Examining the Performance of Implantable-Grade Lithium-Ion Cells after Overdischarge and Thermally Accelerated Aging

Abstract

For implanted medical devices containing rechargeable batteries, maximizing battery lifetime is paramount as surgery is required for battery replacement. In non-life-sustaining applications (e.g., spinal cord stimulators or sacral nerve modulation), these implants may be left unused and unmaintained for extended periods, according to patient preference or in the case of unexpected life events. In this study, we examine the performance of two commercial lithium-ion cells intended for implantable neurostimulators (using lithium titanium oxide (LTO) and graphite as the negative electrode) when subjected to repeated deep overdischarge and to aging at a high state of charge (SOC). The graphite-based cells exhibited significant performance decline and swelling after overdischarge and became unable to store a charge after 42 days at 0 V. In contrast, the LTO-based cells exhibited minimal changes in performance even after 84 days (the length of the study) at 0 V. When subjected to an accelerated aging protocol at 100% SOC, the graphite-based cells were found to age more rapidly than the LTO cells, which exhibited minimal aging over the course of the study period. These results show that practical LTO-based lithium-ion cells are much more tolerant of abuse as a result of neglect and misuse and are worth considering for use in high-value applications where battery replacement is difficult or impossible.

1. Introduction

Rechargeable batteries for use in implanted medical devices face a unique set of constraints not encountered in most other applications. The human body temperature is 37 °C, which will cause the accelerated aging of any lithium-ion battery (relative to room temperature). In addition, cell lifetime is paramount, as surgery is required to replace any defective or damaged batteries. This puts greater stress on designing cells that are exceptionally long-lived. Particularly in the case of non-life-saving applications, there is a significant likelihood that a patient may elect to leave a device unused for extended periods of time without maintaining or removing it. Therefore, cells need to tolerate potential extended storage at a high state of charge (SOC) as well as at a very low SOC (or even under overdischarge conditions).

Medtronic has recently developed a line of implantable batteries that use lithium titanium oxide (LTO) as the negative electrode, in place of the graphite electrode used in traditional lithium-ion cells. LTO is well-known to be more stable than graphite, as the LTO surface is stable in most non-aqueous electrolytes. Although early reports suggested that LTO did not form an solid electrolyte interphase (SEI) layer (due to its high operating potential), recent studies have shown that an SEI layer builds up on LTO-based negative electrodes [1,2]. Other work has explored the response of LTO electrodes to extended overdischarge [3]. However, few studies have investigated the long-term performance of this category of cells when subjected to implant-like conditions.

In this work, we compare the performance of Medtronic’s LTO-based lithium-ion batteries against implantable-grade graphite-based cells manufactured by a third party. We explore the responses of both types of cells to repeated deep overdischarge (7-day-long holds at 0 V) to examine how these cells might respond to extended periods without being recharged. We also conduct tests on the thermally accelerated aging of cells held at high states of charge, which are then used to develop predictive aging models based on the Arrhenius equation to estimate the long-term performance of cells stored at high states of charge.

Our results indicate that LTO-based cells can be much more stable than graphite-based cells against extended aging at both a high SOC and in overdischarge conditions. These findings can help guide the selection and development of more stable lithium-ion cells for medical devices and other applications that may require the cells to tolerate extended periods of storage.

2. Materials and Methods

2.1. Cells Tested

Medtronic provided twenty-five lithium titanium oxide (LTO)-based cells (manufactured by Medtronic) and ten graphite-based lithium-ion cells (manufactured by a third party, a leading implantable cell manufacturer). All cells were intended for use in implanted sacral neurostimulation stimulation devices. The LTO-based cells used lithium cobalt oxide (LCO) for the positive electrode active material, with a normal operating voltage window of 1.8 V to 2.8 V. The graphite-based cells used lithium nickel cobalt aluminum (NCA) for the positive electrode active material with an operating window of 3.0 V to 4.1 V. Within each population, cells were divided into three different test groups: baseline cycling (5 LTO, 2 graphite), overdischarge cycling (5 LTO, 2 graphite), and accelerated aging (15 LTO, 6 graphite).

