Synthesis of Novel Ether Thionocarbamates and Study on Their Flotation Performance for Chalcopyrite

Abstract: Novel ether thionocarbamates, O-butoxy isopropyl-N-ethoxycarbonyl thionocarbamate (BIPECTC) and O-(2-butoxy-1-methylethoxy) isopropyl-N-ethoxycarbonyl thionocarbamate (BMIPECTC), were synthesized in this study. Their collecting efficiencies in the flotation of chalcopyrite were investigated using flotation tests, adsorption measurements, ultraviolet spectra (UV) and Fourier transform-infrared spectroscopy (FT-IR) and density functional theory (DFT) calculations. The synthesized ether thionocarbamates showed better frothing properties than methyl-isobutyl-carbinol (MIBC) and stronger affinity to chalcopyrite compared with O-isopropyl-N-ethyl thionocarbamate (IPETC) and O-isobutyl-N-ethoxycarbonyl thionocarbamate (IBECTC). UV spectra analysis showed that the ether thionocarbamates react with Cu2+, with the exception of Fe2+, Ni2+, Zn2+ and Pb2+. Additionally, it was further confirmed by FTIR spectra that a chemical reaction occurs between copper ion and BIPECTC and BMIPECTC. The adsorption capacity measurements revealed that chalcopyrite exhibits good adsorption ability for ether thionocarbamates at an approximate pH of 8–10, which agrees with the flotation tests. The quantum chemistry calculation results indicated that the ether thionocarbamates exhibit stronger collecting ability for copper mineral in terms of frontier molecular orbital analysis, binding model simulation with copper ions and the molecular hydrophobicity compared with IPETC and IBECTC. The computational results are in very good agreement with the experimental results.


Introduction
Chalcopyrite (CuFeS 2 ) is the primary, economically important and most abundant copper-bearing mineral, accounting for approximately 70% of the current global copper reserves [1,2].While depletion of high-grade copper resources is of serious concern for the mineral processing industries, its judicious utilization to meet the ever-growing demand of copper has great significance.Xanthates are most commonly used as collectors for separating copper sulfide minerals from gangue minerals using froth flotation.However, because an evident disadvantage of xanthates is their poor selectivity, thionocarbamates are considered more effective collectors for sulfide ores; they also have good selectivity, low dosage and toxicity and are extensively applied worldwide [3,4].As a result, the preparation, modification and performance of thionocarbamates have gained increasing attention since their use in mineral flotation [5][6][7][8][9].Glembotskii [10] reported that the collecting ability of thionocarbamate is directly influenced by the electron density of the reactive center (sulfur atom) such that it is enhanced when the electron density of the reactive center is raised by the electron-donating group.Conversely, the collecting ability is reduced as for the electron-withdrawing group.Furthermore, a growing

Synthesis of Ethoxycarbonyl Isothiocyanate
In this procedure, ethyl chloroformate was added dropwise to the aqueous solution of sodium thiocyanate in the presence of DMA.The mixture was stirred for 4 h, and the reaction temperature was kept at approximately 0-5 °C.The product was extracted using icy water, and ethoxycarbonyl isothiocyanate was obtained after removing the solvent.The reaction is shown in Equation (1) [20]. (1)

Determination of the Frothing Properties
Frothing properties were measured using the airflow method to help gas move across the sand filter plate on which a solution or slurry was to be tested; then, the foam height was measured after foaming in the container [21,22].The foam half-life was recorded as the time for the foam height to attenuate by half after aeration.Tests were performed at room temperature (25 ± 3 °C) from a low concentration solution to a high concentration solution for one reagent.The foam tester must be washed with distilled water before further testing.Each test was repeated three times, and the mean value was adopted.The diagrammatic sketch of the frothing property test is shown in Figure 1.(1)

Synthesis of Ethoxycarbonyl Isothiocyanate
In this procedure, ethyl chloroformate was added dropwise to the aqueous solution of sodium thiocyanate in the presence of DMA.The mixture was stirred for 4 h, and the reaction temperature was kept at approximately 0-5 °C.The product was extracted using icy water, and ethoxycarbonyl isothiocyanate was obtained after removing the solvent.The reaction is shown in Equation (1) [20]. (1)

Determination of the Frothing Properties
Frothing properties were measured using the airflow method to help gas move across the sand filter plate on which a solution or slurry was to be tested; then, the foam height was measured after foaming in the container [21,22].The foam half-life was recorded as the time for the foam height to attenuate by half after aeration.Tests were performed at room temperature (25 ± 3 °C) from a low concentration solution to a high concentration solution for one reagent.The foam tester must be washed with distilled water before further testing.Each test was repeated three times, and the mean value was adopted.The diagrammatic sketch of the frothing property test is shown in Figure 1.

