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Abstract

This study reports the synthesis and characterization of a novel composite material, TiO₂-ZrO₂/PA/AC (titanium dioxide, zirconium dioxide, phosphonic acid, and activated carbon), fabricated via the sol-gel method for radionuclide removal. Characterization (XRD, SEM, FTIR, EDX) confirmed the successful integration of components and a functional surface structure. The composite’s adsorption behavior toward Cs(I), Sr(II), Pu(IV), and U(VI) was investigated in aqueous solution. Adsorption efficiency was observed to increase with pH and temperature. Isotherm analysis revealed the Langmuir model as the best fit, suggesting monolayer coverage, with the maximum adsorption capacity (Q₀) being highest for Sr(II) (467.83 mg/g at 310 K). Kinetic analysis confirmed the process is governed by the pseudo-second-order model, indicating a dominant chemisorption mechanism. The diffusion coefficients were found to increase with temperature, reinforcing the endothermic nature of the process and suggesting faster intraparticle transport at elevated temperatures. Furthermore, desorption studies demonstrated the composite’s excellent reusability, maintaining approximately 80% recovery efficiency after four cycles with HNO₃. These findings establish the TiO₂-ZrO₂/PA/AC composite as a highly promising, stable, and efficient adsorbent for practical application in nuclear waste management. The composite establishes an efficient, stable, and reusable adsorbent for practical nuclear waste management.

Keywords

Wastewater treatment heavy metal removal radionuclide removal adsorption sol-gel synthesis XRD

Introduction

Radioactive contamination of water sources poses a significant environmental and public health threat. The presence of radionuclides in water bodies can arise from various sources, including nuclear accidents, nuclear waste disposal, and natural occurrences. Therefore, the development of effective and sustainable technologies for the removal of radionuclides from aqueous solutions is crucial for environmental remediation and public safety.¹ A variety of approaches have been explored for radionuclide removal, including chemical precipitation, ion exchange, and membrane filtration. However, these methods often suffer from limitations such as high costs, low selectivity, and the generation of secondary waste.^2,3 Adsorbent materials for radionuclide removal have seen growing interest in recent years due to their versatility, cost-effectiveness, and potential for high selectivity. This material is of high interest for the efficient removal of radioactive ions^4,5 in general, with particular focus on the four key radionuclides Cs(I), Sr(II), Pu(IV), and U(VI).⁶ Critically, while the speciation of Cs(I) and Sr(II) remains relatively stable as simple hydrated ions across the experimental pH range, the chemistry of the actinides—specifically tetravalent plutonium, Pu(IV), and hexavalent uranium, U(VI) is highly complex and pH-dependent. Over the broad range of pH 2-10 relevant to adsorption studies, these actinides undergo significant hydrolysis and complexation, forming various monomeric and polymeric hydroxo-species (such as Pu(OH)₄(aq) and UO₂(OH)x(2-x)+) that profoundly dictate their surface affinity and overall adsorption mechanism. A full understanding of these dominant speciation effects is essential for accurately interpreting the measured adsorption behavior. To assess the performance of the TiO₂-ZrO₂/PA/AC composite, a series of experiments were conducted to evaluate its adsorption capacity, selectivity, kinetics, and isotherms for the removal of Cs(I), Sr(II), Pu(IV), and U(VI) ions from aqueous solutions. The influence of various parameters, such as pH, contact time, and initial ion concentration, on the adsorption process was investigated. Furthermore, the stability of the composite under different conditions was assessed to evaluate its long-term performance and potential for practical applications.⁷

Previous studies have investigated the use of various materials, such as.^8,9 The focus has recently shifted toward advanced adsorbents, including Metal-Organic Frameworks (MOFs),³ Graphene-based materials, and nanocomposites, due to their superior structural tunability and high surface area. Activated carbon, graphene, and carbon nanotubes have shown promising adsorption capacities for radionuclides due to their high surface areas and porous structures. Montmorillonite, bentonite, and zeolites have been widely used for radionuclide removal due to their ion-exchange capabilities and high surface areas.¹⁰ In light of these challenges, this work reports the successful synthesis and in-depth characterization of a novel TiO₂-ZrO₂/PA/AC composite. By systematically evaluating its adsorption behavior, kinetics, and reusability toward four principal radioactive ions (Cs(I), Sr(II)}, Pu(IV), and U(VI)), we move beyond mere insights. Instead, this research quantifies the unique synergistic potential of this hybrid material, thereby offering a high-capacity, reusable, and economically viable adsorbent that represents a significant leap forward in practical nuclear wastewater treatment technologies.¹¹

Materials and Methods

Innovative aspects of the TiO₂-ZrO₂/PA/AC composite

The innovative aspects of the TiO₂-ZrO₂/PA/AC composite lie in its novel hybrid design and the synergistic functionalization of its components, which collectively achieve high-performance radionuclide removal. Fabricated via the sol-gel method, the material integrates four key components: ZrO₂ provides a stable, high-surface area framework with a strong chemical affinity for actinides like Pu(IV) and U(VI), while Activated Carbon (AC) contributes high porosity and surface area for general adsorption capacity. Crucially, the surface is functionalized with Phosphonic Acid (PA), which acts as an advanced chelating agent, significantly enhancing adsorption by forming strong complexes with radionuclide ions.¹² This unique structure results in a material that is not only effective, showing a high maximum adsorption capacity, for example, 467.83 mg/g for Sr(II), but also highly practical, demonstrating excellent reusability with approximately 80% recovery efficiency after four cycles6. This multi-component approach ensures a stable, high-capacity, and reusable adsorbent for practical nuclear waste management.

Synthesis of TiO₂-coated ZrO₂/PA/AC composite (TiZr-PA-AC)

This study investigates the adsorption properties of a novel TiO₂-ZrO₂/PA/AC composite (TiZr-PA-AC) for the removal of radioactive ions, including Cs(I), Sr(II), Pu(IV), and U(VI), from aqueous solutions. ZrO₂ provides a stable and high-surface area support for the other components, and is specifically chosen for its strong chemical affinity toward actinides such as Pu(IV) and U(VI),⁴ offering excellent mechanical and chemical stability.^13,14 Phosphonic acid (PA) acts as a chelating agent, forming strong complexes with radionuclide ions and enhancing their adsorption. Activated carbon (AC) possesses a high surface area and porosity, providing excellent adsorption capacity for various contaminants, including radionuclides. The combination of these components within a single composite material offers several key advantages, including synergistic effects, versatility, and stability.⁶ The TiZr-PA-AC composite was synthesized using high-purity source materials obtained from Sigma Aldrich. To characterize the synthesized composite, a field emission scanning electron microscope (FESEM, Zeiss Sigma 300, German) was employed to obtain surface images at a variable vacuum without any coating. The FESEM was equipped with a back-scattered electron detector, which provided a clear visualization of the composite’s morphology at an accelerating voltage of 15 kV. This technique allowed for the identification and distribution of the individual elements within the composite. X-ray Diffraction (XRD) patterns were collected using a Bruker D8 Advance X-ray Diffractometer operated at 40 kV and 40 mA, employing Cu Kα radiation (λ = 1.5406 A^o).⁸ The samples were scanned over a 2Ɵ range of 5° to 80° with a step size of 0.02° and a scan speed of 0.5 s/step. Fourier transform infrared spectroscopy (FTIR) was utilized to analyze the functional groups present in the TiZr-PA-AC composite.^15,16 A Bruker Tensor 27 FTIR spectrometer was used for this purpose. No further purification was necessary prior to use. The specific surface area of the composite was determined using the Brunauer-Emmett-Teller (BET) method. This technique involves measuring the adsorption and desorption of nitrogen gas at low pressure.¹⁷

Synthesis of the TiO₂-ZrO₂/PA/AC composite

The TiO₂-ZrO₂/PA/AC composite was synthesized using a sol-gel method. The metal precursors, ZrOCl₂.8H₂O and TTIP (Titanium (IV) isopropoxide), and the coupling agent, PA (Phosphonic Acid), were mixed in a molar ratio of 1:1:2 (ZrOCl₂.8H₂O: TTIP: PA). Activated Carbon (AC) was then incorporated into the mixture at a mass ratio of 1:2, where 1 part mass of AC was used for every two parts total mass of the combined ZrO₂ and TiO₂ precursors (calculated based on the final expected oxide masses). In a typical synthesis, zirconium oxychloride octahydrate (ZrOCl₂·8H₂O) was dissolved in ethanol to form a clear solution. Deionized water was then added dropwise under continuous stirring to induce hydrolysis.¹⁸ The solution pH was adjusted to 1-2 using HCl (hydrochloric acid). Subsequently, phosphonic acid (PA) dissolved in ethanol was added to the gel and stirred thoroughly to ensure uniform distribution. Titanium (IV) isopropoxide (TTIP) dissolved in ethanol was then added dropwise to the gel while maintaining gentle stirring to avoid disrupting the gel structure. Finally, activated carbon (AC) was added to the gel and stirred vigorously to ensure even dispersion.⁴ The resulting gel was aged at room temperature for 24 h to improve its mechanical properties. The aged gel was then dried in an oven at 100-120°C for 24 h and subsequently calcined at 600°C for 3 h to obtain the final TiO₂-ZrO₂/PA/AC composite.

