Water Interface - The Journal

Article pubs.acs.org/JPCC

Bimodal Acidity at the Amorphous Silica/Water Interface Morgane Pfeiffer-Laplaud,† Dominique Costa,‡ Frederik Tielens,§ Marie-Pierre Gaigeot,†,⊥ and Marialore Sulpizi*,# †

LAMBE CNRS UMR8587, Université d’Evry val d’Essonne, Blvd F. Mitterrand, Bât Maupertuis, 91025 Evry, France Chimie Paristech CNRS, UMR8247, Institut de Recherches de Chimie de Paris, 11 rue P et M Curie, 75005 Paris, France § Sorbonne Universités, UPMC Univ Paris 06, CNRS, Collège de France, Laboratoire de Chimie de la Matière Condensé de Paris, 11 place Marcelin Berthelot, 75005 Paris, France ⊥ Institut Universitaire de France, 103 Blvd St Michel, 75005 Paris, France # Department of Physics, Johannes Gutenberg Universitat, Staudingerweg 7, 55099 Mainz, Germany ‡

ABSTRACT: Understanding the microscopic origin of the acid−base behavior of mineral surfaces in contact with water is still a challenging task, for both the experimental and the theoretical communities. Even for a relatively simple material, such as silica, the origin of the bimodal acidity behavior is still a debated topic. In this contribution we calculate the acidity of single sites on the humid silica surface represented by a model for the hydroxylated amorphous surface. Using a thermodynamic integration approach based on ab initio molecular dynamics, we identify two different acidity values. In particular, some convex geminals and some type of vicinals are very acidic (pKa = 2.9 and 2.1, respectively) thanks to a special stabilization of their deprotonated forms. This recalls the behavior of the out-of-plane silanols on the crystalline (0001) αquartz surface, although the acidity here is even stronger. On the contrary, the concave geminals and the isolated groups present a quite high pKa (8.9 and 10.3, respectively), similar to the one of silicic acid in liquid water.

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INTRODUCTION Knowledge of the acid−base behavior of mineral surfaces is crucial for the understanding of their chemistry, including not only surface dissolution, surface interactions with ligands (especially biomolecules), and heterogeneous catalysis but also the building of charge at the interface with solvent and its consequence on ion transport, and more generally in the context of technological applications. Measuring the acid−base character of insulating mineral oxides often relies on indirect measurements, using pH-sensitive molecules with spectroscopic signatures1−3 or potentiometric titration techniques4,5 that only operate over a limited pH range. Certainly a big step forward was made in 1992 when Eisenthal and co-workers demonstrated that nonresonant second harmonic generation (SHG) spectroscopy can provide a surface-sensitive and label-free method for monitoring the acid−base behavior of fused silica.6 The planar silica/water interface has hence been shown by SHG and other methods to exhibit surface sites with two distinct acidities.1,3,6−9 In particular, the SHG experiments showed that 19% of silanol groups on fused silica surfaces exhibit a pKa of 4.5, whereas 81% exhibit a pKa of 8.5.6 Nonlinear SFG spectroscopy experiments on α-quartz also lead to similar conclusions on a bimodal behavior of silanols on crystalline silica.9 Very recent SHG results from Gibbs−Davis points to a trimodal or bimodal behavior of silica depending on the starting © XXXX American Chemical Society

pH, where the trimodal behavior is only observed when tritation is initiated at high pH.10 Other techniques such as evanescent wave cavity experiments3 have also shown the bimodal character of fused silica, measuring a ratio 4:1 of pKa, respectively for non acidic/acidic sites. See ref 11 and references therein for more description of experimental works showing the existence of two types of silanols in terms of acid−base character at the fused silica/water interface. Beyond the existence of two types of silanols at the surface of silica and their actual pKa values, one challenge is to unravel the microscopic nature of these two populations, which is the goal of the present paper using theoretical simulations. Beforehand, one has to specify the silanols nomenclature that will be used throughout our work. See Figure 1 for a schematic representation and also refs 11 and 12 for more details. Qn refers to a Si atom bonded to n other Si atoms through bridging oxygens, forming Si−O−Si siloxane groups. Upon dissociation of water on the surface, (hydroxylated) Si−OH silanol sites are formed. In the present work we will concentrate on hydroxylated surface sites. On the hydroxylated silica surface, a Q3 Si has one single Si−OH silanol group called Received: March 25, 2015 Revised: November 9, 2015

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DOI: 10.1021/acs.jpcc.5b02854 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

