[System]
You are a **scientific‐rigor auditor**. You will receive the parsed contents of a research paper. Your job is to identify **only** those errors or flaws that directly undermine the **scientific validity** of the paper’s methods, analyses, or conclusions.

Your sole focus is to identify flaws—such as errors in experimental design, data integrity, calculations, statistical inference, or reproducibility—that directly call into question the validity of a specific claim, paragraph, or the paper as a whole.

**Do not** report issues that are purely presentational, rhetorical, stylistic, or related to citation practices.

---

After you’ve done a **detailed walkthrough** of the paper, output exactly in this format—no extra keys or commentary:

```
<analysis>
{detailed walk‑through of how you checked each section/figure and why you flagged (or did not flag) any flaw}
</analysis>

<response>
{
  "has_error": <true|false>,
  "errors": [
    {
      "location": "Section 2.1",
      "description": "Claim that ‘all X are Y’ is contradicted by citation [5], which shows examples of non‑Y X."
    },
    {
      "location": "Figure 3",
      "description": "XAxis labeled ‘Time (s)’ but units appear to be milliseconds; scale bar mismatches caption."
    }
    // …more entries…
  ]
}
</response>
```

- **Do not** include any other keys or prose outside these two tagged blocks.
- **Do not** report stylistic or citation issues.
- Be as precise as possible about **where** (section ID or figure/table) and **what** the scientific flaw is.
- Each description for the errors must be rooted in a scientific rationale explaining why it is 'wrong' (not how it could be improved).

Begin your analysis now.

[User]
Cerium oxide nanoparticles (nanoceria) are distinguished by their unique chemical properties, primarily composed of cerium dioxide and capable of fluctuating between Ce(III) and Ce(IV) oxidation states. These properties underpin their diverse applications in catalyzing chemical reactions and combating oxidative stress. The fluorite structure of CeO2 nanoparticles is crucial, facilitating their roles in various catalytic and antioxidant processes [1,2].

Initially, cerium oxide found use in gas mantles, glass polishing, and as a decolorizing agent in glass manufacturing, capitalizing on its stability and optical properties [3–5]. The versatility of CeO2 nanoparticles is utilized across various sectors. Industrially, they improve fuel cell efficiency and reduce emissions, supporting cleaner energy and better air quality. Environmentally, they are integral to water purification technologies, effectively removing organic pollutants and heavy metals, demonstrating their potential for environmental remediation [6,7].

In healthcare, the antioxidant properties of cerium oxide nanoparticles provide therapeutic benefits, mimicking crucial enzymes to neutralize free radicals. This offers promising treatments for diseases linked to oxidative stress, such as Alzheimer’s, Parkinson’s, and various cancers. Their biomimetic capabilities are driving research into CeO2 NP-based therapies that are more targeted and less toxic than traditional options [8–10].

The synthesis of CeO2 NPs is a critical area of research, with methods such as hydrothermal synthesis, sol-gel processes, and precipitation

Reactions being refined to produce nanoparticles with specific sizes, shapes, and surface characteristics. These attributes directly influence their reactivity, stability, and suitability for different applications. The ongoing development of synthesis techniques aims to optimize these parameters for enhanced functionality and application specificity [11, 12].

The incorporation of sonochemistry and the use of ultrasound waves in the synthesis of cerium oxide nanoparticles represents a promising approach to overcome some of the limitations of traditional synthesis methods. By offering precise control over nanoparticle characteristics and potentially lower energy consumption, sonochemical synthesis contributes to the advancement of CeO₂ NPs research and application, paving the way for the development of more efficient, effective, and environmentally friendly nanomaterials [13,14].

Despite the promising attributes and applications of CeO₂ NPs, their deployment is not without challenges. Issues related to nanoparticle aggregation, stability under varying environmental conditions, and potential cytotoxicity are at the forefront of current research efforts. Addressing these challenges requires a multidisciplinary approach, combining insights from materials science, chemistry, biology, and environmental science to ensure the safe and effective use of CeO₂ NPs [15,16].

The potential of CeO₂ NPs is expanding in medical and environmental fields. Their capabilities are being explored in drug delivery, bio-imaging, and tissue regeneration, aiming to create less invasive and more effective treatments. Additionally, their role in sustainable energy and pollution control highlights the importance of nanotechnology in tackling global environmental challenges [17,18].

