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Optimization of Binary Adsorption of Metronidazole and Sulfamethoxazole in Aqueous Solution Supported with DFT Calculations

Centro de Investigación y Estudios de Posgrado, Facultad de Ciencias Químicas, Universidad Autónoma de San Luis Potosí, Av. Dr. Manuel Nava 6, San Luis Potosí 78210, Mexico
Grupo de Investigación de Materiales con Impacto, Mat&mpac. Facultad de Ciencias Básicas, Universidad de Medellín, Medellín 050026, Colombia
Research Group in Carbon Materials, Inorganic Chemistry Department, Faculty of Sciences, University of Granada, Campus Fuente Nueva s/n, 18071 Granada, Spain
Authors to whom correspondence should be addressed.
Processes 2023, 11(4), 1009;
Received: 28 February 2023 / Revised: 22 March 2023 / Accepted: 23 March 2023 / Published: 27 March 2023
(This article belongs to the Special Issue Municipal Wastewater Treatment and Removal of Micropollutants)


Sulfamethoxazole [SMX] and metronidazole [MNZ] are emergent pollutants commonly found in surface water and wastewater, which can cause public health and environmental issues even at trace levels. An efficient alternative for their removal is the application of adsorption technology. The present work evaluated single and binary adsorption processes using granular activated carbon (CAG F400) for SMX and MNZ in an aqueous solution. The binary adsorption process was studied using a Box–Behnken experimental design (RSD), and the results were statistically tested using an analysis of variance. Density functional theory (DFT) modeling was employed to characterize the interactions between the antibiotics and the CAG F400 surface. For the individual adsorption process, adsorption capacities (qe) of 1.61 mmol g−1 for SMX and 1.10 mmol g−1 for MNZ were obtained. The adsorption isotherm model that best fit experimental data was the Radke–Prausnitz isotherm model. The adsorption mechanism occurs through electrostatic and π-π dispersive interactions. For the binary adsorption process, the total binary adsorption capacity achieved was 1.13 mmol g−1, evidencing competitive adsorption. The significant factors that determine the removal of SMX and MNZ from a binary solution were the solution pH and the initial concentration of antibiotics. From DFT studies, it was found that SMX adsorption on CAG F400 was favored with adsorption energy (Eads) of −10.36 kcal mol−1. Finally, the binary adsorption results corroborated that the adsorption process was favorable for both molecules.

