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# Understanding the hard carbon's closed pore formation and Na-ion storage beyond the first charge/discharge cycle

Camélia Matei Ghimbeu, Adrian Beda, Cyril Vaulot

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Camélia Matei Ghimbeu, Adrian Beda, Cyril Vaulot. Understanding the hard carbon's closed pore formation and Na-ion storage beyond the first charge/discharge cycle. Carbon, 2025, 240, 10.1016/j.carbon.2025.120331. hal-05360208

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# Understanding the hard carbon's closed pore formation and Na-ion storage beyond the first charge/discharge cycle

Camélia Matei Ghimbeu<sup>a,b,c,*</sup> <sup>‡</sup>, Adrian Beda<sup>a,b,c</sup>, Cyril Vaulot<sup>a,b</sup>

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## ARTICLE INFO

**Keywords:**

Hard carbon

Na-ion batteries

Open/closed porosity

Initial Coulombic efficiency

Slope/plateau capacity

## ABSTRACT

The lack of accurate determination of hard carbon's (HC) open and closed pores, but also the systematic analysis of only the first charge/discharge cycle, in half-cells, impedes understanding of Na-ions storage. Therefore, a combined approach based on the adsorption of multiple gases (N₂, O₂, H₂ and CO₂) and He density is proposed to understand the HC's open porosity evolution and closed pores formation during pyrolysis. At 900 °C the pores are completely open, they partially close in the range of ~1100-1300 °C, and completely close starting from 1500 °C. The narrower pores (<0.7 nm) close firstly, with the formation of few larger open pores and plenty of closed pores, which increase with temperature. Examination of property-performance relationships from both 1st and 2nd cycles, revealed that the 1st cycle sloping capacity increases with open porosity, O-functional groups and defects, and is associated not only with reversible Na-storage but also with irreversible reactions (SEI formation). On the contrary, the 2nd cycle is only linked with reversible Na-storage, and an optimal property threshold was established. The plateau capacity was found to increase with the increase in graphitic domains and closed pores, no matter the cycle. These findings suggest an adsorption-insertion-filling mechanism.

## 1. Introduction

Sodium-ion batteries (NIBs) have emerged as an exciting technology for energy storage, particularly for large-scale grid applications. There are several key reasons why researchers assign a major interest for this technology, including cost-effectiveness, environmental benefits, and performance advantage. Sodium is localized all over the world, is much more abundant than its competitor lithium, cheaper and easier to extract, therefore, with less impact on the environment, while the "know-how" of lithium-ion battery (LIB) manufacturing proves to be easily adapted for NIBs. In terms of performance, Na-ion technology stands out by their safety for transportation when fully discharged (LIBs require partial charge), low-temperature tolerance and significant long-term cycling.

The anode material, hard carbon (HC), plays an important role in the above-mentioned benefits. Derived from renewable resources (e.g. bio-masses, biopolymers) or synthetic precursors (e.g. phenolic resins) [1], its production is generally less expensive compared to other anode materials (e.g. synthetic graphite, alloys, metal oxides, etc.). It delivers a high reversible capacity, superior to 300 mAh g⁻¹, sometimes

approaching the theoretical capacity of graphite in LIBs (i.e. 372 mAh g⁻¹) [2]. Moreover, its low operating voltage, of around 0.1 V vs. Na/Na⁺, and its high capacity retention make HC an important anode candidate for NIBs. All these benefits are largely related to the unique structure of HC, which combines high disorder with short and randomly oriented pseudo-graphitic domains and closed (restricted) porosity [3]. However, the presence of open pores (micropores), defects and surface functionalities can be detrimental to the initial Coulombic efficiency (iCE), due to the undesired reactions with the electrolyte, leading to the formation of solid electrolyte interphase (SEI) [4].

Among the properties of HC, the accurate assessment of porosity remains a major challenge. The determination of open porosity relies on gas adsorption concepts, where nitrogen (N₂), the most commonly used gas molecule, has very limited access to this porosity, reason why CO₂ appeared as a better alternative [5-7] for deeper evaluation of the narrow pores existing in the HC structure. Recently, however, a more precise description of the HC open porosity was achieved by using more exotic gases, such as O₂ and H₂ that allowed the detection of a complex network of pores with different size ranges [8]. The narrow pores (ultra-micropores) have been shown to favor the irreversible reactions

<footnote><sup>a</sup> Université de Haute-Alsace, Institut de Science des Matériaux de Mulhouse (IS2M), CNRS, UMR 7361, F-68100, Mulhouse, France</footnote>

<footnote><sup>b</sup> Université de Strasbourg, F-67081, Strasbourg, France</footnote>

<footnote><sup>c</sup> Réseau sur le Stockage Electrochimique de l'Energie (RS2E), HUB de l'Energie, FR CNRS 3459, 80039, Amiens, France</footnote>

<footnote>* Corresponding author. Université de Haute-Alsace, Institut de Science des Matériaux de Mulhouse (IS2M), CNRS, UMR 7361, F-68100, Mulhouse, France.
E-mail address: camelia.ghimbeu@uha.fr (C. Matei Ghimbeu).</footnote>
with the electrolyte, thus decreasing the iCE [4,8]. Besides open porosity, closed porosity is also thought to contribute to Na⁺ storage, being particularly responsible for the “filling” mechanism in the plateau region. SAXS (Small-Angle X-ray Scattering) is mainly used to characterize this type of porosity, however, the discrimination of open/closed porosity is sometimes difficult to achieve [9]. Another method used to qualitatively estimate the closed porosity is based on He density and the total open pore volume [10]. The difficulty here is to accurately determine the total open pore volume, by selecting the appropriate gas, taking into account the challenges related to open porosity mentioned above. It is worth to emphasize the importance of precisely characterizing not only the porosity but also other HC key properties, as these significantly influence various electrochemical performance, including Na⁺ insertion/extraction, iCE, irreversible reactions, and long-term cycling stability, among others.

The mechanism of sodium storage in HC is still under debate, although NIBs have been intensively studied for about two decades. The typical electrochemical signature of HC consists of a sloping region that goes down to ~0.1 V, while below this threshold potential, a plateau region is seen. According to previous work [11–13], sodium ions can: i) intercalate between the graphene layers, ii) adsorb onto HC’s surface, defect sites, or heteroatoms, and iii) fill the pores, without clear distinction between open/closed pores. Under certain conditions, pore filling induces formation of Na clusters or pooling of Na atoms. Consequently, several mechanisms have been proposed in the literature including: intercalation-filling, adsorption-intercalation, adsorption-filling and adsorption-insertion-filling [14–17]. Their simultaneous existence only raises more questions to clearly identify the HC’s properties contributing to Na⁺ sloping/plateau regions, and their further optimization to enhance the performance.

For example, Stevens and Dahn [18,19] initially proposed a mechanism based on insertion of Na⁺ in the sloping region and adsorption in the nanopores in the plateau region. Cao et al. [20] suggested a rather opposite mechanism, where Na⁺ intercalation occurs between the graphitic layers in the plateau region, based on X-ray diffraction (XRD) measurements and theoretical approach. Our group confirmed Na⁺ adsorption into the open porosity, in the sloping region, by using gas adsorption [6]. Other authors revealed correlations of the sloping capacity with either the carbon structural defects [11] or the functional groups and heteroatoms [21]. More recently, the contribution of closed porosity to the Na⁺ filling storage mechanism has also been highlighted. Meng et al. [22] demonstrated its contribution to the plateau capacity using true density measurements, while Ilic et al. [22] reached a similar conclusion employing SAXS (Small Angle X-ray Scattering).

In addition to the mechanisms described above, the electrolyte decomposition on the carbon surface leads to the formation of the SEI and irreversible trapping of a part of the Na inventory, which is critical for battery performance and life. This phenomenon occurs particularly in the first cycle and contributes significantly to the sloping region. However, to the best of our knowledge, this sloping region is mainly related to the reversible storage capacity provided by the material, while the part linked to SEI formation and irreversible capacity is often neglected. Therefore, is not well understood to what extent the slope capacity is related to reversible Na-ion storage or SEI formation and other irreversible reactions.

