Materials

The chemical reagents used in this study included phosphomolybdic acid (H₃[P(Mo₃O₁₀)₄]), ammonium chloride (NH₄Cl), tin dichloride (SnCl₂), ferric chloride (FeCl₃), tin tetrachloride (SnCl₄), cesium nitrate (CsNO₃), strontium nitrate (Sr(NO₃)₂), samarium trinitrate (Sm(NO₃)₃), lanthanum nitrate hexahydrate (La(NO₃)₃₆H₂O), gadolinium nitrate hexahydrate (Gd(NO₃)₃₆H₂O), cerium nitrate (Ce(NO₃)₄), europium nitrate(Eu(NO₃)₃), dysprosium nitrate hexahydrate (Dy(NO₃)₃₆H₂O), holmium nitrate pentahydrate (Ho(NO₃)₃₅H₂O), thulium nitrate pentahydrate (Tm(NO₃)₃₅H₂O), ytterbium nitrate (Yb(NO₃)₃), lutetium nitrate pentahydrate (Lu(NO₃)₃₅H₂O), potassium niobate (KNbO₃) and nitric acid (HNO₃). These reagents were procured from Macklin Biochemical Co., Ltd. All of the reagents had a purity of greater than 99.5%, except for SnCl₄ (98%) and HNO₃ (65.0%–68.0%).

Preparation of the Adsorbent

The SnII_xSnIV_y(NH₄)_3-x-y[P(Mo₃O₁₀)₄] was synthesized via a chemical co-precipitation method, which involved the gradual addition of a hybrid solution containing various components into a soluble solution to ensure uniform mixing and controlled precipitation [40]. First, 100 mL of a 0.05 mol/L phosphomolybdic acid solution was prepared in a beaker. A magnetic stirrer was placed in the beaker, and the solution was stirred at 500 rpm. Appropriate amounts of SnCl₄, FeCl₃, and SnCl₂ hybrid element solutions were then added dropwise to the phosphomolybdic acid solution while maintaining stirring for 30 min. This ensured a complete reaction between the hybrid elements and phosphomolybdic acid. Finally, an adequate amount of NH₄Cl solution was added to enhance the crystallization performance of the material. The solid–liquid mixture was allowed to stand and age for 24 h to facilitate the full development of the microcrystals of the hybrid material. After aging, the mixture was separated using a water aspirator and a Buchner funnel to remove any undeveloped or damaged particles. The material was then washed with deionized water and centrifuged to remove insoluble impurities. Finally, the centrifuged material was dried in a constant-temperature vacuum oven. The resulting adsorbent materials contained various hybrid elements and different hybrid contents. Specific data for each formulation are presented in Table 1 and undried samples are shown in Fig. 2 (In this study, x and y represent the number of ammonium ions replaced in each AMP).

Fig. 2Full-screen View

(Color online) Synthesis products: AMP (a), SnIV₁(NH₄)₂[P(Mo₃O₁₀)₄](b) and SnII_0.5SnIV_0.5(NH₄)₂[P(Mo₃O₁₀)₄](c)

Characterization

The surface morphology was examined using a scanning electron microscope (HITACHI, SU 8600, Japan) and a transmission electron microscope (JEOL, JEM-2100F, Japan). The composition and content of the adsorbent before and after adsorption were analyzed using an energy-dispersive spectroscope (FEI, NOVA NanoSEM 230, America). The unit cell size of the adsorbent was determined using a multifunctional X-ray diffractometer (BRUKER-AXS, D8 ADVANCE Da Vinci, German). The functional groups of the adsorbent were characterized using a Fourier transform infrared spectroscope (THERMO FISHER, Nicolet 6700, America). The thermal decomposition of the adsorbent was evaluated using a thermogravimetric analyzer (Perkin Elmer, TGA8000, America). The valence states and proportions of the main elements were investigated using an X-ray photoelectron spectroscope (AXIS Ultra DLD, Shimadzu, Japan).

Adsorption Experiments

Batch experiments were conducted to investigate the adsorption capacity and characteristics of the synthesized adsorbents for metal ions. First, the adsorption capacity for Cs and the stability of various materials were examined. The optimal hybrid material was then selected for studying the multi-ion adsorption selectivity. Additionally, the changes in isotherm models at different temperatures for this material were analyzed. Finally, the kinetics of various adsorbents were studied to assess the impact of hybridization on their adsorption rates. A specified amount of adsorbent was added to a glass bottle, followed by the experimental solution (with varying metal ion compositions and concentrations). The bottle was sealed and placed in a pre-set temperature-controlled shaking bath for oscillation. After ensuring complete adsorption (except for kinetic tests), the bottle was removed. The mixture was then filtered to separate the solid from the liquid, and the concentration of target radionuclides in the solution was measured. Unless otherwise specified, the experimental conditions were: V/m=100 cm³/g, T=25 ℃, pH=7. The concentrations of Cs and other metal ions were measured using an atomic absorption spectroscopy (Shimadzu, AA-660, Japan) and inductively coupled plasma atomic emission spectroscope (Shimadzu, ICPS-7510, Japan).

