High Gradient Magnetic Separation of Pure Gd₂O₃ Particles from Pure La₂O₃ Particles

Abstract

Rare earth oxides such as La₂O₃ and Gd₂O₃ are abundant in waste optical glass. The separation of rare earth oxides is beneficial to the recycling of rare earth resources. In this study, the rare earth oxide Gd₂O₃ particles were separated from La₂O₃ particles using high gradient magnetic separation, and the influence of different fluid media (i.e., water, anhydrous ethanol, and their mixture) on the separation results was investigated. By using the measured zeta potential of oxide particles in water/ethanol of different pH and water with different dispersants (Na₂SiO₃ 9H₂O, citric acid, Na₂CO₃, and sodium hexametaphosphate), the DLVO (Derjaguin–Landau–Verwey–Overbeek) potential calculations and their analysis applied to high gradient magnetic separation results were also performed. The results showed that using anhydrous ethanol or adding a dispersant in water as a fluid medium can promote the separation of magnetic Gd₂O₃ particles under a high-gradient magnetic field. Among the different conditions, anhydrous ethanol can improve the grade of Gd₂O₃ to 95% from 70% with water. Furthermore, ethanol can be reused after filtration, making it an environmentally friendly fluid medium. Among the four dispersants, sodium hexametaphosphate, Na₂SiO₃, and Na₂CO₃ can also increase the separation rate of La₂O₃ and Gd₂O₃ to about 95%. The effect of citric acid on the separation performance is slightly worse, and the recovery rate of Gd₂O₃ is 80%. This study provides a new reference for selecting a fluid medium for magnetic separation.

1. Introduction

Rare earth elements (REE) refer to the lanthanide elements with atomic numbers 57–71 and include scandium (Sc) and yttrium (Y), which have similar chemical properties. Due to the uniqueness of their 4f valence electron shells [1], they have special electrical, magnetic, thermal, and physicochemical properties. The global demand for rare earth is increasing and exceeds its supply. The primary sources of rare earth are ores [2,3,4,5,6,7], where REE usually exists in the state of +3 valent oxides, and rare earth oxides are their most stable forms.

The rare earth optical glass [8] waste contains 30–60 wt.% rare earth and some other valuable metal elements. Its recycling offers a secondary source of rare earth and is one of the ways to solve the so-called rare earth crisis. Due to the similar physical and chemical properties of REE, it is usually difficult to separate them from each other [9]. The standard extraction methods [10,11,12,13,14] and the ion exchange separation of REE are relatively complex, and the ion exchange cycle is too time-consuming. Some studies used the REDOX method, alkaline leaching, chromatographic separation, and biological separation [15,16,17,18]. Cerium has significant photoredox properties, and Hu et al. [19] studied the photocatalysis. Dtpa-chitosan–silica was used as the stationary phase to separate the following rare earth ion mixtures: Nd³⁺/Ho³⁺, Pr³⁺/Nd³⁺, and Pr³⁺/Nd³⁺/Ho³⁺ by medium-pressure liquid chromatography (MPLC) [20].

High gradient magnetic separation (HGMS) [21] is a unique technology for enriching or removing weakly magnetic particles. The particles are attracted by the magnetic force to overcome the resistance and gravity of the fluid so that they can be separated and recovered. This technology can recover particle size up to a few micron meters [22]. Because of its environmental protection, high efficiency, and simple operation advantages, it is widely used in mineral processing [23,24,25,26], clean energy [27], sewage treatment [28,29], and biological engineering [30], among other fields. The HGMS process uses a magnetic matrix that generates a high magnetic field gradient near magnetic lines in a uniform background magnetic field. In turn, this resulted in a strong magnetic force to separate the magnetic particles from a slurry. The main ways to improve the selectivity of HGMS are the matching and arrangement of magnetic media, the properties and flow of fluid media, material dispersion, and minimizing mechanical entrapment. For the liquid medium, its viscosity, surface tension, specific magnetic susceptibility, pH, and flow state play an important role in improving the efficiency of magnetic separation. For fine particles, heterogeneous aggregation is the main factor negatively affecting mineral separation [21].

