Energy Density Limitation of Lithium-Sulfur Battery By Lithium Polysulfide Solubility in Electrolyte
Authors: Zheng Jim P. , Shen Chao , Xie Jianxin , Zhang Mei , Andrei Petru , Hendrickson Mary A. , Plichta Edward J. 
Published: February 2020

Li-S batteries are among the most promising candidates for the next generation rechargeable batteries due to their high energy density, low raw material cost and environmental friendliness [1]. Despite this great potential, the complicated electrochemical process introduces many challenges for Li-S batteries, including low conductivity of both elemental sulfur and end discharge product Li2S, large volume expansion of 80% upon discharge, and unfavorable redox shuttle effect due to soluble nature of intermediate lithium polysulfide LiPS [2,3].
Although Li-S batteries possess a high theoretical cathode specific capacity of 1,672 mAh g-1, the energy density of practical Li-S batteries is much smaller and depends on electrolyte/sulfur (E/S in mL g-1) ratio. From previous works, successful operation of Li-S batteries under lean electrolyte conditions can be challenging, especially in the case when the solubility of LiPS sets an upper bound for polysulfide dissolution. Very recently, we have demonstrated that the E/S ratio of Li-S cells has a significant effect on both performance and theoretical energy density of Li-S batteries. Since the lower-bound for E/S ratio is restricted by the solubility of LiPS in the organic electrolyte, the theoretical energy density of Li-S batteries is significantly reduced. Experimentally, it was approved that when the LiPS concentration reached to the solubility limitation in the electrolyte, the reaction rate of reducing sulfur to LiPS in the cathode will reduce significantly [4].
In this talk, we will discuss the relationship between theoretical specific energy and the solubility of LiPS in the electrolyte. The theoretical specific energy of a Li-S battery can be expressed as:
e=CLVcell/(MC+MA+Mele) (1)
where, CL is the lower capacity in amount of cathode and anode, Vcell is the cell voltage (e.g. 2.1 V), MC, MA, Mele are weights of sulfur (cathode), lithium (anode), and electrolyte, respectively. In an ideal case, capacities of cathode and anode are equal and to be MA=2×6.94MC/32.065, the atomic weights of lithium and sulfur are 6.94 and 32.065 g/mol, respectively, the capacity is CL=cSMC where cS=1,672 mAh/g is the theoretical specific capacity of sulfur. The minimum weight ratio of electrolyte to sulfur is:
Mele/MC=rele/32.065S (2)
where, rele is the mass density of electrolyte (e.g. 1.2 g/cm3) and S is the solubility of LiPS in unit of M[S]/L; therefore, the theoretical specific energy for a Li-S battery is:
e=3511/(1.4327+37.42/S[M/L])[Wh/kg] (3)
Fig. 1 shows the theoretical specific energy of Li-S batteries when the LiPS solubility is considered as an intrinsic limitation for Li-S battery capacity. Here only the weight of active electrode material, such as sulfur and lithium, as well as electrolyte weight is included in calculation. From Fig. 1, it can be seen that for commonly used electrolytes with LiPS solubility less than 8 M[S]/L, the theoretical energy is less than 575 Wh/g. Fig. 2 further presents a series of specific energy calculation for Li-S battery with different E/S ratios. From Fig. 2(a), it can be seen that the electrolyte weight would dominate in a Li-S battery even in relatively low E/S conditions. Fig. 2(b) plots the effective theoretical specific capacity of a Li-S battery. Fig. 2(c) that the reduced effective specific capacity introduced by LiPS solubility limit would offset electrolyte weight loss under low E/S conditions, making the theoretical specific energy curve relatively flat under low E/S region, while without considering LiPS solubility the specific energy will increase sharply when E/S ratio is decreased. The above results imply that reducing E/S ratio would become pointless when LiPS solubility is reached. For further boosting capacity of Li-S batteries, electrolyte with even higher LiPS solubility is favorable. Fig. 2(d) plots the specific energy of an ideal Li-S cell under different LiPS solubility.
Reference:
[1] A. Manthiram, Y. Fu, S. Chung, C. Zu, Y. Su, Rechargeable Lithium–Sulfur Batteries, Chem. Rev. 114 (2014) 11751–11787.
[2] Z.W. Seh, Y. Sun, Q. Zhang, Y. Cui, Designing high-energy lithium–sulfur batteries, Chem. Soc. Rev. (2016).
[3] W. Kang, N. Deng, J. Ju, Q. Li, D. Wu, X. Ma, et al., A review of recent developments in rechargeable lithium-sulfur batteries, Nanoscale. 1 (2016) 16541–16588.
[4] C. Shen, J. Xie, M. Zhang, J.P. Zheng, M. Hendrickson, and E.J. Plichta, J. Electrochem. Soc., 164 (2017) A1220-A1222.

Figure 1