DFT Calculations

DFT is a powerful tool for accurately calculating and predicting the electronic properties of crystal structures. DFT avoids the need to solve complex multibody Schrödinger equations by assuming that the energy of the system can be expressed as a function of electron density, which significantly reduces computational load and saves time. In this study, DFT was employed to analyze the adsorption process and mechanism of the hybrid adsorbent for Cs. All of the calculations were performed using the Vienna Ab Initio simulation package (VASP 6.2) with plane-wave spin-polarized periodic DFT methods. The projector augmented wave method was used to describe electron–ion interactions and electron exchange and correlation energies were treated using the Perdew-Burke-Ernzerhof generalized gradient approximation function. A cutoff energy of 500 eV, was applied, and the gamma grid was used for Brillouin zone sampling. First, the AMP model was optimized [42], with a force convergence threshold set to less than 0.05 eV/Å. Subsequently, the single-point energies of the system were calculated, with total energy convergence set to less than 10^-6 eV.

SEM TEM and EDS

The microstructure of AMP and the SnII_xSnIV_y(NH₄)_3-x-y[P(Mo₃O₁₀)₄] series was initially examined via scanning electron microscopy (SEM). According to the SEM results, the synthesized AMP predominantly exhibited a cubic structure (Fig. 3a1), with most particles displaying surface defects that impair the mechanical properties of the material. After hybridizing with Sn(IV) alone (Fig. 3a2), the increase in unit volume charge was smaller, and owing to the absence of Fe, complete particles did not form because of the lack of copolymerization effects. Therefore, further investigation of this material will not be pursued. When Sn(IV) and Sn(II) were added simultaneously but without Fe (Fig. 3a3), due to a smaller increase in unit volume charge and the absence of Fe, no complete particles were formed due to the lack of copolymerization effects. Subsequent experiments will not involve further investigation of this material. With the simultaneous addition of Sn(IV) and Sn(II) but without Fe (Fig. 3a4), the material exhibited reduced defects, and the microscopic particles transitioned from a cubic to a spherical structure under the high unit volume charge. Finally, when Fe was added alongside Sn(IV) and Sn(II) (SnII_0.5SnIV_0.5(NH₄)₂[P(Mo₃O₁₀)₄] with Fe) (Fig. 3a5), the copolymerization effect between Sn(II) and Fe(III) enhanced the crystallinity of the material, which resulted in well-formed spherical particles with intact surfaces and significantly improved mechanical properties. After adsorption of cesium ions, the microscopic spheres of SnII_0.5SnIV_0.5(NH₄)₂[P(Mo₃O₁₀)₄] with Fe (Fig. 3a6) showed no significant changes, which indicated that the material retained its stable fundamental structure throughout the adsorption process.

Fig. 3Full-screen View

(Color online) SEM, TEM iand EDS results of AMP and Sn-doped-AMP (a1-a6 SEM images, b1-b5 TEM images and c1-c4 EDS results)

Further, the SnII_0.5SnIV_0.5(NH₄)₂[P(Mo₃O₁₀)₄] (add Fe) hybrid material, which featured spherical microparticles, was further analyzed via a transmission electron microscopy (TEM). The TEM images reveal distinct lattice fringes with no noticeable disruptions or displacements, and the consistent spacing between parallel fringes confirms a typical face-centered cubic unit cell structure. The lattice spacing within the unit cell was uniformly distributed. The lattice spacing of the sample was determined to be 2.55 Å by measuring and averaging the spacing between multiple sets of parallel fringes (Fig. 3b5). Figure 3b4 sdisplays uniform reflection rings produced by the numerous brightened nanoscale grains of SnII_0.5SnIV_0.5(NH₄)₂[P(Mo₃O₁₀)₄] (add Fe), as observed through selected area electron diffraction.

