Trackable galvanostatic history in phase separation based electrodes for lithium-ion batteries: a mosaic sub-grouping intercalation model

Kyu-Young Parkab, Jihyun Hongc, Won-Mo Seongab, Jung-Joon Kimab, Kyojin Kuab, Byungju Leeab and Kisuk Kang*ab
aDepartment of Materials Science and Engineering and Research Institute of Advanced Materials (RIAM), Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul 151-742, Korea. E-mail:
bCenter for Nanoparticle Research at Institute for Basic Science (IBS), Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul, Korea
cDepartment of Materials Science and Engineering, Stanford University, Stanford, CA 94305, USA

Received 29th July 2017 , Accepted 18th September 2017

First published on 18th September 2017

An in-depth understanding of electrode reactions is essential to achieve a breakthrough in lithium-ion battery technology, the new ‘engine’ for electric vehicles. Recent studies have continued to reveal unexpected electrode behaviors, providing a more refined view of the operating mechanisms of electrodes from the atomistic to particle level and offering new perspectives to design better battery systems. Herein, it is observed for the first time that the history of applied current densities is memorized in electrode materials that operate via a two-phase reaction and systematically induces a transient galvanostatic profile variation of the electrode. These unforeseen profile changes can be explained by a new proposed intercalation model in which active particle sub-groupings are intermittently generated with a non-uniform chemical potential distribution at the end of charge or discharge. The types of active particle groupings are determined by the current density of the prior charge or discharge, resulting in distinct signatures in the electrochemical profile in the subsequent galvanostatic process. Our proposed intercalation model affords a more comprehensive view of the behavior of electrodes containing many-body particles by elucidating the effect of the applied current densities.

Broader context

Recent studies have continued to refine the view of the intercalation mechanisms of many-body particle electrodes, offering new insights towards designing a better battery system. Under an identical current density, an electrochemical cell would display indistinguishable charge/discharge profiles (relationship between voltage and capacity) regardless of the history of applied current densities unless different degradation of the electrodes occurs. Here we firstly report that the current density history that has been applied to the system also affects the galvanostatic voltage profile, which is named as the pre-current effect, in phase separation based electrode materials. This unforeseen phenomenon enables us to track a new aspect of the intercalation mechanism of an electrode containing many-body particles, which reveals a grouping of active particles with chemical potential gaps that are intermittently generated during galvanostatic charging and discharging. Our proposed intercalation model affords a more comprehensive view of the behavior of electrodes containing many-body particles by elucidating the effect of the applied current densities, and indicates that control of the chemical potential inhomogeneity arising from the thermodynamic and kinetic origins is the key for designing better phase-separating electrode materials.


Electrochemical systems such as lithium-ion batteries, fuel cells, and supercapacitors can provide eco-friendly and cost-effective energy storage solutions; therefore, optimization and development of these systems have been extensively conducted in the past several decades.1–3 A general characteristic of electrochemical energy storage systems is that they exhibit inherent galvanostatic voltage profiles in anodic and cathodic reactions depending on the input/output current density. According to classical electrochemistry, practical voltage profiles are determined by several factors, such as the chemical potential of guest ions, temperature, and polarizations from kinetic factors. Hence, it is expected that under an identical current density and kinetic environment, an electrochemical cell would display indistinguishable galvanostatic charge/discharge profiles, regardless of the history of applied current rates unless different degradation of the electrodes occurs. However, our elaborate electrochemical experiments on a lithium-ion battery system composed of phase-separating electrode materials reveal that the current density history also affects the galvanostatic voltage profiles.

Fig. 1 and Fig. S1 (ESI) present various histories of electrochemical cycling of (a and b) LiFePO4 (LFP) and (c and d) Li4Ti5O12 (LTO) electrode materials in current-density-dependent galvanostatic experiments. The figures on the right in Fig. 1 present zoomed-in profiles of the first (orange), second (green), and third (purple) cycles after pre-cycling, which are plotted together as a function of state of charge (SoC). We conducted these electrochemical experiments under two conditions: case (i) the pre-cycling current density (200 mA g−1) was higher than those of the first, second, and third cycles (30 mA g−1, Fig. 1(a) and (c)) and case (ii) the pre-cycling current density (30 mA g−1) was lower than those of the subsequent cycles (200 mA g−1, Fig. 1(b) and (d)). It is clearly shown that the applied current densities mainly determine the overall overpotential of the cycles (right inset figures in Fig. 1). However, surprisingly, the first galvanostatic profiles (orange) directly after high-current pre-cycling (with 200 mA g−1) systematically shifted down for the LFP cathode (charge) and up for the LTO anode (discharge) compared with the subsequent second and third cycles, as observed in Fig. 1(a) and (c), respectively. In this case, the voltage of the first galvanostatic profile becomes closer to the respective thermodynamic equilibrium potentials of 3.42 V (vs. Li/Li+) and 1.56 V (vs. Li/Li+) than those of the second and third cycles. On the other hand, pre-cycling with a relatively low current density (case ii) caused the voltage of the first galvanostatic charge profile to shift up (LFP) and that of the discharge profile to shift down (LTO) compared with the second and third profiles, which moved farther from the equilibrium potentials, as observed in Fig. 1(b) and (d). Moreover, we confirm that these galvanostatic profile variation tendencies are generally observed for various current density histories and regardless of the sequence numbers of pre-cycling (see Fig. S1 and S2, ESI), and would like to note that it is not caused by other extrinsic factors such as electrode degradation or lithium metal counter electrodes (see Fig. S3 and S4, ESI). Hereinafter, we denote the dependence of the first galvanostatic profile variation on the current density history the ‘pre-current effect’ for convenience. Our experimental results clearly demonstrate that even though the applied current density primarily determines the overall overpotential of the first charge profile, the pre-cycling current density also greatly affects the shape of subsequent galvanostatic charge or discharge profiles, and, counterintuitively, a lower current history induces higher hysteresis (farther from the equilibrium potentials) in the following cycle.

