# Understanding the role of pollutant confinement during the thermal regeneration of activated carbons

F. Olivier, S. Schaefer, Kana Maiga, Marjolie Roulet, I. Laidin, Conchi O.

Ania, Benoît Cagnon

► To cite this version:

F. Olivier, S. Schaefer, Kana Maiga, Marjolie Roulet, I. Laidin, et al. Understanding the role of pollutant confinement during the thermal regeneration of activated carbons. Carbon, 2025, 234, pp.120003. 10.1016/j.carbon.2025.120003. hal-05101945

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# Understanding the role of pollutant confinement during the thermal regeneration of activated carbons

F. Olivier<sup>a,b</sup> <sup>●</sup>, S. Schaefer<sup>a,**</sup> <sup>●</sup>, K. Maiga<sup>b</sup>, M. Roulet<sup>a</sup>, I. Laidin<sup>c</sup>, C.O. Ania<sup>b,*</sup> <sup>●</sup>, B. Cagnon<sup>a,***</sup>

## ARTICLE INFO

### Keywords:

- Thermal regeneration

- Activated carbon

- Phenol adsorption

- Desorption phenomena

## ABSTRACT

The thermal regeneration of activated carbons is the most commonly used approach to allow their reuse. While the process aims to restore the original porosity of the carbon adsorbent, the thermal treatment very often leads to a drop in textural properties due to the thermal degradation of the pollutants inside the porosity of the carbon adsorbent. Despite being widely reported, understanding of the key parameters of the activated carbons governing the efficiency of the regeneration is yet not well understood. In this study, we have carried out a detailed study on the impact of the textural and chemical characteristics of commercial pristine activated carbons on their regeneration upon several cycles. The activated carbons were saturated with phenol from aqueous solution, and characterized after several cycles of thermal regeneration. Our results show that the confinement state of the adsorbed molecule is important to determine the efficiency of the regeneration. Hence, activated carbons with wide micropores displayed poor regeneration efficiency, due to the occurrence of various adsorbed states in those pores (i.e. dimers, clusters, stacking). Carbons with high oxygen contents also presented low regeneration efficiencies due to specific interactions with the oxygen moieties.

## 1. Introduction

Activated carbons (ACs) represent one of the best available environmental control technologies by means of adsorption processes. ACs are used to purify drinking water, wastewater and air. These materials are probably still the most effective adsorbents for organic contaminants due to its high surface area, low specificity and fast adsorption kinetics [1]. After exhaustion, activated carbon must be regenerated or replaced by fresh carbon. The first option is preferred by the industrials due to the high cost of this adsorbent [2]. Moreover, from an environmental regeneration point of view is recommended because the exhausted spent carbon could be landfilled.

At the same time, the treatment of industrial wastewater is increasing in industrializing countries as industrial activity rises and the need to reuse water and reduce effluent pollution becomes greater [3]. The need for activated carbon is increasing and when the AC reached its capacity, no longer was possible to simply take to the landfill and

discarded. Regeneration is an important part of some industrial AC markets, as the regenerated carbons can be sold or used in other suitable applications [4]. In addition, AC regeneration is more conductive to protect the environment and conserve resources. Moreover, the possibility of using an AC in successive adsorption-regeneration cycles is essential from the economic and energetic point of view.

The literature has reported several methods for the regeneration of saturated activated carbons, such as: chemical [2], electrochemical [5–8], supercritical fluids [9–13], microwave-assisted [3,14–16], bio-regeneration [17,18], pH swing-related (alkaline or acidic) [19,20], solvent regeneration [21,22], sonochemical [23], oxidative methods coupling various approaches [24,25] and thermal treatment [26–31]. Despite the good performance of many of these processes (in terms of regeneration efficiency over the number of cycles and porosity recovery), the thermal regeneration under inert or mild oxidative atmosphere is currently the only approach applied worldwide for the regeneration of saturated activated carbons at industrial scale [32], due to its inherent

<footnote><sup>a</sup> ICMN, UMR 7374 - CNRS, Univ. d'Orléans, 45071, Orléans, France</footnote>

<footnote><sup>b</sup> CEMHTI CNRS (UPR 3079), Univ. d'Orléans, 45071, Orléans, France</footnote>

<footnote><sup>c</sup> Jacobi Carbons, Vierzon, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>** Corresponding author.</footnote>

<footnote>*** Corresponding author.</footnote>

<footnote>E-mail addresses: sebastien.schaefer@univ-orleans.fr (S. Schaefer), conchi.ania@cnrs-orleans.fr (C.O. Ania), benoit.cagnon@univ-orleans.fr (B. Cagnon).</footnote>
simplicity of design and ease of application. The thermal regeneration of saturated activated carbons consists on inducing the desorption/de-composition of the pollutants adsorbed inside the porosity of the activated carbon upon a thermal treatment at high/moderate temperatures. Such thermal treatment can be associated to various disadvantages such as long regeneration times and high energy consumption (leading to high operational costs), as well as to undesirable modifications of the properties of the activated carbon (basic/acidic character, attrition of the carbon particles) [14,32].

In this context, the objective of this study is to investigate thermal regeneration of spent commercial ACs currently used in different industrial facilities, emphasizing on the impact of the regeneration conditions after several adsorption/regeneration cycles in the porosity and uptake capacity of the regenerated carbons. A detailed study of the textural properties and surface chemistry of the ACs saturated with phenol (taken as reference molecule) was carried out to understand the mechanisms associated with the regeneration process and the impact of the textural parameters and the surface chemistry of the activated carbon on the regeneration. In addition, a deep insight into the direct link between the initial textural properties of the activated carbons (i.e. prior to phenol adsorption) on the kinetics of phenol thermodesorption and on the well-known pore blocking phenomenon occurring during the thermal regeneration upon the degradation of the pollutants was also obtained.

From this perspective, while the optimum pore size for an efficiency adsorption of phenol on porous carbons has been widely investigated -e.g., some authors report 0.6-0.7 nm [33,34]; others suggest 0.8-1.4 nm and wider pores [35,36]-, the correlation between the porosity of the activated carbon and the thermal desorption of phenol has been scarcely addressed with a similar degree of refinement. In this study, we have combined experimental results with our recent data treatment methodology involving simple modelling [37], to assess the thermal regeneration of activated carbons saturated with phenol, and the critical roles of the pore size distribution of the pristine carbon and its surface chemistry. Our results provide a rational analysis on the correlation between the adsorption performance of activated carbons for an efficient removal of pollutants and their regeneration behavior in consecutive cycles.

## 2. Materials and methods

### 2.1. Materials

Three activated carbons obtained from the activation of coconut shells and supplied by Jacobi Carbons group (Vierzon, France) were selected for this study; they are labeled AS2 and AS5 (physical activation) and L39 (phosphoric acid activation). Phenol (Across organics, 99 % extra pure) was used as model pollutant. Deionized water (Milli-Q system) was used for the preparation of all the solutions.

