Use of Pb 2+ as a Selective Activator in Selective Flotation Separation of Specularite, Aegirine, and Chlorite: A DFT Study

: Despite being one of the main sources of iron, specularite is often associated with gangue minerals such as aegirine and chlorite. Flotation separation is challenging in the mineral processing industry because of the similar surface properties of specularite, aegirine, and chlorite. This study investigates the role and selective activation mechanism of Pb 2+ in the ﬂotation separation of specu-larite, aegirine, and chlorite using micro-ﬂotation experiments, solution chemistry calculations, zeta potential analysis, and the density functional theory (DFT). The results of the micro-ﬂotation experiments show that the addition of lead ions can signiﬁcantly improve the ﬂoatability of specularite, but has little impact on the ﬂoatability of aegirine and chlorite. Additionally, the solution chemistry calculations results show that PbOH + is the main component of selectively activated specularite. The zeta potential analysis shows that Pb 2+ is more inclined to adsorption on the surface of specularite, and that more collectors are adsorbed on the surface of specularite after the addition of Pb 2+ . Finally, the DFT calculations show that different chemical bonds are formed during the interaction between CuOH + and the mineral surface, resulting in different adsorption energies.


Introduction
Iron has a wide range of industrial applications. In recent years, the demand for and consumption of high-quality iron ores have shown a continuous growth trend with the continuous development of the world economy, deepening resource development, and continuous expansion of the field of iron applications [1,2]. Consequently, high-grade and easily processed iron ore resources are gradually being exhausted, and the efficient development and utilization of low-grade, complex, and refractory iron ore resources has gradually attracted attention [3,4].
Specularite is one of the main sources of iron and an indispensable mineral resource [5]. Specularite is a common iron-bearing mineral with the chemical formula Fe 2 O 3 and a cubic crystal system. Specularite is rich in impurities and is often associated with other gangue minerals such as aegirine and chlorite [6][7][8]. Aegirine (NaFeSi 2 O 6 ) is a chainlike iron-containing silicate mineral with a monoclinic system comprising long columnar or needle-shaped crystals [9]. The chemical formula of chlorite can be expressed as Y 3 [Z 4 O 10 ](OH) 2 ·Y 3 (OH) 6 , which is a general term for monoclinic, triclinic, or orthorhombic

Materials
The specularite, aegirine, and chlorite ore samples used in this investigation were obtained from mining locations in Yunnan, China. The ore samples were broken down into fragments having a size of 2 mm. To obtain pure samples, impure particles were manually removed under a microscope. The samples were then graded to produce two particle fractions (38-74 µm and 38 µm) by grinding them using a three-headed grinder. The 38-74 µm fraction was used for the micro-flotation experiments, whereas the 38 µm fraction was employed for the thorough mechanistic analyses. The X-ray diffraction (XRD) patterns of the pure samples are shown in Figure 1. The results of this study demonstrate the high purity of the samples, which allows them to be classified as pure individual minerals. 38-74 µm fraction was used for the micro-flotation experiments, whereas the 38 µm fraction was employed for the thorough mechanistic analyses. The X-ray diffraction (XRD) patterns of the pure samples are shown in Figure 1. The results of this study demonstrate the high purity of the samples, which allows them to be classified as pure individual minerals. 10 20 All the reagents used in the tests were of analytical grade. NaOL was used as the collector and lead nitrate (Pb(NO3)2) was used as the activator. The solution pH was modified using 0.1 mol/L NaOH or H2SO4 solutions.

Micro-Flotation Experiments
An RK/FGC5-35 flotation machine was used to conduct micro-flotation investigations on the single minerals under an air flow rate of 15 cm 3 /min and a stirring speed of 1600 rpm. The examination was conducted as follows: (1) the flotation tank was filled with All the reagents used in the tests were of analytical grade. NaOL was used as the collector and lead nitrate (Pb(NO 3 ) 2 ) was used as the activator. The solution pH was modified using 0.1 mol/L NaOH or H 2 SO 4 solutions.

