# Sustainable Photodegradation of Amoxicillin in Wastewater with a Nickel Aluminate and ZnO Heterosystem Oxides: Experimental and Gaussian Process Regression Modeling Studies

Mohammed Kebir, Rachida Bouallouche, Noureddine Nasrallah, Hichem Tahraoui, Noureddine Elboughdiri, Farid Ait Merzeg, Faycal Dergal, Saifi Amirouche, Aymen Amine Assadi, Abdeltif Amrane, et al.

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Mohammed Kebir, Rachida Bouallouche, Noureddine Nasrallah, Hichem Tahraoui, Noureddine Elboughdiri, et al.. Sustainable Photodegradation of Amoxicillin in Wastewater with a Nickel Aluminate and ZnO Heterosystem Oxides: Experimental and Gaussian Process Regression Modeling Studies. *Catalysts*, 2024, 14 (12), pp.875. 10.3390/catal14120875. *hal-04833079*

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Article

# Sustainable Photodegradation of Amoxicillin in Wastewater with a Nickel Aluminate and ZnO Heterosystem Oxides: Experimental and Gaussian Process Regression Modeling Studies

Mohammed Kebir <fnref n="1" />,<fnref n="2" /> ID, Rachida Bouallouche <fnref n="3" />, Noureddine Nasrallah <fnref n="3" />, Hichem Tahraoui <fnref n="4" />,<fnref n="5" /> ID,
Noureddine Elboughdiri <fnref n="6" /> ID, Farid Ait Merzeg <fnref n="1" />,<fnref n="2" />, Fayçal Dergal <fnref n="1" />,<fnref n="7" /> ID, Saifi Amirouche <fnref n="1" />, Aymen Amine Assadi <fnref n="8" /> ID,
Abdeltif Amrane <fnref n="5" />,* ID, Mohamed Trari <fnref n="9" /> and Jie Zhang ¹⁰ ID

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**Citation:** Kebir, M.; Bouallouche, R.; Nasrallah, N.; Tahraoui, H.; Elboughdiri, N.; Ait Merzeg, F.; Dergal, F.; Amirouche, S.; Assadi, A.A.; Amrane, A.; et al. Sustainable Photodegradation of Amoxicillin in Wastewater with a Nickel Aluminate and ZnO Heterosystem Oxides: Experimental and Gaussian Process Regression Modeling Studies.
*Catalysts* **2024**, *14*, 875. https://doi.org/10.3390/catal14120875

Received: 6 October 2024

Revised: 20 November 2024

Accepted: 22 November 2024

Published: 29 November 2024

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**Copyright:** © 2024 by the authors.
Licensee MDPI, Basel, Switzerland.
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Attribution (CC BY) license (https://
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4.0/).

**Abstract:** The wastewater generated by the pharmaceutical industry poses a risk to the environment due to undesirable characteristics such as low biodegradability, high levels of contaminants, and the presence of suspended solids, in addition to the high load of organic matter due to the presence of drugs and other emerging products in the effluent. This study aims to reduce the impact of wastewater pollution by removing amoxicillin (AMO) antibiotics as an organic pollutant. In this concept, two synthesized catalysts, NiAl₂O₄ and ZnO, are sensitive oxides to light energy. The prepared materials were then characterized using X-ray diffraction, UV-vis solid reflectance diffuse, Raman spectroscopy, scanning electron microscopy, BET, and ATR-FTIR spectroscopy. The effects of principal operating parameters under sunlight, namely, the percentage of the mixture of NiAl₂O₄ and ZnO, the pH of the medium, and the initial concentration of the antibiotic were studied experimentally to determine the optimal conditions for achieving a high degradation rate. The results showed that photodegradation is higher at a pH of 6, with a weight percentage of the mixture of 50% for both catalysts in 1 g/L of the total catalyst dose. Then, the effect of the initial concentration of AMO on the photodegradation reaction showed an important influence on the photodegradation process; as the degradation rate decreases, the initial AMO concentration increases. A high degradation rate of 92% was obtained for an initial AMO concentration of 10 mg/L and a pH of 6. The kinetic study of degradation established that the first-order model and the Langmuir-Hinshelwood (LH) mechanism fit the experimental data perfectly. The study showed the success of using heterosystem photocatalysts and sustainable energy

<footnote n="1">¹ Centre de Recherche Scientifique et Technique en Analyses Physico-Chimiques (CRAPC), BP 384, Bou-Ismail, Tipaza 42004, Algeria; medkebir@yahoo.fr (M.K.); farid.aitmerzeg@gmail.com (F.A.M.); dergalf@yahoo.fr (F.D.); say.amirouche@yahoo.fr (S.A.)</footnote>

<footnote n="2">2 "Unité de Recherche en Analyses Physico-Chimiques des Milieux Fluides et Sols", Centre de Recherche Scientifique et Technique en Analyses Physico-Chimiques (URAPC-MFS/CRAPC), 11, Chemin Doudou Mokhtar, Ben Aknoun 16100, Algeria</footnote>

<footnote n="3">3 Laboratory of Reaction Engineering, Faculty of Mechanical Engineering and Process Engineering, University of Science and Technology Houari Boumediene (USTHB), BP 32, Algiers 16111, Algeria; r.bouallouche@mesrs.dz (R.B.); nas_nour@yahoo.fr (N.N.)</footnote>

<footnote n="4">4 Laboratoire de Biomatériaux et Phénomènes de Transports (LBMPT), Université Yahia Fares de Médéa Pôle Urbain, Médéa 26000, Algeria; hichemm.tahraouii@gmail.com</footnote>

<footnote n="5">5 National Center for Scientific Research (CNRS), National School of Chemistry of Rennes, University of Rennes, ISCR—UMR6226, F-35000 Rennes, France</footnote>

<footnote n="6">6 Chemical Engineering Department, College of Engineering, University of Ha'il, P.O. Box 2440, Ha'il 81441, Saudi Arabia; ghilaninouri@yahoo.fr</footnote>

<footnote n="7">7 Laboratoire de Catalyse et Synthèse en Chimie Organique (LCSCO), Faculté des Sciences, Université de Tlemcen, BP 119, Tlemcen 13000, Algeria</footnote>

<footnote n="8">8 College of Engineering, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia; aaassadi@imamu.edu.sa</footnote>

<footnote n="9">9 Laboratory of Storage and Valorization of Renewable Energies (LSVER), Faculty of Chemistry, University of Science and Technology Houari Boumediene (USTHB), BP 32, Algiers 16111, Algeria; mtrari.usthb@yahoo.fr
10 School of Chemical Engineering and Advanced Materials, Newcastle University, Newcastle upon Tyne NE1 7RU, UK; jie.zhang@newcastle.ac.uk</footnote>

<footnote>* Correspondence: abdeltif.amrane@univ-rennes1.fr</footnote>
for effective pharmaceutical removal, which can be extended to treat wastewater with other organic emerging pollutants. On the other hand, modeling was introduced using Gaussian process regression (GPR) to predict the degradation rate of AMO under sunlight in the presence of heterogeneous ZnO and NiAl₂O₄ systems. The model evaluation criteria of GPR in terms of statistical coefficients and errors show very interesting results and the performance of the model used. Where statistical coefficients were close to one (R = 0.9981), statistical errors were very small (RMSE = 0.1943 and MAE = 0.0518). The results suggest that the model has a strong predictive power and can be used to optimize the process of AMO removal from wastewater.

**Keywords:** pharmaceutical industry; wastewater; photodegradation; heterosystem; kinetic; Gaussian process regression

# 1. Introduction

The availability of drinking water for safe consumption is a challenge and a determining factor in the prevention of water-related diseases, and so it must be given special attention. Around the world, many raw water sources contain toxic chemicals, harmful microorganisms, or other substances that make the water unfit for human consumption [1,2]. The discharge of wastewater laden with emerging pollutants into the environment without any prior treatment is also a growing cause for concern, given the undesirable effects it can have on human health and the ecosystem [3,4]. The poor water quality is due to problems of natural and/or man-made origin. The presence of pharmaceutical molecules in the environment, whether in water, soil, or living organisms, has given rise to concern due to their potential impact on ecosystems. The increase in their concentration in the environment has cascading effects on the ecosystem [5]. These compounds enter the environment via several routes, such as residues and waste from the pharmaceutical industrial process, excretion by humans and animals, and the disposal of expired or unused products [6].