1. Introduction

Pharmaceutical compounds include a variety of organic compounds, referred to as emerging pollutants (EPs), which represent a potential risk to human health and the environment [1]. Among the most common drugs are antibiotics, which are a great environmental concern because most of these have low biodegradability in aerobic conditions [2]. Antibiotics are used in humans and animals, but the organisms cannot fully absorb them, and they are released into the environment in an active form [3]. Then, antibiotics can create an adverse effect on aquatic fauna through bioaccumulation, and consequently, enter the food chain and the human body again [3]. Thus, the ingestion of antibiotic residues can alter the human microbiome and promote emergence and selection for bacteria resistance in the body [4]. Currently, one of the main concerns about the presence of antibiotics is that wastewater treatment plants have low removal efficiencies for these compounds, which facilitates their accumulation in surface, groundwater bodies [5,6,7]. This situation increases the possibility of creating a selection pressure on environmental microbiomes, which can lead to the generation of antibiotic resistance reservoirs in the environment [4]. In this sense, to avoid the presence of these compounds in the environment, the design of efficient treatment systems for drug elimination at the source (manufacturing industries and hospital facilities) is necessary [8,9].
Sulfonamides and nitroimidazoles belong to the group of drugs that are generating the greatest interest, since these drugs are among the antibiotics most widely used for the treatment of bacterial infections in humans and animals [10,11]. Nitroimidazoles, are characterized by high water solubility and low biodegradability, leading to their accumulation and persistence within ecosystems [2], while sulfonamides are less soluble in water and are highly resistant to degradation [2,12]. Recent studies have focused on the removal of these compounds through several technologies, such as adsorption, membrane separation, biological processes, electrochemical oxidation, and advanced oxidation processes (UV/H2O2, Fe2+/H2O2, O3) [13,14,15].
Adsorption processes, considered a conventional technology, have been widely studied for the removal of pharmaceutical compounds due to their easy application, low cost, high efficiency, large-scale application, and above all, because they do not involve the generation of toxic by-products or intermediates [16,17]. This technology has been applied successfully to 30 different antibiotic compound elimination [3]. Several adsorbents have been used for the adsorption of SMX and MNZ, such as clays, metal-organic frameworks, and activated carbon materials (AC). The last one is the most useful due to its excellent physicochemical stability and high specific surface area (500–2000 m2 g−1) [18,19]. In this sense, Ariyanto et al. [19] studied the effect of pore structure and surface oxidation of a nanoporous carbon on the adsorption performance of MNZ, finding that the oxidized carbon material favored MNZ adsorption. In the case of SMX, Li et al. [3] have evaluated the adsorption of SMX on AC, finding a maximum adsorption capacity of 26.77 mg g−1. In our research group, the single adsorption of MNZ and SMX on AC has been carried out, finding that the adsorption process is dominated by π-π dispersive interactions [2,20]. Hence, previous studies have focused on the elucidation of the type of adsorption in single systems [21,22]. However, few studies have been orientated on understanding the interactions involved during the adsorption process in multicomponent systems [23] or have reported the modeling and optimization of multicomponent adsorption systems [24,25,26].
In some cases, more than a single pharmaceutical compound is present in an aqueous sample, making it necessary to optimize the adsorption process to promote the removal of all compounds present in the sample [27]. Particularly, there are no studies reported until now for the combination of sulfonamides and nitroimidazoles. In this sense, the aim of this work is to evaluate the single and binary adsorption of metronidazole and sulfamethoxazole in an aqueous solution using a commercial activated carbon. The results have been statistically analyzed to determine the best conditions for maximizing the removal of both pharmaceuticals as a function of the solution pH, temperature, and initial concentrations of both pharmaceuticals. Additionally, the interactions between functionalities on carbon surfaces and pharmaceutical molecules have been elucidated through theoretical models. The density functional theory framework was used to determine the order of adsorption of SMX and NMZ on activated carbon.

2. Materials and Methods

2.1. Materials

Sulfamethoxazole [SMX] and metronidazole [MNZ], supplied by Sigma Aldrich with 99% purity, were used as model pollutants. Table 1 shows the physicochemical properties of both molecules. The speciation diagrams (Figure 1 and Figure 2) were constructed for both molecules considering the pKa values. SMX is mostly present in its cationic form (SMX+) at pH < 3 due to the protonation of the amino group, while at pH values between 4 and 6.5, the molecule is neutral [SMX]. Finally, at pH > 8, the anionic form (SMX) predominates due to the deprotonation of the amino group. MNZ can also present in three forms when dissolved in water: at pH < 4, the protonated form of the molecule predominates (MNZ+), at pH values in the range from 4 to 12, the molecule will be found mostly in its neutral form [MNZ], while at pH > 12, the anionic form of the molecule (MNZ) will be predominant.

2.2. Adsorbent

Filtrasorb 400 (F400) granular activated carbon (GAC F400), provided by Carbon Calgon Corporation, was used as an adsorbent. CAG F400 is made from select grades of bituminous coal through a process known as reagglomeration. The carbon was sieved to an average particle size of 0.541 mm. The chemical and textural properties of F400 GAC have been previously reported by Serna-Carrizales et al. [22]. The textural characterization of the GAC F400 is shown in Table S1 and Figure S1 of the supplementary material. The material presents a surface area (SBET) of 756 m2 g−1 and is mainly microporous. In terms of chemical properties, GAC F400 is characterized by a high concentration of total basic sites (0.486 meq g−1) and a point of zero charge value (pHpzc) = 9.43 [22].

2.3. Concentration Determination of Sulfonamides and Nitroimidazoles

The concentration of sulfamethoxazole [SMX] and metronidazole [MNZ] in an aqueous solution were determined by high-performance liquid chromatography (HPLC) using Alliance e2695 equipment equipped with a diode array detector (wavelength 265 nm). The mobile phase consisted of a 0.1% acetic acid solution and acetonitrile in a 70/30 ratio, respectively, which were fed to the apparatus at a flow rate of 1 mL min−1. The injection volume of both samples was 10 µL and the retention time was 1.3 and 2.9 min for MNX and SMX, respectively.

