Influence of duck eggshell powder modifications by the calcination process or addition of iron (III) oxide-hydroxide on lead removal efficiency

Lead-contaminated wastewater causes toxicity to aquatic life and water quality for water consumption, so it is required to treat wastewater to be below the water quality standard before releasing it into the environment. Duck eggshell powder (DP), duck eggshell powder mixed iron (III) oxide-hydroxide (DPF), calcinated duck eggshell powder (CDP), and calcinated duck eggshell powder mixed iron (III) oxide-hydroxide (CDPF) were synthesized, characterized, and investigated lead removal efficiencies by batch experiments, adsorption isotherms, kinetics, and desorption experiments. CDPF demonstrated the highest specific surface area and pore volume with the smallest pore size than other materials, and they were classified as mesoporous materials. DP and DPF demonstrated semi-crystalline structures with specific calcium carbonate peaks, whereas CDP and CDPF illustrated semi-crystalline structures with specific calcium oxide peaks. In addition, the specific iron (III) oxide-hydroxide peaks were detected in only DPF and CDPF. Their surface structures were rough with irregular shapes. All materials found carbon, oxygen, and calcium, whereas iron, sodium, and chloride were only found in DPF and CDPF. All materials were detected O–H, C=O, and C–O, and DPF and CDPF were also found Fe–O from adding iron (III) oxide-hydroxide. The point of zero charges of DP, DPF, CDP, and CDPF were 4.58, 5.31, 5.96, and 6.75. They could adsorb lead by more than 98%, and CDPF illustrated the highest lead removal efficiency. DP and CDP corresponded to the Langmuir model while DPF and CDPF corresponded to the Freundlich model. All materials corresponded to a pseudo-second-order kinetic model. Moreover, they could be reusable for more than 5 cycles for lead adsorption of more than 73%. Therefore, CDPF was a potential material to apply for lead removal in industrial applications.

The release of lead-contaminated wastewater from battery, steel, dye and pigment, plastic, and electronic industries causes environmental problems through its toxicity to aquatic life and water quality to water consumption. In addition, the dysfunctional systems of nerves, reproductive, respiration, blood, and many diseases of anemia, lead poisoning, and Alzheimer have been caused by receiving lead into the human body 1 . Therefore, it recommends removing lead from wastewater under the water quality standard which does not exceed 0.2 mg/L following USEPA standards before releasing it into the environment.
Many methods have been applied for eliminating heavy metals in wastewater such as chemical precipitation, oxidation-reduction, coagulation-flocculation, and ion exchange; however, they also leave many concerns of incomplete treatment, expensive operating costs, and creating toxic sludges 2 . As a result, an alternative method of adsorption method is a good choice because it is an efficient and simple method with suitable operating cost including many choices of adsorbents to deal with the specific target pollutants. Various food wastes to eliminate heavy metals in wastewater in 2020-2022 are illustrated in Table 1. In the case of lead removals, eggshells are popularly used because they consist of calcium carbonate (CaCO 3 ) and a hydroxyl group (-OH) which could highly adsorb lead in wastewater. Especially, duck eggshells are more CaCO 3 content and porous than chicken Table 1. Various food wastes for eliminating heavy metals in wastewater.
The synthesis of duck eggshell powder mixed iron (III) oxide-hydroxide (DPF) and calcined duck eggshell powder mixed iron (III) oxide-hydroxide (CDPF). Firstly, 5 g of DP or CDP were added to 500 mL of Erlenmeyer flask containing 160 mL of 5% FeCl 3 ·6H 2 O, and they were mixed by an orbital shaker (GFL, 3020, Germany) of 200 rpm for 3 h. Next, they were filtrated and air-dried at room temperature for 12 h. Then, they were added to 500 mL of Erlenmeyer flask containing 160 mL of 5% NaOH, and they were mixed by an orbital shaker of 200 rpm for 1 h. After that, they were filtered and air-dried at room temperature for 12 h. Finally, they were kept in a desiccator before use called duck eggshell powder mixed iron (III) oxide-hydroxide (DPF) or calcined duck eggshell powder mixed iron (III) oxide-hydroxide (CDPF).