Electron dispersive spectroscopy (EDS) analysis was conducted on SnII_0.5SnIV_0.5(NH₄)₂[P(Mo₃O₁₀)₄] (add Fe) to examine the elemental composition and proportions before and after adsorption. Surface scanning results (Figure 3c1 and c2) confirmed the presence of Sn both before and after adsorption, while Cs is detected only post-adsorption. These findings suggested that Sn was successfully hybridized into AMP and that the hybridized adsorbent retained its Cs adsorption capacity. In addition, there was no significant change in the Sn content or energy relative to Mo, which indicated that Sn does not directly react with Cs. Line scan results (Fig. 3c3 and c4) revealed a good overlap of characteristic peaks for Sn and Cs after adsorption and demonstrated that both elements coexisted in a similar form within the material and that a substitution reaction with ammonium ions occurred [43].

The Sn-doped-AMP

To identify the optimal hybrid adsorbent, a series of microstructural characterizations and batch adsorption experiments were performed on the Sn-doped AMP.

The crystalline structure of AMP and Sn-doped AMP was analyzed using X-ray diffraction (XRD). The relative intensity and distinct peaks confirmed the good crystallinity of the products (Fig. 4a1). For the Sn-doped AMP, the diffraction peaks shifted to the right compared with those of AMP in the order of Sn(II) >Sn(II) + Sn(IV) > Sn(IV). This shift indicated a reduction in lattice constants, which was attributed to the smaller ionic radii of the hybrid elements compared with ammonium ions (ionic radii: ${\text{NH}}_4^{+}$, 0.143nm; ${\text{Sn}}_2^{+}$, 0.093nm; ${\text{Sn}}_4^{+}$, 0.069nm). Additionally, the higher ionic charge of the hybrid elements further reduced the unit cell volume. The formation of Sn(II)-O-Sn(IV) bonds might also contribute to the peak shift and the contraction of the unit cell volume. As shown in Figure 4a1, the sample containing added Fe exhibited sharper diffraction peaks, which highlighted improved crystallinity due to the copolymerization effect of Fe(III) and Sn(II).

Fig. 4Full-screen View

(Color online) XRD, FT-IR, TGA, adsorption capacity and stability results of AMP and Sn-doped-AMP (a1-a2 XRD results, b FT-IR image, c TGA image, d adsorption capacity and e stability)

Furthermore, the effect of various hybrid concentrations ((${\text{NH}}_4^{+}$ substitution ratios) on the structure of the Sn-doped AMP was analyzed. Figure 4a2 demonstrates that within a specific range of hybrid concentrations, the peak intensity of the samples increased with rising concentrations, which indicated that the hybrid elements promote crystal growth. According to the width and intensity of the diffraction peaks, the Scherrer equation was applied to calculate the average grain size of the samples [44]: $D=\frac{0.89\lambda }{\beta \cos \theta }$ (1) where $D$ represents the average grain size, $\lambda$ denoted the wavelength of the incident X-rays, $\beta$ referred to the full width at half maximum of the diffraction peak, and $\theta$ indicated the diffraction angle.

According to the Scherrer equation, the AMP samples exhibited an average particle size of 73.5 nm, while the hybridized samples showed a reduced average particle size ranging from 55 nm to 65 nm. This indicates a noticeable decrease in particle size due to hybridization.

Second, Figure 4b shows the Fourier Transform Infrared Spectroscopy (FT-IR) analysis results for AMP and the Sn-doped-AMP samples. Both AMP and Sn-doped-AMP exhibited characteristic peaks at 1063 cm^-1 (O=P-OH groups), 965 cm^-1 (Mo-O absorption), 868 cm^-1 (Mo-O-Mo absorption), and 765 cm^-1 (antisymmetric stretching vibration of ${\text{PO}}_4^{3-}$), which confirmed that the Keggin structure of the hybridized samples remained intact. Some samples display a bending vibration peak of H-O-H at 1630 cm^-1 and a stretching vibration peak of H-O-H at 3210 cm^-1 attributed to insufficient drying and the presence of crystallization water. Additionally, the N-H bending vibration peak at 1385 cm^-1 confirmed the presence of ammonium ions in the samples. These ammonium ions contributed to enhanced material crystallinity. Notably, after adsorption, the intensity of the N-H bending vibration peak decreased relative to the characteristic O=P-OH group peak and the Keggin structure peak of [PMo₁₂O₄0]^3- in the infrared spectra. This decrease indicated a reduction in ammonium ion content, which suggested their involvement in the adsorption process. In the infrared spectra of the Sn-doped-AMP samples, a characteristic peak for Sn at 2976 cm^-1 was observed. This peak remained detectable after adsorption, which confirmed the successful hybridization and stability of metal ions within the material as they did not detach during adsorption. Lastly, although the functional groups of the samples were similar, the Sn-doped-AMP exhibited a shift towards lower wavenumbers, which were attributed to structural changes induced by hybridization and are consistent with the XRD results.

