Anomalous Discharge Product Distribution in Lithium-Air Cathodes

Article pubs.acs.org/JPCC

Anomalous Discharge Product Distribution in Lithium-Air Cathodes Jagjit Nanda,*,† Hassina Bilheux,*,‡ Sophie Voisin,‡ Gabriel M. Veith,† Richard Archibald,§ Lakeisha Walker,‡ Srikanth Allu,§ Nancy J. Dudney,† and Sreekanth Pannala*,§ †

Materials Science and Technology Division, ‡Neutron Scattering Science Division, and §Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States S Supporting Information *

ABSTRACT: Using neutron tomographic imaging, we report for the first time the three-dimensional spatial distribution of lithium products in electrochemically discharged lithium-air cathodes. Neutron imaging finds a nonuniform lithium product distribution across the electrode thickness, with the lithium species concentration being higher near the edges of the Li-air electrode and relatively uniform in the center of the electrode. The experimental neutron images were analyzed in context of results obtained from 3D modeling that maps the spatiotemporal variation of the lithium product distribution using a kinetically coupled diffusion based transport model. The origin of such anomalous behavior is due to the competition between the transport of lithium and oxygen and the accompanying electrochemical kinetics. Quantitative understanding of these effects is a critical step toward rechargeability of Li-air electrochemical systems.

1. INTRODUCTION Lithium-air chemistry1,2 potentially offers a promise for very high energy density (3450 Wh/kg, calculated on the basis of Li2O2 weight) that if successful would revolutionize the world of electric vehicles by extending their range to 500 miles or beyond. The high energy density is due to two main reasons: (a) the cathodic component, in this case, oxygen, is not stored in the cell unlike the lithium-ion intercalated compounds; and (b) it uses Li-metal as the anode, which has close to an order of magnitude higher specific capacity as compared to commonly used carbon anodes (372 mAh/g). However, to make this happen, major fundamental scientific breakthroughs3 are needed that could address various bottlenecks associated with its poor cycle life and power performance.2 One major issue has been deposition of various insulating lithium decomposition products on the surface of the porous carbon foam (normally referred to as the air-electrode) during the discharge process, commonly referred to as the oxygen reduction reaction, ORR.4,5 Recent studies have found that the discharge reaction is strongly affected by electrolyte and solvent composition and driven by complex reaction kinetics under chemical and electrochemical condition, resulting in more complicated discharge products than Li2O2.5−8 The buildup of the discharge products over time could lead to a drastic reduction of the electronic conductivity due the insulating nature of ORR products impeding the electrochemical process at the interface with a concomitant decrease in the overall porosity of the glassy carbon electrode that could affect the ion transport. Understanding the origin of the electronic passivation on the reaction surface (in this case, graphite carbon foam) due to the complex electrochemical and chemical decomposition of electrolyte− © 2012 American Chemical Society

solvent system and the resulting charge transfer kinetics at various current densities is therefore critical.9 While recent studies have focused on the temporal aspects of the discharge profiles as a function of various electrochemical transport parameters and have provided a guide for the overall performance,9,10 there has been no attempt to understand the discharge (or charge) mechanism spatially in terms of local lithium species concentration across the thickness of the electrode. A three-dimensional imaging and tomographic method11 that could spatially map the lithium discharge product distribution inside the 3D pores across the entire electrode thickness during the discharge step could provide important insights into the ionic mass transport as well as the limiting electronic conduction occurring across these thick electrodes. This study reports for the first time neutron imaging12 and 3D computed tomography (CT) mapping of the lithium discharge products in Li-air cathodes to obtain a semiquantitative estimate of the spatial lithium concentration across the 3D volume element of discharged Li-air cathodes, which then directly relates to the distribution of the reaction products during the ORR.

