Molecular Insight into Fatty Acids Adsorption on Bare and Hydrated

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Molecular Insight into Fatty Acids Adsorption on Bare and Hydrated (111) Fluorite Surface Yann Foucaud, Sébastien Lebègue, Lev O. Filippov, Inna V. Filippova, and Michael Badawi J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.8b08969 • Publication Date (Web): 27 Nov 2018 Downloaded from http://pubs.acs.org on December 2, 2018

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The Journal of Physical Chemistry

Molecular Insight into Fatty Acids Adsorption on Bare and Hydrated (111) Fluorite Surface Yann Foucaud1,*, Sébastien Lebègue2,*, Lev O. Filippov1,*, Inna V. Filippova1,*, Michaël Badawi2,* 1

Université de Lorraine, Laboratoire GeoRessources, UMR 7359 – CNRS, 2 rue du Doyen

Marcel Roubault, 54 505 Vandœuvre-lès-Nancy-Cedex, France. E-mail: [email protected]; [email protected]; [email protected]. 2

Université de Lorraine, Laboratoire Physique et Chimie Théoriques, UMR 7019 – CNRS,

BP239, Boulevard des Aiguillettes, 54 506 Vandoeuvre-lès-Nancy-Cedex, France. E-mail: [email protected]; [email protected].

ACS Paragon Plus Environment

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Abstract

The adsorption of fatty acids with various chain structures on the (111) fluorite surface is investigated using density functional theory including a correction for dispersive interactions. In the case of the acidic form, we observe that the molecular form is preferred over the dissociated one and the molecule adsorbs on a surface calcium atom with an energy of -78.2 kJ mol-1. Also, we show that the carboxylate anion adsorbs on the surface under two possible configurations, a bidentate binuclear one or a monodentate one, the bidentate binuclear being favored. At both 0 K and 300 K, the chain length does not affect the geometry of the carboxyl group, but it strongly impacts the global geometry of the molecule adsorption on the fluorite surface: the “flat” adsorption mode, i.e. when the molecule is parallel to the surface, is favored when the number of carbon atoms is equal or higher to 6, due to dispersion forces. However, when the molecule is in hydrated conditions, the chain folds up on itself to reduce the interactions with water, while the carboxylate group adsorbs in monodentate configuration. In aqueous conditions, the chain length does not impact anymore the adsorption energies, the vertical adsorption mode being always favored.


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Introduction Fluorite is considered as a Critical Raw Material by the European Union due to its high supply risk, its very low recycling rate and the difficulties to substitute it in the industry.1 It is the most important source for hydrofluoric acid (HF), which is the basis for all the industrial uses of fluorine in the world.2,3 In particular, aluminum fluoride is crucial to produce metallic aluminum by electrolysis.2–4 Fluorite is also widely used as a flux for metallurgy of various metals, making this mineral essential for many related industries. The production of hydrofluoric acid requires strict specifications (>97% CaF2, pKa + 1, it is the –COO-. However, most of the minerals can be floated at acidic and alkaline pH,64 proving that both acidic and anionic form of the carboxyl group can adsorb onto minerals surface. It is assumed that a physisorption occurs for the carboxylic acid64–66 while the carboxylate chemisorbs.8,35– 38,67,68

At the moment, the adsorption mechanisms are not well understood for both forms

although some authors confirmed the adsorption of the methanoic acid onto the (111) fluorite surface, reporting adsorption energies of -56.3 to -75.9 kJ·mol-1 but without a dispersion correction.45 a. Adsorption under Acidic Form Methanoic acid was used to study the geometry of an adsorbed carboxyl group on the (111) fluorite surface. Six different configurations are possible to set the molecule on the surface (see Figure 1S in Supporting Information): 1. Each oxygen atom is set on a calcium atom, doing a “monodentate” adsorption; 2. The two oxygen atoms are placed on the same calcium atom, forming a “bidentate” adsorption; 3. The double-bonded oxygen is placed on a calcium atom, the –O-H pointing away to the surface; 4. The –O-H is set on a calcium atom, the double-bonded oxygen pointing away to the surface.