2.2. Baseline Cycling

Cells subjected to baseline cycling were kept in a 37 °C test chamber and cycled using the following parameters: a charge at the cell’s manufacturer’s recommended charge rate, using a constant-current (CC) charging rate (LTO: 2.5C; graphite: 0.5C) to the cell manufacturer’s specification and recommendation maximum voltage (LTO: 2.8 V; graphite: 4.1 V), with a constant voltage (CV) hold sustained at that voltage until the current fell below 0.1C. Cells were then allowed to rest at an open circuit for 30 min, before being discharged at a constant current rate of 0.5C to the minimum operating voltage (LTO: 1.8 V; graphite: 3.0 V). Cells were again rested for 30 min prior to recharge. On a periodic basis (described below), two characterization discharges were performed: a CC discharge at a rate of C/24 ($0.0416\overline{6}\mathrm{C}$; “C/24 discharge”), and a CC discharge at 0.5C with a 10-min rest at open circuit every 12 min (“DC internal resistance (DCIR) discharge”). The same charge protocol was used for all cycles. The C/24 discharge cycles were performed on cycle numbers 2, 52, 102, 202, …, and the DCIR discharge cycles were performed on cycle numbers 3, 53, 103, 203, …. Baseline cycling continued indefinitely and continued for the duration of the study.

2.3. Overdischarge Cycling

Cells subjected to overdischarge cycling were kept in a 37 °C test chamber and were cycled using a modified version of the baseline cycling protocol described in Section 2.2 above. During selected overdischarge cycles, the cells were first discharged normally and allowed to rest for 30 min. After this, they were subjected to a CV hold maintained at the lower operating voltage until the current fell below 0.01C. Each cell was then discharged at constant current, at 0.01C to 0 V, and then held at 0 V for 168 h (7 days). Following this, the cells were recharged at a 0.1C constant current rate at the lower operating voltage limit. Cycling was suspended at this point, to allow for thickness measurement, before resuming.

Overdischarge cycles were performed at the end of cycles 50, 100, 150, 200, …. The C/24 and DCIR discharge cycles were performed using the same schedule as for the baseline cycling protocol.

After 400 cycles (8 weeks in total at 0 V), the cycling protocol was modified for the remaining (LTO) cells, to extend each overdischarge period to last for 4 weeks (672 h), in order to accelerate the aging process. In addition, the C/24 and DCIR discharge cycles were included after every overdischarge period (rather than after every 100 cycles).

Graphite cells were removed from testing when they were no longer capable of storing a charge. LTO cells were subjected to 10 overdischarge periods (500 cycles) for a total of 112 days at 0 V.

2.4. Thermally Accelerated Aging

For the accelerated aging study, cells were divided evenly into three groups for aging at 45 °C, 50 °C, and 55 °C. Prior to aging and approximately every two weeks thereafter, all test chambers were set to 37 °C, and cells were subjected to a characterization protocol consisting of an initial constant current discharge at 0.5C, a standard discharge cycle, a C/24 discharge cycle, and a DCIR discharge cycle (following the conditions specified in Section 2.2). Cells were then fully charged, after which the chamber temperatures were raised to the experimental set point and the aging protocol was initiated.

During aging, each cell’s voltage was continuously monitored. If the cell voltage fell below the voltage estimated to reflect 95% SOC (LTO: 2.47 V; graphite: 4.03 V), then the cell was recharged. Cells were allowed to rest indefinitely between recharges.

The recharge voltage limits were determined using an open-circuit voltage (OCV) determination cycle, in which cells were charged and then discharged at a constant current rate of 0.1C. All cells undergoing aging were subjected to this cycle, prior to the first characterization measurements. The cell recharge voltage was selected to be consistent with an SOC of 95% for that population.