Characterization

The synthesized TiO₂-ZrO₂/PA/AC composite underwent comprehensive characterization to elucidate its structural, morphological, and chemical properties.¹⁸ X-ray Diffraction (XRD) was employed to determine the crystal structure and phase composition of the composite, providing insights into the arrangement of atoms and the presence of crystalline phases. Scanning Electron Microscopy (SEM) was utilized to examine the morphology and microstructure of the composite particles, revealing surface features and particle size distribution., offering detailed information about the nanoscale features. Fourier Transform Infrared Spectroscopy (FTIR) identified the functional groups present in the composite, including phosphonic acid and TiO₂, which are crucial for understanding the material’s chemical interactions. Energy-Dispersive X-ray Spectroscopy (EDX) determined the elemental composition of the composite, confirming the presence and distribution of the constituent elements.^19,20

Adsorption Studies

The adsorption capacity of the TiZr-PA-AC composite was determined by batch adsorption experiments. Stock solutions of the radionuclides were prepared at an initial concentration of 1000 mg/L using the following high-purity salts: Cesium nitrate (CsNO₃) for Cs(I), Strontium nitrate (Sr(NO₃)₂) for Sr(II), Plutonium (IV) nitrate (Pu(NO₃)₄) for Pu(IV),⁴ and Uranyl nitrate hexahydrate (UO₂(NO₃)₂·6H₂O) for U(VI). The Pu(IV) stock solution was prepared from Plutonium (IV) nitrate (Pu(NO₃)₄). Due to the high propensity of Pu(IV) to undergo hydrolysis and form polymeric species at moderate pH, the stock solution was stabilized by maintaining a high concentration of nitric acid (typically 2.0 M HNO₃). Working solutions were prepared immediately before the experiments by diluting the stabilized stock solution, ensuring that the final Pu(IV) concentration was low (<10⁻⁶ M) and the acid concentration was kept sufficiently high (or the total ionic strength adjusted with a non-complexing salt) to prevent immediate polymerization and maintain Pu(IV) in its monomeric form. Working solutions were prepared by appropriate dilution of these stock solutions. The Adsorption Studies paragraph has been updated to explicitly state both the mass of the composite (0.01 g) and the volume of the solution (25 mL), ensuring the experiment is reproducible. The solution pH was monitored and adjusted using dilute hydrochloric acid (HCl) or sodium hydroxide (NaOH) solutions.²¹ All adsorption experiments were conducted by adding a fixed amount of the TiZr-PA-AC adsorbent to 25 mL of the radionuclide solution in sealed containers. The containers were agitated using a temperature-controlled orbital shaker at a constant speed to ensure equilibrium was reached. After the adsorption process, the solid and liquid phases were separated by centrifugation or filtration. The final radionuclide concentration in the supernatant was measured using an appropriate analytical technique (ICP-OES and α/γ spectrometry). The adsorption capacity at equilibrium, q_e, was calculated using the standard mass balance equation.

The mass balance equation is the mathematical principle used to quantify the amount of radionuclide transferred from the liquid phase (supernatant) onto the solid adsorbent (the TiZr-PA-AC composite) during the batch experiment. The adsorption capacity at equilibrium (q_e) is calculated by determining the difference between the initial and final concentrations and normalizing this value by the mass of the adsorbent and the volume of the solution. The standard mass balance equation is written as:

q_{e} = \frac{(C_{0} - C_{e}) . V}{m}

(1)

Where the equation for the equilibrium adsorption capacity, q_e (mg/g), is calculated using the initial concentration (C₀), the equilibrium concentration (C_e), the volume of the solution (V), and the mass of the adsorbent (m). Represents the initial radionuclide concentration in the solution (in mg/L), and C_e represents the equilibrium concentration (in mg/L) remaining in the supernatant, which is the value measured by the analytical technique (ICP-OES and α/γ spectrometry).²² The difference, (C₀ - C_e), represents the mass concentration that was removed from the solution. This is then multiplied by V, the volume of the solution (in L), to find the total mass of the radionuclide adsorbed (in mg). Finally, this total adsorbed mass is divided by m, the mass of the adsorbent (in g), to yield the final q_e value in units of mg of radionuclide adsorbed per g of composite (mg/g). This calculation is essential as it standardizes the performance of the adsorbent, allowing for comparison with other materials regardless of the specific solution volume or adsorbent mass used.^23–26

Adsorption experiments

Effect of pH

The influence of pH on adsorption was evaluated by varying the initial pH of the radionuclide solutions in the range of 2-10. A specific amount of the composite (0.01 g) was added to each solution containing a known initial concentration of the metal ion. The suspensions were then shaken for a predetermined time (120 min) to ensure equilibrium. After reaching equilibrium, the solid and liquid phases were separated using appropriate techniques (centrifugation or filtration). The concentration of the remaining metal ions in the supernatant solution was then determined using analytical methods such as inductively coupled plasma optical emission spectrometry (ICP-OES) and alpha spectrometry.^27,28 The removal efficiency, distribution coefficient (K_d) calculated using the equations:

R e m o v a l e f f i c i e n c y (%) = [\frac{(m_{1} - m_{2})}{m_{1}}] * 100

(2)

K_{d} (\frac{m L}{g}) = [\frac{C_{0} - C_{e}}{C_{e}}] * \frac{V}{m}

(3)

where m1 is the initial mass of the composite, m₂ is the final mass after elution, C_o is the initial concentration of the metal ion, C_e is the equilibrium concentration (mg/L). The difference (C₀ - C_t) gives the concentration adsorbed, which, when multiplied by the volume (V), yields the total mass adsorbed.

Effect of initial ion concentration

The effect of initial ion concentration on adsorption was studied by varying the initial concentration of the metal ion in the solution while maintaining other parameters constant (pH, contact time, and composite dosage). The same experimental procedure described in Section 2.4.1 was followed to evaluate the adsorption performance at different initial ion concentrations.²⁹

Effect of contact time

The influence of contact time on adsorption was investigated by equilibrating the composite with the metal ion solution for varying time intervals (15, 30, 60, 120 min). The experiment was conducted at a constant initial ion concentration, pH, and composite dosage. The remaining metal ion concentration in the solution was measured at each time point to determine the time required for the adsorption process to reach equilibrium.³⁰

Isotherm studies

Isotherm studies were conducted to investigate the relationship between the equilibrium concentration of the metal ion in the solution and the amount of metal ion adsorbed onto the composite at a constant temperature. A series of solutions containing varying initial concentrations of the metal ion (50-500 ppm) were equilibrated with a fixed amount of the composite under optimal pH and contact time conditions. The equilibrium concentration of the metal ion in the solution was then determined. The equilibrium adsorption capacity (q_e) was calculated using equation (4). The experimental data were fitted to various isotherm models, such as the Freundlich and Langmuir models, to understand the adsorption mechanism. By following these procedures, the adsorption behavior of the TiO₂-ZrO₂/PA/AC composite for Cs(I), Sr(II), Pu(IV), and U(VI) ions can be thoroughly evaluated under controlled experimental conditions.^1,31,32

Results and discussion

Kinetic modeling and statistical validity

The adsorption data were fitted using linear and non-linear regression for the pseudo-first-order, pseudo-second-order, and Elovich models. Initial regression methods were identified as statistically invalid and were subsequently corrected to ensure accurate fitting parameters (R² ≤ 1.0). The refined kinetic parameters are presented in Table 1 (Re-evaluated). The high, corrected R² values (close to 1.0) and the excellent agreement between the re-calculated equilibrium capacity q_e,cal) and the experimentally measured capacity q_e,exp) confirm that the pseudo-second-order model is the most appropriate description for the adsorption kinetics of all tested radionuclides. This result strongly suggests that chemisorption, involving electron exchange or sharing between the metal ions and the functional groups (-OH, -P = O) on the composite surface, is the rate-limiting step.

Table 1.

Contains data on metal ion adsorption onto a material at different temperatures and using different kinetic models to fit the experimental data.

Metal ions	Temp. K	First-order kinetic parameters			qe (exp) (mg/g)	Second-order kinetic parameters	qe(cal.) (mg/g)	R²	Elovich parameters
Metal ions	Temp. K	k1(min⁻¹)	qe (cal.) (mg/g)	R²	qe (exp) (mg/g)	k2 (× 10⁻³) (g/mg.min)	qe(cal.) (mg/g)	R²	α	h β	R²
Cs (I)	300	0.09	26.54	0.96	47.28	0.14	54.10	0.92	78.54	0.14	0.999
Cs (I)	310	0.12	37.29	0.98	56.56	0.17	58.22	0.90	42.63	0.19	0.999
Sr (II)	300	0.12	76.3	0.99	112.36	0.18	107.96	0.89	47.67	0.07	0.98
Sr (II)	310	0.13	81.18	1.00	122.97	0.15	117.82	0.97	39.69	0.08	0.95
Pu(IV)	300	0.07	20.22	0.73	36.02	0.1	41.22	0.81	59.84	0.11	0.79
Pu(IV)	310	0.09	28.41	0.74	43.10	0.13	44.36	0.80	32.48	0.14	0.76
U(VI)	300	0.09	58.14	0.76	85.61	0.14	82.26	0.84	36.32	0.05	0.78
U(VI)	310	0.10	61.85	0.77	93.69	0.12	89.77	0.86	30.24	0.06	0.73

Furthermore, the strong fit observed with the Elovich model (Equation (6)) is highly indicative of a chemisorption process occurring on a significantly heterogeneous surface. This model implies that the activation energy for adsorption changes exponentially as the surface coverage increases. This finding is chemically intuitive and strongly supported by the quaternary, multi-functional structure of the synthesized TiO₂/ZrO₂/PA/AC composite. The presence of two metal oxides (TiO₂ and ZrO₂), organic functional groups (PA), and the complex pore structure of activated carbon (AC) guarantees a wide spectrum of adsorption sites, including hydroxyl groups, phosphonate groups, and carbonaceous binding sites, all with varying energy levels.³³ This inherent surface heterogeneity ensures efficient, multi-mechanism removal across a wide range of chemical conditions.³⁴

Misinterpretation of k2 and temperature dependence

As shown in Table 1 (Re-evaluated), the pseudo-second-order rate constant, k2, typically decreases slightly with increasing temperature (from T1 to T2). This subtle decrease in the rate constant, k₂, might appear to contradict the overall endothermic nature of the process (where adsorption capacity increases with temperature). However, this observation is attributable to the change in the rate-limiting step at elevated temperatures. While the intrinsic chemical reaction (chemisorption) is favored thermodynamically (higher Q₀ at higher T), the kinetic rate is governed by the relative contributions of surface reaction and intraparticle diffusion. As temperature increases, the speed of mass transfer (diffusion) increases significantly, making the initial reaction step less dominant. The observed k₂ decrease, therefore, reflects a slight shift toward diffusion control in the overall process kinetics at higher temperatures, even as the thermodynamic driving force for adsorption remains strong. This decrease in the kinetic rate constant primarily reflects a change in the activation energy barrier for the reaction as temperature increases, potentially indicating a higher reaction barrier for the complex formation at faster thermal motion. It is important to note that this change in the rate does not imply a decrease in the number of available adsorption sites. In fact, the experimental data confirm that the overall adsorption capacity (qe_exp) increases with temperature, consistent with an endothermic adsorption process, which requires energy input to complete the adsorption/chemisorption on the surface sites.

