Sulfur Battery by Small Angle Neutron

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Operando Analysis of a Lithium/Sulfur Battery by Small Angle Neutron Scattering Sebastian Risse, Eneli Härk, Ben Kent, and Matthias Ballauff ACS Nano, Just Accepted Manuscript • DOI: 10.1021/acsnano.9b03453 • Publication Date (Web): 23 Aug 2019 Downloaded from pubs.acs.org on August 24, 2019

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Operando Analysis of a Lithium/Sulfur Battery by Small Angle Neutron Scattering Sebastian Risse a†, Eneli. Härk a, Ben Kent a and Matthias Ballauff a,b Institute for Soft Matter and Functional Materials, Helmholtz-Zentrum Berlin für Materialien und Energie, Hahn Meitner Platz 1, 14109 Berlin, Germany. Institute of Physics, Humboldt-University Berlin, Unter den Linden 6, 10099 Berlin, Germany. † Corresponding author: [email protected]. a

b

ABSTRACT

This study reports the use of operando small angle neutron scattering to investigate processes in an operating Li/S battery. The combination with impedance spectroscopy yields valuable insights into the precipitation and dissolution of lithium sulfide during ten cycles of galvanostatic cycling. The use of deuterated electrolyte increases strongly the sensitivity to detect the sulfur and Li2S precipitates at the carbon host electrode and allows us to observe the time dependent initial wetting of the system. No correlation of the scattering signal of the micropores with neither lithium sulfide nor sulfur are observable during the whole course of the experiment. Hence both reaction products do not precipitate inside of the microporous structure though on the outer surface of the micrometre sized carbon fibres used in this study. The excellent scattering contrast allows a detailed analysis of the formation and dissoulution process of nanoscopic Li2S structures. While lithium sulfide particles grow homogeneously during the precipitation period, smaller Li2S particles dissolve first followed by a sudden dissolution of the larger Li2S particles. Keywords: operando analysis, small angle neutron scattering, lithium sulfur battery, impedance spectroscopy, nanoscopic lithium precipitation, microporous carbon Lithium sulfur (Li/S) batteries are a promising candidate for the next generation energy storage systems. They exhibit a theoretical gravimetric energy density that is five times higher than the theoretical value of state-of-the-art lithium ion batteries.1–3 The operation temperature of Li/S cells can be as low as -50°C and sulfur is an abundant element as well as environmentally friendly. However, the major drawback of this system is a pronounced capacity fading with cycle number which relates to complicated processes that take place within the cell.4 During the operation of the cell, lithium sulfide (Li2S) and sulfur (S8) form at the end of the discharge and charge step, respectively, and our understanding of these processes is still

lacking. Operando methods that yield insights into the formation and dissolution of solid products are central for a better understanding of capacity fading.5 In particular, operando X-ray diffraction (XRD)6–10 and X-ray imaging methods11–13 have been used to trace the appearance/disappearance of solid Li2S and S8 while operating the cell. The main result of these studies is the observation that macroscopic β-sulfur with a size up to several micrometers12 is formed while Li2S is precipitated in form of crystals of only a few nanometers 14. However, no information is available from these methods on the locus of precipitation. Since S8 and Li2S form at the cathode, which in general consists

Fig.1 Scheme of the expected small angle neutron scattering curves for the cases if sulfur or lithium sulfide precipitate inside or outside of the micropores of the carbon fiber electrode. a) Scanning electron microscopy image of the cloth-like electrode material ACN-157-15 by Kynol®. b) The carbon matrix mainly consists of slit-like micropores and lateral structures on the nanoscale. c) Simulated contrast match of the micropore scattering signal (black) by the deuterated electrolyte (blue). d) Case A: Precipitation of S8 or Li2S inside of the micropores would recover the micropore scattering multiplied by a constant factor (strong correlation with micropore scattering). e) Case B: No correlation with micropore scattering means precipitation of S8 or Li2S particles outside of the micropores. Both red curves were simulated with the Schultz-Zimm model by using a distribution parameter of 25% and a spherical particle diameter of 2 nm and 12 nm for the “sub-10 nm particle” curve and “>10 nm particle” curve, respectively. A small constant background and a q-4 term were also added to simulate realistic data.