### 2.2. Saturation of the carbons

Initially, a kinetic study was carried out to determine the time needed to equilibrium phenol adsorption in the studied carbons in our experimental conditions. To this end, ca. 50 mg of ACs were suspended in a volume of 50 mL of phenol solution (initial concentration at 500 ppm) under stirring at 25 °C. The concentration of the solution was measured over time by UV spectrophotometry (Cary 60 UV-Vis, Agilent) at 270 nm, after filtering out the carbon (Syringe filter sterile porosity 0.45 µm, ClearLine). The equilibrium time was determined when the variation of the concentration in solution of two consecutive measurements represented less than 10 %. The retrieved equilibrium times were used for saturating the carbons, using the operating conditions described above (ca. 50 mg of carbon dispersed in 50 mL of a phenol solution of initial concentration 500 ppm). After equilibration, the suspensions were filtered out (Whatman 0.45 µm, Grade 40 Ashless Filter Paper,

Cytiva), and the saturated carbons were dried at room temperature for 12 h and kept in the desiccator until further use. The amount of phenol adsorbed during the saturation assays was determined by spectrophotometry, to compare the different adsorption/regeneration cycles.

### 2.3. Thermal regeneration

The thermal regeneration of the saturated carbons was performed in a tubular furnace (Thermolyne 21 100), upon heating from ambient temperature up to 800 °C under a nitrogen flow (160 mL min⁻¹), using a heating rate of 20 °C.min⁻¹ and a dwelling time at the final temperature of 1 h. The inert atmosphere was also maintained during the cooling step to room temperature. Three consecutive adsorption/regeneration steps were carried out, in order to obtain four cycles. The nomenclature of the samples after each regeneration cycle is ZZ-Rn, where ZZ stands for the carbon acronym, and n indicates the regeneration cycle. For instance, L39-R3 stands for carbon L39 submitted to three regeneration cycles (after the corresponding adsorption ones). The raw activated carbons were also thermally treated before carrying out the saturation, in order to evaluate the impact of the thermal treatment on the characteristics of the carbons (control samples). The nomenclature of these control samples is ZZ*, where ZZ stands for the carbon acronym. To evaluate the efficiency of the thermal regeneration, a parameter accounting for the residual fractional mass of carbon after the thermal regeneration (Yc) was calculated as the ratio between the amount of adsorbed phenol that remains in the carbon matrix after the regeneration (calculated as the mass of saturated carbon after the regeneration minus the mass of activated carbon in the saturated sample), and the amount of phenol adsorbed in the saturated sample (calculated from the uptake experiments):

$$Y_c(\text{wt.}\%) = \frac{(m_{\text{phenol adsorbed remaining in the sample after regeneration}})}{(m_{\text{phenol adsorbed in the saturated sample}})} \cdot 100 \quad (1)$$

This parameter accounts for the yield of desorption of the pollutant during the thermal regeneration, and differs from typical regeneration yields focused on the mass loss referred to the initial mass of saturated carbon.

### 2.4. Characterization of the pristine, saturated and regenerated carbons

The porosity of the activated carbons (both as-received, saturated and after regeneration) was determined by N₂ adsorption/desorption isotherms at -196 °C in volumetric analyzer (Triflex, Micromeritics). The samples were previously outgassed under vacuum at 80 °C for 12 h. The gas adsorption isotherms were used to evaluate the specific surface area, S<sub>BET</sub>, calculated by the Brunauer-Emmett-Teller (BET) method in the appropriate range of relative pressures [38], the total pore volume, V<sub>tot</sub> determined at relative pressures of 0.99 and the pore size distributions (PSDs). The latter were obtained using the 2D-NLDFT-HS model for porous carbons with corrugated and chemically heterogeneous surfaces [39].

The average (volume weighted) micropore size was calculated as:

$$L_0(dV)(\text{nm}) = \frac{\sum_{i} w_i \cdot dV_i}{\sum_{i} dV_i} \qquad (2)$$

where dVᵢ (cm³·g⁻¹) is the differential pore volume around a given pore size -wᵢ- (nm).

After each adsorption and regeneration step, the modification of the porosity was evaluated upon evaluating the decrease in the pore volume (V<sub>loss</sub>) around the pore size w and in the pore fraction [39,40]. This parameter is defined as follows:

$$V_{\text{loss}}(w)(\text{cm}^3 \cdot \text{g}^{-1}) = \int_{w-0.125}^{w+0.125} \text{PSD}_{n-1}(w) \, dw - \int_{w-0.125}^{w+0.125} \text{PSD}_n(w) \, dw \quad (3)$$
<figure><img src="image_3.png" /><figcaption>Fig. 1. (A,C) High resolution N₂ adsorption/desorption isotherms at 77 K of the pristine activated carbons and after thermal treatment (series ZZ*); (B,D) Pore size distributions calculated by application of the 2D-NLDFT-HS model for carbon materials to the nitrogen adsorption data. (A colour version of this figure can be viewed online.)</figcaption></figure>

where *PSD*<sub>n-1</sub>(*w*) and *PSD*<sub>n</sub>(*w*) refer to the values of the differential pore volume (*dV/dw*) obtained on the pore size distributions over a 0.25 nm step of pore sizes before (saturated sample) and after (regenerated sample) a nth regeneration cycle (the complete set of PSD data is shown in Fig. S1, Supplementary Information). The chemical composition of the bulk activated carbons was determined by elemental analysis using a Thermo Scientific CHONS flash 2000 analyzer operating under helium and using a catharometer detector coupled to gas elution chromatography. The samples were dried before the analyses, and preconditioned in tin (for C, H, N, and S analyses) and silver capsules (for O). About 0.8 and 1.1 mg of material were used for the analysis, each of it performed in triplicate (average values are presented). To determine the sulfur content, vanadium oxide (ca. 0.8–1.1 mg) was added as internal standard to the tin capsule. The surface pH was measured by triplicate by dispersing 150 mg of the carbons in 75 mL of 0.01 M NaNO₃ under constant stirring (500 rpm), after 72 h of equilibration.

## 2.5. Thermogravimetric analysis

Thermogravimetric analyses were performed using a TGA STA 449 F5 Jupiter (Netzsch) thermobalance. About 10–20 mg of sample was placed in an alumina crucible under a 160 mL min⁻¹ argon flow (a

buoyancy correction was recorded for each measurement). The pristine, saturated and regenerated carbons were heated from ambient temperature up to 800 °C at various heating rates between 5 and 30 °C.min⁻¹, followed by a 1 h at the final temperature and a cooling step to room temperature. For analyzing the desorption of the pollutant after each saturation cycle, the first derivative of the mass evolution with the temperature was calculated and fitted using multiple peak functions and asymmetric gaussian functions.