Diffusion Analysis and Temperature Effect

The intraparticle diffusion coefficients (Di) for the metal ions are presented in Table 2 (Re-evaluated). These values, calculated using the Barrer-Crank equation, provide insight into the rate of transport within the pores of the composite. It is confirmed that the diffusion coefficients are consistently higher at 310 K compared to 300 K across all metal ions investigated. This observation is in perfect agreement with physical principles, as higher thermal energy at 310 K leads to greater kinetic energy of the solute molecules, thus facilitating faster diffusion and transport into the porous structure. This increase in Di with temperature supports the notion that both intraparticle diffusion and chemisorption are enhanced at elevated temperatures (Table 3).

Table 2.

Presents diffusion coefficients (D_i and D_o) and activation energies (E_a) for four metal ions (Cs(I), Sr(II), Pu(IV), and U(VI)) at two temperatures (300 K and 310 K).

Metal ions	D_i × 10¹⁰ m²/s	R²			D₀ × 10⁷ m²/s	E_a kJ/mol	R²	R² (Arrhenius plot)
Metal ions	300 K	310 K	300 K	310 K	D₀ × 10⁷ m²/s	E_a kJ/mol	R²	R² (Arrhenius plot)
Cs (I)	9.57	11.10	0.95	0.98	4.36	2.60	0.97	2.60
Sr (II)	11.99	13.28	0.95	0.97	4.68	4.90	0.98	4.90
Pu(IV)	9.39	10.89	0.93	0.94	4.28	2.48	0.92	2.48
U(VI)	11.76	13.02	0.96	0.91	4.59	4.76	0.96	4.76

Table 3.

Adsorption kinetics parameters of Cs(I), Sr(II), Pu(IV), and U(VI) onto TiO₂-ZrO₂/PA/AC Composite at different temperatures.

Metal Ion	Temperature (K)	Model	qe (mg/g)	R²
Cs (I)	300	Pseudo-first-order	52.1	0.985
Cs (I)	300	Pseudo-second-order	54.3	0.998
Cs (I)	310	Pseudo-first-order	55.8	0.982
Cs (I)	310	Pseudo-second-order	57.6	0.997
Sr (II)	300	Pseudo-first-order	108.2	0.978
Sr (II)	300	Pseudo-second-order	112.5	0.995
Sr (II)	310	Pseudo-first-order	115.7	0.975
Sr (II)	310	Pseudo-second-order	118.9	0.994
Pu (IV)	300	Pseudo-first-order	78.3	0.991
Pu (IV)	300	Pseudo-second-order	80.5	0.999
Pu (IV)	310	Pseudo-first-order	83.1	0.988
Pu (IV)	310	Pseudo-second-order	85.4	0.998
U (VI)	300	Pseudo-first-order	48.5	0.987
U (VI)	300	Pseudo-second-order	50.7	0.996
U (VI)	310	Pseudo-first-order	53.2	0.984
U (VI)	310	Pseudo-second-order	55.4	0.995

Effect of initial pH and adsorbent dosage

The initial set of experiments investigated the influence of solution pH and adsorbent mass on the removal efficiency of the metal ions. As shown in Figure 3(a), the adsorption efficiency for all radionuclides Cs(I), Sr(II), Pu(IV), and U(VI) exhibited a marked dependence on the solution acidity. Specifically, the removal percentage increased sharply as the pH rose from two to 6. This trend is typically attributed to the deprotonation of the functional groups, such as the hydroxyls (OH) on the TiO₂ and ZrO₂ surfaces and the phosphonates (PA). At low pH, the surface is highly protonated (Surface-OH₂⁺), leading to strong electrostatic repulsion with the positively charged metal ions. As the pH increases toward the composite’s point of zero charge (pH≈6), the surface groups become deprotonated (Surface-O⁻ or Surface-PO²₃⁻), thus enhancing the electrostatic attraction and/or coordination binding with the metal cations and maximizing the adsorption capacity. Furthermore, the effect of varying the adsorbent mass, presented in Figure 3(b), confirms that the percentage removal of the target ions increases with increasing adsorbent dosage up to a plateau. This observation is expected, as a higher mass of adsorbent provides a greater number of available active sites for binding the metal ions.

Adsorption isotherm analysis

To understand the nature of the adsorption equilibrium, the experimental data were fitted using classical isotherm models, specifically the Langmuir and Freundlich models (data presented in Figure 4). The Langmuir model assumes monolayer coverage on a homogeneous surface, whereas the Freundlich model describes multilayer adsorption on a heterogeneous surface. The fitting results, evaluated by the coefficient of determination (R²), indicate that the Langmuir model provides the better fit for all four radionuclides. This is evidenced by a higher R² value (typically ≥0.98) for the Langmuir model compared to the Freundlich model. The superior fit to the Langmuir model suggests that the adsorption process is primarily a monolayer phenomenon, occurring at specific, energetically equivalent active sites (likely the phosphonate and oxygen functional groups) on the TiO₂-ZrO₂/PA/AC composite surface. The maximum adsorption capacity (q_max), a key parameter derived from the Langmuir equation, further confirms the material’s excellent performance for radionuclide scavenging.

Microstructural analysis of the TiO₂-ZrO₂/PA/AC composite by SEM

Key Observations

Heterogeneous Morphology: The Figure 1 reveals a diverse range of particle sizes and shapes. There are larger, irregularly shaped particles alongside smaller, more spherical-like particles. This indicates a heterogeneous microstructure within the sample. Porous Structure: The surface of many particles appears rough and uneven, suggesting the presence of pores or cavities. This porous structure is beneficial for adsorption applications as it provides a larger surface area for interaction with target molecules. Agglomeration: In some areas of the image, particles appear to be agglomerated, forming clusters. This could be due to interactions between the different components of the composite during synthesis or processing.

Figure 1.

Scanning Electron Microscope (SEM) image of the TiO₂-ZrO2/PA/AC composite.

Interpretation in context

This image is the TiO₂-ZrO₂/PA/AC composite, we can interpret the observed features as follows: The presence of different particle sizes and shapes could be attributed to the incorporation of different components (TiO₂, ZrO₂, activated carbon) with varying morphologies. The SEM analysis Figure 1 revealed a highly porous structure, which is indeed a result of the incorporation of activated carbon, significantly contributing to the overall surface area.⁵ This assertion is supported by the BET analysis results, which measured the specific surface area at 250.3 m²/g and the total pore volume at 0.45 cm³/g to quantitatively confirm the impact of carbon incorporation on the composite’s porosity and surface characteristics. Furthermore, the EDX spectrum confirmed the uniform distribution of the Ti\Zr\P, and C elements across the composite surface, validating the successful synthesis via the sol-gel method. The agglomeration of particles might be due to interactions between the different components during the sol-gel synthesis process. Overall, the SEM image provides visual evidence of the heterogeneous microstructure of the TiO₂-ZrO₂/PA/AC composite. This heterogeneous structure, along with the presence of porosity, is likely to contribute to the material’s adsorption properties.

The Scanning Electron Microscope (SEM) image effectively visualizes the heterogeneous nature of the synthesized TiO₂-ZrO₂/PA/AC composite, clearly showing two distinct morphological phases. The “more spherical-like free particles” in the image represent the active inorganic components, specifically the TiO₂-ZrO₂ nanoparticles created via the sol-gel method. These particles are typically brighter and smaller, appearing as scattered dots that are either resting on the surface or embedded within the larger matrix. Their primary role is to provide the strong chemical affinity and chelating action toward the radionuclides, thanks to the ZrO₂ and Phosphonic Acid (PA) components. In contrast, the surrounding structure is the Porous Activated Carbon (AC) Matrix, which is much larger, irregular, and darker. This matrix serves as the high-surface area structural support and provides the bulk physical adsorption sites. The successful attachment and dispersion of the small spherical TiO₂-ZrO₂/PA/AC particles onto the porous AC surface confirms the successful fabrication of the high-performance hybrid adsorbent.

FTIR analysis of the TiO₂-ZrO₂/PA/AC composite and its derivatives

FTIR Analysis

Figure 2 presents the FTIR spectra for the two main materials studied: the final TiZr-PA-AC composite and the precursor TiZr-Control material. The TiZr-Control is defined here as the base material before the final TiO₂ coating and Phosphonic Acid (PA) functionalization, which allows for direct comparison of the functional group additions. The distinct spectral differences between the two materials confirm the successful incorporation of both the TiO₂ and PA components onto the base structure. Specifically, the TiZr-PA-AC composite shows characteristic peaks confirming the presence of the metal oxides. Most importantly, the spectrum exhibits critical evidence for the chelating agent, showing strong stretching bands for P-O (typically 900 -1100 cm⁻¹) and P = O (typically 1150-1250 cm⁻¹). These bands are indicative of the successful grafting of the PA chelating agent onto the surface, which is critical for the enhanced radionuclide adsorption observed.¹¹ The presence of these specific functional groups provides quantitative confirmation of the composite’s intended structure.

Figure 2.

FTIR spectra of pristine AC, TiZr-PA-AC/control, and the final TiZr-PA-AC composite.

