Mesoscale Elucidation of Self-Discharge-Induced Performance Decay

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Mesoscale Elucidation of Self-Discharge Induced Performance Decay in Lithium-Sulfur Batteries Feng Hao, Zhixiao Liu, Perla B. Balbuena, and Partha P. Mukherjee ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.9b02282 • Publication Date (Web): 20 Mar 2019 Downloaded from http://pubs.acs.org on March 20, 2019

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ACS Applied Materials & Interfaces

Mesoscale Elucidation of Self-Discharge Induced Performance Decay in LithiumSulfur Batteries

Feng Hao,1 Zhixiao Liu,2 Perla B. Balbuena,3 and Partha P. Mukherjee1,* 1School

of Mechanical Engineering, Purdue University, West Lafayette, Indiana 47907, USA

2College 3Department

of Materials Science and Engineering, Hunan University, Changsa 410082, China

of Chemical Engineering, Texas A&M University, College Station, Texas 77843, USA

*Correspondence:

[email protected]

Keywords: lithium-sulfur battery; self-discharge; sulfur solubility; reaction rate; interlayer

1

ACS Paragon Plus Environment

ACS Applied Materials & Interfaces 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract Polysulfide shuttle phenomenon substantially deteriorates the electrochemical performance of lithium-sulfur (Li-S) batteries, resulting in continued self-discharge and capacity fade during cycling. In this study, a mesoscale analysis is presented to explore the mechanisms of selfdischarge behavior in the Li-S battery during rest state. It is found that self-discharge rate is determined by the sulfur solubility, desorption capability, diffusion kinetics, and reaction rate on the anode surface. Three regimes have been identified: desorption control, diffusion control, and charge transfer control. Correspondingly, strategies are suggested to increase the capacity retention, such as enhancing the binding of sulfur molecules to the host, reducing dissolved sulfur diffusivity, and improving the chemical stability of active materials with Li metal anode. Furthermore, the use of interlayer with high diffusion barriers can effectively suppress the selfdischarge rate due to the confinement effect.

TOC

2


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1. Introduction Rechargeable batteries have attracted tremendous interest due to the emerging demand for electrical energy storage.1-3 However, the state-of-the-art Li-ion batteries are approaching their theoretical limits.4 Lithium-sulfur battery is one of the most promising high-energy-density rechargeable battery chemistries.5-11 Paired with Li anode, sulfur offers a high theoretical capacity of 1672 mAh g-1 through phase-transformation chemistry.12 Currently, the commercialization of Li-S batteries has critical obstacles, primarily originating from the high intrinsic resistance of sulfur cathode, large volumetric changes, and parasitic reactions between polysulfides and the metallic Li anode. To circumvent the drawbacks, various approaches are proposed. For instance, nanoporous carbon network can enhance the charge transport, buffer the volume strain, and increase sulfur loading.13-14 Novel cell configurations with trapping interlayers or modulated separators can suppress the migration of polysulfides to Li anode and thus improve capacity retention.15-18 Intermediate lithium polysulfides dissolve into organic electrolyte during the conversion reactions, which improves the reaction kinetics and cell capacity. On the other side, the high solubility of polysulfides in the ether-based electrolyte leads to the diffusion of active materials between two electrodes, which is named as “shuttle effect” .19 Parasitic reactions of polysulfides with Li anode could result in problematic issues, such as low cycling efficiency, poor safety, and high self-discharge rate.20 During cycling, the reactions continuously consume active sulfur species and corrode Li anode, leading to a blocking surface of insoluble Li2S/Li2S2 and increased charge transfer resistance.21-22 To suppress the shuttle effect, a stable protective layer on Li anode is needed, which could be directly created by using coating layers23 and indirectly 3