2.5. Cell Cross-Sectioning

Selected cells were cross-sectioned after the completion of testing. Cross-sectioning was performed by puncturing the cell can, soaking the cell in dimethyl carbonate, then filling the cell with metallographic epoxy. Once cured, the cells were cut with a bandsaw and backfilled with additional epoxy; a water-free polish was then applied and the cells were optically imaged. The samples were then ion polished and imaged with a scanning electron microscope.

2.6. Equipment Used

All charge/discharge testing was performed using a Maccor 4000 battery cycler (current accuracy 0.03 mA during cycling, 0.03 µA during overdischarge; voltage accuracy 2 mV). Cell thickness measurements were performed using a flat anvil thickness gauge (resolution 0.01 mm, accuracy ± 0.025 mm, model 547-520S, Mitutoyo America Corporation, Aurora, IL, USA). Cells tested at 37 °C, 45 °C, and 50 °C were tested in benchtop incubators (Heratherm General Protocol Microbiological catalog number 51028063, ThermoFisher Scientific, Waltham, MA, USA), temperature uniformity ± 0.6 °C, temperature stability ± 0.2 °C). Cells tested at 55 °C were tested in a benchtop oven (±0.3 °C accuracy, ±1.0 °C uniformity, model Symphony 414004-564, VWR International, Radnor, PA, USA). Cross-sections were imaged using an optical microscope (Model UC50, Olympus Scientific, Tokyo, Japan). Ion polishing was performed using an ion-beam polisher (JEOL USA, Peabody, MA, USA). Scanning electron microscopy (SEM) imaging and energy-dispersive X-ray spectroscopy (EDS) maps were collected with a JEOL JSM-IT800 SEM (JEOL USA, Peabody, MA, USA). EDS spectra were acquired with a JEOL JSM-6390LV scanning electron microscope (JEOL USA, Peabody, MA, USA).

3. Results

3.1. Baseline Cycling

Five LTO and two graphite cells were cycled under the baseline cycling protocol detailed above at 37 °C. Figure 1 shows the normalized discharge capacity and DCIR at 50% of the rated SOC for these cells. The method used for calculating DCIR is described in Appendix A. The data in Figure 1 represent approximately 254 days of active cycling for the graphite cells and approximately 260 days of active cycling for the LTO cells; the difference in the total number of cycles achieved reflects the faster charge rate used for LTO cells.

The LTO cells retained more than 99.5% of their original capacity after 1600 cycles (more than 8 months) of continuous cycling at 37 °C. No significant change in the DCIR at 50% of the rated depth-of-discharge (DoD) was observed for these cells over this period. After 1000 cycles at 37 °C, the graphite cells had approximately 87% of their rated capacity, which agrees well with the manufacturer’s specification sheet for these cells (88% of the rated capacity after 1000 cycles at 37 °C and C/2). They also exhibit an increase of about 50% in DCIR at 50% DoD.

Both cells continued to follow an approximately linear trend on both metrics, consistent with cells that are not yet at their end-of-life [4,5,6]. The capacity loss and growth in DCIR that were observed in the graphite cells were as expected for a traditional lithium-ion cell, where SEI growth over time (especially at high states of charge) is expected to consume the lithium (leading to capacity loss) and increase the charge transfer resistance at the negative electrode (increasing cell internal resistance and further decreasing capacity) [7,8].

Both the LTO and graphite cells exhibited significant capacity hysteresis following each characterization period, showing an elevated discharge capacity for several cycles following each C/24 discharge cycle. For the LTO cells, 19.8 cycles were required on average before the cell’s discharge capacity fell to the level it had been at prior to each C/24 discharge. The graphite cells required 13.4 cycles on average to reach the same level. Investigating the cause of this phenomenon is outside the scope of this study, but it can be attributed to the formation of stable lithium concentration gradients within larger particles in one or both electrodes during high-rate cycling [9]. The C/24 discharge cycles effectively disrupt these concentration gradients, as more time is provided for the lithium to diffuse within the electrodes’ active material particles at the end of discharge. We note that this effect is an artifact of the accelerated cycling regime; practical applications for these cells will use slow discharges (over the course of days) and would not develop the proposed concentration gradients.