A consensus on the microscopic nature of the acidity bimodal character of silanols at silica surfaces is clearly far from achieved, showing the need for a theoretical molecular methodology that would provide a robust way of calculating pKa values of surface sites in the presence of the solvent and simultaneously provide a microscopic rationalization of these values. This can be achieved through ab initio molecular dynamics (AIMD) simulations of the full silica−water interface, as already shown in refs 15 and 17. One can indeed generate controlled surface models on which the pKa of selected sites can be calculated, taking into account the presence of the liquid at the interface. Following such a method and using multiple representative crystalline silica surfaces, Leung has calculated the deprotonation free energies of silanol groups with different structural motifs.15 He showed that a plausible candidate for the most acidic silanols observed in the experiments (pKa = 4.5)6 could be located on locally strained or defected regions with sparse silanol coverage.15 These AIMD simulations lend support to the role of interfacial water, finding that silanol groups on hydrophobically restructured quartz exhibited the lowest pKa.15 In this study it was also observed that the pKa of silanols increased as the number of water layers increased. The less acidic sites were shown to exhibit a pKa ≈ 9, which is similar to that of the monomeric form of silica, i.e., monosilicic acid (pKa(Si(OH)4) = 9.9).18 In a recent work17 we have addressed the special case of the α-quartz (0001)/water interface. The acidity of the surface groups were calculated from AIMD simulations using our developed proton insertion technique.19−22 The (0001) αquartz surface certainly represents a special case because the surface exhibits a regular pattern of Q2 silanol distribution and an associated regular hydrogen bond arrangement.17 Indeed, when the (0001) α-quartz surface is in contact with water, we showed that half of the silanols maintain an “in-plane” orientation, donating hydrogen bonds to nearby silanols, whereas the other half of the silanols adopt an out-of-plane orientation, and act as H-bond donors to interfacial water molecules in the first adsorbed layer.17 With our calculations we could conclude that (0001) α-quartz exhibits a bimodal behavior with two different acidity constants, namely calculated at pKa= 5.6 and 8.5, respectively for the out-of-plane and inplane silanols, and relate these pKa values to the H-bond strengths that the silanols make with the first adsorbed water layer, i.e., strong (out-of-plane) and weak (in-plane) H-bonds. From the experimental data it is clear that the bimodal acidity character is also present at the fused silica/water interface,3 i.e., a noncrystalline surface. So the question is how do silanols behave on an amorphous silica surface in terms of interactions with their environment (amorphous silica being taken as a model for fused silica)? Can we predict and explain silanol acidities in terms of local environment? In this paper we provide an explanation for the bimodal acidity behavior for the amorphous silica/liquid water interface, considering an extended model of the amorphous silica surface. In particular, our model is based on an original structure developed by Garofalini23 and subsequently relaxed via ab initio simulations.24 This surface has been characterized in both dry and microsolvated conditions,24,25 and more recently in contact with bulk water.26 The model presents a distribution of tetrahedral (SiO4) rings in the bulk solid mainly composed of four-, five-, and six-membered rings, in good agreement with the experimental data.24 It is important to note that besides the flexible Si−O−Si bond,27 no strained 3R-rings are present, by

Figure 1. Scheme of silanols encountered at the surface of silica: isolated Q3, H-bonded Q3, vicinal Q3, geminal Q2. This scheme does not take into account the presence of an aqueous interface.

“isolated” because it does not share H-bonds with any other silanol. This occurs whenever the distance between this Si−OH and the closest Si−OH neighbor (d[(Si−O)−H···O−(Si)]) is larger than 3.3 Å.11 See Figure 1a for a graphical representation. A Q3 silanol can also form hydrogen bonds, as shown in Figure 1b. A Q3 Si with one single Si−OH is called “vicinal” whenever this silanol shares a common oxygen vertex in its tetrahedra with another silanol, as illustrated in Figure 1c. A Q2 Si has a pair of geminal Si−OH, as illustrated in Figure 1d. All Si−OH silanols of Q3 type are generally labeled as terminal silanols. The key issue is to provide a microscopic interpretation of the two silanol surface acidities measured in experiments in relation with Q3 and Q2 types of Si silica sites, and in relation with their local environment (i.e., interactions with the surface and with water at the wet surface). This is far from being fully understood from experiments alone. The main reason is that the 4:1 ratio of nonacidic versus acidic sites measured experimentally3 is concomitant with several microscopic structural properties with (i) the average ratio between Hbonded and isolated silanols (IR experiments13) but also with (ii) the ratio of Q2 versus terminal silanols (NMR experiments11). Whether the 4:1 ratio of nonacidic/acidic sites on silica corresponds to one or the other population, or to another one, is still unknown. Things are even more complicated, as Chuang and Maciel showed that these populations overlap, as terminal and Q2 silanols may/may not be H-bonded, depending on the local surface topology14 and on these sites’ interactions with the solvent at the wet surface. Several hypotheses for explaining the bimodal acidity character of silica have been put forward. We list here some of them, with a special emphasis on the most acidic character. This one has been hypothesized to be due to Q3-isolated silanols15 (e.g., near a strained cycle that forms upon dehydration) because they become engaged in interactions with the solvent once the surface is wetted; alternative hypotheses are that this more acidic character could be due to any H-bonded site,11 or on the contrary, to silanols lacking hydrogen bonds,1 or to silanoliums (doubly protonated silanols).16 In a previous theoretical work17 we have provided an explanation for the bimodal character of silanols at the (0001) α-quartz interface in terms of H-bond strengths, showing that the more acidic silanols (pKa = 4.56) form the stronger hydrogen bonds to interfacial water whereas the less acidic silanols (pKa = 8.56) form the weaker H-bonds with interfacial water. B


