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Surface acidity of quartz: understanding the crystallographic control Xiandong Liu,*a Jun Cheng,b Xiancai Lua and Rucheng Wanga We report a first principles molecular dynamics (FPMD) study of surface acid chemistry of the two growth surfaces of quartz, (101% 0) (including Alpha and Beta terminations) and (101% 1) facets. The interfacial hydration structures are characterized in detail and the intrinsic pKas of surface silanols are evaluated using the FPMD based vertical energy gap method. The calculated acidity constants reveal that every surface termination shows a bimodal acid–base behavior. It is found that all doubly-protonated forms (i.e. SiOH2) on the three terminations have pKas lower than 2.5, implying that the silanols hardly get protonated in a
Received 6th July 2014, Accepted 24th October 2014
common pH range. The pKas of surface silanols can be divided into 3 groups. The most acidic silanol is the donor SiOH on the (101% 0)-beta surface (pKa = 4.8), the medium includes the germinal silanol on (101% 0)-alpha and the outer silanol on (101% 1) (pKa = 8.5–9.3) and the least acidic are inner silanols on the
DOI: 10.1039/c4cp02955k
(101% 1)-facet, acceptor SiOH on (101% 0)-beta, and the secondly-deprotonated OH (i.e. Si(O–)(OH)) on (101% 0)-alpha (pKa 4 11.0). With the pKa values, we discuss the implication for understanding metal cations
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complexing on quartz surfaces.
1. Introduction Quartz is one of the most abundant minerals in the Earth’s crust.1 Due to the ubiquitous distribution on the Earth’s surface, quartz plays important roles in interfacial processes in nature, e.g.2–4 The interfacial chemistry of quartz is also of great interest in biology,5 and technology.6,7 Based on the connectivity to the rest of the quartz crystal, the surface silanols can be grouped into Q1, Q2 and Q3 sites (Qn means that it has nSi–O bonds to the bulk and 4-nOH bonds to the solution). These silanol groups are amphoteric, which makes the quartz surface show pH-dependent behaviors, and therefore, the interfacial properties of quartz are strongly dependent on the environmental pH. Numerous titration experiments have been carried out for quartz and other silica phases. The pHiep (isoelectric point) value of quartz is found to be within 0.5–3.5.8 The fitted acidity constants for quartz in the literature are pKa1 = 1.2 and pKa2 = 7.2.9 Experiments show that several types of facets can coexist for quartz, for example, (101% 0), (101% 1) and (0001).10 But up to now, the crystallographic control on surface acidity of silanols remains unclear. Aiming at the understanding of chemical weathering of quartz, dissolution experiments have been extensively carried out, e.g. ref. 11–13 and references therein. The interpretation of a
State Key Laboratory for Mineral Deposits Research, School of Earth Sciences and Engineering, Nanjing University, Nanjing 210093, P. R. China. E-mail: [email protected]; Fax: +86 25 83686016; Tel: +86 25 83594664 b Department of Chemistry, University of Aberdeen, Aberdeen, AB24 3UE, UK
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these experiments must rely on the detailed knowledge of interfacial properties, such as the identity, density, and deprotonation free energies of reactive sites.14–16 The applications of advanced spectroscopic techniques and atomistic simulations have significantly promoted the exploration of molecular-level interfacial properties of quartz. Schlegel et al.10 derived the atomic-scale structures of (101% 0) and (101% 1) facets with X-ray reflectivity and atomic force microscopy. By using the phasesensitive surface spectroscopy, Ostroverkhov et al.17 obtained the microscopic interfacial structure of the quartz(0001) facet and found that there are two types of silanols on this surface. Static quantum mechanical modeling has been applied to investigate surface relaxation and hydrolysis of silica for decades.18–26 Classical and first principles molecular dynamics (FPMD) techniques have also been employed to study the interfaces between silica and water.27–33 By using both classical and FPMD simulations, Skelton et al.31,32 revealed the microscopic interfacial structures of (101% 1) and (101% 0) facets, which provided fundamental models for future research. According to their analyses, (101% 0) surfaces have two different terminations and several types of silanols have been identified. By combining FPMD and free-energy perturbation theory, the Sprik group developed a vertical energy gap technique for pKa calculation,34,35 which has been successfully applied on molecular systems34–38 and solid surfaces.39–44 Systematic tests on molecules of over 20 pKa units show that most acidities can be reproduced within 2 pKa units. Using this method, Sulpizi et al.40 obtained pKas 4.5 and 8.5 for the two kinds of silanols of the quartz(0001) surface. By using a FPMD based potential of
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the mean force calculation technique, Leung et al.45 investigated 6 facets of silica, including the beta-cristobalite(100) surface, the hydroxylated beta-cristobalite(100) surface with one SiOH replaced with SiH to break the chain of H-bonds, two reconstructed betacristobalite(100) surfaces, (H3SiO)3SiOH clusters, a reconstructed quartz(0001) surface containing a cyclic silica trimer (Si–O)3, and they showed a bimodal acid–base behavior of the silica surface, which is consistent with that proposed by Ong et al.46 They found that only the strained silica surface represents the low pKa value of about 4.5 and all the others are higher than 7.0. To form a complete view of the acid chemistry of quartz, the intrinsic acidity constants of all possible surfaces are needed. To our knowledge, the surface acidity of the two growth surfaces ((101% 1) and (101% 0)) has not been quantified. In this study, we employ FPMD simulations to evaluate the pKas of the silanol groups on those two facets. From the simulations, the interfacial structures are characterized in detail and with the derived acidity values, the crystallographic control on the pKa has been discussed.