produced through electrolyte additives, such as LiNO3, Li2S6, and P2S524-25. Nonetheless, the shuttle effect could not be completely eliminated.22 Parasitic reactions could also occur during cell resting, leading to self-discharge and capacity fading. Ryu et al. reported the self-discharge in lithium-sulfur battery and found the open-circuit voltage decreased from 2.48 to 2.16 V after 30 days of storage.26 Mikhaylik and Akridge reported a capacity loss of 43% after 24 h storage.27 Chung and Manthiram observed that a typical self-discharge caused a loss of 65% of the charge-storage capacity in the initial 15-day rest period.28 As the resting time increases, three features can be captured for the discharge profile: the upper discharge plateau begins to disappear, the open-circuit voltage gradually decreases, and the discharge capacity significantly decreases. All these features indicate that the active materials from the cathode, including bulk sulfur, continue to dissolve into the electrolyte and react with the anode.29 However, the self-discharge rates were quite different during resting in the previous experiments.26-31 In this regard, we aim to explore the underlying mechanism that dominates the self-discharge rate during resting. A previous study examined the effects of cell operating conditions on self-discharge, including the depth of discharge, temperature, and idling time.31 Herein, our focus is on the factors related to material properties. Specifically, the following effects are considered: sulfur desorption rate from the cathode, sulfur solubility, diffusion kinetics in the electrolyte, chemical reaction rate on the anode surface, and the interlayer with high diffusion barriers. Using a mesoscale model, the roles of these factors and their competition in self-discharge behavior are assessed, and the results are qualitatively compared with previous experiments. This work offers a fundamental understanding of the self-discharge 4


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in lithium-sulfur battery and suggests promising strategies towards reducing the capacity loss during resting. 2. Model and Method In the cathode film, bulk sulfur is adsorbed on the carbon backbone. Fig. 1 illustrates the self-discharge behavior. During cell resting, sulfur molecules are desorbed from the carbon host. Because of the concentration gradient across the system, the dissolved S8 molecules diffuse out of the cathode through the electrolyte. In the vicinity of Li anode, S8 is reduced on the anode surface. To simplify the model, certain assumptions are made below. In addition to the dissolution of elemental sulfur into the electrolyte, two chemical reactions are considered on the anode surface. S8(𝑠)→S8(𝑙),

(1)

S8(𝑙) +4Li→2Li2S4,

(2)

Li2S4 +6Li→4Li2S.

(3)

Eq. 2 represents one cyclo-S8 molecule is reduced to two lithium tetrasulfide Li2S4, which is responsible for the disappearance of the upper discharge plateau.29 In Eq. 3, Li2S4 is reduced to insoluble lithium sulfide Li2S, which is directly deposited on the anode surface. In fact, there are more types of polysulfides involved. In this simplified model, soluble polysulfides are represented by Li2S4, and insoluble polysulfides are represented by Li2S. The self-discharge originates from the chemical reactions on the anode surface, and the capacity fade caused by the reactions between polysulfides and current collectors (or cathode) is not taken into account. In Li-S batteries, the principal chemical reactions considered on the anode surface are Eqs. (2) and (3). The reaction rate is governed by the chemical stability between active sulfur species 5



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and the anode. For a single lattice site at the Li anode-electrolyte interface, the local reaction rate is given as 𝑘𝐽 = {0, 𝑘1, 𝑘2},

(4)

Three scenarios exist for a single lattice site at the reaction front. If no S8 molecule or Li2S4 is at the site, the local rate is zero. If a S8 molecule resides at the site, the local rate is set to the second term k1 on the right-hand side in Eq. 4. If Li2S4 presents at the site, the local rate is set to k2. The chemical reaction rates are expressed as32

(

𝑘 = 𝑘0𝑒𝑥𝑝 ―

𝐸𝑎𝑐𝑡 𝑅𝑇

)𝑒𝑥𝑝 (𝛼

),

𝑧𝐹 𝑅𝑇𝛥𝜙

(5)

where k0 is the preexponential factor, Eact is the thermal activation energy, R is the gas constant, T is the operating temperature, α is the symmetry factor, z is the number of electrons involved in the reaction, F is the Faraday constant, and 𝛥𝜙 is the potential difference at the reaction front. During cell resting, these parameters are assumed to be constants. Hence, k1 and k2 are constant in the model. In the electrolyte, the diffusion of cyclo-S8 and Li2S4 is driven by the difference of concentrations in adjacent regions. The diffusion rates are assumed to obey the Arrhenius formulation33 𝑘𝑑 = 𝜈𝑒𝑥𝑝