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of microporous carbonaceous materials with a high surface area, the question arises whether both solid products precipitate within the pores or not. Small angle neutron scattering (SANS) is the ideal tool to answer this question. SANS and small-angle X-ray scattering (SAXS) have been used recently to elucidate the microstructure of the carbon materials used as cathodes for Li/S-cells.15–17 Both methods give quantitative information about the internal surface as well as of the average size and shape of the pores. While photons are scattered at the electron shell of the atom in SAXS, neutrons are scattered at the core of the atom in SANS. This major difference leads to complementary applicability of these techniques due to clearly different interaction cross sections. The distinct advantage of SANS over SAXS is the high penetration depth and the low interaction energy of several tenth meV with matter. Many materials used as cathodes consist of partially graphitized and highly disordered carbon that contains mainly micropores with an average pore size around one nanometer and less. The scattering contribution of these micropores is strong at medium and high scattering angles where they give a characteristic scattering signal. Figures 1a,b display a scheme of the microscopic structure resulting from the previous study.15 In particular the SANS technique allows us to match the scattering density of carbon with deuterated solvents so that

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the scattering contribution of the microporous host matrix significantly reduces (figure 1c, blue curve). Hence, the scattering intensity of a Li/S-cell should be at a minimum at the half-charged state where both solid products are not present. Precipitation of S8 or Li2S will lead to a new phase, which will be clearly visible in the SANS-experiments. Here we present an operando SANS-study of a Li/S-cell. The main question here is the locus of the precipitation of both solid materials, that is, will S8 or Li2S precipitate within or outside of the micropores of the carbonaceous cathode. Figures 1d,e depict the possible outcomes for the two scenarios: In case A (figure 1d) both materials precipitated in the micropores, that is, directly at the surface of the cathode. Since the scattering contrast between carbon and sulfur or lithium sulfide is large (see table 1), there will be a pronounced signal from the micropores so that the scattering signal of the dry cathode should recover. It should be mentioned that the precipitation of small molecules of sulfur with a gravimetric density that differs by 50% compared to α-sulfur would still result in a significant intensity increase. When, on the other hand, precipitation takes place outside of the micropores in case B (figure 1e), the scattering signal is mainly due to the solid particles of S8 or Li2S. Possible scattering curves resulting for spherical particles of various size are shown in Figure S1a. Hence, both scenarios lead to different SANS-signal, which are clearly discernible.

Fig. 2 Summary of the operando neutron scattering experiment starting with a 0.1M Li2S8 solution. The upper row shows the voltage curve of the cycles 1-3 and 8-10. The red dots mark characteristic point on the voltage curve that coincide with local minima of the scattering intensity (vertical dashed lines). The inset numbers represent the capacity per each charge or discharge step in mAh/g of sulfur. The second row summarizes the SANS results. The periodic appearance of local maxima correlates well with the charged (S8) and discharged state (Li2S) of the operando cell. The precipitation of Li2S shows as expected the highest intensity due to its stronger contrast with the carbon matrix. The third and fourth row show the results of the solution resistance 𝑅𝑆 as well as 𝐴𝑊 and the distribution of relaxation times (DRT), respectively. These parameters were obtained by a fitting algorithm described elsewhere.18 The DRT plot is subdivided into slow and fast relaxation time regimes (horizontal dashed line). The dotted and dashed/dotted ellipses in the lower right corner of this figure 2 lithium sulfide respectively. highlight the charge transfer processes that are assigned to the phases sulfur and

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the fully discharged state and the dissolution of lithium sulfide. Thus, SANS clearly shows that the dissolution of lithium sulfide is not homogeneous. This could be explained by a higher stability of larger Li2S particles towards their dissolution and will be discussed in more detail at the end of the next section. The scattering intensity slightly increases again after the dissolution of Li2S (right vertical dashed line in figure 2) until the charged state is reached. This local maximum of the scattering intensity is less distinct as this for Li2S. This is caused on the one hand by the macroscopic precipitation of sulfur (>10 µm) as shown recently by operando X-ray imaging techniques.11,12 Because of the large size of these particles only their final slope is visible in the qrange of this experiment. On the other hand the lower contrast of the sulfur phase with respect to the deuterated electrolyte (see table 1) yields lower intensities. The scattering signal decreases again in the following discharge step and the pattern of the scattering intensity repeats as discussed above.

