Archimedes-Based Glycerol Displacement for Electrode Porosity Measurement in Lead-Acid Batteries

Summary

Here, we present a simple and low-cost glycerol displacement method based on Archimedes' principle for measuring lead-acid battery electrode porosities. The method demonstrates good reproducibility and is safer than traditional techniques, requiring low-hazard chemicals and equipment. Combining the technique with microstructural analysis by X-ray diffraction provides information on battery electrode properties and degradation.

Abstract

The performance of lead-acid batteries is highly dependent on the structural and surface properties of the electrodes' active materials. Besides the importance of the material's phase composition at any given time in application, its surface area and porosity contribute to the overall performance of the battery. Mercury porosimetry, which uses a representative sample of the active material for its analysis, has traditionally been used to measure the porosity of battery plates. Apart from the possibility of inducing cracks and cavities in the material while taking the sample, many laboratories have moved away from the use of mercury due to its toxicity. The Archimedes-based glycerol displacement technique has the advantage of being a simple method that considers the porosity of the entire battery plate. Even though the method might not give detailed information on the material's pore volume distribution, reproducibility is achieved for individual plates as well as groups of plates taken from either a single cell or six cells from a battery. The method calculates porosity based on the material's absolute and envelope density, which makes use of absorbed glycerol volume to measure the average porosity over the entire plate. Lead-acid batteries are usually subjected to aging mechanisms that affect the active material's structural integrity and surface properties. This study describes the use of the glycerol displacement technique for the measurement of battery plate porosities, combined with powder X-ray diffraction material characterization to understand the degradation mechanisms of batteries that were subjected to capacity life cycling and calendar aging or shelf life, respectively. The results showed that the failure mechanisms of batteries are significantly different and that both the chemical and physical properties of the active material are interdependent; therefore, one cannot rely on a single analytical tool only to interpret a failure mechanism.

Introduction

The lead-acid battery is one of the oldest commercial rechargeable batteries. In 1859, French physicist Gaston Plante demonstrated the battery's working principle by submerging two lead plates in sulfuric acid. The potential for commercialization was realized only 20 years later, when improvements to the technology were made in using pasted plates that allowed the battery to be discharged and charged through a reverse current¹.

Even in the early stages of the invention, the significance of the exposed surface area and the porosity of the battery material became evident. It was understood that the larger the surface area of the material, the greater the battery's capacity². At the time, the commercialization of the battery found a unique application in the emerging automotive industry¹, enabling the starting of internal combustion engines of not only passenger vehicles but also larger engines that were used in the military, such as tanks and airplanes^3,4,5.

As the manufacturing technologies improved over the years, so did the advancements in chemical analysis and the understanding of the processes that occur within the battery. There will always be a need to improve the manufacturing process to ensure a consistent product that is not only price competitive but also of good quality and that can provide electrical backup for longer periods of time.

The chemistry that occurs in the battery, referred to as a double sulphate theory, is unique when compared to other battery types. In this case, the electrolyte or acid forms part of the reaction mechanism during the discharge and charge process⁶.

Figure 1: Schematic illustration of the charging and discharging reaction mechanisms of a lead-acid battery. Please click here to view a larger version of this figure.

Here, the electrodes or plates that can conduct electricity react with the acid to form lead sulphate, which can be seen as an insulator (Figure 1). Not all the material that is on a plate is used in the discharge process. The electrochemical reaction predominantly occurs at the surface of the material that is exposed to the acid, and when the battery is charged, the insulating lead sulphate material then converts back to the conductive lead dioxide and lead on the two plates that are referred to as the cathode and anode, respectively⁵. The larger the surface area, the more discharge reactions can take place and the more capacity can be obtained. Plates are designed to be relatively thin and usually specific to the application. For high power over short periods of time, as in the starting of a car, a large area is desirable where the acid can easily travel or diffuse to the middle of the plate, whereas for batteries intended to provide more capacity over longer periods of time at lower discharge rates, usually thicker plates are then used. This becomes a trade-off between the available material that the acid can easily migrate or diffuse into, and providing a thicker, more rigid support for the plate to last longer in application.

Analysis of the active material inside a battery has always been challenging due to its destructive nature. The battery has to be cut open and the plates disassembled; that can then only provide a snapshot in time of what the battery's state or condition is. This usually relates to the scientists wanting to know the battery's state of charge (SoC) and state of health (SoH). In a battery, the most important and probably the only chemical parameters one can comfortably measure as an analyst are the chemical properties that include its elemental and phase composition. These techniques usually rely on atomic absorption or X-ray fluorescence-type techniques, as well as advanced methods such as scanning electron microscopy and powder X-ray diffraction. There are also electrochemical analytical techniques that can be applied, including impedance spectroscopy and cyclic voltammetry, among others.

