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Adsorption of different PAM structural units on kaolinite (0 0 1) surface: Density functional theory study
Journal Pre-proofs Full Length Article Adsorption of different PAM structural units on kaolinite (001) surface: Density functional theory study Bao Ren, Fanfei Min, Lingyun Liu, Jun Chen, Chunfu Liu, Kai Lv PII: DOI: Reference:
S0169-4332(19)33140-X https://doi.org/10.1016/j.apsusc.2019.144324 APSUSC 144324
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Applied Surface Science
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Please cite this article as: B. Ren, F. Min, L. Liu, J. Chen, C. Liu, K. Lv, Adsorption of different PAM structural units on kaolinite (001) surface: Density functional theory study, Applied Surface Science (2019), doi: https:// doi.org/10.1016/j.apsusc.2019.144324
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Adsorption of different PAM structural units on kaolinite (001) surface: Density functional theory study Bao Ren, Fanfei Min*, Lingyun Liu, Jun Chen, Chunfu Liu, Kai Lv
Department of Materials Science and Engineering, Anhui University of Science and Technology, Huainan 232001, China * Corresponding author: Tel: +86-554-6668885, Fax: +86-554-6668885 E-mail address: [email protected]
Abstract The objectives of this study are to explore the adsorption mechanisms for how the polyacrylamide (PAM) interact with kaolinite (001) surface. Three structural unit models (P-AM, P-AA, and P-DAC) were developed from the structure of PAM. The adsorption energies were calculated with density functional theory (DFT) to determine the optimal adsorption system of PAM structural units on the kaolinite (001) surface. From the Mulliken population analysis, electron density difference, electronic density of states, and electron localization function of the optimal adsorption system, the adsorption mechanism of each adsorption system was derived and their differences were understood. The results show that these reactive sites of the three PAM structural units are O atoms. P-AM and P-AA can be adsorbed on the kaolinite (001) surface by forming hydrogen bonds. The interaction of kaolinite (001) surface using P-DAC is driven by both hydrogen bonds and electrostatic attraction, electrostatic attraction as a prevailing role is determined simultaneously. The strength of the hydrogen bonds of the P-AM adsorbed on the kaolinite (001) surface is higher than that of P-DAC and P-AA. However, the order of the adsorption interaction of the PAM structural units adsorbed onto the kaolinite (001) surface is P-DAC > P-AM > P-AA. 1
Keywords: Polyacrylamide; Kaolinite; Structural units; (001) surfaces; Density functional theory; Adsorption mechanism
1 Introduction The mechanization of coal mining has sharply increased in the last decade, the grade of coal that can be sorted has become worse. Therefore, a significant number of high-solids tailings have been produced during the raw coal preparation process [1]. It has been shown using various techniques that coal and tailings water contains a large amount of these fine clay minerals particles [2]. The most common clay minerals are kaolinite, montmorillonite, illite, or mixed-layer illite/montmorillonite clays. The kaolinite is also the main component of these clay minerals in coal slurry water [3, 4]. The fine kaolinite particles have strong electronegativity on high surface areas, which can disperse in tailings water [5]. Colloidal clay minerals can cause serious damage in the cleaning process of coals, and this is also a great challenge in other mining wastewater treatments. Proper disposal of clay minerals in mining wastewater has important environmental and economic benefits. PAM is the most economical and effective flocculant for treating industrial wastewater [6-9]. Generally, PAM is synthesized by copolymerization methods. It is divided into non-ionic polyacrylamide (NPAM), anionic polyacrylamide (APAM), and cationic polyacrylamide (CPAM) according to the structure of PAM. P-AM (C3H7ON), P-AA (C3H6O2), and P-DAC (C5H9O2N+) are the basic structural units of these PAM [10-12]. The employment of structural units as compared to the PAM used in industry has potential for chemical reactions and needs to be considered. Any chemical reaction seen between the structural units and clay minerals can also occur between the polymers and clay minerals. [13]. Therefore, studies on the adsorption mechanisms of PAM structural units with kaolinite surfaces can provide important insights into PAM-clay interaction. 2
The influence of PAM on the adsorption and flocculation behavior of stable kaolinite dispersions were investigated during macro-sedimentation experiments [14, 15]. The interfacial structures and interactions of kaolinite with adsorbate have been extensively characterized using nuclear magnetic resonance (NMR) [16], atomic force microscopy (AFM) [17], and chemical force microscopy (CFM) [18]. Lourenço et al. [19] indicated that the flocculation mechanisms of polymer coupled with solid particles cause interactions, such as charge neutralization, polymer bridging, and electrostatic patches interactions. However, the influence of the experimental scale is not able to explain the microscopic adsorption mechanism of the mineral and flocculant. So, it remains a challenging task to accomplish using conventional experimental techniques. Computer simulations have been widely used in this study of electronic structures of solids, as well as the computational errors that were comparable to those between high-precision experiments [20-22], were also highly reliable. A theoretical method of quantum chemistry was employed to study the adsorption and diffusion behavior of the metal atoms on the kaolinite surface [23, 24]. The theoretical aspects of organic functional groups and surfactants on the mineral surface were investigated by utilizing DFT [18, 25-28]. The interaction of kaolinite surface with small molecules was extensively studied [29-32]. In fact, the adsorption of polymers on the kaolinite surface was also studied. There are routine investigations where time restrictions can limit the atomic quantity of models. Researchers can utilize the basic structural unit that helps to represent the interaction between polymers and kaolinite. For example, Lee et al. [33] used DFT to study the adsorption of cellulose on the kaolinite surface. Jacquet et al. [34] provided valuable insights into the simulation and experiments aspects of cationic polymer on the kaolinite surface. However, only a few and simple analyses have been applied to PAM structural units and kaolinite adsorption. [35]. 3
Beyond that, the molecular dynamic of PAM on the mineral surface was focused [36]. The purpose of our study is to understand the adsorption characteristics and mechanisms for how the PAM structural units interact with kaolinite. In this paper, the DFT simulations were carried out on the different PAM structural units for this study’s kaolinite models. The reactive atoms of the three PAM structural units were considered by utilizing the frontier orbital, Mulliken charges, and Fukui indexes. The optimal adsorption models for the different PAM structural units on the kaolinite surface were presented based on their adsorption energies. Mulliken population, electron density difference, electronic density of states and electron localization function were also analyzed in detail to: firstly, evaluate the relevant charge transfers; secondly, explore the bonding nature of adsorption models. The insights provided by this study will help to explain macroscopic adsorption and flocculation experiments, provide useful information for the molecular design and development of a more effective flocculant.
2 Computational methods and models DFT calculations were implemented using the CASTEP [37] and Dmol3 [38] program in Material Studio version 2017 software (Accerly Corporation). Optimization of the different PAM structural units molecule was calculated in a 15×15×15Å3 cubic box using the CASTEP program, while electronic cross-correlation was described with a Perdew-Burke-Ernzerhof (PBE) of the generalized gradient approximation (GGA) functional theory [39]. The plane-wave basis set was truncated with cutoff energy of 400eV, using 1×1×1 grid of k-point sampling and 2.0×10-6eV/atom for self-consistent field tolerance. The atomic positions were optimized using Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithms [40], the threshold values of the convergence criteria were: force less than 0.05eV/A; 2×10-3Å for maximum 4
displacement; stress less 0.1GPa; and 2.0×10-5eV/atoms for energy. The harmonic vibrational frequency of the three PAM structural units were positive, the optimal models as shown in Fig. 1. The frontier molecular orbital, Mulliken charges, and Fukui indexes of geometrically optimized structural units were calculated in the Dmol3 program. The calculation using GGA with PBE was also implemented. The core electrons were treated with Effective Core Potentials and the double numerical basis set with polarization (DNP) functions on hydrogen atoms. The Brillouin zone sampling was applied to Γ-point, and 1.0×10-6eV/atom for self-consistent field tolerance.
Fig. 1. Models and structural formulas of three PAM structural units. (a: P-AM; b: P-AA; c: P-DAC). The most easily dissociated kaolinite (001) and ( 00 1 ) surface [41, 42] was selected as the adsorption surface. The (2×1) periodic supercell of a single-layer slab model contains 78 atoms. The vacuum thickness used was 20Å to prevent the interaction between the adjacent levels. The geometry optimization of kaolinite primitive unit cell and (001) surface were investigated using the CASTEP program. Brillouin zone sampling of (2×2×1) and (1×1×1) k-points was restricted to the kaolinite primitive unit cell and kaolinite surface models optimization, respectively. The remaining calculation parameters were the same as the PAM structural unit. The pseudopotentials were preliminarily generated for the atoms: H:1s1, O:2s22p4, Si:3s23p2, Al:3s23p. All the atoms of the kaolinite models were free relaxation, so the computation to be trustworthy. The optimized cell parameters of kaolinite bulk were: 𝑎=5.196Å, b=9.009Å, c=7.372Å, α=92.996°, β=105.979°, γ=89.877°, the error was within 1.2% when comparing the results to the experiment test values of 𝑎=5.153Å, b=8.942Å, c=7.391Å; α=91.926°, 5
β=105.046°, γ=89.797° [43]. This proved that the optimization parameters were reliable. It was reasonable to the PAM that the structural unit was placed on the appropriate kaolinite surface to form an initial adsorption model. The geometry optimization and electronic properties of the adsorption model were also calculated in the CASTEP program, the calculation parameters were the same for kaolinite surface optimization. Electronic properties were considered based on the optimal adsorption model. The adsorption mechanism of the PAM structural units on the kaolinite surface was obtained by analyzing Mulliken population analysis, electron density difference, electronic density of states and electron localization function of the adsorption system. All calculations were done in reciprocal space. Adsorption mechanism analysis of PAM structural units and the kaolinite ( 00 1 ) surface were studied in the text of the Supplementary Material.