Results/Discussion

Multidimensional operando Analysis Figure 2 gives a general overview on the operando experiment and illustrates the first and last three cycles of the study. The first row shows the time dependent cell voltage during the galvanostatic cycling. The scattering intensity is displayed in the second row of this panel as a heat plot. The third row summarizes the solution resistance 𝑅𝑆 and the Warburg coefficient 𝐴𝑊 that results from the fitting procedure of the intermediately recorded impedance data as described in the experimental section. Selected impedance spectra are shown in figure S8 as Nyquist plots. The last row illustrates the time dependent charge transfer processes with the distribution of relaxation times 𝛾(𝜏). Thus, Figure 2 connects electrochemical information (voltage curve) with structure (SANS) and dynamic (charge transfer, ion concentration) insights. Figure 2 demonstrates that the operando cell shows an excellent performance with respect to electrochemical cycling. Thus, the capacity exhibits a value of more than 1200 mAh/g after the 10th discharge. Furthermore, the regular increase and decrease of the scattering intensity demonstrates immediately the reversibility of the charge and discharge of the cell. The mounting of the cell in the neutron beam just after the addition of the deuterated electrolyte allows us to monitor the wetting process during the open circuit (OCP) conditions within the first 22 hours. The scattering intensity decreases within the initial five hours accompanied by a drop of the OCP from 2.4 V to 2.2 V. The reason for this is the continuous wetting of the carbon electrode by the deuterated electrolyte. An increasing filling of the micropores by the matching solvent leads to a decrease of their scattering contribution (figure 1c). Concomitantly, the overall wetted surface increases, which in turn reduces the inner resistance of the cell. Hence, SANS can be used to assure a proper wetting of the porous cathode in the operando cell. Six selected SANS curves of the first ten hours of the experiment are plotted in figure S7 for better visualization. After the wetting period, the galvanostatic cycling starts with an initial charge to form solid S8 from the dissolved polysulfides (0.1 M Li2S8) in the electrolyte. The specific capacity of 230 mAh/g in this first charge step corresponds to 24.8 µM of electrons. This is in the range of the expected value of 22.6 µM that is equivalent to the absolute amount of sulfur (2.9 mg) in the cell. The voltage curve and the temporal evolution of the scattering intensity show a clear correlation for all cycles. In particular, there are two characteristic points on the voltage curve (red dots, vertical white dashed lines) that correlate to the scattering intensity around the discharged state. The first characteristic point is located between both discharge plateaus approximately at 2.050±0.01 V which is known as the transition from long to short chain polysulfides.19,20 The viscosity reaches a maximum at this point of the voltage curve as shown by Ding et al..21 While in-situ X-ray absorption6,22,23 and XRD studies8,14,24 show an onset of the formation of lithium sulfide at the middle of the second discharge plateau, the scattering intensity of this SANS experiment starts to increase from this characteristic voltage on. This can be attributed to the high contrast of lithium sulfide to the deuterated electrolyte that results in a high sensitivity towards lithium rich sulfur species (see table 1). The dissolution of Li2S is finished (second vertical dashed line) at the other characteristic point on the voltage curve with the value of 2.385±0.01 V. This point is characterized by an S-shape of the voltage curve (see right inset in figure 2, top row). This end of the dissolution process is in good agreement with previous in-situ XRD studies.8,14 Another feature that is present for all discharge steps is the appearance of a local maximum of the scattering intensity between

Evaluation of SANS Data This section describes the quantitative evaluation of the SANSintensities. The neutron beam penetrates different layers of the Li/S cell during the operando experiment, namely two aluminum windows, one Kapton foil, the metallic lithium chip, the PP separator a)

b)

