Unraveling the Operation Mechanisms of Lithium Sulfur Batteries with

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Unraveling the operation mechanisms of Lithium Sulfur Batteries with ultramicroporous carbons Yinghui Yin, and Alejandro A. Franco ACS Appl. Energy Mater., Just Accepted Manuscript • DOI: 10.1021/acsaem.8b01159 • Publication Date (Web): 08 Oct 2018 Downloaded from http://pubs.acs.org on October 11, 2018

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ACS Applied Energy Materials

Unraveling the Operation Mechanisms of Lithium Sulfur Batteries with Ultramicroporous Carbons Yinghui Yin,a,b Alejandro A. Francoa,b,c,d,*

a

Laboratoire de Réactivité et Chimie des Solides (LRCS), UMR CNRS 7314, Université

de Picardie Jules Verne, HUB de l’Energie, Rue Baudelocque, 80039 Amiens Cedex, France b Réseau

sur le Stockage Electrochimique de l’Energie (RS2E), FR CNRS 3459, HUB

de l’Energie, Rue Baudelocque, 80039 Amiens Cedex, France c

ALISTORE European Research Institute, FR CNRS 3104, HUB de l’Energie, Rue

Baudelocque, 80039 Amiens Cedex, France d Institut

Universitaire de France, 103 Boulevard Saint-Michel, 75005 Paris Cedex,

France

Corresponding Author

ACS Paragon Plus Environment

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* [email protected].

KEYWORDS. Energy storage, Li-S battery, ultramicroporous carbon, quasi-solid-state reaction, mechanism, modeling.


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ABSTRACT. Quasi-solid-state lithium-sulfur batteries (QSS-LSBs) constitute a new type of lithium sulfur batteries (LSBs) having a cathode usually based on ultramicroporous carbon and presenting only one voltage plateau in their discharge profile. As the discharge of QSS-LSBs does not involve polysulfide dissolution, shuttle effects can be suppressed in this system. Here, we report a kinetic model to simulate the discharge process of QSS-LSB based on a two-step reaction mechanism. The simulation results well reproduce the one-plateau discharge profile and reveal that the high Li+ transport resistivity of Li2S and Li2S2 is the key capacity limiting factor.

Driven by the escalating demand for renewable energy storage, lithium-sulfur batteries (LSBs) have attracted increasing attention in recent years due to the high theoretical capacity of sulfur cathode (~ 1675 mAh/g) as well as the abundance of sulfur in nature.1 For a conventional LSB, the discharge process undergoes through a solid-liquid-solid reaction path and the discharge profile consists of two voltage plateaus.2 The first plateau at ~ 2.3 V is correlated to the reduction of S8 to soluble long chain polysulfide Li2Sx (4 ≤ x


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≤ 8) and the second plateau at ~ 2.1 V is linked to the further reduction of polysulfides to insoluble Li2S.3,4 However, another type of LSB has been reported more recently showing only one voltage plateau in their discharge profile (Figure 1(a)), in spite of having almost the same cell configuration as the conventional LSB.5–18 This type of LSB shows the following characteristics: (1) S/C composite in these LSB is usually based on ultramicroporous carbon materials which have a pore width smaller than 1 nm; (2) the electrolyte is mostly carbonate-based, while glyme-based electrolyte is also found in a few cases; (3) there is a large irreversible capacity between the first discharge and the later cycles. Fu et al.19 and Dominko et al.20 showed that the discharge of sulfur confined in ultramicropores undergoes via a solid-solid mechanism where the dissolution of polysulfides is absent. As liquid electrolyte is still used in this system, such a discharge mechanism is named as “quasi-solid-state” (QSS) mechanism.5 Different mechanisms have been proposed to attribute the one plateau behavior to the existence of short-chain sulfides,6 C-S interactions21 and formation of a passivation layer12. Nevertheless, the detailed discharge mechanism of QSS-LSB and its dependence on textural properties of carbon host materials are still obscure. Here, a simple kinetic model has been developed


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to simulate the discharge process of QSS-LSB, with the aim to provide an alternative operational mechanism for this system. In this paper, we firstly describe the assumptions and theoretical considerations on which the model builds, followed by the investigations of the impacts of Li2S2 resistivity, pore width and depth on the performances of QSS-LSB.

Figure 1. (a) Experimental discharge profile of a QSS-LSB (reprinted from ref. 6); (b) The schematic illustration of the two-step QSS discharge mechanism, together with the


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simulated (c) discharge profile and (d) evolution of the cathode speciation of the reference case.

