Optimisation of the removal of antibiotics from aqueous environments through ultrasonic processing with α-hematite nanoparticles using response surface methodology (case study: cefixime)

Abstract

The occurrence of contamination of emerging concerns (CECs) has turned into a significant challenge. In the present study, the elimination of Cefixime from the aquatic media was optimized. The ultrasonic method, combined through α-hematite nanoparticles, was studied using the response surface methodology (RSM). In this examination, various factors were evaluated to determine their impact, including pH levels (ranging from 5 to 11), nanoparticle dosage (0.05–0.3 g/L), contact time (10–90 min), primary Cefixime concentration (25–100 mg/L), and ultrasound wave frequencies (35–130 kHz). Nanoparticle characteristics were determined through Brunauer–Emmett–Teller (BET) and X-ray diffraction (XRD) analysis. The chemical oxygen demand (COD) was measured to monitor the removal of Cefixime. The outcomes of the data analysis revealed that the catalyst dosage and contact time were the most significant factors influencing the Cefixime removal rate. The optimal conditions determined during the experiments included a pH of 3, an ultrasound wave frequency of 37 kHz, an initial Cefixime concentration of 25 mg/L, a catalyst dosage of 0.25 g/L, and a reaction time of 90 min. Under these conditions, a COD elimination efficiency of 98.7% was attained for Cefixime. The process kinetics adhered to a pseudo-second-order (PSO) model, achieving an R² value of 0.9905. The findings of this research demonstrate the high efficiency of the sonocatalytic removal technique in eliminating Cefixime antibiotics from aqueous solutions.

Introduction

With the expansion of the water crisis in the world, access to safe drinking water has gained particular importance as a vital necessity and health indicator (Mujtaba et al. 2024). Aquatic ecosystems are threatened by several pollutants, including pharmaceuticals as contamination of emerging concerns (CECs) (Espíndola et al. 2024; Sun et al. 2021). Water pollution is increasingly emerging as a major global concern (An et al. 2024).

Among the ways of entering these emerging contaminants into the environment are pharmaceutical industries, pharmaceutical waste with improper disposal, improper use in agriculture and animal husbandry, and disposal through human feces (Jonidi Jafari et al. 2024; Roy et al. 2021). Medicinal compounds hold specific significance due to their frequent use and intake, so the use of medicinal compounds has increased by more than 30% during the past decade with the spread of pandemics such as COVID-19 and influenza (Vinayagam et al. 2022). Antibiotics rank among the most commonly used medications (Abdipour & Hemati 2023). This group of medicinal compounds has a significant effect in controlling infections and inhibiting the growth and survival of microorganisms (Goodarzi et al. 2024; Zhang et al. 2025). Currently, antibiotics are the most significant group of microbial biotechnological products by global sales of about 16 billion dollars (Tabatabaei et al. 2020a, b). According to the World Health Organization (WHO), nearly 8.5 tons of Antibiotics are manufactured on a global scale daily (Goodarzi et al. 2024; Truong et al. 2021). Based on the WHO report, Iran ranks as the second-highest consumer of antibiotics globally, following Mongolia (Truong et al. 2021). Beta-lactam antibiotics are considered the most widely used group of drugs, characterized by two main features: high clinical efficacy and low toxicity (Stachurová et al. 2021). Due to the high demand, various families of beta-lactam antibiotics have been linked to the emergence of antibiotic resistance genes (Dinh et al. 2022). These antibiotics include a wide range of penams, cephaloms, carbapenems, monobactams, and beta-lactamase inhibitors that are effective against the cell wall and cell envelope of bacteria (Hamadamin et al. 2024). Cefixime, with the chemical formula C₁₆H₁₅N₅O₇S₂, is one of the common antibiotics and a subgroup of beta-lactams (Sheydaei et al. 2018). Cefixime plays a crucial role in treating infections related to the skin, gastrointestinal tract, respiratory system, urinary system, prostate, and bronchial airways (Paidar et al. 2024). However, its significant stability in the environment presents notable ecological challenges (Rasouli et al. 2023). Eliminating this antibiotic from the environment could facilitate the breakdown of similar compounds, as its complex and robust structure often hampers degradation processes. Another concern is the presence of organic components in its structure, which cannot be ignored. When these substances interact with chlorine during water treatment processes, they can form carcinogenic and highly toxic compounds, further contributing to environmental risks (Sheikhmohammadi et al. 2024; Wang et al. 2023).

Some of the physicochemical features of Cefixime antibiotic are presented in Table 1. This antibiotic is part of the cephalosporin class and exhibits antibacterial properties. The effectiveness of this antibiotic in the treatment of pneumonia, urinary tract diseases, respiratory infections, and bone infections has been proven (Tabatabaei et al. 2020a, b). Approximately half of the Cefixime consumed via the digestive system is excreted in urine, ultimately making its way into aquatic ecosystems (Anyat et al. 2025; Pourtaheri and Nezamzadeh-Ejhieh 2015).