2.4. Obtaining Adsorption Equilibrium Data: Individual and Multicomponent

Experimental adsorption equilibrium data for both molecules were obtained using a batch adsorber. This system has been previously reported by Serna-Carrizales et al. [22] and consists of a set of vials of 50 mL capacity, which are immersed in a temperature-controlled bath. For the single adsorption process, the initial concentrations were set in a range from 0.02 to 2.3 mmol g−1 for MNZ, and from 0.089 to 1 mmol g−1 for SMX. For the binary adsorption process, the initial concentrations of both molecules were set in a range from 0.02 to 0.3 mmol L−1, due to the solubility limitations of the SMX molecule. In all cases, 50 mL of a solution of known initial concentration was placed in the adsorbers, and a sample of 10 mL was taken from each vial to verify the initial concentration. Subsequently, 0.01 g of GAC F400 was added to each adsorber and immersed in a bath at a constant temperature until equilibrium was reached. During this period, the pH of the solution was kept constant by adding drops of NaOH or HCl as needed. After equilibrium was reached, a 1 mL aliquot was taken from each adsorber, and the concentration of the solute(s) present was quantified. The individual adsorption capacity of the GAC F400 was obtained by the following mass balance:
q = V C A 0 C e m
where q is the amount of drug adsorbed (mmol g−1); V is the volume of the solution (L); CA0 is the initial concentration of the solution (mmol L−1); Ce is the equilibrium concentration (mmol L−1); and m is the mass of GAC F400 employed (g).
The total adsorption capacity of GAC F400 for the binary system was calculated by summing the individual adsorption capacity according to the following relationship:
q T = q M N Z + q S M X
To evaluate the effect of the system operating variables (pH, temperature, initial SMX concentration, and initial MNZ concentration), a Box–Behnken response surface design of experiments was used. Table S2 shows the experimental design used to obtain the binary equilibrium data, which consisted of four factors at three levels, each with three replicates of the central point, resulting in a total of 27 experiments. The minimum and maximum pH values were set in a range from 2 to 10, while the temperatures were set in a range from 10 to 40 °C. Finally, the experimental data were fitted to a second-order polynomial regression model, which is represented by the following general equation:
q = β 0 + β 1 × p H + β 2 × T + β 3 × [ M N Z ] + β 4 × [ S M X ] + β 5 × p H × T + β 6 × p H × [ M N Z ] + β 7 × p H × [ S M X ] + β 8 × T × [ M N Z ] + β 9 × T × [ S M X ] + β 10 × [ M N Z ] × [ S M X ] + β 11 × p H 2 + β 12 × T 2 + β 13 × [ M N Z ] 2 + β 14 × [ S M X ] 2
where β0 is the independent term; β114 are the model coefficients; [MNZ] and [SMX] are the initial concentrations of metronidazole and sulfamethoxazole, respectively, (mmol L−1); T is the temperature of the system (°C); and q represents the adsorption capacity of MNZ or SMX (mmol g−1).

2.5. Characterization of the Antibiotic-Surface Interaction

The interactions between the antibiotics and the carbonaceous material were characterized through theoretical models. First-principles calculations were performed using the density functional theory framework (DFT). The calculations were performed with the Gaussian09 software using the DFT-B3LYP method and the 6–31+g(d,p) set of bases, which has been widely used for the study of these systems. The geometry optimization calculations were carried out considering the solvent effect, using the IEFPCM approximation (integral equation formalism variant of the polarized continuum model). The values of the local potential energy minima for each structure were confirmed by the non-occurrence of imaginary frequencies. The adsorption energy was calculated using the following expression:
E a d s = E a n t i b i o t i c + s u r f a c e E a n t i b i o t i c E s u r f a c e
where Eads represents the adsorption energy; Eantibiotic+surface corresponds to the total energy of the antibiotic complex/carbonaceous surface; Eantibiotic is the energy of the antibiotic; and Esurface is the energy of the carbonaceous surface.