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5. The double-bonded oxygen is placed between two calcium atoms, the –O-H pointing away to the surface; 6. The –O-H is set between two calcium atoms, the double-bonded oxygen pointing away to the surface. Among all the tested cases, the monodentate adsorption (1) is the most favored (Figure 1). The calculated adsorption energy is ΔE ads = -78.2 kJ·mol-1, which can be decomposed in ΔEdisp = -17.6 kJ·mol-1 and ΔEPBE = -60.6 kJ·mol-1. Our PBE contribution is in nice agreement with the computed adsorption energy of -56.3 kJ·mol-1 with the PW91 functional without dispersion correction reported by Cooper and de Leeuw.45 In this configuration, the doublebonded oxygen atom adsorbs onto the calcium atom with d Ca-O = 2.44 Å while the hydrogen of the –O-H group points towards the closest fluorine atom with dH-F = 1.48 Å (Figure 1). The same geometry is reformed during the relaxation when the methanoic acid is set in a bidentate configuration (2) and in configuration 6 (Figure 1). The adsorption energies are very similar. For cases 4 and 5, the methanoic acid becomes sub-parallel to the surface, and the two oxygen atoms are in interaction with two calcium atoms with both d Ca-O = 2.84 Å. The H of the – O-H group also points towards the closest fluorine atom with d H-F = 1.48 Å. The calculated adsorption energies are ΔEads ≈ -58.4 kJ·mol-1 including ΔEdisp ≈ -29.4 kJ·mol-1. The absolute value of the energy is lower than for the cases 1, 2 and 6 whereas the dispersive forces contribution is significantly higher. It can be explained by the increase of the induced dipoleinduced dipole forces when the oxygen of the –O-H group interacts with the calcium atom. Finally,

the

case

3

is

the

least

favored,

with

ΔEads = -41.3 kJ·mol-1

including

ΔEdisp = -15.4 kJ·mol-1. Even if the double-bonded oxygen atom adsorbs onto a calcium atom,


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the H atom of the –O-H group cannot interact with any fluorine atom, which could explain the low adsorption energy in absolute value.

Figure 1. Adsorption of a methanoic acid molecule on the (111) fluorite surface after DFT relaxation, in side view (left) and in top view (right). The blue, grey, red, marron, and white balls represent the calcium, fluorine, oxygen, carbon, and hydrogen atoms, respectively. The dashed line corresponds to a hydrogen bond. b. Adsorption under Carboxylate Form In flotation, carboxylic acids are mostly used at alkaline pH, in the range where pH >> pKa + 1. Then, different configurations were tested for the adsorption of the methanoate molecule, HCOO- (see Figure 2S in Supporting Information): 1. Each oxygen atom is set on a calcium atom, doing a bidentate binuclear adsorption; 2. The two oxygen atoms are placed on the same calcium atom, forming a “bidentate” adsorption;


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3. One oxygen is placed on a calcium, the other one is pointing away to the surface, forming a monodentate adsorption; 4. One oxygen is placed between two calcium atoms, the other one is pointing away to the surface; The most favored case is the bidentate binuclear adsorption (1). The calculated adsorption energy is ΔEads = -226.4 kJ·mol-1 including ΔEdisp = -18.5 kJ·mol-1. Each oxygen atom establishes a bond with a surface calcium atom, with dCa-O = 2.33 Å for both (Figure 2, a). The hydrogen atom of the C-H is pointing away the surface. The bidentate adsorption (2) and the case (4) reform the same geometry with very similar adsorption energies. The case (3) leads to a different configuration. Only one oxygen atom establishes a bond with a surface calcium atom, the other oxygen pointing away the surface (Figure 2, b). However, the bond is shorter, dCa-O = 2.19 Å and the adsorption energy is lower in absolute value, ΔEads = -167.6 kJ·mol-1 including ΔEdisp = -11.2 kJ·mol-1. The significantly lower adsorption energy in absolute value indicates that this adsorption is possible but occurs more rarely than the monodentate one.


