Mesoscale Elucidation of Surface Passivation in the LiâSulfur Battery

Research Article www.acsami.org

Mesoscale Elucidation of Surface Passivation in the Li−Sulfur Battery Cathode Zhixiao Liu and Partha P. Mukherjee* Department of Mechanical Engineering, Texas A&M University, College Station, Texas 77843, United States S Supporting Information *

ABSTRACT: The cathode surface passivation caused by Li2S precipitation adversely affects the performance of lithium−sulfur (Li−S) batteries. Li2S precipitation is a complicated mesoscale process involving adsorption, desorption and diffusion kinetics, which are affected profoundly by the reactant concentration and operating temperature. In this work, a mesoscale interfacial model is presented to study the growth of Li2S film on carbon cathode surface. Li2S film growth experiences nucleation, isolated Li2S island growth and island coalescence. The slow adsorption rate at small S2− concentration inhibits the formation of nucleation seeds and the lateral growth of Li2S islands, which deters surface passivation. An appropriate operating temperature, especially in the medium-to-high temperature range, can also defer surface passivation. Fewer Li2S nucleation seeds form in such an operating temperature range, thereby facilitating heterogeneous growth and potentially inhibiting the lateral growth of the Li2S film, which may ultimately result in reduced surface passivation. The high specific surface area of the cathode microstructure is expected to mitigate the surface passivation. KEYWORDS: lithium−sulfur battery, Li2S precipitation, surface passivation, morphology evolution, mesoscale modeling

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affinities to PSs than carbon-based material.16 Nazar’s group reported that 2D Ti2C as cathode host material can achieve high specific capacity and good cycling stability because of the strong interactions between PSs and surface Ti atoms.17 Recently, we evaluated silicene as the potential host material in Li−S battery.18 We found that silicene has a strong affinity to PSs and it can facilitate the reduction and dissociation of longchain PSs. However, the strong affinity causes very fast surface passivation, which also harmful for Li−S battery. Surface passivation is attributed to the deposition of insoluble Li2S during the discharge process. It is known that crystalline Li2S is an electronic insulator,19,20 hence the electrochemical reactions for PSs reduction are difficult to happen at the electrolyte/Li2S interface. The lateral growth of Li2S precipitation can reduce the fresh cathode surface area which supplies electrons for electrochemical reactions. Gerber et al. reported a method to inhibit the lateral growth of Li2S film on the carbonbased substrate by using benzo[ghi]peryleneimide (BPI) as the redox mediator. They found that the specific capacity is doubled by using the mediator.21 In this regard, it is necessary to control the surface passivation of the carbon-based substrate caused by Li2S precipitation during the discharge process. The growth of solid Li2S involves three transition events, which are Li2S molecule

INTRODUCTION Lithium-ion batteries (LIBs) have been successfully applied in EVs.1−4 However, the specific energy density of LIB is limited by the Li intercalation mechanism for energy storage.5−7 The development of EVs requires energy storage system with higher specific energy density and lower cost. Lithium−sulfur (Li−S) battery is a promising next-generation electrochemical energy storage system which can deliver a theoretical specific energy as high as 2567 Wh kg−1. Li−S battery will be cheap because its active material sulfur is abundant on Earth. However, Li−S battery has a far way to go before the commercialization. One key challenge for Li−S battery is the internal shuttle effect.8 During the discharge, solid sulfur is dissolved into the electrolyte as the form of S8 molecule, and then S8 is gradually reduced to insoluble Li2S with dissoluble polysulfides (PSs) as intermediate discharge products. PSs can diffuse to anode side due to the potential and concentration gradients. PSs can chemically react with Li metal anode to form insulating Li2S film on the anode surface.9 The shuttle effect reduces the utilization of active material and leads to an irreversible capacity loss and poor cycling stability. To alleviate the shuttle effect, researchers have proposed a variety of novel electrode architecture design and electrocatalytic approaches to trap polysulfides.10−14 Cui and his colleagues presented a concept that the weak PS−carbon interaction is not helpful for PSs retention,15 and they suggested the use of polarized two-dimensional (2D) materials to immobilize PSs because these materials have much stronger © 2017 American Chemical Society