2. EXPERIMENTAL AND ELECTROCHEMICAL MODELING Electrode Preparation for Neutron Imaging and Li-Air Cell Electrochemistry. The Li-air cathodes used in this work Received: February 17, 2012 Revised: March 19, 2012 Published: March 22, 2012 8401

dx.doi.org/10.1021/jp3016003 | J. Phys. Chem. C 2012, 116, 8401−8408

The Journal of Physical Chemistry C

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were made from a graphitized carbon foam (0.035 g, 1 mm thick, surface area 2.2 m2/g as measured by N2 physisorption on a Quantachrome Autosorb 1C) made at ORNL.13,14 The graphite foam was formed from Mitsubishi ARA24 pitch at 1000 °C followed by graphitization in Ar at 2800 °C to give highly conductive foam with open cells (0.4 mm diameter). Manganese oxide-coated electrodes were prepared by soaking the carbon cathodes in an excess of a 0.1 M NaMnO4 (Alfa Aesar) + 0.1 M Na2SO4 (Aldrich) solution for 5.5 h.15 The cathodes were washed with 18 MΩ water until the wash solution was clear, and then soaked in 100 mL of water for 10 min, followed by vacuum drying for 18 h. Swagelok cells were constructed in an argon-filled glovebox using 0.75 mm thick Li foil (99.99%, Alfa), a Celgard 2500 separator, and 1.5 mL of 1.2 M LiPF6 in 1:1 wt % ethylene carbonate/dimethyl carbonate (EC/DMC) (Ferro), which is a widely used electrolyte for Liion batteries and Li-air cells.16−23 The cells were assembled in a vertical geometry with the cathode located at the top of the cell closest to the oxygen/argon supply. Research grade oxygen (Air Liquide) was used, and the cells were operated with 20 PSI O2 with enough electrolyte to saturate the cathode. Cells were discharged at 5 μA of current to 2.2 V on a Maccor battery cycler. For comparison, we also prepared samples coated with lithium peroxide on porous carbon foams. For this experiment, we used commercial glassy carbon foams obtained from Duocel Co. These foams have various pore sizes, described in terms of pores per inch (PPI). The slurry-based coating of lithium peroxide was performed inside an argon controlled atmosphere. In a typical batch, about 1 wt % colloidal mixture of Li2O2 was prepared using N-methyl pyrolidone (NMP) as the solvent. For effective dispersion of Li2O2 in the solvent, the mixture was sonicated for about 10−15 min. The carbon foams were soaked in the slurry for 1 h, and then the excess slurry was wiped from the surface using soft tissue paper. The foams were then dried under vacuum for about 12 h leaving a thin layer of Li2O2 inside the pores of the foam. The excess dried Li2O2 comes out from the surface of the foams. For initial experiments, we used 45 and 100 PPI carbon foams. Because the neutron imaging resolution was originally about 100 μm, then improved to approximately 50 μm for the latest results, there was no need to use finer pores sizes. The typical dimensions of the foams used for imaging were 1 cm (length) × 0.5 cm (width). The samples were packed and sealed inside aluminum cylinders for the neutron experiments. Detailed information about neutron imaging and tomography analysis of air cathodes is discussed in the Supporting Information. 3D Spatial Modeling of Li-Air Cathodes. The electrochemical transport across a three-phase boundary system such as air cathode is driven by (i) the interplay between the reaction kinetics and rate, (ii) changes in the electronic conductivity due to insulating nature of discharge product buildup, and (iii) mass transport of the dissolved oxygen species and lithium across the porous electrode. More importantly, these effects are interrelated and affected by the dynamical change of porosity of the carbon foam as the discharge proceeds. Therefore, the equations to be solved are coupled reaction−diffusion of the following form:

∂(εcO2) eff = ∇·(εDO2 (ε)∇cO2) + 9 O2 ∂t ∂(εc X) = ∇·(εDXeff (ε)∇c X) + 9X ∂t

Here, ε is the porosity in the air-cathode, CO2 and CX stand for the mass fraction of the soluble O2 and reactants (such as Li+, lithium oxides, carbonates, lithium alkyl carbonates) concentration, Deff stands for the effective diffusion (here, we take it as diffusion coefficient times ε0.5), and ℛ stands for the reaction terms leading to depletion of these species from the electrolyte. For lack of detailed knowledge about the exact products decomposition and the associated reaction steps and kinetics,24 t h e o v e r a l l r ea c t i o n i s s im p l i s t ic a ll y g i ve n a s :

The reaction rate factor, k, was modified to include buildup of the decomposition product on the surface of the carbon by the expression: ⎧ d[Li 2CO3] exp(x Li) ⎫ ⎬*[Li]2 [O2 ]1.5 [EC] = k*εs⎨1 − dt exp(1) ⎩ ⎭

along with proper boundary conditions. The transport and reaction equations were solved on the basis of the rigorous volume averaging approach typical of multiphase formulation. In this method, we have a unified, single-domain approach where complex geometries are naturally incorporated by including the local volume fraction of the different phases and corresponding species concentration within each of the phases. The discharge product formation was analyzed under various limiting transport conditions, and specific results are discussed in the Supporting Information.