Table 1. Physicochemical characteristics of Cefixime

Structure of Cefixime
Chemical formula	C16H15N5O7S2
Melting point	210 °C
Boiling point	315 °C
Molar mass	456.42 g/mol
Density	1.33 g/cm3

According to the latest statistics of Iran, after Amoxicillin, Cefixime is the second most used antibiotic in Iran, and it consumes about 150 kg annually (Almasi et al. 2020). Stability, disturbance in the environment, absence of biological interaction, toxicity for aquatic animals, and bacterial resistance are among the characteristics of this drug, which make it an environmental challenge in the environment, especially in water resources (Rasouli et al. 2023; Ribeiro et al. 2018). Therefore, it is necessary to eliminate it from water sources. Removing antibiotic residues from water has been the focus of many researchers. The non-destructive and semi-resistant nature of drugs has caused the common methods of treatment in wastewater treatment plants are not very effective in removing them (Khurana et al. 2021; Patel et al. 2023). Therefore, the effluents containing the mentioned compounds should be treated with modern techniques to minimize the risks for humans and the environment. To date, many physical, chemical, and biological techniques on a laboratory scale such as absorption by activated carbon (92.8% removal), membrane processes (98.6% removal) and ozonation, ultraviolet radiation, ultrasonic (93.4% removal), ion exchange (88% removal), electrochemical processes (91/8% removal), and biological methods (70/5% removal) have been utilized to remove antibiotics from water media. All of these techniques come with their own set of limitations and drawbacks (Asgari et al. 2023; Mahmoudabadi et al. 2022; Xu et al. 2024). Some of the limitations of the used methods are the lack of elimination of the precursor and its phase transfer in absorption, as well as problems of procedure and preservation, obstruction of filters and high costs of maintenance and investment in filtration, and the non-destruction of microorganisms in biological treatment (Khazaei et al. 2019). In recent decades, the almost complete removal of emerging pharmaceutical agents by advanced oxidation processes (AOPS) has captured the interest of researchers (Khan et al. 2023). Using ultrasonic processes to decompose contaminants in water surroundings is one of the AOPs (Rao et al. 2024). In this process, ultrasonic waves break chemical bonds and decompose pollutants through the formation, growth, and finally destruction of bubbles that form inside the liquid (exotic cavitation) (Hasani et al. 2020). This phenomenon generates a chemical environment where the temperature exceeds 5000 K, accompanied by a pressure of 108 pa (Zhuo et al. 2023).

This amount of heat causes the thermal degradation of water molecules and, resulting in the formation of free radicals such as Ho, OH°, and O°, as well as oxidizing agents like a hydrogen peroxide, which can interact with organic compounds (Kamani et al. 2023; Yang et al. 2020; Zhu et al. 2010). To increase the efficiency of the sonolysis oxidation process and accelerate the decomposition ratio of organic molecules, incorporating nanoparticles into the process can be an effective approach (Al-Hakkani et al. 2021; Ren et al. 2025). Nanoparticles enhance the frequency of collisions during cavitation by supplying extra nuclei that facilitate the process (Khalooei et al. 2024; Torabideh et al. 2024).

In addition, nanoparticles smaller than the bubbles can freely pierce the interface between the bubbles and water, allowing them to interact with pollutants while the bubbles act as carriers and transporters (Torabideh et al. 2024).

The small size of nanoparticles causes their effective and straightforward subsurface allocation. Their large cross-sectional area results in high reactivity and the swift decomposing of contaminants (Abdipour et al. 2024a, b; Al-Hakkani et al. 2022; Asgari et al. 2024; Hu et al. 2024). The advantages of the ultrasonic process are that it has few side effects on the environment and is considered one of the clean processes. Increasing heat and pressure can increase the decomposition of organic pollutants such as antibiotics. These reasons lead to the use of this process in removing the antibiotic Cefixime.