## 2.6. Evaluation of selected parameter indicators to discuss the desorption mechanism

The desorption energy (*E*<sub>des</sub>), frequency factor (ν), desorption rates (V), standard entropy of adsorbed phase (*S*<sup>0</sup><sub>aa</sub>) and the average minimum Steele's adsorption potential (<S>) for phenol adsorption on carbon materials were used to discuss the desorption mechanism of phenol in the confined nanopores space. *E*<sub>des</sub> and V are related to the binding energy of the adsorbed molecules and the desorption rate, respectively. The frequency factor is related to the entropy change involved in the system when the adsorbed molecules are desorbed. The complete mathematical demonstrations for the assessment of these parameters is shown in the supplementary information as well as in relevant literature
<caption>**Table 1**</caption>

Main textural parameters and selected chemical characteristics (oxygen content and surface pH) of the raw activated carbons before and after (series ZZ*) the thermal treatment.

<table><thead><tr><th></th><th>S<sup>0</sup><sub>BET</sub> (m<sup>2</sup>.g<sup>-1</sup>)</th><th>V<sub>tot</sub><sup>a</sup> (cm<sup>3</sup>.g<sup>-1</sup>)</th><th>V<sub>micro</sub><sup>a</sup> (cm<sup>3</sup>.g<sup>-1</sup>)</th><th>V<sub>meso</sub><sup>a</sup> (cm<sup>3</sup>.g<sup>-1</sup>)</th><th>V<sub>micro</sub><sup>a</sup> (%)</th><th>V<sub>meso</sub><sup>a</sup> (%)</th><th>S<sub>micro</sub><sup>a</sup> (m<sup>2</sup>.g<sup>-1</sup>)</th><th>O<sup>b</sup> (wt.%)</th><th>pH<sub>surface</sub><sup>c</sup></th></tr></thead><tbody><tr><td>AS2</td><td>1030</td><td>0.48</td><td>0.38</td><td>0.10</td><td>79.3</td><td>20.7</td><td>889</td><td>1.26</td><td>9.3</td></tr><tr><td></td><td>966</td><td>0.43</td><td>0.35</td><td>0.08</td><td>82.5</td><td>17.5</td><td>814</td><td>0.93</td><td>9.9</td></tr><tr><td>AS2*</td><td>1155</td><td>0.72</td><td>0.39</td><td>0.33</td><td>54.8</td><td>45.2</td><td>938</td><td>1.55</td><td>8.3</td></tr><tr><td>AS5</td><td>1166</td><td>0.73</td><td>0.38</td><td>0.35</td><td>52.7</td><td>47.3</td><td>905</td><td>0.76</td><td>9.2</td></tr><tr><td>AS5*</td><td>1601</td><td>1.10</td><td>0.53</td><td>0.57</td><td>48.7</td><td>51.3</td><td>1118</td><td>11.58</td><td>2.9</td></tr><tr><td>L39</td><td>1254</td><td>0.87</td><td>0.44</td><td>0.43</td><td>50.8</td><td>49.2</td><td>1111</td><td>6.84</td><td>7.2</td></tr><tr><td>L39*</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr></tbody></table>

a Obtained from gas adsorption data.

b Obtained from elemental analysis.

c Surface pH at the point of zero charge.

[34,40–46].

The desorption activation energy and frequency factor were calculated from equation (4); plotting $ln(\frac{\beta}{T_p^2})$ versus $\frac{1}{T_p}$ allows evaluating the desorption activation energy from the slope and the frequency factor from the intercept.

$$ln(\frac{\beta}{T_p^2}) = ln(\frac{\nu.R}{E_{des}}) - \frac{E_{des}}{R} \frac{1}{T_p} \quad (4)$$

where $\beta$ stands for the heating rate (in K.s$^{-1}$), $T_p$ (K) is the average temperature of the peak, $E_{des}$ for the desorption energy in J.mol$^{-1}$, $\nu$ is the frequency factor and $R$ is the perfect gas constant.

The desorption rate $V$ (s$^{-1}$) for a first order kinetic was calculated as follows:

$$V(s^{-1}) = \nu.\theta^1.e \left( \frac{E_{des}}{k_b.T_p} \right) \quad (5)$$

where $\theta$ is the fractional coverage, $k_b$ is the Boltzmann's constant, $T$ is the desorption temperature (K), and $E_{des}$ for the desorption energy in J. mol$^{-1}$.

Setting $\theta \approx 1$ and $\beta \approx 0$ lead to the calculation of the maximum desorption rate under infinitesimally low heating rate ($V_{max}$). Such approximation allows to simulate a desorption near equilibrium conditions and to avoid any coverage-induced differences of desorption rate when comparing the different porous carbons.

The standard entropy of adsorbed phase ($S_{ad}^0$) for a given desorption peak was calculated assuming that phenol is adsorbed parallel to the carbon surface, as follows [40]:

$$S_{ad}^0 (\text{J.mol}^{-1}.\text{K}^{-1}) = S_{gas}^0 - S_{gas,1D-trans}^0 - R \ln \left( \frac{\nu.h}{k_b.T_p} \right) \quad (6)$$

where $h$ is the Planck's constant (J.s), $S_{gas}^0$ (J.mol$^{-1}.K^{-1}$) is the standard entropy of the desorbing molecule in its gas phase and $S_{gas,1D-trans}^0$ (J.mol$^{-1}.K^{-1}$) is the entropy contribution due to one translational degree of freedom within a molecule.

The average minimum Steele's adsorption potential ($\langle s \rangle$) for phenol adsorption on a carbon surface with a specific pore size distribution as a function of the pore size ($w$) was calculated as:

$$\langle s \rangle (\text{kJ.mol}^{-1}) = \frac{\sum_i s(w_i) dV_i}{\sum_i dV_i} \quad (7)$$

where $dV_i$ (cm$^3$.g$^{-1}$) is the differential pore volume around a given pore size $w_i$.

# 3. Results and discussion

## 3.1. Textural and chemical characteristics of the pristine activated carbons

Fig. 1 shows the N$_2$ adsorption/desorption isotherms at 77 K and the pore size distributions of the activated carbons. The main textural parameters (specific surface area, total specific pore volumes and fraction of micropores and mesopores) obtained from the analysis of the gas adsorption data are compiled in Table 1. As seen, the N$_2$ adsorption/desorption isotherms of the studied activated carbons are characteristic of materials with a broad distribution of pores in the micropore and mesopore ranges. Samples AS5 and L39 displayed broad knees in the low range of relative pressures of their adsorption isotherms, pointing out to the presence of pores of wider dimensions compared to sample AS2. Both carbons also displayed marked hysteresis loops indicating the presence of mesopores. Comparatively, the nitrogen uptake was significantly higher for carbon L39 in all the range of relative pressures, indicating a more developed porosity for this material in the full nanopore range. This is confirmed by the textural parameters shown in Table 1. Indeed, the PSDs of carbons AS2 and AS5 are rather similar, showing a multimodal pattern in the microporosity with distinctive domains centered at about 0.6, 0.9 and 1.7–1.8 nm (at the boundary of mesoporosity). Comparatively, carbon AS5 shows a larger contribution of mesopores than sample AS2. For carbon L39, two main domains in the micropore region were distinguished (ca. 0.6 and 1.1 nm), along with a well-developed mesoporosity (see the broad hump in the PSD between 2 and 10 nm).

