First-Principles Density Functional Theory Calculations for Formic Acid Adsorption onto Hydro-Garnet Compounds

Abstract

Efficient and large-scale removal of humic acid (HA) from aqueous environments is required since HA causes human health and esthetic issues. Hydro-garnet compounds, Ca₃Al₂(SiO₄)_3–x(OH)_4x, have recently been suggested as HA adsorbents not only due to their superior adsorption behaviors but also because they are ubiquitous element-derived compounds. In this study, the adsorption behavior of formic acid to hydro-garnets was investigated by means of first-principles density functional theory (DFT) computations. Formic acid was chosen owing to its reasonable computational cost and inclusion of carboxylic acid as HA. Comparisons of adsorption energies for formic acid among various compounds (including platinum and kaolinite) indicate that hydro-garnet compounds are promising due to their lower (more stable) adsorption energies. Also, the optimization of composition x enables selective adsorption of formic acid against solvent water molecules. Relationships between surface electronic/atomistic structures and adsorption properties are discussed.

Introduction

Humic acid (HA) is a mixture of various organic molecules consisting of a motif of aromatic nuclei with phenolic and carboxylic substituents. In aqueous environments, HA is produced by biodegradation of dead organisms and is a water pollutant. For example, harmful trihalomethanes are generated through chlorination of HA compounds.^1,2 Therefore, HA removal from water is required at water purification plants to prevent human health issues. Also, small amounts of HA contamination in water cause brown coloring. Thus, HA causes health and esthetic issues,^3,4 and efficient, low-cost, large-scale, and complete removal of HA is highly demanded for water purification.

Several methods, such as membrane separation and coagulation techniques, have been suggested to remove HA.^5,6 Adsorption of HA onto inorganic substrates is also promising. Indeed, activated carbon (which is used as an adsorbent for various materials in water purification plants) also shows high HA adsorption performance.⁷ Libbrecht et al. demonstrated an improvement of HA adsorption by controlling the pore size of carbon.⁸ Oxides, such as kaolinite, also show HA adsorption properties.⁹ We have recently suggested the use of hydro-garnet compounds, Ca₃Al₂(SiO₄)_3–x(OH)_4x, as an HA adsorbent, where this material shows superior adsorption performance compared to kaolinite or zeolite.¹⁰ Furthermore, these compounds are composed only of ubiquitous elements, which potentially satisfies the conditions of low cost and large scale for installing water purification plants. Hydro-garnets are also byproducts of autoclaved cement production.¹¹ Lacivita et al. indicated the existence of a miscibility gap using density functional theory (DFT) calculations,¹² while we reported a wide range of compositions controlled by autoclaved synthesis.¹³

In this study, the organic and/or water molecule adsorption behavior of hydro-garnet compounds was investigated to acquire fundamental knowledge on the adsorption mechanism and materials design to optimize the HA adsorption performance. First-principles DFT calculations were adopted to evaluate quantitative thermodynamics and the electron/molecular-level adsorption mechanism. Instead of HA, formic acid (HCOOH) adsorption properties were investigated in this study, since the molecular size of HA molecules is too large to compute adsorption using the DFT technique (number-average molecular weight is >10 000¹⁴). As HA contains carboxylic substituents, knowledge in formic acid adsorption behavior aids in designing materials for HA adsorption. Particular attention was paid to the compositional dependence of the hydro-garnet adsorbent, to understand the role of surface functional groups such as Si–O(H) and Al–O(H). Also, the adsorption properties of kaolinite and platinum substrates as control compounds were evaluated.

