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Electrode Surface Area Characteristics of Batteries Margot L. Wasz 1 The Aerospace Corporation, Los Angeles, CA, 90009-2957 The electrodes from different battery types were studied using a gas physisorption technique to better understand how changes in surface area and pore size distribution affect performance variables such as capacity, impedance, and rate capability. This paper demonstrates the advantages of quantifying surface area changes and the unique considerations required when applying gas physisorption methods to different types of electrodes. Particular emphasis is given to changes in silver oxide, the hydrogen electrode used in fuel cells, and two different types of carbon powders. Nomenclature R = correlation coefficient for the BET surface area equation (unit-less) I. Introduction HE microstructures of battery electrodes are increasingly being manipulated to attain better performance characteristics for capacity, high discharge currents, rapid charging, and long life. Pore size, particle size, and surface area control are used to optimize the transport of ions to the electrode, charge conduction within the electrode matrix, and to minimize capacity losses over life. Never before have these techniques been put to greater use than in the present development of electrodes using intercalation hosts to hold the mobile ions in the cathode and anode as is the case with lithium-ion batteries. Compared to more traditional electrochemical couples used for energy storage, the conductivity of charged ions in the different types of lithium-ion couples is relatively poor. However, because modern material fabrication methods are able to produce nanoscale features and high surface areas, present day lithium-ion cells, previously only suitable for low rate electronic devices, are proving to be attractive for higher power applications requiring high currents and low system weights. By means of example, a cursory review of the recent technical literature shows compelling capacity and rate capability improvements for high surface area materials such as nanotubes 1 and graphite anodes, 2 along with several detailed models predicting additional benefits should the particle size, porosity, and surface area of the active materials, conductivity agents, and binders be optimized. 3-5 The importance of electrode porosity and surface area on cell performance is not limited to lithium-ion batteries. High surface areas permit high rates of conduction, but also may cause significant capacity impacts due to active material losses incurred by stabilizing the electrode/solution interface. However, for more traditional battery cell chemistries, such as nickel-cadmium or silver-zinc, electrode surface area is not commonly measured as a manufacturing control, in part due to difficulties in conducting and interpreting analytical methods such as mercury porisimetry which has traditionally been used to measure surface area and pore size characteristics. Mercury porisimetry is particularly problematical for analyzing zinc electrodes due to the ease with which mercury amalgamates with zinc. Gas physisorption has been used for decades to quantify the surface area of materials by measuring the amount of adsorption of gas molecules on a sample at cryogenic temperatures. Known volumes of a chemically inert gas, typically nitrogen or krypton, are introduced to the sample and the amount of condensed gas measured as the difference between the expected pressure change from the gas laws and the pressure difference measured. High fidelity using this method requires high resolution pressure gages, accurate system volume measurement, ultra high purity test gases, and contamination-free manifolds. Recent advances in test equipment design optimizing these parameters has made it possible to perform accurate, repeatable measurement of low surface areas previously inaccessible by this technique, making possible the study of electrodes such as nickel sinter and zinc. Surface area is most commonly calculated using the BET (Brunauer, Emmett, and Teller) equation which assumes that adsorbing gas has only two energy levels – that of the first monolayer of gas molecules adsorbed 1 Senior Scientist, Energy Technology Dept., P.O. Box 92957, Mail Stop M2-275, AIAA Senior Member. T 7th International Energy Conversion Engineering Conference 2 - 5 August 2009, Denver, Colorado AIAA 2009-4503 Copyright © 2009 by The Aerospace Corporation. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.
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Page 1: [American Institute of Aeronautics and Astronautics 7th International Energy Conversion Engineering Conference - Denver, Colorado (02 August 2009 - 05 August 2009)] 7th International

Electrode Surface Area Characteristics of Batteries

Margot L. Wasz1

The Aerospace Corporation, Los Angeles, CA, 90009-2957

The electrodes from different battery types were studied using a gas physisorptiontechnique to better understand how changes in surface area and pore size distribution affectperformance variables such as capacity, impedance, and rate capability. This paperdemonstrates the advantages of quantifying surface area changes and the uniqueconsiderations required when applying gas physisorption methods to different types ofelectrodes. Particular emphasis is given to changes in silver oxide, the hydrogen electrodeused in fuel cells, and two different types of carbon powders.

