# Understanding and predicting CO2 capacity loss in activated carbons under humid conditions

R. Morales-Ospino, M. Aoun, J. Castro-Gutiérrez, M.T. Izquierdo, A.

Celzard, V. Fierro

► To cite this version:

R. Morales-Ospino, M. Aoun, J. Castro-Gutiérrez, M.T. Izquierdo, A. Celzard, et al.. Understanding and predicting CO2 capacity loss in activated carbons under humid conditions. Chemical Engineering Journal, 2026, 530, pp.173366. 10.1016/j.cej.2026.173366. hal-05483905

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https://hal.univ-lorraine.fr/hal-05483905v1

Submitted on 3 Feb 2026

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# Understanding and predicting CO₂ capacity loss in activated carbons under humid conditions

R. Morales-Ospino<sup>a, *,</sup>, M. Aoun<sup>a</sup>, J. Castro-Gutiérrez<sup>a</sup>, M.T. Izquierdo<sup>b</sup>, A. Celzard<sup>a, c</sup>, V. Fierro<sup>a, *</sup>

## ARTICLE INFO

Keywords:

Water vapor

Activated carbons

KOH activation

CO₂ capture

Do and Do adsorption model

## ABSTRACT

This study demonstrates that water isotherm measurements can reliably predict moisture tolerance in activated carbons (ACs), reducing the need for extensive CO₂ isotherm testing under varying humidity and guiding the design of hydrophobic, high-capacity adsorbents for post-combustion and direct-air capture. We investigate how water vapor adsorption influences CO₂ capture by combining systematic AC synthesis, detailed textural and chemical characterization, and mechanistic modeling of water isotherms. ACs were produced from wood charcoal via mechanochemical KOH activation at different ratios (AC1.5–AC4), yielding materials with increasing surface areas (≈1700–2900 m² g⁻¹) and pore volumes (0.74–1.21 cm³ g⁻¹), spanning ultramicroporous to supermicroporous/mesoporous structures. Two commercial high-surface ACs were also included in this study. Their water vapor isotherms showed S-shaped cooperative adsorption and were accurately described by the Do and Do (DD) model. For the first time, DD parameters were linked to AC physicochemical properties: initial water affinity scales with surface heteroatom density (N + O per surface area), while pore-filling parameters correlate with pore volume and micropore width. Under humidity, ACs exhibited decreasing CO₂ capacity, and we show that a 50% capacity loss can be predicted directly from the pure water isotherm.

## 1. Introduction

Interest in water adsorption on carbon-based materials has grown due to its significant impact on industrial processes such as carbon capture, where water vapor hinders CO₂ separation. A similar challenge is observed in benchmark CO₂ adsorbents such as zeolite 13× [1,2], whose CO₂ capacity is markedly reduced in the presence of humidity [3–5]. Working under conditions that closely mimic real-world humidity is essential to understanding and mitigating these effects, especially given the specific interactions between water molecules and polar groups on the surface of graphene layers [6]. Water adsorption on activated carbons (ACs) arises from the interplay between surface chemistry, pore structure, and hydrogen-bond interactions [7]. With their high surface area and tunable porosity, ACs are highly effective water vapor adsorbents [8], and their performance depends on the type and distribution of oxygen- and nitrogen-containing groups that control adsorption affinity, while textural properties determine total uptake capacity. Water molecules interact with these functional sites mainly

through hydrogen bonds and electrostatic forces, producing S-shaped adsorption isotherms (type IV or V) due to cooperative cluster formation and pore filling at higher humidity [9–11]. The role of surface sites in enhancing water adsorption at low relative pressures has already been demonstrated by experimental studies and grand canonical Monte Carlo simulations [12]. Although early research on surface polar groups focused primarily on oxygen-containing functionalities [13–19], subsequent studies have shown that other heteroatoms, such as nitrogen, can also promote water adsorption at low relative pressures [20–25]. These surface groups act as nucleation centers for these clusters, giving rise to the characteristic S-shaped behavior [26]. Due to their strong polarity and higher binding energy, water molecules can out-compete CO₂ for the same adsorption sites, blocking access to micropores and active centers and thus reducing CO₂ capture capacity as humidity increases [25,27,28].

Empirical and theoretical approaches have been developed to model water adsorption on ACs, with the aim of correlating their structural and chemical features with their adsorption capacities and energies.