The differential capacity (dQ/dV) profiles in Figure 2 show that little had changed in the discharge profile of the LTO cells between cycle 1402 and cycle 2. The method for calculating differential capacity is described in Appendix B. All cells showed a dominant peak at 2.327–2.329 V, reflecting the primary plateau for the intercalation of lithium into the lithium cobalt oxide positive electrode, used in these cells, and the flat voltage profile of LTO [10]. The graphite cells did not exhibit a single primary discharge plateau, even when new, which is consistent with the complex dQ/dV profile of NCA/graphite cells [11]. After 1200 cycles, these cells showed a slight downward shift in peak positions (reflecting the impact of elevated internal resistance) and a reduction in peak intensity, especially at lower voltages, which is consistent with other studies of NCA/graphite cells after extended cycling [11].

3.2. Overdischarge Cycling

Figure 3 shows the results for five LTO and two graphite cells that were subjected to repeated overdischarge to 0 V. Every 50 cycles, each cell was discharged to 0 V and maintained under a constant voltage (CV) hold at 0 V for 7 days. The graphite cells were removed from cycling after six overdischarge periods (42 days at 0 V). After eight overdischarge periods (56 days at 0 V), the test protocol was altered to expose the LTO cells to 4-week-long 0 V holds, in order to accelerate the rate of aging. This study design (repeated overdischarge of individual cells) was chosen to maximize the research value of the limited number of cells available, by measuring the response of a small number of cells to overdischarge conditions over time.

After each overdischarge period, the graphite cells exhibited a short-lived (~10 cycle) and rapid loss of capacity, after which the rate of capacity loss per cycle declined (although it remained significant throughout each 50-cycle period). The rate of capacity loss also accelerated after each overdischarge period, as shown in Figure 3, with each overdischarge period resulting in a progressively larger capacity loss. Following the sixth overdischarge period (42 days at 0 V), the graphite cells were incapable of storing a charge above 3.0 V, after which they were removed from cycling. After nine overdischarge periods (84 days at 0 V), the LTO cells continued to exhibit nearly unchanged discharge capacities (>99% of their original capacity). These cells exhibited a similar hysteresis response, with a small capacity increase for several cycles after each overdischarge, like the one observed for both cell types following the C/24 discharge during baseline cycling.

Figure 2d shows the relative change in DCIR at 20% of the rated DoD for both cell types, after spending an increasing period of time at 0 V. A value of DCIR at 20% DoD is used here because the graphite cells lost more than 50% of their capacity before the DCIR measurement was performed at cycle 203. This shows that the graphite cells experienced accelerating growth in DCIR with the passage of time at 0 V, which is consistent with repeated degradation of the SEI and consumption of the electrolyte. Slight (< 10%) changes in DCIR were observed for the LTO cells after a total of 84 days at 0 V.

Figure 2e shows the relative change in battery cell thickness with the passage of time at 0 V. Both cells had a hard metal case with two flat faces that limited the cells’ ability to swell. The graphite cells exhibited accelerating swelling (up to a maximum of 14%) after each overdischarge, which was likely due to the production of significant quantities of gas during each subsequent recharge. No measurable swelling was observed on the LTO cells. No evidence of electrolyte leakage or other indications of the cell case being compromised were observed in either cell type, even after the graphite cells no longer functioned.

The C/24 discharge profile and differential capacity plot for selected cycles for both cell types are shown in Figure 4. In the C/24 discharge following the first overdischarge period, some loss of peak resolution was apparent in the graphite cells, but the largest peak at 3.6 V remains prominent. After 14 days at 0 V, this peak has been largely eliminated, resulting in a nearly linear discharge profile for most of the discharge. The LTO cells exhibited a single large discharge plateau around 2.326–2.330 V throughout cycling without a change, which is consistent with the cell’s behavior during baseline cycling. A very slight increase in the differential capacity was seen at the start of discharge relative to the uncycled cell; we attribute this as being another manifestation of the excess capacity observed in these cells, following a deep discharge.

