Identification of the Underlying Processes in Impedance Response of Sulfur/Carbon Composite Cathodes at Different SOC

Commercially available KB EC-600 JD (Akzo Nobel) representing mesoporous C and synthesized CAs as an example of microporous C along with S powder (99.5%, Alfa Aesar) are used for preparation of the composite cathodes. The pore size distributions of the employed C host materials are depicted in Fig. S1 (available online at stacks.iop.org/JES/169/030505/mmedia). Detailed information on synthesis route of the CAs can be found in our previous publication. ¹⁷ Thereby, the CAs densities and porous structure can be configured by the use of certain reagents, such as Ar, CO₂ or N₂. Different preparation methods, i.e. mechanical mixing and gas infiltration, are undertaken to prepare C/S composites. Firstly, a non-infiltrated, mixed C/S composite was fabricated by ball-milling the S and C components for 15 min at 700 rpm. C/S mixtures with ratios of 7:3 and 3:7 were prepared to allow further comparisons with regard to the active material percentage. Moreover, gas S-infiltrated cathodes were fabricated via the application of heat treatments in order to incorporate the S into the porous C structure. Thereby the ball-milled C/S mixture was heated at 600 °C for 6 h for gas infiltration. ¹⁷ In order to remove remaining non-infiltrated surficial S, the infiltrated C/S compounds were treated with a second heating process step in a tube furnace by heating up to 200 °C and holding for 12 h.

Subsequently, an aqueous slurry was prepared by mixing the C/S composites with the binders CMC (carboxymethyl cellulose, Walocel CRT 2000 PA, Dow Wolff) and PEO (polyethylene oxide, m _V = 600 000, Sigma Aldrich) at a weight ratio of 90:3:7 (C/S: CMC: PEO) in a tumbling mixer. After mixing, the homogenous slurry was doctor-bladed with different coating thicknesses on a C-primed aluminum foil. The full list of the herein prepared cathodes can be found in Table SI (see supplementary).

All measurements were conducted in ECC-PAT-Core cells (EL-CELL) with a symmetrical 2E or 3E setup. The cells were assembled in an argon-filled glovebox (Jacomex GPTFF, < 1 ppm H₂O, < 3 ppm O₂). For a 2E setup, two identical C/S cathodes were separated by a GF/C glass fiber sheet (Whatman, 21.6 mm diameter, 260 μm thickness). As electrolyte, 160 μl ether-based DOL/DME electrolyte containing 1 m Lithium bis(trifluoromethanesulfonic)imide (LiTFSi) conducting salt (Alfa Aesar) was added. To enable measurements at various SOCs/DODs, a Li reference ring with a thickness of 0.6 mm, 19 mm inner and 21.6 mm outer diameter was utilized as third electrode/anode. Prior to each measurement, the cells underwent a rest time of 1 h to allow proper wetting of the separator and the porous electrodes in order to reach steady state conditions.

EIS measurements were performed using a Zahner IM6 and ZENNIUM Pro workstation. All measurements were conducted in potentiostatic mode in a frequency range from 5 MHz to 100 mHz with an amplitude of 10 mV. In addition to the impedance measurements at the OCV, EIS evolution at different SOCs or rather DODs were investigated. Therefore, a 3E cell configuration with Li metal reference ring serving as anode was utilized. To allow automatic impedance measurements at specified cycling states, the battery cycling system BaSyTec and the Zahner impedance measurement setup were combined, see Fig. S2. Therefore, an advanced wiring of the test cell was necessary on the hardware side. The connection on the software side was implemented by a Raspberry Pi single-board computer, which connects both systems and has access to a database specifying the impedance measurement conditions. For all SOC/DOD related impedance measurements the same test plan and the same impedance measuring properties as described before were applied. Before discharging the cells, a prolonged resting period of at least 5 h with hourly impedance recording steps was included to the test plan.

Discharging/charging was performed at C/10 in between the cut-off voltages 3.5 V and 1 V with intermediate EIS measurements at equidistant capacity steps of 1/10 of the theoretical capacity. A resting time of two hours was included between every discharge/charge step and the subsequent EIS measurement, as equilibrium conditions are crucial to exclude non-linear effects on impedance spectra.

