Energy of Lithium Batteries and Their

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On the Theoretical Capacity of Lithium Batteries and Their Counterparts Ali Eftekhari ACS Sustainable Chem. Eng., Just Accepted Manuscript • DOI: 10.1021/ acssuschemeng.7b04330 • Publication Date (Web): 19 Mar 2018 Downloaded from http://pubs.acs.org on March 20, 2018

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ACS Sustainable Chemistry & Engineering

On the Theoretical Capacity/Energy of Lithium Batteries and Their Counterparts

Ali Eftekhari Belfast Academy, 2 Queens Road, Belfast BT3 9FG, United Kingdom

Abstract Since the commercial success of lithium-ion batteries (LIBs) and their emerging markets, the quest for alternatives has been an active area of battery research. Theoretical capacity, which is directly translated into specific capacity and energy capacity, defines the potentials of a new alternative. However, the theoretical capacities relied upon in both research literature and industrial/commercial reports are somewhat superficial values. This tiny mistake has overshadowed the potentials of some battery systems while pictured illusive targets for others. Although the battery researchers know the basis of these theoretical values, misinterpretations have caused a severe misunderstanding in the market research and public reports. Therefore, it is of vital importance to highlight the appropriate theoretical capacities, which can make sense in the commercial batteries. The present comparisons clarify that there are serious misconceptions about the advantages and disadvantages of various electrode materials and batteries. From a theoretical perspective (regardless of the performance of available materials), the capacity advantage of Li−S and Li−O2 over LIBs is not as huge as what currently has been pictured. Replacing LIB with a counterpart sodium-ion battery (NIB) is accompanied by only 20% sacrifice in the overall capacity. And NIB has no considerable advantage over potassium-ion battery (KIB) in terms of specific energy. Keywords: Lithium-ion batteries; Sodium-ion batteries; Li−S battery; Energy density; Specific energy Email: [email protected]

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Lithium Anode

It is often mentioned that the theoretical capacity of a metallic Li anode is 3,842 mAh g–1, but this value is that of lithium rather than a Li anode because we cannot consume all the anode. In fact, one gram of the Li charge carrier can provide 3,842 mAh of electricity. The anode releases the charge carrier during the discharge process, but the anode cannot be fully transformed into the charge carrier. One may argue that this is a known fact, but in the fast pace of battery development, it is often interpreted as the target. As will be discussed later, this inappropriate reasoning has caused more severe problems in the battery industry.

Table 1 compares the theoretical capacities of different battery systems with respect to the weight of various components in a 18650 battery, which is currently among the most common types of lithium-ion batteries (LIBs). One may argue that the scientific community is aware of these considerations by common sense, but to the best of knowledge, no paper has ever mentioned that the target energy density of a sodium-ion battery (NIB) or a potassiumion battery (KIB) is only 20% lower than that of LIB or NIB has no considerable advantage over KIB in terms of the specific energy. Instead, most of the research papers promoting NIB somehow highlight that the theoretical capacity of NIB is half of LIB. On the other hand, the opening sentence of most papers considering Li−S and Li−O2 batteries emphasises the unrealistic specific capacities of Li anode as the potential target. In fact, the data shown in Table 1 are known by common sense but never taken into consideration in planning the research strategy.

Calculating the Data

Table 1 is indeed a set of data for the sake of comparison between various system rather than being considered as reference theoretical specific energies. The cell specifications were taken from a commercial 18650 LIB by Sony in which the thickness of the graphite anode is 0.165 mm, the LiCoO2 cathode 0.159 mm, the separator 0.010 mm, the anode Cu current collector 0.013 mm, and the cathode Al current collector 0.019 mm.1 Although the cell technology is advancing, these thicknesses can be fairly considered as the optimum design in this cell architecture. The volumetric ratios of the components can be simply calculated from the given thicknesses. However, for calculating the specific capacity/energy, we need the total volume of each component. For the sake of simplicity, we assume that the layers are in cylindrical shape rather than spiral (the difference is negligible). Then, the full length of the sheet can be calculated by (1)

where L is

the length, h the sheet thickness (sum of all layers), R the cell inner radius (i.e., about 8 mm for 18650 cell which has an outer diameter of 18mm), r the radius of the inner rod (i.e., about 1 mm). Therefore, the sheet length is about 526 mm. Considering that the width of the sheet within a 18650 cell is about 60 mm, the total area of the sheet is about 316 cm2. Hence, the total volume of Cu current collector is 0.41 cm2. Considering the density of 8.96 g cm–3 for copper, the total weight of the Cu current collector in the cell is 3.67 g. Similarly, the total weight of the Al current collector is 1.11 g, and that of the separator 0.63 g (assuming that the separator is fully soaked in the electrolyte). Since the anode and cathode are the active materials in each cell, the overall volume and weight are of interest, which are 10.24 cm3 and Page 2 of 10