3. RESULTS AND DISCUSSION Figure 1 shows the discharge profiles of air cathodes at a current density of 5 μA/cm2 with and without the presence of an active catalyst layer MnO2 on the surface of the graphite foam. The samples were discharged to their full capacity to enable maximum discharge product formation for the neutron imaging experiments. Detailed analysis of the discharge product formation and their possible mechanism was recently reported

Figure 1. Discharge voltage profiles of Li-air cathodes without (top curve) and with catalyst layer MnO2 on the carbon foam (bottom curve). For neutron imaging and tomography experiments, the electrodes were discharged at 5 μA/cm2. 8402



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by our group.6 A plausible reaction mechanism for carbonate electrolyte decomposition was proposed recently by Bruce and co-workers. Briefly, in the presence of LiPF6−carbonate electrolyte system, the discharge product is dominated by the electrolyte decomposition product such as lithium alkyl carbonates and lithium carbonates instead of the ideal peroxide or superoxides for lithium-air chemistry. The electrodes were discharged for >500 h to allow a significant deposition of discharge products for neutron contrast imaging (see Supporting Information). Neutron Imaging and Tomography. Neutron imaging or radiography is a powerful imaging method based on the relative attenuation contrast between the atoms determined by their respective scattering and absorption cross-sections as governed by the Beer−Lambert law, I(λ) = I0(λ)e−μ(λ)Δx, where I0 and I are, respectively, the incident and transmitted neutron beam intensities for a given wavelength λ, μ is the attenuation coefficient, and Δx is the thickness of the sample. The attenuation coefficient μ is given by μ(λ) = σt(λ)(ρNA)/M, where σt(λ) is the material’s total cross-section for neutrons, ρ is its density, NA is Avogadro’s number, and M is the molar mass. Because of the fundamental nature of the interaction of neutrons with matter, some light nuclei such as hydrogen and its isotope deuterium greatly scatter neutrons, whereas some heavier elements such as Cu or Pb are not strong scatterers or absorbers of neutrons and can therefore be easily penetrated. In case of this study, that is, Li distribution in C foam electrodes, the contrast obtained in the neutron radiograph and the neutron tomography set is strongly dominated by the Li content, as illustrated in Table 1. This table displays the

Figure 2. Schematic diagram of the neutron imaging setup at the HIFR neutron imaging prototype facility at Oak Ridge National Laboratory. The incident neutrons have a wavelength range between 1.8 and 6 Å.

than the exact chemistry and composition of the discharge products.25 The color contrast shows the lithium density distribution with brighter color representing higher lithium content across the porous carbon surface. It is expected that the amount of lithium concentration should be a direct measure of the discharge products. The experimental Li-images of the discharged air cathodes were compared to results from coupled 3D transport model (see Supporting Information) shown in Figure 3C and D. The essential elements in the 3D model include (i) a reaction rate dependence of the charge transfer kinetics to account for the gradual buildup of discharge product formation on the surface of the porous carbon, (ii) Li-ion and dissolved oxygen transport in the electrolyte across the porous electrodes, and (iii) coupled spatiotemporal changes in the overall porosity of the electrode during the discharge period. Similar to the experimental discharge conditions, the 3D model calculations were carried for about 23 000 s with a starting porosity of 70% at a moderate kinetic rate factor of 5.0 × 104 (cm3/mol)3.5/s. The reaction rate factor is related to the current density, a parameter that determines the rate under which the air cathodes are discharged. The calculated spatial product distribution and porosity distribution at 23 000 s (close to the discharge time of the air cathodes) are shown in Figure 3C and D with very good qualitative agreement with experiment in terms of spatial lithium distribution. Most notably, the reaction rate expression9 is modified to include the discharge product layer that is formed on the carbon surface. We model the rate expression as:

