Research on the Preparation of Kaolin from Coal Gangue by Flotation Decarburization with Different Collectors

Abstract

In order to find a better collector for the separation of carbon and kaolin from coal gangue flotation, and to explore the action mechanism of collectors, this paper selected 12 kinds of collectors for systematic comparison, including five non-polar organics with different carbon chain lengths, and polar organic matters with double bonds, triple bonds, benzene, as well as cycloalkyl, ester, carboxyl, and aldehyde groups. The flotation results show that the longer carbon chain (with a carbon atom number of 13~15), the better the flotation effect, the better the effect of the collector with the phenyl group (among the four hydrocarbon groups), and the better the effect of the collector with the ester group (among the three functional groups). In order to explore the flotation mechanism at the microscopic level, the molecular structure of carbon in coal gangue was detected using a solid nuclear magnetic test. Afterwards, the organic macromolecule model of carbon was simulated. Finally, the interaction energy values between carbon and collectors were calculated in accordance with the density functional theory, and the order of the acting force of collectors was obtained, which was consistent with that of the collectors in the macro experiment.

1. Introduction

Coal gangue is the waste produced during coal mining and processing, accounting for about 10~15% of the total coal production [1]. The accumulation of coal gangue leads to environmental pollution, including soil and water pollution caused by the weathering and leaching of coal gangue, harmful gas and dust caused by the spontaneous combustion of coal gangue, and a waste of land resources caused by coal gangue stacking [1,2,3]. However, the processing and utilization of coal gangue not only reduces the impact of coal gangue on the environment, but it also turns coal gangue into a resource to increase economic benefits. It has been proven that kaolin can be prepared from coal gangue with more than 80% kaolin mineral content [4,5]. The technology of kaolin preparation from coal gangue has been applied industrially in numerous countries, which alleviates the shortage of high-quality, non-coal measured kaolin. However, it must be noted that the impurities in coal gangue must be removed to prepare qualified kaolin. The impurities in coal gangue mainly include carbon, iron, titanium, quartz, and so on [6], among which, carbon is the most abundant. At present, some research has been conducted on the removal of carbon from coal gangue. Zhang [7] found that the optimum calcination temperature was 700 °C by calcining coal gangue for decarburization. Cheng [8] found that decarbonization via calcination was a two-step reaction, with the temperature ranges of the first and second steps being 350–550 °C and 580–830 °C, respectively. Yuan [9,10,11] conducted a comparative study on the convective calcination and static calcination of coal measured kaolin, finding that under the same calcination temperature, kaolin products with higher whiteness and lower COD (Chemical Oxygen Demand, such as pyrite and organic matter) values can be obtained via fluidized calcination. Yuan [9] also discovered that the COD value of coal gangue decreased with an increase in calcination temperature. At 500 °C, the COD value of the kaolin product decreased to 2217 μg/g, and at 900 °C, the COD value was reduced to 460 μg/g. He [12] separated carbon from kaolin in coal measures using the electric separation method. When the voltage was 32 kv, the feed frequency was 5 Hz, and the flow rate was 20 cm³/s; the decarbonization efficiency was higher, reaching 27.78%. Peng [13] used the gravity separation method to remove carbon from coal gangue. The ignition loss (LOI) of the kaolin product obtained via a float and sink experiment was 44.22% lower than that obtained from raw materials. The kaolin decarburized by the gravity separation method was whiter than that carburized by raw materials. Huang [14] confirmed that carbon had a great influence on the COD value of coal gangue, removing carbon from raw materials via the flotation method. The COD value of carbon products obtained after flotation was 216,202 μg/g, much higher than that of raw materials and kaolin products. Huang [15] also found that the COD value of coal gangue existed in different grain sizes in raw materials. Regarding the employment of the calcination method for decarburization, the optimum grain size for reducing the COD value of raw materials was in the range of −74~+60 μm when the calcination temperature was 450 °C, indicating the COD value of raw materials could be reduced from 27,517 μg/g to 585 μg/g. Huang [16] also studied the combined process of flotation and calcination, finding that the COD value of the kaolin obtained via flotation was 3533 μg/g. When the kaolin was calcined under the condition of 300 °C, the COD value of the calcined kaolin was close to 2700 μg/g, and the temperature was much lower than that of direct calcination without flotation. If the kaolin obtained from flotation was calcined at 450 °C, the COD value of the calcined kaolin could be as low as 290 μg/g. Therefore, compared with direct calcination, the process of flotation followed by calcination reduced the calcination temperature, calcination cost, and COD value of kaolin products.

