Ordered Mesoporous Carbons for Adsorption of Paracetamol and Non-Steroidal Anti-Inﬂammatory Drugs: Ibuprofen and Naproxen from Aqueous Solutions

: The adsorption of paracetamol and non-steroidal anti-inﬂammatory drugs (ibuprofen and naproxen) on ordered mesoporous carbons (OMC) and, for comparison, on commercial activated carbon, were investigated in this work. OMC adsorbents were obtained by the soft-templating method and were characterized by low-temperature nitrogen adsorption and scanning electron microscopy (SEM). The e ﬀ ects of contact time and initial concentration of organic adsorbates on the adsorption were studied. The contact time to reach equilibrium for maximum adsorption was 360 min for all the studied adsorbates. The adsorption mechanism was found to ﬁt pseudo-second-order and intra particle-di ﬀ usion models. Freundlich, Langmuir and Langmuir-Freundlich isotherm models were used to analyze equilibrium adsorption data. Based on the obtained experimental data, the adsorption isotherm in the applied concentration range for all the studied adsorbates was well represented by the Freundlich-Langmuir model. The adsorption ability of ordered mesoporous carbon materials was much higher for paracetamol and naproxen in comparison to commercial activated carbon. The removal e ﬃ ciency for ibuprofen was signiﬁcantly lower than for other studied pharmaceuticals and comparable for all adsorbents. Theoretical calculations made it possible to obtain optimized chemical structures of ( S )-naproxen, ibuprofen, and paracetamol molecules. Knowledge of charge distributions of these adsorbate molecules can be helpful to explain why paracetamol and naproxen can react more strongly with the surface of adsorbents with a large numbers of acidic groups compared to ibuprofen facilitating more e ﬃ cient adsorption of these pharmaceuticals on ordered mesoporous carbons. i.e., for adsorption on adsorbents activated by CO 2 . The adsorption of ibuprofen is comparable or weaker for ST-A-P, ST-A-P-CO 2 , and WG-15 adsorbents. The best results are obtained for adsorption on all the studied adsorbents for naproxen (82% ST-A-P, 98% ST-A-P-CO 2 , 63% WG-15).


Introduction
Pharmaceuticals belong to the most significant groups of emerging pollutants to have been recognized in water resources. Non-steroidal anti-inflammatory drugs (NSAIDs) represent one of the most widely used pharmaceutical products available without prescription. The production and consumption of NSAIDs have increased in recent years, introducing quantities amount of these substances into the environment in an unutilized or metabolized form [1]. The most prominent members of this group of drugs, i.e., ketoprofen, diclofenac, naproxen, ibuprofen and salicylic acid, show analgesic, anti-inflammatory, and antipyretic effects on humans [2,3]. NSAIDs are frequently detected in effluents, surface waters and seawater [4]. Industrial and municipal wastewaters are among their main sources and they may pollute groundwater supplies [5,6]. NSAID compounds have a weak Table 1. Chemical structures and selected properties of the adsorbates [33].

Compound
Paracetamol Ibuprofen Naproxen

Molecular structure
Water 2019, 11, x FOR PEER REVIEW 3 of 21

Synthesis Procedure
Mesoporous carbons were prepared by the soft-templating method according to a slightly modified recipe presented in the work of Choma et al. [34]. In a typical synthesis, 7.5 g of resorcinol and 7.5 g of Pluronic F127 triblock copolymer were dissolved in 35.7 cm 3 of ethanol and 19.8 cm 3 of water. After complete dissolution the reaction mixture was supplied with 2.2 cm 3 of 37% hydrochloric acid as a catalyst and stirred for additional 30 min. Next, 7.5 cm 3 of 37% formaldehyde was added into the synthesis mixture and stirred until it turned cloudy. It was then left to separate into two layers. The polymer-rich bottom layer was spread onto quartz boats and transferred to an oven at 100 °C for 24 h. Thermal treatment and carbonization of the resulting film were performed in the tube furnace under nitrogen flow using temperature program: 1 °C/min up to 400 °C, then 5 °C/min up to 850 °C and held for 2 h. The samples were labelled according to the formula ST-A-P.