α-Fe₂O₃ was used in this work due to their high efficiency and highly recyclable magnetic attractions. Hematite possesses remarkable features including moderate magnetic saturation, excellent chemical stability, and pronounced anisotropy, making it highly significant (Yilmaz et al. 2022). The cheapness and high oxidizing power of hematite have made this compound be used as a catalyst in advanced oxidation processes. Recently, statistical models have been proper for optimizing various processes in pollutant removal (“Elimination of nickel and chromium(VI) ions from industrial wastewater by electrodialysis/characteristics/impact of parameters,” 2024). The advantages of using the sonocatalytic process with alpha hematite nanoparticles (α-Fe₂O₃) for the removal of the antibiotic Cefixime include high efficiency in removing contamination by creating free radicals, accelerating reactions with the alpha hematite catalyst, reducing reaction time, activity at different temperatures and pH levels, producing minimal by-products, reusing the catalyst, reducing costs, increasing process stability, environmental compatibility, and the possibility of application on an industrial scale. Additionally, using these methods for the removal of antibiotics not only helps protect water resources but can also lead to a reduction in drug resistance. A statistical model ordinarily utilized in experimental design is the response surface method (RSM). Determining the optimum theoretical circumstances, fewer experiments, the interaction of parameters, and selecting the last removal formula have been beneficial (Hasanzade et al. 2022; Wan et al. 2024). The response level technique serves as a study methodology commonly used in experimental design and related scientific fields. Through the response surface method, efforts are directed at identifying strategies to estimate interactions, quadratic impacts, and even the local structure of the examined response surface by employing an appropriate experimental framework (Khalooei et al. 2024). To put it differently; the response surface method deals with designing an experimental experiment that models the various impacts of parameters. Then, through the introduction of a regression model, a connection is established between the response and its influencing factors (Kamani et al. 2024). Simultaneously, several key objectives are actively pursued, with the primary goal being the enhancement of the process. This is achieved by identifying optimum inputs, addressing weaknesses and issues, and ensuring process stability. Additional aims of this approach include optimizing the response curve for faster accessibility, assessing the impact of specific variables, and producing a detailed report on changes within the process. Notably, stabilization plays a crucial role in quality statistics, focusing on reducing the influence of secondary or uncontrolled parameters (disturbance). Therefore, considering that there is no report on the removal of the antibiotic Cefixime through the sonocatalytic method using α-Fe₂O₃ nanoparticles, this study was conducted with the general aim of evaluating the efficiency of the aforementioned process for the removal of Cefixime through RSM based on the central composite design (CCD) model and the specific objectives of investigating the effects of various factors, including pH, nanoparticle dose, reaction time, initial antibiotic concentration, and frequency of sound waves on the combined process, as well as analyzing the characteristics of the nanoparticles using BET and XRD analysis. Finally, the reaction kinetics was also calculated.

Materials and methods

Chemicals and equipment

In the present work, triethylamine and hydrochloric acid, zinc nitrate hexahydrate (Zn (NO₃)₂·6H₂O), sodium hydroxide (1 N), iron nitrate (III) monohydrate (Fe (NO₃)₃·9H₂O) from Merck, Germany, and oxide nanoparticles hematite iron produced by Fine Nano Company were obtained. Cefixime 400 mg drug was obtained from Kausar Pharmaceutical Company in Tehran. Deionized water and high-purity chemicals were used in all stages. A stock solution of Cefixime antibiotic with a concentration of 1000 mg/L was prepared through distilled water, and then, it was diluted to the desired concentration in terms of mg/L if needed. During the tests, a pH meter Artico model, a 4.5 L Sky model 30 s ultrasonic device, an Agilent HPLC model equipped with a DAD UV–Vis detector, and a UNICO spectrophotometer were used. After complete mixing, the wastewater samples produced for 10, 50, and 90 min were exposed to ultrasonic light at frequencies (35, 37, and 130) kHz. Then, the samples were filtered through a syringe filter. To conclude, the COD value of the samples was determined through a spectrophotometer at a wavelength of 600 nm with a colorimetric technique.

Preparation of α-Fe₂O₃ nanoplatelets

A mixture of 673 g of Fe(NO₃)₃·9H₂O and 0.195 g of NaCl (or alternatively 0.343 g of NaBr) was dissolved in a solvent composed of 25 mL of distilled water and 25 mL of ethanol, using ultrasound to aid the process. The consequential solution was then transferred into a 100 mL Teflon-lined stainless steel autoclave, where it was sealed, heated to 140 °C, maintained at this temperature for 12 h, and subsequently allowed to cool to room temperature. This process led to the formation of iron oxides (Wang and Huang 2016). Fe₂O₃ nanosheets will undergo synthesis into monodisperse nanocrystals using the hydrothermal technique. For this process, 4 mmol of hematite and 5 mmol of Fe(CO) are combined and mixed with 14 ml of surfactant. During the reaction, triethylamine is subjected to heating in an atmosphere of nitrogen. As the process advances, a distinct color change is observed, transitioning from yellow to black. The Fe nanocrystals are maintained at the temperature where the color change occurs for 1 h before the solution is allowed to cool to room temperature. Subsequently, the mixture is heated at two temperature points, 130 °C and 230 °C, for a duration of 2 h. After being cooled for an additional hour, the particles precipitate and are carefully washed with ethanol. The resulting hematite nanocrystals can subsequently be effortlessly redispersed in hexane (Sreeja & Joy 2007).