Regarding the above, it is obvious that the main methods of decarbonization include calcination, electric separation, gravity separation, flotation, etc. In fact, although carbon in coal gangue is an impurity during the preparation of kaolin, it becomes a valuable energy after being enriched, especially for low ash coal gangue with higher carbon contents. However, at present, the most commonly used method of decarbonization is calcination, which often results in the loss of carbon. In addition to consuming heat energy, calcination also brings certain atmospheric pollution, and it sometimes leads to the destruction of the layered structure of the kaolinite’s crystal phase. Flotation is an effective method to recover carbon resources, but there are very few studies on the removal of carbon from coal gangue via flotation, and the published research results on flotation all focus upon fixed and commonly used flotation agents, such as kerosene or diesel. At present, there is no comparative study of different flotation agents in the flotation process of coal gangue. Therefore, this paper mainly compares the interaction between coal molecules in coal gangue and various flotation agents, and it reveals the mechanism of action. Since collectors play a very important role in flotation reagents, it is necessary to study collectors in depth. During industrial production processes, kerosene and diesel are often used as collectors, and they have different carbon chain lengths. Therefore, it is essential to examine the interaction between agents with different carbon chain lengths and coal molecules. In addition, considering that kerosene and diesel oil interact with coal molecules in gangue through their alkyl groups, it is necessary to study the mechanism of action between other groups and coal molecules, except alkyl groups. In short, this paper focused on researching the interaction mechanism between collectors with different chain lengths and different groups and coal molecules; it also attempted to explore the mechanism concerning the flotation decarbonization of coal gangue.

2. Experimental Materials and Methods

2.1. Experimental Raw Materials

The raw material used in this experiment was coal gangue. In order to fully explain the properties of raw materials, especially the contents of carbon and kaolinite, as well as the functional group composition of coal gangue, the ingredients comprising the raw materials were tested. The test results are described as follows.

Firstly, industrial component analysis of the coal gangue raw material was conducted, in which water was tested using a drying oven, ash and volatile components were tested using a Muffle furnace, and the fixed carbon content was calculated by subtracting the water, ash, and volatile components. The results are shown below in

Table 1. Industrial analysis results of coal gangue.

Raw Material	Aad	Mad	Vad	Cad
Coal gangue	53.45%	1%	20.88%	24.67%

. More specifically, Aad, Mad, Vad, and Cad represent ash, moisture, volatile components, and the fixed carbon content of coal gangue, respectively, in a natural air drying state, and the lower corner mark “ad” represents the state of air drying.

As is evident in the table above, the ash content is 53.45%. The water and volatile component contents are 1% and 20.88%, respectively. Fixed carbon accounts for 24.67%, indicating the relatively high carbon content.

Second, the chemical composition of the coal gangue was analyzed using an X-ray fluorescence spectrometer (XRF, S8 Tiger, Bruker, Berlin, Germany). The XRF worked at 20–60 kV and 10–100 mA, with a collimator angle of 0.23°. The XRF test results are summarized in

Table 2. XRF analysis results of gangue.

Analyte	Na	Mg	Al	Si	S	K	Ca	Ti	Fe
Compound formula	Na2O	MgO	Al2O3	SiO2	SO3	K2O	CaO	TiO2	Fe2O3
Concentration (%)	0.13	0.34	44.77	49.65	0.356	1.16	0.44	1.39	1.54

. Only elements with content greater than 0.1% are listed in the table, and inorganic elements were mainly analyzed. According to the calculations, the Al₂O₃/SiO₂ ratio was 0.9, which was higher than the theoretical value of kaolinite, which is 0.85.

From the analysis of raw materials, the kaolin and carbon contents in the coal gangue after separation were high, and the raw materials exhibited separation and enrichment values.

Third, in order to understand the types and approximate proportions of the functional groups of the carbon molecule in coal gangue, a Fourier transform infrared spectrometer (FT-IR, Vertex 80v, Bruker, Berlin, Germany) was used for the infrared detection of coal gangue. Samples were prepared into pellets with KBr (the ratio of the sample to KBr is 1–100). A Perkin Elmer Spectrum 2000 model spectrometer was employed to record the spectra at a 2 cm⁻¹ resolution between 4000 and 400 cm⁻¹. The test results are described below in Figure 1.