Examination, modelling and fitting of the recorded spectra were performed with the stand-alone impedance analysis software RelaxIS3 (rhd instruments). Previous to fitting, the quality of the measured data was verified using Kramers-Kronig ⁴⁰ transformation. The quality of the obtained fitting values and the suitability of the used equivalent circuit model was evaluated with various quality criteria, such as Chi-square, residual analysis and mathematical error values for single fitting parameter which are shown/mentioned as error bars. Furthermore, DRT analysis was applied (using RelaxIS3 software) wherever necessary to distinguish the overlapping processes.

The characteristic Nyquist plots of symmetrical 2E cells comprising two cathodes of pure KB (KB_pure, red line) and mixed KB/30 wt% S cathodes (KB/S_mixed,30, blue line) are shown in Fig. 1a. In case of pure C, the typical blocking response of the porous electrode (in the absence of the faradic reaction at the surface) is recorded, which is manifested in the Nyquist diagram in a 45° incline in the middle frequency (MF) region characteristic for the resistance of ions within the pores (R_ion) followed by a straight line with an angle of almost 90° featuring the blocking behavior due to the absence of active material. Latter is described with Q_dl, a constant phase element (CPE), characterizing the local charge accumulation and double layer formation at the interface. The equivalent circuit (EC), depicted in Fig. 1b, is adopted to fit the experimental data for this sample which is comprised of a blocking TLM describing the aforementioned processes in series with a resistance (R_s) attributed to the ohmic response originating mainly from the electrolyte. The overall impedance (Z) hereby is calculated using Eq. 1:

$$\begin{eqnarray}&&Z={R}_{{\rm{s}}}+{\left[\frac{{R}_{\mathrm{ion}}}{{Q}_{\mathrm{dl}}{\left({\rm{j}}\omega \right)}^{\alpha }}\right]}^{\frac{1}{2}}\cdot \,\coth \left\{L{\left[{R}_{\mathrm{ion}}\cdot {Q}_{\mathrm{dl}}{\left({\rm{j}}\omega \right)}^{\alpha }\right]}^{1/2}\right\}\end{eqnarray} \tag{ 1 }$$

where ω is the angular frequency of the excitation signal and L the pore length in the porous electrode. The extent of the x-axis intercept corresponds to 1/3 of the ionic resistance in the pore. Of note, the blocking condition appears non-ideal due to parasitic reactions such as the formation of a passivation layer on the blocking electrode. This indeed leads to a deviation of the R_ion values measured by the above-mentioned analysis from the true values. Therefore the reported R_ion values should be considered as apparent rather than the true values. ⁴¹

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An additional process can be distinguished for an active-material containing cathode: a semicircle (RQ)_int at high frequencies (HF; 0.1 MHz ≤ f ≤ 1 MHz) assigned to the interparticle effects of the electrical network of the composite electrode, ^43–45 shown in Fig. 1c. Surprisingly, the composite electrode appears to be blocking despite the presence of the active material at the OCV. This is due to the relatively small excitation (10 mV) at OCV potentials. Since the CT reactions cannot be fully excluded given the presence of S, a non-blocking TLM is expected. In this case the impedance is given by Eq. 2:

$$\begin{eqnarray}&&Z={R}_{{\rm{s}}}+{\left[{R}_{\mathrm{ion}}\,\cdot \,\zeta \right]}^{1/2\,}\,\coth \left[L{\left(\frac{{R}_{\mathrm{ion}}}{\zeta }\right)}^{1/2}\right]\end{eqnarray} \tag{ 2 }$$

with

$$\begin{eqnarray}&&\zeta ={\left[\displaystyle \frac{1}{{R}_{{\rm{ct}}}}+{Q}_{{\rm{dl}}}{\left({\rm{j}}\omega \right)}^{\alpha }\right]}^{-1}\end{eqnarray} \tag{ 3 }$$

This yields extremely large CT resistances (R_ct) values which mathematically, as shown in Eqs. 4 and 5, equals the impedance of the blocking electrode.