Determination of the Frothing Properties
Frothing properties were measured using the airflow method to help gas move across the sand filter plate on which a solution or slurry was to be tested; then, the foam height was measured after foaming in the container [21,22].The foam half-life was recorded as the time for the foam height to attenuate by half after aeration.Tests were performed at room temperature (25 ± 3 • C) from a low concentration solution to a high concentration solution for one reagent.The foam tester must be washed with distilled water before further testing.Each test was repeated three times, and the mean value was adopted.The diagrammatic sketch of the frothing property test is shown in Figure 1.In this procedure, ethyl chloroformate was added dropwise to the aqueous solution of sodium thiocyanate in the presence of DMA.The mixture was stirred for 4 h, and the reaction temperature was kept at approximately 0-5 °C.The product was extracted using icy water, and ethoxycarbonyl isothiocyanate was obtained after removing the solvent.The reaction is shown in Equation (1) [20]. (1)

Determination of the Frothing Properties
Frothing properties were measured using the airflow method to help gas move across the sand filter plate on which a solution or slurry was to be tested; then, the foam height was measured after foaming in the container [21,22].The foam half-life was recorded as the time for the foam height to attenuate by half after aeration.Tests were performed at room temperature (25 ± 3 °C) from a low concentration solution to a high concentration solution for one reagent.The foam tester must be washed with distilled water before further testing.Each test was repeated three times, and the mean value was adopted.The diagrammatic sketch of the frothing property test is shown in Figure 1.

Micro Flotation Experiments
The micro flotation experiments for pure mineral were performed in an XFG type laboratory flotation cell (Jilin Prospecting Machinery Factory, Changchun, China) with a volume of 40 mL.In each test, 2.0 g of sample was dispersed in the cell with distilled water for 1 min.The pH was adjusted using a pH regulator (hydrochloric acid or sodium hydroxide) for 2 min.Then, the collector was introduced and the pulp was conditioned for 3 min, which was followed by flotation for 6 min.

Batch Flotation Tests
Laboratory experiments were conducted for a porphyry copper-molybdenum ore from different deposits of Dexing Copper Mine (Dexing, China).Results of Chemical Analysis and X-ray Diffraction are shown in Tables 1 and 2, respectively.In each test, one sample of 1000 g was ground in a conical ball mill, and the concentration of ore pulp was 62.5%.An XFD type flotation machine (Jilin Prospecting Machinery Factory, Changchun, China) with a volume of 3 L was used in flotation, and one-step rougher flotation was employed.The ore flotation tests were conducted as in the flow sheet shown in Figure 2.

Micro Flotation Experiments
The micro flotation experiments for pure mineral were performed in an XFG type laboratory flotation cell (Jilin Prospecting Machinery Factory, Changchun, China) with a volume of 40 mL.In each test, 2.0 g of sample was dispersed in the cell with distilled water for 1 min.The pH was adjusted using a pH regulator (hydrochloric acid or sodium hydroxide) for 2 min.Then, the collector was introduced and the pulp was conditioned for 3 min, which was followed by flotation for 6 min.

Batch Flotation Tests
Laboratory experiments were conducted for a porphyry copper-molybdenum ore from different deposits of Dexing Copper Mine (Dexing, China).Results of Chemical Analysis and X-ray Diffraction are shown in Tables 1 and 2, respectively.In each test, one sample of 1000 g was ground in a conical ball mill, and the concentration of ore pulp was 62.5%.An XFD type flotation machine (Jilin Prospecting Machinery Factory, Changchun, China) with a volume of 3 L was used in flotation, and one-step rougher flotation was employed.The ore flotation tests were conducted as in the flow sheet shown in Figure 2.

Adsorption Capacity Measurement
The adsorption quantity of collectors on the pure mineral surface was measured by ultraviolet spectrophotometry.The mineral sample (0.5 g) with collectors of different concentrations was oscillated at 30 °C for 10 h.The pH was adjusted by hydrochloric acid or sodium hydroxide.The concentration of supernatant was measured after centrifugation.Finally, the adsorption quantity of collectors on chalcopyrite was calculated with the following Equation (3):

Adsorption Capacity Measurement
The adsorption quantity of collectors on the pure mineral surface was measured by ultraviolet spectrophotometry.The mineral sample (0.5 g) with collectors of different concentrations was oscillated at 30 • C for 10 h.The pH was adjusted by hydrochloric acid or sodium hydroxide.The concentration of supernatant was measured after centrifugation.Finally, the adsorption quantity of collectors on chalcopyrite was calculated with the following Equation (3): Minerals 2016, 6, 97 5 of 16 Q is the adsorption quantity (mol/g); m is the mass of mineral sample (g); V is solution volume (L); and c 1 and c 2 are the solution concentrations before and after adsorption, respectively (mol/L).

