Insights on Relationship between Deterioration and Direct-Current Internal Resistance of Valve Regulated Lead-Acid Battery by Addition of Granular Carbon Additives under HRPSoC Duty

VC 72 was purchased from Cabot Co., USA (some physical characteristics of VC 72 are tabulated in Table S1). Leady oxide (LO) was used to prepare the NAMs; and the degree of oxidation of the LO was 89.1 wt%. The composition of LO are listed in Table S2–S3. The grid for the negative plate was Pb-Ca alloy. To investigate the performance of the negative plates, commercial positive plates were used. Some common additives, barium sulfate, sodium lignosulphonate, and polyester fiber were also used in the preparation of the negative plates, and their dosages were 0.5, 0.25, 0.1 wt% vs. LO, respectively. All the LO, grids, positive plates and additives were supplied by Changguang Co. Ltd (Wuhan, China).

Eight dosages of VC 72 (0, 0.2, 0.5, 0.8, 1.0, 1.2, 1.5, 1.8 wt% vs. LO) were introduced into the NAMs, denoted as C-0, C-0.2, C-0.5, C-0.8, C-1.0, C-1.2, C-1.5, and C-1.8, respectively.

LO, sulfuric acid (1.4 sp.gr.; 8 wt%), deionized water (13.5 wt%), barium sulfate, sodium lignosulphonate, polyester fiber and VC 72 were all homogeneously mixed through stirring for 20 minutes to fabricate the NAMs pastes. Each grid of 35 × 60 × 1.2 mm³ was densely coated with 27.5 g of the NAMs paste to form a negative plate. After an identical curing (as shown in Supporting Information) and formation procedure (as shown in Table S4), all the ripe negative plates were sent to a local battery plant for battery assembling.

Each testing battery consisted of one negative plate and two positive plates, separated by an absorbent glass mat (AGM) separator. The schematic and specific parameters of testing battery are shown in Fig. S2. The performance of the testing batteries, including initial capacity at different electric current density (C/20, C/10, C/5, 0.5 C, 1 C, 2 C), the charging DCIR, and HRPSoC cycle life, were all acquired using a Neware battery test system (CT-4008-5V6A-S1). Based on Ohm's law, the voltage of the battery would increase linearly during charging. Under HRPSoC duty, the charging current (I) is fixed. Once the initial voltage (V₀) and termination voltage (V₁) were recorded, the charging DCIR (R) could be then defined as R = V₁-V₀/I.¹⁶ A typical simulated HRPSoC cycle program consisted of the following steps:⁷ a testing battery was firstly discharged to 50% of its initial capacity at 1 C and then cycled as follows: (i) charged at 2 C rate for 60 s, (ii) hold for 60 s, (iii) discharged at 2 C rate for 60 s, then (iv) hold for another 60 s. The discharging and charging cutoff potential were set as 1.7 and 2.83 V, respectively. Once the battery reached cutoff voltage, it means that the battery couldn't work normally under HRPSoC duty unless full recharged. At this point, a "set" is finished, and the accomplished cycle numbers were recorded as the cycle life of this "set". Each battery experienced five consecutive sets of HRPSoC cycle test to evaluate its reliability and performance.

The Raman spectra of VC 72 were acquired using LabRAM HR800 (Horiba Jobinyvon, France) with a Nd-YAG laser beam (wavelength = 532 nm). The electric conductivity of VC 72 was measured using a conductivity meter (Rooko FT-300I, China). The X-ray diffraction (XRD) patterns of the NAMs were collected utilizing X'Pert PRO XRD (Philips, PAN Analytical B.V., Holland) in the 2θ ranging from 5 to 75°, with X-ray source of Cu-Kα radiation (λ = 0.15418 nm). The NAMs were scraped from negative plate and homogeneously ground into powder before and after HRPSoC cycle tests for XRD analysis. The morphologies of the NAMs of the negative plates and VC 72 were characterized by transmission electron microscopy (TEM) (Tecnai G2 20, FEI, Holland & JEM-2100, JEOL, Japan) and scanning electron microscopy (SEM) (Sirion 200 SEM, FEI, Holland). The NAMs powders were uniformly distributed in ethanol and deposited on carbon grid for TEM analysis. The negative plates were cut into small pieces, and the surface morphology of negative plates before cycle tests were characterized. For a better observation of lead sulfate crystals, both surface and cross-section of negative plates after cycle tests were characterized, as shown in Fig. S3.