Activation of Mesoporous Carbon
The obtained ST-A-P material was activated with CO2, according to a slightly modified recipe of Wickramaratne and Jaroniec [35]. Post-synthesis activation of mesoporous carbon (ST-A-P) was performed by placing a quartz boat with 3 g of ST-A-P in a ceramic tube furnace under flowing nitrogen with a heating rate of 10 °C/min up to 850 °C. After reaching this temperature, the activating gas was introduced to the tube furnace (50 cm 3 /min) for 8 h, and then switched back to nitrogen to prevent further activation during the cooling process. The selection of activation conditions was based on previous studies (activation time 4-8 hours). Taking into account the structural parameters,

Synthesis Procedure
Mesoporous carbons were prepared by the soft-templating method according to a slightly modified recipe presented in the work of Choma et al. [34]. In a typical synthesis, 7.5 g of resorcinol and 7.5 g of Pluronic F127 triblock copolymer were dissolved in 35.7 cm 3 of ethanol and 19.8 cm 3 of water. After complete dissolution the reaction mixture was supplied with 2.2 cm 3 of 37% hydrochloric acid as a catalyst and stirred for additional 30 min. Next, 7.5 cm 3 of 37% formaldehyde was added into the synthesis mixture and stirred until it turned cloudy. It was then left to separate into two layers. The polymer-rich bottom layer was spread onto quartz boats and transferred to an oven at 100 °C for 24 h. Thermal treatment and carbonization of the resulting film were performed in the tube furnace under nitrogen flow using temperature program: 1 °C/min up to 400 °C, then 5 °C/min up to 850 °C and held for 2 h. The samples were labelled according to the formula ST-A-P.

Activation of Mesoporous Carbon
The obtained ST-A-P material was activated with CO2, according to a slightly modified recipe of Wickramaratne and Jaroniec [35]. Post-synthesis activation of mesoporous carbon (ST-A-P) was performed by placing a quartz boat with 3 g of ST-A-P in a ceramic tube furnace under flowing nitrogen with a heating rate of 10 °C/min up to 850 °C. After reaching this temperature, the activating gas was introduced to the tube furnace (50 cm 3 /min) for 8 h, and then switched back to nitrogen to prevent further activation during the cooling process. The selection of activation conditions was based on previous studies (activation time 4-8 hours). Taking into account the structural parameters,

Synthesis Procedure
Mesoporous carbons were prepared by the soft-templating method according to a slightly modified recipe presented in the work of Choma et al. [34]. In a typical synthesis, 7.5 g of resorcinol and 7.5 g of Pluronic F127 triblock copolymer were dissolved in 35.7 cm 3 of ethanol and 19.8 cm 3 of water. After complete dissolution the reaction mixture was supplied with 2.2 cm 3 of 37% hydrochloric acid as a catalyst and stirred for additional 30 min. Next, 7.5 cm 3 of 37% formaldehyde was added into the synthesis mixture and stirred until it turned cloudy. It was then left to separate into two layers. The polymer-rich bottom layer was spread onto quartz boats and transferred to an oven at 100 °C for 24 h. Thermal treatment and carbonization of the resulting film were performed in the tube furnace under nitrogen flow using temperature program: 1 °C/min up to 400 °C, then 5 °C/min up to 850 °C and held for 2 h. The samples were labelled according to the formula ST-A-P.

Activation of Mesoporous Carbon
The obtained ST-A-P material was activated with CO2, according to a slightly modified recipe of Wickramaratne and Jaroniec [35]. Post-synthesis activation of mesoporous carbon (ST-A-P) was performed by placing a quartz boat with 3 g of ST-A-P in a ceramic tube furnace under flowing nitrogen with a heating rate of 10 °C/min up to 850 °C. After reaching this temperature, the activating gas was introduced to the tube furnace (50 cm 3 /min) for 8 h, and then switched back to nitrogen to prevent further activation during the cooling process. The selection of activation conditions was based on previous studies (activation time 4-8 hours). Taking into account the structural parameters,

Synthesis Procedure
Mesoporous carbons were prepared by the soft-templating method according to a slightly modified recipe presented in the work of Choma et al. [34]. In a typical synthesis, 7.5 g of resorcinol and 7.5 g of Pluronic F127 triblock copolymer were dissolved in 35.7 cm 3 of ethanol and 19.8 cm 3 of water. After complete dissolution the reaction mixture was supplied with 2.2 cm 3 of 37% hydrochloric acid as a catalyst and stirred for additional 30 min. Next, 7.5 cm 3 of 37% formaldehyde was added into the synthesis mixture and stirred until it turned cloudy. It was then left to separate into two layers. The polymer-rich bottom layer was spread onto quartz boats and transferred to an oven at 100 • C for 24 h. Thermal treatment and carbonization of the resulting film were performed in the tube furnace under nitrogen flow using temperature program: 1 • C/min up to 400 • C, then 5 • C/min up to 850 • C and held for 2 h. The samples were labelled according to the formula ST-A-P.

