The lignite from Shanxi Fuhong Mineral Products Co., Ltd. (China) is crushed and passed through 150 mesh, 200 mesh and 250 mesh sieves respectively, deionized water is washed 2–3 times and then dried at 80°C. 200 mL iron solution with a total iron concentration of 0.7 mol/L was prepared according to the Fe²⁺ to Fe³⁺ molar ratio of 1:2 and heated in a constant temperature water bath at 60°C. 10 g of lignite was added into the iron solution and stirred at 350 r/min for 1 h. The concentrated ammonia water with a mass fraction of 25% was added drop by drop to a pH value of 9, continued stirring for 1 h, and then stood for 2 h. The precipitate was cleaned with deionized water, separated from solid and liquid by a rubidium magnet, repeatedly cleaned to the supernatant as neutral, dried in a vacuum for 12 h, and taken out. The sample solutions were prepared with analytically pure FeSO₄⋅7H₂O, Fe₂(SO₄)₃, CuSO₄⋅5H₂O, ZnSO₄⋅7H₂O, Pb(NO₃)₂ and NaOH. The concentration of the sample solution was prepared according to the actual AMD water quality parameters in a mining area in Huludao: Cu²⁺ concentration was 30 mg/L, Zn²⁺ concentration was 30 mg/L, Pb²⁺ concentration was 50 mg/L, and pH was 4.

In this experiment, the concentrations of Cu²⁺, Zn²⁺ and Pb²⁺ were measured by a Z-2000 flame atomic spectrophotometer (GB/T 7475-2015), and the pH was measured by PHS-3C pH meter through the glass electrode method (GB/T 6920-2015).

Previous studies have shown that the main influencing factors for the preparation of Fe₃O₄ particles by chemical co-precipitation are particle size, the ratio of Fe²⁺ to Fe³⁺ species, total iron concentration, water bath temperature, type of precipitant and pH [22,23]. When Fe₃O₄ particles are prepared by chemical co-precipitation, Fe²⁺ can be completely precipitated only when the pH reaches 8.9. Therefore, the preparation of Fe₃O₄ particles by chemical co-precipitation method needs to add an alkaline precipitant to adjust the pH [24]. Common precipitants include NaOH and NH₃·H₂O. NaOH is a strong base and has a high alkali concentration of −OH, which is beneficial to the growth of the cell nucleus and can improve the speed of a chemical reaction, but the particle size of the generated Fe₃O₄ particles grows too fast and is prone to agglomeration [24,25]. NH₃·H₂O is a weak base, and its reaction rate is slightly slower than that of NaOH, which can better control the particle size of Fe₃O₄. Generally, NH₃·H₂O is used as the precipitant. A large number of research results show that pH will have a certain influence on the magnetic properties of Fe₃O₄ particles. When the pH value is 9, the prepared Fe₃O₄ particles have the best magnetic properties [24,26]. For lignite: the active ingredient HA in lignite will continuously dissolve under low alkalinity, which is beneficial to adsorption. However, HA will be degraded into small molecules under strong alkalinity, which reduces the chelating ability of metal ions and affects the inhibitory effect of HA on the release of metals in adsorption products [27,28]. Therefore, in this study, NH₃·H₂O was chosen as the precipitant to prepare Fe₃O₄-L under the condition of pH = 9.

Fe₃O₄-L is prepared by loading Fe₃O₄ particles on the lignite matrix. The performance of Fe₃O₄-L is affected by the loading capacity of lignite and the properties of Fe₃O₄ particles. The particle size of lignite is different, the surface area is different, and the loading amount of Fe₃O₄ particles on the lignite surface is also different. Therefore, the particle size of lignite should be discussed as a single factor of preparation conditions. When Fe₃O₄ particles are prepared by chemical co-precipitation, the particle size and magnetic properties of Fe₃O₄ particles can be strictly controlled by changing the reaction temperature [23]. The desired magnetization and nanoparticle size can be achieved by adjusting the concentration of iron salts in the solution and the molar ratio of Fe²⁺ to Fe³⁺ [22,24]. Therefore, the ratio of the amount of Fe²⁺ to Fe³⁺, the total iron concentration, and the temperature of the water bath should also be considered as single factors of the preparation conditions.