(

― 𝐸𝑎 𝑅𝑇

)

𝑁𝑎 ,

(6)

where ν is the frequency, Na is the Avogadro constant, and Ea is the activation energy that needs to be overcome for the transport of S8 and Li2S4 through electrolyte. The kinetic Monte Carlo algorithm is used to perform the self-discharge behavior.34-39 During the self-discharge, S8 molecules and Li2S4 diffuse from one lattice site to an adjacent site, and Li2S is deposited at the lattice sites on the anode surface. In the model, the lattice 6


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constant is assumed to be 6.0 Å based on two facts: the dimensions of sulfur allotropes are around 6.0 Å,40 and the measured lattice constant of crystalline Li2S (four S atoms and eight Li atoms in the unit cell) is 5.722 at temperature 295 K.41 For the two-dimensional model, the Li-S system has a length of 60 nm and a height of 60 nm, composed of a 100×100 grid of 10000 lattice sites. The interlayer has a size of 60 nm (length) by 3 nm (thickness). In the horizontal direction, the periodic boundary condition is applied. Table 1 lists all the parameters used in the kinetic model. In the electrolyte domain, the reference solubility of S8 is assumed to be 19 mol m-3,42 which is equivalent to 0.25% lattice sites in the electrolyte that are occupied by dissolved S8 molecules, and the solubility of Li2S4 is assumed to be 100 mol m-3.43-44 To compensate the dissolved S8 consumption at the Li anodeelectrolyte interface, new S8 molecules are therefore desorbed from the carbon backbone. The calculation runs until the capacity loss reaches 10%, equivalent to the complete reduction of 96 cyclo-S8 molecules. For the precipitation of Li2S, the reference reaction rate k20 in Eq. 3 is assumed to be 10% of the reference rate k10 in Eq. 2, as shown in Table 1. For the diffusion of S8 and Li2S4 in electrolyte, the reference activation energies are assumed to 31 kJ/mol and 33 kJ/mol, respectively. Table 1. Parameters used in the kinetic model. Parameters

Values

Units

k10

Reaction rate in Eq. 2

2320

s-1

k20

Reaction rate in Eq. 3

232

s-1

χ10

S8 solubility

19

mol m-3

χ20

Li2S4 solubility

100

mol m-3

7



Ea

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Activation energy (S8)

31

kJ/mol

(Li2S4)

33

kJ/mol

ka

Desorption rate (S8)

100

s-1

a

Lattice constant

6.0

Å

R

Gas constant

8.314

J mol-1 K-1

F

Faraday constant

96,487

C mol-1

Na

Avogadro constant

6.022×1023

mol-1

T

Operating temperature

300

K

ν

Frequency

2×1012

s-1

3. Results and discussion To begin with, a representative simulation is carried out by using the parameters in Table 1. Fig. 2(a) illustrates the system configuration at the capacity loss of 10%. Initially, all the sulfur molecules (blue) are adsorbed on the carbon backbone (brown). During the resting time, the desorption of sulfur continues until the electrolyte is saturated with S8 molecules, approximately 21 S8 molecules in the electrolyte corresponding to a solubility of 19 mol m-3. The concentration gradient drives S8 molecules to transport from the cathode to Li anode. After the elemental sulfur is reduced at the Li anode-electrolyte interface, other S8 molecules are desorbed from the cathode to replenish the dissolved S8 in the electrolyte. Meanwhile, the reaction product of Li2S4 (grey) diffuses from the Li anode surface to the cathode under the concentration gradient. Alternatively, Li2S4 could be reduced to Li2S (red), which is directly deposited over the anode surface. Though no current runs through the system, charge transfer takes place between the active 8


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materials and the anode. Herein, the involved electrons in the chemical reactions are converted to the “imaginary current density”, which is calculated as 𝑖 =