3 Results and discussion 3.1 Reactive sites 3.1.1 Frontier orbital analysis Fukui’s Frontier molecular orbital (FMO) theory [44] indicates that the highest occupied molecular orbital (HOMO), the lowest unoccupied molecular orbital (LUMO) play an important role in predicting chemical reactivity. For example, the HOMO of the molecule is more relaxed in its electron bound and can provide electrons in chemical reactions, where an electrophilic reaction occurs preferably when the HOMO electron density is of the highest value. The extra electrons will occupy the LUMO and these electrons are removed from the HOMO, the nucleophilic reaction is further likely to take place in the molecular sites having higher LUMO density [45]. In general, the reaction between substances is the electrons transfer 6
at the molecular levels of HOMO and LUMO. There are two types of interaction when the PAM structural unit is adsorbed on the surface of kaolinite. Firstly, the electrons transfer from HOMO of kaolinite (001) surface to LUMO of the structural unit where the HOMO/LUMO gap is denoted ΔE1. Secondly, the other concerns the electrons transfer from HOMO of the structural unit to LUMO from the kaolinite (001) surface where the HOMO/LUMO gap is denoted ΔE2. The lower the absolute value of the HOMO/LUMO gap of the orbital energy difference between the HOMO and LUMO, this means that interaction is more likely to occur [46, 47]. The frontier orbital was analyzed to determine the reactive activity of each model, and the frontier orbital energies and HOMO/LUMO gaps of the structural units and the kaolinite (001) surface are displayed in Table 1. The energy gaps ΔE of the structural units on kaolinite (001) surface was computed as the following equations: E E
1
2
E
E
sur HOMO
pol HOMO
E
E
pol
(1)
LUMO
sur
(2)
LUMO
Where ΔE is the energy gap between PAM structural unit and the kaolinite (001) surface sur
sur
frontier orbital, E HOMO and E LUMO are HOMO and LUMO orbital energy of the kaolinite (001) surface, respectively.
E
pol HOMO
pol
and E LUMO are HOMO and LUMO orbital energy of the PAM
structural unit, also respectively. Table 1 Frontier orbital energies and the HOMO/LUMO gaps of the PAM structural unit and the kaolinite (001) surface.
According to frontier orbital theory, ΔE1 are larger than the corresponding ΔE2, which indicates that the HOMO of the three PAM structural units easily reacted with the LUMO of the kaolinite (001) surface. This is consistent with the results documented in [13]. To better 7
observe the reactive atoms of structural units and the kaolinite (001) surface, the HOMO distributions of structural units and LUMO distributions of the kaolinite (001) surface are depicted in Fig. 2. The HOMO contribute mainly to the kaolinite (001) surface. On the PAM structural units (Fig. 2a, b and c), HOMO is localized close to the O atoms. Conversely on the kaolinite (001) surface (Fig. 2d), the LUMO is mainly localized near the H atoms.
Fig. 2. The HOMO distributions of P-AM (a), P-AA (b), and P-DAC (c), respectively. The LUMO distributions of the kaolinite (001) surface (d). (the isosurface value are 0.03 electrons /Å3).
3.1.2 Mulliken charge distribution and Fukui index analysis
Mulliken charge is used to calculate the space atomic charge distribution. It is an important application field to describe atomic electronegativity. It is also important for analyzing bonding properties and the altered charge in local orbitals [48], which will be discussed later in this paper in more detail. The frontier orbital of the molecule has been suggested as explaining the chemical reactivity. The Fukui function index can visually represent the electronic state at the HOMO and LUMO orbitals, indicating the electrophilic and nucleophilic sensitivity of the molecules in the chemical reaction, where f −(r) and f +(r) are the electrophilic and nucleophilic Fukui function indices [49], respectively. The reactive sites of the molecules can be more accurately analyzed and determined, excluding the main chain atoms of the structural unit, the Mulliken charge distributions and Fukui function indexes of some atoms on the three PAM structural units that were selected and
8
calculated. Table 2 shows the Mulliken charge distribution and Fukui function index for the atoms of the three PAM structural units. Table 2 Mulliken charge distribution and Fukui function index of the three PAM structural units.
The electrophilic and nucleophilic Fukui function index of O1 atom on P-AM is the highest, and the Mulliken charge of O1 is calculated as being -0.460e (Table 2). It demonstrates the strongest electronegativity, this result indicates that the O1 atom is the main reactive site of the P-AM. The f −(r) and f +(r) of the O2 atom on P-AA (0.404 and 0.239, respectively) are obtained (see Table 2). Therefore, the electrophilic and nucleophilic reactions are more likely to take place on the O2 atom. The O2 atom have more negative charges, which shows that the O2 atom is the main reactive site of P-AA. Similarly, the O1 atom is the main reactive site of P-DAC for adsorption on the kaolinite (001) surface. Kaolinite is a typical 1:1 dioctahedral clay minerals with a structural formula of Al4Si4O10(OH)8. The kaolinite (001) surface Al-OH groups [50-52] showed that the adsorption of molecules on the kaolinite (001) surface can be the top site, the bridge site, and the hollow site. Considering the periodicity of kaolinite, 5 top sites, 4 bridge sites, and 5 hollow sites were established on the kaolinite (001) surface as the initial adsorption sites of the three PAM structural units. The initial adsorption sites on the kaolinite (001) surface are shown in Fig. 3. The 9 initial adsorption sites on the kaolinite ( 00 1 ) surface are shown in Fig. S1. The orientation of the main reaction sites is very important [34]. Based on the adsorption site, the plane containing the reaction sites was placed on the kaolinite (001) surface in different postures. The reaction sites pointed toward the adsorption sites, and the plane mainly has parallel, inclined and vertical postures. 9
Fig. 3. The initial adsorption site of the PAM structural unit on the kaolinite (001) surface. Structure of the kaolinite layer, top (upper) and side (lower) views. (Blue T: top site; blue solid line: bridge site, which can be represented by Tm-Tn; blue S: hollow site)
3.2 Adsorption energies and characteristics The stability of adsorbate on the different adsorption sites can be represented using the adsorption energy [53]. The adsorption energies of the PAM structural unit on the kaolinite (001) surface were calculated by the following formula:
E
ads
E
system
E
polymer
E
surface
(3)
where E ads is the adsorption energies, E system is the system energy of the PAM structural unit on the kaolinite (001) surface. E polymer is the energy of an isolated PAM structural unit molecule.
E
surface
is the energy of the kaolinite (001) surface. Of these, E ads is negative, indicating that
the reaction is exothermic, and the adsorption system is stable; E ads is positive, meaning that the reaction is endothermic, and the adsorption system is unstable; the smaller the E ads value, the more stable the adsorption. The geometry optimization of the three PAM structural units on the initial adsorption sites of the kaolinite (001) surface was calculated, it was evident that the adsorption system remained stable with the interaction between the three PAM structural units and the kaolinite (001) surface. Three kinds of stable configurations with relatively small adsorption energies were analyzed. Predicted position changes and optimized adsorption energies are shown in Table 3. It can be seen that the optimal adsorption sites of P-AM, P-AA, and P-DAC on the kaolinite (001) surface are S2, S3, and S2, respectively. And the adsorption postures are 10
vertical, parallel, and vertical postures, respectively. The corresponding adsorption energies are -1.109, -0.982, and -1.823 eV, respectively. The adsorption stability of PAM structural units on the kaolinite (001) surface is in the order of P-DAC > P-AM > P-AA. Table 3. Predicted adsorption positions and energies of the three PAM structural units on the kaolinite (001) surface.
The optimal adsorption configurations of the three PAM structural units on the kaolinite (001) surface as shown in Fig. 4. The optimal adsorption systems of PAM structural units /kaolinite ( 00 1 ) surface as shown in Fig. S2. The most likely bonded atoms of the optimal adsorption system P-AM/kaolinite (001) surface are H1, O8, O1, H2, H4, and H5. The most likely bonded atoms of P-AA on the kaolinite (001) surface are O1, H2, O2, H4, and H8. The most likely bonded atoms of the optimal adsorption system P-DAC/kaolinite (001) surface are O1, H2, H4, and H5.