Micro-Flotation Experiments
An RK/FGC5-35 flotation machine was used to conduct micro-flotation investigations on the single minerals under an air flow rate of 15 cm 3 /min and a stirring speed of 1600 rpm. The examination was conducted as follows: (1) the flotation tank was filled with 60 mL of deionized water, 2 g of the mineral sample, and pH-modifying solutions to change the pH of the pulp. (2) After stirring for two minutes, lead ions were added followed by NaOL.
(3) A manual froth scraper was then used to collect the concentrate after agitation for 3 min. (4) Finally, the tailings and concentrate were filtered, dried, and weighed. The flotation recovery (%) of minerals was calculated as follows: where m 1 and m 2 are the masses of the concentrate and tailings, respectively, and each test was repeated three times. To create samples for examination in future studies, the optimal depressant concentration was determined in the micro-flotation experiments. Visual MINTEQ (version 3.1) software was used to calculate the hydrolytic component distribution of the lead ions in the pulp systems at different pH values. Visual MINTEQ software is widely used to simulate the equilibrium of ions and minerals in environmental water equilibrium solutions. It can theoretically calculate the interaction between chemical substances using thermodynamic data such as equilibrium constants and the Gibbs free energy to determine the morphological distribution of chemical substances through mass-action expressions, thereby predicting the adsorption mode of metal ions on the mineral surface.

Zeta Potential Experiments
The zeta potential of the specularite sample was assessed at 20 • C using a Malvin Zetasizer (Nano-ZS900; Malvin & Co., Malvern, UK). The typical background electrolyte, KCl, was used (5 × 10 −3 mol/L). Each experiment involved the addition of 100 mg of a mineral sample to 100 mL of a potassium chloride solution and stirring the mixture using a magnetic stirrer. After adjusting the pH to the correct level, the solution was then treated for 6 min under a predetermined concentration of the reagent (copper ions or NaOL) and at a predefined pH level. Subsequently, the suspension was left standing to allow the larger particles to settle. The zeta potential at room temperature was then determined by pouring the suspension's tiny mineral particles into a measurement device. At least three measurements were made, and the average zeta potential was calculated.

DFT Details
Density functional theory (DFT) computations of the flotation reagent adsorption systems on the mineral surfaces were performed using the CASTEP program in Material Studio 8.0 [23]. The electron exchange correlation was described using the Perdew-Burke-Ernzerhof (PBE) function and generalized gradient approximation (GGA), and the interaction between the ions and valence electrons was described using the ultrasoft pseudopotential (USPP). Brillouin zone integrations were performed using the Monkhorst-Pack technique with a (2 × 2 × 1) k-point grid and plane wave cutoff energy of 400 eV. The self-consistent field convergence criterion was set to 1.0 × 10 −6 eV/atom. The Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm and the following convergence conditions were used for geometry optimization: a maximum atom displacement of 1 × 10 −4 nm and total energy convergence within 1.0 × 10 −5 eV/atom.
technique with a (2 × 2 × 1) k-point grid and plane wave cutoff energy of 400 eV. The selfconsistent field convergence criterion was set to 1.0 × 10 −6 eV/atom. The Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm and the following convergence conditions were used for geometry optimization: a maximum atom displacement of 1 × 10 −4 nm and total energy convergence within 1.0 × 10 −5 eV/atom. The surfaces of specularite (001), aegirine (110), and chlorite (001) were chosen as the research objects, and a (2 × 2 × 1) supercell model with periodic borders was built for the simulation to guarantee unrestricted adsorption. Furthermore, the crystal structure of specularite, as shown in Figure 2, was obtained by optimizing the above parameters, where a = b = 9.45 Å, c = 13.75 Å, α = β = 90°, and γ = 120°.   The crystal structure of chlorite, as shown in Figure 4, was obtained by optimizing the above parameters, where a = 10.0 Å, b = 10,14 Å, c = 27.27 Å, α = β = 90°, and γ = 60°.  The crystal structure of chlorite, as shown in Figure 4, was obtained by optimizing the above parameters, where a = 10.0 Å, b = 10,14 Å, c = 27.27 Å, α = β = 90°, and γ = 60°. For structural optimization, improved metal ion ligands were added to the mineral surfaces to produce a stable adsorption structure. The exchange-correlation function, pseudopotential approach, cutoff energy, and convergence criteria utilized for calcite crystal calculations were applied for energy calculations and geometry optimization of the surface models and interaction systems. To analyze the interaction of the metal ion ligands with the mineral surface, Einteraction, which is related to the adsorption energy, was calculated as follows: where E1 is the single-point energies of the metal ion ligand, E2 is the single-point energy of the mineral crystal, and Etotal is the total energy of the interaction system. Therefore, a stable interaction was represented by a negative Einteraction. Moreover, a higher negative energy produces a stronger connection and better inhibitory effect [24,25]. For structural optimization, improved metal ion ligands were added to the mineral surfaces to produce a stable adsorption structure. The exchange-correlation function, pseudopotential approach, cutoff energy, and convergence criteria utilized for calcite crystal calculations were applied for energy calculations and geometry optimization of the surface models and interaction systems. To analyze the interaction of the metal ion ligands with the mineral surface, E interaction , which is related to the adsorption energy, was calculated as follows: where E 1 is the single-point energies of the metal ion ligand, E 2 is the single-point energy of the mineral crystal, and E total is the total energy of the interaction system. Therefore, a stable interaction was represented by a negative E interaction . Moreover, a higher negative energy produces a stronger connection and better inhibitory effect [24,25].

