Introduction

Emerging pollutants (EPs) are defined as “chemical substances that have no regulations, are suspected to affect the environment, or their effects are unknown” (Barrios-Estrada et al. 2018). In addition, EPs are found in low concentrations, but still may cause adverse consequences on human health or environment (Lopez de Alda et al. 2003). A common feature of emerging pollutants is that they are introduced into the environment in very low quantities but at a continuous rate. Sulfonamides (SMs) are antibiotics related to this group of pollutants due to their high consumption and low biodegradability, which increases their bioaccumulation (Chen and Xie 2018). SMs are used for the systemic treatment of bacterial infections in humans, and they are effective for combating both gram-positive and gram-negative bacteria, as well as different protozoa.

A number of conventional technologies have been applied to remove SMs from water, including chlorination, chemical oxidation, and biodegradation (Chen and Xie 2018; Mulla et al. 2018; Vila-Costa et al. 2017). In general, these methods efficiently degrade SMs; however, secondary problems are generated since these systems are not capable of achieving complete mineralization. Yang et al. (2018) analyzed the degradation of sulfadiazine using permanganate and studied the effect of solution pH and degradation byproducts toxicity. The results showed that the degradation of sulfadiazine follows a pseudo-first order kinetics with a rate constant in the range of 1.68 × 10−3 to 4.98 × 10−1 min−1. In addition, it was proven that the highest degradation percentage is achieved at pH < 3. Nevertheless, under the experimental conditions employed ([sulfadiazine]0 = 0.02 mM, [Mn(VII)]0 = 0.5 mM), sulfadiazine was not mineralized, and the degradation byproducts presented a higher toxicity than the original compound. Zhang et al. (2018) investigated the degradation of sulfamethazine and sulfadiazine by chlorination after an oxidation process with ferrate (VI). According to the results, the pre-oxidation radically reduces both the formation of THMs and the toxicity of degradation byproducts, but high amounts of Fe (VI) are necessary to ensure the water quality.

In contrast to conventional methods, advanced oxidation processes (AOPs) employ highly reactive species for the degradation of pollutants, such as SO4−•, HO•, eaq−, and H● radicals which can be generated by activation of H2O2 or S2O8−2 with UV light (Xiao et al. 2020a; Yang et al. 2017), photocatalysis (Kim and Kan 2016), radiolysis (Sági et al. 2018), and Fenton process (Martínez-Costa et al. 2018), for instance. The degradation of SMs from water by AOPs has extensively been studied over the last decade (Baran et al. 2011). Zhou et al. (2019) investigated the elimination of sulfamethoxazole, sulfisoxazole, sulfathiazole, and sulfamethizole by persulfate at temperatures from 30 to 60 °C. The results revealed that degradation rate constants increased almost linearly as the temperature augmented for all SMs. Moreover, it was confirmed that five-membered heterocyclic rings could serve as reactive moieties toward SO4•− attack. Acosta-Rangel et al. (2018) analyzed the effectiveness of UVC, UVC/H2O2, and UVC/K2S2O8 on the degradation of sulfamethazine, sulfadiazine, and sulfamethizole obtaining that SMs with a penta-heterocycle presented the highest degradation rates; moreover, an increase in the solution pH enhanced the degradation process. Finally, the presence of radical promoters generates a greater increase in the degradation rate.

Response surface methodology (RSM) is a statistical method, which reduces the research workloads, and provides a more appropriate model for optimization than the conventional variable control approaches (Montgomery 2019). This methodology was applied by Wang et al. (2019) to optimize the amount of Fe+3, CaO2, and the solution pH during sulfanilamide degradation by the Fenton-like process. However, in the case of SM degradation with UV/H2O2 and UV/ S2O8−2, there is no evidence in regard to the application of this methodology optimizing the process variables, reducing energetic cost, and the demand of chemicals. Therefore, the main aim of this work was to investigate the degradation of sulfamethazine, sulfadiazine, and sulfamethoxazole using UV light, HO•, and SO4•− radicals generated by the photoactivation of H2O2 and S2O8−2. An experimental Box-Behnken response surface design was applied in order to optimize operational conditions, and density functional theory (DFT) studies were applied in order to corroborate the degradation mechanism using UV light.

Experimental methods

Sulfonamides

In this work, three SMs were used, sulfamethazine (SMT), sulfadiazine (SMD), and sulfamethoxazole (SMX). Table 1 summarizes their main physicochemical properties (Garoma et al. 2010). SMs are polar molecules with amphoteric characteristics, where the amine nitrogen is protonated at a pH of 2–3, while amidic nitrogen is deprotonated at a pH of 6.5 to 14; i.e., they act as acids and bases of Brönsted-Lowry.

Table 1 Physicochemical properties of SMD, SMT, and SMX
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Figures S1 and S2 show the optimized structures for SMT, SMD, and SMX in vacuum and water environments, respectively, by DFT. The structures share a common planar shape because of their phenyl rings and sulfone moiety. The oxygen atoms of the sulfone generate a non-classic hydrogen (~ 2.4 Å) bond in neutral state with the atoms H9, H10, and H18 for SMT, H9, H10, and H27 for SMD and H7, H8, and H18 for SMX.

Determination of the concentration of SMs in aqueous phase

The concentrations of SMT, SMD, and SMX were determined by high-performance liquid chromatography (HPLC) using a Waters e2695 liquid chromatograph with Nova-Pack® C18 column. The mobile phase was 10 mM acetic acid solution and acetonitrile at a ratio of 70 and 30%, respectively, in isocratic mode at a flow of 1.0 mL min−1. The detector wavelength was 265 nm, and the injection volume was 10 μL. The retention times were 5.5, 3.4, and 2.4 min for SMX, SMD, and SMT, correspondingly.