Third, Fig. 4c and Table 2 present the thermogravimetric analysis (TGA) results for AMP and the Sn-doped-AMP, which showed that all four materials underwent three stages of decomposition. The first stage involved weight loss due to the release of crystalline water from the material. The second stage corresponded to the decomposition of ammonium ions into NH3 gas. In this stage, AMP exhibited a weight loss of 2.58%, while the Sn-doped-AMP showed a weight loss of approximately 1.6%, which aligned with theoretical values of 2.79% and 1.76%, respectively. The final weight loss stage resulted from the decomposition of phosphomolybdic acid into phosphorus and molybdenum compounds, leading to the destruction of the Keggin structure and loss of cesium adsorption capability [45]. Despite the similar pyrolysis processes, the thermal stability of the materials improved following hybridization. Notably, the SnII₁(NH₄)₂[P(Mo₃O₁₀)₄] sample began releasing ammonia only at 765 ℃, whereas AMP initiated ammonia release at 710 ℃. The improved thermal stability is attributed to the enhanced interaction forces between the internal components of the molecules after hybridization, resulting in a significant increase in pyrolysis temperature compared to other materials.

Fourth, a comparison of the adsorption capacities of various adsorbents was conducted. Adsorption capacity experiments involved using 50 mg of each hybridized material with a 1200 ppm Cs aqueous solution (Fig. 4d). the main components of the samples from various hybrid formulations still showed a high degree of similarity to AMP, which resulted in adsorption capacities comparable to those of AMP. However, the adsorption capacity of all materials increased with the doping amount, except for those hybridized with Sn(II) alone. Linking this with the SEM results, it can be inferred that the increase in adsorption capacity is due to the transition of the material’s microstructure from cubes to polyhedra and eventually to spheres, which led to an increase in the specific surface area. Compared with AMP, the SnII_0.5SnIV_0.5(NH₄)₂[P(Mo₃O₁₀)₄] (add Fe) exhibited the highest adsorption capacity of 106.8 mg/g, which represented an increase of approximately 10%. In contrast, the decreased adsorption capacity of the Sn(II)-doped AMP could be attributed to the presence of Sn(II) alone, which lacked the high charge of Sn(IV) to enhance material performance. Additionally, it did not form a stable crystal configuration through copolymerization with Fe(III).

Finally, stability is a crucial factor for the practical use of materials. To assess this, chemical stability experiments were conducted on several hybrid materials with good adsorption capacities by immersing the materials in distilled water and measuring the Mo leaching rate at various time intervals.(SnII_0.5SnIV_0.5(NH₄)₂[P(Mo₃O₁₀)₄] (add Fe))demonstrated excellent stability, with Mo leaching rates of 0.69% and 1.18% after 1 and 3 days, respectively (Fig. 4e). These values were significantly lower than those of AMP, which indicated that the copolymerization effect of ${\text{Sn}}_2^{+}$ and ${\text{Fe}}_3^{+}$ during synthesis enhanced the crystallization of the hybrid material. Additionally, the high charge and small volume of ${\text{Sn}}_4^{+}$ reduced the unit charge volume and further improved the stability of the material. This improvement in stability also reduced the leakage of metal ions during the material’s practical application, which was beneficial for environmental protection.

According to the experimental results, the SnII_0.5SnIV_0.5(NH₄)₂[P(Mo₃O₁₀)₄] (add Fe), which retained the effective Keggin structure and exhibited good thermal stability, demonstrated the highest adsorption capacity and excellent chemical stability among the various Sn-doped-AMP materials. Therefore, it was selected as the hybrid material for subsequent in-depth research.

The SnII_0.5SnIV_0.5(NH₄)₂[P(Mo₃O₁₀)₄] (add Fe) hybridized material

First, X-ray photoelectron spectroscopy (XPS) analysis was conducted to investigate the adsorption mechanism of Cs on SnII_0.5SnIV_0.5(NH₄)₂[P(Mo₃O₁₀)₄] (add Fe). Figure 5a1 shows the full spectrum of SnII_0.5SnIV_0.5(NH₄)₂[P(Mo₃O₁₀)₄] (add Fe) before and after Cs adsorption. Distinct Cs 3d peaks were observed, which confirmed the successful adsorption of Cs onto the hybrid material. Additionally, no Fe-related peaks were detected in the full spectra before or after adsorption. This absence was attributed to the small ionic radius of Fe(III), which might prevent it from forming stable products with the Keggin structure of AMP. Further peak deconvolution of the main elements revealed no significant changes in their binding energies.

