Understanding Rate and Capacity Limitations in Li-S Batteries based on Solid-state Sulfur Conversion in Confinement

1 Understanding Rate and Capacity Limitations in Li-S Batteries based on Solid-state Sulfur Conversion in Confinement Ayca Senol Gungor1, Jean-Marc von Mentlen1, Jean G. A. Ruthes2, Francisco Javier García-Soriano3, Sara Drvarič Talian3, Volker Presser2,4,5, Lionel Porcar6, Alen Vizintin3, Vanessa Wood1,*, Christian Prehal1,7 * 1 Department of Information Technology and Electrical Engineering, ETH Zürich, Gloriastrasse 35, 8092 Zürich, Switzerland 2 INM - Leibniz Institute for New Materials, Campus D2 2, 66123 Saarbrücken, Germany 3 Department of Materials Chemistry, National Institute of Chemistry, Hajdrihova 19, 1000 Ljubljana, Slovenia 4 Department of Materials Science and Engineering, Saarland University, Campus D2 2, 66123 Saarbrücken, Germany 5 saarene – Saarland Center for Energy Materials and Sustainability, Campus C4 2, 66123 Saarbrücken, Germany 6 Institut Laue–Langevin, 71 Avenue des Martyrs, Grenoble, 38042, France 7 Department of Chemistry and Physics of Materials, Paris-Lodron University of Salzburg, Jakob-Haringer-Straße 2a, 5020 Salzburg, Austria Corresponding authors’ email: christian.preha[email protected]c.at, [email protected] Keywords Lithium-sulfur batteries, nanoporous carbons, operando scattering, impedance spectroscopy, solid-state sulfur conversion, electrochemical performance Abstract Li-S batteries with an improved cycle life of over one thousand cycles have been achieved using cathodes of sulfur-infiltrated nanoporous carbon with carbonate-based electrolytes. In these cells, a protective cathode-electrolyte-interphase (CEI) is formed, leading to solid-state conversion of S to Li2S in the nanopores. This prevents the dissolution of polysulfides and slows capacity fade. However, there is currently little understanding of what limits the capacity and rate performance of these Li-S batteries. Here, we aim to deepen the understanding of the capacity and rate limitation using a variety of structure-sensitive and electrochemical techniques, such as operando small angle neutron scattering (SANS), operando X-ray diffraction (XRD), electrochemical impedance spectroscopy (EIS), and galvanostatic charge/discharge. Operando SANS and XRD give direct evidence of CEI formation and solid-state sulfur conversion occurring inside the nanopores. Electrochemical measurements using two nanoporous carbons with different pore sizes suggest that charge transfer at the active material interfaces and the specific CEI/active materials structure in the nanopores play the dominant role in defining capacity and rate performance. This work helps defining strategies to increase the sulfur loading while maximizing sulfur usage, rate performance, and cycle life. 2 Introduction Lithium-sulfur (Li-S) batteries are promising candidates to outperform current Li-ion batteries in terms of cost, environmental friendliness, and storage capacity1,2. However, they are not yet largely commercialized because of poor cycle life3-6 and problems reaching their theoretical capacities. In standard Li-S batteries with ether-based electrolytes7, the conversion from sulfur (S) to Li2S is realized via a solid-liquid-solid process8. During discharge, solid sulfur is reduced to soluble polysulfides, eventually precipitating to solid Li2S9,10. Dissolving the polysulfides improves the reaction kinetics11 compared to a solid-state conversion but requires high amounts of electrolyte,12 which significantly reduces the practical cell capacities and energy densities. In addition, polysulfides cause self-discharge, active material loss, and capacity degradation3,13,14. These issues can, in principle, be circumvented with Li-S batteries using sulfur-infiltrated nanoporous carbon (pores < 2 nm) and carbonate-based electrolytes, where conversion from S to Li2S happens in the solidstate15. The solid-state conversion is enabled by the in-situ formation of a cathode-electrolyte interphase (CEI) during the first discharge16-19 from a nucleophilic reaction of soluble polysulfides with carbonates and the electrochemical formation of CEI components such as LiF20-25. The CEI prevents the further dissolution of S into polysulfides, enabling a direct conversion between solid S and solid Li2S in the carbon nanopores26. As polysulfides in the bulk electrolyte are largely avoided, the cycle life compared to Li-S batteries with ether-based electrolytes is improved, and, in principle, practical energy densities are increased due to lower electrolyte-to-sulfur (E/S) ratios. However, while the nanoporous carbon supports the formation of the CEI, mitigates polysulfide shuttling16, and offers good electronic conductivity; the