Received: November 24, 2016 Accepted: January 23, 2017 Published: January 23, 2017 5263

DOI: 10.1021/acsami.6b15066 ACS Appl. Mater. Interfaces 2017, 9, 5263−5271

Research Article

ACS Applied Materials & Interfaces adsorption, diffusion and desorption. Our previous firstprinciple studies have demonstrated that both graphene and crystalline Li2S surface are energetically favored for Li2S molecule adsorption.20,22 The adsorption is an exothermic reaction; therefore, the adsorption rate is the function of concentration. Contrary to the adsorption event, the Li2S molecule desorption is an endothermic reaction. The desorption rate is determined by the reaction barrier and the temperature. Similarly, the diffusion rate is also determined by the diffusion barrier and temperature. In the presented study, a mesoscale interfacial model is developed to study how species concentration and temperature affect the Li2S film growth. This model is expected to provide efficient strategies to defer surface passivation in Li−S battery cathode.

Based on experimental and computational findings discussed above, a coarse-grained (CG) lattice-based mesoscale model is developed to represent the Li2S formation and growth with the following assumptions: (1) Li2S is the only discharge product. (2) The film grows along the normal direction of Li2S (111) surface. (3) The film growth is only attributed to the direct deposition of Li2S molecules rather than Li2S2 deposition and reduction. (4) The structure of the Li2S is represented by a coarsegrained model. Each triatomic Li2S unit is simplified to a lattice site, and the position of a Li2S unit in the solid phase is represented by the position of the S atom. Therefore, the antifluorite structure of crystalline Li2S is converted to a face-centered cubic (fcc) structure. The coarse-grained model neglects the geometric parameters (i.e., bond length, bond angle and molecule orientation) at the atomistic scale. (5) The adsorption and diffusion of a Li2S unit on the solid substrate is restricted by a solid-on-solid model,33 in which an empty cell cannot accept a Li2S site unless this site coordinates with three occupied sites in the sublayer. A kinetic Monte Carlo (KMC) algorithm is employed to implement transition events taking place at the electrolyte/solid substrate interface. Three transition events are considered in the present model, which are Li2S adsorption, desorption, and diffusion on the surface (schematically illustrated in Figure S1). As discussed above, Li2S adsorption can only happen at an empty site cooperating with three occupied sites in the sublayer. The adsorption rate at an available site is calculated by

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MODEL DETAILS The formation of Li2S during discharge undergoes multistep reactions including23,24 S8(s) = S8(l)

(i)

S8 + 2e− = S82 −

(ii)

S82 − + 2e− = 2S24 −

(iii)

S24 − + 2e− = 2S22 −

(iv)

S22 − + 2e− = 2S2 −

(v)

Reaction i represents the dissolution of α-S into the electrolyte. Reactions ii−v represent electrochemical reactions, in which long-chain polysulfides (PSs) are gradually reduced into shortchain PSs. Short-chain PSs tend to precipitate on the substrate due to the low solubility in the electrolyte, as shown in reactions vi and vii. 2Li+ + S22 − = Li 2S2 ( ↓ ) +

2−

2Li + S

= Li 2S( ↓ )

R ads = k 0NaV

(vi)

(1)

In eq 1, k0 is the reaction rate constant, and Na is the Avogadro constant. V and S are the pore volume and cathode surface area in the porous cathode framework, respectively. Sa is the area of a lattice site projected to Li2S (111) surface. Ci is the reactant concentration and Θ is the Li2S solubility term. The values of reaction rate constant k0 and solubility Θ are adopted from previous simulation work.24 The diffusion rate is calculated by

(vii)

Besides the direct precipitation of Li2S (reaction vii), solid Li2S2 can also be converted to Li2S. Li 2S2 + 2Li+ + 2e− = 2Li 2S

