Transport Properties of Polysulfide Species in Lithium-Sulfur Battery Electrolytes: Coupling of Experiment and Theory.

A comprehensive experimental and theoretical analysis of the isothermal transport of species for the two model ternary-electrolytes with LiTFSI-Li2S4/dioxolane (DOL)-dimethoxyethane (DME) and LiTFSI-Li2S6/DOL-DME formulations is presented. An unambiguous picture of the polysulfide's mobility is set forth after a detailed investigation of the macroscopic transference number and diffusion coefficients. The new findings of incongruent diffusion for Li2S4 species and high significance of cross-term diffusion coefficients reformulate a fledgling view of the prevalent redox-shuttle phenomena. The practical implications of this complex mechanism are discussed in detail.

Introduction

Successful penetration of lithium–sulfur (Li–S) technology into the rechargeable battery market could serve the thirst for higher energy density battery systems in the electric-transport sector. These batteries that utilize lithium metal as the negative electrode and sulfur as positive electrode benefit from high theoretical specific capacity and energy density compared to lithium-ion batteries, coupled with low cost.[1−3] However, before their practical realization, there are many hurdles to overcome such as the insulating character of the active material end members (sulfur and Li2S) on discharge and charge;[4] the corresponding large volume change;[5] lithium dendrite formation[6] during cell operation; and—most importantly—dissolution of the intermediate lithium polysulfide redox species into the electrolyte.[7] Unlike conventional Li-ion battery technologies, in a Li-sulfur battery, formation of a stable anode/electrolyte interface is mainly challenged by the intermediate species produced at the cathode. Understanding the underlying mechanisms of operation in Li–S cells especially remains a major obstacle to their continued improvement.[8] Extensive research is currently ongoing to minimize lithium polysulfide shuttles in Li–S batteries and to eliminate all its concomitant risks to the battery state of health. Much effort has been expanded in attempts to confine the soluble polysulfides via modification of cathode and cell design.[9−11] Some of these approaches include physical entrapment[12,13] or chemical adsorption[14,15] of polysulfides within the cathode network.

Moreover, electrochemical and operando spectroscopic studies reveal that the exact composition of these intermediates is solvent dependent and can be influenced by a series of chemical disproportionation reactions in the electrolyte.[16,17] Lu et al. used a rotating-ring disk electrode technique to probe the kinetics of the electrochemical reactions in Li–S cells,[18] while other researchers[19−21] focused more on the dominant soluble polysulfide species. These are effectively Li2S6 and Li2S4 in solvents of intermediate polarity such as dioxolane/dimethoxyethane (1:1 DOL/DME), which serves as the classical Li–S battery electrolyte, where lithium bis-trifluoromethane-sulfonimide (LiTFSI) is the conducting salt. Many studies show that Li2S8 is unstable toward disproportionation to these species, and Li2S2 is either unstable and/or insoluble.[20] In highly polar media such as dimethyl amide (DMA) and dimethyl sulfoxide (DMSO), the hexa-sulfide and tetra-sulfide dianions undergo cleavage to their monoanion radicals. In such media, S3–• the product of S6–2 cleavage is especially prominent and is strongly favored in dilute solutions. This gives rise to the characteristic deep blue color of such solutions.[22,23] However, cleavage in DOL/DME is not favored at room temperature, and hence the concentration of the trisulfide radical is neglible.[24,25] Despite these many experimental studies to elucidate polysulfide speciation, very limited modeling work on Li–S batteries has been conducted that could provide an understanding of polysulfide transport properties, and hence their behavior in the cell. Only a few seminal and important studies have been reported,[7,26,27] contrary to lithium ion battery systems.[28−31] An accurate picture of species transport in the electrolyte is not only of fundamental importance, but is a prerequisite for any meaningful macroscopic modeling/optimization of the cell performance in a Li–S battery.[32−34] In this regard, experimental measure of a minimum number of the ion-transference numbers and diffusion coefficients for neutral combination of the ions, together with the ionic conductivity of the electrolyte is required.