<footnote><sup>a</sup> Université de Lorraine, CNRS, IJL, F-88000, Epinal, France</footnote>

<footnote><sup>b</sup> Instituto de Carboquímica (ICB-CSIC), 50018, Zaragoza, Spain</footnote>

<footnote><sup>c</sup> Institut Universitaire de France (IUF), 75231, Paris, France</footnote>

<footnote>* Corresponding authors.</footnote>

<footnote>E-mail addresses: rafael.morales-ospino@univ-lorraine.fr (R. Morales-Ospino), vanessa.fierro@univ-lorraine.fr (V. Fierro).</footnote>
Furmaniak et al. [29] provided a comprehensive review of water adsorption models on ACs up to 2008, evaluating both classical and modern approaches. These include the semi-empirical models of Dubinin-Serpinsky (DS) [30], Mahle [31], and Barton [32], as well as theoretical frameworks by D'Arcy and Watt (DW) [33], Talu & Meunier [34], and Do and Do (DD) [35]. These models were assessed based on their ability to predict experimental isotherms and enthalpy profiles while accounting for surface heterogeneity, finite adsorption space, and partial chemisorption at hydrophilic centers. They consider heterogeneous cluster models, in particular the DD model, which provides the most reliable description of adsorption capacity and energy. In 2009, Do and Do [36] extended their model to interpret both adsorption and desorption branches of water vapor isotherms, accurately reproducing the experimental hysteresis over a wide humidity range and attributing the desorption hysteresis mainly to the breakdown of metastable clusters rather than pore blocking. The DD model remains one of the most widely used to describe water adsorption on ACs, capturing the two-stage process of initial cluster formation on hydrophilic sites, followed by progressive pore filling with increasing humidity. It offers a more physically meaningful interpretation than classical models such as those of DS or Dubinin-Astakhov (DA), although the latter has been identified as a good adsorption model approach for ACs in the absence of specific interactions [37].

The present work aims to deepen the understanding of water adsorption mechanisms and their link to CO₂ capture performance by synthesizing and characterizing AC samples with varying N- and O-containing functional groups. It seeks to correlate the structural and chemical properties of such materials with DD model's parameters obtained from experimental isotherm fitting, thereby using the model both as a fitting tool and as a diagnostic framework to link adsorption behavior to intrinsic physicochemical properties. Moreover, since evaluating CO₂ adsorption at different relative humidity (RH) levels is time-consuming and requires specialized equipment, this work proposes a methodology to assess the impact of humidity using only the water vapor adsorption isotherm, which is more accessible and easier to obtain. The analysis quantifies how initial water adsorption, driven by cluster formation and interactions with surface functional groups, affects CO₂ capture. By combining experiments with model-based interpretation, the study clarifies the relationship between water-carbon interactions and CO₂ capture efficiency.

## 2. Materials and methods

### 2.1. Commercial materials

Commercial ACs, MSC30 and MSP20X (Kansai Coke and Chemicals, Japan), were used as reference materials to facilitate comparison of certain results with the AC samples synthesized in this work. Commercial Zeolite 13× (Sigma Aldrich, USA) was also employed to compare CO₂ adsorption under dry and humid conditions of synthesized ACs.

### 2.2. Synthesis of activated carbons

Wood charcoal (20–40 mm, batch B201027) supplied by Groupe Bordet (oak and beech biomass, Grand Est region, France) was used as a precursor for the preparation of ACs. The as-received material was first pre-ground manually in an agate mortar, then in a planetary ball milling (Retsch, 500 rpm, 10 min) to produce a powder in which 90% of the particles were smaller than 550 µm.

The resulting charcoal powder was subsequently mixed with different amounts of KOH powder exclusively by mechanosynthesis, performed using planetary ball milling (Retsch, 500 rpm, 1 h), to obtain various KOH/charcoal weight ratios. The KOH/carbon mass ratios (1.5, 2.25, 4) were selected based on previous KOH activation studies [38–43] to yield ACs with BET surface areas between 1500 and 3000 m² g⁻¹, allowing a systematic correlation between the evolution of pore

features, in particular the gradual broadening of the pore size distribution (PSD), and the parameters of the Do and Do (DD) model.

The mixtures were then subjected to heat treatment at 1073 K in a nitrogen atmosphere (150 SCCM, heating rate 3 K min⁻¹, dwell time 1 h, and natural cooling). The AC samples obtained were designated ACX, where X represents the KOH/charcoal weight ratio, as summarized in Fig. 1. After carbonization, the samples were washed with a 1 M HCl solution and filtered, then rinsed repeatedly with distilled water until a neutral pH (≈7) was achieved. The washed materials were subsequently dried in an oven at 378 K for 24 h. The yield (%) was then calculated by comparing the final mass of the dried AC to the initial mass of the charcoal.

### 2.3. Materials characterization

The ACs were characterized by nitrogen and hydrogen adsorption–desorption measurements at 77 K using a Micromeritics 3Flex manometric analyzer. The nitrogen adsorption data were used to determine the Brunauer–Emmett–Teller (BET) area ($A_{BET}$). In order to study the porous structure in more detail, a combined analysis of nitrogen and hydrogen isotherms was performed using the two-dimensional non-local density functional theory (2D-NLDFT) model. This method provided the PSD, specific surface area ($S_{2D-NLDFT}$), micropore volume ($V_{micro}$), ultramicropore volume ($V_{umicro}$), supermicropore volume ($V_{super}$), mesopore volume ($V_{meso}$) and total pore volume ($V_{pore}$).