limited pore volume leads to low S loadings27. An open challenge is therefore to increase S loading, thereby achieving high capacities while reaching high rates and long cycle life. To do so, a better understanding of the capacity and ratelimiting processes in these types of Li-S batteries is needed. Several hypotheses exist about to what drives solid-state conversion in Li-S cells using S-infiltrated nanoporous carbons and carbonate electrolytes. Some early works argued that the confinement in pores is the main reason for the solid-state conversion28-30. Smaller pores would only host the small S allotropes like S2-4 and no solvent molecules; therefore, are suppressing polysulfide formation/dissolution4,31. However, later studies indicated that solid-state conversion is also possible in pores > 1 nm16,32 as long as carbonate electrolytes form a CEI17,27,33,34. Several X-ray photoelectron spectroscopy (XPS) studies have shown the presence of thiocarbonates, alkyl carbonates, lithium carbonate (Li2CO3), and lithium fluoride (LiF) on the carbon-sulfur cathodes21,26,35,36, but no long-chain polysulfides5. X-ray absorption spectroscopy (XAS) indicated no intermediate polysulfides formed during further cycling with carbonate electrolyte27. These results suggest that the pore structure facilitates the encapsulation of CEI and the solid-state conversion. Overall, the mechanisms of CEI formation, solid-state conversion, and the relation between structure, transport, and performance are still poorly understood. There is no consensus on what limits capacity and rate performance. This study aims to gain more insight on where CEI forms and the capacity and rate-limiting processes. We use a combination of techniques: operando X-ray diffraction (XRD), operando small-angle neutron scattering (SANS), electrochemical impedance spectroscopy (EIS), galvanostatic intermittent titration technique (GITT), and galvanostatic cycling. We systematically vary parameters such as the activated carbon pore size (AC08 with 0.8 nm pore size and AC12 with 1.2 nm pore size), the sulfur loading in the C/S cathodes, and the cycling rate. 3 Experimental section Materials Elemental sulfur (powder, 99.98% trace metals basis, Sigma Aldrich and without any further processing) and nanoporous activated carbons (dried at 200°C under vacuum overnight), MSP20 (denoted as AC08), and YP80F (denoted as AC12) were mixed manually with different weight ratios in an agar mortar. AC08 and AC12 have mean pore sizes of about 0.8 nm and 1.2 nm, respectively, provided by Kansai Coke and Chemicals and Kuraray Chemicals Co. Before melt-infiltration, the AC08 and AC12 carbons were mixed with elemental sulfur at different sulfur-tocarbon mass ratios: 2:1, 1:1, and 1:2. The prepared mixture was melt-infiltrated at 155°C for 7-8 h in a sealed evacuated glass oven (Büchi, Switzerland). The final sulfur mass content was verified by weight and thermogravimetric analysis (TGA). TGA results indicate that the nominal C/S ratios are kept during melt infiltration (Figure S1). For the higher C/S ratios (C/S 1/2), a certain fraction of sulfur is present outside the nanopores. The specific pore volume before and after sulfur infiltration further confirm that sulfur fills primarily the nanopores (Figure S2). The free-standing film electrodes were prepared by mixing carbon with polytetrafluoroethylene (PTFE, 60 mass% suspensions in water, Sigma Aldrich) at 9/1 mass ratio with isopropanol (≥ 99.8 %, Sigma Aldrich). The resulting dough-like material was rolled into a 50-80 μm thick film and dried at 50°C under vacuum (10 mbar) for 2h. After drying, the electrodes were cut (puncher diameter 13 mm), resulting in a geometrical surface area of 1.32 cm2. The sulfur loadings varied from 1.7–6.0 mgS cm-2, depending on the S/ C ratio. As an electrolyte, a solution of 1 M lithium hexafluorophosphate (LiPF6) in fluoroethylene carbonate (FEC): dimethyl carbonate (DMC) (by volume 1:4) was used. All solvents were dried with molecular sieves (3Å, beads, 8-12 mesh, Sigma Aldrich), and the salt was dried under vacuum overnight. Methods The gas adsorption measurements were conducted at INM Saarbrücken. To examine the effect of sulfur infiltration into the carbon structure, nitrogen adsorption analyses at -196 °C were carried out using a Quadrasorb IQ system (Anton Paar, formerly Quantachrome). Before each measurement, the pristine carbon materials were outgassed for 12h at 300 °C, while the infiltrated samples were outgassed for the same duration at 50 °C, both under vacuum. A quenched solid density functional theory (QSDFT) approach, part of the Quadrasorb IQ software, was applied to determine the cumulative specific surface area and pore size distribution (PSD). Specifically, the