2. Methodology 2.1.
Models
The crystal parameters of the used alpha-quartz model are a = 4.9137 Å, b = 4.9137 Å, c = 5.4047 Å and a = g = 901, b = 1201.47 The surface structures were cut from the bulk crystal and all dangling Si–O bonds were saturated by H. The (101% 0) surface has two possible terminations denoted Alpha and Beta (Fig. 1A and B). The Alpha termination contains only Q2 Si and therefore the
silanols are germinal (Fig. 1A). The Beta termination contains Q3 Si, and the silanols are vicinal (Fig. 1B). On the (101% 1) surface, two types of silanols are identified, which are marked SiOHInner and SiOHOuter (the definitions are based on the relative positions of Si atoms) (see Fig. 1C and 7). The models were placed in 3D periodically repeated cells, which have a solution space of about 12 Å in the direction vertical to surfaces (see Fig. 1). The two solution regions of (101% 0) and (101% 1) boxes contain 42 and 54 water molecules, respectively, which approximately reproduce the density of bulk water under ambient conditions. 2.2.
First principles MD
The CP2K/QUICKSTEP package48 was used to carry out the FPMD simulations. In this package, the electronic structures were calculated with a hybrid Gaussian plane wave (GPW) implementation of density functional theory.42 BLYP functional49,50 and Goedecker–Teter–Hutter pseudopotentials51 were used. The cutoff of the plane wave basis for the electron density was set to be 280 Ry. All H atoms in the systems were assigned a mass of 1.008 u. Bohn-Oppenheimer type FPMD simulations were performed with a wave function optimization tolerance of 1.0 106 and a time step of 0.5 fs. To avoid the glassy behaviour of BLYP water,52 ´–Hoover the temperature was controlled at 330 K using the Nose chain thermostat. For each simulation, an equilibration step was for at least 2.0 ps and a production run was for 8.0–10.0 ps. 2.3.
pKa calculation
The half-reaction scheme of the FPMD based vertical energy gap method was applied to evaluate pKas of surface silanol groups.35,53 Using this scheme, the proton of the acid marked AH is gradually transformed into a dummy (i.e. a classical particle with no charge). The free energy change (DdpAAH) of this process is calculated using the thermodynamic integration technique: ð1 Ddp AAH ¼ dZ Ddp EAH rZ (1) 0
where DdpE stands for the vertical energy gap (defined as the difference of potential energies of the reactant state and the product state). The averages of vertical energy gaps (DdpE) are derived from the FPMD trajectories generated by sampling the auxiliary Hamiltonian: HZ = (1 Z)HR + ZHP + Vr
(2)
where HR and HP stand for the reactant and product states, respectively. Z is a coupling parameter, which is increased from 0 (reactant) to 1 (product). The restrained harmonic potential (Vr) is used to keep the dummy in a location, which resembles that of the acid proton of the reactant state: X1 X1 kd ðd d0 Þ2 þ ka ða a0 Þ2 Vr ¼ (3) 2 2 bonds angles Fig. 1 The snapshots of (A) (101% 0)-alpha, (B) (101% 0)-beta and (C) (101% 1) surfaces of quartz. O = red, H = white, and Si = yellow.
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This potential consists of the bonding and angle bending terms whose equilibrium values are d0 and a0 respectively.
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Table 1 The parameters used in the harmonic potentials (eqn (3)) restraining the dummy protons for the surface sites. Hd means the dummy proton. See Fig. 4 for Si(OH)A and Si(OH)D. Equilibrium bond lengths (d0) are in Bohr and equilibrium angles (a0) and torsions (w0) are in radians. All the coupling constants are in a.u.
Acids
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(101% 0) Alpha Si(OH2)(OH)
Beta
(101% 1)
nd d0
kd
na a0
2
1.89 1.89 1.89 1.89 1.89 1.89 1.89 1.89
0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1
2
1.90 1.90 1.89 1.90 1.90 1.89 1.89
0.1 0.1 0.1 0.1 0.1 0.1 1.0
Si(OH)(OH) Si(O)(OH) Si(OH)A Si(OH2)A
1 1 1 2
Si(OH)D
1
Si–(OH2)Inner
2
Si–(OH)Inner 1 Si–(OH2)Outer 2 Si–(OH)Outer H 3 O+
1 3
1 1 1 2 1 2 1 2 1 2
ka
1.92 2.09 2.01 2.01 1.99 1.92 2.09 1.99
(H–O–Hd) (Si–O–Hd) (Si–O–Hd) (Si–O–Hd) (Si–O–Hd) (H–O–Hd) (Si–O–Hd) (Si–O–Hd)
0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1
1.90 2.01 1.99 1.90 2.01 2.13 1.94 1.94
(H–O–Hd) (Si–O–Hd) (Si–O–Hd) (H–O–Hd) (Si–O–Hd) (Si–O–Hd) (H–O–Hd) (H–O–Hd)
0.1 0.1 0.1 0.1 0.1 0.1 0.1
The equilibrium values used for each surface group are obtained from the prior simulations without restraints and the restraining parameters have been selected according to the prescriptions of our previous studies.34,35 Details of Vr are collected in Table 1. For the pKa calculation of the SiOHD site on the (101% 0)-beta surface (see Fig. 4), in the simulation of the deprotonated state (i.e. SiOD–), the dangling O can capture one proton from a neighboring SiOH within 0.5 ps. To prevent this from happening, the O–H bonds of neighboring silanols are restrained with harmonic potentials. For the pKa calculation of the Si(OH)(O–) site on the (101% 0)-alpha surface, in the simulation of the deprotonated state (i.e. Si(O–)2), the solvating water molecules may donate a proton to one dangling O due to the high pKa value of Si(OH)(O–). To avoid this proton transfer, all O–H bonds of water molecules are also restrained with harmonic potentials in the simulation. With the same procedure used for the deprotonation of the surface acidic site, one proton of a hydronium ion located in
the solution region of the simulation box is transformed into a dummy and the free energy of the transformation is denoted ð1 D E þ Ddp AH3 O ¼ dZ Ddp EH3 Oþ (4) rZ
0
The 3-point Simpson rule is applied to calculate the integral in eqn (1) and (4), which requires the simulations at Z = 0, 0.5 and 1: Ddp A ¼
2 1 hDEi0 þ hDEi1 þ hDEi0:5 6 3
The final pKa calculation formula reads: ð1 ð1 D E 2:30kB T pKa ¼ dZ Ddp EAH rZ dZ Ddp EH3 Oþ 0
þ kB T ln c0 LHþ 3
0
(5)
rZ
(6)
c0 = 1 mol L1 is the unit molar concentration and LH+ means the thermal wavelength of the proton. The kBT ln[c0LH+3] term accounts for the translational entropy generated from the acid dissociation and it is approximated by the chemical potential of a free proton at standard concentration. This term is equal to 0.19 eV or equivalently 3.2 pKa units.