$$\begin{eqnarray}&&{Z}_{\left(RQ\right)}=\,\displaystyle \frac{1}{\displaystyle \frac{1}{{Z}_{{\rm{Rct}}}}+\displaystyle \frac{1}{{Z}_{{\rm{Qdl}}}\,}}=\displaystyle \frac{1}{\displaystyle \frac{1}{{R}_{{\rm{ct}}}}+{Q}_{{\rm{dl}}}{\left({\rm{j}}\omega \right)}^{\alpha }}\end{eqnarray} \tag{ 4 }$$

$$\begin{eqnarray}&&{Z}_{\left(RQ\right),R\to \infty }=\,\displaystyle \frac{1}{0+{Q}_{{\rm{dl}}}{\left({\rm{j}}\omega \right)}^{\alpha }}={Z}_{{\rm{Qdl}}}\end{eqnarray} \tag{ 5 }$$

In order to identify the potential physical as well as the underlying chemical and electrochemical processes occurring in the impedance behavior of C/S composite cathodes during cycling, three differently fabricated composite cathodes (CA(Ar)/S_gas, KB/S_mixed,30 and CA(Ar)/S_mixed,30) are considered as model systems. In particular, these case studies represent the typical galvanostatic cycling characteristics and the occurring redox reaction mechanism in a Li-S cell reported in literature. ^17,42

Figure 2 summarizes these plausible voltage profiles depending on the porosity of the C host material as well as the employed infiltration method. As explained in the introduction section, infiltration and anchoring of active material into the UMC host material alters the nature of the occurring CT mechanisms, whereby the voltage profile and the potentials of the characteristic discharge and charge plateaus adopt accordingly as shown in Fig. 2a. For the CA(Ar)/S_gas cathode, a distinct discharge plateau around a considerably lower potential of 1.6 V can be observed corresponding to the QSS-CT reaction of S_{8, polymorph} → Li₂S (QSS-CT). ^16,18 In addition to the expected long plateau at 1.6 V, a negligible plateau around 2.1 V is visible at the beginning of the discharge region, pointing that the dissolution of the remaining surficial S has proceeded to a small extent. In contrast to this, upon charge a second (2.3 V) and third (2.4 V) plateau corresponding to the S₄ ²⁻ → S₈ ²⁻ (PS-CT₁) and S₈ ²⁻ → S₈ (PS-CT₂) oxidation reactions can be observed in addition to the oxidation step of QSS-CT (at 1.8 V). This leads to dissolution of PS and irreversible capacity upon first cycle in such systems. ¹⁷ The main reason for the appearance of this oxidation steps upon charge is the formation and dissolution of semisolid Li₂S₄ upon oxidation of Li₂S. ⁴³

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Figure 2b depicts the recorded voltage profile of a cell with KB/S_mixed,30 cathode. As KB consists of solely mesopores and no thermal infiltration process was carried out, the voltage profile upon discharge shows the characteristic plateaus corresponding to the PS-based CT mechanisms (solid-liquid-solid) around 2.3 V and 2.1 V attributed to the reduction steps of S₈ → S₈ ²⁻ (PS-CT₂) and S₄ ²⁻ → Li₂S₂/Li₂S (PS-CT₃), respectively. ^44,45 Upon charge, corresponding plateaus for the oxidation reactions of S₄ ²⁻ → S₈ ²⁻ (PS-CT₁) and S₈ ²⁻ → S₈ (PS-CT₂) steps can be observed at 2.3 V and 2.4 V, respectively. Additionally, the initial oxidation step of Li₂S₂/Li₂S ↔ S₄ ²⁻ (PS-CT₃) arising at the very beginning of the charge process and leading to a sharp incline, is expected to be still active within the 2.3 V plateau due to sluggish charge transfer kinetics of solid Li₂S/Li₂S₂ oxidation. ⁴⁶ The foregoing discussion is for simplification and does not exclude the formation of S₆ ²⁻, the S₃ ^·− radical and correspondingly the intermediary reaction steps, e.g. the discharge reactions such as S₈ → S₈ ²⁻ → S₆ ²⁻(S₃ ^·−) and S₄ ²⁻ ↔ S₆ ²⁻(S₃ ^·−) as well as the charge reaction of S₆ ²⁻ → S₈. ⁴² In contrast to these two samples, both CT mechanisms, i.e. QSS-CT and PS-CT, are observed for the CA(Ar)/S_mixed,30 sample as depicted in Fig. 2c, resulting from elemental S₈ on the C surface as well as S_8,polymorph species protected by the micropores. ⁴⁷ The charge process for this sample appears to face a strong PS-shuttle whereby the full oxidation to higher potentials is hindered.