For the separation of rare earth oxides, although Chen et al. [31] designed Brønsted acid based on polyols and organic acids, which can be used to dissolve and separate rare earth oxides due to differences in their solubility, this study used the non-dissolved oxide particles’ separation. Therefore, Gd₂O₃ were separated from La₂O₃ by wet high-gradient magnetic separation based on their different magnetic susceptibilities in this study. Furthermore, the effects of water, absolute ethanol, and fluid medium supplemented with different dispersants on the separation of Gd₂O₃ from La₂O₃ by magnetic separation were compared.

2. Experiment

2.1. Materials and Their Characteristics

For the basic study, gadolinium oxide (Gd₂O₃, purity 99.9%), lanthanum oxide (La₂O₃, purity 99.9%), and lanthanum hydroxide (La(OH)₃, purity 99.9%) were utilized in the optimum particle mixture. The optical glass contains a variety of additives, such as boron oxide, lead, zinc oxide, fluorite, and barium oxide, to enhance its ability to transmit light at specific wavelengths. Thus, the magnetic separation of pure oxides is completely different from the behavior that these oxides in the glass matrix may have. To disperse the particles well, the absolute ethanol and the additives in the water of sodium silicate (Na₂SiO₃), sodium carbonate (Na₂CO₃), sodium hexametaphosphate (SHMP, NaPO₃)₆), citric acid (CA, C₆H₈O₇.H₂O), and concentrated nitric acid (HNO₃) were purchased from Shanghai Macklin Biochemical Co., LTD, Shanghai, China.

The particle size and morphology of the samples were observed using the images taken by scanning electron microscopy (SEM) (SU8020, Hitachi, Ltd., Tokyo, Japan), and the particle size was statistically analyzed. As shown in Figure 1, the average particle size of Gd₂O₃ and La₂O₃ were 3.5 μm and 1.5 μm, respectively. If the sample size is too large, the sample needs to be ground. In addition, the magnetic susceptibility of the samples was measured using a vibrating sample magnetometer (VSM) (7410, Lake shore Temperature Co., Columbus, OH, USA). The particle dispersion state by adding reagent in the water/ethanol was observed by optical microscope, and the particle size was measured by dynamic light scattering method (DLS, NanoBrook Omni, Brookhaven Instruments, Holtsville, NY, USA).

2.2. Methods

The high gradient magnetic separator used in this experiment is described in Figure 2. The separator consists of two electromagnetic coils with a stainless steel canister containing a flux-converging element located between magnetic poles and connected with inlet and outlet valves. The dimension of the canister is 200 mm × 50 mm × 25 mm (high × wide × deep). A funnel is supplied for hand-feed operation. Generally, the magnetic polymer media are generally divided into lattice plates, steel rods, steel rings, steel hair, etc. They are all made of magnetic conductive stainless steel. In our experiment, the steel mesh made of SUS (steel use stainless) 430 is used as the magnetic polymer medium. The length and width of the mesh are 225 mm × 49 mm, and the diagonal dimension of the rhomboid hole is 5.1 mm × 2.5 mm. The standard elements of expanded metal sheets have many sharp edges to which the feed material is exposed. Each edge becomes highly induced during operation and provides the necessary high-intensity, high-gradient field to remove the weakly magnetic particles.

Before the experiment, different fluid media needed for the experiment were prepared. The ethanol concentration of the fluid medium used in this experiment was 1, 3, 25, 50 vol% in the water–ethanol mixture or absolute ethanol (100 vol%). NaOH was used to adjust the pH of pure water to 7, 9, 10, 11, or 12, respectively. The dispersants sodium hexametaphosphate (SHMP) [32] 2.5 g, sodium silicate 0.5 g, citric acid (CA) [33] 0.2 g, or sodium carbonate [34] 0.4 g was dissolved in pure water, and 1.5 L of the fluid medium was prepared for each experiment.