The drug AMO is part of the large family of antibiotics mostly prescribed for the treatment of various bacterial infections in humans and animals. Like any emerging pollutants, AMO can enter and pass through wastewater treatment plants and end up in rivers, lakes, and groundwater, and, therefore, carries with it certain potential risks and adverse effects. Studies have also shown that exposure to antibiotics in surface waters, even at trace concentrations, can have adverse effects on non-target organisms in the environment, such as algae, fish, and invertebrates [7]. Numerous studies conducted over the past few years have confirmed the potential risk of antibiotics in surface waters to the environment and human health [5]. Some of these antibiotics are shown to have carcinogenic, teratogenic, genotoxic, and allergenic properties [8]. With this in mind, considerable efforts have been made by researchers around the world to better understand and reduce the environmental impact of pharmaceutical products such as AMO [9]. These include regulating the manufacture and use of pharmaceuticals, improving wastewater treatment technologies, and developing highly efficient disposal methods [10]. However, wastewater from the pharmaceutical industry and hospitals is not always treated before discharge into the environment and, in most cases, only physical processes are used [11]. Therefore, measures must be taken to ensure that water intended for human consumption does not contain any dangerous chemical substances or germs that are harmful to human health.

However, most current wastewater treatment processes are not designed to remove pharmaceutical pollutants and antibiotics such as AMO with the application of cost-effective and efficient methods. As a result, researchers have been considering less expensive alternatives, based on materials, such as biomaterials and catalysts for pollutant removal [12]. In recent times, there has been a growing interest among scientists in the development of visible light photocatalysts due to the limitations of conventional methods in effectively removing pollutants [13–16]. This area of research has gained significant attention and has become highly active. These photocatalysts offer a novel approach to
harness renewable energies, such as sunlight, more efficiently and expand their applica-
tions, particularly in environmental contexts such as carbon dioxide reduction, hydrogen
production, and the treatment of pollutants through photoreduction or photodegradation,
depending on the specific nature of the pollutants [17].

It is shown that the combination of semiconductors leads to a synergistic effect that enhances the overall catalytic activity and constitutes a significant strategy for improving the catalytic performances of the materials utilized in order to increase the separation of electron-hole pairs (e⁻, h⁺) between oxides and during the photodegradation process, which lowers the rate of recombination [18–20]. This approach has some benefits, and it can overcome the limitations associated with individual semiconductors. In the context of photocatalysis, heterogeneous photocatalysis expands on the absorption of sunlight photons by a semiconductor material [21,22]. Specifically, this process involves the absorption of photons with energy equal to or above the band gap (Ec-Ev) of the semiconductor, which boosts the photocatalytic activity under sunlight, offering resistance against photocorrosion or degradation. As a result of enhanced charge separation, electrons are able to transition from the valence band (Ev) to the conduction band (Ec). Electronic gaps, often referred to as holes (h⁺), are produced inside the valence band, resulting in the formation of a redox system [17]. During their lifespan, electrons have the ability to be transported to electron acceptors, whereas holes may be filled by electron donors. Chemical transformations referred to as *p*-type occur when the resultant chemical species undergo reactions prior to the occurrence of reverse electron transfers [23].

In general, the utilization of many components within a heterosystem for photo-
catalysis yields synergistic effects and results in improved performance, as opposed to
the utilization of a single component in isolation [24]. The optimal selection of compo-
nents is contingent upon the specific photocatalytic reaction and the desired attributes of
the system, including selectivity, efficiency, and stability [25–27]. The novel heterojunc-
tion materials used in recent studies have shown exceptional photocatalytic effectiveness
of over 96%. Over 80 min, yolk–shell nanostructures such as Fe₃O₄@void@CuO/ZnO
demonstrated an amoxicillin degradation efficiency of up to 97.6% [28]. Within an hour, the
FeS₂/g-C₃N₅ heterojunction achieved a remarkable 96% tetracycline degradation rate under
ideal conditions [29]. Nevertheless, the artificial photocatalyst, known as O20gCN/ZIS20,
demonstrated exceptional photocatalytic performance, achieving a 98.9% ciprofloxacin
degradation rate in less than 60 min [30].

Effective techniques must be used in order to maximize the utilization of operational
data and improve the decision-making process. Artificial intelligence (AI) is an advanced
technology that may be employed in this task owing to its advantages in anticipating
different influencing factors in wastewater treatment processes on achieving high accu-
racy, increasing productivity, gaining time, lowering costs, and improving environmental
sustainability [31–33]. Artificial neural networks, support vector regression, genetic algo-
rithms, particle swarm algorithms, random forests, and Gaussian process regression (GPR)
are the approaches most often employed in modeling and optimization in the wastewater
treatment area [34].

In this study, we focus on the use of heterogeneous photocatalysis for the degradation
of pharmaceutical contaminants using heterosystem NiAl₂O₄/ZnO due to their potential
synergetic effect under sunlight energy. In addition, the effect of some operating parameters
is studied. The synthesis of the NiAl₂O₄ is carried out using the nitrate method while the
ZnO is obtained by the sol-gel modified method. Both oxides are subjected to different
characterization techniques of crystallite phase, morphology, chemical composition, and
chemical functional groups by TGA/DTA, XRD, SEM, DRS, BET, RAMAN, and ATR-
FTIR to confirm if the synthesis is successful. In addition, the photodegradation of AMO
under sunlight is verified by optimizing the effect of operating parameters such as pH, the
heterogenous weight percentage, and the initial concentration of AMO. Furthermore, AMO
photodegradation mechanism in the presence of a ZnO and NiAl₂O₄ system is proposed
and discussed in detail. Additionally, the photodegradation of AMO is analyzed using
the LH kinetic model. AI is used in this study to achieve optimal control of photocatalytic
reaction conditions for predicting the removal efficiency of AMO.

The novelty of this work lies in the synthesis and comprehensive characterization of NiAl₂O₄ and ZnO catalysts, combined with the innovative application of Gaussian process regression (GPR) to predict the degradation rate of AMO under sunlight in the presence of these catalysts. The study provides an in-depth analysis of the catalysts' properties. Furthermore, the use of GPR, with the optimization of ten different kernel functions, offers a novel approach to modeling complex, non-linear relationships in photodegradation processes, enhancing the prediction accuracy and understanding of the factors influencing AMO degradation. This work presents a contribution of using heterogeneous photocatalysis as an advanced oxidation process favored under sunlight; this clean, sustainable, and new avenue constitutes an easy green solution in the field of pharmaceutical effluents treatment compared to other technologies limited or lacking in treatment efficiency.

**2. Results and Discussion**

2.1. *Structural, Morphological, and Chemical Analysis*

The thermal stability of the ZnO and NiAl₂O₄ catalysts was investigated at high temperatures by the use of thermogravimetry analysis (TGA) and differential thermal analysis (DTA) in a nitrogen atmosphere, and the results are displayed in Figure 1a,b. The obtained data for ZnO are shown in Figure 1a. As shown, a preliminary reduction in mass of 10% was found within the temperature range of 25 to 150 °C, which may be attributed to the evaporation of water molecules and the removal of moisture content. The observed decrease in weight, amounting to 44%, may be attributed to the emission of carbon dioxide and carbon monoxide in the gaseous state. Subsequently, a plateau is seen in the temperature range up to 400 °C, suggesting that 500 °C is the optimal temperature for achieving the desired pure phase of zinc oxide [35]. The presence of two endothermic peaks seen in the differential thermal analysis (DTA) curve, occurring at temperatures of 190 °C and 539 °C, provides evidence for a two-step breakdown process of the precursor reagents.

Figure 1b illustrates the thermal characteristics of the NiAl₂O₄ mixture precursors prior to the process of defining the best calcination temperature. As can be seen from the thermogravimetric analysis, it is evident that there are two principal stages of mass loss that can be noted. The initial stage involves a decrease in weight mass within the temperature range from 25 to 250 °C. This decrease is mostly related to the removal of physically adsorbed water molecules accompanied by the beginning of nitrate decomposition [36,37]. Whereas, the subsequent phase of gradual and continuous weight loss, occurring within the detected temperature ranging from 250 to 500 °C, is associated with the disintegration of all nitrates. In this regard, a modest decrease in weight was seen at temperatures ranging up to 500 to 1000 °C. This analysis indicated that the desired crystallite phase of spinel should be achieved at an approximate temperature of 850 °C; a further increase in temperature did not show any mass modification [38]. Also, NiAl₂O₄ spinal exhibits much better thermal stability at temperatures up to 850 °C [39].