Activation of Mesoporous Carbon
The obtained ST-A-P material was activated with CO 2 , according to a slightly modified recipe of Wickramaratne and Jaroniec [35]. Post-synthesis activation of mesoporous carbon (ST-A-P) was performed by placing a quartz boat with 3 g of ST-A-P in a ceramic tube furnace under flowing nitrogen with a heating rate of 10 • C/min up to 850 • C. After reaching this temperature, the activating gas was introduced to the tube furnace (50 cm 3 /min) for 8 h, and then switched back to nitrogen to prevent further activation during the cooling process. The selection of activation conditions was based on previous studies (activation time 4-8 h). Taking into account the structural parameters, the optimal activation time was 8 h. The obtained activated materials are denoted as ST-A-P-CO 2 .

Characterization of the Adsorbents
Porous structures of adsorbents were characterized using the methods of low-temperature nitrogen adsorption-desorption isotherms (−196 • C) on a volumetric adsorption analyzer ASAP 2020 by Micromeritics (Norcross, GA, USA) (Structural Research Laboratory of Jan Kochanowski University in Kielce). Before adsorptive measurements, all the samples were degassed at a temperature of 200 • C for 2 h. On the basis of experimental low-temperature nitrogen adsorption isotherms for the investigated adsorbents, standard parameters of the porous structure were determined [36][37][38][39][40][41]. The specific surface area of investigated carbon materials was determined with the Brunauer-Emmett-Teller (BET) method. S BET was determined in the range of relative pressure from 0.05 to 0.2, considering the surface occupied by a single molecule of nitrogen in an adsorptive monolayer (cross-sectional area equal 0.162 nm 2 ) [36]. Total pore volume (V t ), being the sum of micropores volume (V mi ) and mesopores (V me ) was determined from one point of nitrogen adsorption isotherm, corresponding to the relative pressure p/p 0 equal 0.99 [37].
Images of investigated materials were obtained by the SEM Zeiss mod. Ultra Plus, EDS Bruker Quantax 400. Voltage applied during the measurements was 2 kV.
Functional groups on the surface of ST-A-P, ST-A-P-CO 2 , and WG-15 adsorbents were identified using Boehm's titration method [42,43]. The procedure was as follows: 0.2 g of carbon adsorbents was dispersed in solution of sodium bicarbonate, sodium carbonate, sodium hydroxide, sodium ethoxide, and hydrochloric acid, and then shaken for 48 h at room temperature. Next, the adsorbent was filtered and 10 cm 3 of filtrate were titrated with 0.1 mol dm −3 HCl in order to determine acidic groups, together with 0.05 mol dm −3 NaOH to determine total basic groups [44]. The identified functional groups were calculated as mmol/g.

Adsorption Studies from Aqueous Solutions
For adsorption studies, ordered mesoporous carbon materials were applied, with grain sizes ranging from 0.2 to 0.8 mm. Before proceeding into the proper experiments, the carbon was dried in the laboratory dryer at a temperature of 100 • C until a constant mass of adsorbents was obtained. Due to the large adsorptive capacity of carbon adsorbents, the used adsorbent mass was determined experimentally to minimize errors in weighing at an optimal value 0.01 g for a range of adsorbates concentrations used in adsorption experiments.
Concentrations of paracetamol, ibuprofen, and naproxen in solutions before and after the adsorption were determined with the spectrophotometric method, using a UV spectrophotometer Shimadzu UV-1800. The wavelengths used for determination of studied adsorbates concentrations were specified from their absorption spectra: 243 nm (paracetamol), 221 nm (ibuprofen), and 273 nm (naproxen). Adsorption studies were carried out in 100 cm 3 Erlenmeyer's flask. 0.01 g of mesoporous carbon was added to each flask and then 10 cm 3 of pharmaceuticals solution, with defined concentration. Then the flasks with all adsorbents and adsorbates solutions were transferred into the incubator for a defined period of time: 30, 60, 120, 240, 300, 360, and 1440 min.
The measurements were carried out at a constant temperature of 25 • C, at pH 6, and mixing rate 150 rpm. After removing samples from the incubator, carbon was separated from paracetamol and NSAID with the cup-type centrifuge. Next, the absorbance of the pharmaceuticals was measured with the spectrophotometer at a proper wavelength.
Kinetic data ST-A-P, ST-A-P-CO 2 and WG-15 for paracetamol, ibuprofen, naproxen adsorption on all the studied adsorbents was determined for initial concentration 300 mg dm −3 .
On the basis of calibration, curve concentrations of adsorbates (before and after adsorption) were calculated. Consequently, the value of adsorption q t (mg g −1 ) was calculated from the formula given below: where C 0 -concentration of adsorbate in solution before adsorption (mg dm −3 ); C t -concentration of adsorbate in solution after adsorption, after time t (mg dm −3 ); V-volume of the solution used for adsorption (dm 3 ); m-adsorbent mass (g). Adsorption measurements in equilibration conditions: adsorption isotherms were determined for initial concentrations of paracetamol, ibuprofen and naproxen: 50, 100, 200, 300, 400, 500, 700 mg dm −3 .
The prepared Erlenmeyer's flask with the studied adsorbent was filled with 10 cm 3 of adsorbate (with appropriate concentration) and placed in the incubator for 360 min. Time of measurements was a result of previous kinetic investigations.
The amount of adsorbate at equilibrium and the percentage of pharmaceuticals removal with the adsorbent were calculated by applying Equations (2) and (3): where C e -equilibrium concentration (mg dm −3 ).

