantitatively compare the capacity fade values of the cells. Since the capacity of LIB varies based on the temperature, an experiment was performed after socking the cells in a chamber at 25^oC for more than 8 h for comparison under identical conditions.

In CC mode, the cell is charged at a fixed current of 0.2 C, such that the cell voltage rapidly rises at the beginning and gradually saturates, reaching 4.2 V. Once the cell voltage reaches 4.2 V, the charging stage changes to the CV mode, and the charging current gradually decreases while the cell voltage remains fixed at 4.2 V. When the decreasing charging current reaches 0.02 C, the charging of the cell is terminated, and following a rest period of 5 min, the cell is discharged until the cell voltage reaches 2.7 V with a constant current of 0.2 C. Accordingly, the capacity of the cell can be determined by

where I_d and T_d denote the discharge current and time in the capacity verification experiment, respectively. The capacities of the three test cells before the cycle experiment were determined as 4.857, 4.736, and 4.903 mAh. These pre-experimental capacities are identified as the initial capacity. Considering that each test cell has a different initial capacity, the capacity measured after the cycle experiment was normalized by the initial capacity, as shown in Eq. 11, to compare the accurate capacity fade.

where C(%) denotes the normalized capacity, C_actual indicates the capacity after the cycle experiment, and C_initial indicates the initial capacity.

Fig. 8 shows the typical Nyquist impedance plot and equivalent circuit of the LIB [37,38], and the Nyquist impedance plot of all test cells before the cycle experiment. The Nyquist impedance plot contains two semicircles from the high-frequency domain to the low-frequency domain. These two semicircles are related to each component of the equivalent circuit, as shown in Fig. 8a.

Here, R_b denotes the bulk resistance of the battery, which includes the electrical resistance of the electrolyte, separator, and electrode terminal. C_sei and R_sei denote the capacitance and resistance, respectively, of the SEI layer formed at the junction of the electrode and electrolyte; they are represented by a left semicircle in the high-frequency domain. R_ct and C_dl denote the charge transfer resistance of lithium ions and the capacitance of the charge double layer, respectively, which are represented by the semicircle in the middle frequency domain. Thus, the change in the state of the SEI layer can be confirmed from the changes in the values of C_sei and R_sei, while the change in the reaction dynamics of the cell can be verified from the change in R_ct and C_dl.

As indicated in Fig. 8b, all test cells have similar results with two semicircles. The degree and cause of cell performance degradation can be confirmed more accurately by comparing the impedance values obtained before and after the cycle experiment.

Fig. 9 presents the results of 10 cycle experiments for each test cell, where the three charging profiles were applied independently. In the CC cycle experiment results shown in Fig. 9a, when a charging current of 7 mA is applied, the voltage instantly increases by 0.3 V from 3.67 V to 3.96 V because of the overvoltage. The internal resistance of the cell at –10^oC is considerably high, approximately 43 Ω. The primary reasons for the high resistance include the slower diffusion of lithium ions and decreased charge transfer dynamics in the charge double layer, which increase R_ct at low temperatures [14]. Fig. 9b shows the results of the PC cycle experiment. Unlike CC, t_c and t_d are 9 ms and 1 ms, and i_c and i_d are 8 mA and 0 mA, respectively; therefore, the current is expressed as a value within 0–8 mA of the charging current curve. Fig. 9c presents the results of the RPC cycle experiment. Similar to a PC, t_c and t_d are 9 ms and 1 ms, and i_c and i_d are 8 mA and –2 mA, respectively. Thus, the range of –2 mA to 8 mA of the current curve is expressed as being filled.

Fig. 10 presents a comparison of the accumulated charging capacity for each profile in the cycle experiment. Since the charging process is terminated when the cell voltage reaches 4.2 V, the actual charging time and capacity vary based on the charging profile and cycle. In particular, the durability becomes more degraded if the LIB is more charged at –10^oC; therefore, the accumulated charging capacity during the cycle experiment for each cell should be considered for an objective comparison.