The structure crystalline of ZnO and NiAl₂O₄ semiconductors was examined by X-ray
diffraction (XRD) analysis; the obtained data are presented in Figure 2a,b. The XRD pattern
of ZnO (Figure 2a) exhibited diffraction peaks at the following positions: 31.73°; 34.37°;
36.21°; 47.52°; 56.56°; 62.84°; 67.91°; and 69.06°; these peaks are attributed to the indexed
(100), (002), (101), (102), (110), (103), (112), and (201) plans according to the ICDD-Card:
01-080-5081 [40], which confirmed the (P63mc) crystalline hexagonal wurtzite structure
with lattice parameters of a = b = 3.2488 Å and c = 5.2054 Å, after comparing the diffraction
angles with those reported on the ICDD-Card: 01-080-5081.
<figure><img src="image_5.png" /><figcaption>**Figure 1.** TGA and DTA plot of the reagents mixture used for (a) ZnO and (b) NiAl₂O₄ synthesis under air environment.</figcaption></figure>

Figure 2b shows an X-ray diffractogram of spinel NiAl₂O₄ prepared by the nitrate method; the peaks were recorded for 10 s at each step of 0.02° over the interval 5–85°; the peaks observed are fine and with high intensity indicating the formation of the spinel structure in perfect agreement with the ICDD-Card: 00-010-0339 and with the P63mc sample [41]. The lattice parameters are a = b = 3.2417 nm and c = 5.1876 nm. At 850 °C, the spinel obtained is bluish green in color and the DRX spectrum showed the main peaks corresponding to the crystal planes for the spinel were the hkl reflection of 220, 311, 400, 420, 511, 440, 620, and 533. The clear peak reveals the single-phase purity of NiAl₂O₄ with improved crystallinity. The average crystallite size calculated according to the full width at
half maximum (FWHM) formula, which typically involves the Scherrer equation, revealed 13.07 nm and 22.10 nm for NiAl₂O₄ and ZnO, respectively.

<figure><img src="image_6.png" /><figcaption>**Figure 2.** XRD patterns of (a) the spinel NiAl₂O₄ synthesized by nitrate route and (b) ZnO prepared by sol-gel mediated green synthesis process.</figcaption></figure>

The SEM micrograph of the ZnO prepared by the modified sol-gel synthesis method is shown in Figure 3a, revealing regular spherical morphology ZnO particles; the formation of bigger nanoparticles may potentially lead to the blockage of holes due to the potential aggregation phenomenon.
<figure><img src="image_7.png" /><figcaption>**Figure 3.** SEM micrographs of prepared (a) ZnO and (b) spinel NiAl₂O₄.</figcaption></figure>

On the other hand, SEM was used to investigate the morphological characteristics of NiAl₂O₄ that had been produced using the nitrate technique and heated until 900 °C. The results are shown in Figure 3b. The micrograph displays a heterogeneous structure with potential for aggregation and agglomeration.

The spinel NiAl₂O₄ has an optical bandgap of 1.72 electron volts (eV), but the synthesized ZnO demonstrates a bandgap energy of 3.26 eV, making it highly compatible with the solar spectrum. Additionally, the ZnO displays a considerable level of conductivity with *p*-type conduction. The *n*-type semiconductor ZnO acts as a mediator between the conduction band of the *p*-type spinel NiAl₂O₄ and the ionic species of AMOX. However, the concurrent use of these semiconductors facilitates enhanced charge separation via a synergistic mechanism, hence extending the spectrum sensitivity of ZnO to include higher wavelengths of light absorption. As a result, this process effectively impedes the rate at which charge carriers recombine.
The BET surface analysis is a common technique used to determine surface properties such as the specific surface area of a material as an essential parameter in catalyst and photocatalyst fields; in our study, BET analysis gives particular specific surface area values of 0.7198 m²/g and 12.35 m²/g for NiAl₂O₄ and ZnO catalysts, respectively. The obtained data confirmed the mesoporous structures.

Raman spectroscopy is a powerful analytical technique that exploits the Raman scattering effect to provide non-destructive information about molecular vibrations, rotations, and other low-frequency modes, acting as a molecular fingerprint [42]. In the context of the multi-component, Raman spectroscopy allows for the identification of characteristic Raman peaks corresponding to different materials.

The image taken by Raman microscopy shows two zones in the NiAl₂O₄ materials (BLUE and WHITE); therefore, we performed a spectrum for each zone and a spectrum for ZnO alone. Figure 4 shows the characteristic peaks of ZnO corresponding to the incident light of the Raman laser, and were directed along the axis [0001] orientation at 98 cm⁻¹ and 437 cm⁻¹, respectively [42].

<figure><img src="image_8.png" /><figcaption>**Figure 4.** Raman spectra of ZnO, NiAl₂O₄ (white zone), and NiAl₂O₄ (blue zone).</figcaption></figure>

The Raman spectrum of the catalyst is presented in Figure 4. A mixture of ZnO and NiAl₂O₄ was the small band at 372 cm⁻¹ and the more intense one at 1042 cm⁻¹, which corresponds to the fingerprint of the second order of ZnO Raman. In fact, the second-order Raman spectrum can be obtained using the Resonance Raman effect and the choice of the exciting line is important. Our experimental conditions are not the same as those used by Joshi et al. and particularly the laser radiation. With the same exciting line at 633 nm [43], we observe the same band between the blue and white zones with low intensities for the blue zone at 352, 595, 748, and 842 cm⁻¹; Sousa et al. reported the same peaks in their works [43,44]. The other bands observed at 1140 cm⁻¹ and also present in the Raman spectra of references [44,45], are in our case, representative of fundamental modes but have too high wavenumber values to be assigned to nickel oxide species. They are in agreement with carbonate stretching vibrations resulting from CO₂ absorption at the surface of the zinc oxide phase.

The difference in zones demonstrated by Raman and by microscopy led us to perform a Raman mapping of our materials in order to see the distribution of the two compounds; we took as a reference the peak at 437 cm⁻¹ of ZnO (in red) and the peak at 1042 cm⁻¹ of
NiAl₂O₄ (in blue). Figure 5 shows the homogeneous distribution with areas that contain both materials.

<figure><img src="image_9.png" /><figcaption>**Figure 5.** Raman mapping of NiAl₂O₄.</figcaption></figure>

The ATR-FTIR spectra of ZnO oxide nanopowder illustrated in Figure 6a shows several peaks at 407 cm⁻¹, 430 cm⁻¹, 594 cm⁻¹, 782 cm⁻¹, 1096 cm⁻¹, 1334 cm⁻¹, 1572 cm⁻¹, 1976 cm⁻¹, 2046 cm⁻¹ and 3324 cm⁻¹; the presence of many chemical components, including alkaloids, glycosides, flavonoids, and steroids in citron lemon may account for the observed number of functional groups [46]. These compounds are known to have reducing and capping properties. It was observed that the sharp peak positioned at 430 cm⁻¹ can be deduced to the Zn–O stretching bonds [47,48]. However, the bands shown in Figure 6a. are in the region of 600–1700 cm⁻¹ and correspond to the functional groups C=O, C–O, and C–H, respectively [40,49]. Another, broad peak at 3324 cm⁻¹ can be due to the O–H stretching vibrations and bending modes of the adsorbed water [50].

Figure 6b illustrates the ATR-FT-IR spectra of the prepared NiAl₂O₄ compound, which showed a discernible vibrational peak within the range of 500–900 cm⁻¹, which accounts for the vibrations of metal-O, Al-O, and metal-O-Al bonds [51]. Furthermore, the high-frequency peaks observed at 715, 490, and 417 cm⁻¹ may be due to the stretching vibrations of Al-O and Ni-O bonds in both octahedral and tetrahedral locations, specifically involving Ni⁺² and Al³⁺ ions. These data indicated the formation of a pure single phase of NiAl₂O₄ [52].

## 2.2. *Sunlight Photocatalytic Degradation of AMO*

The typical procedure for the amoxicillin (AMO) (Sigma-Aldrich, 99.5%) photodegradation experiment is as follows: 1 g/L of the NiAl₂O₄ and ZnO heterosystems ((100 − x) NiAl₂O₄ / x ZnO)) were x is varied from 0 to 100%, the two photocatalysts were dissolved in 200 mL of AMO of well-defined concentration, the pH of the solution was adjusted to 4.5 and then to 10 by the addition of a few drops of NaOH (1 M) or HCl (0.1 N), and their value is made by pH-meter (Hanna pH 211). Next, the solution was left to stir in the dark for 2 h to ensure the formation of an adsorption–desorption equilibrium between the NiAl₂O₄ and ZnO heterosystem oxides; samples of the adsorption were taken prior to the sun irradiation. The solution was subsequently exposed to solar irradiation, while kept under magnetic stirring. Samples of the suspension were taken at regular intervals, and then centrifuged to settle the photocatalytic particles, the temperature of the mixture solution was controlled with a thermostated bath (Julabo). The filtrates obtained were
analyzed at wavelength 270 nm using a Shimadzu 1800 UV-visible spectrophotometer, manufactured by Nakagyoku, Kyoto, Japan [53].

