Recycling of Walnut Shell Biomass for Adsorptive Removal of Hazardous Dye Alizarin Red from Aqueous Solutions Using Magnetic Nanocomposite: Process Optimization, Kinetic, Isotherm, and Thermodynamic Investigation

Abstract

Dye wastewater poses significant risks to human health and aquatic ecosystems, necessitating efficient remediation strategies. This study developed a magnetic Fe₂O₃ nanocomposite (MNC) derived from phosphoric acid-treated walnut shell biomass carbon to remove Alizarin red S (AR) dye from polluted water. Characterization techniques confirmed the nanocomposite’s mesoporous structure, superparamagnetic properties (61.5 emu/g), and high crystallinity. Optimization using Response Surface Methodology (RSM) revealed a maximum adsorption efficiency of 94.04% under the following optimal conditions: A pH of 2, AR dye concentration of 85 mg/L, adsorbent dose of 1.5 g/L, and particle size of 448.1 nm. Adsorption followed pseudo-second-order (PSO) kinetics (R² = 0.9999) and Langmuir isotherm models (R² = 0.9983), with thermodynamic studies indicating spontaneous and endothermic chemisorption. The intra-particle diffusion model, Bangham, and Boyd plots describe the adsorption process, and external boundary layer diffusion of AR dye molecules in the aqueous phase limits the adsorbate removal rate. Regeneration tests demonstrated reusability over three cycles, with a desorption efficiency of 50.52% using 30 mM HCl. The MNC exhibited a maximum adsorption capacity (Q_max) of 115.35 mg/g, outperforming other adsorbents, making it an efficient and sustainable alternative solution for AR dye removal from water bodies.

1. Introduction

Recycling industrial waste and its related environmental hazards are major concerns in today’s world. The primary source of environmental contamination is wastewater from industrial activities [1]. The ecosystem is negatively impacted when wastewater is released into surface waterways. Rapid industrialization and urbanization increase the need for clean water supplies [2]. Industrial processes, particularly those in the textile, paper, and leather industries, are primary contributors to water contamination by organic dyes. These industries often use large volumes of synthetic dyes, which are not fully retained in the final products and are discharged into water bodies through wastewater [3]. Many existing wastewater treatment facilities are not equipped to remove these dyes, leading to significant contamination adequately. Environmental hazards arise from the global disposal of different kinds of dye effluents into water bodies through industries [4]. The pollution of water resources poses problems for many biological, environmental, and aquatic species [5]. Currently, the global trend of the researchers is to convert to a sustainable future through the circular economy approach. Hence, water contamination management is an essential technology worldwide. Anthraquinone-based structure dyes are more environmentally stable and have lower biodegradability [6]. Organic dyes are highly carcinogenic and mutagenic pollutants that pose serious health risks because they are toxic and difficult to break down owing to their structure and physicochemical qualities. Given the capacity of dyes in the hydrosphere to cause major pollution even at very low concentrations due to their highly toxic nature and persistence in the environment, maintaining clean water sources has emerged as a priority [7]. Alizarin red S (AR, Molecular formula = C₁₄H₇NaO₇S 1,2-dihydroxy-9,10 anthraquinone sulfonic acid sodium salt) is a water-soluble anionic dye pollutant released primarily by textile industries. Moreover, it is used for dyeing biological samples such as mineralized bones and tiny invertebrate embryos in vertebrate groups, as an acid-base indicator, staining and positioning calcium deposits in tissues in histology, and identifying carbonate minerals in geology. AR has excellent chemical and photolytic stability, making it inefficient for biodegrading. Still, it is also carcinogenic, poisonous, mutagenic, or teratogenic, as do most dyes [8], necessitating its removal from industrial effluents.

There are numerous methods for treating wastewater, including coagulation/flocculation, membrane filtration, photocatalytic degradation, ozonation, ion exchange membranes, electrochemical oxidation, adsorption, and so on [2]. Among these, adsorption is the most extensively studied and well-known technique for removing dye from contaminated water because of its high effectiveness, low cost, ease of operation, and reliability, among other advantages [9,10]. Many substances have been researched as possible adsorbents for wastewater treatment, including activated carbon, metal–organic frameworks, and biopolymers [11,12,13]. Due to its porous structure and large specific surface area, activated carbon has demonstrated a strong adsorption ability for various contaminants among these materials. One significant disadvantage of powder-activated carbon is that extracting it from treated aqueous solutions might be challenging. Magnetic composite powders based on activated carbon have garnered much interest as a solution to this issue [14]. In recent years, the magnetic separation technique using magnetic nanocomposites (MNC) has been widely used to remove pollutants due to its spectacular significance in accelerating separation speed and improving the efficiency of water treatment [15]. Nanocomposites involving magnetic nanoparticles can be quickly recovered from the solution by applying an external magnetic field (no need for centrifugation or filtration process to remove the magnetic nanoparticles). The ease of collection promotes the adsorbent reusability [16]. Several techniques, including sol–gel, hydrothermal, solvothermal, reduction, co-precipitation, pyrolysis of organometallic compounds, and combustion, have been employed in the synthesis of MNC. Most of these techniques have drawbacks, including lengthy reaction durations, hazardous raw ingredients, several stages in the synthesis process, and difficult-to-control reactions. Conversely, the alkali precipitation technique employed in this work has shown to be workable, adaptable, straightforward, and secure. It can save time and energy because it is a simple and rapid operation requiring essential tools. The alkali precipitation approach also makes it possible to synthesize a wide range of nanocomposites with high yields, large surface areas, and adaptable adsorption capacities in an effective manner [17].

Recently, different types of carbon derived from agricultural biomass have demonstrated potential for adsorbing environmental pollutants. This effectiveness can be attributed to their surface area and porosity. The shells of walnuts are considered waste and have no economic value, leading to extra disposal issues and associated costs. The leftover biomass from walnut shells has limited applications due to challenges such as high emissions, which arise from the low melting point of the ash produced when burnt, causing negative environmental impacts. Constraints on landfill capacity combined with a growing demand for walnut shells have led researchers to explore alternative disposal methods. Consequently, there is a significant global interest in exploring alternative technologies to utilize walnut shells for addressing environmental challenges. Recently, there has been a growing interest in recycling agricultural waste due to more stringent environmental regulations. Annually, the worldwide output of walnuts and walnut shells is approximately 2 million tons and 890,000 tons, respectively [18]. The processing of walnuts generates significant walnut shells, which can serve as an excellent energy resource. Walnut shells contain a limited amount of cellulose (25.5%) and hemicellulose (22.2%), but their high lignin content (52.3%) results in a substantial energy yield that is comparable to that of coal [19]. The price of raw walnut shell biomass powder is $0.82 per kg. To the best of our understanding, the obtained price of the ultimate production of activated carbon from walnut shell biomass is considerably lower than the commercially available activated carbon, which stands at $3.15 per kg and is used for eliminating toxic pollutants from wastewater [20]. Due to their ease of cultivation from seeds, walnuts are widely planted in India. The annual increase in walnut production in India is approximately 2.9%. Both raw and processed walnut shell biomass have shown a remarkable ability to adsorb heavy metal ions, organic substances, and dyes from wastewater [21]. Many researchers have reported the removal of AR dye from aqueous solutions using various adsorbents, such as graphene nanocomposites, SnO₂/CeO₂ nanocomposites, mesoporous sponge polyaniline nanocomposites, chemically treated avocado seed, Fe₃O₄@magnesium hydroxy silicate, cellulose combined with ferromagnetic particles, and multi-walled carbon nanotubes [4,22,23]. Several studies have been reported for the adsorption of toxic pollutants such as Tetracycline, Crystal violet, Acid orange, Methyl orange, Congo red, Reactive black, brilliant blue, Acid yellow, Rhodamine B, and Methylene Blue from synthetic effluent using MNC as an adsorbent [24].

In experiments, low-cost agricultural biomass has demonstrated promising efficacy as an adsorbent in treating hazardous effluents [25]. However, there has not been much research carried out on the removal of AR dye from wastewater using magnetic nanocomposites made from the biomass-activated carbon adsorbent of Juglans nigra (walnut shell). To the best of our knowledge, no research has been published that discusses the possibility of employing carbon-Fe₂O₃ magnetic nanocomposites made from walnut shell biomass as an adsorbent in batch or continuous mode to remove AR dye from simulated effluent. The previously published studies were followed about the influence of different process parameters on the expulsion of AR dye from polluted water, but not for the combination of AR dye and MNC adsorbent. Studying the use of MNC as an inexpensive adsorbent for the expulsion of AR dye from contaminated water is necessary to lower the energy required for processing the wasted adsorbent. In batch investigations, adsorption kinetics and isotherm models must be created to explain the appropriate adsorption procedure for decolorizing artificial dye wastewater with AR utilizing MNC adsorbent. Consequently, an attempt has been made to use MNC produced from activated carbon to remove AR dye from an aqueous solution. This work aims to synthesize activated carbon from biomass derived from walnut shells, which yields magnetic iron oxides when combined with FeSO₄ and NaOH. It has been reported that the produced magnetic nanocomposites were used in the adsorption of AR from aqueous solution after their structural, morphological, and magnetic characteristics were examined.