NomenclatureR = correlation coefficient for the BET surface area equation (unit-less)

I. IntroductionHE microstructures of battery electrodes are increasingly being manipulated to attain better performancecharacteristics for capacity, high discharge currents, rapid charging, and long life. Pore size, particle size, and

surface area control are used to optimize the transport of ions to the electrode, charge conduction within theelectrode matrix, and to minimize capacity losses over life. Never before have these techniques been put to greateruse than in the present development of electrodes using intercalation hosts to hold the mobile ions in the cathode andanode as is the case with lithium-ion batteries. Compared to more traditional electrochemical couples used forenergy storage, the conductivity of charged ions in the different types of lithium-ion couples is relatively poor.However, because modern material fabrication methods are able to produce nanoscale features and high surfaceareas, present day lithium-ion cells, previously only suitable for low rate electronic devices, are proving to beattractive for higher power applications requiring high currents and low system weights. By means of example, acursory review of the recent technical literature shows compelling capacity and rate capability improvements forhigh surface area materials such as nanotubes1 and graphite anodes,2 along with several detailed models predictingadditional benefits should the particle size, porosity, and surface area of the active materials, conductivity agents,and binders be optimized.3-5

The importance of electrode porosity and surface area on cell performance is not limited to lithium-ion batteries.High surface areas permit high rates of conduction, but also may cause significant capacity impacts due to activematerial losses incurred by stabilizing the electrode/solution interface. However, for more traditional battery cellchemistries, such as nickel-cadmium or silver-zinc, electrode surface area is not commonly measured as amanufacturing control, in part due to difficulties in conducting and interpreting analytical methods such as mercuryporisimetry which has traditionally been used to measure surface area and pore size characteristics. Mercuryporisimetry is particularly problematical for analyzing zinc electrodes due to the ease with which mercuryamalgamates with zinc.

Gas physisorption has been used for decades to quantify the surface area of materials by measuring the amountof adsorption of gas molecules on a sample at cryogenic temperatures. Known volumes of a chemically inert gas,typically nitrogen or krypton, are introduced to the sample and the amount of condensed gas measured as thedifference between the expected pressure change from the gas laws and the pressure difference measured. Highfidelity using this method requires high resolution pressure gages, accurate system volume measurement, ultra highpurity test gases, and contamination-free manifolds. Recent advances in test equipment design optimizing theseparameters has made it possible to perform accurate, repeatable measurement of low surface areas previouslyinaccessible by this technique, making possible the study of electrodes such as nickel sinter and zinc.

Surface area is most commonly calculated using the BET (Brunauer, Emmett, and Teller) equation whichassumes that adsorbing gas has only two energy levels – that of the first monolayer of gas molecules adsorbed

1 Senior Scientist, Energy Technology Dept., P.O. Box 92957, Mail Stop M2-275, AIAA Senior Member.

T

7th International Energy Conversion Engineering Conference 2 - 5 August 2009, Denver, Colorado

AIAA 2009-4503

Copyright © 2009 by The Aerospace Corporation. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

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directly to the sample surface, and that of successive layers of gas molecules adsorbed to each other. In practice,BET surface area measurements are performed at low pressure ratios relative to the condensation pressure for thetest gas, with a number of points sampled and fitted to the BET equation. Therefore, it is important to note whetherthe data fits the BET equation, as indicated by the correlation coefficient, R, to assess whether BET theory isappropriate for the sample studied. Significant deviations from the BET theory may result from chemisorption ofthe test gas and more complicated gas-gas interactions in the adsorbed layers.

The information that can be gained from a material from the characteristics of gas physisorption extends wellbeyond surface area measurement. Isotherms of the amount of gas condensed as a function of partial pressure mayprovide insight into the pore size and structure of a material as well as offer insight into interaction between theabsorbate and absorbent material. Once coupled with an appropriate model for the pore structure, hysteresis in thepressure isotherms provides the basis for quantifying pore dimensions. Comprehensive discussion of the manydifferent models available and their relative merits for different types of materials is outside the scope of this paper,however, the reader is referred to Ref. 6 for an excellent discussion of the models available, many of which, areroutinely provided with the analytical equipment software. In the examples to follow, unless noted, the BETequation was used for measuring surface area, and the BJH (Barrett, Joyner, Halenda) method for reporting pore sizedistribution. The BJH method relies on the assumption that, during evacuation, lower pressures are required toremove gas from the smaller pores relative to the larger pores. However, the model does not account for differencesin surface tension of the condensed gas caused by changes in the curvature that can occur in pores with differentmorphologies.