3. Results 3.1.
(101% 0) surface-alpha
On this surface, all SiOH groups are germinal silanols (i.e. Q2). The two OHs on the Si atom are equivalent. As shown in Fig. 2A, the RDF peak of the H-bond between silanol H and water O is centered at around 1.7 Å (Fig. 3), which amounts to about 0.75 on the running CN curve. The oxygen of silanols also accepts H-bonds from solvating water molecules, which shows a peak at around 1.9 Å on the RDF plot (Fig. 2B and marked in Fig. 3). The calculated pKa of Si(OH2)(OH) is 4.3 (i.e. for reaction Si(OH2)(OH) - Si(OH)(OH) + H+) (Table 2), indicating that an additional proton hardly stays on this site. The 1st and 2nd pKas of Si(OH)(OH) are 8.5 and 13.6 respectively (i.e. for
Fig. 2 RDFs (radial distribution functions) and running CNs (coordination numbers) for (A) water O around H of Si–OH and (B) water H around O of Si– OH on the (101% 0)-alpha surface.
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Fig. 3 The snapshot of the (101% 0)-alpha surface. O = red, H = white, and Si = yellow.
receive H-bonds from solvating water molecules (Fig. 4 and 5A). Fig. 5B shows that SiOHA accepts approximately one H-bond from solvating water molecules. Therefore, more possibly, the SiOHA silanols can get a second proton from solutions than SiOHD. On this facet, the donor and acceptor silanols have pKas of 4.8 and 11.0, respectively (Table 3), indicating that the donor SiOH is significantly more acidic than the acceptor silanol. A similar pattern was also found for the silanols on the quartz(0001) facet in the report of Sulpizi et al.,40 where 5.6 and 8.5 were obtained for the donor and acceptor silanols respectively. This also indicates that O of SiOHA has higher basicity, which supports our deduction above that it is more possible that SiOHA gets a second proton than SiOHD. As shown in Table 3, Si(OH2)A has a pKa of 7.2, implying that the doubly protonated forms of donor and acceptor silanols are not stable under normal pH conditions (because the pKa of Si(OH2)D should be lower than 7.2). 3.3.
(101% 1) surface
It can be seen in Fig. 6A that SiOHOuter donates 1 H-bonds on average to solvating water molecules whereas SiOHInner donates only 0.5 H-bonds. Fig. 6B shows that SiOHOuter oxygen accepts approximately 1.8 H-bonds from water but SiOHInner oxygen has 0.5 H-bonds only. These findings imply that it is more possible that SiOHOuter forms H-bonds with solvating water molecules, which is consistent with the study of Skelton et al.31 The pKas of SiOHOuter and SiOHInner are 9.3 and 12.2, respectively (Table 4), implying that SiOHOuter can deprotonate but SiOHInner hardly deprotonates in the normal pH range. The protonated forms of both kinds of silanols show pKas of around 2.7. Fig. 4 The snapshot of the (101% 0)-beta surface. O = red, H = white, and Si = yellow.
Table 2 Calculated deprotonation free energies DA (see the left side of eqn (1) and (4)) and pKa values of surface groups of the quartz (101% 0)-alpha surface
Sites
Z = 1.0
Z = 0.5
Z=0
DdpA/eV
pKas
Si(OH2)(OH) Si(OH)(OH) Si(OH)(O–) H3O+
15.23 15.98 16.6 14.98
18.23 18.98 19.18 18.3
20.25 21.1 21.32 20.56
18.07 18.83 19.11 18.12
4.3 8.5 13.6 —
Si(OH)(OH) - Si(O–)(OH) + H+ and Si(O–)(OH) - Si(O–)2 + H+, respectively). This implies that Si(OH)(OH) and Si(OH)(O–) are the most possible surface groups in common solutions whereas Si(O–)2 rarely happens. 3.2.
(101% 0) surface-beta
During the simulation period of this surface, it is found that some SiOHs (marked SiOHD in Fig. 4) always donate H-bonds to solvating water molecules and at the same time they receive H-bonds from other silanols (marked SiOHA in Fig. 4), which
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4. Discussion The derived pKas of quartz surfaces are collected in Table 5. The theoretical PZC (point of zero charge) of one individual surface can be estimated from the calculated pKas. For example, the PZC of (101% 0)-alpha is 2.2, which is determined by Si(OH2)(OH) and Si(OH)(OH). As shown in Table 5, Alpha, Beta and (101% 1) facets have the PZCs of 2.2, 1.2 and 3.3 respectively. Therefore, the theoretical overall PZC of quartz should be within 1.2 and 3.3, which is generally consistent with the experimental range, 0.5–3.5.8 According to the acidity constants, the SiOH groups can be divided into 3 groups: 4.8 (Si(OH)D on Beta), 8.5–9.3 (Si(OH)(OH) on Alpha and Si(OH)Outer on (101% 1)) and 11.0–12.2 (Si(OH)A on Beta and Si(OH)Inner on (101% 1)). The three groups are well separated and therefore may be distinguished on experiments. Interestingly, the pKas of donor (5.6) and acceptor (8.5) silanols on the quartz(0001) facet calculated in the previous study,40 can be assigned to the first two groups, respectively. However, it is difficult to make a comparison with the fitted pKas (e.g. ref. 9). The procedures such as the 1-pK and 2-pK approaches give pKas of presumed sites through fitting the titration curve. The presence of so many different sites on real samples make the fitting based on a
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Fig. 5 RDFs (radial distribution functions) and running CNs (coordination numbers) for (A) water O around H of Si–OHD and (B) water H around O of Si– OHA on the (101% 0)-beta surface.