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Figure 2. Two possible configurations for the adsorption of a methanoate molecule onto the (111) fluorite surface after DFT relaxation, in side views; a: bidentate binuclear adsorption; b: monodentate adsorption. The dashed line represents a hydrogen bond. Two possible configurations for the carboxylate adsorption onto the fluorite surface were reported in the literature using spectroscopic methods.35,43 The first identified configuration was a monodentate adsorption, which is accordance with what we found in the present study. The second one was a bidentate adsorption, a configuration which was not possible to get from our simulations in vacuum. However, these experimental investigations were performed in aqueous medium at room temperature while this part of our study was realized without water and at 0 K. c. Dissociation on the Surface The adsorption of the methanoic acid could be possible by the dissociation of HCOOH into HCOO- and H+ at the vicinity of the surface. This dissociation was investigated, comparing the system where the carboxylate and the hydrogen atom are both adsorbed to the system where the HCOOH is set far from the surface. The methanoate was set on the surface with the most favored configuration we determined previously, namely the bidentate binuclear configuration. The


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proton was set between two fluorine atoms, at different distances of the carboxyl group. When it is placed close to the carboxyl group, at d Carboxyl-H = 2.5 Å, the carboxylic acid is reformed and adsorbs as described previously, in a monodentate configuration, see Figure 1. When the H is placed far enough, at dCarboxyl-H = 7.1 Å, it establishes two H-F bonds, while the carboxylate adsorbs onto calcium atoms with the bidentate binuclear configuration as displayed in Figure 2. The adsorption does not compensate the dissociation as the global reaction energy is ΔEr = 75.2 kJ·mol-1 including ΔEr-disp = -29.2 kJ·mol-1. It indicates that, when the carboxylic acid is under acidic form, it adsorbs as it, without dissociating at the vicinity of the surface.


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Global Geometrical Configuration of the Adsorbed Molecule The fatty acids used as flotation collectors can be written as R-COO-, R being a linear aliphatic chain composed of between 11 and 17 carbons. This parameter can impact strongly the global configuration of the adsorption. We then investigated the adsorption of fatty acids with different chain lengths on the (111) fluorite surface. The choice was made to study only the carboxylate forms as they are the stable form in flotation conditions. For each saturated-chain length, the adsorption with the molecule being perpendicular to the surface (“vertical” adsorption) was compared to the case where the molecule is parallel to the surface (“flat” adsorption). Results are presented in Figure 3.

Figure 3. Evolution of the total adsorption energy and its PBE and dispersive components as a function of the number of carbon atoms in the aliphatic chain for vertical and flat adsorptions. 1 carbon means the ethanoate molecule, 4 means the butanoate…


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The chain length does not impact significantly the adsorption energies when the molecules are adsorbed in “vertical” configuration, which are around -240 kJ·mol-1. The corresponding contribution of dispersion interactions to the total adsorption energies are also similar whatever the chain length, around -20 kJ·mol-1. We can conclude that for the “vertical” adsorption mode, the adsorption is mainly controlled by the short range interaction between the carboxylate group and the surface. Regarding the “flat” adsorptions, the adsorption energies increase in absolute values when the chain length is increased, ranging between -200 kJ·mol-1 for R = CH3 to -292.5 kJ·mol-1 for R = C17H35. Moreover, the contribution of dispersive energy increases in absolute values with the chain length, from -21.0 kJ·mol-1 for R = CH3 to -132.3 kJ·mol-1 for R = C17H35. It proves that induced dipole-induced dipole interactions exist between the hydrogen atoms of the chain and the surface fluorine atoms. These forces are the main parameter explaining the increase of the global adsorption energies when the chain length increases, the adsorption energies and the contribution from dispersion following the same trend. Also, the PBE contribution decreases slightly when the chain length is increased. It can be explained by a twist of the first C-C bond following the carboxyl group that occurs to allow the “flat” adsorption (Figure 4). Dispersion forces make the “flat” adsorption much more favored than the “vertical” adsorption for chain length longer than R = C5H11. For short chains, there is no difference in terms of adsorption energy between the “vertical” and the “flat” configurations. Also, the chain length and the adsorption mode (“flat” or “vertical”) do not impact the geometry of the carboxyl group as it constantly adsorbs in bidentate binuclear configuration with dCa1-O1 = dCa2-O2 = 2.33 Å (Figure 4). After the relaxation, the distances between the hydrogen atoms of the chain and their


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closest fluorine atom were measured for the different chain lengths in “flat” adsorption (Figure 4). The dH-F ranges between 2.35 Å and 3 Å with a mean value of 2.59 Å.