Fig. 5Full-screen View

(Color online) XPS, adsorption selectivity and PZC of SnII_0.5SnIV_0.5(NH₄)₂[P(Mo₃O₁₀)₄] (add Fe) (a1-a5 XPS results, b1 Adsorption Selectivity, b2 the PZC curve)

Figures 5a2 and a3 display the high-resolution Mo 3d spectra. Before adsorption, the binding energies for Mo were 233.11 eV, 236.26 eV (Mo6+, as well as 232.19 and 235.27 eV (Mo5+), with corresponding proportions of 51.17%, 35.30% (Mo6+) and 8.00%, 5.52% (Mo5+), respectively. After adsorption, the binding energies shifted to 232.72 eV, 235.87 eV (Mo6+) and 231.53 eV, 234.76 eV (Mo5+), with proportions of 53.27%, 36.72% (Mo6+) and 5.93%, 4.09% (Mo5+), respectively. The binding energies and peak area proportions for the various valence states of Mo showed no significant changes, which indicated that no redox reactions involving Mo occurred during the adsorption process.

Figures 5a4 and a5 present the high-resolution Sn 3d spectra. Before adsorption, the binding energies for Sn were 487.25 eV and 495.66 eV (Sn²⁺) and 487.49 eV, 496.10 eV (Sn⁴⁺), with proportions of 28.23%, 19.55% (Sn²⁺) and 31.33%, 20.89% (Sn⁴⁺), respectively. After adsorption, the binding energies shifted to 486.85 eV, 495.25 eV (Sn²⁺) and 487.39 eV, 495.79 eV (Sn⁴⁺), with proportions of 23.77%, 16.46% (Sn²⁺) and 35.69%, 24.08% (Sn⁴⁺), respectively. Similar to the Mo results, the binding energies and peak area proportions of the various valence states of Sn showed no significant changes, which confirmed the absence of redox reactions involving Sn during the adsorption process. Combined with the IR spectroscopy results, it can be concluded that the adsorption mechanism of Cs on the SnII_0.5SnIV_0.5(NH₄)₂[P(Mo₃O₁₀)₄] (add Fe) mainly involved an ion-exchange reaction.

Second, radioactive wastewater contained various metal ions, which often interfered with each other during industrial processes, leading to a reduced adsorption capacity of the adsorbent for target radionuclides [46]. Therefore, it is essential to assess the adsorption selectivity of SnII_0.5SnIV_0.5(NH₄)₂[P(Mo₃O₁₀)₄] (add Fe). SnII_0.5SnIV_0.5(NH₄)₂[P(Mo₃O₁₀)₄] (add Fe) was introduced to mixed ion solutions at different pH values and adsorption capacity curves for various ions were plotted (Fig. 5b1). In mixed ion solutions at different pH values, SnII_0.5SnIV_0.5(NH₄)₂[P(Mo₃O₁₀)₄] (add Fe) demonstrated a high adsorption capacity for Cs, with almost no adsorption of other metal elements in the solution (e.g., Sr, Eu). This result indicated that SnII_0.5SnIV_0.5(NH₄)₂[P(Mo₃O₁₀)₄] (add Fe) retained good adsorption selectivity for cesium under various conditions. Additionally, as the pH decreased, the adsorption capacity of SnII_0.5SnIV_0.5(NH₄)₂[P(Mo₃O₁₀)₄] (add Fe) decreased, mainly owing to the competition between H⁺ and Cs⁺ during the adsorption process. The point of zero charge (PZC) pH value of SnII_0.5SnIV_0.5(NH₄)₂[P(Mo₃O₁₀)₄] (add Fe) was measured via the mass titration method [47]. As shown in the Figure 5b2, the PZC ofSnII_0.5SnIV_0.5(NH₄)₂[P(Mo₃O₁₀)₄] (add Fe) is 4.91. When the solution pH was lower than 4.91, a large amount of H⁺ ions accumulated on the surface of the adsorbent. The high concentrations of H⁺ ions could electrostatically interact with metal cations and reduce the adsorption capacity of the material [48, 49].

Third, to evaluate the effect of temperature on the adsorption process, the thermodynamic parameters of the adsorption reaction were calculated using the Van’t Hoff equation: $\ln K_{\text{d}}=\frac{-\text{Δ}H}{RT}+\frac{\text{Δ}S}{R}$ (2) $\text{Δ}G=\text{Δ}H-T\text{Δ}S$ (3) As shown in Fig. 6a, the (K_d) values at different temperatures were fitted to the Van’t Hoff equation, which yielded a correlation coefficient ($R^2$) of 0.9623. Further analysis of the fitted equation provided the thermodynamic parameters–standard enthalpy (ΔH), standard entropy (ΔS), and Gibbs free energy (ΔG) for this adsorption experiment, as presented in Table 3.