Table 1. Total Neutron Scattering Cross-Section (in barns) of Isotopes of Lithium and Carbon element

isotope %

coherent crosssection

Li6 Li7 C12 C13

7.5 92.5 98.9 1.1

0.51 0.619 5.559 4.81

incoherent crosssection

scattering crosssection

absolute crosssection

0.46 0.78 0 0.034

0.97 1.4 5.559 4.84

940 0.0454 0.00353 0.00137

scattering (coherent and incoherent) and absorption crosssections for the selected isotopes of Li and C. The total crosssection, which is necessary to calculate the transmission through a sample, is the sum of all cross-sections at 1.5 Å. Clearly, the major isotope contributing to a strong attenuation of neutrons is Li6, with an attenuation cross-section of 940 barns. Figure 2 shows a schematic diagram of the neutron imaging experimental setup currently operated at the High Flux Isotope Reactor (HIFR) at Oak Ridge National Laboratory. Briefly, a collimated neutron beam is incident on the sample mounted on a 3D rotatable stage for collecting image snapshots across the entire sample cross-sections. As mentioned above, with an objective toward understanding the underlying electrochemical transport and the spatial distribution of the discharge products on the pores of the Liair cathodes, we performed imaging and neutron tomographic reconstruction of discharged air cathodes shown in Figure 3. Figure 3A and B shows 2D image slices of discharged Li-air cathodes labeled as Li-Air-1 and Li-Air-2 (same as cathode-1 except with a MnO2 catalyst layer coating). It is noteworthy that in the context of the current experiment, the neutron attenuation contrast is only sensitive to atomic lithium rather

⎧ d[Li 2CO3] exp(x Li) ⎫ ⎬*[Li]2 [O2 ]1.5 [EC] = k*εs⎨1 − dt exp(1) ⎭ ⎩

where xLi is the mass fraction of the deposited lithium product, and εs is the starting porosity of the matrix. The reaction rate order was taken to be 4.5 on the basis of approximate global reaction corresponding to the detailed reaction mechanism proposed by Bruce and workers for carbonate electrolyte decomposition in the presence of reduced oxygen species and lithium salt.24 The dissolved oxygen concentration value [O2] was obtained from measurement reported by Read and coworkers26 for similar electrolyte composition and was kept constant. The coupled transport equations described in the Supporting Information (eqs 1,2) were solved self-consistently to calculate the spatial discharge products and the spatiotemporal changes of porosity as shown in Figure 3C and D. In the absence of a quantitative estimation of the reaction rate 8403



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Figure 3. Normalized two-dimensional reconstructed slices of discharged Li-air cathodes showing spatial distribution of lithium concentration: (A) Li-Air-1, (B) Li-Air-2 (includes the catalyst layer MnO2). (C) Calculated Li-product spatial distribution at 23 000 s. The color code shows the relative lithium compound or discharge product formation. (D) Calculated porosity changes at 23 000 s as a result of the discharge product 8404



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Figure 3. continued formation. (E) Reconstructed 3D tomography image of Li-Air-1. (F) Reconstructed 3D tomography image of Li-Air-2. The 3D pictures are intentionally sliced at the edges to show the spatial Li-variation. (G) A typical cross-sectional lithium distribution derived from the bulk of Li-Air-1 cathode. (H) A typical cross-sectional lithium distribution derived from the bulk of Li-Air-2 cathode. The scale bars for the 3D figures are the same as those given in (A) and (B).

Figure 4. Calculated line profile showing the relative Li volume percent in Li-air cathodes. The line profiles are calculated at different thresholds (Lisignal in the voxel) for uncertainty quantification. See Supporting Information for details. (A) Li-concentration profile for Li-Air-1 and (B) Li-Air-2. (C) Results obtained from modeling of the Li-discharge products after 23 000 s.