The chemical composition of the AC samples was determined by elemental analysis (EA) using a Vario El Cube elemental analyzer (Elementar). The elemental composition of the surface was further examined by X-ray photoelectron spectroscopy (XPS) with an ESCAPlus OMICRON system equipped with a hemispherical electron energy analyzer. The analyses were conducted under vacuum across an area of 1.75 mm × 2.75 mm, employing a non-monochromatized magnesium X-ray source (1253.6 eV) operated at 15 kV and 20 mA. XPS survey spectra were acquired at 0.5 eV steps (50 eV pass energy, 0.2 s dwell time) for elemental trends, while high-resolution spectra used 0.1 eV steps (20 eV pass energy, 0.5 s dwell time) processed in CASA software [44]. Charge correction applied C1s adventitious carbon reference [45], Scofield sensitivity factors [46], and Shirley background; peak fitting used GL (70) line shape validated on ion-sputtered graphite with constrained positions/FWHM and iterative residual minimization for reliable chemical state quantification.

### 2.4. Pure water vapor isotherms

Water vapor adsorption measurements were performed at 323 K using a Belsorp Max II manometric system (Microtrac), which employs precise pressure-volume-temperature (PVT) analysis for high-accuracy isotherm determination. The procedure involved dosing purified water vapor into the evacuated sample cell (~100 mg adsorbent, pre-outgassed at 383 K under secondary vacuum for 12 h), with equilibrium at each step established to <1% pressure change. Pressure transducers (0.01–100 kPa range, ±0.15% accuracy) and temperature control (±0.1 K stability) ensure reliable data across 0.01–0.9 P/P₀. The adsorption model developed by Do and Do [36] (Eq. 1) to describe water vapor adsorption in ACs was used to fit the experimental adsorption isotherms. The model describes the water vapor adsorption mechanism in two parts: the first represents a multiple clustering of water molecules around the functional groups of the AC (first term of Eq. 1), and the second is related to the filling of the micropores of the adsorbent (second term of Eq. 1).

$$q_{eq} = S_0 \frac{K_f \sum_{n=a+1} n(P/P_0)^n}{1 + K_f \sum_{n=a+1} (P/P_0)^n} + C_{\mu s} \frac{K_{\mu} \sum_{n=a+1} (P/P_0)^n}{K_{\mu} \sum_{n=a+1} (P/P_0)^n + \sum_{n=a+1} (P/P_0)^{n-a}} \quad (1)$$
<figure><img src="image_2.png" /><figcaption>Fig. 1. Schematic of the preparation of ACs (AC1.5, AC2.25, AC4) from wood charcoal and KOH by ball milling, followed by activation under N₂ at 1073 K.</figcaption></figure>

$S_0$ (mmol g⁻¹) represents the initial interaction force between water molecules and active sites (functional groups) on the carbon surface. $K_f$ (dimensionless) is the so-called chemisorption equilibrium constant. The parameter $\alpha$ (n-1, dimensionless) refers to the size of water clusters in the micropores, and $P/P_0$ is the relative water vapor pressure. $C_\mu$ (mmol g⁻¹) is the saturation concentration in the micropores, and $K_\mu$ (dimensionless) is the micropore equilibrium constant.

## 2.5. CO₂ adsorption isotherms under dry and pre-loaded humidity conditions

Equilibrium CO₂ adsorption isotherms at 323 K under controlled pre-humidified conditions (5–70% RH) were measured using a Dynamic Vapor Sorption (DVS) gravimetric analyzer (Surface Measurement Systems, UK), which provides ultrahigh-resolution mass detection (±0.05 µg, <0.1% RH control) for precise uptake quantification. Samples (10–20 mg) were pre-outgassed at 383 K under high vacuum (<10⁻⁶ mbar, 12 h) to eliminate pre-adsorbed species. Water vapor was then dosed to target RH values using a mass flow controller (reservoir with water, 200 sccm total flow).

CO₂ partial pressures were incrementally applied up to 1 bar after water vapor equilibrium was achieved. Equilibrium was defined in accordance with the manufacturer's guidelines, i.e., when the rate of mass change (dm/dt) fell below 0.004% min⁻¹, a threshold established for reliable measurements with typical sample masses in the 10–20 mg range. Once this equilibrium criterion was fulfilled, the adsorption isotherms were collected. The CO₂ isotherms obtained under pre-loaded humidity were then systematically compared to reference isotherms collected under dry conditions (i.e., without prior exposure to water), also measured at 323 K up to 1 bar and under identical experimental conditions.

# 3. Results and discussion

## 3.1. Physicochemical characterization of materials

The yields of the synthesized ACs, calculated relative to the initial charcoal weight, were 50% for AC1.5, 49% for AC2.25, and 49% for AC4. Information regarding gas physisorption characterization and PSD of the synthesized materials are presented in Fig. 2.