As illustrated in Figure 1 (b), we consider in our model that all elementary sulfur is loaded in cylindrical pores, having uniform width and depth, of the porous carbon. There are different opinions reported in literature about the form of the elementary sulfur in the ultramicropores. While Xin et al. proposed that due to the narrow pore size, sulfur is more likely to be short-chain S2-4 molecules,6 Markevich et al. point out that at the temperature of S/C preparation, the major component in sulfur vapor is still S6-8.2 Moreover, Li et al. reported that the same S/C composite electrode can switch from QSS mechanism to conventional mechanism just by changing carbonate-based electrolyte with glyme-based electrolyte.7 This observation indicates that sulfur in ultramicropores is not necessarily in the form of small molecules. Thus, in the current model, elementary sulfur is considered to be in the form of S8 which is reduced successively to Li2S2 (Eq.1) and Li2S (Eq.2): 𝑆8 + 8 𝐿𝑖 + + 8 𝑒 ― = 4 𝐿𝑖2𝑆2

(1)

𝐿𝑖2𝑆2 + 2 𝐿𝑖 + + 2 𝑒 ― = 2 𝐿𝑖2𝑆

(2)


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The formation of Li2S2 is supported by the molecular dynamics (MD) modeling results reported by Burgos et al. who showed that Li2S2 could be stabilized in nanoscale confined structures.22 Moreover, it is assumed that the lithiation of sulfur proceed via a layer-bylayer manner, thus, the formation of Li2S2 as well as Li2S can be viewed as a two-phase reaction with a moving interphase (video S1). Then, to describe the kinetics of these reactions, Tafel relation is used in our model:

𝑖1 = 𝑛1𝐹𝑘1𝑎8𝐿𝑖 + 𝑎𝑆8exp [ ―

𝛽𝑛1𝐹 𝑅𝑇

𝑖2 = 𝑛2𝐹𝑘2𝑎2𝐿𝑖 + 𝑎𝐿𝑖2𝑆2exp [ ―

(𝐸 ― 𝐸𝑜1 + i1𝑅𝑠1)]

𝛽𝑛2𝐹 𝑅𝑇

(𝐸 ― 𝐸𝑜2 + 𝑖2𝑅𝑠2)]

(3) (4)

where i1 and i2 are the current density (or Li+ flux density across the sulfur/electrolyte boundary), k1 and k2 are kinetic constants, a refers to the activities, E is the electrode potential, Eo is the standard potential and R is the resistance of Li+ transport through the discharge product layer(s). While the activities of solid species (𝑎𝑆8 and 𝑎𝐿𝑖2𝑆2) are defined to have a value of 1 if they exist in the system, the activity of Li+ is dimensionless, defined as the ratio between the actual and standard concentrations:

𝑎𝐿𝑖 + =

𝑐𝐿𝑖 +

(5)

𝑐𝑜𝐿𝑖 +


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To focus more on the impacts on the local reaction kinetics, it is assumed that the Li+ transport from anode is fast enough to maintain the Li+ concentration unchanged during the discharge process. For other cases where the Li+ transport is the limiting factor, the variation of Li+ concentration should be also considered accordingly. Moreover, the resistances can be written as a function of the resistivity (𝜌) and thickness (𝛿) of Li2S2 and Li2S as following: 𝑅𝑠1 = 𝜌𝐿𝑖2𝑆2𝛿𝐿𝑖2𝑆2 + 𝜌𝐿𝑖2𝑆𝛿𝐿𝑖2𝑆

(6)

𝑅𝑠2 = 𝜌𝐿𝑖2𝑆𝛿𝐿𝑖2𝑆

(7)

Summing up the current densities from the surface area of the electrochemical active zone (A) gives the applied current: 𝐼 = (𝑖1 + 𝑖2)A

(8)

Considering the insulating nature of S8 and Li2S2, the electron transfer may rely mainly on electron tunneling. Thus, the electrochemical active zone corresponds to the area within the maximum electron tunneling distance (rtn). As a result, A can be expressed as:

𝐴=

{

𝜋𝑟2, 𝑟 ≤ 𝑟𝑡𝑛 2 2 𝜋𝑟 ― 𝜋(𝑟 ― 𝑟𝑡𝑛) , 𝑟 > 𝑟𝑡𝑛

(9)

where r is the radius of the pore. The discharge rate with respect to the mass of sulfur can be obtained by


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𝑅𝑎𝑡𝑒 =

(𝑖1 + 𝑖2)𝐴

(10)

2

𝜋𝑟 𝐿𝜔𝑆8

where 𝜔𝑆8 is the density of S8. With the discharge process going on, the thicknesses of Li2S2 and Li2S vary with time. Their growth rate can be obtained as following: 𝑑𝛿𝐿𝑖2𝑆2 𝑑𝑡

=

(

4𝑖1 𝑛1𝐹

𝑑𝛿𝐿𝑖2𝑆 𝑑𝑡

=

―

𝑖2

)