parameters for the intermediate steps during LiPF6−carbonate salt decomposition,24 the 3D model simulations27,28 described here only provide a qualitative picture of spatial discharge profile and the transport limiting mechanism. One of the significant observations from modeling results is that while we certainly see a gradient in lithium distribution across the spatial dimension of the electrode, the overall changes in the porosity were only of the order of 3%. This may not be sufficient to limit the mass transfer effects due to pore clogging.9,29 To further substantiate our results, the individual 2D slices are then reconstructed into 3D tomographic structures (described in the Supporting Information) as shown in Figure 3E and F. These tomographic images contain information about the bulk lithium product distribution (within the resolution) that can be then extracted along any internal cross-sectional planes of the electrode to obtain the lithium distribution. An example of this is shown in Figure 3G and H. Further along these directions, an analysis was carried out to estimate the total integrated lithium volume expressed as %

lithium, along with the electrode thickness that shows the average variation of lithium concentration across the bulk thickness of the electrode. This can be obtained, in absolute terms, by using a reference lithium standard along the beam in parallel with the discharge air-cathodes. In the absence of a such a standard, here we calculated the Li content in the individual 2D image slices at various lithium signal or count thresholds (T) (T can vary between 0 and 1) and then integrated along the individual volume dimensions to estimate the total lithium volume (in %) across the total thickness of the electrode as shown by the line profiles for the air cathode structures 1 and 2, in Figure 4A and B. Strikingly, these results clearly show a double peak profile near the top and bottom region and a relatively flat profile in the central part, signifying a higher lithium product formation at the region of cathode that is close to the lithium metal/separator and also near the oxygen/air front. These are qualitatively in agreement with 3D modeling results (Figure 3D) that essentially capture the various transport limiting phenomena that could drive uneven product 8405



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Figure 5. Normalized two-dimensional reconstructed slices of lithium peroxide-coated carbon foams: (A) 45 pores per inch (PPI) foam, (B) 100 PPI carbon foam, (C) reconstructed 3D tomography image of 45 PPI Li2O2-coated carbon foam, (D) reconstructed 3D tomography image of 100 PPI Li2O2-coated carbon foam, (E) cross-sectional lithium distribution of 45 PPI reconstructed carbon foam, and (F) cross-sectional lithium distribution of 100 PPI reconstructed carbon foam. (G) Calculated line profile showing the relative Li volume percent in 45 PPI Li2O2-coated carbon foam. (H) Calculated line profile showing the relative Li volume percent in 100 PPI Li2O2-coated carbon foam. The line profiles are calculated at different thresholds (Li-signal in the voxel) for uncertainty quantification. 8406



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cathodes ideal for Li-air chemistry. Efforts are underway to improve the spatial resolution of the neutron imaging technique to few micrometers, further increasing the usefulness of this method to monitor lithium transport in electrodes at a more local level.30

distribution both at the Li front as well as the oxygen end. This is further validated by comparing the calculated lithium discharge product profile using an experimental condition similar to that shown in Figure 4C for lithium carbonate discharge product formation. Ignoring the experimental artifacts such as edge effects and various factors that can lead to broadening of the experimental line profiles, we notice a higher concentration of Li-product deposition at the edges confirming to the experimental trends. As was alluded to before, the discharge product profile is strongly driven by competition between the reaction rate (kinetics), diffusion, or mass transfer effects; these factors fundamentally determine the current density or rate that the air cathodes could sustain to provide a uniform spatial product distribution or a transport limited scenario in which case there is an uneven distribution of discharge product. The Supporting Information (Figure 4A−C) describes the results based on transport limiting conditions within the limits of our 3D model. Briefly, under limited oxygen or lithium diffusion, the product distribution profile falls steeply across the cathode thickness, leading to a gradient in discharge product concentration (Figure 4B). Further, by adjusting the diffusion coefficients (of Li and oxygen species) and the rate kinetic factor, one can also be able to sustain a uniform spatial distribution, which could practically translate to lower discharge currents. In the present case, the air-cathodes were discharged at 5 μA/cm2, which as per our previous report9 is a high enough current density to produce transport driven polarization, leading to buildup of discharge product at the electrode edges. To further ascertain that the observed anisotropy in the discharge air-cathodes is a result of the electrochemistry driven effects, we performed a control experiment in which lithium peroxide (Li2O2) was chemically deposited on the carbon foam having two pore sizes, 45 and 100 pores per inch (PPI). The neutron imaging and tomographic reconstruction results are briefly discussed here in context of Figure 5. The analyzed 2D reconstructed image slices showing the relative lithium concentrations for 45 and 100 PPI carbon foams are shown in Figure 5A and B, and the corresponding reconstructed 3D tomography images are shown in Figure 5C and D. The Lithreshold calculated line profile (Figure 5E and F) showed relatively uniform lithium concentration across the bulk thickness of the carbon foam for both 45 and 100 PPI Li2O2coated foam. This behavior is expected because, in this case, lithium peroxide was uniformly coated from the solution (dipped and dried under vacuum) and was not subjected to electrochemical cycling unlike the air cathodes.