Sa 2 (C Li+CS2− − Θ) S

(viii)

There is a controversy about the composition of the discharge products in Li−S batteries. Barghamadi et al. reported that the direct formation of solid Li2S is the predominant reaction and reaction viii is kinetically slow.25 Xiao et al. detected Li2S2 by using an in situ nuclear magnetic resonance (NMR) technique.26 However, Li2S2 is not a thermodynamically stable phase according to experimental observations27 and the firstprinciples calculations,28 and the XRD pattern of the final product matches the crystal structure of Li2S rather than the structure of Li2S2 predicted by the first-principles calculations.28 Cuisinier et al. and Dominko et al. independently analyzed products during the discharge/charge cycling by operando Xray absorption spectroscopy, and they found that Li2S is the only detectable crystalline phase among discharge products.23,29 Cuininier et al. also tracked the PSs evolution during discharge with NMR, but they did not detect solid Li2S2 as reported by Xiao et al.26 Cañas et al. analyzed discharge products with in situ XRD technique and they did not find solid Li2S2.30 Cañas et al. also found that (111) surface dominates the facets of crystalline Li2S, which is also confirmed by first-principle calculations.20,31,32

⎛ E ⎞ R dif = ν exp⎜ − b ⎟ ⎝ κT ⎠

(2)

In eq 2, Rdif is the number of diffusion attempts per second. The term “ν” is the jumping frequency. T is the temperature, and κ is the Boltzmann constant. Previous first-principle calculation demonstrated that the chemical adsorption energy (Eads) of a single Li2S molecule on graphene is only −0.55 eV,22 hence the desorption of a Li2S from the cathode surface should be considered and the desorption rate is calculated by R des =

⎛E ⎞ 2κT exp⎜ ads ⎟ ⎝ κT ⎠ h

(3)

where h represents the Planck constant. Table S1 lists the values of input parameters in eqs 1−3. Previous first-principles calculation showed that there is a strong attractive interaction between a Li2S molecule and preadsorbed Li2S.20,22 Thereby, the adsorbed Li2S molecule will not implement desorption or diffusion once it coordinates with other Li2S sites. The details of how to implement these transition events in KMC are 5264


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diffusion). The desorption rate dominates the total transition rates. The high desorption rate is attributed to the weak chemical interaction between the single Li2S molecule and the carbon substrate.21 It is worth pointing out that previous DFT simulaions demonstrated that (Li2S)n (n ≥ 2) clusters have much stronger chemical interactions with the carbon substrate than the single Li2S molecule. If a single adsorbed Li2S molecule collides with other adsorbed Li2S molecules, a stable (Li2S)n forms on the surface of the carbon substrate. In this case desorption of the Li2S is difficult because of the strong chemical interaction. These clusters act as seeds for Li2S film growth. As shown in Figure 1, the coverage keeps increasing in the second stage (pink region) and the third stage (yellow region). The slope of the coverage curve represents the coverage growth rate, and the larger slope indicates higher coverage growth rate (faster lateral growth). In the second stage, Li2S islands experience the isolated growth which associates an increase of coverage growth rate. In the third stage, the coverage growth rate gradually decreases to zero. The decrease in the coverage growth rate is attributed to the coalescence of Li2S islands. In Figure 1, the solid black line represents the average thickness of the Li2S precipitation; and the slope represents the thickness growth rate. It is found that the thickness growth in the second stage (the stage isolated island growth) is slower than the thickness growth in the third stage (the stage of island coalescence). The adsorption makes contributions only to the lateral growth and the thickness growth of Li2S islands. For a specified temperature and species concentrations, the adsorption rate is a constant and independent of the time. In the second stage, the lateral growth is dominant. Consequently, the thickness growth is suppressed. In the third stage, the coalescence of islands eliminates the lateral growth, which leads to an increase in the thickness growth rate. The film thickness grows linearly after the cathode surface being fully covered by the discharge product. According to Figure 1, it can be inferred that the formation of Li2S film undergoes three stages: cluster formation (nucleation), isolated island growth, and island coalescence. Snapshots in Figure 2a−c depict the represented topographies of carbon with different Li2S coverages. In Figure 2a, isolated islands are observed on the carbon substrate when the coverage is 30%. The coalescence of islands is observed at 50% coverage