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The Journal of Physical Chemistry C −SiOH + H 2O(aq) → −SiO− + H3O+(aq)

construction. The bulk slab is about 10 Å thick (vertical spacing), with an in-plane cell size of 13 Å × 17.5 Å, which resulted in Si27O67H26 composition (120 atoms as a whole). The slab is about three-layers thick, with thickness locally varying between 5 and 8 Å, reflecting the surface rugosity, see Figure 2. The OH density of 5.8 OH/nm2 mimics the behavior of an hydroxylated amorphous silica surface (4.5/4.9 OH/ nm2).

(1)

The transfer process is implemented using the thermodynamic integration. The charge of the acidic proton of a surface OH group is gradually switched off, transforming the proton into a neutral “dummy” particle. Simultaneously, a similar dummy proton attached to a water molecule is charged up, creating a hydronium in the Eigen form. The fractional charges on the two groups always add up to unity. Following the approach that we have discussed in detail in ref 22, the discharge integral is calculated according to ΔdpA =

∫0

1

dη⟨ΔdpE⟩r η

(2)

where ΔdpE is the vertical energy gap, defined as the potential energy difference between product P (MO−+H3O+(aq) in eq 1) and reactant R (−MOH + H2O(aq)) for instantaneous configurations of a molecular dynamics trajectory. The subscript rη indicates that the averages are evaluated over the restrained mapping Hamiltonian /η = (1 − η)/R + η /P

(3)

where η is a coupling parameter that is gradually increased from 0 (−MOH + H2O(aq)) to 1 (−MO− + H3O+(aq)). This Hamiltonian also contains a harmonic restraining potential Vrestr keeping the dummy atom close to the equilibrium position of the H+ nucleus in the protonated system. The Simpson rule (three-point approximation) is used to evaluate the integral in eq 2:

Figure 2. Amorphous silica slab used for calculations. Color code: yellow, Si; red, O; white, H atoms. The five studied silanol sites are highlighted in blue and use a larger size.

The acidity of the silanols at the dry surface has been characterized in ref 24. The terminal Q3 hydroxyl groups were found to have a deprotonation energy of ∼650 kJ/mol and the Q2 ones of ∼600 kJ/mol, with geminal silanols thus slightly more acidic. The small 50 kJ/mol difference in the deprotonation energies may, however, not be enough to confidently predict the order of acidity in the presence of an aqueous phase. Vacuum DFT calculations of the adsorption of lutidine (2,6-dimethylpyridine) on Q2- and Q3-isolated silanols of this surface furthermore confirm the slightly higher acidity of Q2 sites.28 In the same spirit, we identified that the convex silanol nest formed around the Q2 site exhibits a higher chemical reactivity than Q3-isolated silanols, being typically an attracting site for the adsorption of glycine, and stabilizing basic adsorbates.25 Is the higher chemical reactivity of Q2 silanols maintained at the aqueous interface?