In all charge profiles, the open-circuit voltage is high because the first and eleventh cycles were performed after potentiostatic EIS; thus, the charging capacity is significantly smaller than those in other cycles. Overall, except for the first and eleventh cycles, the PC and RPC have relatively constant and high increasing rates of the accumulated charging capacity. Consequently, the accumulated charging capacities of the PC and RPC are 9% higher than that of CC after 20 cycles. In other words, the PC and RPC can charge the LIB more reliably at low temperatures than CC; however, they are more likely to degrade the durability of the LIB. By contrast, CC exhibits a relatively lower increase in the rate of accumulated charging capacity, which gradually decreases as the cycle progresses; the primary reason is that the use of CC charging at –10^oC degrades the cell characteristics. Accordingly, a large overvoltage is formed by the higher internal resistance. Thus, the degradation in the durability of the cell caused by CC charging can be alleviated by applying PC and RPC charging at –10^oC.

As described in Section 2.1, charging an LIB at low temperatures degrades the cell capacity and durability because of the occurrence of lithium plating and the formation of dendrites. Therefore, the effect of each charging profile was confirmed by comparing the capacity fade after the cycle experiment. Fig. 11 illustrates a graph that compares the results of the capacity verification experiment with those of the simulation after the cycle experiment using the three charging profiles. The experimental and simulation results agree in all cases except after 20 cycles of CC. This difference can be attributed to the relatively smaller actual charge amount in the cycle experiment, as shown in Fig. 10 in the case of CC charging. Both experimental and simulation results reveal that the capacity fade of the RPC is significantly less than that of CC. As shown in Fig. 4, an excessive increase in the lithium-ion concentration at the anode interface during low-temperature charging is the primary reason for the cell capacity fade, and the RPC alleviates the durability degradation of the cell by considerably reducing the concentration increase relative to CC.

Fig. 12 presents a comparison between the change in the cell capacities for each charge profile following the cycle experiment. In the CC, PC, and RPC charging methods, a capacity reduction of 13%, 8%, and 4%, respectively, after 10 cycles, and a capacity reduction of 20%, 19%, and 8%, respectively, after 20 cycles, is evident. Compared to the CC, the capacity degradation decreases by 38% for the PC and 69% for the RPC after 10 cycles, and it decreases by 5% for the PC and 60% for the RPC after 20 cycles. Therefore, the CC caused the most severe capacity fade, whereas the RPC exhibited the smallest capacity fade. The PC caused a similar capacity fade with CC after 20 cycles because of the difference in the total charge capacity during the cycle experiment, as shown in Fig. 10. Because the durability of the cell is more degraded as the total charge capacity at –10^oC increases, the capacity fade of the cell should be compared in accordance with the total charge capacity at –10^oC to perform an objective comparison. Fig. 13 shows the capacity fade according to the low temperature charging capacity during the cycle experiments. The capacity fade rate of CC is the highest at 2.33, the PC has a capacity fade rate of 1.99, which is 15% less than that of CC, and the RPC has a capacity fade rate of 0.91, which is 61% less than that of CC. Therefore, the experimental results indicate that CC causes the most severe degradation in durability during low-temperature charging, whereas PC and RPC effectively prevent it.

After each test cell is charged using a different charge profile at –10^oC during the cycle experiment, the cells deteriorate differently as the charging progresses. Thus, the value of each component of the equivalent circuit may also differ. Fig. 14 shows the impedance change before and after 10 cycles, and after 20 cycles of the CC, PC, and RPC charging. As shown in Fig. 14a–b, the CC and PC charging profiles drastically change the impedance of the test cells. In contrast, the RPC charging profile results in a considerably smaller change in the impedance even after 20 cycles. In particular, the left semicircle, which indicates the impedance of the SEI layer, exhibits minimal change, as shown in Fig. 14c. Hence, RPC charging effectively alleviates degradation of the cell durability when charging LIBs at low temperatures. Moreover, the results of this impedance analysis reasonably explain the capacity change following the cycle experiment shown in Fig. 12.

