Adsorption of methylamine cations on kaolinite basal surfaces: A DFT study

To explore the interaction of alkylamine surfactants with kaolinite, the density functional theory (DFT) method was used to calculate the single adsorption of different methylamine cation on kaolinite basal surfaces and the competitive adsorption of methylamine cation and water molecule on kaolinite basal surfaces, respectively. Different methylamine cations can adsorb on kaolinite basal surfaces by electrostatic interaction and hydrogen bonds, and the methylamine cations more easily adsorbed on kaolinite Si-O surface. In the case of competitive adsorption with water molecule, the methylamine cation is capable of flushing out the surrounding water molecule to get rid of its steric effect and stably adsorbing on kaolinite basal surfaces, and the adsorption state of the competitive adsorption system is more stable. The adsorption mechanism of methylamine cation on kaolinite basal surface should be the result of electrostatic interaction and hydrogen bonds, and the electrostatic interaction plays the main role.


Introduction
Clays are highly muddied associated minerals (gangue) (Zhao et al., 2018;Zhang et al., 2019;Zhao et al., 2019a), and it usually exists in microparticles at less than 2 µm (Bergaya et al., 2013;Xiong et al., 2017) in most industrial mine tailings (Pendharker et al., 2017;Zhao et al., 2019b), which has a very adverse effect on the sedimentation Chen et al., 2017), separation (Yu et al., 2017;Xing et al., 2017;Jeldres et al., 2019) and dewatering  of mine tailings. This is because clay mineral characterized as strong hydrophilic surfaces, extraordinarily fine granularity and strong electronegativity of the particle surfaces. The hydrophobic modification of particle surfaces using hydrophobic surfactants is one of the main ways to generate efficient agglomeration settlement Min et al., 2014) and separation (Lee et al., 2011;Huang et al., 2019) of the clay mineral particles, and improving the hydrophobicity of particle surface can further promote dewatering of the particles . Chen et al. (2017) pointed out the adsorption of amine/ammonium salts on kaolinite surface can induce a strong hydrophobic aggregation of kaolinite particles to promote its settlement. Huang et al. (2019) used dodecyl dimethyl ammonium bromide to hydrophobic-modify the montmorillonite surface, which can effectively enhance the selective separation of montmorillonite. Min et al. (2020) pointed out hydrophobic modification can promote the high efficiency dewatering of clay particles by weakening the hydration layer. Recently, the hydrophobic surfactants of alkyl amine salts (Hu et al., 2013;Jiang et al., 2014) have been studied and proven to be effective reagents for the hydrophobic modification of clay particles.
Much research has been done recently about the hydrophobic agglomeration behavior of clay particles with amine surfactants (Rodrigues et al., 2013;Shen et al., 2017;Gibsona et al., 2017), but few have actually examined the micro interaction mechanism between amine surfactants and clay particles. Therefore, it is important to analyze the microscopic mechanism of alkyl amine surfactants adsorption on clay particle surface (Peng et al., 2018). Generally, the computer simulations have employed to investigate and evaluate the adsorption mechanism of surfactants on solid surfaces recently (Rath et al., 2014;Sarvaramini et al., 2017;Xia et al., 2019;Mabudi et al., 2019;Xia et al., 2019). Specifically, the DFT method has recently enjoyed extensive application in this field, in an effort to understand the electronic structure and atomic structure of adsorbed surfactants (Wang et al., 2013;Geatches et al., 2013;Han et al., 2016;Liu et al., 2019).
Kaolinite is the main fine clay particle in coal slurry water, which has significant influence on the high efficiency solid-liquid separation of coal slurry water. In this study, four different methylamine cations (methyl primary amine cation (MPA + (CH6N + )), methyl secondary amine cation (MSA + (C2H8N + )), methyl tertiary amine cation (MTA + (C3H10N + )) and methyl quaternary amine cation (MQA + (C4H12N + ))) were constructed, and the single adsorption of different methylamine cation and competitive adsorption of methyl amine cation with water molecule on kaolinite basal surfaces were investigated using DFT calculations. The frontier orbital analysis, adsorption position analysis and adsorption energy calculation, adsorption configurations and bond populations, and charge analysis were presented and discussed. The adsorption mechanism is discussed in detail, which can provide a theoretical basis for developing new technology development and pharmaceutical design of sedimentation and clarification for coal slurry water.