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20.48 g, respectively. The density of LiCoO2 is 4.98 g cm–3 and that of graphite is 2.27 g cm–3, but it is a fair approximation to consider the overall density of 2 g cm–3 for the anode and cathode materials owing to their porosity. Note that the purpose is just a comparison between different batteries. Since it is unlikely to make a major improvement in the cell architecture, these values can be considered as maximum theoretical capacities of 1865 cells by reducing the weight of other components including the electrolyte. Moreover, the weight of the current collectors is not too much to make major improvement.

The theoretical capacity of LiCoO2 is usually calculated 278 mAh g–1 and its reversible capacity 139 mAh g–1, because half of the Li ions are extractable and the extraction of the other half results in the structural breakdown. Note that the difference highlighted between LiCoO2 and LiNi1/3Mn1/3Co1/3O2 is not the actual difference between these two cathode materials, but the symbolic difference between full and half Li extraction from this class of layered metal oxides. In the table, the theoretical capacity is calculated based on the content of extractable lithium. As an analogue, the cathode material could be synthesised in the form of Li0.5Na0.5O2.

Alkali Metal Charge Carriers

Owing to the natural scarcity of lithium and the abundance of two neighbouring elements, NIB and KIB, are among the most promising candidates for the new generation of rechargeable batteries. However, their theoretical capacities are considered much lower than that of lithium. With the same way of calculation, the theoretical capacity of a Na anode is 1166 mAh g–1 and that of a K anode is 685 mAh g–1. However, the metallic anode has never been a commercial option for LIBs (except a few cases in the early years); then, why comparing the potentials of NIBs and KIBs with an imaginary rival. Instead, graphite was the common anode for hosting the Li charge carrier during charging. The theoretical capacities for LiC6, NaC6, and KC6 are 339, 282, 241 mAh g–1, respectively. In fact, the superiority of lithium is less significant in an appropriate theoretical comparison (Table 1). This superiority further diminishes when calculating the specific energy of the whole cell in which the weight of common components such as electrolyte, current collector, etc. should be considered. Note that the purpose is a theoretical comparison of the alkali metals, as potassium tends to form KC8 and sodium has thermodynamical unfavourability for intercalation into graphite.2 It should be noted that metallic anode has been recently reconsidered3 but still far from a practical development to be used as the basis of comparison between alkali metals.

Conversion Electrodes

Since the theoretical capacity of graphite anode has already been achieved, the current focus is on new options to increase the anode capacity. Conversion-based electrode materials obviously provide a higher capacity as compared with the intercalation materials such as graphite. Several new anode materials have been reported to have an experimental capacity of over 4,000 mAh g–1 .4 This causes confusion as this value is higher than the theoretical capacity of metallic Li anode (which itself is unattainable as discussed above). Some authors highlight that the theoretical capacity of Si anode is 10 times higher than graphite4-5 and 24 times higher than Li4Ti5O126, and "it has Page 3 of 10



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the highest specific capacity (4,200 mAh g–1) than any other anodes studied to date".7 These statements give an impression that Si anode even outperforms the metallic Li anode and can revolutionise the battery industry. The point is that these capacities are calculated with respect to the base material rather than the whole anode when the cell is charged (lithiated anode). Note that it is not a matter of preference; if calculating the theoretical capacity of a metallic Li anode with this approach, the capacity tends to infinity. The theoretical capacity of Li4.4Si is 2,011 mAh g–1, and this is the value, which can be appropriately compared with the theoretical capacity of lithium. The superficial value of ca. 4,200 mAh g–1 seems higher than that of a metallic Li anode, and thus, can revolutionise the future of LIBs. Despite the fact that it is almost impossible to achieve this capacity due to the inevitable volume changes, Table 1 shows that the specific energy of a LIB employing a Si anode is high but not revolutionary.