Here, for the first time, we determine a complete set of transport properties for the binary electrolytes composed of Li2S6, Li2S4 (and the electrolyte salt, LiTFSI) dissolved in DOL/DME (1:1). These measurements are performed according to the original approach developed by Ma and Newman.[35] The theoretical/experimental frames provided by the thermodynamics of irreversible processes are further applied to estimate the transport properties for the more practical ternary cases where the polysulfide and lithium salt are both present in the electrolyte.[36]

Results

The restricted diffusion (RD), transference-polarization (TP), and concentration-cell (CC) experiments were all carried out on 1 mL of the electrolyte confined inside a Teflon (PFA) Swagelok cell. A schematic of this symmetric cell is presented in Figure where a 12 mm PFA tube with an internal diameter of 10 mm is positioned between the two lithium electrodes and filled with the electrolyte. In the concentration-cell (CC) experiments, the internal PFA tube is divided in two compartments separated with a 3 mm ultrafine porous glass frit to avoid mixing among the two compartments. The binary and ternary electrolytes with Li2S (n = 6, 4) and LiTFSI as solutes were prepared in a 1,3 dioxolane/1,2 dimethoxyethane (DOL/DME) solvent (1–1 volume ratio) over a concentration range of 0.05–1.1 M in solute. Additional details are provided in Experimental Methods (see below).

Figure 1

Schematic of the Swagelok cell used in this study for the electrochemical characterization of the electrolytes.

Development of the Theoretical Framework

In a Li–S battery, the concentrated binary electrolyte (i.e., a primary lithium salt dissolved in a solvent) upon assembly turns into an electrolyte with a single cation (Li+) and multiple anions (i.e., polysulfides in addition to the primary lithium-salt anion) over the course of battery operation.[20] Hence, in a Li–S battery and in the presence of n independent series of polysulfides, transport properties are required to describe the isothermal transport of species in the electrolyte. This means that in the simplest case where only one of the high-order lithium-polysulfides (Li2S, 4 ≤ n ≤ 8) is dominant, one is left with a ternary electrolyte and six transport properties to be measured.

Here, our target is to provide consistent estimates of diffusion coefficients and transference numbers for a typical electrolyte used in Li–S cells. To do so, first, an appropriate formulation of species transport is presented for a general ternary electrolyte composed of a primary lithium salt, a single lithium-polysulfide (Li2S), and a solvent. Further, the two approaches of Miller[37,38] and Ma et al.[35] are combined and adopted to the ternary electrolytes of LiTFSI and Li2S6 (Li2S4) dissolved in DOL/DME (namely, the binary coefficients were determined with the aid of three orthogonal experiments as set forth by Ma et al., and the ternary data are estimated according to Miller et al.).

Fundamental Transport Coefficients in a Ternary Electrolyte with a Common Cation

A ternary electrolyte with a common cation (C) and A1 and A2 as two anions can be represented as the following:where, ϑ and ϑ are the stoichiometries of the cation and anions in the ith solute (i = 1, 2), and the charge numbers of the common cation and two anions are represented by z1, z2, and z3, respectively. Isothermal transport of species in such a system is described by two independent transference numbers, four diffusion coefficients for neutral combinations of ions (out of which three are independent) and the ionic conductivity of the electrolyte. These measurable macroscopic properties are expressed with the aid of nine fundamental transport coefficients (l) where only six are independent according to the Onsager reciprocal relations.[36] In a solvent-fixed frame (SF), hereafter represented by 0 in the superscript, the flux equations for the ions (i.e., JC0, JA10, JA20) in one dimension arewhere I is the total current density and F is the Faraday constant. In these flux equations, ∇μ12 and ∇μ13 are the electrochemical potential gradients of the neutral combination of the common cation (denoted as subscript 1) with the first (2) and second (3) anions, respectively, and are related to their concentration counterparts (i.e., ∇c12, ∇c13) according to the following equation:[39]where δ is the Kronecker delta function, R is the universal gas constant, and T is temperature. The molar concentrations and mean-molar ionic activity coefficients of the two solutes (i.e., Cϑ1,cA1ϑ1,a and Cϑ2,cA2ϑ2,a) are represented by (c12, c13) and (f±12, f±13), respectively.