On the other hand, physicochemical properties include the strength of the plates, the available surface area, and the porosity of the active material. Surface area analysis is typically done by nitrogen adsorption techniques, and in this study, the porosity of the plates used in the lead-acid battery was measured. Porosity relates to the available free space that is within the active material for the acid to move freely into and to be in contact with the active sites that will then allow for an electrochemical reaction to take place. If the porosity is too high, there will be limited connective pathways between the various active material particles, increasing the likelihood of disconnection. If the porosity is too low, less of the acid will be able to reach the active sites, thereby reducing the available capacity.

Traditionally, the porosity of solid materials that have micro- to meso-sized pores is measured by mercury porosimetry. This required the active material to be physically removed from the plate in order to fit into the instrument's sample holder. This has a number of disadvantages, namely, only a representative sample from a plate area is taken; the sample as such is disconnected from the grid or current collector, thereby inducing additional cracks and cavities in the material; and many laboratories have moved away from the use of mercury due to its toxicity. The advantage of the technique is its ability to provide an estimate of the pore size distribution of the material within a certain range.

This study proposes a technique that makes use of the entire plate in measuring the total porosity of the active material by using Archimedes' principle. In its context of determining material density, Archimedes' principle states that the buoyant force on an object that is immersed in a fluid is equal to the weight of the fluid displaced by that object. This principle allows one to calculate an object's density by measuring its weight in air and its weight when submerged in a known fluid. This buoyant force is then used to calculate the volume of the displaced fluid, which is equal to the volume of the object.

The technique can be easily set up in a laboratory to measure the porosity of lead-acid battery plates that have been subjected to certain manufacturing or testing conditions. Even though the technique is still destructive in the sense of having to cut the battery open to remove the plates for analysis, the porosity of the entire plate is considered. Hence, the method measures the average porosity over the entire plate, capturing variations of certain regions of the plate that are usually not taken into account. These variations typically occur when working with relatively large plates, where possible manufacturing inconsistencies and the effects of acid stratification can affect specific plate regions over time. However, a limitation of the glycerol displacement method is that it measures porosity based on permeable pores. This means that it is possible to underestimate the plate's porosity if glycerol does not fully penetrate the pores of the active mass. When closed pores are present, the technique indirectly correlates with what happens inside the battery during application, since the acid would also not be able to completely penetrate areas of the active mass that have closed pores. Despite this limitation, the method remains safe and cost-effective and is suitable for measuring the porosity of battery plates.

In this study, the porosities of both the negative and positive plates of a relatively small 7.2 Ah valve-regulated lead-acid (VRLA) battery are measured. These batteries are typically used in household alarm and gate motor control systems. The effect on the batteries' plate porosity and chemical phase composition was studied in terms of the possible aging mechanism to which the battery was exposed. One being excessive calendar aging or shelf life, and the other being repeated capacity cycling without sufficient recharging. These are typical conditions that such batteries are exposed to. Those that remain on the electrical wholesaler's shelves for many months and sometimes years without receiving a boost charge. Moreover, those batteries that are used in standby power supply systems are subjected to repeated "load-shedding-type" capacity cycling, where the inverter system's recharge is insufficient to provide the necessary energy to fully recharge the battery during the short recharge periods available.

Protocol

NOTE: The protocol is similar to the one previously described by Ferg et al.⁷. The equipment and reagents used in the study are listed in the Table of Materials. An image of the equipment used for the porosity measurement of the electrodes is presented in Figure 2.

Figure 2: Simple equipment used for glycerol displacement-based porosity measurement of electrodes. The setup comprises (1) a digital electronic balance, (2) a balance attachment with crocodile clips, (3) a sturdy frame structure, (4) a negative battery plate, (5) a container with glycerol, and (6) a laboratory Jack Please click here to view a larger version of this figure.