The novelty of this work lies in the development of a magnetic Fe₂O₃ nanocomposite from phosphoric acid-treated walnut shell biomass carbon, offering a sustainable and efficient solution for AR dye removal from wastewater, addressing a critical research gap. Unlike prior studies, MNC uniquely utilizes agricultural waste as a precursor for adsorbent materials, combining sustainability with exceptional adsorption performance. The research encompasses the comprehensive characterization of the MNC, optimization of operational parameters using response surface methodology, and thorough analysis of adsorption kinetics, isotherms, and thermodynamics, offering valuable insights into the mechanisms of dye removal. Furthermore, the study highlights the reusability of the MNC across multiple cycles, emphasizing their economic and environmental benefits, making it a comprehensive and sustainable approach to wastewater remediation. By focusing on sustainable material innovation and practical applicability, this work significantly contributes to advancing wastewater treatment technologies.

2. Materials and Methods

2.1. Chemicals and Reagents

All chemicals were of analytical reagent grade. The synthetic dye AR was purchased from Sigma Aldrich, India. The remaining chemicals were purchased from Merck, India. AR dye was prepared as 1000 mg/L stock solution, and the experimental solution of required dye concentrations was obtained by diluting the stock solution with pH-adjusted distilled water by adding 0.1 N HCl or 0.1 N NaOH.

2.2. Instrumentation

The UV–visible spectrophotometry device (Shimadzu UV-1800, Kyoto, Japan) at a wavelength of 421 nm was employed to measure the AR dye concentration in solutions. The sample’s magnetic properties were measured using a vibrating sample magnetometer (VSM, Quantum Design, San Diego, CA, USA), which operates on the principle of vibrating sample magnetometry. In addition, nanoparticle size (nanoparticle size analyzer, Horiba SZ-100, Horiba, Kyoto, Japan), Thermogravimetric (TG, TA Instruments, Newcastle, DE, USA), Brunauer–Emmett–Teller (BET, Smart Instruments, Dombivli, India), zeta potential, zero-point charge (pH_zpc), X-ray photoelectron spectroscopy (XPS, JEOL, JAMP-9500F Tokyo, Japan), Fourier transform infrared spectroscopy (FT-−IR, Shimadzu 8400S, Kyoto, Japan), Field emission-scanning electron microscopy/Energy-dispersive X-ray spectroscopy (FE-SEM/EDS, JEOL 6300, JEOL, Tokyo, Japan) analyzers were applied for characterizing the physical, chemical, and morphological structure of magnetic nanocomposite adsorbent. The degree of crystallinity of the MNC adsorbent was studied using an X-ray diffraction (XRD, Rigaku Ultima IV, Tokyo, Japan) analyzer. The scan measurements were performed in a 2θ range of 10–90° with a scan speed of 2° min⁻¹ with a step size of 0.02. A digital pH meter (Systronics 335, Bengaluru, India) was used for pH measurements. An incubator shaker (Lead Instruments, Bengaluru, India) was applied to stir the dye solutions with an MNC adsorbent.

2.3. Synthesis of Walnut Shell-Activated Carbon Magnetic Nanocomposites Adsorbent

The walnut biomass was thoroughly rinsed with distilled water to remove any surface-adherent dirt particles, and it was then dried for 24 h at 383 K in a hot air oven. The dehydrated materials were crushed into a fine powder with a crusher and heated for two hours to 773 K in a muffle furnace. Following sieving, the appropriate amount of powdered walnut shell carbon was combined with phosphoric acid in a proportion of 1:2.5 (w/v), meaning 1 g of powdered walnut shell carbon was mixed with 2.5 mL of phosphoric acid [26]. After separating the activated carbon, it was washed with deionized water and 1% NaOH solution until the pH was neutral. The contents were then oven-dried for 24 h at 373 K to obtain pure activated carbon. An amount of 5.56 g of walnut shell activated carbon and 2.78 g of ferrous sulfate (weight ratio 2:1) were combined with 100 mL of distilled water to create the magnetic nanocomposite, which was then aggressively agitated for one hour. To this, 1% NaOH was added dropwise till pH reached 12 and kept in a water bath at 353 K for one hour. After recovering the resulting magnetic product, it was oven-dried (338 K, 24 h), ground, and sieved [27]. The powdered materials were stored in an airtight container to be used in further adsorption experiments.

2.4. Batch Adsorption Studies

To examine the impact of variables like starting pH, MNC adsorbent dosage, initial dye concentration, electrolytes, and temperature on AR adsorption, multiple batch tests are conducted in a 250 mL Erlenmeyer glass flask holding 100 mL of dye solution. One factor is varied while maintaining a constant level of the other variables. The solutions were mixed for six hours at a predetermined temperature in a temperature-controlled shaker at a steady speed of 150 rpm. After each variable’s investigation, the optimal quantity was measured to investigate the subsequent parameter [28]. Adsorption equilibrium tests were conducted by changing the starting adsorbate concentration (35–210 mg/L) while maintaining a constant adsorbent dose. After that, the mixture was put on a shaker with temperature control and shaken for 24 h at room temperature at 150 rpm. Following adsorbent saturation, the aqueous solution was separated, and spectrophotometry was used to determine the amount of residual AR in suspensions in the clear liquid. The following formula was used to calculate the amount of AR dye adsorption capacity at equilibrium (q_e), where C_o, C_e (mg/L), V (L), and W (g) represent the initial AR concentration, equilibrium AR concentration, dye solution volume, and adsorbent mass, respectively [28].

$${\mathrm{q}}_{\mathrm{e}}={\displaystyle \frac{\left({\mathrm{C}}_{\mathrm{o}}-{\mathrm{C}}_{\mathrm{e}}\right)\mathrm{V}}{\mathrm{W}}}$$

(1)

The different AR dye concentrations from 35 to 210 mg/L were examined in kinetic experiments. The appropriate volume of the aqueous phase was taken at predefined intervals and instantly separated by an adscititious magnet to gather the adsorbent [29]. The adsorption capacity of AR (q_t, mg/g) on adsorbents at a given time t (min) and removal effectiveness (R, %) was calculated as follows [30], where C_t (mg/L) is the AR concentration at a particular time t.

$${\mathrm{q}}_{\mathrm{t}}={\displaystyle \frac{\left({\mathrm{C}}_{\mathrm{o}}-{\mathrm{C}}_{\mathrm{t}}\right)\mathrm{V}}{\mathrm{W}}}$$

(2)

$$\mathrm{R}(\mathrm{\%})={\displaystyle \frac{\left({\mathrm{C}}_{\mathrm{o}}-{\mathrm{C}}_{\mathrm{t}}\right)}{{\mathrm{C}}_{\mathrm{o}}}}\times 100$$

(3)

2.5. Desorption and Reusability Studies

The ability to recycle adsorbent materials is crucial for making the adsorption process cost-effective and environmentally friendly. In terms of use, an advanced and superior adsorbent should possess features like removal efficiency, stability, and reproducibility. When adsorbent materials can be easily regenerated and reused, it reduces disposal issues and enhances environmental purity. The removal effectiveness increases with increasing acidity of the solution, and the adsorption is extremely pH-dependent. As a result, the solution’s pH can be lowered to initiate the desorption of AR. This implies that using an acidic solution to wash the loaded MNC adsorbent might aid in their renewal [31]. Desorption investigations were carried out separately for Alizarin red dye solution (100 mL) in a 165 mg/L concentration. The MNC adsorbent loaded with dye molecules was rinsed with 100 mL of various solvents such as methanol, acetone, 30 mM HCl, and 30 mM NaOH [32]. After adding the desorbing reagent, the solution was stirred at 150 rpm with a contact time of 12 h. The concentration of each eluent was measured using the obtained standard curve from the spectrophotometry method. After three water washes, the regenerated MNC adsorbent was magnetically isolated from the water and dried at 353 K until a consistent weight was reached. Following desorption, the regenerated MNC was used in the adsorption studies conducted by the adsorption experiments previously indicated in Section 2.4. This adsorption/desorption cycle was carried out four times. Every experiment was performed twice to ensure repeatable findings, and the Section 3 report the average values of these repetitions.