In order to prepare Fe₃O₄-L adsorption materials with excellent performance, NH₃·H₂O was chosen as the precipitant in this study, and the preparation conditions were explored under the condition of pH = 9. A single-factor experimental method was used to investigate the effects of particle size, the molar ratio of Fe²⁺ to Fe³⁺, total Fe concentration and water bath temperature on the removal performance of Cu²⁺, Zn²⁺ and Pb²⁺ under a single metal system in AMD-treated with Fe₃O₄-L.

Effect of particle size: Fe₃O₄-L was prepared in a constant temperature water bath at 60°C in the molar ratio of Fe²⁺ to Fe³⁺ of 1:2 and a total Fe concentration of 0.7 mol/L. The prepared Fe₃O₄-L was crushed and screened to 150 mesh, 200 mesh and 250 mesh. A 250 mL, pH = 4 solutions containing 30 mg/L Cu²⁺, 30 mg/L Zn²⁺, and 50 mg/L Pb²⁺ were prepared, respectively. 1.0 g of 150-mesh, 200-mesh, and 250-mesh Fe₃O₄-L were weighed and added to Cu²⁺, Zn²⁺ and Pb²⁺ solutions, respectively. Three replicates of each experiment were made. The adsorption was shaken at 150 r/min and samples were collected every 30 min to detect the concentrations of Cu²⁺, Zn²⁺ and Pb²⁺ in different Fe₃O₄-L particle size systems.

The following experimental procedures for the preparation of Fe₃O₄-L to remove Cu²⁺, Zn²⁺ and Pb²⁺ are the same as the above experiments except that the materials of Fe₃O₄-L are different. Effect of the molar ratio of Fe²⁺ to Fe³⁺: The Fe₃O₄-L with 250 mesh particle size was prepared in a constant temperature water bath at 60°C according to the molar ratio of Fe²⁺ to Fe³⁺ of 1:1, 1:1.5 and 1:2, respectively, and the total Fe concentration of 0.7 mol/L. Effect of total Fe concentration: The Fe₃O₄-L with a particle size of 250 mesh was prepared in a constant temperature water bath at 60°C according to the molar ratio of Fe²⁺ to Fe³⁺ of 1:2 and the total iron concentration of 0.5, 0.7 and 0.9 mol/L, respectively. Effect of water bath temperature: The Fe₃O₄-L with a particle size of 250 mesh was prepared in a constant temperature water bath of 50°C, 60°C and 70°C with the molar ratio of Fe²⁺ to Fe³⁺ of 1:2 and the total Fe concentration as 0.7 mol/L, respectively.

In this study, the Box-Benhnken method (BBD) was used to design response surface experiments using the results of single-factor experiments. Three independent variables, particle size (A), total Fe concentration (B) and the molar ratio of Fe²⁺ to Fe³⁺ (C), were used as response factors, which were varied at low (−1), medium (0) and high (1) levels, respectively, and the removal rates of Cu²⁺, Zn²⁺ and Pb²⁺ from the experimental sample solutions were used as response values (Y) to design 17 sets of experiments. The response experimental design scheme and the results are given in Table 1. The second-order polynomial model was fitted using Design-Expert software, as in Eq. (1), to obtain the regression equation. Statistical significance of the model was assessed by analysis of variance (ANOVA), and variable interaction effects were analyzed using response surface plots [5,24].(1) Y=β0+∑i=1kβiXi+∑i=1kβiiXi2+∑i=1k−1∑j=kβijXiXj+ε where, Y is the system response value; β₀ is the offset factor of the offset term; β_i is the linear offset coefficient; β_ii is the second-order offset coefficient; β_ij is the interaction effect coefficient; X_i, X_j and X_iX_j are the main and interaction effects of each factor for each factor level value analysis [29].

Fe₃O₄-L was prepared for the adsorption of Pb²⁺, Cu²⁺, and Zn²⁺ according to the optimal results of RSM. To investigate the adsorption effect of Fe₃O₄-L at different reaction times, 1.0 g Fe₃O₄-L was injected into the solutions of Cu²⁺ (30 mg/L), Zn²⁺ (30 mg/L) and Pb²⁺ (50 mg/L) at pH = 4, respectively. Adsorption by shaking at 150 r/min. The remaining ion concentrations were measured at 5, 10, 15, 30, 45, 60, 90, 120, 150 and 180 min. Each experiment was repeated three times. To investigate the removal effect of Fe₃O₄-L on metal ions at different initial concentrations in different temperature systems, 1.0 g Fe₃O₄-L was added to different concentrations of Cu²⁺ solution (10, 20, 30, 40, 50 mg/L), Zn²⁺ solution (10, 20, 30, 40, 50 mg/L) at pH = 4, and Pb²⁺ solution (10, 20, 30, 50, 70 mg/L) at pH = 4. The adsorption was carried out at temperatures of 25°C, 35°C and 45°C, respectively, for 180 min at an oscillation speed of 150 r/min. Each experiment was repeated three times. The residual Cu²⁺, Zn²⁺ and Pb²⁺ concentrations were detected at different initial concentrations in different temperature systems.