<figure><img src="image_10.png" /></figure>

<figure><img src="image_11.png" /><figcaption>**Figure 6.** ATR-FTIR spectra of (a) ZnO and (b) NiAl₂O₄ spinel.</figcaption></figure>
The photodegradation efficiency (R%) of AMO on the NiAl₂O₄/ZnO heterosystem was calculated from the initial concentrations (Co) and (Ct) at a time (t) according to the following equation:

$$R\% = \left( \frac{Co - Ct}{Co} \right) \times 100 \quad (1)$$

### 2.2.1. Effect of Heterosystem Percentage on AMO Elimination Rate

It is important to note that the combination of material oxides exhibited different gap energy and with different weight ratios can lead to involving a new heterosystem with high performance because it offers a synergy effect, light absorption, and emission characteristics. Therefore, it is crucial to consider this parameter in the optimization of operating parameters. To evaluate the effect of this parameter on the AMO performance photodegradation, a series of solutions have been prepared where the weight percentages were varied between NiAl₂O₄ and ZnO materials (mg catalysts/mL solution). For instance, a pollution solution containing 0, 25, 50, 75, and 100% of the weight percentage of NiAl₂O₄ in a global catalysts concentration of 1 g/L at a pH of 6 and an initial AMO concentration of 30 mg/L. The mixture solution was irradiated under sunlight. Figure 7 shows the removal efficiency of AMO photodegradation by studying the effect of the percentage heterosystem of two oxides.

<figure><img src="image_12.png" /><figcaption>Figure 7. The photodegradation efficiency of AMO as a function of different percentages of (100 - x) NiAl₂O₄ / x ZnO under sunlight irradiation.</figcaption></figure>

According to Figure 7, it was observed that the removal efficiency of the photodegradation of the heterosystem for different percentages of composition was increased compared to bare NiAl₂O₄ (100%) and ZnO (100%). Otherwise, the excess 150% of ZnO or NiAl₂O₄ decreases the photodegradation activity of AMO.

According to the obtained data, it was noted the percentage of 50% NiAl₂O₄ (50%) ZnO for a total weight of 1 g/L of catalysts exhibited a high photodegradation efficiency of AMO within 160 min, this can be explained by the synergy effect of the heterosystem between NiAl₂O₄ and ZnO, which promotes the photodegradation efficiency of AMO under sunlight irradiation. In addition, the present heterosystem ensures a good charge separation (electron-hole pairs) and consequently increases the charge carrier lifetime.
### 2.2.2. Effect of pH

Previous studies have shown that pH is a parameter that can impact the photodegradation process of AMO in aqueous media, and also that the catalyst surface charge can be positive, negative or neutral. However, the specific effects may vary depending on the AMO and the experimental conditions [54].

To study the effects of this parameter on the photodegradation activity of the heterosystem, different pH values ranging from 3 to 10 of the solution of 30 mg/L of AMO are obtained by adding the HCl or NaOH with 0.01 M; the initial AMO concentration is taken. The rate efficiency of AMO photodegradation is illustrated in Figure 8.

<figure><img src="image_13.png" /><figcaption>**Figure 8.** The effect of pH on the photodegradation of AMOX at different pH values (AMO = 30 mg/L, total weight of catalyst 1 g/L (50% ZnO (0.5 g/L) et 50% NiAl₂O₄ (0.5 g/L)).</figcaption></figure>

From Figure 8, an increase is observed in the photodegradation with increasing pH; the high removal efficiency is obtained at a pH value of 6 within 160 min of irradiation time; this finding can be due to the good electrostatic interactions that occur between the surface of two oxides and AMO molecules. It can also be explained by the availability of concentrated active hydroxyl radicals in the solution; these radicals are responsible for the oxidation of AMO molecules [55].

Moreover, the low value of the removal efficiency of photodegradation can be due to the instability of the ZnO at an acidic medium, in addition to the low production of radical hydroxyl at these pH values.

In addition, the efficiency of the photocatalytic process is directly linked to the surface charges of the two catalysts and the distribution of the pollutant molecules. Furthermore, the ionic nature of the antibiotic can cause electrostatic interactions between the catalyst and the pollutant [56]. Based on the previous study, the considered optimal pH of the AMO solution is 6.

### 2.2.3. Effect of Initial Concentration of AMO

The concentration of pollutants in industrial, urban, and hospital effluents varies over time. It is, therefore, essential to study the parallel behavior of photochemical degradation over a very wide concentration range of the AMO molecule chosen as the pollutant of interest in this work. It is clear that the initial concentration of AMO can affect the catalytic photodegradation process, on one hand, by influencing the reaction kinetics, and on the
other hand, the limitation of light absorption and the phenomenon of mass transfer and catalyst poisoning. To investigate the effect of this parameter, experiments are carried out in the range between 20 and 60 mg/L of AMO at a pH value of 6 for a fixed total concentration of 1 g/L (50% NiAl₂O₄/50% ZnO).

Figure 9 shows the evolution of AMO disappearance kinetics at various initial concentrations.

<figure><img src="image_14.png" /><figcaption>Figure 9. Photodegradation plots of AMOX removal efficiency as a function of time.</figcaption></figure>

Figure 9 displays the effect of different AMOX concentrations that varied from 20 to 60 mg/L on the photodegradation process in the presence of the heterosystem NiAl₂O₄/ZnO and under the optimized condition previously. It was observed that an increase in AMO initial concentration leads to an increase in the amount of decomposed organic molecules along with a decrease in the photodegradation efficiency.

This study revealed a significant rate efficiency of 98% obtained for the initial AMO concentration of 20 mg/L; these data are consistent with the literature studies that found the same behavior when raising the initial pollutant concentration [57,58]. However, determining the optimal initial concentration of the pollutant is a crucial factor for the target to overcome the problems limiting the removal efficiency, such as the increase in the turbidity of solution, which reduces the light penetration to reach the catalyst surface, thereby causing a decrease in the oxidation reaction [59].

Moreover, the reduction of the photodegradation efficiency can be explained in several ways: for the low initial AMO concentration, a more ready active site on the catalyst surface was available; however, with increasing initial concentration for the same amount of catalyst, the same free active sites were filled, and the rate of the reactions and the production of hydroxyl radicals were reduced. Consequently, fewer hydroxyl radicals are produced for the photocatalytic reaction of the heterosystem NiAl₂O₄/ZnO [60].

## 2.3. Kinetic Study of Photodegradation

The utilization of a kinetic approach is commonly employed to gain a comprehensive understanding of the heterogeneous catalytic photodegradation of organic molecules, such as AMO. This approach enables the determination of the reaction order and the values of different kinetic constants associated with the process. Moreover, this approach is based on the Langmuir–Hinshelwood model, widely applied to describe experimental results of
heterogeneous photocatalysis reactions, linking the rate of disappearance of a compound to its concentration in solution. This model is based on the adsorption of the substrate onto the oxide, which is considered the most important step in the process, followed by a photochemical reaction due to the absorption of light energy and the regeneration of the electron-hole pairs involved in the catalytic reaction, as described by the Hinshelwood model, according to the following equation:

$$V = -\frac{dC}{dt} = k_{\text{app}} \times C \qquad (2)$$

where

V: Photodegradation rate (mg L⁻¹·min⁻¹)

k<sub>app</sub>: Apparent photodegradation constant (min⁻¹)

C: Pollutant solution concentration (mg L⁻¹)

t: Irradiation time (min)

Integrating Equation (1) yields the following relationship, with C = Co at t = 0, where Co is the initial concentration in the bulk solution after reaching the equilibrium dark adsorption and t is the reaction time.

