Molecular Dynamic Simulation of the Interaction of a Deep Eutectic Solvent Based on Tetraethylammonium Bromide with La³⁺ in Acidic Media

Abstract

In recent years, noticeable progress has been made in the development of alternative extraction systems characterized by greater sustainability. In this context, deep eutectic solvents (DESs) have emerged as a promising alternative to the conventional solvents commonly used in metal extraction. This work focuses on investigating the extraction of lanthanum in an aqueous solution of sulfuric acid using a deep eutectic solvent, employing molecular dynamics simulations (MD). The structural characteristics of the solvent and its interactions with the components of the aqueous solution are explored. In this study, tetraethylammonium bromide (TEABr) is combined with ethylene glycol (EG) to form a DES, in which sodium cyanide (NaCN) is subsequently solubilized. According to the results obtained from the MD simulation, the primary interactions in the DESs are established through hydrogen bonds between the bromine and the hydrogens of the methyl group of tetraethylammonium at 3.5 Å, as well as between the bromine and the hydrogens of the methylene group of ethylene glycol at 3.5 Å. Similarly, the main interactions between the binary DES and sodium cyanide occur through the hydrogens of the hydroxyl group of EG and the carbon of cyanide at 1.7 Å, and between the oxygen of the hydroxyl group of EG and the sodium at 2.5 Å. In the acidic solution, the primary interaction is highlighted between the lanthanum ion and the oxygen of the bisulfate at 2.8 Å. Additionally, it is observed that the interaction between the DES and the aqueous solution occurs between the lanthanum and the oxygen of the hydroxyl group of EG, as well as between the lanthanum and the carbon of cyanide at 4.4 Å. It is important to note that, when increasing the temperature from 25 to 80 °C, the interaction distance between the lanthanum and the carbon of cyanide decreases to 2.4 Å, suggesting a possible correlation with the increase in lanthanum extraction, as experimentally observed. Overall, this study underscores the importance of considering the fundamental structural interactions of the DES with the lanthanum acid solution, providing an essential theoretical basis for future experimental investigations.

1. Introduction

The rare earth elements (REEs) constitute a group of chemical elements encompassing all lanthanides, yttrium, and scandium. Commonly, they are classified into two distinct categories: light rare earth elements (LREEs), comprising from lanthanum to samarium, and heavy rare earth elements (HREEs), spanning from europium to lutetium [1,2,3]. REEs are dispersed throughout the earth’s crust as mixtures in various rock formations such as basalt, granite, gneiss, shale, and silicate rocks [4].

Approximately 95% of the global rare earth resources are concentrated in just three minerals: monazite ((Ce, La, Nd) PO₄), bastnäsite ((Ce, La, Y) CO₃F), and xenotime ((Y, Yb) PO₄). These minerals represent the primary sources for the extraction of rare earth elements [5,6,7]. REEs are crucial components in key technologies for clean energy, such as wind turbines and electric vehicles. Therefore, the energy transition from fossil fuel-based energy to decarbonized energy relies heavily on the intensive use of critical elements like REEs [8], leading to a notable increase in the industrial demand for these elements [9]. It is projected that this demand will grow at an approximate annual rate of 10% during the period 2023–2028 [10].

REEs are typically leached from their processed mineral (concentrate) using aqueous inorganic acids, such as sulfuric or nitric acid [3]. The individual separation of REEs is a technical and economic challenge, often requiring multiple stages of solvent extraction (SX) from loaded leach solutions to achieve commercially viable separations [11]. The SX technique is widely recognized for transferring metal ions from the aqueous phase to an organic solution, which generally contains an extraction agent diluted in a molecular solvent. The back-extraction (or reverse extraction) of the loaded organic phase into an aqueous solution facilitates the concentration of the target metal, ready for selective recovery through methods such as electrodeposition or precipitation [12].

SX has been a subject of academic interest, both from a fundamental perspective, to understand extraction mechanisms [13], and from an applied perspective. Over time, highly efficient solvent-based systems using molecular organic solvents have been developed to treat various aqueous phases containing metals. However, with increasing environmental concerns, it is recognized that molecular organic solvents are toxic and hazardous compounds. Therefore, one of the main challenges lies in conceiving highly efficient extraction systems that adhere to the principles of green chemistry. In this context, there is a growing interest in alternative approaches to conduct extraction processes [14].