𝑁𝑞 𝑡𝑆 ,

(7)

where N is the total number of electrons transferred in the reactions during a resting time t, S is the area of the electrolyte-anode interface, and q is the elemental charge. Fig. 2(b) shows the “imaginary current density” as the function of time. In the early stage, the current density remarkably increases. During this period, S8 molecules rapidly diffuse to the anode. After the concentrations of S8 molecules and Li2S4 reach the equilibrium states, the current density is stable at 0.25 mA cm-2. As indicated in Fig. 2(c), the concentration of Li2S4 gradually increases with time. Meanwhile, the precipitation of insoluble Li2S results in a passivation layer on the anode surface. Fig. 2(c) shows that the average thickness of the passivation layer progressively increases with the resting time. In addition, the interphase layer features a porous Li2S structure, as illustrated in Fig. 2(a), which is consistent with the recently reported results.22 In the experiments, the failure of lithium-sulfur battery was attributed to the continued growth of a porous passivation layer on Li metal anode, with the thickness up to 440 μm, which was identified as Li2S by X-ray diffraction.22 The formation of Li2S interphase degrades the performance by means of consuming the electrolyte and Li anode, eventually leading to a dead cell.22 Because of the nanoscale system used in the model, the resting time is only 0.26 s when the capacity loss is 10% in Fig. 2. To scale up to the system comparable to a practical lithiumsulfur system, the dimensionless time and “imaginary current density” are employed 𝐷𝑡

𝑖𝐿

𝑡 = 𝐿2 , 𝑖 = 𝐷𝑐0𝐹, 9


(8)


where L is the system height, 𝑐0 is the concentration, and D is the diffusivity. We have D = d2kd,33 where kd is the diffusion rate in Eq. (6), and d is the distance between two adjacent sites, i.e. 6.0 Å. The calculated reference diffusivities are D10 = 2 × 10-8 cm2/s and D20 = 1 × 10-9 cm2/s for S8 and Li2S4, respectively. Using the dimensionless time and current density, the diffusion equation can be transformed into non-dimensional forms.45 For the capacity loss of 10%, the resting time of 0.26 s and “imaginary current density” of 0.25 mA cm-2 in our model are equivalent to 3 days and 0.0025 mA cm-2 for a practical system with the thickness of 600 μm. In fact, the self-discharge rate varies from experiment to experiment. Mikhaylik and Akridge reported a capacity loss of 43% after 24 h storage.27 Manthiram et al. observed that the discharge capacity loss was about 50% after a resting time of 1 week.29 Ryu et al. found the self-discharge rate of Li/TEGDME/S battery using Al current collector was 34% during initial 80 days.30 Self-discharge rate could depend on various factors,31 and the effects of solubility, diffusion kinetics, reaction rate, and interlayer resistance will be focused in the following. The nature of the electrolyte controls the solubilities of S8 and Li2S4, which determines their maximum concentrations in the electrolyte. Given that concentration could significantly affect the reaction rate, its effect on self-discharge behavior is examined. Table 1 presents the reference solubilities, i.e. χ10 = 19 mol m-3 for S8 and χ20 = 100 mol m-3 for Li2S4. For a capacity loss of 10%, Fig. 3(a) shows the dimensionless self-discharge time in terms of two dimensionless parameters χ1/χ10 and χ2/χ20, where χ1 and χ2 are the solubilities of S8 and Li2S4, respectively. As illustrated in Fig. 3(a), high solubilities greatly reduce the self-discharge time, implying that the self-discharge rate is increased. Due to the high solubility, more S8 and Li2S4 are available in the electrolyte, which enhances the reaction kinetics on the anode surface during 10