Methods

First, relaxed structure calculations were performed for the bulk structures of a series of hydro-garnet compounds, Ca₃Al₂(SiO₄)_3–x(OH)_4x (where x = 0, 0.5, 1.5, 2.5, and 3), using DFT. Both the ends of the composition are known as grossular (x = 0) and katoite (x = 3). Ca and Al ions are located at the dodecahedral and octahedral sites, respectively. The tetrahedral cavities are occupied by Si or H ions. We adopted the special quasi-random (SQS) technique¹⁵ to determine the Si and H arrangement for the intermediate composition (0.5 < x < 2.5), due to the numerous arrangements of Si and H inside the tetrahedral cavities. In detail, we only considered pair interactions, and the Monte Carlo approach was used for SQS structure search, as the nearest-neighbor (NN) coordination number distribution derived from this approach renders randomly configured cation–cation interactions. The constraint that the interatomic distance between Si and H was longer than 1.4 Å due to strong Coulombic repulsion was applied for the SQS structure search. DFT computations for the above structure models were performed using the generalized gradient approximation (GGA-PBEsol)^16,17 using the plane-wave basis set and the projector-augmented wave (PAW) method as implemented in the Vienna ab initio simulation package (VASP).^18,19 The kinetic energy cutoff was set as 500 eV, and a 2 × 2 × 2 k-point mesh was applied.

After determining the cubic lattice parameters of hydro-garnets, the surface structures were computed using the slab technique, in which a set of infinite layers separated by vacuum layers are repeated periodically along the surface normal. Low-index facets of the (001), (011), and (111) surfaces with various terminations were targeted in this study, as reported previously.¹³ In this study, charge-balanced stoichiometric slabs were treated by adjusting the number of surface atoms. A total of six termination models for each composition (i.e., total 30 structure models for 5 compositions) were constructed as follows: Ca- and CaAlSi-terminated {001} surfaces, CaSi- and Al-terminated {011} surfaces, and CaSi- and Al-terminated {111} surfaces (see the Supporting Information; Figure S1). Surface structure relaxations were carried out using the DFT technique as for the bulk model, except for the condition that the k-point mesh along the c-axis (normal to the slab layer) was unity.

Formic acid (HCOOH) adsorption reactions onto three compositions (x = 0, 1.5, and 3.0) in Ca₃Al₂(SiO₄)_3–x(OH)_4x were performed using DFT-based first-principles molecular dynamics (FPMD) simulations. The initial structure models were inputted as the HCOOH molecules were placed at the vacuum layer. The cutoff energy was set to 420 eV, and a 1 × 1 × 1 k-point grid (only Γ point) was employed to reduce the computational cost. The difference in the total electron energy was <4 meV atom^–1, which was obtained by comparing the structure relaxation calculation settings described above (500 eV in cutoff energy and 2 × 2 × 2 k-point grid). The time step was set to 1 fs, and our FPMD simulations were carried out in the canonical (NVT) ensemble, in which the amount of substance (N), volume (V), and temperature (T) are conserved, using a Nosé thermostat²⁰ at 298 K, until the energy of the system became stable (after 20–40 ps). We also computed structure models without any adsorbate or with H₂O (solvent) molecules as adsorbates. Likewise, adsorption reaction calculations onto the other substrates (platinum metal [Pt] and kaolinite [Al₄Si₄O₁₀(OH)₈] surfaces) were performed for comparison purposes.

Results and Discussion

The calculated cubic lattice parameters for bulk Ca₃Al₂(SiO₄)_3–x(OH)_4x (0 ≤ x ≤ 3) are plotted in Figure 1. The compounds obey Vegard’s law, as the lattice parameter increases linearly with composition x. Also, the results are in accordance with experimental observations.

Figure 1.

Variation of the calculated cubic lattice parameter of hydro-garnets as a function of composition x in Ca₃Al₂(SiO₄)_3–x(OH)_4x.

Table 1 and Figure 2 show the calculated surface energies of various low-index facets. In general, the surface energies are monotonically decreased (stabilized) with composition x regardless of the facets, indicating that the surface of Si-rich compounds is more reactive. We infer that H⁺ stabilizes the dangling bonds of oxide ions at the top surface. Figure 3a displays the optimized particle morphologies for various compositions, and Figure 3b shows the ratio of facets’ area. The Wulff construction was used to estimate the particle morphology, in which the distance to the central point {hkl} from the origin was taken to be proportional to the surface energy.²¹ At x = 0, the {001} and {111} facets were dominant, whereas {001} and {110} became more significant for the composition x > 0. Hence, introducing H⁺ largely stabilized the {110} facets with respect to the {111} facets.