Figure 4. Adsorption of a hexadecanoate (palmitate) molecule (15 carbon atoms in the chain) in flat adsorption (left) and in vertical adsorption (right) after DFT relaxation. Ab Initio Molecular Dynamics Calculations a. On the Bare (111) Fluorite Surface Our previous calculations were conducted at T = 0 K and on bare surfaces. Therefore, to approach more realistic conditions, we have conducted ab initio molecular dynamics simulations at T = 300 K. Calculations with the methanoic acid and with the methanoate (R = H) were performed and, to gain understanding on the influence of the chain length, with the ethanoate (R = CH3), the butanoate (R = C3H7) and the octanoate (R = C7H15). The objectives were to determine the geometries of the carboxyl group, of the chain and the adsorption energies when they adsorb onto the (111) fluorite bare surface at T = 300 K. The methanoic acid adsorbs staying perpendicular to the (111) fluorite surface with a monodentate configuration, which is in accordance with the results obtained at 0 K. The double-


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bonded oxygen atom establishes a bond with a calcium atom with an average distance of 2.51 Å and a standard deviation of 0.16 Å. The hydrogen of the carboxyl group interacts with a surface fluorine atom, with an average distance dH-F = 1.54 Å and a standard deviation of 0.16 Å. The calculated internal adsorption energy is ΔE ads = -86.1 kJ·mol-1, which is higher in absolute value that the values found at T = 0 K. Under carboxylate form, the collector molecule adsorbs on bidentate binuclear configuration as found for T = 0 K, whatever the chain length. Each oxygen atom adsorbs on a different calcium atom with dCa-O = 2.40 Å on average and a standard deviation being only 0.12 Å. As at T = 0 K, the chain length impacts the global geometry of the collector: the octanoate molecule becomes sub-parallel to the surface over time as the hydrogen atoms are getting closer to the fluorine atoms, between 2 and 3 Å on average. Also, the calculated internal adsorption energies increase in absolute value with the chain length (Figure 5), highlighting the same phenomenon observed previously at T = 0 K: the hydrogen bonds between the chain hydrogen atoms and the surface fluorine atoms make the “flat” adsorption more favored. Overall, at T = 300 K, the internal adsorption energies range from -175.6 kJ·mol-1 for the methanoate molecule to -189.5 kJ·mol-1 for the octanoate molecule.


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Figure 5. Evolution of the adsorption energy as a function of the aliphatic chain length at T = 0 K and T = 300 K. b. On the Hydrated (111) Fluorite Surface The flotation process is conducted in aqueous phase and the fatty acids adsorb onto a hydrated surface, in presence of water. Therefore, we conducted calculations where the collector molecule is placed at the vicinity of the surface and the cell filled with water molecules. Notice that in our previous study,69 we have investigated the mechanisms leading to the hydration of the (111) fluorite surface but without the presence of the collector molecule. When adsorption energies were calculated, we compared the total energy of this system to the energy of the system where the collector molecule is placed in the bulk water at 10 Å far from the surface. First, the adsorption of collector under acidic form was investigated: the octanoic acid (R = C7H15) was set at the vicinity of the surface, in the most favored configuration demonstrated


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previously. During the simulation, the molecule moves away from the surface and the two oxygen atoms of the carboxyl group establish hydrogen bonds with water molecules. Moreover, when the octanoic acid reaches the water bulk, the dissociation of the carboxylic acid to the carboxylate form occurs after few picoseconds. This observation is in accordance with the pKa of the octanoic acid, which is 4.85, indicating that, in pure water, i.e. at pH = 7, the carboxylate form is more than 100 times more favored than the acidic form. Under the carboxylate form, the octanoate molecule (R = C7H15) was set in a bidentate binuclear configuration, which represents the most favored geometry found without water. In this configuration, each oxygen atom (O1 and O2) is close to a calcium atom (Ca 1 and Ca2, respectively) with dCa1-O1 = dCa2-O2 = 2.3 Å. In the first 8 ps of the simulation, the two oxygen atoms are going away from their respective calcium atom. However, O 1 is getting closer to Ca2 and the distance between the two atoms radically decreases from 4.0 Å to 2.5 Å between 8.4 ps and 8.7 ps. For the rest of the simulation, the distance between O 1 and Ca2 oscillates around an average of 2.81 Å with a standard deviation of 0.30 Å, indicating that a bond has been established between the two atoms. The other oxygen atom points towards the water bulk, forming H-bonds with the water molecules (Figure 6). It induces that the molecule is globally tilted, resulting to the existence of a global angle of around 20° between the surface and the line joining the two oxygen atoms (Figure 6).