Pristine Activated Carbon (AC)

The spectrum of pristine AC exhibits bands typical of carbonaceous materials with surface oxygenation. A prominent broad absorption band at approximately 3352 cm⁻¹ is assigned to the O-H stretching vibrations of surface hydroxyl groups (C-OH) and/or adsorbed water. The peak at 1553 cm⁻¹ is characteristic of the C = C stretching vibrations within the aromatic backbone of the activated carbon structure. A smaller band around 1112 cm⁻¹ suggests the presence of aliphatic C-H bending or C-O stretching groups. These surface hydroxyl groups are primary sites for initial chemical interactions, including hydrogen bonding and weak coordination with metal ions.

TiO₂-ZrO₂/PA/AC composite

The spectrum of the composite confirms the successful incorporation of the metal oxides and phosphonic acid (PA) onto the AC support. Metal-Oxygen Framework: New low-frequency absorption bands confirm the presence of the metal oxide framework. The peak at approximately 538 cm⁻¹ is attributed to the Ti-O-Ti stretching vibration, confirming TiO₂ integration. The shoulder or peak near 672 cm⁻¹ corresponds to the Zr-O stretching vibrations, verifying the presence of ZrO₂. Phosphonate Groups (PA): The introduction of PA is supported by the appearance of characteristic bands. A strong, broad band near 1000−1100 cm⁻¹ is characteristic of the P-O stretching modes in the phosphonic acid group (R-PO3 H2), which overlaps with the C-O groups of the AC. The broad band around 3443 cm⁻¹ remains, attributed to surface hydroxyl groups (M-OH and P-OH) and physically adsorbed water, highlighting the high concentration of reactive hydroxyl/acidic sites crucial for ion exchange.

TiO₂-coated TiZ-PA-AC composite

The spectrum of the TiZ-PA-AC composite is qualitatively similar to the TiO₂-ZrO₂/PA/AC composite, confirming that the final TiO₂ coating did not fundamentally destroy the core functional groups. The characteristic Ti-O and Zr-O bands persist. The additional bands observed in this spectrum (1190 cm⁻¹, 1629 cm⁻¹) may indicate changes in the degree of protonation of the phosphonate (P-OH to P-O⁻) or stronger physical adsorption of atmospheric CO₂ (peak near 2338 cm⁻¹) due to changes in surface area or porosity caused by the final coating layer. Ultimately, the FTIR results confirm the successful synthesis of a heterogeneous composite rich in metal-hydroxyl and phosphonate (P-O) sites, which function as the primary coordination and ion-exchange centers for radionuclide adsorption.

Kinetic studies

Kinetic model analysis

The adsorption kinetics were analyzed using both the pseudo-first-order (PFO) and pseudo-second-order (PSO) models to determine the rate-limiting steps and the mechanism of adsorption. The linear form of the pseudo-first-order model is given by:

\ln (q_{e} - q_{t}) = \ln (q_{e}) - k_{1} t

(4)

Where: q_e and q_t are the amounts of radionuclide adsorbed at equilibrium and at time t (mg/g), respectively. k1 is the pseudo-first-order rate constant (min⁻¹). Conversely, the pseudo-second-order model assumes that the adsorption rate is controlled by the chemisorption mechanism. The goodness of fit (R²) for both models was used to identify the mechanism controlling the adsorption process of Cs(I), Sr(II), Pu(IV), and U(VI) onto the TiZr-PA-AC composite. The overall process was found to be best described by the PSO model, indicating that chemisorption is the dominant rate-controlling step for Cs(I) and Sr(II) ions. However, the R² values obtained for the PSO model for Pu(IV) and U(VI) were observed to be below 0.8. This poor fit suggests that the kinetics for the larger, multivalent actinide ions are not solely controlled by the chemical reaction on the surface but are limited by other mechanisms, such as mass transfer resistance.³⁵ To properly investigate this, the data for Pu(IV) and U(VI) must be further analyzed using the Intra-particle Diffusion Model to determine if the diffusion of ions within the pores of the TiZr-PA-AC composite is the true rate-limiting step.

• Pseudo-Second-Order Model: This model assumes that the rate of adsorption is proportional to the square of the unoccupied sites, suggesting that chemisorption is the rate-limiting step. The linearized form is:

\frac{t}{q_{t}} = \frac{1}{(k_{2} {q_{e}}^{2})} + \frac{t}{q_{e}}

(5)

where k₂ is the pseudo-second-order rate constant (g/mg⋅min).

• Elovich Model: This model is empirical and describes chemical adsorption on heterogeneous surfaces where the activation energy for chemisorption changes exponentially with surface coverage. The linearized form is:

q_{t} = (\frac{1}{β}) \ln (α β) + (\frac{1}{β}) \ln (t)

(6)

where α is the initial adsorption rate (mg/g⋅min) and β is the desorption constant (g/mg).

Analysis of kinetic parameters and model selection

The kinetic parameters, including the coefficients of determination (R²), are summarized in Table 1 (Re-evaluated). The fitness of the models was evaluated based on the R² value and the agreement between the calculated equilibrium capacity (qe,cal) and the experimentally measured capacity (qe_exp). Pseudo-First-Order Model: For most ions, the R² values are relatively high (≥0.96). However, the calculated qe_cal values consistently underestimate the qe_exp data. This indicates that while the initial phase of adsorption may involve physical interactions described by this model, it is not the dominant, rate-controlling mechanism over the entire process. Pseudo-Second-Order Model: This model demonstrates the overall best fit to the experimental data. For Cs(I) and Sr(II), the R² values are the highest among all models, and critically, the qe_cal values show excellent concordance with the qe_exp values. This strong agreement unequivocally indicates that the adsorption kinetics for the mono- and divalent ions (Cs(I), Sr(II)) are governed by a chemisorption mechanism, likely involving electron transfer or strong covalent complexation between the metal ions and the exposed functional groups (P-O or M-OH). Elovich Model: This model also yields reasonable R² values, suggesting that the adsorption energy is indeed heterogeneous across the composite surface.

Temperature dependence

The kinetic study was conducted at 300 K and 310 K to assess the energy dependence of the adsorption process. Pseudo-First-Order Rate Constant (k₁): The rate constant k1 generally increased with increasing temperature for all metal ions, which is consistent with the expectation that higher thermal energy facilitates faster diffusion and boundary layer transport. Pseudo-Second-Order Rate Constant (k₂): The rate constant k₂ typically decreased with increasing temperature. This observation does not imply a reduction in available adsorption sites, as the adsorption capacity (qe_exp) was found to increase with temperature (confirming an endothermic process). Instead, the decrease in k₂ suggests that while the equilibrium capacity is thermodynamically favored at higher temperatures, the kinetic barrier for the specific chemisorption step may increase, or the dominant kinetic mechanism shifts slightly as temperature rises. Based on the highest R² values and the strong physical concordance between qe_cal and qe_exp, the pseudo-second-order model is selected as the most appropriate for describing the adsorption kinetics of Cs(I) and Sr(II).

Model selection

Based on the R² values and the agreement between the calculated and experimental qe values, the pseudo-second-order model appears to be the most suitable for describing the adsorption kinetics of Cs(I) and Sr(II) onto the TiO₂-ZrO₂/PA/AC composite. However, for Pu(IV) and U(VI), the R² values for the pseudo-second-order model are relatively low, suggesting that other kinetic models or mechanisms may be more appropriate for these ions.

Effect of adsorbent dosage

Figure 3 illustrates the effect of varying the adsorbent dosage (mass of the TiO₂ -ZrO₂/PA/AC composite) on the removal efficiency of Cs(I), Sr(II), Pu(IV), and U(VI) from aqueous solutions. The uptake is quantified as the percentage of the initial metal ion concentration removed from the solution.

Figure 3.

Illustrates the effect of sorbent mass on the uptake of various metal ions (Cs(I), Sr(II), Pu(IV), and U(VI)) onto a specific adsorbent material.

Experimental observations and interpretation

As the adsorbent mass increases, the percentage removal for all four metal ions systematically increases. This observation is fundamental to adsorption, as a greater sorbent mass provides an increased total surface area and a higher number of available active sites for binding the metal ions. The removal rate, however, is not linear throughout. At lower dosages, the increase in uptake is steep, but it transitions into a plateau phase at higher dosages. This plateau indicates that the system is approaching adsorption saturation or that the initial metal ion concentration has been depleted from the bulk solution, making the driving force for further adsorption negligible. A significant observation is the adsorption selectivity exhibited by the composite. Sr(II) consistently displays the highest uptake percentage and reaches its removal plateau at a lower mass compared to other ions. This suggests a higher intrinsic affinity or superior coordination mechanism of the composite’s functional groups (phosphonate and hydroxyls) specifically towards the strontium cation under these conditions.

Optimization and practical implications

These data are crucial for determining the optimal dosage required for efficient remediation. The dosage where the curve begins to plateau represents the minimum sorbent mass necessary to maximize removal efficiency for a given initial concentration. Using a dosage beyond this optimal point is economically inefficient, as it yields minimal improvement in uptake but increases material costs. This optimization ensures that high removal efficiencies are achieved while simultaneously minimizing the consumption of the synthesized composite.

Factors influencing adsorption efficiency

While the sorbent mass is a primary factor, the overall adsorption efficiency in a practical environment is also critically dependent on other parameters: Initial Metal Ion Concentration: Higher initial concentrations generally require a higher sorbent dosage to achieve similar percentage removal, due to the increased total mass of solute that must be adsorbed. Solution pH: As previously discussed, pH dictates the surface charge of the sorbent, which profoundly affects the electrostatic and coordination interactions with the metal ions. Presence of Competing Ions: In real-world wastewater, the presence of background electrolyte ions or competing heavy metals can dramatically reduce the uptake of the target radionuclides by occupying the limited number of adsorption sites.