The types of functional groups and their approximate proportions in coal gangue were obtained from the analysis of Figure 1. Specific details are organized below in

Table 3. Analysis table of the infrared detection results of the carbon molecule in coal gangue.

Peak Position (cm−1)	Functional Group Type	Proportion
3693, 3620	-OH (dissociation)	15.75%
1606	C=C	6.61%
1440	-OH(In-plane bending vibration)	1.32%
1033, 1009	C-O	40.19%
913	-COOH	7.75%
796, 753, 694, 2921, 2852	C-H	7.92%
539, 470	Si-O-Si, Si-O-Al	20.46%

.

2.2. Experimental Agents

2.2.1. Collectors

Five kinds of collectors with different carbon chain lengths, and seven kinds of collectors with different groups were selected for comparison. Information concerning these collectors is listed in the following

Table 4. Summary of collectors.

Collectors	Molecular Formula	Purity	Molecular Weight	Characteristics
Hexane	C6H14	97%	86.18	The length of the carbon chain is different
Octane	C8H18	>99%	114.23
Decane	C10H22	99%	142.28
Tridecane	C13H28	98%	184.36
Pentadecane	C15H32	99%	212.41
Dodecene	C12H24	96%	168.32	With double bond
Dodecyne	C12H22	>95%	166.31	With triple bond
Octylbenzene	C14H22	98%	190.33	With phenyl
Octylcyclohexa	C14H28	≥98%	196.38	Alicyclic
Dodecanoic Acid	C12H24O2	98%	200.32	With carboxyl group
Methyl laurate	C13H26O2	99.7%	214.34	With an ester group
Lauraldehyde	C12H24O	95%	184.32	Aldehydic

.

2.2.2. Dispersant and Foaming Agents

The dispersant was fixed with sodium metaphosphate (molecular formula Na₆O₁₈P₆, AR grade, content of 98%), and the foaming agent was fixed with sec-octanol (molecular formula C₈H₁₈O, AR grade, content of 98%).

2.3. Experimental Method

First, 60 g of the raw material was weighed and placed into the flotation tank, and 1 L tap water which was measured using a measuring cylinder was poured into the flotation tank. The mixture was stirred using the flotation machine stirring device at a speed of 2000 r/min. Then, 2‰ sodium hexametaphosphate was added and stirred for 2 min. The collector accounted for 2.5‰ of the raw material’s weight, it was added and stirred for 2 min, and then 1‰ foaming agent was weighed, added, and stirred for 1 min. When the stirring process was complete, the mixture was aerated for 30 s using the aeration device of the flotation machine. Subsequently, the foam products floating on the pulp were scraped using the bubble scraping device. Finally, the foam products and the slurry in the tank were filtered and dried, respectively, and they were kept as samples for later sample testing and data processing. The foam product was carbon, and the slurry in the tank was enriched kaolin.

The flotation machine used in this experiment is shown below Figure 2.

First, the raw material powder and water was poured into the plastic tank located in the middle of the machine, and the stirring device was activated by setting the stirring speed on the operation panel on the right side of the machine. The agitator located in the middle of the plastic tank then began to stir, as per the set speed. During the stirring process, the dosing process was completed in accordance with the adding order and time that the flotation agents were added, as described above. Finally, the air switch was opened on the left side of the machine to let air in. At this time, both hydrophilic and hydrophobic components in the material began to separate, at which point, the hydrophobic carbon floated on the pulp with air bubbles, and it was scraped into the basin; the hydrophilic enriched kaolin remained in the pulp. This was the process by which carbon products were separated from enriched kaolin. The two products were extracted using a filter, and they were dried in a drying oven, after which, the yield of the products was calculated and the ash content was detected.

