Mechanistic Evaluation of Pb(II) Adsorption on Magnetic Activated Carbon/Fe₃O₄ Composites: Influence of Hydrothermal and Ultrasonic Synthesis Routes

Abstract

This study presents a comparative analysis of two synthesis approaches for fabricating magnetic sorbents based on activated carbon (AC) incorporated with magnetite (Fe₃O₄) nanoparticles: hydrothermal synthesis and ultrasonic treatment. The results demonstrate that ultrasonic-assisted synthesis yields a magnetically responsive composite, us-AC/Fe₃O₄, exhibiting a Pb²⁺ removal efficiency of 92.84%, which is comparable to that of pristine activated carbon (99.0%). A key advantage of the synthesized composite lies in its facile recovery via magnetic separation following adsorption, rendering it a promising candidate for the remediation of heavy metal-contaminated water. Kinetic modeling suggests a dual adsorption mechanism: initial stages are governed by physisorption, while chemisorption dominates in the later phases. Adsorption isotherm modeling demonstrated that the Langmuir model provided the best description of Pb²⁺ adsorption on AC and us-AC/Fe₃O₄, with the highest sorption capacities observed for pristine activated carbon, followed by the ultrasonically modified composite, and comparatively lower values for the hydrothermally treated material. These findings underscore the potential of ultrasonic processing as an effective route for developing magnetically separable sorbents with high performance in aqueous heavy metal removal.

1. Introduction

Contamination of water resources with heavy metals remains one of the most pressing environmental issues, largely driven by intensive anthropogenic activities such as mining, battery manufacturing, electronics, metallurgy, and the chemical industry [1,2,3]. Heavy metal ions such as Pb²⁺, Cd²⁺, As³⁺/As⁵⁺, and Hg²⁺ are characterized by high toxicity, resistance to biodegradation, and a strong tendency to bioaccumulate in living organisms. These properties make them extremely hazardous to both the environment and human health, leading to neurotoxic, carcinogenic, reproductive, and mutagenic effects [4,5,6].

Particular concern is raised by lead (Pb²⁺), which exhibits high neurotoxicity and accumulates in bone tissue. Its effects are especially dangerous for children, as it impairs the development and function of the central nervous system, potentially leading to irreversible cognitive and behavioral disorders [7]. In aquatic systems, lead may exist in various forms, including free ions (Pb²⁺), hydroxyl complexes, carbonate and chloride complexes, as well as poorly soluble precipitates and colloidal particles [8,9,10,11]. The dominant forms depend on pH, redox conditions, and the presence of other ions in the medium. This complex chemical nature complicates the removal of lead, necessitating the development of universal and highly efficient sorbent materials. Various methods are employed for the removal of heavy metal ions from water, including chemical precipitation, membrane processes, ion exchange, electrochemical techniques, and adsorption [12]. Among these, adsorption is considered one of the most promising due to its simplicity, availability of raw materials, low cost, high efficiency, and the potential for sorbent reuse [13,14].

Activated carbon (AC) plays a particularly important role among adsorbents due to its high specific surface area (up to 3000 m²/g), well-developed meso- and microporous structure, significant pore volume, and the presence of oxygen-containing functional groups (carboxyl, phenolic, hydroxyl), which facilitate metal ion complexation [15,16,17]. Additionally, the use of renewable biomass sources for AC production enhances its sustainability and cost-effectiveness [18]. However, despite its outstanding adsorption properties, AC has several limitations, including difficulties in separating it from water after adsorption, as well as limited selectivity and adsorption rate for target ions. One effective strategy to overcome these drawbacks is the modification of AC with metal oxide nanoparticles, particularly magnetite (Fe₃O₄) [19,20]. Magnetite is a spinel-structured iron oxide with a high saturation magnetization, high adsorption capacity, and surface functionality that can be tailored to enhance selectivity toward specific ions [21,22,23]. These properties make Fe₃O₄ nanoparticles widely used as modifiers that impart magnetic properties to adsorbents, enabling rapid and complete separation from water using an external magnetic field, thereby preventing secondary pollution [24].

A key factor determining the effectiveness of such composites is the interaction between Fe₃O₄ nanoparticles and the porous structure of AC. Despite the extensive research on Fe₃O₄/AC-based sorbents, the effect of the nanoparticle incorporation method on the morphology, distribution of active sites, and adsorption properties of the material remains insufficiently explored. In particular, comparative analysis of different modification methods—such as ultrasonic treatment and hydrothermal synthesis—is of significant relevance, as these approaches lead to varying degrees of nanoparticle penetration into meso- and macropores, as well as differences in surface defect density and functionalization. The integration of magnetic nanoparticles into the macro- and mesopores of the carbon matrix not only prevents their aggregation and loss of activity in aqueous environments, but also significantly increases the active surface area and the number of available adsorption sites [25]. The porous AC framework serves as a stabilizing platform, ensuring uniform nanoparticle distribution, protection against oxidation and aggregation, and enhanced hydrophilicity of the material. At the same time, Fe₃O₄ nanoparticles embedded in the adsorbent structure enhance electrostatic interactions with metal ions and promote faster mass transfer through magnetic gradients [26].

Recent studies have shown that the synergistic effect resulting from the combination of activated carbon with Fe₃O₄ nanoparticles significantly enhances the sorption performance of the composite. This includes high Pb²⁺ ion removal efficiency, improved sorption kinetics, regeneration stability, and the potential for repeated use without a notable decline in activity [27,28]. However, the key factor determining the functionality of such composites remains their microstructural organization—particularly the degree of nanoparticle incorporation into the porous carbon matrix, their distribution within the pores, defect formation, and changes in surface chemistry. The structural and chemical integration of Fe₃O₄ nanoparticles not only affects the accessibility of active sites but may also induce textural rearrangement, formation of oxygen-containing functional groups, and the emergence of additional sorption sites due to defects and heterogeneous functionalization, as summarized in

Table 1. Overview of modern carbon-based composite adsorbents for lead ion removal.

Composite Sorbent	AC Precursor	Component Synthesis Method	Composite Synthesis Approach	Pollutant	Adsorption Capacity (mg/g)	Ref.
AC/PANi	Waste biomass from fruit skins and pits	PANi—Polymerization	Polymerization	Pb (II)	6.81	[29]
AC/HAP	Commercial product	HAP—Co-precipitation	Co-precipitation	Pb (II)	401.58	[30]
AC/NiO−CuO	Arabo-khata leaves	NiO, CuO—Commercial product	Ultrasonic treatment	Pb (II)	182.78	[31]
AC/NC/GO	Sugar beet	Nanoclay—Carbonization, graphene oxide—Hummers’ method	Mixing	Pb (II)	208	[32]
AC	Rapeseed straw	-	Hydrothermal method	Pb (II)	253.2	[33]
AC/GO	Glucose	GO—Chemical exfoliation, Hummers’ method	Ultrasonic treatment	Pb(II)	217	[34]

.