The transference numbers (t0) and fundamental diffusion coefficients () are expressed with the aid of more fundamental transport coefficients (l0) set forth by the thermodynamics of irreversible processes according to eqs and 8, respectively.[36−38]where, in eq and 8, κ is the electrolyte conductivity:However, the transference numbers and diffusion coefficients are dependent on the chosen frame of reference. Transference numbers are experimentally measured in a solvent-fixed (SF) frame, whereas the practical diffusion coefficients are usually measured in a volume-fixed frame of reference (VF). Practical diffusion coefficients (D) and fundamental ones () are related according to eq

It is more convenient to set forth the transport equations in SF and further use the following equation to transform the practical diffusion coefficients between the two frames of reference (i.e., SF and VF):[40]where V̅12 and V̅13 are the partial molar-volumes of Cϑ1,cA1ϑ1,a and Cϑ2,cA2ϑ2,a, respectively, and are experimentally measured with the aid of the following equation:[41]where M12 and M13 are the molar masses of Cϑ1,cA1ϑ1,a and Cϑ2,cA2ϑ2,a, respectively, and ρ is the density of the ternary electrolyte.

Note that in Miller’s original treatment of ternary electrolytes with a common anion,[38] he distinguished between the chemical and electrical potentials in the entropy production term. This separation is unnecessary,[39] though similar results are obtained when the thermodynamic force is defined in terms of the electrochemical potentials.

Estimation of Ternary Transport Properties from Experimental Binary Data

The six fundamental transport coefficients (l0) for the system defined by eqs and 2 are estimated based on the measured coefficients (l0,b) for the two isolated binary systems, defined by eqs and 2, and application of the following correlations after Miller:38where l+ −0,b, l+ +0,b, and l– −0,b are the cation–anion, cation–cation, and anion–anion interaction coefficients in the binary electrolytes, respectively. These binary coefficients are evaluated at a total (N) number of equivalents in the ternary electrolyte:

In eqs –16, x12 and x13 are the equivalent fractions and are defined as the following:

Transference numbers, conductivity, and fundamental diffusion coefficients () for the ternary system (eqs and 2) are readily available (eqs –9) after estimation of l0. Derivatives of mean-molar ionic activity coefficients (f±12 and f±13) are required, however, in order to obtain practical diffusion coefficients (D0). Providing that these thermodynamic parameters are known for the binary constituents (f±12,b and f±13,b), the Scatchard’s neutral-electrolyte description can be used to estimate f±12 and f±13 in the ternary system:[42]where c0 and (c0b)1 are the solvent concentrations in the ternary and binary electrolytes, respectively, ρ0 is the solvent density, and M0 is molar mass of the solvent. In eqs and 21, all the binary parameters are evaluated at the total ionic-strength of the ternary electrolyte and y defines the ionic-strength fraction[42] of each solute in the ternary electrolyte according to

Fundamental Transport Coefficients for the Binary Electrolytes of LiTFSI and Li2S (n = 6, 4) in DOL/DME

Here, we are interested at experimental measure of l+ −0,b, l+ +0,b, and l– −0,b for the three binary systems described by eqs –25

It is straightforward to show that in a binary electrolyte, the three fundamental transport coefficients can be expressed as a function of three macroscopic and measurable transport properties (i.e., κb, t0,b, and DV,b) in eq where V̅0b and c0b are the partial molar-volume and concentration of the solvent, respectively, and cb is the solute concentration in the binary electrolyte.

The value κb is readily attained with the application of AC-impedance spectroscopy. The high frequency intercept on the x (real)-axis in a Nyquist plot is a sufficiently accurate measure of the ohmic resistance of the electrolyte. This resistance, together with the known geometry of the cell, provides us with the specific ionic conductivity of the electrolyte which is independent of the frame of reference used during the measurement. However, the experimental measurement of t0,b and DV,b is not trivial. In the following, the elegant approach originally developed by Ma et al.[35] and lately improved by Hafezi and Newman[43] is applied to the case of binary electrolytes investigated in this study (eqs –25). Here, and for the sake of simplicity, the solvent system (DOL/DME) is treated as a single component. The transference number of lithium ions (t+0,b) and the mean-molar ionic activity coefficient of the solutes (f±b) are coupled together according to eq in the absence of current (I = 0)[41]where Φ is a well-defined potential in the electrolyte with respect to a lithium reference electrode.