Fig. 4. The optimal adsorption systems of three PAM structural units on the kaolinite (001) surface. The most likely bonded atoms of the optimal adsorption systems. (a: P-AM/kaolinite (001) surface; b: P-AA/kaolinite (001) surface; c: P-DAC/kaolinite (001) surface)
3.3 Mulliken bond populations analysis Displayed here are the most likely bonds that make up the optimal adsorption systems as represented by Hn-Om (e.g. H1-O8). All the Mulliken bond population of PAM structural units on the kaolinite ( 00 1 ) surface are M(Hn-Om) =0 (Table S1). The Mulliken bond populations of the optimized adsorption system of P-AM, P-AA, and P-DAC on the kaolinite (001) surface are given in Table 4. The Mulliken bond population of H1-O8 is M(H1-O8) =0.10 and the bond 11
length is L(H1-O8) =1.812 Å (Table 4). The values of the Mulliken bond populations of P-AM on the kaolinite (001) surface are in the order of M(H1-O8) > M(H4-O1) > M(H5-O1) > M(H2-O1), and the bond lengths are in a sequence of L(H1-O8) < L(H4-O1) < L(H5-O1) < L(H2-O1). So, the bonding trends of the P-AM/kaolinite (001) surface are in this order of H1-O8 > H4-O1 > H5-O1 > H2-O1. The Mulliken bond populations of P-AA on the kaolinite (001) surface are following order M(H4-O2) = M(H8-O2) > M(H2-O1), and the bond lengths are in the order of L(H4-O2) < L(H2-O) < L(H8-O2). The bonding trend of H4-O2 is stronger than that of H8-O2, and H2-O1. The Mulliken bond populations of P-DAC on the kaolinite (001) surface are in a sequence of M(H2-O1) = M(H5-O1) > M(H4-O1), and the bond lengths are in this order of L(H2-O1) < L(H5-O1) < L(H4-O1), the bonding trends of the P-DAC/kaolinite (001) surface are following order H2-O1 > H5-O1 > H4-O1. The average Mulliken bond populations of the optimized adsorption system of P-AM, P-AA, and P-DAC on the kaolinite (001) surface are 0.063, 0.027, and 0.047, their average bond lengths are 1.868, 2.164, and 1.983 Å, respectively. The bonding interactions only of three PAM structural units on the kaolinite (001) surface are in the order of P-AM > P-DAC > P-AA. Table 4. The Mulliken bond populations of the three PAM structural units on the kaolinite (001) surface.
3.4 Charge analysis The Mulliken charge populations of the three adsorption systems were computed and summarized in Table 5. In P-AM/kaolinite (001) surface, the H1 atom of the P-AM obtained 0.07e charge, the O1 atom gained 0.04e, where the s orbit lost 0.02e and the p orbit received 12
0.06e. The H2, H4, and H5 atoms of the kaolinite (001) surface obtained 0e, 0.01e, and 0.02e, respectively. The p orbit of the O8 atom lost 0.07e while the s orbit did not lose any electrons. The adsorption system of the P-AA and the kaolinite (001) surface. The O1 and O2 atoms of the P-AA lost 0.01e and obtained 0.03e in the p orbit, respectively. Meanwhile there was no electrons change in the s orbit. The H4, H8, and H2 atoms of the kaolinite (001) surface lost 0.01e, obtained 0.03e and 0e, respectively. The P-DAC adsorption on the kaolinite (001) surface. The O1 atom of the P-DAC gained 0.07e, where the s orbit lost 0.01e and the p orbit obtained 0.08e. The H2, H4, and H5 atoms of the kaolinite (001) surface obtained 0.01e, 0e, and 0.02e, respectively. Table 5. Mulliken charge populations before and after the three PAM structural units adsorption on the kaolinite (001) surface.
The electron density difference can visually display the electron rearrangement of the adsorption system. In order to further determine the bonding properties, the electron density difference is analyzed based on the Mulliken charge analysis of the optimal adsorption system. Fig. 5 shows the electron density difference of the three PAM structural units on the kaolinite (001) surface, the blue region indicates electron accumulation, while the yellow region indicates electron depletion. It is worth noting that the hydrogen bond has directionality and saturation. In the P-AM/kaolinite (001) surface adsorption system, the electrons accumulated in the outermost layer of the O1 atomic orbit, whilst then shifting to the H5 and H4 atoms, the hydrogen bonds O−H4···O1 and O−H5···O1 are formed between O1 and H4, H5 atoms. The electrons of O8 atom shifted toward H1 atom to form a hydrogen bond N−H1···O8. The P-AA adsorption on the kaolinite (001) surface. Electrons are mainly accumulated at O2 atom and 13
shifted toward H4 and H8 atoms. Meanwhile, the electrons of the H4 and H8 atoms are depleted. The adsorption of P-AA/kaolinite (001) surface is driven by hydrogen bonds O−H4···O2 and O−H8···O2. Similarly, the hydrogen bonds formed by the P-DAC/kaolinite (001) surface are O−H2···O1 and O−H5···O1. In addition to the electron accumulation at the O1 atom, it is apparent that electron depletion occurs at the H atom of the P-DAC. There are no hydrogen bonds according to the Mulliken charge analysis. Combine with the calculation results for adsorption energies and Mulliken bond populations, it can be seen that the P-DAC adsorbs on the kaolinite (001) surface as well as the hydrogen bonds. It is evident that electrostatic attraction occurred and dominated the process. The electronic analysis in Table S2 shows that PAM structural units adsorption on the kaolinite ( 00 1 ) surface, while no hydrogen bond formation, there is a potential for hydrogen bonding. It can be seen from Fig. S3 that P-DAC has higher potential for hydrogen bonding with kaolinite ( 00 1 ) surface than P-AA and P-AM. The P-DAC and kaolinite ( 00 1 ) surface are only adsorbed by electrostatic attraction.
Fig. 5. The electron density difference of three PAM structural units on the kaolinite (001) surface (a: P-AM/kaolinite (001) surface; b: P-AA/kaolinite (001) surface; c: P-DAC/kaolinite (001) surface, the isosurface value is 0.01 electrons/Å3).
3.5 Electronic density of states analysis Fig. 6 and Fig. 7 illustrate the partial density of states (PDOS) of the interacting atoms between three PAM structural units and the kaolinite (001) surface in the optimal adsorption system. From Fig. 6, it can be seen that the energy levels of the atoms forming the hydrogen bond in the optimal adsorption configurations negatively shifted relative to that before 14
adsorption. This subsequently indicates that the adsorption system is more stable. After P-AM is adsorbed on the kaolinite (001) surface, the PDOS peak of interacting atoms decreased, the valence band widens and delocalization is enhanced. Overlaps of H1 1s with O8 2p are very clearly observed in -9eV ~ -6.5eV energy range of Fig. 6a. This is consistent with the analysis of the charge, indicating the hydrogen bond of N−H1···O8 is formed in the P-AM/kaolinite (001) surface. From -7.5eV to 5eV energy can be seen H4 s and H5 s contribute to O1 s and p states in of Fig. 6b. The interaction between O1 and H5, H4 are hydrogen bonds O−H4···O1 and O−H5···O1. Similarly, states of O2 and H4 s, H8 s of P-AA/kaolinite (001) surface adsorption system form resonance are presented in -7.5eV ~ 5eV energy range of Fig. 7a. Overlaps of O1 2p and H2 1s, H5 1s states of P-DAC/kaolinite (001) surface are obvious in part of Fig. 7b. The hydrogen bonds formed by P-AA/kaolinite (001) surface and P-DAC/kaolinite (001) surface are O−H4···O2, O−H8···O2 and O−H2···O1, O−H5···O1. These results are consistent with the charge analysis.
Fig. 6. PDOS of interacting atoms between P-AM and the kaolinite (001) surface. (a: H1 and O8; b: O1, H5, and H4).
Fig. 7. PDOS of interacting atoms of P-AA (a) and P-DAC (b) on the kaolinite (001) surface. (a: O2, H4, and H8; b: O1, H2, and H5). The density of states (DOS) of three PAM structural units adsorbed on kaolinite (001) surface is shown in Fig. 8. The energy of the P-DAC/kaolinite (001) surface adsorption system is much lower than that of the P-AM and P-AA adsorbing system on the kaolinite (001) surface. The more stable energy of the adsorption system indicates that the interaction between P-DAC 15
and kaolinite (001) surface is stronger. The results are consistent with the above analysis results.
Fig. 8. DOS of three PAM structural units adsorbed on the kaolinite (001) surface in the optimum adsorption system.
3.6 Electron localization function analysis The localization of atoms extranuclear electrons at different positions can be described by Electron localization function (ELF) [54]. ELF as defined runs from 0 to 1, which when closer to 1 localization increases and is equal to 0.5 for the homogeneous electron gas. Thus, ELF of 1.0 corresponds to perfect localization and ELF of 0.5 to perfect delocalization, which is important for describing the intensity of hydrogen bonds [55]. The ELF plot for three of the optimal adsorption systems is depicted in Fig. 9. In the P-AM/kaolinite (001) surface, the critical values of ELF(N−H1···O8), ELF(O−H4···O1), and ELF(O−H5···O1) are 0.063, 0.048， and 0.042, respectively. Hydrogen bonds formed by P-AM and the kaolinite (001) surface, the critical values of ELF(O−H4···O2) and ELF(O−H8···O2) are 0.017 and 0.018, respectively. The critical values of ELF(O−H2···O1) and ELF(O−H5···O1) are 0.025 and 0.022, respectively, while P-DAC was adsorbed on the kaolinite (001) surface. The average critical values of ELF for hydrogen bonding in the three adsorption systems are 0.0510, 0.0175 and 0.0235, respectively. The hydrogen bonding strength of P-AM and the kaolinite (001) surface is higher than that of P-AA and P-DAC.
16
Fig. 9. ELF of three PAM structural units adsorption on the kaolinite (001) surface. (a: P-AM/kaolinite (001) surface; b: P-AA/kaolinite (001) surface; c: P-DAC/kaolinite (001) surface).