3. Results and Discussion

3.1. Characterization of Synthesized MNC Adsorbent

3.1.1. FT-IR Analysis

The FT-IR spectra of untreated and AR dye-treated MNC, represented by red and blue lines in Figure 1A, respectively, display distinct vibrational modes at 556.32, 996.79, 1130.87, 1215.69, 1691.72, 2263.57, 3124.48, and 3721.84 cm⁻¹. The peak at 556.32 cm⁻¹ corresponds to Fe–O bond vibrations in both tetrahedral and octahedral sites, confirming the presence of Fe₂O₃ particles, as typically observed below 900 cm⁻¹ [33,34]. Peaks at 996.79 cm⁻¹ and 1130.87 cm⁻¹ are assigned to C–OH bond vibrations and C–N stretching of aliphatic amines, respectively. The peak at 1215.69 cm⁻¹ is associated with C–O stretching, indicating changes in surface chemistry following AR dye adsorption. Broader absorption bands at 1691.72 cm⁻¹, 2263.57 cm⁻¹, and 3124.48 cm⁻¹ correspond to C=C stretching (alkenes), C≡N stretching (nitriles), and O–H stretching (hydroxyl groups), respectively [35]. Additionally, the high-frequency band at 3721.84 cm⁻¹ is attributed to free O–H stretching vibrations, where a decrease in intensity after dye adsorption suggests interactions between hydroxyl groups and AR dye molecules. Minor peaks observed in the untreated MNC spectrum likely arise from organic impurities introduced by the activated carbon component derived from walnut shells. Notably, shifts in peak positions and intensities between untreated and dye-treated samples indicate electrostatic interactions and possible hydrogen bonding between AR dye molecules and functional groups such as hydroxyl, amine, and nitrile groups on the MNC surface. These observations confirm successful dye adsorption and highlight these functional groups as active binding sites. After adsorption, a peak shift to 549.02 cm⁻¹ is observed, corresponding to Fe–O stretching vibrations, further supporting the interaction between AR dye and the MNC surface.

3.1.2. Morphological Analysis of MNC by FE-SEM/EDS

Figure 1B,C show the images of the FE-SEM of the activated carbon-Fe₂O₃ nanocomposite before and after removing the AR dye. Figure 1B (1 μm, 10,000× resolution) shows that the nanocomposite formed a very rough, irregular surface with spherical particles of different sizes, uniform size distribution, large pores, and some agglomeration, which enabled high surface area and directly promoted the adsorption capacity of the nanocomposite [26,36]. After adsorption, the MNC material surface became smoother, confirming the presence of AR dye molecules onto the particle surface interior pores of the material (Figure 1C). Figure 1D represents the EDS spectrum results, showing that a sharp peak at 0.3 keV confirmed the presence of carbon, while another prominent peak at 0.5 keV belonged to oxygen. The 1 and 2.2% peaks correspond to sodium and sulfur, respectively. The smaller peaks between 0.7 and 6.4 keV are attributed to iron. The weight percentage of iron and oxygen is 12.31% and 39.28%, respectively, proving the formation of Fe₂O₃ nanoparticles [29]. The weight and atomic proportion of carbon, oxygen, sodium, and sulfur rose upon adsorption, compared with before adsorption, indicating that AR dye molecules were accumulated on the MNC adsorbent (Figure 1E).

3.1.3. XPS Analysis

The nanocomposite adsorbent XPS was characterized to investigate the chemical composition of the as-prepared walnut shell biomass carbon-modified magnetic nanocomposite. XPS data are typically displayed as a graph showing counts against binding energy, with the peak positions indicating the elements and their corresponding electronic structures. The total survey XPS spectra allow for the co-existence of carbon, oxygen, and iron elements in the as-proposed adsorbent of MNC, as demonstrated in Figure 1F through the black curve line. FE-SEM confirmed this discovery in conjunction with EDS, which revealed that the magnetic nanoparticles (NPs) comprised components including carbon, oxygen, and iron (Figure 1F) [29]. Iron originates from Fe₂O₃ nanoparticles, while sulfur is produced due to alizarin red sorption, an organic pigment. Considering this characteristic, it seems that the nanoparticle, in its current state, is an excellent candidate for the adsorption of organic dye AR removal. From Figure 1F, it can be determined that the surface of the MNC material shows peaks at 283.96, 529.49, 710.12, and 721.80 eV, which correspond to the C1s, O1s, Fe2p, and Fe2p states, respectively. The wide oxygen peak observed at 529.49 eV may be related to the C–O and O–H functionalities found in the sample and the oxygen associated with the Fe₂O₃ nanoparticles, aligning with what has been reported in the literature. The C1s peak observed at 283.96 eV is attributed to alkyl or aliphatic carbons in the biomass. The two peaks at 710.12 eV and 721.80 eV are associated with the Fe³⁺ oxidation state, aligning with the oxidation state of iron in Fe₂O₃ [37].

The additional description for the XPS analysis of MNC adsorbent is given in Section S2.1.1 in the Supplementary Information (Figure S1).

3.1.4. XRD Analysis

The XRD pattern of the carbon-magnetic nanocomposite (Figure 2A) shows several peaks at 2θ = 16.60°, 18.96°, 20.67°, 23.04°, 26.91°, 32.96°, and 34.88°, which are segmented according to the (110), (111), (110), (002), (140), (102), and (311) planes, respectively. XRD results reveal that the prepared α-Fe₂O₃ nanocomposite materials have a rhombohedral structure with a space group of R-3c corresponding to α-Fe₂O₃ [38,39]. The peak at 2θ values of 26.91° and 34.88° correspond to activated carbon and homohematite (α-Fe₂O3), respectively [26]. The results agree with the Inorganic Crystal Structure Database (ICSD) code 88418, which is concordant with the literature [40]. Furthermore, the appearance of sharp, narrow, and highly intense characteristic peaks at 16.60°, 18.96°, 20.67°, 23.94°, and 32.96° in the spectrum indicates that the MNC adsorbent exhibits the crystalline nature and purity of the synthesized material. The average crystallite size (D) was computed from the two most intense peaks (18.96° and 34.88°) utilizing the Debye-Scherrer’s Formula [41]:

D = Kλ/(β_D-S cos θ)

(4)

where the diffraction angle is θ, the full width at half maximum (FWHM) is β_D-S, a constant value of K is 0.9, and the X-ray wavelength is λ. The typical size of a crystallite diameter was discovered to be 24.36 nm. The synthesized Fe₂O₃ samples displayed characteristic peak positions consistent with the standard iron oxide (Fe₂O₃) pattern (Joint Committee on Powder Diffraction Standards, JCPDS 33-0664) reported in earlier studies [42], closely aligning with the current findings rather than other phases such as Fe₃O₄ (magnetite) or β-FeOOH. Hematite exhibits unique diffraction peaks at specific 2θ angles, and their precise alignment with the Fe₂O₃ pattern further supports its identification (Figure S2) [43]. The thermal degradation profile in Figure 2D indicates the stability of the Fe₂O₃ phase. In contrast, other iron-based compounds, such as β-FeOOH, would decompose into different phases at lower temperatures, leaving a stable oxide residue, which is consistent with the behavior of Fe₂O₃. The saturation magnetization (Ms) value of the MNC material (~61.5 emu/g) is lower than that of Fe₃O₄ (~75.3 emu/g), which is consistent with hematite’s weak magnetic properties [44]. The XRD pattern, thermal stability data, and magnetic behavior support the conclusion that the material is Fe₂O₃ (hematite) rather than Fe₃O₄ or other iron-based phases.

3.1.5. BET Surface Area, Zero-Point Charge and Particle Size Investigations

The surface area of the prepared MNCs was investigated using the BET technique in the presence of nitrogen. The adsorption–desorption isotherm is shown in Figure 2B. The type IV isotherm of the prepared material is a hysteresis loop. It reflects the difference between the adsorption and desorption processes. The isothermal adsorption of activated carbon-Fe₂O₃ nanocomposites often exhibits hysteresis loops. This type of hysteresis indicates the presence of narrow pores. Microporous or mesoporous MNCs usually exhibit hysteresis loops in their physical adsorption isotherms, most of which are relatively higher than 0.29 [45]. The BET area of surface, volume of the pore, pore size, and average particle size of the MNC adsorbent are 188.749 m²/g, 0.1081 cm³/g, 4.8706 nm, and 448.1 nm, correspondingly, confirming the mesoporous pores. Therefore, the high surface area and the existence of mesoporous pores give good results in removing various contaminants. The iso-electric point charge (pH_zpc) of the MNC adsorbent was determined to be at pH 6.7 (Figure 2C). This means that the surface of MNC material will be protonated in an acidic solution with a pH value below 6.7 due to the excess H⁺ ions, resulting in a positively charged adsorbent surface. Conversely, at pH levels above pHzpc, the surface sites are deprotonated by OH⁻ ions, rendering the adsorbent negatively charged [46]. The zeta potential of the MNC material is −26.8 mV, suggesting that the prepared material is environmentally stable.