discussed in the Supporting Information (schematically illustrated in Figure S2). In the current CG-KMC model, periodic boundary condition is applied along X and Y direction. In this case, an appropriate computational domain size should be selected because the simulation results show significant fluctuation if the domain size is too small to avoid the noise.34,35 It is found computational domain with 175 × 175 lattice sites is large enough to study surface passivation (Figure S3).

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RESULTS AND DISCUSSION Three stages during the Li2S film formation are identified by the present mesoscale interfacial model. Figure 1 shows the

Figure 1. Surface coverage as a function of time with constant reaction concentrations (CLi+ = 1 × 103 mol m−3 and CS2− = 1 × 10−4 mol m−3 and constant operation temperature T = 20 °C.

Li2S film coverage variation and thickness variation as a function of time. The simulation in Figure 1 is performed with T = 20 °C, CLi+ = 1 × 103 mol m−3 and CS2− = 1 × 10−4 mol m−3. The formation of Li2S film cannot be observed in the first duration (the orange region in Figure 1). In this stage, Li2S desorption inhibits other transition events (adsorption and

Figure 2. Snapshots in the upper row depict the simulation results of Li2S growth on carbon substrate with the coverage of (a) 30, (b) 50, and (c) 90%. In the simulation, the temperature is set to T = 20 °C, and the reactant concentration are CLi+ = 1 × 103 mol m−3 and CS2 = 1 × 10−4 mol m−3. SEM images in the bottom row depict the morphology evolution of precipitated Li2S on carbon fiber cathode after (d) 2.5, (e) 4, and (f) 6 h with potentiostatic discharge at 2.02 V. SEM images adapted with permission from ref 36. Copyright 2015 Wiley. 5265


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ACS Applied Materials & Interfaces as shown in Figure 2b. The continuum film appears when 90% of carbon surface is covered by the Li2S precipitation. Fan et al. also observed the similar growth kinetics in an experimental study.36 In the experiment, the battery is discharged with a constant voltage of 2.02 V. It was found that the carbon fiber cathode was sparsely covered by Li2S islands after 2.5 h (Figure 2d), island coalescence happened after 4 h (Figure 2e), and the continuum Li2S film was observed on the carbon fiber after 6 h (Figure 2f). It is known that Li2S is an electrical insulator and the resistivity is larger than 1 × 1014 Ω cm.19 Therefore, Fan et al. argued that it is difficult for electrochemical reductions to happen at the surface of Li2S film, and the three-phase boundary (the boundary between electrolyte, Li2S and carbon) is electrochemically active for PS reduction.36 According to Figure 2, it can be inferred that the island coalescence reduces the length of the three-phase boundary, which leads to the decrease in active sites for electrochemical reactions. Recent theoretical studies revealed that the Li vacancy (V−Li) is the main charge carrier in crystalline Li2S,37 and transition metal doping can increase V−Li concentration.38 It was also found that transition metal dopant can generate gap states between fully occupied valence band below Fermi level and empty conduction band above Fermi level, which is also helpful for increasing the electronic conductivity.38 The final discharge product Li2O2 in Li−air battery is also an electrical insulator, which is similar to the discharge product Li2S in the Li−S battery. Theoretical studies also demonstrated that vacancies and dopants can increase the electrical conductivity of crystalline Li2O2.39−41 Besides point defects, grain boundaries in crystalline Li2O2 can also increase the electronic conductivity.42 According to these theoretical findings, we hypothesize that electrochemical reductions can happen at the surface of Li2S films. The reason is that defects in the Li2S film can provide pathways for electron migration from carbon cathode to the Li2S/electrolyte interface. However, the spread and growth of Li2S film will generate voltage drop because of Ohm’s law. Hence, it is necessary to control the passivation of the cathode surface to improvement the battery performance. The effects of S2− concentration and temperature on surface passivation are studied by the present mesoscale model. Figure 3 shows the effects of S2− concentration and temperature on saturation time (τS). τS is defined the time for the cathode surface getting completely covered by Li2S film. Figure 3 clearly demonstrates that the saturation time monotonically decreases as S2− concentration decreases. At room temperature (20 °C), the cathode surface will be passivated faster with a relatively higher S2− concentration. The top panel in Figure 4 shows the coverage variation as a function of time with different Cs2−. With a high S2− concentration Cs2− = 5 × 10−3, the surface coverage linearly grows to 100% with a large slope. In this case, the zerocoverage stage is not observed, which means that the nucleation happens very fast. According to eq 1, the higher S 2− concentration indicates a higher adsorption rate. Therefore, Li2S molecules have a high probability to get clustered and stabilized on the carbon surface. The zero-coverage duration appears when the concentration is decreased to 1 × 10−3 mol m−3. Since the concentration is reduced, the adsorbed single Li2S molecule will desorb from the cathode surface before it gets another Li2S molecule to form a stable cluster. The further decrease in S2− concentration can elongate the zero-coverage duration.