Fig. 3 a) SANS curves of the cloth-like carbon electrode (ACN-157-15 by Kynol®) under different conditions. Black circles: Carbon in the operando cell after subtraction of the scattering contributions from both Al-windows, lithium anode, Kapton foil and PP (Celgard) separator. Green triangles: Scattering curve of carbon measured in a quartz cuvette. Orange diamonds: Background scattering contribution of the carbon electrode obtained by contrast matching (see figure S3 and ref.15). Red squares: Carbon electrode and electrolyte in the operando cell after a wetting period of 22 hours. b) Comparison between scattering curves after the 8th charge and discharge with the dry carbon host matrix. ∆𝐼inc marks the amount of the q-independent background that is introduced by the liquid electrolyte.

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(Celgard 2700), the d-electrolyte solution (as described in experimental section) and the dry carbon electrode (see figure 6b). Only processes at the carbon electrode contribute to changes of the SANS-intensity, all other cell components yield only a constant scattering signal in the observed q-range during the experiment that must be subtracted. The loose packing of the cloth-like carbon electrode is addressed by further normalization of the scattering intensity dΣ/dΩ(𝑞) to the apparent scattering volume to obtain the carbon mass normalized macroscopic cross-section dΣm/dΩ(𝑞). d𝛴m d𝛺

(𝑞) =

d𝜎 1 (𝑞) 𝜌app ∙ 𝑉skd𝛺

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squares, after 22h) carbon electrode in figure 4 shows that the scattering contribution of the micropores decreases by a factor of approximately 20. Although the pore scattering diminishes by 95%, there is still a contribution to the surface scattering of the wetted electrode indicated by a 𝑞 ―4 slope for low 𝑞-values (red solid line), which originates from macroscopic structures that were not fully enclosed by the electrolyte. The SANS intensities recorded during the galvanostatic cycling are always above this macroscopic scattering contribution of the wetted state. The discharged state (blue diamonds, figure 4) shows a clear shoulder at around 2 nm-1 while the SANS curve in the charged state exhibits a similar shape like the wetted carbon curve. This qualitative difference indicates already that lithium sulfide precipitates as nanoscopic structure, while sulfur forms large structures that give no significant scattering within the present 𝑞-range. This result is in good agreement with recent operando imaging studies 11,12 and operando X-ray diffraction results6,10,25 that show the macroscopic solidification of sulfur of several micrometer and the nanoscopic precipitation of Li2S, respectively. The scattering intensities of the last three cycles in the fully charged and discharged state are shown in figure S4 for comparison. Figure 4 shows that there is no correlation of the scattering curve of the dry carbon and the SANS curve of the Li/S cell in the charged or discharged state. The precipitation of sulfur or lithium sulfide in the micropores would recover the scattering curve of the dry carbon electrode multiplied by a constant factor (see figure 1d). Hence, neither sulfur nor lithium sulfide are formed in the micropores of the

(1)