3. Results and Discussion

3.1. Results of Flotation Experiment

After the flotation of coal gangue with collectors of different groups and different carbon chain lengths, results were obtained, which are listed in Figure 3, Figure 4 and Figure 5. The concentrate marked in the legend represents the floating foam product obtained from the flotation process, namely, the carbon product, whereas the corresponding tailings refer to the enriched kaolin product left in the pulp. Before analyzing the changing trend of the flotation results, the objective of flotation should first be clarified; it should aim to remove as many carbon impurities in coal gangue as possible, and it should try to reduce the kaolin content while removing carbon. In other words, the yield of the carbon product should be as high as possible, and the lower the ash content of the carbon product, and the higher ash content of the enriched kaolin, the better the results. The flotation results were analyzed as follows.

As mentioned above, the yield and ash content of products are the two indicators that are being focused upon in this paper. The two products obtained via flotation in this paper are carbon products and enriched kaolin products, with their yield and ash tested using a drying oven and Muffle furnace. The test results are listed below. In order to discuss the flotation effect of collectors with different characteristics, all the test results were organized into three tables, including the flotation results of collectors with different carbon chain lengths, collectors with different hydrocarbon groups, and collectors with different functional groups.

Figure 3. The variation diagram of the flotation results of collectors with different carbon chain lengths.

Figure 3. The variation diagram of the flotation results of collectors with different carbon chain lengths.

3.1.1. The Flotation of Coal Gangue Using Collectors with Different Carbon Chain Lengths

The flotation results are presented in

Table 5. The flotation results of collectors with different carbon chain lengths.

Collectors	The Name of the Products	Yield (%)	Ash Content (%)
Hexane	carbon	19.98	36.83
	enriched kaolin product	80.02	55.60
Octane	carbon	31.37	35.12
	enriched kaolin product	68.63	56.74
Decane	carbon	31.14	36.25
	enriched kaolin product	68.86	57.21
Tridecane	carbon	41.39	33.11
	enriched kaolin product	58.61	57.57
Pentadecane	carbon	43.67	34.68
	enriched kaolin product	56.33	60.78

.

According to the above table, as the carbon chain length of the collectors changed, so did the yield and ash content of the carbon products and enriched kaolin products obtained through flotation. To observe this changing trend more clearly, the data in the above table were plotted in the following figure, and corresponding changes were analyzed in detail.

As observed, the black yield curve of carbon products essentially increased as the carbon chain length of the collector increased, but the amplitude of these increases varied. More specifically, the yield of n-octane with 8 carbon atoms increased by about one-third compared with n-hexane which has 6 carbon atoms, whereas the yield of n-decane with 10 carbon atoms was approximately the same as that of n-octane. Tridecane with 13 carbon atoms increased its yield by approximately one third more than n-decane, and pentadecane with 15 carbon atoms slightly increased its yield compared with tridecane, but only slightly. Regarding the blue yield curve concerning enriched kaolin products, the changing trend was opposite to that of the carbon product yield; that is, as the collector chain length increased, the yield presented a downward trend. Regarding the red ash curve of the carbon products, in general the range of change was not large, first showing a downward trend and then an upward trend, with the lowest point reaching 33.11%, indicating that when the number of carbon atoms was about 13, the ash content of the carbon products was low. Regarding the green ash curve of enriched kaolin products, the range of change for ash was also small, showing a constantly rising trend overall. When the number of carbon atoms exceeded 13, the range for ash became larger.

By synthesizing these four curves, it is evident that the carbon chain of collectors should not be too short. Carbon chain that are too short may result in a carbon yield that is too low, which may lead to a relatively high ash content in carbon products and a relatively low ash content in enriched kaolin. Moreover, it is not necessary to use the longest carbon chain, because the increased carbon yield is not significant when the carbon chain reaches a certain length, and it would lead to an increase in the ash content of the carbon products.

3.1.2. Flotation of Coal Gangue using Collectors with Different Hydrocarbon Groups

The flotation results of collectors with different hydrocarbon groups were discussed. The test data of the flotation products are listed in the

Table 6. The flotation results of collectors with different hydrocarbon groups.

Collectors	The Name of the Products	Yield (%)	Ash Content (%)
Dodecene	carbon	38.19	33.73
	enriched kaolin product	61.81	61.70
Dodecyne	carbon	40.28	34.50
	enriched kaolin product	59.72	60.88
Octylbenzene	carbon	45.89	36.12
	enriched kaolin product	54.11	63.76
Octylcyclohexa	carbon	40.63	35.89
	enriched kaolin product	59.37	59.90

below.