Figure 3. Effect of S2− concentration (CS2−) and temperature (T) on surface passivation. The saturation time (τS) represent the time for the cathode surface getting completely covered by Li2S film. The surface passivation can be mitigated by decreasing the S2− concentration in the electrolyte and operating the battery in an appropriate temperature window.

Figure 4. (a) Coverage variation vs time with different S 2− concentrations at room temperature T = 20 °C. Snapshots demonstrate the Li 2S film growth process with different S 2− concentration: (b) CS2− = 5 × 10−3 mol m−3, (c) CS2− = 1 × 10−3 mol m−3, and (d) CS2− = 5 × 10−3 mol m−3.

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ACS Applied Materials & Interfaces Snapshots in Figure 4 clearly show the effect of S2− concentration on the morphology evolution of Li2S islands. It can be clearly seen that many small Li2S islands appear on the cathode surface at 10% coverage when S2− concentration is 5 × 103 mol m−3. For the lower S2− concentration, only a few large Li2S islands are observed at 10% coverage. Without cooperating with predeposited solid Li2S, the adsorbed Li2S is always ready dissolved into the electrolyte from the carbon surface due to the weak physical interaction. On the other hand, our previous DFT simulation demonstrated that Li2S molecule has a strong affinity to the solid Li2S due to strong chemical bonds.20 For a certain surface coverage, the decrease in the island size leads to increasing the number of Li2S islands. Also, small islands always have a larger total perimeter than a large island. Therefore, smaller islands can provide more chemical interaction sites to capture Li2S molecules from the ambient environment. As shown in Figure 3, decreasing S2− concentration is a way to defer the surface passivation. One method to reduce S2− concentration is to discharge the battery with a low current density to limit the electrochemical reduction reactions from S8 to S2−. A recent experimental study on sodium−air batteries also demonstrated that the surface passivation could cause the “sudden death” when the cell was operated with a high discharge current density.43 However, the low discharge current density cannot supply high power. Another way to reduce S2− concentration is to facilitate the backward reaction of the 2− + S8. However, disproportionation reaction such as S2− n ⇔ S the long-chain PSs produced by backward disproportionation reaction can increase the shuttle effect, which leads to irreversible capacity loss. Another method to defer the surface passivation is discharging the battery at an appropriate temperature. Figure 3 shows that the low temperature (T < − 20 °C) leads to a fast surface passivation (τ S < 3 h) even though the S 2− concentration is as low as 1 × 10−4 mol m−3. It is found that the saturation time τS increases as temperature increases to T = 60 °C, which means that the surface passivation will be alleviated by increasing the temperature in an appropriate range. Over this critical temperature point, a further increase in temperature contrarily decreases the saturation time as shown in Figure 3. Figure 5 shows the effect of temperature on coverage variation. It is found that the adsorption−desorption competition duration is very short at T = −20 °C. The reason is that the desorption kinetic rate is significantly reduced by the low temperature according to Arrhenius equation. For a given S2− concentration, the adsorption rate is a constant in the present model, and the desorption rate is proportional to e−1/T. More desorption events can happen at a relatively higher temperature condition, which slows down Li2S cluster formation. Hence, the adsorption−desorption competition duration with T = 40 °C is longer than that with T = −20 °C. However, the high temperature (T > 40 °C) also decreases the adsorption−desorption competition duration as shown in Figure 5. The increase of temperature facilitates the diffusion of Li2S molecules. Therefore, Li2S molecules have more chances to collide to form clusters at T = 80 °C, thus the zero-coverage duration is reduced. Snapshots in Figure 5 depict morphology evolution during deposition at different temperatures. Snapshots in the first column show the temperature effect on the Li2S island distribution at 10% coverage. It is found that some small Li2S nanoislands appear on the cathode surface at T = −20 °C,