The resulting integration leads to the following equation:

$$\ln\left(\frac{C_o}{C_t}\right) = k_{\text{app}} \times t \qquad (3)$$

plotting Ln(C/Co) as a function of time (t) is linear, with k<sub>app</sub> being the apparent rate constant of the first-order reaction, and Ce being the equilibrium concentration of the catalysts after adsorption.

k<sub>app</sub> is the apparent rate constant. Thus, if we plot ln (Co/C) as a function of time, and if degradation follows an L-H mechanism, a straight line is obtained. The slope of this line is then used to determine the apparent rate constant k<sub>app</sub>. To determine Kr and Ks, it is necessary to degrade the substrate at different concentrations of AMO.

$$\frac{1}{k_{\text{app}}} = \frac{1}{k_{r}k_{s}} + \frac{C_{o}}{k_{r}} \qquad (4)$$

The graphical representation of -Ln(C/Co) as a function of time is given in Figure 10. These later representations give straight lines with good linearity, as the correlation coefficients are greater than 0.985. These results suggested that the photodegradation of AMO approximately follows the kinetics of apparent first-order regarding the initial concentration of the pollutant in the concentration range studied. Also, the values of the apparent constants, half-reaction times, and the coverage rate of the catalyst surface for the pharmaceutical pollutant is shown in Table 1.

<table><caption>**Table 1.** Photocatalysis degradation kinetic parameters for different concentrations.</caption><thead><tr><th>C (mg/L)</th><th>K<sub>app</sub> (1/min)</th><th>t<sub>1/2</sub> (min)</th><th>R<sup>2</sup></th><th>K<sub>C</sub> (L/mg)</th><th>K<sub>H</sub></th><th>θ</th></tr></thead><tbody><tr><td>20</td><td>0.0086</td><td>80.5</td><td>0.9941</td><td rowspan="3">0.0619</td><td rowspan="3">0.1893</td><td>8.526 × 10<sup>-3</sup></td></tr><tr><td>30</td><td>0.0074</td><td>93.6</td><td>0.9419</td><td>7.345 × 10<sup>-3</sup></td></tr><tr><td>40</td><td>0.0065</td><td>106.63</td><td>0.9588</td><td>6.458 × 10<sup>-3</sup></td></tr></tbody></table>

On the other hand, from the data in the table, we can see that the rate of photodegradation is strongly related to solution loading in the case of AMO and varies slightly in the case of AMO. Moreover, the apparent kinetic constants decrease with increasing initial concentration for both molecules. This is explained by the fact that at high pollutant con-
centrations, photons cannot reach their target due to the impermeability of the solution to be treated.

<figure><img src="image_15.png" /><figcaption>**Figure 10.** The kinetic photodegradation of AMO for different initial concentrations.</figcaption></figure>

Another way of checking order one is to calculate the product Kapp, t1/2, which should be constant and equal to Ln(2). The table clearly shows that the product is constant and its numerical value is very close to Ln(2) for kinetics.

From the values of the constants of both adsorption and photocatalysis models, we observe that KH (0.189288 L/mg) is significantly higher than Kc (0.061954 L/mg), as seen in Table 1. This result is frequently encountered in the literature, i.e., the constant calculated under irradiation KH is stronger than Kc calculated in the dark. Several hypotheses have been put forward to explain this difference between the two constants Kc and KH. For example, this increase in KH is due to photoadsorption, and the photodegradation reaction takes place not only on the surface but also in the solution. In addition, the decline in the coverage rate θ of the heterosystem surface is attributed to the propensity of AMO molecules to cluster and create a dense layer that obscures the catalyst's active sites [61,62].

According to the results obtained for each concentration, the Langmuir-Hinshelwood model is confirmed in the photodegradation of our pollutant.

## 2.4. Photodegradation Mechanism

The mechanistic study proposed to illustrate the photodegradation of the antibiotic molecule AMO in the presence of the NiAl₂O₄/ZnO heterosystem and under sunlight shows that the various oxidizing radicals such as h⁺ holes, *OH hydroxyl radicals, and *O₂⁻ superoxide radicals are generated on the surface of the photocatalysts and play a key role in the photocatalytic degradation activity of AMO. This combination of the two semiconductors helped in the separation of the photogenerated carriers.

During the photodegradation process and under solar irradiation (hv > Eg), the valence band electrons (e⁻) move to the conduction band with the production of electron-hole pairs, and consequently in the conduction band, the electrons (e⁻) are excited from *p*-NiAl₂O₄-CB to *n*-ZnO-CB. However, the holes (h⁺) in the valence band pass from *n*-ZnO-VB to *p*-NiAl₂O₄-VB, react with *OH*⁻ or H₂O, and contribute to the production of hydroxyl radicals depending on the oxidation reactions of the water molecules near the surface of the semiconductor. On the other hand, photoinduced electrons react with adsorbed oxygen molecules, leading to the formation of superoxide radicals *O₂⁻*. *O₂⁻*· The radicals formed
have the potential for oxidizing the AMO molecules present in the aqueous solution under natural sunlight [63].

The reduction of dissolved oxygen molecules or adsorbed O₂ to superoxide anion radicals (*O₂⁻*) by CB(e⁻) eCB is described in Equations (7) and (8). Also, superoxide radicals *O₂⁻* are transformed to hydrogen peroxide (H₂O₂) by disproportionation with protons (Equation (13)) or they take the form of HO₂ by protonation, knowing that the lifetime is short due to the rapid rate of this reaction with *O₂⁻* or *HO₂* to form stable H₂O₂ (Equations (14) and (15)) [64–66].

$$ \mathrm{NiAl_2O_4} + \mathrm{h\nu} \rightarrow \mathrm{NiAl_2O_4} (\mathrm{CBe}^{-} + \mathrm{VBh}^{+}) \qquad (5) $$

$$ \mathrm{ZnO} + \mathrm{h\nu} \rightarrow \mathrm{ZnO} (\mathrm{CBe}^{-} + \mathrm{VBh}^{+}) \qquad (6) $$

$$ \mathrm{NiAl_2O_4} (\mathrm{CBe}^{-}) + \mathrm{O_2} \rightarrow \mathrm{NiAl_2O_4} + *\mathrm{O_2}^{-} \quad (\text{superoxide radical}) \qquad (7) $$

$$ \mathrm{ZnO} (\mathrm{CBe}^{-}) + \mathrm{O_2} \rightarrow \mathrm{ZnO} + *\mathrm{O_2}^{-} \quad (\text{superoxide radical}) \qquad (8) $$

$$ \mathrm{NiAl_2O_4} (\mathrm{VBh}^{+}) + \mathrm{H_2O} \rightarrow \mathrm{NiAl_2O_4} + \mathrm{H}^{+} + *\mathrm{OH}^{-} \quad (\text{hydroxyl radical}) \qquad (9) $$

$$ \mathrm{ZnO} (\mathrm{VBh}^{+}) + \mathrm{H_2O} \rightarrow \mathrm{ZnO} + \mathrm{H}^{+} + *\mathrm{OH}^{-} \qquad (10) $$

$$ \mathrm{ZnO} + (\mathrm{VBh}^{+}) + \mathrm{OH}^{-} \rightarrow \mathrm{ZnO} + *\mathrm{OH}^{-} \qquad (11) $$

$$ 2*\mathrm{O_2}^{-} + 2\mathrm{H_2O} \rightarrow \mathrm{H_2O_2} + 2\mathrm{OH}^{-} + \mathrm{O_2}^{-} \qquad (12) $$

$$ *\mathrm{O_2}^{-} + \mathrm{H}^{+} \rightarrow *\mathrm{HO_2}^{-} \qquad (13) $$

$$ *\mathrm{HO_2}^{-} + (\mathrm{CBe}^{-}) + \mathrm{H}^{+} \rightarrow \mathrm{H_2O_2}^{-} \qquad (14) $$

$$ *\mathrm{HO_2}^{-} + *\mathrm{HO_2}^{-} \rightarrow \mathrm{H_2O_2}^{-} + \frac{1}{2}\mathrm{O_2}^{-} \qquad (15) $$

$$ \mathrm{AMO} + \mathrm{h\nu} \rightarrow *\mathrm{AMO} \rightarrow \text{Degraded product} \qquad (16) $$

$$ *\mathrm{AMO} + \mathrm{ZnO} + (\mathrm{VBh}^{+}) \rightarrow *\mathrm{AMO} + \mathrm{ZnO} \qquad (17) $$

$$ *\mathrm{AMO} + \mathrm{h}^{+} + *\mathrm{OH}^{-} / *\mathrm{O_2}^{-} \rightarrow \text{Degraded products} + \mathrm{H_2O} + \mathrm{CO_2}^{-} \qquad (18) $$

The various detailed reactions occurring on the surface of the *p*-NiAl₂O₄/*n*-ZnO heterosystem to degrade AMO molecules can be illustrated by the proposed AMO photodegradation mechanism scheme in Figure 11.