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cell resting. Conversely, low solubility decreases the cell self-discharge rate, which contributes to good capacity retention after resting. In experiments, using concentrated electrolytes could inhibit the dissolution of polysulfides, thereby suppressing the parasitic reactions between polysulfides and Li anode.46-47 However, there is a trade-off.48 In contrast to the blockage of electronic path due to insoluble products, highly soluble polysulfides help to improve the cell capacity. For a fixed S8 solubility in Fig. 3(a), as the solubility of Li2S4 increases, the selfdischarge rate first dramatically increases and then approaches a relatively stable value. Similarly, for a fixed Li2S4 solubility, as the solubility of S8 increases, the self-discharge rate gradually increases to a stable value. To reveal the underlying mechanism, Fig. 3(b) shows the calculated Li2S4 concentration c2 in the electrolyte under varying solubilities, where c20 is reference concentration (100 mol m-3) corresponding to the reference solubility χ20 (100 mol m-3). For the solubility of S8, two examples are taken: χ1/χ10 = 0.25 and χ1/χ10 = 1.0. It can be seen that as χ2/χ20 increases, c2/c20 gradually deviates from the dashed line and reaches a stable value for the case of χ1/χ10 = 0.25. It implies that a low solubility of S8 will greatly limit the Li2S4 concentration even if the electrolyte has a high Li2S4 solubility, which accounts for the stable self-discharge rate in Fig. 3(a). Further, Fig. 3(c) shows Li2S4 concentration c2, influenced by the solubility of sulfur χ1 and the solubility of χ2. A decrease in the solubility of sulfur or the solubility of Li2S4 will decrease the Li2S4 concentration in the electrolyte. The solubility of Li2S4 is an inherent material property, which determines the limit of Li2S4 concentration, namely the maximum concentration c2max. Li2S4 is consumed on the anode, which leads to the formation of insoluble interphase. The reduction of sulfur produces Li2S4. If the solubility of sulfur is relatively low, 11



there are not sufficient polysulfides produced to maintain the limit c2max, thereby resulting in a relatively low self-discharge rate. As demonstrated in Fig. 3(b), the concentration of Li2S4 deviates from the limit (the dashed line). In the cathode, desorption rate describes the capability of bulk sulfur desorption from the carbon backbone, which determines the soluble S8 content in the electrolyte. On the anode surface, the reaction in Eq. (2) consumes dissolved S8 and provides Li2S4 for the reaction in Eq. (3), and thus, the rate in Eq. (2) plays a critical role in the self-discharge during cell resting. Fig. 4 shows the effects of the two factors on self-discharge rate by means of the dimensionless time for a fixed discharge capacity loss of 10%, where kd (kd0) is the desorption rate (the reference desorption rate) of bulk sulfur, and k1 (k10) is the local rate (the reference rate) for the chemical reaction in Eq. (2). kd0 and k10 can be obtained from Table 1. For each case, three individual simulations are used to yield the average dimensionless time. For a fixed desorption rate, as the reaction rate k1 increases, the dimensionless selfdischarge time first dramatically decreases and then slightly varies. Comparing the four curves in Fig. 4, it is evident that the self-discharge time decreases with increasing desorption rate. Therefore, two strategies could be proposed to reduce the self-discharge rate during cell resting: increasing the affinity of bulk sulfur to the carbon backbone and enhancing the chemical stability between dissolved S8 and Li metal anode. For the first strategy, nanostructured carbon materials are widely used, such as nanoporous carbon, carbon nanotube, and graphene, which possesses a high surface area to immobilize the active materials.49 In addition, strong adsorption could be achieved by tailoring the chemical interactions between sulfur species and host materials.50 The second strategy is to reduce the reaction kinetics in Eq. (2). A stable 12


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passivation layer, with a highly ionic conductive, is critical to alleviating the shuttle effect. For instance, using LiNO3 as an electrolyte additive could create a protective film of LixNOy and LixSOy on the anode,25 which is chemically stable against polysulfide and Li metal, thereby reducing the reaction kinetics on the anode surface. In Fig. 4, the results are governed by different mechanisms. For the influences associated with sulfur molecules, three regimes can be roughly identified: charge transfer control (I), desorption control (II), and diffusion control (III). In Regime I, charge transfer is the ratedetermining step. In Regime II, sulfur desorption dominates the entire reaction. However, charge transfer and sulfur are not the dominating factors in Regime III, where the self-discharge rate is controlled by S8 diffusion. The diffusivity of S8 (D10) affects the limiting current density in Eq. (2), which takes the form 𝑖𝐿 ∝