The relevance of the present study lies in addressing a clear gap in understanding how different modification methods affect the structure and performance of activated carbon/Fe₃O₄ composites. Although these materials have been extensively studied, most reports focus mainly on adsorption capacity, while the relationship between synthesis method, morphology, nanoparticle distribution, and functional properties remains insufficiently explored [35,36,37,38,39,40]. A comparative analysis of hydrothermal and ultrasonic modification is therefore of particular importance, as these approaches exert distinct effects on pore formation, nanoparticle dispersion and anchoring within the carbon matrix, and the density and accessibility of active sites [41,42,43,44,45]. Such insights are essential for identifying optimal modification conditions to improve sorbent efficiency. Furthermore, the sorption of Pb²⁺ proceeds through a combined mechanism: initial stages dominated by physical adsorption and intraparticle diffusion, followed by chemisorption involving carbon functional groups and Fe₃O₄ surface sites, as supported by recent studies [46,47].

Thus, the aim of the present study is to conduct a comparative investigation of the sorption properties of magnetic nanocomposites based on activated carbon and Fe₃O₄ nanoparticles synthesized via hydrothermal and ultrasonic methods. Special attention is given to the impact of synthesis conditions on adsorption efficiency and the feasibility of magnetic separation of the sorbent from aqueous solutions. Comprehensive physicochemical characterization and kinetic modeling were carried out to identify the key mechanisms underlying the sorption behavior of these materials and to propose rational design strategies for the development of next-generation sorbents for heavy metal ion removal from water.

2. Materials and Methods

The following chemical reagents were used in this study: rice husk (Kyzylorda region, Kazakhstan), potassium hydroxide (KOH), FeSO₄·7H₂O, FeCl₃·6H₂O, 25% aqueous ammonia solution, and Pb(NO₃)₂—all of analytical grade and purchased from LLP “Labor-Pharma (Almaty, Kazakhstan)” and LLP “Labhimprom(Almaty, Kazakhstan)”. Argon gas (Ar, 99.999%) was obtained from LLP “Ikhsan Technogaz (Almaty, Kazakhstan).”

2.1. Synthesis of Activated Carbon

Activated carbon was synthesized from rice husk using a two-step process consisting of carbonization followed by thermochemical activation. Prior to carbonization, the raw biomass was pretreated by thorough washing with hot water, rinsing with distilled water, and subsequent drying in a laboratory oven at 110 °C for 12 h to remove impurities and reduce moisture content. Carbonization was carried out at 550 °C for 100 min in a vertical tubular furnace under a constant nitrogen flow of 150 SCCM to ensure an inert atmosphere. The resulting biochar was then chemically activated using potassium hydroxide in a 1:4 mass ratio (carbon:KOH). The activation process was conducted in a stainless-steel reactor (AISI 321 grade), where the mixture was heated to 850 °C at a ramp rate of 7 °C/min under a continuous argon flow of 150 SCCM. The target temperature was maintained for 120 min to complete the activation. Passive cooling to ambient temperature was employed after both the carbonization and activation steps. A detailed description of the synthesis process can be found in [48].

2.2. Synthesis of Fe₃O₄ Nanoparticles

Magnetite nanoparticles were synthesized by a chemical co-precipitation method [49]. An aqueous solution of ferric chloride (FeCl₃) with a concentration of 0.32 mol/L and a ferrous sulfate (FeSO₄) solution with a concentration of 0.20 mol/L were prepared separately. Equal volumes of the two solutions (325 mL each) were transferred into a heat-resistant flask, and 200 mL of 25% aqueous ammonia solution was added dropwise at a rate of one drop per second under continuous stirring using a magnetic stirrer. The reaction temperature was maintained at 50 °C throughout the process. A black precipitate of Fe₃O₄ formed, which was separated by filtration and washed repeatedly with distilled water by decantation until a neutral pH was reached. The resulting precipitate was dried in an oven at 60 °C for 24 h to remove residual moisture.

2.3. Synthesis of AC/Fe₃O₄ Composites

2.3.1. Ultrasonication-Assisted Synthesis of us-AC/Fe₃O₄ Composite

The composite AC/Fe₃O₄ was synthesized via an ultrasonication-assisted method. To prepare the composite, activated carbon and the pre-synthesized Fe₃O₄ nanoparticles were mixed at a mass ratio of 2:1 and dispersed in 20 mL of distilled water. The resulting suspension was subjected to ultrasonication for 1 h in an ice bath using a Bandelin ultrasonic bath (Germany) operating at a frequency of 35 kHz, with a high-frequency power of 80 W and a peak ultrasonic power of 320 W. After sonication, the product was filtered, washed with distilled water, and dried at 60 °C. The resulting composite was designated as us-AC/Fe₃O₄, where “us” refers to ultrasonication.

2.3.2. Hydrothermal Synthesis of h-AC/Fe₃O₄ Composite

Magnetite nanoparticles supported on activated carbon were synthesized via a co-precipitation method followed by hydrothermal treatment. Initially, 100 mL of a 0.052 M FeSO₄ solution and 150 mL of a 0.069 M FeCl₃ solution were prepared and mixed under vigorous stirring at 70 °C. Subsequently, 6.4 mL of 25% aqueous ammonia was added dropwise until the pH of the mixture reached approximately 11. The appearance of a dark brown color indicated the formation of magnetite, after which 2.4 g of activated carbon was introduced into the reaction mixture. These conditions yielded a composite with an activated carbon to magnetite ratio of 2:1. The suspension was continuously stirred at 70 °C for 2 h, then allowed to stand at room temperature for 24 h.

The resulting composite was magnetically separated, thoroughly washed several times with distilled water and ethanol, and dried in an oven at 90 °C for 12 h. The intermediate product, obtained in a yield of 3.4 ± 0.18 g, was then subjected to hydrothermal treatment. Specifically, 0.230 ± 0.002 g of the composite was dispersed in 30 mL of deionized water and ultrasonicated for 30 min to ensure uniform dispersion. The suspension was transferred into a Teflon-lined stainless-steel autoclave and hydrothermally treated at 150 °C for 24 h. After cooling to room temperature, the product was magnetically separated, thoroughly washed with distilled water and ethanol, and dried in an oven at 80 °C for 12 h.

The final material, obtained in a yield of 0.210 ± 0.005 g, was designated as h-AC/Fe₃O₄, where “h” denotes hydrothermal treatment. The chosen mass ratios ensured sufficient material for 3–4 repeated sorption experiments (50 mg of h-AC/Fe₃O₄ per sorption test).

2.4. Adsorption Performance Test

To evaluate the adsorption properties of the synthesized composites, the lead ion adsorption capacity was measured. In a typical test, 50 mg of activated carbon or composite (us-AC/Fe₃O₄ or h-AC/Fe₃O₄) was dispersed in 50 mL of an aqueous Pb(NO₃)₂ solution with a concentration of 50 mg/L (based on Pb²⁺ ions) and stirred on a laboratory shaker at 250 rpm at room temperature (25 °C). An initial Pb(II) concentration of 50 mg/L was selected for the adsorption experiments based on two key considerations: practical relevance and scientific comparability. Pb(II) levels in industrial effluents vary widely depending on the source; for example, wastewater from the wood-processing industry has been reported to contain Pb(II) concentrations in the range of 51.8–414.4 mg/L [50]. Moreover, a concentration of 50 mg/L is frequently employed in the literature as a benchmark for assessing the performance of novel adsorbents, thereby enabling meaningful comparisons with previously published studies [51,52]. To evaluate the adsorption kinetics and identify the equilibrium time, experiments were conducted at different contact times (2, 4, and 6 h). After adsorption, the suspension was filtered, and the residual concentration of Pb²⁺ ions was analyzed using a Shimadzu AA-6200 (Kyoto, Japan) atomic absorption spectrometer. The adsorption capacity (q, mg/g) was calculated using the following equation:

$$q_e={\displaystyle \frac{(C_0-C_e)·V}{m}}$$

(1)

where C₀ and C_e are the initial and equilibrium concentrations of Pb²⁺ (mg/L), V is the volume of the solution (L), and m is the mass of the sorbent (g).