Herein, the in-situ impedance data was recorded at defined DODs/SOCs during the first discharge/charge cycle for these three cathode materials in order to gain a broader understanding on the underlying mechanisms and kinetics of the CT mechanisms. Therefore, a symmetrical configuration consisting of two C/S cathodes and a Li reference, serving as the anode, was implemented. The charge/discharge profile recorded for such cell design was compared to a 2-electrode (2E) setup to ensure the elimination of the originated geometrical effect from the 3E cell setup, see Fig. S3.

The capacity, efficiency and long-time cycling performance of these various systems has already been investigated in detail in one of our previous studies. ¹⁷ As evident from Fig. S4a, the infiltration and anchoring of the active material within the UMC carbon host indeed exhibits the highest specific capacity and most stable long-term cyclability. For mixed CA(Ar)/S and KB/S cells however, lower and slowly decaying performances are found due to their tendency to side reactions and PS-shuttle effect, as discussed above.

In Fig. 3a, the recorded discharge/charge profile of a full cell in 3E setup with CA(Ar)/S_gas cathodes is depicted. A prolonged OCV-phase of 50 h was chosen in order to investigate undesired effects such as self-discharge upon relaxation period. The colored dots mark the recordings of impedance data. The voltage peaks at the EIS measurement points can be attributed to the relaxation breaks, which are not depicted in the plateaus.

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Figure 3b shows the corresponding EIS spectra at different DODs. At the OCV state (0% DOD, measurement 0), the impedance spectrum of the cell exhibits the same characteristics as observed in previous OCV investigations for mixed electrodes, i.e. a blocking response in the LF region, an inter-particle response in the HF area and the ionic pore resistance in between. Indeed, the impedance remains unchanged after relaxation, implying that the self-discharge reactions are suppressed by entrapment of the active material. Interestingly upon discharge initiation, a remarkable change in the LF section with an emerging semicircle is recorded. The LF branch with appendant semicircle decreases during progressing along the 1.6 V plateau and further until the end of the discharge process. The observed semicircle is attributed to the QSS-CT mechanism (RQ)_QSS-CT. The spectra recorded for 8%–72% DOD are fitted with the EC shown in Fig. 3c. With further discharge, R_ct decreases and an additional branch appears in the LF range for deeper DOD (72%–100% DOD, measurement 9–13), describing a nearly infinite diffusive process i.e. the solid diffusion of Li-ions fitted using Q_diff (see the EC in Fig. 3d). To make sure the low branch is corresponding to the diffusion but no other CT processes, the EIS of a fully discharged cell is recorded up to ultra-low frequencies (32 μHz), see Fig. S5. Distribution of relaxation times (DRT) analysis was employed to carry out a more precise classification of the identified processes with respect to the corresponding frequency ranges as well as the relaxation times, see Fig. 3e. In addition to the R_ct, the evolution of R_s, R_ion and R_int is explored, see Fig. 3f. Interestingly, R_s remains almost unchanged at 1.5 Ω upon discharge process. This steady behavior can be attributed to the lack of PS dissolution in the bulk electrolyte as a consequence of the QSS-CT. The formation of PSs is shown to increase the viscosity of the electrolyte, resulting in a higher resistance. ⁴⁸ For the presented system however, since the trapped S in the micropores is not dissolved in the electrolyte, no substantial viscosity changes in the electrolyte and thus no significant resistance alteration arises in the further discharge steps. Similar trend is observed for the R_ion at the OCV as well as early DODs due to the same reason. At the deeper DOD however R_ion increases steadily due to the consumption of Li-ions in the pores and the local depletion in the concentration of the ionic carriers, and consequential reduction in pore ionic conductivity. Such an effect is not observed for the bulk, where the depletion of the cation is compensated fast enough from the anode during discharge. In the case of R_int, a stable value can be noted before plateau. Afterwards R_int keeps falling explainable by the higher ionic conductivity of the solid product Li₂S/Li₂S₂ (σ_Li2S = 1·10⁻¹⁷ S cm^{−1 49} ) relative to elemental S (σ_S8 = 5·10⁻³⁰ S cm^{−1 50} ). Interestingly, after the plateau (from 1.5 V to 1 V) R_int begins to increase again, as eventually the Li₂S precipitation overlies the surface of the conductive C material, also in corroboration with rerise of the R_ion after plateau.