Table 3 Calculated deprotonation free energies DA (eV) and pKa values of surface groups of the quartz (101% 0)-beta surface
Sites
Z = 1.0
Z = 0.5
Z=0
DdpA/eV
pKas
Si(OH2)A Si(OH)D Si(OH)A H3O+
16.0 15.94 15.07 15.58
18.27 19.04 19.82 18.64
20.37 21.50 21.43 20.77
18.24 18.93 19.30 18.46
7.2 4.8 11.0 —
limited number of sites hard to reveal the real site-specific pKas. Furthermore, the lack of titration data at the low-pH end limits the exploration of the surface sites of very low pKas. As shown in Table 5, all doubly-protonated silanols have pKas below 0, but the commonly used pH range for titration is 3–9, which makes the fitting approach lack a basis. The experimental difficulty is the inevitable dissolution at low pH. Our results show that Si(OH)D on the natural Beta termination has the low pKa of 4.8 and all the others have pKas higher than 7.0. Leung et al.45 found that only the artificially strained defect sites on b-cristobalite(100) have low pKas within 3.8–5.1, whereas all the other silanols (including isolated, H-bonded, Q2 and Q3 sites) present pKas ranging from 7.0 to 8.9. These
Fig. 6
Fig. 7 The snapshot of the (101% 1) surface. O = red, H = white, and Si = yellow.
computational findings coincide with the conclusion of Ong,46 which identifies two types of Si–OH groups on fused silica surfaces: only 19% of silanols with pKa = 4.5 and 81% of silanols with pKa = 8.5. The derived atomic scale structure and acidity data can be used to understand the interfacial processes of quartz.54 The first two groups of silanols discussed above can dissociate in
RDFs and running CNs for (A) water O around H of Si–OH and (B) water H around O of Si–OH on the (101% 1) surface.
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Table 4 Calculated deprotonation free energies DA (eV) and pKa values of surface groups of the quartz(101% 1) surface
Sites
Z = 1.0
Z = 0.5
Z=0
DdpA/eV
pKas
Si(OH2)Inner Si(OH2)Outer Si(OH)Inner Si(OH)Outer H3O+
16.61 16.06 16.38 16.08 15.90
18.92 19.04 20.01 19.88 18.93
20.72 21.0 21.98 21.75 21.32
18.84 18.87 19.73 19.56 18.82
2.8 2.7 12.2 9.3 —
Table 5 pKas of surface sites and point of zero charge (PZCs) of individual surfaces of quartz
Surfaces (101% 0)
Alpha Beta
(101% 1)
Sites
pKas
PZC
Si(OH2)(OH) Si(OH)(OH) Si(OH)(O–) Si(OH2)A Si(OH)D Si(OH)A
4.0 8.5 13.6 7.2 4.8 11.0
2.2
Si(OH2)Inner Si(OH2)Outer Si(OH)Inner Si(OH)Outer
2.8 2.7 12.2 9.3
1.2
3.3
the common pH range, but the last does not due to their relatively high pKa. Therefore, the silanols in the first two groups are available for complexing metal cations. As pH increases, the silanols on the (101% 0)-beta surface first dissociate, and then the germinal silanols on the (101% 0)-alpha surface and the silanol on (101% 1) facets. On the Beta facet, the nearest two silanols are 2.6 Å apart, so the foreign metal cations can form binuclear bidentate complexes. On Alpha termination, the second pKa is 13.6 and therefore, it hardly gets deprotonated, so the foreign cations may prefer to form monodentate complexes but cannot form bidentate ones (i.e. mononuclear). The distance between the two nearest silanols is around 3.8 Å, so the binuclear complexes could form on two neighboring silanol sites. On the (101% 1) surface, the Inner silanol sites are not available for complexing cations due to the high pKa and therefore, complexes can only form on Outer silanol sites.
5. Summary The FPMD simulation technique is applied to investigate the acid chemistry of the two growth surfaces of quartz (two (101% 0)type terminations and the (101% 1) facet). The microscopic interfacial structures are characterized. The intrinsic pKas of surface silanols are derived by using the FPMD based vertical energy gap method. The results indicate that all doubly-protonated forms (i.e. SiOH2) have very low pKas (o2.5), implying that the silanols hardly get protonated under common pH. It is found that the silanols can be subdivided into 3 groups with respect to the intrinsic pKas. The donor SiOHs on the (101% 0)-beta surface is the most acidic silanol (pKa = 4.8). The Si(OH)2 groups (i.e. germinal silanol) on the (101% 0)-alpha surface and the Outer silanols on (101% 1) show similar pKas ranging from 8.5 to 9.3.
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Inner silanols on the (101% 1) facet, acceptor silanols on the (101% 0)-beta surface, the Si(OH)(O–) groups (i.e. the second OH of the germinal silanol) on the (101% 0)-alpha surface are the least acidic groups, which have pKas higher than 11.0 and therefore remain inert in the common pH range. Overall, this study shows that quartz has a complicated surface acid chemistry due to the multiple facets. The calculated acidity values can be applied to understand interfacial processes of quartz and related silica phases.
Acknowledgements We acknowledge the National Science Foundation of China (No. 41002013, 40973029, 41273074 and 41222015), the Foundation for the Author of National Excellent Doctoral Dissertation of PR China (No. 201228), Newton International Fellow Program, the Natural Science Foundation of the Jiangsu Province (BK2010008) and the financial support from the State Key Laboratory for Mineral Deposits Research. We are grateful to the High Performance Computing Center of Nanjing University for providing us the IBM Blade cluster system.