QSDFT with slitpore geometry was used to determine the PSD37. The pore volume was derived from the cumulative PSD data up to 35 nm. The average pore size is defined as the pore size at which half of the total pore volume is reached. Thermogravimetric analysis (TGA) to determine the sulfur content was performed on a STA 449 F3 Jupiter under an argon atmosphere, with a heating rate of 10 °C min⁻1 up to a maximum temperature of 900 °C. All custom-built coin-cell-type electrochemical cells were assembled under an inert atmosphere in an argonfilled glovebox. The cells consisted of an aluminum current collector (18 mm in diameter), a free-standing C/S cathode, a glass fiber separator (20 mm in diameter, Whatman GF/A glass microfiber filters), and a metallic lithium anode (18 mm in diameter, 110 μm thick, FMC Lithium corporation). The electrolyte-to- 4 sulfur-ratio was kept at 20-40 μL mgS-1 to ensure that the electrolyte amount does not limit the electrochemical performance. All electrochemical characterization was performed with a Biologic VMP3 or MPG2 potentiostat/galvanostat. Galvanostatic cycling was done between 3.0 V and 0.5 V vs. Li/Li+ with a rate of C/10 rate (0.167 A/gS, 0.31 mA/cm2 depending on the loading, except for the rate performance tests). The lower potential limit of 0.5 V was chosen to achieve the maximum capacities, in line with a previous study4,38. During rate capability measurements, the first discharge was done with a rate of C/10, and then three charge/discharge cycles were completed at each rate. Electrochemical Impedance Spectroscopy (EIS) measurements were conducted in potentiostatic mode during GITT (galvanostatic intermittent titration technique). For every 100 mAhgS-1 (every 200 mAhgS-1 during first discharge), the cells were rested at the open-circuit voltage for 1h; then the impedance spectrum was measured between 1 MHz and 0.5-1 mHz with a 5 mV perturbation amplitude. Relaxation times at open circuit voltage (OCV) were chosen for 1 hour, before EIS measurements started. The relaxation voltage vs. time indicates sufficient equilibration while maintaining experimental efficiency. Samples for Scanning Electron Microscopy (SEM) were extracted from the cells, washed with diethylene glycol dimethyl ether (2G, anhydrous, 99.5%, Sigma Aldrich), and dried under vacuum. All steps were completed in an Ar-filled glovebox, and the samples were transferred to the SEM inside a vacuum transfer holder. SEM micrographs were taken with a Hitachi SU-8200 at 1 kV acceleration voltage with backscattered and secondary electron detectors. Operando small angle neutron scattering (operando SANS) measurements during galvanostatic cycling were conducted at the D-22 small angle neutron scattering beamline at the ILL neutron source (Grenoble, France). The experimental setup was identical to a previously used setup39 (Figure S3). A wavelength of 0.5 nm, a beam diameter of 10 mm, and two areal detectors (sample-to-detector distance of 17.6 m and 1.4 m) were employed to ensure an overlapping q-region40. The custom-built operando SANS cell (Figure S4) is identical to the previously used SANS cell39. Aluminum windows, each with a diameter of 12 mm, were employed to maintain a low background and uniform pressure throughout the cell assembly. The cell assembly comprised a copper foil current collector (≥ 99.9 %, Schlenk Metallfolien), a Li metal anode (≥ 99.9 %, Alfa Aesar, 0.75 mm thickness, 16 mm diameter), a glass fiber separator (Whatman GF/A, 21 mm diameter, 260 µm thickness), an AC08/S cathode (13 mm in diameter, 180 µm thick), and an aluminum current collector (≥ 99.5 %, Korf). The assembly was infilled with 200 µl of electrolyte (1M LiPF6 in FEC/DMCdeuterated, in a volume ratio of 1:4). The neutron beam irradiated all components of the cell, but discernible and reversible structural alterations were only observed in the cathode. The 2D detector intensity signal was subjected to azimuthal averaging, corrected for sample holder scattering and electronic background, and then normalized using transmission values. The corresponding SANS intensities and electrochemical data are shown in Figures S5 and Figure 1c. To determine the low-q background mainly originating from the AC08 particle scattering, we fitted a power-law model of the form 𝐼𝑚𝑜𝑑(𝑞)=𝐵𝐺0+ 𝐼0𝑞−𝛼 to the average of five consecutive SANS curves right after the high voltage plateau at 2.3 V vs. Li/Li+) during the first discharge (see Figure S5a)41. After the high voltage plateau, S has at least in parts dissolved into polysulfides, and Li2S and CEI have not yet formed. What remains is approximately the scattering from nanopores and any nanostructure inside the nanopores39,42. We subtracted the sodetermined power-law