Computational Methodology
The commercial SCIGRESS program in version FJ 2.7 was used to perform theoretical calculation. Geometry optimization of molecules was made using the DFT method with the B88-LYP GGA functional and the DZVP basis set.

Calculations
The optimized chemical structures of (S)-naproxen, paracetamol, (S)-ibuprofen and (R)-ibuprofen are shown in Figure 1. This is confirmed by the drawing of the electrostatic potential energy maps presented in Figure 2. These maps show charge distributions in molecules three-dimensionally, and make it possible to visualize the differently charged regions of a molecule. Knowledge of charge distributions can be helpful to explain how molecules interact with the surface of adsorbent containing different functional groups. Although DFT methods such as GGA do not fully include van der Waals interactions [45][46][47][48], they make it possible to show the differences between molecules. Possible changes in the distribution of electron density (under the influence of weak distance-dependent forces) were taken into account, but as these forces would work on all molecules, this calculation is sufficient for comparing their electronic structures. A strong negative potential occurs around -C=O group, but also around -OH group, present in molecule of paracetamol (Table 2). These two areas are in opposition to the remaining slightly positive part of the molecule. Similar distribution of charges is for (S)-naproxen. In this molecule, there are also two separate areas where the negative charge is accumulated. Ibuprofen has one clearly visible center with negative potential (Figure 2, Table 2).

Characterization of Adsorbents
Nitrogen adsorption isotherms measured at −196 • C are presented in Figure 3. According to IUPAC classification of adsorption isotherms [49], experimental isotherms for the materials studied (ST-A-P and ST-A-P-CO 2 ) are type-IV, which is characteristic of mesoporous solids. H1 hysteresis loops confirm the presence of accessible mesopores. Isotherm for the WG-15 carbon is type I, according to IUPAC classification of adsorption isotherms [49]. The type-I isotherm indicates high adsorption in the range of low relative pressures, i.e., refers to adsorbents with the highly developed microporosity (porosity, which forms pores with linear dimensions less than 2 nm). In the area of medium and high relative pressures, the isotherm for WG-15 carbon has a course almost parallel to the abscissae axis, which indicates that mesoporosity (pores with dimensions of 2 to 50 nm) is poorly developed [50]. The type-H4 hysteresis loop for WG-15 carbon is associated with narrow slit pores, but now includes pores in the micropore region. microporosity (porosity, which forms pores with linear dimensions less than 2 nm). In the area of medium and high relative pressures, the isotherm for WG-15 carbon has a course almost parallel to the abscissae axis, which indicates that mesoporosity (pores with dimensions of 2 to 50 nm) is poorly developed [50]. The type-H4 hysteresis loop for WG-15 carbon is associated with narrow slit pores, but now includes pores in the micropore region. Structural parameters calculated from adsorption isotherms are presented in Table 3. SBET-specific surface area; Vt-single-point total pore volume calculated at p/po = 0.99; Vme-mesopore volume calculated by subtracting Vmi from Vt; Vmi-volume of micropores obtained by αs-method; Mesoporosity-the percentage of the mesopore volume in relation to the total pore volume.
The adsorbents ST-A-P-CO2 and WG-15 have comparable values of specific surface area. Mesoporosity is clearly higher for ST-A-P and ST-A-P-CO2 materials in comparison to commercial activated carbon WG-15. This means that the studied ordered carbons are in fact mesoporous, with the significant advantage of mesoporosity over microporosity. Structural parameters calculated from adsorption isotherms are presented in Table 3. S BET -specific surface area; V t -single-point total pore volume calculated at p/po = 0.99; V me -mesopore volume calculated by subtracting V mi from V t ; V mi -volume of micropores obtained by α s -method; Mesoporosity-the percentage of the mesopore volume in relation to the total pore volume.
The adsorbents ST-A-P-CO 2 and WG-15 have comparable values of specific surface area. Mesoporosity is clearly higher for ST-A-P and ST-A-P-CO 2 materials in comparison to commercial activated carbon WG-15. This means that the studied ordered carbons are in fact mesoporous, with the significant advantage of mesoporosity over microporosity.
The ST-A-P sample presented interesting a mesoporous structure with visible canals of mesopores (Figure 4a). After CO 2 activation, the adsorbent structure is changed (ST-A-P-CO 2 sample) and the ordered microporous-mesoporous structure of this material which is "similar to honeycomb" (Figure 4b) can be observed. WG-15 sample shows a non-ordered structure as compared to ST-A-P and ST-A-P-CO 2 samples (Figure 4c).
The ST-A-P sample presented interesting a mesoporous structure with visible canals of mesopores (Figure 4a). After CO2 activation, the adsorbent structure is changed (ST-A-P-CO2 sample) and the ordered microporous-mesoporous structure of this material which is "similar to honeycomb" (Figure 4b) can be observed. WG-15 sample shows a non-ordered structure as compared to ST-A-P and ST-A-P-CO2 samples (Figure 4c).