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Figure 6. Snapshot of a side view of the (111) fluorite surface with an octanoate molecule adsorbed onto the surface and the cell completely filled with water molecules so that the density is 1 g·cm-3. Dashed lines represent H-bonds. Lone atoms are due to the periodicity of the cell. Nevertheless, our results at T = 0 K and T = 300 K, in the absence of the water, demonstrated that each oxygen atom is bonded with a calcium atom. It means that the presence of water impacts the geometry of the carboxyl group during the adsorption, changing the most favored configuration from “bidentate binuclear” to “monodentate”. This adsorption has been described by Fourier transform infrared spectroscopy (FT-IR) through the internal reflection spectroscopy (IRS) where authors demonstrated that a “uni-dentate” adsorption occurs for low fatty acids coverage onto the (111) fluorite surface.35 They also reported that a global angle of around 10° exists between the line joining the two oxygen atoms and the surface.35 We observed both of these statements but also that, during the simulation, the global conformation of the molecule is changing due to the free rotation on the C-C axis (Figure 6). Several C-C bonds transform from – trans conformer to –cis conformer to maximize the van der Waals interactions between the hydrogen atoms of the chain, resulting in the folding up of the molecule on itself. This


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phenomenon has also be described in the literature for low surface coverage by fatty acids.39 Nevertheless, even if the molecule tilts over time, it does not desorb the water molecules from the surface so that the “flat” adsorption observed previously occurs only on a bare surface. The adsorption energies calculated for water are around -55 kJ·mol-1 69 while a “flat” adsorption of an octanoate molecule would result in the desorption of at least two water molecules, corresponding to -110 kJ·mol-1. The difference between a “flat” and a “vertical” adsorption is lower than -110 kJ·mol-1, inducing that the adsorption occurs in a sub-vertical configuration in presence of water. The global calculated internal adsorption energy is -6.6 kJ·mol-1, which is a very low value compared to the adsorption energies calculated on the bare surface, in accordance with the literature.47,50 It can be linked to the fact that the octanoate molecule is quite stable in aqueous phase due to hydrogen bonds established between water molecules and the carboxyl group. Overall, in aqueous conditions, the chain length does not impact anymore the adsorption energies: the vertical adsorption mode is always favored even if the aliphatic chain folds up to minimize the contact with the water. Conclusion In this work, the interaction between various carboxylic acids, their corresponding carboxylates and the (111) surface of the fluorite crystal was investigated using density functional calculations including a correction for dispersion forces, at 0 K and at 300 K. The behaviors of the two forms of the carboxyl group (acidic and carboxylate) were compared. All the results are summarized in Table 1. First, only the bare surface was studied. At T = 0 K, the methanoic acid adsorbs with the double-bonded oxygen on a calcium atom and the hydrogen atom on a fluorine atom with ΔEads = -78.2 kJ·mol-1

including

ΔEdisp = -17.6 kJ·mol-1 and

dCa-O = 2.44 Å.

Under

the

carboxylate form, the molecule adsorbs with its two oxygen atoms bonded with two neighboring


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calcium atoms of the surface with ΔE ads = -226.4 kJ·mol-1 including ΔEdisp = -18.5 kJ·mol-1 and dCa-O = 2.33 Å. The adsorption of carboxylic acids under acidic form exhibits lower adsorption energies than under anionic form, which is in agreement with AFM studies.47,50 When the chain length of the molecules is increased, they become sub-parallel to the surface to establish hydrogen bonds with fluorine atoms, increasing the adsorption energies. At T = 300 K, the same conclusions are observed in terms of adsorption geometries, the bond being yet slightly longer and the adsorption energy lower. When the water is introduced, at T = 300 K, the molecule under acidic form does not adsorb and dissociates to form the carboxylate form. Besides, the molecule under carboxylate form adsorbs with only one oxygen atom bonded to a calcium, with dCa-O = 2.81 Å on average. A significant lower adsorption energy is exhibited for the adsorption in water compared to the adsorption in vacuum, which is in accordance with experimental results.47,50 Overall, when the chain length is high, the molecule folds up to minimize the interactions with water. The results presented in this study contribute to a better understanding of the adsorption of carboxylic acids and their carboxylates onto the (111) fluorite surface. The understanding in the formation of a monolayer of carboxylic acid is crucial to reach a selective separation of minerals with similar surface properties by flotation, and we hope that our work will stimulate further research in this direction. Table 1. Summarizing table of the adsorption geometries (bond lenghts, configurations) and adsorption energies as a function of the conditions, the temperature, the molecule and its form.