UV Spectra
Various levels of the collector solution were mixed with the metal ion solution, and the concentrations of two solutions were both 1 × 10 −4 mol/L.Then, the mixture was sufficiently oscillated.Absorption spectra between 220 and 320 nm were recorded for the supernatant using an Ultraviolet Spectrometer (UV-1750, Shimadzu, Kyoto, Japan).

FTIR Spectra
The FTIR spectra were obtained with AVATAR360 FTIR (Nicolet Corporation, Madison, WI, USA) to characterize the nature of the interaction between the collectors and minerals.The sample for testing was prepared as follows.The collector and chalcopyrite (<2 µm) were mixed in aqueous solution.The precipitate was obtained after oscillation and set quietly for a while before it was washed 2-3 times using clean water and then dried in a vacuum.

Computation
Density Functional Theory (DFT) computations with the hybrid exchange-correlation functional B3LYP [23] were performed using Gaussian 09 [24] package.Initial molecular structures of the title products were drawn and pre-optimized by MM2 (a modified version of Allinger's MM2 force field) and PM3 (Parameterized Model Revision 3) methods.The molecular geometry was further optimized with the basis set 6-31 + g* [25,26].The binding model and molecular energy were calculated with the same basis set.The IEF-PCM model (the integral equation formalism for the polarizable continuum model) was adopted to calculate the properties of molecules in aqueous solution.ChemBioOffice 2010 was employed for predicting the clogP of molecules.

Frothing Performance of Ether Thionocarbamates
Frothing properties of the ether thionocarbamate solution were evaluated by characterizing the frothing ability and foam stability through recording the height and half-life, which were compared with those for methyl-isobutyl-carbinol (MIBC).To evaluate frothing characteristics in practical flotation, the frothing properties of the ether thionocarbamates in slurry were also determined.The foam height and half-life at different reagent concentrations are shown in Figures 3 and 4.
In general, the foam height and half-life reflect the frothing ability and foam stability, respectively.As seen in Figure 3, compared with the traditional frother MIBC, the synthesized ether thionocarbamates have a higher foam height and longer half-life, indicating they have a stronger frothing ability and better stability.Additionally, the frothing ability of BMIPECTC is stronger than Minerals 2016, 6, 97 6 of 16 that of BIPECTC.At a lower concentration, the foam half-lives of BIPECTC and BMIPECTC are almost the same; however, when the collector concentration is higher than 20 mg/L, the foam half-life of BMIPECTC is longer than that for BIPECTC.From Figure 4, the frothing characteristics of the ether thionocarbamate decreases in the slurry.This may be due to the reaction with minerals.The frothing properties of the synthesized ether thionocarbamates are better than that for IPETC and IBECTC, which are used for comparison.As a result, in practical flotation, less frother is required when using BIPECTC and BMIPECTC as the collectors.almost the same; however, when the collector concentration is higher than 20 mg/L, the foam half-life of BMIPECTC is longer than that for BIPECTC.From Figure 4, the frothing characteristics of the ether thionocarbamate decreases in the slurry.This may be due to the reaction with minerals.The frothing properties of the synthesized ether thionocarbamates are better than that for IPETC and IBECTC, which are used for comparison.As a result, in practical flotation, less frother is required when using BIPECTC and BMIPECTC as the collectors.The relationship between the foam height and half-life was fit to compare the foam properties, as shown in Figure 5.  almost the same; however, when the collector concentration is higher than 20 mg/L, the foam half-life of BMIPECTC is longer than that for BIPECTC.From Figure 4, the frothing characteristics of the ether thionocarbamate decreases in the slurry.This may be due to the reaction with minerals.
The frothing properties of the synthesized ether thionocarbamates are better than that for IPETC and IBECTC, which are used for comparison.As a result, in practical flotation, less frother is required when using BIPECTC and BMIPECTC as the collectors.The relationship between the foam height and half-life was fit to compare the foam properties, as shown in Figure 5.The relationship between the foam height and half-life was fit to compare the foam properties, as shown in Figure 5. almost the same; however, when the collector concentration is higher than 20 mg/L, the foam half-life of BMIPECTC is longer than that for BIPECTC.From Figure 4, the frothing characteristics of the ether thionocarbamate decreases in the slurry.This may be due to the reaction with minerals.The frothing properties of the synthesized ether thionocarbamates are better than that for IPETC and IBECTC, which are used for comparison.As a result, in practical flotation, less frother is required when using BIPECTC and BMIPECTC as the collectors.The relationship between the foam height and half-life was fit to compare the foam properties, as shown in Figure 5.  Figure 5 indicated that the foam height is linearly correlated with the foam half-life.We can easily compare the foam properties by the gradient of the fitting lines.The foam stability is better when the gradient is smaller.In this way, the foam stabilities conform to the following sequence: BMIPECTC > BIPECTC > MIBC.