image file: c7ee02138k-f1.tif
Fig. 1 Current history-dependent galvanostatic profile variation of LiFePO4 and Li4Ti5O12 electrodes. (a–d) The whole galvanostatic history of the LFP (a and b) and LTO (c and d) electrodes. The right inset figures exhibit the overlapped first, second and third charge or discharge profiles for each experiment. (a and c) Experiment sets are operated with 30 mA g−1 cycling after 200 mA g−1 current histories. (b and d) Experiment sets are conducted with 200 mA g−1 cycling after 30 mA g−1 current histories. The galvanostatic charge/discharge voltage range is 2.5–4.6 V (vs. Li/Li+) and 1.25–2.0 V (vs. Li/Li+) for the LFP and LTO electrode, respectively, and 1 hour relaxation is conducted after a half-cycle process.

The pre-current effect raises important issues concerning practical aspects of battery operations. LFP and LTO are important electrode materials for next-generation lithium-ion batteries because of their long-term cyclability, superior safety, and fast charge/discharge behaviors. In particular, their high current rate capability is a key electrochemical property that enables their applications in electric or hybrid electric vehicles for commercialization.1,4–7 However, the pre-current effect is evident for phase-separating electrodes and becomes stronger as the difference in current densities between the pre-cycling and subsequent cycles is amplified according to further studies illustrated in Fig. S5–S7 (ESI). Consequently, the usage of LFP or LTO electrodes and the corresponding misrepresentation of the voltage would cause a problem with the SoC estimation for automobiles after the fast charge/discharge process along with the memory effect as reported by Sasaki et al.8 Moreover, the prediction would be more demanding in a typical driving mode, where various accelerating and regenerative breaking situations would occur. Fundamentally, this phenomenon requires a new understanding of the effect of varying current densities on phase-separating electrode reactions. Recently, important progress has been made in elaborating electrode mechanisms concerning the distinctive intercalation behaviors of phase-separating electrode materials that are dependent on the current density.9–13 For the nano-sized LFP electrode, it was investigated that the large interface energy between two phases in a small particle leads to particle-by-particle intercalation under relatively low current densities to avoid an intra-particle two-phase coexistence.6,14,15 As the applied current density increases, it shifts from particle-by-particle intercalation to concurrent intercalation behavior to accommodate the high current.11,12 Furthermore, a very recent report by Lim et al. visualized the relationship between the cycling rates and variations in composition within LFP particles.16 Theoretical approaches also have elucidated the intercalation process in more detail.10,17 It was reported that lithium-rich and lithium-poor particle groups are generated through mosaic instability during de/lithiation, and the electrodes require an incubation time to extract/insert sufficient lithium ions for the next mosaic instability. This sequence of intercalation behavior leads to an intermittent phase transformation, which is called the group-by-group intercalation behavior. Although offering much more polished views of the operating mechanisms of electrodes than previously available, the models or experiments in these studies cannot explain the effect of the cycling history with varying current densities on the de/intercalation behaviors of electrodes, which will be addressed in more detail later. The pre-current effect suggests that a new comprehensive model is required to describe the observed behavior of phase-separating electrodes.

In the following work, we conducted a series of electrochemical experiments and proposed a new electrode mechanistic model using an LFP electrode as an example because it is a well-established system for investigating phase-separating intercalation behavior.11,14,18–23 In addition, we focused on the dependence of the first galvanostatic charge behavior on pre-cycling current densities to simplify the electrochemical experiments because the pre-current effect in the first discharge is affected by not only the pre-cycle but also its first charge process history for the cathode (see Fig. S8, ESI). A relatively high ratio of conductive agent (active material[thin space (1/6-em)]:[thin space (1/6-em)]carbon[thin space (1/6-em)]:[thin space (1/6-em)]binder = 7[thin space (1/6-em)]:[thin space (1/6-em)]2[thin space (1/6-em)]:[thin space (1/6-em)]1 weight ratio) with an electrode thickness less than 40 μm (Fig. S9, ESI) and nanosized LFP particles (approximately 30–70 nm; the particle size distribution is shown in Fig. S10, ESI) was used to minimize the impedance of the cells.11 In addition, about 3 wt% residual carbon was found to be homogeneously coated on the surface as shown in Fig. S11 (ESI). The entire electrochemical experiment was conducted at a constant temperature of 30 ± 0.5 °C and within 30 cycles to avoid changes in the galvanostatic profiles that may arise from temperature change, cell degradation or side reactions.