3.1.6. TG Analysis

The TG studies analyzed the thermal behavior and stability of the activated carbon-Fe₂O₃ nanocomposite by monitoring the sample’s weight change when heated at different temperatures (Figure 2D). From the TG analysis graph, the weight percentage of the MNC adsorbent diminished from 99.98% to 67.054% when the temperature increased from 299.27 to 966.41 K. The MNC adsorbent showed two-step weight loss; the initial weight loss of approximately 24.43% was rapid from 299.27 K to 375.97 K on the TGA curve, which was attributed to the desorption of moisture content physically adsorbed on the oxide surface [21]. Afterwards, a substantial weight loss was found from 376 K to 966.41 K, wherein a maximum weight loss of 32.926% occurred from its initial weight. At the end of 966.41 K, the residual mass of the nanocomposite was found to be 67.054%, which could represent the thermal stability of iron-oxides and other carbon-containing compounds [47].

3.1.7. VSM Analysis

To investigate the magnetic characteristics of Fe₂O₃ nanoparticles and MNC material at room temperature, a superconducting quantum interference device (SQUID) magnetometer was used (Figure 2E). The lower magnetization saturation value of magnetic nanocomposite (61.5 emu/g) results from the less-magnetic behaviors of Fe₂O₃ NPs. This contrasts with the value of bare Fe₂O₃ NPs, which is 79.3 emu/g [48]. Furthermore, in response to an applied magnetic field at ambient temperature, the magnetic properties of MNC material manifested themselves in the form of remanence-free and zero coercivity magnetization curves with S-shaped hysteresis lines. This was a comparable phenomenon to the magnetic characteristics of Fe₂O₃ nanoparticles. Hence, the VSM analysis may conclude that the Fe₂O₃ nanoparticles have a super-paramagnetic characteristic [26].

3.2. Investigation of Experimental Studies Conducted in Batch Mode to Eliminate AR Dye from Wastewater Using MNC Adsorbent

3.2.1. Effect of Acidity and Alkalinity on AR Dye Solution

The acidity and alkalinity of the aqueous phase in an AR dye solution are crucial factors affecting the electrostatic interactions between the adsorbate and nano adsorbent, as they influence the charge on the particle surface, the extent of ionization of dye molecules and the dissociation of different functional groups on the adsorbent. A series of batch experiments were performed to obtain the impact of pH on the adsorption effectiveness of AR using MNC as an adsorbent by changing the solution’s pH within the range of 2–12 while keeping all other operating parameters constant at room temperature. The adsorption results at various experimental factors described here are reported in

Table 1. Influence of various experimental factors on AR dye removal using MNC adsorbent.

pH	Co (mg/L)	MNC Dosage (g/L)	Dp (nm)	Agitation Speed (rpm)	Temperature (K)	Time (h)	% AR Dye Adsorption
2	165	1.20	448.1	150	301	24	84.93
3	165	1.20	448.1	150	301	24	83.12
4	165	1.20	448.1	150	301	24	80.24
5	165	1.20	448.1	150	301	24	78.46
6	165	1.20	448.1	150	301	24	75.34
7	165	1.20	448.1	150	301	24	70.96
8	165	1.20	448.1	150	301	24	63.54
10	165	1.20	448.1	150	301	24	50.64
12	165	1.20	448.1	150	301	24	37.45
2	35	1.20	448.1	150	301	24	94.43
2	70	1.20	448.1	150	301	24	91.24
2	105	1.20	448.1	150	301	24	88.65
2	140	1.20	448.1	150	301	24	86.12
2	175	1.20	448.1	150	301	24	81.48
2	210	1.20	448.1	150	301	24	72.29
2	165	0.50	448.1	150	301	24	62.54
2	165	0.75	448.1	150	301	24	71.44
2	165	1.00	448.1	150	301	24	78.69
2	165	1.25	448.1	150	301	24	86.24
2	165	1.50	448.1	150	301	24	87.43
2	165	1.80	448.1	150	301	24	89.01
2	165	1.25	1084.6	150	301	24	75.36
2	165	1.25	786.7	150	301	24	81.52
2	165	1.25	448.1	0	301	24	31.19
2	165	1.25	448.1	45	301	24	44.36
2	165	1.25	448.1	90	301	24	58.72
2	165	1.25	448.1	135	301	24	75.64
2	165	1.25	448.1	180	301	24	87.63

. Figure S3A and Table 1 show that when pH was raised from 2 to 12, the effectiveness of AR removal dropped from 84.93 to 37.45%, respectively. The amount of H⁺ ions on the particle’s surface is high in the acidic range, leading to more electrostatic interactions between the AR dye anions and the positively charged nanomaterials. Hence, the adsorption efficiency reaches its maximum at pH 2. At pH 2, the competition between hydrogen ions and AR dye anions is less, and many AR dye molecules can bind to the functional groups of the adsorbent material, so the ion concentration in the solution decreases, which increases the adsorption efficiency. When the pH level rises, the protons on the particle surface are removed, and the OH⁻ ion concentration on the nanomaterial surface begins to increase. The negatively charged areas on the nanomaterial surface do not promote the adsorption of AR dye anions due to electrostatic repulsion. Additionally, at pH 12, the adsorption effectiveness is at its lowest because of the increased competition between excess hydroxyl ions and anionic AR ions for the surface of the adsorbent containing active sites [49,50]. Under acidic conditions (pH < pHzpc), the electrostatic attraction between the positively charged MNC surface and the negatively charged AR dye anions enhances adsorption. However, a competitive effect also exists: the abundant H⁺ ions compete with dye anions for adsorption sites at very low pH. Despite this competition, the strong electrostatic attraction between the protonated MNC surface and AR anions dominates, leading to high dye adsorption at pH 2.

3.2.2. Impact of Initial Concentration of AR Dye

The impact of starting AR concentration on the effectiveness of adsorption was investigated within the 35–210 mg/L range, and the findings are shown in Figure S3B (Table 1). As a result, AR dye’s adsorption on the surface of MNC adsorbent particles at saturation increased from 22.47 to 110.35 mg/g, and the adsorption efficiency diminished from 94.43 to 72.29% with a rise in the initial adsorbate concentration between 35 and 210 mg/L. At low concentrations, the mass of AR is small, and the adsorption medium can adsorb the mass of dye anions, so the adsorption efficiency increases. More adsorbate molecules compete with one another for the established active sites of the adsorbent when the mass of AR is higher at high concentrations, causing the buildup of AR dye molecules on the adsorbent’s vacant sites. As a result, the adsorption efficiency decreases when there are not enough accessible active sites on the particle surface. The rise in the adsorption of dye uptake at equilibrium is because of the rise in the gradient of adsorbate concentrations between the surface of MNC solid particles and the solution’s concentration of AR. This concentration gradient is the primary motivator behind the movement of AR dye molecules onto the particle’s surface from the aqueous solution [51].

3.2.3. Influence of MNC Adsorbent Particle Size (Dp)

The adsorption effectiveness of AR varies greatly depending on the area of the surface of the particles accessible for dye removal. The impact of the MNC adsorbent’s average particle diameter on the dye removal was investigated by changing the particle diameter from 1084.6 nm to 448.1 nm. The size of the MNC adsorbent particles is inversely correlated with the AR dye’s adsorption effectiveness, as shown in Figure S3C. Consequently, the effectiveness of AR’s adsorption dropped from 87.11% to 75.36% as the particle size increased from 448.1 nm to 1084.6 nm (Table 1). Based on this correlation, powdery materials are preferred over granular materials. The greater surface area of the smaller particles being adsorbed per unit mass is responsible for higher adsorption effectiveness. Also, the smaller the particle, the shorter the diffusion path, so the AR dye molecules can be adsorbed quickly and penetrate deeply into the surface of the adsorbent particles [21,52].