1. Sample preparation

1. Extraction of the plates for porosity measurement
   1. Using a plastic-cutting saw, carefully open the lead-acid battery by slowly cutting along the seam between the casing and the lid.
      CAUTION: Review the material safety data sheet (MSDS) for all materials used in this protocol. A lead-acid battery contains corrosive sulfuric acid and toxic lead plates. Cut open slowly in a well-ventilated chemical fume hood while wearing full personal protective equipment, including acid-resistant gloves, in order to prevent potential injuries. Also, keep neutralizing agents and emergency facilities nearby.
   2. Carefully disassemble the lead-acid battery.
   3. Remove each battery cell and separate its components, ensuring the positive and negative plates are extracted without any alteration.
2. Preparation of the plates for porosity measurement
   1. Gently rinse the plates with water to remove the residual acid.
      NOTE: Ensure that the plates are free of any residual acid, as this might react when immersed in the glycerol.
   2. Dry the negative plate in an oven under an inert atmosphere such as nitrogen to prevent the oxidation of lead. Dry at 110 °C for 6 h or until constant mass is achieved.
   3. Dry the positive plate in the oven at 110 °C for 24 h.
      ​NOTE: In the case of pasted plates, the outer paper should be removed before drying in the oven.
   4. Remove the plates from the oven and allow them to cool in a desiccator to prevent moisture absorption.
   5. Cut off the lugs of the plates and ensure the plates are dry before commencing the porosity measurement in order to record accurate masses.

2. Porosity measurement

NOTE: A Digital Electronic Balance (maximum capacity: 500 g; accuracy: 0.01 g) was used in this study.

1. Place an electronic balance on a sturdy frame structure above a suitable container that contains the glycerol of a known density.
   NOTE: The glycerol density will be used later in the calculations.
2. Remove the dry plate from the desiccator, place it onto a tared electronic balance, and record the mass as the mass of the dry plate.
3. Attach the telescopic (extendable) crocodile clip to the top of the lead grid.
4. Submerge the plate completely in glycerol, ensuring that the extended portion of the clip is kept above the liquid for easy removal of the plate from the glycerol. Bubbles that are trapped in the plate should start to emerge.
5. Put the lid onto the container and insert the stopper.
   NOTE: The container lid should be designed to enable vacuum application.
6. Connect the setup to a low vacuum supply and apply a vacuum of approximately 100 mbar until the sides of the container show a slight indent, then turn off the vacuum. This is to ensure that glycerol penetrates all the pores.
7. Keep the plate under vacuum for at least 15 min.
   NOTE: If air bubbles are still visibly emerging from the lead plate after this period, extend the vacuum time for a little longer. The average porosity of the plates can be underestimated if glycerol does not fully penetrate all the pores.
8. Place the balance attachment onto a tared scale and record the mass.
9. Remove the plate from the glycerol and attach it to the two crocodile clips on the balance attachment. Make sure the plate is level and adjust if necessary.
10. Place the balance attachment with the soaked plate onto the scale and let the plate hang above the glycerol for 8 min to remove the excess glycerol that is on the surface of the plate.
11. Wipe off any drops on the bottom of the plate.
12. Place the balance attachment on the scale and record the mass as the mass of the glycerol-saturated plate.
13. Slowly raise the glycerol container by using the laboratory jack until the top of the plate is just submerged. Record this mass as the mass of the glycerol submerged plate.
14. Repeat the experiment in triplicate.
    NOTE: Dispose of all residues as hazardous chemical waste, following the institution's waste management guidelines.

3. Analysis of the porosity data

NOTE: The data required to calculate the porosity of the plates were adapted from Ferg et. al.⁷, and a detailed derivation of the formulas is provided in Supplementary file 1^7,8,9.

1. Data required to calculate the porosity of the electrode
   1. Define the parameters required. The parameters required for analyzing the percentage porosity are defined as follows:
      Mass of dry plate (g) = A
      Mass of glycerol saturated plate (g) = B (To be measured in triplicate)
      Mass of glycerol submerged plate (g) = C (To be measured in triplicate)
      Mass of the grid alloy (g)= D
      Density of the grid alloy (g/cm³) = E (NOTE: this is determined by the type of lead alloy used)
      Density of glycerol (g/cm³) = F
      Active material mass (g), G = (A - D)
      Active material absolute density (g/cm³),  
      Specific pore volume (cm³/g),
      Bulk density (g/cm³),  
      % Porosity, K = IJ x 100
2. Generating the remaining data needed for the calculations
   1. Determine the mass of the grid by carefully removing the active material of the electrode.
      NOTE: Figure 6A,B show positive and negative formed lead-acid battery plates with corresponding active materials, while Figure 6C, D show the respective grids.
3. Data analysis
   1. Open a spreadsheet and input each parameter listed in step 3.1 and the corresponding formulas into the appropriate columns.
   2. Input the mass of the dry plate, A into a column.
   3. Input the triplicate masses of the glycerol saturated plate, B, into a column.
   4. Input the triplicate masses of the submerged plate, C, into a column.
   5. Input the mass of the grid alloy, D, into a column.
   6. Input the density of the grid alloy, E, into a column. (Depending on the type of lead alloy used).
   7. Input the density of the glycerol, F, into a column.
   8. Input the formula for determining the active material mass of the plate, G, into a column by subtracting the mass of the dry plate, A, from the mass of the grid alloy, D, to compute the corresponding values.
      The active material mass of the plate, G = (A -D)      (1)
   9. Input the formula for determining the absolute density of the active material, H, into a column to compute the corresponding values.
      