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Surface acidity of quartz: understanding the crystallographic control Xiandong Liu,*a Jun Cheng,b Xiancai Lua and Rucheng Wanga We report a first principles molecular dynamics (FPMD) study of surface acid chemistry of the two growth surfaces of quartz, (101% 0) (including Alpha and Beta terminations) and (101% 1) facets. The interfacial hydration structures are characterized in detail and the intrinsic pKas of surface silanols are evaluated using the FPMD based vertical energy gap method. The calculated acidity constants reveal that every surface termination shows a bimodal acid–base behavior. It is found that all doubly-protonated forms (i.e. SiOH2) on the three terminations have pKas lower than 2.5, implying that the silanols hardly get protonated in a
Received 6th July 2014, Accepted 24th October 2014
common pH range. The pKas of surface silanols can be divided into 3 groups. The most acidic silanol is the donor SiOH on the (101% 0)-beta surface (pKa = 4.8), the medium includes the germinal silanol on (101% 0)-alpha and the outer silanol on (101% 1) (pKa = 8.5–9.3) and the least acidic are inner silanols on the
DOI: 10.1039/c4cp02955k
(101% 1)-facet, acceptor SiOH on (101% 0)-beta, and the secondly-deprotonated OH (i.e. Si(O–)(OH)) on (101% 0)-alpha (pKa 4 11.0). With the pKa values, we discuss the implication for understanding metal cations
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complexing on quartz surfaces.
1. Introduction Quartz is one of the most abundant minerals in the Earth’s crust.1 Due to the ubiquitous distribution on the Earth’s surface, quartz plays important roles in interfacial processes in nature, e.g.2–4 The interfacial chemistry of quartz is also of great interest in biology,5 and technology.6,7 Based on the connectivity to the rest of the quartz crystal, the surface silanols can be grouped into Q1, Q2 and Q3 sites (Qn means that it has nSi–O bonds to the bulk and 4-nOH bonds to the solution). These silanol groups are amphoteric, which makes the quartz surface show pH-dependent behaviors, and therefore, the interfacial properties of quartz are strongly dependent on the environmental pH. Numerous titration experiments have been carried out for quartz and other silica phases. The pHiep (isoelectric point) value of quartz is found to be within 0.5–3.5.8 The fitted acidity constants for quartz in the literature are pKa1 = 1.2 and pKa2 = 7.2.9 Experiments show that several types of facets can coexist for quartz, for example, (101% 0), (101% 1) and (0001).10 But up to now, the crystallographic control on surface acidity of silanols remains unclear. Aiming at the understanding of chemical weathering of quartz, dissolution experiments have been extensively carried out, e.g. ref. 11–13 and references therein. The interpretation of a
State Key Laboratory for Mineral Deposits Research, School of Earth Sciences and Engineering, Nanjing University, Nanjing 210093, P. R. China. E-mail: [email protected]; Fax: +86 25 83686016; Tel: +86 25 83594664 b Department of Chemistry, University of Aberdeen, Aberdeen, AB24 3UE, UK
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these experiments must rely on the detailed knowledge of interfacial properties, such as the identity, density, and deprotonation free energies of reactive sites.14–16 The applications of advanced spectroscopic techniques and atomistic simulations have significantly promoted the exploration of molecular-level interfacial properties of quartz. Schlegel et al.10 derived the atomic-scale structures of (101% 0) and (101% 1) facets with X-ray reflectivity and atomic force microscopy. By using the phasesensitive surface spectroscopy, Ostroverkhov et al.17 obtained the microscopic interfacial structure of the quartz(0001) facet and found that there are two types of silanols on this surface. Static quantum mechanical modeling has been applied to investigate surface relaxation and hydrolysis of silica for decades.18–26 Classical and first principles molecular dynamics (FPMD) techniques have also been employed to study the interfaces between silica and water.27–33 By using both classical and FPMD simulations, Skelton et al.31,32 revealed the microscopic interfacial structures of (101% 1) and (101% 0) facets, which provided fundamental models for future research. According to their analyses, (101% 0) surfaces have two different terminations and several types of silanols have been identified. By combining FPMD and free-energy perturbation theory, the Sprik group developed a vertical energy gap technique for pKa calculation,34,35 which has been successfully applied on molecular systems34–38 and solid surfaces.39–44 Systematic tests on molecules of over 20 pKa units show that most acidities can be reproduced within 2 pKa units. Using this method, Sulpizi et al.40 obtained pKas 4.5 and 8.5 for the two kinds of silanols of the quartz(0001) surface. By using a FPMD based potential of
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the mean force calculation technique, Leung et al.45 investigated 6 facets of silica, including the beta-cristobalite(100) surface, the hydroxylated beta-cristobalite(100) surface with one SiOH replaced with SiH to break the chain of H-bonds, two reconstructed betacristobalite(100) surfaces, (H3SiO)3SiOH clusters, a reconstructed quartz(0001) surface containing a cyclic silica trimer (Si–O)3, and they showed a bimodal acid–base behavior of the silica surface, which is consistent with that proposed by Ong et al.46 They found that only the strained silica surface represents the low pKa value of about 4.5 and all the others are higher than 7.0. To form a complete view of the acid chemistry of quartz, the intrinsic acidity constants of all possible surfaces are needed. To our knowledge, the surface acidity of the two growth surfaces ((101% 1) and (101% 0)) has not been quantified. In this study, we employ FPMD simulations to evaluate the pKas of the silanol groups on those two facets. From the simulations, the interfacial structures are characterized in detail and with the derived acidity values, the crystallographic control on the pKa has been discussed.