The examples below detail the information gained from using gas physisorption on common battery and fuel cellelectrodes and materials. They were selected to illustrate the utility of gas physisorption analysis on materials onceconsidered unsuitable for the technique. Physisorption measurements were taken using a Micromeritics ASAP 2020surface area and pore size analyzer equipped with a high vacuum module. Samples were out-gassed at thetemperatures noted with a dwell of four hours. The absorption of UHP nitrogen gas was measured starting from apartial pressure of 0.06 to saturation in liquid nitrogen. Desorption was measured to 0.15 partial pressure limit.Calculations for surface area used a 6-point linear curve fit to the BET equations from 0.06 to 0.20 partial pressure.A Mettler balance model AE-160, with an accuracy of 0.5 milligrams, was used to measure sample and sample tubeweights. Reference standards for 214 m2/g and 0.28 m2/g were used to verify the instrument accuracy. All electrodeplate samples were cut to 0.25 x 0.25 inch dimensions to fit in the analysis tube.

II. Silver OxideSilver oxide is a strong oxidizer, producing a power-dense electrochemical couple when combined with zinc,

cadmium or iron anodes in alkaline solutions.7 Silver oxides are commonly formed electrochemically from asintered silver powder and current collector matrix in a strong alkaline bath using proprietary processes. Theprocess precipitates a combination of AgO and Ag2O, referred to as the peroxide and monoxide phases respectively,on the conductive silver particle cores and current collector mesh. Retaining a conductive silver network throughoutthe electrode is crucial to making low impedance electrodes because the bulk resistivity for these three materialsranges fourteen orders of magnitude, with silver = 1.6 x 10-6, AgO = 10, and Ag2O = 10+8 Ohm-cm.8

Despite the large increase in bulk resistivity of the monoxide phase, the transition from the peroxide to monoxidephase, shown schematically in Figure 1, is commonly accompanied by a significant drop in cell impedance. Oneinterpretation for this seemingly inconsistent observation is that the discharge of the AgO phase forms both metallicsilver and Ag2O in the positive electrode, and that the higher conductivity is the result of the newly-formed,conductive, silver paths in the active material. It is important to note that while in practice, the open circuit voltageis used to describe the silver active material as either in the peroxide (~1.85V) or monoxide (1.6V) state, in reality,both peroxide and monoxide phases are often present but electrically isolated from the current collector.

Thermogravimetric (TGA) data for electrochemically-formed silver oxide displays two peaks, the first onecorresponding to the thermal decomposition of the less-stable peroxide phase followed by the decomposition of themonoxide phase. Figure 2 is an example from the author’s laboratory. The percent weight loss for each phasecorresponds to the stoichiometric loss of oxygen.

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Figure 1. Schematic of the change in Ohmicresistance during discharge of silver oxide.From thin film work reported in Ref. 9.

Figure 2. Example of TGA data for thethermal decomposition of the active materialfrom a silver oxide electrode.

Figure 3 shows the percent weight loss and the percent change in surface area with progressively higherannealing temperatures for a silver oxide plate nominally processed to the peroxide phase. A 7.7 gram sample wassuccessively annealed at the temperatures shown with intervening BET measurements made, and full isothermsmeasured after annealing at 30, 110, 150, 225, 350 and 400oC. BET correlation coefficients, R, ranged from0.99967 to 0.99999. After measuring each of these isotherms, a piece of was removed from the analysis tube forscanning electron microscopy (SEM) and x-ray diffraction (XRD) analysis. Note that the % weight loss shows thesame two-plateau structure as the TGA data in Figure 2. The determination of the silver oxide phases labeled onFigure 3 were based on the surface color of the electrode. This determination was fairly easy to make, given that theperoxide phase is dull gray, the monoxide phase is dark black, and the metallic silver phase is white. Figure 4details the results of the XRD measurements indicating at points A – E shown in Figure 2. The XRD results agreewith the visual phase identifications.

Figure 3. Surface area and percent weight loss changes in silver oxide as a function of annealingtemperature.

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Figure 4. XRD results for samples A – E after gas physisorption measurement as indicated on Figure 3.

