Daniel Lee

Harish Banda

Sandy Périé

Coralie Marcucci

Yves Chenavier

Lionel Dubois

Pierre-Louis Taberna

Patrice Simon

Gaël De Paëpe

Florence Duclairoir

Revealing Electrolytic Ion Sorption in Layered Graphene Galleries through Low-Temperature Solid-State NMR

Keywords: Supercapacitors, pillared graphene materials, low-temperature solid state NMR, ion sieving

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INTRODUCTION

The ever-increasing demand for clean and reliable energy in mobile applications calls for the development of efficient energy storage devices. Among various electrochemical devices, supercapacitors (SCs) have emerged as excellent candidates that can handle rapid charge and discharge processes over millions of cycles. SCs consist of two porous electrodes that are immersed in an electrolytic solution and are separated by an ion-permeable membrane. Upon polarization of the electrodes, ions in the electrolyte form an electric double layer of opposite polarity and offer reliable charge-storage. In order to maximize the charge stored, nano-porous materials with high specific surface areas, such as activated carbons and carbide-derived carbons, are often used as electrodes. [START_REF] Simon | Materials for Electrochemical Capacitors[END_REF][START_REF] Béguin | Carbons and Electrolytes for Advanced Supercapacitors[END_REF][START_REF] Miller | Electrochemical Capacitors for Energy Management[END_REF][START_REF] Chmiola | Anomalous Increase in Carbon Capacitance at Pore Sizes Less Than 1 Nanometer[END_REF] With increasing demand for enhanced energy storage capabilities in SCs, other carbon-based materials, such as onion-like carbon [START_REF] Pech | Ultrahigh-Power Micrometre-Sized Supercapacitors Based on Onion-like Carbon[END_REF] , carbon nanotubes [START_REF] Frackowiak | Supercapacitor Electrodes from Multiwalled Carbon Nanotubes[END_REF] , and graphene [START_REF] Chen | Graphene Materials for Electrochemical Capacitors[END_REF] , are extensively studied. In this context, graphene-based materials are potential candidates for SCs owing to the excellent electrical conductivity and high theoretical capacitance of 550 F/g offered by graphene. [START_REF] Xia | Measurement of the Quantum Capacitance of Graphene[END_REF] However, spontaneous restacking of graphene sheets due to π-π interactions has led to experimental capacitances well below this theoretical capacitance, achieved in the range of 100 F/g for reduced graphene oxide (RGO), a graphene-like material. [START_REF] Stoller | Graphene-Based Ultracapacitors[END_REF] Recently, pillared graphene materials have emerged as a new class of materials that prevent spontaneous restacking of individual graphene sheets by separating them with a chemical linker. [START_REF] Bourlinos | Graphite Oxide: Chemical Reduction to Graphite and Surface Modification with Primary Aliphatic Amines and Amino Acids[END_REF][START_REF] Matsuo | Synthesis of Polyaniline-Intercalated Layered Materials via Exchange Reaction[END_REF][START_REF] Herrera-Alonso | Intercalation and Stitching of Graphite Oxide with Diaminoalkanes[END_REF][START_REF] Garberoglio | Gas Adsorption and Separation in Realistic and Idealized Frameworks of Organic Pillared Graphene: A Comparative Study[END_REF][START_REF] Jiang | Functional Pillared Graphene Frameworks for Ultrahigh Volumetric Performance Supercapacitors[END_REF][START_REF] Sun | Porous Graphite Oxide Pillared with Tetrapod-Shaped Molecules[END_REF][START_REF] Lee | Tunable Sub-Nanopores of Graphene Flake Interlayers with Conductive Molecular Linkers for Supercapacitors[END_REF] Among different approaches, the strategy to use graphene oxide as the precursor and alkyl diamines as chemical pillars has offered facile synthetic and design control. [START_REF] Banda | Ion Sieving Effects in Chemically Tuned Pillared Graphene Materials for Electrochemical Capacitors[END_REF][START_REF] Yuan | Straightforward Generation of Pillared, Microporous Graphene Frameworks for Use in Supercapacitors[END_REF][START_REF] Hung | Cross-Linking with Diamine Monomers To Prepare Composite Graphene Oxide-Framework Membranes with Varying d-Spacing[END_REF] Alkyl diamines bridge graphene sheets through covalent and non-covalent interactions and offer a robust pillared-graphene architecture with chemically-engineered "galleries" available for ion sorption in SCs. [START_REF] Lee | Tunable Sub-Nanopores of Graphene Flake Interlayers with Conductive Molecular Linkers for Supercapacitors[END_REF][START_REF] Banda | Ion Sieving Effects in Chemically Tuned Pillared Graphene Materials for Electrochemical Capacitors[END_REF][START_REF] Yuan | Straightforward Generation of Pillared, Microporous Graphene Frameworks for Use in Supercapacitors[END_REF] An ion-sieving study using cations of varied sizes provided an indirect evidence for ion-sorption inside the 2D galleries, wherein cations smaller than the inter-layer spacing deliver enhanced capacitances. [START_REF] Banda | Ion Sieving Effects in Chemically Tuned Pillared Graphene Materials for Electrochemical Capacitors[END_REF][START_REF] Banda | Investigation of Ion Transport in Chemically Tuned Pillared Graphene Materials through Electrochemical Impedance Analysis[END_REF] In addition, lowering the number of pillars inside the 2D galleries was also shown improve ion transport characteristics in SCs. [START_REF] Banda | Sparsely Pillared Graphene Materials for High-Performance Supercapacitors: Improving Ion Transport and Storage Capacity[END_REF] Together, these findings present the idea of ion sorption inside the 2D galleries as an avenue towards achieving enhanced capacitances in graphene-based materials. Nevertheless, atomic-scale information on ion-sorption inside the 2D galleries is still lacking and is necessary to further understand ion sorption mechanisms in these materials. Solid-state nuclear magnetic resonance (ssNMR) spectroscopy has proved to be a powerful tool for direct characterization of ion sorption in SCs from in-situ [START_REF] Wang | In Situ NMR Spectroscopy of Supercapacitors: Insight into the Charge Storage Mechanism[END_REF][START_REF] Griffin | In Situ NMR and Electrochemical Quartz Crystal Microbalance Techniques Reveal the Structure of the Electrical Double Layer in Supercapacitors[END_REF][START_REF] Wang | Real-Time NMR Studies of Electrochemical Double-Layer Capacitors[END_REF][START_REF] Oukali | In Situ Magnetic Resonance Imaging of a Complete Supercapacitor Giving Additional Insight on the Role of Nanopores[END_REF] and ex-situ studies. [START_REF] Deschamps | A Solid-State NMR Study of C70: A Model Molecule for Amorphous Carbons[END_REF][START_REF] Deschamps | Exploring Electrolyte Organization in Supercapacitor Electrodes with Solid-State NMR[END_REF][START_REF] Fulik | Electrolyte Mobility in Supercapacitor Electrodes -Solid State NMR Studies on Hierarchical and Narrow Pore Sized Carbons[END_REF][START_REF] Borchardt | Interaction of Electrolyte Molecules with Carbon Materials of Well-Defined Porosity: Characterization by Solid-State NMR Spectroscopy[END_REF][START_REF] Forse | NMR Study of Ion Dynamics and Charge Storage in Ionic Liquid Supercapacitors[END_REF] The investigation of ion-sorption in electrode micropores through soaking in increasing amounts of electrolyte has allowed for decisive differentiation of ion sorption sites. [START_REF] Wang | Real-Time NMR Studies of Electrochemical Double-Layer Capacitors[END_REF][START_REF] Deschamps | Exploring Electrolyte Organization in Supercapacitor Electrodes with Solid-State NMR[END_REF] This is possible because the chemical environment of ion/solvent is directly related to the NMR chemical shift and that adsorbed species on microporous graphitic materials undergo specific shifts due to ringcurrent effects. [START_REF] Forse | Ring Current Effects: Factors Affecting the NMR Chemical Shift of Molecules Adsorbed on Porous Carbons[END_REF] The strength of NMR experiments is thus to allow differentiating ions/solvent molecules that are present inside the pores (in-pore) from the ones lying outside the pore (expore). [START_REF] Deschamps | Exploring Electrolyte Organization in Supercapacitor Electrodes with Solid-State NMR[END_REF][START_REF] Forse | NMR Study of Ion Dynamics and Charge Storage in Ionic Liquid Supercapacitors[END_REF] For instance, ex-situ studies by Deschamps et al. have analysed the relative concentrations of anions, cations and solvents in "in-pore" and "ex-pore" sites and identified a strong influence of the nature of porous carbon on electrolyte reorganization upon polarization. [START_REF] Deschamps | Exploring Electrolyte Organization in Supercapacitor Electrodes with Solid-State NMR[END_REF] Extensive in-situ studies by Grey and co-workers on various carbons have provided substantial insight into ion dynamics during charge-discharge processes. [START_REF] Griffin | In Situ NMR and Electrochemical Quartz Crystal Microbalance Techniques Reveal the Structure of the Electrical Double Layer in Supercapacitors[END_REF][START_REF] Forse | Direct Observation of Ion Dynamics in Supercapacitor Electrodes Using in Situ Diffusion NMR Spectroscopy[END_REF][START_REF] Forse | New Perspectives on the Charging Mechanisms of Supercapacitors[END_REF] Another study of a graphene film in SCs, using ex-situ ssNMR, found two distinct processes of co-ion expulsion and counterion adsorption upon polarization. [START_REF] Li | Solid-State NMR Study of Ion Adsorption and Charge Storage in Graphene Film Supercapacitor Electrodes[END_REF] Herein, we show that ssNMR under low temperature (LT) magic angle spinning (MAS) conditions is a powerful approach to study ion-sorption in the 2D galleries of a state-of-the-art pillared graphene material (6-GH). A washing procedure, similar to that of Deschamps et al., [START_REF] Deschamps | Exploring Electrolyte Organization in Supercapacitor Electrodes with Solid-State NMR[END_REF] reveals signals from adsorbed species and the use of low temperatures limits residual motion of the adsorbed species, enabling improved nuclear polarization transfer. This, combined with MAS conditions, provides the necessary high resolution and sensitivity for detailed investigations of the adsorbed species in the in-pore regions of this complex system. In this work, we use polarization transfer from nuclei in the pillars to receptive 31 P nuclei in purposefully-selected phosphonium electrolyte ions to probe the presence of these ions inside the chemicallyengineered graphene galleries. This methodology, along with the ion-sieving property of the 2D galleries confirmed through an electrochemical study of electrolyte cations with varied sizes, revealed the presence of cations between the graphene sheets. This approach provides direct information about ion sorption in pillared materials and will thus help further optimize such materials towards high-energy SCs.