3. Results and Discussion

3.1. Single and Multicomponent Adsorption Equilibrium

3.1.1. Individual Adsorption Equilibrium

To perform a comparative analysis, the individual adsorption isotherms of MNZ and SMX were obtained (Figure 2). Both isotherms present an asymptotic “L’’ type behavior, which, according to Giles’ classification, indicates that the aromatic rings present in the structure of SMX and MNZ adsorb parallel to the graphitic planes of the GAC F400; this behavior has been previously documented by Serna-Carrizales et al. [22] and Carrales-Alvarado et al. [20,31]. In Figure 2, it can be observed that at equilibrium concentrations (Ce) lower than 0.15 mmol L−1, the carbon surface showed a slightly better affinity by MNZ, however, at higher concentrations at equilibrium, SMX adsorbed much better than MNZ. As an example, at an equilibrium concentration of 0.6 mmol L−1, the adsorption capacity towards SMX and MNZ were 1.3 and 1.04 mmol g−1, respectively.
This can be attributed to the isoxazole and aniline aromatic rings providing a high electron density in SMX; besides in SMX, more resonance structures can be proposed to stabilize this molecule. The two aromatic rings infer coplanarity, enhancing the π-π stacking interactions that it has with the GAC F400 surface. Moreover, at the experimental conditions (pH = 7 and T = 25 °C) the GAC F400 surface is positively charged. If we analyze the speciation diagram of both molecules (Figure 1), at a pH of 7, the SMX molecule is found mostly in its deprotonated form with the presence of neutral species, favoring adsorption through attractive electrostatic interactions and π-π interactions. In the case of the MNZ molecule, it is in its neutral form in a range of pH from 6 to 12. Thus, π-π interactions will be predominant in the adsorption process. However, MNZ has two disadvantages in the adsorption process. The first one is that, although MNZ possesses an imidazole ring, the electron density is diminished due to the nitro group, which is an electron-withdrawing group. This decreases the electronic density over the aromatic ring. The second disadvantage is the structure of MNZ; this molecule is only planar in the imidazole ring, therefore, the interaction area for π-π stacking interactions is smaller than SMX. The discussion about this behavior during adsorption will be supported by the computational results presented in Section 3.2, associated with the different established interactions between the antibiotics and the surface of GAC F400.
The experimental data were interpreted using the Langmuir, Freundlich, and Radke–Prausnitz isotherm models (see the supplementary material). The isotherm parameters were determined by the non-linear least-squares method using the Levenberg–Marquardt optimization algorithm and are shown in Table S3. The average deviation percentage (%D) was calculated to determine the best fit between the experimental data and the model (see supplementary material). Considering the values of the regression coefficient (R2) and the average deviation percentage (%D) of each model, the Radke–Prausnitz and Langmuir isotherm models (Figure 2) describe the experimental data adequately. The maximum adsorption capacities from the Langmuir model were 1.61 mmol g−1 and 1.10 mmol g−1 for SMX and MNZ, respectively. These values are similar to those obtained in the literature using activated carbon [20,22].