ΔA TP =

1 2 (⟨ΔE⟩0 + ⟨ΔE⟩1) + ⟨ΔE⟩0.5 6 3

(4)

This requires generation of three trajectories corresponding to values of η = 0, 0.5, 1. This formula is often a good compromise between computational cost and accuracy of the free energy change.19,36 The pKa value of a surface group is obtained from the proton transfer integral of eq 2 by adding a thermochemical correction. The leading term in this correction adds in the translational entropy generated by the acid dissociation. This term is missing in reaction 1, which is formally a proton transfer reaction conserving the number of translational degrees of freedom. Indeed, this translational entropy term is related to the definition of our solvated proton, which is assumed to be in the Eigen form, namely, as H3O+(aq), where instead the proton is actually free to diffuse around and should be instead represented as H+(aq). The simplification is motivated by the necessity to have a well-defined position for the proton insertion. A detailed explanation about this issue can be found in ref 22. The overall formula used for the pKa calculation becomes

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METHODS Calculation of the Acidity Constants. The acidity constants of surface groups are computed using the reversible proton insertion/deletion method.19−22 The method was initially developed and tested on a series of aqueous compounds,19−22 and then applied to the calculation of the acidity of surface groups of several oxides in contact with water.17,26,33−35 The advantage of this approach is that the solid (mineral) surface and the solvent (water) are treated at the same level of theory, and therefore the approach is particularly suitable for heterogeneous environments such as interfaces. The acidity constants are calculated from the free energy for transferring a proton from a group on the surface (in our case the silanol OH) to a water molecule in the bulk solution. The following reaction is considered:

2.30kBTpK a =

∫0

1

dη ΔdpE η + kBT ln[c o Λ 3H+]

(5)

where co = 1 mol dm−3 is the unit molar concentration and ΛH+ is the thermal wavelength of the proton. We refer the reader to ref 22 for a detailed derivation of such a formula. The logarithm of the product coΛ3H+ accounts for the liberation entropy of the proton and is responsible for a correction of −3.2 pK units to the thermodynamic integral. We comment that all the pKa values have been calculated on a neutral surface, so at the point of zero charge condition. It is expected that if the overall charge of the surface varies, in C


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Figure 3. Representative snapshots of the local structures around the SiOH groups at the water/amorphous silica interface. Hydrogen bonds appear in white dashed lines.

Table 1. Energies (eV) Obtained in the pKa Calculations of the Geminal, Isolated, and Vicinal Silanols on Amorphous Silicaa system

traj

Q2-Gem. 1

Whole Half1 Half2 Whole Half1 Half2 Whole Half1 Half2 Whole Half1 Half2 Whole Half1 Half2

Q2-Gem. 2

Q3-Iso.

Q3-Vic. 1

Q3-Vic. 2

ΔE0 −7.18 −7.45 −6.91 −6.34 −6.23 −6.45 −5.49 −5.62 −5.36 −8.30 −8.62 −7.99 −5.24 −5.31 −5.18

± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

ΔE0.5 1.62 1.59 1.60 1.45 1.49 1.40 0.67 0.63 0.69 2.82 3.31 2.18 0.64 0.72 0.55

0.35 0.51 0.19 0.77 0.75 0.78 0.75 0.66 0.76 0.63 0.70 0.56 1.42 1.39 1.46

± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.54 0.53 0.51 0.52 0.53 0.50 0.54 0.48 0.54 0.53 0.57 0.47 0.50 0.52 0.49

ΔE1

ΔA

pKa

ΔpKa

± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.28 0.36 0.15 0.67 0.68 0.66 0.79 0.67 0.86 0.23 0.31 0.23 1.15 1.13 1.19

2.9 4.1 0.9 8.9 9.0 8.7 10.3 8.4 11.3 2.1 3.4 2.1 16.2 15.9 16.9

1.6

7.09 7.16 7.01 7.30 7.30 7.33 7.24 7.04 7.45 7.40 7.66 7.14 6.43 6.56 6.49

1.03 0.98 1.06 1.09 1.08 1.10 1.28 1.31 1.23 1.53 1.59 1.43 1.06 1.03 1.06

0.2

1.5

0.7

0.5

ΔE represents vertical energy gaps and ΔA is the difference in free energy. Uncertainties on the final values are qualitatively evaluated via an estimation on the pKa in the first half (Half1) and in the second half (Half2) of the trajectories. This last part confirms the convergence of the calculations. a

and 2 ps for the isolated SiOH) with a time step of 0.5 fs. On average, the lengths of the trajectories (true data collection) are 10 ps for geminal 1 and vicinal 1, 15 ps for the isolated site, and 20 ps for geminal 2 and vicinal 2. These sites are described in the next section.