Characterizations of duck eggshell materials. Various characterized techniques were used for characterizing duck eggshell powder (DP), duck eggshell powder mixed iron (III) oxide-hydroxide (DPF), calcined duck eggshell powder (CDP), and calcined duck eggshell powder mixed iron (III) oxide-hydroxide (CDPF). Firstly, Brunauer-Emmett-Teller (BET) (Bel, Bel Sorp mini X, Japan) by isothermal nitrogen gas (N 2 ) adsorption-desorption at 77.3 K and degas temperature of 80 °C for 6 h was used to identify their specific surface area, pore volumes, and pore sizes. Second, an X-ray diffractometer (XRD) (PANalytical, EMPYREAN, UK) in a range of 2θ = 5-80° was used for investigating their crystalline structures. Third, Field emission scanning electron microscopy and focus ion beam (FESEM-FIB) with energy dispersive X-ray spectrometer (EDX) (FEI, Helios NanoLab G3 CX, USA) which the samples were placed on aluminum stubs with gold-coating for 4 min using a 108 auto Sputter Coater with thickness controller MTM-20 model (Cressington, Ted Pella Inc, USA) by  (1,3,5,7,9), and initial lead concentration (10-70 mg/L). The initial lead concentration of 50 mg/L, a sample volume of 200 mL, pH 5, a shaking speed of 200 rpm, and a temperature of 25 °C were applied as the control condition. The lowest value with the highest lead removal efficiency of each affecting factor was selected as the optimum value, and it was used for the next affecting factor study. The triplicate experiments were conducted for confirming their results. An atomic adsorption spectrophotometer (PerkinElmer, PinAAcle 900 F, USA) was used for analyzing lead concentrations, and Eq. (1) was used to calculate lead removal efficiency in the percentage: where C 0 is the initial lead concentration (mg/L), and C e is the equilibrium of lead concentration in the solution (mg/L). where C e is the equilibrium of lead concentration (mg/L), q e is the amount of adsorbed lead on duck eggshell materials (mg/g), q m is indicated the maximum amount of lead adsorption on duck eggshell materials (mg/g), K L is the adsorption constant (L/mg). K F is the constant of adsorption capacity (mg/g)(L/mg) 1/n , and 1/n is the constant depicting the adsorption intensity. R is the universal gas constant (8.314 J/mol K), T is the absolute temperature (K), b T is the constant related to the heat of adsorption (J/mol), and A T is the equilibrium binding constant corresponding to the maximum binding energy (L/g). q m is the theoretical saturation adsorption capacity (mg/g), K DR is the activity coefficient related to mean adsorption energy (mol 2 /J 2 ), and ε is the Polanyi potential (J/mol) 14 . Graphs of linear Langmuir, Freundlich, Temkin, and Dubinin-Radushkevich isotherms were plotted by C e /q e versus C e, log q e versus log C e , q e versus ln C e , and ln q e versus ε 2 , respectively whereas graphs of their nonlinear were plotted by q e versus C e 39 . For adsorption isotherm experiments, 15 g/L of DP or 10 g/L of DPF or 7.5 g/L of CDP, or 5 g/L of CDPF were added to 500 mL Erlenmeyer flasks with initial lead concentrations from 10 to 70 mg/L. The control condition of DP or DPF or CDP or CDPF was a sample volume of 200 mL, a shaking speed of 200 rpm, pH 5, a temperature of 25 °C, and a contact time of 4 h for DP, 3 h for DPF, 3 h for CDP, and 2 h for CDPF. Adsorption kinetics. The adsorption kinetics of duck eggshell powder (DP), duck eggshell powder mixed iron (III) oxide-hydroxide (DPF), calcined duck eggshell powder (CDP), and calcined duck eggshell powder mixed iron (III) oxide-hydroxide (CDPF) were identified by various adsorption kinetics of linear and nonlinear pseudo-first-order kinetic, pseudo-second-order kinetic, elovich, and intraparticle diffusion models to (1) Lead removal efficiency (%) = (C 0 − C e )/C 0 × 100 Linear : log q e = log K F + 1/n log C e  where q e is the amount of adsorbed lead on adsorbent materials (mg/g), q t is the amount of adsorbed lead at the time (t) (mg/g), k 1 is a pseudo-first-order rate constant (min −1 ), and k 2 is a pseudo-second-order rate constant (g/mg•min). α is the initial adsorption rate (mg/g/min) and β is the extent of surface coverage (g/mg). k i is the intraparticle diffusion rate constant (mg/g•min 0.5 ) and C i is the constant that gives an idea about the thickness of the boundary layer (mg/g). Graphs of linear pseudo-first-order, pseudo-second-order, elovich, and intraparticle diffusion models were plotted by ln (q e − q t ) versus time (t), t/q t versus time (t), q t versus ln t, and q t versus time (t 0.5 ), respectively whereas their nonlinear graphs were plotted by the capacity of lead adsorbed by adsorbent materials at the time (q t ) versus time (t) 39 . For adsorption kinetic experiments, 15 g/L of DP or 10 g/L of DPF or 7.5 g/L of CDP, or 5 g/L of CDPF were added to 1000 mL of breaker with the initial lead concentration of 50 mg/L. The control condition of DP or DPF or CDP or CDPF was a sample volume of 1000 mL, a shaking speed of 200 rpm, pH 5, a temperature of 25 °C, and a contact time of 6 h.