Pre-cycling-dependent electrochemical properties

Note that the pre-cycling current density also affects other electrochemical characteristics of LFP electrodes. First, the current history affects the length of the one-phase region near a SoC of 0% at the next galvanostatic cycle. Fig. S12(a) and (b) (ESI) present zoomed-in views of three cycles of the experiments as shown in Fig. 1(a) and (b), respectively, near the beginning of the two-phase plateaus. The profiles affected by the pre-current effect, i.e., the first cycle after pre-cycling, exhibit distinguishable one-phase reaction behaviors compared with those in the second and third cycles; for example, the two-phase plateau of the LFP electrode after high-current-density (200 mA g−1) pre-cycling appears at an SoC of ∼7.5%; however, those of the second and third cycles appeared at a relatively higher SoC of ∼8.2%, as observed in Fig. S12(a) (ESI). However, the two-phase plateau begins later (SoC of ∼8.2%) with low-current-density (30 mA g−1) pre-cycling compared with those of the second and third cycles (an SoC of ∼7.3%), indicating that the one-phase reaction region is affected by the history of applied current densities, as observed in Fig. S12(b) (ESI). The underlying reason for this phenomenon will be discussed in a later section. This behavior was also consistently observed in other series of experiments with various current rates, as demonstrated in Fig. S12(c)–(f) (ESI), confirming that prior cycling with a relatively lower current density induces a longer one-phase reaction region in the subsequent cycle. Second, the pre-cycling history affects the relaxation behavior during the rest at the same SoCs. The electrochemical protocol illustrated in Fig. 2(a) was performed, where the electrodes were pre-cycled at a current density of 200 mA g−1, followed by partial charging with a current density of x mA g−1 (x = 30, 80, 130, or 200 mA g−1) to an SoC of 23.6% (corresponding to a capacity of 40 mA h g−1 within a two-phase region). After the partial charging process, the cells were relaxed until dV dt−1 reached 1.0 × 10−6 V s−1 and the voltages were measured. The voltages were also measured for low-current-history experiments with identical partial charging (30, 80, 130, or 200 mA g−1) and relaxation processes; however, the pre-cycling step was performed at a current density of 30 mA g−1, as described in Fig. 2(b). The measured voltages of these experiments are shown in Fig. 2(c). Slightly higher potential values than the thermodynamic equilibrium potential of 3.422 V (vs. Li/Li+)14 were observed, and the two experimental sets exhibited similar tendencies, where the measured voltages monotonously increased as the current density of partial charge decreased. The higher measured voltage, i.e., larger deviation from 3.422 V (vs. Li/Li+), observed after partial lower-current-density charging was applied is counterintuitive. Slow charging is expected to lead to less deviation from the ‘equilibrium potential’ if the deviation stems from kinetic polarization and not from a thermodynamic origin. Moreover, the relaxed voltages vary more with the current density of x for low-current-density pre-cycling (30 mA g−1), which is approximately twice as large (∼5.2 mV) as that of the 200 mA g−1 pre-cycling experiment (∼2.5 mV). Results from Fig. 2(c) clearly demonstrate that the voltages after relaxation of the electrodes with two different pre-cycling histories systematically differed even at the same SoC and at a current density of x.
image file: c7ee02138k-f2.tif
Fig. 2 Demonstration of relaxation behavior depending on the pre-cycling current density of the LFP electrode. (a and b) Representative full electrochemical history of voltage measurement after relaxation with 200 mA g−1 pre-cycling (a) and a 30 mA g−1 pre-cycling (b); after pre-cycling, the cells are charged to 40 mA h g−1 (corresponding with an SoC of 23.6% within a two-phase region) with a current density of x mA g−1 (x = 30, 80, 130 or 200 mA g−1). Cells are relaxed until dV dt−1 reaches 1.0 × 10−6 V s−1, and voltages are measured. (c) The measured voltages of both electrochemical experiment set-ups. The dashed black-dotted line is 3.422 V (vs. Li/Li+) corresponding to a two-phase equilibrium potential of LFP. The error range of each point is calculated from at least three identical measurements.

The observed alternation of the measured voltages with respect to the current density x can be partly explained by the spinodal decomposition de/intercalation behavior which could have multi-equilibrium potentials.14,15 Moreover, several theoretical and experimental studies have indicated that the current density basically determines the intercalation paths and the ratio of the active LFP electrode from particle-to-particle to concurrent intercalation, which might affect the subsequent electrode behavior.11,12,24 Therefore, it is expected that varying the current rates of partial charge will result in the difference in the OCVs and relaxation behavior of the electrodes. However, our experimental results indicate that the dependency of the relaxed voltage on the current density is more dramatic for electrodes with low-current-density pre-cycling, implying that not only the current density itself but also the history of the current density in the prior cycle affect the voltage relaxation, which can hardly be explained by the previous models. Nevertheless, the fact that the OCVs in phase-separating electrodes can be dependent on the state of the active particles hints that the observed pre-current effect is related to the difference in the intercalation states of the electrode imposed by pre-cycling.