term from all SANS intensities (assuming it would remain approximately constant during cycling). In the next step, we subtracted a flat background originating from diffuse/incoherent scattering. To determine the background (BG) for each recorded SANS intensity (Figure S5b), we fitted the SANS intensities between 5-6 nm-1 with a Porod power law decay of the form 𝐼𝑚𝑜𝑑(𝑞)=𝐵𝐺 + 𝑃𝑞−4 (Figure 5 S5b). The resulting background-corrected data is given in Figure S5c. The SANS intensities in Figure 1 are averaged over five consecutive SANS intensities to reduce noise and improve visualization. The operando XRD measurements were conducted with an equivalent custom-made operando cell design adjusted for X-rays in transmission mode (Figure S3, S4). A small hole (2 mm) protected by a Mylar window guaranteed the penetration of the primary X-ray beam and the diffracted X-rays. The cells comprised a Li metal anode, electrolyte (1 M LiPF6 in FEC/DMC, v/v 1/4), separator, and the S-C composite cathode (with S loading 3.84 mgS/cm-2 and the corresponding E/S ratio 40 μLmgS-1). During in-situ XRD measurements, a Biologic SP240 potentiostat/galvanostat was used for electrochemical cycling. Ex-situ and in-situ XRD measurements were carried out on a Rigaku SmartLab 9 kW System, with a rotating Cu anode and 2D solid-state detector (HyPix-3000 SL). All experimental (raw-)data of this study are available under DOI:10.5281/zenodo.14048781. Results and Discussion: Operando small-angle neutron scattering and X-ray diffraction To understand structural changes of the nanoporous activated carbon-sulfur during galvanostatic cycling, the AC08-S cathode (C/S ratio of 1:1) was first studied via operando SANS and operando XRD. The small angle scattering (SAS) intensity in Figure 1a (data taken from an ex-situ SAXS measurement in Ref42) shows the scattering contribution of the empty AC08 nanopore structure. The hump at approximately 3 - 4 nm-1 indicates a mean pore size of approximately 0.85 nm (π/3.7 nm-1 ≈ 0.85 nm), which fits the mean pore size determined via gas adsorption (0.8 nm)41 (Figure S2). Using Gaussian random fields, we generate a statistically representative real space nanopore structure (Figure 1b, top) from the SAS model fit in Figure 1a. The scattering length density (SLD) difference between the carbon matrix and pore (Figure 1b, bottom) determines the absolute intensity value of the scattering curve. The SLD values sketched in Figure 1b correspond to the SLD values for the operando SANS measurements. If the nanopores are filled with a material of random shape and distribution, the entire SAS curve will retain its shape but shift on the logarithmic intensity axis. If a new structure appears outside the pores with a length scale larger than ≈ 1.5 nm and smaller than ≈ 20 nm, additional features at q < 2nm-1 would emerge. The galvanostatic (dis)charge profiles of the operando SANS and operando XRD measurements are given in Figure 1c and Figure S6, respectively. The first discharge shows an irreversible capacity slightly higher than the theoretical capacity of sulfur, which can be explained by CEI formation16. The shape of the later charging and discharging cycle without a second high-voltage plateau gives evidence for solid-state conversion43. During the first discharge, the SANS intensity increases by about a factor of 4 without a significant change in the shape. This increase indicates solid Li2S and CEI components forming in the nanopores, replacing S and electrolyte44 (Figure 1j). As shown in the sketch in Figure 1b, the SLD contrast and, thus, the SANS intensity increases when these components are formed (Table S1 shows SLD values for carbon, Li2S, and possible CEI components). The fact that the SANS intensity curve has a similar shape to the SAXS intensity of the empty nanopore structure (Figure 1a) indicates that Li2S and CEI components are formed inside the nanopores and not only on the outer surface of the AC08 particles (as shown by the surface sensitive XPS data in Ref33). The SANS intensities remain nearly identical during further charging (Figure 1e) and discharging (Figure 1f). Hence, the solid components in the nanopores stay largely intact and are not dissolved during electrochemical conversion (Figure 1j). The slight q-shift of the SANS intensity during solidstate conversion (Figure 1e-f) might be attributed to the detailed SLD change and swelling/shrinking of the 6 active materials inside the pores or the pore structure itself upon lithiation/de-lithiation45,46. Also, the pore structure itself is expected to show some degree of swelling / shrinking during lithiation / delithiation. However, the effect on the SANS and XRD intensities is minimal and does not impact the conclusions drawn from