Desorption experiments.
The desorption experiments of duck eggshell materials were studied to investigate the possible material reusability which is referred from the study of Praipipat et al. 14 . The adsorption-desorption experiments in 5 cycles were used for confirming the abilities of duck eggshell powder (DP), duck eggshell powder mixed iron (III) oxide-hydroxide (DPF), calcined duck eggshell powder (CDP), and calcined duck eggshell powder mixed iron (III) oxide-hydroxide (CDPF) for lead adsorption. The saturated DP or DPF or CDP or CDPF after lead adsorption was added to 500 mL of Erlenmeyer flask containing 200 mL of 0.5 M HNO 3 solution, then it was shaken by an incubator shaker (New Brunswick, Innova 42, USA) at 200 rpm for 4 h. After that, it was washed with deionization water and dried at room temperature, and DP or DPF or CDP or CDPF is ready for the next adsorption cycle. Equation (17) was used for calculating the desorption efficiency in percentage.
where q d is the amount of lead desorbed (mg/mL) and q a is the amount of lead adsorbed (mg/mL).

Result and discussion
The physical characteristics of duck eggshell materials. The physical characteristics of duck eggshell powder (DP), duck eggshell powder mixed iron (III) oxide-hydroxide (DPF), calcined duck eggshell powder (CDP), calcined duck eggshell powder mixed iron (III) oxide-hydroxide (CDPF) are demonstrated in Fig. 2a-d. DP was a white color powder demonstrated in Fig. 2a while DPF was a dark brown color powder which might be from the color of iron (III) oxide-hydroxide color added illustrated in Fig. 2b. For CDP, it was a white color similar to DP, but it was a finer powder than DP shown in Fig. 2c. Finally, CDPF was a light brown color powder shown in Fig. 2d. Therefore, a calcination process might affect to the material colors and their characteristics.