Experimental system

SM degradation experiments were carried out in a photoreactor with similar dimensions and configuration as the one used in a previous study (Hermosillo-Arellano et al. 2019). The photoreactor was equipped with a medium-pressure 700 W TQ 718 mercury lamp which emitted radiation at 240–320 nm. The rate of energy irradiated by the lamp at 90, 270, 540, and 630 W was determined by actinometry with a solution of 5 μM atrazine as actinometer (Canonica et al. 2008) obtaining photon irradiances of 1.07 × 10−5, 7.65 × 10−5, 17.06 × 10−5, and 20.19 × 10−5 Einstein m−2 s−1, respectively.

Collecting of experimental data from the degradation of SMT, SMD, and SMX through UV radiation

Experimental data on the degradation of SMs were obtained by the following procedure: solutions with a known initial concentration (CA0 = 7.18 × 10−5 mol L−1) of each SM were prepared in volumetric flasks of 50 mL. These solutions were poured into the 60 mL quartz tubes and introduced into the photoreactor, where the operating temperature and stirring speed were set. Once the system reached operating temperature, the lamp and chronometer were turned on to start the degradation kinetics. The concentration of each SM within the photoreactor over time was monitored by withdrawing and quantifying 1 mL aliquots at time intervals of as follows: 0, 1, 3, 5, 10, 15, 30, 45, and 60 min for SMT and SMD, and 0, 0.5, 1, 3, 5, 10, 15, 20, and 30 min for SMX. The degradation rate of the three drugs was analyzed by studying the effect of the lamp power (90, 180, 270, and 360 W), maintaining a temperature of 25 °C and a constant CA0 value. In addition, the effect of solution pH was studied by conducting experiments at pH values corresponding to pKa1, and pKa2 of each sulfonamide. Besides, pH = 5 for SMT, pH = 4 for SMD and SMX, and a pH = 11 for the three sulfonamides. The desired pH values were obtained by adding HCl or NaOH solutions.

Collection of experimental data from the degradation of SMT and SMD through the UV/H2O2 and UV/K2S2O8 systems

The degradation kinetics of SMT and SMD using the UV/H2O2 and UV/K2S2O8 systems were obtained through a process like the one described in the previous section. The only difference was that an aliquot of a concentrated solution of H2O2 or K2S2O8 was added to the reactor before turning the lamp, in order to obtain the desired initial concentration of each radical promoter. The effect of the operating conditions of the system on the degradation rate was investigated by using a Box-Behnken-type response surface experiment design with three factors and three repetitions of the center point, consisting of 15 experiments. The solution pH, the initial concentration of H2O2 or K2S2O8, and the temperature were selected as study factors, while the response was the apparent degradation rate constant, kap. Table S1 presents the decoded values of the corresponding variables.

Computational details

DFT calculations were carried out to know the influence of the medium in the lability of the fragmented bonds. The critical points of bond were determined for the systems in gas phase and in aqueous medium. The compounds were structurally modified, simulating the different solution pH, adding, or removing a hydrogen atom (positive or negative charge). Figure 1 shows as an example the molecular structures for SMT (anionic form), SMD (cationic form), and SMX (cationic form), where the letters represent the sites of possible fragmentation in the systems, whereas Figures S1 and S2 illustrate the molecular bond distances for the nine structures in water and vacuum.

Fig. 1
figure 1

Molecular graphs of the SMTw, SMDw, and SMXw systems. All optimized structures were obtained at a M06/def2-TZVP/CPCM (Water)

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Molecular structures were submitted to a geometry optimization without symmetry constraint, employing DFT framework in ORCA code (Neese 2018). DFT calculations were performed using the M06 hybrid functional of Zhao and Truhlar (2008) and the def2-TZVP electronic basis set (Holzmann et al. 2011; Weigend and Ahlrichs 2005). These systems were evaluated in vacuum and water within the conductor-like polarizable continuum model (CPCM) (Takano and Houk 2005). In all cases, a frequency analysis was carried out to verify the stationary points. Finally, QTAIM analysis was permomed by the Multiwfn package (Lu and Chen 2012) using the def2-TZVP/M06 ORCA output. The images were rendered by the molecular visualizers Chemcraft (Zhurko and Zhurko 2015) and VMD (Humphrey et al. 1996).

Results and discussion

Direct photolysis

Kinetics degradation of SMD, SMT, and SMX at 270-W power and CA0 = 7.18 × 10−5 mol L−1 are shown in Fig. 2. In this figure, it is observed that while SMT and SMD require a time of 60 min for their complete degradation, SMX shows a much faster degradation, since it only takes 8 min, which is 8.5 times faster than SMT and SMD. In addition, experimental data showed a slightly faster degradation rate for SMD than SMT. For example, at a time of 30 min, the degradation of SMT is 70%, while that for SMD is almost 83%. These results reveal that the chemical structure of the molecules plays a main role in their photodegradation.