𝑐10𝐷10 𝐿

,

(9)

where c10 is the bulk concentration of S8. Therefore, S8 diffusion kinetics could be an important factor that determines the upper limit of self-discharge rate during cell resting. In addition to the influence of S8 in Region III, the reduction rate of Li2S4 plays a key role in self-discharge rate, as shown in Fig. 4(b). For a fixed capacity loss of 10%, the self-discharge time decreases with increasing k2/k20, where k2 is the reaction rate in Eq. (3), and D2 is the diffusivity of Li2S4 in the electrolyte. For the three cases, the diffusivity of Li2S4 has little impact on the selfdischarge rate, because the diffusion is not the rate-determining step for the range considered in Fig. 4(b). Finally, the effect of interlayer on self-discharge is explored. In our model, the interlayer is assumed to have a higher diffusion barrier for sulfur and polysulfides than the electrolyte. 13



Hence, we have Di/D0 < 1, where Di is the diffusivity in the interlayer, D0 is the diffusivity in the electrolyte. In practical applications, the interlayer should not affect Li-ion transport. Fig. 5(a) shows the capacity loss in terms of log (D1i/D10) and log (D2i/D20) for a fixed self-discharge time of D10t/L2 = 150 during resting. D1i is the diffusivity of S8 in the interlayer, and D2i is the diffusivity of Li2S4 in the interlayer. For dissolved S8, when the interlayer has a much higher diffusion barrier than the electrolyte, the self-discharge rate primarily depends on D1i/D10. As the diffusion barrier of S8 in the interlayer becomes close to that in the electrolyte, the diffusion kinetics of Li2S4 in the interlayer dominates the self-discharge behavior. For instance, the right side in Fig. 5(a) shows that the self-discharge rate increases with increasing diffusion barrier of Li2S4 in the interlayer. In addition, for a fixed high diffusion barrier of Li2S4 in the interlayer, a slight change of self-discharge rate is caused with decreasing diffusion barrier of S8 in the interlayer, shown in the lower right corner in Fig. 5(a). For the above results, Fig. 5(b) illustrates the mechanism. For sulfur molecules, the interlayer with a high diffusion barrier will resist the diffusion of dissolved S8 through it. Therefore, sulfur molecules are largely confined in the space above the interlayer. Consequently, the decreased S8 concentration at the Li anode-electrolyte substantially reduces the selfdischarge rate during cell resting. The result is consistent with the experiments, where excellent overall performance could be obtained by using an ultrathin dense interlayer.16 In contrast, a special case is that the interlayer has a moderate diffusion barrier for S8 but a high diffusion barrier for Li2S4, and thus, Li2S4 is largely confined in the space below the interlayer. Because of the confinement, the accumulated Li2S4 could increase Li2S4 concentration and its gradient between the interlayer and the anode, which contributes to a relatively larger self-discharge 14


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rate. For a practical Li-S battery, the artificial interlayer needs to be designed to hinder the diffusion of sulfur and polysulfides, aimed at effectively suppressing the self-discharge during resting.

Table 2. Self-discharge rates of three Li-S systems references

27

28

30

cathode

sulfur

sulfur

sulfur

acetylene black

super P carbon

acetylene black

graphite, binder

PVDF

PVDF-co-HFP

LiN(CF3SO2)2

LiCF3SO3

LiCF3SO3

DOL, DME

DOL, DME

TEGDME

Separator

polyolefin

polypropylene

polypropylene

Anode

Li

Li

Li

65% after 15 days

34% after 80 days

electrolyte

Self-discharge rate 43% after 1 day

Table 2 lists the self-discharge rates of three Li-S systems during resting. Based on the aforementioned results, many factors and their competition affect the self-discharge behavior: the binding of sulfur to the cathode (ka), sulfur solubility and diffusivity in the electrolyte (χ1 and kd), and chemical stability of sulfur species against Li anode (k1 and k2). These factors contribute to the self-discharge rate differences in experiments. For practical Li-S batteries, the use of interlayers alleviates self-discharge. Self-discharge rate could also be reduced by improving the separator and electrolyte, such as enhancing the resistance to the diffusion of sulfur species, but without compromise of Li-ion diffusion kinetics. In this study, qualitative