Characterizations of duck eggshell materials. BET. The specific surface area, pore sizes, and pore volumes of duck eggshell powder (DP), duck eggshell powder mixed iron (III) oxide-hydroxide (DPF), calcined duck eggshell powder (CDP), and calcined duck eggshell powder mixed iron (III) oxide-hydroxide (CDPF) by BET analysis are demonstrated in Table 3. For DP and DPF, their specific surface area, pore volumes, and pore sizes were 0.955 m 2 /g, 0.0009 cm 3 /g, 3.703 nm and 12.313 m 2 /g, 0.0081 cm 3 /g, 2.617 nm which DPF had a higher specific surface area and pore volume approximately than 13-fold and ninefold of DP, whereas its pore size was smaller than approximately 1.4-fold of DP. Thus, the addition of iron (III) oxide-hydroxide helped to increase the specific area and pore volume with decreasing pore size 14,44-46 . For CDP, its specific surface area, pore volume, and pore size were 10.781 m 2 /g, 0.0065 cm 3 /g, and 2.540 nm which had the higher specific surface area and pore (10) Linear : ln q e − q t = ln q e − k 1 t www.nature.com/scientificreports/ volume of approximately 11-fold and 7-fold of DP, and it had smaller pore size approximately 1.45-fold than DP which might result from the calcination process similar to previous studies 47,48 . For CDPF, its specific surface area, pore volume, and pore size were 34.930 m 2 /g, 0.0943 cm 3 /g, and 2.092 nm which demonstrated the highest specific surface area and pore volume with the smallest pore size than other materials resulting in the high lead adsorption capacity. Therefore, the calcination process along with adding iron (III) oxide-hydroxide is recommended to increase the specific surface area and pore volume with a small pore size for higher lead adsorption by duck eggshells than only the calcination process or adding iron (III) oxide-hydroxide. Moreover, since their pore sizes were in a range of 2-5 nm, all materials were mesoporous materials by the classification by the International Union of Pure and Applied Chemistry (IUPAC) 49 .   www.nature.com/scientificreports/ mixed iron (III) oxide-hydroxide (CDPF) by FESEM-FIB analysis at 1500× magnification with 100 µm illustrated in Fig. 4a-d. For DP and DPF, they were irregular structures with heterogeneous particle sizes, so iron (III) oxide-hydroxide added to DPF did not affect its surface morphology similar reported by another study 14 . In addition, the distributions of EDX mapping of DP and DPF are demonstrated in Fig. 4e,f. Carbon (C), oxygen (O), and calcium (Ca) were found in DP and DPF, whereas iron (Fe), sodium (Na), and chloride (Cl) were found in only DPF which might be from chemicals used in a process of the addition of iron (III) oxide-hydroxide   14,28,39,51 . For CDP and CDPF, their surfaces were irregular shapes similar to DP and DPF; however, they were smaller in size than DP and DPF which might result from a calcination process. The smaller particle sizes of CDP and CDPF might support higher lead adsorptions than DP and DPF similarly reports by other studies that calcined eggshells had a higher or developer porous structure than non-calcined eggshells 48 . Moreover, adding iron (III) oxide-hydroxide also did not affect the surface structure of CDPF similar to DPF. The distributions of EDX mapping of CDP and CDPF are demonstrated in Fig. 4g,h which found the same chemical elements of C, O, and Ca similar to DP and DPF, whereas CDPF had the same chemical elements as DPF with observing iron distribution on the surface of DPF and CDPF. The chemical compositions of duck eggshell powder (DP), duck eggshell powder mixed iron (III) oxidehydroxide (DPF), calcined duck eggshell powder (CDP), and calcined duck eggshell powder mixed iron (III) oxide-hydroxide (CDPF) by EDX analysis are reported in Table 4, and their distributions of EDX mapping are demonstrated in Fig. 4e-h. Carbon (C), oxygen (O), and calcium (Ca) were the main chemical components of all materials, whereas iron (Fe), sodium (Na), and chloride (Cl) were only found in DPF and CDPF which could be confirmed the successful addition of iron (III) oxide-hydroxide in both materials. For DP and DPF comparison, the mass percentages by weight of O, Ca, and C of DPF were decreased, whereas the mass percentages by weight of Fe, Na, and Cl were increased which might be from chemicals ferric chloride hexahydrate (FeCl 3 ·6H 2 O) and sodium hydroxide (NaOH) used for the DPF synthesis. For DP and CDP comparison, the mass percentages by weight of O and C of CDP were decreased, whereas the mass percentage by weight of Ca was increased resulting from the effect of the calcination process similar to another study 52 . For CDP and CDPF comparison, the mass percentages by weight of O, Ca, and C were decreased. While, the mass percentages by weight of Fe, Na, and Cl were increased similar reason to DPF from chemicals used in the CDPF synthesis. The point of zero charge. The point of zero charge (pH pzc ) refers to a pH value at the net charge equal to zero of the adsorbent for realizing which pH value is good for adsorption by that adsorbent. In this study, the pH pzc of duck eggshell powder (DP), duck eggshell powder mixed iron (III) oxide-hydroxide (DPF), calcined duck eggshell powder (CDP), and calcined duck eggshell powder mixed iron (III) oxide-hydroxide (CDPF) was investigated to identify which a pH value was good for lead adsorption for each material, and their results are demonstrated in Fig. 6. The pH pzc values of DP, DPF, CDP, and CDPF were 4.58, 5.31, 5.96, and 6.75, respectively. As a result, the calcination process and the iron (III) oxide-hydroxide increased the pH pzc of materials. Since a negatively charged material surface is preferred for capturing lead (II) ions, the pH of the solution (pH solution ) should be higher than pH pzc (pH solution > pH pzc ) to support a high lead adsorption. Therefore, the high lead adsorptions of all materials should be observed at pH > 4.   Fig. 7a. Their lead removal efficiencies increased with increasing of dosages which might be from increasing active sites for capturing the lead. Their highest lead removal efficiencies were 99.74% at 15 g/L for DP, 100% at 10 g/L for DPF, 100% at 7.5 g/L for CDP, and 100% at 5 g/L for CDPF, respectively. Therefore, they were used as optimum adsorbent dosages of DP, DPF, CDP, and CDPF for the effect of contact time.