## 2.5. Gaussian Process Regression (GPR)

As previously mentioned during the creation of the GPR model, we conducted optimization on ten kernel functions (Exponential, Squared Exponential, Matern32, Matern52, Rational Quadratic, ARD Exponential, ARD Squared Exponential, ARD Matern32, ARD Matern52, and ARD Rational Quadratic) using four distinct base functions (constant, linear, zero, and Pure Quadratic). Each of these kernel functions was optimized with its specific parameters (SigmaM and SigmaF), along with Sigma.

Table 2 provides a detailed summary of the best results achieved through the optimization of the ten kernel functions, in conjunction with their four respective base functions and corresponding specific parameters. The statistical coefficients and errors (R, RMSE, MAE) are also listed for the training data, validation data, and the entire dataset (combining training and validation).

The results in Table 2 show that the “ARD Exponential” kernel with the “Constant” basis function exhibited an exceptional model in terms of performance compared to other kernels. The coefficient R measures the strength of the linear relationship between the model’s predictions and the actual values of the degradation rate of AMO under sunlight in the presence of the heterogeneous ZnO and NiAl₂O₄ systems. For the training data, R is 0.9959, indicating a strong positive correlation between the model’s predictions and the actual data. The validation data show an even higher R, reaching 0.9999, suggesting that
the model can generalize impressively to new data. Lastly, for the complete dataset, R is 0.9981, demonstrating a strong overall correlation.

<figure><img src="image_16.png" /><figcaption>**Figure 11.** Schematic illustration of the photocatalytic degradation of AMO by NiAl₂O₄/ZnO heterosystem under sunlight.</figcaption></figure>

<table><caption>**Table 2.** Performance of GPR model tested.</caption><thead><tr><th rowspan="2">Kernel Function</th><th rowspan="2">Basis Function</th><th colspan="2">Kernel Scale</th><th colspan="2">Sigma</th><th colspan="2">R</th><th colspan="3">RMSE/MAE</th></tr><tr><th>SigmaM</th><th>SigmaF</th><th>Train</th><th>Val</th><th>ALL</th><th>Train</th><th>Val</th><th>ALL</th></tr></thead><tbody><tr><td rowspan="4">GPR</td><td rowspan="4">ARD-Exponential</td><td>69.1958</td><td rowspan="4">68.1417</td><td rowspan="4">1.1558</td><td rowspan="4">0.9959</td><td rowspan="4">0.9999</td><td rowspan="4">0.9981</td><td>0.2595</td><td>0.1305</td><td>0.1943</td></tr><tr><td>146.4862</td><td>0.0637</td><td>0.0429</td><td>0.0518</td></tr><tr><td>39.9120</td><td></td><td></td><td></td><td></td></tr><tr><td>203.3687</td><td></td><td></td><td></td><td></td></tr><tr><td></td><td></td><td>40.0221</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr></tbody></table>

On the other hand, the RMSE measures the model's accuracy in terms of error prediction. For the training data, RMSE is 0.2595, which is relatively low, indicating adequate precision. RMSE is even lower for the validation data, at 0.1305, showing that the model maintains its accuracy on new data. The complete dataset displays an RMSE of 0.1943, signifying an overall high precision. Similarly, these findings are corroborated by the MAE, which measures the average absolute error between the model's predictions and the actual values. For the training data, MAE is 0.0637, indicating a relatively high adequacy of the model. MAE is even lower for the validation data, at 0.0429, suggesting that the model maintains its accuracy when applied to new data. The complete dataset records a MAE of 0.0518, indicating an overall high adequacy.

In light of these results, it can be concluded that the model using the "ARD Exponential" kernel with the "Constant" basis function excels in data prediction, with a strong correlation, low RMSE, and low MAE. These results suggest that this model is highly performant and could be valuable for predicting AMO degradation under conditions similar to those in the study. These results are presented graphically in Figure 12a-c.
<figure><img src="image_17.png" /><figcaption>Figure 12. *Cont.*</figcaption></figure>
<figure><img src="image_18.png" /><figcaption>**Figure 12.** Comparison between experimental and predicted values: (a) training phase, (b) validation phase, and (c) all phases.</figcaption></figure>

### 2.5.1. Model Performance Test

The 15% portion of the database that had been previously set aside during the initial data partitioning was utilized to assess the performance of the best GPR model obtained through interpolation. The results of this evaluation are presented in Table 3, showcasing statistical coefficients and associated errors.

<table><caption>**Table 3.** Model test performance.</caption><thead><tr><td>R</td><td>RMSE/MAE</td><td>MAE</td></tr></thead><tbody><tr><td>0.9997</td><td>0.0116</td><td>0.0116</td></tr></tbody></table>

The results presented in Table 3 provide an evaluation of the GPR model's performance on the test segment, representing 15% of the previously reserved database.

The R obtained through interpolation is particularly remarkable, reaching 0.9997 for the test segment. This value indicates an extremely strong and positive correlation between the GPR model's predictions and the actual values of the degradation rate of AMO under sunlight in the presence of the heterogeneous ZnO and NiAl₂O₄ systems. Such a high correlation coefficient suggests that the model is highly accurate in its predictions and effectively captures data variations. Regarding the RMSE, the model displays an RMSE of only 0.0116 for the test segment. This value is very low, indicating that the GPR model's predictions deviate on average by only 0.0116 units from the actual values. Such a low RMSE signifies high precision when the model is applied to the test segment. Similarly, the MAE exhibits a value of 0.0391 for the test segment. MAE measures the average absolute error between the model's predictions and the actual values. A MAE of 0.0391 means that, on average, the model's predictions differ by only 0.0391 units from the actual values. This high level of precision on the test segment is confirmed.
These results emphasize that the GPR model with the “ARD Exponential” kernel and “Constant” basis function performs exceptionally well. It demonstrates a correlation coefficient close to one, a low RMSE, and a similarly low MAE. These results reinforce the notion that this model is robust and capable of predicting the degradation rate of AMO with a high degree of accuracy under the specific conditions of the study. To provide a visual representation of these performances, experimental values and predicted values are graphically represented in Figure 13.

<figure><img src="image_19.png" /><figcaption>Figure 13. Comparison between experimental and predicted values to assess performance.</figcaption></figure>

2.5.2. Residues Study

In this part, both the residual method and error histogram were employed to rigor-
ously assess the effectiveness and performance of the selected model across the training,
validation, and test phases [67,68]. Subsequently, a comparative analysis was conducted by
juxtaposing experimental values with predicted values, encompassing all the data points
(Figure 14a), including those from the training, validation, and test datasets. Furthermore,
the error was meticulously quantified by calculating the disparity between experimental
and predicted values for the entire dataset, encompassing data from the training, validation,
and test sets [67,69,70]. This error was then graphically represented (Figure 14b) using
residual analysis methods.

Figure 14a illustrates a perfect overlap between the predicted values of AMO degra-
dation rate and the experimental values in all three phases of the study. Conversely, the
analysis of Figure 14b reveals an instance distribution with high values, with a majority of
errors exceeding 120, observed across the training, validation, and test data phases. In light
of these observations, we can confidently conclude regarding the precision and outstanding
performance of our obtained model.
<figure><img src="image_20.png" /><figcaption>**Figure 14.** Residuals relating to the models established by the different techniques according to the estimated values: (a) relationship between experimental data and the predicted data of samples, and (b) instances distribution of errors.</figcaption></figure>

### 2.5.3. Optimization of the Optimal and Validation

In the pursuit of optimizing the degradation conditions of AMO, the formidable capabilities of the improved gray wolf optimization (IGWO) algorithm were harnessed [71].
IGWO, inspired by the collaborative hunting strategies of gray wolves, stands out as a robust metaheuristic optimization technique renowned for its adeptness at navigating intricate solution spaces [70]. What distinguishes IGWO are its dual-pronged strengths: an exploratory phase for wide-ranging search and an exploitative phase for pinpointing local optima [71]. This dynamic equilibrium ensures a comprehensive exploration of the solution landscape, making IGWO an invaluable tool for optimization challenges [71]. Within the research framework, upper and lower limits for the input parameters were meticulously defined, initiating the optimization process with IGWO, steered by the GPR model that had been meticulously crafted. During the optimization phase, the concentration levels (20, 30, 40, 50, and 60 mg/L) were systematically adjusted to identify optimal conditions under varying scenarios. Subsequently, the GPR model underwent a stringent validation process. After obtaining the optimal conditions for each concentration, meticulous laboratory experiments were conducted to validate these findings. The culmination of this rigorous endeavor is encapsulated in Table 4, where the results of the optimization and validation efforts are meticulously presented, including a comprehensive analysis of the error between predicted and experimental degradation rates.