particular when a nearby group gets deprotonated, this can have a strong impact on the site pKa. Model Systems. Our AIMD simulations follow the same general setups used in our previous investigations of solid− liquid interfaces.17,26,33−35 DFT-based Born−Oppenheimer molecular dynamics (BOMD) simulations have been performed with the CP2K/Quickstep package,37 using the hybrid Gaussian and plane wave method. The Perdew−Burke− Ernzerhof (PBE) exchange−correlation density functional was used. Goedecker−Teter−Hutter pseudopotentials,38,39 a double-ζ DZVP plus polarization Gaussian basis set for the orbitals and a density cutoff of 400 Ry were used. Only the Γ point was considered in a supercell approach. The box dimensions are 12.77 × 17.64 × 25.17 Å3. Periodic boundary conditions are applied in all directions of space. Dynamics were conducted in the canonical NVT ensemble (after 9 ps of equilibration for geminal 1, 5 ps for geminal 2 and vicinal 2, 10 ps for vicinal 1

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RESULTS AND DISCUSSION In our recent work26 we have shown that this amorphous silica/ water interface is characterized by a strongly adsorbed layer of water at the interface. In particular, three zones were identified, with increasing “local ordering” of the interfacial water, namely, Q3-isolated silanols and concave and convex geminal Q2 silanols. A picture showing the local environment for a few selected groups can be found in Figure 3. For our pKa analysis we have chosen different types of sites that are representative of different Qn sites (namely silanols with different number of D


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The Journal of Physical Chemistry C bridging oxygens) and different types of local environment and solvation. In particular, we chose two different types of geminals, namely Geminal 1 (panel a in Figure 3), which is a convex Q2 silanol, and Geminal 2, which is a concave Q2 silanol (panel b in Figure 3). From our detailed analysis of the solvation structure at the interface with the amorphous silica, we could already suggest that the convex Q2 silanol represents possibly low acidity sites.26 Additional investigated sites include two Q3 vicinals with very diffferent environments and a Q3isolated site. The two vicinals are reported in Figure 3, panels c and d, and are characterized by two distinct exposures to solvent. Vicinal 1 (panel c) corresponds to a hydroxyl group fully immersed into liquid water. It is H-bonded to a neighboring silanol through a bridging water molecule and is part of a four-membered H-bond ring. In particular, it receives and donates 2 H-bonds with two water molecules. Conversely, Vicinal 2 (panel d) is a completely buried site, almost inaccessible to solvent. It only shares its proton directly with a nearby silanol. Finally, the isolated site is depicted in panel e of Figure 3 and is H-bonded with one water molecule. We provide here a quantitative estimate of these site acidities, applying our proton insertion approach19−22 as in ref 17. pKa values will be compared to those calculated for the in-plane and out-of-plane Q2 silanols of the crystalline quartz−water interface. The pKa values found are 2.9 for the convex Q2 silanol and 8.9 for the concave Q2 silanol. This first result suggests that the acidity is not depending on the type of site only (Q2 for both cases) but is strongly influenced by the local environment, namely, by the solvent accessibility and H-bond network around the OH site. A similar conclusion also holds for the Q3 sites. Indeed, vicinals with different local environments can have very different acidities. The Q3 vicinal 1, which is characterized by steady hydrogen bonds with interfacial water, has a pKa value of 2.1, whereas another vicinal with its hydrophobic environment, namely, our Q3 vicinal 2, has a much higher pKa value of 16.2. Finally, the Q3-isolated silanol has a pKa of 10.3. (A summary of the pKa analysis is reported in Table 1). The (convex) geminal 1 and the vicinal 1 are thus very acidic, even more acidic than the Q2 out-of-plane silanols at the αquartz/water interface (pKa = 5.6),17 whereas the geminal 2 and the isolated sites have a relatively high pKa that is similar to the one of the silanols in silicic acid (pKa ≈ 9.9 from our previous AIMD simulations17). Finally, the pKa of vicinal 2 is outside the water window and would possibly not be probed in titration experiments. Overall, we recover a bimodal behavior at the water/amorphous silica with a first acidity around 2−3 pKa units and a second one around 9−10. Now the key question is where does the strong/weak acidity come from? To provide an answer to such a question, we have analyzed in detail the solvation structure of both the protonated and the deprotonated forms of the silanols. To guide the structural analysis, a scheme is reported in Figure 4, which shows a silanol in the protonated form (left panel) and a silanol in the deprotonated form (right panel) and their hydrogen bond networks obtained from our AIMD simulations. In the scheme, the average hydrogen bond distances for the Q2- and Q3-isolated silanols at the amorphous silica/water interface, and for the Q2 aqueous quartz out-of-plane silanols,17 are reported for discussion. Note that for clarity, we do not report here all the sites. On the basis of the average distances reported in Table 2 for the neutral form of the amorphous silica sites, the convex Q2

Figure 4. Schematic view of the solvation of the different surface sites of silica (amorphous and crystalline quartz) obtained from our AIMD simulations: amorphous Q2 convex geminal (red); amorphous Q3isolated (black); quartz Q2 out-of-plane (OP) (green). Left: neutral Si−OH form of the silanol site. Right: deprotonated Si−O− form of the silanol site (conjugated base, silanolate). Labels show the average number of hydrogen bonds formed between the Si−OH (left)/Si−O− (right) and their surrounding (silanols and water molecules).