Fig. 2a shows the N₂ adsorption isotherms at 77 K with typical type I behavior, confirming microporosity. AC1.5 displays a type I(a) profile, while higher KOH/carbon ratios shift the isotherm towards type I(b), indicating wider micropores and emerging mesoporosity [47]. N₂ uptake increases from AC1.5 to AC4, consistent with higher porosity. H₂ adsorption at 77 K (Fig. 2b) follows the same trend, with AC4 exhibiting the highest uptake. The 2D-NLDFT PSDs (Fig. 2c) reveal peaks at ~0.4 nm and 0.7–0.9 nm, corresponding to ultra- and supermicropores, respectively. AC1.5 is dominated by ultramicropores, while AC4 features broader pores and small mesopores, leading to the largest

cumulative pore volume as shown in Fig. 2d. Fig. 2e illustrates how the total pore volume increases from 0.74 cm³ g⁻¹ (AC1.5MS) to 0.90 cm³ g⁻¹ (AC2.5MS) and 1.21 cm³ g⁻¹ (AC4PM). Although the relative micropore fraction decreases slightly with activation (from 96% to 87%), the absolute micropore volume continues to rise (from 0.71 to 1.05 cm³ g⁻¹). Similarly, the PSD shifts from ultramicropores to larger supermicropores, whose share increases from 62% (AC1.5) to 81% (AC4), as shown in Fig. 2f. Thus, more intense activation introduces more mesopores while favoring supermicropores over ultramicropores.

Table S1 summarizes the textural properties of these ACs, together with those of the two commercial ACs, including specific surface area and different average pore widths ($w_{x,avg}$ where x denotes ultra-, super-, micro-, mesopores or total pore width). Both $A_{BET}$ and $S_{2D-NLDFT}$ values reveal higher KOH/carbon ratios increase the specific surface area, confirming that more intense activation promotes pore development. Although the $S_{2D-NLDFT}$ values for AC1.5 and AC 2.25 exceed the $A_{BET}$ values, both exhibit the same trend. The BET model tends to underestimate the surface area of highly microporous samples due to the limited accessibility of N₂ in ultramicropores (<0.7 nm), as in samples AC1.5 and AC2.25, and to overestimate it in samples such as AC4, where supermicroporosity and mesoporosity promote multilayer adsorption. Pore size analysis (2D-NLDFT) reveals predominantly microporous structures, mainly supermicropores (~1.1 nm) with some ultramicropores (~0.5 nm) and minor mesopores (~2.5 nm). The average total pore width ($w_{pore,avg}$) increases from 0.91 nm (AC1.5) to 1.25 nm (AC4).

Table S1 also summarizes the elemental composition of the synthesized ACs (AC1.5, AC2.25, and AC4). Elemental analysis (EA, wt% / at. %) and X-ray photoelectron spectroscopy (XPS, at.%) both indicate that C is the dominant element and O is the main heteroatom. Increasing the activation ratio slightly raises the percentage of C while reducing the O and N contents. The elemental composition reveals a decrease in O content with increasing KOH/carbon ratios. This trend results from redox reactions that occur during activation [48], where higher doses of KOH promote carbon gasification and the formation of metallic potassium and potassium carbonate [49], which ultimately reduces the oxygen content. XPS results confirm a predominantly carbonaceous surface with minor oxygen functionalities. The EA results are also expressed as atomic percentage (at.%) to allow direct comparison between bulk and surface compositions.

XPS consistently shows slightly higher oxygen contents compared to EA, reflecting the enrichment of O-containing functional groups at the carbon surface. The C1s, N1s, and O1s XPs spectra of the synthesized samples are shown in Fig. S1. Fig. 3 compares the relative abundances of O-functional groups in the three AC samples. As the KOH/carbon ratio rises, the percentage of OI (quinone/carbonyl) decreases from 29.3% (AC1.5) to 23.2% (AC4), while OII (hydroxyl/ether/anhydride) also declines slightly from 49.7% to 44.8%. The proportion of OIV species (Chemisorbed oxygen species or water vapor) rises from 0% to 13% with increasing KOH/carbon ratios, indicating greater formation of oxygen
<figure><img src="image_3.png" /><figcaption>**Fig. 2.** Gas adsorption and PSD of ACs. (a) N₂ adsorption–desorption isotherms at 77 K with inset showing the low-pressure region. (b) H₂ adsorption isotherms at 77 K. (c) PSD obtained by NLDFT, and (d) the cumulative pore volume, highlighting ultramicropores, supermicropores, and mesopores. (e) Evolution of total pore, micropore and supermicropore volumes. (f) Micropore distribution with KOH/carbon ratio.</figcaption></figure>

species in the gas phase and sites accessible to water. At the same time, OIII (carboxylic acids) decreases slightly, suggesting limited additional oxidation on the edge. These trends are in line with reports in the literature showing that higher doses of KOH enhance porosity but promote gasification and loss of stable oxygen groups (e.g., carbonyls, phenols) [50–52]. Accordingly, moderately activated materials (KOH/carbon ratios 1–2) retain more bound oxygen species (OI, OII), whereas highly activated ones (KOH/carbon ratios ≥4) have lower stable oxygen content but higher OIV, as observed for AC4.