The peroxide to monoxide phase transition was accompanied by a greater than 2000% increase in surface area.The change in microstructure accompanying this surface area increase is shown in Figure 5. Utilizing the back-scattering mode on the instrument, the silver peroxide appears as dark, angular particles with very small isolatedareas of monoxide which appear as white particles on the surface of the darker peroxide. The higher oxide contentof the white particles was also confirmed by energy dispersive analysis (EDX). After the monoxide transition, thesample has a finer microstructure because of the phase formation process. It is believed that this large surface areaincrease is the cause for the lower electrode impedance characteristic despite the higher resistivity of the Ag2Ophase.

Figure 5. Back-scattered SEM images at 5000x for samples annealed at 30oC (left), and 150oC (right) The30oC sample is mostly peroxide with small isolated monoxide particles appearing as small white spots whereasthe 150oC sample is nearly all high-surface area monoxide.

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Figure 6 shows the gas physisorption isotherm for the 30oC and 150oC silver oxide samples, and Figure 7displays the pore size distribution as calculated by the BJH model for the same two conditions. After the monoxidetransition, increases in gas physisorption were greatest at the higher relative pressures, suggesting an increase in thelarger pore sizes in the electrode as was evident in the SEM images. Results of the BJH analysis, Figure 7, confirmsthis, but also revealed a small increase in the number of pores in the 10 – 20 Å, a range which eluded detection bySEM microscopy.

Figure 6. Gas physisorption isotherms forsilver oxide samples after 30oC annealing(green), and 150oC annealing (red).

Figure 7. BJH pore size distribution for silveroxide samples after 30oC annealing (green),and 150oC annealing (red).

III. Hydrogen ElectrodeHydrogen electrodes are used in alkaline fuel cells and in certain batteries where hydrogen is stored in the gas

phase during charge. The electrodes are made from a slurry of platinum black particles and a Teflon emulsion thatis coated on a metallic current conductor. Figure 8 shows the cross section of a hydrogen electrode and themicrostructure of the Pt/Teflon surface. Note that the Pt/Teflon active material is highly porous and the surfacecontains many surface cracks. This microstructure is critical to the proper operation of the electrode, for not onlymust the electrode easily wick in electrolyte and reject water, it must also stabilize the solid-gas-liquid interfaceduring charge and discharge.10 Early work on these electrodes often reported electrode “drowning”, i.e. the filling ofpores with water, as a failure mode for sustaining high currents in these structures.11

Gas physisorpion was selected to characterize the porous character of these electrodes. For all gas physisorptionwork, it is important to remove the absorbed gas present on samples prior to measuring an isotherm. This isgenerally done by heating the sample under vacuum to remove water and gases adhering to the surface. Hightemperatures are preferred when not detrimental to the sample microstructure, and bake-out temperatures of 350 –450oC for silicon and alumina calibration standards are often used. However, it was unknown how high atemperature the hydrogen electrodes could sustain without suffering changes in microstructure. Furthermore, whileprior investigations reported significant performance improvements when sintering temperatures used to process theelectrodes were increased from 310 to 335oC due to the better water rejection rate by the electrode microstructure,11

the maximum suitable processing temperature was not known. To measure the surface area and pore size responseto annealing temperature, a virgin hydrogen electrode was sectioned for gas physisorpion analysis, and isothermscollected as progressively higher annealing temperature were applied. A virgin electrode was selected instead of anelectrode from a fuel cell to reduce the risks posed by residual electrolyte inaccessible by washing. Upon exposureto air, any electrolyte left in the pores of these electrode has been observed to cause damage to the material due tothe higher relative volume of the carbonate phase formed by reacting with the carbon dioxide in the air.

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Figure 8. Back-scattered SEM images of a hydrogen electrode: Cross section (left) and surface view ofPt-Teflon slurry (right). The large white area in the cross-section image is a nickel current collector, and the toplayer is a hydrophobic polymer membrane used to facilitate gas into the structure.