2. Methodology 2.1.
Models
The crystal parameters of the used alpha-quartz model are a = 4.9137 Å, b = 4.9137 Å, c = 5.4047 Å and a = g = 901, b = 1201.47 The surface structures were cut from the bulk crystal and all dangling Si–O bonds were saturated by H. The (101% 0) surface has two possible terminations denoted Alpha and Beta (Fig. 1A and B). The Alpha termination contains only Q2 Si and therefore the
silanols are germinal (Fig. 1A). The Beta termination contains Q3 Si, and the silanols are vicinal (Fig. 1B). On the (101% 1) surface, two types of silanols are identified, which are marked SiOHInner and SiOHOuter (the definitions are based on the relative positions of Si atoms) (see Fig. 1C and 7). The models were placed in 3D periodically repeated cells, which have a solution space of about 12 Å in the direction vertical to surfaces (see Fig. 1). The two solution regions of (101% 0) and (101% 1) boxes contain 42 and 54 water molecules, respectively, which approximately reproduce the density of bulk water under ambient conditions. 2.2.
First principles MD
The CP2K/QUICKSTEP package48 was used to carry out the FPMD simulations. In this package, the electronic structures were calculated with a hybrid Gaussian plane wave (GPW) implementation of density functional theory.42 BLYP functional49,50 and Goedecker–Teter–Hutter pseudopotentials51 were used. The cutoff of the plane wave basis for the electron density was set to be 280 Ry. All H atoms in the systems were assigned a mass of 1.008 u. Bohn-Oppenheimer type FPMD simulations were performed with a wave function optimization tolerance of 1.0 106 and a time step of 0.5 fs. To avoid the glassy behaviour of BLYP water,52 ´–Hoover the temperature was controlled at 330 K using the Nose chain thermostat. For each simulation, an equilibration step was for at least 2.0 ps and a production run was for 8.0–10.0 ps. 2.3.
pKa calculation
The half-reaction scheme of the FPMD based vertical energy gap method was applied to evaluate pKas of surface silanol groups.35,53 Using this scheme, the proton of the acid marked AH is gradually transformed into a dummy (i.e. a classical particle with no charge). The free energy change (DdpAAH) of this process is calculated using the thermodynamic integration technique: ð1 Ddp AAH ¼ dZ Ddp EAH rZ (1) 0
where DdpE stands for the vertical energy gap (defined as the difference of potential energies of the reactant state and the product state). The averages of vertical energy gaps (DdpE) are derived from the FPMD trajectories generated by sampling the auxiliary Hamiltonian: HZ = (1 Z)HR + ZHP + Vr
(2)
where HR and HP stand for the reactant and product states, respectively. Z is a coupling parameter, which is increased from 0 (reactant) to 1 (product). The restrained harmonic potential (Vr) is used to keep the dummy in a location, which resembles that of the acid proton of the reactant state: X1 X1 kd ðd d0 Þ2 þ ka ða a0 Þ2 Vr ¼ (3) 2 2 bonds angles Fig. 1 The snapshots of (A) (101% 0)-alpha, (B) (101% 0)-beta and (C) (101% 1) surfaces of quartz. O = red, H = white, and Si = yellow.
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This potential consists of the bonding and angle bending terms whose equilibrium values are d0 and a0 respectively.
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Table 1 The parameters used in the harmonic potentials (eqn (3)) restraining the dummy protons for the surface sites. Hd means the dummy proton. See Fig. 4 for Si(OH)A and Si(OH)D. Equilibrium bond lengths (d0) are in Bohr and equilibrium angles (a0) and torsions (w0) are in radians. All the coupling constants are in a.u.
Acids
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(101% 0) Alpha Si(OH2)(OH)
Beta
(101% 1)
nd d0
kd
na a0
2
1.89 1.89 1.89 1.89 1.89 1.89 1.89 1.89
0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1
2
1.90 1.90 1.89 1.90 1.90 1.89 1.89
0.1 0.1 0.1 0.1 0.1 0.1 1.0
Si(OH)(OH) Si(O)(OH) Si(OH)A Si(OH2)A
1 1 1 2
Si(OH)D
1
Si–(OH2)Inner
2
Si–(OH)Inner 1 Si–(OH2)Outer 2 Si–(OH)Outer H 3 O+
1 3
1 1 1 2 1 2 1 2 1 2
ka
1.92 2.09 2.01 2.01 1.99 1.92 2.09 1.99
(H–O–Hd) (Si–O–Hd) (Si–O–Hd) (Si–O–Hd) (Si–O–Hd) (H–O–Hd) (Si–O–Hd) (Si–O–Hd)
0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1
1.90 2.01 1.99 1.90 2.01 2.13 1.94 1.94
(H–O–Hd) (Si–O–Hd) (Si–O–Hd) (H–O–Hd) (Si–O–Hd) (Si–O–Hd) (H–O–Hd) (H–O–Hd)
0.1 0.1 0.1 0.1 0.1 0.1 0.1
The equilibrium values used for each surface group are obtained from the prior simulations without restraints and the restraining parameters have been selected according to the prescriptions of our previous studies.34,35 Details of Vr are collected in Table 1. For the pKa calculation of the SiOHD site on the (101% 0)-beta surface (see Fig. 4), in the simulation of the deprotonated state (i.e. SiOD–), the dangling O can capture one proton from a neighboring SiOH within 0.5 ps. To prevent this from happening, the O–H bonds of neighboring silanols are restrained with harmonic potentials. For the pKa calculation of the Si(OH)(O–) site on the (101% 0)-alpha surface, in the simulation of the deprotonated state (i.e. Si(O–)2), the solvating water molecules may donate a proton to one dangling O due to the high pKa value of Si(OH)(O–). To avoid this proton transfer, all O–H bonds of water molecules are also restrained with harmonic potentials in the simulation. With the same procedure used for the deprotonation of the surface acidic site, one proton of a hydronium ion located in
the solution region of the simulation box is transformed into a dummy and the free energy of the transformation is denoted ð1 D E þ Ddp AH3 O ¼ dZ Ddp EH3 Oþ (4) rZ
0
The 3-point Simpson rule is applied to calculate the integral in eqn (1) and (4), which requires the simulations at Z = 0, 0.5 and 1: Ddp A ¼
2 1 hDEi0 þ hDEi1 þ hDEi0:5 6 3
The final pKa calculation formula reads: ð1 ð1 D E 2:30kB T pKa ¼ dZ Ddp EAH rZ dZ Ddp EH3 Oþ 0
þ kB T ln c0 LHþ 3
0
(5)
rZ
(6)
c0 = 1 mol L1 is the unit molar concentration and LH+ means the thermal wavelength of the proton. The kBT ln[c0LH+3] term accounts for the translational entropy generated from the acid dissociation and it is approximated by the chemical potential of a free proton at standard concentration. This term is equal to 0.19 eV or equivalently 3.2 pKa units.