After the battery assembly, all the testing batteries were first subjected to charging/discharging cycles at different rates, ranging from C/20 to 2 C, and the capacities are shown in Fig. 1a. There are 2 testing batteries in each group, they showed similar performance under HRPSoC duty, therefore, only one battery was selected for analysis in each group. It can be observed that a lower VC 72 dosage (<0.5 wt%) in the NAMs enhanced the initial capacity at all rates, while the capacities decreased slightly at higher dosages, and battery exhibited maximum capacity with 0.2 wt% of VC 72. The nominal capacities of all batteries ranged from 3.1 to 3.6 Ah (or from 113 mAh g⁻¹ to 131 mAh g⁻¹). With a theoretical value of 240 mAh g⁻¹, the calculated utilization efficiencies were all greater than 46.9%. The subtle capacity reduction from C-0.8 to C-1.8 might be related to the modified pore system of the NAMs, induced by the agglomeration of redundant carbon particles.³³ The capacity decreased as electric current increased, which could be further explained by Peukert equation:

where C is the capacity, Ah; I is the electric current, A; and K and n are empirical constants. Peukert plots in the double Napierian logarithm are presented in Fig. 1b, which enables the linearization fitting of curves in Fig. 1a. The constants n, usually referred to as the coefficient, could be calculated from Fig. 1b. The value of n increases as the battery efficiency decreases; and the typical n value of LABs is 1.3.⁴² So the capacity (C) would decrease conspicuously as electric current (I) increased based on Eq. 1 (Figs. 1a–1b).

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The consequence of 20 h rate capacity (initial capacity) and the calculated value of n are presented in Table I. The n values ranged from 1.25 to 1.36, similar to the typical value of LABs. It implies that the correlation between the electric current density and the capacity is relatively independent of carbon dosages.

The discharging potential during the first set of HRPSoC cycle is presented in Fig. 1c. With the presence of certain amounts of VC 72 in the NAMs, the HRPSoC cycle life was extended. Specifically, battery C-1.2 accomplished 16706 HRPSoC cycles before reaching the cutoff potential, which is five times longer than that of the control testing battery (C-0) in the first cycle set. A similar phenomenon could be observed in all cycle sets (Fig. 1d). With the VC 72 dosage in the NAMs ranging from 0 to 1.2 wt%, batteries accomplished increasing numbers of cycles as the VC 72 dosages increased, followed by slightly declined cycleability with further increases of VC 72 (1.2-1.8 wt%). After all five sets of HRPSoC cycles, battery C-1.2 completed the maximum number of cycles, 51624 specifically, while battery C-0 accomplished only 15586 cycles. The enhancement of HRPSoC performance brought by VC 72 is even better than some kind of activated carbon or graphene.²⁹ The discharging capacity of every cycle was 0.0667 Ah, so the total discharging capacity of battery C-1.2 was nearly 3300 Ah. The HRPSoC cycle life of VRLA batteries has been prolonged significantly with the addition of VC 72.

To analyze the effect of VC 72 on the cycle life of VRLA batteries, the charging DCIR behaviors during each cycle were investigated. Since battery C-1.2 has the longest cycle life, a comparison of the charging DCIR behaviors between battery C-0 and C-1.2 is illustrated in Fig. 2. As shown in Figs. 2a–2e, the relationship of the charging DCIR vs. the cycle number could be linearly fitted in each cycle set, and the relationship could be described by the following equation:

where R is the charging DCIR (mΩ), N is the cycle number, k is the slope (ΔR/ΔN), which stands for increasing rate of the charging DCIR vs. cycle number (N), and R₀ is the initial charging DCIR in each cycle set. The specific parameters of k and R₀ during each cycle set are shown in Table II. During the first four sets, the charging DCIR of the control battery C-0 increased rapidly, in comparison with those of battery C-1.2. However, the variation of two increasing rates became insignificant in the 5^th set.

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It is worth mentioning that, the values of the charging DCIR at the end of each testing set were almost the same after the 1^st set. For battery C-0, the charging DCIR reached approximately 45 mΩ when the HRPSoC cycle life terminated, compared with the charging DCIR of 55 mΩ for battery C-1.2. The charging DCIR behaviors at the end of each set of all testing batteries followed a similar trend as presented in Fig. 2f. Typically, a battery failed when its charging DCIR reached the same maximum limit during different cycle sets. Since the charging DCIR varied linearly with cycles under HRPSoC duty, the service life (N) could be reliably predicted by monitoring the variation of DCIR.