To address this dilemma, this study attempts to better understand the evolution of open and closed porosity of HC with the pyrolysis temperature, using multiple gas adsorption, without overlooking the other HC properties (i.e., structure, surface chemistry, and defects). To achieve this goal, a series of HCs were prepared over a wide range of temperatures (i.e., 900–1700 °C), characterized by multiple gas adsorption and complementary techniques, while the main physicochemical properties were linked with the iCE and sloping/plateau capacity of the HCs. We focused not only on property-performance in the first discharge/charge cycle, as traditionally done in most previous studies, but also explored the slope/plateau capacity correlations of the 2nd cycle. This

approach allowed to better discriminate the impact of HC properties on the sloping/plateau capacity and particularly their importance on SEI build-up.

## 2. Experimental part

### 2.1. Hard carbon synthesis

Hard carbon materials were prepared according to our previous work [23]. First, a phenolic resin was obtained by reacting phloroglucinol (3.26 g) and glyoxylic acid (3.6 g) in 40 mL of ethanol for 72 h. The resulting phenolic-resin gel was first thermopolymerized in air at 80 °C for 12h to increase the cross-linking degree, then pyrolysed in an oven under Ar (15L h⁻¹) for 1 h at different temperatures: 900 °C, 1100 °C, 1300 °C, 1500 °C and 1700 °C. The materials obtained were manually ground and thereafter denoted by HCT, where T is the pyrolysis temperature.

### 2.2. Material characterisation

#### 2.2.1. Textural properties

Gas adsorption isotherms were recorded on HC materials using several gas probe molecules: N₂, O₂, and H₂ at 77 K and CO₂ at 273K, using Micromeritics ASAP 2420 and ASAP 2020 instruments. The materials were outgassed at 300 °C under vacuum for 12 h on the degassing port, to remove the volatile molecules. A further two additional hours of degassing were performed on the analysis port, to remove the backfill gas. To ensure accurate isotherm acquisition, the dead space volume of the analysis tube was measured at the end, and separately from the analysis [24]. Low-pressure incremental gas doses were applied, ranging from 0.1 to 10.0 cm³ g⁻¹, depending on the surface area of the materials. The equilibration time (equilibration interval) was set to 10s for N₂, O₂ and H₂ and 5s for CO₂, considering the faster diffusion rate at high temperature (273K). Where mentioned, the equilibration time was varied between 10 and 200s. The Brunauer-Emmett-Teller (BET) specific surface area (SSA) was determined from the linear plot (1/((P₀/P)-1) vs. P/P₀) in the relative pressure range: 0.01-0.05 P/P₀ for N₂, O₂ and H₂ and 0.01-0.03 for CO₂, following the Rouquerol conditions [24]. The adsorption branch of the isotherms was used to determine the pore size distribution (PSD) by using the two-dimensional nonlocal density functional theory (2D-NLDFT) and the heterogeneous surface pore model for carbon materials. SAIEUS (Solution of Adsorption Integral Equation Using Splines) software (Micromeritics) was used for this purpose [25]. The average diameter of the pores (L₀) was calculated as described elsewhere [8].

He density was measured with a Micromeritics AccuPyc II 1340 gas pycnometer on vacuum degases samples (300 °C/12h). The average value of 100 cycles was used. The obtained He densities were used together with the O₂/N₂ total pore volumes to calculate the ratios of open and closed pores according to Refs. [10,26].

#### 2.2.2. Structural properties

The local microstructure of HC materials was evaluated by high-resolution transmission electron microscopy (HR-TEM) using a JEOL ARM-200F instrument operated at 200 kV. Global structural insights were obtained by X-ray diffraction (XRD). The diffractograms were obtained with a Bruker D8 Advance diffractometer having a flat-plate Bragg-Brentano θ-θ geometry equipped with a LynxEye XE-T high-resolution energy dispersive 1D detector (Cu Kα₁,₂, λ = 1.54 Å). The graphitic interlayer spacing (d₀₀₂) was assessed using the Bragg equation on the diffraction peak (002), while the crystallite height (L_c) and lateral width (L_a) were deduced from the Scherrer equation [27] based on the peaks (002) and (100/101) [28], respectively. Raman spectra were acquired with a LabRAM 300 instrument from Horiba Jobin-Yvon, which was equipped with a solid state Laser (Compass 315 M from Coherent) as excitation source with a wavelength of 532 nm. Several
spectra were measured and the average spectrum was fitted with: i) two-peaks using Lorentz function and ii) four-peaks using Voigt function based on a modified Sadezki method [29]. The $I_D/I_G$ was determined by the ratio of the areas under the peaks obtained with the two-peak fit procedure.

### 2.2.3. Surface chemistry and active sites

Temperature-programmed desorption coupled with mass spectrometry (TPD-MS) was employed to determine the O-containing surface functionalities and the active surface area (ASA) of HC. Specific details of the protocol used are provided elsewhere [6]. Briefly, the HC was heated under vacuum ($10^{-7}$ Torr) to 950 °C using a constant heating rate of 5 °C min$^{-1}$. The O-based functionalities are decomposed as CO and $CO_2$ gases, and they are monitored by a mass spectrometer. However, other gases such as $H_2$ and $H_2O$ can also be released. The total amount of each released gas can be quantified by time integration of the TPD curves. After this step, the samples were subjected to $O_2$ chemisorption at 300 °C for 10 h, and a second TPD was performed, and the desorbed $CO/CO_2$ gas quantities were used for the calculation of ASA, according to an equation previously established [4].

TPD-MS was also used to assess the $N_2$ and $O_2$ trapping in the HC. Two main scenarios were considered: i) the samples exposed to ambient air were outgassed under secondary vacuum, prior to TPD-MS analysis, using different vacuum time and temperature conditions: 25 °C–30 min, 25 °C–15 h and 300 °C–15 h; ii) HC sample is outgassed at 300 °C–15 h, then exposed to 760 torr of $N_2/O_2$ (for 2 h), before TPD-MS evaluation (vacuum done at 25 °C–30 min).

### 2.3. Electrochemical characterization

To obtain the electrodes, 90 wt% of HC active material was mixed with 5 wt% polyvinylidene fluoride binder (PVDF – Alfa Aesar) and 5 wt % carbon black conductive additive (Super C65 from TIMCAL), in presence of N-methyl-2-pyrrolidone solvent (NMP, Sigma–Aldrich). The resulting slurry was coated onto an aluminium current collector with the help of an automatic film applicator, using a 150 µm gap. Electrodes of 11 mm in diameter were punched (3–3.5 mg cm$^{-2}$ mass loading) and dried for 15 h under dynamic vacuum, at 120 °C, in a Büchi® oven. CR2032-type coin cells were assembled in a glove box under an Ar atmosphere ($O_2 < 2$ ppm, $H_2O < 3$ ppm) and sodium metal (Sigma–Aldrich, 99.9 % purity) was used as both reference and counter electrodes, thus a half-cell configuration. 1 M $NaPF_6$ in a mixture of ethylene carbonate and dimethyl carbonate (EC:DMC, 1:1 vol) (purchased from E-Lyte Innovations GmbH) was used as electrolyte to ensure ion conductivity. The electrochemical tests were performed at room temperature using a Biologic BCS-800 battery cycler. Testing consisted of galvanostatic cycling with potential limitation (GCPL) and it was performed in two stages during $Na^+$ insertion: (i) a galvanostatic step in the voltage range of 2.1–0.005 V vs. $Na^+/Na$ at a current density of 37.2 mA g$^{-1}$ and (ii) a potentiostatic step at 0.005 V vs. $Na^+/Na$ until the current density dropped to 3.72 mA g$^{-1}$. $Na^+$ extraction was performed in galvanostatic mode only, considering a current density of 37.2 mA g$^{-1}$ and a similar potential window, 0.005–2.1 V vs. $Na^+/Na$. The theoretical specific capacity was considered 372 mA g$^{-1}$, (1C rate), in analogy with $Li^+$ intercalation into graphite. For the calculation of the specific capacity of the electrodes, only the mass of the active material was taken into account (3–4 mg). Electrochemical impedance spectroscopy (EIS) was performed on coin cells at different stages: before electrochemical testing of the electrodes (fresh cells), after five cycles at 5 C/10 rate and after a further five cycles at 1 C rate. A working frequency range of 100 kHz–1 mHz was considered.