Here 𝜌app is the apparent density measured by compressing a disk of the cloth-like electrode material between two rigid plates to its minimum thickness. 𝑉sk is the skeletal volume that is calculated with 𝑉sk = 𝑚Carb/𝜌sk. The skeletal density 𝜌sk was measured with a pycnometer and equals to 2.0 g/cm3.15 𝑚Carb is the mass of carbon that is exposed to the neutron beam. The mass normalized scattering intensity of the dry carbon electrode in the operando cell is shown in figure 3a (black open circles). The scattering contributions of the PP separator, the aluminum windows, the Kapton foil and the lithium metal chip were subtracted. This corrected curve is in an excellent agreement with the scattering curve of another dry carbon electrode from the same batch measured inside of a quartz cuvette (green filled circles, figure 3a) with the same SANS instrument. This demonstrates the precision of the subtraction applied and the negligible neutron absorption of 6Li. The scattering of the carbon electrode after the wetting period of 22 hours (red squares, figure 3a) with the deuterated electrolyte is also shown. Although the incoherent background introduced by the liquid electrolyte leads to a vertical shift of the scattering intensity, the matching of the microporous structure in the middle-q range is already apparent. The amplitude of the unavoidable incoherent contribution (∆𝐼inc) can be estimated with the aid of the background scattering curve of the carbon electrode (orange diamonds). This curve was obtained by following the data processing steps like in our previous study15 that is described in detail in the supporting information (Figure S3). This carbon background curve represents the scattering contribution of internal density fluctuations15 in the bulk carbon structure, which is assumed to remain constant during the whole galvanostatic cycling experiment. Since this constant scattering is always present, irrespective of whether contrast matching is applied or not, it has to be subtracted in a first step from all SANS curves. The respective values of ∆𝐼inc are also subtracted from all SANS curves in a second step to remove this not relevant scattering contribution. Figure 3b compares the scattering curves of the 8th charge and discharge step with the scattering intensity of the dry carbon before both subtraction steps are applied. A qualitative comparison with figure 1d immediately shows that that neither Li2S nor S8 precipitate in the micropores of the cathode. This point can be discussed in a quantitative fashion as follows: Figure 4 shows the same scattering curves after the subtraction of the carbon background and the incoherent background. The contribution of lateral fluctuations that scale with 𝑞 ―2 was additionally subtracted from the dry carbon SANS curve.15 Hence a 𝑞 ―4-regime is obtained for large q-values of the dry carbon curve (solid black line). The Porod constant from this linear slope in the log-log representation yields a specific surface area of the carbon electrode of 1006±242 m2/g. This is comparable to previous values of this electrode material of around 1000 m2/g.15 The comparison of the dry (black open circles) and the wetted (red

Fig. 4 SANS curves after the subtraction of the incoherent scattering contribution of the electrolyte and the carbon background (see legend). The solid black lines at high q-values represents the Porod regime where the Porod constant 𝑃𝑚 can be extracted from the dry carbon electrode. The calculated specific surface from 𝑃𝑚 is 1006±242 m2/g that is comparable with previous results.15 The solid red line at low q-values is also proportional to q-4 and indicates surface scattering of macroscopic structures. The solid blue and orange line represent simulated scattering curves obtained with the model described in equation 3.

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carbon host matrix. However, it should be stressed that this finding could be different if doping or surface modification of the carbon host are used to achieve lithiophilic inner surfaces. The time dependent evolution of the precipitated phases is qualitatively analyzed in the following. The fitting model used consists of two major contributions to the scattering signal that superimpose. First, there is the surface scattering of macroscopic structures that scales with 𝑞 ―4 that contributes to the scattering intensity at low q. Second, the precipitated structures are modeled as polydispersed spheres. The solid blue and orange lines in figure 4 are fits of this approach. While the precipitate in the discharged state (blue solid curve) exhibits a particle diameter of 1.8 nm and a polydispersity of 22%, the SANS curve of the charged state (orange solid curve) yield a fit result of 1.3 nm and a polydispersity of 28%. The four fitting parameter of this model are the Porod constant 𝑃m, the amplitude of the scattering intensity of the poly dispersed spheres 𝐴pds∆𝑆𝐿𝐷2, the average particle radius 𝑅0 and the polydispersity 𝜎. Furthermore, 𝑃(𝑞) is the scattering form factor and 𝑆(𝑞) is the structure factor that is set to one for small concentrations. The function Γ(𝑥) is the gamma function, 𝑛(𝑅) the Schultz-Zimm distribution26 and 𝑉p the radius 𝑅 dependent particle volume 4/3𝜋 𝑅3. The complete model is summarized in the equations 2-6. d𝛴m d𝛺

(q) = 𝑃m

4

( ) 2𝜋 𝑞

d𝛴pds + 𝐴pds∆𝑆𝐿𝐷2 (𝑞) d𝛺

d𝛴pds (𝑞) = 𝑃(𝑞)𝑆(𝑞) with 𝑆(𝑞) ≈ 1 d𝛺

d𝛴pds (𝑞) = d𝛺

∞

𝑛(𝑅)𝑉p2 3(sin (𝑞𝑅) ― 𝑞𝑅cos (𝑞𝑅))