Figure 5 presents the charge extracted from each cell during each overdischarge period. Both cell types exhibited an initial decay in the current passed during the first several hours (as the cell relaxes from the C/100 discharge and approaches a steady state). During the first overdischarge period, the graphite cells passed 7.0% to 8.0% of their rated capacity during the CV hold at 0 V (see Figure 6). During the second overdischarge, this decreased from 6.5% to 6.8%, after which the amount of charge passed increased with each successive overdischarge period. The LTO cells passed a much smaller fraction of their rated capacity during the first overdischarge period (1.1–1.3%), which declined during the second overdischarge period (0.7–0.9%). Subsequent overdischarge periods behaved similarly, with only a very slight change in accumulated charge (0.8–1.0% of rated capacity) by the 8th week of overdischarge.

3.3. Cross-Sectioning of Tested Cells

After testing, four cells were selected for metallurgical cross-sections: one of each type after overdischarge testing, and one of each type after aging at 45 °C. Optical microscopy (OM; Figure 7) and scanning electron microscopy (SEM; Figure 8) were used to collect images.

Evidence of the dissolution of the copper current collector is apparent throughout the overdischarged graphite cell. Additional copper was visible in both OM and SEM (as bright deposits) within the negative electrode of this cell, which is a result of the spontaneous redeposition of copper during subsequent charges. Energy-dispersive X-ray spectroscopy (EDS) was also performed on each electrode (see Figure 9). These spectra show that the LTO cells use lithium titanium oxide as the negative electrode and lithium cobalt oxide as the positive electrode (lithium is not detected in these EDS results). The graphite cells use graphite in the negative electrode (with no discernable additives), and lithium nickel cobalt aluminum oxide (NCA) in the positive electrode.

Copper was present in the EDS spectra of the graphite negative electrode after overdischarge, as shown in Figure 9, even though the collection area did not include the current collector. This is consistent with the signs of copper in the OM and SEM micrographs. Figure 10 shows an EDS map of the copper signal in the graphite cells; low-intensity copper signals are visible in several regions of the overdischarged cell’s negative electrode, in addition to the regions where the current collector was completely dissolved. The map of the aged graphite cell shows no detectable Cu signal in the negative electrode outside of the current collector.

Phosphorous and fluorine can be attributed to the residual electrolytes present in the cells. Silicon can be attributed to residues from the grinding media (silicon carbide). Trace titanium in the positive electrode of the LTO cells can be attributed to contamination from the negative electrode during polishing. The aluminum in both LTO cell electrodes and the graphite cell’s positive electrode can be attributed to the current collector.

3.4. Analysis of Overdischarge Results

The baseline cycling results are consistent with the cell manufacturer’s specification (where available) and reflect the behavior of cells that have not yet reached end-of-life (where accelerating capacity loss and/or growth in resistance are expected) [4,5,6,13]. This provides a reasonable foundation by which to compare the overdischarge performance.

Significant damage to the graphite cells is immediately apparent after the first overdischarge period. On cycle 49 (just prior to the first overdischarge), graphite cells from both groups (baseline and overdischarge) exhibited a discharge capacity of 99.5% of the original capacity. On cycle 51 (immediately following the first overdischarge), the capacity of the overdischarge cells dropped to 97.6–97.8% of the initial capacity. By cycle 99, this had fallen to 91.8–92.9% of the initial capacity. Each subsequent overdischarge further accelerated the rate of capacity loss.