𝑛2𝐹

( ) 2𝑖2

𝑛2𝐹

𝑉𝑒,𝐿𝑖2𝑆2

𝑉𝑒,𝐿𝑖2𝑆

(11) (12)

where 𝑽𝐞 refers to the molar volume. By solving numerically Eq. 3-12, one obtains the evolution of the cathode potential and the speciation. The baseline values of parameters used in the model are summarized in Table 1. The values of pore geometry parameters and discharge rate were set in a reasonable range as reported in the literature. Though there are already theoretical investigations of Li2S2/Li2S resistivities via DFT calculations reported in literature, it is not clear if these values are applicable in our model as they refer mainly to the bulk phase.23,24 Lacking of available experimental references, the reaction rate constants and Li2S2/Li2S resistivities used in the reference case were fitted through an automatic parameter sensitivity screening with a home-made MATLAB script to obtain a similar discharge


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shape and discharge voltage in comparison to the experimental curve.6 The simulated discharge profile of the reference case is presented in Figure 1 (c) and it reproduces well the one-plateau behavior reported in experimental literature. The evolution of the cathode speciation (Figure 1 (d)) shows that the voltage plateau corresponds mainly to the formation of Li2S2. With the growth of the Li2S2 layer, the discharge potential decreases slowly due to the gentle increasing of the Li+ resistance. Then, Li2S starts to be formed when the potential decreases by ~ 0.1 V due to a lower standard potential. However, the formation of highly resistive Li2S results in a fast drop of discharge potential and the discharge stops when the potential reaches the cut-off set at ~ 1V. The simulated cathode speciation indicates that the final discharge product is a mixture of Li2S2 and Li2S, which is in agreement with experimental observations20 and MD modeling results.21,22 This incomplete conversion from S8 to Li2S also explains the simulated specific capacity about 900 mAh/gs, which is similar to the reversible capacity but much smaller than the initial capacity reported in literature.6,14,17 This simulation result is not surprising considering that the dramatic initial specific capacity fading can be attributed to the side reactions, such as electrolyte decomposition and solid-electrolyte-


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interface (SEI) formation as proposed by

2,12

Markevich et al., other than the intrinsic

discharge mechanism. Though it is not included in the present model, it is worth to note that the large volume expansion from Li2S2 to Li2S can also contribute into the incomplete conversion and the impact of the mechanical stress on the discharge potential will be addressed in a future work.

Table 1. Summary of parameters and their baseline values in the model.

Symbols

Parameters

Values and Units

𝒅𝒑𝒐𝒓𝒆

Pore width

1 nm

𝑳

Pore depth

7.5 nm

𝝆𝑳𝒊𝟐𝑺𝟐

Li+ resistivity Li2S2

1×1010 Ω∙m


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𝝆𝑳𝒊𝟐𝑺

Li+ resistivity Li2S

1×1012 Ω∙m

𝑬𝒐𝟏

Standard potential of S8/Li2S2

2.26 V v.s. Li+/Li

𝑬𝒐𝟐

Standard potential of Li2S2/Li2S

2.15 V v.s. Li+/Li

𝝎𝑺𝟖

Density of S8

Rate

Current density with respect to

2.17 g/cm3

0.1 A/g

the sulfur mass

𝒌𝟏

Kinetic constant of S8 reduction

1×10-10 mol/(s∙m2)

𝒌𝟐

Kinetic constant of Li2S2 reduction

1×10-10 mol/(s∙m2)

𝒂𝑳𝒊 +

Activity of Li+

1

As the impact of reaction kinetic constants (k1,k2) are less pronounced comparing to Li2S2/Li2S

resistivities, here we discuss only the latter. The Li+ transport resistivity of Li2S2

and Li2S are assumed to be 1×1010 Ω∙m and 1×1012 Ω∙m, respectively. Such a resistivity


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difference between Li2S2 and Li2S is necessary to obtain the one-plateau voltage profile. If this difference become smaller, there will be two separated voltage plateaus appearing in the discharge profile (Figure S1). Thus, in the investigation of the resistivity impact, a series of simulations have been conducted by varying the Li2S2 resistivity from 109 to 1012 Ω m while maintaining Li2S resistivity always two orders of magnitude higher than that of Li2S2. As shown in Figure 2 (a), the discharge profile is intimately linked to the resistivity of Li2S2 and Li2S. When the resistivity becomes larger, slopes of both plateau and incline region in the discharge profile increases, which can be attributed to the increased ohmic drop. Moreover, it is found that the discharge capacity decreases with the increasing resistivity of Li2S2 and Li2S as consistent with the simulated cathode speciation displayed in Figure 2 (b). When the resistivity of discharge products is high, very limited amount of S8 is converted into Li2S2 and Li2S before the discharge potential drops to the cut-off voltage, resulting in extremely low specific capacity. Lowering such a resistivity leads to a better utilization of S8, more formation of Li2S and higher discharge capacity. This specific capacity dependence on the resistivity also implies that the enhancing of Li+


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transport in Li2S2 and Li2S layers by doping or introducing defects can be a way to improve the discharge capacity of QSS-LSB.