To investigate the kinetic models, sorption experiments were conducted at various contact times. For this purpose, 50 mg of activated carbon or composite (us-AC/Fe₃O₄ or h-AC/Fe₃O₄) was dispersed in 50 mL of an aqueous Pb(NO₃)₂ solution with a concentration of 50 mg/L (based on Pb²⁺ ions) and stirred on a laboratory shaker at 250 rpm at room temperature (25 °C). Aliquots were taken at 5, 10, 20, 40, 60, and 120 min, respectively, to determine the residual concentration of Pb²⁺.

For constructing adsorption isotherms, solutions with Pb²⁺ ion concentrations of 25, 50, 75, 100, 125, and 150 mg/L were prepared. To each flask containing 50 mL of solution, 50 mg of activated carbon or composites (us-AC/Fe₃O₄ or h-AC/Fe₃O₄) was added. The flask with the solution and sorbent was continuously agitated on an orbital shaker. The adsorption time for all sorbents was set at 4 h. After the adsorption process, the sorbent was separated by centrifugation for activated carbon and by magnetic separation for the us-AC/Fe₃O₄ and h-AC/Fe₃O₄ composites. Subsequently, an aliquot of the post-adsorption solution was taken, and the residual Pb²⁺ concentration was determined using an atomic absorption spectrometer (Shimadzu AA-6200, Japan).

2.5. Determination of the Point of Zero Charge

The point of zero charge (PZC) of the composites were determined using the pH-drift method [53]. A fixed amount of the sorbent (25 mg) was added into 25 mL of mixture in a series of glasses. The pH of the mixture was adjusted by using 0.1 N HCl and/or 0.1 N NaOH solution. The pH was measured with a pH meter. Potassium chlorate (KCl) with 0.1 N concentrations was made to be added to the mixture of adsorbent and water to obtain ionic strengths.

The initial pH values of the suspensions were adjusted to 3, 5, 6, 7, 8, 10, and 12 by adding small amounts of standard HCl or NaOH solutions of various concentrations to 25 mL glasses of deionized water. The suspensions were shaken on an orbital shaker for 1 h at 25 °C, and the initial pH values were recorded as pHᵢ (pH_water).

After equilibration, 1 mL of KCl solution (0.1 N) was added to each beaker to maintain constant ionic strength, yielding a final volume of 26 mL. The suspensions were further agitated for 30 min under the same conditions, and the final pH values (pHf) were measured. The difference ΔpH was calculated as:

ΔpH = pH_f − pH_i

(2)

The ΔpH values were plotted against the initial pH values (pHᵢ). The PZC was identified as the pH at which the curve intersects the line ΔpH = 0.

2.6. Characterization

The structural and morphological characteristics of the synthesized samples were comprehensively examined using a range of advanced analytical techniques. Field-emission scanning electron microscopy (SEM, Auriga Crossbeam 540, Carl Zeiss, Oberkochen, Germany), equipped with an energy-dispersive X-ray spectroscopy (EDS) system (Oxford Instruments, AZtec 6.0 software, UK), was employed to investigate the surface morphology and elemental composition of the materials. Additionally, a Helios CX5 system (Thermo Fisher Scientific, Waltham, MA, USA) was utilized for high-resolution morphological and structural analysis of the composites. All microscopic analyses were performed at Nazarbayev University (Astana, Kazakhstan). X-ray diffraction (XRD) measurements were conducted using a PANalytical X’Pert PRO MPD diffractometer (Netherlands) equipped with Cu Kα radiation (λ = 1.5406 Å), operating at 40 kV and 40 mA. Diffraction data were collected over a 2θ range of 5° to 90° to determine the crystalline structure and phase composition of the magnetite-containing samples. Raman spectroscopic analysis was performed using an NT-MDT NTegra Spectra system (Russia, Moscow) with laser excitation wavelengths of 473 nm and 633 nm. These measurements were conducted at the National Nanotechnology Laboratory of Open Type, al-Farabi Kazakh National University (Almaty, Kazakhstan). Nitrogen adsorption–desorption isotherms were measured using Static multi-purpose gas adsorption analyzer SSA-4000 (Henan Mingguan Scientific Instruments Co., Ltd., Zhengzhou, China), and the specific surface area and porosity characteristics were subsequently calculated using the Brunauer–Emmett–Teller (BET) method.

3. Results and Discussion

The structural and chemical transformation of activated carbon to impart magnetic properties—enabling magnetic separation while preserving its porous structure and active adsorption sites—is crucial for the development of novel, sustainable, and safe sorbents. This study focuses on evaluating the influence of different methods for incorporating magnetite nanoparticles into the carbon matrix of activated carbon on its surface structure, porosity, and surface chemistry. Particular attention is given to maintaining high adsorption performance, demonstrated through the removal of lead ions from aqueous solutions.

Activated carbon is a well-established material for water purification, effective against a wide range of contaminants including metal ions, organic pollutants, and others [54]. The adsorption performance of AC is influenced not only by the type of raw precursor used but also by the carbonization and post-treatment conditions, which may include various activation and functionalization methods [55]. These factors collectively affect the material’s structure and morphology, porosity, surface chemistry, defect density, and degree of graphitization—all of which directly impact its adsorption capacity. Figure 1 shows SEM images of activated carbon derived from rice husk, revealing its heterogeneous surface morphology

The material exhibits a rough, porous texture with micro- and mesopores, which is typical for carbonaceous adsorbents prepared via thermochemical activation. These pores enhance the specific surface area and provide numerous active sites for interaction with adsorbates. In addition to the porous structure, certain regions display layered arrangements, indicative of partial graphitization. The presence of these lamellar features may suggest the formation of graphitic carbon domains during high-temperature treatment [56]. Such structures can improve the material’s electrical conductivity and mechanical stability, and may contribute to π–π interactions with adsorbed metal ions or organics. EDS elemental analysis confirms that the sample is primarily composed of carbon (C, 78.88 ± 0.33 wt. %) and oxygen (O, 20.26 ± 0.54 wt. %), with trace amounts of silicon (Si, 0.35 ± 0.04 wt. %) and potassium (K, 0.51 ± 0.05 wt. %). Silicon likely originates from residual silica inherent in rice husk, while potassium is introduced during the activation process. These results suggest that the rice husk-derived activated carbon possesses a well-developed porous structure combined with partially graphitized carbon domains, making it a promising material for adsorption-based water purification [57].