Figure 5. (a) Coverage variation vs time with CS2− = 1 × 10−4 mol m−3 at different temperatures. Snapshots demonstrate the Li2S growth processes at different temperatures: (b) T = −20 °C, (c) T = 20 °C, (d) T = 40 °C, and (e) T = 80 °C.

whereas fewer nanoislands are observed at T = 20 °C. Only one nanoisland is found in the computational domain when the temperature is larger than 40 °C. At low temperature, adsorbed Li2S molecules can be easily stabilized on the cathode surface due to the low desorption rate. As temperature increases, more preadsorbed Li2S molecules will desorb from the cathode surface to the ambient electrolyte environment, hence the number of island decreases. As shown in Figure 5, the temperature affects the morphology variation of the precipitation film. At T = −20 and 20 °C, the island coalescence happens at 50% coverage. When the temperature is above 40 °C, the island coalescence happens after 70% coverage. The density of the lateral sites of Li2S islands is calculated to quantitatively show the morphology evolution of the precipitation. Lateral sites are empty sites adjacent to Li2S 5267


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Because surface passivation is harmful to the electrochemical reactions due to the insulating nature of the solid Li2S, lowtemperature operation of Li−S batteries can adversely affect the discharge performance. Mikhaylik and Akridge studied the effect of temperature on the discharge performance of Li−S battery with graphite cathode.44 They found that the decrease of temperature (from 25 °C to −40 °C) reduced the discharge capacity and voltage. In addition, a higher temperature was helpful for achieving a better cycling stability. Huang et al. fabricated a cathode with hierarchical porous graphene and tested the high rate performance in the temperature range from −40 to 60 °C.45 They also found that the decrease in temperature (from 25 °C to −40 °C) reduced the discharge capacity. They also studied the effect of high temperature on the capacity. Their experiments demonstrated that the discharge capacity at 60 °C is also less than the capacity at 25 °C. These experimental observations coincide with the conclusion from our modeling work. A salient message from our work is that the Li−S batteries should be performed within an appropriate temperature window in order to achieve better discharge performance. It can be inferred that the temperaturecontrolled surface passivation affects the battery performance. The root-mean-square surface roughness Rrms is calculated to quantitatively represent the heterogeneity variation during Li2S film growth. A lower surface roughness indicates a more uniform distribution of Li2S film thickness, while the larger roughness always corresponds to a more heterogeneous Li2S distribution. Figure 7a clearly demonstrates that Li2S film prefers to grow heterogeneously at a higher temperature. The heterogeneous growth of Li2S film is beneficial for reducing capacity loss. Figure 7b shows the average film thickness as a function of coverage at different temperature conditions. A thicker Li2S film indicates a greater utilization of active material (solid sulfur). Operation at a high temperature can accommodate more Li2S precipitation, thereby leading to a higher discharge capacity. Recently, Gerber et al. reported a method to control Li2S growth by using benzo[ghi]peryleneimide (BPI) as the redox mediator.21 They found that the discharge capacity was significantly improved by using BPI to control the morphology of the Li2S precipitation. BPI can facilitate the film growing along the thickness direction. Thereby, the surface passivation can be alleviated and a higher discharge capacity could be achieved.