## 3.2. *Pure CO₂ and H₂O adsorption, and CO₂ adsorption under pre-humidified conditions*

The CO₂ adsorption isotherms in Fig. 4a show uptake in the order AC2.25 > AC1.5 > AC4. The adsorption capacities of AC2.25 and AC1.5 are very similar, with only a slight difference, while AC4 shows a somewhat lower uptake. Although this trend does not directly reflect the overall surface area or total porosity, the CO₂ adsorption capacity correlates linearly with the average size of ultramicropores (w<sub>umicro,avg</sub>), as
<figure><img src="image_4.png" /><figcaption>**Fig. 3.** Deconvolution of O1s XPS spectra for (a) AC1.5, (b) AC2.25, and (c) AC4, showing the relative percentages of oxygen-containing functional groups (O1, OII, OIII, and OIV). (d) Scheme of oxygen-containing functional groups in the carbon lattice, color-coded as indicated.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>**Fig. 4.** (a) CO₂ adsorption isotherms at 323 K up to 1 bar. (b) Water vapor adsorption–desorption isotherms at 298 K. (c) Percentage of CO₂ adsorption under humid conditions relative to dry conditions. (d) Absolute CO₂ adsorption capacity as a function of RH for the different samples.</figcaption></figure>

shown in Fig. S2. This relationship highlights the key role of ultra-
micropores in governing CO₂ uptake at low pressures (≤ 1 bar), where
adsorption occurs mainly through strong confinement effects rather
than by overall pore volume [53–58].

The water vapor adsorption isotherms at 298 K (Fig. 4b) exhibit type V behavior, as expected for ACs, characterized by low initial uptake at low relative pressures, followed by a sharp rise at intermediate P/P₀ values. The position of this sharp increase shifts towards higher relative

pressures as the KOH/carbon ratio increases, indicating that pore filling
occurs later in samples with wider pores. Moreover, the hysteresis loop
widens from AC1.5 to AC4, reflecting the evolution towards a more open
pore structure and a higher fraction of mesopores. These larger pores
facilitate multilayer adsorption and capillary condensation, contributing
to a wider hysteresis.

Fig. S3 shows CO₂ adsorption isotherms at 323 K up to 1 bar under dry (green) and pre-humidified (blue) conditions. As the RH increases,
CO₂ adsorption progressively decreases, although not always propor-
tionally to the RH level. For most samples, the CO₂ uptake remains
relatively constant up to 30% RH, and then gradually decreases as RH
increases. Among the ACs, AC1.5 loses its CO₂ adsorption capacity at
around 50% RH, whereas AC2.25 and AC4 show better moisture toler-
ance, maintaining measurable adsorption even at 50% RH. AC4 in
particular demonstrates the greatest resistance to the presence of water
vapor. The ACs recovered their initial mass after humid CO₂ adsorption-
desorption isotherms, indicating the complete reversibility of the
adsorption process. For comparison, we have performed the same ex-
periments on 3 commercial adsorbents: one zeolite and two commercial
ACs (Fig. S3 d-f). Zeolite 13× was included because it is a benchmark
CO₂ adsorbent due to its high uptake and selectivity under dry condi-
tions. The commercial ACs MSC-30 and MSP-20× were selected because
they are widely used in gas adsorption applications [50–52], possess

high surface areas (A<sub>BET</sub> > 2000 m<sup>2</sup> g<sup>-1</sup>; see Table S1 for a detailed
presentation of textural properties) and feature mixed micro-
–mesoporous structures, providing a broader range of textural and
chemical characteristics for correlation analysis.

Although zeolite 13× has significantly higher CO₂ uptake in dry conditions (4 mmol g⁻¹ at 1 bar and 323 K), its performance deteriorates markedly after pre-humidification, with CO₂ adsorption capacity falling to 0.5 mmol g⁻¹, corresponding to a reduction of approximately 87%. In contrast, the ACs retain a significant portion of their CO₂ uptake at moderate humidity levels, as illustrated in Fig. 4c and d. These graphs clearly show that zeolite 13× loses nearly all of its CO₂ adsorption above only 10% RH, while the ACs maintain approximately 70% of their CO₂ adsorption capacity in dry conditions up to 60% RH (for MSC-30), confirming their superior resistance to water vapor. Although the commercial AC MSC-30 exhibits the best water tolerance, its CO₂

<figure><img src="image_6.png" /><figcaption>Fig. 5. Determination of slope 1 and slope 2 from the water vapor adsorption isotherms of (a) AC1.5, (b) AC2.25, and (c) AC4. (d) Linear fits and determination coefficients (R²) corresponding to the low-relative pressure region (slope 1) and the high-relative pressure region (slope 2) for the same samples. Circles with a black arrow indicate the RH at the intersection of slopes 1 and 2. (e) Relative humidity values causing a 50% loss of CO₂ adsorption capacity. (f) Correlation between the relative humidity at the intersection of the slopes of water vapor isotherms and the relative humidity causing a 50% loss of CO₂ adsorption capacity.</figcaption></figure>
adsorption capacity below 1 bar is the lowest because it has the smallest ultramicropore volume ($V_{umicro}$) among all samples (see Table S1).