<table><caption>**Table 4.** Results of optimization and validation.</caption><tbody><tr><td colspan="2">Agent search number: 50<br>Number of iterations: 100</td></tr><tr><td colspan="2">Concentration of AMO: 20 mg/L</td></tr><tr><td>Optimal conditions</td><td>X1: 360 min, X2 = 20 mg/L, X3 = 50%,<br>X4 = 50%, X5 = 6</td></tr><tr><td>Predicted rate of AMO degradation</td><td>96.5951%</td></tr><tr><td>Experimental rate of degradation of AMO</td><td>96.9230%</td></tr><tr><td>Error</td><td>0.3279%</td></tr><tr><td colspan="2">Concentration of AMO: 30 mg/L</td></tr><tr><td>Optimal conditions</td><td>X1: 360 min, X2 = 30 mg/L, X3 = 50%,<br>X4 = 50%, X5 = 6</td></tr><tr><td>Predicted rate of AMO degradation</td><td>79.7620%</td></tr><tr><td>Experimental rate of degradation of AMO</td><td>79.7570%</td></tr><tr><td>Error</td><td>0.005%</td></tr><tr><td colspan="2">Concentration of AMO: 40 mg/L</td></tr><tr><td>Optimal conditions</td><td>X1: 360 min, X2 = 40 mg/L, X3 = 50%,<br>X4 = 50%, X5 = 6</td></tr><tr><td>Predicted rate of AMO degradation</td><td>67.0476%</td></tr><tr><td>Experimental rate of degradation of AMO</td><td>66.8760%</td></tr><tr><td>Error</td><td>0.1716%</td></tr><tr><td colspan="2">Concentration of AMO: 50 mg/L</td></tr><tr><td>Optimal conditions</td><td>X1: 360 min, X2 = 50 mg/L, X3 = 50%,<br>X4 = 50%, X5 = 6</td></tr><tr><td>Predicted rate of AMO degradation</td><td>62.3582%</td></tr><tr><td>Experimental rate of degradation of AMO</td><td>62.3076%</td></tr><tr><td>Error</td><td>0.0506%</td></tr><tr><td colspan="2">Concentration of AMO: 60 mg/L</td></tr><tr><td>Optimal conditions</td><td>X1: 360 min, X2 = 60 mg/L, X3 = 50%,<br>X4 = 50%, X5 = 6</td></tr><tr><td>Predicted rate of AMO degradation</td><td>60.1924%</td></tr><tr><td>Experimental rate of degradation of AMO</td><td>60.2207%</td></tr><tr><td>Error</td><td>0.0283%</td></tr></tbody></table>

The findings presented in Table 4 offer a profound understanding of our endeavors in optimizing and validating different AMO concentrations. This table provides comprehen-
sive data for five distinct concentration levels, alongside their respective optimal conditions, and facilitates a meticulous comparison between the predicted and experimental rates of AMO degradation.

At a concentration of 20 mg/L, the predicted rate of AMO degradation closely aligns with the experimental rate, standing at 96.5951% and 96.9230%, respectively, resulting in a negligible error of only 0.3279%. For the 30 mg/L concentration, the predicted degradation rate mirrors the experimental rate almost identically, with values of 79.7620% and 79.7570%, respectively, leading to an extraordinarily low error of just 0.005%. Moving to a concentration of 40 mg/L, the predicted degradation rate registers at 67.0476%, while the experimental rate is 66.8760%, resulting in a modest error of 0.1716%. At the 50 mg/L concentration, the predicted degradation rate stands at 62.3582%, closely paralleling the experimental rate of 62.3076%, yielding a minimal error of 0.0506%. Finally, for the concentration of 60 mg/L, the predicted degradation rate is 60.1924%, an exceptionally close match to the experimental rate of 60.2207%, yielding a mere error of 0.0283%.

It is noteworthy that all these results were obtained under constant conditions, encompassing a contact time of 360 min, an initial AMO concentration, a 50% ZnO percentage, a 50% NiAl₂O₄ percentage, and a pH level of 6. The consistent observation of errors not exceeding 0.2% across all experiments underscores the remarkable performance of the GPR model in predicting AMO degradation rates. This unwavering alignment between predictions and experimental observations underscores the significant advantage of leveraging the IGWO algorithm to optimize these conditions. This amalgamation of techniques unequivocally showcases the robustness of the approach employed in attaining highly precise optimal degradation conditions.

### 2.5.4. Discussion on the Predictive Power and Practical Applications of GPR Models

The robustness of the GPR model, demonstrated by its remarkable accuracy in predicting AMO degradation rates under different conditions, emphasizes its potential in real-world wastewater treatment applications. This study validates the model's predictive power across varying concentrations and experimental setups, affirming its adaptability to diverse scenarios.

Moreover, the IGWO-GPR framework exemplifies a reliable approach for optimizing and scaling treatment processes. The consistently low error margins between predicted and experimental outcomes highlight its utility in designing efficient treatment systems. Future studies could further investigate its application to other pollutants and mixed effluent systems, paving the way for practical implementations in industrial and municipal wastewater treatment.

### 2.5.5. Interface for Optimization and Prediction

A highly sophisticated application has been meticulously developed within the user-friendly MATLAB interface (Figure 15). This application has been specifically designed to address two crucial tasks: optimizing the degradation conditions of AMO using the IGWO algorithm and predicting the degradation rate of this substance when exposed to sunlight in the presence of heterogeneous systems such as ZnO and NiAl₂O₄, utilizing a GPR model. This revolutionary application offers an invaluable opportunity to fine-tune input parameters, thereby achieving optimal conditions for the degradation of AMO. Equally importantly, it also enables a highly accurate prediction of the degradation rate based on the input parameters introduced. This powerful technological solution represents a significant advancement in the field of pharmaceutical compound photodegradation, paving the way for substantial progress in research and the development of more efficient and environmentally friendly medical treatments. It serves as an essential tool for researchers and scientists determined to optimize their experiments and precisely forecast AMO degradation performance under variable conditions.
<figure><img src="image_21.png" /><figcaption>**Figure 15.** Application for the optimization and prediction of the degradation rate of AMO under sunlight in the presence of heterogeneous ZnO and NiAl₂O₄ systems.</figcaption></figure>

# 3. Materials and Methods

## 3.1. *Chemical Reagents*

Zn(CH₃COO)₂·2H₂O zinc acetate (99%, Merck Co., Rahway, NJ, USA), citric acid (99%, Merck Co., Rahway, NJ, USA), Ni(NO₃)₂ 6H₂O (99%, Fluka Co., Ronkonkoma, NY, USA), Al(NO₃)₃ 6H₂O (99%, Sigma-Aldrich Co., Saint Louis; MO, USA), HNO₂ (69%, Merck Co., Rahway, NJ, USA), NH₄OH (25%, Sigma-Aldrich Co., Saint Louis; MO, USA), polyethylene glycol - 400 (PEG-400 Da, > 95%, Sigma-Aldrich Co., Saint Louis; MO, USA), amoxicillin C₁₆H₁₉N₃O₅S and all other reagents and solvents for syntheses were purchased from commercial sources and used without further purification. NaOH and H₂SO₄ solutions were used for pH adjustment.

## 3.2. *Synthesis of the NiAl₂O₄ Catalyst*

Bimetallic catalysis NiAl₂O₄ is a spinel distinguished by its unique structure, thermal stability, and favorable properties, which facilitate the formation of vacancies in its lattice. It is synthesized via the nitrate method, utilizing a ½ molar ratio of the initial precursors [72]. First, a solution containing 1 mole of Ni(NO₃)₂ 6H₂O and 2 moles of Al(NO₃)₃ 6H₂O was dissolved in distilled water with a minimum of HNO₃ (69%) separately to ensure good homogenization. The two solutions were then mixed at room temperature, stirred, and then slowly heated to prevent ejection into a ventilated area. Water and other NOₓ fumes were gradually eliminated by heating. Lastly, we obtained a bluish green cake which was ground to a fine powder in an agate mortar and heated at 5 °C/min to 900 °C at a temperature for 22 h with intermediate mechanical regrinding.