The experimental procedure is described in Figure 3. At first, the discharge port valve at the bottom was closed, and the liquid filled in the separation zone, and the magnetic field was turned on by the DC power supply. The total 2 g of the mixture of La₂O₃ and Gd₂O₃ powders at a mass ratio of 1:1 and 200 mL of fluid medium were then put into a 200 mL beaker and stirred thoroughly to make a slurry and then fed into the high gradient magnetic separation (HGMS) zone by opening the bottom discharge valve. The non-magnetic particles were continuously flushed out and recovered as non-magnetic products. Then, the DC power supply was turned off, and the magnetic particles were washed out and collected in the vessels by feeding and rinsing with deionized water. Finally, the non-magnetic and magnetic products were filtered and dried to obtain the oxide powder after magnetic separation. Then, 0.1 g powder of the dried products was dissolved and diluted with nitric acid, and the contents of La and Gd elements were measured by plasma atomic emission spectrometer (ICPS-7510, Shimadzu Co., Tokyo, Japan). In order to analyze the influence principle of dispersant on high gradient magnetic separation, La₂O₃ powder before and after exposure to water was tested by X-Ray Diffractomer (XRD), and La₂O₃ and Gd₂O₃ powder were soaked, filtered, and dried in different dispersant solutions before FTIR tests were conducted.

2.3. Theoretical Basis

In this session, the particle capture on the ferromagnetic matrix between the magnet and competing forces are described from the particle separation point of view. A schematic diagram of major forces on a magnetic particle is shown in Figure 4a. The cylindrical magnetic line with cross-section diameter 2a is in the separation region, where the uniform magnetic field H₀ is applied, and the volume of paramagnetic particles is V. The flow rate of paramagnetic particles is v_0, and the flow rate is perpendicular to the metal wire. The separated particle is passed through a tube in a magnetic fluid medium and subjected to magnetic forces F_mq and F_mr, which depend on the relative effective susceptibility of the fluid medium and the particle itself. In addition, the particles are also subjected to gravity force F_g and hydrodynamic force F_d. Additionally, the interaction forces between particles (containing particle and matrix), such as van der Waals force and electrostatic force of double electric layers. When the magnetic force F_mq is greater than the F_dq + F_gq force, there is enough F_mr, and there is a certain migration time within the force range when the particles can be captured by the magnetic media [21]. Figure 4b shows the magnetization curves of Gd₂O₃ and La₂O₃ particles, and the magnetic susceptibilities of Gd₂O₃ and La₂O₃ are 147 × 10⁻⁶ emu/g and −0.24 × 10⁻⁶ emu/g at 1 T, indicating that Gd₂O₃ has a high magnetic susceptibility, while La₂O₃ is diamagnetic, in agreement with the literature [35]. The paramagnetic Gd₂O₃ can be easily captured on the ferromagnetic wire matrix under a magnetic field.

2.3.1. Magnetic Force

The magnetic force acting on a particle subjected to a magnetic field can be expressed as:

$$F_m={\mathsf{\mu }}_0\mathrm{V}\left({\mathrm{k}}_{\mathrm{p}}-{\mathrm{k}}_{\mathrm{m}}\right)H\mathrm{grad} H$$

(1)

where ${\mathsf{\mu }}_0$ refers to magnetic permeability in free space, H is applied magnetic field intensity in particle volume, grad H is magnetic field gradient, ${\mathrm{k}}_{\mathrm{p}}$ is material volume magnetic susceptibility of magnetic particle, and ${\mathrm{k}}_{\mathrm{m}}$ is material volume magnetic susceptibility of the fluid medium.

As shown in Figure 4a, the radial and tangential components of the magnetic force [36] are expressed by the following equations:

$$F_{mr}=-\frac{1}{3}\mathsf{\pi }{d}^2\left({\mathrm{k}}_{\infty }{H}_0+{\mathrm{fM}}_0\right)H_0\frac{{\mathrm{Da}}^2}{{\mathrm{r}}^3}\left(\cos 2\theta +\frac{{\mathrm{Da}}^2}{{\mathrm{r}}^2}\right)$$

(2)

$$F_{m\theta }=-\frac{1}{3}{d}^2\left({\mathrm{k}}_{\infty }{H}_0+{\mathrm{fM}}_0\right)H_0\frac{{\mathrm{Da}}^2}{{\mathrm{r}}^3}\sin 2\theta$$