In recent years, significant progress has been made in the development of alternative extraction systems with more sustainable characteristics. In this context, deep eutectic solvents (DESs) have emerged as a promising option. DESs are formed through the complexation of an organic salt, typically a quaternary ammonium salt, with a metal salt, a hydrated metal salt, or a hydrogen bond donor (HBD) [15]. DESs can also be prepared by mixing hydrates of metal salts with HBD [16]. The charge delocalization resulting from the formation of these complexes occurs between the anion of the organic salt and the HBD species, leading to a reduction in the lattice energy of the organic salt [15]. This reduction in lattice energy results in a decrease in the melting point of the mixture compared to the individual components [17].

Due to their high polarity, DESs emerge as potential substitutes for traditional aqueous organic solvents in the separation of polar substances. The notable electrical conductivity of DESs, as well as the high solubilities of metals and metal salts in these solvents, position them as favorable compounds for applications in mineral refining, metal extraction in solution, purification by electrodeposition, and metal recovery from primary sources or waste recycling [18].

However, DESs present a series of challenges that limit their potential application in hydrometallurgical processes. One of the main issues associated with DESs is their high viscosity, which impedes mass and heat transfer in these processes. This necessitates specific operational conditions to prevent alterations in the molecular structure of the DESs, which could lead to their decomposition and, consequently, affect the efficiency of the process [19,20]. Furthermore, the design and optimization of DESs require a profound understanding of their physicochemical properties, as well as the interactions between their components and the target metals. These properties and interactions are contingent upon the molecular structure of the DES, which is complex and heterogeneous, thereby influencing the solubility, selectivity, kinetics, and thermodynamics of the hydrometallurgical processes [21].

Molecular dynamics (MD) simulation is a sophisticated computational technique employed to investigate atomic systems by numerically solving Newton’s equations of motion for each atom within the system. This approach offers a microscopic perspective on physical phenomena, facilitating a comprehensive analysis of the molecular interactions and the temporal evolution of the system. In the context of deep eutectic solvents (DESs), MD simulations are utilized to model the structural, dynamic, thermodynamic, and transport properties of these solvents. The atomistic insights into molecular interactions and the prediction of thermodynamic properties derived from MD simulations can significantly complement experimental findings, thereby enhancing our understanding of DESs [22,23,24,25,26]. In this study, to gain in-depth knowledge of the extraction of rare earth elements using deep eutectic solvents, a potentially applicable DES was synthesized for REE extraction. A series of molecular dynamics simulations were conducted to understand the mechanisms involved in the extraction process and how eutectic solvents can enhance extraction efficiency. The results obtained from MD simulations can be employed to optimize extraction conditions and develop more efficient and sustainable methods for extracting rare earth elements.

2. Materials and Methods

2.1. Synthesis of the Deep Eutectic Solvent (DES)

Considering previous experiments [27], a binary deep eutectic solvent was synthesized, composed of tetraethylammonium bromide (TEABr) and ethylene glycol (ETG), in which sodium cyanide (NaCN) was dissolved. The molar ratio of the synthesized DES was 1:4:0.2. Each of the components was mixed in a beaker at a temperature of 80 °C, with constant stirring at 600 rpm until a clear liquid was formed. The process was conducted in an extraction hood, and the temperature was controlled using an oil bath. The effect of temperature on the extraction of lanthanum using the synthesized deep eutectic solvent was investigated at temperatures of 25, 40, 50, 60, 70, and 80 °C. Equal volumes of 10 mL of a 2.0 M sulfuric acid aqueous solution (containing 2563 mg/L of La, sourced from a prior monazite leaching process) and the DES were contacted for 10 min. Subsequently, the aqueous phase and DES were separated using a separatory funnel; following phase separation, the concentration of lanthanum in the aqueous phase was analyzed using ICP-OES. During the extraction experiments, the concentration of lanthanum in the DES was determined by mass balance. The extraction efficiency (%E) was calculated as shown in Equations (1) and (2).

$$D=\frac{{\left[C\right]}_t-{\left[C\right]}_a}{{\left[C\right]}_a}$$

(1)

$$\%E=\frac{100·D}{D+\left(\raisebox{1ex}{$V_{aq}$}\!\left/ \!\raisebox{-1ex}{$V_{DES}$}\right.\right)}$$

(2)

where [C]_t is the initial concentration of lanthanum in the aqueous phase before extraction, [C]_a is the concentration of the metal in the aqueous phase after extraction, V_aq is the volume of the aqueous solution, and V_DES is the volume of the DES.