Since conversion materials such as sulphur cathode are entrapped within a conducting matrix such as carbon, the theoretical capacity of the S/C cathode is no longer that of the pure S cathode.8 The reversible capacity with respect to the mass of sulphur is of fundamental interest to understand the degree of the conversion reaction. However, this value might be misleading when judging about the practical potential of the electrode under consideration. Many papers do not even mention if the capacity has been calculated for the mass of S or the whole electrode. As depicted in Table 1, the practical potential of Li−Se batteries, which has a considerable advantage due to its significantly higher electrical conductivity of Se, is not less than the Li−S counterpart.9

Lithiated vs Deliathiated

The problem of theoretical capacity in the lithiated or delithiated form is not limited to the conversion anodes only. Li2S is an alternative cathode for Li−S batteries8 whose theoretical capacity is reported to be 1167 mAh g–1 as compared with the theoretical capacity of 1672 mAh g–1 for a pure S cathode. Almost all papers on Li2S cathodes mention the specific capacity as a disadvantage, but it is not at all. In the whole cell, the capacity contribution of Li2S and S cathodes are the same. The total amount of the charge carrier in the anode and cathode is the same regardless of the initial cell assembly. If using an S cathode, the anode should be LiC6; and for the Li2S cathode, the anode is C. In other words, whether assembling the cell with the structure of C|Li2S or LiC6|S, the overall specific capacity of the cell is the same (Table 1). The key point is that S cathode has no capacity advantage over the Li2S cathode, but the theoretical capacities reported in the literature are interpreted as a capacity disadvantage of Li2S.

Similar to the case of Si anode discussed above, it is always more appropriate (and safer) to report the capacity of an electrode material (both anode and cathode) with respect to its lithiated form for the Li extraction. The capacity of all electrode materials can be calculated in their lithiated form, but that of a metallic Li anode cannot be calculated in its delithiated form. This problem is significant for high capacity materials such as Si anode and S cathode, which are usually new candidates, where the capacities in the lithiated and delithiated forms are noticeably different; otherwise, there is only 2% error if calculating the capacity of LiCoO2 in its lithiated or delithiated form.

Full Cell Capacity Page 4 of 10


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The battery market is expanding quickly, faster than its research, as the market demand is ahead of the technological advancement. All the theoretical capacities considered for the individual electrodes (anode or cathode) are just the basis for estimation of the full cell capacity. However, the problem of targeting the potential battery systems based on the aforementioned superficial theoretical capacities is much more severe. Mentioning these theoretical capacities in the research literature is in a highlighting fashion, but the policymaking and market research reports consider these superficial theoretical capacities are the practical targets.

For instance, the Deutsche Bank markets research report on lithium10 has been the basis for numerous other official reports and policymaking documents. In this report, NIB, which is considered as the closest possible alternative to LIB by the scientific community, has not been mentioned as a potential candidate (probably due to the capacity disadvantage highlighted above). Instead, Li−S and Li-air batteries have been considered as the emerging revolutions. This is obviously an inappropriate comparison building a superficial target to increase the specific capacity of the lithium batteries by 10 and 20 folds. Although a commercial prototype of NIB as an alternative to the 18650 batteries of Tesla Motors has been fabricated (Table 1), the market is waiting for the revolution promised by the superficial theoretical capacities.

The report claims that the theoretical specific capacity of Li−S battery is 1,675 Wh kg–110 (as presented in the last row of Table 1). If assembling a Li−S battery with the anode and cathode of LiC6/S, the cell theoretical specific energy is 460 mAh g–1 (Table 1). The former value can be obtained if assuming that the cell is composed of a Li2S cathode only, which is obviously a superficial assumption. One may argue that this is just the theoretical value, but note that these theoretical values are compared with the current LIBs to picture possible alternatives. On the other hand, all these calculations are based on the assumption of a metallic Li anode. Despite the fact that the problem of the theoretical capacity of a metallic Li anode as discussed above, a metallic anode is not a practical choice. If developing the cell technology to include a metallic Li anode, the specific energy of the available LIBs can be doubled (Table 1); then, what is the point of dealing with the difficulties of the S cathodes? This does not mean that Li−S battery does not have commercial potentials, but it is not a revolutionary alternative. Instead, it will have its own advantages and applications in the future. It should be taken into account that the theoretical capacity reported in the last row of Table 1 is superficial because we cannot use pure Li anode and S cathode.