Model and methods
Owing to fine kaolinite particles almost perfectly cleavaged along (001) basal surfaces (Vaz et al., 2002;Šolc et al., 2011) to form two different surfaces (Al-OH surface and Si-O surface), and these two different kaolinite basal surfaces were used as the main research objects in this study. DFT calculations of single adsorption and competitive adsorption on kaolinite basal surfaces were used with the CASTEP program in the software Material Studio 8.0, BIOVIA Corporation (Clark et al., 2005;Segall et al., 2002). The exchange-correlation function was used the Perdew, Burke, and Ernzerhof (PBE) functional with generalized gradient approximation (GGA) (Perdew et al., 1996), and the plane-wave cutoff was 400 eV. Grimme method (Zhang et al., 2012) was used for DFT-D dispersion corrections. The unbalanced charges in the adsorption systems of different methylamine cation adsorption on kaolinite basal surfaces are balanced by Cl-ions. The other specific parameter settings and computational method were implemented according to the process detailed by (Chen et al., 2019 a;Chen et al., 2019 b). The optimizations of different methylamine cations (MPA + , MSA + , MTA + and MQA + ) and water molecule were calculated in a 15 Å ×15 Å ×15 Å cubic box, and the optimization parameters were the same for primitive unit cell optimization. Fig. 1 and Fig. 2 illustrate the surface structure of kaolinite and the equilibrium configurations of different methylamine cation and water molecule, respectively.
The adsorption energies of different methylamine cation or water molecule on the kaolinite basal surfaces were calculated as: where Eads is the adsorption energy, kJ/mol; Etotal is the energy of the kaolinite basal surface with cation or (and) water molecule adsorbed, kJ/mol; Ecation/water is the energy of different methylamine cation or water molecule in 15 Å×15 Å×15 Å cubic box, kJ/mol; and Esurface is the energy of different kaolinite basal surface, kJ/mol. The Dmol 3 module was used to calculate the frontier orbital properties of kaolinite basal surface and different methylamine cations with energy optimization, and the k points of Brillouin zone were sampled using Gamma point . Frontline orbit calculation parameters were as follows: exchange correlation function uses GGA-PBE, Effective Core Potentials and DNP basis sets, the precision is set to fine, and the self-consistent field convergence criterion is set to 1.0×10 -6 eV/atom.

Frontier orbital analysis
According to frontier orbital theory, the smaller the absolute value of the energy difference (DE) between the highest occupied molecular orbital (HOMO) of one reactant and the lowest unoccupied molecular orbital (LUMO) of another reactant, the more easily the two reactants react (Chen et al., 2015). In order to understand the reactivity of each model and the optimal adsorption sites of cations on kaolinite basal surface, the frontier orbital energy differences of different methylamine cations and kaolinite were calculated. The results are summarizing in Table 1.  The adsorption energies of different methylamine cation or water molecule on the kaolinite basal surfaces were calculated as: Eads= Etotal (Ecation+Esurface), (1) where Eads is the adsorption energy, kJ/mol; Etotal is the energy of th e kaolinite basal surface with cation or (and) water molecule adsorbed, kJ/mol; Ecation/water is the energy of different meth ylamine cation or water molecule 15 15 15 , / ; Esurface is the energy of different kaolinite basal surface, kJ/mol. The Dmol 3 module was used to calculate the frontier orbital properties of kaolinite basal surface and different methylamine cations with energy optimization, and the k points of Brillouin zone were sampled using Gamma point (Ch en et al., 2020). Frontline orbit calculation parameters were as follows: exchange correlation function uses GGA -PBE, Effective Core Poten tials and DNP basis sets, the precision is set to fine, and th e self-consistent field 1.0 10 -6 eV/atom.