Batch adsorption experiments.
The effect of contact time. The contact times from 1 to 6 h of duck eggshell powder (DP), duck eggshell powder mixed iron (III) oxide-hydroxide (DPF), calcined duck eggshell powder (CDP), and calcined duck eggshell powder mixed iron (III) oxide-hydroxide (CDPF) were applied for the effect of contact time, and the results are shown in Fig. 7b. Their lead removal efficiencies increased with increasing of contact time, and the highest lead removal efficiency is found at the constant contact time. Their highest lead removal efficiencies were 98.96% at  www.nature.com/scientificreports/ 4 h for DP, 99.29% at 3 h for DPF, 99.54% at 3 h for CDP, and 99.87% at 2 h for CDPF, respectively. Therefore, they were used as the optimum contact time of DP, DPF, CDP, and CDPF for the effect of pH.
The effect of pH. The pH values of 1, 3, 5, 7, 9, and 11 of duck eggshell powder (DP), duck eggshell powder mixed iron (III) oxide-hydroxide (DPF), calcined duck eggshell powder (CDP), and calcined duck eggshell powder mixed iron (III) oxide-hydroxide (CDPF) were used for the effect of pH, and the results were presented in Fig. 7c. Their lead removal efficiencies were increased with the increase of pH values from 1 to 5, then they were decreased. At pH < 5, the increase of proton (H + ) at pH 1-3 affected low lead adsorptions of all materials because of the competition of H + and Pb (II) ions (Pb 2+ ) agreed with the previous studies 14, 16,54 . At pH > 5, their lead removal efficiencies were decreased because the hydroxide formation of lead such as PbOH + (aq), Pb 2 (OH) 3 + (aq), Pb(OH) 2 (aq) similarly reported by a previous study 55 including the occurrence of lead precipitation (Pb(OH) 2 (s)) resulted to lead removals at high pH values. The highest lead removal efficiencies of all materials were found at pH 5 for 95.12%, 96.78%, 98.41%, and 99.76% for DP, DPF, CDP, and CDPF, respectively. These results corresponded to the results of pH pzc in this study and other studies that pH > 4 illustrated the highest lead removal efficiency related to pH pzc of lead removals in wastewater 6,14,28,39,56 . Therefore, pH 5 was used as the optimum pH of DP, DPF, CDP, and CDPF for the effect of concentration.
The effect of initial lead concentration. Initial lead concentrations from 10 to 70 mg/L of duck eggshell powder (DP), duck eggshell powder mixed iron (III) oxide-hydroxide (DPF), calcined duck eggshell powder (CDP), and calcined duck eggshell powder mixed iron (III) oxide-hydroxide (CDPF) were applied for the effect of initial lead concentration, and the results are shown in Fig. 7d. Their lead removal efficiencies of duck eggshell materials were decreased with the increasing of initial lead concentration from 10 to 70 mg/L resulting from lack active sites for adsorb lead ions similarly found by other studies 6,14,28,39,45,51,56 . Lead removal efficiencies at 50 mg/L of DP, DPF, CDP, and CDPF were 98.35%, 98.94%, 99.04%, and 99.24%, respectively, and CDPF demonstrated a higher lead removal efficiency than others.