∫ 4/3𝜋𝑅 | 3 0

0

𝑛(𝑅) =

( )

with 𝑧 =

𝑅0

𝑅𝑧 𝑧+1 exp ― 𝑅 Γ(𝑧 + 1) 𝑅0

(

2

() 𝜎

(𝑞𝑅)

𝑧+1

𝑧+1 𝑅0

|

3

― 1 and

∫

2

d𝑅

(4)

)

(5)

𝑛(𝑅)d𝑅 = 1

(6)

∞ 0

Figure 5 summarizes the major results of the SANS curve fitting. A detailed summary can be found in figure S5. The top row shows the time dependent cell voltage of the last three cycles until the end of the 10th charge step. The vertical dashed and solid lines mark the discharged and charged state, respectively. The second row displays the Porod constant 𝑃m for each SANS curve during galvanostatic cycling. Almost all values of 𝑃m are above the red dashed line that represents the 𝑃m value extracted from the wetted carbon electrode in figure 4. Since the 𝑃m values are proportional to the specific surface area, the 𝑃m curve indicates the formation of macroscopic precipitates that are not observable in the q-range of this SANS experiment. The third row of figure 5 shows the fit results of the parameters 𝑅0 and 𝐴pds∆𝑆𝐿𝐷2. The time dependent scattering intensity amplitude 𝐴pds∆𝑆𝐿𝐷2 is proportional to the volume fraction of the scattering species. It shows two local maxima in the charged and discharged state. The symmetric and triangular shape around both end states indicates a continuous precipitation and dissolution rate of the respective sulfur phase. However, the average particle diameter (2𝑅0) exhibits a clear asymmetry with respect to the discharged state where Li2S is formed. This can be explained by the initial dissolution of the smallest lithium sulfide particles at the beginning of the charge step and a higher stability towards dissolution of the remaining larger particles. A sudden decrease of particle diameter sets in and 2𝑅0 and 𝐴pds∆𝑆𝐿𝐷2 reach a local minimum. This point marks the complete dissolution of all nanoscopic Li2S particles and coincide with the second characteristic voltage of 2.385 V discussed above. The S-shape of the voltage curve at this point is a clear indicator for this phase transition.

(2)

(3)

Impedance Spectroscopy The two rows at the bottom of figure 2 summarize the results of the potentiostatic impedance spectroscopy that was performed during potentiostatic stops of the galvanostatic cycling. The solution resistance 𝑅𝑆 and the Warburg coefficient 𝐴𝑊 allow us conclusions about the time dependent ion concentration in the electrolyte. The ionic conductivity of the deuterated electrolyte is determined by the contribution of all ions in the solution, namely, Li+, Sx2-, TFSI- and NO3-. The combined salt concentration of LiNO3 (0.6 M) and LiTFSI (0.29 M) is almost nine times higher than the Li2S8 polysulfide concentration (0.1 M). Also the diffusion constants of Li+ and TFSI- are slightly higher than this of Sx2-.27 Apart from the initial passivation layer formation28, the concentration of both conducting salts does not change significantly. Therefore, the contribution of the time dependent polysulfide concentration to the ionic conductivity can be neglected. However, as shown by Ding et al.21 the presence of polysulfides in the electrolyte increases the viscosity of the solution, which in turn reduces the diffusion constants of the other ions and finally reduces the ionic conductivity. Since the solution resistance 𝑅𝑆 is inversely proportional to the ionic conductivity, the increase in polysulfide concentration will always increase the value of 𝑅𝑆. On the one hand, this explains the local minima of the 𝑅𝑆 curve in the charged and discharged states where polysulfides are removed from the solution and precipitate as solid product. On the other hand, the

Fig. 5 Summary of the fitting results obtained with processed SANS curves and the model in equation 3. Top row: Time dependent cell voltage curves. The dashed and solid vertical lines mark the discharged and charged state, respectively. Middle row: Time dependent values of the fitting parameter 𝑃m. Bottom row: Time dependent particle diameter (black curve) and SANS 2

intensity factor 𝐴pds∆𝑆𝐿𝐷 (red curve).