3. Results 3.1.
(101% 0) surface-alpha
On this surface, all SiOH groups are germinal silanols (i.e. Q2). The two OHs on the Si atom are equivalent. As shown in Fig. 2A, the RDF peak of the H-bond between silanol H and water O is centered at around 1.7 Å (Fig. 3), which amounts to about 0.75 on the running CN curve. The oxygen of silanols also accepts H-bonds from solvating water molecules, which shows a peak at around 1.9 Å on the RDF plot (Fig. 2B and marked in Fig. 3). The calculated pKa of Si(OH2)(OH) is 4.3 (i.e. for reaction Si(OH2)(OH) - Si(OH)(OH) + H+) (Table 2), indicating that an additional proton hardly stays on this site. The 1st and 2nd pKas of Si(OH)(OH) are 8.5 and 13.6 respectively (i.e. for
Fig. 2 RDFs (radial distribution functions) and running CNs (coordination numbers) for (A) water O around H of Si–OH and (B) water H around O of Si– OH on the (101% 0)-alpha surface.
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Fig. 3 The snapshot of the (101% 0)-alpha surface. O = red, H = white, and Si = yellow.
receive H-bonds from solvating water molecules (Fig. 4 and 5A). Fig. 5B shows that SiOHA accepts approximately one H-bond from solvating water molecules. Therefore, more possibly, the SiOHA silanols can get a second proton from solutions than SiOHD. On this facet, the donor and acceptor silanols have pKas of 4.8 and 11.0, respectively (Table 3), indicating that the donor SiOH is significantly more acidic than the acceptor silanol. A similar pattern was also found for the silanols on the quartz(0001) facet in the report of Sulpizi et al.,40 where 5.6 and 8.5 were obtained for the donor and acceptor silanols respectively. This also indicates that O of SiOHA has higher basicity, which supports our deduction above that it is more possible that SiOHA gets a second proton than SiOHD. As shown in Table 3, Si(OH2)A has a pKa of 7.2, implying that the doubly protonated forms of donor and acceptor silanols are not stable under normal pH conditions (because the pKa of Si(OH2)D should be lower than 7.2). 3.3.
(101% 1) surface
It can be seen in Fig. 6A that SiOHOuter donates 1 H-bonds on average to solvating water molecules whereas SiOHInner donates only 0.5 H-bonds. Fig. 6B shows that SiOHOuter oxygen accepts approximately 1.8 H-bonds from water but SiOHInner oxygen has 0.5 H-bonds only. These findings imply that it is more possible that SiOHOuter forms H-bonds with solvating water molecules, which is consistent with the study of Skelton et al.31 The pKas of SiOHOuter and SiOHInner are 9.3 and 12.2, respectively (Table 4), implying that SiOHOuter can deprotonate but SiOHInner hardly deprotonates in the normal pH range. The protonated forms of both kinds of silanols show pKas of around 2.7. Fig. 4 The snapshot of the (101% 0)-beta surface. O = red, H = white, and Si = yellow.
Table 2 Calculated deprotonation free energies DA (see the left side of eqn (1) and (4)) and pKa values of surface groups of the quartz (101% 0)-alpha surface
Sites
Z = 1.0
Z = 0.5
Z=0
DdpA/eV
pKas
Si(OH2)(OH) Si(OH)(OH) Si(OH)(O–) H3O+
15.23 15.98 16.6 14.98
18.23 18.98 19.18 18.3
20.25 21.1 21.32 20.56
18.07 18.83 19.11 18.12
4.3 8.5 13.6 —
Si(OH)(OH) - Si(O–)(OH) + H+ and Si(O–)(OH) - Si(O–)2 + H+, respectively). This implies that Si(OH)(OH) and Si(OH)(O–) are the most possible surface groups in common solutions whereas Si(O–)2 rarely happens. 3.2.
(101% 0) surface-beta
During the simulation period of this surface, it is found that some SiOHs (marked SiOHD in Fig. 4) always donate H-bonds to solvating water molecules and at the same time they receive H-bonds from other silanols (marked SiOHA in Fig. 4), which
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4. Discussion The derived pKas of quartz surfaces are collected in Table 5. The theoretical PZC (point of zero charge) of one individual surface can be estimated from the calculated pKas. For example, the PZC of (101% 0)-alpha is 2.2, which is determined by Si(OH2)(OH) and Si(OH)(OH). As shown in Table 5, Alpha, Beta and (101% 1) facets have the PZCs of 2.2, 1.2 and 3.3 respectively. Therefore, the theoretical overall PZC of quartz should be within 1.2 and 3.3, which is generally consistent with the experimental range, 0.5–3.5.8 According to the acidity constants, the SiOH groups can be divided into 3 groups: 4.8 (Si(OH)D on Beta), 8.5–9.3 (Si(OH)(OH) on Alpha and Si(OH)Outer on (101% 1)) and 11.0–12.2 (Si(OH)A on Beta and Si(OH)Inner on (101% 1)). The three groups are well separated and therefore may be distinguished on experiments. Interestingly, the pKas of donor (5.6) and acceptor (8.5) silanols on the quartz(0001) facet calculated in the previous study,40 can be assigned to the first two groups, respectively. However, it is difficult to make a comparison with the fitted pKas (e.g. ref. 9). The procedures such as the 1-pK and 2-pK approaches give pKas of presumed sites through fitting the titration curve. The presence of so many different sites on real samples make the fitting based on a
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Fig. 5 RDFs (radial distribution functions) and running CNs (coordination numbers) for (A) water O around H of Si–OHD and (B) water H around O of Si– OHA on the (101% 0)-beta surface.