Figure 2. Simulated (a) discharge profiles and (b) final cathode speciation of QSS-LSBs with different value of Li2S2 resistivity. In all cases, the resistivity of Li2S is assumed to be two orders of magnitude higher than that of Li2S.

To understand why the QSS mechanism is always linked to the ultramicroporous carbon, we further investigated the impact of pore size with the present model. Figure 3 (a) shows the simulated discharge profile considering various pore widths. It is found that the electron tunneling distance acts as a threshold for the pore size effects. The discharge profiles are overlapped when the pore radius are smaller than the electron tunneling


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distance. However, when the pore radius is larger than the electron tunneling distance, increasing the pore size leads to an obvious decrease of the specific capacity. This can be explained by the electron transport limitation. Due to the small size, all the sulfur loaded in the ultramicropores can be considered as electrochemical active. In contrast, in large pores, only part of sulfur can be accessed by the electrons and be reduced. Therefore, the sulfur utilization decreases by increasing the pore size as displayed in Figure 3 (b). Moreover, bearing in mind that the applied current density in experiment is usually with respect to the overall sulfur loading, the local current density experienced by the electrochemical active sulfur in mesopores is much larger than the apparent value. As a result, the ohmic drop in mesopores is much higher and the discharge potential decreases faster, leading to a lower S8 utilization even inside the electrochemical active zone.


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Figure 3. Simulated (a) discharge profiles and (b) final cathode speciation of QSS-LSBs based on carbon with different pore widths.

Apart from the pore width, the simulation results also show impact on the discharge performance of QSS-LSB. Though there is only a slight decrease in discharge capacity when the pore depth increases from 5 to 7.5 nm, further increasing the pore depth to 10 nm leads to a pronounced decrease in the specific discharge capacity (Figure 4(a)), which is attributed to the insufficient sulfur utilization as illustrated in Figure 4 (b). In the latter case, when the Li2S2 and Li2S grow until reaching a certain thickness, the resistance for Li+ transport becomes so high that the ohmic drop brings the discharge potential down to the cut-off voltage, leaving the sulfur at the bottom of the pore unchanged. Moreover,


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despite varying the discharge capacity, the final thickness of the Li2S layer in all cases is similar. This indicates that the end of the discharge process is correlated to the formation of a 1.1 nm thick Li2S layer, highlighting again the high resistivity of the discharge product as the key capacity limiting factor. The above simulation results provide a new insight into the texture-performance relationship of electrodes for QSS-LSB. It suggests that shallow pores are favored for QSS-LSBs to obtain better sulfur utilization and higher specific capacity.

Figure 4. Simulated (a) discharge profiles and (b) final cathode speciation of QSS-LSBs based on carbon with various pore depths.


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In conclusion, considering a two-step reaction mechanism and layer-by-layer conversion, we proposed a simple kinetic model to simulate the discharge process of QSS-LSB. The simulation results show that the final discharge product in QSS-LSB is a mixture of Li2S and Li2S, whose resistivity is the key capacity-limiting factor in such a system. At the same time, the model provides novel mechanistic insights into the textureperformances relationship of the ultramicroporous carbon in QSS-LSBs. According to the model, the pore size dependence of the QSS mechanism can be explained through the electron transport limitation. Moreover, the failure of the QSS mechanism in mesopores is mainly due to the low ratio of electrochemical active sulfur and high local current density. In addition, other textural properties, such as the pore depth also shows impact on the discharge performance of QSS-LSB and shallow pores are favored for a better utilization of sulfur.

ASSOCIATED CONTENT


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Supporting Information. The following files are available free of charge. Simulation results showing the impacts of Li2S resistivity, Li2S2 resistivity and current density on discharge performances of QSS-LSB. (PDF) Evolution of discharge voltage and speciation (avi)

Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

Funding Sources This work is funded by the European Union’s Horizon 2020 research and innovation program for the funding support through the HELIS project under grant agreement No. 666221, and by a grant from Institut Universitaire de France to Prof. Alejandro A. Franco.

Notes The authors declare no competing financial interests.


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ACKNOWLEDGMENT

Dr. Robert Dominko at NIC (Ljubljana, Slovenia) and Mr. Vigneshwaran Thangavel are gratefully acknowledged for fruitful discussions. Prof. Alejandro A. Franco also acknowledges the Institut Universitaire de France for the support.

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