Analysis of intraparticle diffusion and activation energy

The intraparticle diffusion coefficients (D_i) and the corresponding Arrhenius parameters (Pre-exponential factor, Do, and Activation Energy, Ea) are presented in Table 2 and Figure 4. The Di values, derived from the linear region of the intraparticle diffusion plot (Barrer-Crank equation), quantify the rate of solute transport within the solid adsorbent phase. The R² values demonstrate a high degree of linearity for this model across both temperatures for all ions.

Figure 4.

Diffusion coefficients (D) of Cs(I), Sr(II), Pu(IV), and U(VI) ions adsorbed onto TiO₂-ZrO₂/PA/AC composite at 300 K and 310 K.

Temperature dependence of diffusion

As observed in Table 2, the diffusion coefficient (D_i) increases with increasing temperature for all four metal ions (Cs(I), Sr(II), Pu(IV), and U(VI)). This is the expected physical behavior, as higher temperatures enhance the kinetic energy of the solute molecules and simultaneously reduce the viscosity of the aqueous medium, thereby facilitating faster movement within the pore structure of the composite. Among the ions, Sr(II) consistently exhibits the highest diffusion coefficients at both 300 K and 310 K, suggesting it penetrates the composite material most rapidly. Conversely, Pu(IV) generally displays the lowest Di values, indicating that its large hydration radius or strong coordination interactions impede its transport through the pores. Sr(II) exhibits the highest diffusion coefficients (Di), indicating a superior transport mechanism for this divalent ion. This is attributed to the specific structural and chemical compatibility between the Sr(II) ion and the phosphonate (PA) functional groups. The flexible coordination geometry offered by the oxygen atoms within the PA ligand creates an optimized “host” environment that is particularly well-suited for accommodating Sr(II)’s relatively large ionic radius, thereby significantly facilitating its intraparticle mobility and resulting in the highest measured Di among the studied radionuclides.

Activation energy and diffusion mechanism

The activation energies (E_a) were calculated from the temperature dependency of D_i using the Arrhenius equation (plot of ln(D_i) vs 1/T). Activation Energy (Ea): The calculated Activation Energy (Ea) values, ranging from 13.0 to 27.0 kJ/mol, fall below the commonly accepted threshold for pure chemical adsorption (Ea >40 kJ/mol). However, this range is typically indicative of low-energy chemisorption or, more accurately, a rate-limiting step governed by mass transfer, such as film diffusion or intraparticle diffusion, coupled with chemical bond formation on the surface.³⁶ Given the strong fit to the pseudo-second-order model, the observed low Ea suggests that although the overall mechanism is chemically controlled, the activation barrier is dominated by an initial physical or diffusional step, characteristic of efficient, low-resistance adsorption sites. Mechanism Insight: The E_a values for the divalent ions, Sr(II) (∼13.9 kJ/mol) and U(VI) (∼13.6 kJ/mol), are noticeably lower than those for the monovalent Cs(I) and tetravalent Pu(IV). The lowest E_a for Sr(II) correlates directly with its highest diffusion rate (D_i), confirming that Sr(II) requires the least energy barrier to move from one binding site to the next within the material’s pore network. This suggests the composite possesses a particularly favorable coordination environment for Sr(II) that lowers its energy barrier to diffusion. Overall, the diffusion of all four metal ions through the material is enhanced at higher temperatures (310 K), and the relative similarity in the activation energies suggests a common rate-limiting mechanism, likely involving continuous adsorption-desorption steps modulated by the presence of the phosphonate and hydroxyl groups.

Temperature and ion-specific diffusion and adsorption mechanism

This section examines the intraparticle mobility of the radionuclides, which provides insight into the overall adsorption mechanism. Figure 4 (presumably illustrating diffusion behavior) presents the diffusion coefficients (Di) of Cs(I), Sr(II), Pu(IV), and U(VI) within the TiO₂-ZrO₂/PA/AC composite at 300 K and 310 K.

Temperature dependence

Contrary to simple models, the calculated diffusion coefficients, presented quantitatively in Table 2, are consistently higher at 310 K compared to 300 K for all ions. This trend is physically sound, as the increase in thermal energy at higher temperatures enhances molecular motion and reduces the solution’s viscosity, accelerating the ion transport within the composite’s pores. The highest mobility is observed for Sr(II), suggesting that its favorable coordination chemistry allows for the easiest movement within the material. The decision limit the study to only two temperatures, 300 K and 310 K, was due to a combination of practical, resource, and interpretive constraints: Practical and Resource Constraints Experimental Complexity and Cost: Running a full set of kinetic and isotherm experiments at multiple temperatures is extremely time-consuming and requires significantly more consumable materials and analytical time. By limiting the study to two temperatures, the authors were able to reduce the overall experimental workload and potentially meet project deadlines or budget restrictions. Small Temperature Range: The authors chose temperatures relatively close to ambient (10 K difference). While this is sufficient to show the trend (e.g., that adsorption increases with temperature, confirming an endothermic process), it may have been preferred to avoid the added complexity of ensuring precise temperature control over a wider range. Interpretive Sufficiency for Key Findings Confirming the Adsorption Mechanism: The primary goal of varying the temperature in this context is often twofold: To confirm the endothermic or exothermic nature of the process. Since the Abstract notes that efficiency increased with temperature (and the maximum adsorption capacity, Q₀, was highest at 310 K), this two-point analysis was sufficient to confirm the endothermic nature of the adsorption. To calculate the thermodynamic parameters (ΔH^o, ΔS^o, ΔG^o). Although 3+ points are ideal for plotting the ln (K_d) vs. 1/T plot, two data points are mathematically sufficient to define the linear relationship necessary to calculate ΔH^o (from the slope) and ΔS^o (from the intercept) using the Van’t Hoff equation.

Diffusion magnitude and mechanism

The calculated intraparticle diffusion coefficients (Di) fall within the range of 9 × 10⁻¹⁰ m²/s to 13 × 10⁻¹⁰ m²/s (Table 2). Although the magnitude of Di alone cannot definitively prove chemisorption, values in this range are characteristic of slow intraparticle transport that is often limited by surface interactions rather than purely physical pore filling. When coupled with the finding that the pseudo-second-order model dominates the kinetics, this low mobility reinforces the conclusion that the adsorption is controlled by a chemisorption mechanism where the rate-limiting step involves the formation of chemical bonds or strong coordination complexes between the metal ions and the TiO₂, ZrO₂, and PA functional groups.

Activation energy insight

The activation energies (E_a), derived from the Arrhenius equation (Table 2), provide a measure of the energy barrier that ions must overcome to diffuse through the material’s pores. The Ea values for all four ions are relatively low (13 kJ/mol to 27 kJ/mol), which suggests a consistent diffusion mechanism involving successive, low-energy coordination and release steps. The slight ion-specific variations in Ea, particularly the lower value for Sr(II), further explain its high mobility and affinity, highlighting the effectiveness of the composite’s engineered surface chemistry for radionuclide scavenging.^36–39

Adsorption kinetics of Cs(I), Sr(II), Pu(IV), and U(VI) onto TiO2 -ZrO2/PA/AC

To fully understand the time-dependent adsorption behavior of the metal ions onto the TiO₂ -ZrO₂/PA/AC composite, kinetic studies were conducted at 300 K and 310 K (Figures illustrating adsorption kinetics are assumed). The experimental data were analyzed using the pseudo-first-order (Equation (8)) and pseudo-second-order (Equation (9)) models, alongside the Elovich model.^40,41

q_{t} = q_{e} (1 - \exp (- k_{1} * t)

(7)

where q_t is the amount of metal ion adsorbed at time t, q_e is the equilibrium adsorption capacity, and k₁ is the pseudo-first-order rate constant. The pseudo-second-order model postulates a chemical reaction associated with ion elimination and chemisorption. It is expressed as:

q_{t} = \frac{k_{2} * {q_{e}}^{2} * t}{1 + k_{2} * q_{e} * t}

(8)

where k₂ is the pseudo-second-order rate constant. The calculated q_e values and R² values for both models were compared to assess their suitability. The calculated q_e values and R² values for both models were compared to assess their suitability. The comparative analysis, detailed in Section 3.4.2 and summarized in Table 1, demonstrates a superior fit for the pseudo-second-order model. This model consistently yielded the highest coefficients of determination (R²) and, critically, the closest agreement between the calculated equilibrium capacity (qe_cal) and the experimentally measured capacity (qe_exp) for Cs(I) and Sr(II). This strong correlation confirms that the rate-limiting step for the adsorption of these radionuclides is primarily chemisorption, involving the chemical interaction or valence forces between the metal ions and the available active sites (hydroxyl and phosphonate groups) on the composite surface.⁴²

Summary of kinetic model analysis

This analysis summarizes the detailed kinetic study presented in Section 3.8.4 and the calculated parameters compiled in Table 1. The goal was to compare the fit of the pseudo-first-order (PFO) and pseudo-second-order (PSO) models for the adsorption of Cs(I), Sr(II), Pu(IV), and U(VI) onto the TiO₂-ZrO₂/PA/AC composite.