The Raman spectrum of the rice husk-derived activated carbon exhibits two prominent peaks located at approximately 1346 cm⁻¹ and 1581 cm⁻¹, which correspond to the D–and G–bands, respectively (Figure 2). The G–band (~1581 cm⁻¹) is attributed to the E2g vibration mode of sp²-hybridized carbon atoms in graphitic structures. It indicates the presence of ordered graphitic domains and is a signature of crystalline carbon networks. The D–band at ~1346 cm⁻¹ (disordered-induced) associated with defects or disorders within the carbon lattice, such as edge planes, vacancies, and functional groups.

The intensity ratio I_D/I_G provides insight into the degree of disorder and graphitization. The intensity ratio I_D/I_G was calculated to be 0.95. A relatively high intensity of the D-band compared to the G-band suggests a significant amount of structural defects or amorphous carbon, which is typical for activated carbon materials derived from biomass. This value implies that while the material retains some graphitic character, a significant proportion of amorphous or defect-rich carbon is present [58,59]. Such structural disorder is beneficial for adsorption, as it enhances surface reactivity by providing more active sites for Pb(II) ion binding. Overall, the Raman spectrum confirms that the synthesized material contains both disordered carbon regions and partially graphitized structures, in agreement with the SEM observations of layered domains. This hybrid structure enhances both the surface reactivity and the mechanical stability of the adsorbent.

Magnetite nanoparticles obtained by the co-precipitation method were also characterized using SEM, XRD, and BET analyses. Analysis of the SEM images (Figure 3) revealed that the Fe₃O₄ nanoparticles possess a nearly spherical morphology with a relatively uniform size distribution in the range of 20 to 35 nm. Additionally, larger particles exceeding 50 nm were observed, which is attributed to agglomeration driven by the intrinsic magnetic interactions between particles. EDS elemental mapping confirmed the high purity of the synthesized material, consisting primarily of iron and oxygen. Minor signals of carbon, silicon, and gold detected in the spectrum are ascribed to the substrate and sample preparation process.

The X-ray diffraction (Figure 4) pattern of the magnetite nanoparticles exhibited six distinct diffraction peaks at 2θ values of 30.3°, 35.6°, 43.4°, 53.6°, 57.2°, and 62.9°, corresponding to the characteristic crystallographic planes of the magnetite phase: (220), (311), (400), (422), (511), and (440), respectively. A weak reflection at 2θ = 19.7° and a minor peak at 18.8° may be attributed to lattice disorder, which is commonly observed in nanoparticles, or to the presence of trace impurities. The average crystallite size (t) was estimated using the Scherrer equation (t = λ/βcos θ), where λ is the wavelength of the Cu Kα radiation, θ is the Bragg angle, and β is the full width at half maximum of the diffraction peak in radians. The calculated crystallite size was approximately 21.04 nm. In comparison, scanning electron microscopy analysis revealed an average particle size of approximately 31.41 nm, suggesting possible agglomeration or that individual particle might consist of multiple crystalline domains. Such discrepancies are common, as the XRD method determines the size of coherently diffracting domains, whereas SEM reflects the actual physical dimensions of the particles. According to the Brunauer–Emmett–Teller analysis, the specific surface area of the obtained magnetite nanoparticles was found to be 68.42 m²/g, indicating a high degree of dispersion and nanoscale morphology. These properties render them highly promising for applications in adsorption, catalysis, and magnetic separation.

The us-AC/Fe₃O₄ composite was synthesized by combining rice husk-derived activated carbon with magnetite nanoparticles prepared via the co-precipitation method, followed by ultrasonication treatment. The SEM images of the us-AC/Fe₃O₄ composite illustrate a textured and heterogeneous surface morphology (Figure 5). The activated carbon matrix retains its porous, irregular structure, which is favorable for adsorption. At higher magnifications (×50,000–×120,000), it can be observed that the magnetite nanoparticles tend to agglomerate [60]. The elemental composition includes carbon (C, 69.58 ± 0.17 wt%), oxygen (O, 25.04 ± 0.29 wt%), and iron (Fe, 4.94 ± 0.10 wt%), along with trace amounts of silicon (Si, 0.20 ± 0.02 wt%) and potassium (K, 0.24 ± 0.02 wt%). Silicon is present as a trace component in the activated carbon, originating from the rice husk precursor, whereas potassium may arise from residual activating agents. As a result of ultrasonication, magnetite nanoparticles are uniformly distributed across the surface of the activated carbon particles, thereby imparting the required magnetic properties to the material and enabling its subsequent magnetic separation after the sorption processes.

The XRD pattern of the us-AC/Fe₃O₄ composite (Figure 6) displays distinct diffraction peaks at 30.2°, 35.6°, 43.3°, 53.7°, 57.3°, and 62.9°, which can be indexed to the (220), (311), (400), (422), (511), and (440) planes of magnetite (Fe₃O₄) in accordance with JCPDS card no. 19-0629. These reflections confirm the characteristic cubic spinel structure of Fe₃O₄ [61,62], indicating that the crystalline framework of magnetite remains preserved after ultrasonic treatment. In addition, the broad diffraction band observed near 26.2° is attributed to the amorphous structure of activated carbon, whereas the sharp peaks correspond to well-crystallized Fe₃O₄ nanoparticles uniformly embedded within the carbon matrix [63,64].

The h-AC/Fe₃O₄ composite was synthesized by co-precipitating magnetite nanoparticles onto activated carbon, followed by hydrothermal treatment. The SEM images of the h-AC/Fe₃O₄ composite at various magnifications reveal a heterogeneous surface morphology typical of magnetically modified carbon materials (Figure 7).

Distributed across the activated carbon surface are numerous spherical and quasispherical nanoparticles of magnetite Fe₃O₄ formed during co-precipitation. At higher magnifications (×20,000–×120,000), these nanoparticles appear uniformly anchored to the carbon surface, forming tight clusters or aggregates.

The EDS mapping confirms the presence of key elements: carbon (C, 70.00 ± 0.18 wt%), oxygen (O, 25.01 ± 0.31 wt%), and iron (Fe, 4.88 ± 0.10 wt%), with minor traces of silicon (Si, 0.11 ± 0.02 wt%). The significant iron content confirms the successful incorporation of Fe₃O₄ into the composite. The detected silicon originates from residual silica inherently present in the rice husk precursor used for the production of activated carbon. The combined SEM and EDS results demonstrate that the hydrothermal method enables uniform deposition of Fe₃O₄ nanoparticles onto the carbon substrate, yielding a composite with structural stability, and magnetically responsive properties.

The XRD pattern of the h-AC/Fe₃O₄ composite (Figure 8) exhibits distinct reflections at 26.0°, 30.3°, 35.6°, 43.2°, 44.7°, 48.3°, 53.8°, 57.4°, and 63.0°. The broad peak at 26.0° is attributed to the (002) plane of graphitic carbon with sp² hybridization [65]. The diffraction peaks at 30.3°, 35.6°, 43.2°, 53.8°, 57.4°, and 63.0° correspond to the characteristic reflections of magnetite (Fe₃O₄), confirming the preservation of its crystalline spinel structure. In addition, the weak peak observed at 44.7° may suggest a minor contribution from metallic Fe or Fe₃C phases [66].