Chemical potential distribution in a mosaic instability model and its limitation

A similar transient change of the galvanostatic profile, which originates from different thermodynamic states of the electrode, has been reported as the SoC memory effect.8 Sasaki et al. observed that after partial charge/discharge, the subsequent galvanostatic cycle exhibits a small voltage bump at a specific SoC and attributed this phenomenon to a memory effect based on the particle-by-particle intercalation behavior of the LFP electrode as follows: the partial charge and discharge process forms two active particle groups with slightly different chemical potentials. Afterwards, when the electrode is recharged, the leading active particle group first finishes the particle-by-particle de/intercalation, and the subsequent second particle group subsequently moves toward the spinodal decomposition point. In this situation, the second activated group induces the delayed initial overshooting, resulting in the SoC memory bump.8

Returning to our results in Fig. 1, it is difficult to explain the pre-current effect with the SoC memory effect model. If the SoC memory effect model were applied, indistinguishable galvanostatic charge/discharge profiles would be expected rather than the overall up/down shift of the charge/discharge profile because the electrochemical experiment in Fig. 1 was conducted using the full charge/discharge protocols. Moreover, the different one-phase regions and voltage variations after relaxation depending on the pre-cycling current histories, as observed in Fig. S12 (ESI) and Fig. 2(c), respectively, would not be expected. According to the SoC memory effect model, particles with the same chemical potential simultaneously move toward the phase transition barrier and subsequently undergo phase transformation. Regardless of the current history, the particles would follow an identical intercalation behavior if the same current density were applied. Even though the SoC memory effect does not explain the pre-current effect, it provides important information about LFP electrodes: particle groups with distinct chemical potentials can be generated in the electrode through certain charge/discharge protocols, and the potential gaps do not merge sufficiently fast during the relaxation or re-charge/discharge process. This phenomenon is attributed to the intrinsically slow ionic and electronic conductivities of LFPs.

The formation of active particle groups with different chemical potentials in LFP electrodes suggests that the electrode can have various states of chemical potential distributions depending on the electrochemical protocols. This finding naturally motivated us to consider two types of hypothetical states of electrodes with (i) uniform and (ii) non-uniform chemical potential distributions, as illustrated in Fig. 3(a) and (e), respectively. It should be noted that these hypothetical states could be established only if the electrodes reach an SoC of ∼0%, which is not the ideal SoC of 0% because there is an only uniform state in the absolute zero SoC state. Among the various intercalation models,5,6,25–27 the recently proposed group-by-group charge/discharge model with mosaic instability can provide a starting platform to understand the pre-current effects based on the two hypothetical electrodes.10,13,17 Experimental and theoretical studies have demonstrated that a realistic electrode containing many-body particles has a driving force for lithium-ion redistribution between interconnected particles upon charge or discharge,11,13,20,24,28 which reduces the free energy of the particles, triggering active particles to rapidly undergo phase transformation with groupings, i.e., mosaic instability.17

image file: c7ee02138k-f3.tif
Fig. 3 Comparison of intercalation behaviors between uniform and non-uniform chemical potential distribution electrodes. (ad) The chemical potential conditions scenario from the initial state to the first mosaic instability for the uniform potential electrode (denoted as the U-electrode). (e–h) The scenario for the non-uniform potential electrode (denoted as the N-electrode) from the initial state to the first mosaic instability. The initial state of the hypothetical U-electrode and the N-electrode (a and e). The beginning of the galvanostatic charge process (b and f). The conditions just before the first mosaic instability occurred (c and g). The chemical potential distribution after mosaic instability of the electrodes (d and h). A and C points indicate a two-phase equilibrium potential of lithium-rich and lithium-poor states, respectively. The B point is the phase transformation barrier under very slow charge/discharge.14

Let us now conduct the thought experiments mentioned above based on the mosaic instability, in which the same moderate current is simultaneously applied (charge process) to electrodes with a uniform chemical potential (denoted as the U-electrode, Fig. 3(a)) and a non-uniform chemical potential (denoted as the N-electrode, Fig. 3(e)). For simplification, we assumed that the particle size of LFP in the electrodes was identical with a nano-size and that the particles did not exhibit any geometric or kinetic differences. The individual particles are defined as primary particles, as in previous reports.14,20 In addition, the total chemical potential state (i.e. total sum of the chemical potential of each particle in the system) of two electrodes is also assumed to be the same. Each LFP particle in the electrodes was denoted as 1, 2, 3,… n and 1′, 2′, 3′, … n′ for the U-electrode and N-electrode, respectively. During initial charging, the active particles of both electrodes move toward the phase transition barrier, point B (see Fig. 3(b) and (f)). For the U-electrode, when particles 1, 2, 3, … n pass over the transition barrier (Fig. 3(c)), some particles are rapidly charged into the lithium-poor state (particles 1 and 2), whereas the rest of the active particles move back near point A (particles 3 to n) because of its internal exchange current (Fig. 3(d)). However, for the N-electrode, even when particle 1′ first reaches the phase transition barrier of point B (Fig. 3(f)), the electrode cannot undergo phase separation because an insufficient number of particles have the driving force for the lithium-ion redistribution (i.e., the number of active particles overcoming the phase transformation barrier is insufficient). Thus, a longer time is required, during which the chemical potential of particle 1′ continues to increase.10,17 Therefore, the mosaic instability in the N-electrode is relatively suppressed and requires a prolonged one-phase region compared with the U-electrode.24 As a result, some of the active particles will be positioned slightly over point B, as shown in Fig. 3(g), exhibiting an additional overpotential for further charging. When a sufficient number of particles reach point B to induce phase separation in the N-electrode, the mosaic instability rapidly occurs and the particles participating in the lithium-ion redistribution move to either point A or C, as illustrated in Fig. 3(h) (see Supplementary Discussion 1 for a more detailed discussion, ESI). During the entire charge process, phase separation in the N-electrode is delayed and requires a higher overpotential than in the U-electrode. The higher overpotential at the individual particle level implies that the N-electrode ‘continuously’ exhibits the initial voltage overshooting for all the SoCs.