In order to establish a relationship between the shape of the water vapor isotherms and the CO₂ adsorption capacity after pre-humidification, two characteristic slopes were derived from the water adsorption curves (Figs. 5a-c). The first, slope 1, corresponds to the low-relative pressure region (P/P₀ < 0.2) and is associated with the material's affinity for water. A higher slope 1 indicates stronger water-surface interactions. As shown in Fig. 5d, AC1.5, despite having the lowest overall water uptake near saturation, exhibits the highest slope 1, suggesting a stronger affinity for water. Conversely, AC2.25 and AC4 show lower slope 1 values, consistent with their greater stability in CO₂ adsorption under humid conditions (Fig. 4). Among them, AC4 presents the lowest slope 1, confirming its lower hydrophilicity and higher resistance to moisture. The second, slope 2, corresponds to the steep region of the isotherm at higher relative pressures (P/P₀ ≈ 0.5-0.8), where capillary condensation and micropore filling occur after reaching the critical formation of water cluster. A steeper slope 2 reflects a greater

adsorption capacity at saturation. The intersection points between slope 1 and slope 2 (values in Table S2) provide an indicative RH threshold at which a significant decrease in CO₂ uptake occurs, as previously observed in Fig. 4.

To validate this relationship further, the RH corresponding to the intersection of the slopes was correlated with the CO₂ adsorption capacity under wet conditions compared to dry conditions (Figs. 5e and f). This analysis revealed that, for ACs, the intersection points correlate well with the RH at which the material loses approximately 50% of its CO₂ adsorption capacity (values in Table S2). It is worth mentioning the same commercial ACs MSC-30 and MSP-20× were included to strengthen this correlation. The water vapor adsorption isotherm of MSC-30 and MSP-20× at 298 K showing the intersection of slope 1 and slope 2 is shown in Fig. S3. This approach demonstrates that water vapor isotherms alone can provide predictive insights into the humidity threshold at which ACs lose half of their CO₂ capture performance and reduce the need for time-consuming CO₂ adsorption experiments.

<figure><img src="image_7.png" /></figure>

### C Do and Do model equation

$$q_{eq} = S_0 \frac{K_f \sum_{n=\alpha+1} n(P/P_0)^n}{1 + K_f \sum_{n=\alpha+1} (P/P_0)^n} + C_{\mu s} \frac{K_{\mu} \sum_{n=\alpha+1} (P/P_0)^n}{K_{\mu} \sum_{n=\alpha+1} (P/P_0)^n + \sum_{n=\alpha+1} (P/P_0)^{n-\alpha}}$$

### Do & Do model parameters correlations

<figure><img src="image_8.png" /><figcaption>Fig. 6. Experimental water vapor adsorption isotherms (symbols) with DD model fits (lines) plotted up to (a) P/P₀ = 1 and (b) P/P₀ = 0.2. (c) DD model equation and best linear correlations for the DD model parameters as a function of the physicochemical properties of samples AC1.5, AC2.25, AC4, and commercial ACs MSC30 and MSP20X.</figcaption></figure>
### 3.3. Correlation between DD model parameters and the physiochemical properties of ACs

The adsorption branches of the synthesized ACs (AC1.5, AC2.25, and AC4) and two commercial ACs (MSC-30 and MSP-20×) were fitted using the DD model, showing excellent agreement with the experimental water vapor isotherms over the entire range of relative pressures (Fig. 6a) and in the low-pressure region ($P/P_0 \le 0.2$; Fig. 6b). The corresponding fitting parameters for the five samples are summarized in Table S3.

The DD model parameters ($S_0$, $K_f$, $\alpha$, $K_{ub}$, $C_{us}$) of the five samples were systematically correlated with the textural properties of the same samples, such as specific surface area ($A_{BET}$, $S_{NLDFT}$) and different categories specific pore volumes: total pore volume ($V_p$), micropore volume ($V_{micro}$), ultramicropore volume ($V_{umicro}$), supermicropore volume ($V_{super}$), mesopore volume ($V_{meso}$) and the sum of super-and mesopore volumes ($V_{super+meso}$). The DD parameters were equally correlated to the chemical composition of the samples in terms of heteroatom content (N + O, at. %). Although the DD parameters can, in theory, be related to specific textural and chemical features of adsorbents, the objective of this correlation exercise is to assess these relationships beyond theoretical assumptions and identify new potential correlations that could provide deeper insight into the mechanisms of water adsorption on ACs. Analysis of the determination coefficients ($R^2$) between the DD model parameters and the textural and chemical properties of ACs reveals distinct relationships that help elucidate their water adsorption behavior. The complete set of $R^2$ values is presented in Table S4, while the corresponding best linear fits are shown in Fig. 6c. Additionally, Table S5 lists the values of DD model parameters previously reported in the literature.