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ASSOCIATED CONTENT

S Supporting Information *

Additional discussion and figures. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (J.N.); [email protected] (H.B.); [email protected] (S.P.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research is sponsored by the Laboratory Directed Research and Development Program of Oak Ridge National Laboratory, managed by UT-Battelle, LLC, for the U.S. Department of Energy. The user facility at the High Flux Isotope Reactor is sponsored by the U.S. Department of Energy Office of Science, Office of Basic Energy Sciences (BES). ORNL is managed by UT-Battelle, LLC, for the U.S. DOE under contract DE-AC05-00OR22725. We sincerely thank Drs. Keely Willis, Jack Wells, Thomas Proffen, Gene Ice, and Partha Mukherjee for scientific discussions and support.

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REFERENCES

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CONCLUSION This study reports the first experimental evidence of the spatial variation of discharge products across the bulk of the Li-air electrode using neutron tomography imaging, virtually allowing one to “see through” inside the bulk electrode. The results were analyzed in context of the 3D transport model that includes reaction kinetics and mass transport across the air cathode thickness. Neutron imaging finds a nonuniform lithium product distribution across the electrode thickness, the lithium species concentration being higher near the edges of the Li-air electrode and relatively uniform in the center of the electrode. The origin of such anomalous product distribution is related to the polarization factors due to the kinetic and diffusion barriers that could lead to a discharge product gradient. Our result provides key insights into the discharge mechanism in thick air cathodes at a 3D spatial scale that could lead to the design of air 8407



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(18) Ngala, J. K.; Alia, S.; Dobley, A.; Crisostomo, V. M. B.; Suib, S. L. Chem. Mater. 2007, 19, 229. (19) Debart, A.; Paterson, A. J.; Bao, J.; Bruce, P. G. Angew. Chem., Int. Ed. 2008, 47, 4521. (20) Ogasawara, T.; Debart, A.; Holzapfel, M.; Novak, P.; Bruce, P. G. J. Am. Chem. Soc. 2006, 128, 1390. (21) Zhang, D.; Fu, Z. H.; Wei, Z.; Huang, T.; Yu, A. S. J. Electrochem. Soc. 2010, 157, A362. (22) Read, J. J. Electrochem. Soc. 2002, 149, A1190. (23) Read, J.; Mutolo, K.; Ervin, M.; Behl, W.; Wolfenstine, J.; Driedger, A.; Foster, D. J. Electrochem. Soc. 2003, 150, A1351. (24) Freunberger, S. A.; Chen, Y.; Peng, Z.; Griffin, J. M.; Hardwick, L. J.; Bardé, F.; Novák, P.; Bruce, P. G. J. Am. Chem. Soc. 2011, 133, 8040. (25) Neutron Data Booklet, Institute Laue-Langevin, 2nd ed.; Dianoux, A.-J., Ed.; OCP Science, 2003. (26) Read, J.; Mutolo, K.; Ervin, M.; Behl, W.; Wolfenstine, J.; Driedger, A.; Foster, D. J. Electrochem. Soc. 2003, 150, A1351. (27) Mukherjee, P. P.; Pannala, S.; Turner, J. A. Modeling and Simulation of Battery Systems. In Handbook of Battery Materials, 2nd ed.; Daniel, C., Besenhard, J. O., Eds.; Wiley-VCH Verlag GmbH & Co. KGaA: Weinheim, 2011; p 843. (28) Computational Gas-Solid Flows and Reacting Systems: Theory, Methods and Practice; Pannala, S., O’Brien, T., Eds.; IGI Global: Hershey, PA, 2010. (29) Zhang, S. S.; Foster, D.; Read, J. J. Power Sources 2010, 195, 1235. (30) Nanda, J.; Remillard, J.; O’Neill, A.; Bernardi, D.; Ro, T.; Nietering, K. E.; Go, J.-Y.; Miller, T. J. Adv. Funct. Mater. 2011, 21, 3282.

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Anomalous Discharge Product Distribution in Lithium-Air Cathodes

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