Experimental setup

In this work, the response surface methodology was employed to assess and predict the optimal response value among two models: the Box–Behnken design and the central composite design (CCD). The CCD technique was ultimately selected to investigate the effect of autonomous parameters on response performance. The primary objective was to assess the elimination effectiveness of the antibiotic Cefixime, which served as the dependent parameter. Using Minitab.16 software, autonomous features including pH (X1), hematite nanoparticle dose (X2), reaction time (X3), primary Cefixime concentration (X4), and frequency of sound waves (X5), each at 3 separate levels within the frame, the sonocatalytic process (Table 2) was formed. The experimental setup, encompassing a total of 64 runs, with 12 central replicate points and two replicates to diminish general mistake, was generated as instructed.

Table 2. Factors and diverse ranks of experimental project

Autonomous factors	The mark	Level
		Low(− 1)	Medium(0)	Much(+ 1)
pH	X1	5	7	11
α-Fe2O3 nanoparticles dose g/L	X2	0.1	0.25	0.5
Reaction time min	X3	10	50	90
Primary Cefixime concentration mg/L	X4	25	50	100
Frequency of sound waves kHz	X5	35	37	130

Quality control and quality assurance

Quality control in this process includes a set of activities to check and verify the quality of products or processes. Selecting high-quality raw materials, such as nanoparticles and pure antibiotics, is one of its key steps. Designing reproducible experiments with precise control of temperature, pH, and reaction time is also essential. Using accurate instruments to measure concentrations and validated analysis methods, such as HPLC, helps ensure the accuracy of the results. Accurate recording of data, laboratory conditions, and results in detailed reports are another important part of quality control.

Quality assurance in this process consists of activities aimed at preventing quality problems. Determining quality standards for raw materials, processes, and final results is of great importance. Establishing specific protocols for conducting experiments and analyzing data is also essential. Training employees in testing methods, the use of equipment, and quality control principles play a key role in quality assurance. Periodic inspections to assess compliance with quality protocols, identify weaknesses, and plan for continuous process improvement are other quality assurance activities. Validation of measurement methods and regular calibration of laboratory equipment ensures measurement accuracy.

Statistical analysis and evaluation of model quality

The significant expense of nanoparticles, the requirement to reduce sample volumes, and the importance of identifying an efficient equation encouraged researchers to use statistical models.

The implementation of the statistical model was carried out by trials following statistical techniques. The criteria of R² and adjusted R² were used to assess the quality of the polynomial model. The responses were analyzed via Analysis of Variance (ANOVA), and three-dimensional graphs were generated to provide clearer insights into the effects of the parameters. For the study, an importance level of P ≤ 0.05 was established.

Results and discussion

α-Fe₂O₃ features

The synthesized α-Fe₂O₃ nanoparticles were analyzed using a BET analyzer to determine their surface area, pore volume, and pore diameter. The BET surface area was recorded as 1020.6588 m²/g.

The pore volume decreased from 0.4556 to 0.4165 cm³/g after synthesis, indicating a reduction in pore distance and a rise in wall thickness (from 17.07 to 18.04 nm) due to α-Fe₂O₃ saturation according to the structural characteristics and porosity analysis. Additionally, there was a rise in the nanoparticle pore diameter, suggesting a reduction in α-Fe₂O₃ pore volume due to adsorption.

Figure 1 demonstrates the XRD patterns of the synthesized α-Fe₂O₃ nanoplates. As revealed, the highest peak occurred at 30 degrees. All diffraction peaks are clearly attributed to the hexagonal phase of α-Fe₂O₃, specifically the hematite phase. The lack of any contaminants confirms that the sample consists solely of pure nano-Fe₂O₃ layers. The presence of α-Fe₂O₃ peaks suggests that the phase structure includes a mixture of α-Fe₂O₃ phases. Evidently, the incorporation of α-Fe₂O₃ plays a significant role.

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Fig. 1

XRD pattern of a α-Fe₂O₃ nanoplatelets

The elimination efficiency at to each phase of the experiment was determined by improving the model’s effectiveness. An equation was used to calculate the elimination of Cefixime antibiotic in the samples by considering the primary volume present and assessing the residual antibiotic. The COD antibiotic elimination was calculated through a particular equation, and the outcomes are found in Table 3.

1

$$\text{COD}\text{removal}\text{efficiency}=\frac{C_0-C_1}{C_0}\times 100$$C₀ = COD of the initial Cefixime and C₁ = COD antibiotics after process.