islands. In the present interfacial model, the Li2S molecule placed at the lateral site cannot desorb from the carbon substrate due to the strong attraction between Li2S molecules. The increase of density corresponds to the isolated island growth and the decrease of density corresponds to the island coalescence. The variation of lateral site density vs time is shown in Figure 6. The saddle point of the density curve is

Figure 6. Density of lateral sites as a function of coverage. The lateral site of a Li2S island is defined as the empty lattice site adjacent to the island. If a Li2S molecule is placed at the lattice site, the molecule cannot desorb from the carbon substrate due to the strong attraction between Li2S molecules. The formation and isolated growth of islands will increase the density of lateral sites, whereas the coalescence of islands will decrease the density of lateral sites.

shifted to a high coverage by increasing the temperature. As discussed in the above, the low temperature produces smallersized Li2S islands, which lead to a larger density of lateral sites. Once a Li2S molecule is located at a lateral site, it is stabilized on the carbon surface due to the strong attraction between this adsorbed Li2S molecule and the predeposited Li2S island. Hence, the cathode surface with smaller islands (larger density of lateral sites) always has a higher coverage growth rate, which leads to a faster surface passivation.

Figure 7. (a) Root-mean-square surface roughness of Li2S film vs coverage. A higher roughness represents a more heterogeneous distribution of local thickness. (b) Average Li2S film thickness vs coverage. The film with higher temperature can accommodate more Li2S molecules before the carbon substrate being fully covered. 5268


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Figure 8. Effects of (a) factional groups and (b) specific surface area on the carbon cathode surface passivation. All simulations are performed with T = 20 °C, CLi = 1 × 103 CLi = 1 × 103 mol m−3, and CS2− = 1 × 10−4 mol m−3.

enhanced surface passivation. Our work points to an important open question, hitherto unanswered in Li−S batteries: What dominates, shuttle effect or surface passivation, and what are the potential trade-offs on the cell performance?. The geometric properties (pore volume, surface area and architecture) of the cathode microstructure also influence the Li2S film growth. Figure 8b shows the effect of the specific surface area on the surface passivation. The specific surface area is defined as the ratio of cathode surface area to the pore volume. It is found that the increase in specific surface area can be helpful toward deferring the surface passivation. According to eq 1, the adsorption rate is inversely proportional to the specific surface area. Therefore, the high specific surface area can potentially reduce Li2S precipitation. The electrolyte can also affect Li2S precipitation. The interaction between Li2S molecules and electrolyte molecules determines the solubility of Li2S. Higher solubility can decrease the adsorption rate according to eq 1. Kamphaus and Balbuena theoretically studied long-chain polysulfides adsorption on the cathode substrate, and they found that the chemistry of the solvent in the electrolyte system significantly affects the adsorption energy.49 It also can be expected that varying the composition of the electrolyte may affect the Li2S adsorption energy and diffusion barrier on the carbon cathode surface, which consequently can impact the morphology evolution of the Li2S island formation and growth. If the choice of electrolyte improves the attraction between Li2S and the cathode surface, the surface passivation may be enhanced. The influence of electrolytes on surface passivation is an important aspect that warrants comprehensive investigation and is left as a future exercise.