4 Conclusion In this work, the DFT was employed to calculate the reactive sites, adsorption energies, and characteristics of the PAM structural unit on the kaolinite (001) surface. The PAM structural unit was developed from the industrial PAM structure itself. The simulation results show that the electrophilic and nucleophilic reaction are more likely to take place on the reactive atoms. The reactive atoms of the three PAM structural units, i.e. P-AM, P-AA, and P-DAC are all O atoms, these atoms have high electronegativity. The optimal adsorption sites of PAM structural unit on the kaolinite (001) surface are the hollow site and the adsorption energies are -1.109, -0.982, and -1.823eV, respectively. The hydrogen bonds of P-AM are adsorbed on the kaolinite (001) surface are N−H1···O8, O−H4···O1, and O−H5···O1. The hydrogen bonds of O−H4···O2 and O−H8···O2 did form in the P-AA/kaolinite (001) surface. Hydrogen bonds formed between atoms in the adsorption system are responsible for atomic orbital resonance. The main adsorption mechanism of P-AM or P-AA/kaolinite (001) surface is a hydrogen-bond interaction. The P-DAC adsorption on the kaolinite (001) surface as well as the hydrogen bonds O−H2···O1 and O−H5···O1, suggest there is electrostatic attraction and this process dominated. The P-AM or P-AA does not form hydrogen bonds with the kaolinite ( 00 1 ) surface, but there is adsorption potential. The adsorption of P-DAC with the kaolinite ( 00 1 ) surface is driven only by electrostatic attraction. By doing the ELF analyses, the hydrogen-bond interaction of the PAM structural units on the kaolinite (001) surface was as follows: P-AM > P-DAC > P-AA. However, the adsorption interaction between P-DAC and 17
the kaolinite (001) surface is higher than that of P-AM and P-AA. The present study provided an insight into the adsorption mechanism of PAM and kaolinite, which could serve as a guidance to choose PAM structural unit for its further applications in the molecular design and development of a more effective flocculant.
Acknowledgements The financial supports for this work from the National Natural Science Foundation of China under the grant No. 51874011 and the National Natural Science Foundation of China under the grant No. 51804009 are gratefully acknowledged.
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Adsorption of different PAM structural units on kaolinite (001) surface: Density functional theory study Bao Ren, Fanfei Min*, Lingyun Liu, Jun Chen, Chunfu Liu, Kai Lv
Department of Materials Science and Engineering, Anhui University of Science and Technology, Huainan 232001, China * Corresponding author: Tel: +86-554-6668885, Fax: +86-554-6668885 E-mail address: [email protected]
Fig. 1. Models and structural formulas of three PAM structural units. (a: P-AM; b: P-AA; c: P-DAC).
Fig. 2. The HOMO distributions of P-AM (a), P-AA (b), and P-DAC (c), respectively. The LUMO distributions of the kaolinite (001) surface (d). (the isosurface value are 0.03 electrons /Å3). 22
Fig. 3. The initial adsorption site of the PAM structural unit on the kaolinite (001) surface. Structure of the kaolinite layer, top (upper) and side (lower) views. (Blue T: top site; blue solid line: bridge site, which can be represented by Tm-Tn; blue S: hollow site)
Fig. 4. The optimal adsorption systems of three PAM structural units on the kaolinite (001) surface. The most likely bonded atoms of the optimal adsorption systems. (a: P-AM/kaolinite (001) surface; b: P-AA/kaolinite (001) surface; c: P-DAC /kaolinite (001) surface)
23
Fig. 5. The electron density difference of three PAM structural units on the kaolinite (001) surface (a: P-AM/kaolinite (001) surface; b: P-AA/kaolinite (001) surface; c: P-DAC /kaolinite (001) surface, the isosurface value is 0.01 electrons/Å3).
Fig. 6. PDOS of interacting atoms between P-AM and the kaolinite (001) surface. (a: H1 and O8; b: O1, H5, and H4).
24
Fig. 7. PDOS of interacting atoms of P-AA (a) and P-DAC (b) on the kaolinite (001) surface. (a: O2, H4, and H8; b: O1, H2, and H5).
Fig. 8. DOS of three PAM structural units adsorbed on the kaolinite (001) surface in the optimum adsorption system.
25
Fig. 9. ELF of three PAM structural units adsorption on the kaolinite (001) surface. (a: P-AM/kaolinite (001) surface; b: P-AA/kaolinite (001) surface; c: P-DAC /kaolinite (001) surface).
26
Adsorption of different PAM structural units on kaolinite (001) surface: Density functional theory study Bao Ren, Fanfei Min*, Lingyun Liu, Jun Chen, Chunfu Liu, Kai Lv
Department of Materials Science and Engineering, Anhui University of Science and Technology, Huainan 232001, China * Corresponding author: Tel: +86-554-6668885, Fax: +86-554-6668885 E-mail address: [email protected]
Table 1. Frontier orbital energies and the HOMO/LUMO gaps of the PAM structural unit and the kaolinite (001) surface. Model P-AM P-AA P-DAC Kaolinite (001) surface
Frontier orbital energy/eV
HOMO/LUMO Energy gap/eV
HOMO
LUMO
ΔE1
ΔE2
-5.519 -6.253 -5.063 -7.060
-0.471 -1.131 0.094 -2.130
6.589 5.929 7.154 −
3.389 4.123 2.933 −
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Table 2. Mulliken charge distribution and Fukui function index of the three PAM structural units. Model
atom
Mulliken charge/e
f −(r)
f +(r)
P-AM
C1 N1 O1 H1 H2 C1 O1 O2 H1 C1 C2 C3 C4 N1 O1 O2 H1 H2 H3
0.432 -0.380 -0.460 0.210 0.194 0.496 -0.395 -0.392 0.264 0.428 0.105 -0.027 -0.058 -0.358 -0.480 -0.471 0.043 0.043 0.067
0.106 0.105 0.399 0.059 0.070 0.124 0.125 0.404 0.071 0.062 0.019 0.031 0.038 0.009 0.074 0.020 0.047 0.053 0.047
0.215 0.124 0.216 0.066 0.067 0.233 0.134 0.239 0.069 0.060 0.019 0.030 0.037 0.008 0.073 0.020 0.047 0.052 0.048
P-AA
P-DAC
Table 3. Predicted adsorption positions and energies of the three PAM structural units on the kaolinite (001) surface. Adsorption system
Initial position
Final position
Adsorption energy/eV
P-AM/kaolinite (001) surface
S2 S3 T5 S1 S3 T2-T1 T6 S2 T5-T8
S2 T5 T5 S1 S3 T2-T1 T6 S2 T5-T8
-1.109 -0.911 -0.904 -0.890 -0.982 -0.816 -1.771 -1.823 -1.779
P-AA/kaolinite (001) surface
P-DAC/kaolinite (001) surface
28
Table 4. The Mulliken bond populations of the three PAM structural units on the kaolinite (001) surface. Adsorption system
Bond
Bond populations
Bond lengths /Å
P-AM/kaolinite (001) surface
H1-O8 H2-O1 H4-O1 H5-O1 H2-O1 H4-O2 H8-O2 H2-O1 H4-O1 H5-O1
0.10 0.03 0.07 0.05 0.02 0.03 0.03 0.05 0.04 0.05
1.812 1.946 1.845 1.899 2.156 2.147 2.189 1.898 2.073 1.977
P-AA/kaolinite (001) surface
P-DAC/kaolinite (001) surface
Table 5. Mulliken charge populations before and after the three PAM structural units adsorption on the kaolinite (001) surface. Adsorption system
Atom
Mulliken charge population Before
P-AM/kaolinite (001) surface
P-AA/kaolinite (001) surface
P-DAC/kaolinite (001) surface
H1 O1 H2 H4 H5 O8 O1 O2 H2 H4 H8 O1 H2 H4 H5
After
s
p
Charge/e
s
p
Charge/e
0.53 1.83 0.55 0.56 0.54 1.85 1.82 1.82 0.55 0.56 0.55 1.82 0.55 0.56 0.54
— 4.76 — — — 5.21 4.86 4.72 — — — 4.75 — — —
0.47 -0.59 0.45 0.44 0.46 -1.06 -0.68 -0.54 0.45 0.44 0.45 -0.57 0.45 0.44 0.46
0.60 1.81 0.55 0.57 0.56 1.85 1.82 1.82 0.55 0.55 0.58 1.81 0.56 0.56 0.56
— 4 .82 — — — 5.14 4.85 4.75 — — — 4.83 — — —
0.40 -0.63 0.45 0.43 0.44 -0.99 -0.67 -0.57 0.45 0.45 0.42 -0.64 0.44 0.44 0.44
29
Adsorption of different PAM structural units on kaolinite (001) surface: Density functional theory study Bao Ren, Fanfei Min*, Lingyun Liu, Jun Chen, Chunfu Liu, Kai Lv
Department of Materials Science and Engineering, Anhui University of Science and Technology, Huainan 232001, China * Corresponding author: Tel: +86-554-6668885, Fax: +86-554-6668885 E-mail address: [email protected]
Graphical Abstract
30
Adsorption of different PAM structural units on kaolinite (001) surface: Density functional theory study Bao Ren, Fanfei Min*, Lingyun Liu, Jun Chen, Chunfu Liu, Kai Lv
Department of Materials Science and Engineering, Anhui University of Science and Technology, Huainan 232001, China * Corresponding author: Tel: +86-554-6668885, Fax: +86-554-6668885 E-mail address: [email protected]
The adsorption mechanism of the PAM structural unit on the kaolinite (001) surface has been studied by utilizing DFT. The adsorption interaction of P-DAC with the kaolinite (001) surface higher than P-AA and P-AA. P-AM or P-AA adsorption on the kaolinite (001) surface through hydrogen bonding. Both hydrogen bonds and electrostatic attraction contribute to the adsorption process of P-DAC/ kaolinite (001) surface.