Cerium oxide nanoparticles are at the forefront of nanotechnology, demonstrating its potential to convert theoretical science into practical solutions for critical global issues. As research progresses, the full scope of CeO₂ nanoparticles' capabilities remains to be tapped, forecasting a future where their application in health, environmental protection, and technology continues to evolve and expand. This ongoing exploration and utilization signal a transformative era in nanotechnology, poised to significantly impact human health and environmental sustainability [19,20].

Nanotechnology's appeal stems from the enhanced catalytic, stability, and redox properties of materials like CeO₂ NPs compared to their bulk forms. Recognizing that nanoscale materials behave differently spurred advancements in their synthesis. Methods like hydrothermal synthesis, sol-gel processes, and later sonochemistry, enabled precise control over nanoparticle size, shape, and crystallinity, crucial for customizing their properties for specific applications [21,22].

Research into CeO₂ NPs expanded rapidly, exploring their potential in diverse fields. In catalysis, nanoceria showed promise in improving the efficiency of fuel cells and reducing emissions from vehicles. In biomedicine, its antioxidant properties opened avenues for therapeutic applications, including neuroprotection and cancer treatment. The environmental sector saw the potential of CeO₂ NPs in treating pollutants and in energy conversion technologies [17,23].

The historical trajectory of CeO₂ nanoparticles is documented extensively in scholarly articles, detailing their evolution from basic insights to sophisticated applications in biomedicine and environmental science. Beginning with Carl Walkey’s work in 2014–2015, which highlighted their catalytic and antioxidant properties and the biological challenges for medical use, the research narrative progressed with Atul Dhall in 2018, who focused on synthesis methods and their implications for personalized medicine, emphasizing the importance of green synthesis for enhanced biocompatibility [4,21,24,25].

In 2020, Kshitij R. B. Singh and his team contributed a comprehensive review on the biosynthesis and wide-ranging biomedical applications of CeO₂ NPs, highlighting their pivotal role across various fields, including their significant impact on medicine and environmental protection. Furthermore, the contribution to the literature by authors in an IntechOpen book chapter delves into the structural nuances of CeO₂ nanostructures, especially focusing on the crucial role of oxygen vacancies and their potential applications in technologies like solid oxide fuel cells (SOFCs) [3,26].

CeO₂ nanoparticles have a substantial surface area relative to their volume, enhancing their catalytic efficiency and interaction with various substances. They retain their crystalline structure under various conditions, demonstrating durability. Notably, their properties are size-dependent; smaller particles exhibit greater surface reactivity, crucial for catalytic and antioxidant functions. Quantum effects further modify their optical, electrical, and magnetic properties, expanding their potential uses [27,28].

The high surface area and presence of defects like oxygen vacancies endow CeO₂ NPs with exceptional catalytic activities, crucial for speeding up chemical reactions, including pollutant degradation and chemical synthesis. In biomedicine, their nanoscale properties enable enzymatic mimetic activities, offering potential in anti-inflammatory, neuroprotective, and anticancer therapies [29].

Despite their promise, CeO₂ nanoparticles encounter several challenges, including toxicity concerns and environmental impacts, such as potential oxidative stress in biological systems and bioaccumulation risks that necessitate thorough risk assessments. Additionally, manufacturing challenges such as achieving consistent nanoparticle characteristics are crucial for ensuring industrial scalability and effective application [30,31].

Addressing the challenges associated with CeO₂ nanoparticles requires a multidisciplinary approach to refine synthesis techniques, boost functionality, and ensure safety and sustainability. Progress in understanding their mechanisms and interactions is essential for developing new technologies and applications. This study builds on prior research by introducing a novel sonochemical approach using glucose as a capping agent, aiming to provide innovative solutions to environmental, energy, and biomedical challenges. Utilizing (NH₄)₂[Ce(NO₃)₆] as the cerium source, we explore the efficacy of both sodium hydroxide and ammonium hydroxide as precipitating agents, with a particular focus on the innovative use of ultrasonic waves to provide the necessary energy for the synthesis process. This sonochemical synthesis method not only enhances the reaction kinetics but also enables precise control over the nanoparticle characteristics, offering a greener and more efficient alternative to conventional synthesis techniques.

After a thorough optimization of the reaction conditions, the optimal nanoparticles were systematically characterized to elucidate their physicochemical properties. The characterization process involved a comprehensive analysis of the nanoparticles’ size, morphology, crystallinity, and surface chemistry, providing valuable insights into how the use of glucose as a capping agent influences these parameters.