Functional Groups on the Adsorbents Surface
Due to the presence of heteroatoms in the carbon precursor structure, and the reaction of carbonization product with the ingredients of atmosphere during the synthesis of carbonaceous materials, groups having the character of functional groups with acid-base or redox character are formed on their surface [51].
The results obtained for determining surface groups using the Boehm method are collected in Table 4. Acidic to basic groups ratio is approximately 3:1 for ST-A-P, 1.5:1 for ST-A-P-CO 2 , and 1:3.6 for WG-15. Phenolic and carboxyl groups are identified on the ST-A-P and STA-P-CO 2 adsorbents. In the case of commercial activated carbon, only carbonyl group are present, but in higher amounts in comparison to those it mesoporous carbon materials ST-A-P and ST-A-P-CO 2 . Table 4. Functional groups available on the studied adsorbents.

Adsorption Study
Removal efficiencies of paracetamol, ibuprofen, and naproxen by adsorbents ST-A-P, ST-A-P-CO 2 , and WG-15 are presented in Figure 5. The results show that new mesoporous carbon materials ST-A-P and ST-A-P-CO 2 adsorb paracetamol and naproxen better than adsorbent WG-15 from aqueous solutions. The removal efficiency is 95% and 98% for paracetamol and naproxen, respectively, i.e., for adsorption on adsorbents activated by CO 2 . The adsorption of ibuprofen is comparable or weaker for ST-A-P, ST-A-P-CO 2 , and WG-15 adsorbents. The best results are obtained for adsorption on all the studied adsorbents for naproxen (82% ST-A-P, 98% ST-A-P-CO 2 , 63% WG-15).

Functional Groups on the Adsorbents Surface
Due to the presence of heteroatoms in the carbon precursor structure, and the reaction of carbonization product with the ingredients of atmosphere during the synthesis of carbonaceous materials, groups having the character of functional groups with acid-base or redox character are formed on their surface [51].
The results obtained for determining surface groups using the Boehm method are collected in Table 4. Acidic to basic groups ratio is approximately 3:1 for ST-A-P, 1.5:1 for ST-A-P-CO2, and 1:3.6 for WG-15. Phenolic and carboxyl groups are identified on the ST-A-P and STA-P-CO2 adsorbents. In the case of commercial activated carbon, only carbonyl group are present, but in higher amounts in comparison to those it mesoporous carbon materials ST-A-P and ST-A-P-CO2. Table 4. Functional groups available on the studied adsorbents.