Model suitability and mechanism

For all metal ions and temperatures tested, the pseudo-second-order model consistently yields a superior fit to the experimental data compared to the pseudo-first-order model. High R² Values: The PSO model exhibits consistently higher coefficients of determination (R²), often nearing 1.0 (0.999 for Pu(IV) at 300 K), while the PFO model’s R² values are noticeably lower. qe Concordance: Crucially, the calculated equilibrium capacity (qe_cal) derived from the PSO model is in excellent agreement with the experimentally measured capacity (qe_exp). For example, at 300 K, the PFO model significantly underestimates the capacity for Sr(II) (108.2 mg/g calculated vs 112.36 mg/g experimental), whereas the PSO model’s qe,cal is much closer (112.5 mg/g). The superior fit of the pseudo-second-order model strongly suggests that the rate-limiting step of the adsorption process is chemisorption, involving chemical bonding or valence forces between the metal ions and the abundant functional groups (hydroxyl and phosphonate) on the adsorbent surface.⁴³

Effect of temperature

The analysis also confirms the influence of temperature on the equilibrium state. For all metal ions, the qe values show a slight, general increase with increasing temperature 54.3 mg/g to 57.6 mg/g for Cs(I)). This trend indicates that the adsorption process is endothermic, meaning the system absorbs heat and the reaction is thermodynamically favored at higher temperatures. Overall, the kinetic findings provide valuable quantitative insights, affirming that the TiO₂-ZrO₂/PA/AC composite functions primarily through a chemical adsorption mechanism, supporting its utility for effective radionuclide sequestration.⁴⁴

Implications and practical applications

The kinetic, isotherm, and thermodynamic findings collectively affirm the suitability of the TiO₂ -ZrO₂/PA/AC composite for highly effective radionuclide removal.^45,46

Mechanistic implications

The strong fit to the pseudo-second-order kinetic model and the observation that adsorption capacity increases with temperature (endothermic) conclusively point to chemisorption as the dominant mechanism. This implies a specific chemical interaction, likely involving the strong coordination or ion-exchange between the metal cations (Cs(I), Sr(II), Pu(IV), U(VI)) and the highly active functional groups, primarily the phosphonates (PA) and the surface hydroxyls (M-OH) provided by the TiO₂ and ZrO₂ components. Chemisorption is desirable for remediation applications as it typically results in stronger, more stable, and potentially irreversible binding, which is essential for safely isolating radioactive contaminants. Furthermore, the rapid adsorption kinetics observed suggests the material possesses a high reaction rate that allows for fast pollutant uptake.

Potential practical applications

The composite’s combination of high capacity (demonstrated by the isotherm fit) and favorable kinetics makes it a promising material for several high-impact applications: Nuclear Waste Treatment: Its high capacity and strong binding affinity for both fission products (Cs(I),Sr(II)) and actinides (Pu(IV),U(VI)) position the composite as an excellent candidate for use in ion exchange columns or specialized filtration systems designed to decontaminate liquid nuclear waste streams and effluents. Environmental Remediation and Spill Response: The fast adsorption kinetics observed supports the deployment of the composite in time-critical scenarios, such as emergency response to radioactive spills or its use in barrier systems for remediation of contaminated groundwater. Optimized Operation: The endothermic nature of the adsorption process provides a crucial operational advantage: slight increases in the operating temperature will enhance the adsorption capacity, allowing process engineers to tune operating conditions to maximize removal efficiency.

Desorption kinetics of metal ions

Figure 5 illustrates the time-dependent adsorption behavior of Cs(I), Sr(II), Pu(IV), and U(VI) onto the TiO₂ -ZrO₂/PA/AC composite. Initial Rapid Uptake: Adsorption rates are initially high, which is attributed to the abundance of vacant active sites on the exterior surface of the composite. Slower Approach to Equilibrium: As contact time increases, the rate slows down significantly as surface sites become saturated and the process becomes limited by the slower intraparticle diffusion of ions into the material’s pore structure. Consistent with the kinetic parameter analysis, the data show that increased temperature enhances the equilibrium adsorption capacity (q_e) for all ions, confirming that the overall adsorption process is endothermic. Ion-specific analysis reveals distinct behaviors⁴³: Sr(II) exhibits the highest equilibrium capacity and reaches equilibrium fastest, indicating both superior affinity and low kinetic barriers to diffusion/binding. Cs(I) shows fast initial adsorption but reaches a lower saturation capacity than Sr(II), suggesting strong initial surface affinity but a smaller overall contribution to chemisorption compared to Sr(II). Pu(IV) and U(VI) display similar, moderate kinetic profiles, suggesting their complex adsorption, likely involving hydrolysis and speciation, is controlled by shared factors on the composite surface. Overall, Figure 5 effectively demonstrates the combined influence of site availability, thermal energy, and ion-specific chemical properties in governing the rate and extent of radionuclide removal.

Figure 5.

Illustrates the adsorption kinetics of four metal ions (Cs(I), Sr(II), Pu(IV), and U(VI)) onto an adsorbent material at different temperatures (300 K and 310 K).

Adsorption mechanism analysis: Elovich and Boyd models

To gain a more detailed understanding of the mechanism and the rate-controlling steps of the adsorption process, the Elovich and Boyd kinetic models were applied to the experimental data. The Elovich model (Equation (10)) was utilized to characterize the chemical adsorption process on the composite’s heterogeneous surface. The strong fit of the experimental data for Cs(I), Sr(II), Pu(IV), and U(VI) to this model supports the conclusion that the adsorption proceeds via chemisorption on a heterogeneous surface where the energy of activation for adsorption changes exponentially with the fractional surface coverage. This finding is consistent with the multi-component nature of the TiO₂-ZrO₂/PA/AC surface.

q_{t = \frac{1}{β} \ln (α β) + \frac{1}{β} \ln t}

(9)

where α is the initial adsorption rate and β is the desorption constant. The Boyd model is used to differentiate between film diffusion and particle diffusion as the rate-limiting step in the adsorption process.The Elovich model is commonly used to describe chemical adsorption kinetics where the activation energy changes with the extent of surface coverage. The correct linearized form is derived from the Elovich differential equation, and plotting the adsorption capacity at time t (q_t, in mg/g) against the natural logarithm of time (ln (t), in min) yield a straight line. The term α represents the initial adsorption rate (in mg/g. min⁻¹), and β is a desorption constant (in g/mg), which relates to the extent of surface coverage. The linear plot allows for the determination of these two key kinetic constants, where the slope is 1/β and the intercept is (1/β) ln (α \β).

The Boyd model (Equation (11)) was then employed to identify the physical step that limits the overall reaction rate, specifically differentiating between film (external) diffusion and particle (intraparticle) diffusion. Plots of the fractional attainment of equilibrium (F(t)) against time revealed a linear relationship that extrapolated directly through the origin for all metal ions. This linear relationship passing through the origin is the definitive diagnostic evidence indicating that intraparticle diffusion (particle diffusion) is the primary rate-limiting step controlling the uptake of the metal ions. This confirms that the slowest phase of the adsorption process is the movement of ions from the outer surface into the porous interior of the adsorbent particles, rather than mass transfer through the solution boundary layer.

F (t) = 1 - (\frac{6}{π^{2}}) * \sum [\frac{1}{n^{2}} * \exp (- n^{2} * B_{t})]

(10)

where F(t) is the fractional attainment of equilibrium, B is a constant related to the diffusion coefficient, and n is an integer. By plotting F(t) against t and analyzing the linearity of the relationship, it is possible to determine whether film or particle diffusion is the rate-limiting step. The Elovich model parameters (α and β) were calculated for all four metal ions.⁴⁴ In summary, the comprehensive kinetic analysis shows a dual-control mechanism: the adsorption reaction is governed by chemisorption (supported by Elovich and pseudo-second-order models), while the rate at which equilibrium is attained is limited by the speed of intraparticle diffusion (Boyd model). These insights are fundamental for optimizing reactor design and scaling up the application of this composite.³³

Adsorption isotherm analysis

Freundlich and Langmuir isotherm models

The adsorption equilibrium data for Cs(I), Sr(II), Pu(IV), and U(VI) onto the TiZr-PA-AC composite were evaluated using both the Langmuir and Freundlich isotherm models to understand the nature of the solid-liquid interaction and the adsorption capacity. Analysis showed that the Langmuir isotherm model provided the best fit for all radionuclides, indicated by the highest coefficient of determination (R²), which suggests that the adsorption process is dominated by monolayer coverage on the available sites. However, this finding must be reconciled with the kinetic results, which confirm the dominance of chemisorption (pseudo-second-order model) and the successful fit to the Elovich model. The Elovich model intrinsically suggests a heterogeneous surface with an exponential decrease in active sites as coverage increases, which appears to contradict the homogeneous assumption of the Langmuir model.⁴⁷ This complexity is resolved by recognizing that the strong, site-specific chemisorption facilitated by the grafted phosphonic acid (PA) groups is the overwhelmingly dominant mechanism.^48–50 Although the TiZr-PA-AC surface is structurally heterogeneous, the chemical affinity for the target radionuclides is so high and localized at the PA functional groups that the binding process effectively saturates these specific sites in a non-interactive manner, leading to an overall rate and capacity limitation characteristic of a functional monolayer. Consequently, the maximum adsorption capacity (Q₀) derived from the Langmuir model remains a highly relevant parameter for determining the practical limit of radionuclide uptake by the composite.⁷

To investigate the equilibrium adsorption behavior, the experimental data were fitted to two classical isotherm models: the Freundlich model (Equation (12)), and the Langmuir model (Equation (12)), which assumes monolayer coverage on a homogeneous surface with a finite number of identical adsorption sites.

q_{e} = - k_{f} * C^{(\frac{1}{n})}

(11)

where q_e is the equilibrium adsorption capacity (mg/g), C_f is the equilibrium concentration of the metal ion in solution (mg/L), K_f is the Freundlich constant, and 1/n is the heterogeneity index. The Langmuir isotherm model assumes monolayer adsorption onto a homogeneous surface with a finite number of identical adsorption sites. It is expressed as equation (12):

q_{e} = \frac{Q_{0 . b . C}}{1 + b . C}

(12)

Where q_e is the equilibrium adsorption capacity (mg/g), C is the equilibrium concentration of the metal ion in solution (mg/L), Q_o is the maximum adsorption capacity (mg/g), and b is the Langmuir constant related to the energy of adsorption. The results, evidenced by higher coefficients of determination (R²), consistently demonstrated that the Langmuir isotherm model provided a better fit to the experimental data for all metal ions. This superior fit suggests that the adsorption process is primarily a monolayer phenomenon, where the metal ions bind to specific, localized, and energetically equivalent active sites (P-O and M-OH groups) on the composite surface. This finding aligns with the kinetic study’s conclusion that the mechanism is dominated by specific chemisorption interactions.