The culmination of our work lies in the application of these optimized CeO₂ NPs for the degradation of organic pollutants. Demonstrating a significant enhancement in catalytic performance, these nanoparticles exhibit a remarkable ability to break down various organic compounds, underscoring their potential as a sustainable solution for environmental remediation efforts. In a pioneering approach within the field of materials science, this study introduces the sonochemical synthesis of CeO₂ nanoparticles employing glucose as a capping agent for the first time. This innovative method leverages the unique properties of glucose to control the nanoparticle morphology and size, which significantly enhances their photocatalytic efficiency. The choice of glucose, a naturally derived capping agent, not only offers a green synthesis route but also optimizes the surface characteristics crucial for photocatalytic activity. This synergistic combination of sonochemistry and glucose has led to notable improvements in the photocatalytic efficiency of CeO₂ nanoparticles.

For this research, NH4OH and NaOH were sourced from Merck Company and used as received, without additional purification. (NH4)2[Ce(NO3)6] was purchased from Sigma-Aldrich and served as the cerium source. D-glucose was employed as a capping agent and also purchased from Sigma-Aldrich. The deionized water used was produced by an ultra-pure water system (Smart-2-Pure, TKA Co., Germany). Acid Red 14 and Malachite Green were obtained from Alvan Co., Iran. Amlodipine and Captopril, provided in analytical grade by Merck Company, were used for photocatalytic experiments.

The XRD analysis of the nanocomposites was performed using a Philips X-ray diffractometer equipped with Ni-filtered Cu Kα radiation, with peak matching and phase identification aided by HighScore Plus software. The software matched the observed diffraction patterns to database entries using crystallographic parameters. The scanning rate was set to 1°/min over a 2θ range of 20°–80°. The morphology and size of the nanoparticles were examined using a Philips XL-30ESM SEM. UV–Vis absorption spectra were acquired with a PerkinElmer Lambda2S spectrophotometer in the 200–800 nm range.

An ultrasonic probe device was operated with a power output of 100 W. First, 0.3 g of the cerium source and glucose are dissolved in 60 mL of water using a magnetic stirrer. Following this, an ultrasonic probe is inserted into the container holding the solution and exposed to radiation for the duration specified in the table above, while an ammonia solution is added dropwise simultaneously. The pH is adjusted to 11. Subsequently, the mixture is centrifuged, and the precipitate is washed and then dried at 80–90 °C. Finally, the residue is calcined at 500 °C for 2 h (Schematic 1).

To identify the optimal conditions for synthesizing cerium oxide nanoparticles through sonication, the process was carried out under different conditions as detailed in Table 1. The investigation focused on several parameters, including the power (in Watts), duration of sonication (in minutes), concentration of the capping agent (in millimoles), and the type of precipitator used.

Upon a detailed examination of the SEM images of cerium oxide nanoparticles synthesized at varying ultrasonic powers (Fig. 1), it appears that the use of 60 W presents the most favorable conditions, producing smaller and more uniformly distributed nanoparticles with reduced agglomeration. This observation is particularly evident in image c, where the average particle size is approximately 90 nm.

The dense nanoparticle population observed in Fig. 1a, at a 1 μm scale, along with images b and c at a 200 nm scale, underscores a robust nucleation process, leading to the formation of numerous nanoparticles. These images suggest a delicate balance between nucleation and growth rates achieved at 60 W, facilitating the synthesis of nanoparticles that are less prone to clumping as opposed to the larger, more sparse particles produced at 30 W.

At the 30 W power setting, the SEM images, particularly image d at the 1 μm scale and images e and f at the 200 and 100 nm scales, depict larger particles, implying a lower nucleation rate with a tendency for the particles to grow larger rather than to form new nucleation sites. This condition seems to be less ideal for the synthesis goals, as it leads to increased agglomeration.

On the other hand, at a higher power of 90 W, SEM images g and h, although showing discrete particles at a microscale, do not align with the desired nanoparticle characteristics observed at the optimal 60 W setting. Here, the higher power may have introduced different dynamics in the growth and nucleation process, leading to a distinct particle morphology that may not be as beneficial for the application of interest [32].