3.2.4. Effect of Dosage of MNC Adsorbent

The MNC adsorbent for the adsorption of AR dye was performed as a function of particle dosage. When the adsorbent dosage was raised from 0.5 to 1.8 g/L, Figure S3D shows a significant improvement in adsorption efficiency (Table 1). Furthermore, with 1.25 g/L MNC adsorbent, more than 85% AR dye molecules can be adsorbed from 165 mg/L AR solution. As the dosage increases, the surface area of the material increases, which means that the functional groups that can bind with AR ions increase, expanding the distribution of active sites on the adsorption surface, and thus the adsorption efficiency increases. At the same time, the adsorption capacity (q_e) decreases, as shown in Figure S3D. This means a decrease in the adsorbent dosage leads to a larger adsorption capacity and vice versa. This primarily results from the difference in concentration gradients between the AR dye concentrations in the solution and those at the MNC adsorbent’s surface. As a result, when the adsorbent dosage increases, the competition for the active sites available for AR dye adsorption reduces. This might result from MNC adsorbent particles interacting, such as aggregation or overlapping of adsorption binding sites due to high adsorbent concentration. This accumulation may lengthen the diffusion channel and decrease the adsorbent’s active surface area [53].

3.2.5. Impact of Agitation Velocity

The impact of the stirring speed on the AR dye pollutant from aqueous solution was examined in the range of 0–180 rpm, and Figure S3E and Table 1 display the findings. The results show that the relationship between the variables is direct, and the adsorption efficiency increases from 31.19% to 87.63% when the stirring speed increases from 0 to 180 rpm. This outcome could be explained by increasing agitation speed during adsorption is essential for minimizing external mass transfer resistance. Agitation promotes the efficient movement of AR dye molecules from the bulk solution to the adsorbent surface by disrupting the stagnant boundary layer. This reduction in boundary layer thickness enhances the diffusion rate of dye molecules toward the active sites of the MNC adsorbent more quickly, leading to improved adsorption efficiency and ensuring that the process reflects the actual interaction between the dye molecules and the adsorbent rather than being limited by diffusion barriers [54].

3.2.6. Effect of Ionic Strength

The wastewater from textile industries has a large concentration of dissolved inorganic salt ions, which can impact adsorption effectiveness. As such, it is crucial to investigate the effects of ionic strength on the adsorption process [52]. To examine the impact of ionic strength on AR adsorption, several concentrations of electrolytes, including K₂SO₄, NH₄Cl, and NaCl, were introduced in different batches. The findings of changing the electrolyte concentration in a 165 mg/L AR dye solution from 0% to 1% (w/v) are displayed in Figure S3F. It can be concluded that the investigated electrolytes enhance the adsorption of AR dye. Moreover, as the electrolyte concentration increases, the adsorbent’s efficiency in removing MNCs improves. This effect arises from the increased positive charge on the solid surface, strengthening the electrostatic interaction between the solid particles and AR dye molecules [55].

3.3. Designing Experiments to Optimize Process Parameters and Analyze Empirical Data

The process parameters, i.e., initial pH (X₁), initial AR dye concentration (X₂), MNC adsorbent dosage (X₃), and particle size (X₄), were optimized using response surface methodology (RSM). The interactions between the independent variables and the associated responses were characterized using central composite design (CCD) using Minitab 16 statistical software.

Table 2. Central composite design (CCD) method used independent variables and their levels.

Independent Variables	Range and Level
	−2	−1	0	1	2
Initial pH (X1)	1.6	1.8	2.0	2.2	2.4
Initial AR pollutant concentration, mg/L (X2)	85	125	165	205	245
MNC adsorbent dose, g/L (X3)	1.0	1.25	1.5	1.75	2.0
Nanoadsorbent particle diameter, nm (X4)	260.3	354.2	448.1	542	636

presents the range and levels of each independent variable incorporated into the model, with adsorption efficiency as the dependent response variable.

A total of 31 experiments were conducted, including 16 factorial points, 8 axial points, and 7 replicate points, according to 2⁴ CCD. The following second-order polynomial model approximates the relationship between the experimental factors and the predicted responses [56].

$${\mathrm{Y}}_{\mathrm{e}\mathrm{s}\mathrm{t}}={\mathrm{b}}_{\mathrm{o}}+\sum _{\mathrm{i}=1}^{{\mathrm{n}}_{\mathrm{v}}}\left({\mathrm{b}}_{\mathrm{i}}{\mathrm{x}}_{\mathrm{i}}\right)+\sum _{\mathrm{i}=1}^{{\mathrm{n}}_{\mathrm{v}}}\left({\mathrm{b}}_{\mathrm{i}\mathrm{i}}{\mathrm{x}}_{\mathrm{i}}^2\right)+\sum _{\mathrm{i}=1}^{{\mathrm{n}}_{\mathrm{v}}-1}\sum _{\mathrm{j}=\mathrm{i}+1}^{{\mathrm{n}}_{\mathrm{v}}}\left({\mathrm{b}}_{\mathrm{i}\mathrm{j}}{\mathrm{x}}_{\mathrm{i}}{\mathrm{x}}_{\mathrm{j}}\right)$$

(5)

where n_v is the number of variables, x_i and x_j are the coded values of the process components, and b₀, b_i, b_ii, and b_ij are the coefficient constant, linear, quadratic, and interaction coefficients, respectively. Additionally, Y_est is the predicted adsorption efficiency.

3.3.1. Fitting of the Experimental Data in the Quadratic Model

Thirty-one trials were conducted using the RSM approach, and

Table 3. Batch adsorption experiments involve utilizing the CCD matrix to remove AR dye with MNC adsorbent (Stirring speed: 150 rpm, contact time: 10 h, and temperature: 301 K).

Run No.	X1	X2 (mg/L)	X3 (g/L)	X4 (nm)	AR Dye Adsorption Efficiency (%)
					Experiment	Computed
1	2.0	165	6.0	448.1	87.45	87.36
2	1.8	125	5.0	542.0	88.72	88.33
3	2.2	125	5.0	542.0	86.68	86.43
4	1.8	125	7.0	542.0	91.24	92.39
5	1.8	205	7.0	354.2	79.98	81.91
6	2.0	165	6.0	448.1	86.94	87.40
7	2.0	165	6.0	448.1	87.36	87.40
8	2.0	165	6.0	448.1	87.75	87.40
9	2.4	165	6.0	448.1	83.47	82.52
10	2.0	245	6.0	448.1	69.10	67.94
11	2.0	85	6.0	448.1	94.04	93.10
12	2.2	125	7.0	354.2	89.66	91.41
13	1.8	125	5.0	354.2	86.18	87.00
14	2.2	205	5.0	354.2	76.43	76.97
15	2.0	165	6.0	260.3	87.54	85.96
16	1.8	125	7.0	354.2	92.38	92.89
17	1.8	205	5.0	354.2	79.55	79.02
18	2.0	165	6.0	448.1	88.12	87.46
19	2.2	125	5.0	354.2	87.94	87.39
20	2.2	205	5.0	542.0	72.34	72.25
21	2.2	125	7.0	542.0	87.67	88.62
22	2.0	165	8.0	448.1	88.72	85.31
23	2.2	205	7.0	354.2	77.18	77.99
24	2.0	165	4.0	448.1	78.92	80.23
25	1.8	205	7.0	542.0	76.68	77.65
26	1.6	165	6.0	448.1	89.48	88.34
27	2.2	205	7.0	542.0	70.58	71.44
28	2.0	165	6.0	636.0	81.26	80.74
29	1.8	205	5.0	542.0	76.65	76.59
30	2.0	165	6.0	448.1	86.89	87.40
31	2.0	165	6.0	448.1	87.28	87.34

compares the predicted response values with the experimental results for batch adsorption. Among the experimental runs, Experiment No. 11 achieved the highest adsorption efficiency (94.04%). Analysis of variance (ANOVA) was performed to evaluate the adsorption efficiency data, as presented in Table S1. The second-order model was chosen based on the proposed model’s statistical findings. With a regression coefficient (R²) of 0.9727, the estimated response values strongly agree with the experimental data, meaning that 97.27% of the response variation can be explained through this framework. The predicted (0.9264) and adjusted R² (0.9488) values are in close agreement, indicating a good relationship between the experimental and predicted responses. A higher predicted R² value indicates a better predictive ability of the model.

Table S1 represents information related to ANOVA for the proposed quadratic model, including the goodness-of-fit and model F-statistics value. The probability F value (40.74) showed that the proposed model is significant for optimizing AR dye adsorption, while the error function is insignificant. Even though the F value is lower than 0.05, there is no statistically significant lack of goodness-of-fit. In the model chosen with the appropriate coefficients, lower p values (p < 0.05) and higher T statistics for the linear, quadratic, and interaction effects indicate greater significance [55,57]. Equation (6) was developed with four independent variables for dye adsorption efficiency. The optimization of model parameters is achieved by assigning importance to each variable to achieve the maximum percentage of dye adsorption.