An important highlight of the current study is to understand how the operating temperature affects the surface passivation of carbon-based cathodes. However, Li−S batteries with carbon based cathode suffer from the internal shuttle effect due to the weak affinity of the polysulfides to the carbon surface. Silecene is a potential cathode material which can ameliorate the detrimental shuttle effect because of its strong attraction to polysulfides according to our previous study. We also applied this mesoscale model to evaluate the surface passivation of the silicene-based cathode for Li−S batteries.18 It was found that the silicene cathode suffers from severe surface passivation due to the strong attraction between polysulfides and the substrate, and the increase in the operating temperate cannot alleviate the surface passivation. Cui and his colleagues also found that metal chalcogenides demonstrate strong affinity to polysulfides.16 Therefore, based on the present mesoscale interface model, it can be inferred that these cathode materials will also likely suffer from severe passivation. Beyond surface passivation, there are other temperaturedependent physicochemical interplays (i.e., electrochemical reaction rates, side reaction rates, and species diffusivity) that can potentially affect the Li−S battery performance. The present mesoscale interfacial model can be coupled with a macroscale performance model and cathode microstructure analysis to identify the dominant physical factors determining the Li−S battery performance. For typical carbon-based cathodes, the cathode surface is usually decorated with functional groups to trap polysulfides because the functional groups exhibit strong attraction to polysulfide molecules.46−48 The mesoscale model is also employed to evaluate the effect of the population of functional groups on the surface passivation. In these mesoscale simulations, functional groups are randomly distributed on the cathode surface. It is also hypothesized that the Li2S molecule cannot desorb or diffuse once it is situated at a functionalized site. Figure 8a clearly shows that saturation time is dependent on the population of the functionalized site. The cathode surface with more functional groups is passivated much faster. Functional groups can serve as nucleation agents, which can produce many small Li2S islands on the carbon surface and facilitate the lateral growth of the Li2S precipitation. Hence, a typical carbon cathode decorated with functional groups may also suffer from severe passivation. In summary, a strong affinity of the cathode surface to polysulfides is required to mitigate the shuttle effect. However, this will also result in faster and

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CONCLUSIONS Li2S film formation and growth involve Li2S molecule adsorption, diffusion, and desorption, which happen at atomistic scale. The kinetic rates of these events are functions of macroscale properties including reactant concentrations and ambient temperature. In the present work, an interfacial model is developed to elucidate the surface passivation due to the growth of Li2S film on the carbon-based cathode surface. Cathode microstructure properties (i.e., pore volume and surface area) are also incorporated in the mesoscale interfacial model. The current work focuses on understanding the effect of S2− concentration and temperature on Li2S film growth and resulting surface passivation. The low S2− concentration can 5269



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lower the adsorption rate, which leads to inhibiting the formation of Li2S nucleation seed and the growth of Li2S film. An appropriate temperature is also required to reduce the adversely surface passivation. At a low-temperature condition, Li2S molecules are frozen on the carbon surface due to the low desorption rate, and lots of nucleation seeds form on the surface. Li2S desorption becomes more active as temperature increases. Therefore, the formation of nucleation seeds is inhibited, and only a few seeds can grow large, which leads to a heterogeneous film growth. The heterogeneous film growth can facilitate the thickness growth and inhibit the lateral growth of Li2S islands, which consequently defers cathode surface passivation. The geometric properties of cathode microstructure also affects the Li2S film growth. It is found that the high specific surface area is helpful for alleviating the surface passivation. Functional groups are usually employed to reduce the shuttle effect, but a high population of functional groups can lead to a fast surface passivation.

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REFERENCES

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsami.6b15066. Schematic illustration of transition kinetics (Figure S1), schematic illustration of the data flow of the whole simulation process (Figure S2), and the effect of the size of the computational domain on the simulation stability (Figure S3) (PDF)

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Research Article

AUTHOR INFORMATION

Corresponding Author

*Email: [email protected]. ORCID

Partha P. Mukherjee: 0000-0001-7900-7261 Notes

The information, data, or work presented herein was funded in part by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The information, data, or work presented herein was funded in part by the Office of Energy Efficiency and Renewable Energy (EERE), U.S. Department of Energy, under Award DEEE0006832. Supercomputer resources from Texas A&M University High Performance Computer are gratefully acknowledged. The authors thank Dr. Perla B. Balbuena from Texas A&M University for helpful discussions. 5270


Research Article

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