the data. If carbon swelling were substantial during cycling, we would expect noticeable changes between 20 and 30° around the carbon 002 peak. Figure 1: Operando SANS and XRD measurements. (a) Small angle X-ray scattering (SAXS) intensity of the AC08 carbon (grey) versus momentum transfer q, and after subtraction of the particle scattering at low q and the subtraction of a constant background (black). The blue solid line corresponds to a model fit based on Gaussian Random Fields (GRFs). The data is taken from Reference41. (b) Top: 3D and 2D visualization of the AC08 nanopore structure based on the GRF model fit in (a)41. Bottom: Sketch of scattering length densities (SLD) of different phases in the C -S composite. Detailed numbers are given in Table S1. (c) Galvanostatic (dis)charge curves of the insitu SANS cell (AC08/S cathode with C/S ratio of 1/1). (d) SANS intensities versus scattering vector length q during first discharge. An increasing SLD difference (as shown in b) and the resulting SANS intensity increase indicate the CEI formation. (e) SANS intensities versus scattering length q during first charge. (f) SANS intensities versus scattering length q during 2nd discharge. Operando X-ray 7 diffraction (XRD) intensity of an identical cell (AC08/S ration of 1/1) during (g) first discharge (h) first charge (i) second discharge. The absence of sharp crystalline S diffraction peaks during any cycling step confirms the solid-state conversion inside the nanopores. The XRD pattern of the pristine C/S powders is given in red. (j) Schematic summary of the processes occurring during first discharge, first charge, and second discharge. The conversion takes place without causing any changes in nanopore structure and with no crystalline products. The operando XRD measurements in Figure 1g-i are also consistent with the solid-state S/Li2S conversion occurring inside the AC pores. Figures S7-S8, show the reference data of pristine AC, S, AC-S powder and the AC electrode impregnated with sulfur. Orthorhombic S8 crystals exhibit sharp diffraction peaks (Figure S8c), whereas the electrode after sulfur impregnation shows only a broad peak between 10 – 30° 2θ and no distinct peaks that would indicate bulk sulfur crystals. The broad peak is likely caused by amorphous or nanocrystalline S clusters inside the carbon nanopores, as the Scherrer crystallite size is in the order of 0.81.0 nm. (Figure 1g-i, red curves, and Figure S7). TGA measurements of the pristine AC08/S powder at C/S 1/1 confirm that essentially all S is present inside the nanopores (Figure S1). Comparable to the pristine AC08-S electrode, the XRD patterns after discharge and charge show a broad peak between 10 - 30° 2θ. This indicates that no bulk crystalline phase is formed outside the nanopores throughout cycling and that sulfur and other discharge products (Li2S, Li2Sx) are present in their amorphous state47, most likely in the nanopores. Scanning electron microscopy (SEM) of the AC08-S electrode in its pristine state, after the first discharge and after the first charge, reveals the formation of cracks and some surface deposits48,49, which are likely CEI components (Figure S9)35. Particle fracture after the first discharge is likely caused by the formation of CEI components and Li2S inside the nanopores5,46,50,51. In summary, operando SANS and operando XRD measurements provide evidence that the solid-state S/Li2S conversion occurs inside the carbon nanopores, and that the CEI also exists within the nanopore network (Figure 1j). Using electrochemical measurements, we explore two factors that could potentially limit the cathode’s rate performance and capacity (Figure 2): 1) Li-ion (mass) transport into and in the carbon particles (Figure 2a), and 2) charge transfer between the active material and the electronically conductive carbon (Figure 2b). Figure 2: Possible rate and capacity limiting factors during solid-state conversion in confinement. Both (a) Li ion transport into the carbon particle and (b) charge transfer between carbon and active material could be rate-limiting factors. 