Similarly, the theoretical capacity of a Li-air battery is not 3,842 mAh g–1, as stated in the corresponding report10, which is indeed the theoretical capacity of Li only as discussed above. The theoretical capacity of a Li-air is higher than its counterparts because oxygen is not stored in the cathode, but it does not mean that a Li-air battery does not have a cathode. The electrocatalytic cathode is relatively heavy because of metallic electrocatalysts, which should be provided over a large surface area.11 This also reduces the energy density (per unit of volume). On the other hand, the cell technology of Li-air is significantly different from the architecture of the present batteries, and thus, it is a long way for the commercial development of Li-air batteries. The problem here is that the theoretical capacity of lithium for carrying the charge is directly translated into commercial/market research reports, as the theoretical capacity (i.e., ideal target capacity) of a battery system. Not only this creates false hope and inappropriate planning but also causes a public mistrust that the battery technology is far behind the scientific possibilities. Page 5 of 10



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Note that this is not a lame mistake by non-technical people. As emphasised above, these numbers are frequently mentioned in the research literature without considering their scientific significance. In a different context, Gogotsi and Simon pointed out that calculating the specific energy of supercapacitors without considering the weight of the current collectors is misleading, and wrongfully has made an impression that the specific energy of supercapacitors can compete with that of LIBs.12 The fancy values are always a result of neglecting the weight of other components in a battery. The cell technology has been dramatically advanced during the last years due to the growing market, and the cell design has already minimised the weight of other components. However, their weight is still high in comparison with high-energy materials.

Concluding Remarks

The discussion made here may seem simple but the impact of the corresponding misleading is enormous. Theoretical capacity and specific energy are not just fancy values, but the targets for improving an energy storage system. Therefore, they should be realistic and meaningful. Battery research is now one of the most active areas of research owing to a rapidly growing market. Battery advancements during the forthcoming years may substantially change our everyday life and address global issues such as the climate change. Hence, the requirement for a practical perspective even in the fundamental studies is vital at this particular time. Reporting unrealistic values, though theoretical in a sense, is not useful and may cause serious misleading, as it has happened already. Theoretical capacity (or specific energy) is the target for the practical development of future batteries. It does not lead us very far to repeat unattainable theoretical values for advertising a specific battery system.

The cost of LIBs has been dramatically dropped during the past years due to the economy of scale and the cell technology advancement rather than materials discovery, as the LIB architecture is somewhat similar to the first commercial products. However, the cell design has reached its limitations to further reduce the cost or improve the specific energy. Now, the materials chemistry plays a more crucial role in the next generation of LIBs or their counterparts. In this direction, we should plan a roadmap with realistic targets. The purpose of this paper is to emphasise that the comparisons should be made with the appropriate conditions. It is pointless to compare a full cell LIB with the cathode of its counterparts, or a graphite-based LIB with a battery employing a metallic Li anode. Furthermore, comparisons of the base materials only can show promising differences, but if considering the cell architecture, these attractive differences are no longer huge.

The battery research today is all about comparisons between the performances of different materials to choose the best materials to maximise the battery performance. Thus, it is of vital importance to have commonly accepted standards to report both theoretical and experimental data in comparative forms. It should be taken into account that thanks to the rapid growth of the demand and market, the battery literature is now read by a broad range of audience, the outlets for possible misinterpretations should be specifically avoided.