The three pristine carbons also presented large differences regarding composition. Carbon L39 displays high oxygen content and low surface pH, while carbons AS2 and AS5 are of basic nature as inferred from their low oxygen content and values of surface pH (Table 1). These characteristics are typical of activated carbons obtained by physical (AS2 and AS5) and chemical (L39) activation of lignocellulosic precursors [47].

Fig. 1 (plots C,D) shows the N$_2$ adsorption/desorption isotherms of the pristine activated carbons exposed to the similar thermal treatment used during the regeneration (samples AS2*, AS5* and L39*). For carbons AS2 and AS5, the thermal treatment had a negligible impact in the porosity as seen in the minor changes in the textural parameters (Table 1). For carbon L39, the thermal treatment brought about a marked decrease in the pore volumes and surface area, although the shapes of the gas adsorption isotherms are similar. The analysis of the PSD before (sample L39) and after the thermal treatment (sample L39*) confirmed that the thermal annealing only affected the pore volumes as the pore size distributions remained similar. Besides porosity, the thermal treatment of carbon L39 also modified the acidic/basic character of this carbon, since the fall in the oxygen content render carbon L39* hydrophobic (Table 1). This behavior has been widely described in the
<figure><img src="image_4.png" /><figcaption>**Fig. 2.** Evolution of phenol adsorption capacity relative to the pristine materials (bars, left axis) and the area of micropores (squares, right axis) of the pristine and regenerated activated carbons after several cycles. Data corresponding to the activated carbons after the thermal treatment at a similar temperature than the regeneration (series ZZ*) is also shown for comparison purposes. (A colour version of this figure can be viewed online.)</figcaption></figure>

**Table 2**

Evolution of the residual fractional mass of carbon ($Y_c$) and the desorption energies corresponding to peaks I and II in the thermogravimetric profiles upon several cycles of adsorption/regeneration of the activated carbons.

<table><thead><tr><th rowspan="2"></th><th colspan="3">Residual fractional mass of carbon Y<sub>c</sub> (wt. %)</th><th colspan="3">E<sup>peak I</sup><sub>des</sub> (kJ.mol<sup>-1</sup>)</th><th colspan="3">E<sup>peak II</sup><sub>des</sub> (kJ.mol<sup>-1</sup>)</th></tr><tr><th>AS2</th><th>AS5</th><th>L39</th><th>AS2</th><th>AS5</th><th>L39</th><th>AS2</th><th>AS5</th><th>L39</th></tr></thead><tbody><tr><td>Cycle 1</td><td>58.4</td><td>50.3</td><td>-<sup>a</sup></td><td>66.9</td><td>56.2</td><td>92.3</td><td>243.4</td><td>88.6</td><td>-<sup>a</sup></td></tr><tr><td>Cycle 2</td><td>51.8</td><td>51.6</td><td>71.3</td><td>70.6</td><td>70.2</td><td>124.4</td><td>133.4</td><td>110.8</td><td>84.1</td></tr><tr><td>Cycle 3</td><td>58.2</td><td>49.9</td><td>64.4</td><td>68.6</td><td>78.1</td><td>90.0</td><td>126.7</td><td>120.0</td><td>138.2</td></tr><tr><td>Cycle 4</td><td>56.9</td><td>48.9</td><td>60.8</td><td>58.1</td><td>55.3</td><td>86.2</td><td>144.9</td><td>186.0</td><td>116.7</td></tr><tr><td>Annealed carbons</td><td>AS2*</td><td>AS5*</td><td>L39*</td><td>AS2*</td><td>AS5*</td><td>L39*</td><td>AS2*</td><td>AS5*</td><td>L39*</td></tr><tr><td></td><td>70.2</td><td>70.6</td><td>72.1</td><td>63.2</td><td>65.4</td><td>62.3</td><td>243.5</td><td>167.6</td><td>-</td></tr></tbody></table>

literature [33–35,47]. All these modifications of both the texture and the chemical composition of the carbons as a result of the thermal treatment are important, since they will have a strong impact in the adsorption ability for phenol retention. This will be further discussed below.

## 3.2. Cyclic adsorption capacities

To evaluate the effect of thermal regeneration on the cyclic performance of the activated carbons, the adsorption capacity of phenol was evaluated upon subsequent thermal regeneration cycles and compared to that of the pristine materials (Fig. 2). Details on the kinetics of adsorption for the pristine carbons are shown in the supplementary information (Fig. S2, Table S2). The evolution of the area of the micropores ($S_{micro}$) over the subsequent adsorption/regeneration cycles is also shown in Fig. 2 as a performance indicator accounting for the textural properties and the uptake, since it is rather well established that phenol adsorption predominantly occurs upon a micropore filling mechanism [33–36,48–51].

As seen, the pristine carbons displayed different trends upon the adsorption/regeneration cycles. For carbon AS2, both the uptake of phenol and $S_{micro}$ decreased gradually with the adsorption/regeneration

cycles (Fig. 2), indicating a loss in the active sites during the regeneration. The uptake loss after 4 cycles represents ca. 20 %, similar to the drop in the surface area of the micropores. We attribute this behavior to a partial structural annealing of the carbon during the thermal heating at high temperatures and the decomposition of phenol molecules inside the micropores, causing a partial blockage of the microporosity [3,14].

For carbon AS5, the uptake followed a smooth drop with a loss of ca. 10 % after the fourth cycle (Fig. 2); this agrees with the small fall in $S_{micro}$ along the cycles for this carbon (note that this is also consistent with the smaller drop in the textural properties observed for sample AS5*, Table 1). On the other hand, the uptake for this carbon increased after the first regeneration cycle (sample AS5-R1); this is attributed to increased affinity of this carbon towards phenol adsorption after the removal of oxygen-surface groups during the first regeneration (Table 2) [49–52]. A similar effect was observed in carbon L39, although much more pronounced owing to its high oxygen content (Table 1). Indeed, it is well-known that oxidized carbons (hydrophilic) are less favorable for phenol adsorption than hydrophobic (basic) ones, due to the withdrawal effect of the O-groups on the π electronic density of the basal planes and the competitive water adsorption [1,48–52]. The thermal regeneration provoked not only the desorption of phenol, but also the removal of the

<footnote><sup>a</sup> Values for the first cycle of carbon L39 have not been calculated to avoid overestimation, since the amount desorbed corresponds to both phenol desorption and the decomposition of the O-groups.</footnote>
<figure><img src="image_5.png" /><figcaption>Fig. 3. Differential thermogravimetric profiles of the pristine, saturated and regenerated (first cycle, R1) of the studied activated carbons. Arrows show the distinctive peaks (peak I, II) that have been analyzed in the discussion. (A colour version of this figure can be viewed online.)</figcaption></figure>

O-containing groups of this carbon, thereby increasing its basicity. As a result, the uptake of phenol increased significantly after the first and second regeneration cycles (samples L39-R1 and L39-R2). After the third cycle, the uptake started to decrease, following a similar behavior than that observed for carbons AS2 and AS5 (Fig. 2). This is consistent with the trends of uptake observed for the annealed carbons (series ZZ*), showing the effect of the thermal treatment alone in the adsorption capacity.