(3)

where ${\mathrm{k}}_{\infty }$ is the magnetic susceptibility in the infinite magnetic field, r is the distance between the particle and the central axis of the metal wire, a is the radius of the cross-section of the metal wire, d is particle diameter, and the magnetic field factor $\mathrm{f}$ is given by the following equation:

$$\mathrm{f}=\frac{1}{2{\left(1+\frac{2{\mathrm{Da}}^2}{{\mathrm{r}}^2}\cos 2\theta +\frac{D^2{a}^4}{{\mathrm{r}}^4}\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}$$

(4)

D is the perturbation term of the cylindrical matrix, which can be given by the following equation:

$$D=\frac{2{\mathsf{\pi }\mathrm{M}}_{\mathrm{w}}}{H_0}$$

(5)

where ${\mathrm{M}}_{\mathrm{w}}$ is the magnetization of the matrix.

2.3.2. Fluid Drag Force

Particles are subject to hydrodynamic resistance:

$$F_d=3\mathsf{\pi }\mathsf{\eta }d\left(v_l-v_p\right)$$

(6)

where $v_l$ refers to the flow rate of fluid, $v_p$ refers to the flow rate of particles, and h is the viscosity of the fluid.

2.3.3. Gravitational Force

The gravitational force F_g acting on a particle can be expressed as:

$$F_g=\left({\mathsf{\rho }}_{\mathrm{p}}-{\mathsf{\rho }}_{\mathrm{l}}\right)\mathrm{gV}$$

(7)

where ${\mathsf{\rho }}_{\mathrm{p}}$ and ${\mathsf{\rho }}_{\mathrm{l}}$ are the densities of particles and fluids, respectively.

The components of gravity are expressed by the following equations:

$$F_{gr}=\left({\mathsf{\rho }}_{\mathrm{p}}-{\mathsf{\rho }}_{\mathrm{l}}\right)\mathrm{gVcos}\theta$$

(8)

$$F_{g\theta }=\left({\mathsf{\rho }}_{\mathrm{p}}-{\mathsf{\rho }}_{\mathrm{l}}\right)\mathrm{gVsin}\theta$$

(9)

The particles are retained by the wire, requiring the magnetic force to overcome all other physical forces. The necessary (but not sufficient) conditions are as follows:

$$\{\begin{array}{c}{F}_{mr}\ge F_{gr} \\ F_{m\theta }\ge F_{g\theta }+F_{d\theta }\end{array}$$

(10)

2.3.4. Surface Force

The surface interactions are mainly particle–particle interactions, including electric double-layer interaction, van der Waals interaction, and magnetic dipole interaction.

DLVO (Derjaguin–Landau–Verwey–Overbeek) theory [37,38] and its extension to different particle systems’ so-called heterocoagulation theory state that the interactions between two homogeneous or heterogeneous colloid particles can be expressed by the summation of the electric double layer interaction potential energy V_R and the van der Waals interaction potential energy V_A. The following equation expresses V_R between two heterogeneous spherical particles:

$${\mathrm{V}}_{\mathrm{R}}=\frac{{\mathsf{\epsilon }a}_1{a}_2\left({\phi }_1{}^2+{\phi }_2{}^2\right)}{4\left(a_1+a_2\right)}\left[\frac{2{\phi }_1+{\phi }_2}{{\phi }_1{}^2+{\phi }_2{}^2}\times \ln \frac{1+{\mathrm{e}}^{-\mathsf{\kappa }h}}{1-{\mathrm{e}}^{-\mathsf{\kappa }h}}+\ln \left(1-{\mathrm{e}}^{-2\mathsf{\kappa }h}\right)\right]$$

(11)

where $a_1$ and $a_2$ refer to particle radius, ${\phi }_1$ and ${\phi }_2$ to the surface potential of two heterogeneous particles, $\mathsf{\epsilon }$ to the dielectric constant of the medium, h to the surface distance between the interacting particles, and κ to the Debye–Hückel reciprocal length, which can be described by the following equation:

$$\mathsf{\kappa }=\sqrt{2{\mathrm{nz}}^2{\mathrm{e}}^2/({\mathsf{\epsilon }}_{\mathrm{r}}{\mathsf{\epsilon }}_0\mathrm{kT})}$$