31
Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:
We declare that we have no conflict of interest.
32
S0169-4332(19)33140-X https://doi.org/10.1016/j.apsusc.2019.144324 APSUSC 144324
To appear in:
Applied Surface Science
Received Date: Revised Date: Accepted Date:
31 March 2019 30 September 2019 7 October 2019
Please cite this article as: B. Ren, F. Min, L. Liu, J. Chen, C. Liu, K. Lv, Adsorption of different PAM structural units on kaolinite (001) surface: Density functional theory study, Applied Surface Science (2019), doi: https:// doi.org/10.1016/j.apsusc.2019.144324
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Adsorption of different PAM structural units on kaolinite (001) surface: Density functional theory study Bao Ren, Fanfei Min*, Lingyun Liu, Jun Chen, Chunfu Liu, Kai Lv
Department of Materials Science and Engineering, Anhui University of Science and Technology, Huainan 232001, China * Corresponding author: Tel: +86-554-6668885, Fax: +86-554-6668885 E-mail address: [email protected]
Abstract The objectives of this study are to explore the adsorption mechanisms for how the polyacrylamide (PAM) interact with kaolinite (001) surface. Three structural unit models (P-AM, P-AA, and P-DAC) were developed from the structure of PAM. The adsorption energies were calculated with density functional theory (DFT) to determine the optimal adsorption system of PAM structural units on the kaolinite (001) surface. From the Mulliken population analysis, electron density difference, electronic density of states, and electron localization function of the optimal adsorption system, the adsorption mechanism of each adsorption system was derived and their differences were understood. The results show that these reactive sites of the three PAM structural units are O atoms. P-AM and P-AA can be adsorbed on the kaolinite (001) surface by forming hydrogen bonds. The interaction of kaolinite (001) surface using P-DAC is driven by both hydrogen bonds and electrostatic attraction, electrostatic attraction as a prevailing role is determined simultaneously. The strength of the hydrogen bonds of the P-AM adsorbed on the kaolinite (001) surface is higher than that of P-DAC and P-AA. However, the order of the adsorption interaction of the PAM structural units adsorbed onto the kaolinite (001) surface is P-DAC > P-AM > P-AA. 1
Keywords: Polyacrylamide; Kaolinite; Structural units; (001) surfaces; Density functional theory; Adsorption mechanism
1 Introduction The mechanization of coal mining has sharply increased in the last decade, the grade of coal that can be sorted has become worse. Therefore, a significant number of high-solids tailings have been produced during the raw coal preparation process [1]. It has been shown using various techniques that coal and tailings water contains a large amount of these fine clay minerals particles [2]. The most common clay minerals are kaolinite, montmorillonite, illite, or mixed-layer illite/montmorillonite clays. The kaolinite is also the main component of these clay minerals in coal slurry water [3, 4]. The fine kaolinite particles have strong electronegativity on high surface areas, which can disperse in tailings water [5]. Colloidal clay minerals can cause serious damage in the cleaning process of coals, and this is also a great challenge in other mining wastewater treatments. Proper disposal of clay minerals in mining wastewater has important environmental and economic benefits. PAM is the most economical and effective flocculant for treating industrial wastewater [6-9]. Generally, PAM is synthesized by copolymerization methods. It is divided into non-ionic polyacrylamide (NPAM), anionic polyacrylamide (APAM), and cationic polyacrylamide (CPAM) according to the structure of PAM. P-AM (C3H7ON), P-AA (C3H6O2), and P-DAC (C5H9O2N+) are the basic structural units of these PAM [10-12]. The employment of structural units as compared to the PAM used in industry has potential for chemical reactions and needs to be considered. Any chemical reaction seen between the structural units and clay minerals can also occur between the polymers and clay minerals. [13]. Therefore, studies on the adsorption mechanisms of PAM structural units with kaolinite surfaces can provide important insights into PAM-clay interaction. 2
The influence of PAM on the adsorption and flocculation behavior of stable kaolinite dispersions were investigated during macro-sedimentation experiments [14, 15]. The interfacial structures and interactions of kaolinite with adsorbate have been extensively characterized using nuclear magnetic resonance (NMR) [16], atomic force microscopy (AFM) [17], and chemical force microscopy (CFM) [18]. Lourenço et al. [19] indicated that the flocculation mechanisms of polymer coupled with solid particles cause interactions, such as charge neutralization, polymer bridging, and electrostatic patches interactions. However, the influence of the experimental scale is not able to explain the microscopic adsorption mechanism of the mineral and flocculant. So, it remains a challenging task to accomplish using conventional experimental techniques. Computer simulations have been widely used in this study of electronic structures of solids, as well as the computational errors that were comparable to those between high-precision experiments [20-22], were also highly reliable. A theoretical method of quantum chemistry was employed to study the adsorption and diffusion behavior of the metal atoms on the kaolinite surface [23, 24]. The theoretical aspects of organic functional groups and surfactants on the mineral surface were investigated by utilizing DFT [18, 25-28]. The interaction of kaolinite surface with small molecules was extensively studied [29-32]. In fact, the adsorption of polymers on the kaolinite surface was also studied. There are routine investigations where time restrictions can limit the atomic quantity of models. Researchers can utilize the basic structural unit that helps to represent the interaction between polymers and kaolinite. For example, Lee et al. [33] used DFT to study the adsorption of cellulose on the kaolinite surface. Jacquet et al. [34] provided valuable insights into the simulation and experiments aspects of cationic polymer on the kaolinite surface. However, only a few and simple analyses have been applied to PAM structural units and kaolinite adsorption. [35]. 3
Beyond that, the molecular dynamic of PAM on the mineral surface was focused [36]. The purpose of our study is to understand the adsorption characteristics and mechanisms for how the PAM structural units interact with kaolinite. In this paper, the DFT simulations were carried out on the different PAM structural units for this study’s kaolinite models. The reactive atoms of the three PAM structural units were considered by utilizing the frontier orbital, Mulliken charges, and Fukui indexes. The optimal adsorption models for the different PAM structural units on the kaolinite surface were presented based on their adsorption energies. Mulliken population, electron density difference, electronic density of states and electron localization function were also analyzed in detail to: firstly, evaluate the relevant charge transfers; secondly, explore the bonding nature of adsorption models. The insights provided by this study will help to explain macroscopic adsorption and flocculation experiments, provide useful information for the molecular design and development of a more effective flocculant.
2 Computational methods and models DFT calculations were implemented using the CASTEP [37] and Dmol3 [38] program in Material Studio version 2017 software (Accerly Corporation). Optimization of the different PAM structural units molecule was calculated in a 15×15×15Å3 cubic box using the CASTEP program, while electronic cross-correlation was described with a Perdew-Burke-Ernzerhof (PBE) of the generalized gradient approximation (GGA) functional theory [39]. The plane-wave basis set was truncated with cutoff energy of 400eV, using 1×1×1 grid of k-point sampling and 2.0×10-6eV/atom for self-consistent field tolerance. The atomic positions were optimized using Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithms [40], the threshold values of the convergence criteria were: force less than 0.05eV/A; 2×10-3Å for maximum 4
displacement; stress less 0.1GPa; and 2.0×10-5eV/atoms for energy. The harmonic vibrational frequency of the three PAM structural units were positive, the optimal models as shown in Fig. 1. The frontier molecular orbital, Mulliken charges, and Fukui indexes of geometrically optimized structural units were calculated in the Dmol3 program. The calculation using GGA with PBE was also implemented. The core electrons were treated with Effective Core Potentials and the double numerical basis set with polarization (DNP) functions on hydrogen atoms. The Brillouin zone sampling was applied to Γ-point, and 1.0×10-6eV/atom for self-consistent field tolerance.
Fig. 1. Models and structural formulas of three PAM structural units. (a: P-AM; b: P-AA; c: P-DAC). The most easily dissociated kaolinite (001) and ( 00 1 ) surface [41, 42] was selected as the adsorption surface. The (2×1) periodic supercell of a single-layer slab model contains 78 atoms. The vacuum thickness used was 20Å to prevent the interaction between the adjacent levels. The geometry optimization of kaolinite primitive unit cell and (001) surface were investigated using the CASTEP program. Brillouin zone sampling of (2×2×1) and (1×1×1) k-points was restricted to the kaolinite primitive unit cell and kaolinite surface models optimization, respectively. The remaining calculation parameters were the same as the PAM structural unit. The pseudopotentials were preliminarily generated for the atoms: H:1s1, O:2s22p4, Si:3s23p2, Al:3s23p. All the atoms of the kaolinite models were free relaxation, so the computation to be trustworthy. The optimized cell parameters of kaolinite bulk were: 𝑎=5.196Å, b=9.009Å, c=7.372Å, α=92.996°, β=105.979°, γ=89.877°, the error was within 1.2% when comparing the results to the experiment test values of 𝑎=5.153Å, b=8.942Å, c=7.391Å; α=91.926°, 5
β=105.046°, γ=89.797° [43]. This proved that the optimization parameters were reliable. It was reasonable to the PAM that the structural unit was placed on the appropriate kaolinite surface to form an initial adsorption model. The geometry optimization and electronic properties of the adsorption model were also calculated in the CASTEP program, the calculation parameters were the same for kaolinite surface optimization. Electronic properties were considered based on the optimal adsorption model. The adsorption mechanism of the PAM structural units on the kaolinite surface was obtained by analyzing Mulliken population analysis, electron density difference, electronic density of states and electron localization function of the adsorption system. All calculations were done in reciprocal space. Adsorption mechanism analysis of PAM structural units and the kaolinite ( 00 1 ) surface were studied in the text of the Supplementary Material.