Fig. 2
figure 2

Direct photolysis of sulfonamides, CA0 = 7.18 × 10−5 M; T = 298 K; pH 0 = 6.5; P = 270 W

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Absorption bands of SMD, SMT, and SMX in a range of 200 to 320 nm are shown in Fig. 3a along with the lamp spectrum. It is evident that the maximum emission of the lamp is in the range of 255 to 270 nm and from 310 to 320 nm, whereas that the main absorption bands for the three SMs are present from 240 to 280 nm; i.e., the energy emitted by the lamp at wavelengths greater than 290 nm is weakly absorbed by the SMs. The absorption band near to 240 nm corresponds to the pyrimidine ring present in the SMT and SMD. Phenyl ring of SMT, SMD, and SMX influenced by the amine and sulfone group exhibits an absorption band at 260 nm. The substituents contribute to improve the π electrons’ delocation through the molecule causing a higher intensity in the absorption bands (Pretsch 2002). The isoxazole N-O bond possesses weak energy, about 201 kJ/mol, meanwhile for C-N and C=N bonds, the energy is 305 and 615 kJ/mol, respectively. Reactivity of isoxazole is susceptible to ring opening through N-O bond cleavage. Ring opening triggers formation of new functional groups to obtain new stabilized species (Zoltewicz and Deady 1978). Since this process involves the formation of new products, it is possible to attribute the rapid degradation of SMX to such phenomena.

Fig. 3
figure 3

a Emission spectrum of the lamp and absorption spectra for SMT, SMD, and SMX at CA0 = 7.18 × 10−5 M, and their evolution as a function of treatment time for (b) SMT, (c) SMD, and (d) SMX

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Figure 3b–d show a similar evolution through time for the phenyl absorption band in the three SMs. A reduction of absorption through time can be noticed; once the degradation process is completed, the phenyl band shows up to only half of the initial intensity for the SMX. This indicates partial rupture of the molecule, reducing the resonance area for the byproducts of degradation. The new absorption band at 255 nm is attributed to the byproducts degradation of the SMT and SMD, while for SMX is observed near 250 nm. Phenyl and pyrimidine bands are not missing completely since a fraction of the structure is still present in the degradation byproducts, such as, C-N and C=N.

Effect of the lamp power and initial concentration of sulfonamides

The effect of the lamp power was carried out by obtaining the degradation kinetics of SMs at powers of 90, 180, 270, and 360 W. These powers corresponded to irradiation intensities of 1.07 × 10−5, 7.65 × 10−5, and 17.06 × 10−5 y 20.19 × 10−5 Einstein s−1 m−2 (Hermosillo-Arellano et al. 2019). It is important to mention that due to the high degradation rate of SMX, its kinetics was obtained in a 30-min period, while for SMT and SMD was 60 min. Figures S3–S5 illustrate the experimental results obtained from the degradation of SMT, SMD, and SMX to different lamp radiation powers, respectively. These figures show that the degradation of the three drugs drastically depends on the intensity of the lamp, since at 90 W, only 12% of SMT and 20% of SMD are degraded in 60 min of exposure, while a complete degradation is achieved at 270 W in periods of 45 and 30 min, correspondingly. In the case of SMX, a more drastic behavior is obtained since a complete degradation is acquired in only 5 min of exposure at 270 W. These results are explained by considering that an increase in irradiation power leads to an increase in the number of photons in the medium available to degrade SMT, SMD, and SMX.

Equation (1) was used to interpret experimental data at different lamp powers. The kap value was determined from a nonlinear fit of the model to the experimental data using the software STATISTICA 7. Table 2 summarizes the values found for the three drugs, where the model correctly interpreted the experimental data since R2 values were obtained near the unit. Additionally, notice that an increase in the lamp power exponentially increases the kap value for the three compounds. It is also observed that the kap values for SMD are between 1.5 and 2 times greater than SMT. Finally, the kap values for SMX are much higher than those found for SMT and SMD.

$$ \frac{{\mathrm{dC}}_{\mathrm{i}}}{\mathrm{dt}}=-{\mathrm{k}}_{\mathrm{ap},\mathrm{i}}{\mathrm{C}}_{\mathrm{i}} $$
(1)

where Ci is the concentration of the compound i, mg L−1; kap,i is the reaction rate constant of the compound i, min−1; and t is the time, min.

Table 2 Apparent rate constants, quantum efficiencies, and degradation percentages of SMT, SMD, and SMX obtained at different lamp powers by direct photolysis. CA0 = 7.18 × 10−5 mol L−1, pH 6.5
Full size table

The efficiency of a photochemical process is determined by calculating the quantum efficiency of the process, which is defined as the number of molecules that have undergone a photochemical process for each photon absorbed by the system (Canonica et al. 2008). For the photochemical reaction that occurs during direct photodegradation of SMs using a polychromatic lamp, the quantum efficiency can be expressed as (Canonica et al. 2008):

$$ {\Phi}_{{\left(200-325\mathrm{nm}\right)}_{\mathrm{i}}}=\frac{{\mathrm{k}}_{{\mathrm{ap}}_{\mathrm{i}}}}{2.303{\mathrm{E}}_{\left(200-325\right)}{\sum}_{\uplambda =200\mathrm{nm}}^{\uplambda =325\mathrm{nm}}\left({\mathrm{f}}_{\uplambda}{\upvarepsilon}_{\uplambda_{\mathrm{i}}}\right)} $$
(2)

where Φ(200–325nm) is the quantum efficiency of the compound i (mol·Einstein−1); E200–325 is the is the photon fluence rate (Einstein·s−1 m−2) in the wavelength interval of 200–325 nm, whose values were reported in the “Experimental system” section; kap,i is the apparent reaction rate constant of the compound i (s−1); ελi is the absorption coefficient of the compound i for a value of λ (m2·mol−1); and fλ is the normalized fraction of energy emitted by the lamp at a determined wavelength; i.e., \( {\sum}_{\lambda =200\mathrm{nm}}^{\lambda =325\mathrm{nm}}{\mathrm{f}}_{\lambda }=1 \).