Si−OH (geminal 1) donates a strong hydrogen bond to water (1.57 Å, (Si)O−H···Ow intermolecular distance), stronger than the one formed by the concave Q2 Si−OH (1.69 Å) and slighly stronger than that formed by the Q2 out-of-plane silanol from the (0001) quartz crystalline surface (1.60 Å). This is also clear from the (Si−O)H···Ow distances reported in Table 2 taken from the position of the first peak in the radial distribution functions between silanol H atoms and Ow oxygens of water (curves reported in Figure 5). Maybe, more importantly, from these curves one can obtain the information concerning the position of the second peaks in the H···Ow radial distribution functions and their microscopic interpretation. The second peak of H···Ow for the amorphous Q2 silanol (Figure 5, red line) corresponds to the interaction of this site with three nearby silanols and four water molecules from the liquid. A very similar strong coordination from the environment was also found for the Q2 out-of-plane silanol of the crystalline (0001) quartz, as it is also surrounded by two to three neighboring SiOH groups and by two to three water molecules. The high computational cost of our AIMD proton-insertion method for pKa calculations prevents us from determining the intrinsic acidity of each surface site. However, we could envisage estimating acidic heterogeneities within the same type of silanol group by looking at the local environment around the protonated and deprotonated forms. The rdfs of all the convex geminals are reported in Figure 6. The red lines (continuous and dashed) refer to a pair sharing the same Si, and the blue lines (continuous and dashed) refer to another pair sharing the same Si. We only have two concave geminals at the surface, which is clearly a very limited statistics. A comparison of the rdfs is nonetheless reported in Figure 7. Note that the color code in Figures 6 and 7 to the same code chosen in the previous figures; namely, the continuous red line corresponds to the convex geminal 1 and the continuous orange line is for the concave geminal 2. The position of the first peaks in the H/O rdfs (Figures 6 and 7), corresponding to proton sharing with a nearby hydroxyl (from silanol or water), are all shifted to larger distances with respect to the continuous red line of convex geminal 1. From considering only the H/O rdfs, the weaker H-bond donor character could reflect lower acidity. Considering that for more acidic sites, the OH bond is more polarized implying a greater negative charge on the oxygen, its H-bond acceptor character should be enhanced. Indeed, from the O/H rdfs, the more acidic convex geminal 1 and the less acidic concave geminal 2 correspond to the extreme H-bond acceptor behaviors, the more acidic site being a very strong acceptor and the less acidic E


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Table 2. Positions and Heights of the First Two Peaks from the Radial Distributions Functions (rdf) around the Q2-Geminal 1 (Gem. 1), Q2-Geminal 2 (Gem. 2), Q3-Isolated (Iso.), Q3-Vicinal 1 (Vic. 1), Q3-Vicinal 2 (Vic. 2), and Out-of-Plane (OP) Silanols first peak

second peak

rmax(Å)

Imax

rmin(Å)

H−O Gem. 1

1.57

3.65

2.14

0

H−O H−O H−O H−O H−O O−H

Gem. 2 Iso. Vic. 1 Vic. 2 OP Gem. 1

0 0 0 0 0 0.11

Gem. 2 Iso. Vic. 1 Vic. 2 OP

2.78 3.83 2.73 3.44 4.10 1.42 1.49 0.61 1.34 0.40 0.69 2.34

2.24 2.19 2.28 2.16 2.03 2.56

O−H O−H O−H O−H O−H

1.69 1.60 1.74 1.65 1.55 1.69 1.89 1.87 1.78 2.21 3.41 1.58

2.46 2.39 2.42 4.27 2.16

0.12 0.10 0.31 0.19 0

1.57 1.63 1.70 1.58 1.50 1.53

4.08 3.85 3.66 3.39 3.36 4.77

2.23 2.11 2.48 2.36 2.14 2.28

0.06 0.00 0.23 0.15 0.04 0.08

O−−H O−−H O−−H O−−H O−−H O−−H

Gem. 1 Gem. 2 Iso. Vic. 1 Vic. 2 OP

Imin

Figure 5. Radial distribution functions (rdf) around SiOH and SiO− on amorphous silica or on α-quartz. The black line correspond to the Q3-isolated sites, the red and orange ones to the Q2-convex (geminal 1) and concave (geminal 2) geminals, respectively. Blue lines represent the Q3-vicinals, dark blue for vicinal 1 and light blue for the buried vicinal 2. The green line is used for the out-of-plane silanol on quartz. Top panel: rdfs. Lower panel: integrated densities.