When we intentionally stop charging, both the U- and N-electrodes will undergo lithium-ion redistribution similar to the situations as illustrated in Fig. 3(c and d) and (g and h). However, the U- and N-electrodes will exhibit clearly distinguishable relaxation behaviors due to their different initial chemical uniformity states. For example, particles 1, 2, 3,…,n in the U-electrode will actively participate in the mandatory chemical potential redistribution because all the particles are in an unstable state and have the same exchange current density (over point B, see Fig. 3(c)).17,24 In contrast, the limited number of active particles over point B, such as particles 1′, 2′, 3′, and 4′ in Fig. 3(g) and (h), will mainly regulate the redistribution of chemical potentials in the N-electrode due to their relatively higher driving force for the redistribution and exchange current density than those of other particles 5′, … n′. This result implies that the relaxation behavior of electrodes will be sensitively affected by the number of active particles residing at unstable states. Indeed, Li et al. showed that the number of actively intercalating particles with the reaction overpotential is dependent on the current density for LFP electrodes;11 thus, it is highly expected that the different initial chemical distribution state in the U-electrode and N-electrode will result in a distinguishable relaxation tendency with the applied current density. Even though the mosaic instability or relaxation behavior in actual cells is more complicated, depending on both the particle size and kinetic environment,29 this thought experiment on two hypothetical electrodes provides us with a clue to understand the observed electrochemical behavior of LFP.

If we assume that a high-current-density history induces a relatively uniform chemical potential distribution in the electrode (U-electrode) and a low-current-density history induces non-uniformity (N-electrode), our hypothetical thought experiments can explain the pre-cycling effect. In this scenario, an identical electrode can swing between the U-electrode-type and N-electrode-type behaviors depending on the history of the prior current density. For example, if pre-cycling is performed at a relatively high current density, the subsequent cycle (first cycle) follows the U-type behavior, and if it is performed at a relatively low current density, the electrode in the subsequent cycle follows the N-type behavior. Thus, depending on the relative current density applied during the first cycle, the second cycle would follow either an N-type (low current) or a U-type (high current) behavior. According to this scenario, the first charge in Fig. 1(a) should follow the U-type electrode behavior because of the high-current-density pre-cycling history (200 mA g−1); however, the second and third charge cycles will begin in the N-type electrode state because of the low-current density history in the first and second cycles (30 mA g−1), respectively. Therefore, the second and third profiles should exhibit higher overpotentials and wider one-phase regions than the first galvanostatic profile (see Fig. S12(a), ESI), which agrees with our observation. Likewise, the first charge in Fig. 1(b) should follow the N-type electrode behavior because of low-current-density pre-cycling history (30 mA g−1); however, the second and third charge cycles should begin in the U-type electrode state because of the high-current density history in the first and second cycles (200 mA g−1), respectively. Thus, the first cycle profile exhibits a higher overpotential and a wider one-phase region compared with those in the second and third galvanostatic profiles (see Fig. S12(b), ESI). Furthermore, the different relaxation behaviors observed in Fig. 2 can be addressed based on this scenario. As discussed in the thought experiment, for the N-type electrode, the number and distribution of active particles near the transition point critically affects the relaxation behavior, unlike in the U-type electrode, and are dependent on the current density applied to the electrode. Accordingly, the relaxation behavior of the N-type electrode would be more sensitively affected by the current density than the U-type electrode. The findings for the electrode with low-current-density pre-cycling in Fig. 2, i.e., the N-type electrode, agree well with this explanation. Then, one question remains: Is it a plausible assumption that the high (or low) current rate of galvanostatic pre-cycling yields a uniform (or non-uniform) chemical potential distribution state of the electrode?