(12)

$$\mathrm{n}=1000{\mathrm{N}}_{\mathrm{A}}\mathrm{C}$$

(13)

where $\mathrm{n}$ is the number concentration of anion or cation in the solution, $\mathrm{z}$ represents the valence of ion, $\mathrm{e}$ represents the electron charge, ${\mathsf{\epsilon }}_{\mathrm{r}}$ represents the relative dielectric constant, ${\mathsf{\epsilon }}_0$ represents the permittivity of vacuum, $\mathrm{T}$ represents the temperature (K), ${\mathrm{N}}_{\mathrm{A}}$ represents the Avogadro number, and $\mathrm{C}$ represents the concentration of anion or cation (mol/L).

The van der Waals interaction potential energy between heterogeneous spherical particles is:

$${\mathrm{V}}_{\mathrm{A}}=-\frac{\mathrm{A}}{6}\mathrm{C}\frac{2a_1{a}_2}{{\mathrm{A}}^2+2\left(a_1+a_2\right)h}+\frac{2a_1{a}_2}{{\mathrm{A}}^2+2\left(a_1+a_2\right)h+4a_1{a}_2}+\ln \frac{h^2+2\left(a_1+a_2\right)h}{h^2+2\left(a_1+a_2\right)h+4a_1{a}_2}$$

(14)

where A is Hamaker’s constant.

The van der Waals interaction potential energy between homogeneous spherical particles is:

$${\mathrm{V}}_{\mathrm{A}}=-\frac{\mathrm{A}}{6}\mathrm{C}\frac{2a_1{}^2}{4a_{1}h+h^2}+\frac{2a_1{}^2}{{(2a_1+h)}^2}+\ln \frac{4a_{1}h+h^2}{{(2a_1+h)}^2}$$

(15)

The potential energy of magnetic dipole interaction between particles is:

$${\mathrm{V}}_{\mathrm{m}}=\frac{8{\mathsf{\pi }\mathsf{\epsilon }}_0{\mathrm{x}H}^2{a}_1{}^6}{9{\left(\mathrm{x}+2a_1\right)}^3}$$

(16)

where H is the external magnetic field intensity, x is the particle volume susceptibility, and ${\mathsf{\epsilon }}_0$ is the vacuum permeability.

The total potential energy of interaction between magnetic and non-magnetic particles can be expressed by Equations (11) + (14). The total potential of interaction between magnetic and similar/homogeneous particles can be expressed by Equations (11) + (15) + (16). The total potential energy between non-magnetic particles can be expressed by Equations (11) and (15). Regulating and controlling the potential energies of these interactions plays an important role in improving the efficiency of magnetic separation and optimizing the properties of fluid media, mainly by regulating the electrochemical properties such as pH. In high-gradient magnetic separation, it is necessary for particles to disperse stably and to reduce mechanical entrapment and blockage. In order for particles to disperse and prevent aggregation, repulsive interactions between them should be dominant.

3. Results and Discussion

3.1. Ethanol as a Fluid Medium

In this experiment, the ethanol concentration of 1, 3, 25, 50, or 100 vol% in the water–ethanol mixture was selected as the fluid medium to study the influence of different ethanol concentrations on magnetic separation. As shown in Figure 5a, when the ethanol concentration was 1, 3, 25, or 50%, the purity/grade of Gd₂O₃ in the magnetic product was about 70%, and the recovery of La₂O₃ was about 55%. However, when absolute ethanol was used, the grade and recovery of La₂O₃ and Gd₂O₃ in the non-magnetic and magnetic products reached 95%. This shows that absolute ethanol has a good dispersive effect on oxide particles. Figure 6 shows the XRD patterns of La₂O₃ particles before and after the experiment that soaked La₂O₃ in water. Through comparative analysis with standard cards and the change in characteristic peak intensities, the initial La₂O₃ particles containing some La(OH)₃ reacted with moisture in the air and generated a small amount of La(OH)₃. In contrast, the soaked La₂O₃ particles showed that most peaks were La(OH)₃. As a fluid medium, aqueous ethanol made La₂O₃ become La(OH)₃ and then was aggregated with Gd₂O₃ by optical micrograph observation. Because La(OH)₃ particles showed that structures such as colloid and Gd₂O₃ were not well dispersed and captured by the matrix irrelevant to their magnetic susceptibilities, the purity of Gd₂O₃ in the magnetic product and the recovery rate of La₂O₃ in the non-magnetic product was low due to the entrapment of undesired particles. On the other hand, in anhydrous ethanol liquid, La₂O₃ did not change to La(OH)₃ by XRD observation. The high grade and recovery rate results were obtained in the HGMS. On the other hand, Gd₂O₃ peaks by XRD did not change initially and after soaking in water.