Table 3 Calculated deprotonation free energies DA (eV) and pKa values of surface groups of the quartz (101% 0)-beta surface
Sites
Z = 1.0
Z = 0.5
Z=0
DdpA/eV
pKas
Si(OH2)A Si(OH)D Si(OH)A H3O+
16.0 15.94 15.07 15.58
18.27 19.04 19.82 18.64
20.37 21.50 21.43 20.77
18.24 18.93 19.30 18.46
7.2 4.8 11.0 —
limited number of sites hard to reveal the real site-specific pKas. Furthermore, the lack of titration data at the low-pH end limits the exploration of the surface sites of very low pKas. As shown in Table 5, all doubly-protonated silanols have pKas below 0, but the commonly used pH range for titration is 3–9, which makes the fitting approach lack a basis. The experimental difficulty is the inevitable dissolution at low pH. Our results show that Si(OH)D on the natural Beta termination has the low pKa of 4.8 and all the others have pKas higher than 7.0. Leung et al.45 found that only the artificially strained defect sites on b-cristobalite(100) have low pKas within 3.8–5.1, whereas all the other silanols (including isolated, H-bonded, Q2 and Q3 sites) present pKas ranging from 7.0 to 8.9. These
Fig. 6
Fig. 7 The snapshot of the (101% 1) surface. O = red, H = white, and Si = yellow.
computational findings coincide with the conclusion of Ong,46 which identifies two types of Si–OH groups on fused silica surfaces: only 19% of silanols with pKa = 4.5 and 81% of silanols with pKa = 8.5. The derived atomic scale structure and acidity data can be used to understand the interfacial processes of quartz.54 The first two groups of silanols discussed above can dissociate in
RDFs and running CNs for (A) water O around H of Si–OH and (B) water H around O of Si–OH on the (101% 1) surface.
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Table 4 Calculated deprotonation free energies DA (eV) and pKa values of surface groups of the quartz(101% 1) surface
Sites
Z = 1.0
Z = 0.5
Z=0
DdpA/eV
pKas
Si(OH2)Inner Si(OH2)Outer Si(OH)Inner Si(OH)Outer H3O+
16.61 16.06 16.38 16.08 15.90
18.92 19.04 20.01 19.88 18.93
20.72 21.0 21.98 21.75 21.32
18.84 18.87 19.73 19.56 18.82
2.8 2.7 12.2 9.3 —
Table 5 pKas of surface sites and point of zero charge (PZCs) of individual surfaces of quartz
Surfaces (101% 0)
Alpha Beta
(101% 1)
Sites
pKas
PZC
Si(OH2)(OH) Si(OH)(OH) Si(OH)(O–) Si(OH2)A Si(OH)D Si(OH)A
4.0 8.5 13.6 7.2 4.8 11.0
2.2
Si(OH2)Inner Si(OH2)Outer Si(OH)Inner Si(OH)Outer
2.8 2.7 12.2 9.3
1.2
3.3
the common pH range, but the last does not due to their relatively high pKa. Therefore, the silanols in the first two groups are available for complexing metal cations. As pH increases, the silanols on the (101% 0)-beta surface first dissociate, and then the germinal silanols on the (101% 0)-alpha surface and the silanol on (101% 1) facets. On the Beta facet, the nearest two silanols are 2.6 Å apart, so the foreign metal cations can form binuclear bidentate complexes. On Alpha termination, the second pKa is 13.6 and therefore, it hardly gets deprotonated, so the foreign cations may prefer to form monodentate complexes but cannot form bidentate ones (i.e. mononuclear). The distance between the two nearest silanols is around 3.8 Å, so the binuclear complexes could form on two neighboring silanol sites. On the (101% 1) surface, the Inner silanol sites are not available for complexing cations due to the high pKa and therefore, complexes can only form on Outer silanol sites.
5. Summary The FPMD simulation technique is applied to investigate the acid chemistry of the two growth surfaces of quartz (two (101% 0)type terminations and the (101% 1) facet). The microscopic interfacial structures are characterized. The intrinsic pKas of surface silanols are derived by using the FPMD based vertical energy gap method. The results indicate that all doubly-protonated forms (i.e. SiOH2) have very low pKas (o2.5), implying that the silanols hardly get protonated under common pH. It is found that the silanols can be subdivided into 3 groups with respect to the intrinsic pKas. The donor SiOHs on the (101% 0)-beta surface is the most acidic silanol (pKa = 4.8). The Si(OH)2 groups (i.e. germinal silanol) on the (101% 0)-alpha surface and the Outer silanols on (101% 1) show similar pKas ranging from 8.5 to 9.3.
26914 | Phys. Chem. Chem. Phys., 2014, 16, 26909--26916
Inner silanols on the (101% 1) facet, acceptor silanols on the (101% 0)-beta surface, the Si(OH)(O–) groups (i.e. the second OH of the germinal silanol) on the (101% 0)-alpha surface are the least acidic groups, which have pKas higher than 11.0 and therefore remain inert in the common pH range. Overall, this study shows that quartz has a complicated surface acid chemistry due to the multiple facets. The calculated acidity values can be applied to understand interfacial processes of quartz and related silica phases.
Acknowledgements We acknowledge the National Science Foundation of China (No. 41002013, 40973029, 41273074 and 41222015), the Foundation for the Author of National Excellent Doctoral Dissertation of PR China (No. 201228), Newton International Fellow Program, the Natural Science Foundation of the Jiangsu Province (BK2010008) and the financial support from the State Key Laboratory for Mineral Deposits Research. We are grateful to the High Performance Computing Center of Nanjing University for providing us the IBM Blade cluster system.
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