Two primary reactions are of concern during the deep overdischarge of graphite-based Li-ion cells: solid electrolyte interphase (SEI) decomposition and the dissolution of the copper current collector. SEI decomposition occurs when the negative electrode potential rises above the stability window of the SEI. Once decomposed, a new layer of SEI will be spontaneously re-formed the next time the cell is recharged (when the negative electrode potential drops below the stability window of the electrolyte). This process damages the cell by (a) consuming the electrolyte (both solvent and salt), (b) generating gas within the cell, and (c) forming a new and less uniform layer of SEI. Notably, even with a trickle recharge at a low voltage, the SEI formation that occurs after deep overdischarge is not as controlled as that which occurs during the formation process during battery manufacturing. Many cell manufacturers include sacrificial additives that promote the formation of a stable SEI; these additives are often fully consumed during the initial formation and would not be present during the reformation occurring after overdischarge [14]. The gas formed during SEI reformation is also trapped within the cell. For pouch cells, this may result in the cell swelling and, in extreme cases, a rupture of the pouch. For prismatic cells (like the cells investigated here), this gas increases the internal pressure and can result in the case bulging.

The SEI reformation process continues even after the first recharge. This is apparent here through the continued capacity loss during the 50 cycles between each overdischarge period (at a rate in excess of that observed in the baseline cycling). SEI formation is hypothesized to continue throughout a cell’s life, but at a rate that slows with time [8,15,16]. By overdischarging and then continuing to cycle these cells, this process is restarted, resulting in accelerating damage to the cells.

In addition to SEI decomposition, copper dissolution is a concern for cells that are deeply overdischarged. Copper is universally used as the current collector for graphite negative electrodes because of its electrochemical stability at the necessary potentials. However, if the electrode potential rises above the stability window, the copper will dissolve into the electrolyte. This dissolved copper will redeposit (often in dendrite or cloud-like formations) upon subsequent recharge [17,18,19]. The copper dissolution potential is 3.38 V, vs. Li/Li⁺ in a standard aqueous solution [20]. Despite this, we observed evidence of copper dissolution and replating in the post-overdischarge cross-section of these cells. This suggests that repeated and sustained discharging to 0 V (as may occur when a battery-containing device is left unused for an extended period) is sufficient to drive copper dissolution within a graphite-based lithium-ion battery.

Both SEI decomposition and copper dissolution are electrochemical processes, and the excess charge passed from the graphite cells at 0 V likely reflects the rate of reaction of both processes. We observed that the current decayed over the first several days of each overdischarge. This suggests that the SEI decomposition reaction may gradually decelerate before reaching a steady state. Subsequent overdischarges were found to exhibit progressively higher currents (especially in the latter days of each discharge), suggesting that the SEI decomposition reaction may be accelerated as a result of repeated overdischarges. In the final two overdischarge periods, the current at 0 V became increasingly erratic, which is consistent with the higher rates of pitting corrosion of the copper electrode [21].

No evidence of any detrimental impacts to the LTO cells was observed after multiple extended overdischarge periods, although the LTO electrodes have been shown to form SEI layers [1,2]. These cells also used an aluminum current collector and are, thus, not susceptible to copper dissolution. As a result, deeply discharging the LTO cells fully delithiated the LTO negative electrode and lithiated the positive electrode, both of which are stable in this state. Both LTO and cobalt oxide-based positive electrode materials have very steep voltage profile curves in this state, so relatively little current is passed during the overdischarge process. As with the graphite cells, the current at 0 V started out relatively high (close to the C/100 discharge rate) and declined as the electrodes become fully (de)lithiated. After this, the current reached a steady (slightly non-zero) value, resulting in a gradual increase in accumulated charge over the period of time at 0 V. The cause of this current is currently unexplained; however, it does not appear to result in any lasting damage to the cells.

3.5. Accelerated Aging at High SOC

Ordinary charge/discharge cycling serves as a useful way to accelerate the aging reactions in Li-ion batteries that occur during active use (especially during charge). However, this type of test does not capture the effect of calendar aging and/or the degradation that occurs chemically when cells are stored at a fixed SOC for extended periods. To examine this, we also performed thermally accelerated aging at a fixed SOC for both the LTO and graphite cells.