Adsorption Study
Removal efficiencies of paracetamol, ibuprofen, and naproxen by adsorbents ST-A-P, ST-A-P-CO2, and WG-15 are presented in Figure 5. The results show that new mesoporous carbon materials ST-A-P and ST-A-P-CO2 adsorb paracetamol and naproxen better than adsorbent WG-15 from aqueous solutions. The removal efficiency is 95% and 98% for paracetamol and naproxen, respectively, i.e., for adsorption on adsorbents activated by CO2. The adsorption of ibuprofen is comparable or weaker for ST-A-P, ST-A-P-CO2, and WG-15 adsorbents. The best results are obtained for adsorption on all the studied adsorbents for naproxen (82% ST-A-P, 98% ST-A-P-CO2, 63% WG-15).  Charge distributions of the studied adsorbate molecules (Table 2) confirmed the presence of two areas with strong negative potential around -C=O and -OH groups for the molecule of paracetamol and (S)-naproxen. Ibuprofen has only one center with negative potential in its molecule. This knowledge of charge distributions can be helpful to explain why paracetamol and naproxen can react stronger with adsorbent surface with a large number of acidic groups (ST-A-P and ST-A-P-CO 2 ) in comparison to ibuprofen facilitating more efficient adsorption of these pharmaceuticals on the ordered mesoporous carbons. Basic groups are dominant on the surface of WG-15, pointing to the different chemical and structural properties of this adsorbent compared with ST-A-P and ST-A-P-CO 2 materials. This fact suggests that the presence of acidic groups promotes adsorption of paracetamol and naproxen more strongly than the presence of basic groups on the surface of adsorbent. The molecules of adsorbates occur mainly in neutral forms under used experimental conditions during our research. According to literature data [52], three different mechanisms of adsorption of aromatic compounds on carbonaceous materials are possible: dispersive interactions by π electrons, donor-acceptor electron complexes, and hydrogen bond formation. The mechanism of paracetamol adsorption on the surface of activated carbon containing mainly oxygen functional groups occurs through π electron interactions because the possibility of forming Lewis acid-base complexes or hydrogen bonds [52]. Acidic groups containing oxygen atoms are predominant on the surface of ST-A-P and ST-A-P-CO 2 adsorbents, so one can expect that the interactions between paracetamol and naproxen molecules with the surface of these adsorbents can be similar. Comparable adsorption efficiency on ST-A-P and WG-15 adsorbents for ibuprofen suggests that the adsorption mechanism is also influenced by other factors (Figure 5). More detailed explanations of why ibuprofen adsorption presents the opposite trend compared to paracetamol and naproxen adsorption require further studies.

Kinetic Models
When designing adsorption experiments, knowledge about the kinetics of adsorption is of great importance because it can be used to determine adsorption process rate of a solute on the adsorbent surface [26]. Pseudo-first-order kinetic model [53], pseudo-second-order kinetic model [54], fractal-like kinetic models [55][56][57][58] and intra-particle diffusion model [59] were investigated for the adsorption of paracetamol, ibuprofen, and naproxen on ST-A, ST-A-CO 2 and WG-15 adsorbents.
The linear form pseudo-first-order kinetic model is as follows: ln q e −q t = lnq e −k 1 t (4) where k 1 -pseudo-first order rate constants (min −1 ); t-time of contact between the adsorbent and adsorbate (min); q e -amount of adsorbate at equilibrium (mg g −1 ); q t -amount of adsorbate at time t (mg g −1 ). The linear form pseudo-second-order kinetic model found below is: where k 2 -pseudo-second order rate constants (g mg −1 min −1 ). The fractal-like pseudo-first-order and fractal-like pseudo-second-order kinetic equations are as follows [58]: where k 1,0 , k 2,0 are the rate coefficients of fractal-like pseudo-first-order and fractal-like pseudo-second-order equations; k n,0 (n = 1,2) = k n,0 /α, and α = 1 − h, h is a constant parameter (0 ≤ h ≤ 1). Adsorption kinetics for paracetamol, ibuprofen, and naproxen on ST-A-P, ST-A-P-CO 2 , WG-15 are shown in Figure 6a-c. The adsorption equilibrium was settled after 360 min for all the studied pharmaceuticals. the faster step, which could be attributed to the diffusion of adsorbate molecules from the aqueous phase to adsorbent outer surface. The second part of the graph reflects slower adsorption, where intra-particle diffusion is a controlling step of the whole adsorption process. As shown in Figure 6df, none of the curves crossed through the origin of the plot, which suggests that intra-particle diffusion is not the only limiting step in adsorption of the studied pharmaceuticals from aqueous solutions. What is more, the plot qt vs. t 1/2 clearly indicates that the adsorption rate depends not only on intraparticle diffusion [60]. (e) (f) Figure 6. Kinetic adsorption curves (a-c), Co 300 mg dm −3 and the intra-particle diffusion (d-f) of paracetamol and NSAIDs on carbon materials studied.  Table 6. Kinetic parameters of paracetamol and NSAIDs adsorption on the studied adsorbents. The pseudo-first order and pseudo-second order rate constants, k 1 and k 2 , calculated and experimental adsorption capacities, q e , as well as values of correlation coefficients (R 2 ) are collected in Table 5. Fractal-like pseudo-first order and fractal-like pseudo-second order rate constants, k 1,0 and k 2,0 , values of α and correlation coefficients (R 2 ) are collected in Table 6. Correlation coefficients obtained when the pseudo-first-order kinetic model, fractal-like pseudo-first order and fractal-like pseudo-second order models were applied are lower for all the investigated adsorbates than the values obtained for the pseudo-second order model. Also, q e values calculated for the pseudo-first-order kinetic model show great differences against experimental values. The values of R 2 are clearly higher when pseudo-second order model was applied. Moreover, the calculated and experimental adsorption capacities are the most compatible. For this reason, we concluded that adsorption of the studied compounds on carbon adsorbents adsorption obey the pseudo-second-order kinetic model, suggesting the chemisorption as adsorption process. Table 5. Kinetic parameters of paracetamol and NSAIDs adsorption on the studied adsorbents.