In conclusion, 15 g/L, 4 h, pH 5, 50 mg/L, 10 g/L, 3 h, pH 5, 50 mg/L, 7.5 g/L, 3 h, pH 5, 50 mg/L, and 5 g/L, 2 h, pH 5, 50 mg/L, respectively were the optimum conditions in dose, contact time, pH, and concentration of DP, DPF, CDP, and CDPF, so CDPF demonstrated the highest lead removal efficiency at high lead removal of 99.24% than other materials because it spent less material dosage and contact time than others. In addition, they could be arranged in high material efficiency to low being CDPF > CDP > DPF > DP. Therefore, adding iron (III) oxide-hydroxide along with the calcination process improved material efficiency, and CDPF was a potential material to apply in the wastewater treatment system. Adsorption isotherms. The adsorption patterns of duck eggshell powder (DP), duck eggshell powder mixed iron (III) oxide-hydroxide (DPF), calcined duck eggshell powder (CDP), and calcined duck eggshell powder mixed iron (III) oxide-hydroxide (CDPF) for lead adsorptions were identified by linear and nonlinear models of Langmuir, Freundlich, Temkin, and Dubinin-Radushkevich models. For linear models, Langmuir, Freundlich, Temkin, and Dubinin-Radushkevich isotherms were plotted by C e /q e versus C e , log q e versus log C e , q e versus ln C e , and ln q e versus ε 2 , respectively. For nonlinear models, all isotherms were plotted by C e versus q e. The plotting graph results are illustrated in Fig. 8a-h, and the equilibrium isotherm parameters are illustrated in Table 5.
For linear models, the Langmuir maximum adsorption capacities (q m ) of DP, DPF, CDP, and CDPF were 4.655, 7.358, 9.643, and 14.205 mg/g, and Langmuir adsorption constants (K L ) of DP, DPF, CDP, and CDPF were 2.672, 3.259, 4.548, and 6.579 L/mg. For Freundlich isotherm, the 1/n values of DP, DPF, CDP, and CDPF were 0.405, 0.410, 0.417, and 0.422. Freundlich adsorption constants (K F ) of DP, DPF, CDP, and CDPF were 2.888, 5.138, 7.528, and 11.402 (mg/g)(L/mg) 1 For R 2 value consideration, since R 2 values of DP and CDP in both linear and nonlinear Langmuir models were higher than Freundlich, Temkin, and Dubinin-Radushkevich models, its adsorption patterns corresponded to Langmuir isotherm relating to physical adsorption. While R 2 values of DPF and CDPF in both linear and  Moreover, the comparison of the maximum adsorption capacity (q m ) value of eggshell adsorbents for lead adsorption is illustrated in Table 6. All duck eggshell materials in this study had a higher q m value than the studies of Alamillo-López et al. 64 , Bayu et al. 65 , Kasirajan et al. 66 , and Peigneux et al. 30 . In addition, CDPF also had a higher q m value than the study of Hajji and Mzoughi 54 .
Adsorption kinetics. The adsorption kinetics of duck eggshell powder (DP), duck eggshell powder mixed iron (III) oxide-hydroxide (DPF), calcined duck eggshell powder (CDP), and calcined duck eggshell powder mixed iron (III) oxide-hydroxide (CDPF) for lead adsorptions were investigated to describe by linear and nonlinear kinetic models of pseudo-first-order kinetic, pseudo-second-order kinetic, elovich, and intraparticle diffusion. For linear models, they were plotted by ln (q e − q t ) versus time (t), t/q t versus time (t), q t versus ln t, and q t versus time (t 0.5 ) for pseudo-first-order kinetic, pseudo-second-order kinetic, elovich, and intraparticle diffusion models, respectively. For nonlinear models, they were plotted by q t versus time (t). The plotting graph results are illustrated in Fig. 9a-h, and the adsorption kinetic parameters are presented in Table 7. Table 5. The comparison of linear