Table 3. The experimental design matrix showing various levels of variables and the efficiency of COD elimination using the Cefixime, in both current and estimated situations

Run	pH	US (kHz)	α-Fe2O3 (g/L)	Cefixime concentration (mg/L)	Time (min)	COD degradation Cefixime %
						Expt. Pred	Actual removal
1	0	0	− 1	0	0	65.8	68.50
2	1	− 1	− 1	1	1	80.5	78.60
3	0	0	0	0	0	68.44	70.50
4	0	1	0	0	0	63.33	64.66
5	0	0	0	0	0	67.50	68.40
6	− 1	− 1	− 1	1	− 1	80.55	82.50
7	− 1	− 1	1	− 1	− 1	90.22	91.66
8	− 1	1	− 1	1	1	63.80	62.60
9	1	1	− 1	1	− 1	55.60	56.66
10	0	− 1	0	0	0	87.33	86.05
11	0	0	0	− 1	0	85.62	80.45
12	0	0	0	1	0	66.50	70.50
13	0	0	0	0	0	72.15	73.66
14	− 1	1	1	− 1	1	78.61	80.50
15	− 1	− 1	− 1	1	− 1	83.60	82.40
16	0	0	0	0	1	77.70	75.44
17	− 1	1	1	1	− 1	62.25	63.42
18	− 1	1	1	1	− 1	60.40	60.90
19	1	− 1	− 1	− 1	− 1	89.45	88.00
20	0	0	0	0	1	77.50	73.66
21	1	− 1	1	− 1	1	95.60	94.20
22	0	− 1	0	0	0	87.36	85.66
23	− 1	− 1	− 1	− 1	1	97.20	97.50
24	0	0	0	0	0	70.40	73.24
25	− 1	− 1	1	1	1	87.65	87.07
26	− 1	1	− 1	− 1	− 1	72.63	74.20
27	0	1	0	0	0	61.57	64.40
28	0	0	0	0	0	67.49	68.23
29	1	− 1	1	− 1	1	93.50	95.00
30	1	0	0	0	0	73.80	74.50
31	1	1	1	− 1	− 1	72.66	70.50
32	0	0	0	0	0	74.25	75.00
33	1	1	1	1	1	63.45	61.00
34	− 1	0	0	0	0	82.80	76.50
35	− 1	1	− 1	− 1	− 1	70.40	71.50
36	− 1	1	1	− 1	1	80.70	82.80
37	0	0	0	0	0	73.66	72.20
38	1	1	− 1	1	− 1	60.50	57.33
39	0	0	0	− 1	0	88.50	83.00
40	1	0	0	0	0	69.50	74.80
41	1	− 1	− 1	1	1	88.00	84.66
42	− 1	0	0	0	0	75.46	74.20
43	− 1	− 1	− 1	− 1	1	98.20	98.7
44	1	1	− 1	− 1	1	75.54	76.54
45	0	0	1	0	0	80.55	76.00
46	0	0	0	0	0	78.00	63.66
47	1	− 1	1	1	− 1	84.46	83.20
48	0	0	0	0	0	76.50	74.00
49	− 1	0	0	0	0	83.40	78.77
50	0	0	0	0	− 1	65.66	69.00
51	0	0	0	0	0	75.00	74.02
52	1	1	1	− 1	− 1	73.20	73.50
53	− 1	1	− 1	1	1	63.0 5	63.20
54	− 1	− 1	1	1	1	87.55	86.20
55	0	0	− 1	0	0	68.00	73.00
56	1	1	1	1	1	63.50	61.40
57	− 1	− 1	1	− 1	− 1	95.60	96.00
58	0	0	0	0	− 1	71.00	74.56
59	1	1	− 1	− 1	1	90.00	83.00
60	0	0	1	0	0	79.50	76.00
61	0	0	0	0	0	75.60	73.81
62	0	0	0	1	0	65.60	70.00
63	1	− 1	1	1	− 1	84.00	82.56
64	1	− 1	− 1	− 1	− 1	88.22	90.66

After analyzing the response surface method, the equations below were developed to demonstrate the empirical connection between the factors studied and coding efficiency.

Cefixime antibiotic COD degradation efficiency = 70.24 − 1.42X₁ − 12.05X₅ + 1.12X₂ − 6.5X₄ + 3.02X₃ − 1.40(X₄X₃) + 2.23(X₁)² + 2.72(X₅)² + 0.08(X₂)² + 2.52(X₄)² − 1.52(X₃)² + 0.09(X₁X₅) + 0.16(X₁X₂) + 0.25(X₁X₄) − 0.6(X₁X₃) + 0.35(X₅X₂) + 0.9(X₅X₂) + 0.04(X₅X₃) − 0.25(X₂X₄) − 0.6(X₂X₃).

The study examined the factors influencing the removal of Cefixime antibiotics through a sonocatalytic process. In the equations, X1 through X5 represents pH, α-Fe₂O₃ nanoparticles dose, duration of contact, initial Cefixime concentration, and sound wave frequency, respectively. Table 2 provides a comprehensive overview of these influential factors, their individual effects on the process efficiency, and a comparison between the actual and predicted Cefixime elimination rates.

When comparing the experimental and predicted efficiencies of the sonocatalytic process by α-Fe₂O₃ nanoparticles, researchers found a strong and meaningful correlation. The response surface model’s variance analysis results, as shown in Table 2, highlight the significant impact of all five factors on the model. Interestingly, the catalyst dosage (P-value = 0.045) and reaction time (P-value < 0.002) emerged as the most influential variables affecting the response variable, which was the percentage of COD (Chemical Oxygen Demand) reduction in Cefixime.