According to the above table, when collectors with different hydrocarbon groups were used for flotation, the yield and ash content of the carbon products and enriched kaolin products were also different. To observe the changing trend more clearly, the data in the above table were used to create the following figure, and corresponding changes were analyzed in detail.

The flotation results are shown in Figure 4.

Figure 4. The comparison of the flotation effects of collectors with different hydrocarbon groups.

Figure 4. The comparison of the flotation effects of collectors with different hydrocarbon groups.

As is evident from the figure above, the black yield curve representing carbon products generally presented a trend that first increased and then decreased. The collector with double bonds provided the lowest yield, the collector with phenyl provided the highest yield, and the collector with triple bonds provided the same yield as the collector with cycloalkyl. The red ash curve representing carbon products also exhibited a trend that first increased and then decreased overall, but with a small range of change. The blue yield curve representing the enriched kaolin generally revealed a trend that first decreased and then increased, which contrasted with the black curve representing the carbon product yield. The green ash curve representing the enriched kaolin generally revealed a trend that first increased and then decreased. The maximum ash content was obtained from the collector with a phenyl group, whereas the ash content of the enriched kaolin was very similar to that produced by collectors with the other three kinds of hydrocarbon group.

Based on the above curve, it is evident that the carbon product yield of the collector with double bonds achieved the lowest carbon yield, the ash content of the carbon product was not significantly lower than that of other hydrocarbon-based collectors, and the ash content of the enriched kaolin was not the highest. The flotation effect of the collector with triple bonds was similar to that of the collector with cycloalkyl, but the flotation effect was neither the best nor worst. The yield of carbon products obtained from benzene collectors was higher, indicating that the benzene ring structure presented stronger interactions with the carbon molecule. In addition, the ash content of carbon products obtained using this collector slightly increased, whereas the ash content of the enriched kaolin increased to a greater extent, indicating that the collector with benzene exhibited a weak interaction with kaolin molecules when it reacted with the carbon molecule. In other words, the collector exhibited good selectivity. Therefore, the collector with the benzene ring structure could achieve a better flotation effect than other hydrocarbon groups.

3.1.3. Flotation of Coal Gangue Using Collectors with Different Functional Groups

The flotation results of collectors with different functional groups were explored. The test data are listed below

Table 7. The flotation results of collectors with different functional groups.

Collectors	The Name of the Products	Yield (%)	Ash Content (%)
Methyl laurate	carbon	51.22	37.85
	enriched kaolin product	48.78	66.55
Lauraldehyde	carbon	40.25	42.62
	enriched kaolin product	59.75	55.83
Dodecanoic Acid	carbon	42.53	36.22
	enriched kaolin product	57.47	61.27

, as follows.

According to the above table, when collectors with different functional groups were used for flotation, the yield and ash content of carbon products and enriched kaolin products were also different. In order to compare these changes more clearly, the data in the above table were used to create the following figure, and corresponding changes were analyzed in detail.

The flotation results are presented in Figure 5.

Figure 5. The comparison of the flotation effect of collectors with different functional groups.

Figure 5. The comparison of the flotation effect of collectors with different functional groups.

As is evident from the figure above, the black floater yield curve showed a trend that first increased and then decreased, with the decreasing range being larger than the increasing range. The floater yield of methyl laurate was the highest, that of dodecaldehyde was the lowest, and that of dodecanic acid was the median. The red floater ash curve essentially showed an upward trend. The ash contents of the floater collected using dodecanic acid and methyl laurate were very similar, although the ash content of the floater collected using dodecaldehyde was highest. Regarding the blue curve representing the tail mineral yield, the tail mineral yield first decreased and then increased. Methyl laurate produced the minimum tail mineral yield, and dodecaldehyde produced the maximum. The green ash curve showed a trend that first increased and then decreased. There was no significant difference in the ash content of tailings obtained using dodecanic acid and methyl laurate, although the ash content of tailings obtained using dodecaldehyde was the lowest. In sum, the carbon yield obtained using methyl laurate was the highest, and the carbon ash content was also low. The effect of dodecanic acid was moderate. Lauraldehyde produced the worst results. Thus, flotation using an ester group reagent can produce the best effects.