2.2. Molecular Dynamics Simulation

This study addressed the structural analysis of a binary DES composed of tetraethylammonium bromide (TEABr) and ethylene glycol (ETG). Subsequently, the effect on the structure of the DES formed by incorporating sodium cyanide (NaCN) was investigated. Additionally, the interaction of this DES with an acidic aqueous solution of lanthanum (H₂O, HSO₄⁻ and La³⁺), was investigated through molecular dynamics simulations. The identification of each atom associated with the various species comprising the DES and the lanthanum aqueous solution is presented in detail in Figure 1 and Figure 2.

Molecular dynamics simulations were conducted using the LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator) simulation package [28]. System visualization was performed with VMD 1.9.3 software [29]. The system’s temperature and pressure were kept constant using a Nose–Hoover thermostat and barostat [30]. The models of the systems to be simulated were created using the Materials Studio 2017 5.5.2 package (Accelrys Software Inc., San Diego, CA, USA). Initial configurations were generated using the Packmol software v20.15.0 [31].

In the initial step, a simulation box was generated for the system composed of tetraethylammonium bromide (TEABr) and ethylene glycol (ETG), establishing a TEABr–ETG ratio of 1:4. Subsequently, NaCN was integrated into the system to achieve a TEABr–ETG–NaCN ratio of 1:4:0.2. Next, the aqueous lanthanum solution and HSO₄⁻ were generated. Finally, the system composed of [TEABr–ETG–NaCN] was integrated with the aqueous lanthanum solution [H₂O–La³⁺–HSO₄⁻], inserting a spherical cluster with a radius of 25 Å, consisting of 40 TEABr molecules, 150 ETG molecules, and 10 NaCN molecules, into a cubic box of 120 Å. This box was composed of the lanthanum aqueous solution, comprising 15,000 water molecules, 1500 HSO₄⁻ molecules, and 500 La³⁺ ions, as illustrated in Figure 3.

The previously defined system was subjected to a minimization process at temperatures of 298 K and 353 K, utilizing the canonical NVT ensemble for a period of 200 ps. Subsequently, the NPT ensemble was applied for 1000 ps with the purpose of adjusting the density of the systems under analysis. Finally, the NVE ensemble was employed for a duration of 5000 ps to ensure the conservation of the systems’ energy, during which radial distribution functions (RDF) were generated and analyzed. The simulation procedure carried out is shown in Figure 4.

The force field parameters for tetraethylammonium bromide, La³⁺, and HSO₄⁻ were taken from ligpargen based on the OPLS-AA force field [32,33], the force field parameters for ethylene glycol were adopted from Doherty’s work [25], and the behavior of water was simulated using the SPC/E model parameters [34]. The previously indicated parameters can be seen in

Table 1. Charges and Lennard-Jones parameters for tetraethylammonium, sodium, and lanthanum cations, as well as for bromide, cyanide and sulfate anions.

Ion	Atom Type	q (e)	σ (Å)	ɛ (kcal/mol)
Tetraethylammonium	HS	0.034	2.50	0.0300
	CS	−0.086	3.50	0.0660
	CT	−0.002	3.50	0.0660
	HT	0.022	2.50	0.0300
	N	−0.057	3.25	0.1700
Br	Br	−0.179	4.28	0.7100
Cyanide	CM	−1.00	3.30	0.0660
	NM	0.00	3.20	0.1700
Na	Na	1.00	4.07	0.0005
Sulfate	OT	−0.535	2.96	0.7113
	S	0.802	3.55	1.0460
	OM	−0.622	3.12	0.7113
	HM	0.425	0.00	0.0000
La	La	3	3.75	0.0600

,

Table 2. Nonbonded parameters for ethylene glycol and water.