3.1.2. Binary Adsorption Equilibrium

The binary adsorption process was analyzed through a response surface design of experiments. The experimental data were analyzed using Design-Expert 7.0 software. A significance level of 95% (α = 0.05) was used to analyze the significance of the model and its respective coefficients. In this sense, the p-value is used to denote the significance of each factor as follows: the factor is statistically significant if the p-value is <0.05, while a p-value > 0.05 lacks statistical significance. However, because some factors were around 5%, a refinement of the factors was performed by increasing the significance level to 90% (α = 0.1) to cover all the factors that were affecting the system. Table S4 shows the analysis of variance (ANOVA) for the variable qSMX. The statistically significant factors for this variable are the linear terms pH, T, and [SMX], the interaction between the pH and [SMX] and the quadratic terms pH2, T2, and [SMX]2. From the values of F and p reported in Table S4, the [SMX] term is the factor most influencing the qSMX given that it shows the largest F value and the smallest p value. Finally, the model showed a p value < 0.0001 with no significant lack of fit, which indicates that the model can describe the change of qSMX as a function of the factors studied.
The final model to describe the qSMX, after a depuration process and considering the factors hierarchy, is represented by the following equation:
q S M X = ( 0.0160 + 0.0576 × p H 8.955 × 1 0 3 × T + 5.278 × [ S M X ] 0.173 × p H × [ S M X ] 4.340 × 10 3 × p H 2 + 1.920 x 10 4 × T 2 7.945 × [ S M X ] 2 ) 2
A similar analysis was performed to identify the significant terms during the adsorption of MNZ, qMNZ, supported by the ANOVA analysis showed in Table S5. For this case, the statistically significant factors were the pH, [SMX], [MNZ], pH2, and the interaction between pH and [MNZ]. The mathematical model to describe the qMNZ is given by the following equation:
q M N Z = 0.0169 + 0.0613 × p H + 0.830 × [ M N Z ] 0.374 × [ S M X ] + 0.171 × p H × [ M N Z ] 6.867 × 1 0 3 × p H 2
Figure S2a,b shows the correlation between the experimental data for qSMX and qMNZ, respectively, and a random distribution can be observed over the 45° line for both cases when using Equations (5) and (6). Furthermore, the values of R2 for the mathematical models were 0.9658 and 0.9426, respectively, which indicates that Equations (5) and (6) can predict the response successfully.
Finally, for the variable qTOTAL (Table S6), the significant parameters are the linear terms pH, [MNZ], and [SMX], the interaction between pH and [SMX], and the quadratic factors pH2 and [SMX]2. In this sense, the expression for qTOTAL, considering the statistically significant terms, is described below:
q T o t a l = 0.541 + 0.214 × p H + 1.661 × [ M N Z ] + 5.411 × [ S M X ] 0.360 × p H × [ S M X ] 0.0162 × p H 2 8.220 × [ S M X ] 2
From the above equations, response surface curves were obtained for qMNZ and qSMX as a function of significant variables defined in Tables S4–S6. In Figure 3a, the variation of qMNZ as a function of pH and [SMX] at initial MNZ concentrations of 0.03, 0.16, and 0.30 mmol L−1 is shown. The results reveal that qMNZ is drastically dependent on the initial MNZ concentration, increasing favorably as the concentration of MNZ increases. As an example, at pH 6 and an initial SMX concentration of 0.2 mmol L−1 the values of qMNZ were 0.6, 0.4, and 0.2 mmol g−1, at initial MNZ concentration of 0.30, 0.16 and 0.03 mmol L−1, respectively. In Figure 3a, it can also be seen that pH has a significant influence on qMNZ, but mainly at initial concentrations greater than 0.16, regardless of the presence of SMX.
Generally, it is observed that an increase in pH solution and initial MNZ concentration increases the adsorption capacity of MNZ. This effect is maximized at pH ≈ 8, which is associated with the fact that π-π stacking interactions are favored at this pH. Moreover, it can be observed that the presence of SMX during MNZ adsorption has a slight effect, i.e., the qMNZ only decreases by 10% by increasing the initial SMX concentration from 0 to 0.3 mmol L−1, indicating non-competitive adsorption during MNZ adsorption. At acidic pHs (≈pH 2), the adsorption capacity for MNZ presents the lowest values, since MNZ is mostly positively charged with a slight presence of a neutral charge, and GAC F400 is positively charged. This leads into the establishment of repulsive electrostatic interactions that decrease the adsorption capacity. In addition, MNZ in neutral form decreases significatively the electron density in the imidazole ring due to the nitro group disfavoring the π-π stacking interactions at this pH. Finally, during the adsorption of MNZ in the presence of SMX, the temperature was not a significant parameter. Carrales-Alvarado et al. [20] showed that during single adsorption of MNZ on activated carbon, the adsorption capacity at 10, 20, and 35 °C was not affected by temperature.