3.2. Mechanism-Based Interpretation of the Experimental Results

According to the above experimental results, for non-polar carbon chain collectors, the best flotation effect can be achieved when the carbon atom number is 13–15. When this is the case, the coal yield is higher, the ash content is lower, and the corresponding kaolin ash content is also higher, which suggests that the coal and kaolin have been separated well, leading to a lower mixing rate of the two. Regarding collectors with different hydrocarbon groups, collectors with a phenyl group can achieve the highest carbon enrichment yield, the lowest carbon ash content, and the highest kaolin ash content. Collectors with triple bonds or a naphthenic group achieve the second highest flotation effect, and collectors with double bonds achieve the worst flotation effect. Regarding collectors with different functional groups, collectors with an ester group produce a better separation effect, along with the highest flotation yield, a lower ash content, and a higher kaolin ash content. Collectors with a carboxyl group rank second, and collectors with an aldehyde group exhibit the worst flotation effect.

To provide a microcosmic explanation of the above experimental phenomena, the molecular structure of carbon in coal gangue should first be determined, and then, the molecular diagram should be drawn. In order to achieve this, solid nuclear magnetic detection was conducted on coal gangue, and the results are displayed in the Figure 6 below.

As is evident from the figure above, the peak at 0–55 ppm is the lipid carbon peak, 55–90 ppm is the ether oxygen peak, 90–165 ppm is the aromatic carbon peak, and 165–220 ppm is the carboxyl and carbonyl carbon peaks. Pulverized coal produced two peaks, which were the lipid carbon peak and aromatic carbon peak. The analysis results from peak attribution revealed that aliphatic carbon accounted for 27.26% of the total, ether oxygen carbon accounted for 6.08%, aromatic carbon accounted for 64.89%, and carboxyl and carbonyl carbon accounted for 1.77% of the total. These results essentially corresponded with the infrared detection results. The specific results are introduced in the following

Table 8. The solid nuclear magnetic test results of coal gangue.

Serial Number	Chemical Shift	C Atom Attribution	Percentage (%)
1	13.35	Lipid methyl carbon	7.315
2	29.43	Methylene carbon linked to lipid methyl group	14.614
3	43.92	Quaternary carbon, hypomethylene carbon	5.331
4	58.46	Methoxy group and oxygen to methylene carbon	0.729
5	72.97	Oxygen bonded to methylidene carbon	0.698
6	80.89	Epoxy-bonded lipocarbon	4.661
7	121.05	Protonated aromatic carbon	19.575
8	131.69	Bridging aromatic carbon	16.939
9	142.14	Collateral aromatic carbon	21.158
10	160.26	Oxygen substitution of aromatic carbon (phenolic hydroxyl, ether, etc.)	7.218
11	178.50	Carboxyl carbon	1.762

.

According to the data in the above table, the carbon molecule structure of the coal gangue was simulated, and the molecular diagram was drawn as follows.

In Figure 7, the red balls represent oxygen atoms, the gray balls represent carbon atoms, the white balls represent hydrogen atoms, the yellow balls denote sulfur atoms, and the blue balls refer to nitrogen atoms.

Due to the simple molecular structures of the different collectors, their known molecular structures can be employed directly.

In order to calculate the interaction energy between the carbon molecule and the collector molecules, interaction models between the carbon molecule and the collector molecules were first created. These models were divided into three graphs which corresponded with the three categories of collectors, as follows: collectors with different carbon chain lengths, collectors with different hydrocarbon groups, and collectors with different functional groups. These models are shown in Figure 8, Figure 9 and Figure 10 below.

As is evident in Figure 8, in these five interaction models, there are no chemical bonds or hydrogen bonds between the collector molecules and the carbon molecules; they can only interact through van der Waals forces (between hydrocarbon chains). Van der Waals forces mainly produce the association energy between hydrocarbon chains.

In Figure 9, hydrogen bonds are represented by dashed blue lines. It is evident that hydrogen bonds are formed between coal molecules and collector molecules with double bonds, triple bonds, and benzene ring structures. Moreover, there are both hydrogen bonds and van der Waals forces between hydrocarbon chains. In addition, only van der Waals forces exist between collector molecules with cyclohexane and coal molecules; hydrogen bonds are not present.

It is evident from Figure 10 that hydrogen bonds are formed between collector molecules with functional groups and coal molecules, and both hydrogen bonds and van der Waals forces (between hydrocarbon chains) exist between the two.