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References

[1] Xu, J.; Liu, B.; Wang, X.; Hu, D. Computational Model Of 18650 Lithium-Ion Battery With Coupled Strain Rate And SOC Dependencies. Appl. Energy, 2016, 172, 180–189. DOI 10.1016/j.apenergy.2016.03.108 [2] Wang, Z.; Selbach, S. M.; Grande, T. Van Der Waals Density Functional Study Of The Energetics Of Alkali Metal Intercalation In Graphite. RSC Adv., 2014, 4, 4069–4079. DOI 10.1039/C3RA47187J [3] Lin, D.; Liu, Y.; Cui, Y. Reviving The Lithium Metal Anode For High-Energy Batteries. Nat. Nanotech., 2017, 12, 194–206. DOI 10.1038/nnano.2017.16 [4] Wu, H.; Cui, Y. Designing Nanostructured Si Anodes For High Energy Lithium Ion Batteries. Nano Today, 2012, 7, 414–429. DOI 10.1016/j.nantod.2012.08.004 [5] Hwang, T. H.; Lee, Y. M.; Kong, B.; Seo, J.; Choi, J. W. Electrospun Core–Shell Fibers For Robust Silicon Nanoparticle-Based Lithium Ion Battery Anodes. Nano Lett., 2012, 12, 802–807. DOI 10.1021/nl203817r [6] Sun, Y.; Lopez, J.; Lee, H.; Liu, N.; Zheng, G.; Wu, C.; Sun, J.; Liu, W.; Chung, J. W.; Bao, Z.; Cui, Y. A Stretchable Graphitic Carbon/Si Anode Enabled By Conformal Coating Of A SelfHealing Elastic Polymer. Adv. Mater., 2016, 28, 2455–2461. DOI 10.1002/adma.201504723 [7] Chen, L. B.; Xie, J. Y.; Yu, H. C.; Wang, T. H. An Amorphous Si Thin Film Anode With High Capacity And Long Cycling Life For Lithium Ion Batteries. J. Appl. Electrochem., 2009, 39, 1157–1162. DOI 10.1007/s10800-008-9774-1 [8] Eftekhari, A.; Kim, D. Cathode Materials For Lithium–Sulfur Batteries: A Practical Perspective. J. Mater. Chem. A, 2017, 5, 17734–17776. DOI 10.1039/C7TA00799J [9] Eftekhari, A. The Rise Of Lithium–Selenium Batteries. Sustainable Energy Fuels, 2017, 1, 14–29. DOI 10.1039/C6SE00094K [10] Deusche Bank Markets Research, Lithium 101, 9 May, 2016. [11] Eftekhari, A.; Ramanujam, B. In Pursuit Of Catalytic Cathodes For Lithium–Oxygen Batteries. J. Mater. Chem. A, 2017, 5, 7710–7731. DOI 10.1039/C7TA01124E [12] Gogotsi, Y.; Simon, P. True Performance Metrics In Electrochemical Energy Storage. Science, 2011, 334, 917–918. DOI 10.1126/science.1213003

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Table 1. Estimations of the theoretical capacities for various battery systems. The battery architecture is assumed the commercial 18650 cell. The specific capacity is calculated by considering the weight of anode+cathode+separator only. It is assumed that the electrodes are dense as the electrolyte is injected in the separator only and not the electrodes. For the sake of simplicity, the weight of all other components including the binders/additives, excess electrolyte, the external stainless steel cylinder, and lead connections is considered to be equal to the weight of the current collectors. This is an underestimate since the current collectors are fairly thin in a 18650 cell, but appropriate for estimating the theoretical targets.

Battery AN / mAh g–1

LIB

LIB

LIB

LIB

LIB

NIB

KIB

Li−S

CA / mAh g–1

AN+CA / mAh g–1

LiC6

LiNi1/3Co1/3Mn1/3 LiC6|Ni1/3Co1/3Mn1/3O O2 2

339

278

Li

LiNi1/3Co1/3Mn1/3 Li|Ni1/3Co1/3Mn1/3O2 O2

3861

278

278

Li4.4Si

LiCoO2

Li4.4Si|8.8Li0.5CoO2

2011

139

133

Li

LiCoO2

Li|2Li0.5CoO2

3861

139

137

LiC6

LiCoO2

LiC6|2Li0.5CoO2

339

139

100

NaC6

NaCoO2

NaC6|2Na0.5CoO2

282

118

89

KC6

KCoO2

KC6|2K0.5CoO2

241

103

81

LiC6

Li2S

LiC6|0.5S

339

1167

282

Li2Se

LiC6|0.5Se

577

226

Li−Se LiC6 339

159

Specific Commercial 18650 / AN+CA+CCs+Se Voltag Energy / Wh –1 e / V p / mAh g Wh kg–1 –1 kg

Tesla/Panasonic

117

3.6

421

205

3.7

756

98

3.3

323

101

3.8

384

272

Sony

74

3.7

279

185 CNRS

66

3.5

231

59

3.7

218

208

2

416

166

2

332

90

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Battery AN / mAh g–1

Li−S

CA / mAh g–1

AN+CA / mAh g–1

Li

Li2S

Li|0.5S

3861

1167

1167

Specific Commercial 18650 / AN+CA+CCs+Se Voltag Energy / Wh –1 e / V p / mAh g Wh kg–1 –1 kg

858

2.1

1802

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Graphical Abstract This paper provides a realistic perspective on the theoretical values of specific capacity and energy of various batteries.

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Energy of Lithium Batteries and Their

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