3 Results and discussion 3.1 Reactive sites 3.1.1 Frontier orbital analysis Fukui’s Frontier molecular orbital (FMO) theory [44] indicates that the highest occupied molecular orbital (HOMO), the lowest unoccupied molecular orbital (LUMO) play an important role in predicting chemical reactivity. For example, the HOMO of the molecule is more relaxed in its electron bound and can provide electrons in chemical reactions, where an electrophilic reaction occurs preferably when the HOMO electron density is of the highest value. The extra electrons will occupy the LUMO and these electrons are removed from the HOMO, the nucleophilic reaction is further likely to take place in the molecular sites having higher LUMO density [45]. In general, the reaction between substances is the electrons transfer 6
at the molecular levels of HOMO and LUMO. There are two types of interaction when the PAM structural unit is adsorbed on the surface of kaolinite. Firstly, the electrons transfer from HOMO of kaolinite (001) surface to LUMO of the structural unit where the HOMO/LUMO gap is denoted ΔE1. Secondly, the other concerns the electrons transfer from HOMO of the structural unit to LUMO from the kaolinite (001) surface where the HOMO/LUMO gap is denoted ΔE2. The lower the absolute value of the HOMO/LUMO gap of the orbital energy difference between the HOMO and LUMO, this means that interaction is more likely to occur [46, 47]. The frontier orbital was analyzed to determine the reactive activity of each model, and the frontier orbital energies and HOMO/LUMO gaps of the structural units and the kaolinite (001) surface are displayed in Table 1. The energy gaps ΔE of the structural units on kaolinite (001) surface was computed as the following equations: E E
1
2
E
E
sur HOMO
pol HOMO
E
E
pol
(1)
LUMO
sur
(2)
LUMO
Where ΔE is the energy gap between PAM structural unit and the kaolinite (001) surface sur
sur
frontier orbital, E HOMO and E LUMO are HOMO and LUMO orbital energy of the kaolinite (001) surface, respectively.
E
pol HOMO
pol
and E LUMO are HOMO and LUMO orbital energy of the PAM
structural unit, also respectively. Table 1 Frontier orbital energies and the HOMO/LUMO gaps of the PAM structural unit and the kaolinite (001) surface.
According to frontier orbital theory, ΔE1 are larger than the corresponding ΔE2, which indicates that the HOMO of the three PAM structural units easily reacted with the LUMO of the kaolinite (001) surface. This is consistent with the results documented in [13]. To better 7
observe the reactive atoms of structural units and the kaolinite (001) surface, the HOMO distributions of structural units and LUMO distributions of the kaolinite (001) surface are depicted in Fig. 2. The HOMO contribute mainly to the kaolinite (001) surface. On the PAM structural units (Fig. 2a, b and c), HOMO is localized close to the O atoms. Conversely on the kaolinite (001) surface (Fig. 2d), the LUMO is mainly localized near the H atoms.
Fig. 2. The HOMO distributions of P-AM (a), P-AA (b), and P-DAC (c), respectively. The LUMO distributions of the kaolinite (001) surface (d). (the isosurface value are 0.03 electrons /Å3).
3.1.2 Mulliken charge distribution and Fukui index analysis
Mulliken charge is used to calculate the space atomic charge distribution. It is an important application field to describe atomic electronegativity. It is also important for analyzing bonding properties and the altered charge in local orbitals [48], which will be discussed later in this paper in more detail. The frontier orbital of the molecule has been suggested as explaining the chemical reactivity. The Fukui function index can visually represent the electronic state at the HOMO and LUMO orbitals, indicating the electrophilic and nucleophilic sensitivity of the molecules in the chemical reaction, where f −(r) and f +(r) are the electrophilic and nucleophilic Fukui function indices [49], respectively. The reactive sites of the molecules can be more accurately analyzed and determined, excluding the main chain atoms of the structural unit, the Mulliken charge distributions and Fukui function indexes of some atoms on the three PAM structural units that were selected and
8
calculated. Table 2 shows the Mulliken charge distribution and Fukui function index for the atoms of the three PAM structural units. Table 2 Mulliken charge distribution and Fukui function index of the three PAM structural units.
The electrophilic and nucleophilic Fukui function index of O1 atom on P-AM is the highest, and the Mulliken charge of O1 is calculated as being -0.460e (Table 2). It demonstrates the strongest electronegativity, this result indicates that the O1 atom is the main reactive site of the P-AM. The f −(r) and f +(r) of the O2 atom on P-AA (0.404 and 0.239, respectively) are obtained (see Table 2). Therefore, the electrophilic and nucleophilic reactions are more likely to take place on the O2 atom. The O2 atom have more negative charges, which shows that the O2 atom is the main reactive site of P-AA. Similarly, the O1 atom is the main reactive site of P-DAC for adsorption on the kaolinite (001) surface. Kaolinite is a typical 1:1 dioctahedral clay minerals with a structural formula of Al4Si4O10(OH)8. The kaolinite (001) surface Al-OH groups [50-52] showed that the adsorption of molecules on the kaolinite (001) surface can be the top site, the bridge site, and the hollow site. Considering the periodicity of kaolinite, 5 top sites, 4 bridge sites, and 5 hollow sites were established on the kaolinite (001) surface as the initial adsorption sites of the three PAM structural units. The initial adsorption sites on the kaolinite (001) surface are shown in Fig. 3. The 9 initial adsorption sites on the kaolinite ( 00 1 ) surface are shown in Fig. S1. The orientation of the main reaction sites is very important [34]. Based on the adsorption site, the plane containing the reaction sites was placed on the kaolinite (001) surface in different postures. The reaction sites pointed toward the adsorption sites, and the plane mainly has parallel, inclined and vertical postures. 9
Fig. 3. The initial adsorption site of the PAM structural unit on the kaolinite (001) surface. Structure of the kaolinite layer, top (upper) and side (lower) views. (Blue T: top site; blue solid line: bridge site, which can be represented by Tm-Tn; blue S: hollow site)
3.2 Adsorption energies and characteristics The stability of adsorbate on the different adsorption sites can be represented using the adsorption energy [53]. The adsorption energies of the PAM structural unit on the kaolinite (001) surface were calculated by the following formula:
E
ads
E
system
E
polymer
E
surface
(3)
where E ads is the adsorption energies, E system is the system energy of the PAM structural unit on the kaolinite (001) surface. E polymer is the energy of an isolated PAM structural unit molecule.
E
surface
is the energy of the kaolinite (001) surface. Of these, E ads is negative, indicating that
the reaction is exothermic, and the adsorption system is stable; E ads is positive, meaning that the reaction is endothermic, and the adsorption system is unstable; the smaller the E ads value, the more stable the adsorption. The geometry optimization of the three PAM structural units on the initial adsorption sites of the kaolinite (001) surface was calculated, it was evident that the adsorption system remained stable with the interaction between the three PAM structural units and the kaolinite (001) surface. Three kinds of stable configurations with relatively small adsorption energies were analyzed. Predicted position changes and optimized adsorption energies are shown in Table 3. It can be seen that the optimal adsorption sites of P-AM, P-AA, and P-DAC on the kaolinite (001) surface are S2, S3, and S2, respectively. And the adsorption postures are 10
vertical, parallel, and vertical postures, respectively. The corresponding adsorption energies are -1.109, -0.982, and -1.823 eV, respectively. The adsorption stability of PAM structural units on the kaolinite (001) surface is in the order of P-DAC > P-AM > P-AA. Table 3. Predicted adsorption positions and energies of the three PAM structural units on the kaolinite (001) surface.
The optimal adsorption configurations of the three PAM structural units on the kaolinite (001) surface as shown in Fig. 4. The optimal adsorption systems of PAM structural units /kaolinite ( 00 1 ) surface as shown in Fig. S2. The most likely bonded atoms of the optimal adsorption system P-AM/kaolinite (001) surface are H1, O8, O1, H2, H4, and H5. The most likely bonded atoms of P-AA on the kaolinite (001) surface are O1, H2, O2, H4, and H8. The most likely bonded atoms of the optimal adsorption system P-DAC/kaolinite (001) surface are O1, H2, H4, and H5.