Mosaic sub-grouping intercalation model

From kinetic considerations alone, our assumption may be difficult to be realized. It is well known that reaction inhomogeneity in practical electrochemical cells becomes serious with increasing current density because diffusion is typically a limiting factor of reactions at high current rates.30,31 Therefore, the formation of a non-uniform chemical potential electrode is expected after high-current-density cycling. However, the thermodynamic reaction mechanism of the group-by-group intercalation behavior provides the possibility of forming a more uniform electrode because a higher current density induces more active particles in the electrode to share their intercalation paths with the same chemical potential.10,11,17,24 Let us conduct a further thought experiment on the charging process of the U-electrode after the first mosaic instability. In Fig. 4(a), we denote the lithium-poor and lithium-rich particles after the first mosaic instability as 1, 2,…,m near point C and m + 1, m + 2,…,n near point A, respectively. During the incubation time for the next mosaic instability, particles m + 1, m + 2,…,n move toward the phase transformation barrier, and simultaneously particles 1, 2,…,m are also charged to slightly higher chemical potentials because the lithium-poor active groups still have small amounts of lithium ions to be extracted (Fig. 4(b)). When the lithium-rich group arrives at the phase decomposition barrier (Fig. 4(c)), the new lithium-rich and lithium-poor groups are rapidly generated and move to points A and C, respectively (Fig. 4(d)). Note that it would be difficult for the 1, 2,…,m particle group to participate in this second mosaic instability with lithium-ion re-distribution because of the relatively poor exchange current density near the Li0FePO4 or Li1FePO4 compositions;10,16 thus this group for 1, 2,…,m particles is still in a slightly more charged position than the following group, and a chemical potential gap is generated between the old and new lithium-poor groups (red arrow in Fig. 4(d)). Consequently, the gap is temporarily memorized on the chemical potential landscape (red arrow in Fig. 4(d)). The mosaic instability continuously occurs during charging, resulting in the formation of several lithium-poor groups with gaps, as illustrated in Fig. 4(e). In short, a thermodynamically driven grouping history will be temporarily memorized on the electrode even after cycling due to the low exchange current density of LFP beyond the spinodal decomposition region (Fig. 4(e) and (f)).16 Similarly, several lithium-rich active particle groupings with gaps are also generated independently during the discharge through the lithiation mosaic instability as illustrated in Fig. 4(f), and finally, the electrode has a non-uniform chemical potential sub-grouping after several mosaic instabilities (see Supplementary Discussion 2 for a more detailed discussion, ESI).
image file: c7ee02138k-f4.tif
Fig. 4 Possible scenario of group-by-group memorizing intercalation in a many-body particle system. (a) The condition after the first mosaic instability of the uniform electrode. (b) The condition at the initial charging. (c) Just before the second mosaic instability occurred. (d) The condition after the second mosaic instability. (e and f) The final condition of the grouping scenario. The end of the galvanostatic charge (e) and discharge (f) states of the phase separation electrode. Note that the groups at the discharged state (Fig. 4(f)) are independently and newly generated by the discharge mosaic instability, but not by the groups transferred from the charged state (Fig. 4(e)). The chemical potential distribution states (g) after the concurrent intercalation and (h) after the particle-by-particle intercalations. The number of particles in each group will be determined by the frequency of mosaic instability, which determines whether the electrode is uniform or non-uniform.

Our mosaic sub-grouping model suggests that the electrodes can be either U-type or N-type depending on the number of groups and their sizes generated from the mosaic instability frequency. For example, if all the active particles are de/lithiated concurrently (i.e. low mosaic instability frequency), the number of sub-groups is unity and it will be a U-type electrode as shown in Fig. 4(g). On the other hand, the number of the group can be as large as the number of particles present in the electrode (i.e. high mosaic instability frequency); in this case, the electrode will follow N-type behavior (Fig. 4(h)). Recent theoretical work on the phase transformation behavior with 26 LFP particles revealed that the number of mosaic instabilities is affected by the applied current density.10 Several mosaic instabilities occur when a sufficiently low current density is applied to the electrode; however, increasing the current density reduces the number of mosaic instabilities. In addition, it was previously demonstrated that the size of the phase-transformed group (i.e., the number of particles in the group) has an inverse relationship with its mosaic instability frequency,10 which is consistent with the porous electrode model proposed by Bazant's group.13 The combination of our mosaic sub-grouping model and previous theoretical works supports our assumption that the electrode can have distinct states depending on the current history. A high current density results in less mosaic instabilities; therefore, the electrode will have a relatively more uniform chemical potential distribution, i.e., behave as a U-electrode.

To further verify the proposed mosaic sub-grouping model, we performed a modified memory effect experiment, which has been known to be effective because of the two sub-groupings of active particles, by inducing various current histories. According to our new model, the chemical potential uniformity of the electrode or the degree of sub-groupings should be mainly determined by the applied current density (the number of mosaic instabilities). If so, the pre-current effect can be intentionally controlled for different SoC ranges by varying the current densities through partial charge/discharge or pre-cycle protocols. In the following experiments, the electrochemical conditions were identical to those in a previous SoC memorizing test performed by Sasaki et al.;8 however, we systemically changed the current densities to 30 or 200 mA g−1 for pre-cycling, memory-writing, memory-releasing (first charge/discharge), and memory-free cycle (second charge/discharge) steps. The steps that are different from the reference experiment shown in Fig. 5(a) are indicated in green in Fig. 5 (b)–(d). The memory-releasing and memory-free profiles are plotted together on the right of Fig. 5 for a better comparison. The black vertical dotted lines in the right figure indicate an SoC of 23.6% (corresponding to a capacity of 40 mA h g−1), where we stopped partial charging.

image file: c7ee02138k-f5.tif
Fig. 5 History-dependent SoC memory effect experiment. (a–d) The whole history of the SoC memory effect experiment of the LFP electrode. The right inset figures are overlapped memory-releasing and free cycles as a function of SoC for each experiment. Typical SoC memory effect with a fixed current density of 30 mA g−1 (a). The higher current density (200 mA g−1) at the memory-writing step experiment (b). The 200 mA g−1 memory effect experiment except for pre-cycling step (30 mA g−1) (c). The higher current density (200 mA g−1) at the memory free and releasing step experiment (d).