Table 1. Calculated Surface Energies of Various Facets and Terminations for Hydro-Garnet Compounds^a.

x	facet	termination	surface energy (eV Å–2)
0	{100}	CaSi	0.0924
		CaAlSi	0.1014
	{110}	CaSi	0.1134
		Al	0.1247
	{111}	CaSi	0.1024
		Al	0.0980
0.5	{100}	CaSi	0.0741
		CaAlSi	0.0795
	{110}	CaSi	0.0721
		Al	0.0801
	{111}	Al	0.0809
1.5	{100}	CaSi	0.0452
		CaAlSi	0.0495
	{110}	CaSi	0.0541
		Al	0.0464
	{111}	Al	0.0545
2.5	{100}	CaSi	0.0272
		CaAlSi	0.0398
	{110}	CaSi	0.0272
		Al	0.0330
	{111}	Al	0.0363
3	{100}	Ca	0.0143
		CaAl	0.0203
	{110}	Ca	0.0151
		Al	0.0199
	{111}	Ca	0.0197
		Al	0.0260

^aDetailed atomic arrangements for each model are shown in Figures S2–S4 (Supporting Information).

Figure 2.

Variation of the surface energies for the selected surface model listed in Table 1 as a function of composition x in Ca₃Al₂(SiO₄)_3–x(OH)_4x.

Figure 3.

Composition dependence of (a) optimized particle morphologies and (b) ratio of the corresponding facet area as a function of composition. Blue, green, and orange correspond to the {100}, {110}, and {111} facets.

Due to limitations in computational resources, FPMD calculations were only conducted for the selected facets and composition x, as described below. Since the {100} surfaces commonly appeared for all of the compositions, as well as small surface energy changes attributed to facets and terminations (Table 1 and Figure 2), we focused solely on the {100} facet, hereinafter, for studies on the adsorption of formic acids and H₂O molecules. Moreover, three adsorbent compositions (i.e., x = 0, 1.5, and 3.0) were selected for the FPMD studies to account for monotonic surface energy changes as a function of composition x (Figure 2). The lowest surface energy terminations (i.e., CaSi- (x = 0 and 1.5) or Ca-terminated (x = 3) facets) were chosen for the {100} facets of each composition model. Formic acid (HCOOH) or H₂O adsorption onto the {100} facets was simulated by FPMD calculations at 298 K. Due to the limitations in computational resources and composition-dependent surface energy monotonic changes (Figures 2 and S2), the adsorbate molecules were adsorbed on the slab (adsorbent) surfaces within 20 ps at 298 K in this study. It was also confirmed that no molecules were released to the vacuum layer after the 20 ps MD run. The adsorption reaction and the adsorption energies (E_ads) are as follows