Micro Flotation
Compared with IPETC and IBECTC, the influences of the pH and collector dosage on the collecting ability of ether thionocarbamates to chalcopyrite were investigated, as shown in Figure 6.In Figure 6a, the collector dosage is 60 mg/L and in Figure 6b, pH = 10.
Minerals 2016, 6, 97 7 of 16 Figure 5 indicated that the foam height is linearly correlated with the foam half-life.We can easily compare the foam properties by the gradient of the fitting lines.The foam stability is better when the gradient is smaller.In this way, the foam stabilities conform to the following sequence: BMIPECTC > BIPECTC > MIBC.

Micro Flotation
Compared with IPETC and IBECTC, the influences of the pH and collector dosage on the collecting ability of ether thionocarbamates to chalcopyrite were investigated, as shown in Figure 6.In Figure 6a, the collector dosage is 60 mg/L and in Figure 6b, pH = 10.As shown in Figure 6, the flotation performances of the synthesized ether thionocarbamates for chalcopyrite are obviously better than with IPETC and IBECTC.Additionally, Figure 6a shows that the recovery of chalcopyrite increases with increasing pH when pH < 10, and the recoveries reach a maximum at pH = 10. Figure 6b indicates that the recovery of chalcopyrite gradually increases as the collector dose increases from 10 to 60 mg/L.At the same concentration, the collecting ability to chalcopyrite conforms to the following sequence: BMIPECTC > BIPECTC > IBECTC > IPETC.
To evaluate the recovery changes with changes in both the pH and dosage levels, their response surface plots with both the pH level and dosage as the axes were drawn for BIPECTC and BMIPECTC, as shown in Figure 7.As shown in Figure 6, the flotation performances of the synthesized ether thionocarbamates for chalcopyrite are obviously better than with IPETC and IBECTC.Additionally, Figure 6a shows that the recovery of chalcopyrite increases with increasing pH when pH < 10, and the recoveries reach a maximum at pH = 10. Figure 6b indicates that the recovery of chalcopyrite gradually increases as the collector dose increases from 10 to 60 mg/L.At the same concentration, the collecting ability to chalcopyrite conforms to the following sequence: BMIPECTC > BIPECTC > IBECTC > IPETC.
To evaluate the recovery changes with changes in both the pH and dosage levels, their response surface plots with both the pH level and dosage as the axes were drawn for BIPECTC and BMIPECTC, as shown in Figure 7.
Minerals 2016, 6, 97 7 of 16 Figure 5 indicated that the foam height is linearly correlated with the foam half-life.We can easily compare the foam properties by the gradient of the fitting lines.The foam stability is better when the gradient is smaller.In this way, the foam stabilities conform to the following sequence: BMIPECTC > BIPECTC > MIBC.

Micro Flotation
Compared with IPETC and IBECTC, the influences of the pH and collector dosage on the collecting ability of ether thionocarbamates to chalcopyrite were investigated, as shown in Figure 6.In Figure 6a, the collector dosage is 60 mg/L and in Figure 6b, pH = 10.As shown in Figure 6, the flotation performances of the synthesized ether thionocarbamates for chalcopyrite are obviously better than with IPETC and IBECTC.Additionally, Figure 6a shows that the recovery of chalcopyrite increases with increasing pH when pH < 10, and the recoveries reach a maximum at pH = 10. Figure 6b indicates that the recovery of chalcopyrite gradually increases as the collector dose increases from 10 to 60 mg/L.At the same concentration, the collecting ability to chalcopyrite conforms to the following sequence: BMIPECTC > BIPECTC > IBECTC > IPETC.
To evaluate the recovery changes with changes in both the pH and dosage levels, their response surface plots with both the pH level and dosage as the axes were drawn for BIPECTC and BMIPECTC, as shown in Figure 7.The effects of the slurry pH and collector dosage on the mineral recovery are more straightforward in the surface plots.In Figure 7, the dark red region represents the higher copper recovery and the dark blue region represents the lower one.From Figure 7, the slurry pH has a weak influence on the recovery of chalcopyrite, however, the copper recovery is better at pH = 8-10 with low collector dosage (less than 20 mg/L) for both BIPECTC and BMIPECTC; meanwhile, the effect of the collector dosage is significant until it exceeds 60 mg/L.The recovery of chalcopyrite increased little when collector dosage is more than 60 mg/L.