Fig. 15 shows the changes of each component in the equivalent circuit extracted from the impedance analysis result using the ZFit software (Biologic). As shown in Fig. 15a, C_sei decreases by 0.43 μF for the CC charging and 0.46 μF for the PC charging, whereas there is little change (an increase of 0.01 μF) for the RPC charging after 20 cycles. As depicted in Fig. 15b, R_sei increases by 1.03 Ω for the CC charging and 0.59 Ω for the PC charging, whereas there is little change (increase of 0.11 Ω) for the RPC charging after 20 cycles. The reason for the increase in the resistance of the SEI layer and the decrease in the capacitance is the increase in the thickness of the SEI layer. This is an indicator of lithium plating and dendrite formation during the low-temperature charging, and an additional SEI layer was formed via the reaction with the electrolyte. This causes cell capacity fade and increased resistance, which conforms with the capacity change following the cycle experiment shown in Fig. 12. Thus, CC charging accelerates lithium plating and the formation of dendrites due to the continuous accumulation of lithium ions at the anode interface. However, PC charging provides a relaxation time for the injected lithium ions to intercalate into the anode, thereby suppressing lithium plating and dendrite formation. RPC charging can suppress lithium plating and dendrite formation more effectively by converting the lithiumion state through a discharge (reverse reaction) before the formed plating and dendrite react with an electrolyte to form an SEI layer. In particular, the effect is maximized because the electric field that exists during the short discharge process is concentrated on sharp or uneven lithium plating and dendrite formation. Therefore, compared to the CC and PC profiles, the RPC induces a relatively small change in the resistance and capacitance of the SEI layer, effectively improving the capacity fade. Moreover, as shown in Fig. 15c, the CC and PC charging profiles also significantly reduce C_dl, whereas the RPC induces a relatively smaller change in C_dl. The charge double layer is a region where lithium ions intercalate into the graphite anode to form an open-circuit voltage of the battery in a charge state. Thus, the reduction in C_dl indicates that part of the structure forming the graphite anode is collapsed or a path is blocked by the generated plating and dendrites, which reduces the site in which lithium ions exist. Therefore, the CC and PC charging profiles actively form plating and dendrites, thus degrading the cell durability; however, the RPC effectively suppresses such side reactions to prevent durability degradation. As shown in Fig. 15d, R_ct exhibits a significant increase in the case of the CC and PC charging. However, in the case of the RPC charging, the increase in R_ct is relatively small. An increase in R_ct means that the activation energy of the reaction is increased to reduce the dynamics of the reaction, and the increase in the activation energy is caused by the products formed when electrolytes decompose under a high potential [38]. Thus, the RPC charging can effectively reduce electrolyte decomposition by suppressing internal potential formation. In other words, at low temperatures, the RPC charging method can maintain the durability of the cell most stably.

The impedance analysis revealed that the RPC effectively suppresses lithium plating and dendrite formation, compared to the CC and PC, while effectively maintaining the durability of the cell. To confirm that the proposed charging method is also effective for batteries applied to actual EVs, the same experiment was performed using a commercial 18650 cylindrical battery (INR18650-25R) with a capacity of 2500 mAh. Using the CC and RPC profiles specified in Table 1, the cycle experiment was performed 500 times, and the capacity fade of the 18650 batteries was compared. Fig. 16 shows the change in capacity of each battery as the cycle experiment progresses. Even though the two charging profiles had the same average current, in the case of CC charging, a capacity fade of 221 mAh occurred after 500 cycles; however, in the case of RPC charging, a capacity fade of 104 mAh occurred. The RPC charging profile reduced the capacity fade by 53%, compared to the CC charging profile. Therefore, through the proposed RPC charging method, the durability of EV and HEV batteries can be maintained more reliably at the same charging rate at low temperatures without making additional battery configuration changes.