Moving forward, the synthesis process appears to benefit from further optimization of other parameters such as sonication time, the concentration of the glucose capping agent, and the type of precipitator used. Modulating the sonication time could potentially decrease the tendency of nanoparticles to agglomerate, thereby increasing their individual stability. Adjusting the concentration of the glucose capping agent may offer a refined control over particle growth and could prevent excessive agglomeration. Lastly, exploring different precipitators might alter the pH and ionic strength of the solution, which in turn could significantly impact the final morphology of the nanoparticles. Such optimization is anticipated to further enhance the capabilities of CeO₂ nanoparticles for the degradation of organic pollutants, aligning with the specific objectives of the research.

Fig. 2 depicts the SEM images provide a comparative visualization of cerium oxide nanoparticles (CeO₂ NPs) synthesized under varying ultrasonication durations, specifically 20 min (images a-c) and 5 min (images d-f). The images a-c, corresponding to a 20-min ultrasonication, depict a landscape of CeO₂ NPs characterized by distinct separations and less surface coverage, suggesting that prolonged exposure to ultrasonication leads to overgrown particles with a propensity towards coarser and more distinct structures. This is especially apparent in image a (1 μm scale), where the fractured morphology implies substantial particle growth, potentially reducing the available reactive surface area.

Upon closer examination at the 200 nm and 100 nm scales (images b

Fig. 3. FE-SEM images of CeO2 NPs after using 2 mmol glucose (a–c) and 0.5 mmol glucose (d–f).

The SEM analysis corroborates the hypothesis that a 5-min sonication, or interactions with larger polyanions, the nanoscale nature of the particles in importance in ensuring uniformity.

Show a tightly bound nanoparticle network, indicative of a synthesis regime that favors the formation of nanoparticles with a high surface area relative to volume. Such characteristics are particularly advantageous for catalytic processes, as they provide a greater active site density.

Sonication time is beneficial in producing a nanoparticulate matrix that is less agglomerated and finely dispersed, with an average particle size of approximately 20 nm. However, the suggestion to employ a 10-min sonication time as the optimum condition proposes an intermediate approach—potentially optimizing the balance between nucleation and particle growth to yield CeO2 NPs with morphological characteristics tailored for enhanced reactivity in environmental applications.

Certainly, the tendency towards agglomeration is pronounced.

Particles at a 100 nm scale, a high density or highly clustered regions even at larger pronounced at 200 nm or 100 nm closer in-

Further magnified views at 200 nm and 100 nm (images e and f)

Intense particle growth can occur.

During the sonication-assisted synthesis of CeO2 nanoparticles,

images.

From these observations, it is inferred that a glucose concentration of consistent sizes and shapes.

Despite this irregularity, the nanoscale nature of the particles in

aggregation. The right-density packing observed in image a (1 μm scale) suggests a rapid nucleation process that is curtailed before sig-

and d, the CeO2 particles appear to have clear boundaries and are less clustered, indicating that extended sonication times may encourage in-

Individual particle growth over collective nucleation. Conversely, the SEM images e-f associated with a 5-min sonication duration reveal a markedly different scenario—a densely populated nanoparticulate field where the CeO2 NPs are in closer proximity, displaying minimum growth but aggregation.

Following the scrutiny of SEM images that identified sample 5 as the optimum sample, additional characterizations were performed to understand its composition and structure in detail. The Energy-Dispersive X-ray Spectroscopy (EDS) analysis, complemented by the elemental mapping images, provides a detailed insight into the composition and distribution of elements in the CeO₂ nanoparticles characterized in sample 5 (Fig. 5). The EDS spectrum reveals the presence of distinctive peaks for cerium (Ce) and oxygen (O), establishing the material’s identity as CeO₂. Atomic percentage data from the EDS quantification shows oxygen at approximately 76.62% and cerium at 23.38%, a ratio that slightly exceeds the expected stoichiometric ratio for CeO₂ but could be indicative of surface-adsorbed oxygen rather than a fundamental compositional imbalance.

The morphological SEM image exhibits well-defined grain boundaries and a cracked structure typical of nanoparticles post-synthesis, indicating a crystalline formation with the characteristic drying patterns. The elemental maps, displayed in a composite overlay and individually for cerium and oxygen, portray a homogeneous elemental distribution. Cerium’s presence, shown in green, is densely spread across the nanoparticles, and the oxygen distribution, depicted in red, mirrors this uniformity. The consistency in the intensity of the colors across the maps indicates an even distribution of both cerium and oxygen, confirming a uniform chemical composition throughout the sample.