### 3.3. Analysis of phenol desorption mechanism

Thermogravimetric analysis of the carbons before and after phenol adsorption were measured to investigate the desorption phenomenon upon cycling. The differential thermogravimetric (DTG) curves corresponding to the pristine, saturated and first regeneration cycle carbons are shown in Fig. 3. For the hydrophobic carbons (samples AS2 and AS5), the profiles after saturation showed an intense first peak (labeled as peak I) featuring between 150 and 400 °C, and a small hump (labeled as peak II) between 400 and 500 °C. Owing to their low

<figure><img src="image_6.png" /><figcaption>Fig. 4. (A) Steele adsorption potential for the $O_{phenol}$ active site on a graphitic surface within a slit pore versus the position (z) in the pores for different pore sizes (h); (B) minimum of the Steele's adsorption potential as a function of the pore size (w). (A colour version of this figure can be viewed online.)</figcaption></figure>
<figure><img src="image_7.png" /><figcaption>**Fig. 5.** Correlation between (A,C) the activation energy for the desorption of phenol related to peak I and (B,D) the residual fractional mass of carbon with the average micropore size ($L_0$). Solid lines and percentages are a guide for the eye, and represent the general regression over the data in which the pre-exponential factor and the exponent in the previous power laws were obtained using a power law and a linear law depending on the pore volume fractions $V_{0.8-1.4 \text{ nm}}$ (A, B) and $V_{0.4-1.25 \text{ nm}}$ (C,D). Colors correspond to the pore volume fractions. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)</figcaption></figure>

functionalization, both peaks are assigned to the desorption of phenol retained in the pores; this is also confirmed by the lack of peaks in this range for the raw carbons (control experiments). Similar profiles for the desorption of phenol from activated carbons have been reported in the literature [51]. In the case of carbon L39, the raw material displays a broad peak above 400 °C due to the decomposition of the surface functional groups [53,54]. Hence in the thermogravimetric profiles of saturated carbon L39, only the first peak can be clearly assigned to the desorption of adsorbed phenol. The presence of a second (peak II) associated to the desorption of phenol cannot be clearly identified: it is either absent or overlapped with the broad desorption band above 400 °C owing to the simultaneous decomposition of the surface functional groups in this carbon.

The profiles of the regenerated carbons (after the first cycle) were similar to those of the pristine materials, with the exception of carbon

L39 due to the above-mentioned decomposition of functional groups. In either case, the lack of peaks in the profiles of the regenerated carbons indicates either a complete desorption of phenol. A partial thermal degradation of phenol retained in the porosity of the carbons (forming a carbonaceous residue) is also possible due to the high temperature of the regeneration [51]. From the DTG curves, the desorption energies ($E_{des}$) of both peak I and II were evaluated for the series of saturated carbons upon subsequent regeneration cycles and for the series ZZ* after saturation (i.e., carbons previously heated at the same temperature of regeneration); the values are compiled in Table 2.

The residual fractional mass of carbon ($Y_C$) was used as an indicator accounting for the efficiency of the regeneration considering the fraction of phenol desorbed during the thermal treatment (red curves in the DTG profiles in Fig. 3). $Y_c$ ranged between 50 and 60 wt% for carbons AS2 and AS5, and slightly higher values for carbon L39 after the first
<figure><img src="image_8.png" /><figcaption>**Fig. 6.** Correlations between the minimum potential of phenol adsorption *<S>* and (A) the activation energy for phenol desorption peaks ($E_{des}^{peak I}$ and $E_{des}^{peak II}$; (B) the frequency factor ($\nu$); (C) the hypothetical maximum desorption rate ($V'_{max}$) for a maximum fractional coverage ($\theta = 1$). Plots A-C refer to peak I, and plots D-F refer to peak II in the thermogravimetric profiles. Linear correlation regression coefficients are shown. Note that data of samples L39\* and L39-R1 are not considered for the fittings. Green diamonds with a thin outline refer to carbons with $L_0$ close to 0.90 nm, while those with thick outlines refers to carbons with $L_0$ close to 1–1.1 nm (plots B and C). (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)</figcaption></figure>

regeneration cycle (60–70 wt%). This is attributed to the differences in uptake of the carbons (Fig. S2, Table S2). Interestingly, the residual fractional mass of carbon ($Y_c$) of the annealed carbons was significantly higher than those of the pristine counterparts (and rather similar among them), which agrees with the improved adsorption capacity after the annealing (Fig. 2).

The desorption energies of peak I ($E_{des}^{peak I}$) were rather similar for carbons AS2 and AS5, with higher values (on average) for L39 series. We attribute this to the different porosity and surface chemistry of the carbons (i.e., hydrophilic character), that govern the interactions of adsorbed phenol with the carbon matrix [48–51]. The desorption energy of peak II ($E_{des}^{peak II}$) was higher than $E_{des}^{peak I}$, which is expected peak I appears at a higher temperature in the DTG profiles. Interestingly, $E_{des}^{peak II}$ follows an opposite trend than $E_{des}^{peak I}$ with the nature of the carbons, as the values are higher for carbon AS2 -compared to the series AS5 and L39-, particularly for the first two regeneration cycles.

### 3.3.1. Desorption mechanism and porosity

To further understand and analyze these differences, we have correlated several indicators associated to the adsorption and desorption process $-E_{des}$, *<S>* and $Y_c$-with the physicochemical parameters of the saturated carbons -series ZZ-Rx-. Calculations were performed in the pore range between 0.4 and 1.25 nm. The upper limit cut-off was selected considering that the minimum of Steele's adsorption potential

reaches 98 % of its nominal value in pores of 1.25 nm (over this limit, *⟨s⟩* reaches a constant value, Fig. 4), which agrees with the experimentally reported optimal pore size range for phenol adsorption in carbons (i.e., below 1.4 nm) [39,40]. The lower limit cut-off of 0.4 nm was selected based on several factors: i) the minimum of the Steele's adsorption potential for phenol adsorption is located at 0.45–0.5 nm (Fig. 4), in agreement with the kinetic diameter of phenol (ca. 0.37–0.43 nm) [55–57]; thus accessibility to pores smaller than 0.4 nm is expected to be restricted; ii) the lack of accuracy of the estimation of PSD below 0.4–0.5 nm pore size range, owing to gas diffusion limitations at cryogenic temperatures (e.g., $N_2$ at 77K) [42].