## 3. Results and discussion

### 3.1. Textural properties

The porosity of HC materials remains intriguing and challenging to assess and understand. This can change with the precursors used for the HC preparation, but also with the operating synthesis conditions such as the pyrolysis temperature, time, and atmosphere [1]. Herein, the impact of the pyrolysis process on HC textural properties (SSA, pore volume and size) and kinetics of adsorption are studied by measuring gas adsorption isotherms using $N_2$, $O_2$, $H_2$ and $CO_2$ (Fig. 1). Some of these gases proved to be of particular interest for determining the SSA or a specific range of pore size, as we have shown in our previous works [4,8]. However, the study was conducted in a limited pyrolysis temperature range (1300–1400 °C) while using several precursor-derived HCs. It appears important to understand the evolution of HC porosity (open and closed porosity) in a larger temperature interval (e.g., 900–1700 °C) by using one single precursor. As can be seen in Fig. 1, which presents the gas adsorption/desorption isotherms, the material treated at the lowest temperature (900 °C) exhibits the highest amount of adsorbed gas, regardless of the probe molecule used. The $N_2$ and $O_2$ isotherms are characterised by a type I shape according to the IUPAC classification [24], implying a steep increase in the amount of adsorbed gas at low relative pressure ($P/P_0 < 0.1$), corresponding to progressive filling of the micropores, and a plateau at higher $P/P_0$ indicating the gas monolayer coverage formation (Fig. 1a and b). These isotherms are specific to materials with narrow pores and, therefore, to microporous materials (pore size < 2.0 nm). Worth noting that in the case of $H_2$ and $CO_2$ isotherms (Fig. 1c and d), the plateau is less defined (or not present) suggesting that the gas monolayer coverage is not complete. For $H_2$, this might be due to the fact that $H_2$ is under supercritical conditions at 77 K, hindering the condensation in larger pores [7]. In such case, the shape of isotherm become less sensitive to the pore shape/size. In respect to $CO_2$, the relative pressure range is limited to $P/P_0 = 0.03$ at 273 K, due to the high saturation pressure (26142 torr), which once again inhibits the gas condensation in larger pores and affects the isotherm's shape.

We also note that the adsorbed volumes vary with the pyrolysis temperature but also with the type of gas used. At 900 °C, the following order of gas adsorbed volume is established: $O_2 > N_2 > H_2 > CO_2$, while for higher temperature pyrolysed samples, the order changes as: $O_2 > H_2 > CO_2 > N_2$. Thus, $N_2$ proves to be the least suitable to properly detect the porosity of HCs heat-treated above 1000 °C.

When the pyrolysis temperature is increased from 900 to 1100 °C, a very significant decrease in the adsorbed gas is observed, in particular for $N_2$ (from 155 to 15 cm$^3$ g$^{-1}$ at $P/P_0 = 1$), thus ~ 10 times lower. For the other gases, although the adsorbed volume is diminished, this behaviour is less visible, i.e. 2.1 times for $O_2$, 1.6 times for $H_2$ and 1.4 times for $CO_2$. These observations suggest that some of the open pores close or partially close, by heating the material from 900 to 1100 °C, and become inaccessible particularly to $N_2$, while some of them are still accessible to the other gases.

The accessibility of a given molecule to porosity is dependent on both its size and the analysis temperature. For example, the size of $H_2$ (0.289 nm) < $CO_2$ (0.330 nm) < $O_2$ (0.346 nm) < $N_2$ (0.364 nm), Table S1 [8], might explain the improved diffusion of $H_2$ since it presents the smallest size, while in the case of $CO_2$, the diffusion is improved by the higher analysis temperature used (273 K vs. 77 K). However, for $O_2$ and $N_2$ molecules which have rather similar size and the same analysis temperature (77 K), very distinct results were obtained: diffusion through the carbon network is the highest for $O_2$ and the lowest for $N_2$, respectively. If the possible interactions between the HC and the gas molecules are taken into consideration by comparing the quadrupole moment of the molecules, the preferential diffusion of $O_2$ cannot be explained either, since its value is smaller than that of $N_2$ [7]. It is possible that the higher diffusivity coefficient of $O_2$ compared to $N_2$ enhances the adsorption of $O_2$ through narrow pores [30,31]. In addition, at 77 K, $O_2$
<figure><img src="image_5.png" /><figcaption>**Fig. 1.** Gas adsorption/desorption isotherms (quantity adsorbed vs. relative pressure) obtained on the hard carbons, with different gas probe molecules: (a) N₂ at 77 K, (b) O₂ at 77 K, (c) H₂ at 77 K and (d) CO₂ at 273 K. For comparison purpose, the absolute pressure (P) for the H₂ adsorption isotherms was divided by the atmospheric pressure (760 mmHg) to obtain P/P₀ (the “real” saturation pressure (P₀) cannot be reached at 77 K). Full symbols denote: adsorption, and empty symbols: desorption.</figcaption></figure>

is in liquid state since its boiling point is 90.95 K (Table S1), which allow better condensation in the pores. For the HC treated at 1300 °C, the decrease in the adsorbed gas volume continues and becomes almost null for N₂, while for the other gases, values very close to zero could be seen starting with the HC heat-treated at 1500 °C. Therefore, above this temperature, most open pores close and are no longer detectable by gas adsorption.

Very important to remark that for HC900, the adsorption process is completely reversible no matter the gas used, as attested by the overlap of the adsorption and desorption isotherm branches. This behaviour is different from the other materials. For HC1100 and HC1300, the isotherms of all gases do not close, thus, adsorption is not completely reversible, and present a hysteresis shape in some cases. This behaviour, also observed in other studies, remains poorly understood [32,33]. One possible explanation is the formation of narrow pores with small openings, resembling the “ink-bottle” shape reported by Buiel et al. [34]. We propose here a more insightful explanation: gas trapping in the narrow pores, preventing complete desorption of the gas. To investigate this hypothesis, TPD-MS studies were conducted under different outgassing conditions (see experimental part, and Fig. 2).

At first, the HC1300 was outgassed at 25 °C for 30 min, before being heated under vacuum. The evolved gases were monitored by MS and presented in Fig. 2a and b - black curve. It can be seen that the sample releases N₂ with a very broad desorption profile in the temperature range of 50–400 °C. The same behaviour is observed for O₂, however, the peak is narrower (50–250 °C) and less intense. They both originate from the exposure of HC to air. The release of these gases at such high temperatures suggests that they are either trapped in the porosity or

strongly bound to the carbon surface. N₂ shows more interaction/
confinement in the pores considering its larger peak compared to O₂.
The slightly larger size of N₂ vs. O₂ (0.364 nm vs. 0.346 nm) and its
higher quadrupole moment (–4.91X10⁴⁰ cm² for N₂ and –1.33X10⁴⁰ cm²
for O₂) might explain such behaviour. To attempt to remove these gases
from the porosity, HC1300 was outgassed under secondary vacuum by
applying more stringent vacuum and temperature conditions: 25 °C for
12h or 300 °C for 12h, prior to TPD-MS analyses (red/blue curves of
Fig. 2a and b). It can be noticed that the gases can be progressively
removed with longer outgassing times, but heating (300 °C) is manda-
tory to remove all the gas molecules trapped in the material (blue
curves).

To mimic conditions similar to those during gas adsorption-
desorption measurements, the material was first outgassed, then
exposed to either N₂ or O₂ at 760 torr (equivalent of a relative pressure
P/P₀ = 1 as used in N₂ gas adsorption measurements) and finally ana-
lysed by TPD-MS (Fig. 2c). Moreover, to explore this trapping phe-
nomenon under different textural conditions, HC900 was also
considered (Fig. 2d). This material does not show isotherm hysteresis,
contrary to HC1300 where the adsorption/desorption branches do not
overlap.