In order to explore the reusability of Fe₃O₄-L, adsorption-desorption cycle experiments were carried out. Add 1.0 g Fe₃O₄-L to Cu²⁺ (30 mg/L), Zn²⁺ (30 mg/L), and Pb²⁺ (50 mg/L) solutions at pH = 4, and shake at 150 r/min for 180 min at 25°C. The remaining Cu²⁺, Zn²⁺, and Pb²⁺ concentrations in the supernatant were detected. Then, Fe₃O₄-L after adsorption of Cu²⁺, Zn²⁺, and Pb²⁺ was added to 250 mL of 0.1 mol/L HNO₃ and desorbed by shaking at 150 r/min for 180 min at 25°C to achieve the desorption of Cu²⁺, Zn²⁺, and Pb²⁺. The desorbed Fe₃O₄-L was washed with deionized water until neutral, dried under vacuum for 12 h, and the above adsorption-desorption process was repeated five times. Each group of experiments was repeated three times.

A scanning electron microscope (JSM-7610Plus, Japan) was used to observe the surface morphology of lignite as well as Fe₃O₄-L. The lignite and Fe₃O₄-L adsorbent before and after adsorption of metal ions were analyzed for elemental composition testing using an UltraDry EDS detector (Thermo ScientificTM, USA). The changes in the composition and surface functional groups of Fe₃O₄-L adsorbent before and after modification and adsorption were determined by an X-ray diffractometer (Shimadzu XRD-6100, Japan) and Fourier transform infrared spectrometer (Thermo Fisher Scientific IS10, USA).

The removal rates of Cu²⁺, Zn²⁺ and Pb²⁺ by the prepared Fe₃O₄-L gradually rise with the increase of the particle size mesh (Figs. 1a–1c). The growth in particle size leads to an increase in the specific surface area and porosity of Fe₃O₄-L particles, which leads to an increase in the adsorption activity sites and facilitates the adsorption reaction.

The removal rates of Cu²⁺, Zn²⁺ and Pb²⁺ by Fe₃O₄-L gradually increase as the ratio of Fe²⁺ to Fe³⁺ substance decreases (Figs. 1d–1f). The Fe³⁺ content affects the purity and porosity of Fe₃O₄-L. When the Fe³⁺ content in the solution is low, the prepared Fe₃O₄-L has more impurities and low purity. In the process of loading Fe₃O₄, the dissolution of Fe³⁺ will lead to the increase of H⁺ content in the solution, resulting in the decomposition of some components of lignite that can produce new pore channels and increase the surface area and porosity [15,23,30]. The content of Fe²⁺ affects the Fe₃O₄ nanocrystal properties and yields. The increase of Fe²⁺ facilitates the reaction to produce Fe₃O₄ nanocrystals with larger particle size and better crystallinity, but the low yield leads to the reduction of Fe₃O₄ particles loaded on the surface of lignite, which affects the adsorption performance [23,24,30].

The removal rates of Cu²⁺, Zn²⁺ and Pb²⁺ by Fe₃O₄-L show an increasing and then decreasing trend with the increase of total Fe concentration (Figs. 1g–1i). The total concentration of iron salts affects the crystallization of Fe₃O₄ nanoparticles. The process of preparing nanoparticles by chemical co-precipitation is divided into two stages: the crystal nucleation stage and the grain growth stage [31]. The iron salt concentration is low mainly in the nucleation stage, generating a large number of nuclei. However, the particle size of the product at this time is small, and the adsorption effect of Fe₃O₄-L is minimal. With the increase of iron salt concentration, the grain growth stage is entered. The grain growth rate is accelerated, the product particle size, surface area and porosity increase, and the adsorption capacity is strong. The total concentration of iron salts is getting higher and higher, and the iron salts react rapidly to generate nuclei after adding precipitant and grow continuously, with a large specific surface area and more adsorption sites. However, when the concentration is already too high, the generated Fe₃O₄ agglomerates seriously, and the pores of Fe₃O₄-L are gradually blocked, which affects the adsorption effect [32].