and nonlinear isotherm parameters for lead adsorptions on duck eggshell powder (DP), duck eggshell powder mixed iron (III) oxide-hydroxide (DPF), calcined duck eggshell powder (CDP), and calcined duck eggshell powder mixed iron (III) oxide-hydroxide (CDPF). www.nature.com/scientificreports/ For linear models, the adsorption capacities (q e ) of DP, DPF, CDP, and CDPF on a pseudo-first-order kinetic model were 2.641, 3.186, 3.805, and 8.144 mg/g, and their reaction of rate constants (k 1 ) were 0.016, 0.018, 0.019, and 0.020 min −1 . For a pseudo-second-order kinetic model, the adsorption capacities (q e ) of DP, DPF, CDP, and CDPF were 3.505, 5.015, 6.892, and 10.730 mg/g, and their reaction of rate constants (k 2 ) were 0.014, 0.015, 0.018, and 0.025 g/mg min. For the elovich model, the initial adsorption rates (α) of DP, DPF, CDP, and CDPF were 0.671, 0.712, 0.830, and 0.857 mg/g/min, and their extents of surface coverage (β) were 1.619, 0.935, 0.842, and 0.557 g/mg. For the intraparticle diffusion model, the reaction of rate constants (k i ) of DP, DPF, CDP, and CDPF were 0.153, 0.217, 0.281, and 0.432 mg/g min 0.5 , and their constant C i values were 0.963, 1.737, 2.431, and 3.455 mg/g. For nonlinear models, the adsorption capacities (q e ) of DP, DPF, CDP, and CDPF on a pseudo-first-order kinetic model were 2.850, 3.310, 3.954, and 8.217 mg/g, and their reaction of rate constant (k 1 ) were 0.017, 0.020, 0.021, and 0.022 min −1 . For a pseudo-second-order kinetic model, the adsorption capacities (q e ) of DP, DPF, CDP, and CDPF were 3.520, 5.024, 6.998, and 10.792 mg/g, and their reaction of rate constants (k 2 ) were 0.017, 0.019, 0.023, and 0.030 g/mg min. For the elovich model, the initial adsorption rates (α) of DP, DPF, CDP, and For R 2 value consideration, since R 2 values of DP, DPF, CDP, and CDPF in both linear and nonlinear pseudosecond-order kinetic models were higher than the pseudo-first-order kinetic, elovich, and intraparticle diffusion models, so their adsorption rate and mechanism of both materials corresponded to a pseudo-second-order kinetic model which was chemisorption process with heterogeneous adsorption. Finally, it also recommended plotting both linear and nonlinear kinetic models for protecting against data mistranslations 34,57-63 . Desorption experiments. Before duck eggshell materials are used in industrial applications, it is necessary to estimate the cost and economics of them and whether they can be reused. As a result, the desorption experiments investigated the possible reuse of duck eggshell materials for lead adsorption. The adsorption-desorption  Fig. 10a-d. In Fig. 10a, DP could be reused in 5 cycles with high adsorption and desorption in ranges of 73.37-98.41% and 67.04-96.09%, respectively which adsorption and desorption were decreased by approximately 25% and 29%, respectively. For DPF, it also confirmed to be reusability in 5 cycles with high adsorption and desorption in ranges of 79.94-98.97% and 72.38-96.43%, respectively which adsorption and desorption were decreased by approximately 19% and 24%, respectively shown in Fig. 10b. For CDP could be reused in 5 cycles with high adsorption and desorption in ranges of 85.10-99.12% and 78.66-96.73%, respectively which adsorption and desorption were decreased by approximately 14% and 18%, respectively shown in Fig. 10c. For CDPF, it also confirmed to be reusability in 5 cycles with high adsorption and desorption in ranges of 89.49-99.54% and   Fig. 10d. Therefore, all duck eggshell materials could be reused more than 5 cycles by more than 73%.