Figure 11 presents the change in several metrics over the course of aging at various temperatures for 135 days. The ells were stored at 100% of SOC at the specified temperature, based on the standard charge condition for each cell. Voltage was monitored throughout aging and the cells were recharged when the OCV fell below the estimated 95% SOC voltage. Recharge frequency was found to decrease with aging; most cells were recharged at least once during the first aging period, while only two cells were recharged during the third aging period (50 days), and no cells were recharged while aging after the fourth aging period (64 days) was completed (see Appendix C and Figure A1).

Graphite cells exhibited significant changes in all three of the metrics investigated here (the DCIR at 50% DoD, the discharge capacity of the DCIR cycle, and the C/24 discharge capacity) at all temperatures after the first aging period. These changes continued to grow along with additional aging, with an increase of more than 40% in DCIR and a loss of at least 4% of the initial capacity at both rates after 135 days of aging. One graphite cell that had been aged at 55 °C (shown in bright yellow in Figure 11) appeared to enter a second phase of reaction after ~100 days of aging, exhibiting an increased rate of capacity loss and DCIR growth after this point.

LTO cells exhibited no significant change in any of the metrics over the study period at any temperature. No cell exhibited more than a 1% loss in capacity after aging at any temperature, and the rise in DCIR was not more than 10% for all cells. A slight (<1%) variation in capacity was observed during the initial characterization cycle prior to aging (relative to subsequent cycles), which can be attributed to these cells still “breaking-in” after manufacturing. Additionally, two LTO cells that were later aged at 55 °C exhibited an anomalously low C/24 discharge capacity during the pre-aging characterization cycle.

3.6. Thermally Accelerated Aging and Predictions

Aging the cells at various temperatures and measuring their performance enabled a predictive model to be built that reflects the long-term aging expected to occur in these cells at normal operating temperatures. This is performed using a modified version of the Arrhenius equation, shown in Equation (1) below:

$$\mathsf{\Delta }M=k\cdot b{t}^x=A{e}^{-\frac{E_A}{RT}}\cdot t^x=e^{C-\frac{E_A}{RT}}\cdot t^x$$

(1)

This formula states that the change in a measurable cell property (such as discharge capacity or DCIR) is proportional to the reaction rate constant $k$ and a power-law time-dependence. The choice of a power-law time-dependent relationship is arbitrary but is well justified in practice, as it can describe a range of reaction regimes (both accelerating and decelerating) with a single variable. In addition, the growth of a passivating layer on a surface is theoretically described by $t^{1/2 }$, and this has been used to model the rate of SEI growth and DCIR [6,7,8,22,23]. The reaction rate constant, $k,$ can be substituted with the right-hand side of the Arrhenius equation to produce an explicit temperature component to the formula, which is controlled by the activation energy, $E_A$. This results in a formula where the change in a given metric ($\mathsf{\Delta }M$) is dependent on two experimental conditions (time, $t$, and the absolute aging temperature, $T$), the ideal gas law constant, $R$, and three empirically derived parameters: the prefactor $A$ (or the prefactor exponential, $C$), the activation energy, $E_A$, and the time-dependent power-law factor, $x$. In addition to the assumption about time dependence, this model also assumes that the measured change in performance is controlled by the same reaction mechanism in all cells and at all temperatures. Heating cells to too high a temperature can defeat this assumption, resulting in poor model fits and/or necessitating the exclusion of that data. For this reason, the maximum temperature for this study was limited to 55 °C.

With this formula, we used all the collected aging data for a particular cell type and metric and produced a model that relies on only three adjustable parameters. For each metric of interest, the change in the metric was calculated with the formula $\mathsf{\Delta }M=1-\frac{M}{M_0}$ or $\mathsf{\Delta }M=\frac{M}{M_0}-1$ (depending on the expected direction of the expected change in the metric). This value, along with the total aging time and absolute aging temperature, was then fitted against Equation (1), as defined above, to solve it for $C$, $E_A$, and $x$. The details of this fitting process are described in Appendix D.