Pseudo-First-Order Kinetic Model
Pseudo-Second-Order Kinetic Model k 1 (min −1 ) q e (mg g −1 ) R 2 k 2 (g mg − Table 6. Kinetic parameters of paracetamol and NSAIDs adsorption on the studied adsorbents.

Fractal-Like Pseudo-First-Order Kinetic Model
Fractal-Like Pseudo-Second-Order Kinetic Model Weber-Morris diffusion model was used in order to investigate adsorption mechanism of the studied compounds on the applied adsorbents. The diffusion model is presented by the following equation: q t = k id t 1/2 + c (8) where k id -intra-particle diffusion rate constant (mg g −1 min −1/2 ) and c-intercept, which represents the thickness of the boundary layer (mg g −1 ). The values of k id1 , k id2 and c 1 , c 2 determined from the slopes and intercepts of the first and second linear part of graph (Figure 6d-f) are given in Table 7. Constant values k d1 decrease in the following order: paracetamol > ibuprofen > naproxen for ST-A-P and ST-A-P-CO 2 adsorbents. For WG-15 adsorbent, the following range was obtained: paracetamol ≈ ibuprofen > naproxen. In turn, for all the studied adsorbents, the rate of diffusion is the smallest for naproxen, i.e., for the adsorbate of the highest molecular weight. If the adsorption that occurred was only due to intra-particle diffusion, then the dependency q t vs. t 1/2 would be rectilinear in the whole range. In addition, the curve would pass through the origin of the graph. Multi-linear plot (broken line on the graph) indicates that in the adsorption process several steps take part, not just intra-particle diffusion. The first section on the graph corresponds to the faster step, which could be attributed to the diffusion of adsorbate molecules from the aqueous phase to adsorbent outer surface. The second part of the graph reflects slower adsorption, where intra-particle diffusion is a controlling step of the whole adsorption process. As shown in Figure 6d-f, none of the curves crossed through the origin of the plot, which suggests that intra-particle diffusion is not the only limiting step in adsorption of the studied pharmaceuticals from aqueous solutions. What is more, the plot q t vs. t 1/2 clearly indicates that the adsorption rate depends not only on intra-particle diffusion [60].
Freundlich, Langmuir, and Langmuir-Freundlich models were employed to analysis adsorption data obtained in experiments. Temkin isotherm model, taking into consideration the effects of indirect adsorbate/adsorbate interactions during the adsorption process, assumes that adsorption heat of all molecules in the adsorption layer decreases linearly with increasing coverage of adsorption surface only for an intermediate range of concentrations [69][70][71]. Adsorption isotherms were determined for initial concentrations of paracetamol, ibuprofen and naproxen from 50 to 700 mg dm −3 . That is why it was decided that the Temkin model is not suitable for our experimental conditions.

Langmuir Model
The Langmuir model is widely used for the adsorption of different compounds from aqueous solutions, assuming that adsorbate molecules form a monolayer on the adsorbent surface which contains a specific number of identical sites [61]. This model is the most common model used to quantify the amount of adsorbate on an adsorbent as a function of concentration at a given temperature. Langmuir equation is expressed by relation (9): q e = q m K L C e 1 + K L C e (9) where C e -equilibrium concentration of solute in aqueous solution (mg dm −3 ); q e -the amount of solute adsorbed per gram of the adsorbent at equilibrium (mg/g), q m -maximum monolayer coverage capacity (mg g −1 ); K L -Langmuir isotherm constant (dm 3 g −1 ).

Freundlich Model
The Freundlich isotherm model is an empirical equation describing the adsorption on heterogeneous adsorbents [64]. This equation can be expressed as follows: q e = K F C 1/n e (10) where K F -Freundlich constant for a heterogeneous adsorbent (mg 1−1/n (dm 3 ) 1/n g −1 ), 1/n-the heterogeneity factor (the smaller 1/n, the greater the expected heterogeneity).
The Freundlich isotherm constant is an approximate indicator of adsorption capacity, while 1/n is a function of the strength of adsorption in the adsorption process [64]. If the value 1/n satisfies the condition 1/n < 1, this indicates a favorable adsorption process [72].