The possible mechanisms of lead adsorption by duck eggshell materials
The possible mechanisms of lead adsorptions on duck eggshell powder (DP), duck eggshell powder mixed iron (III) oxide-hydroxide (DPF), calcined duck eggshell powder (CDP), and calcined duck eggshell powder mixed iron (III) oxide-hydroxide (CDPF) were explained by referring idea from the study of Praipipat et al. 14 shown in Fig. 11a 3 . For electrostatic interaction, the surface charge of the adsorbent plays an important role in lead adsorption which depends on the pH of the solution. In addition, the point of zero charge (pH pzc ) of the adsorbent is used to indicate which charge of the adsorbent surface is. If the pH solution is lower than pH pzc (pH solution < pH pzc ), the surface charge of the adsorbent is positively charged which affects low lead adsorption because of the competition of lead (II) ions (Pb 2+ ) and proton (H + ) at an acidic pH condition. As a result, the high lead adsorption should be found at the pH of solution higher than pH pzc (pH solution > pH pzc ) with a negatively charged of adsorbent surface. Since the pH pzc of DP, DPF, CDP, and CDPF were 4.58, 5.31, 5.96, and 6.75, their lead adsorptions should occur at pH of solution > pH

Conclusion
Duck eggshell powder (DP), duck eggshell powder mixed iron (III) oxide-hydroxide (DPF), calcined duck eggshell powder (CDP), and calcined duck eggshell powder mixed iron (III) oxide-hydroxide (CDPF) were successfully synthesized. CDPF demonstrated the highest specific surface area and pore volume with the smallest pore size than other materials, so the calcination process along with adding iron (III) oxide-hydroxide helped to increase specific surface area and pore volume with decreasing pore size which supports a high lead adsorption. In addition, all materials were classified as mesoporous materials with a range pore size of 2-50 nm. DP and DPF demonstrated the semi-crystalline structures with specific calcium carbonate peaks, whereas CDP and CDPF illustrated the semi-crystalline structures with specific calcium oxide peaks. In addition, the specific iron (III) oxide-hydroxide was detected in only DPF and CDPF because of the addition of iron (III) oxide-hydroxide. Their surface morphologies were rough with irregular shapes, and the additional iron (III) oxide-hydroxide did not affect changing their surface characteristic. All materials were found carbon (C), oxygen (O), and calcium (Ca). Iron (Fe), sodium (Na), and chloride (Cl) were only found in DPF and CDPF from using chemicals in a process of addition of iron (III) oxide-hydroxide. In addition, they also found iron distribution on DPF and CDPF surfaces. They consisted of carbon (C), oxygen (O), and calcium (Ca), whereas iron (Fe), sodium (Na), and chloride (Cl) were found only in DPF and CDPF which could be confirmed the successful addition of iron (III) oxide-hydroxide in both materials. Three main function groups of O-H, C=O, and C-O were found in all www.nature.com/scientificreports/ materials similar found in other studies of eggshells, whereas Fe-O was only found in DPF and CDPF because of the addition of iron (III) oxide-hydroxide. The point of zero charges (pH pzc ) of DP, DPF, CDP, and CDPF were 4.58, 5.31, 5.96, and 6.75, respectively, so the calcination process and addition of iron (III) oxide-hydroxide increased pH pzc of materials. For batch experiments, the optimum conditions of DP, DPF, CDP, and CDPF were 15 g/L, 4 h, pH 5, 50 mg/L, 10 g/L, 3 h, pH 5, 50 mg/L, 7.5 g/L, 3 h, pH 5, 50 mg/L, and 5 g/L, 2 h, pH 5, 50 mg/L, respectively, and their lead removal efficiencies were 98.35%, 98.94%, 99.04%, and 99.24%, respectively. Thus, CDPF illustrated a higher lead removal efficiency than other materials because it spent less adsorbent dosage and contact time than DP, DPF, and CDP. Thus, adding iron (III) oxide-hydroxide along with the calcination process improved material efficiencies for lead adsorption. For the isotherm study, the Langmuir model was the best-fit model for DP and CDP explained by a physical adsorption process. While the Freundlich model was a good fit model for DPF and CDPF described by a physicochemical adsorption process. For the kinetic study, a pseudo-second-order kinetic model was the best-fit model for all materials related to a chemisorption process with heterogeneous adsorption. Moreover, all duck eggshell materials could reuse for more than 5 cycles for lead adsorption of more than 73%. As a result, all duck eggshell materials were high-potential materials for lead adsorption in an aqueous solution, and CDPF demonstrated the highest lead removal efficiency. Therefore, CDPF was suitable to apply for industrial wastewater treatment applications in the future. For future works, the continuous flow study and the competing ions such as sodium (Na + ) and magnesium (Mg 2+ ) contaminated in real wastewater are recommended to study for confirming the specific lead adsorption by duck eggshell materials before applying in industrial applications.

Data availability
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