For the Cefixime antibiotic, the predicted R-squared (R²) value was calculated to be 0.9440, representative an excellent fit with the adjusted R-squared value of 0.925. This strong correlation between the model’s predictions and the experimental results further validates the reliability of the study’s findings.

Table 4 shows the outcomes of the analysis of variance (ANOVA) for a quadratic model used to study the elimination of Cefixime antibiotic COD through sonocatalytic procedure.

Table 4. Studies focused on AOPs have been conducted with the objective of removing Cefixime

Type of AOP	Concentration (mg/L)	Operation condition	Removal efficiency	References
Sonophotocatalyst Cu–ZnO	20	Time = 30 min [H2O2] = 5 mM	89%	(Khitab et al. 2024)
Sonophotocatalyst Ni-ZnO			91%
O3/Active Carbon	10	Adsorbent dose = 1 g/L pH = 4 Time = 30 min; ozone = 60 g/m3	96%	(Oskoue et al. 2019)
Sono-electro-Fenton	40	pH = 3 Time = 81.5 min [H2O2] = 0.85 mM	97.5%	(Hasani et al. 2020)
UV/peroxymonosulfate	5	Time = 30 min; catalyst dose = 1.37 mmol; pH = 7.5	93.18%	(Khazaei et al. 2019)
Ultrasonic/α-Fe2O3@TiO2	20.5	pH = 4.76 Time = 8 min Catalyst dose = 0.012 g/L	98.8%	(Rasouli et al. 2023)
UV/H2O2	9 mg/L	H2O2/= 5; time = 3 h; pH = 3;	100%	(Belghadr et al. 2015)

This study on sonocatalytic removal of Cefixime antibiotics revealed strong correlations between experimental and predicted efficiencies. The response surface model highlighted significant impacts of pH, α-Fe₂O₃ nanoparticle dosage, initial Cefixime concentration, sound wave frequency, and reaction time. Notably, catalyst dose and contact time emerged as the most influential factors affecting COD reduction.

Analysis of variance confirmed these parameters’ undeniable effects on the model. The R² value derived from the second-order model is 0.9958, showing a correlation between the model and the deterioration, aligned well with the adjusted R² of 0.9926, indicating a robust relationship between model predictions and experimental outcomesThe distribution of actual data compared to the predicted reduction in COD efficiency in the removal of cefixime is presented in Fig. 2.

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Fig. 2

The distribution of actual data compared to the predicted reduction in COD (Chemical Oxygen Demand) efficiency of the Cefixime antibiotic using the Sonocatalyst method with iron oxide nanoparticles

Response surface analysis

Using diagrams such as one-factor diagrams, 3D plots, and contour plots is a method to analyze how a reaction system is influenced by operating features. The 3D graphs in Fig. 3 illustrate the relationships between pH and various factors influencing removal efficiency. Notably, at pH 5 and with a reaction time of 90 min or more, the removal rate reached an impressive 98.7%. The efficiency was enhanced by two key factors: lowering the pollutant concentration and increasing the nanoparticle dosage (Delavari et al. 2024). The superior performance observed under acidic conditions can be attributed to two main reasons: firstly, the increased production of hydroxyl radicals, and secondly, the favorable surface charge interactions between the antibiotic molecules and the adsorbent material (Abdipour et al. 2024; Sheikhmohammadi and Sardar 2013). The ability to remove waste in acidic conditions may be related to the reactions that follow (Tamimi et al. 2008).

2

$$2{\text{HO}}_2^0\to {\text{O}}_2^0+{\text{H}}_2{\text{O}}_2$$

3

$${\text{H}}_2{\text{O}}_2+{\text{O}}_2^0\to {\text{OH}}^0+{\text{OH}}^{-}+{\text{O}}_2$$

4

$${\text{e}}^{-}+{\text{O}}_2\to {\text{O}}_2^{0-}$$

5

$${\text{O}}_2^{0-}+{\text{H}}^{+}\to 2{\text{HO}}_2^0$$

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Fig. 3

Display case a three-dimensional diagrams representing the combined effects of pH factors and reaction time (a), pH and initial concentration of Cefixime antibiotic (b), pH and dose of α-Fe₂O₃nanoparticles (c), and pH and frequency of sound waves (d)

Table 4 presents a compilation of studies from the past decade focusing on Cefixime removal using advanced oxidation processes. Our current study shows the work of Belghadr and Hasani K, who employed UV/H₂O₂ and sono-electro-Fenton processes, respectively, for Cefixime removal. Additionally, our findings closely align with Fazlzadeh et al. (Fazlzadeh et al. 2016)’s research on amoxicillin removal. However, it is worth noting that the present study similarities to from the work conducted by Mohammadi et al. (Mohammadi et al. 2023).