Frontier orbital analysis
According to frontier orbital th eory, the smaller th e absolute value of the energy difference ( E ) between the high est occupied molecular orbital (HOMO) of one reactant and the lowest unoccupied molecular orbital (LUMO) of another reactant, the more easily the two reactants react (Chen et al., 2015). In order to understand the reactivity of each model and the optimal adsorption sites of cations on kaolinite basal surface, the frontier orbital energy differences of different methylamine cations and kaolinite were calculated. The results are summarizing in Table 1.
It can be seen from Table 1 that the values of DE2 are less than that of DE1. Namely that, the HOMO of different methylamine cations and the LUMO of kaolinite can react easily. In this regard, the frontier orbital distribution of kaolinite and different methylamine cations were analyzed. Fig. 3 shows the LUMO of kaolinite, the yellow and blue portions in orbital graph represent α and β electrons in the spin, respectively, which are equivalent. The LUMO of kaolinite appears on the first layer of hydrogen atoms in the Al-OH surface, the hydrogen atoms in the lattice, and the oxygen atoms in each layer, and the intensity of the hydrogen atoms is the largest, while the intensity on the oxygen atoms of each layer is uniform but very small. Fig. 4 shows the HOMO of different methylamine cations. It is observed that the HOMO of different methylamine cations appears on the head hydrogen atom (HN) and have the highest intensity at this position ( Fig. 4 (a)~(c)). Then the HOMO of the methyl quaternary amine cation appears in the triangular region composed of three adjacent methyl hydrogen atoms (Fig. 4 (d)). Since the LUMO of kaolinite has the highest intensity on the first layer of hydrogen atoms on the Al-OH surface, different methylamine cations should be more easily adsorbed on the kaolinite (001). This is what frontier orbital theory asserts, but the actual adsorption should also consider hydrogen bondings and other interactions, for example electrostatic interaction.

Single adsorption
The adsorption energies of different methylamine cation on different initial position of kaolinite basal surfaces were calculated as shown in  Fig. 3 shows the LUMO of kaolinite, th e yellow and blu e portions in o b a a a electrons in the spin, respectively, which are equivalent. The LUMO of kaolinite appears on the first layer of hydrogen atoms in th e Al-OH surface, the h ydrogen atoms in th e lattice, and the oxygen atoms in each layer, and the intensity of the hydrogen atoms is the largest, while th e intensity on the oxygen atoms of each layer is uniform but very small. Fig. 4 shows the HOMO of different methyla mine cations. It is observed that the HOMO of different methyla mine cations appear on the h ead hydrogen atom (HN) and have the highest intensity at this position (Fig. 4 (a)~(c)). Then the HOMO of the methyl quaternary amine cation appears in the triangular region composed of three adjacent methyl hydrogen atoms (Fig. 4 (d)). Since th e LUMO of kaolinite has the highest intensity on the first layer of h ydrogen atoms on the Al-OH surface, different methylamine cations should be more easily adsorbed on the kaolinite (001). This is what frontier orbital theory asserts, but the actual adsorption should also consider hydrogen bondings and other interactions, for example electrostatic interaction.