EXPERIMENTAL METHODS

Material Synthesis

Graphene oxide (GO) was synthesized following procedures reported elsewhere. [START_REF] Banda | Sparsely Pillared Graphene Materials for High-Performance Supercapacitors: Improving Ion Transport and Storage Capacity[END_REF] Pillared graphene hydrogels (6-GHs) were synthesized using a mixture of 5 ml of aqueous GO (5 mg/ml) solution and 32.5 mg of 1.6-hexanediamine ( 15 N-labelled) pillar molecule (Fig. 1a). The reaction mixture was sonicated for 10 min, transferred into a 23 ml Teflon vessel and heated at 180 o C for 17 h. The resulting hydrogel was cleaned with excess ethanol and water sequentially, and freezedried (sample freezing was carried out using liquid N 2 ) to obtain 6-GH aerogels.

Electrochemical tests

The synthesized aerogels were tested in a three-electrode supercapacitor configuration (Fig. S1) with porous carbon (YP50) as counter and silver wire as pseudo-reference electrodes, respectively. A 25 μm thick cellulose sheet served as a separator. The working electrodes were fabricated as a slurry by mixing active materials, polyvinylidene fluoride (PVDF), and acetylene black carbon in a ratio of 80:10:10 using N-methyl-2-pyrrolidone and were coated onto 0.5 cm 2 stainless steel disks. The as-prepared electrodes were dried at 65 o C in air for 3 h prior to drying under vacuum at 120 o C overnight. The dried electrodes had an active mass loading of 2-3 mg.cm -2 . 1 M Tetralkylphosponium tetrafluoroborate (TAPBF 4 ) salt solutions in anhydrous acetonitrile (ACN) with varying cation sizes; ethyl (TEPBF 4 ) -0.68 nm, butyl (TBPBF 4 ) -0.82 nm and octyl (TOPBF 4 ) -1.12 nm were used as electrolytes. TEPBF 4 and TBPBF 4 were purchased from TCI. TOPBF 4 was prepared through an ion-exchange procedure between TOPBr (purchased from TCI) and NaBF 4 in a mixture of ACN/acetone (50:50). A multichannel VMP3 potentiostat with EC-Lab software (Biologic) was used for all electrochemical studies.

ssNMR experimental techniques

Conventional and DNP-enhanced solid-state nuclear magnetic resonance (ssNMR) spectroscopy were performed using a Bruker AVIII 9.4 T 263 GHz / 400 MHz DNP-NMR spectrometer equipped with a 3.2 mm low-temperature-capable magic angle sample spinning (MAS) probe. DNP was not attempted for the pillared materials due to the known challenges with hyperpolarizing conductive materials. [START_REF] Svirinovsky-Arbeli | The Effects of Sample Conductivity on the Efficacy of Dynamic Nuclear Polarization for Sensitivity Enhancement in Solid State NMR Spectroscopy[END_REF] Here, instead, we show the usefulness of lowtemperature measurements. All experiments were performed using cryogenic nitrogen gas to cool and spin the sample at 100 K with a MAS frequency of 8 kHz unless otherwise specified.

The sample temperature was externally calibrated using the T 1 of 79 Br in KBr. [START_REF] Thurber | Measurement of Sample Temperatures under Magic-Angle Spinning from the Chemical Shift and Spin-Lattice Relaxation Rate of 79Br in KBr Powder[END_REF] { 1 H-} 31 P and { 1 H-} 15 N cross-polarization (CP)MAS NMR experiments were recorded using 100 kHz nutation for 1 H /2 pulses and 65 kHz for 1 H heteronuclear continuous wave decoupling, a ramped (50-100%) power to match a Hartmann-Hahn CP condition when using 50 kHz for 31 P or 36 kHz [START_REF] Sun | Porous Graphite Oxide Pillared with Tetrapod-Shaped Molecules[END_REF] N nutation during 1 ms CP spin-locking and using a spin-echo of one rotor period total duration (50 kHz for 31 P or 36 kHz 15 N -pulses) before free-induction decay (FID) acquisition. Between 444 and 8192 and 444 and 1664 transients were recorded for the { 1 H-} 31 P and { 1 H-} [START_REF] Sun | Porous Graphite Oxide Pillared with Tetrapod-Shaped Molecules[END_REF] N CPMAS experiments, respectively, using a recycle delay of ~1 s between transients and 50 Hz exponential apodization before Fourier transformation of the FID. The 2D z-filtered TEDOR 15 N-31 P dipolar correlation spectrum of 6-GH was recorded with a starting { 1 H-} 31 P CP step of 0.5 ms, 7 ms total TEDOR mixing, 2048 transients for each of 6 complex (States-TPPI) t 1 increments of 123.3 s, using a recycle delay of ~1 s between transients and 300 and 50 Hz exponential apodization in the direct and indirect dimensions, respectively, before double Fourier transform. [START_REF] Jaroniec | 3D TEDOR NMR Experiments for the Simultaneous Measurement of Multiple Carbon-Nitrogen Distances in Uniformly 13C,15N-Labeled Solids[END_REF] For the 1D { 15 N-} 31 P z-filtered TEDOR experiments of 6-GH with various electrolytes, 7, 14, or 20 ms total TEDOR mixing (as stated) was employed for up to 10240 transients. The other parameters were as for the 2D version. For the DNP-enhanced 2D [START_REF] Sun | Porous Graphite Oxide Pillared with Tetrapod-Shaped Molecules[END_REF] N-31 P z-filtered TEDOR experiment of 25 mM guanosine-15 N 5 5'-monophosphate sodium salt solution (GMP), a starting { 1 H-} 31 P CP step of 2.25 ms and a 7 ms total TEDOR mixing period were employed, with 32 transients for each of 16 complex (States-TPPI) t 1 increments of 123.3 s acquired, using a recycle delay of 3.4 s between transients and 50 Hz exponential apodization in both dimensions before double Fourier transform.

Sample preparation for ssNMR

6-GH samples for ssNMR studies were prepared as pellets (~7 mg) that were either soaked in an electrolyte for 90 min or polarized for 90 min at a constant potential of -1.3 V or +1.5 V vs.

Ag in a three-electrode Swagelok cell (Fig S1). Wet pellets of 6-GH (soaked/polarized) were then transferred to a P4 fritted Buchner filter (10-15 μm) and mildly washed with ~10 ml of acetonitrile under applied vacuum. Later, the dried powder was further dried in a vacuum oven at 65 o C for 4 h. Samples were also prepared without the washing step by directly transferring wet pellets into vacuum oven.