Figure 3b shows the variation of qSMX as a function of [MNZ] and the solution pH at different initial SMX concentrations. For an initial SMX concentration of 0.16 and 0.3 mmol L−1, the adsorption capacity of SMX decreases by increasing the pH. This is congruent with the behavior found in the single system because, at pH values higher than 10, SMX is mostly negatively charged, as is the GAC F400 surface, causing repulsive electrostatic interactions. The highest adsorption capacity of SMX is found at low pH (pH = 2) regardless of the presence of MNX, where SMX is neutral and positive in a 1:1 ratio [2]. At this pH there is a protonated amido group that generates a positive charge in the molecule, but it seems that is not a positive charge strong enough to have significant repulsive interactions with GAC F400. Besides, the aniline and isoxazole rings possess high electron densities that favor the π-π stacking interactions [2]. In Figure 3b it can be seen that the presence of MNZ in the binary process does not affect the adsorption of SMX regardless of solution pH. However, at [MNZ] concentrations of 0.16 and 0.30 mmol L−1 at pH 2, the presence of MNZ significantly affects the adsorption capacity of SMX. As an example, at [SMX] of 0.16 mmol L−1 in the absence of MNZ, the adsorption capacity is qSMX = 0.2 mmol g−1, but in the presence of MNZ (0.3 mmol L−1) the adsorption capacity is duplicated. Thus, SMX adsorption increased because the MNZ molecules provide order to adsorption process. We propose that MNZ is adsorbed between SMX molecules, and this action generates a stable adsorption process. Furthermore, π-π stacking interactions between SMX and MNZ contribute to a more stable stacking process. Since SMX and MNZ’s electron densities in their aromatic rings are different, this generates stronger π-π interactions. MNZ rings are deactivated by the nitro group, and SMX is an amino group-activated ring. This difference in electron density favored stacking among different rings.
Figure 3c shows the behavior of total adsorption capacity concerning SMX concentration and pH. The total adsorption capacity increases with the rising solution concentration of both MNZ and SMX. This is consistent with the results shown in Table S2 since the highest qTOTAL was found using the highest initial concentrations of SMX and MNZ (Exp 13). Additionally, comparing the maximum adsorption capacities found in individual systems (qSMX = 1.61 mmol g−1 and qMNZ = 1.10 mmol g−1) with the maximum total adsorption capacity found in the binary system (qTOTAL = 1.13 mmol g−1), it is evident that the adsorption of SMX is affected by the presence of MNZ and vice versa in the binary system. This indicates that both molecules adsorb on the same active sites.
The effect of pH on qTOTAL was also analyzed. It was found that at pH = 6, the qTOTAL value is maximized. At this pH value, the MNZ molecule is entirely neutral, while the SMX molecule is 40% in its anionic form and 60% neutral, promoting π-π stacking interactions between the graphitic rings of GAC F400 and the aromatic rings of SMX and MNZ. Therefore, the best option is pH 6, since this will enhance the use of the active sites available in the GAC F400. According to these results, the mechanism that predominates during the binary adsorption of both antibiotics is governed by the occurrence of π-π stacking interactions, which are maximized at pH 6 with SMX concentrations higher than 0.15 mmol L−1, and MNZ concentrations lower than 0.16 mmol L−1. This can see in Table S6, from ANOVA, the interaction of [SMX] and pH is significant because, in this pH range, the adsorption capacity of SMX is larger than de MNZ.
The effect of [MNZ] and pH over the total adsorption capacity is shown in Figure 3d. The values of qTOTAL increase as the [MNZ] and [SMX] increase; this effect is observed at lower [SMX] values (0.03 mmol L−1). On the other hand, the pH value that maximizes the qTOTAL was a value of 6. A similar behavior was found for SMX (see Figure 3c). Furthermore, the interaction between [MNZ] and pH in the model design is not significant, therefore, pH does not affect the adsorption. Moreover, as is shown in Figure 1a, the speciation of MNZ does not change in a wide range of pHs.