The removal of all three metal ions by Fe₃O₄-L increases with increasing reaction temperature, but then decreases when the temperature is too high (Figs. 1j–1l). The higher the reaction temperature, the greater the crystal growth rate and the larger the product particle size, which provides more adsorption sites and facilitates adsorption. However, the higher temperature tends to lead to crystal aggregation and blockage of Fe₃O₄-L pores, which is not conducive to adsorption [31]. Temperature affects the purity of Fe₃O₄-L. When the temperature increases, Fe²⁺ is easily oxidized to Fe³⁺, and it is difficult to control the molar ratio of Fe²⁺ to Fe³⁺, which leads to the increase of impurities in the product and reduces the adsorption capacity. Temperature affects the stability of Fe₃O₄ particles and thus the rate of their production. At lower temperatures, the solute energy is weak and the crystal formation rate is slow. As the temperature increases, the rate of crystal formation gradually reaches its maximum. The continued increase in temperature will cause the kinetic energy of molecules in solution to increase too fast, which is not conducive to the formation of stable particles and reduces the rate of crystal formation [33].

ANOVA was used to assess the adequacy of the second-order regression model developed by BBD, and the results were shown in Tables 2–4. The F value and P-value of the model (Prob > F) determined the model significance. The model F values for Cu²⁺, Zn²⁺, and Pb²⁺ were 48.90, 137.74, and 27.31, respectively. The P-values (Prob > F) for the Cu²⁺ and Zn²⁺ models were less than 0.001, indicating that the Cu²⁺ and Zn²⁺ models were highly significant. The P-value for the Pb²⁺ model was 0.001, which was less than 0.05, indicating that the model was significant. The P values (Prob > F) for the model items A, B, C, AB, AC in the Cu²⁺ model, A, B, C, A², B², C² in the Zn²⁺ model, and A, B, AB, AC, BC, A² in the Pb²⁺ model were less than 0.05, indicating that the above model terms were significant in each model [1,29]. The closer the R² value is to 1, the better the fit between the calculated results and the observed results of the model. The R² values of the three models in this experiment were 0.9670, 0.9944, 0.9723, all very close to 1. R²_Adj were 0.9473, 0.9872, 0.9367, indicating that the models could explain 94.73%, 98.72%, 93.67% of the changes in response values, respectively, and the regression models could better predict the experimental results and optimize the process parameters [31]. The AP values of the models in this experiment were 24.562, 34.144, 18.622, all greater than 4, while the coefficients of variation CV were 0.63%, 0.52%, 1.06%, all less than 10%, indicating that the models are highly accurate and stable [34,35]. In summary, RSM can better simulate the removal patterns of magnetically modified lignite for Cu²⁺, Zn²⁺, and Pb²⁺, and is a meaningful model.

The removal rate of Cu²⁺ increases with increasing particle size, and the increased speed is faster when the total Fe concentration and the molar ratio of Fe²⁺ to Fe³⁺ are low. The removal rate of Cu²⁺ decreases with increasing total iron concentration and declines more rapidly at a larger particle sizes and a higher molar ratio of Fe²⁺ to Fe³⁺. The removal rate of Cu²⁺ increases with the decrease of the molar ratio of Fe²⁺ to Fe³⁺, and the change rate increases with the increase of total Fe concentration and particle size (Fig. 2). Combining the response surface plots, considering the response surface and ANOVA results, indicates that the AB and AC interactions are very significant and the BC is not.

The Zn²⁺ removal rate increases with increasing particle size, and decreases and then increases with increasing total Fe concentration and decreasing molar ratio of Fe²⁺ to Fe³⁺ (Fig. 3). The curvature of the response surface plot of AB, AC, and BC interaction is larger and the interaction effect of the binary parameters is higher, and the variance results verify this conclusion.

In a certain range, the Pb²⁺ removal rate increases with the increase of particle size. When the particle size is too large, the Pb²⁺ removal rate decreases and the decrease is most obvious at the molar ratio of Fe²⁺ to Fe³⁺ of 1:1. Pb²⁺ removal rate decreases with increasing total Fe concentration, and the decrease is more obvious when the molar ratio of Fe²⁺ to Fe³⁺ is higher. When the particle size is small and the total Fe concentration is low, the Pb²⁺ removal rate decreases with the molar ratio of Fe²⁺ to Fe³⁺, and vice versa (Fig. 4). Combined with the response surface diagram, contour diagram, and variance analysis results, the pairwise interaction of AB, AC and BC is highly significant.