RESULTS AND DISCUSSION

Pillared graphene materials are generally synthesized through a direct reaction of aqueous GO solution with alkyl diamines as pillars. [START_REF] Herrera-Alonso | Intercalation and Stitching of Graphite Oxide with Diaminoalkanes[END_REF] The amine groups react with epoxy and carboxylic groups on adjacent graphene oxide sheets and result in covalently-bridged graphene sheets. However, owing to the reducing nature of alkyl diamines, GO sheets undergo partial and simultaneous chemical reduction and restack into graphitic particles, resulting in a biphasic material that consists of domains of both covalently-bridged and restacked graphene. [START_REF] Banda | Ion Sieving Effects in Chemically Tuned Pillared Graphene Materials for Electrochemical Capacitors[END_REF] The obtained pillared materials are then reduced further to remove residual oxygen functionalities, improve electrical conductivity and facilitate their application in SCs. Recently, we synthesized a pillared graphene hydrogel (6-GH) through simultaneous pillaring and reduction of GO in a onestep hydrothermal process using 1,6-hexanediamine as the pillar molecule. [START_REF] Banda | Sparsely Pillared Graphene Materials for High-Performance Supercapacitors: Improving Ion Transport and Storage Capacity[END_REF] This material demonstrated a high specific capacitance of ~225 F/g, benefitting from an enhanced ion sorption in the synthesized 2D galleries. In order to investigate this ion-sorption through ssNMR techniques, herein, the pillar molecules were isotopically-enriched using [START_REF] Sun | Porous Graphite Oxide Pillared with Tetrapod-Shaped Molecules[END_REF] Ions adsorb in the inter-layer nanopores and the inter-particular micropores (together termed as in-pore ions) whereas, the ions in meso-macro pores (termed as ex-pore ions) serve as buffer stock for the bulk electrolyte.

The synthesized 6-GH displays a 3D monolithic structure and a strong presence of both crosslinked (pillared graphene) and restacked (RGO-like) domains in the X-ray diffraction (XRD) patterns (Fig. 1b &S3). Scanning electron microscopy shows the presence of an extended 3D macroporous structure throughout the monolith (Fig. 1b). From XRD patterns, an inter-layer separation of 7.8 Å has been assigned between the graphene sheets, in line with earlier reports on diamine-pillared graphene materials. [START_REF] Bourlinos | Graphite Oxide: Chemical Reduction to Graphite and Surface Modification with Primary Aliphatic Amines and Amino Acids[END_REF][START_REF] Herrera-Alonso | Intercalation and Stitching of Graphite Oxide with Diaminoalkanes[END_REF] X-ray photoelectron spectra (XPS) show that the majority of N in 6-GH occur as amines in pillars with smaller contributions from N as pyrrolic and graphitic moieties (see Fig. S4). Low temperature { 1 H-} [START_REF] Sun | Porous Graphite Oxide Pillared with Tetrapod-Shaped Molecules[END_REF] N CP MAS NMR spectra of 6-GH show the distinct presence of secondary amines (at { 15 N} ~80 ppm) in 6-GH (see Fig. S5a) indicating the covalent bridging between alkyl diamines and graphene layers, as well as primary amines (at { 15 N} ~20-50 ppm) and secondary amides, pyrrolic, pyridinic, and graphitic N (at Tetrafluoroborate (BF 4 -) 0.48 Table 1. Ion sizes of the various electrolytic salts used in this study. These values were obtained from prior reports in the literature. [START_REF] Levi | Electrochemical Quartz Crystal Microbalance (EQCM) Studies of Ions and Solvents Insertion into Highly Porous Activated Carbons[END_REF][START_REF] Mysyk | Confinement of Symmetric Tetraalkylammonium Ions in Nanoporous Carbon Electrodes of Electric Double-Layer Capacitors[END_REF] They were calculated using molecular modelling approaches and verified by crystallographic measurements, correspond to ions in their unsolvated states.

{ 15 N} ~100-200 ppm). 38
6-GH was tested for its electrochemical properties through cyclic voltammetry (CV) using a family of 1M (TAP + BF 4 -/ACN) electrolytes since the large NMR receptivity of 31 P in the cations results in an excellent probe for NMR analysis (compared to 14/15 N and [START_REF] Garberoglio | Gas Adsorption and Separation in Realistic and Idealized Frameworks of Organic Pillared Graphene: A Comparative Study[END_REF] C in tetraalkylammonium ions). Alkyl phosphonium cations of varied sizes with increasing alkyl chain lengths of ethyl (TEP + ), butyl (TBP + ) and octyl (TOP + ) (Table 1) allowed for analysis of size-based ion sieving [START_REF] Eliad | Ion Sieving Effects in the Electrical Double Layer of Porous Carbon Electrodes: Estimating Effective Ion Size in Electrolytic Solutions[END_REF][START_REF] Levi | Electrochemical Quartz Crystal Microbalance (EQCM) Studies of Ions and Solvents Insertion into Highly Porous Activated Carbons[END_REF][START_REF] Mysyk | Confinement of Symmetric Tetraalkylammonium Ions in Nanoporous Carbon Electrodes of Electric Double-Layer Capacitors[END_REF] in 6-GH. CVs were recorded at 20 mV/s after electrowetting of the electrodes during several initial cycles and the obtained curves were normalized using the weight of graphene material in the electrode (Fig. 2). CVs obtained in TEP + BF 4 -/ACN, TBP + BF 4 -/ACN, and TOP + BF 4 -/ACN for 6-GH show similar rectangular curves for potentials higher than 0.2 V vs Ag -the initial OCV -but differ greatly for potentials lower than 0.2 V vs Ag. Since anion adsorption is recognized as a major process under positive polarization, the similarity in the curves is expected as the BF 4 -anion (with a smaller diameter than the d-spacing of 6-GH) is used in all cases. However, under negative polarization with respect to OCV, a gradual decrease in the intensity of currents can be seen with increasing cation size. Considering that TEP + is smaller than the inter-layer gallery spacing of 7.8 Å in 6-GH, it shows a rectangular behaviour which is consistent with a facile ion sorption within the carbon material. However, TBP + and TOP + , which are, respectively, in the same range or larger than the d-spacing have increasingly limited access to the galleries and thus the CVs show a fairly symmetric deformation at negative voltages with substantial decrease in current. As a result, it turns out 6-GH's electrochemical behaviour, in such electrolytes, upon negative polarization is correlated with the cation size: the larger the cation, the lower the current. It is noteworthy that CVs recorded using TEPBF 4 electrolyte displayed relatively similar curves from the 1 st to 100 th cycles (Fig. S6a). However, CVs using larger TAPBF 4 salts displayed a gradual enhancement in current in the first 100 cycles (Fig. S6b). We suspect that a gradual activation and enhancement of electrochemically active in-pore surface area may cause this gradual increase in currents for ions that experience more difficulties to access the inter-layer galleries. These electrochemical results of 6-GH in TEP + BF 4 -, TBP + BF 4 -, and TOP + BF 4 -/ACN thus demonstrate a sieving based on ion size versus d-spacing of a graphene-based material, and highlight 6-GH as well-suited for NMR characterization of ion sorption in inter-layer graphene galleries.

LT-MAS NMR experiments were performed on pristine and polarized 6-GH electrodes that were prepared by washing the excess electrolyte from the meso/macro pores in order to get a clearer picture of only species that are close to graphene surfaces. This washing is similar to the approach taken by Deschamps et al. [START_REF] Deschamps | Exploring Electrolyte Organization in Supercapacitor Electrodes with Solid-State NMR[END_REF] The scope of the work here is to analyse whether ions are only adsorbed in the inter-particle micro porosity and/or also in the inter-layer pores (Fig. 1b), and the low temperature experiments enable the sensitive detection required to probe these distinctions via NMR spectroscopy. Samples were also prepared without the washing step as a comparison. Here, the combination of [START_REF] Forse | Ring Current Effects: Factors Affecting the NMR Chemical Shift of Molecules Adsorbed on Porous Carbons[END_REF] The { 1 H-} 31 P LT CPMAS NMR spectra of 6-GH unpolarized and soaked in electrolyte and washed with ACN, shown in Fig. 3, qualitatively demonstrate that the low temperature methodology provides good NMR signal-to-noise ratios for small amounts of remaining electrolyte, which are quite different to those of unwashed samples. Notably, the 31 P spectrum of 6-GH soaked in TEP + BF 4 -/ACN and unwashed displays a major peak at 42 ppm with minor shoulders at lower chemical shifts (30-38 ppm). This is in stark contrast to the washed sample that shows the most intense peak at 30 ppm, with a remaining low intensity and broad contribution centred at ~38 ppm (see Fig. 3a). The observed [START_REF] Forse | Ring Current Effects: Factors Affecting the NMR Chemical Shift of Molecules Adsorbed on Porous Carbons[END_REF] P spectrum of the unwashed sample is comparable to that observed for earlier work with the same electrolyte but with porous carbon electrodes and corresponds to free ex-pore (~41 ppm) and adsorbed in-pore (~34 ppm) cations, respectively. [START_REF] Griffin | In Situ NMR and Electrochemical Quartz Crystal Microbalance Techniques Reveal the Structure of the Electrical Double Layer in Supercapacitors[END_REF] It is interesting to note that the 31 P peak around 42 ppm in the soaked and unwashed sample is also present in the bare salt although the resonance is less broadened. This suggests the presence of an ion-pairing effect between TEP + and BF 4 -in the unwashed sample (at the concentration used in this study). Interestingly, for the washed sample, this large contribution at 42 ppm is mostly removed. The remaining 31 P resonance appears around 30 ppm and is tentatively assigned to ex-pore TEP + ions that are shielded by distance from BF 4 -(possibly owing to a full solvation shell of ACN). The resonance at 38 ppm, which is clearly present in the sample polarized at -1.3 V and washed, can be attributed to adsorbed in-pore cations. The effect of the graphene ring current can clearly be seen here because of the relatively small size of the TEP + cations.