The results show that HC1300 traps more N₂/O₂, which are released
at slightly higher temperatures compared to HC900. However, the later
material has more O-based functionalities (see COₓ in Table 1), there-
fore, it should be more susceptible to interact with N₂ and O₂, and to
observe larger TPD-MS peaks and gas adsorption hysteresis. However,
no hysteresis could be seen on the N₂ adsorption/desorption isotherm of
HC900, indicating that the pores are completely open, and the
<figure><img src="image_6.png" /><figcaption>**Fig. 2.** TPD-MS measurements of HC1300 outgassed under different temperature and time conditions, showing the release of: (a) N₂ and (b) O₂ trapped in material; O₂ and N₂ gas desorption profiles of (c) HC1300 and (d) HC900 after exposure to a gas pressure of 760 torr and outgassing at 25 °C for 30 min.</figcaption></figure>

<caption>**Table 1**</caption>

Textural properties of hard carbon materials including BET specific surface areas determined by different gas probe molecules, ratio of closed pores (R<sub>CP</sub>) obtained by O₂ adsorption and He density, the COₓ-derived from oxygen functionalities decomposition, the active surface area (ASA), the graphitic interlayer space (d<sub>002</sub>) and the ratio I<sub>D</sub>/I<sub>G</sub>.

<table><thead><tr><th>Material</th><th>SSA N<sub>2</sub> m<sup>2</sup> g<sup>-1</sup></th><th>SSA O<sub>2</sub> m<sup>2</sup> g<sup>-1</sup></th><th>SSA H<sub>2</sub> m<sup>2</sup> g<sup>-1</sup></th><th>SSA CO<sub>2</sub> m<sup>2</sup> g<sup>-1</sup></th><th>R<sub>CP</sub> %</th><th>CO<sub>x</sub> mmol g<sup>-1</sup></th><th>ASA m<sup>2</sup> g<sup>-1</sup></th><th>d<sub>002</sub> Å</th><th>I<sub>D</sub>/I<sub>G</sub></th></tr></thead><tbody><tr><td>HC900</td><td>613</td><td>652</td><td>198</td><td>448</td><td>10.9</td><td>0.625</td><td>12.4</td><td>3.88</td><td>2.40</td></tr><tr><td>HC1100</td><td>48</td><td>299</td><td>113</td><td>315</td><td>3.8</td><td>0.383</td><td>9.4</td><td>3.85</td><td>2.04</td></tr><tr><td>HC1300</td><td>8</td><td>119</td><td>45</td><td>74</td><td>11.4</td><td>0.231</td><td>4.1</td><td>3.77</td><td>1.79</td></tr><tr><td>HC1500</td><td>5</td><td>3.4</td><td>1.0</td><td>20</td><td>25.5</td><td>0.095</td><td>1.2</td><td>3.72</td><td>1.59</td></tr><tr><td>HC1700</td><td>4</td><td>2.6</td><td>0.5</td><td>28</td><td>37.0</td><td>0.021</td><td>0.4</td><td>3.59</td><td>1.51</td></tr></tbody></table>

adsorption/desorption process is reversible. Thus, these observations suggest that the N₂ and O₂ gases are rather trapped in the narrow (partially closed) pores of HC1300, instead of being localised on the surface of the O-functional groups (HC900). Therefore, this gas trapping effect explains the isotherm hysteresis observed in the case of HC1300.

It was also found that the amount of trapped gas increases when increasing equilibration time interval during adsorption/desorption isotherm measurement (Fig. S1). The hysteresis becomes much larger and the volume of N₂ adsorbed doubles when the equilibration time is increased from 10 to 200 s. Moreover, the analysis time takes much longer, i.e. 76 h (for 200 s equilibration time) vs. < 1h (for 10 s equilibration time). Therefore, the gas adsorption/desorption in narrow pores takes longer to assess due to steric limitations, and the equilibration time appears to be an important parameter to be precise in the experimental part of the articles for better comparison. However, this is rarely mentioned in published works involving gas adsorption. In this work, an equilibration interval of 10 s was found to be a good compromise for comparing several samples and different gas probe molecules.

Fig. 3 shows the total analysis time necessary to record the gas

adsorption branch of HC materials, using different gases. In all cases, the analysis time steeply increases in the low pressure region, corresponding to the filling of the micropores, and then a plateau is observed for higher relative pressures. In the case of N₂ (Fig. 3a), the analysis time is the highest for HC900, then decreases with increasing pyrolysis temperature, which is directly proportional to nitrogen adsorbed volume and BET specific surface area (Table 1). This is somewhat expected behavior for many carbon materials, as a high open porosity triggers a longer analysis time. Unlike N₂, for O₂ and H₂, the longest analysis time is observed for HC1300, followed by HC1100 (Fig. 3b and c), although their adsorbed volume of gas and BET SSA are smaller than those found for HC900. The slow adsorption kinetics of O₂ and H₂ in these two materials can be attributed to the presence of very narrow pores with small necks (entrances), which hinder gas adsorption. Consequently, pore closure seems to begin at 1100 °C and progresses at 1300 °C, before being completely closed at high temperatures (>1500 °C). At 1300 °C, the pores appear to have the smallest necks, considering the longest analysis time, and then they completely close, as indicated by the low adsorbed gas volume and short acquisition time.

If one compares the acquisition time of O₂ and H₂ isotherms for
<figure><img src="image_7.png" /><figcaption>**Fig. 3.** Gas adsorption isotherms (adsorption time vs. relative pressure, P/P₀) obtained on the hard carbon materials with different gas probe molecules: (a) N₂ at 77 K, (b) O₂ at 77 K, (c) H₂ at 77 K and (d) CO₂ at 273 K.</figcaption></figure>

HC1100 and HC1300, it can be seen that this is 4–5 times longer for O₂ than for H₂. The smaller molecular size of H₂ (0.289 nm) compared to O₂ (0.346 nm) and the supercritical conditions of H₂ at 77 K allow for faster diffusion of this gas in the narrow pores. Regarding CO₂ gas (Fig. 3d), the acquisition time is the shortest among all gases (e.g., 1.5 h for CO₂ compared to 184 h for O₂ for HC1300, Table S2), which can be explained by the faster diffusion rate of CO₂ occurring due to the higher analysis temperature (273 K vs. 77 K) [35]. Therefore, the analysis time is affected by the analysis temperature, the properties of the probe molecule and the compatibility between pore size and gas molecule.

The pore size distribution, PSD, was determined and the results are presented in Fig. 4. Although all materials have sizes in the micropore range, regardless of the gas probe used, some differences could be seen. In the case of N₂ (Fig. 4a), a broad and intense peak is observed at ~0.6 nm, along with a second less intense and broader peak around ~ 1.1 nm. Interestingly, when the pyrolysis temperature of HC increases from 900 to 1100 °C, the main peak completely disappears, while the secondary peak at 1.1 nm decreases in intensity and slightly shifts to a smaller width. A further increase in temperature, i.e., 1300 °C, leads to the loss of both peaks. This would suggest that the small pores close first at ~1100 °C followed by the larger ones at 1300 °C. When O₂ and H₂ are used (Fig. 4b and c), a rather similar behavior is observed, but the temperature at which the pores are no longer observed is higher, i.e., 1500 °C. It can also be noticed that the PSD is different from that of N₂. For O₂ and H₂, the main peak is located at lower values than for N₂, i.e., 0.53 nm and 0.4 nm, respectively (vs. 0.58 nm), and it is narrower. This indicates a better diffusion and compatibility for these two gases to analyze smaller pores. In fact, both gases have a smaller molecular size than N₂, i.e., 0.289 nm for H₂ and 0.346 nm for O₂ (vs. 0.364 nm for N₂) [8], which facilitates the access to very narrow pores. For O₂ (Fig. 4b), two other small peaks are seen at 0.9 and 1.3 nm, which decrease with temperature and disappear starting with 1500 °C. Thus, O₂ can access

both ultramicropores ($d_{pore} < 0.7$ nm) and supermicropores ($0.7 < d_{pore} < 2$ nm). For H₂ (Fig. 4c), the secondary peak is observed at ~ 0.75 nm, following the same behaviour vs. temperature as O₂. It is worth mentioning that the detection of pores larger than 0.8 nm is not possible with this gas, due to the supercritical conditions of H₂ at 77 K, which do not allow gas condensation [7]. For CO₂, only one intense and broad peak is seen, with a maximum centred at ~0.55 nm (Fig. 4d). Its intensity gradually decreases with temperature, and is no longer observed above 1500 °C. The smaller molecular size of CO₂ (0.33 nm) compared to O₂ and N₂, combined with its higher diffusion rate promoted by the high analysis temperature (273 K), allows to efficiently detect the ultramicropores. However, its high saturation pressure limits the detection range to pores smaller than 1 nm.