The response surface BBD experimental design and the analysis of the results showed that all three factors had an effect on the ability of the prepared Fe₃O₄-L to adsorb metal ions, and there was an interactive effect between the three factors. Using the optimization function of Design Expert, the optimal preparation conditions for the preparation of Fe₃O₄-L by chemical co-precipitation were optimized as follows: the particle size of 250 mesh, the total Fe concentration of 0.5 mol/L, and the molar ratio of Fe²⁺ to Fe³⁺ of 1:2. The removal rates of Cu²⁺, Zn²⁺, and Pb²⁺ in AMD by Fe₃O₄-L prepared under these conditions were 94.52%, 88.49% and 96.69%.

The removal of all three ions by Fe₃O₄-L shows an increasing trend as the reaction progressed. In the first 60 min, the adsorption sites on the adsorbent surface are sufficient, the mass transfer driving force between the solution and the adsorbent surface is large, and the adsorption rate increases significantly. In the middle and late stages, the adsorption sites on the surface gradually reach adsorption saturation. The adsorption of metal ions is transferred from the surface to the adsorption sites in the internal pores and the adsorption rate is slowed down. The adsorption basically reaches the equilibrium state at 180 min. The removal rates of Fe₃O₄-L for Cu²⁺, Zn²⁺ and Pb²⁺ at equilibrium are 99.99%, 85.27% and 97.48%, respectively (Fig. 5a). Fe₃O₄-L is a porous adsorbent with a high adsorption rate loaded with Fe₃O₄ nanoparticles on the lignite matrix, which has a good prospect for the rapid removal of heavy metal cations from polluted wastewater [23,24].

The solute adsorption rate controls the residence time of the adsorbate at the solid-solution interface, so understanding the adsorption kinetics is important for the study of pollutant removal. In order to study the adsorption mechanism and potential rate-controlling steps throughout the adsorption process, pseudo-first-order models (such as Eq. (2)), pseudo-second-order models (such as Eq. (3)), and intraparticle diffusion models (such as Eq. (4) were utilized) to fit and analyze the kinetic process of removing Cu²⁺, Zn²⁺, and Pb²⁺ from Fe₃O₄-L prepared by chemical co-precipitation method. The results are shown in Table 5 and Figs. 5b–5d.

(2) ln⁡(qe−qt)=ln⁡qe−K1t

(3) t/qt=1/(K2qe2)+t/qe

(4) qt=K3⋅t1/2+C

where, q_t and q_e are the adsorption capacity at time t (min) and equilibrium, respectively (mg/g), K₁ is the rate constant of quasi-first-order kinetic reaction (min⁻¹), K₂ is the rate constant of quasi-second-order kinetic reaction (mg/g⋅min), K₃ is the reaction rate coefficient of intra-particle diffusion (mg/g⋅min^0.5), and t is the adsorption time (min) [6,36,37].

From Table 5, Figs. 5b–5d, it can be seen that the R² of Fe₃O₄-L adsorption process of Cu²⁺, Zn²⁺, Pb²⁺ fit pseudo-first-order, pseudo-second-order kinetics and intraparticle diffusion models are: 0.8155, 0.8316, 0.8249, 0.9981, 0.9939, 0.9947, 0.9046, 0.7195, 0.8904, 0.8878, 0.8778, 0.8974. The value of R² can be judged that the pseudo-second-order kinetic equation can better describe the adsorption process of Fe₃O₄-L to three heavy metal ions. According to the mechanism established by the pseudo-second-order kinetic equation, it can be inferred that in the process of Fe₃O₄-L adsorption of three heavy metals, physical adsorption and chemical adsorption coexist, and chemical adsorption is the main one [38,39]. All the curves of Fe₃O₄-L adsorption of Cu²⁺, Zn²⁺, Pb²⁺ with time can be divided into two parts, and do not pass through the coordinate origin, which indicates that the adsorption process is determined by both surface adsorption and slow channel diffusion, but the effect of diffusion adsorption on chemisorption rate Impact can be ignored [36].