Batch Flotation Tests
Batch flotation tests were used to investigate the behavior of the synthesized ether thionocarbamates for the porphyry copper-molybdenum ore.The yields of rough concentrate, copper grade and recovery are listed in Table 3, where RSD is the relative standard deviation.Table 3 indicates that the copper recoveries are improved by the synthesized ether thionocarbamates compared with IPETC and IBECTC, even with fewer MIBC, which serves as frother.The results are consistent with the pure mineral flotation experiments.Furthermore, the assumption was confirmed that the introduction of alkoxyl group endows the thionocarbamates with good frothing properties.We can also conclude that the collecting ability of ether thionocarbamates for copper increases with increasing carbon chains.

Adsorption Tests
The adsorption capacity of a collector is known to affect the mineral floatability.The adsorptive capacity for chalcopyrite was measured by the solution pH and initial concentration of collectors.The influence of the solution pH on the adsorptive capacity of chalcopyrite for ether thionocarbamates is shown in Figure 8.At an approximate pH of 8-10, chalcopyrite exhibited better adsorption ability for ether thionocarbamates compared with other pH values.Additionally, the adsorption quantities of the synthesized ether thionocarbamates are stronger than those of IPETC and IBECTC, which is also in agreement with the micro flotation experiments.The adsorptive capacities of chalcopyrite for ether thionocarbamates with different concentrations were measured at pH 9, as shown in Figure 9.The adsorptive capacities for ether thionocarbamates significantly increased with their concentrations.It can be concluded that the adsorptive capacity of chalcopyrite for BMIPECTC is better than for BIPECTC.

UV Spectra of Collectors and Metal Ions
UV spectra of the synthesized ether thionocarbamates have been adopted to evaluate the interaction between the collectors and Cu 2+ , Fe 2+ , Ni 2+ , Zn 2+ or Pb 2+ ions, as shown in Figure 10.As seen in Figure 10, the absorption peaks for both BIPECTC and BMIPECTC are located at approximately 255 nm.It is apparent that their UV spectrum intensities significantly decreased after

UV Spectra of Collectors and Metal Ions
UV spectra of the synthesized ether thionocarbamates have been adopted to evaluate the interaction between the collectors and Cu 2+ , Fe 2+ , Ni 2+ , Zn 2+ or Pb 2+ ions, as shown in Figure 10.As seen in Figure 10, the absorption peaks for both BIPECTC and BMIPECTC are located at approximately 255 nm.It is apparent that their UV spectrum intensities significantly decreased after

UV Spectra of Collectors and Metal Ions
UV spectra of the synthesized ether thionocarbamates have been adopted to evaluate the interaction between the collectors and Cu 2+ , Fe 2+ , Ni 2+ , Zn 2+ or Pb 2+ ions, as shown in Figure 10.

UV Spectra of Collectors and Metal Ions
UV spectra of the synthesized ether thionocarbamates have been adopted to evaluate the interaction between the collectors and Cu 2+ , Fe 2+ , Ni 2+ , Zn 2+ or Pb 2+ ions, as shown in Figure 10.As seen in Figure 10, the absorption peaks for both BIPECTC and BMIPECTC are located at approximately 255 nm.It is apparent that their UV spectrum intensities significantly decreased after As seen in Figure 10, the absorption peaks for both BIPECTC and BMIPECTC are located at approximately 255 nm.It is apparent that their UV spectrum intensities significantly decreased after Minerals 2016, 6, 97 10 of 16 they mixed with Cu 2+ solution compared with other metal ion solutions.The results indicated that the title products have stronger affinity to copper ion than to other metal ions.

FTIR Spectra of Chalcopyrite
The FTIR spectra of chalcopyrite and chalcopyrite adsorbed by BIPECTC and BMIPECTC are shown in Figure 11.
they mixed with Cu 2+ solution compared with other metal ion solutions.The results indicated that the title products have stronger affinity to copper ion than to other metal ions.