Considering the findings made following the use of these four gases, it can be concluded that a large variety of open pores are present in the HC materials, which cannot be detected by a single gas. In addition, the results converge on the direction that smaller pores close before larger ones, no matter the gas used.

Based on the adsorption/desorption isotherms and pore size distributions, the evolution of the HCs' textural properties with the pyrolysis temperature was determined using the four probe molecules (Fig. 5). For all gases, the BET SSA reveals a decreasing trend with temperature, as previously reported [1,36]. However, the values are rather dependent on the gas used, especially in the low temperature range. At 900 °C, the most important differences are observed, and the BET SSA varies in the following order: O₂ (652 m² g⁻¹) ≈ N₂ (613 m² g⁻¹) > CO₂ (448 m² g⁻¹) ≫ H₂ (198 m² g⁻¹). At 1100 °C, the BET SSA analysed by N₂ drops most significantly, to 48 m² g⁻¹ (more than 10 times vs. 900 °C), as compared to the ones obtained by the other gases (2.2 times lower for O₂ and ~0.7 times lower for H₂ and CO₂, Table 1). At 1300 °C, there are still significant differences in the SSAs obtained by the four gases (Table 1 and Fig. 5a), while from 1500 °C, the BET SSA is very low/similar, regardless
<figure><img src="image_8.png" /><figcaption>Fig. 4. 2D-NLDFT pore size distribution of the hard carbons pyrolysed at different temperatures obtained using different gas probe molecules: (a) N₂ at 77 K, (b) O₂ at 77 K, (c) H₂ at 77 K and (d) CO₂ at 273 K.</figcaption></figure>

of the gas used.

These low SSAs also correspond to shorter analysis times (Fig. 5b). Interestingly, for very high SSA (HC900), the analysis time is only slightly longer than for HC1500, while for the intermediate samples (HC1300), the analysis time is the longest, even though the SSA is significantly lower than that of HC900. This increase in the analysis time can be mainly attributed to the modification of the pore size and/or architecture. The pores are completely open and accessible at 900 °C and they become less accessible at 1300 °C due to partial closure.

The pore architecture could also have been modified, as suggested elsewhere [34], with the large openings being reduced with temperature and thus becoming narrower, impeding the diffusion of the gas in the main pore body. When the average micropore size ($L_0$) was calculated (Fig. 5c and Table S3), an increase with temperature was noticed, from ~0.5 nm (900 °C) to 1.1 nm (1300 °C). A further increase in temperature enlarges the mean pore size even more (up to ~ 2.4 nm at 1500 °C) for all gases, except H₂ – for the reasons explained before. Although the average pore size increased with the pyrolysis temperature, it is important to note that the total pore volume decreases significantly (Fig. 1, Table S4). This suggests that most of the small pores are progressively closing, and the remaining pores become larger in size but fewer in number.

The open and closed porosity ratios of the materials were calculated considering He density and their total pore volume obtained by $O_2$, as presented in Fig. 5d and Table S4. The He density increases from 1.95 to 2.21 $g cm^{-3}$ by increasing the HC pyrolysis temperature from 900 to 1100 °C, due to the open pore closure and structure densification. Further increase in HC temperature leads to a decrease in He density, i. e., 1.42 $g cm^{-3}$ at 1700 °C, indicating the formation of closed pores. It is worth mentioning that in previous works [10,37], N₂ data were used for

determination of open/closed pore ratio, however, N₂ is not able to properly detect all open pores (i.e., total pore volume), while $O_2$ seems to be more appropriate, as shown by the comparison provided in Table S4. As a general tendency, the ratio of open pores, $R_{OP}$ (which are detectable by gas adsorption), decreases with temperature, whereas the ratio of closed pores, $R_{CP}$, shows the opposite behaviour, i.e., more closed pores (not detectable by gas adsorption) are formed with increasing temperature above 1100 °C.

## 3.2. Structural properties

Although the quantification of closed porosity is rather challenging, HR-TEM represents an interesting tool to visualise them (Fig. 6). It can be seen that at low temperature (900 °C, Fig. 6a), the closed pores are not visible as the HC matrix is rather compact and consists of randomly oriented graphitic domains with 2-3 stacked graphene planes. By increasing the temperature to 1300 °C, some spherical spaces surrounded by stacked graphene layers can be observed, representing the closed pores (Fig. S2a). They become much more visible at 1700 °C (Fig. 6b), when the internal structure of HC becomes more ordered. The graphene layers are now stacked in multiple, elongated layers with reduced interlayer spacing. In fact this corresponds very well to the “falling card” model proposed by Dahn et al. [34,38] to explain the formation of closed pores. This process involves the coalescence of neighbouring open pores as a result of the reorganisation of the graphene planes at high temperature, forming larger pores enclosed by stacked graphene layers.

Further insight into the structural evolution of the materials was obtained by XRD and Raman. The XRD patterns (Fig. 6c) show three peaks corresponding to the (002), (100/101) and (110) diffraction
<figure><img src="image_9.png" /><figcaption>Fig. 5. Evolution of the adsorption data with the pyrolysis temperature of the hard carbons by using different gas probe molecules: (a) specific surface area, (b) adsorption time, (c) average micropores size and (d) ratio of closed and open pores determined using He density and $O_2$ adsorption.</figcaption></figure>

planes of graphite (Crystallography Open Database, COD 9011577) and their broad shape indicates a typical HC structure [40]. With increasing the temperature, the broad 002 peak become narrower and shifts to higher 2 theta values (22° at 900 °C to 24.3° at 1700 °C), thus, closer to the position of ordered graphite structure (26°), indicating an increase in the pseudo-graphitic domains number and size of the materials. In addition, the graphene interlayer spacing, $d_{002}$, decreases with the temperature (Fig. 6d) from 3.88 Å (900 °C) to 3.59 Å (1700 °C), an expected tendency [1,41]. The average height of the crystallites, Lc, varies from 9.3 to 12.9 Å, while the lateral length of the crystallites, La, varies from 32.5 to 46.1 Å, when the temperature is raised from 900 to 1700 °C. The average number of stacked graphene layers, N, ranges from 3.4 to 4.6 (Table S5). All these observations indicate an increase in the crystallite size and structural order with the pyrolysis temperature, in agreement with the HR-TEM results.

In addition, the Raman spectra (Fig. 6e) show the presence of two intense bands at low Raman shift values, i.e., the D (defect) and G (graphite) bands. The D band (~1342 cm⁻¹) arises from structural defects or edges in the aromatic rings, while the G band (~1596 cm⁻¹) corresponds to the in-plane vibrations of doubly bonded carbon atoms, Csp² in hexagonal graphene layer, indicating the crystalline order [42]. The widths of the D and G bands become narrower with increasing temperature, while the second order 2D band (specific to graphite) visible at high Raman shift (2682 cm⁻¹) becomes more defined and intense, especially for HC1500 and HC1700. This indicates a decrease in the defects and an increase in the structural order of the materials. Indeed, the disordered degree $I_D/I_G$ determined considering the two-peak areas, decreases from 2.40 (for HC900) to 1.51 (for HC1700), confirming the decrease in disorder and defects in the materials. In order to gain further insights into the HC structural defects, the spectra were deconvoluted with four-peaks according to Sadezki et al. [39] and the results are presented in Fig. 6f (HC900) and S2b (HC1700). It can be seen that the D4 peak (~1200 cm⁻¹), which is associated with amorphous carbon and Csp³/Csp² bonds in C–C and C≡C in polyene-like

carbon [39], is clearly visible on HC900, while it almost disappears on HC1700. In addition, the D3 peak (~1520 cm⁻¹) related to the functional groups bonded to the carbon sp², becomes less intense and broader for HC1700, as result of their removal at high temperature. Therefore, the assembly of these results indicates a decrease in the structural defects, amorphous carbon and functional groups with temperature, as well as an increase in the structural order, in agreement with XRD and HR-TEM observations.