% AR dye adsorption = 87.39 − 1.45 X₁ − 6.29 X₂ + 1.27 X₃ − 1.30 X₄ − 0.49 X₁² − 1.72 X₂²
− 1.16 X₃² − 1.01 X₄²− 0.61 X₁ X₂ − 0.47 X₁ X₃ − 0.57 X₁X₄ − 0.75 X₂X₃ − 0.94 X₂X₄ − 0.46 X₃X₄

(6)

3.3.2. Analysis of Surface of Response as Well as Contour Figures

The optimal response level for each parameter was determined using response surface and contour plots to analyze the interactions between variables. A three-dimensional response surface plot was employed to identify each variable’s optimal response level and understand the linear effects of factor interactions [58]. The response surface curves for AR adsorption are displayed in Figure 3A,B.

Figure 3A displays a graph of the response variable surface as a function of starting pH and dye concentration. It unequivocally demonstrates that adsorption effectiveness falls when pH and adsorbate concentration rise. The adsorbate concentration, which ranges from 85 to 245 mg/L, significantly impacts the AR adsorption rate, while the pH value in the range of 1.6–1.95 has no significant effect. Figure 3B shows that the adsorption rate improves with increasing MNC dosage and decreasing adsorbent particle diameter. The adsorption of AR dye was significantly affected by the MNC dosage response plot, which ranges from 1 to 2 g/L with particle diameter in the 260.3–636 nm range. The response surface plot gives the best response values, which agree with the experimental values and the regression model equation.

Figure 4A,B show the elliptical contour plots for the AR dye adsorption efficacy. The minimum curvature coordinates on each contour plot show the highest value of the respective components, yielding maximum percentage removal. Figure 4A displays the contour graphs for AR dye elimination efficacy as a function of starting pH and adsorbent concentration. When the starting pH is between 1.6 and 1.95, the MNC concentration is between 1.44 and 2 g/L, and the interaction impact is negligible, the maximum adsorption occurs. Figure 4B indicates that the highest adsorption efficiency is achieved within an AR dye concentration range of 85–145 mg/L and an adsorbent particle size range of 307.25–636 nm.

Table 4. Optimal experimental conditions of process variables for the maximum removal of AR dye using the MNC adsorbent.

Experimental Parameters	Optimum Value	AR Dye Removal Efficiency (%)
		Experiment	Computed
Initial pH (X1)	2.0	94.04	93.10
Initial AR dye concentration, mg/L (X2)	85
MNC adsorbent dosage, g/L (X3)	1.5
MNC adsorbent particle size, nm (X4)	448.1

lists the optimal process parameter values for maximal responsiveness. The comparison of the calculated and empirical responses shows a positive relationship between them, so the design of the empirical model can also be used to explain the relationship between the experimental factors. The optimization test unequivocally demonstrated that RSM is a valuable method for predicting the optimal experimental conditions for maximum adsorption efficiency.

3.4. Kinetic and Isotherm Models for Abatement of AR Dye from Simulated Wastewater

To evaluate the effectiveness of the process, it is crucial to research the adsorption kinetics as it provides an understanding of the controlling rate and mechanism of adsorption. This is especially valuable for establishing the correlation between contact time and adsorption capacity and examining the adsorption process to enhance efficiency in eliminating pollutants and making significant advancements. To predict batch adsorption kinetics for designing industrial adsorption columns, it is essential to develop mathematical models to explain the process [57]. Several mathematical models are used to estimate adsorption kinetics and validate the adsorption process. The various kinetic models are represented by the following equations [35,55].

• Pseudo-first-order (PFO) kinetic model:

  $$\mathrm{l}\mathrm{n}\left({\mathrm{q}}_{\mathrm{e}}-{\mathrm{q}}_{\mathrm{t}}\right)=\mathrm{l}\mathrm{n} {\mathrm{q}}_{\mathrm{e}}-{\mathrm{K}}_1\mathrm{t}$$

  (7)
• Pseudo-second-order (PSO) kinetic model:

  $${\displaystyle \frac{\mathrm{t}}{{\mathrm{q}}_{\mathrm{t}}}}={\displaystyle \frac{1}{{{\mathrm{K}}_2\mathrm{q}}_{\mathrm{e}}^2}}+{\displaystyle \frac{\mathrm{t}}{{\mathrm{q}}_{\mathrm{e}}}}$$

  (8)
• Intra-particle diffusion (ID) model:

  $${\mathrm{q}}_{\mathrm{t}}={\mathrm{K}}_{\mathrm{i}}{\mathrm{t}}^{0.5}+\mathrm{C}$$

  (9)
• Elovich model:

  $${\mathrm{q}}_{\mathrm{t}}=\left({\displaystyle \frac{1}{\mathsf{\beta }}}\right)\mathrm{l}\mathrm{n}\left(\mathsf{\alpha }\mathsf{\beta }\right)+\left({\displaystyle \frac{1}{\mathsf{\beta }}}\right)\ln \mathrm{t}$$

  (10)

  where t is reaction time (min), K₁, K₂, K_i, C, $\mathsf{\alpha }$ and $\mathsf{\beta }$ are the PFO, PSO, ID rate, film thickness, and Elovich constants expressed in (1/min), (g/(mg·min)), (mg/(g·min^1/2)), (mg/g), (mg/(g·min) and (g/mg), respectively. The results of various kinetic model parameters and their regression correlation coefficients are displayed in

  Table 5. Kinetic and isotherm model parameters for AR dye removal using MNC adsorbent.

  Kinetic Model	Model Parameters	Initial AR Dye Pollutant Concentration, Co (mg/L)
  		35	70	105	140	175	210
  AR dye uptake at equilibrium, qe, empirical (mg/g)		22.4768	48.9507	64.4210	81.3736	98.4892	110.348
  PFO	qe, calculated (mg/g)	9.5048	18.2346	29.6894	38.3752	45.6481	54.943
  	K1 (1/min)	0.0909	0.0560	0.0416	0.0197	0.0148	0.0115
  	R2	0.9960	0.9812	0.9990	0.9846	0.9875	0.9832
  	NSD (%)	21.8134	25.7978	23.1461	23.8064	22.6051	22.9536
  PSO	qe, calculated (mg/g)	23.278	49.216	65.574	82.237	99.403	110.987
  	K2 (g/(mg·min))	0.0291	0.0110	0.0078	0.0061	0.0047	0.0022
  	h (mg/(g·min))	14.7112	26.3848	32.7267	39.8758	45.9248	53.6472
  	R2	0.9999	0.9999	0.9999	0.9999	0.9999	0.9999
  	NSD (%)	1.3463	0.3733	0.5964	0.3198	0.2680	0.1608
  Intra-particle diffusion	Ki (mg/(g·min1/2))	0.0824	0.1432	0.1917	0.3662	0.5916	0.6309
  	C (mg/g))	21.6534	42.5042	61.3787	75.1872	88.0301	98.1263
  	R2	0.7228	0.7466	0.7812	0.9066	0.9764	0.9788
  Elovich	$\mathsf{\alpha }$ (mg/(g·min)	2305.207	3472.416	5534.045	7645.394	8824.728	9690.639
  	$\mathsf{\beta }$ (g/mg)	0.4272	0.2392	0.1892	0.1546	0.1338	0.1173
  	R2	0.9588	0.9544	0.9697	0.9819	0.9867	0.9588
  Isotherm Model	Model Parameters	Values of the Parameters			Predicted Model Expression
  Freundlich	KF (L/g)	24.0076			${\mathrm{q}}_{\mathrm{e}}=24 {{\mathrm{C}}_{\mathrm{e}}}^{0.4260}$
  	n	2.3474
  	R2	0.9762
  	${\chi }^2$	3.8432
  Langmuir	Qmax (mg/g)	115.35			${\mathrm{q}}_{\mathrm{e}}={\displaystyle \frac{{22.0264 \mathrm{C}}_{\mathrm{e}}}{{1+0.1909 \mathrm{C}}_{\mathrm{e}}}}$
  	KL (L/mg)	0.1909
  	RL	0.0243–0.1301
  	R2	0.9966
  	${\chi }^2$	0.2116
  Temkin	RT/bT	24.1968			${\mathrm{q}}_{\mathrm{e}}=4.1968 \mathrm{l}\mathrm{n}\left({1.9522 \mathrm{C}}_{\mathrm{e}}\right)$
  	KT (L/g)	1.9522
  	R2	0.9902
  	${\chi }^2$	0.7372
  Dubinin-Radushkevich	qs (mg/g)	84.0086			${\mathrm{q}}_{\mathrm{e}}=84.0086 \mathrm{e}\mathrm{x}\mathrm{p}\left(-0.6642 {\mathsf{ϵ}}^2\right)$ $\mathsf{\epsilon }=\mathrm{R}\mathrm{T}\ln \left(1+{\displaystyle \frac{1}{{\mathrm{C}}_{\mathrm{e}}}}\right)$
  	KDR (mole2/kJ2)	0.6642
  	E (kJ/mole)	0.8675
  	R2	0.9276
  	${\chi }^2$	14.2877

  Where NSD = Normalized standard deviation (%); ${\chi }^2$ = Chi-square error.