It can be concluded that presence of VC 72 in the NAMs contributed to hindering the rapid increase of the charging DCIR as shown in Figs. 2a–2e. Meanwhile, the charging DCIR at the end of each cycle set also changed with different dosages of VC 72 as illustrated in Fig. 2f.

The phenomenon that the charging DCIR increased continuously and reached a maximum limit upon failure might be explained by the Percolation theory. The specific electric conductivity (σ) of the NAMs could be described as:¹¹

where x₁ is the volume fraction (%) of the conductive phase (metallic Pb); x_c is the critical volume fraction (%), and b is a numeric exponent.⁴³ The critical volume fraction could be defined as:

where d_c is a constant, and f is the filling rate, which depends on the compositions of the NAMs.⁴⁴ Both the volume fraction of the conductive phase (x₁) and the filling rate (f) could be defined as follow:¹¹

where V₁ is the volume of the conductive phase (%), V₂ is the volume of the insulating phase (%), r is the conversion rate of the NAMs (i.e., the volume ratio of the insulating phase to the whole electrode, as shown in Eq. 7), f₀ is the initial filling rate, and C is a constant determined by the molar volumes of different phases.

The specific electric conductivity (σ) could be deduced from Eqs. 3–7, as presented in Eq. 8:

where the parameters of f₀, b, d_c are listed in Table S5.¹² We assumed that negative plate was almost all metallic lead before cycle test, i.e., r = 0, thus the specific electric conductivity (σ) equals to that of metallic lead(σ₁), and internal resistance (R) is inversely proportional to the specific electric conductivity (σ):

However, the addition of VC 72 changed this value of testing battery as shown in Table II, and the value of R₀of C-0 and C-1.2 are 25.72 and 17.59 mΩ, respectively, indicating a variation of parameter d_c for battery C-1.2. The specific parameters of battery C-0 and C-1.2 are shown in Table S6. Combining Eqs. 8–10, the ratio of maximum limit of R_max(C-0)/R_max(C-1.2) was calculated to be 0.85, and the corresponding conversion rate of testing battery C-0 and C-1.2 were nearly 0.75 and 0.82, respectively. The measured maximum limit value of R_max(C-0)/R_max(C-1.2) was approximately 0.82 (i.e., 45/55), in accordance with theoretical values.

Based on the above analysis, the specific electric conductivity (σ) can be regarded as a function of the conversion rate (r) of the NAMs. With higher volume fraction of insulating phase of PbSO₄ (V₂), the conversion rate (r) would increase, and the specific electric conductivity (σ) of the NAMs decreased correspondingly. Therefore, the charging DCIR would rise with an increase of volume fraction of PbSO₄. When the content of lead sulfate reached a threshold, for example, the conversion rate reached 0.75 for battery C-0 or 0.82 for battery C-1.2, the ratio of active mass became insufficient for the proceeding of discharging reaction,¹⁴ and the testing battery would reach the cutoff potential at this point. A battery was then fully recharged before the next set of cycle test. After being recharged, most of lead sulfate would be transformed to conductive metallic lead that resulted in a decrease of the charging DCIR.

The Eq. 8 helps to establish a quantitative correlation between the inner compositions of negative plate and charging DCIR, by which HRPSoC cycle life can be predicted and the deterioration process through battery testing can be described. An optimal dosage of VC 72 in the NAMs could provide a favorable effect to enhance electric conductivity during charging, thus hindering the rapid increase of the charging DCIR. This effect was most likely related to alleviation of sulfation.

The morphology and structure of VC 72 were characterized by SEM, Raman, and XRD, as shown in Fig. S4. The morphology (Fig. S4(a)) and size distribution of VC 72 (Fig. S4(b)) indicate that VC 72 particles are spherical in nanometer size (∼20 nm), which might provide nuclei for formation of PbSO₄ crystals and conductive pathway for electron exchange. As shown in the Raman spectrum (Fig. S4(c)), the peaks located at 1355 and 1580 cm⁻¹ are correlated with the disordered (D) band and the graphitic (G) band, respectively; and the ratio of integrated intensity (I_D/I_G) was 0.73. A relatively low integrated Raman intensity ratio of the D and G bands implies an increasing amount of graphene clusters in the structure, attributing to the improved electric conductivity of VC 72.⁴⁵ The electric conductivity of VC 72 was measured to be 3.0 mS mm⁻¹. As shown in Fig. S4(d), only two broad peaks at 25° and 43° are observed in the XRD pattern, with no other miscellaneous peaks, indicating no other impurity is discernible. The main peak at 25° is associated with lattice plane (1 1 0) with an interplanar spacing of 0.367 nm.