Fig. 5(a) presents the reference memory effect experiment for an SoC of 23.6% with a fixed current density of 30 mA g−1. As shown in the right figure, a small memory bump is observed at an SoC of 23.6% in the memory-releasing cycle, whereas the other regions of the SoCs exhibit almost identical profiles as the memory-free cycle, which is consistent with a previous report.8 The next memory effect experiment shown in Fig. 5(b) was conducted with a higher current density (200 mA g−1) in the memory-writing step, which resulted in a remarkably different behavior. The voltage profile corresponding to the capacity of the memory-writing cycle (40 mA h g−1 or an SoC of 23.6%) exhibits a down-shifted pre-current effect at the specific SoC in the memory-releasing cycle; however, the voltage profile for the rest of the capacity is identical to that of the memory-free cycle. This marked change in the SoC memory behavior with a simple change in the current density of the memory-writing step is interesting but can be explained by our model. The SoC range before 23.6% is associated with a more uniform state (U-electrode) because of the high-current-density memory-writing step; therefore, the overpotential of this range in the memory-releasing cycle is substantially decreased. However, the rest of the capacity is determined under pre-cycling conditions, which is identical to that of the memory-releasing cycle; thus, no appreciable change is observed. If the memory-releasing cycle is performed at the same high current as shown in Fig. 5(c), the down-shifted pre-current effect disappears in the SoC range before 23.6%, and a regular voltage bump appears. However, we observe that the other SoC range (beyond an SoC of 23.6%), which had a 30 mA g−1 current density pre-cycling history, now exhibits a relatively high overpotential in the memory-releasing cycle compared with the memory-free cycle. This result occurs because the memory-releasing cycle in the region is performed in the N-type electrode because of the low-current-density pre-cycling history. However, the subsequent memory-free cycle should exhibit a lowered overpotential profile because the memory-releasing cycle was performed with a high current density that generates a U-type state at the end of discharge. Thus, the memory-releasing cycle in the region appears to be relatively up-shifted compared with the memory-free cycle. Finally, the up-shifted pre-current effect can also be observed in the entire memory-releasing cycle if the cell is operated with a relatively low current density (30 mA g−1) for both the pre-cycling and the memory-writing cycle (see Fig. 5(d)). In this case, the entire electrode becomes N-type because of the low current density before memory releasing and exhibits a higher overpotential in all the SoCs compared with the memory-free cycle, whose prior history is the high current density of the memory releasing cycle. Because of the higher overpotential in all the SoCs, the signature of the voltage bump at the specific SoC is only slightly observable. This profile is similar to the previous result for the pre-current effect shown in Fig. 1(b), indicating that the chemical potential distribution of the overall electrode is non-uniform. Moreover, it is observed that the pre-current effect become blurred with increasing rest time between cycles, proving that the sluggish kinetic property of solid solution phases of LFPs (i.e. Li∼1FePO4 or Li∼0FePO4) cause the memorization of thermodynamic driven mosaic instabilities (see Fig. S13 and S14, ESI). The series of modified SoC memory effects and electrochemical experiments clearly confirms that the current density history is memorized on the electrode and supports our mosaic sub-grouping model.

The chemical potential sub-grouping model can also offer an explanation for the overshooting phenomenon of LFP electrodes, which has not been clearly understood to date. The origin of the activation of overshooting at the beginning of charge/discharge has been attributed to an unknown resistance before the phase transformation of active particles.8,32 We observe that the initial overshooting of the LFP electrode is remarkably reduced after high-rate pre-cycling; however, it clearly reappears and increases after a few cycles with relatively low-current-density cycling, as observed in Fig. S15 (ESI). This finding indicates that the resistance of the initial charge/discharge is also related to the chemical potential non-uniformity of the electrodes. As discussed in Fig. 3, the N-electrode requires an overpotential for the mosaic instability to induce phase separation because of the insufficient number of leading active particles toward point B and the small particle-to-particle exchange current. This phenomenon implies that after high-current-density cycling, less overshooting will be observed for the U-type electrode. In addition, the overpotential in the N-type electrode will be comparatively larger and affected by the size of the active particle group. According to our mosaic sub-grouping model, the size of the active particle group for charging is determined by the frequency of mosaic instabilities during discharge (see Fig. 4(f)). In addition, the absolute number of phase-transformed particles through mosaic instability continuously decreases with decreasing applied current density and depth of discharge.10 Thus, it is expected that the size of the active particle group is small with low-current-density cycling and decreases as the discharge proceeds, resulting in the smallest group of active particles at the end of discharge. Upon initial charge, the smallest group in the sub-groupings should be located at the highest chemical potential in Fig. 4(f); thus, it is the first to be charged. The smallest group of active particles will follow the most N-type-like behavior, causing the particularly large overpotential at the beginning of the charge, i.e., the initial overshooting of the LFP electrode.

The electrode mechanism involving many-body particles has been intensively investigated using various experimental tools and mathematical modeling in recent years.11,12,17,20,31,33 For example, the solid-solution bypass intercalation of an LFP electrode at room temperature has been theoretically predicted by ab initio calculation,20 and the non-equilibrium phase transformation behavior at a high current rate has been experimentally captured by in situ synchrotron X-ray diffraction techniques.12 Furthermore, the direct redox state analysis tool has proven that the fraction of active particles is largely determined by current rates and reaction directions,11,34 explaining the contradictory reports of particle-by-particle and concurrent intercalation behaviors.6,12 Even though this advanced technique enables the observation of the phase transformation path at the individual particle level,30,31,33,35 the precise chemical potential distribution at the end of charge/discharge and its effect on the intercalation behavior in the actual cells are still unknown because of the limited compositional resolution of in situ or ex situ observation tools and lack of knowledge. The pre-current effect suggests that the electrode can have a regularly non-uniform or uniform state depending on the pre-cycling current density, which can be one of the factors affecting the intercalation paths of the phase-separating electrode. In addition, our observation provides insight that not only geometric and kinetic factors but also the thermodynamic paths of electrode materials yield inhomogeneous potential distribution problems even at a low current rate.