8 Electrochemical processes Electrochemical processes in a full-cell Li-S battery were monitored with GITT-EIS during galvanostatic charging and discharging between 0.5 V and 3 V vs. Li/Li+ with a rate of C/10. Every 100 (200 for first discharge) mAhgS-1 , the cells rest for 1 h at open circuit voltage (OCV) at which point EIS is performed. Full cell impedance measurements are rich in information and contain features from both the cathode and anode. Developing a quantitative equivalent circuit model where each element has a physicochemical origin is difficult. Here, we compare full-cell EIS/GITT data of two cells with two different nanoporous carbons, AC08 and AC12, with a mean nanopore size of 0.8 nm and 1.2 nm, but otherwise identical cells components. This helps us to identify impedance features that are linked to the nanopore structure of the cathode particles. Identifying trends during charging and discharging can hint at the origin of certain features. The complete data set of EIS/GITT measurements over the entire frequency range is given in Figure S10 (AC08) and Figure S11 (AC12). The impedance spectrum of a symmetric cell consisting of two cathodes after the first discharge, first charge, and second discharge shows that Li metal impedance does contribute to the mid-frequency range features (10 – 1000 Hz) of the full cell. However, the symmetric cell results also show that this contribution is small and that the full cell impedance is dominated by processes in the cathode (Figure S12). The first discharge curves (Figure 3a-b, Figure S10a, Figure S11a) show two potential plateaus. The first plateau at ~2.3 V vs. Li/Li+ indicates the reduction of S to dissolved long-chain polysulfides10,52. This plateau is shorter in the smaller-pored carbon (Figure 3a) than in the large-pored carbon (Figure 3b), indicating that more S is reduced to polysulfides in the larger carbon pores. However, the plateau for both nanoporous carbons is short compared to that observed in ether-based systems7, indicating that impregnating S in nanopores reduces the amount of S reduced to long-chain polysulfides. At the second part of the plateau is a ~1.5 V vs. Li/Li+, with the equilibrium voltage reached during OCV ~2.0 V vs. Li/Li+, pointing to solid-state Li2S formation5 (in ether-based electrolytes, a plateau at 2.15 V vs. Li/Li+ is common53). The overpotentials are high for both carbons (0.4 V – 0.7 V). Lower overpotentials after the CEI formation in further cycles suggest that the large overpotential could be related to dissolved polysulfides and their reactions with the carbonate solvent and the formation of CEI components54. Notably, the first discharge profiles for AC08 and AC12 differ: AC12 displays a relatively flat plateau near 1.5 V, while AC08 exhibits a marked curvature. Given that equilibrium potentials are similar for both, this curvature in AC08 is likely attributable to distinct kinetic properties arising from its nanopore structure and particle morphology, possibly introducing a mass transport limitation for Li ions or polysulfides. This interpretation is complemented by EIS data (Figure S10a-c and Figure S11a-c and further discussion in the Supporting Note 1). 9 Figure 3: Galvanostatic intermittent titration technique (GITT) . GITT measurements during the first discharge at a rate of C/10 for (a) AC08/S (C/S 1/1) and (b) AC12/S (C/S 1/1) electrodes. Figure 4 shows the EIS/GITT results for solid-state conversion after the CEI has been formed. Results for AC08 are shown in Figure 4a-f and AC12 in Figure 4g-l. During charging (Figures 4a,g) and discharging (Figures 4b,h), there are single potential plateaus around 2.0 V vs. Li/Li+ and 1.8 V vs. Li/Li+ , confirming that after the initial formation of the CEI, there is no further dissolution of S to polysulfides and solid-state S/Li2S conversion dominates5. The overpotentials decrease at the end of discharge, indicating that the final slope reflects a specific capacitive contribution, which is reversible at the beginning of charging. In the EIS, we will focus on the mid-frequency region (10 – 1000 Hz), as it shows the most distinct difference between AC08 and AC12. A distinct arc emerges between 200–700 Hz, with resistance increasing during charge and decreasing during discharge for both materials. AC12, with larger nanopores, shows resistance values 6–10 times higher than AC08. It´s difficult to determine the origin of this feature; we speculate that the increase in resistance values with larger nanopores may suggest some form of increased charge transfer resistance. If the Li metal impedance would dominate the mid-frequency full cell impedance, we would expect opposite trends with charging and discharging (see symmetric anode-anode tests in Figure S12e-f). The Bode plots in Figures S13 and S14 reveal the same trends in the mid-frequency region. The time-dependent potential relaxation during OCV (normalized and shown in Figures 4e,f–k,l) reveals decreasing relaxation time constants 𝜏 during charging and increasing times during discharge for both materials (consistent with Ref. 38), with overall shorter relaxation time constants for AC12. Lower relaxation times with larger nanopores may suggest Li-ion diffusion in and out of the particle to be a dominating factor55, even though slower processes of another origin may also contribute. 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