All the negative plates were subjected to phase and morphology characterizations before the battery tests. The XRD patterns of the NAMs in the formed negative plates with different dosages of VC 72 are shown in Fig. 3. In the absence or low dosages of VC 72, the NAMs consisted of metallic lead alone. With the VC 72 dosages increased to higher than 0.5 wt%, the phases of the NAMs stayed constant, comprising major crystalline phase of metallic lead and a small amount of lead oxide. The generation of lead oxide could be attributed to the impeded transport of ions.³³

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The surface morphologies of the NAMs of the negative plates in each testing battery are shown in Fig. 4. From the SEM images of lower VC 72 dosages (<1 wt%, Figs. 4a–4d), spongy morphologies could be observed. While when VC 72 dosages increased to higher than 1 wt%, cubic particles were substituted by interconnected granules (Figs. 4e–4h). Besides, particles of more uniform in shape and size could be observed in Figs. 4d–4f, which are favorable for promoting battery cycle performance.

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After all five sets of HRPSoC tests, all the batteries were fully recharged, and then disassembled before subsequent analysis. The XRD patterns of the disassembled negative plates are illustrated in Fig. 5. Metallic lead, lead sulfate, and lead oxide were identified as the main crystalline phases in the NAMs, while no XRD peaks matched with carbon due to its low mass percentage. It is worth mentioning that, when the VC 72 dosages were between 0 to 0.5 wt% (Figs. 5a–5c), lead sulfate was identified as the major crystalline phase. It indicates that most of the lead sulfate existed as irreversible phase. At higher VC 72 dosages (0.8 to 1.8 wt%), metallic lead was the major phase, indicating that most of lead sulfate existed as reversible phase and could be converted to metallic lead after being fully recharged.

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The morphologies of surface and cross-section of each negative plate are shown in Fig. S5 and Fig. 6. No evident differences could be observed among the surfaces of all the plates (Figs. S5(a-h)), a dense layer on the surface of negative plates could be found. So the internal morphologies of each plates were characterized. The internal structure of the negative plates was completely transformed with the addition of VC 72. In the absence of VC 72, dendritic crystals of several micrometers in diameter was observed (Fig. 6a). When the VC 72 dosage increased to 0.2-0.5 wt%, the dendritic crystals were gradually transferred to a cubic shape (Figs. 6b–6c). With the further increase of VC 72 dosage (>0.8 wt%), the cubic crystals could no longer be found. Instead, numerous tiny grains, uniformly distributed around the larger amorphous agglomerates, could be observed in Figs. 6d–6h. The size distribution of different NAMs of each testing battery are shown in Fig. S6. With the increase dosage of VC 72 from 0 to 1.2 wt%, the particle size becomes smaller, than it gets larger with further increase of VC 72. This trend is in consistence with SEM images. It has been reported that lead sulfate crystals with large particle sizes were more strenuous to be converted to metallic lead.⁴⁶ Thus, the generation of irreversible sulfate appear to be alleviated effectively with excessive dosages of VC 72.

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The EDS mapping of batteries C-0 and C-1.2 in fully recharged state after all five sets of HRPSoC cycle test are presented in Fig. 7 to confirm the postulation from morphology analyses. As shown in Fig. 7a, Pb and S are the dominant elements in negative plate of C-0, with nearly no C discernible. Combined with XRD and SEM analysis in Fig. 5a and Fig. 6a, the crystal could be identified as lead sulfate. In contrast, both Pb and C elements were homogeneously dispersed in negative plate of C-1.2, while S element was almost invisible as shown in Fig. 7b. From the XRD and SEM analysis in Fig. 5f and Fig. 6f, the Pb element mainly existed as metallic lead. Furthermore, the dosage of VC 72 in the NAMs is only 1.2 wt%. It indicated that the small amount of VC 72 particles were uniformly dispersed in the metallic Pb grains. The unique morphology of metallic lead combined with uniform distribution of carbon particles could be beneficial for hindering the rapid growth of lead nuclei due to steric hindrance.^47,48