Application of eq to the results from a series of concentration-cell experiments provides one with the product of thermodynamic factor () and the transference number of the anion (i.e., 1 – t+0,b). In the concentration-cell experiments, the potential difference is recorded (I = 0) between the two lithium electrodes (ΔΦ) in a cell filled with different concentrations of a given solute at the left (cb) and right (cb) compartments. Transference-polarization (TP) tests are performed to compensate for the dearth of data regarding the thermodynamic factor of the solute (which could be obtained independently via vapor pressure or isopiestic measurements with great effort). In TP experiments, a short pulse of current is applied to an equilibrated symmetric cell made of the lithium electrodes and the binary electrolyte under study at a given initial concentration (c∞b). The difference of solute concentration (Δcb) between the vicinity of the two electrodes created by the current pulse is[43]where tp is the pulse duration and D∞V,b is the diffusion coefficient of solute in the electrolyte at cb = c∞b and in VF. τ is a dimensionless time and is defined by eq :

In eq , t is the time elapsed from the beginning of the TP experiment and extends to the relaxation period to the point where the cell retrieves its equilibrium (Δcb = 0). During the TP experiment, this is the potential across the cell and not the concentration difference which is recorded. For sufficiently small perturbations (I√tp → 0), Δcb can be evaluated from eq :where the denominator on the right-hand side of the equality is the slope of a ΔΦ–ln cb plot evaluated at cb = c∞b and is accessible through the data analysis of the concentration-cell experiments. Accordingly, combination of eqs and 30 results in the following correlation between ΔΦ and τ in TP experiments

The slope of ΔΦ–τ plots are calculated for a series of TP tests with different values of I√tp. The quantity inside the bracket in eq is then plotted against I√tp and the resulting slope represented by m is used for unequivocal resolution of transference number:

An a priori knowledge of D∞V,b enables us to calculate both the thermodynamic factor and the transference number at the same concentration of solute by the application of eq and eq , respectively. Here, D∞V,b is obtained with the application of the method of the restricted diffusion (RD) to a similar cell used in TP experiment.[44] Contrary to the TP experiment where tp is in the order of few minutes, in RD, the cell is held under polarization for a very long time (i.e., few hours). The natural logarithm of the potential relaxation is plotted against time of which a linear trend is found toward equilibrium. The slope of the linear tail (sD) is related to D∞V,b according to eq where L is the distance between the two electrodes.

Discussion

It is important to note that the application of eqs –33 for the case of polysulfide systems (eqs and 25) is subject to two main assumptions. First, any disproportionation reactions cannot be explicitly accounted for owing to the complexity involved (and lack of experimental data on their kinetics), and second, the flux of polysulfide anions (i.e., S4–2 and S6–2) is taken to be zero at both electrodes. A more comprehensive analysis would be possible only with a priori access to the kinetic parameters of the polysulfides in the disproportionation and side reactions at the bulk of electrolyte and surface of the lithium electrode, respectively. We believe these are both reasonable assumptions. Under dilute conditions, and in a solvent of intermediate polarity such as DOL/DME, disproportionation reactions at static Li/S ratios as used here are not expected to be high.[45]