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𝑅𝑆 curve exhibits local maxima between both end states where the polysulfide concentration reaches its maximum. The Warburg coefficient describes the strength of the diffusion control in a charge transfer reaction.29 In contrast to the solution resistance, 𝐴𝑊 is determined by the ion species that are involved in the charge transfer processes at both electrodes, namely, Li+ and Sx2-. Since lithium ions have a higher concentration and possess a higher diffusion constant, the polysulfides are the limiting factor in the diffusion controlled charge transfer reaction. This means high Warburg coefficients represent low polysulfide concentrations and vice versa. The distribution of relaxation times 𝛾(𝜏) gives the strength and the characteristic time 𝜏 of a charge transfer process. It allows conclusions about the presence of certain phases in the system. We showed in a previous X-ray imaging study12 that the appearance of macroscopic sulfur crystals can be correlated to a charge transfer process between the characteristic times 0.1 and 10 s. With these statements the correlations between SANS curves and the analyzed impedance data from figure 2 can be summarized as follows:  The coincidence of local minima and maxima of 𝐴𝑊 and 𝑅𝑆, respectively, with the local minima of the SANS intensity is a clear indication for a high concentration of polysulfides and the absence of solid phases.  In contrast to this, the periodic maxima of the SANS intensities are in good agreement with the maxima and minima of 𝐴𝑊 and 𝑅𝑆, respectively, which in turn shows the presence of the solid phases sulfur or lithium sulfide and the depletion of polysulfides at the same time.  The charge transfer processes between 0.1 and 10 s in the DRT plot (above horizontal dashed line) can be assigned to the maxima of the SANS signal. These processes are exemplarily highlighted by dashed and dashed/dotted ellipses in the 8th and 9th cycle. Here, the narrow and broad ellipse corresponds to the presence of sulfur and lithium sulfide, respectively.  An asymmetric shape of the 𝐴𝑊 curve in the 8th and 9th cycle reflects the slower dissolution of largerLi2S particles as shown in figure 5.  The overall decrease of the SANS intensities with cycle number and the accompanied steady increase in the solution resistance and the Warburg coefficient indicates gradual capacity fading of the Li/S cell that is always present. The maximum of 𝛾(𝜏) in the discharged state for relaxation lower than 10-3 s is ascribed to the charge transfer process at the lithium anode.18,30,31

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The good contrast between lithium sulfide and the deuterated electrolyte as well as the subtraction of non-relevant scattering contributions from the SANS curves allows the application of a simple fitting model. The asymmetry of the particle diameter around the discharged state indicates that lithium sulfide does not dissolve homogenously. The smallest Li2S particles are dissolved at first followed by the dissolution of the larger particles. The results of the impedance spectroscopy show a consistent correlation with the SANS intensities and are a suitable tool to substantiate conclusions derived from the scattering experiment. The high sensitivity with respect to both precipitation phases, and the good spatial resolution qualify operando SANS as an appropriate non-invasive tool for further investigations to elucidate the mechanisms of capacity fading in lithium sulfur cells. The results of this work make us optimistic to investigate systems such as mesoporous carbons that are decorated by catalysts.

Methods/Experimental

The cathode used in the present study is ACN-157-15 by Kynol®, noted as dry carbon electrode in text.12 The diameter of the electrodes was 14 mm and were cut out with a punching die. The electrically conductive material consists of matted carbon fibers with an average diameter of 10 µm and a length of around 7 mm. The electrode exhibits by virtue of its isotropic structure a certain elastic modulus that causes a proper pressure on the current collector. In addition, the absence of a binder phase facilitates the evaluation of the SANS data and allows the consideration as a quasi-two-phase scattering system. The inner surface of around 1000 m2/g (SAXS method15) originates mainly from micropores that were created by a CO2 activation process. Scanning electron microscopy images of this cloth-like material can be found in the supporting information (Figure S2). For more detailed information see ref.15 The electrolyte consists of deuterated tetrahydrofuran (Eurisotop Cambridge Isotope Laboratories Inc., 99.5%D, water