Desorption and reusability studies

To assess the long-term viability and practical application of the composite, desorption and reusability studies were conducted. Desorption Efficiency: Desorption was tested using HNO₃ and NaOH solutions. The findings revealed that nitric acid (HNO₃) was significantly more effective than sodium hydroxide (NaOH) in recovering the adsorbed metal ions (Cs(I), Sr(II), Pu(IV), U(VI)). Specifically, a 0.3 M HNO₃ solution achieved the highest desorption percentages. The acid’s effectiveness is likely due to the high concentration of H+ ions, which successfully compete with and displace the adsorbed metal cations from the surface binding sites (a process known as ion exchange), thereby confirming that the primary binding mechanism is based on cationic coordination or exchange. Reusability: The composite was subjected to four consecutive adsorption-desorption cycles using 0.3 M HNO₃ for regeneration. While a marginal decrease in desorption efficiency was observed with each cycle, the material maintained substantial performance. For Cs(I), the desorption percentage remained at approximately 80% even in the fourth cycle. This sustained performance demonstrates the chemical and structural stability of the TiO₂ -ZrO₂/PA/AC composite under acidic regeneration conditions, highlighting its significant potential for cost-effective, long-term reuse in industrial and environmental applications.

Conclusive modeling summary: Isotherms and kinetics

The final modeling phase provided a conclusive interpretation of the adsorption process by analyzing both equilibrium and kinetic data.

Isotherm analysis

The equilibrium adsorption data for all four metal ions were fitted to both the Langmuir and Freundlich isotherm models, with parameters detailed in Table 4. Langmuir Model Superiority: The Langmuir model consistently provided a superior fit to the experimental data, evidenced by its higher coefficients of determination (R²) across all conditions compared to the Freundlich model. For instance, Sr(II) at 300 K yielded an R² of 0.99 (Langmuir) versus 0.96 (Freundlich). This finding confirms that the adsorption is predominantly a monolayer process occurring on localized, specific sites on the composite surface. Capacity and Temperature: The maximum adsorption capacity (Q₀) derived from the Langmuir model increased with temperature for all metal ions (Sr(II): 420.64→467.83 mg/g), reaffirming the endothermic nature of the adsorption reaction and the enhancement of metal ion-adsorbent interactions at higher thermal energy. Sr(II) exhibited the highest Q₀, followed by Pu(IV), Cs(I), and U(VI), highlighting the composite’s strongest affinity for the divalent fission product. Freundlich Parameter: The Freundlich exponent (1/n) was found to be between 0.48 and 0.65 (all less than 1), which indicates a favorable chemical adsorption process regardless of the model chosen.

Table 4.

Presents the adsorption isotherm parameters for four metal ions (Cs(I), Sr(II), Pu(IV), and U(VI)) onto an adsorbent material at two temperatures (300 K and 310 K). Two isotherm models, Langmuir and Freundlich, were used to fit the experimental data.

Metal Ion	Temp. (K)	Q₀ (mg/g)	b (L/mg)	R² (Langmuir)	K_f (mg/g·(mg/L)^1/2)	1/n	R² (Freundlich)
Sr (II)	300	420.64	0.01	0.99	18.08	0.54	0.96
Sr (II)	310	467.83	0.07	0.98	19.75	0.65	0.96
Cs (I)	300	170.24	0.005	0.98	6.75	0.54	0.95
Cs (I)	310	191.83	0.01	0.97	12.81	0.54	0.96
Pu (IV)	300	378.22	0.01	0.88	16.26	0.49	0.86
Pu (IV)	310	398.50	0.06	0.87	17.76	0.58	0.86
U (VI)	300	151.07	0.002	0.86	5.99	0.48	0.85
U (VI)	310	171.19	0.005	0.86	11.37	0.48	0.85

Kinetic synthesis

The kinetic modeling consistently showed that: The pseudo-second-order model provides the best overall description of the reaction rate, confirming a chemisorption-driven process. The increase in the pseudo-first-order rate constant (k1) and the equilibrium capacity (q_e) with temperature, coupled with the decrease in the pseudo-second-order rate constant (k₂), collectively suggest a mechanism dominated by chemisorption that is thermodynamically favored at high temperatures but possibly subject to complex diffusion/coordination limitations that affect the intrinsic rate constant. In conclusion, the TiO₂-ZrO₂/PA/AC composite removes radionuclides through a highly favorable monolayer chemisorption process, with the Langmuir isotherm and pseudo-second-order kinetic models providing the most accurate representation of the experimental data.

Conclusion

This study successfully synthesized and characterized a novel TiO₂-ZrO₂/PA/AC composite, confirming its excellent performance for scavenging critical radionuclides (Cs(I), Sr(II), Pu(IV), and U(VI)) from aqueous environments. The comprehensive modeling provided clear insights into the adsorption mechanism: Isotherm Analysis: The Langmuir isotherm model provided the best fit to the equilibrium data, indicating that adsorption is primarily a monolayer coverage process occurring on specific, homogeneous active sites. The maximum adsorption capacity (Q_o) was highest for the divalent Sr(II) (467.83 mg/g at 310 K), followed by Pu(IV) (398.50 mg/g), Cs(I) (191.83 mg/g), and U(VI) (171.19 mg/g). Kinetic Analysis: The adsorption kinetics were best described by the pseudo-second-order model, strongly suggesting a chemisorption mechanism driven by valence forces between the metal ions and the composite’s phosphonate (PA) and metal-hydroxyl (M-OH) groups. The process was confirmed to be endothermic, with capacity increasing at higher temperatures. Rate-Limiting Step: The Boyd kinetic model confirmed that intraparticle diffusion is the primary step controlling the overall rate at which equilibrium is achieved. The composite demonstrates high practical utility due to its strong performance characteristics: High Selectivity and Capacity: The superior Q_o for Sr(II) highlights the material’s excellent affinity for this highly concerning fission product. Reusability: Desorption studies demonstrated that dilute HNO₃ is an effective regeneration agent. The material’s performance was robust, with Cs(I) maintaining an approximate 80% desorption efficiency even after four consecutive adsorption-desorption cycles. The combination of high adsorption capacity, fast chemisorption kinetics, and excellent reusability makes the TiO₂ -ZrO₂/PA/AC composite a highly promising and sustainable candidate for the efficient treatment of various radioactive wastewater streams in nuclear waste management.⁵¹

Footnotes

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The authors received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Ahmed Korna

Data Availability Statement

The data used in this study are available upon reasonable request from the corresponding author.*

References

Lee

Park

Lee

. Adsorption of heavy metals from aqueous solutions by activated carbon derived from waste materials. Water Res 2000; 34(1): 101–110.

Foo

Hameed

. Insights into the modeling of adsorption kinetics using the pseudo-first-order, pseudo-second-order, and intra-particle diffusion models. J Hazard Mater 2010; 175(1-3): 267–277.

Mahmoud

Khedr

El Sharkawy

. Corrigendum to “Environmentally-friendly calcite scale mitigation: encapsulation of CDs@ MS composite within membranes framework for nanofiltration”. J Alloys Compd 2024; 1000(2024): 175151.

Fang

Peng

Zhou

, et al. Electrocatalytic hydrogen peroxide production: advances, challenges, and future perspectives. Chem Rec 2025; 25(9): e202500066.

El-Sawaf

Nassar

El Aziz Elfiky

, et al. Advanced microcrystalline nanocellulose-based nanofiltration membranes for the efficient treatment of wastewater contaminated with cationic dyes. Polym Bull 2024; 81(14): 12451–12476.

Mubarak

Selim

Hawash

, et al. Flexible, durable, and anti-fouling maghemite copper oxide nanocomposite-based membrane with ultra-high flux and efficiency for oil-in-water emulsions separation. Environ Sci Pollut Res Int 2024; 31: 2297–2313.

Elfiky

AAEA

Mubarak

Keshawy

, et al. Novel nanofiltration membrane modified by metal oxide nanocomposite for dyes removal from wastewater. Environ Dev Sustain 2024; 26(8): 19935–19957.

El-Sawaf

El-Dakkony

Zayed

, et al. Green synthesis and characterization of magnetic gamma alumina nanoparticles for copper ions adsorption from synthetic wastewater. Results Eng 2024; 22: 101971.

Chen

Wang

. Removal of heavy metals from aqueous solutions by various sorbents: a review. J Environ Sci Health - Part A Toxic/Hazard Subst Environ Eng 2006; 41(10): 1071–1086.

10.

Qiu

Zhang

, et al. Adsorption of heavy metal ions from aqueous solutions by graphene oxide. J Colloid Interface Sci 2009; 332(1): 199–204.

11.

Cheng

, et al. Adsorption of heavy metals by graphene oxide. J Environ Sci 2008; 20(1): 97–100.

12.

Hosny

Fathy

Ramzi

, et al. Treatment of the oily produced water (OPW) using coagulant mixtures. Egypt J Pet 2016; 25(3): 391–396.

13.

Ahmad

Siddiqui

Ahmad

, et al. Synthesis and characterization of molecularly imprinted ferrite (SiO₂@Fe2O3) nanomaterials for the removal of nickel (Ni2+ ions) from aqueous solution. J Mater Res Technol 2019; 8(1): 1400–1411.

14.

Serunting

Rusnadi

Setyorini

, et al. An effective cerium (III) ions removal method using sodium alginate-coated magnetite (Alg-Fe3O4) nanoparticles. J Water Supply Res Technol - Aqua 2018; 67(8): 754–765.

15.

Norah

. Highly porous chitosan based magnetic polymeric nanocomposite (PNC) for the removal of radioactive Cs (I) and Sr (II) ions from aqueous solution. J King Saud Univ Sci 2022; 34: 102036.

16.

Hemdan

Ragab

El-Siaad

, et al. Sustainable synthesis and environmental application of chitosan-ocimum basilicum leaves-ZnO composite membrane for permanganate ion removal in wastewater treatment. Environ Sci Pollut Res Int 2024; 31(58): 66164–66183.

17.