### 3.3. Surface chemistry and active sites

The formation of graphitic domains and porosity is closely related not only to temperature but also to the precursor employed [1]. A phenolic resin is used, which contains aromatic rings in its structure, but also a large amount of O-based groups such as carboxylic acid, phenol, or lactone [43]. These functional groups are involved in the cross-linking process of the phenolic resin and are further involved, during thermal pyrolysis, in the formation of the carbon skeleton, porosity, and surface functionalities [44]. TPD-MS was used to identify and quantify the O-based functional groups of the materials. When the sample is heated under vacuum, these O-groups decompose into $CO_2$ and CO gases, at temperatures closely related to their thermal stability (Fig. 7a and b). Acidic groups, such as carboxyl, anhydrides, and lactone, have a lower decomposition temperature and release $CO_2$ in the temperature range of 100–600 °C (Fig. 7a) [45,46]. The $CO_2$ desorption profiles of the HCs are large, indicating the presence of several acidic groups such as: carboxyl (~300 °C), anhydride (~450 °C) and lactone (~600 °C). The latter two O-groups release $CO_2$ simultaneously with CO, as observed from the $CO_2$ and CO desorption profiles (Fig. 7a and b). Furthermore, at temperatures above 600 °C, the desorption of phenol (~650 °C), ether (~700 °C) and quinones (>700 °C) occurs, with the formation of CO gas [47,48]. It is worth noting that the intensity of CO peaks is higher than that of $CO_2$ peaks, indicating the presence of more basic groups on the carbon surface. With an increase in the pyrolysis
<figure><img src="image_10.png" /><figcaption>**Fig. 6.** HR-TEM images of hard carbon materials pyrolysed at different temperatures: (a) 900 °C, (b) 1700 °C, (c) XRD of HC materials, (d) evolution of graphitic interlayer space ($d_{002}$), crystallite height (Lc) and crystallite width (La) with the pyrolysis temperature, as determined by XRD, (e) Raman spectra of the HC materials and (f) deconvoluted Raman spectra of HC900 according to Ref. [39].</figcaption></figure>

temperature, the intensity of the peaks decreases, and the shape of the peaks changes slightly. This resulted in a decrease in the total amount of acidic and basic groups (COx) from 0.625 mmol g⁻¹ (HC900) to 0.021 mmol g⁻¹ (HC1700), as illustrated in Fig. 7c and Table 1. Because these groups are localized at the carbon surface, on the graphene planes and pores, their removal induces structural rearrangement of the carbon matrix.

By exposing the materials to O₂ chemisorption followed by TPD-MS analysis, the active surface area (ASA) comprising the edges, defects, dislocations, vacancies [49], etc. can be quantified (Fig. 7c). The highest ASA value was found for HC900 (12.4 m² g⁻¹) and it gradually decreases with the pyrolysis temperature, reaching a value close to 0 (0.4 m² g⁻¹) for HC1500. This trend is in agreement with other works [1,6]. It is interesting to note that the active sites decrease almost linearly with the removal of O-based functionalities (Fig. 7c). This correlation suggests that the O-functional groups are probably anchored to the active sites and defects. Furthermore, a decrease of ASA with BET SSA is seen (Fig. 7d), and might be related to the surface of the edges and basal planes of HC. In fact, BET SSA measures the total surface area of the

material (edge planes + basal planes), while ASA considers only the surface of HC edges and defects in the basal planes [4]. Therefore, when the BET SSA is high, the surface area of basal/edge planes is high, and in most cases, the ASA is also superior [4,46]. It is important to mention that both BET SSA and ASA were found to have a strong impact on the iCE of HCs in NIBs [4].

### 3.4. Electrochemical performance

It appears important to understand the effect of HC properties on its electrochemical behaviour, in half-cells (vs. Na metal). In Fig. 8a, the first galvanostatic charge-discharge curves show a typical behaviour of HC, characterised by a high voltage region, >0.1 V (sloping region) and a low voltage region, <0.1 V (plateau region). All materials have a very high 1st discharge capacity, ranging between 382 and 412 mAh g⁻¹ (Table 2), however, the 1st charge capacity significantly varies and three different temperature-dependent behaviours are observed.

For HC900, the major part of the gained discharge capacity is represented by a sloping region (>90 %), while the plateau capacity is very
<figure><img src="image_11.png" /><figcaption>Fig. 7. TPD-MS gas desorption profiles including (a) CO₂ and (b) CO of hard carbon materials, (c) evolution of active surface area, ASA, with the total amount of desorbed gases, COₓ, coming from the decomposition of O-functional groups, and (d) evolution of ASA with BET specific surface area determined by the four probe molecules (the pyrolysis temperature of hard carbons is also indicated).</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>Fig. 8. (a) First discharge - charge cycle vs. Na⁺/Na for the hard carbon materials; evolution of sloping and plateau capacity for (b) 1st discharge cycle, (c) 2nd discharge cycle. Correlations between iCE and (d) specific surface area, SSA (e) average pore size, L₀, determined using different gas probe molecules, and (f) active surface area, ASA.</figcaption></figure>
<table><caption>**Table 2**
Electrochemical performance of hard carbon materials prepared at different pyrolysis temperatures.</caption><thead><tr><th>Material</th><th>Discharge capacity mAh g<sup>-1</sup></th><th>Charge capacity mAh g<sup>-1</sup></th><th>iCE %</th><th>Plateau capacity mAh g<sup>-1</sup></th><th>Slope capacity mAh g<sup>-1</sup></th></tr></thead><tbody><tr><td>HC900</td><td>383</td><td>108</td><td>28.2</td><td>37</td><td>346</td></tr><tr><td>HC1100</td><td>387</td><td>245</td><td>63.3</td><td>97</td><td>290</td></tr><tr><td>HC1300</td><td>412</td><td>349</td><td>84.7</td><td>182</td><td>230</td></tr><tr><td>HC1500</td><td>398</td><td>346</td><td>86.9</td><td>245</td><td>153</td></tr><tr><td>HC1700</td><td>382</td><td>324</td><td>84.8</td><td>266</td><td>116</td></tr></tbody></table>

limited. In addition, the capacity obtained during Na extraction is very low (~108 mAh g⁻¹), which correspond to an iCE of only 28.2 %. The formation of SEI is mainly responsible for the high irreversibility observed and is largely identified with the sloping region. For the material heat-treated at 1100 °C, the sloping region is reduced (compared to HC900) and the plateau capacity becomes more important (25 %). In addition, there is also a significant improvement in the reversible capacity to 245 mAh g⁻¹ and in iCE to 63.3 %. Starting from 1500 °C, the plateau capacity is predominant (up to 70 %), the irreversible reactions are mitigated, thus improving both the reversible capacity (up to 349 mAh g⁻¹) and the iCE (up to 87 %). As a general tendency, the iCE increases with increasing pyrolysis temperature, in agreement with other works [50]. Based on these observations, the best compromise in terms of iCE and reversible capacity is provided by HC1500.

However, as the SEI layer forms mainly during the 1st cycle, it is judicious to evaluate the impact of HC properties on the sloping/plateau capacity without the SEI contribution. This can be achieved by examining the 2nd cycle (Fig. S3a). One can see in Fig. 8c that the total discharge capacity (slope + plateau) is smaller in the 2nd cycle, and this is related to the decrease in capacity in the sloping region, especially in the case of HC900 and HC1100. At the same time, the contribution of the plateau capacity improves for all materials. Moreover, the CE is very close to 100 %, i.e. 98 %, except for HC-900 (94 %) (Fig. S3b), confirming that the SEI formation is mainly complete in the second cycle, therefore, its contribution to the sloping region in the 2nd cycle is minimized. Interesting, one can notice in Fig. S3b that the 2nd cycle CE follows the same trend as the one observed for the iCE: HC900 the lowest %, while HC1500 the highest.

To gain further insight on SEI, Electrochemical Impedance Spectroscopy (EIS) measurements were performed (Fig. S4). To clearly highlight a trend, three out of the five samples were selected: HC900, HC1100 and HC1500. Different testing conditions were considered for EIS evaluation: before cycling (assembled cells), after cycling for five cycles at C/10 rate (to ensure good SEI formation) and after five additional cycles at 1C rate, to evaluate SEI stability. Interesting, one can see in Fig. S4a that initially (after cell assembly), the charge transfer resistance measured (the semicircle) is higher for HC1100 and HC1500 (~115 Ω) compared to HC900 (90 Ω). This suggests a chemical-driven SEI formation, more favourable in the case of HC900, due to its higher SSA and richer surface chemistry [51,52]. Therefore, even at this early stage, the SEI is more developed on the HC900, resulting in a lower internal resistance. However, once the cells are cycled (5 cycles) and the SEI is well formed (Fig. S4b), one can see that the charge transfer resistance changes significantly and the trend is totally different. HC1500 presents the lowest resistance (~42 Ω), around two times lower than HC1100 and HC900. This implies a more stable and homogeneous SEI layer formed on HC1500 compared to the other materials, which explains its high iCE, (particularly vs. HC900 and HC1100). The diffusion-controlled straight line observed in the low-frequency region is rather identical for the three electrodes, at around 45° (Warburg Impedance).