Unwashed 6-GH prepared with TBP + BF 4 -/ACN gave a { 1 H-} 31 P LT CPMAS NMR spectrum of similar intensity to that of unwashed TEP + BF 4 -/ACN, but displayed a broad signal (see Fig. 3b) around 31-34 ppm; we note that peak intensities are discussed here as a crude approximation but the study remains qualitative. It is interesting to note that these chemical shifts are also consistent with an ion-pairing effect since they match the resonances present in the bare salt.

Nevertheless, TBP + cations are larger, so one should expect the effect of the BF 4 -anions on the [START_REF] Forse | Ring Current Effects: Factors Affecting the NMR Chemical Shift of Molecules Adsorbed on Porous Carbons[END_REF] P chemical shift to be reduced. It is also interesting to note that there is a diversity in 31 P chemical shift visible for both pure TEPBF 4 and TBPBF 4 (Fig. 3a inset and Fig. 3b). The pure salts are similar to organic ionic plastic crystals, with disorder leading to different 31 P chemical shifts. [START_REF] Armel | Ionic Liquids and Organic Ionic Plastic Crystals Utilizing Small Phosphonium Cations[END_REF] Upon washing, the resulting spectrum of 6-GH with TBP + BF 4 -/ACN shows a dramatic decrease in the 31 P signal intensity, as could be expected; most free TBP + are washed away. This is not the case after the sample has been polarized to -1.3V where one can detect a large signal centred at 31 ppm, which is thus attributed to adsorbed in-pore TBP + .

The relatively small difference in [START_REF] Forse | Ring Current Effects: Factors Affecting the NMR Chemical Shift of Molecules Adsorbed on Porous Carbons[END_REF] P chemical shift between the in-pore signals (31 ppm) and free cations (34 ppm) for TBP + BF 4 -/ACN could be attributed to the lesser influence of ring currents from the graphene electrode and interactions with BF 4 -anions, respectively, on the 31 P spins in the larger cations. Overall, this analysis shows that washing the samples is an efficient way to focus mainly on adsorbed cations. Hereafter, all discussion will hence be focused on washed samples.

After being polarized at -1.3 V vs. Ag in TEP + BF 4 -/ACN (Fig. 3a), TBP + BF 4 -/ACN (Fig. 3b) or TOP + BF 4 -/ACN (Fig. S7), 6-GH samples exhibit a tremendous increase in the intensity of adsorbed cation signal, compared to that of the corresponding soaked sample (~50 times). This indicates, as expected, that negative polarization results in enhanced adsorption of cations. TEP + displays a major, broad [START_REF] Forse | Ring Current Effects: Factors Affecting the NMR Chemical Shift of Molecules Adsorbed on Porous Carbons[END_REF] P signal at 38 ppm, thus corresponding to adsorbed species. The intense TBP + 31 P signal is clearly recorded at 31 ppm. Here again, this negligible shift between bulk and adsorbed species is explained by the graphene shielding effect [START_REF] Forse | Ring Current Effects: Factors Affecting the NMR Chemical Shift of Molecules Adsorbed on Porous Carbons[END_REF] and interactions with BF 4 -anions being minimized by the lengthier alkyl chains from this cation. This interpretation is further confirmed by the absence of shift between bulk and adsorbed peaks for TOP + (both ~30 ppmsee Fig. S7).

Contrary to expectations, the { 1 H-} 31 P LT CPMAS NMR spectra of 6-GH soaked with electrolyte and polarized directly to +1.5 V vs. Ag (from its pristine state) for 90 min show peaks corresponding to adsorbed cations (see Fig. 3). This could also indicate that charge diffusion upon cycling does not rely on a full anion/cation exchange or on full cation depleting mechanisms. [START_REF] Griffin | Ion Counting in Supercapacitor Electrodes Using NMR Spectroscopy[END_REF] Another interpretation could be that the ions enter the inter-layer graphene galleries upon soaking 6-GH, and cations are then not fully removed with simple polarization up to +1.5 V. This presence of adsorbed cations even under positive polarization is interesting and supports our earlier impedance studies, wherein ion transport was found to depend strongly on both counter ions and co-ions. [START_REF] Banda | Investigation of Ion Transport in Chemically Tuned Pillared Graphene Materials through Electrochemical Impedance Analysis[END_REF] The presence of adsorbed cations under positive polarization was also observed with room temperature ssNMR spectroscopy (see Fig. S5b). A comparison to the corresponding ssNMR spectrum recorded at low temperature (Fig. 3 and Fig. S5b) demonstrates the sensitivity gains from these low temperature measurements where a worse signal-to-noise ratio was obtained at room temperature even after 25 times more accumulated scans.

Although interactions between electrolyte ions and graphene have been inferred in the above ssNMR data, no clear evidence was observed to differentiate ion sorption in the in-pore interparticular and in-gallery 2D porosities. (i) TEP + and TBP + cations may enter the inter-layer spaces in 6-GH under negative polarization and be in sufficiently close proximity to the pillar molecules; (ii) relatively more cations may enter the inter-particular porosity under negative polarization, leading to shorter cation-pillar distances on average than when the sample is only soaked. To distinguish scenario (i), an electrolyte with cations of diameter larger than the inter-gallery d-spacing of 6-GH was employed; TOP + BF 4 -/ACN contains cations with a diameter of ~ 11.2 Å (cf. 7.8 Å for the dspacing). [START_REF] Levi | Electrochemical Quartz Crystal Microbalance (EQCM) Studies of Ions and Solvents Insertion into Highly Porous Activated Carbons[END_REF] Although { 1 H-} 31 P LT CPMAS NMR experiments of 6-GH in TOP + BF 4 -/ACN provide good signal-to-noise (see Fig. S7), no signal is observed for the { 15 N-} 31 P zf-TEDOR experiment (see Fig. 4a and Fig. S8). This suggests that there is not a sufficient amount of TOP + ions in proximity to [START_REF] Sun | Porous Graphite Oxide Pillared with Tetrapod-Shaped Molecules[END_REF] N from the electrode and thus that the large TOP + ions do not enter into the graphene galleries of 6-GH. This corroborates the conclusions from the electrochemical measurements (vide supra).

To ensure that the absence of { 15 N-} 31 P zf-TEDOR signal for 6-GH with TOP + BF 4 -/ACN is not due to the larger distance between 31 P and 15 N because of the octyl chains of TOP, a reference experiment was performed. A guanosine derivative was chosen (Guanosine-15 N 5 5'monophosphate sodium salt solution, GMP) that bears a variety of 31 P-15 N distances, from approximately 6 to 11 Å (cf. TOP + radius of <10 Å). From a 2D LT CPMAS 15 N-31 P zf-TEDOR NMR spectrum (using the same TEDOR recoupling time as for the experiments on 6-GH) for diluted (25 mM) GMP, cross peaks for even the furthest 15 N-31 P spin pairs are observed (see Fig. S9). Moreover, longer TEDOR recoupling times (up to 20 ms) were also attempted for 6-GH in TOP + BF 4 -/ACN, with still no observed signal (see Fig. S8). This rules out the longer alkyl chain length of TOP + as the reason for absence of { 15 N-} 31 P zf-TEDOR signal. Therefore, this shows that TOP + cations do not enter the graphene galleries as expected considering their size and, by extension, confirms that the NMR signal observed for { 15 N-} 31 P zf-TEDOR experiments of 6-GH with TEP + BF 4 -/ACN and TBP + BF 4 -/ACN does indeed come from cations confined between the pillared layers. The proximity between electrolyte and the pillars is only detected here through { 15 N-} 31 P zf-TEDOR experiments when there is a sufficient number of dipolar (through-space) coupled nuclei, as is the case when the electrolyte can enter high-surface area pillared graphene interlayers. To gain further information on specific interaction sites within the graphene galleries, a 2D LT CPMAS [START_REF] Sun | Porous Graphite Oxide Pillared with Tetrapod-Shaped Molecules[END_REF] N-31 P zf-TEDOR NMR spectrum of 6-GH with TEP + BF 4 -/ACN and negative polarization was acquired, and is shown in Fig. 5. It can be seen that 31 P spins from the electrolyte cations correlate to [START_REF] Sun | Porous Graphite Oxide Pillared with Tetrapod-Shaped Molecules[END_REF] N in a variety of different environments found in the pillared graphene material: free amines, N in α of the graphene sheet, N from amides, and N from pyridinic or pyrrolic moieties. Moreover, it appears that different [START_REF] Sun | Porous Graphite Oxide Pillared with Tetrapod-Shaped Molecules[END_REF] N environments correlate more or less strongly to two particular 31 P chemical shifts (evidenced by the relative intensity of the contours and via cross-sectional slices (see Fig. S11)), at 39 and 36 ppm. Amines and amides that could be expected near to the edges of the graphene sheets correlate to the higher-shifted 31 P resonance at 39 ppm, which could be expected if cations near the edges were then less affected by ring currents in the graphene. [START_REF] Forse | Ring Current Effects: Factors Affecting the NMR Chemical Shift of Molecules Adsorbed on Porous Carbons[END_REF] Conversely, cations in the centre of the sheets would be most affected by the ring currents. Indeed, the 31 P resonance showing the lower shift, at 36 ppm, correlates most strongly to [START_REF] Sun | Porous Graphite Oxide Pillared with Tetrapod-Shaped Molecules[END_REF] N-containing moieties that are expected to covalently link the graphene sheets together (N in α of the graphene and pyridinic-or pyrrolic-N). This tentative assignment indicates that the broadness (~ 9 ppm) of the 31 P NMR signal from adsorbed TEP + cations is at least partly due to varied positions of the electrolyte cations with respect to the pillared graphene electrode.