Micro-Flotation Results
The effects of the activator concentration (1, 2, 5, 10, and 15 mg/L) and pulp pH on the flotation behavior of the three minerals using NaOL as the collector and Pb 2+ as the activator are shown in Figure 5.
As shown in Figure 5a, under natural pH conditions (pH = 6-7), the recovery rates of specularite, aegirine, and chlorite without the addition of Pb 2+ are 68.26, 2.07, and 3.16%, respectively. After the addition of Pb 2+ , the recovery rates of all three minerals increased with increasing Pb 2+ concentration. When the Pb 2+ concentration is more than 10 mg/L, the recovery rate of specularite stabilizes. As shown in Figure 5b, the maximum difference in the floatability of specularite and the two types of gangue minerals occurs when the Pb 2+ concentration is 10 mg/L and the pulp pH is 8. At this point, the recovery rates of specularite, aegirine, and chlorite are 91.69, 10.25, and 5.78%, respectively. These results indicate that the addition of Pb 2+ can significantly improve the floatability of specularite, but has little effect on the floatability of aegirine and chlorite. In other words, Pb 2+ can selectively activate the specularite.

Micro-Flotation Results
The effects of the activator concentration (1, 2, 5, 10, and 15 mg/L) and pulp pH on the flotation behavior of the three minerals using NaOL as the collector and Pb 2+ as the activator are shown in Figure 5.

Solution Chemistry Calculations
To explore the morphology and content of the activator lead ions in the solution, Visual MINTEQ (Version 3.1) software was used to calculate the effect of the pH on the morphology and lead ion content in each component of the solution system, and the results are shown in Figure 6.

Solution Chemistry Calculations
To explore the morphology and content of the activator lead ions in the solution, Visual MINTEQ (Version 3.1) software was used to calculate the effect of the pH on the morphology and lead ion content in each component of the solution system, and the results are shown in Figure 6. At a pH of 6, the component content is mainly PbOH + and follows the order: PbOH + > Pb 2+ > Pb(OH)2(aq) > Pb2(OH)3 + > Pb(OH)3 − , as shown in Figure 6; this indicates that PbOH + may be the main component of the selectively activated specularite. Based on the calculated ion products, we infer that the chemical reactions occurring in solution are as follows: Pb + 3OH ⇋ Pb OH (7) Figure 6. Effects of the pH on the lead speciation in the pulp solution system.
At a pH of 6, the component content is mainly PbOH + and follows the order: Figure 6; this indicates that PbOH + may be the main component of the selectively activated specularite. Based on the calculated ion products, we infer that the chemical reactions occurring in solution are as follows:

Zeta Potential Analysis
The adsorption of reagents can lead to changes in the charge of the specularite surface. Therefore, zeta potential testing was used to evaluate the charge changes on the surface of a mineral. Figure 7 shows the relationship between the zeta potential and pH of specularite, aegirine, and chlorite when Pb 2+ was used as an activator. Figure 7a shows that the isoelectric point (IEP) of specularite occurs at pH of 4.4. After adding NaOL, the surface potential of specularite decreases over the entire pH range, and the IEP shifts to 3.7. This is mainly because NaOL is a polar molecule that adsorbs and replaces water molecules on the mineral surface and arranges them directionally, thereby forming an additional adsorption dipole layer that changes the interphase potential difference between the remaining charges on the mineral surface. Consequently, a negative shift occurs in the mineral surface potential. After treatment with Pb 2+ , the potential of the specularite shifts significantly and positively over the entire pH range, with an IEP of 8.9, indicating that Pb 2+ was adsorbed onto the surface of the specularite. After simultaneous treatment with NaOL and Pb 2+ , the zeta potential of specularite decreased significantly over the entire pH range. Additionally, its IEP shifted from 8.9 to 5.1, indicating that a large amount of NaOL was adsorbed onto the surface of the specularite after lead ion activation.
Comparing the zeta potential changes of natural specularite and specularite treated with Pb 2+ before and after NaOL treatment, the zeta potential difference of specularite treated with lead ions is greater than that of natural specularite, particularly in the pH range of 6-8. This indicates that more oleic acid species were adsorbed on the surface of specularite after lead ion treatment, which may have been due to the increase in the number of reaction sites on the surface of specularite after treatment with Pb 2+ . Consequently, the adsorption of oleic acid substances on the surface of the modified minerals was promoted and the hydrophobicity of the specularite particles was improved.

Zeta Potential Analysis
The adsorption of reagents can lead to changes in the charge of the specularite surface. Therefore, zeta potential testing was used to evaluate the charge changes on the surface of a mineral. Figure 7 shows the relationship between the zeta potential and pH of specularite, aegirine, and chlorite when Pb 2+ was used as an activator.  Figure 7a shows that the isoelectric point (IEP) of specularite occurs at pH of 4.4. After adding NaOL, the surface potential of specularite decreases over the entire pH range, and the IEP shifts to 3.7. This is mainly because NaOL is a polar molecule that adsorbs and replaces water molecules on the mineral surface and arranges them directionally, thereby forming an additional adsorption dipole layer that changes the interphase potential difference between the remaining charges on the mineral surface. Consequently, a negative shift occurs in the mineral surface potential. After treatment with Pb 2+ , the potential of the specularite shifts significantly and positively over the entire pH range, with an IEP of 8.9, indicating that Pb 2+ was adsorbed onto the surface of the specularite. After simultaneous treatment with NaOL and Pb 2+ , the zeta potential of specularite decreased significantly over the entire pH range. Additionally, its IEP shifted from 8.9 to 5.1, indicating that a large amount of NaOL was adsorbed onto the surface of the specularite after lead ion activation. Comparing the zeta potential changes of natural specularite and specularite treated with Pb 2+ before and after NaOL treatment, the zeta potential difference of specularite treated with lead ions is greater than that of natural specularite, particularly in the pH range of 6-8. This indicates that more oleic acid species were adsorbed on the surface of specularite after lead ion treatment, which may have been due to the increase in the number of reaction sites on the surface of specularite after treatment with Pb 2+ . Consequently, the adsorption of oleic acid substances on the surface of the modified minerals was promoted and the hydrophobicity of the specularite particles was improved.
As shown in Figure 7b,c, the zeta potential changes of the aegirine and chlorite treated with sodium oleate or Pb 2+ are relatively small over the entire pH range compared with those of specularite. This indicates that the addition of Pb 2+ has a small impact on the adsorption quantity of sodium oleate on the surface of aegirine and chlorite.

DFT Results
Using the above research methods, the mechanism of action of lead ions and their effects on the adsorption of the NaOL collector on the mineral surfaces were analyzed. As shown in Figure 7b,c, the zeta potential changes of the aegirine and chlorite treated with sodium oleate or Pb 2+ are relatively small over the entire pH range compared with those of specularite. This indicates that the addition of Pb 2+ has a small impact on the adsorption quantity of sodium oleate on the surface of aegirine and chlorite.