Figure 5b shows the magnetic separation results obtained with the absolute ethanol at 0.3, 0.6, 0.8, 1, or 1.2 T field strengths. It was found that even at the lowest field strength of 0.3 T, the grades of La₂O₃ in the non-magnetic product and Gd₂O₃ in the magnetic product are about 94%, and the recovery rates of La₂O₃ and Gd₂O₃ are 96.2% and 91.5%, respectively. With the increase in the magnetic field strength, the grade and recovery of both of them improved slightly. When the field strength reaches 1 T, the results tend to be stable, the grade of La₂O₃ and Gd₂O₃ reaches 98% and 94.5%, and the recovery reaches 95.2% and 98%. This shows that using absolute ethanol as a fluid medium can effectively disperse the two oxides and separate them well, even at low field strengths.

Figure 7 shows the zeta potential changes of La₂O₃ and Gd₂O₃ in pure water. The point of zero charges of La₂O₃ and Gd₂O₃ in water are at pH 8.2 and 7.3, respectively. In the higher alkaline region, the zeta potential becomes significantly negative, and each particle can have good dispersion. The zeta potential of oxide in water reaches the lowest value of −28 mV at pH 11. In order to explore the effect of pH on the results of high-gradient magnetic separation, pure water with pH 7, 9, 10, 11, and 12 was selected, as shown in Figure 5c. With the increase in pH, the recovery of La₂O₃ and the purity of Gd₂O₃ increased slightly, reaching the maximum value at pH 11. The recovery of La₂O₃ increased from 54% to 63%, and the grade of Gd₂O₃ increased from 65% to 72%, as shown in Figure 5c.

As shown in Figure 5d, when pure water with 1% ethanol content was used as the fluid medium, the purity of Gd₂O₃ in the magnetic product was stable at 70%, and the recovery of La₂O₃ in the non-magnetic product was about 58%. However, by increasing the pH value, the recovery of La₂O₃ was slightly increased from 58% to 65% at pH 10. Moreover, in this experiment, pH has no obvious effect on the magnetic separation of the two oxides.

3.2. Different Dispersants

3.2.1. Magnetic Separation Results, Zeta Potential, and Infrared Analysis

The results of the magnetic separation of La₂O₃ and Gd₂O₃ particles using four dispersants, SHMP, Na₂SiO₃, CA, and Na₂CO₃, are shown in

Table 1. Results of HGMS with four kinds of dispersants added in water.

Dispersant	Product *	Weight (g)	Grade (%)		Recovery (%)
			La2O3	Gd2O3	La2O3	Gd2O3
SHMP	M	0.437	4.53	95.47	3.78	91.31
	NM	0.615	92.71	7.29	96.22	8.69
Na2SiO3	M	0.8245	3.65	96.35	4.18	99.08
	NM	0.8247	98.94	1.06	95.82	0.92
CA	M	1.1	19.83	80.17	27.96	97.48
	NM	0.603	96.11	3.89	72.04	2.52
Na2CO3	M	0.8345	5.43	94.57	5.63	94.39
	NM	1.01	94.19	5.81	94.37	5.61

*—M = Magnetic product; *—NM = Non-magnetic product.