Molecule	Atom Type	q (e)	σ (Å)	ɛ (kcal/mol)
Ethylene glycol	HO	0.348	0.00	0.0000
	OG	−0.56	3.00	0.2975
	CG	0.116	3.50	0.1155
	HG	0.048	2.50	0.0525
Water	O	−0.82	3.17	0.1554
	H	0.41	0.00	0.0000

,

Table 3. Bond and angle force constants, k_r (kcal mol⁻¹ Å⁻²) and k_θ, (kcal mol⁻¹ rad⁻²), and equilibrium distances and angles, r₀ (Å) and θ₀ (degrees), for the tetraethylammonium cation and cyanide anion.

Ion	Bonds	r0	kr	Angles	θ0	kθ
Tetraethylammonium	CS–CT	1.529	268	CS–CT–HT	110.7	37.5
	CS–HS	1.090	340	CS–CT–N	111.2	80.0
	CT–HT	1.090	340	CT–CS–HS	110.7	37.5
	N–CT	1.471	367	CT–N–CT	113.0	50.0
				HS–CS–HS	107.8	33.0
				HT–CT–HT	107.8	33.0
				HT–CT–N	109.5	35.0
Cyanide	CM–NM	1.157	650
Sulfate	HM–OM	0.945	463	HM–OM–S	110	61.9
	OM–S	1.670	376	OM–S–OT	108.7	61.9
	OT–S	1.440	586	OT–S–OT	119	87.0

and

Table 4. Bond and angle force constants, k_r (kcal mol⁻¹ Å⁻²) and k_θ, (kcal mol⁻¹ rad⁻²), and equilibrium distances and angles, r₀ (Å) and θ₀ (degrees), for ethylene glycol.

Molecule	Bonds	r0	kr	Angles	θ0	kθ
Ethylene glycol	OG–HO	0.945	553	HO–OG–CG	108.5	55.0
	CT–OG	1.410	320	OG–CG–CG	108	50.0
	CT–CT	1.529	268	OG–CG–HG	109.5	35.0
	HC–CT	1.090	340	CG–CG–HG	110.7	37.5
				HG–CG–HG	107.8	33.0
Water	H–O	1.000	600	H–O–H	109.47	75.0

.

3. Results and Discussion

3.1. Effect of DES Temperature on Lanthanum Extraction

A series of experiments were conducted at different DES temperatures to observe their effect on the extraction of lanthanum. As shown in Figure 5, the extraction of La is directly proportional to the temperature of the DES. The results indicate that increasing the temperature from 25 to 80 °C enhances the extraction of La from 7.2% to 93.3%. To understand this phenomenon, a series of molecular dynamics simulations were performed.

3.2. Density

Density is one of the most accessible properties to calculate through simulation and serves as an initial test to validate the selected force fields [35].

Table 5. Comparison of the densities of the simulated and experimental systems.

System	Temperature (K)	Experimental Density (g/cm3)	Simulated Density (g/cm3)	Error (%)
TEABr–ETG	298	1.05	1.00	4.76
	353	-	0.93	-
TEABr–ETG–NaCN	298	1.06	1.01	4.72
	353	-	0.94	-
lanthanum solution	298	1.62	1.59	2.45

presents the densities of the simulated systems at 298 K and 353 K under one atmosphere of pressure. The deviation of the densities from the experimental values at 298 K ranges between 2.45% and 4.76%. Therefore, the force fields used in the simulations reasonably predict the densities at different temperatures.

3.3. Interaction among the Components of the DES

With the purpose of obtaining a more detailed understanding of the structure of the DES composed of tetraethylammonium bromide, ethylene glycol, and sodium cyanide, the calculation of radial distribution functions (RDFs) was carried out between the bromine atom and the hydrogens of ethylene glycol (H_G and H_O), as well as with the hydrogens of tetraethylammonium (H_S and H_T). Figure 6a,b clearly illustrate that both the Br–H_S and Br–H_G RDFs exhibit a prominent peak at 3.5 Å, suggesting the presence of significant interactions. On the other hand, the Br–H_T and Br–H_O RDFs show peaks at 3.5 Å and 5.8 Å, respectively. The interaction peak between Br–H_T pairs at 3.5 Å is less pronounced compared to the interaction peak of Br–H_S. This suggests that, although there is a probability of finding H_S -type hydrogen atoms at 3.5 Å from the bromine atom, the interaction is less intense. On the other hand, the secondary interaction peak between Br–H_O pairs at 5.8 Å suggests a high probability of finding H_O -type hydrogen atoms at this distance from the bromine atom, indicating the presence of a secondary structure at 5.8 Å.