Fig. 6Full-screen View

Adsorption performance of SnII_0.5SnIV_0.5(NH₄)₂[P(Mo₃O₁₀)₄] (add Fe) (a Thermodynamic experiment, b1-b3 isotherm capacity, c1 contact time and fitted curves of AMP, c2 contact time and fitted curves of SnII_0.5SnIV_0.5(NH₄)₂[P(Mo₃O₁₀)₄] (add Fe), c3 the intraparticle diffusion model, c Adsorption-Desorption

From the table, it can be observed that the ΔH value is negative, which indicated that the reaction is exothermic. The negative ΔS value suggests that the driving force of the reaction decreased with increasing temperature, which means the K_d value decreased as temperature rose [50]. Additionally, calculations revealed that the ΔG values for the adsorption reaction remain negative up to 215.48 ℃.

Fourth, the adsorption isotherms illustrated the relationship between the amount of adsorbate adsorbed by the adsorbent at equilibrium and the concentration of the target radionuclide in the solution. These isotherms can be used to identify specific adsorption mechanisms and calculate the saturated adsorption capacity of the adsorbent.

The Langmuir model assumes that the adsorption reaction is a monolayer adsorption process with constant adsorption energy. The fitting equation is: $Q_{\text{e}}=\frac{Q_{\text{m}}{K}_{\text{L}}{C}_{\text{e}}}{1+K_{\text{L}}{C}_{\text{e}}}\mathrm{,}$ (4) where Q_e is the adsorption capacity, Q_m is the maximum adsorption capacity, C_e is the equilibrium concentration of Cs in the solution, and K_L is the Langmuir constant.

The Freundlich model assumes that the adsorption occurs on a heterogeneous adsorbent surface with multiple layers of adsorption. The fitting formula is: $Q_{\text{e}}=K_{\text{F}}{C}_{\text{e}}^{\frac{1}{n}}\mathrm{,}$ (5) where K_F is the Freundlich constant, and 1/n is the Freundlich isotherm coefficient.

The Temkin model accounts for adsorbate-adsorbate interactions and assumes that the adsorption energy decreases linearly as the surface coverage increases. The fitting formula is: $Q_{\text{e}}=\frac{RT}{b_{\text{T}}}\ln C_{\text{e}}+\frac{RT}{b_{\text{T}}}\ln K_{\text{T}}\mathrm{,}$ (6) where R is the gas constant, T is the absolute temperature, K_T is the Temkin isotherm equilibrium binding constant, and b_T is the Temkin isotherm constant related to the heat of sorption.

The Dubinin-Radushkevich (D-R) model assumes that the adsorption process follows a porous filling mechanism with a Gaussian distribution of adsorption energies. The fitting equation is: $\ln Q_{\text{e}}=\ln Q_{\text{m}}-K_{\text{D}}{\epsilon }^2$ (7) $\epsilon =RT\ln \left(1+\frac{1}{C_{\text{e}}}\right)$ (8) $E={\left(2K_{\text{D}}\right)}^{-\frac{1}{2}}$ (9)

The nonlinear Langmuir and Freundlich fitting results for the hybrid materials at different temperatures are shown in Fig. 6b1, with the estimated isotherm parameters listed in Table 4. For all temperature conditions, the Langmuir model consistently provided better fits, with correlation coefficients ($R^2$) exceeding 0.975. This suggested that the adsorption process of SnII_0.5SnIV_0.5(NH₄)₂[P(Mo₃O₁₀)₄] (add Fe) followed a monolayer adsorption mechanism. According to the Langmuir isotherm model fitting, the maximum adsorption capacities of SnII_0.5SnIV_0.5(NH₄)₂[P(Mo₃O₁₀)₄] (add Fe) at 25 C, 35 C, and 45 C were 115.00 mg/g, 108.78 mg/g, and 102.06 mg/g, respectively. These values indicated that SnII_0.5SnIV_0.5(NH₄)₂[P(Mo₃O₁₀)₄] (add Fe) possessed significant adsorption capacity over a wide temperature range, which demonstrated its effectiveness in purifying Cs from radioactive wastewater. Moreover, the maximum adsorption capacities obtained from the model fit at different temperatures were in close agreement with the experimental results, which further validated the suitability of the Langmuir isotherm model.

However, in some cases, the best-fit model for adsorption materials cannot be determined solely by $R^2$, which might introduce some ambiguity [51]. The Langmuir isotherm model suggested that monolayer, uniform adsorption dominated under non-competitive equilibrium conditions. In contrast, the Freundlich isotherm model mainly examined the adsorption mechanism through the K_F and $1/n$ values, which helped infer the favorability of metal ion adsorption onto the adsorbent [52]. The Freundlich model fitting results indicated that the $1/n$ values for SnII_0.5SnIV_0.5(NH₄)₂[P(Mo₃O₁₀)₄] (add Fe) at different temperatures fell within the range of 0.1-10, specifically 0.21 (25 ℃), 0.20 (35 ℃), and 0.20 (45 ℃), which were considered favorable for adsorption.