For the charging process shown in Fig. 4a at the earlier states, in addition to the interparticle reaction and the ionic pore resistance, the QSS-CT semicircle and the LF branch representing solid diffusion are distinctly evident. At higher SOCs (>70% SOC), different impedance responses are identified, see Fig. 4b. Considering the voltage profile, the second plateau at 2.3 V linked to the oxidation step of S₄ ²⁻ → S₈ ²⁻ (PS-CT₁) arises at about 70% SOC. This naturally faster PS-CT reaction (relative to QSS-CT) is emerging at higher frequencies. In the last EIS spectrum recorded at 100% SOC, a semicircle becomes ultimately fully visible in the MF region. With regard to the position in the voltage plateau, this response conforms the oxidation of long-chain PSs to solid S, S₈ ²⁻ → S₈ (PS-CT₂). Apparently, this process and the ionic pore response share similar relaxation times, the 45° incline is superimposed by the oxidation reaction disabling the application of the TLM. Instead, a serial connection of two (RQ)-circuit elements is assigned to inter-particle effects (RQ)_int, oxidation to solid S (S₈ ²⁻ → S₈, (RQ)_PS-CT2) as well as the CPE element Q_diff describing the solid diffusion, see Fig. 4c. The evolution of other resistances upon charge is shown in Fig. S6. The series resistance, which originates mostly from the electrolyte, steadily increases from 1.5 V to 1.9 Ω. The reason therefore is the mentioned second oxidation step forming semisolid Li₂S₄ which results in further dissolution to PS. This agrees with the maximum R_s appearing at the end of the second charge plateau. Furthermore, an increase of R_ion can be observed within the second half of the charge process which is in accordance with the overall rise of the R_s. Since the inter-particle resistance R_int is not falling but slightly growing during charging of the cell, it is evident that the effect of the cathode passivation occurring due to Li₂S₂/Li₂S formation at the end of the discharge process is indeed irreversible.

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In contrast to the CT processes identified for gas infiltrated CA(Ar)/S cathodes, pure PS-CT mechanism was observed in the mesoporous C host system mixed with S (KB/S_mixed,30). As expected, two characteristic PS-based discharge plateaus at 2.3 V and 2.1 V can be noticed, see Fig. S7. Recorded EIS spectra for this sample during discharge are shown in Fig. 5a. Due to the significant overlapping of different CT processes, the EIS data has been interpreted by means of DRT analysis, see Fig. S8a. The influences can be attributed to the various, complex reactions taking place inside the cell during PS reduction. While in OCV phase the expected TLM with blocking conditions is visible, a MF semicircle arises shortly after starting the discharge process, see Fig. 5a, DOD = 17%. With regard to the discharge profile, EIS measurement 1 at 17% DOD was recorded at the 2.3 V plateau. Thus, the spectrum represents the impedance response of the first discharge plateau at which the dissolution of solid S (PS-CT₂) occurs and where no distinct ionic pore resistance contribution is evident. Instead, a semicircle superimposes the relevant frequency region. Moreover, the transformation of the LF branch toward a semicircle indicates that another process has already initiated. With further discharge and reaching the plateau at 2.1 V where the process S₄ ²⁻ → Li₂S₂/Li₂S (PS-CT₃) is dominated, the semicircle at LF becomes visible. The assignment of the appearing LF semicircle to PS-CT₃ is corroborating with the early growth of the HF semicircle which indicates a greater inter-particle resistance induced by deposition of reduction product at the surface, similarly observed upon solid reaction in previous discussed samples. Preceding aforementioned, for the first discharge EIS spectrum at DOD = 17%, fitting was performed with a serial combination of three (RQ)-elements and a series resistance depicting the ohmic resistances, see Fig. 5b. The following EIS spectra from 34% to 68% DOD, recorded at the plateau are fitted employing an EC illustrated in Fig. 3c as well, where the increase of the (RQ)-element describing the PS-CT₃ is increasing with time at the plateau.