DFT Results
Using the above research methods, the mechanism of action of lead ions and their effects on the adsorption of the NaOL collector on the mineral surfaces were analyzed. However, the underlying mechanisms remain unclear. Therefore, DFT was used to clarify the mechanisms of the interactions between the agents and mineral surfaces from an atomic point of view. The results of the solution chemistry calculations indicate that PbOH + may be the main component of the selectively activated specularite. Therefore, this section discusses the adsorption configuration of PbOH + on the mineral surface, further revealing the selective activation mechanism of metal ion activators on specularite. According to the calculation results, PbOH + can interact with the O atom and the Fe atom on the surface of specularite to form three chemical bonds, Fe 1 -O 1 , Pb 1 -O 2 , and Pb 1 -O 3 , with bond lengths of 1.922, 2.647, and 2.661 Å, and bond populations of 0.29, 0.05, and 0.04, respectively. The adsorption energy of the interaction between PbOH + and specularite is −3.58 eV, indicating that the reaction occurred spontaneously. Figure 8 and Table 1 show the adsorption configuration and bonding characteristics of PbOH + on the surface of specularite.
atomic point of view. The results of the solution chemistry calculations indicate that PbOH + may be the main component of the selectively activated specularite. Therefore, this section discusses the adsorption configuration of PbOH + on the mineral surface, further revealing the selective activation mechanism of metal ion activators on specularite. Figure 8 and Table 1 show the adsorption configuration and bonding characteristics of PbOH + on the surface of specularite.  According to the calculation results, PbOH + can interact with the O atom and the Fe atom on the surface of specularite to form three chemical bonds, Fe1-O1, Pb1-O2, and Pb1-O3, with bond lengths of 1.922, 2.647, and 2.661 Å, and bond populations of 0.29, 0.05, and 0.04, respectively. The adsorption energy of the interaction between PbOH + and specularite is −3.58 eV, indicating that the reaction occurred spontaneously. Figure 9 and Table 2 present the adsorption configuration and bonding characteristics of PbOH + on the aegirine surface.

Adsorption Energy (eV)
Bond Type Bond Length (Å) Popula  According to the calculation results, PbOH + can interact with the O and Fe atoms on the surface of aegirine to form two chemical bonds, Pb 1 -O 2 and Fe 1 -O 1 , with bond lengths of 2.402 Å and 1.965 Å, and bond populations of 0.02 and 0.20, respectively. The adsorption energy of the interaction between PbOH + and aegirine is −1.84 eV, which is lower than that of PbOH + and specularite (−3.58 eV). Figure 10 and Table 3 present the adsorption configuration and bonding characteristics of PbOH + on the chlorite surface.

Adsorption Energy (eV) Bond Type Bond Length (Å) Population −2.29
Pb1-O1 2.269 0.08 According to the calculation results, PbOH + can interact with the O atom on the surface of chlorite, forming a Pb1-O1 bond with a bond length of 2.269 Å and bond population of 0.08. The adsorption energy of the interaction between PbOH + and chlorite is −2.29 eV. These results indicate that the interaction strength between PbOH + and the surface of chlorite is also lower than that of specularite, which may be the main reason why lead ions can selectively activate specularite and have a smaller effect on the flotation of aegirine and chlorite.
To further determine the electron transfer between atoms in the system during the surface bonding process of lead ions with specularite, aegirine, and chlorite, the Mulliken population and charge changes of the relevant atoms in each system were analyzed before and after the action of Pb ions.
The Mulliken populations of the related elements before and after the interaction between PbOH + and the surface of the specularite are shown in Figure 11 and Table 4.  According to the calculation results, PbOH + can interact with the O atom on the surface of chlorite, forming a Pb 1 -O 1 bond with a bond length of 2.269 Å and bond population of 0.08. The adsorption energy of the interaction between PbOH + and chlorite is −2.29 eV. These results indicate that the interaction strength between PbOH + and the surface of chlorite is also lower than that of specularite, which may be the main reason why lead ions can selectively activate specularite and have a smaller effect on the flotation of aegirine and chlorite.
To further determine the electron transfer between atoms in the system during the surface bonding process of lead ions with specularite, aegirine, and chlorite, the Mulliken population and charge changes of the relevant atoms in each system were analyzed before and after the action of Pb ions.
The Mulliken populations of the related elements before and after the interaction between PbOH + and the surface of the specularite are shown in Figure 11 and Table 4.  According to the results, there is a strong interaction between the Fe1 and O1 atoms, and between the Pb1 and O2 atoms, after the adsorption of PbOH + . This is accompanied by an evident shared electron behavior, indicating an interaction between the two forms of Fe-O and Pb-O bonds.
After the interaction between PbOH + and the surface of specularite, the charge of the Fe1 atom on the surface of specularite increased from 0.84 e to 1.02 e, an increase of 0.18 e, and its electron loss mainly occurs in the Fe 4s orbital. The charge of the O1 atom in PbOH + decreased from −0.95 e to −0.97 e, a decrease of 0.02 e, and its electrons are mainly located in the O 2p orbital. These results indicate that the charge in the Fe-O bond formed by the adsorption of PbOH + on the surface of specularite is mainly transferred from the 4s orbital of the Fe1 atom to the 2p orbital of the O1 atom. Moreover, the charge of the O2 atoms on the surface of specularite decreased from −0.58 e to −0.60 e, a decrease of 0.02 e. The charge Figure 11. Electron density difference before and after the interaction between PbOH + and the surface of specularite: (a) before and (b) after the interaction. Table 4. Mulliken population of related atoms before and after the interaction between PbOH + and specularite.