Fig. 5A shows the evolution of the activation energy of the first desorption peak ($E_{des}^{peak I}$) with the porosity of the carbons. The desorption temperature of peak I (ca. 150-400 °C) is too low to decompose phenol molecules by effect of the temperature [51,58,59], thus this peak is mainly associated to the desorption of phenol (gas phase) retained in the porosity. As seen, $E_{des}^{peak I}$ follows a power law (such representation is commonly used in the literature to describe adsorption processes [37,60, 61]) with the average micropore size ($L_0$), suggesting that the confinement state of the adsorbed molecules is important in the thermal desorption.

The analysis of the goodness of the (power law) regression coefficient to fit $E_{des}^{peak I}$ shows that the quality of these regressions is maximized for materials with contributions of volume of micropores within 0.8–1.4 nm
<figure><img src="image_9.png" /><figcaption>Fig. 7. (A) Correspondence between the pore size domains of existence of the different adsorbed states (i.e. states I, II, III, IV, V, see discussion and supplementary information) and the pore size distributions of carbons AS2 and AS5 (where “R” stands for regeneration cycle); (B,C,D) loss of pore volume ($V_{loss}$) for carbons AS2 (B), AS5 (C) and L39 (D) over the pore range after subsequent regeneration cycles. (A colour version of this figure can be viewed online.)</figcaption></figure>

($V_{0.8-1.4 	ext{ nm}}$) between 30 and 46% (Fig. 5A, 5.B). This points out that pores in these ranges are important in the adsorption/desorption of peak I, and agrees with the reported optimal pore size for phenol adsorption in carbons [35,36].

Fig. 5B shows a similar trend for the correlation of the residual fractional mass of carbon ($Y_C$) and $L_0$, underlining the importance of pore size in the desorption of the adsorbed molecules during the thermal regeneration (magnitude assessed by $Y_C$). As a first approach, high values of $Y_C$ may be associated to a less efficient regeneration and to an important blockage of the porosity of the carbon, which would eventually lead to a decrease in the uptake in subsequent adsorption cycles. Thus, understanding the dependence of $Y_C$ with the textural parameters of the activated carbons is important to control the regeneration efficiency. Fig. 5B shows higher $Y_C$ values for pores around 1 nm, which agrees with the optimal pore size for phenol adsorption.

Similar representations using the fraction of pores in the 0.4–1.25 nm range lead to different trends (Fig. 5C, 5.D). $E_{des}^{peak I}$ and $Y_C$ decrease with increasing $L_0$ (as in Fig. 5A, 5.B) which is interesting since according to Fig. 1 this range of pore sizes is favorable for the uptake of phenol. This suggests that adsorption in this pore range cannot be explained only by dispersive forces. Nevertheless, data points in Fig. 5B and 5D ($Y_C$ correlation with $L_0$) are quite scattered, suggesting that $L_0$ is not an accurate

parameter to describe the role of the textural features on the thermal desorption. On the other hand, $E_{des}^{peak I}$ showed a logic linear increasing correlation with $Y_C$ (Fig. S3A) that was not observed for peak II ($Y_C$ vs $E_{des}^{peak II}$, Fig. S3B), suggesting that the porosity plays a secondary role in the second desorption peak.

Contrarily to the trend observed for peak I, $E_{des}^{peak II}$ increases with $L_0$ (Fig. S3C). Note that the temperature of peak II (between 400 and 500 °C) is not high enough for the decomposition of phenol molecules by the effect of the temperature [58,59], thus peak II is associated to a high-energy adsorbed state of phenol molecules. Hence, the increasing trend in Fig. S3C suggests that high-energy adsorbed states of phenol are more likely retained in micropores above 1 nm (Fig. S6).

To understand the reversed order for the relative positions of the groups of carbons accounting for pore volume fractions either within 0.4–1.25 nm or 0.8–1.4 nm ranges of pore sizes, a further analysis of the thermodesorption process was carried out considering the evolution of the adsorption potential $<S>$ (Fig. 6). With the exception of samples L39*-R1 and L39-R2, plotting the thermal desorption parameters ($E_{des}$, $\nu$ and $Y_C$) and $<S>$ showed two distinct linear trends for pores above and below 1.1 nm (Fig. 6A). The goodness of these linear dependences ($R^2 > 0.99$ for plots in Fig. 6A–C) justifies the interest of the use of $<S>$ over $L_0$.
<figure><img src="image_10.png" /><figcaption>**Fig. 8.** Correlations between the oxygen content of the pristine carbons and (A) the activation energy for the desorption of phenol; (B) the frequency factor; (C) the hypothetical maximum desorption rate ($V_{max}$) for a maximum fractional coverage. Plots A-C refer to peak I, and plots D-F refer to peak II in the thermogravimetric profiles. Dashed lines are a guide for the eye. Notes: i) due to the large uncertainty on the desorption parameters on peak II, data of sample L39-R1 is not considered in plots D, E and F; ii) green diamonds with a thin outline refer to carbons with $L_0$ close to 0.90 nm. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)</figcaption></figure>

as indicator. The assessments of the regression coefficients varying the upper cut-off limit of the pore size up to 5 nm are shown in Figs. S4 and S5, giving optimal results for a cut-off of 1.25 nm.

Our previous studies analyzing the thermal desorption of phenol retained in activated carbons using a mass spectrometer to identify the nature of the desorbed products have demonstrated that peak I is due to the simultaneous desorption of phenol and water molecules co-adsorbed in the carbon pores [51]. These observations are consistent with the formation of water-phenol clusters of different sizes [62–64], owing to the multiple possible H-bonding interactions between phenol and water molecules. Indeed, considering the reported effective size of phenol molecule of ca. 0.75 nm [65], those water-phenol clusters are likely to be formed in pores above 0.8 nm. As an example, water-mediated phenol dimers ($H_2O(\phi OH)_2$) could be formed in pores of ca. 1.2 nm through cooperative adsorption process (i.e. phenol bridges within the pore walls). [62,66–68]. Cooperative adsorption processes through multiple $\pi$-$\pi$ stacking of phenol molecules have also been proposed in the literature [66–68]; these structures would display ca. 1.1 nm size. Some other authors have suggested the occurrence of linear water percolating clusters in pores close to 2 nm size [69,70]. All these observations are consistent with the observed increase in $E_{des}^{peak I}$ for average micropore sizes above 1.10 nm (Fig. 6A), with water-phenol clusters formed in pores above 0.8 nm, and $\pi$-$\pi$ stacked phenol collaborative adsorption in pores above 1.1 nm (Fig. S6).

Fig. 6B shows the dependence of the frequency factor ($\nu$) for peak I with $<S>$. This parameter can be seen as an entropic contribution to the

desorption process [40,71,72]. The higher values of frequency factor of carbons exhibiting average micropore sizes above 1.1 nm can be interpreted as the entropically favored desorption of phenol-water clusters and/or phenol-phenol dimers adsorbed in those pores. Fig. 6C shows that this entropic contribution does not balance the increase in the desorption energy with the hypothetical maximum desorption rate at infinitesimally slow heating rate ($V_{max}$'). We attribute this to the exponential function in the estimation of the frequency factor. Interestingly, $V_{max}$' is lower for carbons with $L_0$ close to 1–1.1 nm (green diamonds with thick outlines). This is counterintuitive considering the higher variation of $<S>$ for pores above 1 nm, and points out differences in the adsorption-desorption rate in pores filled with a disordered adsorbed layer. Such disorder can be induced by a statistical change of orientation of the phenol molecule [73] or by the presence of small and isolated phenol-water clusters in those wide micropores [74,75].