   10. Input the formula for determining the specific pore volume, I, into a column to compute the corresponding values.
       
   11. Input the formula for determining the bulk density of the active material, J, into a column to compute the corresponding values.
       The bulk density of the active material, 
   12. Input the formula for calculating the % Porosity of the active material mass on the plate, K, into a column to compute the corresponding values.
       % Porosity, K = IJ x 100      (5)
   13. Determine the average percentage porosity and standard deviation of the plates using the appropriate function on the spreadsheet.

4. Microstructural analysis by powder X-ray diffraction

NOTE: Powder X-ray diffraction microstructural analysis were performed on replicate plates from the same battery that have been exposed to the same condition to ensure that the data obtained is comparable and that there is no structural interference.

1. Sample preparation for X-ray diffraction of the electrode surface
   1. Carefully cut the dried sample of the plate to the appropriate shape to fit into the sample holder.
      NOTE: This should be done carefully to avoid altering the surface of the electrode.
   2. Transfer the sample to a clean sample holder, ensuring that the height of the plate surface is aligned with the top edge of the sample holder.
2. Sample preparation for X-ray diffraction of active material bulk
   NOTE: A sample preparation station obtained from Malvern Panalytical was used to enable easy back-loading of the powder sample into the sample holder.
   1. Remove the dried sample of the active material of the plate from the grid.
   2. Grind the active material to powder with a mortar and pestle to uniformly reduce the particle size and ensure there is sufficient powder to fill a standard sample holder.
   3. Clean the sample holder and the sample preparation table of the sample preparation station.
   4. Place the top plate of the 2-piece powder sample holder flat-side down on the sample preparation table and secure it by pressing and releasing the clamp button of the sample preparation table.
   5. Overfill the top plate of the sample holder with the powder sample using a spatula.
   6. Gently compress the powder onto the top plate of the sample holder by pressing firmly and evenly with the powder press block of the sample preparation station. Ensure the sample height aligns with the top edge of the sample holder.
   7. Clean the edges of the sample holder with a dusting brush to remove the excess powder.
   8. Press the bottom of the 2-piece powder sample holder face-side down onto the top plate until it clicks.
   9. Flip the sample preparation table and press the clamp button to release the sample holder. Confirm that the powder surface is smooth and aligns with the top edge of the sample holder.
3. XRD data acquisition
   NOTE: Powder X-ray diffraction patterns were recorded over a 2-theta range of 5°-80°, in a 15 min scan using a benchtop diffractometer equipped with a cobalt (Co) anode X-ray tube.
   1. Load the sample holder onto the XRD diffractometer.
   2. Select the appropriate measurement program and input the sample details into the diffractometer.
   3. Start the measurement.
   4. After the data has been collected, go to the data management menu of the diffractometer and export the results to the desired folder.
4. Rietveld refinement
   NOTE: The DIFFRAC.EVA version 4.3 and DIFFRAC.TOPAS version 6 were used for the phase identification and quantitative Rietveld refinement, respectively.
   1. Identify the phases available in the sample using a dedicated phase identification software.
   2. Open the DIFFRAC.EVA software and click on the import from files tab to load the XRD scan file (.RAW file) onto the software for peak identification.
   3. Click on the Search/Match (scan) tab in the Data command panel.
   4. Click on the drop-down button beside the chemical filter tab. Right-click to select all elements on the periodic table, then right-click again to change the selected elements to 'discarded'.
   5. Uncheck the elements of interest that are contained in the sample by clicking on the element symbol.
   6. Click on the drop-down button beside the database filter tab and select the database of choice.
   7. Click on the match tab to match the diffraction pattern with the reference database to identify the phases.
   8. Quantify the identified phases in the sample using a dedicated quantitative analysis software.
   9. Open the DIFFRAC.TOPAS software and click on the load scan files to import the raw XRD data into the software for quantitative Rietveld refinement.
   10. Click on the drop-down button beside the name of the raw file.
   11. Right-click on the emission profile tab and load the emission profile.
   12. Click on the background tab and refine the background parameters.
   13. Click on the instrument tab and refine the parameters based on the instrument configuration.
   14. Click on the correction tab and refine the zero error, sample displacement, and Lorentz polarization factors.
   15. Click on the Load STR(s) tab to load the structure files of the identified phases from the CoD database of the TOPAS software.
   16. Refine the lattice parameters and atomic positions of the crystal structure(s).
   17. Click on the Run tab to initiate the refinement.
   18. Continue refining until the goodness-of-fit and weighted-profile R-factor (Rwp) is below the acceptable standard.