Mulliken Population
Total Charge/e s p d According to the results, there is a strong interaction between the Fe 1 and O 1 atoms, and between the Pb 1 and O 2 atoms, after the adsorption of PbOH + . This is accompanied by an evident shared electron behavior, indicating an interaction between the two forms of Fe-O and Pb-O bonds.
After the interaction between PbOH + and the surface of specularite, the charge of the orbital. The charge of the Pb 1 atom is 0.81 e, and compared to that before adsorption, the electron loss is mainly in the Pb 6p orbital. Based on the charge analysis between the above atoms, when PbOH + is adsorbed on the surface of the specularite, the charge of the Pb-O bond formed by the interaction is mainly transferred from the 6p orbital of the Pb 1 atom to the 2p orbitals of the O 2 and O 3 atoms.
The Mulliken populations of related elements before and after the interaction between PbOH + and the aegirine surface are shown in Figure 12 and Table 5. The charge of the Pb1 atom is 0.81 e, and compared to that before adsorption, the electron loss is mainly in the Pb 6p orbital. Based on the charge analysis between the above atoms, when PbOH + is adsorbed on the surface of the specularite, the charge of the Pb-O bond formed by the interaction is mainly transferred from the 6p orbital of the Pb1 atom to the 2p orbitals of the O2 and O3 atoms. The Mulliken populations of related elements before and after the interaction between PbOH + and the aegirine surface are shown in Figure 12 and Table 5.  After the adsorption of PbOH + , the electronic ability of Fe1 on the aegirine surface is significantly reduced. In addition, there is a clear shared electronic behavior between the Pb1 atom in PbOH + and the O2 atom on the surface of aegirine, indicating that the two interacted to form Fe-O and Pb-O bonds.
After the interaction between PbOH + and the surface of aegirine, the charge of Fe1 on the surface of aegirine increases from 0.82 e to 0.96 e, an increase of 0.14 e, and its electron  After the adsorption of PbOH + , the electronic ability of Fe 1 on the aegirine surface is significantly reduced. In addition, there is a clear shared electronic behavior between the Pb 1 atom in PbOH + and the O 2 atom on the surface of aegirine, indicating that the two interacted to form Fe-O and Pb-O bonds.
After the interaction between PbOH + and the surface of aegirine, the charge of Fe 1 on the surface of aegirine increases from 0.82 e to 0.96 e, an increase of 0.14 e, and its electron loss mainly occurs in the Fe 3d orbital. Additionally, the charge of the O 1 atom in PbOH+ decreases from −0.95 e to −0.98 e, a decrease of 0.03 e, and its electrons are mainly located in the O 2p orbital. These results indicate that the charge in the Fe-O bond formed by the adsorption of PbOH + on the surface of aegirine is mainly transferred from the 3d orbital of the Fe 1 atom to the 2p orbital of the O 1 atom. The charge of the O 2 atom on the surface of aegirine decreases from −0.91 e to −0.93 e, a decrease of 0.02 e, indicating that the electrons of the O atom on the surface of specularite are mainly in the O 2p orbital. The charge of the Pb 1 atom is 1.09 e, and compared to that before adsorption, the electron loss is mainly in the Pb 6p orbital. Based on the charge analysis between the above atoms, when PbOH + is adsorbed on the surface of aegirine, the charge in the Pb-O bond formed by this interaction is mainly transferred from the 6p orbital of the Pb 1 atom to the 2p orbital of the O 2 atom.
The Mulliken populations of the related elements before and after the interaction between PbOH + and the chlorite surface are shown in Figure 13 and listed in Table 6. .09 e, and compared to that before adsorption, the electron loss is mainly in the Pb 6p orbital. Based on the charge analysis between the above atoms, when PbOH + is adsorbed on the surface of aegirine, the charge in the Pb-O bond formed by this interaction is mainly transferred from the 6p orbital of the Pb1 atom to the 2p orbital of the O2 atom. The Mulliken populations of the related elements before and after the interaction between PbOH + and the chlorite surface are shown in Figure 13 and listed in Table 6.  After the adsorption of PbOH + , the electron acquisition ability of the O1 atom on the surface of chlorite is significantly reduced, and there is a clear shared electron behavior between the Pb1 atom and O1 atom on the surface of chlorite, further confirming the formation of the Pb-O bond.  After the adsorption of PbOH + , the electron acquisition ability of the O1 atom on the surface of chlorite is significantly reduced, and there is a clear shared electron behavior between the Pb 1 atom and O 1 atom on the surface of chlorite, further confirming the formation of the Pb-O bond.
After the interaction between PbOH + and the surface of chlorite, the charge of the O 1 atom on the surface of chlorite decreases from −0.52 e to −0.67 e, a decrease of 0.15 e, indicating that the electrons of the O 1 atom on the surface of chlorite are mainly in the O 2p orbital. The charge of the Pb 1 atom in PbOH + is 1.08 e, and compared to that before adsorption, the electron loss is mainly in the Pb 6p orbital. Based on the charge analysis between the above atoms, it can be concluded that when PbOH + is adsorbed on the surface of the green mud, the charge in the Pb-O bond formed by the interaction is mainly transferred from the 6p orbital of the Pb 1 atom to the 2p orbital of the O 1 atom.