The chemical potential sub-grouping state after cycling is presumed to be affected by the phase transformation barrier or intrinsic ionic/electronic conductivities of the electrode materials. In this respect, distinct behaviors will be observed for different phase-separating electrodes. Nevertheless, a non-uniform chemical potential is always expected to cause extra overpotential and affect the cycle life or rate capability of several electrode materials because it generally requires an additional driving force and time for the guest ion redistributions.10,13 From a practical viewpoint, the non-uniform chemical potential distribution of electrodes leads to problems with the estimation of the SoC and energy efficiency during the cycling of electrochemical cells. These issues imply that a cell design that easily turns the chemical potential distribution of a multi-particle-nature electrode into a uniform state should be considered. An applicable strategy to increase the uniformity involves the improvement of the chemical potential sharing ability in electrochemical cells. As discussed in the previous sections, the particle-to-particle exchange current capability for the phase transformation will be directly accountable for the uniformity. Recently, there has been growing experimental and theoretical evidence that the thermodynamic properties of phase-separating materials can be tuned using various strategies, such as controlling the particle size18,21 or reducing the lattice misfit through doping,36–38 resulting in the reduction of the phase transformation barrier height with the increased reaction rate of the electrode.10,13,39 Accordingly, the reduced phase transition barrier will not only increase the active populations11 but will also improve the chemical potential redistribution of the electrode. Moreover, the kinetic component of cells will affect the electrochemical exchange between groups; thus, well-structured electron/ion transport networking,40 surface coating,7 and a modified electrolyte can be applied to control the thermodynamic uniformity of the phase-separating electrode.

In summary, we demonstrated for the first time the transient voltage variation occurring dependent on the history of current density induced. Through observation of this unforeseen memory effect, we proposed a new intercalation model based on the sub-groupings of active particles with different chemical potential distributions in the electrode. The types of sub-groupings were determined by the current density of the prior charge or discharge, resulting in distinct signatures in the electrochemical profile. Our proposed intercalation model for phase-separating electrode materials affords a more comprehensive view of the behavior of electrodes containing many-body particles by elucidating the transient states of the electrode materials. We believe that the pre-current effect could occur in other energy storage systems, such as hydrogen storage systems or supercapacitors, using interconnected phase-separating active particles. Our mosaic sub-grouping intercalation model suggests that the control of the chemical potential inhomogeneity arising from the thermodynamic and kinetic origins is the key for designing better phase-separating electrode materials.


Material preparation

LFPs are synthesized using Li2CO3 (Sigma Aldrich, 99.9%), FeC2O4·H2O (Sigma Aldrich, 99%) and (NH4)2HPO4 (Aldrich, 98%) as precursors. Each precursor is pulverized using high-energy ball-milling for 4 hours under Ar conditions. The precursors are mixed by wet ball milling using acetone for more than 20 hours. After drying the mixture, the powder was calcinated at 350 °C with 5–6 °C min−1 heating rate for 10 hours. The calcinated powder is pelletized under more than 300 bar and synthesized at 600 °C under Ar conditions. LTO powder is prepared using Li2CO3 (Sigma Aldrich, 99.9%) and TiO2 (Aldrich, 98%). The two precursors are mixed by high-energy ball milling for 4 hours, and the mixed power is sintered at 850 °C.

Electrochemical analysis

Electrochemical cells are assembled using a CR2032-type coin cell with lithium metal as the counter electrode in an Ar-filled glove box. 1 M LiPF6 in ethyl carbonate/dimethyl carbonate (Panax, EC/DMC, 1[thin space (1/6-em)]:[thin space (1/6-em)]1 v/v) as the electrolyte is used in cell fabrication. The electrode slurry was cast onto Al foil using polyvinylidene fluoride (PVDF, as a binder), super p (carbon, as a conductive agent) and the prepared active materials with a density of ∼1.2 mg cm−2. Galvanostatic electrochemical analysis is evaluated using a WBC-3000 cycler (Wonatech, Korea) within a temperature-controlled chamber at 30 ± 0.5 °C. The cut-off potentials for LFP and LTO cells are used with 2.5–4.6 V (vs. Li/Li+) and 1.25–1.5 V (vs. Li/Li+), respectively. Rest times of 1 minute and 1 hour are always applied between galvanostatic cycles and between half-cycles, respectively. In addition, the cells were cycled with a current density of 30 mA g−1 prior to pre-cycling, and this state is considered to be close to SoC = 0. Note that the SoC of the LFP electrode was calculated based upon a theoretical capacity of 169 mA h g−1.

Conflicts of interest

There are no conflicts to declare.


This work was supported by Project Code (IBS-R006-G1). K.-Y. P., W.-M. S., K. K., and K. K. are grateful for the financial support from IBS.


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Electronic supplementary information (ESI) available. See DOI: 10.1039/c7ee02138k

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