Figure 9 shows the weight loss and surface area changes as a function of annealing temperature from 50 to375oC. As temperatures were increased to 100oC, the BET surface area slightly increased. When water is presenton the sample, the surface area increases as the sample weight is lost due to the evaporation of water and the highernumber of pores accessible to the condensation of nitrogen gas. At temperatures between 100 and 250oC, there wasa 10% loss in surface area that was not reflected by a corresponding loss in sample weight which dropped at aconsistent rate throughout the temperature range studied. At temperatures above 250oC, there is a rapid decline insurface area with a loss of 95% at the highest temperature tested. Correlation coefficients for the BET equationexceeded 0.9990 for all runs, and surpassed 0.9999 for temperatures of 275oC and lower.

Figure 9. Surface area and percent weight loss changes in a hydrogen electrode as a function of annealingtemperature.

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Figure 10. BJH pore size distribution in a hydrogen electrode after successively higher annealingtemperatures.

The cause of the weight loss fluctuations in Figure 9 is unknown, and exceeded the 0.06% accuracy of theMettler balance used. While significant weight losses had been anticipated for temperatures up to 110oC due to theevaporation of water and residual surfactant, it was expected that the sample weight would remain largelyunchanged up to 300 - 380oC.12 Contrary to expectation, the sample linearly lost weight throughout testing, up to atotal of about 0.8% at the highest annealing temperature tested.

Figure 10 shows the porous volume in the electrode as a function of pore size for annealing temperatures of 50,125, 225, and 325oC. Note that the pores at the highest annealing temperature are significantly diminished for poresizes measuring 200 Å or less. These data suggest that some of the losses in surface area detected by BET analysisfor temperatures in excess of 250oC are caused by an annihilation of the smallest pores originally present in theelectrode microstructure.

IV. Carbon PowdersThis final example focuses on characterization of commercial carbon powders. Since the discovery of C60 and

related fullerenes, the material characteristics of the different types of carbon crystalline structures and morphologiessuch as graphite, cokes, and pyrolytic carbons has received a great deal of attention. Carbon’s ability to maintainlarge, stable interstitial sites at a low density makes it a popular intercalation host for lithium, and different types ofcarbon have been widely studied as anodes for different combinations of cathodes, solvents, and salts for lithium-ioncells.13-15 Other types of carbons and carbon-compounds are commonly added to both the anode and the cathodeused in lithium-ion cells to improve the conductivity and mechanical adhesion between particles, and betweenparticles and the metallic current collector.

Two types of carbons offered from Alfa-Aesar were measured to determine how sensitive gas physisorptionwould be to their differences in microstructure. Shown in Figure 11, both had similar particle sizes ranging from 0.4to 12 microns. However, whereas the first sample was wholly spherical, the other sample is commonly described ashaving a “splinter” morphology. The BET surface area measured for the spherical carbon was 3.77 ± 0.04 m2/g (R =0.99979) and for the splinter carbon was 23.5 ± 0.2 m2/g (R = 0.99979). Even though the range in particle sizes wassimilar between the types of powders, a somewhat larger surface area in the splinter carbon was expectable given itslonger aspect ratio. However, a 6 fold increase was not expected. Because of the low porous character of thesepowders, surface area calculations using the Langmuir approximation also show a good correlation, with thesolution indicating a surface area of 5.1 ±0.1 m2/g for the spherical powder and 31.7 ± 0.6 m2/g for the splintercarbon. The Langmuir solution always indicates a higher surface area than the BET solution because it assumes thatall gas condensed contributes to a single monolayer on the sample surface.

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Figure 11. SEM images at 1500x of spherical (left) and splinter carbon (right).

Figure 12 shows the gas physisorption isotherm for both types of carbon powder. As would be expected fromthe surface results, the total gas adsorbed is higher in the splinter carbon, with the largest amount of adsorptionoccurring at the lowest and highest relative pressures. However, the data for the spherical carbon are notable as tohow little adsorption occurs between the completion of the initial monolayer formation at around 0.15 and about 0.7relative pressure. This is reflected in the BJH solution for the pore volume as a function of pore size, Figure 13.The data suggests that the splinter carbon has a high volume of micropores that are absent in the spherical carbonwhich accounts for the larger relative surface area in the splinter carbon. Finally, it is worth noting that the increasein gas adsorption seen in both samples at the maximum relative pressure is due to the condensation of gas betweenthe carbon particles, and differences between the two samples in this region are likely due to differences in thegeometry of the interstices caused by round and splinter-shaped particles.

Figure 12. Nitrogen physisorption isotherms of spherical (red) and splinter carbon (green).