3.2. Characterization of the Antibiotic-Surface Interaction

The possible interactions proposed between the surface functional groups present in the adsorbent and the antibiotics were modeled by computational calculations in monocomponent and multicomponent systems, according to the spectroscopic characterization of this material previously reported [32]. The carbonaceous surface was simulated, including functional groups, such as ether, semiquinone, carboxylic and phenol groups, with the last two of them being protonated species (that is, carboxylic H+ [-COOH2+] and phenol H+ [-OH2+]), considering that under experimental conditions at pH = 5, the surface is positively charged. A systematic study was carried out over these groups, considering the neutral and anionic forms of SMX molecules and the neutral form of MNZ (the neutral and anionic forms were established from speciation curves for both molecules). The adsorption energies (Eads) for both contaminants are shown in Figure 4 (also see Table S7 in the supplementary material), and the stability of these geometries can be deducted based on the adsorption energies (see the most stable structures shown in Figure 5). In monocomponent systems, different interactions were established with the oxygenated groups of the carbonaceous material under fourth adsorption modes, i.e., interactions of a type where hydrogen bonds occurs with ether, semiquinone, and the protonated carboxylic groups with the amine groups of SMX or MNZ molecules (-NH or -NH2) or with the -OH group of MNZ. Also, π-π interactions and electrostatic attraction can take place between the functional groups and SMX (neutral and anionic forms) and MNZ molecules. Specifically, for SMX, aniline, isoxazole, and sulfonamide groups are determinants for interactions. For MNZ, the imidazole ring and nitro group are the principal sites for interactions. From these results, the stability sequence of the geometries obtained decreased in the following order for the proposed model with the SMX molecule: semiquinone > carboxylic H+ > ether groups, while the order was semiquinone > ether > carboxylic H+ groups was displayed with the MZN molecule. Hence, these findings indicate that the affinity of the adsorption sites for each pollutant depends on both; that is, the chemical nature of the adsorbent and the pollutant. In consequence, these results corroborated that the hydrogen bonds, electrostatic attraction, and π-π interaction mechanisms play an important role in the adsorption of the antibiotic molecules in these systems. From these results, it is possible also to propose that SMX adsorption is favored over the carbonaceous material compared to the MZN molecule due to SMX’s larger electron cloud created by the presence of aniline and isoxazole rings, which was evidenced by the experimental equilibrium results in monocomponent systems.
For a multicomponent system, the adsorption of both antibiotics was evaluated over the carbonaceous surface containing the semiquinone group and considering π-π interactions among the surface and the antibiotic molecules (SMX and MNZ). The Eads were favorable for the adsorption of both molecules with a value of −10.36 kcal mol−1, indicating that the SMX adsorption occurs first, followed by the MNZ, in a multicomponent system.

4. Conclusions

In the adsorption process, the concentration of the pharmaceutical compounds and the pH of the solution determined the affinity of GAC F400 towards SMX and MNZ molecules. Therefore, the best conditions to favor the adsorption process in a binary MNZ/SMX system are a pH of 6 and equimolar concentrations of each drug. The adsorption of SMX was affected by the presence of MNZ, so it can be inferred that there is a competitive adsorption process of an antagonistic type. For both drugs, the predominant adsorption mechanism is via electrostatic and π-π stacking interactions.
DFT models confirm the adsorption mechanism proposed. Also, the SMX adsorption is favored over the carbonaceous material compared to the MNZ molecule. In a binary system, SMX adsorption occurs first, followed by MNZ.

Supplementary Materials

The following supporting information can be downloaded at:

Author Contributions

Conceptualization, J.C.S.-C., R.O.-P. and A.I.Z.-G.; methodology, J.C.S.-C. and A.I.Z.-G.; software, J.C.S.-C.; validation, R.O.-P., A.I.Z.-G., J.C.S.-C., A.F., E.B.-G., E.F., A.A.-A. and C.F.A.G.-D.; formal analysis, R.O.-P., A.I.Z.-G., A.F., E.F., A.A.-A. and C.F.A.G.-D.; investigation, J.C.S.-C., R.O.-P. and A.I.Z.-G.; data curation, J.C.S.-C., A.I.Z.-G., A.I.Z.-G. and A.F.; writing—original draft preparation, J.C.S.-C., R.O.-P., A.A.-A., A.F. and A.I.Z.-G.; writing—review and editing, J.C.S.-C., R.O.-P., A.F. and A.I.Z.-G.; visualization, J.C.S.-C., R.O.-P., A.I.Z.-G., A.F., E.F., A.A.-A. and C.F.A.G.-D.; supervision, R.O.-P. and A.I.Z.-G. All authors have read and agreed to the published version of the manuscript.


This research received no external funding.

Data Availability Statement

The data used to support the findings of this study are available from the corresponding author upon a reasonable request.


Juan Carlos Serna-Carrizales thanks the Consejo Nacional de Ciencia y Tecnología (National Council for Science and Technology), CONACyT, Mexico, for the funding granted for postgraduate studies. Dra. Ana I. Zárate-Guzmán thanks CONACyT for the support received through the “Convocatoria 2020: Estancias Posdoctorales por México” and “Convocatoria 2021: Segundo año de continuidad de Estancias Posdoctorales por México modalidades 1 y 2”.