The nitrogen adsorption–desorption isotherms measured at 77 K (Figure 9a) correspond to type Ib with an H4 hysteresis loop, indicating the predominance of micropores [67,68], referred to in [69] as “silt-pores”, as well as a high specific surface area as determined by the Brunauer–Emmett–Teller (BET) method. The pronounced uptake at low p/p₀ is attributed to rapid filling of molecular-scale micropores owing to strong adsorbent–adsorptive interactions [70]. The presence of the characteristic hysteresis loop confirms the existence of capillary pores and a complex porous morphology. At low relative pressures (p/p₀ < 0.1), a steep adsorption uptake is observed, corresponding to micropore filling. At higher relative pressures (p/p₀ > 0.8), a sharp rise in adsorption is evident, particularly for AC and more prominently for us-AC/Fe₃O₄, which is attributed to capillary condensation within pores. The specific surface areas calculated using the BET equation for AC, us-AC/Fe₃O₄, and h-AC/Fe₃O₄ were 1818.2, 1007.2, and 833.1 m²/g, respectively.

The unmodified activated carbon exhibited the highest nitrogen adsorption–desorption capacity, reflecting its well-developed microporous structure typical of plant-derived activated carbons. Following hydrothermal modification with Fe₃O₄ nanoparticles, a pronounced decrease in nitrogen uptake was observed, indicating a significant reduction in accessible surface area and/or pore volume (Figure 9a). This decrease can be attributed to the partial blockage of pores by Fe₃O₄ particles during hydrothermal treatment and precipitation, resulting in denser coverage of the carbon surface. In contrast, ultrasonic treatment facilitated a more homogeneous dispersion of Fe₃O₄ nanoparticles on the carbon framework, thereby reducing excessive pore blockage. Consequently, the surface area of us-AC/Fe₃O₄ remained higher than that of h-AC/Fe₃O₄, but lower than that of pristine AC.

The pore size distribution was obtained from the nitrogen desorption branch using the Horváth–Kawazoe model, which is suitable for the analysis of microporous structures under the assumption of slit-shaped pore geometry. This semi-empirical method is particularly useful for the comparative analysis of microporous materials [70]. The results revealed a narrow distribution predominantly in the range of 0.57–0.84 nm for all three samples (Figure 9b). Such pore-size distribution for the activated carbon derived from rice husk via KOH thermochemical activation is in good agreement with previously reported studies. In particular, in work [71], it was shown that for KOH-activated rice husk carbon the predominant fraction of micropores was also concentrated within the 0.5–0.9 nm range. In work [72], activated carbon was also obtained from oil-tea shell by KOH thermochemical activation, yielding a microporous structure with pore widths predominantly in the range of 0.6–0.8 nm.

At the same time, the pore volume is significantly reduced for the h-AC/Fe₃O₄ and us-AC/Fe₃O₄ composites compared with AC, which also indicates possible pore blocking, since the pore diameter remains in the range of 0.57–0.84 nm for all investigated sorbents. Pores of adsorbents fall within a suitable size range for the sorption of Pb²⁺ ions, whose effective ionic radius is ~120 pm (0.12 nm). This dimensional match allows the ions to penetrate the pores and promotes effective interaction with the active sorption sites. Considering these findings, the us-AC/Fe₃O₄ composite represents an intermediate case, combining a relatively high specific surface area with a uniform dispersion of nanoparticles and effective magnetic separation. This combination of properties makes it a promising candidate for adsorption applications, providing both enhanced performance and convenient recovery via magnetic separation.

The synthesized sorbents were evaluated for their efficiency in removing Pb²⁺ ions. To evaluate the contact time at which the maximum adsorption capacity is achieved, experiments were conducted at 2, 4, and 6 h (SI Table S1). It was found that for AC and the us-AC/Fe₃O₄ composite, the maximum adsorption capacity was reached at 4 h. In the case of the h-AC/Fe₃O₄ composite, the highest value was observed at 6 h. However, due to its comparatively lower adsorption capacity relative to the other materials, the data for this composite are also presented at 4 h in the main text. The results of lead adsorption capacity after 4 h of sorption at actual pH of initial solution equal to 5.7 ± 0.2 are presented in Figure 9. After the sorption processes, an increase in the solution pH was observed with decreasing residual concentrations of lead ions. Specifically, the pH value was 6.5 for activated carbon, 6.3 for the us-AC/Fe₃O₄ composite, and 5.9 for the h-AC/Fe₃O₄ composite. These results indicate that the efficiency of Pb²⁺ removal is directly reflected in the change in the solution’s acid–base environment: the higher the degree of cation removal, the closer the pH shifts toward neutral values. The points of zero charge (PZC) of AC and AC/Fe₃O₄ composites were determined using the pH-drift method. The ΔpH vs. pHᵢ plots clearly demonstrate the crossing of the curve with the ΔpH = 0 axis. It was determined that the point of zero charge (pH_pzc) for the three investigated sorbents corresponded to the following pH values: 6.2 for AC, 6.8 for us-AC/Fe₃O₄, and 7.1 for h-AC/Fe₃O₄ (SI Figure S1). Determination of the PZC is critically important for understanding and optimizing the adsorption performance of AC/Fe₃O₄ in water treatment processes aimed at Pb²⁺ removal. The PZC defines the pH at which the adsorbent surface has no charge, at pH values below the PZC the surface is positively charged. At this pH value, competing adsorption of protons and positively charged lead ions uptake due to electrostatic repulsion can be observed. While at pH values moderately above the PZC the surface becomes negatively charged, thereby enhancing Pb²⁺ adsorption. However, increasing the pH of the solution by adding alkali to the solution leads to the precipitation of insoluble lead hydroxide, which distorts the true adsorption and increases the error [73]. Thus, the sorption characteristics of the sorbents were assessed at the actual pH value, without its correction. The results of lead adsorption capacity after 4 h of sorption at actual pH equal to 5.7 ± 0.2 are presented in Figure 10.

It was found that the adsorption efficiency and adsorption capacity of the studied materials after 4 h of contact time were as follows: AC—99.00%, 42.03 ± 1.82 mg/g, h-AC/Fe₃O₄—56.27%, 23.89 ± 1.19 mg/g, us-AC/Fe₃O₄—92.84%, 39.15 ± 1.64 mg/g. To evaluate the magnetic separation performance, both hydrothermally and ultrasonically synthesized AC/Fe₃O₄ composites were subjected to an external magnetic field. The complete separation of both magnetic composites upon application of an external magnetic field demonstrates the high efficiency of magnetic separation following the sorption process (Figure S2). The observed decrease in adsorption performance in the order AC > us-AC/Fe₃O₄ > h-AC/Fe₃O₄ is consistent with the specific surface area results obtained for the three composites, which showed a reduction from 1818.2 m²/g to 1007.2 and 833.1 m²/g, respectively. Thus, the decrease in active sorption surface area and partial pore blocking lead to reduced adsorption efficiency, which is most pronounced for the h-AC/Fe₃O₄ composite.