CONCLUSIONS

In summary, this study presents low temperature MAS NMR spectroscopy as an efficient and powerful technique to investigate electrolytic ion sorption in pillared graphene hydrogel electrodes suitable for use in supercapacitors. Extensive analysis using electrolytic cations of varied sizes and under different bias potentials has revealed that ions enter inter-layer 2D galleries in 6-GH when chosen appropriately. Specifically, when 6-GH is used in combination with a cation of larger diameter than the d-spacing, nuclear polarization transfer is not observed between the electrolyte cations and the pillars as these ions are too big to enter the 2D galleries.

Only when 6-GH is used in combination with a cation smaller than the d-spacing do cations enter the graphene galleries. Nuclear polarization transfer between cations inside the galleries and isotopically-enriched marker nuclei from the pillars reveals that the cations can be found in various chemical environments within these graphene galleries. Overall, LT MAS ssNMR offers a new atomic-scale method to probe ion-sorption in SCs and similar devices, presenting enormous potential for understanding dynamic mechanisms, thus leading to further improved energy storage materials.

ASSOCIATED CONTENT

Supporting Information

Material characterization, instrumentation details, ssNMR data acquisition protocols, control experiments on guanosine derivates are included in supporting information file.

Present address: HB: Department of Chemistry and Biochemistry, The University of Texas, El ǂ Paso, Texas, USA.

  N-labeled 1,6hexanediamine.

Figure 1 .

 1 Figure 1. (a) Schematic representation of the synthesis of pillared graphene hydrogel (6-GH)

Figure 2 .

 2 Figure 2. Cyclic voltammogram curves of 6-GH in TEPBF 4 , TBPBF 4 and TOPBF 4 / acetonitrile

43 Figure 3 .

 433 Figure 3. { 1 H-} 31 P LT CPMAS NMR spectra at 100 K of 6-GH electrodes with TEP + BF 4 -/ACN

Figure 4 . 15 N

 415 Figure 4. 1D LT CPMAS { 15 N-} 31 P zf-TEDOR NMR spectra of 6-GH electrodes after negative

Figure 5 .

 5 Figure 5. 2D LT CPMAS 15 N-31 P zf-TEDOR NMR spectrum of 6-GH electrodes with negative

Funding Sources

Authors acknowledge funding support by CEA and by the French National Research Agency (SUGGEST-ANR-15-CE05-0022, ANR-12-BS08-0016-01, ANR-11-LABX-0003-01 and RTB) as well as the European Research Council (ERC-CoG-2015, No. 682895). ACKNOWLEDGEMENT Authors appreciate the access to mutualized equipment provided by PFNC Nano-characterization Minatec platforms. Present address: #DL: Department of Chemical Engineering, University of Manchester, Manchester M13 9PL, United Kingdom.

AUTHOR INFORMATION

Corresponding Author

Florence Duclairoir: florence.duclairoir@cea.fr Gaël De Paëpe: gael.depaepe@cea.fr

Present Addresses

Author Contributions DL, HB, FD and GDP proposed and led the project. DL, HB, SP and CM performed experiments. PLT, PS and LD helped interpret results. The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. †These authors contributed equally.


Kangkang Ge

Hui Shao

Pierre-Louis Taberna
email: pierrel-louis.taberna@univ-tlse3.fr

Patrice Simon
email: patrice.simon@univ-tlse3.fr

Understanding Ion Charging Dynamics in Nanoporous Carbons for Electrochemical Double Layer Capacitor Applications

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electrolyte was experimentally investigated in electrolytes with various concentrations by using a cavity micro-electrode. We were able to observe electrolyte depletion and we systematically studied the key parameters that will affect the electrolyte depletion, resulting in major changes in the charging kinetics. Results showed that low concentration, high overpotential potential and small carbon pore size triggered the electrolyte depletion, decreasing the charging kinetics. These findings further push our understanding of the ion dynamics of EDL at charged porous carbon/electrolyte interface.

TOC GRAPHICS

Understanding the formation of the electric double layer (EDL) at porous carbon electrode/electrolyte interface is of high importance in various applications such as energy storage (electrochemical double-layer supercapacitors), [START_REF] Simon | Perspectives for electrochemical capacitors and related devices[END_REF] capacitive deionization, [START_REF] Rubin | Induced-Charge Capacitive Deionization: The Electrokinetic Response of a Porous Particle to an External Electric Field[END_REF][START_REF] Rica | Thermodynamic relation between voltage-concentration dependence and salt adsorption in electrochemical cells[END_REF][START_REF] Zhang | Ionophobicity of carbon sub-nanometer pores enables efficient desalination at high salinity[END_REF] or energy harvesting. [START_REF] Brogioli | Extracting Renewable Energy from a Salinity Difference Using a Capacitor[END_REF][START_REF] Emmerich | Enhanced nanofluidic transport in activated carbon nanoconduits[END_REF][START_REF] Simoncelli | Blue Energy and Desalination with Nanoporous Carbon Electrodes: Capacitance from Molecular Simulations to Continuous Models[END_REF] Classical planar EDL theory, so-called the Gouy-Chapman-Stern model, has been established using two parallel charged planar electrodes immersed in an electrolytic solution, [START_REF] Shao | Nanoporous carbon for electrochemical capacitive energy storage[END_REF] with the Poisson-Nernst-Plank (PNP) equation to address time-dependent charge-relaxation phenomena. [START_REF] Sakaguchi | Charging dynamics of the electric double layer in porous media[END_REF] Nevertheless, moving from 2D planar to a high surface area porous electrode comes with confinement effect, [START_REF] Pean | And Electrosorption Effects on the Diffusion of Ions in Nanoporous Carbon Electrodes[END_REF][START_REF] Merlet | Highly confined ions store charge more efficiently in supercapacitors[END_REF] presence of chemical defects [START_REF] Dupuis | How chemical defects influence the charging of nanoporous carbon supercapacitors[END_REF] , potential distribution, curvature effects [START_REF] Seebeck | Elucidating Curvature-Capacitance Relationships in Carbon-Based Supercapacitors[END_REF] (…) that make porous electrode behavior different from classical planar ones.

A few decades ago, de Levie first proposed a transmission line model (TLM), which considers uniformly distributed capacitance and solution resistance throughout the pores, to model the charge storage behaviors in porous carbon. [START_REF] Levie | On Porous Electrodes in Electrolyte Solutions[END_REF] TLM and their associated equivalent circuits are widely used to describe the frequency behavior under small potential bias in porous carbon electrodes by catching the linear or the early-times nonlinear kinetics. [START_REF] Sakaguchi | Charging dynamics of the electric double layer in porous media[END_REF][START_REF] Bazant | Diffuse-charge dynamics in electrochemical systems[END_REF] To move further, new theoretical models have been proposed. Indeed, the required voltage for a realistic EDL charging process up to about 1.0V in aqueous electrolyte [START_REF] Aslyamov | Relation between Charging Times and Storage Properties of Nanoporous Supercapacitors[END_REF] is always larger when compared to 25 mV (RT/F~25 mV at room temperature), which is the potential derived from the linear approximation of PNP equation [START_REF] Bazant | Diffuse-charge dynamics in electrochemical systems[END_REF][START_REF] David | Effect of Salt Depletion on Charging Dynamics in Nanoporous Electrodes[END_REF] , above which potential the mathematic calculations are challenged. Therefore, Biesheuvel and Bazant [START_REF] Biesheuvel | Nonlinear dynamics of capacitive charging and desalination by porous electrodes[END_REF] derived nonlinear porous-electrode equations and found two domains. At small voltages or early times, a porous electrode acts like a transmission line, governed by a linear diffusion equation that results in a potential distribution inside the porous carbon network; while for large voltages and long times, porous electrode kinetics is governed by coupled, nonlinear diffusion equations and local electrolyte depletion [START_REF] Biesheuvel | Nonlinear dynamics of capacitive charging and desalination by porous electrodes[END_REF] .