Conclusions
In this study, micro-flotation experiments, solution chemistry calculations, zeta potential analysis, and DFT were combined to study the role and selective activation mechanism of Pb 2+ in the flotation separation of specularite, aegirine, and chlorite. The results of the micro-flotation experiments show that Pb 2+ can significantly improve the flotation effect of specularite. After the addition of Pb 2+ , the recovery rates of specularite, aegirine, and chlorite are 90.43, 9.87, and 5.32%, respectively. The solution chemistry calculation results indicate that when the pulp pH is 8, PbOH + is the main component of selectively activated mineral flotation. The zeta potential analysis results show that compared to aegirine and chlorite, Pb 2+ is more inclined to adsorption on the surface of specularite, and after the action of Pb 2+ , more oleic acid species are adsorbed on the surface of specularite. This may be because the number of reaction sites on the surface of specularite increases after treatment with Pb 2+ , promoting the adsorption of oleic acid on the surface of the modified minerals. The DFT results show that PbOH + can interact with the O and Fe atoms on the surface of specularite to form three chemical bonds, Fe 1 -O 1 , Pb 1 -O 2 , and Pb 1 -O 3 , with an adsorption energy of −3.58 eV. Additionally, PbOH + can interact with the O and Fe atoms on the surface of aegirine to form two chemical bonds, Pb 1 -O 2 and Fe 1 -O 1 , with an adsorption energy of −1.84 eV. Finally, PbOH + can also interact with the O atoms on the surface of chlorite to form a Pb-O bond, with an adsorption energy of −2.29 eV. The adsorption energy of the interaction between PbOH + and the surface of specularite is higher than that of aegirine and chlorite. This is the main reason why lead ions can selectively activate the flotation of specularite.