In the Temkin model(Fig. 6b2), the correlation coefficient ($R^2$) for SnII_0.5SnIV_0.5(NH₄)₂[P(Mo₃O₁₀)₄] (add Fe) at different temperatures was greater than 0.97, which indicated a high level of accuracy for this model. The value of b_T was greater than 1, which suggested that the reaction was endothermic and aligned with the thermodynamic results [53]. In the D-R model (Fig. 6b3), the average adsorption energy (E) for SnII_0.5SnIV_0.5(NH₄)₂[P(Mo₃O₁₀)₄] (add Fe) was approximately 1000 kJ/mol, which was significantly higher than 8 kJ/mol and indicated that the adsorption of Cs involved the breaking and reorganization of molecular bonds, characteristic of a chemisorption process [54].

Fifth, the surface characteristics of the adsorbent directly influenced the adsorption rate, mainly due to the significant effect of diffusion resistance on ion transport during the adsorption process.

To describe the change in adsorption of the target nuclide over time, we selected the pseudo-first-order (PFO) and pseudo-second-order (PSO) kinetic models, which corresponded to physical and chemical adsorption, respectively.

The PFO kinetic model was based on membrane diffusion theory and a physical adsorption model. The expressions for the nonlinear and linear PFO kinetic models are as follows:

The pseudo-first-order kinetic model is based on the membrane diffusion theory and a physical adsorption model. The expressions for the nonlinear and linear pseudo-first-order kinetic models include the following: $q_{\text{t}}=q_{\text{e}}\left(1-e^{-k_{1}t}\right)$ (10) $\log \left(q_{\text{e}}-q_{\text{t}}\right)=\log q_{\text{e}}-\frac{k_1}{2.303}t$ (11) where $k_1$ is the adsorption rate constant of the PFO kinetic model, and q_t and q_e are the adsorption capacities of the adsorbent for the target nuclide at time $t$ and equilibrium, respectively.

The PSO kinetic model represents a chemical adsorption process, where electrons are shared or transferred between the adsorbate and the adsorbent. The expressions for the two forms of the PSO kinetic model are as follows: $\frac{\text{d}{q}_{\text{t}}}{\text{d}t}=k_2{\left(q_{\text{e}}-q_{\text{t}}\right)}^2$ (12) $\frac{t}{q_{\text{t}}}=\frac{1}{k_2{q}_{\text{e}}^2}+\frac{t}{q_{\text{e}}}$ (13) where $k_2$ is the adsorption rate constant of the PSO kinetic model, and q_t and q_e represent the adsorption capacities of the adsorbent for the target nuclide at time t and equilibrium, respectively.

Figure 6c1, c2 show the adsorption rates of AMP and SnII_0.5SnIV_0.5(NH₄)₂[P(Mo₃O₁₀)₄] (add Fe), along with the fitted curves for the PFO and PSO models. As observed from the figure, the adsorption of AMP and SnII_0.5SnIV_0.5(NH₄)₂[P(Mo₃O₁₀)₄] (add Fe) achieved uptake ratios of over 96% within 1 minute and reached equilibrium quickly. This indicates that, after hybridization, SnII_0.5SnIV_0.5(NH₄)₂[P(Mo₃O₁₀)₄] (add Fe) retains the extremely high adsorption rate of AMP while improving its adsorption capacity. Table 5 presents the parameters of the fitted curves for AMP and the SnII_0.5SnIV_0.5(NH₄)₂[P(Mo₃O₁₀)₄] (add Fe). Both materials were best described by the PSO kinetic model, with correlation coefficients greater than 0.99. This suggested that the adsorption process of the hybrid materials was chemical in nature, which aligned with the XPS measurement results. Additionally, the PSO kinetic parameters of the hybrid materials were similar to those of AMP, which indicated that hybridization did not alter the kinetic properties of the material, which still retained a high adsorption rate. According to the fitting results, the equilibrium adsorption capacities of SnII_0.5SnIV_0.5(NH₄)₂[P(Mo₃O₁₀)₄] (add Fe) under these conditions were in close agreement with the experimentally measured values, which confirmed the accuracy of the model.