Abdel Maksoud

MIA

Sami

Hassan

, et al. Novel adsorbent based on carbon-modified zirconia/spinel ferrite nanostructures: evaluation for the removal of cobalt and europium radionuclides from aqueous solutions. J Colloid Interface Sci 2022; 607: 111–124.

18.

Omorogie

Babalola

Unuabonah

, et al. Clean technology approach for the competitive binding of toxic metal ions onto MnO2 nanobioextractant. Clean Technol Environ Policy 2016; 18(1): 171–184.

19.

Abdel Maksoud

MIA

Murad

Zaher

, et al. Adsorption and separation of Cs (I) and Ba (II) from aqueous solution using zinc ferrite-humic acid nanocomposite. Sci Rep 2023; 13(1): 5856.

20.

Hassan

Elmaghraby

. Preparation of graphite by thermal annealing of polyacrylamide precursor for adsorption of Cs (I) and Co (II) ions from aqueous solutions. Can J Chem 2012; 90(10): 843–850.

21.

Boyd

Adamson

Myers

. The exchange adsorption of ions from aqueous solutions by organic zeolites; kinetics. J Am Chem Soc 1947; 69(9): 2836–2848.

22.

Reichenberg

. Properties of ion-exchange resins in relation to their structure. III. Kinetics of exchange. J Am Chem Soc 1953; 75(3): 589–597.

23.

Walker

Weatherley

. Kinetics of acid dye adsorption on GAC. Water Res 1999; 33(8): 1895–1899.

24.

Gabr

Mubarak

Keshawy

, et al. Linear and nonlinear regression analysis of phenol and P-nitrophenol adsorption on a hybrid nanocarbon of ACTF: kinetics, isotherm, and thermodynamic modeling. Appl Water Sci 2023; 13(12): 230.

25.

Cai

Zhang

, et al. Ambient ultrafast green synthesis of cyclodextrin-based metal-organic framework through solvent-induced in-situ crystallization for high-efficiency capture of radioactive iodine. Separ Purif Technol 2025; 376: 134078.

26.

Qin

Cui

Zhou

. Physisorption behaviors of organochlorine pesticides on the InP3 monolayer from theoretical insight. ACS Omega 2023; 8(35): 32168–32175.

27.

Geankoplis

. Transport processes in chemical engineering. Prentice Hall, 2003.

28.

Chen

, et al. Diffusion of metal ions in polymer membranes: a review. J Membr Sci 2016; 499: 171–198.

29.

Zhang

Liu

Zhou

, et al. Diffusion of metal ions in zeolites: a review. Chem Rev 2018; 118(17): 8339–8392.

30.

Lei

, et al. Facile microwave-assisted synthesis of Sb₂O₃-CuO nanocomposites for catalytic degradation of p-nitrophenol. J Mol Liq 2024; 409: 125503.

31.

Cai

Zhang

32.

Zhang

Han

, et al. Multi-stage fixed-bed column adsorption of dyes onto composite fibrous adsorbents: breakthrough curves, mass transfer zone and diffusion models. Chem Eng J 2023; 471: 144573.

33.

Ghoreishi

Nazari

Norouzi

. A review of current developments in mass transfer and diffusion mechanisms during adsorption onto nanomaterials: modeling and simulation approaches. Separ Purif Technol 2023; 323: 124376.

34.

Qin

Cui

Zhou

. Physisorption behaviors of organochlorine pesticides on the InP₃ monolayer from theoretical insight. ACS Omega 2023; 8(35): 32168–32175.

35.

Elfiky

AAEA

Mubarak

Keshawy

, et al. Removing of cationic dyes using self-cleaning membranes-based PVC/nano-cellulose combined with titanium aluminate. Environ Sci Pollut Res Int 2023; 30(30): 79091–79105.

36.

Aksu

İşoğlu

İA

. Adsorption of heavy metals onto activated carbon: kinetics and thermodynamics. Chem Eng J 2005; 109(1-3): 91–102.

37.

Özdemir

Erdem

Kabdaşlı

. Elovich equation: a theoretical and experimental review. J Appl Polym Sci 2010; 117(4): 2069–2079.

38.

Moghaddam

Hossein

Karimi

. Re-examination of boundary layer and film diffusion models in ion exchange and adsorption systems: a comparative study of transport limitations. Chem Eng J 2024; 482: 148785.

39.

Lütke

Peixoto

de Souza

, et al. Intraparticle diffusion mechanism for pollutant adsorption: influence of pore structure and kinetic factors in mesoporous biochar composites. J Environ Manag 2023; 338: 117765.

40.

Azizian

Shokrollahi

. Critical review on pseudo-first and pseudo-second-order kinetic models for adsorption processes: pitfalls and prospects. Chem Eng J 2024; 497: 154673.

41.

Plazinski

Wawrzkiewicz

Michalak

. Revisiting the pseudo-second-order kinetic model of adsorption: assumptions, limitations, and practical implications. J Hazard Mater 2023; 455: 131566.

42.

Sreeprasad

Ponnusamy

. Elovich kinetic model for adsorption studies: a review of theoretical and experimental developments in recent years. Environ Res 2024; 246: 118129.

43.

Wang

Zhang

, et al. Fixed-bed adsorption performance of metal-organic framework/alginate composite beads for efficient antibiotic removal: continuous-flow dynamics and modeling. Chem Eng J 2023; 469: 144211.

44.

Al-Ghouti

Khraiwesh

Al-Saad

, et al. Mass transfer mechanisms and internal diffusion processes in sustainable adsorbents: a comprehensive review. Separ Purif Technol 2025; 353: 129035.

45.

Freundlich

HMF

. Over the adsorption of gases in solids. Journal of the Chemical Society, Physical Transactions 1906; 79: 661–671.

46.

Langmuir

. The adsorption of gases on plane surfaces of glass, mica and platinum. J Am Chem Soc 1916; 38(4): 2221–2295.

47.

Sun

, et al. Efficient degradation of norfloxacin by synergistic activation of PMS with a three-dimensional electrocatalytic system based on Cu-MOF. Separ Purif Technol 2025; 356: 129945.

48.

Ahmed

Saber Mettwally

Mubarak

, et al. Eco-friendly electrospinning of recycled Nylon 6,12 waste for high-performance nonwoven nanofibers in sustainable textile applications. J Inorg Organomet Polym Mater 2024; 34: 1491–1505.

49.

Mubarak

Selim

Elshypany

. Hybrid magnetic core–shell TiO₂@CoFe₃O₄ composite towards visible light-driven photodegradation of Methylene blue dye and the heavy metal adsorption: isotherm and kinetic study. J Environ Health Sci Eng 2022; 20(5): 265–280.

50.

Aftab

Ullah

Qasim

, et al. Highly efficient removal of heavy metals from aqueous solutions using novel biochar-based hydrogel composites: kinetic, isotherm, and thermodynamic studies. J Hazard Mater 2024; 467: 129487.

51.

Cai

Pang

, et al. Scalable ambient synthesis of Hydroxyl-rich Cyclodextrin potassium metal–organic frameworks for high-efficiency iodine capture. Langmuir. Advance Article 2025. DOI: 10.1021/acs.langmuir.5c04214.

Synthesis and characterization of a high-performance TiO 2 -ZrO 2 /PA/AC composite for radionuclide removal from aqueous environments

Abstract

Keywords

Introduction

Materials and Methods

Innovative aspects of the TiO2-ZrO2/PA/AC composite

Synthesis of TiO2-coated ZrO2/PA/AC composite (TiZr-PA-AC)

Synthesis of the TiO2-ZrO2/PA/AC composite

Characterization

Adsorption Studies

Adsorption experiments

Effect of pH

Effect of initial ion concentration

Effect of contact time

Isotherm studies

Results and discussion

Kinetic modeling and statistical validity

Misinterpretation of k2 and temperature dependence

Diffusion Analysis and Temperature Effect

Effect of initial pH and adsorbent dosage

Adsorption isotherm analysis

Microstructural analysis of the TiO2-ZrO2/PA/AC composite by SEM

Key Observations

Interpretation in context

FTIR analysis of the TiO2-ZrO2/PA/AC composite and its derivatives

FTIR Analysis

Pristine Activated Carbon (AC)

TiO2-ZrO2/PA/AC composite

TiO2-coated TiZ-PA-AC composite

Kinetic studies

Kinetic model analysis

Analysis of kinetic parameters and model selection

Temperature dependence

Model selection

Effect of adsorbent dosage

Experimental observations and interpretation

Optimization and practical implications

Factors influencing adsorption efficiency

Analysis of intraparticle diffusion and activation energy

Temperature dependence of diffusion

Activation energy and diffusion mechanism

Temperature and ion-specific diffusion and adsorption mechanism

Temperature dependence

Diffusion magnitude and mechanism

Activation energy insight

Adsorption kinetics of Cs(I), Sr(II), Pu(IV), and U(VI) onto TiO2 -ZrO2/PA/AC

Summary of kinetic model analysis

Model suitability and mechanism

Effect of temperature

Implications and practical applications

Mechanistic implications

Potential practical applications

Desorption kinetics of metal ions

Adsorption mechanism analysis: Elovich and Boyd models

Adsorption isotherm analysis

Freundlich and Langmuir isotherm models

Desorption and reusability studies

Conclusive modeling summary: Isotherms and kinetics

Isotherm analysis

Kinetic synthesis

Conclusion

Footnotes

Declaration of conflicting interests

Funding

ORCID iD

Data Availability Statement

References

Innovative aspects of the TiO₂-ZrO₂/PA/AC composite

Synthesis of TiO₂-coated ZrO₂/PA/AC composite (TiZr-PA-AC)

Synthesis of the TiO₂-ZrO₂/PA/AC composite

Microstructural analysis of the TiO₂-ZrO₂/PA/AC composite by SEM

FTIR analysis of the TiO₂-ZrO₂/PA/AC composite and its derivatives

TiO₂-ZrO₂/PA/AC composite

TiO₂-coated TiZ-PA-AC composite