As expected, $S_0$ exhibits a strong correlation with the total content of functional groups (N + O), confirming that the heteroatom concentration plays a decisive role in governing the early stages of water cluster formation at low relative pressures. This parameter represents the fraction of water adsorption attributable to surface functionalities. As illustrated in Fig. 6c, $S_0$ increases the heteroatom density normalized by the material's BET area (N + O/$A_{BET}$), demonstrating that the surface concentration of these groups is a key factor in initiating water uptake. This behavior indicates that nitrogen- and oxygen-containing groups act as primary active sites where water molecules begin clustering through hydrogen bonding. Among the parameters in the DD model, $S_0$ stands out as one of the few that exhibits a clear and consistent relationship with the chemical characteristics of the ACs, as also reflected in Table S4. The values of $S_0$ obtained in this study are consistent with those reported in the literature, which range from 0.12 to 12.78 mmol $g^{-1}$ (see Table S5). It is worth noting that, in most cases, the reported values are less than 2 mmol $g^{-1}$, an amount that corresponds well to the amount of adsorbed water observed at low relative pressures before micropore filling begins.

In the DD model, the parameter $K_f$ represents the chemisorption equilibrium constant associated with primary adsorption sites where water molecules initially interact with surface functional groups. It reflects the overall affinity of these sites, integrating both intrinsic chemical strength (e.g., hydrogen bonding or polarity) and confinement effects imposed by the local pore environment [20,35]. Higher $K_f$ values indicate stronger effective interactions between the adsorbed molecules and the solid surface, resulting in an initial increase in the uptake at lower relative pressures. As shown in Fig. 6a, sample AC1.5 displays the fastest adsorption increase, whereas MSC30 exhibits the slowest, consistent with their respective highest and lowest $K_f$ values. $K_f$ shows a strong dependence on the porous structure of ACs. Among the different textural properties, $K_f$ is most strongly correlated with $A_{BET}$, $V_p$ and $w_{micro,avg}$ ($R^2 \ge 0.95$). This suggests that the chemisorption equilibrium constant is heavily influenced by the accessibility and confinement of adsorption sites within the microporous structure. A higher $A_{BET}$ provides a larger number of accessible functional groups for initial water interaction, while a greater pore volume ($V_p$) facilitates enhanced

molecular accommodation and diffusion. Similarly, a decrease in average micropore width ($w_{micro,avg}$) intensifies confinement effects, promoting stronger adsorbate-surface interactions and thereby higher $K_f$ values.

Lodewyckx et al. [20] proposed a simplified form of the DD equation describing adsorption near functional groups, where $S_0$ and $K_f$ were directly related to their number. $S_0$ was assumed to correspond to a pentamer per functional group (5 [N + O]), and $K_f$ to a kinetic parameter representing the adsorption-desorption driving force, dependent on [N + O] at low relative pressures ($P/P_0 < 0.4$). This led to a Langmuir-type relation linking the [N + O] content, obtained by XPS, to the linear region of the water vapor isotherm (equation in Fig. S4a). In our study, this correlation was not observed directly (Fig. S4b). Instead, the slope 1 of the isotherms up to $P/P_0 \approx 0.2$ of the five selected samples showed a relatively strong correlation with [N + O]/$A_{BET}$ ($R^2 = 0.94$), indicating that the density of functional groups better describes the water adsorption behavior in this low-pressure range (Fig. S4c).

The cluster critical size ($\alpha$) is strongly correlated with the $V_p$, $w_{micro,avg}$, $V_{super+meso}$ ($R^2 \ge 0.96$). This observation supports the assumption that, once this critical cluster size is reached, the adsorption mechanism switches to pore filling. Consequently, materials that possess larger pore volume and micropore size require larger water clusters before pore filling can begin. Interestingly, $\alpha$ shows poor correlation with micropore volume, implying that the critical cluster size depends more on micropore size rather than on micropore quantity. In the original DD model [35], the critical cluster size ($\alpha$) was fixed at five. Values closer to this number were previously reported [7] and have been found to be characteristic of ACs with an average pore diameter between 1.96 and 2.8 nm. Neitsch et al. [59] proposed a modification of the DD model by considering variable water cluster sizes and found values up to 16. Molecular simulation studies [60] have shown that the size of water clusters is influenced by both the density and spatial distribution of adsorption sites, as well as by pore width. In the revised formulation of the DD model in 2009 [36], $\alpha$ became an adjustable parameter, with reported values exceeding 5 ($\alpha$ up to 30; see Table S5 for details) [9,36]. An increase in this value indicates that water adsorption in micropores begins at higher relative pressures. Larger water clusters only form around surface functional groups at these higher vapor pressures before condensing inside the pores [36]. Once formed, these clusters cause a sharp increase in the adsorbed amount due to the larger number of associated water molecules. In this study, the results are more consistent with the assumption of variable cluster size when $\alpha$ increases from 9 in AC1.5 to 10 in AC2.25 and 14 in AC4, producing a steeper increase in the isotherm, consistent with delayed micropore filling, as shown in Fig. 6a.