15



analysis is provided. However, a more rigorous model is further needed to clarify the mechanism of self-discharge. (1) In the model, we focus on the self-discharge caused by the reduction of the dissolved sulfur from the cathode and its produced polysulfides, and the reduction of pre-existing sulfur species in the electrolyte is not considered. (2) In addition to the reactions on the anode surface, parasitic reactions could also occur in the cathode and current collectors.30 (3) This model can only be applied to cell resting; however, self-discharge exists in the entire cell life. 4. Conclusion In summary, we investigate the capacity loss in the lithium-sulfur battery through a mesoscale model, in particular, focusing on the parameters that affect the self-discharge behavior during resting. In this model, we consider the desorption of bulk sulfur from the carbon backbone, diffusion kinetics in the electrolyte, and chemical reactions on the anode surface. Dissolved sulfur molecules react with Li anode, and the final product of lithium sulfide is deposited on the anode surface, forming a porous layer. A low solubility of sulfur can reduce the reaction kinetics, thereby suppressing the capacity loss during cell resting. For sulfur molecules, three regimes are found in determining the self-discharge rate: desorption control, diffusion control, and charge transfer control. In addition, the model demonstrates that selfdischarge rate could be greatly reduced by using the interlayer with a high diffusion barrier of sulfur molecules, originating from its confinement effect. This work offers a fundamental understanding of the capacity loss of lithium-sulfur battery during resting, providing insights into the possible strategies towards reducing the self-discharge rate. Acknowledgement 16


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FIGURES AND FIGURE CAPTIONS

Fig. 1. Schematic of the self-discharge in the simplified model, where soluble polysulfides are represented by Li2S4 (S4-2, the grey circle), and insoluble polysulfides are represented by Li2S (S-2, the red circle). Reaction process: (1) solid sulfur dissolves into the electrolyte; (2) the dissolved S8 diffuses from the cathode to the anode through the electrolyte and reacts with Li anode, which produces soluble Li2S4; (3) Li2S4 is further reduced and deposited on the substrate, forming Li2S interphase.

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Fig. 2. (a) Snapshot of the Li-S system when the capacity loss is 10%. The system includes solid sulfur (blue), dissolved S8 molecules (purple), Li2S4 (gray), Li2S (red), carbon backbone (brown), and Li anode (black). (b) “Imaginary current density” with time. (c) Profiles of the Li2S4 concentration and average thickness of the Li2S interphase.

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Fig. 3. (a) For the capacity loss of 10%, the dimensionless self-discharge time in terms of χ1/χ10 and χ2/χ20. χ1 is the solubility of S8, and χ2 is the solubility of Li2S4. The reference solubilities in the electrolyte: χ10 = 19 mol m-3 and χ20 = 100 mol m-3. (b) Li2S4 concentration with increasing Li2S4 solubility, and the reference concentration c20 = 100 mol m-3. (c) Schematic of the concentration of polysulfides c2 (Li2S4) influenced by the solubility of sulfur χ1 and the solubility of polysulfides χ2.

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Fig. 4. (a) For the capacity loss of 10%, the reaction-rate-dependent dimensionless self-discharge time under various S8 desorption rates. Roughly, the map is divided into three control regimes: charge transfer (I), desorption (II), and diffusion (III). (b) Roles of Li2S4 in the self-discharge rate. k1 and k2 are the reaction rates of S8 → Li2S4 and Li2S4 → Li2S. The reference rates k10 and k20 are in Table 1. kd the desorption rate of solid S8 from the cathode, and kd0 the reference desorption rate. D2 is the diffusivity of Li2S4 in the electrolyte, and D20 is the reference diffusivity.

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Fig. 5. Effect of interlayer on self-discharge kinetics. (a) For a fixed self-discharge time of D10t/L2 = 150, the capacity loss in terms of log(D1i/D10) and log(D2i/D20). D1i is the diffusivity of S8 in the interlayer, and D2i is the diffusivity of Li2S4 in the interlayer. D10 and D20 are the reference diffusivities of S8 and Li2S4 in the electrolyte, respectively. (b) Schematic of the confinement effect from the interlayer with high diffusion barriers for S8 and Li2S4.

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Mesoscale Elucidation of Self-Discharge-Induced Performance Decay

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