The Φ values of the three compounds were estimated based on the kap values reported in Table 2 and the absorption spectra presented in Fig. 3a. Table 2 summarizes the values found, where it is important to point out near-zero values for SMT and SMD, indicating that their photo-transformation requires a high consumption of energy, making the process energetically inefficient. On the other hand, the Φ values for SMX were on average 26- and 57-folds higher than those obtained for SMD and SMT indicating that the degradation process is significantly more favorable energetically. Finally, Table 2 shows that the Φ values for the three drugs were increased by augmenting the power of the lamp; thus, for SMX, a maximum value of 0.259 mol·Einstein−1 at a power of 360 W was reached.

Evaluation of the pH effect on the degradation of SMT, SMD, and SMX and DFT analysis

SMs are amphoteric molecules; i.e., they can act as either Bronsted-Lowry acids at pH greater than 8 or as Bronsted-Lowry bases at pH lower than 3. For this reason, in order to evaluate the effect of the species present in their degradation rate, experiments were carried out at four different pH values. The lowest pH corresponded to the pKa1 value where the molecules are distributed in an equimolar manner in a cationic and neutral form. The following value corresponded to pH = 5 for SMT and pH = 4 for SMD and SMX, since under these conditions, the three molecules are in neutral form. The third pH corresponded to the pKa2 value where the sulfonamide is present in its neutral and anionic form in 1:1 ratio. Finally, a pH value of 11 was chosen to ensure that 100% of the species were in a negative form. Degradation kinetics were obtained at CA0 = 7.18 × 10−5 M and 270-W power for SMT and SMD, while for SMX, the applied power was 90 W.

Figure 4 illustrates the kap values obtained as a function of the solution pH for the three sulfonamides. In this figure, it can see the following: (1) the degradation rate of the three sulfonamides is highly dependent on the solution pH; (2) by increasing the solution pH, the kap values varied differently for the three sulfonamides; (3) the maximum kap value was presented at pH values of 4, 2, and 11 for SMX, SMD, and SMT, respectively, highlighting that at these conditions, the molecules are in their neutral, cation-neutral, and anionic forms; and (4) the lowest kap value was obtained at pH values of 11, 11, and 5 for SMX, SMD, and SMT, corresponding to their anionic, neutral, and anionic forms, respectively. These results demonstrate that the formal charge of the species present in the solution plays a fundamental role in the photodegradation rate. The values of the quantum yield in relation to the pH of the solution are recorded in Table 3. The Φ values for the SMT and SMD remain very low regardless of the pH level, while for SMX, a maximum value is reached at pH = 4, since at this value, the highest kap value is reached with a lower absorption of photons.

Fig. 4
figure 4

Variation of kap as a function of the solution pH. CA0 = 7.18 × 10−5 M, T = 298 K; P = 270 W (SMT and SMD), t = 60 min; P = 90 W (SMX), t = 30 min

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Table 3 Variation of the apparent rate constant and quantum efficiency in relation to the pH of the solution. CA0 = 7.18 × 10−5 M
Full size table

The rate of degradation for the SMT showed to be enhanced at pH = 11, because at this pH level, the anionic species of SMT absorbs a greater amount of energy as shown in Fig. 5a. However, this aspect does not seem to be the only factor to consider, because at pH = 2.65, the SMT had the lowest energy absorption and yet its rate of degradation was higher than that obtained at pH = 5 and similar to that evidenced at pH = 7.65. On the other hand, the degradation of the SMD exhibited very similar behavior to the SMT at pH values greater than 8, the anionic forms increasing the electron density in the molecules caused by relocation of negative charge. However, SMD had the slowest degradation rate at pH = 11, even though it presented the highest energy absorption (Fig. 5b). These results could be explained taking into account that the methyl groups in the R substitute are not present in the SMD, so the charge density decreases in that part of the molecule due to absent of inductive effect promote by methyl groups, favoring the photochemical processes.

Fig. 5
figure 5

UV absorption spectrum of (a) SMT, (b) SMD, and (c) SMX at different values of pH. CA0 = 7.18 × 10−5 M

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The degradation of the SMX (Fig. 5c) is mainly the result of the rupture of the N-O bond of the isoxazole ring. The results show that its rupture is more easily achieved when the solution pH is kept at a value of 4, while at superior pH values, the bond becomes more resistant. The above is reflected in the obtained kap values, where this value decreases as the pH increases above 4. This observation is due to decrease of electron density in the isoxazole ring caused by the protonation of the molecule.

The electron density in the molecules was analyzed by computational study. Electron density confers stability over parts of the molecule, which is reflected by covalency in a bond between two atoms. Thus, analysis of bonds’ length represents a way to measure the covalency in a bond that is potentially breakable. To get a better support in regard to the electron density, DFT analysis was carried out in vacuum and in water. Table S2 presents the main changes in the bond lengths caused by the solvation effects, where it is evident that molecules are mainly affected in the sulfone amine moiety, excepting for the protonated amine bonded to the phenyl ring in SMX. The bond distance of the nitrogen and carbon atoms increases, meanwhile the bounds of the nitrogen and carbon with the sulfur atom are shorted.

As mention above, another point to develop involves the analysis of electron density as a function of the solution pH. For it, the critical points of some labile bonds were determined for the systems in gas and aqueous phase. Figure 1 shows the molecular structures of SMs in water phase, where the letters represent the sites of possible fragmentation in the systems. Topological parameters of bond critical points were analyzed for covalent interaction Laplacian of electron density, ∇2ρ(r), total energy density, H(r) kinetic energy density, G(r), and potential energy density, V(r), such as symbol of covalence (see Tables S3–S11). As shown in these tables, all critical points correspond to negatives Laplacians of electron density and negatives H(r)’s. Evidently, all bonds presented are formal bonds.