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Interestingly, distinct behavior can be found for the discharge impedance data at 85% and 100% DOD where the discharge plateau is already exceeded. Naturally, the CT resistance of the Li₂S₂/Li₂S-forming reduction steps is not detectable anymore given the absence of the formation of respective phase. However, a new individual process starts to appear at frequencies of 5 kHz ≤ f ≤ 0.5 MHz, which is even higher than frequencies corresponding to the porous response and dissolution of the (PS-CT₂). The origin of this puzzling process is not fully clear. This relatively fast process on one hand could be assigned to the reduction of remaining high order PSs (S₈ ²⁻ → S₄ ²⁻ (PS-CT₁)) which fully occurs in liquid state, given the similar time-constant to the PS-CT₁ process for previous sample. Drvarič-Talian et al. reported a tendency for PSs to disproportionate resulting in the local depletion at cathode surface at deep discharge. ⁴⁹ The depleted PS cannot be compensated fast enough by those PSs that are present in more distant areas, e.g. the separator, due to slow wandering. Hence, long-chain PSs are still present in the electrolyte, even though the discharge process has already continued to further reduction steps and fitting is performed with a blocking TLM with two serial (RQ)-elements, see Fig. 5c. On the other hand, an additional plausible interpretation of (RQ)-element appearing at lower DODs is the partial coating of the cathode surface during the formation of Li₂S. Diffusion of Li ions through such a coating layer could result in this additional resistance.

Herein, charging was finished faster than discharging and only four impedance spectra could be recorded, which indicates the loss of active material. For the first two spectra at 32% and 64% SOC recorded in the known 2.3 V charge plateau, the corresponding oxidation reaction Li₂S/Li₂S₂ → S₄ ²⁻ (PS-CT₃) as well as the solid diffusion branch can be observed in the LF region, see Fig. 5d. The ionic pore response in the MF part is superimposed by a distorted, enlarged semicircle shape, indicating two processes with similar relaxation times. With regard to the frequency range and previous information gained by investigation of the discharge spectra, the two MF impedance responses depict most likely oxidation reactions of long-chained PSs, hence S₄ ²⁻ → S₈ ²⁻ (PS-CT₁) and S₈ ²⁻ → S₈ (PS-CT₂). For later charge impedance spectra at approximately 96% and 100% DOD, blocking behavior is observed. The porous response is still partially superimposed by PS-CT₁ apparent from DRT analysis (Fig. S8b), therefore a serial connection of (RQ)-circuits depicting the identified processes are chosen as EC, see Fig. 5e for the first and second charge EIS spectrum and Fig. 5f for later spectra.

Subsequently, the impedance evolution of mixed, i.e. non-infiltrated, CA(Ar)/S_mixed,30 electrode upon first cycle where the characteristics of both kind of CT processes, i.e. PS-CT and QSS-CT, are evident is investigated. In order to maintain comparable conditions a S fraction of 30 wt% is chosen, since the S content of CA(Ar)/S_gas is usually around 20%–30%, see Fig. S9. Observation of impedance spectra recorded during OCV shows a decrease in the LF branch which could indicate a slight self-discharge, see Fig. S10, in contrary to CA(Ar)/S_gas. The recorded discharge impedance spectra are shown in Fig. 6. As observed before, the impedance response of the ionic pore resistance is superimposed by process PS-CT₂ (S₈ → S₈ ²⁻), Fig. 6a. A further semicircle in the LF area can be observed, which increases toward the end of the first discharge plateau at 48% DOD. This behavior is linked to the reduction of S₄ ²⁻ → Li₂S₂/Li₂S (PS-CT₃).

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Simultaneously with the decrease of the LF arc and appearance of the solid-state process, the HF inter-particle response increases analogous to CA(Ar)/S_gas sample. Starting from EIS measurement 6 at 60% DOD, the porous characteristics (45° slope) become visible again in the EIS spectra, see Fig. 6b. In the second discharge plateau, the impedance evolution is similar to spectra of the gas infiltrated CA(Ar)/S cell. The LF branch drops toward the real axis and a semicircle shape becomes apparent.

The distinct presence of both CT mechanisms leads to a more complicated identification of the corresponding responses in the charge impedance data, which are shown in Fig. S11. However, since QSS-CT and PS-CT are dominant in different voltage areas, a simultaneous occurrence is not expected. Hence, modelling and fitting can be achieved by applying the already known TLM as depicted in Fig. 3d.