Three-dimensional models (Fig. 4) illustrate how increasing iron oxide nanoparticle dosage enhances Cefixime degradation, with optimal results at higher nanoparticle concentrations and lower initial antibiotic levels. Under average conditions, efficiency exceeds 90% when nanoparticle dose is maximized and antibiotic concentration minimized. The sonocatalytic process’s effectiveness improves with longer duration and higher nanoparticle dosage, with 0.5 g identified as the ideal amount. Iron oxide nanoparticles boost the process by providing additional cavitation surfaces and promoting radical formation. Their presence catalyzes H₂O₂ breakdown, increasing free radical production and ultimately improving antibiotic elimination efficiency (Abdipour and Asgari 2024; Mason 2002; Samadi et al. 2024). The optimal dosage of α-Fe₂O₃ nanocatalyst is crucial for efficient Cefixime elimination in the sonocatalytic process. Higher nanoparticle doses and lower initial antibiotic concentrations can achieve over 90% removal efficiency. The lag phase duration, influenced by nanoparticle quantity, affects the accumulation of ferrous ions and subsequent antibiotic removal. Increased removal effectiveness at higher doses is attributed to more active sites, enhanced antibiotic–nanoparticle interactions, and amplified sound wave effects (Liao et al. 2003).

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Fig. 4

Demonstrates a three-dimensional graph representing the correlation among the frequency of sound waves (A), the duration of contact (B), the primary concentration of Cefixime antibiotic (C), and the dosage of α-Fe₂O₃ nanoparticles

Reaction time is a critical factor in chemical processes, including oxidation (Shi et al. 2020). Figure 5 shows that longer contact times improve removal efficiency of Cefixime, balancing effectiveness with operational costs. Extended exposure allows for continued hydroxyl radical generation and increased antibiotic decomposition (Bazrafshan et al. 2013). Over time, iron surface corrosion increases available adsorption area, while changes in active sites boost iron–water reaction outputs, enhancing separation efficiency. These findings align with the previous studies, such as Shi et al. (2020)’s work on Ceftriaxone removal using nanocomposite g-C3 N4/MWCNT/Bi2 WO6 with ultrasonic, and Barzegarzadeh et al.’s research on a rifampicin elimination using Cu (BDC)@ Wool Biocomposite (Barzegarzadeh et al. 2024).

[See PDF for image]

Fig. 5

3D plot of interface outcome of sound wave frequency and initial concentration of Cefiximes antibiotic (a), and sound wave frequency and reaction time (b)

Figure .5 illustrates that Cefixime elimination efficiency declines as primary antibiotic concentration increases from 25 to 100 mg/L, with 25 mg/L identified as the optimal starting point. Higher concentrations hinder hydroxyl radical response, reducing bubble disruption and impacting decomposition (Safari et al. 2014). Increased antibiotic levels provide greater driving force, but also more mass transfer resistance between liquid and solid phases. At lower concentrations, the ratio of adsorbed molecules to active sites is lower, maximizing elimination (Rahmani et al. 2014). Conversely, elevated concentrations lead to antibiotic condensation on nanoparticles, obstructing contact and reducing reaction rates (Karagozoglu et al. 2007; Yuan et al. 2011). These findings align with the previous studies such as Moridi (Moridi et al. 2023) and Naghipoura (Naghipoura et al. 2020) demonstrating reduced removal at higher antibiotic concentrations.

Figure 6 illustrates that Cefixime elimination efficiency exceeds 95% at 35 kHz frequency and 25 mg/L initial concentration. Decreasing frequency and increasing iron oxide nanoparticle dosage to 0.3 g further boosts elimination above 99%. The visual representation clearly indicates that antibiotic elimination improves with lower sound wave frequency and longer sonocatalytic duration, reaching over 90% at 35 kHz and 90 min. This significant enhancement through frequency reduction is attributed to factors such as increased bubble lifespan, elevated pressure/temperature, and greater hydroxyl radical generation and diffusion (Kidak and Dogan 2015; Ohl et al. 2015; Ziylan et al. 2013). The previous studies on phenol (Abdelwahab et al. 2009) and ibuprofen (Kang et al. 2015) degradation have reported similar trends of improved elimination at lower ultrasonic frequencies. Kamal Rasouli’s work showed that by using nanocomposite and ultrasound (w 50–90), 82.4% of the antibiotic Cefixime was removed, with the most effective removal occurring at the lowest ultrasonic waves (Rasouli et al. 2023).