5. Modifications and troubleshooting

NOTE: This section outlines critical protocol steps that can affect the accuracy and reproducibility of porosity measurements in lead plates and provides guidance for addressing common issues that can be encountered during the protocol.

1. Fragile plates
   1. Plates exposed to typical battery conditions may become fragile and could disintegrate during handling. Handle plates gently, avoiding pressure on the active material.
2. Incomplete drying of plates
   1. If the plates are not dried completely, residual moisture may cause inaccuracies in the mass of the dry plate and, consequently, in all subsequent calculations. Ensure the plates are fully dry before commencing the porosity measurement, and verify that a constant mass has been achieved.
3. Residual acid plates
   1. Residual acid in the plates may react when submerged in glycerol. Rinse the plates gently but thoroughly with water to remove any remaining acid, ensuring complete removal.
4. Incomplete pore penetration
   1. If glycerol does not fully penetrate all pores, the calculated pore volume will be lower than the actual value, affecting the average porosity of the plates. After 15 min of vacuum-assisted infiltration, the presence of air bubbles indicates that there are pores that are yet to be filled; continue vacuuming until bubble ceases. While 15 min should be suitable for most plate sizes, optimize the infiltration time based on the plate size.

Results

Capacity tests were conducted on three commercially purchased 12 V, 7.2 Ah VRLA lead-acid batteries at the C₁₀ rate to a lower voltage limit of 10.5 V. All capacity tests were performed at 25 °C. Upon receipt, the batteries were recharged at 14.8 V for 10 h, with a maximum current of 2.9 A. This was followed by two C₁₀ capacity tests with a standard recharge step at 14.8 V for 24 h at 2.9 A maximum. The results of the initial C₁₀ capacities are summarized in Table 1.

...

Discussion

Capacity tests showed that Battery 1 delivered 92% of the rated capacity (6.62 Ah), Battery 2 delivered 50% (3.58 Ah) with only a partial recovery of 3.32 Ah even after a repeated recharge step, and Battery 3 delivered 91% of the rated capacity (6.57 Ah) (Table 1).

Variations in the concentration of H₂SO₄ within the PAM pores, resulting from chemical reactions that occur in the plates during capacity cycling, influence the structure and morphology of the ...

Materials

List of materials used in this article

Name	Company	Catalog Number	Comments
Aeris benchtop powder X-ray diffractometer	Malvern Panalytical B.V., Almelo, The Netherland		For the microstructural analysis
Balance Attachment with crocodile clips			To allow for the weighing of the saturated and submerged plate
Battery cells (12 V, 7.2 Ah)	N/A	N/A	Any
DIFFRAC.EVA V 4.3	Bruker AXS GmbH, Karlsruhe, Germany	Version 4.3	Phase identification software
DIFFRAC.TOPAS V6	Bruker AXS GmbH, Karlsruhe, Germany	Version 6	Phase quantification software
Digital Electronic Balance	Dixon Science, China	EG5001-A	Digital Electronic Balance with a maximum capacity of 500 g and an accuracy of 0.01 g
Laboratory central vacuum line			To apply vacuum to the container to facilitate the infiltration of glycerol into the plates.
Laboratory Jack	Karl-Kurt Juchheim Laborgeräte, GmbH, Germany	2290	To raise the glycerol container until the top of the plate is just submerged
Powder sample holders	Malvern Panalytical B.V., Almelo, The Netherland		For holding powder samples for XRD analysis
Sample Preparation Station	Malvern Panalytical B.V., Almelo, The Netherland	9,43,00,17,70,101	To enable easy back-loading of powders into the sample holders for XRD analysis
Sturdy frame structure			Any
Suitable container with lid			Any
Telescopic crocodile clip			For submerging the plates in the glycerol
Vacuum Pressure Guage	WIKA Alexander Wiegand SE & Co. KG, Klingenberg, Germany	Model: 611.10	To measure the pressure of the applied vacuum