A similar analysis of the different parameters extracted from the analysis of peak II shows that the textural indicators do not seem to have a relevant role in this contribution to the desorption mechanism (Fig. 6D-F). Indeed, correlations for this second desorption peak were found with the surface chemistry of the carbons, as it will be discussed after.

The pore size distributions after successive regeneration cycles (series AS2 and AS5) are shown in Fig. 7A do not exactly match the profiles of loss of pore volume ($V_{loss}$, from equation (3)) presented in Fig. 7B,C. This suggests that phenol adsorption states are strongly dependent on specific pore sizes. Indeed, the two main pore volume decreases,
occurring mainly within the 0.4–1.25 nm range and within the 1.25–3 nm, should correspond to different adsorbed states.

For example, experimental data and numerical simulation have shown that pre-adsorbed in hydrophilic narrow pores (i.e., 0.6 nm) [76] can hinder the adsorption of phenol in those pores (adsorbed states I in Fig. S6). This effect would be visible for carbons AS5 (before the third regeneration cycle) and carbon L39 (before the first and second regeneration cycle). The loss in pore volumes between 0.6 and 1.8 nm can be assimilated to the increase of entropy in pores between 0.6 and 0.9 nm due various phenol molecules orientations [73] and the formation of small water-phenol clusters [74,75]. This is seen in the increase of entropy of adsorbed layer when average micropore sizes increases slightly from 0.90 to 1–1.1 nm (adsorbed states II in Fig. S6).

The loss in pore volume for pores close to 0.80 nm can be assimilated to the existence of quasi-crystalline layers of adsorbed phenol molecules embedding single waters monomers [69] or to the existence of partly disordered double layer of adsorbed phenol molecules [34,77] (adsorbed states III in Fig. S6). The tail of this second peak lies within the 1–1.25 nm range and could be associated to adsorption driven by dispersive forces, cooperative adsorption through π-π stacking, water-mediated dimers or trimers (adsorbed states IV in Fig. S6) [78]. Unlike the profiles of the PSDs, the last peak of $V_{loss}$ between 1.8 and 2 nm is sharp (Fig. 7); according to some authors, this peak could correspond to phenol which is compressed onto the surface of the pores by water percolating clusters (adsorbed state V in Fig. S6) [69]. The tail of this peak quickly tends to reach a value close to 0 for pores of about 3 nm, showing the almost nonexistent overlapping of adsorption potential for pores above 2.5–3 nm (adsorbed state VI in Fig. S6). Considering each adsorbed state, a fraction of the adsorbed molecules is decomposed inside the pores of the activated carbons, provoking a pore blockage in considered micropores. The pore blockage is associated to the decomposition of phenol into coke-like products [14,51], thus high pore blocking implies high residual fractional carbon mass after thermal regeneration ($Y_C$). Although the exact nature of these adsorbed states cannot be assessed through thermodesorption and textural characterization, the correlations between $Y_C$ and the average micropore size ($L_0$) suggest that this is a useful indicator for predicting the pore loss in the 0.8–1.4 nm pore size (Fig. S7). Lower pore volume losses and $Y_C$ are obtained for pores below a 1.1 nm threshold, owing to the occurrence of multiple adsorption states in larger pores.

### 3.3.2. Desorption mechanism and surface chemistry

Besides porosity, the surface chemistry of activated carbons needs to be considered, as it is well known to impact the adsorption of phenol on these materials. This is particularly pertinent for carbon L39 that displayed high oxygen content (Table 1), and which phenol uptake increased significantly after the first two regeneration cycles due to the modification of its surface chemistry during the thermal treatment (see discussion above).

Hence, we have performed a similar analysis by correlating several indicators $-V_{0.8-1.4 \text{ nm}}$, $E_{des}$, $<S>$ and $L_0$-with the oxygen content of the carbons. The oxygen content of activated carbons is mainly associated to O-containing moieties at the edges of the graphitic-like sheets, partially withdrawing the π electron density in the carbon pore walls [79]. Thus, increasing the oxygen content provokes a progressive destabilization of the π-π stacking of phenol molecules on the carbon surface [80–82]. These surface functionalities may also lead to specific interactions with phenol molecules (e.g., dipole-dipole interactions, acid-base reactions on ketones and aldehyde-like groups) [83].

Fig. 8 shows a decrease in $E_{des}^{peak I}$ and $\nu$ (i.e., an increase in $V_{max}$) as the oxygen content of the pristine carbons increases. The plots are again differentiated for the carbons displaying average micropores around 1.1 nm.

For carbons with oxygen contents below 2 wt%, the $E_{des}^{peak I}$ strongly depends on the textural features (as discussed above) and the role of

<figure><img src="image_11.png" /><figcaption>Fig. 9. Dependence of the entropy of adsorbed phase ($S^{\circ}_{ad}$) for the second desorption peak with the oxygen content. (A colour version of this figure can be viewed online.)</figcaption></figure>

surface chemistry is negligible. This is reflected in a scattered contribution of the analyzed dataset in this region (oxygen content below 2 wt%). Above 2 wt%, $E_{des}^{peak I}$ increased smoothly pointing out to a contribution of specific interactions. The frequency factor showed higher values as the oxygen content increased (Fig. 8B), suggesting a somewhat higher entropic contribution to desorption (although the trend is smooth).

A stronger impact of surface composition is observed upon analyzing the second peak in the desorption profiles (Fig. 8D to F). As discussed above, this peak corresponds to the desorption of phenol from energetic adsorption sites (compared to peak I) and water molecules [35]. As seen, $E_{des}^{peak II}$ and $\nu$ parameter decreased sharply as the amount of oxygen increases. This is in line with the lower π-electron density in the pore walls of functionalized carbons. Interestingly, the effect of the oxygen content is small for carbons with an average micropore size $L_0$ close to 0.9 nm (green diamonds with a thin outline in Fig. 8D-F). We attribute this to the fact that oxygen groups are hardly expected to be grafted in those small pores due to steric effects. As a result, phenol desorption properties are less influenced by the oxygen content in such narrow un-functionalized pores. On the other hand, no correlation was found between the indicators calculated from the second desorption peak and the textural parameters.

Fig. 9 represents the dependence of the entropy of adsorbed phase ($S^{\circ}_{ad}$) for the second desorption peak with the oxygen content. A similar analysis is shown in Fig. 7D for the dependence of the entropy of adsorbed phase ($S^{\circ}_{ad}$) related to desorption peak I and the average minimum of adsorption potential of phenol $<S>$ (texture contribution). The entropic contribution of the adsorbed phase is more evident for desorption peak I, with linear trends for the subfamilies of carbons with average pore sizes above/below 1.1 nm. For the second peak, the entropic contribution of the adsorbed phase shows a constant behavior with increasing the oxygen content.