Figure 12 presents multiple ways of evaluating the quality of fit of the rise in DCIR at 50% DoD, in both the graphite and LTO cells. For the graphite cells, this metric fitted well with the modified Arrhenius model, with a predicted vs. actual R² value of 98%. In contrast, the LTO cells were not a good fit for this metric, with an R² value of just 19%. Both groups shared similar root mean squared errors (graphite: 0.018, LTO: 0.019), which indicated that the poor LTO fit was due to the lack of signal. As can be seen in the top row of Figure 11 (showing the raw aging data for these values), the LTO cells exhibited very little systematic change in this metric over the study period. Similar data for the DCIR cycle discharge capacity are presented in Appendix E and Figure A2.

Figure 13 shows the aging data and model predictions at the various aging temperatures for DCIR at 50% DoD and the DCIR cycle discharge capacity. For both metrics, the graphite cell model parameters fitted the data reasonably well (R² = 89% and 79%, respectively). In contrast, the LTO cells were not predicted well, as the change in these metrics is small, relative to the measurement error. For the graphite cells, the DCIR at 50% DoD was predicted to have a power-law dependence of 0.67 (95% confidence interval (CI): 0.64–0.71) and an activation energy of 33.2 kJ/mol (95% CI: 29.8–36.7 kJ/mol). The higher-than-expected time dependence suggests that the processes affecting this metric are not following a theoretical film passivation reaction scheme. The DCIR cycle discharge capacity loss was predicted to follow a square root time-dependence (x = 0.48; 95% CI: 0.42–0.55) with a significantly lower activation energy (13.1 kJ/mol; 95% CI: 4.8–21.8 kJ/mol). The LTO cells exhibited very slight changes in DCIR (<5%) and DCIR discharge capacity (<1%) in all conditions. Because of this, the confidence intervals on the fits for these parameters are extremely wide. Additional aging (possibly at higher temperatures) is required to increase confidence in these parameters [24].

Finally, the long-term predictions at 37 °C are shown in Figure 14. Based on these models, the graphite cell population is expected to experience significant aging after 5 years of storage at 100% SOC in a 37 °C environment, with the internal resistance increasing by 2.5× and the DCIR cycle discharge capacity dropping by 30% (only the population average is predicted; confidence intervals for individual cells are not predicted). In contrast, the LTO cells are expected to see a less than 30% increase in DCIR over this period (based on the upper boundary of the 95% CI). It is important to note that the extrapolated predictions here should be viewed as optimistic; these predictions assume that the reactions observed to date will continue to develop at the same rate. Additional reactions that have not been accounted for in the model (such as electrolyte depletion) are generally expected to accelerate the rate of aging above those figures predicted here.

4. Discussion and Conclusions

In this work, we explored the performance of two different commercial lithium-ion batteries intended for use in implanted medical applications; one used a traditional graphite electrode and the other, a lithium titanium oxide (LTO) negative electrode. We investigated their response to two different aging scenarios (deep overdischarge and extended storage at high states of charge). During overdischarge, the graphite-based cells were found to exhibit signs of significant degradation after one 7-day overdischarge period at 0 V, and the degradation accelerated with each subsequent overdischarge session. We identified behaviors consistent with SEI degradation during overdischarge and reformation on subsequent recharge, as well as signs of copper dissolution and replating. Using thermally accelerated static aging at 100% state-of-charge, we observed that the graphite-based cells aged significantly when stored at temperatures of between 45 °C and 55 °C for approximately 4 months, allowing the development of a robust model to predict long-term changes in internal resistance (DCIR) and capacity loss. The LTO-based cells exhibited minimal aging under the same conditions, which limited the precision of the model. Despite this, the very small amount of aging observed suggests that these cells will exhibit excellent long-term (>5 years) performance, even when stored at 37 °C.