## 3.3. *Synthesis of the ZnO Catalyst*

Due to its optical and electrical properties, zinc oxide is considered a versatile compound; the ZnO was synthesized by a sol-gel mediated green synthesis process. Typically, 0.1 mol of Zn(CH₃COO)₂·2H₂O powders were dispersed and dissolved in a known volume of ethanol in a dry glass beaker; after 1 h of stirring, distilled water was added to the mixture under continuous magnetic stirring. Thereafter, ethylene glycol (EG, 20 mL) was added, keeping a temperature at 60 °C. Subsequently, a volume of aqueous NH₄OH was added to the mixture reagent.
Then, the mixture solution was subjected to stirring for 2 h, a 10% of hydrodistilat Citron lemon extract volumetric ratio was dropped, and the solution was aged for 24 h till a yellowish aerogel was observed; after increasing the heating temperature to 110 °C, as a result, a cake was formed. After drying, the final yield was ready for further studies. Finally, the harvested powders were dried in the oven by keeping them at 120 °C for 24 h, after which they were ground and annealed at 500 °C for 2 h in a muffle furnace under an air atmosphere. The obtained powder was crushed using agate mortar into fine nano powder and sieved for further use.

### 3.4. Characterization

The thermal gravimetric (TGA) and differential thermal analysis (DTA) were performed on TEA (SDTQ 600-TGA, TA instruments Corp., New Castle, DE, USA) up to 1100 °C at a heating rate of 10 °C min⁻¹ under air during this process; the weight loss, as a result of the rising temperature, was measured and shown in Figure 1a,b. The crystalline structure was elucidated by X-ray diffraction technique using a X-ray diffractometer (XRD) Bruker D8 Advance, PANalytical Co. Ltd., Almelo, The Netherlands) using Cu Kα radiation (λ = 1.54178 Å). The morphology of the surface microstructure of NiAl₂O₄ spinel and ZnO oxide was performed by a scanning electron microscopy (SEM) (Jeol JSM-7200F Tokyo, Japan); the results are also depicted in Figure 3a,b. The evaluation of the band gap energy was an important part of determining the optical properties. This evaluation was carried out using the UV-visible spectrophotometer model (Specord 210 Analytical Jena instrument Co., Jena, Germany), equipped with an integrated sphere; the PTFE was used as a conventional standard, and the resulting measurements were recorded within the wavelength range of 190 to 1100 nm.

The Brunauer–Emmett–Teller (BET) method was employed to assess the specific surface area of the two oxides with the ASAP 2020 device (Micromeritics Co., Norcross, GA, USA). The analytical procedure was conducted following degassing at 300 °C for a duration of 4 h.

As another supplemental technique, a Raman spectroscopic investigation was conducted utilizing a Raman spectrometer (HORIBA LABRAM HR, Kyoto, Japan) to analyze NiAl₂O₄ and ZnO powders. The instrument operated in a single spectrograph mode featuring a holographic dispersive grating with 600 grooves per millimeter, equipped to handle frequencies of 663, 785, and 325 nm.

The Fourier transform infrared (ATR-FTIR) spectra were acquired using a Bruker Optics Alpha One instrument Co., USA.

### 3.5. Gaussian Process Regression (GPR)

Gaussian process regression (GPR) stands out as a powerful machine learning technique, offering a probabilistic framework for regression analysis [73]. It is based on the concept of modeling the output as a Gaussian distribution, assigning a mean and variance to each data point [69]. This makes GPR particularly adept at capturing complex and nonlinear relationships between input and output variables [67]. Unlike many other regression methods, GPR does not impose a specific functional form on the relationship between input and output variables, making it highly adaptable to a variety of problems [73]. GPR offers several advantages over other regression techniques, such as its ability to estimate uncertainty, its adaptability, its robustness to noise, and its hyperparameter optimization [69].

In this study, the objective was to create a mathematical model using GPR to predict the degradation rate of AMO under sunlight in the presence of heterogeneous ZnO and NiAl₂O₄ systems. The parameters that were optimized for AMO degradation were chosen as independent variables: contact time for each sample (X1), AMO concentration (X2), percentage of ZnO (X3), percentage of NiAl₂O₄ (X4), and pH (X5). Conversely, the degradation rate of AMO under sunlight at each time point (y) was defined as the output variable. After the database was created, a critical step involved normalizing the data within the range [-1,1], followed by splitting it into three separate sets: 70% for training and 15% for
validation. However, an additional 15% was thoughtfully set aside for future use to assess the performance of the best model obtained.

Subsequently, ten different kernel functions were optimized to find the best model, each with a unique set of base functions. These kernel functions included Exponential, Squared Exponential, Matern32, Matern52, Rational Quadratic, ARD Exponential, ARD Squared Exponential, ARD Matern32, ARD Matern52, and ARD Rational Quadratic. Additionally, the parameters of each kernel function, including Kernel Scale [SigmaM, SigmaF] and sigma, were adjusted to improve the accuracy of the GPR model.

### 3.6. Statistical Evaluation Criteria

To assess the performance of each model, the correlation coefficient (R), root mean square error (RMSE), and mean absolute error (MAE) were employed. The respective values were computed utilizing the following equations [74–76]:

$$R = \frac{\sum_{i=1}^{N} (y_{\text{exp}} - \bar{y}_{\text{exp}}) (y_{\text{pred}} - \bar{y}_{\text{pred}})}{\sqrt{\sum_{i=1}^{N} (y_{\text{exp}} - \bar{y}_{\text{exp}})^2 \sum_{i=1}^{N} (y_{\text{pred}} - \bar{y}_{\text{pred}})^2}} \quad (19)$$

$$RMSE = \sqrt{\left(\frac{1}{N}\right) \left(\sum_{i=1}^{N} \left[ (y_{\text{exp}} - y_{\text{pred}}) \right]^2\right)} \quad (20)$$

$$MAE = \left(\frac{1}{N}\right) \sum_{i=1}^{N} |y_{\text{exp}} - y_{\text{pred}}| \quad (21)$$

where N is the number of data samples, $y_{\text{exp}}$ and $y_{\text{pred}}$ are the experimental and the predicted values, respectively, and $\bar{y}_{\text{exp}}$ and $\bar{y}_{\text{pred}}$ are, respectively, the average values of the experimental and the predicted values [70,77,78].

## 4. Conclusions

In the present study, we investigated the synthesis of NiAl₂O₄ by the nitrate way and ZnO by the modified sol-gel method. In the crystalline phase, the morphological and chemical composition of each semiconductor was performed by different techniques such TGA/DTA, DRX, SEM, DRS RAMAN, and ATR-FTIR. Thereafter, the photocatalytic activity potential of the heterosystem (NiAl₂O₄ and ZnO) was tested in the photodegradation efficiency of AMO as an emerging pharmaceutical pollutant through studying the effect of different operating parameters such as the pH of the medium, the percentage of the heterosystem, and the effect of the initial AMO concentration.

The study of the effect of several parameters shows the following: photodegradation depends on the pH of the solution and the best degradation is obtained at a pH for AMO (pH = 6); however, the heterojunction effect leads to an optimum combination of 50% of the two semiconductors used. In addition, the AMO photodegradation kinetics follow the Langmuir–Hinshelwood model. The GPR model exhibited exceptional precision, as evident from the remarkably high statistical coefficients (approaching one) and extremely minimal statistical errors (approaching zero) achieved. Furthermore, the model's efficacy has been validated through various methods, such as test interpolation and residual analyses.

**Author Contributions:** Conceptualization, M.K., R.B., N.N., H.T., N.E., F.A.M., F.D., S.A., A.A.A., A.A., M.T. and J.Z.; data curation, M.K., H.T., A.A. and M.T.; formal analysis, M.K., R.B., H.T., N.E., F.A.M., F.D., S.A., A.A.A., A.A., M.T. and J.Z.; investigation, M.K., R.B., N.N., H.T., N.E., F.A.M., F.D., S.A., A.A.A., A.A., M.T. and J.Z.; methodology, M.K., R.B., N.N., H.T., N.E., F.D., S.A., A.A.A., A.A., M.T. and J.Z.; project administration, M.K., H.T., A.A. and J.Z.; resources, M.K., R.B., N.N., H.T., N.E., F.A.M., F.D., S.A., A.A. and J.Z.; software, M.K., N.N., H.T., N.E., F.A.M., F.D., A.A. and J.Z.; supervision, A.A., M.T. and J.Z.; validation, M.K., R.B., N.N., H.T., N.E., F.A.M., F.D., S.A., A.A.A.,
A.A., M.T. and J.Z.; visualization, M.K., R.B., N.N., H.T., N.E., F.A.M., F.D., S.A., A.A.A., A.A., M.T. and J.Z.; writing—original draft, M.K. and H.T.; writing—review and editing, R.B., N.N., N.E., A.A.A., A.A., M.T. and J.Z. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Data Availability Statement:** Data will be made available on request.

**Conflicts of Interest:** The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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