  , while the outcomes of kinetic studies are depicted in Figure 5A–D.

The correlation coefficient of the PSO model is 0.9999, which is higher than other models and lower value of normalized standard deviation (NSD), indicating a good agreement between the predicted values q_e and adsorption efficacy of different adsorbate concentrations and the actual observations. This verdict suggests that the adsorption of AR onto the surface of MNC particles involves the PSO adsorption mechanism, indicating that the overall rate constant values may be influenced by the chemisorptive process, leading to an enhancement in the amount of AR dye adsorption. The PSO constant value K₂ dropped from 0.029 g/(mg·min) to 0.0022 g/(mg·min) when the starting AR dye concentration grew from 35 to 210 mg/L. This may be because there is more competition for the limited space at the site of the MNC at higher adsorbate concentration [52].

Figure 5C displays the ID plot for the adhesion of AR onto the MNC adsorbent particle surface, revealing three linear segments that indicate the potential influence of three steps on the adsorption process: external film (EF) diffusion, ID, and binding sites in the particle surface pores are becoming saturated. After analyzing the kinetic data, it is clear that the rapid removal of AR was due to the numerous sites of activity within the first five minutes on the MNC adsorbent surface, which corresponds to the initial lines standing up for external diffusion. Pore diffusion (PD), or the flow of adsorbate molecules from the nanomaterial’s surface to the particle pores, is depicted in the subsequent linear section. At last, the third region pertains to the attachment of dye molecules and the filling up of empty spaces in the pores of the adsorbent. Subsequently, the diffusion of AR dye molecules within the pores starts to decelerate due to the reduced concentration of the adsorbate in the water phase. Furthermore, it was noted that the graphs for each concentration did not cross at the starting point, indicating that PD was not the determining factor in the rate-limiting step of the adsorption process [59]. Based on the analysis, the main factor influencing the adsorption rate is the EF diffusion, with only a minor impact from the ID of AR dye anions to the particle’s interior surface. It was observed that the adsorption process may be predominantly influenced by EF diffusion in the initial stages and gradually transition to PD as the solid particles accumulate with dye molecules. The Bangham plot (Figure 5E) and Boyd plot (Figure 5F) display a non-linear profile, indicating that the EF diffusion of AR dye molecules predominantly affects the overall rate of the reaction [60].

Adsorption isotherms are one of the notable features that describe the adsorbent–adsorbate interaction and provide helpful information for designing efficient adsorption processes [61]. The adsorption process was investigated using the Freundlich, Langmuir, Temkin, and Dubinin-Radushkevich isotherm models. The equations for these isotherm models are provided as follows [62].

• Freundlich isotherm

  $$\log {\mathrm{q}}_{\mathrm{e}}=\log {\mathrm{K}}_{\mathrm{F}}+{\displaystyle \frac{1}{\mathrm{n}}} \log {\mathrm{C}}_{\mathrm{e}}$$

  (11)
• Langmuir isotherm

  $${\displaystyle \frac{{\mathrm{C}}_{\mathrm{e}}}{{\mathrm{q}}_{\mathrm{e}}}}={\displaystyle \frac{{\mathrm{C}}_{\mathrm{e}}}{{\mathrm{Q}}_{\mathrm{m}\mathrm{a}\mathrm{x}}}}+{\displaystyle \frac{1}{{\mathrm{Q}}_{\mathrm{m}\mathrm{a}\mathrm{x}}{\mathrm{K}}_{\mathrm{L}}}}$$

  (12)

As depicted in Equation (13), the equilibrium parameter R_L is a crucial feature of the Langmuir isotherm, offering valuable insights into the adsorption process’s nature.

$${\mathrm{R}}_{\mathrm{L}}={\displaystyle \frac{1}{1+{\mathrm{K}}_{\mathrm{L}}{\mathrm{C}}_{\mathrm{o}}}}$$

(13)

Temkin isotherm

$${\mathrm{q}}_{\mathrm{e}}={\mathrm{B}}_{\mathrm{T}} \mathrm{l}\mathrm{n} {\mathrm{K}}_{\mathrm{T}}+{\mathrm{B}}_{\mathrm{T}} \ln {\mathrm{C}}_{\mathrm{e}}$$

(14)

Dubinin-Radushkevich (D-R) isotherm

$$\ln {\mathrm{q}}_{\mathrm{e}}=\ln {\mathrm{q}}_{\mathrm{s}}-{\mathrm{K}}_{\mathrm{D}\mathrm{R}} {\mathsf{\epsilon }}^2$$

(15)

where K_F, K_L, K_T, and K_DR are the Freundlich, Langmuir, Temkin, and D-R model isotherm constants expressed in (L/g), (L/mg), (L/g), and (mole²/kJ²), respectively. The adsorption intensity is 1/n, Q_max is the utmost adhesion capacity of the nanomaterial (mg/g), B_T refers to the heat of accumulating adsorbate, and q_s for D-R isotherm theoretical equilibrium capacity (mg/g). The value of ε can be determined using the following Equation (16)

$$\mathsf{\epsilon }=\mathrm{R}\mathrm{T} \ln \left({\displaystyle \frac{{\mathrm{C}}_{\mathrm{e}}+1}{{\mathrm{C}}_{\mathrm{e}}}}\right)$$

(16)

Figure 6A–D show the linear isotherm models of Freudnlich, Langmuir, Temkin, and D-R for the MNC used for the adsorption of AR dye molecules. Table 5 presents the isotherm model parameters obtained in this study, including q_e and R². The data indicate that the experimental results best fit the Langmuir model, followed by the Freundlich, Temkin, and D-R models for AR dye adsorption. This ranking is based on the R² values of 0.9993, 0.9655, 0.9584, and 0.7099, respectively. It is clear that the removal process of the AR dye over MNC adsorbent is subject to Langmuir’s isotherm better than other models due to the high correlation coefficient value, lower value of chi-square error and the predicted equilibrium data fit experimental data more closely (Figure 6E). This means that the adsorption occurs at a homogenous surface, and monolayer adsorption takes place with a limited number of indistinguishable sites and without any interaction among the adsorbed species under optimal experimental conditions. The MNC adsorbent is anticipated to reach a Q_max of 115.35 mg/g at room temperature. The adsorption process is preferred based on the R_L values ranging from 0.024 to 0.13 at different adsorbate concentrations (35 to 210 mg/L). It was observed that the process becomes more advantageous at greater adsorbate concentrations. The validity of the adsorption process was once again confirmed through the Freundlich exponent value of n (1.753), which falls within the standard range of 1 to 10 [60]. Upon reviewing the Q_max of our MNC adsorbent in comparison to numerous other adsorbents reported in the literature,

Table 6. Comparison of AR dye’s highest monolayer surface assimilation ability (Q_max) with already available adsorbents computed by the Langmuir model.

Adsorbent	Highest Surface Assimilation Capacity, Qmax (mg/g)	Reference
Mustard husk	0.507	[63]
Unmodified walnut shell	2.62	[64]
Polyaniline/carbon hybrids	7.61	[65]
Nano-Fe3O4/corn cover composite	10.52	[66]
Fe3O4@Talc nanocomposite	11.76	[67]
ZnO/TiO2	12.50	[68]
Olive stone	16.01	[69]
Cynodon dactylon	16.30	[70]
Spirulinaplatensis biomass	17.15	[28]
SnO2/CeO2 nano-composite	18.50	[4]
Immobilized Canna indica beads	21.69	[71]
Cucurbituril	22.80	[72]
Powdered activated carbon (PAC)	24.50	[73]
Coal bottom ash-derived zeolite	26.79	[74]
Layered double hydroxide clay	29.41	[75]
Activated clay modified by iron oxide	32.70	[76]
Hydroxyapatite	34.20	[77]
Chitosan-coated Fe3O4 nanoparticles	40.12	[78]
Chitosan	42.48	[79]
Chitosan-clay composite	44.39	[5]
Fe3O4 magnetic nanoparticles	45.80	[80]
Coal bottom ash	49.26	[74]
Nano γ-alumina	54.40	[81]
Nitric acid-treated PAC	57.80	[78]
Acid-treated avocado seed powder	67.08	[82]
Citrullus lanatus peels	79.60	[83]
Epichlorohydrin modified with walnut shells	81.44	[64]
Schima wallichii-based activated carbon	91.69	[84]
Polymer resin and waste cotton fibers	104.00	[85]
Magnetic activated carbon	108.69	[86]
NiFe2O4/PANI composite	110.00	[87]
Walnut shell caron-Fe2O3 nanocomposite	115.35	Present study

clearly shows that the prepared MNC demonstrates a superior adsorption capacity for eliminating AR species from simulated effluent when compared to the listed adsorbents.