Fig. 4. The optimal adsorption systems of three PAM structural units on the kaolinite (001) surface. The most likely bonded atoms of the optimal adsorption systems. (a: P-AM/kaolinite (001) surface; b: P-AA/kaolinite (001) surface; c: P-DAC/kaolinite (001) surface)
3.3 Mulliken bond populations analysis Displayed here are the most likely bonds that make up the optimal adsorption systems as represented by Hn-Om (e.g. H1-O8). All the Mulliken bond population of PAM structural units on the kaolinite ( 00 1 ) surface are M(Hn-Om) =0 (Table S1). The Mulliken bond populations of the optimized adsorption system of P-AM, P-AA, and P-DAC on the kaolinite (001) surface are given in Table 4. The Mulliken bond population of H1-O8 is M(H1-O8) =0.10 and the bond 11
length is L(H1-O8) =1.812 Å (Table 4). The values of the Mulliken bond populations of P-AM on the kaolinite (001) surface are in the order of M(H1-O8) > M(H4-O1) > M(H5-O1) > M(H2-O1), and the bond lengths are in a sequence of L(H1-O8) < L(H4-O1) < L(H5-O1) < L(H2-O1). So, the bonding trends of the P-AM/kaolinite (001) surface are in this order of H1-O8 > H4-O1 > H5-O1 > H2-O1. The Mulliken bond populations of P-AA on the kaolinite (001) surface are following order M(H4-O2) = M(H8-O2) > M(H2-O1), and the bond lengths are in the order of L(H4-O2) < L(H2-O) < L(H8-O2). The bonding trend of H4-O2 is stronger than that of H8-O2, and H2-O1. The Mulliken bond populations of P-DAC on the kaolinite (001) surface are in a sequence of M(H2-O1) = M(H5-O1) > M(H4-O1), and the bond lengths are in this order of L(H2-O1) < L(H5-O1) < L(H4-O1), the bonding trends of the P-DAC/kaolinite (001) surface are following order H2-O1 > H5-O1 > H4-O1. The average Mulliken bond populations of the optimized adsorption system of P-AM, P-AA, and P-DAC on the kaolinite (001) surface are 0.063, 0.027, and 0.047, their average bond lengths are 1.868, 2.164, and 1.983 Å, respectively. The bonding interactions only of three PAM structural units on the kaolinite (001) surface are in the order of P-AM > P-DAC > P-AA. Table 4. The Mulliken bond populations of the three PAM structural units on the kaolinite (001) surface.
3.4 Charge analysis The Mulliken charge populations of the three adsorption systems were computed and summarized in Table 5. In P-AM/kaolinite (001) surface, the H1 atom of the P-AM obtained 0.07e charge, the O1 atom gained 0.04e, where the s orbit lost 0.02e and the p orbit received 12
0.06e. The H2, H4, and H5 atoms of the kaolinite (001) surface obtained 0e, 0.01e, and 0.02e, respectively. The p orbit of the O8 atom lost 0.07e while the s orbit did not lose any electrons. The adsorption system of the P-AA and the kaolinite (001) surface. The O1 and O2 atoms of the P-AA lost 0.01e and obtained 0.03e in the p orbit, respectively. Meanwhile there was no electrons change in the s orbit. The H4, H8, and H2 atoms of the kaolinite (001) surface lost 0.01e, obtained 0.03e and 0e, respectively. The P-DAC adsorption on the kaolinite (001) surface. The O1 atom of the P-DAC gained 0.07e, where the s orbit lost 0.01e and the p orbit obtained 0.08e. The H2, H4, and H5 atoms of the kaolinite (001) surface obtained 0.01e, 0e, and 0.02e, respectively. Table 5. Mulliken charge populations before and after the three PAM structural units adsorption on the kaolinite (001) surface.
The electron density difference can visually display the electron rearrangement of the adsorption system. In order to further determine the bonding properties, the electron density difference is analyzed based on the Mulliken charge analysis of the optimal adsorption system. Fig. 5 shows the electron density difference of the three PAM structural units on the kaolinite (001) surface, the blue region indicates electron accumulation, while the yellow region indicates electron depletion. It is worth noting that the hydrogen bond has directionality and saturation. In the P-AM/kaolinite (001) surface adsorption system, the electrons accumulated in the outermost layer of the O1 atomic orbit, whilst then shifting to the H5 and H4 atoms, the hydrogen bonds O−H4···O1 and O−H5···O1 are formed between O1 and H4, H5 atoms. The electrons of O8 atom shifted toward H1 atom to form a hydrogen bond N−H1···O8. The P-AA adsorption on the kaolinite (001) surface. Electrons are mainly accumulated at O2 atom and 13
shifted toward H4 and H8 atoms. Meanwhile, the electrons of the H4 and H8 atoms are depleted. The adsorption of P-AA/kaolinite (001) surface is driven by hydrogen bonds O−H4···O2 and O−H8···O2. Similarly, the hydrogen bonds formed by the P-DAC/kaolinite (001) surface are O−H2···O1 and O−H5···O1. In addition to the electron accumulation at the O1 atom, it is apparent that electron depletion occurs at the H atom of the P-DAC. There are no hydrogen bonds according to the Mulliken charge analysis. Combine with the calculation results for adsorption energies and Mulliken bond populations, it can be seen that the P-DAC adsorbs on the kaolinite (001) surface as well as the hydrogen bonds. It is evident that electrostatic attraction occurred and dominated the process. The electronic analysis in Table S2 shows that PAM structural units adsorption on the kaolinite ( 00 1 ) surface, while no hydrogen bond formation, there is a potential for hydrogen bonding. It can be seen from Fig. S3 that P-DAC has higher potential for hydrogen bonding with kaolinite ( 00 1 ) surface than P-AA and P-AM. The P-DAC and kaolinite ( 00 1 ) surface are only adsorbed by electrostatic attraction.
Fig. 5. The electron density difference of three PAM structural units on the kaolinite (001) surface (a: P-AM/kaolinite (001) surface; b: P-AA/kaolinite (001) surface; c: P-DAC/kaolinite (001) surface, the isosurface value is 0.01 electrons/Å3).
3.5 Electronic density of states analysis Fig. 6 and Fig. 7 illustrate the partial density of states (PDOS) of the interacting atoms between three PAM structural units and the kaolinite (001) surface in the optimal adsorption system. From Fig. 6, it can be seen that the energy levels of the atoms forming the hydrogen bond in the optimal adsorption configurations negatively shifted relative to that before 14
adsorption. This subsequently indicates that the adsorption system is more stable. After P-AM is adsorbed on the kaolinite (001) surface, the PDOS peak of interacting atoms decreased, the valence band widens and delocalization is enhanced. Overlaps of H1 1s with O8 2p are very clearly observed in -9eV ~ -6.5eV energy range of Fig. 6a. This is consistent with the analysis of the charge, indicating the hydrogen bond of N−H1···O8 is formed in the P-AM/kaolinite (001) surface. From -7.5eV to 5eV energy can be seen H4 s and H5 s contribute to O1 s and p states in of Fig. 6b. The interaction between O1 and H5, H4 are hydrogen bonds O−H4···O1 and O−H5···O1. Similarly, states of O2 and H4 s, H8 s of P-AA/kaolinite (001) surface adsorption system form resonance are presented in -7.5eV ~ 5eV energy range of Fig. 7a. Overlaps of O1 2p and H2 1s, H5 1s states of P-DAC/kaolinite (001) surface are obvious in part of Fig. 7b. The hydrogen bonds formed by P-AA/kaolinite (001) surface and P-DAC/kaolinite (001) surface are O−H4···O2, O−H8···O2 and O−H2···O1, O−H5···O1. These results are consistent with the charge analysis.
Fig. 6. PDOS of interacting atoms between P-AM and the kaolinite (001) surface. (a: H1 and O8; b: O1, H5, and H4).
Fig. 7. PDOS of interacting atoms of P-AA (a) and P-DAC (b) on the kaolinite (001) surface. (a: O2, H4, and H8; b: O1, H2, and H5). The density of states (DOS) of three PAM structural units adsorbed on kaolinite (001) surface is shown in Fig. 8. The energy of the P-DAC/kaolinite (001) surface adsorption system is much lower than that of the P-AM and P-AA adsorbing system on the kaolinite (001) surface. The more stable energy of the adsorption system indicates that the interaction between P-DAC 15
and kaolinite (001) surface is stronger. The results are consistent with the above analysis results.
Fig. 8. DOS of three PAM structural units adsorbed on the kaolinite (001) surface in the optimum adsorption system.
3.6 Electron localization function analysis The localization of atoms extranuclear electrons at different positions can be described by Electron localization function (ELF) [54]. ELF as defined runs from 0 to 1, which when closer to 1 localization increases and is equal to 0.5 for the homogeneous electron gas. Thus, ELF of 1.0 corresponds to perfect localization and ELF of 0.5 to perfect delocalization, which is important for describing the intensity of hydrogen bonds [55]. The ELF plot for three of the optimal adsorption systems is depicted in Fig. 9. In the P-AM/kaolinite (001) surface, the critical values of ELF(N−H1···O8), ELF(O−H4···O1), and ELF(O−H5···O1) are 0.063, 0.048， and 0.042, respectively. Hydrogen bonds formed by P-AM and the kaolinite (001) surface, the critical values of ELF(O−H4···O2) and ELF(O−H8···O2) are 0.017 and 0.018, respectively. The critical values of ELF(O−H2···O1) and ELF(O−H5···O1) are 0.025 and 0.022, respectively, while P-DAC was adsorbed on the kaolinite (001) surface. The average critical values of ELF for hydrogen bonding in the three adsorption systems are 0.0510, 0.0175 and 0.0235, respectively. The hydrogen bonding strength of P-AM and the kaolinite (001) surface is higher than that of P-AA and P-DAC.
16
Fig. 9. ELF of three PAM structural units adsorption on the kaolinite (001) surface. (a: P-AM/kaolinite (001) surface; b: P-AA/kaolinite (001) surface; c: P-DAC/kaolinite (001) surface).