The adsorption kinetics of the investigated materials were analyzed by fitting the experimental data to the pseudo-first-order and pseudo-second-order models, which are expressed by Equations (3) and (4), respectively:

ln (q_e − q_t) = ln q_e − k₁ · t

(3)

$${\displaystyle \frac{t}{q}}={\displaystyle \frac{1}{k_2·q_e^2}}+{\displaystyle \frac{1}{q_e·t}}$$

(4)

where q_t (mg·g⁻¹) is the amount of Pb(II) adsorbed at time t, q_e (mg·g⁻¹) is the adsorption capacity at equilibrium, k₁ is the sorption rate constant for the pseudo-first order model, k₂ is the sorption rate constant for the pseudo-second order model.

In addition, the sorption mechanisms were examined using the intraparticle diffusion model (Weber–Morris), Boyd’s film diffusion model, Bangham’s kinetic model, and the Elovich chemisorption model.

The results obtained from the adsorption kinetics (Figure 11) demonstrate that the adsorption rates vary among the three investigated sorbents. For pristine activated carbon, equilibrium concentration (C_e) is reached within the first 5 min, indicating rapid adsorption. In contrast, for the us-AC/Fe₃O₄ composite, the most significant decrease in lead concentration occurs within the initial 5 min, followed by a comparatively slower adsorption process, reaching equilibrium after approximately 120 min. This behavior may be attributed to the diffusion of Pb²⁺ ions into deeper pores of the sorbent. In the case of the h-AC/Fe₃O₄ composite, the sharpest decline in initial concentration is also observed within the first 5 min, with equilibrium being achieved after 40 min.

Extending the contact time beyond this point results in no significant change in the residual lead ion concentration. The results of the pseudo-first-order model calculations, including the rate constant k₁ and the correlation coefficient R², are presented in

Table 2. Comparison of kinetic parameters for Pb²⁺ ion adsorption by AC and AC/Fe₃O₄ composites.

Sorbent	Pseudo-First-Order		Pseudo-Second-Order
	k1 (min−1)	R2	k2 (g·min·mg−1)	R2
AC	0.0001	0.8649	0.0632	0.9999
h-AC/Fe3O4	0.0065	0.7282	0.1082	0.9994
us-AC/Fe3O4	0.0021	0.8892	0.0671	0.9997

for all three investigated sorbent composites. As shown in Figure 11a,c,e, a similar trend is observed in the pseudo-first-order plots for all samples. However, deviations from linearity become apparent after 10 min of adsorption for the h-AC/Fe₃O₄ and us-AC/Fe₃O₄ composites, and after 20 min for pristine AC. This suggests that the pseudo-first-order model is primarily applicable during the initial stages of the adsorption process [74]. It can be assumed that at the beginning, adsorption is governed by physical mechanisms such as van der Waals interactions or diffusion into readily accessible pores [75].

The adsorption profile shown in Figure 11 supports this behavior: for pristine AC, a rapid attainment of equilibrium concentration is observed within the first 5 min, with no significant change in residual concentration thereafter. In contrast, the adsorption curves for the composites exhibit two distinct stages: an initial rapid decline in lead ion concentration due to physisorption on the sorbent surface, followed by a slower adsorption phase leading to equilibrium. Accordingly, adsorption on AC is primarily governed by physisorption, whereas for the h-AC/Fe₃O₄ and us-AC/Fe₃O₄ composites, the process involves initial physisorption followed by chemisorption at later stages [76]. Physisorption may proceed via both surface diffusion and pore diffusion mechanisms. A comprehensive discussion of the processes represented by the pseudo-second-order kinetic model, along with its inherent limitations, is provided in [77].

The obtained results suggest that the incorporation of magnetite nanoparticles into the AC structure via hydrothermal treatment leads to the partial filling of micro- and mesopores with Fe₃O₄ nanoparticles, significantly reducing the adsorption capacity of the resulting composite [78]. In contrast, the ultrasonic-assisted deposition of magnetite nanoparticles promotes their attachment to the surface without compromising the porosity of the activated carbon. As a result, a composite is formed that is suitable for lead ion adsorption and exhibits magnetic properties [79], enabling efficient magnetic separation of the sorbent after the adsorption process.

The determination of mass transfer parameters is essential for clarifying the adsorption mechanism and for the rational design of sorption processes. As described in [76], the overall kinetics of mass transfer can be divided into three main stages. The first involves external diffusion, where adsorbate molecules migrate through the liquid film surrounding the adsorbent under the driving force of the concentration gradient between the bulk solution and the adsorbent surface. The second stage corresponds to intraparticle diffusion, during which the adsorbate penetrates into the pores and channels of the sorbent. The third stage is the interaction of the adsorbate with the active binding sites of the sorbent surface. Among these, the slowest step controls the overall sorption process and thus determines the rate-limiting stage. Identifying the rate-limiting step is essential for the effective design and optimization of sorption processes. Typically, adsorption is governed by two dominant mass transfer mechanisms: external film diffusion and intraparticle diffusion. To obtain deeper insights into the controlling mechanism, several kinetic models were applied in this study, namely the Weber–Morris intraparticle diffusion model, Boyd’s film diffusion model, Bangham’s kinetic model, and the Elovich chemisorption model.

The Boyd model was employed to illustrate the diffusion of adsorbate through a limiting liquid film. This model is employed to predict the actual rate-determining stage of the adsorption process. The Boyd model is employed to ascertain the governing mechanism of the adsorption process, whether it occurs due to intramolecular (or intradiffusion) diffusion or external diffusion (diffusion through the liquid-solid boundary) [80,81]. The Boyd model is expressed by Equation (5).

B_t = −0.4977 − ln(1 − F)

(5)

where F = q_e/q_t is the proportion of equilibrium sorption at time t, B_t is the Boyd function, q_t is the adsorption at time t (mg/g), and q_e is the equilibrium adsorption capacity (mg/g).

The Elovich model, also referred to as the Elovich equation, is an empirical kinetic model that has gained significant traction in the field of adsorption on heterogeneous surfaces, particularly in scenarios where the sorbent surface exhibits an uneven distribution of active centers [80,82]. The nondifferential form of the equation is expressed by Equation (6):

$$q_t= {\displaystyle \frac{1}{B}}{\log }_e\left(\mathsf{\alpha }\mathsf{\beta }\right)+ {\displaystyle \frac{1}{\mathsf{\beta }}}{\log }_e\left(t\right)$$

(6)

In this equation, q_t denotes the amount of adsorbed substance at time t (mg/g), α is the initial rate of adsorption (mg/g·min), β is the desorption constant associated with energy activation (g/mg), and t is time (min).

Bangham’s kinetic model is employed to elucidate the mechanisms of adsorption, particularly in circumstances where pore diffusion and micropore accessibility are taken into account [83,84]. This model posits that intrapore diffusion functions as a limiting stage in the adsorption process. The model was utilized to ascertain whether diffusion in pores is the sole mechanism governing velocity.

The logarithmic form of the model looks like this (7):

$$\log \left[\log \left({\displaystyle \frac{C_0}{C_0-q_t ·\mathrm{m}}}\right)\right]=\log \left({\displaystyle \frac{k}{2.303 ·\mathrm{V}}}\right)+\mathsf{\alpha }·\log t$$

(7)

where C₀ is the initial concentration of ions in the solution (mg/L), q_t is the amount of adsorbed substance at a time (mg/g), m is the mass of the sorbent (g), V is the volume of the solution (mL), k is the Bangham constant (related to kinetics and porosity), α is the indicator characterizing the mechanism of pore diffusion, t is the time (min).