The fragmentation of molecules with lability in the S-C (SMTw) (Table S5), N-C (SMDw) (Table S6), and N-O (SMXw) (Table S9) bonds was analyzed. These bonds were proposed based on previous literature studies where a degradation pathway was proposed (Batista et al. 2014; Hu et al. 2007). The influence of the medium is such that when analyzing the fragmented bonds corresponding to E in SMT, D in SMD, and E in SMX a decrease in the topological parameters can be observed in comparison with the other bonds involved, where the behavior is opposite, and an increase in the QTAIM values is observed. Thus, based on this analysis, the results presented in Fig. 4 can be explained.

Analysis for SMT (Tables S3 to S5) corroborates experimental observations. In the positively charged system, it can be observed that the values of ρ(r) and ∇2ρ(r) increase when the effects of solvent are included; also, an increase is observed in the value of total energy density; this speaks of an increase in the degree of covalence of bond E when the system is immersed in water. For a neutral state, it does not change the values. Comparing the three systems, the lower values of electron density are found in anionic molecule, indicating at this pH value, easier fragmentation is achieved and therefore a greater kap value is obtained. This phenomenon is related to the resonance in the pyrimidine ring nitrogen and the stabilization through the sulfonamide group. Besides, the inductive effect by the presence of methyl substitutes in the pyrimidine ring increases electron density that leaves S-C bond such as the lowest energy bond in the sulfonamide group.

In neutral and positive state, the resonance stabilization is distributed along the molecule in the same proportion principally in neutral state because in the positive aniline is not available for resonance.

For SMD, it was observed that in the N-C breakable bond of the cationic system (Table S6), the density values remained constant both in the gas phase and in the water phase, but an increase in the value of the ∇2ρ(r) was noted when the system was simulated with the solvent effects. Although, ρ(r) and ∇2ρ(r) parameters diminish from vacuum to water in a negative system, the comparison among the three systems shows that + 1 charged molecules possess the lowest covalence parameters. This is mainly due to the low resonance in the molecule, produced by deactivation of positive charged aniline. In Fig. 4, it is observed that the high value of kap at pH = 2 is related to low covalence. On the other hand, anionic system increases resonance and electron density in the nitrogen of sulfonamide group that involves high increment in covalence parameters. It can be inferred in determinant form that the covalence of the critical point analyzed in the cationic system is affected by pH’s effects.

Finally, in the case of SMX, the topological parameters calculated for the last system are found in Tables S9, S10, and S11; in this case, the main fragmentation occurred in the N-O bond of the isoxazole ring and happened in the system with a positive charge due to the presence of a protonation in the aniline ring. The experimental highest value of kap among the sulfonamides presented was obtained for SMX at pH = 4 but even in pH = 2 is high as well (Fig. 4). Although this slight difference of kap values between pH is not clarified by DFT, it can be inferred that the aniline is not the unique protonated species, could be another one in SMX that modify kap values. Making a comparison of these systems versus those with which there was no rupture of the bond, it was found that the values of ∇2ρ(r) decrease by a value of 0.04 a.u (Table S9), compared with the others, where for the neutral system was obtained a value of 0.01, and for the anionic system, no differences were found; therefore, it can be argued that the N-O bond present in the cationic system suffers a weakening when it passes from gas phase to water phase, so the effect of pH is notorious. In the opposite, in negative charged system, ρ(r) and ∇2ρ(r), 0.01 a.u decreases from gas phase to solvent causing slight effect. The highest values of electron density are observed in neutral state, even H(r) is the highest. In SMX, the Laplacian of density of site E becomes more positive due to protonation form neutral to the cationic species. This lowered in the electronic density in the E bond can be explained by the formation of the intramolecular hydrogen bond between the N21 and H7 (Fig. S1). This hydrogen bond is only made in the cationic structure, explaining why the lability of this bond at acidic pH.

Degradation of the SMT and SMD with HO• and SO4•− radicals

Design of the response surface

The results shown above demonstrated that SMX had much higher quantum yield than those obtained by SMD and SMT. For this reason, degradation for these two compounds was investigated by indirect photolysis using HO• and SO4•− radicals generated by the UV/H2O2 and UV/S2O8−2 systems, respectively. The effect of the pH, temperature, and the initial concentration of the radical promoters was varied according to the experimental design shown in Table S1. A lamp power of 270 W and an initial concentration of SMT and SMD of 7.18 × 10−5 M were employed to obtain their degradation kinetics. The experimental data for Exp1–Exp15 were interpreted by using Eq. 1. The apparent rate constant, kap-i,j, was recorded as a response to the design of experiments, and Table 4 summarizes the results found. The values of kap for each system were fitted with a second-order polynomial regression model in accordance with the following equation:

Table 4 Values of kap obtained when applying the UV/H2O2 and UV/S2O8−2 systems for the degradation of SMT and SMD
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$$ {\mathrm{k}}_{\mathrm{ap}\ \mathrm{i},\mathrm{j}}={\alpha}_0+{\alpha}_1\left[\mathrm{pH}\right]+{\alpha}_2\left[\mathrm{T}\right]+{\alpha}_3\left[\mathrm{C}\right]+{\alpha}_4\left[\mathrm{pH}\right]\left[\mathrm{T}\right]+{\alpha}_5\left[\mathrm{pH}\right]\left[\mathrm{C}\right]+{\alpha}_6\left[\mathrm{C}\right]\left[\mathrm{T}\right]+{\alpha}_7{\left[\mathrm{pH}\right]}^2+{\alpha}_8{\left[\mathrm{T}\right]}^2+{\alpha}_9{\left[\mathrm{C}\right]}^2 $$
(3)

where the subindex i represents the type of sulfonamide, the subindex j represents the oxidation process applied, α0–9 are the coefficients of the regression, and [C] represents the concentration of [H2O2] or [K2S2O8].