Single adsorption
The adsorption energies of differen t methylamine cation on different initial position of kaolinite basal surfaces were calculated as shown in Table 2 surfaces did not differ significantly, but they are lower than that of methyl quaternary amine cation (MQA + ) on kaolinite basal surfaces. It is indicating that the methylamine cations are more stable than the methyl quaternary amine cation adsorption on kaolinite basal surfaces. The adsorption energies of different methylamine cation on kaolinite Al-OH surface are significantly higher than that on the kaolinite Si-O surface, which means that the adsorptions of different methylamine cation on kaolinite Si-O surface are more stable, (Geatches et al., 2012) reported the similar results. According to the results in Table 2   The oxygen atomic numbers in Table 3 are corresponding to that in Fig. 5 and Fig. 6, and the hydrogen atoms forming hydrogen bonds with corresponding oxygen atoms are denoted as H1, H2 and H3, respectively; the same below.   respectively. It is important to note here that the magnitude of the interaction between different methylamine cation and kaolinite basal surface is approximately proportional to the range of electron accumulation and depletion in adsorption system. After the adsorption of MPA + on the kaolinite basal surfaces, there is a large amount of charge transfer. And the electrons transferred from MPA + to the kaolinite basal surface. The electron accumulation mainly distributed around the hydrogen atoms in cation (HA), and electron depletion mainly distributed around the oxygen atoms of kaolinite basal surface (OS). At the same time, it can be seen that the electron rearrangement range between adjacent atoms in adsorption configurations of kaolinite Al-OH surface is significantly smaller than that in adsorption configurations of kaolinite Si-O surface. This suggests the interactions of different methylamine cations on the kaolinite Al-OH surface are weaker than that on the kaolinite Si-O surface. This finding is very consistent with the calculation of adsorption energy. The Mulliken charge populations of the atoms before and after different methylamine cations adsorption on kaolinite basal surfaces are shown in Table 4. In the adsorption configurations of cations on the kaolinite Al-OH surface, the HA atoms lose 0.01-0.15 e electrons, and the charge of the OS atoms forming hydrogen bonds with them does not change or loses a small number of electrons. Indicating that, after different methylamine cations adsorbed on the kaolinite Al-OH surface, the electrons are not only transferred to the Os atoms, but also transferred to the other atoms of kaolinite Al-OH surface which are adjacent to the cation (see Fig. 7). In the adsorption configurations of different methylamine cations on kaolinite Si-O surface, the HA lose 0.05-0.17 e electrons, and the Os atoms forming hydrogen bonds with them get 0.10-0.20 e electrons. Indicated here is the fact that the electron transfer of different methylamine cations after adsorption on kaolinite Si-O surface mainly occurs between the HA and the Os atoms forming hydrogen bonds with the cations. The number of charges lost by the cations of different methylamine cations before and after adsorption on the kaolinite Al-OH surface and Si-O surface confirms that the number of charges lost by different amine cations is not much different. They are, however, larger than that lost by quaternary ammonium cations. The number of charges lost in different methylamine cations after adsorption on the kaolinite Al-OH surface is smaller than that in different methylamine cations after adsorption on the Si-O surface. This outcome is consistent with the results concerning the electron density difference.
The adsorption configurations and charge analysis of MPA + adsorbed on the kaolinite basal surface indicate that the adsorption mechanism of methylamine cations on this surface mainly takes the form of hydrogen bonding and electrostatic attraction. Of these electrostatic attraction takes the dominant position and this is the main reason why the calculation results of adsorption energy are inconsistent with the frontier orbital analysis. First, the methylamine cations mainly form hydrogen bonds between the Os atoms and the HA (H atom in cations) atoms, while the first layer of Hs atoms of the kaolinite Al-OH surface produces a certain degree of steric hindrance to the formation of the hydrogen bond of HA...Os. Secondly, the Os atoms of kaolinite Si-O surface are also distributed with a certain intensity of LUMO orbitals, which also react with methylamine cations. Meanwhile, according to Mulliken charge analysis, the Os atoms of the kaolinite Al-OH surface and Si-O surface have a large amount of negative charge, which has a strong electrostatic attraction to the methylamine cations. Meanwhile each Os atom on the kaolinite Al-OH surface has an Hs atom, which causes the electrostatic attraction between kaolinite Al-OH surface and cations to be weaker than that between kaolinite Si-O surface and cations.