The Weber–Morris Model (intraparticle diffusion model) is used to analyze the mechanism of adsorption and, in particular, to find out whether intraparticle diffusion (pore diffusion) is involved in limiting the rate of the sorption process [85,86]. The linear form of the equation has the form (8):

$$q_t= k_{id }·t^{{\displaystyle \frac{1}{2}}}+C$$

(8)

where q_t is the amount of adsorbed substance at time t (mg/g); k_id is the intraparticle diffusion constant (mg·g⁻¹·min^−0․5), t^1/2 is the square root of time, and C is the parameter reflecting the boundary layer thickness.

The calculation results for each of the models for the studied adsorbents are presented in

Table 3. Comparison of kinetic parameters for Pb²⁺ ion adsorption by AC, us-AC/Fe₃O₄ and h-AC/Fe₃O₄ composites in various models.

Sorbent	Weber-Morris				Boyd		Bangham			Elovich
	kid1 mg/(g/min)	R2 Step 1	kid2 mg/(g/min)	R2 Step 2	kB, min−1	R2	α	k, mg/g·min−α	R2	α (mg g−1 min−1)	β (g mg−1)	R2
AC	0.0648	0.8302	0.0266	0.9982	0.0002	0.8649	0.0681	1.413	0.937	~3.24 × 1030	2.0016	0.9113
h-AC/Fe3O4	0.9125	0.6664	0.0996	0.4905	0.0066	0.7283	0.1407	440.19	0.9138	58.01	0.1883	0.9306
us-AC/Fe3O4	0.8182	0.9781	0.3687	0.9898	0.0022	0.8893	0.1128	74.43	0.9389	52.238	0.3355	0.9215

.

The fitting of the experimental data to the Weber–Morris intraparticle diffusion model is presented in Figure 12, Figure 13 and Figure 14 for the investigated sorbents. As shown by the Weber–Morris calculations, the obtained results were multilinear (Figure 12a), suggesting that the adsorption process is controlled not only by intraparticle diffusion but also by two or more stages. The data are represented by two linear phases: the initial phase corresponds to the influence of the boundary layer with external mass transfer, during which lead ions are rapidly adsorbed. After 60 min, the adsorption rate decreased, leading to the second phase, which lasted up to 120 min. According to [81], this phase is associated with the diffusion of molecules to the internal adsorption sites of the sorbent. A comparison of the two diffusion constants of the Weber–Morris model (k_id) shows that k_id1 > k_id2, as presented in Table 2. The diffusion of molecules inside the sorbent is thus the rate-determining step of the adsorption process, as confirmed by the lower k_id2 value. However, intraparticle diffusion may not be the sole limiting step of the adsorption process, and other interaction mechanisms may act simultaneously.

The parameters of the initial adsorption rate, α and β, calculated using the Elovich model for the sorption of Pb ions on activated carbon, have excessively high values. This indicates that the description of the sorption process using this model is not applicable or incorrect (Figure S3). The parameters of the initial adsorption rate calculated using the Elovich model for the sorption of Pb²⁺ ions on h-AC/Fe₃O₄ are α = 58.01 mg/g·min and β = 0.1883, and for us-AC/Fe₃O₄, α = 52.238 mg/g·min and β = 0.3355, respectively. These results indicate a high initial rate of adsorption and a moderate decrease in the rate with increasing sorption on the surface [82].

In the next step, the applicability of the Bangham model was tested. The ensuing results are delineated in Table 3 and Figure S4. For all three sorbents, the α values range from 0.07 to 0.14. The fact that α < 1 indicates that the process is controlled by both intrapore diffusion and external mass transfer, i.e., a mixed transport mechanism [84]. The highest α value is observed for h-AC/Fe₃O₄ (0.1407), possibly due to the high resistance of the pore structure after hydrothermal treatment, due to complete or partial pore blockage due to blockage by Fe₃O₄ nanoparticles. All values of R² > 0.91, which confirm the model’s suitability for describing diffusive behavior. The optimal data correspondence (R² = 0.937–0.9389) is observed between AC and us-AC/Fe₃O₄, indicating the most suitable description of the kinetics of Pb²⁺ penetration into the porous structure.

The experimental data was also evaluated using the Boyd model [87] (Figure S5). Linear approximation results yielded coefficients of determination (R²) for the sorption process using each sorbent. R² values range from 0.7283 to 0.8893, indicating a relatively weak agreement with the experimental data. Furthermore, all graphs constructed using the Boyd model demonstrate that the line does not pass through the origin, indicating that intraparticle diffusion is not the sole limiting factor.

The adsorption of Pb²⁺ ions by sorbents was modeled using Freundlich and Langmuir isotherms. The adsorption isotherm is defined as the relationship between the amount of substance adsorbed on the surface of the sorbent and its equilibrium concentration in solution. The study of adsorption isotherms is of key importance for understanding the mechanisms of adsorbate–adsorbent interaction and improving the efficiency of sorption materials. To interpret the experimental data in this study, two of the most common models were used: Langmuir and Freundlich. The quality of compliance was assessed using the correlation coefficient. The isotherms obtained in this study facilitate the visualization of the relationship between the amount of substance retained by the adsorbent and its equilibrium concentration in solution.

The Langmuir model was originally proposed to describe the adsorption of gas molecules on homogeneous solid surfaces (crystalline materials) with one type of adsorption centers [88,89]. The model under consideration is of an empirical nature and is predicated on kinetic principles. In a state of equilibrium, the rates of adsorption and desorption on the surface are balanced, and there is no total accumulation. The following assumptions underpin this study: (a) the process proceeds in the form of monolayer adsorption, (b) all active centers of the surface are energetically homogeneous, (c) the adsorption energy remains constant, and (d) there are no lateral interactions between the adsorbed molecules [90]. The Langmuir isotherm can be described by Equation (9):

$$q_e= {\displaystyle \frac{1}{\mathrm{ }{K}_L{q}_{max{C}_e}}}+ {{\displaystyle \frac{1}{q}}}_{max}$$

(9)

where q_e is the amount of adsorbate, adsorbent substance (mg/g), C_e is the equilibrium concentration of adsorbate (mg/L), K_L is the coefficient of adsorption energy (L/mg), q_max is the maximum adsorption capacity (mg/g) [91].

In contrast to the Langmuir isotherm, the empirical Freundlich model is capable of being utilized for multilayer adsorption on heterogeneous sites. The Freundlich model has been demonstrated to be capable of describing experimental data from adsorption isotherms, irrespective of whether adsorption occurs on homogeneous or heterogeneous centers. Additionally, it has been shown to be independent of the formation of a monolayer. Furthermore, the Freundlich isotherm is frequently employed to characterize multilayer adsorption and adsorption on heterogeneous surfaces, where there is an interaction of neighboring adsorbed molecules [92]. The mathematical model can be represented by Equation (10):

$${\log }_e{q}_e= {\displaystyle \frac{1}{n}}{\log }_e{C}_e+ {\log }_e{K}_F$$

(10)

where q_e is the amount of adsorbate, adsorbent substance (mg/g), C_e is the equilibrium concentration of adsorbate (mg/L), K_F is the Freundlich constant (mg/g), heterogeneity factor (dimensionless) [93]. The Pb²⁺ adsorption isotherms (Figure S6) revealed distinct uptake behaviors for the three sorbents, which can be attributed to differences in their chemical composition as well as in their textural and morphological characteristics.