Considering the discussion above, phenol adsorption in activated carbons could be pictured as a complex mechanism based on different adsorption modes upon the size and the surface chemistry of the pores (Fig. 9). In pores below 1 nm, phenol molecules are dominantly adsorbed upon π-π stacking in un-functionalized pores. In wider pores, phenol
<figure><img src="image_12.png" /><figcaption>**Fig. 10.** Correlations between the residual fractional mass of carbon after the thermal regeneration ($Y_c$) with: the hypothetical maximum desorption rate for desorption peak I (A) and peak II (B); the average minimum of the adsorption potential ($<S>$) for the oxygen on phenol on a graphitic flat surface (C) and the oxygen content of the pristine carbons (D). (A colour version of this figure can be viewed online.)</figcaption></figure>

molecules may be adsorbed upon various configurations, including the formation of cluster and dimers through cooperative adsorption stacking. All these mechanisms lead to adsorption modes of different energies where the desorption mechanism is governed by the average pore size. High desorption energies in small pores are characterized by slow desorption rates. On the other hand, functionalized carbons (e.g., above 2 wt% oxygen) display more energetic adsorption sites related to specific interactions with the O- groups, although those interactions have a lower impact in the desorption mechanism and rate.

### 3.3.3. The residual fractional mass of carbon ($Y_c$), porous texture and surface chemistry

Fig. 10 shows the correlations between the residual fractional mass of carbon after the thermal regeneration ($Y_c$) and several indicators, namely: the hypothetical maximum desorption rate ($V_{max}$) for peak I and II, the average minimum of the adsorption potential ($<S>$) for the oxygen on phenol on a graphitic flat surface and the oxygen content of the pristine carbons. As seen, there is no clear correlation between the residual fractional mass of carbon after the thermal regeneration and $V_{max}$ related to peak II, whereas as sigmoid like function is observed for

$V_{max}$ related to peak I, with an onset at ca. 0.01 $s^{-1}$. Such onset can be assimilated to a “kinetic trigger” below which phenol desorption is not fast enough from the pores (Fig. 10A). This would suggest that phenol desorption associated to peak I has a kinetic control over the residual fractional mass of carbon after the thermal regeneration, with less influence from peak II (Fig. 10B).

The dependence of $Y_c$ with the minimum of adsorption potential for phenol ($<S>$) (Fig. 10C) shows that $Y_c$ depends both on the confinement degree and on the pore size itself (i.e. average micropore pore size $L_0(dV)$) due to some of the specific adsorbed states of phenol. More specifically, it suggests that the widest micropores (i.e. above 0.8 nm) in which dimers, trimers and multiple $\pi$-$\pi$ stacking are the more likely to be formed are responsible of this aforementioned dependence between $Y_c$ and $L_0(dV)$ while the high density of adsorbed phenol in the narrowest pores (i.e. below 0.8 nm) is responsible of the dependence between $Y_c$ and $<S>$.

Nevertheless, the high dispersion of the data set in some parts of Fig. 10C suggests that the both confinement degree and pore size cannot explain entirely the behavior of $Y_c$. This is the reason why $Y_c$ was also represented versus oxygen content. The sharp decrease of $Y_c$ whenever
the oxygen content increases up to 2 wt% seems to confirm the hypothesis of the decrease of π - π interactions whenever oxygen functional groups are introduced onto the surface of the carbon. Above 2 wt%, the high density of specific interactions (i.e. strong and polarized phys-isorption or even chemisorption) counterbalances the decrease of π - π interactions, induces a decrease of desorption during peak I (Fig. 8C) and, subsequently, induces an increase of Yc.

4. Conclusions

A comprehensive investigation into the thermal regeneration of saturated activated carbons - employed in a range of industrial facilities- has been carried out by analyzing with a high level of refinement the impact of the porous features and surface chemistry of those activated carbons on the thermal regeneration efficiency and the residual carbon fraction. Experimental data obtained from the sequential regeneration of a series of commercial carbons saturated with phenol from aqueous solutions has been integrated into a processing methodology that employs straightforward modeling to assess the pivotal roles of different indicators on the thermal regeneration of the saturated carbons. This approach correlates the physicochemical parameters of the pristine and saturated activated carbon (pore volume and size, composition) with the desorption phenomenon driving the thermal regeneration (desorption energy, desorption rate, entropy of the adsorbed phase) and the implication in subsequent cycles (uptakes over cycles, carbon yields). This analysis enables to facilitate the choice of specific activated carbons with optimized regeneration performance, allowing for their repeated use with high efficiency.

Among the many correlations that have been identified, the importance of the micropore size on the regeneration has been highlighted. The correlation between the thermal desorption parameters and the minimum of the adsorption potential as textural indicator showed two distinct trends for pores above and below 1.1 nm. Lower values of residual fractional mass of carbon were obtained for pores below the 1.1 nm threshold, owing to the dependence of adsorbed states with average pore sizes (favoring the formation of clusters, dimers and trimers in various configurations). Adsorption in un-functionalized micropores has a high impact on the recovery of the porosity of the regenerated carbons, while high energy adsorption sites -typically accessible in activated carbons with high saturation degrees-play a secondary role in the desorption mechanism. Desorption properties are less influenced by the oxygen content in narrow micropores, since oxygen groups are hardly expected to be grafted in those small pores due to steric effects. Those adsorption sites dominated by dispersive interactions have a kinetic control over the residual fractional mass of carbon after the thermal regeneration, with less influence from the high energy sites. Functionalized activated carbons (e.g. above 2 wt% oxygen) also displayed more energetic adsorption sites related to specific interactions with the O-groups, although these interactions have less influence on the desorption mechanism and rate. The frequency factor related to the thermodesorption of phenol from those energetic sites decreased with the oxygen content of the activated carbons, suggesting a lower entropic contribution to desorption. A sharp decrease in Yc was observed for carbons with increasing oxygen contents, owing to the impact of functionalization in the adsorption dispersive forces.

CRediT authorship contribution statement

**F. Olivier:** Writing – review & editing, Methodology, Investigation.
**S. Schaefer:** Writing – original draft, Supervision, Methodology, Formal
analysis, Conceptualization.
**K. Maiga:** Investigation.
**M. Roulet:** Investigation.
**I. Laidin:** Writing – review & editing, Resources, Funding
acquisition.
**C.O. Ania:** Writing – review & editing, Supervision, Fund-
ing acquisition, Formal analysis, Conceptualization.
**B. Cagnon:** Writing
– review & editing, Supervision, Funding acquisition, Formal analysis,
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.

Acknowledgments

The authors thank the financial support of Region Centre-Val de
Loire (France) through the ARD MATEX Program (subproject Carbone-
4).

**Appendix A. Supplementary data**

Supplementary data to this article can be found online at https://doi.
org/10.1016/j.carbon.2025.120003.

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