The macroscopic transport coefficients for the three binary electrolyte systems (i.e., eqs –25) at 25 °C and for solute concentrations in the range of 0.1–1 M are presented in Figure a–c. The diffusion coefficient of the lithium salt and lithium polysulfides features a decreasing trend upon the concentration increase, and the average DV,b is the same order of magnitude (3.5 × 10–10 < (DV,b)ave < 6.5 × 10–10 m2/s) for the three solutes (Figure a). LiTFSI and Li2S6 have the highest and lowest DV,b over the whole concentration range, respectively. The transference number of lithium ions in LiTFSI-DOL/DME is significantly higher than those of polysulfide systems and falls in a range of 0.47–0.57. The fraction of current (in the absence of a concentration gradient) carried by Li+ in Li2S6-DOL/DME is in the range of 0.001–0.2, whereas the negative transference numbers clearly distinguish the Li2S4-DOL/DME among the three binary systems, i.e., −0.39 < t+0,b < −0.32 (Figure b). These small transference numbers impose a very steep gradient of solute concentrations to the polysulfide binary systems under current control and the Li2S4 species is clearly the most vulnerable. The ionic conductivity (Figure c) of the electrolyte in LiTFSI system is well above 1 mS/cm over the whole concentration range and increases to 14.7 mS/cm at 1 M. The average ionic conductivity in Li2S4-DOL/DME and Li2S6-DOL/DME systems are less than 20% and 29% of the corresponding value in LiTFSI system, respectively. Table summarizes the measured electrolyte density and partial molar volumes of the solute in the binary and ternary electrolytes.

Figure 2

Transport coefficients: (a) practical diffusion coefficient in a volume-fixed frame of reference, (b) transference number of lithium ions in a solvent-fixed frame of reference (c) electrolyte ionic conductivity—in the binary electrolytes of LiTFSI-DOL/DME (dash-dot-○-), Li2S4-DOL/DME (dot-△-), and Li2S6-DOL/DME (dash-*-) at T = 25 °C. Markers are experimental data and lines are shape-preserving fits only for improved visualization.

Table 1

Calculated Partial Molar Volumes of Solvent (i.e., DOL/DME) and Solutes in the Binary and Ternary Mixtures of Li2S4, Li2S6, and LiTFSIa

	component
solution	V̅Li2S4 (cm3/mol)	V̅Li2S6 (cm3/mol)	V̅LiTFSI (cm3/mol)	V̅DOL/DME (cm3/mol)	solution density (g/cm3)
DOL/DME-Li2S4	44			84	ρ = 0.0996c13 + 0.9647
DOL/DME-Li2S6		65		84	ρ = 0.1438c13 + 0.9638
DOL/DME-LiTFSI			134	83	ρ = 0.157c12 + 0.968
DOL/DME-Li2S4–LiTFSI	38		128	84	ρ = 0.1076c13 + 0.1638c12 + 0.9644
DOL/DME-Li2S6–LiTFSI		75	125	83	ρ = 0.1336c13 + 0.1656c12 + 0.9689

Calculations are based on the solution densities measured at 25 °C. Individual solute concentrations are between 0.1 and 1 M.

The thermodynamic factor () of the three solutes in DOL/DME are presented in Figure a. The thermodynamic factor increases with concentration for the three binary systems and significantly deviates from the value expected for an ideal solution (i.e., 1) at lower concentrations. The mean-molar ionic activity coefficients are available by integration of the curves in Figure a and with respect to the secondary state of reference. Figure b presents these activity coefficients for the three binary systems. The activity coefficients are far from unity for the three electrolyte cases and the highest degree of nonideality belongs to the polysulfide solutions. Higher gradients of potential in these electrolytes are further expected as a direct consequence of their extreme nonideality. Application of the Scatchard’s neutral-electrolyte description (i.e., eqs –22) to the binary data (i.e., Figure b) predicts a similar situation (Figure S1) for the ternary electrolytes of LiTFSI with Li2S (n = 6, 4).

Figure 3

(a) Thermodynamic factor and (b) mean-molar ionic activity coefficients of solutes in the binary electrolytes of LiTFSI-DOL/DME (dash-dot-○-), Li2S4-DOL/DME (dot-△-), and Li2S6-DOL/DME (dash-*-) at T = 25 °C. Markers are experimental data and lines represent the empirical fits or processed data.