The X-Ray Diffraction (XRD) patterns of samples 5 and 9, with sample 9 serving as the blank, reveal distinct crystalline characteristics of the cerium oxide nanoparticles synthesized in sample 5 (Fig. 6). The XRD patterns matched the JCPDS card number 00-034-0394, confirming the phase and crystallinity of the synthesized CeO₂ [37]. The sharp and well-defined peaks in the XRD pattern of sample 5 correspond to the fluorite structure of crystalline CeO₂, indicating a high degree of crystallinity and purity in the synthesized nanoparticles. In contrast, the XRD pattern of the blank sample 9 displays diffuse and poorly defined peaks, suggesting a lack of crystalline structure and confirming the amorphous nature of the blank. This stark difference substantiates the effectiveness of the synthesis process for sample 5, culminating in nanoparticles that exhibit the crystalline attributes necessary for enhanced catalytic activity and stability, as compared to the non-crystalline blank.

On the other hand, the crystallite size of CeO₂ nanoparticles, determined using the Scherrer equation from the XRD data, was 5.95 nm for the optimized sample 5 and 11.91 nm for the blank sample 9. The smaller size in sample 5 suggests a controlled synthesis process, enhancing the nanoparticles’ surface area and potential catalytic properties, whereas the larger size in sample 9 indicates a less regulated crystallite formation [38].

The Diffuse Reflectance Spectroscopy (DRS) analysis and the obtained Tauc plot for samples 5 and 9 reveal distinct optical properties of the CeO₂ nanoparticles in Fig. 7. While our approach focuses on spectroscopy and the resulting Tauc plot, some researchers have successfully applied machine learning techniques to predict the band gaps of a wide array of materials, suggesting a complementary pathway for future enhancements in prediction accuracy [39]. Sample 5, with a band gap of 2.5 eV, exhibits a sharp absorption edge in the UV region, suggesting a strong potential for photocatalytic applications under UV and possibly visible light. The corresponding Tauc plot confirms a direct electronic transition, indicative of a material poised for effective light-energy

electrons. These superoxide radicals can participate in oxidation reactions or recombine to form hydrogen peroxide (H₂O₂), which can further dissociate into hydroxyl radicals [36].

In contrast, sample 9 shows a slightly wider band gap of 2.66 eV, as evidenced by its DRS spectrum with a less sharp absorption edge, hinting at the influence of the absent capping agent on the nanoparticles’ electronic structure. This larger band gap could restrict the photocatalytic activity to a narrower UV range [40].

Brunauer-Emmett-Teller (BET) and Barrett-Joyner-Halenda (BJH) analyses were conducted to evaluate the surface properties of CeO2 nanoparticles in samples 5 and 9 (Fig. 8).

The results for sample 5 revealed a high surface area of 102.27 m²/g and a pore volume of 0.06676 cm³/g with pores averaging 2.6112 nm in diameter, suggesting a uniform distribution of mesopores. Such uniformity is crucial for consistent photocatalytic activity as it ensures more predictable diffusion paths for reactants, facilitating effective interactions with the catalyst’s active sites. Conversely, the BJH pore size distribution for Sample 9 is broader with a less distinct peak, indicating a more varied pore size distribution [41]. Also, sample 9 displayed a lower surface area of 72.9 m²/g, a pore volume of 0.06397 cm³/g, and a larger pore diameter of 3.51 nm. The increased pore size and reduced surface area in sample 9, lacking a glucose capping agent, may lead to diminished catalytic efficiency. These findings underscore the significant role of synthesis modifications, particularly the inclusion of a capping agent, in enhancing the textural characteristics essential for photocatalytic applications of CeO2 nanoparticles. A summary of this data can be found in Table 2.

The nitrogen adsorption-desorption isotherms for both Sample 5 and Sample 9 are classified as type IV according to IUPAC standards, indicative of mesoporous materials. This classification is supported by the presence of a capillary condensation step observed within a middle range of relative pressures, typical of mesopores. Both samples exhibit hysteresis loops, which further affirm the mesoporous nature of the materials. The hysteresis loop observed in Sample 5 corresponds to type H3, commonly associated with slit-shaped pores that result from the aggregation of plate-like particles [42]. This loop type suggests non-uniform and irregular pores, characteristic of dynamically synthesized particles under sonochemical conditions [43]. For Sample 9, the type H3 hysteresis loop is also present but is less pronounced, implying a presence of larger, more irregularly shaped pores compared to Sample 5.

utilization.