rmax(Å)

Imax

rmin(Å)

Imin

3.14 3.42 3.42 3.25 3.23 4.03 2.82 3.10

1.40 2.18 1.76 1.30 1.44 0.97 2.67 1.54

4.10 3.66 3.47 3.76 4.35 3.22 3.60

0.57 0.75 0.96 0.73 0.44 0.66 0.31

2.99 3.22 3.07

1.08 1.70 1.60

3.52 3.66 4.40

0.42 0.76 0.53

3.08 3.53 3.06 3.02 3.13 3.11 3.90 3.54

0.93 1.30 1.16 1.41 1.36 1.47 0.65 1.81

3.31 3.77 3.79 3.40 3.34 4.34 4.74 4.17

0.74 0.64 0.36 0.67 0.87 0.39 0.35 0.49

Figure 6. Comparison of the local environment for convex geminal silanols: (left) donated hydrogen bonds from silanol H atoms; (right) accepted hydrogen bonds from water H atoms. The red lines (continuous and dashed) refer to a pair sharing the same Si, and the blue lines (continuous and dashed) refer to another pair sharing the same Si.

If we now turn to the conjugated silanolate bases (Figure 4, right), we observe that they are strongly and equally stabilized for the convex Q2 Si−O− of amorphous silica and the Q2 outof-plane site of crystalline (0001) α-quartz. Note, e.g., that for the amorphous convex Q2 SiO−, one H-bond is accepted by one water (distance 1.64 Å) and two H-bonds are accepted by a nearby silanol (1.64 Å). A pictorial view of the local environment for the deprotonated convex geminal Q2 can be found in Figure 8, panel a. Similarly for the out-of-plane Q2 SiO− on the quartz crystalline surface: two H-bonds are accepted from water

site being a poor one. All the remaining geminals lie in between. Conclusions on their relative acidities are thus not straightforward. Nonetheless, because the two concave sites are not as good H-bond acceptors as the convex ones (maximum 1H-bond is accepted, Figure 7, right panels) we expect both concave silanols to exhibit the similar less acidic pKa. Note that the higher acidity correlated to a stronger H-bond acceptor character also holds for acidic Q3 vicinal 1 vs basic Q3 vicinal 2 on one side and for acidic Q2 out-of-plane geminal vs less acidic Q2 in-plane geminal on quartz on the other side. F


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hydrogen bonds. The isolated site seems not to fit within this scheme. Indeed, its conjugated base has a coordination of 3.5; however, it forms on average the weakest H-bonds with these water molecules (1.82 Å), the weakest among all the H-bonds stabilizing the other deprotonated silanols (also true when looking for the strongest H-bond among the 3.5 possible). This type of stabilization of the isolated silanolate may resemble that of a silicic acid molecule where the base stabilization can only come from solvent molecules, but not from other silanol groups. A pictorial view of the local environment for the deprotonated Q3 site can be found in Figure 8, panels c, d, and e. In addition to the radial distribution functions we have also investigated the orientational distribution of the water around the deprotonated silanols. We find that the orientational distribution is very similar for all the cases (geminal, vicinal, isolated) and the maxima are only displaced by a few degrees. We can conclude that water orientation around the deprotonated oxygen is not a discriminating element characterizing the conjugated base. In some recent analysis of a model of amorphous silica surface the presence of hydrophobic−hydrophilic patches has been suggested in connection to the siloxane density.29,30 It thus may be interesting to comment on the eventual correlation between the density of siloxane groups in vicinity of the silanol groups and their pKa’s. Our analysis shows that low pKa is possible for both Q2 (geminal 1) and Q3 (vicinal 1) sites, which means it is independent of the number of siloxane bridges. Convex and concave geminals have the same number of siloxane bridging groups; however, they exhibit a quite large difference in the pKa. This would suggest that the environment, namely, the local topology and solvent accessibility are the key element to determine silanols acidity. To quantify the local hydrophobicity, we have calculated the rdf of the siloxane O around the silanols with the solvent H, or the nearby silanol H. These are reported in Figure 9. We find that the siloxanes are quite hydrophobic, and no hydrogen bond is formed between the siloxane oxygens and protons from the environment

Figure 7. Comparison of the local environment for concave geminal silanols: (left) donated hydrogen bonds from silanol H; (right) accepted hydrogen bonds from water H. Two OH groups sharing the same Si are investigated. The continuous line refers to an OH group that donates an H-bond to water (similar to convex silanols), and the dashed line, to an OH group which donates an H-bond to a nearby silanol.