In each temperature regime, an increase in the initial concentration increases the concentration difference between the solution and the adsorbent surface, leading to an increase in the adsorption of Cu²⁺, Zn²⁺, and Pb²⁺ per unit mass of Fe₃O₄-L (Figs. 6a, 6c, 6e). However, Fe₃O₄-L has a limited adsorption capacity and cannot further reduce the concentration of the remaining metal ions in the solution after the adsorption reaches saturation. The adsorption capacity of Fe₃O₄-L for Cu²⁺, Zn²⁺ is larger and that for Pb²⁺ is smaller when the temperature increases, which proves that the adsorption reaction of Fe₃O₄-L for Cu²⁺ and Zn²⁺ is an absorbing reaction, and that for Pb²⁺ is an exothermic reaction. Under the same environmental conditions, the adsorption effect of Fe₃O₄-L on Cu²⁺ and Pb²⁺ was better than that of Zn²⁺. Differences in migration rates, ionic radii and hydration energy of Cu²⁺, Zn²⁺ and Pb²⁺ lead to higher adsorption affinity of Fe₃O₄-L for Cu²⁺ and Pb²⁺ than for Zn²⁺ [3].

Adsorption isotherms are often used to describe the interaction of an adsorbent with an adsorbate. The Langmuir and Freundlich adsorption model are important models for describing many adsorption isotherms. Using the Langmuir and Freundlich adsorption models, the adsorption forms of Fe₃O₄-L for Cu²⁺, Zn²⁺, and Pb²⁺ were explored and the maximum adsorption capacity was calculated [37].

The Langmuir temperature model describes monolayer adsorption: when an adsorbent chemisorbs on a fixed number of active centers on the surface of the adsorbent, a monolayer is formed, where each active center is large enough to accommodate one adsorbed cation. All active sites are equivalent, and there is no interaction between species adsorbed on adjacent active sites. Furthermore, adsorption energy and adsorption enthalpy are equivalent. Eq. (5) represents the nonlinear form of the Langmuir isotherm:(5) qe=KLQmCeCeKL+1

where, K_L is the adsorption constant related to the adsorption activation energy, the larger the value, the stronger the adsorption capacity; C_e is the remaining adsorbate concentration in the solution at equilibrium (mg/L), and q_e is the adsorption capacity at equilibrium (mg/g). Q_m is the theoretical saturation capacity of complete monolayer adsorption (mg/g), which is also related to the maximum adsorption capacity.

The Freundlich isotherm describes adsorption occurring on amorphous surfaces. This isotherm involves reversible adsorption and is not limited to monolayer formation. The Freundlich isotherm assumes that adsorption occurs at multiple locations due to the inhomogeneity of the associated surface. Eq. (6) represents the nonlinear form of Freundlich isotherm:

(6) qe=KFCe1/n where, K_F is the Freundlich constant related to the adsorption equilibrium, n is the Freundlich constant related to the number of active centers in the adsorbent required for the adsorption of a metal cation, and C_e (mg/L) is the remaining adsorbate concentration in the solution at equilibrium, q_e (mg/g) is the adsorption capacity at equilibrium [40].

Figs. 6b, 6d and 6f show the adsorption isotherms of Cu²⁺, Zn²⁺, Pb²⁺ three heavy metal ions adsorbed by Fe₃O₄-L at 25°C, 35°C and 45°C, respectively. The relevant parameters of data fitting are shown in Table 6. According to the fitting results, both Langmuir and Freundlich adsorption models can well fit the isotherm adsorption process of Fe₃O₄-L for three heavy metal ions. From the correlation coefficient R², the Langmuir model can better fit the adsorption process. The Langmuir isotherm is related to monolayer adsorption and homogeneous adsorption, so the adsorption of Cu²⁺, Zn²⁺, Pb²⁺ three heavy metal ions by Fe₃O₄-L is more inclined to homogeneous monolayer adsorption [38]. According to the Langmuir model, the theoretical maximum adsorption capacity of Fe₃O₄-L for Cu²⁺, Zn²⁺, and Pb²⁺ at different temperatures can be calculated, which are 14.5273 (25°C), 14.7014 (35°C), 14.9039 (45°C), 11.3407 (25°C), 12.1250 (35°C), 12.6858 (45°C), 14.2771 (25°C), 13.3843 (35°C), 12.8604 (45°C), the theoretical values are similar to the experimental results [41–43].