Conway [START_REF] Conway | Electrochemical supercapacitors: scientific fundamentals and technological applications[END_REF] depicted an electrolyte concentration depletion when there is a limited amount of electrolyte ions at the charged porous carbon/electrolyte interface and pointed out its negative effect on the local ionic conductivity-resulting in power performance limitation. Besides, the increased electrolyte resistance caused by electrolyte depletion makes the charging kinetics slower and nonlinear. [START_REF] David | Effect of Salt Depletion on Charging Dynamics in Nanoporous Electrodes[END_REF][START_REF] Biesheuvel | Nonlinear dynamics of capacitive charging and desalination by porous electrodes[END_REF] Later, Lian and co-workers [START_REF] Lian | Blessing and Curse: How a Supercapacitor's Large Capacitance Causes its Slow Charging[END_REF] proposed a parallel stacked electrode model to describe the carbon charging kinetics. They confirmed the existence of the two relaxation time domains, with the RC relaxation (TLM) at early times or low voltages, and a diffusion limitation domain at longer times. This model well bridged a 5-order of magnitude gap between single slit pore simulation and experimentally observed relaxation time constant at the electrode level. But the key parameters such as finite ion size and pore length/morphology should also be taken into account. Since recently, models have been refined to get closer to actual three-dimensional confinement systems, such as chemically driven charge localization (CDCL) model [START_REF] Dupuis | How chemical defects influence the charging of nanoporous carbon supercapacitors[END_REF] , modified PNP model, [START_REF] Kilic | Steric effects in the dynamics of electrolytes at large applied voltages. II. Modified Poisson-Nernst-Planck equations[END_REF][START_REF] Yang | Simulating the charging of cylindrical electrolyte-filled pores with the modified Poisson-Nernst-Planck equations[END_REF] and dynamic density functional theory (DDFT) [START_REF] Ma | Dynamic density functional theory for the charging of electric double layer capacitors[END_REF] … Together with experimental parameters (for instance the finite pore length, [START_REF] Yang | Simulating the charging of cylindrical electrolyte-filled pores with the modified Poisson-Nernst-Planck equations[END_REF][START_REF] Janssen | Transmission Line Circuit and Equation for an Electrolyte-Filled Pore of Finite Length[END_REF] pore size distribution, [START_REF] Lian | Non-Negligible Roles of Pore Size Distribution on Electroosmotic Flow in Nanoporous Materials[END_REF] curvature, [START_REF] Seebeck | Elucidating Curvature-Capacitance Relationships in Carbon-Based Supercapacitors[END_REF] ion confinement, [START_REF] Pean | And Electrosorption Effects on the Diffusion of Ions in Nanoporous Carbon Electrodes[END_REF][START_REF] Futamura | Partial breaking of the Coulombic ordering of ionic liquids confined in carbon nanopores[END_REF] desolvation and defects [START_REF] Dupuis | How chemical defects influence the charging of nanoporous carbon supercapacitors[END_REF] ), it greatly contributes to the theoretical understanding of ion transport kinetics in porous carbon electrodes. However, experimental approaches are barely proposed to further validate these theoretical approaches, and experimental investigations of the EDL formation and evolution for the subnanopores with confinement are highly desired.

The major obstacle that hinders experimental tracking of ionic dynamics is the fast charge relaxation, namely the fast charge separation and charging of EDL resulting from the electrostatic nature of the charge storage. Dilute electrolyte solutions with lower ionic conductivity are preferred to slow down ion dynamics in order to track the small charging kinetic differences. Also, the use of micro-electrode should be preferred in low electrolyte concentrations to limit the ohmic drops and allow for the electrochemical kinetics study. For instance, Zuleta [START_REF] Zuleta | Determination of diffusion coefficients of inside carbon nanopores using the single particle microelectrode technique[END_REF][START_REF] Zuleta | Determination of the effective diffusion coefficient of nanoporous carbon by means of a single particle microelectrode technique[END_REF][START_REF] Zuleta | Determination of diffusion coefficients of BF4-inside carbon nanopores using the single particle microelectrode technique[END_REF] and co-workers determined the effective diffusion coefficient in porous carbon using a single particle micro-electrode technique. Besides, cavity micro-electrode (CME) was found interesting in exploring electrochemical kinetics of various materials for energy storage applications such as lithium iron phosphate (LFP), [START_REF] Come | Electrochemical Kinetic Study of LiFePO4 Using Cavity Microelectrode[END_REF][START_REF] Kisu | Electrochemical kinetics of nanostructure LiFePO4/graphitic carbon electrodes[END_REF] MXenes 2D metal carbides [START_REF] Come | A Non-Aqueous Asymmetric Cell with a Ti2C-Based Two-Dimensional Negative Electrode[END_REF] and porous. [START_REF] Portet | Electrochemical characterizations of carbon nanomaterials by the cavity microelectrode technique[END_REF] In this work, carbide-derived carbons (CDCs) with high surface area, tunable porosity, controllable average pore size and narrow pore size distributions were used as model porous carbon materials for revealing the EDL charging mechanisms under confinement. [START_REF] Pe´an | On the Dynamics of Charging in Nanoporous Carbon-Based Supercapacitors[END_REF] The use of a CME made it possible to reveal the fundamental electrochemical kinetic behaviors. [START_REF] Cachet-Vivier | Development of cavity microelectrode devices and their uses in various research fields[END_REF] While previous works proposed theoretical approaches built on models describing salt depletion and charge relaxation time scales at largely applied potentials, we provide for the first time, to the best of our knowledge, direct observation of the electrolyte depletion process and a systematic study to show how the electrolyte depletion affects the charging kinetics. The set of results provided here shed light on ion transport and adsorption kinetics at a realistic, charged porous carbon / electrolyte interface.

The Cavity Micro-Electrode (CME) used here consists of a Pt wire embedded inside a silica glass tube. After polishing and controlled dissolution of the Pt wire, a small cavity of ~50 µm diameter and ~20µm depth is prepared, where about 10 -7 -10 -8 g of active material powder can be packed [START_REF] Cachet-Vivier | Electrochemistry of powder material studied by means of the cavity microelectrode (CME)[END_REF] (Figure S1), without the need for conductive additives or binders. Figure 1 shows the cyclic voltammetry (CV) curves of CDC porous carbons in a three-electrode configuration using the CME as a working electrode. The current in CVs was normalized to the potential scan rate [START_REF] Lin | Microelectrode Study of Pore Size, Ion Size, and Solvent Effects on the Charge/Discharge Behavior of Microporous Carbons for Electrical Double-Layer Capacitors[END_REF] .

In conventional 1.0 M of Li 2 SO 4 electrolyte, all normalized CVs exhibit a symmetric and rectangular shape at all scan rates (0.2, 0.5 and 1.0 V s -1 see Figure 1a), indicating a reversible ion adsorption/desorption process with fast ion transport kinetics, as expected for porous carbon electrodes. It also confirms the negligible ohmic drop observed using the CME. The fast kinetics stems from the fast ion transport and ion adsorption and desorption processes. When the electrolyte concentration is decreased by ten times from 1.0 M to 0.1 M, the rectangular shape still remains at a lower scan rate, that is 0.2 V s -1 in our case, while obvious distortion appears at elevated scan rates (Figure 1b). The asymmetry of the CV distortion (Figures 1b and1c) as well as the low current value passed in the electrode (for example, 600 nA at 0.2 V s -1 ) supports the kinetic origin of these limitations. [START_REF] Lin | Microelectrode Study of Pore Size, Ion Size, and Solvent Effects on the Charge/Discharge Behavior of Microporous Carbons for Electrical Double-Layer Capacitors[END_REF] Indeed, an important limitation (drastically reduced current) is observed in 0.01 M Li 2 SO 4 electrolyte during negative polarization (below -0.2 V vs. Ag/AgCl, 0.5 V s -1 ). This limitation is not fully ohmic in nature as the positive polarization is much less affected (Figure 1c)-the distortion is not symmetric as expected for an ohmic limitation-as the result of the different ion species involved in the charge storage mechanism during positive and negative polarization [START_REF] Lin | Microelectrode Study of Pore Size, Ion Size, and Solvent Effects on the Charge/Discharge Behavior of Microporous Carbons for Electrical Double-Layer Capacitors[END_REF][START_REF] Lin | Solvent effect on the ion adsorption from ionic liquid electrolyte into subnanometer carbon pores[END_REF] . The current decrease could arise from local electrolyte depletion, which can only be observed in a specific range of concentration, since for high-concentration electrolytes, adsorbed ion amount is barely noticeable and the depletion space is expected to be fed quickly whereas too low concentration would lead to a resistive signal. [START_REF] David | Effect of Salt Depletion on Charging Dynamics in Nanoporous Electrodes[END_REF] Therefore, the unique electrochemical signature of CDC in Li 2 SO 4 electrolyte obtained at low concentration could be used to emphasize the electrolyte depletion and the ion dynamics during charge/discharge of the EDL in microporous carbons.