. With the addition of those dispersants, the grades of Gd₂O₃ were 95.47%, 96.35%, 80.17%, and 94.19%, and the recovery rates were 91.31%, 99.08%, 97.48%, and 94.39%, respectively. The grades of La₂O₃ in the non-magnetic product were 92.71%, 98.94%, 96.11%, and 94.19%, and the recoveries were 96.22%, 95.82%, 72.04%, and 94.37%, respectively. The effect of Na₂SiO₃ and Na₂CO₃ on the grade of the recovered oxide particles is slightly better than that of SHMP, while the effect of CA is relatively poor. However, compared with pure water, the grade of Gd₂O₃ in the magnetic product increased from 65% to 80.17%, and the recovery of La₂O₃ in the non-magnetic product increased from 54% to 72.04%.

The zeta potentials of oxides in pure water and four dispersants are compared in Figure 7. The results showed that the negative surface charge was enhanced with the addition of CA, SHMP, Na₂SiO₃, or Na₂CO₃ dispersant compared with the pure water, and their effect on zeta potential was arranged from high to low. Therefore, the electrostatic repulsion between oxide particles was enhanced in alkaline pH, and thus they can be well dispersed.

Table 2. The pH of four dispersants before and after adding oxide particles and the size of particle mixture at pH 11.

pH and Particle Size	SHMP	Na2SiO3	CA	Na2CO3	Water
Initial pH	6.62	11.25	3.4	10.68	6.7
pH after adding the oxide particle mixture	10.94	11.25	6.75	10.59	7.11
Size of particle mixture at pH = 11 (μm)	1.21	2.51	1.91	2.37	3.33

shows the initial pH values of the aqueous solution of the four dispersants and pure water, as well as the pH values after mixing Gd₂O₃ and La₂O₃ particles evenly, and measured sizes of the oxide particle mixtures at pH 11. The results showed that the initial solution pH of the pure water and SHMP was neutral, while CA was acidic. After adding the oxide particle mixture, their pH increased due to the adsorption of dispersant on the surface of La(OH)₃. With the oxide particle mixture, the pH of CA and pure water was about seven, and that of the other three was about 11. Moreover, when pH is 11, the well-dispersed particle size by adding four kinds of dispersant is smaller than that of the pure water. Therefore, the dispersants play an excellent role in dispersing the oxide particles. In conclusion, SHMP, Na₂SiO₃, Na₂CO_3, and CA can effectively improve the dispersion of La₂O₃ and Gd₂O₃ particles and thus improve the performance of high-gradient magnetic separation.

In order to study the adsorption of dispersant on the surface of lanthanum oxide and gadolinium oxide, infrared spectroscope analysis was carried out on the oxides before and after adding a dispersant. Figure 8a shows the change in the infrared spectrum of La₂O₃ before and after the addition of a dispersant, and the characteristic peak of La₂O₃ is at 643.1 cm⁻¹ [39]. Compared with the infrared spectrum of La₂O₃ before the addition of a dispersant, the asymmetric stretching vibration peak of Si-O-Si appears at 1092.9 cm⁻¹ after sodium silicate addition [40], and the surface free -OH is at 3610.6 cm⁻¹. After sodium carbonate addition, the stretching vibration peak of C-O-C appears at 1089.1 cm⁻¹, the bending vibration peak of C-H appears at 1469.6 cm⁻¹, and the surface free -OH appears at 3610.1 cm⁻¹. Our results shown in Figure 8a confirmed that both sodium silicate and sodium carbonate are adsorbed on the surface of lanthanum oxide particles. Figure 8b shows the change in the infrared spectrum of Gd₂O₃ before and after the addition of a dispersant, and about 553 cm⁻¹ is the characteristic peak of Gd₂O₃ [41]. After the dispersant of sodium hexametaphosphate, sodium silicate, citric acid, or sodium carbonate, the characteristic peaks moved slightly in the direction of a higher wave number (for example, 545 cm⁻¹).

The average particle sizes of Gd2O3 and La2O3 measured using SEM images were 3.5 μm and 1.5 μm, respectively.