The analysis of variance (ANOVA) was performed to evaluate which factors are significant and to verify the deviation of the model. Statistical analysis of the factors was carried out through the hypothesis test (p value) and the F-test. The confidence interval considered was 90%. Thus, the factors or interactions exhibiting p ≤ 0.10 are significant, and the null hypothesis may be rejected. The ANOVA analysis corresponding to the degradation of SMT using the UV/S2O8 and UV/H2O2 systems is presented in Tables S12 and S13, respectively, while those for the SMD in Tables S14 and S15. These tables show that the main factors affecting response behavior were linear, quadratic, and double interaction. Linear factors include the concentration of the oxidizing agent and the pH of the solution, because these factors directly influence the production of SO4•− and HO• radicals and their reactivity. On the other hand, temperature is a factor that only influences the photodegradation of SMT in both systems. The quadratic factors were only evident for the pH of the solution, indicating the presence of a maximum or a minimum level in the response. For the degradation of SMT with the UV/H2O2 system, the synergy between the pH and [C] variables had significant relevance. Finally, the refined regression models for kap i,j are described by the following equation:

$$ {\mathrm{k}}_{\mathrm{SMT}-\mathrm{UV}/\mathrm{K}2\mathrm{S}2\mathrm{O}8}=7.4678\times {10}^{-3}-7.12781\times {10}^{-3}\left[\mathrm{pH}\right]+3.00473\times {10}^{-3}\left[\mathrm{T}\right]+5.42939\times {10}^{-5}\left[\mathrm{K}2\mathrm{S}2\mathrm{O}8\right] $$
(4)
$$ {\displaystyle \begin{array}{l}{\mathrm{k}}_{\mathrm{SMT}-\mathrm{UV}/\mathrm{H}2\mathrm{O}2}=0.020541-4.6140\times {10}^{-3}\left[\mathrm{pH}\right]+1.3116\times {10}^{-3}\left[\mathrm{T}\right]+2.9707\times {10}^{-5}\left[\mathrm{H}2\mathrm{O}2\right]\ \\ {}-1.4834\times {10}^{-6}\left[\mathrm{pH}\right]\left[\mathrm{H}2\mathrm{O}2\right]+7.2774\times {10}^{-4}\left[{\mathrm{pH}}^2\right]\end{array}} $$
(5)
$$ {\mathrm{k}}_{\mathrm{SMD}-\mathrm{UV}/\mathrm{K}2\mathrm{S}2\mathrm{O}8}={\left(0.62684+0.038\left[\mathrm{pH}\right]+5.19324\times {10}^{-5}\left[\mathrm{K}2\mathrm{S}2\mathrm{O}8\right]-3.18702\times {10}^{-3}\left[{\mathrm{pH}}^2\right]\right)}^2-0.5 $$
(6)
$$ {\mathrm{k}}_{\mathrm{SMD}-\mathrm{UV}/\mathrm{H}2\mathrm{O}2}=0.018508+4.2097\times {10}^{-2}\left[\mathrm{pH}\right]+3.27334\times {10}^{-5}\left[\mathrm{H}2\mathrm{O}2\right]-3.54041\times {10}^{-3}\left[{\mathrm{pH}}^2\right] $$
(7)

Figure 6a–d show the relationship between the experimental values of kap against the values predicted by Eqs. (4)–(7), respectively. These figures highlight that the R2 values for three systems are greater than 0.93, while for the SMD–UV/H2O2 system, a value of 0.88 was achieved. These results indicate that the suggested equations interpret the experimental data relatively well.

Fig. 6
figure 6

Calculated values against experimental values of the degradation kinetic constant of SMT (a, b) and SMD (c, d) by applying the UV/K2S2O8 and UV/H2O2 systems, respectively

Full size image

Effect of the type of radical on the degradation of the SMT and SMD

Figure 7 illustrates the kap variation as a function of the initial concentration of H2O2 or K2S2O8, pH of the solution, and temperature for the degradation of SMT (a and c) and SMD (b and d), respectively. These figures clearly show that the kap value is increased almost linearly by increasing the concentration of H2O2 and K2S2O8, regardless of the pH level of the solution or the temperature. For example, for the SMD-UV/K2S2O8 system (Fig. 7d) at a pH of 6 and a temperature of 30 °C, the predicted values of kap are 0.14, 0.35, and 0.56 min−1 for initial concentrations of 1000, 3250, and 5500 μM. These results show that the recombination of radical species does not occur under the experimental conditions studied. Reports in the literature show similar results in the application of UV/K2S2O8 and UV/H2O2 systems to the SMT (Hermosillo-Arellano et al. 2019; Lin and Wu 2018).