The presence of polysulfides in the ternary electrolytes of LiTFSI is concurrent with a substantial change in the mobility of lithium ions. Figure a,b and Figure d,e present the transference numbers of lithium ions and polysulfides in the ternary electrolytes of LiTFSI-Li2S4-DOL/DME and LiTFSI-Li2S6-DOL/DME, respectively. Analogous to the trends found for the binary electrolytes of lithium-polysulfides (Figure b), the lithium ions have a higher transference number in the ternary electrolyte of Li2S6 (Figure d) in comparison to the Li2S4 ternary system (Figure a). The lithium transference is as low as −0.2 for extremely low concentrations of LITFSI and polysulfide concentrations above 0.1 M. The contribution of polysulfide anions in the ionic current is not negligible (Figure b,e) even at very low concentrations of Li2S (n = 4, 6). A better illustration of the polysulfide’s detrimental impact on the transference of lithium ions is presented in Figure c,f. In these figures, the ratio of ternary and binary transference numbers of lithium ions for the same concentration of LiTFSI is presented for the ternary electrolytes based on Li2S4 (Figure c) and Li2S6 (Figure f). Introduction of the Li2S (n = 4, 6) into the binary electrolyte of LiTFSI is concomitant with up to 20% and 80% of reduction in the transference number of lithium ions for polysulfide concentrations as low as 0.01 and 0.1 M, respectively. At lithium salt concentrations below 0.5 M, the onset of polysulfide-induced decline in the cationic transference number of the LiTFSI binary electrolytes stands at a very low concentration of polysulfide species, e.g., 20% decrease in tLi0 for a 0.3 M LiTFSI is observed as early as polysulfide concentration exceeds 0.005 M.

Figure 4

Lithium transference numbers at T = 25 °C, in the ternary electrolytes (a) LiTFSI-Li2S4 and (d) LiTFSI-Li2S6 and their ratio with respect to the corresponding values in a binary electrolyte of LiTFSI at the same concentration of LiTFSI as in those of ternary (c) LiTFSI-Li2S4 and (f) and LiTFSI-Li2S6. Polysulfide transference numbers in the ternary electrolytes of (b) LiTFSI-Li2S4 and (e) LiTFSI-Li2S6.

The analysis of diffusion in a ternary electrolyte is not trivial since a solute diffuses not only as a response to concentration gradient of its own, but also to that of the second solute (eqs –5). The practical coefficients characterizing the diffusion rate of LiTFSI and Li2S (n = 4, 6) under their own concentration gradient, i.e., D220 and D330, respectively, are presented in Figure . LiTFSI has slightly higher diffusion coefficients (D220) in the presence of Li2S4 (Figure a) rather than Li2S6 (Figure c). The diffusion behavior (D330) of Li2S4 and Li2S6 in ternary electrolytes of LiTFSI is significantly different. In LiTFSI-Li2S6-DOL/DME ternary electrolyte, the diffusion coefficient of Li2S6 (D330 in Figure d) is superior to that of LiTFSI (D220 in Figure c), up to 1 order of magnitude. However, the incongruent diffusion of Li2S4 (D330 in Figure b) is dominant for polysulfide concentrations lower than 0.01 M and higher than 0.1 M over the full range and cLiTFSI < 0.3 M, respectively.

Figure 5

Practical diffusion coefficients of LiTFSI (D220) at T = 25 °C in ternary electrolytes of (a) LiTFSI-Li2S4 and (c) LiTFSI-Li2S6 and those of polysulfides (D330) in (b) LiTFSI-Li2S4 and (d) LiTFSI-Li2S6.