Sample 9, devoid of a glucose capping agent, shows commendable activity with an 83.71% reduction, while sample 8, synthesized without ultrasonic waves, lags behind at 38.21%. Notably, the commercial TiO₂ (P25) nanoparticles exhibit a lower degradation efficiency of 9.7%, unexpectedly underperforming against the synthesized samples. These observations underscore the efficacy of the synthesis process for sample 5, particularly the role of glucose as a capping agent in enhancing photocatalytic performance, and affirm the critical influence of specific synthesis conditions on the functionality of CeO₂ nanoparticles.

The photocatalytic activities of the synthesized CeO₂ nanostructures were assessed by examining their effectiveness in degrading various contaminants in an aqueous medium under visible light exposure from a 125 W Osram lamp. For each assay, 48 mg of the nanocatalyst was dispersed into 50 ml of a solution containing 1.2 mg of the target contaminant. This suspension was stirred in darkness for 30 min to establish an adsorption-desorption equilibrium before the illumination was initiated. The degradation rate of the toxic contaminants was determined by calculating the ratio (Aₜ/A₀) × 100. Subsequently, the rate of degradation as a function of illumination time was graphically represented to evaluate the nanocatalysts’ performance [34]. Fig. 9 delineates the photocatalytic degradation of Acid red 14 using synthesized nanocatalysts from samples 5, 8, and 9 under visible light, with TiO₂ nanoparticles (P25) for comparative analysis and a catalyst-free sample as a control sample without any catalyst to account for self-degradation. The results reveal that sample 5 significantly outperforms the rest, achieving an impressive 97.2% degradation efficiency, highlighting its superior photocatalytic activity.

Fig. 10 showcases the application of the Langmuir-Hinshelwood kinetic model to describe the pseudo-first-order kinetics for the photocatalytic degradation of Acid Red 14 by various nanocatalysts, including commercial TiO₂ (P25) and sonochemically prepared samples 5, 8, and 9. The model, expressed as ln(C/C₀) = -kt, where C₀ is the initial concentration of the contaminant, C is the concentration at time t, and k is the rate constant, is commonly used to analyze the photocatalytic activity.

The logarithmic concentration ratio, ln(C/C₀), plotted against time, demonstrates that sample 5 exhibits the most rapid degradation, as evidenced by the steepest slope and highest rate constant of 0.0701 min⁻¹. This superior performance is significantly greater than that of sample 9 (k = 0.0096 min⁻¹), sample 8 (k = 0.0382 min⁻¹), and notably surpasses the commercial TiO₂, which has the lowest rate constant of 0.0021 min⁻¹. The comparison graph unequivocally establishes sample 5 as the most efficient photocatalyst among those tested, highlighting the effectiveness of the sonochemical synthesis process in optimizing the photocatalytic activity of CeO₂ nanoparticles.

Fig. 11 illustrates the impact of varying doses of CeO₂ nanoparticles from sample 5 and different concentrations of Acid Red 14 on the degradation efficiency. The results indicate that an increase in the nanoparticle dosage leads to higher degradation percentages, with the efficiency climbing from 74.1% at the lowest dosage to a peak of 97.2% at the highest dosage. This suggests that greater quantities of the nanocatalyst enhance the photocatalytic reaction by providing more active sites. Conversely, the degradation efficiency inversely correlates with the concentration of Acid Red 14; higher dye concentrations decrease the degradation percentage to as low as 62.8%, while lower concentrations facilitate a more efficient degradation, achieving up to 97.2%. These findings highlight the significance of nanoparticle dosage and contaminant concentration in optimizing the photocatalytic degradation capabilities of CeO₂ nanoparticles from sample 5.

These findings illustrate the nuanced interplay between catalyst dosage and contaminant concentration, with 50 mg of CeO₂ nanoparticles emerging as the optimal amount for the photocatalytic degradation of Acid Red 14, ensuring maximal degradation performance.