To further investigate the electrolyte depletion and its impact on charging kinetics, the current change over time was monitored during potential step experiments (chronoamperometry, set up is shown in Figure S2). More specifically, the potential of the porous CDC electrode was set at the potential of zero charge (PZC), we measured it at the minimum current from the cyclic voltammograms; then, a negative constant potential was applied with respect to the PZC and the current change vs. time was recorded. The PZC of CDC-600 o C was measured at about 0.2 V vs. Ag/AgCl in 0.01 M Li 2 SO 4 electrolyte (see Figure S3). In fact, the PZC of CDCs should be very

close to the open circuit potential before any electrochemical test, as CDCs are free of functional groups [START_REF] Lin | Microelectrode Study of Pore Size, Ion Size, and Solvent Effects on the Charge/Discharge Behavior of Microporous Carbons for Electrical Double-Layer Capacitors[END_REF][START_REF] Tsai | Electrochemical Quartz Crystal Microbalance (EQCM) Study of Ion Dynamics in Nanoporous Carbons[END_REF] . As expected, it is the same whatever the electrolyte concentration in our studyalthough it is more accurately detected for the lowest concentration, as the minimum capacitance is more pronounced. As the pH of the electrolyte was measured at around 6, all the charges accumulated during the negative potential polarization step should then be mainly associated with Li + adsorption with negligible SO 4 2-ion exchange [START_REF] Wu | Tracking ionic fluxes in porous carbon electrodes from aqueous electrolyte mixture at various pH[END_REF] .

Figure 2a shows the current response with time, once the electrode was polarized from PZC to -1.2 V vs. PZC. In highly concentrated electrolyte (1.0 M Li 2 SO 4 ), the cathodic current decay follows the expected exponential decrease characteristics of a capacitive (electrostatic) charge storage by ion adsorption. Different behaviors were then observed in 0.1 M, 0.01 M and 0.005 M electrolytes, with non-monotonous current decays, are observed and the presence of current peaks in some cases. Those observations may be consistent with a more complex charge mechanism likely linked with electrolyte depletion. Indeed, just after polarization the current varies as expected for a capacitive electrode, exponentially, then it increases and decreasescurrent peak-until the carbon is fully charged. Interestingly, the position of the current peak depends on the electrolyte concentration-it shows up later when the electrolyte concentration is lower. For electrolytes with a high ionic concentration, the current is driven by the migration of ions -no concentration limitation-and changes exponentially; for electrolytes having a low ionic concentration, the current is first driven by the migration flow until ionic depletion occurs leading to a high concentration gradient. As a result, a diffusion current adds up, which may explain a current peak shows up. Interestingly, the phenomenon is more severe for 0.005M than for 0.01M, resulting in a current peak at a longer time when decreasing the electrolyte concentration (Figure 2a). Once the permanent regime is established, the current continuously decays to reach a steady state, at which state the surface charge is mostly screened by electrolyte ions. Figure S4 shows the cumulative charge obtained by integrating the current with the time plots of Figure 1a. Owing to the small leakage current existing in realistic porous carbon electrodes (being not ideally polarizable, as the result of the possible presence of small amounts of redox active impurities on the carbon surface and charge distribution), the background in Figure S4 has been subtracted by removing the average stabilized leakage current of the last two seconds to ensure that the calculated charge corresponds only to the reversible capacitive process. In Figure S4, it is worth noting the maximum charge is directly correlated with the ionic concentration, which is in line with an ionic concentration limitation.

For better comparison of the kinetics, the cumulative capacitive charges were normalized to the total charge at 100 % charge state (defined as Q 0 ), which is the charge calculated at the end of the test, as confirmed by the roughly constant value of the cumulative charge in Figure S5. As expected, the cumulative charge varies with the electrolyte concentration (Figure S5); more specifically, lower concentration delays the charge storage as shown in Figure 2b (Q/Q 0 vs. time), which means the full charge state of the carbon electrode is reached at longer times in low concentration electrolytes. Figure 2b clearly shows a huge charging rate difference at an early time, where the electrolyte depletion occurs, as shown in the (1-Q/Q 0 ) vs. time plot (Figure 2c).

The change of the cumulative charge Q was plotted as 1-Q/Q 0 , to better define the early time charging kinetics. In the rest of this work, we will consider that 90 % state of charge (SOC) of the carbon electrodes is representative of a fully charged system, as the extra 10 % charge would The change of τ t with the charging time t was plotted to better understand the transient kinetics -a dimensionless time was used, corresponding to the actual time divided by the time to reach a state of charge of 90 % (equation 2).

Normalized time equation (2)

Figure 2d gives the change of time constant for the different electrolyte concentrations, where different behaviors can be observed. For the highly concentrated 1.0 M electrolyte, a monotonic increase of the time constant was found, showing increases from 0 to less than 4 s. This change is in line with a time constant distribution as expected for a porous electrode. Interestingly, for the electrolytes with lower concentration, a time constant peak/bump is observed for short times-in the case of 0.1 M, it is followed by a monotonic increase. This peak is assumed to be related to the electrolyte depletion, as a result of the limited amount of ionic species close to the carbon surface. Although it is barely visible for the electrode tested in 0.1 M electrolyte, as on average it behaves roughly as the electrode in 1 M electrolyte, it is very obvious for the lowest electrolyte concentrations. It is worth noting for those concentrations, the time constant peak is then followed by a time constant in the order of magnitude than the other concentrations. For 1 M and 0.1 M electrolytes, the charging process is mainly driven by the ion migration and successive time constants are supposed to be observed as it is a porous electrode. Concerning the 0.01 M and 0.005 M electrolytes, an ionic depletion is present, leading to an ion diffusion flux toward the electrode that adds up to the ion migration flux-this is assumed to translate into the current peak observed in Figure 2a. Such process only appears in low-concentration electrolytes (<0.1 M), since there is no depletion effect in 1 M electrolyte. Beyond being in agreement with previous modeling works, those results allow for the experimental observation of the plateau region for τ t which is related to the time constant of the diffusion process of the ions to reach the adsorption sites on the electrode surface [START_REF] Bazant | Diffuse-charge dynamics in electrochemical systems[END_REF][START_REF] Yang | Simulating the charging of cylindrical electrolyte-filled pores with the modified Poisson-Nernst-Planck equations[END_REF] . The observed shift to a longer time of the plateau when decreasing the electrolyte concentration is the result of increased diffusion limitation [START_REF] Lian | Blessing and Curse: How a Supercapacitor's Large Capacitance Causes its Slow Charging[END_REF] .

Therefore, the plateau is only slightly visible when electrolyte concentration is lowered down to 0.1 M, but is the main feature when further decreasing the electrolyte concentration down to 0.01 M and 0.005 M. As mentioned above, the 0.1 M electrolyte concentration shows an intermediate In the next step, the influence of the applied potential on the depletion and charging kinetics was studied by polarizing the carbon electrode at different constant cathodic potentials vs. PZC, in 0.01 M Li 2 SO 4 electrolyte. Figure S6 shows the change of the current during the constant potential step. The profile is similar to Figure 1a, and an exponential decay of the current is observed during the first second of the polarization as a result of the fast charge process, followed by a current increase when increasing the cathodic overpotential. Such current increase demonstrates that higher cathodic overpotentials result in severe electrolyte depletion: the ion populations near or inside the carbon pores can no longer meet the required amount of ions to screen the applied potential. Consequently, a current peak is observed for a potential of -1.2 V vs. PZC, in the same way as what was observed with decreasing electrolyte concentrations.

Therefore, we fixed the overpotential at -1.2 V vs. PZC to study the pore size effect on the depletion and related charging kinetics.

Porous carbon materials (CDCs) were prepared by chlorination of TiC powders [START_REF] Dash | Titanium carbide derived nanoporous carbon for energy-related applications[END_REF][START_REF] Chmiola | Anomalous increase in carbon capacitance at pore sizes less than 1 nanometer[END_REF] , where the chlorination temperature controls the carbon pore size. CDC-600 o C, CDC-800 o C and CDC-1100 o C with average pore sizes of 0.67 nm, 0.8 nm and 0.9 nm (Table S1), respectively, were prepared and used as model materials to investigate the effect of the pore size on the charging kinetics. The SEM images showed similar morphology of the porous carbon grains, with grain sizes around 5-10 µm for all the samples (Figure S7). Figure 3a shows the current response with time during the polarization from PZC to -1.2 V vs. PZC of the CDC with different pore sizes.