FTIR Spectra of Chalcopyrite
The FTIR spectra of chalcopyrite and chalcopyrite adsorbed by BIPECTC and BMIPECTC are shown in Figure 11.
In the FTIR spectra of chalcopyrite adsorbed by BIPECTC or BMIPECTC, the absorption peak of C=O stretching vibration was observed at 1627 cm −1 .At about 1500 cm −1 , the conjunction vibration of C-O and C-N was observed.The C=S stretching vibration was found at 1095 cm −1 .The stretching vibration of N-H appeared at around 3400 cm −1 .It can be concluded that chemical adsorption occurred on the surface of chalcopyrite.

Molecular Geometry
The optimized molecular structures of IPETC, IBECTC and ether thionocarbamates in water are shown in Figure 12 and labeled with the element symbols for C, N, O and S.
As shown in Figure 12, IBECTC and the ether thionocarbamates contain -C(=S)-N-(O=)Cgroup, and the conjugate -C(=S)-N-(O=)C-group improves the electron delocalization itself, which may result in a stronger ability to accept the back donation electron from mineral metals, such as copper.The dihedral angles of the -C(=S)-N-(O=)C-group in ether thionocarbamates were −0.77987° and 0.57394° for BIPECTC and BMIPECTC, respectively.In other words, it is preferential to form a six-membered ring with a copper ion for the molecular structure.From this point of view, IBECTC may also have a stronger chelating ability for copper ion than IPETC.In the FTIR spectra of chalcopyrite adsorbed by BIPECTC or BMIPECTC, the absorption peak of C=O stretching vibration was observed at 1627 cm −1 .At about 1500 cm −1 , the conjunction vibration of C-O and C-N was observed.The C=S stretching vibration was found at 1095 cm −1 .The stretching vibration of N-H appeared at around 3400 cm −1 .It can be concluded that chemical adsorption occurred on the surface of chalcopyrite.they mixed with Cu 2+ solution compared with other metal ion solutions.The results indicated that the title products have stronger affinity to copper ion than to other metal ions.

FTIR Spectra of Chalcopyrite
The FTIR spectra of chalcopyrite and chalcopyrite adsorbed by BIPECTC and BMIPECTC are shown in Figure 11.
In the FTIR spectra of chalcopyrite adsorbed by BIPECTC or BMIPECTC, the absorption peak of C=O stretching vibration was observed at 1627 cm −1 .At about 1500 cm −1 , the conjunction vibration of C-O and C-N was observed.The C=S stretching vibration was found at 1095 cm −1 .The stretching vibration of N-H appeared at around 3400 cm −1 .It can be concluded that chemical adsorption occurred on the surface of chalcopyrite.

Molecular Electrostatic Potential
The molecular electrostatic potential (MEP) describes the electron density in the target molecule, and it is a very useful descriptor to predict the reactive sites for electrophilic or nucleophilic attacks in various reactions [27,28].The MEP is a plot of the electrostatic potential mapped onto the constant electron density surface.The advantage of the MEP lies in the fact that it simultaneously and visually displays a molecular size and shape as well as positive, negative and neutral electrostatic potential regions in terms of color grading.In the majority of the MEP maps, red and blue represent the regions with the most negative and most positive electrostatic potentials, respectively.The color coding of these maps is in the range between −0.05 (deepest red) and 0.05 a.u.(deepest blue) in compounds.In the present study, 3D plots of MEP for IPETC, IBECTC, BIPECTC and BMIPECTC are shown in Figure 13.

Molecular Electrostatic Potential
The molecular electrostatic potential (MEP) describes the electron density in the target molecule, and it is a very useful descriptor to predict the reactive sites for electrophilic or nucleophilic attacks in various reactions [27,28].The MEP is a plot of the electrostatic potential mapped onto the constant electron density surface.The advantage of the MEP lies in the fact that it simultaneously and visually displays a molecular size and shape as well as positive, negative and neutral electrostatic potential regions in terms of color grading.In the majority of the MEP maps, red and blue represent the regions with the most negative and most positive electrostatic potentials, respectively.The color coding of these maps is in the range between −0.05 (deepest red) and 0.05 a.u.(deepest blue) in compounds.
In the present study, 3D plots of MEP for IPETC, IBECTC, BIPECTC and BMIPECTC are shown in Figure 13.