Fig. 7
figure 7

Response surfaces for the degradation system UV/H2O2 (a, b) and UV/K2S2O8 (c, d) applied to SMT and SMD, respectively, at different concentrations of oxidant; t = 20 min.; P = 270 W

Full size image

Figure 7 shows that the kap values for the UV/K2S2O8 system were approximately double to those obtained by the UV/H2O2 system for both compounds, independently of the experimental conditions. Even though, in terms of energy, the production of HO• radicals is more favorable than the production of sulfate radicals, according to the following reactions (Ocampo-Pérez et al. 2016):

$$ {\mathrm{H}}_2{\mathrm{O}}_2\overset{+46.4\ \mathrm{Kcal}/\mathrm{mol}}{\to }2{\mathrm{H}\mathrm{O}}^{\bullet } $$
(8)
$$ {\mathrm{S}}_2{{\mathrm{O}}_8}^{2-}\overset{+50.8\ \mathrm{Kcal}/\mathrm{mol}}{\to }2\mathrm{S}{{\mathrm{O}}_4}^{\bullet -} $$
(9)

Therefore, the best efficiency of the sulfate radical can be explained by taking into account the following aspects: (a) SO4•− radicals have a reactivity between 4 and 4.6 times higher than the HO• radicals toward SMT and SMD, respectively, according to their reaction rate constants (kSO4•−,SMT = 3.58 × 1010, kSO4•−,SMD = 4.16 × 1010, kHO•,SMT = 8.81 × 109, and kHO•,SMD = 8.78 × 109 M−1 s−1) (Zhang et al. 2016); (b) the sulfate radical has a half-life time of between 30 and 40 μs which is four orders of magnitude greater than that presented by the hydroxyl radical (10−3 μs) (Xiao et al. 2020b; Ocampo-Pérez et al. 2016), which allows the sulfate radical to have more active time to attack the molecule of the SMT or the SMD; (c) the quantum efficiency of the UV/S2O82− system is higher than that presented by the UV/H2O2 system, indicating that more radicals per mol of absorbed photons are produced for the UV/S2O82− system as indicated by reactions (10) and (11), respectively; (d) both sulfate and hydroxyl radicals are generated simultaneously in the activation mechanism of the sulfate radical, which increases the efficiency of the process according to reactions (12) to (15) (Xiao et al. 2020c; Ocampo-Pérez et al. 2010; Baxendale and Wilson 1957).

$$ {\mathrm{H}}_2{\mathrm{O}}_2+\mathrm{h}\upnu \to 2{\mathrm{H}\mathrm{O}}^{\bullet}\kern2.75em \Phi =1.0 $$
(10)
$$ {\mathrm{S}}_2{\mathrm{O}}_8^{2-}\to 2{\mathrm{S}\mathrm{O}}_4^{\bullet -}\kern3.25em {\displaystyle \begin{array}{c}\Phi =1.4\ \left(\mathrm{deoxygenated}\right)\\ {}1.8\ \left(\mathrm{oxygen}-\mathrm{saturated}\right)\end{array}} $$
(11)
$$ {\mathrm{S}}_2{{\mathrm{O}}_8}^{2-}+\mathrm{h}\upupsilon \to 2\mathrm{S}{{\mathrm{O}}_4}^{\bullet -} $$
(12)
$$ \mathrm{S}{{\mathrm{O}}_4}^{\bullet -}+{\mathrm{H}}_2\mathrm{O}\to \mathrm{S}{{\mathrm{O}}_4}^{2-}+{\mathrm{H}\mathrm{O}}^{\bullet }+{\mathrm{H}}^{+}\kern2.25em \mathrm{k}=\left(0.36-1.0\right)\times {10}^3\ {\mathrm{M}}^{-1}\ {\mathrm{s}}^{-1} $$
(13)
$$ {\mathrm{HO}}^{\bullet }+{\mathrm{S}}_2{\mathrm{O}}_8^{2-}\to \mathrm{HS}{{\mathrm{O}}_4}^{-}+\mathrm{S}{{\mathrm{O}}_4}^{\bullet -}+\frac{1}{2}{\mathrm{O}}_2\kern1.75em \mathrm{k}=\left(0.1-1.2\right)\times {10}^7\ {\mathrm{M}}^{-1}\ {\mathrm{s}}^{-1} $$
(14)
$$ \mathrm{S}{{\mathrm{O}}_4}^{\bullet -}+{\mathrm{HO}}^{\bullet}\to \mathrm{HS}{{\mathrm{O}}_4}^{-}+\frac{1}{2}{\mathrm{O}}_2\kern4.5em \mathrm{k}=\left(0.1-1.0\right)\times {10}^{10}\ {\mathrm{M}}^{-1}\ {\mathrm{s}}^{-1} $$
(15)

Effect of pH and temperature on the degradation of SMT and SMD

The variation of pH showed that, compared with the UV system, the SMD presents greater reactivity and as a consequence the highest values of kap at values close to pKa2 in both oxidation systems. The above occurs for the entire range of temperature analyzed since this factor does not influence its degradation. For SMT, the maximum kap values were obtained at a pH = 2 and at a temperature of 40 °C. These same kap values obtained for SMT and SMD were up to 130 and 60 times higher than using only UV light. The minimum kap values occur at temperatures close to 10 °C and a pH less than 6 for SMT, while SMD displays the minimum values at a pH of 2 and 10, regardless of the temperature.

The results for both drugs when using the UV/H2O2 system show that degradation is unfavorable under alkaline conditions, because at these conditions, H2O2 is deprotonated into the hydroperoxide anion (HO2−, E0 = 0.88 V) according to Eq. (16); this anion decreases the concentration of H2O2 in the medium according to Eq. (17), reducing the production of radicals HO•. Another factor that causes a decrease in efficiency in the basic medium is that the HO• radicals are recombined with the HO− anion producing their conjugate base O•− (Eq. 18) which decreases the participation of the hydroperoxide and other radical species oxygenated in the degradation of the pollutants. Finally, the H2O2 becomes highly unstable at a basic pH, and self-decomposition occurs, so it loses its characteristics as an oxidizer (Eqs. (19) and (20)) which decreases the ability to generate HO• radicals (Acosta-Rangel et al. 2018).