Fig. 12 provides a clear visualization of scavenging experiments aimed at identifying the main active species responsible for the photocatalytic degradation of a contaminant by sample 5. With no scavenger present, sample 5 achieves a 97.2% degradation rate, indicating its high intrinsic photocatalytic activity. When isopropyl alcohol (IPA), a known ·OH scavenger, is introduced, the degradation rate dramatically decreases to 28.7%. This significant reduction suggests that hydroxyl radicals are a primary active species in the photocatalytic process of sample 5. The addition of Vitamin C (VIT C), which is an effective scavenger of h⁺ (holes), results in a degradation rate of 48.6%. This indicates that electron vacancies also play a crucial role in the photocatalytic reaction, albeit not as dominantly as the hydroxyl radicals. The presence of potassium iodide (KI), which scavenges ·O₂⁻ (superoxide radicals), shows a lesser impact on the photocatalytic activity, with a degradation rate of 80.9%. This suggests that superoxide radicals do contribute to the photocatalysis but are not the primary reactive species [44,45].

The results from these scavenging experiments reveal that hydroxyl radicals and holes are the predominant oxidative agents driving the photocatalytic degradation in sample 5. The hydroxyl radicals, in particular, are the most influential, considering the substantial decrease.

Fig. 7. DRS and Tauc plots of sample 5 (a, b) and sample 9 (c, d).

| a                                                | b                                               |
| ------------------------------------------------ | ----------------------------------------------- |
| !Graph showing Absorbance vs Wavelength (nm)      | !Graph showing (αhv)² vs hv (eV)                |
| c                                                | d                                               |
| !Graph showing Absorbance vs Wavelength (nm)      | !Graph showing (αhv)² vs hv (eV)                |

Fig. 8. BET-BJH results for sample 5 and sample 9.

| a                               | b                               |
| ------------------------------- | ------------------------------- |
| !Graph with blue background     | !Graph with blue background     |
| c                               | d                               |
| !Graph with pink background     | !Graph with pink background     |

Fig. 9. (a) The photocatalytic activities of as-synthesized nanocatalyst and (b) comparison of photocatalytic efficiency.

| a                                                            |
| ------------------------------------------------------------ |
| !Graph showing C/C₀ vs Time (min) for different samples      |
| b                                                            |
| !Bar graph showing Degradation (%) for different samples      |

Table 2
Summary of BET-BJH results for sample 5 and sample 9.

| Photocatalyst | BET area (m² g⁻¹) | Pore volume (cm³ g⁻¹) | Pore diameter (nm) |
| ------------- | ----------------- | --------------------- | ------------------ |
| Sample 5      | 102.27            | 0.06676               | 2.6112             |
| Sample 9      | 72.9              | 0.06397               | 3.51               |

in degradation observed when they are scavenged.

The reusability of sample 5 nanocatalyst is depicted in Fig. 13a, where the catalyst, at a consistent weight of 50 mg, is used to treat a 50 mL dye solution containing Acid Red 14 with a concentration of 1.2 mg, subjected to visible light for a duration of 50 min, across 11 consecutive cycles. The initial cycle shows a high degradation rate of 97.2 %, which experiences a gradual decrease to 87.8 % by the 11th cycle.

This trend suggests a slow decline in the nanocatalyst's effectiveness, which could be due to the saturation of the catalyst's active sites by the dye or its degradation byproducts, a slight loss of the catalytic material through the repeated reuse, or alterations to the nanocatalyst's characteristics over the course of the treatment cycles. Despite this, the catalyst retains a notable degree of activity over numerous cycles, highlighting its durability and potential for repetitive use.

The XRD pattern presented in Fig. 13b for sample 5 after undergoing 11 photocatalytic cycles can be compared to the initial XRD pattern provided earlier to assess any changes in the crystalline structure of the nanocatalyst. The pattern in Fig. 13b shows sharp peaks corresponding to the characteristic crystal planes of cerium oxide, indicating that the crystalline structure is well-preserved even after multiple cycles of photocatalytic activity. The maintenance of peak positions and intensities when compared to the initial XRD pattern suggests that the crystallinity of the catalyst has not been compromised through reuse. There are no new peaks or noticeable peak broadening, which would indicate structural changes or a decrease in crystallite size. The enduring crystalline integrity as evidenced by the XRD analysis is a likely contributor to the stability and reusability of the photocatalyst. It suggests that the catalytic material does not undergo significant structural degradation or loss of crystallinity, which could otherwise lead to a decline in photocatalytic performance.