When the electrodes are cycled at higher C-rate (1C), the EIS semi-circle diminishes significantly for all three HC electrodes, but in particular for HC1500. This indicates that SEI layer evolved between C/

10 and 1C testing rate, and that it is more stable and conductive, thus limiting charge transfer reactions [52]. Another interesting observation here is related to the Warburg Impedance. The 45-degrees tail present at an intermediate frequency, it is followed by a transition zone as the frequency decreases and then at really low frequencies, the tails are oriented toward lower degrees (limited diffusion layer). This behaviour can be related to faster diffusion kinetics of Na⁺.

The stability of all the electrodes and the rate performance of the HC1500 were also evaluated (Fig. S5). A good cycle stability during 30 and 50 cycles was found for all materials and HC1500, respectively, with no significant capacity drop between C/10 to 1C rate (Figs. S5a and b). Moreover, HC1500 (best material) was selected to evaluate the stability during rate performance measurements (Fig. S5c). Variable charging rates were used (C/10, 1C, 2C, 5C and 10C) while the discharge rate was maintained at 1D (after five initial formation cycles at D/10). One can see that the transition from C/10 to 1C-2C and then 5C is very smooth and that the reversible capacity is still around 300 mAh g⁻¹. However, when passing to 10C-rate (Fig. S5c), the electrode is not very stable and some fluctuations could be observed (capacity drop followed by an important increase). This can be related to SEI layer which underwent modifications and required few stabilization cycles (due to high current applied). Finally, when returning to a charging rate of C/10, most of the initial capacity is recovered (~330 mAh g⁻¹), demonstrating the robustness of the electrode in terms of capacity maintenance under different C-rate regimes.

### 3.5. Property-performance relationship

During the pyrolysis process at elevated temperatures, several modifications occur in the properties of hard carbon, i.e., the BET SSA, O-functional groups, ASA and $d_{002}$ decrease while the crystallite size and closed porosity increase. Among these, the BET SSA has been identified as an important factor that impacts the iCE [4,46]. A high BET SSA leads to electrolyte decomposition, excessive SEI formation, and lower iCE [53,54]. We investigated this aspect taking into account the BET SSA obtained by different probe gases. As can be seen in Fig. 8d, for SSAs below 50 m² g⁻¹ the iCE is high for all materials, and only small differences are noticed. For higher SSAs, comprised between 50 and ~650 m² g⁻¹, the iCE decreases almost linearly with the increase of SSA measured by $O_2$, $H_2$ and $CO_2$. In the case of $N_2$ SSA, this linear correlation is difficult to observe (only two points in this region), since this gas cannot detect all pores. Indeed, these results confirm the tendency observed on other HC materials prepared using various precursors, synthesis processes and pyrolysis conditions [4,6,46].

Other factors affecting the iCE may be linked with the Na trapping in the carbon pores and/or structure [55]. In can be seen (Fig. 8e) that the ultramicropores with sizes smaller than 0.5 nm are more likely susceptible to contribute to this effect, while the active surface area (ASA), which comprises the structural defects, can have a negative effect on the iCE when the value is greater than 4 m² g⁻¹, as suggested by Fig. 8f. Indeed, these results corroborate with our previous works showing the importance of active sites [4,46]. Taking into account that ASA varies in the same way as the O-based functional groups, $CO_x$ (Fig. 7c), the same correlation was found between iCE and $CO_x$ (Fig. S6). Consequently, a lower amount of O-functional groups is beneficial for a reversible sloping capacity gain. In contrast, higher concentrations of O-groups can lead to Na⁺ trapping and undesirable reactions with the electrolyte, which favor SEI layer formation and ultimately reduces the iCE. [56,57]. The nature of the O-functionalities could also influence the iCE; the materials with a high amount of O-groups (HC900 and HC1100) present a large pallet of O-functional groups, in particular they have high contribution of phenol, ether and quinone groups, as shown by the intense CO profile at high temperature (Fig. 7b). These results illustrate that several interplaying properties affect the iCE and are consistent with previous findings, thus confirming the main key properties of HC that influence iCE [4,46].
Next, we tried to correlate individually the sloping and plateau capacity with the HC properties in order to identify the dominant ones. Several studies have reported in this direction, highlighting some trends [4,6,20,58]. It has been shown that the sloping region develops with the increase of HC porosity, active sites, and/or surface functionalities, due to the possible adsorption phenomena with $Na^+$ and/or pseudocapacitive reactions with the electrolyte [6,20,58]. Indeed, the same trends were found for the HCs studied herein (Fig. 9a-c): the sloping capacity increases with $O_2$ SSA, ASA, and $CO_x$ groups, in an almost linear manner. However, the 1st discharge cycle is generally used to understand the property - capacity relationship. An interesting approach would be to consider the discharge capacity from the 2nd cycle in order to better distinguish between the irreversible reactions related to the SEI and the reversible $Na^+$ storage in sloping/plateau regions. One can see that the tendencies between the sloping capacity and the HC properties change significantly for the 2nd cycle (Fig. 9a-c).

In particular, a threshold limit of HC property values is observed, below which the sloping capacity improves and then declines as the value of a certain property increases. More precisely, up to a given value of BET SSA $O_2$ (~100 $m^2 g^{-1}$), ASA (~5 $m^2 g^{-1}$) and $CO_x$ (0.2 mmol $g^{-1}$) the sloping capacity increases, whereas for larger values of these properties the sloping capacity starts to decrease.

This behaviour may indicate that a certain porosity can be useful for reversible adsorption of $Na^+$, a moderate active surface area can promote the reversible $Na^+$ binding, while a reasonable amount of O-functional groups might improve the wettability with the electrolyte and thus $Na^+$ diffusion/adsorption. On the contrary, larger values of these properties are detrimental to performance, most likely due to fact that they promote the electrolyte decomposition and SEI formation. However, materials with high SSA, ASA, and $CO_x$ amounts have larger interlayer spaces and less stacked graphene layers (Fig. 6d and Table 1 and S5), which may allow better $Na^+$ insertion, but they are less

<figure><img src="image_13.png" /><figcaption>**Fig. 9.** Evolution of sloping/plateau capacity during the 1st and 2nd discharge cycle of HC pyrolysed at different temperatures with (a) $O_2$ BET SSA, (b) active surface area, ASA, (c) $CO_x$-derived from decomposition of O-groups, (d) interlayer graphitic space, $d_{002}$, (e) disorder degree, $I_D/I_G$ and (f) ratio of closed porosity.</figcaption></figure>
electronically conductive limiting the charge propagation.

Indeed, during the 1st cycle, the sloping capacity increases with the enlargement of d₀₀₂ (Fig. 9d). A similar trend is observed in the second cycle, for d₀₀₂ values up to ~3.77 Å. Above this threshold, a decrease in sloping capacity was noticed. Similarly, the sloping capacity of the 1st cycle is enhanced with the I₀/I₀ ratio, in agreement with other studies [11,59]. However, if the SEI contribution is excluded (2nd cycle), an optimal I₀/I₀ ratio of 1.8–2 is observed, with higher values leading to a decrease in sloping capacity (Fig. 9e). This can be due to the electronic conductivity that diminishes for highly disordered structures (high d₀₀₂, I₀/I₀ and low La, Lc) [60], but also to the fact that for these HCs, other properties such as SSA, ASA or O-groups also have high values, favourable for irreversible reactions rather than Na⁺ adsorption.