$$ {\mathrm{H}}_2{\mathrm{O}}_2\leftrightarrow {{\mathrm{H}\mathrm{O}}_2}^{-}+{\mathrm{H}}^{+} $$
(16)
$$ {{\mathrm{H}\mathrm{O}}_2}^{-}+{\mathrm{H}}_2{\mathrm{O}}_2\leftrightarrow {\mathrm{H}}_2\mathrm{O}+{\mathrm{O}}_2+{\mathrm{O}\mathrm{H}}^{-} $$
(17)
$$ \mathrm{H}{\mathrm{O}}^{\bullet }+{\mathrm{O}\mathrm{H}}^{-}\overset{\mathrm{k}=1.3\mathrm{x}{10}^{10}{\mathrm{M}}^{-1}{\mathrm{s}}^{-1}}{\to }{\mathrm{O}}^{\bullet -}+{\mathrm{H}}_2\mathrm{O} $$
(18)
$$ {\mathrm{H}}_2{\mathrm{O}}_2+\mathrm{O}{\mathrm{H}}^{-}\leftrightarrow {{\mathrm{H}\mathrm{O}}_2}^{-}+{\mathrm{H}}_2\mathrm{O} $$
(19)
$$ 2{\mathrm{H}}_2{\mathrm{O}}_2\leftrightarrow {\mathrm{O}}_2+2{\mathrm{H}}_2\mathrm{O} $$
(20)

In the UV/K2S2O8 system, one of the main advantages is that sulfate radicals can be thermally activated by applying heat (see reaction 21), resulting in additional activation of SO4•− radicals. Thus, Fig. 7 shows that this synergy was only evident for the degradation of the SMT since the highest kap values were obtained, while for the SMD, temperature was a null factor in the process. For both drugs, degradation at a basic pH with the UV/K2S2O8 system showed low efficiencies, which was attributed to the recombination reactions between sulfate and hydroxyl radicals as demonstrated by Eqs. (22) and (23). Moreover, the reactivity of S2O8−2 is highly dependent on the pH of the solution. Ike et al. (2018) reported that under acidic conditions, the influence of the partially positively charged atom of hydrogen attached to the oxygen in the O-O bond generates a rupture in this bond causing the decomposition of the S2O8−2, with the formation of a single SO4•− radical which is partially transformed into SO3 due to the present acidic environment (Eqs. (26) and (27)).

$$ {\mathrm{S}}_2{{\mathrm{O}}_8}^{2-}+\left[\mathrm{Heat}\right]\to {{2\mathrm{SO}}_4}^{\bullet -} $$
(21)
$$ \mathrm{S}{{\mathrm{O}}_4}^{\bullet -}+\mathrm{H}{\mathrm{O}}^{\bullet}\overset{\mathrm{k}=1.0\mathrm{x}{10}^{10}{\mathrm{M}}^{-1}{\mathrm{s}}^{-1}}{\to }\ \mathrm{HS}{{\mathrm{O}}_5}^{-} $$
(22)
$$ \mathrm{S}{{\mathrm{O}}_4}^{\bullet -}+\mathrm{H}{\mathrm{O}}^{\bullet}\overset{\mathrm{k}=\left(0.01-1.0\right)\mathrm{x}{10}^{10}{\mathrm{M}}^{-1}{\mathrm{s}}^{-1}}{\to }\ \mathrm{HS}{{\mathrm{O}}_4}^{-}+0.5{\mathrm{O}}_2 $$
(23)
$$ {\mathrm{S}}_2{{\mathrm{O}}_8}^{2-}+{\mathrm{H}}^{+}\to {\mathrm{H}\mathrm{S}}_2{{\mathrm{O}}_8}^{-}\to {{\mathrm{S}\mathrm{O}}_4}^{\bullet -}+{{\mathrm{H}\mathrm{S}\mathrm{O}}_4}^{-} $$
(24)
$$ {{\mathrm{SO}}_4}^{\bullet -}\to {\mathrm{SO}}_3+\frac{1}{2}{\mathrm{O}}_2 $$
(25)

Finally, the main advantage of the application of the design of experiments is the capacity to predict the experimental conditions that maximize the SMs degradation, i.e., finding the pH, T, and reagent concentration values that maximize the kap values in the region of study. For SMT and SMD degradation, the optimal coordinates were obtained from the analysis of the stationary points corresponding to Eqs. (4)–(7) using Solver tool of Excel being as follows: pH = 2, T = 40 °C, and [S2O8−2] = 5500 μM for SMT; pH = 2, T = 40 °C, and [H2O2] = 5500 μM for SMT; pH = 6, T = 25–40 °C, and [S2O8−2] = 5500 μM for SMD; and pH = 6, T = 25–40 °C, and [H2O2] = 5500 μM for SMD.

Conclusions

The application of UV radiation proved that SMX can be efficiently degraded independent of operating conditions. However, the quantum yields for SMT and SMD were close to zero, indicating that this system has a low efficiency for these compounds.

The photodegradation of SMX, SMT, and SMD as a function of the solution pH showed that the kap values depend on the amount of radiation absorbed as well as its electronic density. DFT results demonstrated the influence of the medium on the lability of the bonds, obtaining descriptors of atoms in molecules that indicate the weakening of the bonds of S14-C2(SMTw), N17-C18(SMDw), and N22-O22(SMXw).

From a design of experiments using response surface methodology, four statistically reliable equations were obtained to determine the reaction rate constant as a function of the system operating conditions. Moreover, the optimal conditions of pH, temperature, and concentration of H2O2 or S2O8−2 that maximize the degradation of SMT and SMD were identified.

Sulfate radicals proved to have a higher reactivity than hydroxyl radicals to degrade SMT and SMD regardless of the operating conditions of the system, obtaining apparent rate constants almost twofolds higher than those obtained with hydroxyl radicals.