The parameters of the isotherms for the Freundlich and Langmuir models, calculated for the adsorption of Pb²⁺ ions by AC and AC/Fe₃O₄ composites, are presented in

Table 4. The isotherm parameters for Freundlich and Langmuir models for Pb²⁺ ion adsorption by AC and AC/Fe₃O₄ composites.

Sorbent	Langmuir			Freundlich
	qmax, mg/g	KL, L/mg	R2	n	KF, mg/g·(L/mg)1/n	R2
AC	63.6943	7.1364	0.9997	5.3333	40.8413	0.8117
h-AC/Fe3O4	24.1546	0.0478	0.8373	1.8783	1.8569	0.8568
us-AC/Fe3O4	41.3223	0.1367	0.9899	8.4104	22.0445	0.9873

.

According to the obtained results, the following assumptions can be made from the experiments. The maximum sorption capacity (q_max) calculated for AC is 63.69 mg/g. For the us-AC/Fe₃O₄ and h-AC/Fe₃O₄ composites, the calculated capacities are 41.32 and 24.16 mg/g, respectively. These values are in good agreement with the experimental data. The result indicates a strong affinity of AC for Pb²⁺ ions, a typical occurrence for carbons with oxygen-containing groups. For us-AC/Fe₃O₄, K_L is 0.14 L/mg, indicating a moderate affinity for Pb₂₊ and 0.05 L/mg for h-AC/Fe₃O₄, suggesting a weaker affinity for Pb²⁺. The coefficient of determination for all three sorbents ranges from 0.8373 to 0.9997, and it has been demonstrated to be a comparatively superior indicator of compliance with the Langmuir model for describing the processes of adsorption of Pb²⁺ ions of AC and us-AC/Fe₃O₄. The constants of the Freundlich isotherms, K_F and n, are determined from the slope of the graph of log q_e versus log C_e (Figure 15).

In this study, the values of n > 1 indicate chemosorption and reflect the high affinity between adsorbate and adsorbent [94]. The Freundlich constant, K_F, which is associated with the adsorption capacity, exhibits an increase in the range K_F(h-AC/Fe₃O₄) < K_F(us-AC/Fe₃O₄) < K_F(AC) (Table 4). This observation indicates the endothermic nature of the adsorption process. The Freundlich model is a more suitable model for describing the adsorption process on the h-AC/Fe₃O₄ composite, as indicated by its higher coefficient of determination.

Comparative analysis of the adsorption capacity (

Table 5. Comparison of Fe₃O₄-composite sorbents synthesized from different supports for Pb(II) adsorption.

Composite Sorbent	Support Material	Component Synthesis Method	Composite Synthesis Approach	Pollutant	Adsorption Capacity (mg/g)	Ref.
AC/Fe3O4	Rice straw	-	In situ co-precipitation	Pb(II)	33	[95]
AC/Fe3O4(2)	Rice straw	-	In situ co-precipitation	Pb(II)	68
AC/Fe3O4	Castor seed shell	Fe3O4—Co-precipitation	Conventional co-precipitation	Pb(II)	122	[96]
ES/Fe3O4	Eggshell + starch	Fe3O4—Co-precipitation	Ultrasonic-assisted	Pb(II)	57.14	[97]
BC/Fe3O4	Tangerine peel	Fe3O4—Co-precipitation	Co-precipitation on biochar	Pb(II)	125.23	[98]
BC/Fe3O4	Waste wood	-	In situ precipitation on biochar	Pb(II)	40.7	[99]
C/Fe3O4	Pinewood + feedstocks	-	Pyrolysis + magnetic precipitation	Pb(II)	~30
C/Fe3O4	Switchgrass	-	Pyrolysis + magnetic precipitation	Pb(II)	~30
AC/Fe3O4	Commercial AC	-	Co-precipitation with alginate	Pb(II)	36.764	[100]
AC/Fe3O4	Rice husks	Fe3O4—Co-precipitation	Hydrothermal-assisted	Pb(II)	23.89	This work
AC/Fe3O4	Rice husks	Fe3O4—Co-precipitation	Ultrasonic-assisted	Pb(II)	39.15	This work

) shows that the obtained Fe₃O₄/AC composite demonstrates values comparable to a number of well-known nanomaterials.

Despite exhibiting slightly lower rates in comparison to individual highly effective sorbents, the developed samples demonstrate a favorable performance when utilizing affordable raw materials and environmentally friendly synthesis methods. This observation serves to substantiate their practical significance and to underscore their capacity for further optimization.

4. Conclusions

In this study, two approaches to synthesizing magnetic sorbents based on activated carbon from rice husks with the inclusion of magnetite nanoparticles by hydrothermal and ultrasonic treatment were investigated. The experimental results demonstrated that the us-AC/Fe₃O₄ composite exhibited an adsorption capacity of 39.15 mg/g and a removal efficiency of 92.84% when adsorbing lead (Pb²⁺) ions from an aqueous solution with an initial concentration of 50 mg/L over a period of 4 h. These values are comparable with the adsorption capacity of the initial activated carbon (42.03 mg/g and 99.0%). A notable benefit of us-AC/Fe₃O₄ is its capacity for expeditious extraction following sorption via magnetic separation, a process that significantly streamlines the water purification procedure.

The analysis of kinetic models demonstrated that the adsorption of Pb²⁺ occurs in two stages: rapid physical adsorption in the initial stages and subsequent chemosorption. A comparison of experimental data with the Weber–Morris, Elovich, Bangham, and Boyd models indicates a high initial sorption rate and a gradual deceleration due to surface saturation. The investigation revealed that the process is governed by two primary mechanisms: external mass transfer and intraparticle diffusion. The most suitable agreement with the experiment for AC and us-AC/Fe₃O₄ was demonstrated by the Weber–Morris and Bangham models. Conversely, for h-AC/Fe₃O₄, the Weber–Morris and Elovich models provided a more adequate description. Modeling of adsorption isotherms revealed that the maximum calculated sorption capacity (q_max) according to the Langmuir model is 63.69 mg/g for AC, 41.32 mg/g for us-AC/Fe₃O₄ and 24.16 mg/g for h-AC/Fe₃O₄. The determination coefficients confirmed the optimal fit of the Langmuir model for describing the processes of Pb²⁺ adsorption on AC and us-AC/Fe₃O₄.

Therefore, it has been demonstrated that the ultrasonic modification of activated carbon with magnetite nanoparticles facilitates the production of magnetic composites that exhibit high sorption activity, comparable to that of the original carbon. An additional technological benefit of this process is the potential for magnetic separation. This renders us-AC/Fe₃O₄ a promising material for use in water purification systems from heavy metal ions.