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To elucidate the roles of granular carbon particles precisely, transmission electron microscope (TEM) and high-resolution transmission electron microscope (HRTEM) analyses for the NAMs of batteries C-0 and C-1.2 in fully recharged state were also conducted after all five sets of HRPSoC cycle tests (Fig. 8). Battery C-0 exhibited a dendritic structure of a few micrometers in size (Fig. 8a), similar to that in SEM image (Fig. 6a). However, carbon grains were incorporated into the lead bulk, and filled the gaps between lead skeleton (Fig. 8b), thus providing electric pathways for electrons. As shown in the HRTEM image (Figs. 8c–8d), some particles of tens of nanometers in size were embedded in the lead bulk, and the interplanar spacing of them was measured to be approximately 0.366 nm, which is consistent with the (1 1 0) lattice plane of VC 72 as seen in the XRD pattern (Fig. S4(d)), and in agreement with the particle size of VC 72 (around 20 nm) in the SEM image of VC 72 (Fig. S4(a)). Based on the TEM and HRTEM analysis, it can be inferred that some granular carbon particles in nano sizes would be completely covered by lead, as shown in Fig. 8d. While the other part of carbon particles might aggregate among the lead bulk, as shown in the box area of Fig. 8b. Meanwhile, some carbon particles were separated from the lead bulk as pointed in Fig. 8c.

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As reported in the previous literatures, the reduction of Pb²⁺ ions to Pb occurred on the surfaces of both carbon and the lead skeleton.^33,47 When Pb or PbSO₄ was deposited on the surface of VC 72, nano carbon particles acted as nucleation seeds for the growth of them.⁴¹ With the proceeding of this process during battery cycling, some granular carbon particles would then be covered by metallic lead or lead sulfate (Fig. 8c). To the best of our knowledge, this is the first report that carbon particles has been directly detected to be embedded in the lead bulk during HRPSoC duty in LABs. However, when carbon particles were embedded in or separated from the lead bulk, they could no longer perform as the electron pathway.⁴⁹ In summary, the addition of VC 72 has definitely altered the inner structure of the negative plates, thus impeding the formation of large lead sulfate crystals.

Since there is a close correlation between electric resistance and the formation of lead sulfate, the charging DCIR behavior (Fig. 2) could be discussed in detail with characterizations of negative plates, as shown schematically in Fig. S7.

Two points can be concluded from Fig. 2. The first is the increasing rate of the charging DCIR, and the second is the value of the charging DCIR at the end of each cycle. As long as a battery is operating under HRPSoC duty, the generation of lead sulfate is inevitable due to partial charging as shown in Fig. S7. Consequently, the charging DCIR of all testing batteries would increase with the cycles of battery, but may show difference in the increasing rate, as shown in Fig. 2. In the absence of VC 72, metallic lead was converted into large lead sulfate crystals, which were more difficult to be reduced to metallic Pb compared with smaller crystals.⁴⁶ Therefore, the accumulation rate of lead sulfate became accelerated, and the charging DCIR was directly determined by the degree of sulfation as demonstrated in Eq. 8. Via the addition of granular carbon particles in the NAMs, the formation of large lead sulfate crystals could be inhibited, so as the rapid increase of the charging DCIR. However, this effect would be weakened in the last few cycle sets due to the fact that some carbon particles were separated from the lead bulk while some embedded in the lead bulk.

On the other hand, the degree of sulfation of each negative plate was close at the same level of charging DCIR.¹¹ In the absence of carbon particles, the NAMs were occupied by large insulating lead sulfate crystal, hence the paths for electric current were blocked, leading to premature failure. However, the conductive carbon particles could provide extra electric current channels between insulating lead sulfate particles, which enable the reduction of Pb²⁺ ions to Pb to occur. Consequently, battery C-1.2 could still operate normally at a higher charging DCIR with the help of carbon particles.

Although the above mechanism is deduced from granular carbon additives, it can also be applied for the other conductive particles (for example, semiconductor oxide) with a similar morphology, which could produce similar advantageous effects when used as additives in the NAMs as confirmed by some previous studies.^50,51