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Figure 13. BJH pore size distribution in spherical (red) and splinter (green) carbon.

V. ConclusionThis report was prepared as a demonstration of the utility of gas physisorption analysis for gaining insight into

the structure of materials used in battery electrodes. The first example offered a new perspective to the possiblecause for a well-known impedance phenomena associated with silver oxide electrodes when they transition betweenchemical phases. The second example demonstrated how processing temperatures previously indicated forelectrodes containing Teflon emulsions may be precariously close to having negative consequences should thedynamics of an electrode become limited by surface area or pore size. Finally, the last example demonstrated howtwo carbon powders, seemingly identical except for particle geometry, had very different microporous characterwhich could affect how the particular carbon performs as an intercalation host, conductivity agent, or binder.

AcknowledgmentsThis work was supported under The Aerospace Corporation’s Mission-Oriented Investigation and

Experimentation program , funded by the U. S. Air Force Space and Missile Systems Center under contract No.FA8802-04-C-0001. The author is grateful to Yardney Technical Products for supplying the silver oxide samplesfor study and permission to share these results. The author is grateful for the assistance of Paul Adams, KathyrnLaney, and Patti Sheaffer for providing analyses and conducting many of the tests reported here.

References1Yin, J., et al. “Nanostructured Ag-Fe-Sn/Carbon Nanotubes Composites as Anode Materials for Advanced Lithium-Ion

Batteries,” Journal of the Electrochemical Society, Vol. 152, No. 7, 2005, pp. A1341 – A1346.2Buqa, H., et al. “High Rate Capability of Graphite Negative Electrodes for Lithium-Ion Batteries,” Journal of the

Electrochemical Society, Vol. 152, No. 2, 2005, pp. A474 – A481.3Garcia, R.E., et al. “Microstructural Modeling and Design of Rechargeable Lithium-Ion Batteries,” Journal of the

Electrochemical Society, Vol. 152, No. 1, 2005, pp. A255 – A263.4 Srinivasan, V. and Newman, J., “Design and Optimization of a Natural Graphite/Iron Phosphate Lithium-Ion Cell,” Journal

of the Electrochemical Society, Vol. 151, No. 10, 2004, pp. A1530 – A1538.5Sikha, G., Popov, B. N., and White, R.E., “Effect of Porosity on the Capacity Fade of a Lithium-Ion Battery,” Journal of the

Electrochemical Society, Vol. 151, No. 7, 2004, pp. A1104 – A1114.6Lowell, S., Shields, J.E., Thomas, M.A., and Thommes, M, Characterization of Porous Solids and Powders: Surface Area,

Pore Size and Density,” Springer, 2004.7Linden, D., Handbook of Batteries and Fuel Cells, McGraw-Hill, 1984, chapter 21.

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8Frank, H.A., Long, W.L., and Uchiyama, A.A., “Impedance of Silver Oxide-Zinc Cells,” Journal of the ElectrochemicalSociety, Vol. 123, No. 1, Jan. 1976, pp. 1 – 9.

9Fleischer, A. and Lander, J., Zinc-Silver Oxide Batteries, John Wiley & Sons., 1971.10Perry, M. L., and Fuller, T. F., “A Historical Perspective of Fuel Cell Technology in the 20th Century,” Journal of the

Electrochemical Society, Vol. 149, No. 7, 2002, pp. S59-S67.11Handley, L. M.; Meyer, A. P.; and Bell, W. F., “Development of Advanced Fuel Cell System, Phase 3” NASA Publication,

CR-134818, Jan. 30, 1975.12ASTM standard D4441-98, “Standard Specification for Aqueous Dispersions of Polytetrafluoroethylene,” ASTM

International.13Xing, W. and Dahn, J.R., “Study of Irreversible Capacities for Li Insertion in Hard and Graphitic Carbons,” Journal of the

Electrochemical Society, Vol. 144, No. 4, 1997, pp. 1195-1201.14Xing, W., et al., “Correlation Between Lithium Intercalation Capacity and Microstructure in Hard Carbons,” Journal of the

Electrochemical Society, Vol. 143, No. 11, 1996, pp. 3482-3491.15Zheng, T., et al., “Lithium Insertion in High Capacity Carbonaceous Materials,” Journal of the Electrochemical Society,

Vol. 142, No. 8, 1995, pp. 2581-2590.


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