Regarding the plateau capacity, it shows an opposite trend with the sloping capacity, and interestingly, no difference is seen between the 1st and 2nd cycles – the curves almost overlap (Fig. 9b, d-f). This implies that the plateau region is not related to SEI layer formation, but only the sloping region, which evolves significantly between cycle 1 and 2. One can see in Fig. 9d that the plateau capacity increases with the decrease of d₀₀₂, therefore, with the increase of structural order and graphitic domains (Lc, La) in the materials. Similar observations have been reported in the literature [6,61,62]. However, there are studies where the plateau capacity shows an opposite trend, thus it increases with the increase of d₀₀₂ [11,37,63]. Such contradictory results suggest that the relationship between the plateau capacity and d₀₀₂ is impacted by other factors coming from the different HC synthesis procedures, their various properties and electrochemical testing conditions. It is worth to note that a plateau is observed for d₀₀₂ smaller than 3.7 Å, corresponding to the highest plateau capacity, but the lowest sloping capacity. This suggest that narrower interlayer spaces are not favourable for Na⁺ insertion in the slopping region, in agreement with theoretical predictions [64]. However, it appears that an interlayer space comprised between ~ 3.7 and 3.8 Å is the best compromise to maximise the total capacity (sloping + plateau). Regarding the effect of structural defects, I₀/I₀ on the

plateau capacity it was found that materials with fewer defects (lower I₀/I₀) have a higher plateau capacity (Fig. 9e). In fact, a rather negative linear relationship is observed between the plateau capacity and I₀/I₀, which is in line with the relationship observed for the defects quantified as the active surface area, ASA (Fig. 9b) and d₀₀₂ (Fig. 9d). All these correlations indicate that a disordered structure with large interlayer spaces, defects and active sites leads to a lower plateau capacity, while for intermediate values a high total capacity is achieved, as a contribution from both sloping and plateau capacity, *via* Na-ion adsorption and insertion reactions, respectively.

In addition, the attribution of the plateau capacity to the Na⁺ insertion between the graphene layers or closed porosity is also under debate [37,65]. Here, it was found that the plateau capacity increases with the closed porosity ratio (Fig. 9f). Although its influence is not very clear for small ratios of closed porosity (~10 %), higher ratios, above this threshold, are beneficial for Na⁺ storage. In our previous work [37], we found an opposite trend of plateau capacity with closed pores, but also with the interlayer space (Fig. S7a). At a first glance, these results appear contradictory, however, one might consider that in the previous work, all HCs were obtained at the same pyrolysis temperature (1500 °C) but using different precursors, which guarantees very low surface area, O-functional groups and defects, although there are differences in closed porosity (%) and interlayer space distances. Particularly, the range of d₀₀₂ values is rather restrained (3.73–3.79 Å, Fig. S7b), which is very different from the present study, where a wide range of temperatures is used, resulting in HCs with a large range of d₀₀₂ (3.59–3.88 Å) and variety of properties (Table 1, Fig. 10). However, for both series of materials, the range of values of closed pore ratio are similar (7.6–33 % for previous work and 7.7–36 %, in this work, Fig. S7a). Therefore, in the present work both the closed pores and d₀₀₂ are varying with the temperature, whereas in the previous work mostly the closed pores are modified by the precursor used. This means that for the materials prepared herein, the plateau capacity is influenced by both closed pores and d₀₀₂ simultaneously, making difficult to estimate which

<figure><img src="image_14.png" /><figcaption>**Fig. 10.** Schematic representation of the evolution of hard carbon properties during the thermal pyrolysis along with the Na⁺ storage mechanisms: a) 2D view and b) 3D view.</figcaption></figure>
effect is the most predominant one. This is the case in many other works where several HC properties vary with the experimental conditions, but also from one study to another. This somehow explains the controversial results regarding the plateau capacity associated to a certain Na-ion storage mechanism (insertion between the graphene layers or/and into the closed porosity). Moreover, as proposed by some authors [11, 21,66], a three-stage Na-insertion mechanism (adsorption-insertion-filling) can be plausible. In such a case, both the insertion of Na⁺ between the graphene layers and the filling of the closed pores (Fig. 10), occur in the plateau region, but the extent of each contribution could vary with the material, the electrochemical test conditions, and the electrolyte used. These elements could probably explain the different correlations observed here compared to the previous study [37]. However, the improvement of the plateau capacity with the increase of closed pore ratio observed here is consistent with several other papers in the literature [22,67,68]. Nevertheless, complementary studies are required to gain a deeper understanding of such complex mechanisms, in particular by the use of in-operando techniques. In summary, increasing the pyrolysis temperature has multiple effects on HC properties and Na-ion mechanisms (Fig. 10). At low temperature (900 °C), the HC has plenty micropores, reactive O-functional groups, and highly disordered carbon layers with structural defects. These characteristics promote detrimental electrolyte interactions, reduce iCE, and restrict accessible Na⁺ storage sites. Higher temperatures (> 1100 °C) progressively promote micro-pore collapse into closed pores, minimising electrolyte penetration, while the removal of oxygen groups and defects stabilises the surface, boosting the iCE. In addition, the pseudo-graphitic domains and closed pores become more abundant, contributing to the increase in capacity. A compromise between all these HC properties allows the overall capacity (sloping + plateau) to be enhanced, through a three-stage mechanism: (1) adsorption of ions onto surface domains, (2) insertion into the interlayer spacings of the pseudo-graphitic regions, and (3) filling of closed pores.

## 4. Conclusions

The evolution of HCs properties with the pyrolysis temperature and their relationship with the electrochemical performance in Na-ion half-cells were investigated. Firstly, a focus on the textural properties was done, in order to understand the closure of open pores during the pyrolysis process. The use of adsorption measurements with four different gases allowed to identify several important aspects: i) at 900 °C the pores are completely open, the gas diffusion is fast and no hysteresis is observed in the gas sorption isotherm, ii) at 1100 °C, the open pores start to close, and at 1300 °C, they present the smallest neck entries, as indicated by isotherms hysteresis, long analysis time and gas trapping measurements, iii) from 1500 °C, the pores are predominantly closed. The smaller pores close first, resulting in larger pores but fewer in number. N₂ gas proved unsuitable to follow pore closure and textural changes. However, O₂ gas adsorption in combination with He density allowed to clearly track the gradual open pore closure and increase of the closed pore ratio with temperature. Nevertheless, these textural changes are accompanied by structural and surface chemistry modifications. While the defects and O-containing functional groups decrease with the temperature, the graphitic domains become larger in size, and the distance between the graphene sheets narrows.

All these changes in HC characteristics have an impact on the performance, and in general the iCE and capacity increase with the pyrolysis temperature. Differently than many works, we analysed both 1st and 2nd charge/discharge cycles in detail, and the following conclusions could be drawn. In the 1st cycle, the sloping capacity increases with the increase of specific surface area, active surface area, O-functional groups and defects. However, in the 2nd cycle, the correlations between HC properties and sloping capacity are different and a threshold limit of property values is identified, above which the sloping capacity starts to decrease. This clearly suggests that in the 1st cycle, the mentioned

properties contribute to the formation of SEI and irreversible capacity, whereas in the 2nd cycle, their presence in small extent leads only to reversible Na⁺-storage. Regarding the plateau region, it increases with the decrease of the interlayer space and the increase of the closed porosity ratio, regardless of the 1st or 2nd cycle examined, therefore, these properties do not contribute to the SEI formation, but only to the Na⁺-storage. In light of previous literature works, such observed trend of interlayer space and closed porosity with plateau capacity cannot be generalized for all materials, since it depends on the predominant insertion-filling stage. Nevertheless, balancing the Na-ion adsorption on HC surfaces (sloping region), the insertion between graphene layers and pore filling (plateau region) maximises total capacity. Overall, the results converge towards an adsorption-insertion-filling Na-storage mechanism.

## CRediT authorship contribution statement

**Camélia Matei Ghimbeu:** Writing – review & editing, Writing – original draft, Validation, Supervision, Project administration, Methodology, Funding acquisition, Data curation, Conceptualization. **Adrian Beda:** Writing – review & editing, Validation, Methodology, Investigation, Formal analysis, Data curation. **Cyril Vaulot:** Methodology, Investigation, Formal analysis.

## Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Acknowledgements

This work was financially supported by the European Union's Horizon 2020 Program (project NAIMA, call: LC-BAT-02, Contract no. 875629). Dr. Loic Vidal and Dr. Jean-Marc Le Meins are acknowledged for the HRTEM and XRD analyses through IS2M technical platforms. The authors thank Julia Coffre for the help provided with graphical illustrations.

## Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.carbon.2025.120331.

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