All the above discussed processes occurring within cathodes in this study are listed in Table I. The QSS-CT has slower kinetics than the PS-based CT reactions which is mainly due to the limited diffusion within the S particles compared to the fast PS disproportionation steps in solution. ^43,51 Among the PS-based CT mechanisms, the PS-CT₁ reaction which occurs fully in the liquid state owns the lowest relaxation time constants.

The quantified R_ct values for the CA(Ar)/S_gas and KB/S_mixed,30 cathodes and their evolution at the main discharge plateau are depicted in Figs. 7a and 7b. The QSS-CT owns greater R_ct values due to the less exothermic reaction of S₈ → Li₂S compared to PS-based reduction steps. ⁴⁵ Additionally, the confinement of S in the ultramicropores and lack of contact between electrolyte and active material calls for the solid-state diffusion of ions which leads to overpotentials as well. ⁴³

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Interestingly, while R_QSS-CT in the case of CA(Ar)/S_gas cathode decreases upon discharge at the plateau, the resistance of the PS-CT₃ mechanism occurring in the KB/S_mixed,30 cell appears to rise. The opposing trends can be explained with the dominating limiting factor of the different CT mechanisms. Since the QSS-CT mechanism reacts only in the solid phase, it is predominantly controlled by the diffusion of the Li-ions in the cathode. Even though both species, elemental S₈ as well as Li₂S, are generally considered to be insulating, the final discharge product Li₂S shows to have a greater ionic conductivity than elemental S₈ (σ_Li2S = 1·10⁻¹⁷ S cm^{−1 50} vs σ_S8 = 5·10⁻³⁰ S cm^{−1 50} ). Hence, with ongoing discharge process the overall ionic conductivity in the C/S compound cathode grows whereby the diffusion and CT are facilitated. For PS-based CT mechanisms in Li/S cells, CT is mainly controlled by the surface reactions which occur at the three-phase boundary between the PS solution, insulating lithium sulfides precipitates and conductive C. With further discharge a growing amount of insulating Li₂S₂/Li₂S precipitation covers the conductive C surface (evident from the EIS data as discussed) which suppresses the further nucleation and growth of reduction products resulting in an increased CT resistance. Such passivation of the surface by final products of PS-based reduction reaction and increase in CT resistance at plateau is analogously observed and discussed using in situ TEM. ⁵²

The combination of gas infiltration and microporous C enables the application of carbonate-based electrolyte whereby the excessive nucleophilic reaction of the carbonate solvent with the short-chain S-anions could be suppressed. Thereby, great specific discharge capacities can be obtained, see Figs. S4b. To assess the implementation of carbonate-based electrolytes within Li/S batteries employing a S infiltrated UMC host, the evolution of the EIS upon first cycle is compared to the ether-based electrolyte, see Figs. 8a. The observed EC/DMC cell was assembled using CA(Ar)/S_gas cathodes in a symmetrical cell configuration and with cycling parameter analogous to previous investigations executed for ether-based electrolytes. In the voltage profile, the elimination of the 2.1 V voltage plateau in contrary to the ether-electrolyte has been fully achieved. This is originated in the formation of a passivation layer on the cathode in contact with the carbonate electrolyte whereby the S is fully trapped within the carbon matrix. ¹⁷ Figure 8a shows the impedance data recorded during the initial OCV phase as well as the complete first cycle in a 3D Nyquist plot. For the carbonate-based electrolyte, in addition to the LF contributions (CT and the solid diffusion) a second semicircle can be observed in the MF region (50 Hz ≤ f ≤ 0.5 MHz). This MF process which superimposes the ionic pore response appears to grow while discharging the cell. Figure 8b compares the EIS spectra recorded at the end of the discharge process of CA(Ar)/S_gas cells using DOL/DME (blue) and EC/DMC (black). During charging of the cell, a reversed progress of the QSS-CT response in the LF area can be observed. However, the MF semicircle is still growing while charging the cell and still visible at the end of the charging process, see Fig. 8c. This process is assigned to the passivation film to be known forming on the S cathode in contact with the carbonate electrolyte. The irreversibility of the process upon charge corroborates this assumption. Interestingly, the formation of such film on the cathode leads to an increase in the CT resistance (QSS-CT).

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