3.2.2. DLVO Theory Analysis

DLVO theory determines whether particles attract or repel each other by calculating the total potential energy V_T of the system, i.e., the sum of the electric double layer interaction potential energy V_R and the van der Waals interaction potential energy V_A between two spherical particles (i.e., La₂O₃ and Gd₂O₃ particles in this study). The total potential energy can be a key indicator of particle stability and evaluate whether the particles aggregate or disperse. The combination of Equations (11) and (14) leads to the following equation:

$$\begin{gathered} {\mathrm{V}}_{\mathrm{T}}=\frac{\mathsf{\epsilon }{a}_1{a}_2\left({\phi }_1{}^2+{\phi }_2{}^2\right)}{4\left(a_1+a_2\right)}\left[\frac{2{\phi }_1+{\phi }_2}{{\phi }_1{}^2+{\phi }_2{}^2}\times \ln \frac{1+e^{-kh}}{1-e^{-kh}}+\ln \left(1-e^{-2kh}\right)\right] \\ -\frac{\mathrm{A}}{6}\mathrm{C}\frac{2a_1{a}_2}{{\mathrm{A}}^2+2\left(a_1+a_2\right)h}+\frac{2a_1{a}_2}{{\mathrm{A}}^2+2\left(a_1+a_2\right)h+4a_1{a}_2}+ \ln \frac{h^2+2\left(a_1+a_2\right)h}{h^2+2\left(a_1+a_2\right)h+4a_1{a}_2} \end{gathered}$$

(17)

Using the zeta potential values from Figure 7 and particle radius values (a₁ = a₂) calculated from the particle diameters stated in Table 2, Equation (17) was used to calculate V_T. With the four dispersants, the total interaction energy V_T between lanthanum oxide and gadolinium oxide particles varies with the distance between the two particles, and the results are shown in Figure 9. The highest point on the curve is the repulsive potential barrier. In the existence of a high potential barrier, the particles were well dispersed and liberated, and the height of the barrier often indicates the stability of the colloidal particles. If there is no barrier in the total potential energy, it suggests that the particles can aggregate in water. In the four dispersants, the potential barrier between the La₂O₃ particle and Gd₂O₃ particle increased with the order of CA, Na₂CO₃, Na₂SiO_3, and SHMP. Combined with the results of magnetic separation, it can be seen that the four dispersants can play a certain role in the dispersion of oxide particles. As shown in the separation result of Table 1, Na₂SiO₃, Na₂CO₃, and SHMP addition that had significant potential barriers showed good separation results. However, CA did not show the potential barrier, and thus La₂O₃ and Gd₂O₃ particles can be coagulated; therefore, the separation result was slightly worse than the results obtained with the three other dispersants.

4. Conclusions

This study explored the effects of different fluid media used in HGMS on the dispersion and recovery of La₂O₃ and Gd₂O₃ particles in the view of recycling discarded optical glass. Different contents of ethanol (i.e., 1, 3, 25, and 50 vol% ethanol) in a water–ethanol mixture had no significant effect on the recovery of Gd₂O₃. In contrast, the absolute ethanol as a fluid medium made the recovery of La₂O₃ and Gd₂O₃ reach 97.91% and 94.74%, respectively. Pure water with pH values 7, 9, 10, 11, and 12 were also studied as the fluid medium. With the increase in pH value, the recovery of La₂O₃ and the grade of Gd₂O₃ increased slightly, reaching the maximum value (72% of Gd₂O₃ grade) at a pH value of 11. The recovery of La₂O₃ increased from 54% to 63%, and the purity of Gd₂O₃ increased from 65% to 72%. By using the pure water with 1% ethanol addition as the fluid medium and adjusting the pH value, the grade of La₂O₃ in the non-magnetic product was slightly increased from 60% to 65% when the pH was 10. Adding SHMP, Na₂SiO₃, CA, and Na₂CO₃ to the pure water effectively negatively increased the zeta potential of the oxide particle surface and enhanced the particle dispersion. Thus, the recoveries of Gd₂O₃ were 91.31%, 99.08%, 97.48%, and 94.39%, respectively, and the recoveries of La₂O₃ were 96.22%, 95.82%, 72.04%, and 94.37%, respectively. The DLVO potential energy calculations confirmed that SHMP, Na₂SiO₃, and Na₂CO₃ could effectively improve the dispersion of La₂O₃ and Gd₂O₃ particles and, thus, the performance of magnetic separation. This study provides an environmentally friendly and efficient method for separating rare earth oxides, which is of great significance for recovering and separating rare earth oxides.