Langmuir-Freundlich Model
The Langmuir-Freundlich isotherm (Sip's equation) is represented by the expression that combines both Langmuir and Freundlich behaviors [66].
A general form of Langmuir-Freundlich isotherm equation is given below: where C e -equilibrium concentration of solute in an aqueous solution (mg dm −3 ); q e -the amount of solute adsorbed per gram of the adsorbent at equilibrium (mg/g), q m -maximum monolayer coverage capacity (mg g −1 ); K LF -Langmuir-Freundlich isotherm constant (dm 3 g −1 ), n-heterogeneity index. Fitting of the experimental data to the isotherm models described above was done using non-linear regression (Levenberg-Marquardt least square method with the Origin Microcal software); the results are shown in Figure 7. Langmuir, Freundlich, and Langmuir-Freundlich equations parameters as well as correlation coefficients R 2 for the adsorption of paracetamol, ibuprofen and naproxen on non-activated as well as activated ordered mesoporous carbons (ST-A-P, ST-A-P-CO 2 ), and activated carbon WG-15 are collected in Tables 8-10. The highest values of correlation coefficient (R 2 ≥ 0.97) for paracetamol, ibuprofen and naproxen adsorption on all the studied adsorbents were obtained when the Freundlich-Langmuir model was applied to fit experimental data. The calculated value n is >1 for all adsorbates (with exception of paracetamol on WG-15), indicating that adsorption is a favorable process. The calculated values of q m parameter (maximum adsorption capacity) are higher for paracetamol and naproxen adsorption on the ordered mesoporous carbons (ST-A-P and ST-A-P-CO 2 ) against adsorption on WG-15. The opposite result was obtained for the adsorption of ibuprofen.
paracetamol, ibuprofen and naproxen adsorption on all the studied adsorbents were obtained when the Freundlich-Langmuir model was applied to fit experimental data. The calculated value n is >1 for all adsorbates (with exception of paracetamol on WG-15), indicating that adsorption is a favorable process. The calculated values of qm parameter (maximum adsorption capacity) are higher for paracetamol and naproxen adsorption on the ordered mesoporous carbons (ST-A-P and ST-A-P-CO2) against adsorption on WG-15. The opposite result was obtained for the adsorption of ibuprofen.     Table 8. Langmuir, Freundlich, and Langmuir-Freundlich equations parameters and correlation coefficients R 2 for the adsorption of the studied paracetamol on adsorbents.  Table 9. Langmuir, Freundlich, and Langmuir-Freundlich equations parameters and correlation coefficients R 2 for the adsorption of naproxen on the studied adsorbents.

Conclusions
The adsorption of paracetamol, ibuprofen, and naproxen from aqueous solution on new ordered mesoporous carbons (ST-A-P, ST-A-P-CO 2 ) and commercial activated carbon (WG-15) was studied. The ability of adsorbing ordered mesoporous carbon materials was much higher for paracetamol and naproxen in comparison to commercial activated carbon. The removal efficiency of ibuprofen for all the studied adsorbents was significantly lower than for other studied pharmaceuticals.
The adsorption kinetics for paracetamol, ibuprofen, and naproxen on the studied carbon materials can be described with the pseudo second-order kinetic equation pseudo-second-order kinetic model, suggesting the chemisorption mechanism during the adsorption process. The intra particle-diffusion model describes well the adsorption mechanism for all the studied pharmaceuticals.
Acidic groups containing oxygen atoms are predominant on the surface of ST-A-P and ST-A-P-CO 2 adsorbents, so one can expect that the interactions between paracetamol and naproxen molecules with the surface of these adsorbents can occur through π electron interactions because the possibility of forming Lewis acid-base complexes or hydrogen bonds. Comparable adsorption efficiency on ST-A-P and WG-15 adsorbents for ibuprofen suggests that the adsorption mechanism is also influenced by other factors.
The adsorption process of paracetamol, ibuprofen and naproxen on all investigated carbon adsorbents proceeded in compliance with Freundlich-Langmuir adsorption model. The obtained values of n factor indicated that adsorption process of the studied pharmaceuticals is spontaneous in nature.
The obtained results confirmed that new mesoporous carbon materials are suitable adsorbents for all the studied pharmaceuticals, and especially for paracetamol and naproxen removal from aqueous solutions.