1

and

2

where S, M, and n are solid-state adsorbent, adsorbate molecules, and the number of adsorbates, respectively; θ and A correspond to surface coverage and surface area in the model; and E[X] stands for the averaged total electronic energy of compound X for the last 5 ps of MD calculations. Note that surface coverage is defined as the area occupancy of adsorbed molecules against the total surface area of the corresponding slab model, A. Figure 4a displays the variation of adsorption energies of formic acid as a function of surface coverage, θ, onto hydro-garnet {100} facets. The molecular area at the monolayer for formic acids was set as 37.3 Ų using the ChemDraw software package.^22,23 The calculated adsorption energies were abruptly increased (destabilized) at θ > 1, indicating a weak interaction between the two adsorbates, which is linked to multilayer adsorption and strong interactions between the adsorbent and adsorbate. Figure 4b presents the absorption energy for formic acid or H₂O molecules with composition x of hydro-garnet adsorbents around the surface coverage of 0.5 (four adsorbate molecules in the slab model). The adsorption energies were reduced with composition x for both the adsorbates, HCOOH and H₂O. Therefore, the introduction of hydroxy units at the hydro-garnet surface reduced the reactivity with adsorbates. For comparison purpose, the calculated adsorption energies of formic acid onto the platinum metal or kaolinite surfaces are also plotted in Figure 4a. We confirmed that the hydro-garnet compounds showed much larger adsorption energies than kaolinite materials (one of the candidate adsorbate materials for HA) and comparable energies to platinum metal surfaces. Hence, the hydro-garnet material is potentially an attractive adsorbent for formic acid in terms of adsorption energy. However, as shown in Figure 4b, adsorption energies for solvent H₂O molecules onto hydro-garnets were also large, which may lead to the preferential adsorption of H₂O molecules rather than adsorption of formic acids. Considering the phase equilibrium based on eq 1, the relationship between adsorption energy and surface coverage for species M_i can be described as follows

3

where K_i represents the equilibrium constant for species M_i; N, R, and T correspond to the total number of adsorption sites, gas constant, and temperature; and [M_i] is the concentration of species M_i in aqueous solution. There were three species considered in this study; formic acid (HCOOH), water molecules (H₂O), and vacancy (φ, only for adsorbent). Considering the site and mass balance

4

5

and 1 ppm as a concentration of formic acid ([M_HCOOH] = 10^–6) at 298 K, since HA is present at dilute concentrations in aqueous environments. The surface coverage of the three species on hydro-garnets with various compositions x in Ca₃Al₂(SiO₄)_3–x(OH)_4x was determined as listed in Table 2. Although there was large adsorption energy of formic acid for the Ca₃Al₂(SiO₄)₃ (x = 0) adsorbent, H₂O molecules were preferentially covered on the hydro-garnet surface due to a larger adsorption energy of H₂O molecules (Figure 4b) and low formic acid concentrations. On the other hand, hydro-garnet with x = 1.5 showed large coverage by formic acid due to the relatively smaller (more stable) adsorption energy of H₂O molecules than that of formic acid. Therefore, the present computation demonstrates that composition optimization is a useful technique to control the selective adsorption of formic acid. Hydro-garnet compounds containing Ca₃Al₂(SiO₄)_1.31(OH)_6.76 (x = 1.31), Ca₃Al₂(SiO₄)_0.66(OH)_9.37 (x = 0.66), and Ca₃Al₂(SiO₄)_0.31(OH)_10.76 (x = 0.31) exhibited higher HA adsorption capacity than the hydro-garnet compound Ca₃Al₂(SiO₄)_0.42(OH)_10.32 (x = 0.42), which is consistent with the simulation results using formic acid. Further improvement could be achieved by optimizing composition x based on the computational results described herein.

Figure 4.

(a) Averaged adsorption energies of HCOOH onto various adsorbents as a function of surface coverage, θ. Multilayer adsorption is indicated at θ > 1. (b) Comparison of adsorption energies between H₂O and HCOOH as adsorbates onto the {100} surface of Ca₃Al₂(SiO₄)_3–x(OH)_4x (x = 0, 1.5, and 3.0).

Table 2. Surface Coverage of Formic Acid, HCOOH, on the Hydro-Garnet Surface with Various Compositions of x in Ca₃Al₂(SiO₄)_3–x(OH)_4x.