For the micropore equilibrium constant, $K_u$, the obtained values were over 100, ranging between 106 and 236 (Table S4). Ponton et al. [61] also reported $K_u$ values in the order of one hundred (105) for a series of bio-sourced carbon-based materials. According to Vagner et al. [62], this parameter can be interpreted as a partition coefficient that reflects the adsorption equilibrium between water molecule clusters and the micropores at the carbon surface. In their study, only minor variations in $K_u$ were observed, indicating comparable water-carbon interaction behavior between samples. In this work, parameter $K_u$ showed a reasonable agreement with the overall heteroatom concentration and the heteroatom density per surface area [N + O]/$S_{NLDFT}$ ($R^2 \ge 0.85$). This correlation suggests that the formation and stability of water clusters within the micropores are largely governed by the availability and distribution of polar surface functionalities, such as O- and N-containing groups, which enhance the local polarity and facilitate strong hydrogen bonding interactions. Materials with higher heteroatom densities offer more active centers for cooperative adsorption, promoting capillary condensation-like behavior even at low relative pressures. At the same time, similar $K_u$ magnitudes across the samples indicate that the micropore environments share comparable energetic characteristics, likely due to analogous pore size ranges and confinement effects. Nevertheless, it is worth mentioning that values of $K_u$ reported in the
literature vary widely. For instance, Do and Do [36] reported values as high as 37,682, while Legrand et al. [21] observed values ranging from 9.7 to 1072. From this, it can be concluded that further research is needed, and this study is intended to be the first in a series of efforts to understand better the significance of this parameter. The use of chars produced at different carbonization temperatures and ACs with less developed surface areas could be a useful strategy to achieve this.

The micropore saturation concentration ($C_{\mu s}$) correlates well with most textural properties, especially those related to total pore volume ($R^2 = 0.96$) and average micropore size ($R^2 = 0.95$). This behavior can be attributed to the fact that $C_{\mu s}$ represents the amount adsorbed at saturation, as the $C_{\mu s}$ values for the five samples closely match the water uptake experimentally measured at $P/P_0 \sim 1$ (Fig. S6), which is consistent with the findings reported by Li and Li [7]. However, $C_{\mu s}$ does not correlate well with micropore volume ($R^2 = 0.47$). This could be attributed to the fact that pore filling is not limited solely to micropores, but also involves mesopores. This is consistent with the adsorption mechanism proposed by Legrand et al. [21], which describes water uptake progressing through micropore filling up to $P/P_0 \sim 0.8$, followed by the gradual filling of mesopores and, eventually, macropores. Since all samples, particularly AC4 and MSC30, exhibit some degree of mesoporosity, correlations based solely on micropore volume do not adequately describe this behavior. This is also reflected in the good linear correlation with the volumes of supermicropores and mesopores ($V_{super} + meso, R^2 = 0.96$).

## 4. Conclusion

This study presented a predictive framework for assessing the effects of humidity on CO₂ capture in activated carbons (ACs), demonstrating that a 50% loss in CO₂ capture can be predicted from the pure water isotherms. By applying the Do and Do (DD) adsorption model to water vapor isotherms, we obtained excellent fits, and the resulting DD parameters were correlated with surface heteroatom density and textural parameters, enabling reliable predictions of moisture-induced CO₂ capacity loss.

These water adsorption measurements were shown to be a rapid screening tool for identifying moisture-tolerant ACs, reducing the need for time-consuming water/CO₂ adsorption experiments with different relative humidity levels. This approach also provided a rational basis for designing high-capacity, less hydrophilic adsorbents through targeted control of surface chemistry and pore architecture. Future work should extend this framework to a range of carbon materials, including biomass-derived ACs with O-rich surfaces, showing stronger water affinity, templated carbons with uniform pores, allowing for clearer structure-property relationships, and heteroatom-doped (e.g., N-, O-, or S-) ACs that can modify adsorption onset while maintaining overall trends. Additionally, materials with lower specific surface areas and higher heteroatom contents should be explored. This approach can also be applied to other adsorbents, such as zeolites and MOFs, and extended to dynamic multi-component conditions to better support practical CO₂ capture applications.

## CRediT authorship contribution statement

R. Morales-Ospino: Writing – review & editing, Writing – original draft, Supervision, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. M. Aoun: Writing – original draft, Investigation. J. Castro-Gutiérrez: Validation, Investigation. M.T. Izquierdo: Writing – review & editing, Validation, Methodology, Investigation. A. Celzard: Writing – review & editing, Validation, Supervision. V. Fierro: Writing – review & editing, Validation, Supervision, Resources, Project administration, Methodology, Funding acquisition, Formal analysis, Data curation, Conceptualization.

## 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 supported by the CATALPA project (ANR-22-PESP-0007), funded by the ANR France 2030 program. The authors gratefully acknowledge Philippe Gadonneix for his invaluable assistance in the laboratory.

## Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.cej.2026.173366.

## Data availability

Data will be made available on request.

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