Furthermore, this study also investigated particle diffusion during the adsorption process of SnII_0.5SnIV_0.5(NH₄)₂[P(Mo₃O₁₀)₄] (add Fe) using the intraparticle diffusion model (IPD). The equation for the intraparticle diffusion model is as follows: $q_t=K_{\text{I}}{t}^{\frac{1}{2}}+C$ (14) where K_I is the IPD constant and C is the constant associated with the IPD, which is proportional to the boundary layer thickness.

As shown in Fig. 6c3, the adsorption processes of SnII_0.5SnIV_0.5(NH₄)₂[P(Mo₃O₁₀)₄] (add Fe) and AMP for Cs can be mainly divided into two stages. The first stage is the relatively steep surface diffusion stage, during which Cs is rapidly adsorbed onto the surface of SnII_0.5SnIV_0.5(NH₄)₂[P(Mo₃O₁₀)₄] (add Fe). However, it is noteworthy that the curve does not pass through the origin, indicating that internal diffusion is not the sole factor controlling the adsorption process [55]. The second stage is the more gradual internal diffusion stage, where, due to the occupation of a large number of adsorption sites on the surface and within the pores of SnII_0.5SnIV_0.5(NH₄)₂[P(Mo₃O₁₀)₄] (add Fe), the adsorption process transitions to diffusion within the particles, resulting in a significant decrease in the adsorption rate and ultimately reaching equilibrium [56, 57].

Finally, desorption performance and reusability were crucial parameters for evaluating the effectiveness of adsorbents. In this experiment, a 500 ppm Cs solution was used for adsorption, and 3M NH₄Cl was employed as the desorbent. The adsorption-desorption experiments were conducted at pH 7. After each adsorption, the adsorbent was immersed in 3M NH₄Cl for desorption, followed by a new adsorption cycle. This process was repeated for a total of four cycles. As shown in Fig. 6d, the desorption rate did not reach 100% after each cycle, leading to a gradual decline in the adsorption efficiency of SnII_0.5SnIV_0.5(NH₄)₂[P(Mo₃O₁₀)₄] (add Fe). However, both the desorption rate in the third cycle and the adsorption rate in the fourth cycle remained above 85%, which indicated that SnII_0.5SnIV_0.5(NH₄)₂[P(Mo₃O₁₀)₄] (add Fe) exhibited good reusability and could meet the demands of practical industrial applications.

DFT analysis

DFT simulations were performed to model the molecular structure of the synthesized hybrid materials and calculate their energy changes. First, the adsorption process was simulated by systematically replacing ammonium ion sites in AMP with other ions. When Fe atoms were introduced as substitutes, the model results failed to converge, which indicated that Fe could not directly react with AMP. This finding aligned with the microscopic characterization results obtained from EDS and XPS. A series of initial model structures for the hybrid materials were obtained by substituting ammonium ions with Sn atoms (Fig. 7). Table 6 lists the crystal structural parameters of AMP and SnII_xSnIV_y(NH₄)_3-x-y[P(Mo₃O₁₀)₄] after optimization. Calculations were performed to determine the cell parameters of each material, energy changes during synthesis, and energy changes during the adsorption process. Static calculations were conducted on energy changes to obtain the total free energy changes for each system. The energy calculation formula is as follows: $E_{\text{binding}}=E_{\text{free}}-E_{\text{atom}}$ (15) $\begin{array}{ll}{E}_{\text{adsorption}}\hfill & =E_{\text{binding}}+x{E}_{\text{binding}}\left({\text{NH}}_4{}^{+}\right)\hfill \\ \hfill & -E_{\text{binding}}\left(AMP\right)-x{E}_{\text{atom}}\left(Cs\right)\hfill \end{array}$

Fig. 7Full-screen View

The different DFT substitution models of AMP and Sn doped-AMP

According to the DFT calculation results, when Sn ions replaced ammonium ions, the cell size of the crystals decreased, with the simulation results aligning with experimental findings. Additionally, based on the energy calculation results in Table 7, the substitution of Sn was a spontaneous exothermic reaction. The binding energy was lowest when only one Sn ion was substituted, which indicated that this configuration was the most stable. However, during subsequent adsorption processes, if two ammonium ions were replaced by Sn ions during synthesis, the reaction became endothermic and could not proceed spontaneously. Therefore, it was crucial to strictly control the Sn concentration and the drop rate of the solution during the synthesis of hybrid materials to ensure optimal hybridization conditions. According to previous research conducted by our group, two-thirds of the active ammonium ions in AMP underwent ion exchange reactions [58]. The hybrid material demonstrated optimal adsorption performance when one-third of the ammonium ions were substituted. This suggested that the non-active ammonium ions in AMP could be replaced by the hybrid element, which enhanced the stability and mechanical properties of the material while maintaining its adsorption capacity.