composition x	0.0	1.5	3.0
surface coverage θHCOOH	∼0%	∼90%	∼0%

To clarify the molecular-level adsorption mechanism, surface atomistic and electronic structure analyses before and after adsorption were performed. Figure 5 displays selected snapshots in the vicinity of hydro-garnet surfaces after adsorption. It was confirmed that all of the formic acids were dissociated into H⁺ and HCOO^–. H⁺ ions are prone to bind surface oxygen atoms which are connected to Si, i.e., −Si–O–H formation (Figure 5a,b). At a composition of x = 3.0 where no Si atoms were present, H⁺ ions were bonded with surface OH^– forming H₂O molecules, and then H₂O coordinated on the top of Ca²⁺ ions (Figure 5d). On the other hand, HCOO^– ions interacted with surface Ca, forming −Ca–OCHO^– bonds (Figure 5b–d). Similarly, H₂O molecules were dissociated into H⁺ and OH^– and formed surface −Si–O–H and −Ca–OH bonds. Therefore, salt dissociation and acid/base reactions proceed on the surface of the hydro-garnets.

Figure 5.

Snapshots of surface structures after HCOOH adsorption onto the surface of hydro-garnets, Ca₃Al₂(SiO₄)_3–x(OH)_4x. (a–c) Surface at the composition x = 0 and (d) surface at the composition x = 3.0. Numerical values indicate interatomic distances (unit Å). The light pink, brown, red, blue, green, and orange spheres indicate hydrogen, carbon, oxygen, silicon, aluminum, and calcium atoms, respectively.

Figure 6 shows contour plots of the density of states (DOS) for the electronic band against energy level and z-fractional coordinates (perpendicular to the slab facets). It was confirmed that the top of the valence band around the surface was higher than that around the bulk before the HCOOH adsorption, i.e., band bending at x = 0 (Figure 6a). Also, the band bending feature was confirmed for the bottom of the conduction band at x = 0. The band bending feature was reduced with composition x in Ca₃Al₂(SiO₄)_3–x(OH)_4x. (Figure 6b,c). Figure 7a,c displays the partial electron density at the top of the valence band; the energy ranged from −1 to 0 eV vs Fermi level, for the sample at x = 0 and 3.0, respectively, before adsorption. The electron density arising from dangling bonds of the surface O 2p orbitals is clearly visible on the surface oxygen at x = 0 in Figure 7a, whereas electric states corresponding to these dangling O 2p orbitals were faint due to capping of H⁺ ions on surface oxygens at x = 0 (Figure 7c). Therefore, the band bending feature was diminished with the replacement of Si⁴⁺ by H⁺ with composition x. In other words, a strong electron-donating property via the dangling O 2p orbital is indicated for the sample with smaller x in Ca₃Al₂(SiO₄)_3–x(OH)_4x. Indeed, the band bending characteristics were diminished after completion of HCOOH or H₂O adsorption (Figure 6d), due to the H⁺ capping on the surface oxygen. Therefore, we infer that bare surface oxygen sites trigger dissociation of HCOOH or H₂O molecules and the resulting H⁺ ions are bonded to the dangling O 2p orbital. The trend of band bending characteristics agrees with changes in the adsorption energy for both HCOOH and H₂O (Figure 4), where the adsorption energy for both molecules monotonically reduced with composition x. Therefore, the enhancement of salt dissociation by dangling bonds of O 2p at the surface of hydro-garnet would be a primary reason for the observed trend in adsorption energy as a function of composition x.

Figure 6.

Density of states (DOS) for various {100} slab models as a function of energy level and z-axis (normal to the slab surface). (a–c) Slab models without adsorbates at compositions x = 0, 1.5, and 3.0 in Ca₃Al₂(SiO₄)_3–x(OH)_4x. (d) DOS for four HCOOH adsorbed hydro-garnet with x = 0.

Figure 7.

Visualized (a, c), occupied, and (b, d) unoccupied states around the Fermi level at the surface of hydro-garnets (yellow-colored isosurfaces).