The adsorption capacity of the adsorbent is usually represented by the maximum adsorption capacity calculated by the Langmuir model. Table 7 summarizes the ability of other adsorbents reported in the literature to adsorb Cu²⁺, Zn²⁺, and Pb²⁺. Obviously, Fe₃O₄-L is superior to Pellet material of iron tailings (IT) compounded with sodium alginate (SA) [44], GCM2 [45], KOH-RH [46], SiO₂/PAA [47], Sawdust of Populus alba [48] and Magnetite nanospheres [49]. Although some adsorbents such as Nanoporous activated neem bark have a better adsorption effect than Fe₃O₄-L, these adsorbents have the problems of a complicated preparation process, high cost and difficulty in recycling [41–43].

The stability of magnetic materials is an important factor in their adsorption applications. The results of the cyclic adsorption experiment on Fe₃O₄-L are shown in Fig. 7. It can be seen from the figure that the first removal rates of Cu²⁺, Zn²⁺ and Pb²⁺ of Fe₃O₄-L are: 99.76%, 85.17% and 97.18%, respectively. After five cycles of adsorption-desorption experiments, the adsorption rates decreased by 6.92%, 5.84% and 4.79%, respectively. It shows that Fe₃O₄-L has a strong regeneration ability, and has the advantages of stable recycling when treating heavy metal pollution in water [50–52].

Lignite has a dense structure and uneven shape, with many microfractures and large pores distributed on the surface. The surface of Fe₃O₄-L is rougher and covered with a large number of tiny particles (Fig. 8). The elemental composition of lignite is dominated by C, O, Al, Si and Ca, while Fe₃O₄-L adds a large amount of Fe elements compared with lignite (Fig. 9). SEM and EDS results illustrate that the Fe₃O₄-L surface was successfully loaded with a large number of Fe₃O₄ particles and had a larger specific surface area and more pore structure than lignite, which was particularly favorable for the adsorption of heavy metal ions. A large number of precipitates accumulated on the surface and pores of Fe₃O₄-L with adsorbed metal ions, and Cu, Zn and Pb elements obviously appeared on Fe₃O₄-L after adsorption, indicating that Cu²⁺, Zn²⁺ and Pb²⁺ were successfully on Fe₃O₄-L and underwent precipitation reactions.

The X-ray diffraction patterns (XRD) and Fourier transform infrared spectra (FTIR) of lignite and Fe₃O₄-L before and after adsorption are shown in Fig. 10. In the figure, a represents lignite, b represents Fe₃O₄-L, and c, d, and e represent Fe₃O₄-L after adsorption of Cu²⁺, Zn²⁺, and Pb²⁺, respectively.

Analysis of XRD results shows that lignite is mainly composed of conventional mineral components such as SiO₂, and the Fe₃O₄ crystalline phase appears obviously after magnetic modification, which confirms the successful preparation of Fe₃O₄-L. After the adsorption reaction Cu²⁺, Zn²⁺ and Pb²⁺ existed as CuFe₂O₄, Zn(OH)₂, ZnFe₂O₄ and PbS and PbS, respectively, as a result of the ion exchange and complexation reaction of Cu²⁺, Zn²⁺ and Pb²⁺ on the surface of Fe₃O₄-L. Cu²⁺, Zn²⁺ and Pb²⁺ are adsorbed onto the Fe₃O₄-L surface driven by the mass transfer forces generated by the concentration difference between the Fe₃O₄-L surface and the solution, and precipitation occurs to form Cu(OH)₂, Zn(OH)₂, PbS. Cu(OH)₂, some of Zn(OH)₂ and Fe(OH)_3, the hydrolysis product of Fe³⁺, undergo a co-precipitation reaction to form CuFe₂O₄ and ZnFe₂O₄.

Analysis of the FTIR results shows that the typical absorption peak of Fe₃O₄ clearly appears near 582 cm⁻¹ in b compared to a, which is attributed to the stretching vibration of the Fe-O bond, indicating a successful preparation. Before and after the adsorption of heavy metal ions by Fe₃O₄-L, the absorption peaks near 3400, 2922, 1690, 1593 cm⁻¹ were shifted and the series of absorption peaks corresponding to complex C-H out-of-plane bending vibrations were changed in the range of 600–900 cm⁻¹, which verified that the adsorption of Cu²⁺, Zn²⁺, and Pb²⁺ by Fe₃O₄-L was a combination of physical and chemical adsorption. Some collapse of the crystal structure of Fe₃O₄-L after adsorption of heavy metal ions occurs as a result of the reaction between metal ions and Fe-O [23,53,54].