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Final and most stable configuration Molecule

Conditions T (K)

ΔEads (kJ.mol-1)

Ca1-O1

Ca2-O2

bond length

bond length

(Å)

(Å)

Vertical

2.44

N/A

Flat

2.54

N/A

Vertical

2.33

2.33

Flat

2.33

2.33

Flat

2.40

2.40

2.81

N/A

Head

Chain

Monodentate Methanoic acid

Vacuum

0

-78.4 + H-bond Monodentate

Octanoic acid

Vacuum

0

-81.4 + H-bond

Octanoic acid

Hydrated

300

Not adsorbed Bidentate

Methanoate

Vacuum

0

-226.4 binuclear Bidentate

Octanoate

Vacuum

0

-244.5 binuclear Bidentate

Octanoate

Vacuum

300

-189.5 binuclear

Octanoate

Hydrated

300

-6.6

Monodentate Vertical

Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes There are no conflict of interest to declare.


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Acknowledgements This work was granted access to the HPC resources of TGCC under the allocation 2017-A0030910306 made by GENCI. The research leading to these results has received funding from the European Union's Horizon 2020 research and innovation program under grant agreement No 641650 for the FAME project. We also acknowledge the support of Labex Ressources 21 (supported by the French National Research Agency through the national program “Investissements d’Avenir” with reference ANR-10-LABX-21—LABEX RESSOURCES 21). References (1)

European Commission. Critical Raw Materials for the EU: Report of the Ad-Hoc Working Group on Defining Critical Raw Materials. http://ec.europa.eu/enterprise/policies/rawmaterials/documents/index_en.htm. 2010. (2) Féraud, J. Mémento Des Roches et Minéraux Industriels : La Fluorine Ou Spath Fluor (in French). Rap. BRGM R 40825, 102 p., 2 fig., 10 tabl., 2 ann., 1 carte h.t. 1999. (3) Emsley, J. Nature’s Building Blocks: An A-Z Guide to the Elements, New ed., completely rev. and updated.; Oxford University Press: Oxford ; New York, 2011. (4) Beck, T. R.; Brooks, R. J. Electrolytic Reduction of Alumina, September 1989. (5) Jébrak, M.; Marcoux, É.; Laithier, M. Geology of Mineral Resources, Second edition.; Geological Association of Canada: St. John’s, NL, 2016. (6) Magotra, R.; Namga, S.; Singh, P.; Arora, N.; Srivastava, P. K. A New Classification Scheme of Fluorite Deposits. International Journal of Geosciences 2017, 08 (04), 599– 610. https://doi.org/10.4236/ijg.2017.84032. (7) St.Śla̧czka, A. Effects of an Ultrasonic Field on the Flotation Selectivity of Barite from a Barite-Fluorite-Quartz Ore. International Journal of Mineral Processing 1987, 20 (3–4), 193–210. https://doi.org/10.1016/0301-7516(87)90066-4. (8) Marinakis, K. I.; Shergold, H. L. The Mechanism of Fatty Acid Adsorption in the Presence of Fluorite, Calcite and Barite. International journal of mineral processing 1985, 14 (3), 161–176. (9) Zhijie, C.; Zijie, R.; Huimin, G.; Yupeng, Q.; Renji, Z. Effect of Modified Starch on Separation of Fluorite from Barite Using Sodium Oleate. Physicochemical Problems of Mineral Processing; ISSN 2084-4735 2018. https://doi.org/10.5277/ppmp1806. (10) Ren, Z.; Yu, F.; Gao, H.; Chen, Z.; Peng, Y.; Liu, L. Selective Separation of Fluorite, Barite and Calcite with Valonea Extract and Sodium Fluosilicate as Depressants. Minerals 2017, 7 (2), 24. https://doi.org/10.3390/min7020024. (11) Marinakis, K. I.; Shergold, H. L. Influence of Sodium Silicate Addition on the Adsorption of Oleic Acid by Fluorite, Calcite and Barite. International Journal of mineral processing 1985, 14 (3), 177–193.


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