Additionally, calculations of the integrals of the RDFs were performed, providing coordination numbers (NC) as a function of radial distance. In the first solvation layer of the bromine atom, defined by the first minimum value between the first two peaks, values of 6.5 for HS and 7.6 for H_G were obtained. These results align with the number of hydrogens present in tetraethylammonium (TEA) and ethylene glycol (ETG), considering the 1:4 ratio between TEA and ETG, where TEA contains 4 methyl groups, while ETG has 2 methylene groups. Figure 7 provides a graphical representation of the solvation environment of the bromine atom, showing its structure of four molecules of ethylene glycol and one molecule of tetraethylammonium.

Additionally, the radial distribution function was studied at a temperature of 80 °C. Figure 8a,b illustrate that the interaction distance for the Br–H_S and Br–H_G pairs does not experience appreciable variations, although a slight decrease in the intensity of the Br–H_S interaction is observed, and practically no alterations are observed in the intensity of the Br–H_G interaction, showing a slight increase. These results lead to the conclusion that the temperature change from 25 °C to 80 °C does not constitute a determining factor in the distribution of ions and molecules for the system composed of tetraethylammonium bromide and ethylene glycol.

Similarly, the solvation environment at 25 °C of H_G-type hydrogen atoms from ethylene glycol, H_S-type hydrogen atoms from tetraethylammonium, and NaCN in the DES was investigated through the determination of radial distribution functions. Like the scenario observed in the system composed of tetraethylammonium bromide and ethylene glycol, both Br–H_S and Br–H_G interactions exhibited a peak at 3.5 Å, with intensities comparable to the system lacking NaCN. This finding indicates that the presence of NaCN does not alter the interactions of these pairs, as evidenced in Figure 9a,b.

The most notable interactions of sodium cyanide with the system composed of tetraethylammonium bromide and ethylene glycol (TEABr–ETG) manifest primarily between the pairs of atoms C_M–H_O and Na–O_G. As evidenced in Figure 10a,b, the radial distribution function of the C_M-H_O pair exhibits a sharp peak of high intensity at a very short distance of 1.7 Å, while the RDF of the Na–O_G interaction shows a pronounced peak at 2.5 Å. These results indicate the presence of strong interactions between these pairs, and the coordination numbers in the first solvation layer of NaCN are 1.7 for H_O and 2.5 for O_G. Figure 11 provides a graphical representation of the main interactions present in the DES composed of TEABr–ETG–NaCN.

The stability of the structure formed by the (TEA–ETG–NaCN) system was then investigated as the temperature was raised to 80 °C. As depicted in Figure 12a, the RDF of the Br-H_G pair showed no significant changes with increasing temperature, maintaining a constant interaction distance of 3.5 Å. On the other hand, the Br-H_S pair interaction exhibited no variations in the 3.5 Å interaction distance, although a slight decrease in the peak intensity was observed, as depicted in Figure 12b. This phenomenon suggests a subtle modification in the structure with the temperature increase.

As can be observed in Figure 13a, the interaction of the C_M–H_O pair undergoes no changes in the interaction distance, remaining constant at 1.7 Å with the temperature increase. However, the peak intensity significantly decreases as the temperature is raised to 80 °C. On the other hand, the RDF of the Na–O_G pair interaction (Figure 13b) remains unchanged at 2.5 Å. Nevertheless, like the C_M–H_O interaction, the peak intensity decreases considerably with the temperature increase. The reduction in the peak intensities of the RDFs corresponding to the C_M–H_O and Na–O_G interactions, with the temperature elevated to 80 °C, suggests a destabilization in the structure of the system.