[See PDF for image]

Fig. 6

3D Plot of the interaction influence of the initial concentration of Cefixime antibiotic and reaction time

Optimization of the sonocatalytic procedure in COD removal of Cefixime antibiotic

The aim of the optimization process is to determine the best conditions for maximum Cefixime removal via the sonocatalytic method. Response surface software is used to select and predict the optimal levels of factors such as pH, nanoparticle dose, contact time, sound frequency, and primary antibiotic concentration. Under the optimal conditions (which is mentioned in Table 5) identified by the software, the predicted Cefixime removal efficiency is 99.00%.

Table 5. The best values for a parameter and the highest investigational and predicted efficiency for COD elimination with Cefixime

Factors	The optimal value	COD removal efficiency %
		Experimental	Predicted
pH	5	98.7	99.00
α-Fe2O3 nanoparticles dose	0.25 (g/L)
Frequency of sound waves	37 (kHz)
Reaction time	90 (min)
The primary Cefixime concentration	25 (mg/l)

Kinetics study

In order to understand how the decomposition process works, an experiment was conducted to analyze the rate of the process for 90 min. The results showed that the extraction rate follows a first-order reaction, as revealed in Fig. 7. The findings of the kinetic study indicated that it followed the PSO and R² is 0.9905.

[See PDF for image]

Fig. 7

Kinetics of Cefixime removal by α-Fe₂O₃

Economic evaluation

For the economic evaluation of this process, especially in industrial and research fields, the key factors of investment costs (purchase of equipment, nanoparticles, construction, and installation), operating costs (energy, labor, maintenance, and repairs), raw material costs (price of nanoparticles and chemicals, transportation, and storage), environmental costs (waste and pollution management, environmental consequences), income from the sale of products (treated water, by-products, and added value), and social and health benefits (reduction of pollution, improvement of water quality, and reduction of treatment costs) should be considered. With the benefit–cost assessment, which includes identifying and collecting data related to all process costs and calculating the income from sales and social and health benefits, it was found that if the benefit–cost ratio is greater than 1, the project is justified. About 0.09$ is needed for the treatment of each liter of wastewater containing antibiotics. In order to comprehensively assess the axis, sensitivity analysis is necessary to examine the impact of changes in key variables on the benefit–cost ratio.

Study limitations

1. Limited efficiency: The effectiveness of antibiotic removal can fluctuate based on factors such as the type and concentration of the antibiotic and environmental variables such as pH and temperature. Certain antibiotics may prove difficult to eliminate completely.

2. By-product formation: The sonocatalytic process can generate potentially harmful or toxic by-products, which must be thoroughly assessed and appropriately addressed.

3. High-energy consumption: Sonocatalysis typically relies on an external energy source, such as ultrasound, making it a relatively expensive process.

4. Nanoparticle stability: Hematite nanoparticles might lose stability over time, potentially aggregating or precipitating under specific conditions, thereby diminishing their effectiveness.

5. Environmental concerns: The introduction of nanoparticles into environmental systems could lead to negative consequences, necessitating a comprehensive evaluation of potential risks.

6. Limited scope of contaminant removal: While effective for antibiotics, these methods may not be capable of addressing other types of pollutants in the environment.

Conclusion

Antibiotics are medicinal compounds that have low metabolism, high mobility, and resistance to biological degradation in water. Cefixime, a common beta-lactam, has seen an increase in usage in recent years. This research aimed to examine the sonocatalytic degradation procedure of Cefixime using α-Fe₂O₃ to effectively remove the antibiotic. The optimization of the procedure was carried out by the CCD technique of the response surface methodology. COD elimination was found to increase as pH, ultrasonic wave frequency, initial antibiotic concentration decreased, and α-Fe₂O₃ nanoparticles dosage and reaction time increased. The best removal efficiency was achieved under optimal circumstances of a sound frequency of 37 kHz, antibiotic concentration of 25 mg/L, 0.25 g/L dose of α-Fe₂O₃ nanoparticles, and a contact time of 90 min, subsequent in a COD elimination efficiency of 98.7%. The process kinetics followed a PSO with an R² value of 0.9905. The study indicated promise for the removal of the antibiotic Cefixime. The integrated process revealed the ability to meet environmental standards and effectively treat sources contaminated with pharmaceutical wastewater. Considering some challenges and limitations of this study, and in order to develop integrated approaches for antibiotic removal, the sonocatalytic process through the development of new nanoparticles, the study of process by-products, the combination of advanced oxidation with other methods, including adsorption, and process modeling is suggested for future studies.

Acknowledgements

The authors grateful to the Kerman University of Medical Sciences for financially and technically supporting this research (Grant number:502000077 and code of ethics IR.KMU.REC.1402.385).

Author contributions

All persons who meet authorship criteria are listed below.

Funding

The paper was supported by Kerman University of Medical Sciences.

Declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

Code of Ethics approval is not required because no human or animal studies have been conducted.

Consent to participate

Not applicable.

Consent for publication

All the authors agreed with the content and that all gave explicit consent to submit. They obtained consent from the responsible authorities at the institute/organization, where the work has been carried out.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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