Conflicts of Interest

The authors declare no conflict of interest.


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Figure 1. Speciation diagram of (a) MNZ and (b) SMX.
Figure 1. Speciation diagram of (a) MNZ and (b) SMX.
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Figure 2. Individual adsorption isotherms of MNZ and SMX on GAC F400 at 25 °C and pH 7. The dotted line represents the prediction of the Radke–Prausnitz model.
Figure 2. Individual adsorption isotherms of MNZ and SMX on GAC F400 at 25 °C and pH 7. The dotted line represents the prediction of the Radke–Prausnitz model.
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Figure 3. Surface response curves for (a) qMNZ, (b) qSMX, and (c) qTOTAL in the function of [SMX] and pH; (d) qTOTAL in the function of [MNZ] and pH.
Figure 3. Surface response curves for (a) qMNZ, (b) qSMX, and (c) qTOTAL in the function of [SMX] and pH; (d) qTOTAL in the function of [MNZ] and pH.
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Figure 4. Adsorption energies (Eads) for both antibiotics on functional groups of the models for the carbonaceous material in mono- and multicomponent systems.
Figure 4. Adsorption energies (Eads) for both antibiotics on functional groups of the models for the carbonaceous material in mono- and multicomponent systems.
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Figure 5. Most stables adsorption modes of antibiotic molecules on carbonaceous models. The C, O, H, N, and S atoms are symbolized by a dark gray, red, white, blue, and yellow color, respectively. (a) Semiquinone NH2-SMX [32], (b) Semiquinone OH-MNZ, (c) Carboxylic H+ π-π-SMX [−], and (d) Semiquinone π-π-SMX [32]-MNZ.
Figure 5. Most stables adsorption modes of antibiotic molecules on carbonaceous models. The C, O, H, N, and S atoms are symbolized by a dark gray, red, white, blue, and yellow color, respectively. (a) Semiquinone NH2-SMX [32], (b) Semiquinone OH-MNZ, (c) Carboxylic H+ π-π-SMX [−], and (d) Semiquinone π-π-SMX [32]-MNZ.
Processes 11 01009 g005aProcesses 11 01009 g005b
Table 1. Physicochemical properties of MNZ and SMX.
Table 1. Physicochemical properties of MNZ and SMX.
Physicochemical PropertyMNZSMX
StructureProcesses 11 01009 i001Processes 11 01009 i002
Molecular formula C6H9N3O3C10H11N3O3S
Molecular weight (g mol−1)171.15253.28
pKa [28,29]pKa1 = 2.58
pKa2 = 14.44
pKa1 = 1.97
pKa2 = 6.16
Solubility (mol L−1) [28,29]0.0410.001109
Log Kow [30]−0.020.9
Molecular size (nm)x = 0.969
y = 0.736
z = 0.454
x = 1.517
y = 0.676
z = 0.541
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Serna-Carrizales, J.C.; Zárate-Guzmán, A.I.; Aguilar-Aguilar, A.; Forgionny, A.; Bailón-García, E.; Flórez, E.; Gómez-Durán, C.F.A.; Ocampo-Pérez, R. Optimization of Binary Adsorption of Metronidazole and Sulfamethoxazole in Aqueous Solution Supported with DFT Calculations. Processes 2023, 11, 1009.

AMA Style

Serna-Carrizales JC, Zárate-Guzmán AI, Aguilar-Aguilar A, Forgionny A, Bailón-García E, Flórez E, Gómez-Durán CFA, Ocampo-Pérez R. Optimization of Binary Adsorption of Metronidazole and Sulfamethoxazole in Aqueous Solution Supported with DFT Calculations. Processes. 2023; 11(4):1009.

Chicago/Turabian Style

Serna-Carrizales, Juan Carlos, Ana I. Zárate-Guzmán, Angélica Aguilar-Aguilar, Angélica Forgionny, Esther Bailón-García, Elizabeth Flórez, Cesar F. A. Gómez-Durán, and Raúl Ocampo-Pérez. 2023. "Optimization of Binary Adsorption of Metronidazole and Sulfamethoxazole in Aqueous Solution Supported with DFT Calculations" Processes 11, no. 4: 1009.

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