4 Conclusion In this work, the DFT was employed to calculate the reactive sites, adsorption energies, and characteristics of the PAM structural unit on the kaolinite (001) surface. The PAM structural unit was developed from the industrial PAM structure itself. The simulation results show that the electrophilic and nucleophilic reaction are more likely to take place on the reactive atoms. The reactive atoms of the three PAM structural units, i.e. P-AM, P-AA, and P-DAC are all O atoms, these atoms have high electronegativity. The optimal adsorption sites of PAM structural unit on the kaolinite (001) surface are the hollow site and the adsorption energies are -1.109, -0.982, and -1.823eV, respectively. The hydrogen bonds of P-AM are adsorbed on the kaolinite (001) surface are N−H1···O8, O−H4···O1, and O−H5···O1. The hydrogen bonds of O−H4···O2 and O−H8···O2 did form in the P-AA/kaolinite (001) surface. Hydrogen bonds formed between atoms in the adsorption system are responsible for atomic orbital resonance. The main adsorption mechanism of P-AM or P-AA/kaolinite (001) surface is a hydrogen-bond interaction. The P-DAC adsorption on the kaolinite (001) surface as well as the hydrogen bonds O−H2···O1 and O−H5···O1, suggest there is electrostatic attraction and this process dominated. The P-AM or P-AA does not form hydrogen bonds with the kaolinite ( 00 1 ) surface, but there is adsorption potential. The adsorption of P-DAC with the kaolinite ( 00 1 ) surface is driven only by electrostatic attraction. By doing the ELF analyses, the hydrogen-bond interaction of the PAM structural units on the kaolinite (001) surface was as follows: P-AM > P-DAC > P-AA. However, the adsorption interaction between P-DAC and 17
the kaolinite (001) surface is higher than that of P-AM and P-AA. The present study provided an insight into the adsorption mechanism of PAM and kaolinite, which could serve as a guidance to choose PAM structural unit for its further applications in the molecular design and development of a more effective flocculant.
Acknowledgements The financial supports for this work from the National Natural Science Foundation of China under the grant No. 51874011 and the National Natural Science Foundation of China under the grant No. 51804009 are gratefully acknowledged.
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Adsorption of different PAM structural units on kaolinite (001) surface: Density functional theory study Bao Ren, Fanfei Min*, Lingyun Liu, Jun Chen, Chunfu Liu, Kai Lv
Department of Materials Science and Engineering, Anhui University of Science and Technology, Huainan 232001, China * Corresponding author: Tel: +86-554-6668885, Fax: +86-554-6668885 E-mail address: [email protected]
Fig. 1. Models and structural formulas of three PAM structural units. (a: P-AM; b: P-AA; c: P-DAC).
Fig. 2. The HOMO distributions of P-AM (a), P-AA (b), and P-DAC (c), respectively. The LUMO distributions of the kaolinite (001) surface (d). (the isosurface value are 0.03 electrons /Å3). 22
Fig. 3. The initial adsorption site of the PAM structural unit on the kaolinite (001) surface. Structure of the kaolinite layer, top (upper) and side (lower) views. (Blue T: top site; blue solid line: bridge site, which can be represented by Tm-Tn; blue S: hollow site)
Fig. 4. The optimal adsorption systems of three PAM structural units on the kaolinite (001) surface. The most likely bonded atoms of the optimal adsorption systems. (a: P-AM/kaolinite (001) surface; b: P-AA/kaolinite (001) surface; c: P-DAC /kaolinite (001) surface)
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Fig. 5. The electron density difference of three PAM structural units on the kaolinite (001) surface (a: P-AM/kaolinite (001) surface; b: P-AA/kaolinite (001) surface; c: P-DAC /kaolinite (001) surface, the isosurface value is 0.01 electrons/Å3).
Fig. 6. PDOS of interacting atoms between P-AM and the kaolinite (001) surface. (a: H1 and O8; b: O1, H5, and H4).
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Fig. 7. PDOS of interacting atoms of P-AA (a) and P-DAC (b) on the kaolinite (001) surface. (a: O2, H4, and H8; b: O1, H2, and H5).
Fig. 8. DOS of three PAM structural units adsorbed on the kaolinite (001) surface in the optimum adsorption system.
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Fig. 9. ELF of three PAM structural units adsorption on the kaolinite (001) surface. (a: P-AM/kaolinite (001) surface; b: P-AA/kaolinite (001) surface; c: P-DAC /kaolinite (001) surface).
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Adsorption of different PAM structural units on kaolinite (001) surface: Density functional theory study Bao Ren, Fanfei Min*, Lingyun Liu, Jun Chen, Chunfu Liu, Kai Lv
Department of Materials Science and Engineering, Anhui University of Science and Technology, Huainan 232001, China * Corresponding author: Tel: +86-554-6668885, Fax: +86-554-6668885 E-mail address: [email protected]
Table 1. Frontier orbital energies and the HOMO/LUMO gaps of the PAM structural unit and the kaolinite (001) surface. Model P-AM P-AA P-DAC Kaolinite (001) surface
Frontier orbital energy/eV
HOMO/LUMO Energy gap/eV
HOMO
LUMO
ΔE1
ΔE2
-5.519 -6.253 -5.063 -7.060
-0.471 -1.131 0.094 -2.130
6.589 5.929 7.154 −
3.389 4.123 2.933 −
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Table 2. Mulliken charge distribution and Fukui function index of the three PAM structural units. Model
atom
Mulliken charge/e
f −(r)
f +(r)
P-AM
C1 N1 O1 H1 H2 C1 O1 O2 H1 C1 C2 C3 C4 N1 O1 O2 H1 H2 H3
0.432 -0.380 -0.460 0.210 0.194 0.496 -0.395 -0.392 0.264 0.428 0.105 -0.027 -0.058 -0.358 -0.480 -0.471 0.043 0.043 0.067
0.106 0.105 0.399 0.059 0.070 0.124 0.125 0.404 0.071 0.062 0.019 0.031 0.038 0.009 0.074 0.020 0.047 0.053 0.047
0.215 0.124 0.216 0.066 0.067 0.233 0.134 0.239 0.069 0.060 0.019 0.030 0.037 0.008 0.073 0.020 0.047 0.052 0.048
P-AA
P-DAC
Table 3. Predicted adsorption positions and energies of the three PAM structural units on the kaolinite (001) surface. Adsorption system
Initial position
Final position
Adsorption energy/eV
P-AM/kaolinite (001) surface
S2 S3 T5 S1 S3 T2-T1 T6 S2 T5-T8
S2 T5 T5 S1 S3 T2-T1 T6 S2 T5-T8
-1.109 -0.911 -0.904 -0.890 -0.982 -0.816 -1.771 -1.823 -1.779
P-AA/kaolinite (001) surface
P-DAC/kaolinite (001) surface
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Table 4. The Mulliken bond populations of the three PAM structural units on the kaolinite (001) surface. Adsorption system
Bond
Bond populations
Bond lengths /Å
P-AM/kaolinite (001) surface
H1-O8 H2-O1 H4-O1 H5-O1 H2-O1 H4-O2 H8-O2 H2-O1 H4-O1 H5-O1
0.10 0.03 0.07 0.05 0.02 0.03 0.03 0.05 0.04 0.05
1.812 1.946 1.845 1.899 2.156 2.147 2.189 1.898 2.073 1.977
P-AA/kaolinite (001) surface
P-DAC/kaolinite (001) surface
Table 5. Mulliken charge populations before and after the three PAM structural units adsorption on the kaolinite (001) surface. Adsorption system
Atom
Mulliken charge population Before
P-AM/kaolinite (001) surface
P-AA/kaolinite (001) surface
P-DAC/kaolinite (001) surface
H1 O1 H2 H4 H5 O8 O1 O2 H2 H4 H8 O1 H2 H4 H5
After
s
p
Charge/e
s
p
Charge/e
0.53 1.83 0.55 0.56 0.54 1.85 1.82 1.82 0.55 0.56 0.55 1.82 0.55 0.56 0.54
— 4.76 — — — 5.21 4.86 4.72 — — — 4.75 — — —
0.47 -0.59 0.45 0.44 0.46 -1.06 -0.68 -0.54 0.45 0.44 0.45 -0.57 0.45 0.44 0.46
0.60 1.81 0.55 0.57 0.56 1.85 1.82 1.82 0.55 0.55 0.58 1.81 0.56 0.56 0.56
— 4 .82 — — — 5.14 4.85 4.75 — — — 4.83 — — —
0.40 -0.63 0.45 0.43 0.44 -0.99 -0.67 -0.57 0.45 0.45 0.42 -0.64 0.44 0.44 0.44
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Adsorption of different PAM structural units on kaolinite (001) surface: Density functional theory study Bao Ren, Fanfei Min*, Lingyun Liu, Jun Chen, Chunfu Liu, Kai Lv
Department of Materials Science and Engineering, Anhui University of Science and Technology, Huainan 232001, China * Corresponding author: Tel: +86-554-6668885, Fax: +86-554-6668885 E-mail address: [email protected]
Graphical Abstract
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Adsorption of different PAM structural units on kaolinite (001) surface: Density functional theory study Bao Ren, Fanfei Min*, Lingyun Liu, Jun Chen, Chunfu Liu, Kai Lv
Department of Materials Science and Engineering, Anhui University of Science and Technology, Huainan 232001, China * Corresponding author: Tel: +86-554-6668885, Fax: +86-554-6668885 E-mail address: [email protected]
The adsorption mechanism of the PAM structural unit on the kaolinite (001) surface has been studied by utilizing DFT. The adsorption interaction of P-DAC with the kaolinite (001) surface higher than P-AA and P-AA. P-AM or P-AA adsorption on the kaolinite (001) surface through hydrogen bonding. Both hydrogen bonds and electrostatic attraction contribute to the adsorption process of P-DAC/ kaolinite (001) surface.
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Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:
We declare that we have no conflict of interest.
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