3.5. Probable Interactions Among MNC Material and AR Dye Adsorbate

Understanding the adsorption mechanism is crucial for elucidating the accumulation of AR dye onto the MNC adsorbent. Dye uptake is influenced by several adsorbent properties, including morphology, structure, functional groups, and surface area. The diffusion of the adsorbate toward the adsorbent and its subsequent interaction play a significant role in the removal process. Figure 7 illustrates the proposed mechanism for AR dye adsorption onto the MNC particle surface, where dye molecules are primarily retained through electrostatic interactions, π–π bonding, and intermolecular hydrogen bonding, all of which are key factors in the removal system. The AR dye contains a sulfonic group in its structure, which becomes ionized in a water-based solution. This ionization creates colored anions (−SO₃⁻) in addition to aromatic rings, which significantly affects the adsorption process. The chemisorption process between carbonaceous material’s aromatic rings and anionic pollutant molecules is predominantly influenced by robust Π-Π stacking and negative ion–positive ion interaction [29].

3.6. Thermodynamic Investigation on Adsorptive Removal of AR Dye Using MNC Adsorbent

The impact of temperature on AR dye removal onto MNC adsorbent was investigated by conducting equilibrium studies at numerous initial adsorbate concentrations (35 to 210 mg/L) across temperatures from 301 to 323 K. The evaluation of the thermodynamics of the adsorption process involved the calculation of parameters such as the Gibbs free energy, ΔG° (kJ/mole), enthalpy, ΔH° (kJ/mole), and entropy, ΔS° (kJ/(mole K)) changes. The approach assumes a constant Gibbs free energy for all adsorption sites. In this calculation, the equilibrium constant, K_c was derived from the Langmuir fit of empirical equilibrium data [88].

$$\Delta \mathrm{G}°=-\mathrm{R}\mathrm{T} \mathrm{l}\mathrm{n}({\mathrm{K}}_{\mathrm{c}})$$

(17)

The universal gas constant is denoted as R (8.314 J/mole K), and Temperature (K) is represented by T. The Thermodynamic parameters are computed from the Van’t Hoff Equation (18) [89], the values are summarized in

Table 7. Thermodynamic parameters and activation energy are used to remove AR dye onto MNC adsorbent in an aqueous solution.

Temperature (K)	Qmax (mg/g)	Thermodynamic Parameters
		ΔG (kJ/mole)	ΔH (kJ/mole)	ΔS (kJ/mole K)
301	115.35	−25.0251	47.9105	0.2198
313	119.64	−27.2759
323	126.57	−29.9045
Co (mg/L)	Activation Energy, Ea (kJ/mole)
35	46.6328
70	61.8536
105	56.9996
140	50.0526
175	56.4308
210	43.8761

, and the resulting plot can be seen in Figure 8A.

$$\ln {\mathrm{K}}_{\mathrm{c}}=-{\displaystyle \frac{∆\mathrm{H}°}{\mathrm{R}}}\left({\displaystyle \frac{1}{\mathrm{T}}}\right)+{\displaystyle \frac{\Delta \mathrm{S}°}{\mathrm{R}}}$$

(18)

The increasing temperature accentuates the magnitude of the negative ΔG°, signifying a spontaneous adsorption process. The process becomes more favorable at higher temperatures, as indicated by the decreasingly pronounced negative ΔG°. The adsorption process exhibits endothermic behavior, as indicated by the value and sign of ΔH° (47.91 kJ/mole), and ΔS° (0.2198 kJ/(mole K)), which in turn result in increased randomness of adsorbate species on the MNC adsorbent surface. The rise in the value of q_e and adsorption efficacy at elevated temperatures suggests the fast and endothermic nature of the dye uptake process.

The Arrhenius plot in Figure 8B can be used to calculate the activation energy, E_a (kJ/mole), for removing the adsorbate. The E_a values deviate from 43.87 and 61.85 kJ/mole across different adsorbate concentrations covering a range of 35 to 210 mg/L. It could be deduced that the E_a value of 52.64 kJ/mole and the ΔH° value indicate that the accumulation of AR dye species over the MNC adsorbent surface is a chemisorption process [90]. A positive correlation is obtained between q_e and C_e at several temperatures, as revealed in Figure 8C. This can be explained by the fact that the molecules of the AR dye attach to the material surface’s active sites more intensely at higher temperatures. The observed result could be attributed to the improved movement of adsorbate species over the external boundary layer and interior pores in the MNC material. The solid material surface becomes more attractive to many adsorbate molecules as they gain adequate kinetic energy to engage with the binding sites [91]. Upon further examination in Section 3.4, the studied adsorption process aligned with the chemosorption mechanism, which adhered to the PSO kinetics.

3.7. Renewal of MNC Adsorbent and Reusability

In Figure 9A, it can be observed that the desorption efficiency of AR declined as the number of cycles increased when employing various desorbing reagents. The incomplete elimination of adsorbed dye species from the surface of the particles into the desorbing reagent might be caused by insufficient shaking speed and low volume of desorbing reagents used. The findings indicate that using 30 mM HCl as a desorbing reagent to regenerate the MNC adsorbent accumulated with AR dye molecules is more effective (50.52% in the fourth run) than other reagents. This may be due to the increased interaction between H⁺ ions and dye anions [92]. The maximum number of adsorption–desorption cycles were investigated using a diluted solution of 30 mM HCl.

Figure 9B shows the reusability studies of MNC material in several cycles, and it suggests that the MNC recovered using 30 mM HCl had the greatest adsorption efficiency (removal efficacy, R₁ = 89.745%, R₂ = 78.864%, R₃ = 67.384%, and R₄ = 56.454%). A progressive reduction in adsorption efficacy was observed from the first cycle to the fourth cycle. This could be due to changes in the surface structure of the MNC adsorbent, leading to the potential blocking of multiple adsorption sites [93]. The renewed adsorbent could be successfully reutilized for up to four runs by using 30 mM HCl to remove AR dye from simulated effluent. However, there has been a significant decrease in the percentage of adsorption. To improve adsorbent stability, focus on enhancing its structural integrity, chemical resistance, and surface properties through techniques like surface modification, material selection, and optimizing synthesis conditions and develop effective regeneration techniques [94].

4. Conclusions

The agricultural waste walnut shell biomass proved to be a better way to recycle and synthesize the nanocomposite material. This study investigates the adsorption efficiency of the activated walnut shell carbon-iron oxide nanocomposite material and provides valuable insights into its application for removing harmful anionic dyes, specifically Alizarin Red S, from synthetic wastewater. Comprehensive characterization revealed the material’s porous, irregular structure and the presence of functional groups conducive to adsorption. At its point of zero charge (pH_zpc = 6.7), MNC demonstrated a high surface area (188.749 m²/g) and optimal performance under specific conditions: pH 2, AR concentration of 85 mg/L, adsorbent dosage of 1.5 g/L, and particle size of 448.1 nm. Adsorption data aligned with the Langmuir isotherm model and pseudo-second-order kinetics, indicating a chemisorption mechanism with a maximum AR adsorption capacity of 115.35 mg/g. The reaction rate is mainly governed by EF diffusion, as proven by intra-particle diffusion, Bangham, and the Boyd model, which showed that it is the rate-limiting step in the removal system. Thermodynamic studies confirmed a self-driven, endothermic process, with intra-particle diffusion as the primary rate-limiting step. The material also retained its adsorption efficiency for up to four reuse cycles, underscoring its practical applicability. This research highlights a sustainable and cost-effective approach to wastewater treatment, utilizing agricultural waste-derived materials to enhance environmental protection and promote resource recovery. By demonstrating the efficacy of magnetic nanocomposites as a significant and foremost adsorbent for AR removal and their potential for broader applications in removing other anionic pollutants, this work addresses pressing challenges in industrial effluent management and sustainability in a real-life scenario.