In order to compare the forces between the carbon molecules and various collector molecules, the interaction energy between the carbon molecule and the collector molecules can be calculated using the above interaction models and density functional theory. The specific calculation process may be explained, as follows. The collector molecules, coal molecules, and kaolin molecules in a water solvent were geometrically optimized using the software, Avogadro, to enter the starting geometry. Afterwards, the molecules were distorted to form a variety of conformers which were then optimized in order to calculate the global minimum on the potential energy surface. Frequency calculations were performed on all the optimized geometries to ascertain whether they would produce minimum or transition states on the potential energy surfaces. Notably, for locations where transition state geometries were found, it was decided that the bond lengths and angles should be distorted in the direction of vibration, and the structure should be re-optimized until only positive frequencies are obtained. All calculations were carried out using the Gaussian 09 program [17,18] with the hybrid B3LYP functional and the standard 6–31 G(d) basis set.

The calculation method for interaction energy, that is, the calculation equation, is as follows:

E(interaction) = E(AB) − E(A) − E(B)

(1)

Regarding Equation (1), E(interaction) is the interaction energy between two molecules, E(AB) is the binding energy formed by molecules A and B, and E(A) and E(B) represent the energy when molecules A and B exist independently.

The interaction energy values are organized in the

Table 9. The calculation results showing the interaction energy.

Category	Interaction Objects	Interaction Energy (kcal/mol)
The collectors with different carbon chain lengths	Hexane–coal	−50.0376
	Octane–coal	−52.6355
	Decane–coal	−54.3863
	Tridecane–coal	−54.7251
	Pentadecane–coal	−56.5324
The collectors of different hydrocarbon groups	Dodecene–coal	−56.9465
	Dodecyne–coal	−58.7161
	Octyl cyclohexane–coal	−60.5610
	Octyl benzene–coal	−63.4413
The collectors with different functional groups	Lauraldehyde–coal	−58.3584
	Dodecanoic Acid–coal	−65.5120
	Methyl laurate–coal	−72.2892

below.

As is evident from the table above, by comparing collectors with different carbon chain lengths, it was found that the interaction energy value between collectors with longer chain lengths and coal was low, with the interaction objects sorted as follows: Hexane–coal > Octane–coal > Decane–coal > Tridecane–coal > Pentadecane–coal. By comparing different hydrocarbon-based collectors, it was found that the interaction energy value between the phenyl collector and coal was the lowest, with the order of the interaction objects as follows: Dodecene–coal > Dodecyne–coal > Octyl cyclohexane–coal > Octyl benzene–coal. By compaing collectors with different functional groups, it was found that the interaction energy value between collectors with an ester group and coal was the lowest, and the order is as follows: Lauraldehyde–coal > Dodecanoic Acid–coal > Methyl laurate–coal. Therefore, collectors with longer carbon chains, with a phenyl group, and with an ester group could achieve a better flotation effect.

4. Conclusions

(1)

By systematically comparing the flotation effects of non-polar collectors with different carbon chain lengths and polar collectors with different groups, it was found that the flotation effect of longer carbon chains (with the number of carbon atoms ranging from 13~15) produced the best results. The collector with a phenyl group proved to be more suitable for the flotation of coal gangue when comparing different hydrocarbon groups. The sorting effect of the collector with an ester group was found to be best when comparing different functional groups, as it produced the highest carbon yield, the lowest ash content of carbon products, and the highest ash content of enriched kaolin products.

(2)

The complex carbon molecule of the coal gangue was analyzed through nuclear magnetic detection, and the carbon molecule model was simulated. The interaction energy values between carbon and various collectors were calculated in accordance with density functional theory in order to obtain the interaction energy order. It was confirmed that carbon and collectors with long carbon chains, as well as a phenyl or ester group, have the lowest energy. More specifically, the interaction energy of Tridecane–coal is −54.7251 kcal/mol, the interaction energy of Pentadecane–coal is −56.5324 kcal/mol, and the interaction energy of Octyl benzene–coal is −63.4413 kcal/mol, whereas that of Methyl laurate–coal is −72.2892 kcal/mol. The energy values of these interaction objects are low, so the interaction forces between the corresponding agents and carbon are strong, and the corresponding flotation effect is better.