Our exploration of the mechanism governing the photocatalytic decomposition of Acid Red 14 by cerium oxide nanoparticles, initiates with an investigation into the nanoparticles’ responsiveness to visible light, leading to the subsequent formation of reactive species (Schematic 2). The following is a proposed mechanism for the photocatalytic degradation of Acid Red 14 by CeO₂ nanoparticles synthesized with the assistance of ultrasonic waves and glucose as a capping agent [46,47]:

Fig. 14 illustrates the photocatalytic degradation prowess of sample 5, which demonstrates exceptional efficiency in the breakdown of various pollutants under visible light conditions. The nanocatalyst exhibits a remarkable degradation efficiency of 97.2% for Acid Red 14, 98.7% for Malachite Green, an impressive 99.1% for Captopril, and 98.3% for Amlodipine, showcasing its robust performance across a diverse range of contaminants. The UV–Vis spectral data corroborates these findings, with significant reductions in absorbance peaks signifying the effective dismantling of the pollutants’ molecular structures within a 50-min irradiation period. The consistently high degradation percentages for all tested pollutants underscore the versatility and efficacy of sample 5 as a photocatalyst, marking its potential for widespread application in the purification of contaminated water.

Table 3 presents a comprehensive analysis of the photocatalytic efficiencies of various cerium oxide (CeO₂) nanoparticles synthesized through different methods, illustrating the enhanced performance of our sonochemically synthesized nanoparticles. With a degradation efficiency of 97.2% against Acid Red 14 under visible light, our nanoparticles not only demonstrate superior activity but also do so within a relatively short reaction time of 100 min. This marks a significant improvement over nanoparticles produced by traditional hydrothermal methods, which only achieve a 74.04% efficiency against Methylene Blue under sunlight.

Our results are particularly compelling when compared to doped or composite nanostructures such as CeO₂-TiO₂ nanocomposites and Zn-doped CeO₂ NPs. These systems, while effective, often require UV light and longer exposure times to reach high efficiencies. For example, CeO₂-TiO₂ nanocomposites, though achieving a high degradation efficiency of 95%, necessitate 150 min and the presence of UV and visible light, highlighting the time-efficiency and simpler light requirements of our nanoparticles.

Moreover, the broad-spectrum activity of our sonochemically synthesized nanoparticles against various pollutants underscores their versatility and contrasts with other nanostructures that often exhibit selective efficiency. Notably, our nanoparticles outperform CeO₂ nanowires and CeO₂/Bi₂WO₆ composites, which show lower efficiencies and require specific conditions such as different light sources and longer reaction times.

The superior efficiency, shorter reaction time, and ability to operate effectively under visible light without the necessity for UV radiation make our sonochemically synthesized CeO₂ nanoparticles particularly attractive for practical applications in environmental remediation. Their high degradation efficiency across a range of pollutants also highlights their potential to address diverse environmental challenges, providing a versatile and efficient solution for the degradation of complex organic pollutants in water systems.

In this study, we have introduced a novel sonochemical method for synthesizing cerium oxide (CeO₂) nanoparticles using glucose as a capping agent, significantly enhancing their photocatalytic properties under visible light. The optimal formulation achieved an impressive 97.2 % degradation efficiency for Acid Red 14, compared to only 9.7 % degradation using commercial TiO₂. Moreover, the kinetics analysis revealed a rate constant of 0.0701 min⁻¹ for the optimized nanoparticles, markedly higher than that observed for other catalysts, demonstrating the efficacy of our approach.

The application of glucose as a capping agent effectively controlled the nanoparticle morphology and size distribution, which was instrumental in preventing agglomeration and enhancing stability. The resultant nanoparticles exhibited remarkable photocatalytic activity not only against Acid Red 14 but also against other contaminants like Amlodipine and Malachite Green, achieving degradation efficiencies of 98.3 % and 98.7 % respectively. Furthermore, the synthesized nanoparticles maintained their catalytic performance over multiple cycles, with a minimal decrease in activity, from 97.2 % in the first cycle to 87.8 % after 11 cycles, underscoring their durability and reusability.

Sahar Zinatloo-Ajabshir: Writing – review & editing, Writing – original draft, Visualization, Validation, Project administration, Methodology, Investigation, Funding acquisition, Data curation, Conceptualization. Zohreh Mehrabadi: Validation, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. Hossein Khojasteh: Writing – original draft, Visualization, Validation, Investigation, Formal analysis, Data curation, Conceptualization. Fariborz Sharifianjazi: Resources, Investigation, Data curation, Conceptualization.

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.

Authors are grateful to the council of University of Bonab for supporting this work by Grant No (14013).

Not applicable.

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