The dissociated anions (HCOO^– or OH^–) are also captured on surface Ca²⁺ ions by electrostatic interactions or coordination bonding, as shown in Figure 5b–d. Figure 7b,d displays the spatial distribution of density of states around the bottom of conduction bands (energy ranges are shown in the figure). The formation of widely spread states at the surface is visible above Ca²⁺ and neighboring O^2– at the surface in x = 0 (Figure 7b). This is due to the hybridization between the Ca 4s orbital and the unshared electron pairs arising from the O 2p orbital. Hence, these unoccupied states act as electron acceptors, and HCOO^– or OH^– ions (which possess unshared electron pairs) would interact with the unoccupied states above the surface Ca²⁺ ions. This agrees with the fact that HCOO^– adsorbed onto Ca²⁺ ions as shown in Figure 5b–d. On the other hand, these unoccupied states were localized at the composition x = 3.0 (Figure 7d) and the corresponding energy level against the Fermi level largely increased. Since the unshared pair electrons of surface oxide ions were bonded with H⁺ ions, hybridization between Ca 4s and O 2p at the surface was weakened.

The adsorption energy difference between HCOOH and H₂O as a function of composition x appeared rather complicated, where the H₂O adsorption energy was more stable at the end compositions (x = 0 and 3.0), while HCOOH was stable at the intermediate composition (x = 1.5). Indeed, this difference controls the surface coverage of HCOOH adsorption as listed in Table 2.

One of the factors is that an acid/base dissociation reaction in solution is easier in HCOOH (pK_a = 3.75) than in H₂O (pK_a = 15.7). Therefore, dissociation-driven proton adsorption of HCOOH may be enhanced even for compounds with large composition x where there is no enhancement of H⁺ dissociation/adsorption due to no band bending. Another factor is the formation of a coordinate bond between the bottom of the conduction band of the adsorbent and the highest occupied molecular orbital (HOMO) of the anion adsorbate (OH^– or HCOO^–). Figure 8 presents the HOMO and lowest unoccupied molecular orbital (LUMO) of three adsorbent surfaces according to the DFT calculation and electronic potential at the vacuum. The bottom of the conduction band level and the band gap of the adsorbent increased with composition x. Since the HCOO^– anion has a larger molecular size than OH^– and an electronic resonance structure, the coordinate bonding interaction of HCOO^– was much stronger than OH– with adsorbents at low composition x. Such effects (acid/base dissociation and/or coordinate bond formation) are trade-off relationships which may account for the calculated results that the intermediate composition of the adsorbent showed superior HCOO^– adsorption.

Figure 8.

Band diagram for the {100} slab models at compositions x = 0, 1.5, and 3.0 in Ca₃Al₂(SiO₄)_3–x(OH)_4x.

Conclusions

Formic acid or water adsorption behavior onto the surfaces of hydro-garnet compounds has been simulated using first-principles DFT-MD techniques. The results indicated that hydro-garnets show more stable adsorption (smaller in adsorption energy) of formic acid than kaolinite or platinum substrates. Thus, hydro-garnets may be promising compounds for HA adsorption materials.¹⁰ Also, the results suggest the importance of composition optimization for selective adsorption of formic acid, since HA is present at dilute concentrations in aqueous environments. The electronic structure analysis of the hydro-garnets surface revealed compositional changes of band bending at the surfaces, which may affect acid/base dissociation reactions. Further research is needed to characterize the dissociation reaction process in more detail, which could be achieved via the nudged elastic band method²⁴ and blue-moon ensemble techniques²⁵ to assess the free-energy profiles of the reaction. These findings will aid in the rational design of novel hydro-garnet compounds as materials for HA adsorption.

Glossary

Abbreviations Used

HA

humic acid

DFT

density functional theory

FPMD

first-principles molecular dynamics

DOS

density of states

NVT

canonical ensemble

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.9b03746.

• Slab models for Ca₃Al₂(SiO₄)₄ for density functional theory (DFT) calculations; relaxation process of formic acid adsorption process in density functional theory based molecular dynamics (PDF)

Author Contributions

M.N. and H.M. conceived and directed the project. K.I. and K.W. conducted DFT calculations. The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

The authors declare no competing financial interest.