Molecular Electrostatic Potential
The molecular electrostatic potential (MEP) describes the electron density in the target molecule, and it is a very useful descriptor to predict the reactive sites for electrophilic or nucleophilic attacks in various reactions [27,28].The MEP is a plot of the electrostatic potential mapped onto the constant electron density surface.The advantage of the MEP lies in the fact that it simultaneously and visually displays a molecular size and shape as well as positive, negative and neutral electrostatic potential regions in terms of color grading.In the majority of the MEP maps, red and blue represent the regions with the most negative and most positive electrostatic potentials, respectively.The color coding of these maps is in the range between −0.05 (deepest red) and 0.05 a.u.(deepest blue) in compounds.In the present study, 3D plots of MEP for IPETC, IBECTC, BIPECTC and BMIPECTC are shown in Figure 13.From the MEP maps, it is evident that the negative charge covers the C=S and C=O groups, and the positive region is mainly over the hydrogen that is adjacent to the N atom for IBECTC, BIPECTC and BMIPECTC.As for IPETC, a similar situation is observed without the C=O group.The value of the electrostatic potential is largely responsible for the binding sites of a substrate to its receptor because the receptor and corresponding ligand recognize each other at their molecular surfaces.Consequently, the higher electronegativity in the C=S and C=O groups makes them the most reactive parts in the molecule for denoting electrons to the receptor (such as minerals), forming six-membered chelate rings [16].Furthermore, the atom net charge obtained from NBO (natural bond orbital) analysis revealed that the S and O atoms in BIPECTC (S −0.212, O −0.651) and BMIPECTC (S −0.213, O −0.651) possess a more negative charge than IBECTC (S −0.200, O −0.641).In other words, BIPECTC and BMIPECTC have stronger affinity to copper ion than IBECTC.

Frontier Molecular Orbitals
Frontier molecular orbitals (FMO), the highest occupied molecular orbital (HOMO) energy and the lowest unoccupied molecular orbital (LUMO), and their properties, such as energy, are very useful and important parameters for quantum chemistry [29].The energy gap, ∆E HOMO-LUMO is an important value that serves as a stability index.In fact, a large HOMO-LUMO energy gap implies high molecular stability in terms of its lower reactivity in different chemical reactions [30][31][32].The HOMO represents the ability to donate an electron.The LUMO, as an electron acceptor, represents the ability to obtain an electron.The collecting ability of a collector consists of donating electrons to mineral and accepting feedback electrons from mineral.The calculated energies of HOMO and LUMO are listed in Table 4.As shown in Table 4, the energy gap of BMIPECTC is the smallest, indicating that the chemical reactivity of BMIPECTC is strongest among the four collectors, which is followed by BIPECTC.The reactivity of a collector to metal ion can reflect its collecting ability to the corresponding mineral to a certain degree [33][34][35].Accordingly, the binding model between collectors and copper ions is simulated to discuss their collecting ability to chalcopyrite.The optimized geometries of binding model are shown in Figure 14.
To obtain more evidence for the formation of complexes between copper ions and collectors, the bond order is adopted to discuss the bond variation.The bond order is the number of chemical bonds between a pair of atoms, which gives an indication of the stability and strength of a bond.Because the bond order is not a quantum-mechanical observable and this term is not semantically precise, there are many different quantum-chemical definitions of this descriptor among which the Wiberg bond index is useful and extensively used in bond order analysis and is provided by the Gaussian package [36][37][38].
The concerned bonds are shown in Figure 15, and the atom numbers are labeled.As displayed in Table 5, the Wiberg bond indices of S-Cu are approximately 0.50 and those of O-Cu are approximately 0.23, indicating that new bonds formed between copper ion and the four collectors, which can also be clearly observed from the binding model shown in Figure 14.After IBECTC, BIPECTC and BMIPECTC interact with copper ion, the Wiberg bond indices of C=S and C=O became smaller from the electron transfer to copper ion.Consequently, the N atom and other O atoms in the functional group offer their electrons to compensate for the vacant position in the C=S and C=O groups.As a result, the bond orders for other bonds become slightly larger, as shown in Table 5.In summary, the electrons are better distributed in the functional group after interacting with copper ion.With respect to IPETC, although the bond order of S-Cu is a little larger than that of the corresponding bonds for IBECTC, BIPECTC and BMIPECTC, its binding with copper ion may be not as strong as IBECTC, BIPECTC or BMIPECTC because the combination between IPETC and copper only occurs through the C=S group, while the C=S and C=O groups are both involved in the combination for the latter.Moreover, the combination between copper and BIPECTC or BMIPECTC is stronger than with IBECTC due to the larger Wiberg bond indices of S-Cu and O-Cu.
Minerals 2016, 6, 97 13 of 16 Table 5.In summary, the electrons are better distributed in the functional group after interacting with copper ion.With respect to IPETC, although the bond order of S-Cu is a little larger than that of the corresponding bonds for IBECTC, BIPECTC and BMIPECTC, its binding with copper ion may be not as strong as IBECTC, BIPECTC or BMIPECTC because the combination between IPETC and copper only occurs through the C=S group, while the C=S and C=O groups are both involved in the combination for the latter.Moreover, the combination between copper and BIPECTC or BMIPECTC is stronger than with IBECTC due to the larger Wiberg bond indices of S-Cu and O-Cu.Table 5.In summary, the electrons are better distributed in the functional group after interacting with copper ion.With respect to IPETC, although the bond order of S-Cu is a little larger than that of the corresponding bonds for IBECTC, BIPECTC and BMIPECTC, its binding with copper ion may be not as strong as IBECTC, BIPECTC or BMIPECTC because the combination between IPETC and copper only occurs through the C=S group, while the C=S and C=O groups are both involved in the combination for the latter.Moreover, the combination between copper and BIPECTC or BMIPECTC is stronger than with IBECTC due to the larger Wiberg bond indices of S-Cu and O-Cu.