Conclusions

Providing D330 < 0, i.e., incongruent diffusion, the Li2S4 species diffuse against their own concentration gradient. This phenomenon is in favor of polysulfide retention at the cathode and against polysulfide crossover toward the lithium anode during cell discharge. The above-mentioned D330 behavior suggests that the kinetics of Li2S6 to Li2S4 reduction has a pivotal role in the onset of polysulfide crossover phenomena. A longer residence time of Li2S6 at the cathode during cell discharge, i.e., sluggish kinetics of Li2S6 reduction, is readily followed by the fast crossover of these species toward the anode. On the contrary, under the fast kinetics of Li2S6 reduction, Li2S4 species have a very low tendency to shuttle toward the anode during cell discharge. Our diffusion analysis reveals the significant share of Li2S6 in the shuttle mechanism and further aging of the lithium–sulfur batteries with a similar electrolyte formulation (i.e., LiTFSI-DOL/DME). The importance of cross-term diffusion coefficients cannot be overlooked. This is clearly evident from the magnitude orders of D230 and D320 presented in Figure S2 of Supporting Information. Very high values of D320 (Figure S2b,d) indicate that a subtle gradient in the concentration of LiTFSI has a significant impact on the diffusion of polysulfide species (i.e., both Li2S4 and Li2S6). Accordingly, higher rates of cell discharge and charge are counterintuitively in favor of polysulfide retention and crossover, respectively. This might suggest that the relaxation periods after slow rate of discharge and high rate of charge are detrimental to the battery state of health. In contrast to the other two transport properties and not surprisingly, the ionic conductivity of the electrolyte improves upon polysulfide build-up: especially for lower concentrations of LiTFSI (Figure S3).

While it is risky to speculate on the underlying difference in the behavior of the two polysulfides that this analysis clearly points to, we note that under the relatively dilute conditions employed here (<1 M polysulfide) we can expect disproportionation to occur, although it would be less compared to more concentrated solutions. Thus, S62– is probably less prone to disproportionation in DOL/DME—generally being subject to cleavage to S3–• only in EDP solvents[25]—whereas Li2S4 is likely to be the end polysulfide that precedes precipitation of Li2S via disproportionation, as it represents the polysulfide species at the inflection point in a theoretical discharge profile.[20,24−26,45] Computational studies may shed light on the complex dynamics of this system. Further analysis of the system in electron-pair donor (EPD) solvents such as DMSO and DMA where the trisulfide ion dominates the kinetics would be expected to yield very different results, and will be the subject of future studies.

Experimental Methods

All experiments were conducted at 25 °C inside an argon-filled glovebox with oxygen and water contents below 3 ppm. A VMP3 potentiostat was used for the AC-impedance measurements and the galvanostatic polarization studies, together with relaxation tests performed with the aid of a Macpile potentiostat. The density of the electrolytes was measured using an oscillating U-tube digital density meter (DMA 35, Anton-Paar).

To prepare the polysulfides, precise stoichiometric amounts of lithium (as the stabilized powder; FMC Corporation), sulfur, and/or LiTFSI together with the solvent were mixed inside a magnetically stirred glass vial for 4 days. The electrolytes were filtered to remove any leftover reactants.

The 1.27 cm2 circular lithium electrodes were punched out from a lithium foil with a thickness of 150 μm. All the cells were subjected to three formation cycles after assembly in order to partially stabilize the surface of lithium electrodes. A formation cycle consisted of a charge and discharge segment at 0.05 mA and continued for 0.5 h in each segment. The galvanostatic polarization pulses were 0.1–2 mA in magnitude and continued for 20 min and 10 h in the experiments involved in the measure of the transference number and diffusion coefficient, respectively. Relaxation was recorded until equilibrium was reached both during concentration cell studies and after galvanostatic polarization periods in TP and RD. The AC-impedance spectra were obtained over a frequency range of 200 kHz–50 mHz and with a potential amplitude of 15 mV.

The ionic conductivity of three ternary samples (i.e., (0.2 M LiTFSI, 0.2 M Li2S6), (0.4 M TFSI, 0.1 M Li2S6), (0.3 M TFSI, 0.2 M Li2S6)) were measured in order to check the accuracy of the prediction methodology proposed in this work. The predictions overestimate the experimental data with a maximum error of 20%, which is reasonable considering the experimental protocol.

A representative set of data from the restricted diffusion, transference polarization, and concentration-cell experiments are included in the Supporting Information for the Li2S6 electrolytes. Figures S4 and S5 present the data from the TP and RD experiments, respectively, for the binary electrolyte of Li2S6 at 0.5M. The results of the concentration-cell experiments are summarized in Figure S6, for the concentration cells at five different concentrations of Li2S6, i.e., 0.1, 0.3, 0.5, 0.7, and 1 M.