3.4. Interaction among the Components of the Aqueous Solution

The aqueous system composed of H₂O–La³⁺–HSO₄⁻ was studied to determine the primary interactions present through the determination of radial distribution functions. The closest recorded interaction occurred between lanthanum and sulfate, specifically with the oxygen atoms of sulfate (La³⁺–O_T), at 2.8 Å, as illustrated in Figure 14a. It can be observed that this interaction reaches a significant height, indicating a high probability of finding an oxygen atom (O_T) at this distance from the lanthanum ion. This suggests a strong interaction or coordination between La³⁺ and O_T, implying a well-defined structure and specific coordination at this distance. The second peak, located at approximately 4.9 Å, is the highest. This indicates an even higher probability of finding oxygen atoms (O_T) at this distance, suggesting the existence of a second coordination shell or an ordered structure beyond the first layer of immediate neighbors. The third peak appears at approximately 6.9 Å. Although less pronounced than the second peak, it remains significant, indicating a tertiary structure in the system. This greater distance suggests a long-range organization in the environment of La³⁺.

Additionally, a predominant interaction was identified between the lanthanum ion and water molecules, visualized through the La³⁺–O pairs. This phenomenon is evident in Figure 14b, where the radial distribution function exhibits a sharp peak of high intensity at 2.6 Å. Additionally, an interaction between H–O_T pairs of water and sulfate was highlighted. This interaction can be seen in Figure 14c, where a peak is observed at a very short distance of 1.9 Å.

3.5. Interactions between La³⁺ and the DES

With the purpose of examining the interaction between the components of the DES and the aqueous solution of lanthanum (H₂O–La³⁺–HSO₄⁻), molecular dynamics simulations were conducted for these systems at temperatures of 25 and 80 °C. Additionally, an understanding of the structural properties of these systems was sought through radial distribution functions describing the distances between the components of the DES and the aqueous solution. In Figure 15a,b, the main interactions at 25 °C between the aqueous solution and the DES are highlighted, specifically between the La³⁺–O_G and La³⁺–C_M pairs. The radial distribution function of the La³⁺–O_G pair shows a peak at 4.9 Å, while the RDF of the La³⁺–C_M pair presents a peak at 4.4 Å. Considering the intensity of these peaks and the interaction distances, it can be indicated that the predominant interaction occurs between the lanthanum ion and the carbon atom of the cyanide.

Upon increasing the temperature to 80 °C, Figure 16a reveals that the RDF of the La³⁺–O_G pair shows no significant changes with the temperature increase, maintaining a constant interaction distance of 4.9 Å. On the other hand, the primary interaction of the La³⁺ –C_M pair occurs at a shorter distance, 2.4 Å, as the temperature is raised to 80 °C (Figure 16b). This reduction in the interaction distance is possibly associated with the increased lanthanum extraction upon raising the temperature, as observed experimentally. These results suggest a sensitive response of molecular interactions to temperature variation, which may have significant implications in understanding and controlling the processes involving these systems. In Figure 17, the main interactions between the components of the deep eutectic solvent (TEA–ETG–NaCN) and the components of the lanthanum aqueous solution (H₂O–La³⁺–HSO₄⁻) are schematically represented.

4. Conclusions

For a deeper understanding of the structure of a deep eutectic solvent formed by tetraethylammonium bromide, ethylene glycol, and sodium cyanide, and its interaction with an acidic aqueous solution of lanthanum, a series of molecular dynamics simulations were conducted for the TEABr–ETG–NaCN and H₂O–La³⁺–HSO₄⁻ systems. The structural properties were verified by calculating the radial distribution functions of the main interactions. The primary interactions in the deep eutectic solvent, as indicated by the RDFs, occur between the pairs H_S–Br (3.5 Å); H_G–Br (3.5 Å); H_O–C_M (1.7 Å); and O_G–Na (2.5 Å). In the acidic solution, the main interaction between the lanthanum ion and sulfate is observed between the La–O_T pairs (2.8 Å). The interaction between the deep eutectic solvent and the aqueous solution is manifested through the O_G–La (4.9 Å) and C_M–La (4.4 Å) pairs. It is crucial to highlight that, with a temperature increase from 25 to 80 °C, the interaction distance between the C_M–La pair reduces to 2.4 Å; this reduction is possibly associated with the enhanced lanthanum extraction, as observed experimentally.