Figure 1 .
Figure 1.Diagrammatic sketch of the frothing property determined by the airflow method.

Figure 1 .
Figure 1.Diagrammatic sketch of the frothing property determined by the airflow method.

Figure 1 .
Figure 1.Diagrammatic sketch of the frothing property determined by the airflow method.

1 Figure 1 .
Figure 1.Diagrammatic sketch of the frothing property determined by the airflow method.

Figure 2 .
Figure 2. The flow sheet of rougher flotation for chalcopyrite.

Figure 3 .Figure 4 .
Figure 3. Maximum foam height and half-life as a function of the frother concentrations in aqueous solution.(a) Foam height; (b) Foam half-life.

Figure 5 .
Figure 5. Relationship between the foam height and half-life.

Figure 3 .
Figure 3. Maximum foam height and half-life as a function of the frother concentrations in aqueous solution.(a) Foam height; (b) Foam half-life.

Figure 3 .Figure 4 .
Figure 3. Maximum foam height and half-life as a function of the frother concentrations in aqueous solution.(a) Foam height; (b) Foam half-life.

Figure 5 .
Figure 5. Relationship between the foam height and half-life.

Figure 4 .
Figure 4. Maximum foam height and half-life as a function of the collector concentrations in slurry.(a) Foam heigh; (b) Foam half-life.

Figure 3 .Figure 4 .
Figure 3. Maximum foam height and half-life as a function of the frother concentrations in aqueous solution.(a) Foam height; (b) Foam half-life.

Figure 5 .
Figure 5. Relationship between the foam height and half-life.

Figure 5 .
Figure 5. Relationship between the foam height and half-life.

Figure 7 .
Figure 7. Recovery response surface plots with both the slurry pH and collector dosage.

Figure 7 .
Figure 7. Recovery response surface plots with both the slurry pH and collector dosage.

Figure 7 .
Figure 7. Recovery response surface plots with both the slurry pH and collector dosage.

Figure 9 .
Figure 9. Adsorption quantity as a function of the collector concentration (pH = 9).

Figure 9 .
Figure 9. Adsorption quantity as a function of the collector concentration (pH = 9).

Figure 9 .
Figure 9. Adsorption quantity as a function of the collector concentration (pH = 9).

Figure 9 .
Figure 9. Adsorption quantity as a function of the collector concentration (pH = 9).

3. 8 .
Quantum Chemistry Calculation3.8.1.Molecular GeometryThe optimized molecular structures of IPETC, IBECTC and ether thionocarbamates in water are shown in Figure12and labeled with the element symbols for C, N, O and S.As shown in Figure12, IBECTC and the ether thionocarbamates contain -C(=S)-N-(O=)Cgroup, and the conjugate -C(=S)-N-(O=)C-group improves the electron delocalization itself, which may result in a stronger ability to accept the back donation electron from mineral metals, such as copper.The dihedral angles of the -C(=S)-N-(O=)C-group in ether thionocarbamates were −0.77987 • and 0.57394 • for BIPECTC and BMIPECTC, respectively.In other words, it is preferential to form a six-membered ring with a copper ion for the molecular structure.From this point of view, IBECTC may also have a stronger chelating ability for copper ion than IPETC.Minerals 2016, 6, 97 10 of 16

Figure 14 .
Figure 14.The binding model between copper ion and BIPECTC, BMIPECTC and IPETC.

Figure 14 .
Figure 14.The binding model between copper ion and BIPECTC, BMIPECTC and IPETC.

Table 1 .
Chemical analysis of the ore.All percentages are given as weight percentage of the total.

Table 2 .
Ore type for copper minerals.

Table 1 .
Chemical analysis of the ore.All percentages are given as weight percentage of the total.

Table 2 .
Ore type for copper minerals.

Table 3 .
Comparative Cu recoveries by IPETC, IBECTC and the synthesized products.