The current peaks related to electrolyte depletion are observed at 2.5 s and 8.5 s for CDC-800 o C (0.8 nm) and CDC-600 o C (0.67 nm), respectively, as a result of the small pore size. The peak disappears for the large pore size of 0.9 nm (CDC-1100 o C). [START_REF] Yin | The effects of local graphitization on the charging mechanisms of microporous carbon supercapacitor electrodes[END_REF] As expected, a slower charge accumulation rate was observed with decreasing the carbon pore size (Figure 3b), in agreement with former experimental observation in non-aqueous electrolytes [START_REF] Lin | Microelectrode Study of Pore Size, Ion Size, and Solvent Effects on the Charge/Discharge Behavior of Microporous Carbons for Electrical Double-Layer Capacitors[END_REF][START_REF] Lin | Solvent effect on the ion adsorption from ionic liquid electrolyte into subnanometer carbon pores[END_REF] . Previous computational works [START_REF] Pe´an | On the Dynamics of Charging in Nanoporous Carbon-Based Supercapacitors[END_REF][START_REF] Kondrat | Charging Dynamics and Optimization of Nanoporous Supercapacitors[END_REF] also predicted that smaller average pore size results in a slower charging rate at the molecular level. The characteristic charging times to reach 90% SOC were found to range from 0.5 to 4 s, which is also in good agreement with those predicted. [START_REF] Pe´an | On the Dynamics of Charging in Nanoporous Carbon-Based Supercapacitors[END_REF] The pore size-dependent charging kinetics could be attributed to steric hindrance of the pore accessibility 37-38, 42, 45-47 and/or to the ion desolvation process. [START_REF] Dupuis | How chemical defects influence the charging of nanoporous carbon supercapacitors[END_REF] The solvation shell of Li + in aqueous electrolytes usually contains 5 to 6 H 2 O molecules with a Li-O distance (3.5-4.0 Å) for the second hydration shell 48- 49 , making solvated Li + ion sensitive to steric hindrance during transport in subnanometer pores of the porous carbon network. Therefore, the sluggish adsorption kinetics observed for narrow pores could be explained by the hindered transportation of solvated Li + , together with their partial desolvation process when accumulated in the subnanometer carbon pores [START_REF] Tsai | Electrochemical Quartz Crystal Microbalance (EQCM) Study of Ion Dynamics in Nanoporous Carbons[END_REF][START_REF] Levi | Electrochemical Quartz Crystal Microbalance (EQCM) Studies of Ions and Solvents Insertion into Highly Porous Activated Carbons[END_REF] .

Similarly, to further investigate the depletion-related charging kinetics, we plotted 1 -Q/Q 0 vs. time with different pore-sized CDCs. It takes 4.8 s to reach 90 % of Q/Q 0 for cabrons with bigger pore size, while the time is delayed to 6.7 s and 13.0 s for smaller pore size one (Figure 3c). The change of τ t vs. normalized time shown in Figure 3d was used to better highlight the difference in charging kinetics. Similar change of τ t as reported in Figure 2d were observed as well, in relation to electrolyte depletion, but only for carbons with a pore size below 0.9 nm. In Figure 3d, the transient time constant τ t slowly increases for the 0.9 nm sample, which is consistent with the absence of any electrolyte depletion and is controlled by the potential distribution inside the carbon pores due to the RC relaxation (TLM model). Similarly to what was observed in Figure 2d, a time constant bump appears for smaller pore sizes, with a higher average τ t value with decreasing pore size. The electrolyte depletion is only present for small pore size samples and is likely to occur as subnanopores are more easily depleted than larger pores-the pore size being smaller, the total available ions nearby the carbon surface being lower. Also, the ion transport is expected to be slower.

Based on the results discussed above, we could propose a view (Figure 4) of the charging process in porous carbon when electrolyte depletion occurs. At the open circuit potential (OCP), there is no ion concentration gradient in the bulk electrolyte (Figure 4a). When applied an electrical potential difference, the external surface or the orifice of the pores will be first charged before the inner porous network. [START_REF] Levie | On Porous Electrodes in Electrolyte Solutions[END_REF] In the case of electrolyte depletion occurs, that could be triggered by higher applied potential, lower electrolyte concentration or smaller average pore size-the limitation of ion transportation, it results in electrolyte depletion inside the subnanopores and on the external surface, as discussed previously. [START_REF] David | Effect of Salt Depletion on Charging Dynamics in Nanoporous Electrodes[END_REF] Then, a mass transfer film adjacent to the electrode was formed and extended into the pore, which is also called the "stagnant diffusion layer (SDL)" elsewhere. [START_REF] Biesheuvel | Nonlinear dynamics of capacitive charging and desalination by porous electrodes[END_REF] In this case, the ion diffusion and ion migration contribute together to the charge accumulation (Figure 4b). Meanwhile, the limited ion transportation within the depleted area pushes the charge storage process delayed to longer times. At longer times, it reaches the steady charging state of EDL, where the ions migrate toward charged carbon surface and ion diffusion started from carbon surface and extends to the bulk electrolyte and they reach a dynamic balance at the end of charging steady state (Figure 4c). However, there is no electrolyte depletion in a conventional view, that is, in the case of high electrolyte concentrations, small potential bias and/or large pore size. After polarization, the ion concentration and potential gradients then develop inside the pores and in the bulk solution near the external surface as a result of the ion adsorption process. In conclusion, the EDL charging kinetics of microporous carbons with various porosity was experimentally investigated in aqueous electrolytes with different ion concentrations. The use of a cavity micro-electrode helped minimizing the ohmic drops and allowed us to experimentally observe and characterize the electrolyte depletion inside the porous carbon network, responsible for sluggish EDL charging kinetics. We also pointed out several parameters that affect this depletion, such as the pore size, electrolyte concentration and the applied cathodic overpotential.

The set of results allows for a better understanding of the ion dynamics and EDL charging in porous carbon electrodes from an experimental approach, which confirms some recent models predicted by theoretical approaches. Our findings can also help to design experimental set-ups and simulation conditions for further studying the EDL charging behavior in realistic electrodes.

Supporting Information. Electrochemical techniques, equations, set up, additional electrochemical data and carbon material characterization.

Figure 1 .

 1 Figure 1. Cyclic voltammetry plots of CDC-600 o C in Li 2 SO 4 electrolyte were obtained using a

Figure 2 .

 2 Figure 2. Change of the charging kinetics of CDC-600 at a holding potential of -1.2 V vs. PZC in Li 2 SO 4 electrolyte, with concentrations ranging from 0.005 M to 1.0 M. (a) Current response and (b) cumulative normalized charge (Q/Q 0 ) change with time obtained by integration of the plots in (a). (c) Semilog plot of 1-Q/Q 0 change with time. (d) Transient charging time constants ([-dLn(1-Q/Q 0 )/dt] -1 ) change with normalized time (time normalized to time corresponds to 90% of Q/Q 0 ) along the whole charging process.

  need a long time due to the exponential decay of the current. It takes only 2.6 s to reach 90 % of Q/Q 0 for 1 M electrolyte while 4.8 s, 13.0 s and 19.3 s are needed to reach the same state of charge, respectively in 0.1 M, 0.01 M and 0.005 M electrolyte. To further study the charging kinetics, we derivated the Ln(1-Q/Q 0 ) vs. time plot and defined a transient charging time constant τ t as (equation (1), and equation S1-S5): equation (1)

( 4 . 1 M

 41 8 s vs. 2.6 s to reach 90 % SOC, Figure2c) but without a clear plateau for τ t , showing that 0.ion concentration is still high enough to drastically decrease the diffusion limitation under our experimental conditions.

Figure 3 .

 3 Figure 3. Pore size dependent charging kinetics of CDC with potential holding at -1.2 V vs. PZC

18

 18

Figure 4 .

 4 Figure 4. Schematic illustration of the charging process of porous carbon when electrolyte

ACKNOWLEDGMENT K.G. was supported by a grant from the China Scholarship Council (no. 202006340020). H.S., P.S. and P.L.T. acknowledge the support from Agence Nationale de la Recherche (Labex Storeex) and ERC Synergy Grant MoMa-Stor #951513. REFERENCES

AUTHOR INFORMATION Corresponding Authors

Pierre-Louis Taberna-Université Paul Sabatier, CIRIMAT UMR CNRS 5085, 118 Route de Narbonne, 31062 Toulouse, France; Email: pierrel-louis.taberna@univ-tlse3.fr Patrice Simon-Université Paul Sabatier, CIRIMAT UMR CNRS 5085, 118 Route de Narbonne, 31062 Toulouse, France; Email: patrice.simon@univ-tlse3.fr Authors Kangkang Ge -Université Paul Sabatier, CIRIMAT UMR CNRS 5085, 118 Route de Narbonne, 31062 Toulouse, France; Email: kangkang.ge@univ-tlse3.fr Hui Shao -Université Paul Sabatier, CIRIMAT UMR CNRS 5085, 118 Route de Narbonne, 31062 Toulouse, France; Email: hui.shao@univ-tlse3.fr

Notes

The authors declare no competing financial interest.