Competitive adsorption
Taking the methyl primary amine cation with the best adsorption effect as an example, the competitive adsorptions of methylamine cation and water molecule on kaolinite basal surfaces were simulated, the results are shown in Fig. 8 and Fig. 9. Fig. 8 shows the competitive adsorption of MPA + and water on kaolinite Al-OH surface. From the comparative analysis of Fig. 8 (a) and (b), MPA + and water molecule adsorbed on kaolinite Al-OH surface mainly by forming hydrogen bonds. In addition, the MPA + and water molecule are slightly offset from each other to the two sides, which means that the methylamine cations can flush out the surrounding water molecules to get rid of their steric effect and stably adsorb on the kaolinite Al-OH surface. This is very evident when MPA + competes for adsorption with water molecules. As shown in Fig. 8 (c), a large amount of electron transfer occurs in the system after adsorption equilibrium. The electron transfer of MPA + mainly occurs around -NH3 while the electron transfer occurs around all the water molecules. Fig. 9 shows the competitive adsorption of MPA + and water adsorbed on the kaolinite Si-O surface. Here the competitive adsorption law is similar to the adsorption law regarding the kaolinite Al-OH surface, the difference being that the electron transfer range in the competitive adsorption of kaolinite Si-O surface is slightly larger than that of kaolinite Al-OH surface. Specifically, the stability of MPA + and water molecules' competitive adsorption on the kaolinite Si-O surface is stronger.  Table 5 shows the adsorption energies and Mulliken charge populations on the competitive adsorption of MPA + and water adsorbed on kaolinite basal surfaces. According to the results for adsorption energy calculation summarized in Table 5, the total adsorption energy of MPA + and water molecule on kaolinite Al-OH surface is -210.32 kJ/moL, which is significantly lower than that on kaolinite Si-O surface (-216.22 kJ/moL). Indicating that the competitive adsorption system of kaolinite Si-O surface is more stable. Compared to the adsorption energies of single MPA + on kaolinite basal surfaces in Table 2 (-125.385 and -140.961 kJ/moL, respectively), suggesting that the adsorption state of the competitive adsorption system is more stable.
From the results of the Mulliken charge populations in Table 5, it can be seen that in the competition for adsorption on the kaolinite Al-OH surface, the water molecule and kaolinite Al-OH surface received 0.11 and 0.44 e electrons, respectively, and MPA + lost 0.55 e electrons. In the competition for adsorption on the kaolinite Si-O surface, the water molecule charge is unchanged, the Si-O surface received 0.80 e electrons, and MPA + lost 0.80 e, respectively. Furthermore,. the total charge transfer amounts resulting from the competition for adsorption on the kaolinite Al-OH surface and Si-O surface were 0.55 and 0.80 e, respectively. This outcome is very consistent with the adsorption energy calculation. At the same time, according to the analysis done on the Mulliken charge populations of water molecules in different competitive adsorption systems, these water molecules received electrons by interacting with MPA + while losing electrons by hydrogen bonding with kaolinite basal surface (Chen, 2017). Subsequently, the interaction of single MPA + on the surface is smaller, indicating that water molecules to a certain extent inhibit the adsorption of MPA + on kaolinite basal surfaces.
Comprehensive analysis shows that the methylamine cations can adsorb on kaolinite basal surfaces by electrostatic interaction and hydrogen bonds, and realize the effective surface hydrophobic modification of kaolinite particles by its hydrophobic polar groups, which can provide a theoretical basis to synthetic new surfactants and develop new technologies of sedimentation and clarification for high muddied coal slurry water.

Conclusions
(1) The results of frontier orbital analysis indicate that the HOMO orbitals of methylamine cations should react more easily with the LUMO orbitals of kaolinite. contrary to what frontier orbital analysis asserts. The main explanation is that the adsorption mechanism of different methylamine cation adsorbed on kaolinite basal surfaces is mainly hydrogen bonds and electrostatic attraction, in which the electrostatic attraction plays the main role. (4) In the presence of competitive adsorption with water molecule, the methylamine cation is capable of flushing out the surrounding water molecule to get rid of its steric effect and stably adsorbing on kaolinite basal surfaces, and the adsorption state of the competitive adsorption system is more stable.