(1.69 Å) and one H-bond is accepted from a nearby silanol (1.53 Å). Both the amorphous Q2 SiO− and the quartz out-ofplane Q2 SiO− are strongly stabilized by the environment and exhibit an overall 3-fold coordination of the deprotonated oxygen. On the contrary, the concave Q2 SiO− site is not so strongly stabilized. It only accepts two hydrogen bonds, which are also weaker than those stabilizing the deprotonated convex site. A pictorial view of the local environment for the deprotonated concave geminal Q2 can be found in Figure 8, panel b. Let us now turn to the vicinals and the isolated sites. Here we investigated different types of environments on the Q3 sites. For the vicinals a key element to interpret the acidity can be again found in the conjugated base stabilization. Indeed, also here the acidic site (vicinal 1) has a conjugated base that is strongly stabilized by three hydrogen bonds. Instead, for vicinal 2 (higher pKa) the conjugated base is only stabilized by two

Figure 8. Representative snapshots of the local structures around the deprotonated SiO− silanols at the water/amorphous silica interface. Hydrogen bonds appear in white dashed lines. G



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CONCLUSIONS

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AUTHOR INFORMATION

The first conclusion from our structural study is that the silanol acidity does not depend on the actual n value of the Qn site, at least not solely. We find pKa values of 2.9 and 8.9 for a convex, respectively, concave Q2 geminal silanol and pKa of 2.1 and 16.2 for Q3 vicinal silanols with more hydrophilic or hydrophobic environments, respectively. Finally, we find pKa value of 10.3 for the isolated Q3 site. The local environment has a strong impact on the silanols acidity and the geminals are a good example where different environments (local topology (nano-roughness) and hydrophobicity/philicity) can lead to very different pKa. Some convex Q2 silanol at the amorphous/ water interface can form strong hydrogen bonds with water, so exhibiting a major tendency of the proton to be shared with water, thus pointing to a higher acidity (pKa value 2.9). On the contrary, the SiO− deprotonated form of this convex geminal can be more easily stabilized by the presence of nearby OH groups from other surface silanols, which in this nested configuration are particularly prone to solvate the silanolate base. Overall, the convex conjugated base is 3-fold coordinated, whereas the concave conjugated base is only 2-fold coordinated. The same conclusion seems to hold for the vicinals, where the acidic site has a 3-fold coordinated conjugated base, whereas the more basic site has a 2-fold coordinated base. We believe this special anion solvation is the key element to explain the higher acidity of some of the Q2 geminal and some of the Q3 vicinal silanols at the amorphous aqueous silica surface. The corollary is that both Q2-geminal 2 and the Q3-isolated silanols form weaker H-bonds with the solvent, and more importantly their conjugated bases are not stabilized by a substantial H-bond network. This is the key element for the basic character of the Q3-isolated silanol at the silica amorphous aqueous interface, and the intrinsic flexibility of the silica framework that stabilizes the overall H-bond network on the surface. Our analysis supports and explains the acidity bimodal character of amorphous (this work) and crystalline silica silanols (this work and ref 17), as the result of local H-bond organization and strength, that can lead to a strong stabilization of the silanolate base. We have indeed shown that the essential element resides in the stabilization of the conjugated base of the silanol site, by local interactions with the surface and water. The H-bond network that can be formed around the conjugated base is the key factor to understand the ranking in acidity of silica silanol sites.

Figure 9. Local environment for siloxane groups. Upper panel: rdf between the siloxane oxygen and the water hydrogens. Bottom panel: integrated numbers. Black curve: siloxane oxygens around the isolated. Green curve: siloxane oxygens around the quartz geminal. Red curve: siloxane oxygens around the convex Q2-Geminal 1. Orange curve: siloxane oxygens around the concave Q2-Geminal 2. Black: Q3-Iso. Dark blue: Q3-Vicinal 1. Light blue. Q3-Vicinal 2. All are at the water/ amorphous silica interface. Green: siloxane oxygens around the Q2out-of-plane site at the (0001) α quartz surface.

(namely protons from other silanols or from water). In all the cases (geminal, isolated, vicinal, crystalline quartz) the first peak in the radial distribution function appears around 3 Å. For the convex geminal (red curve in Figure 9) the broad band around 3.0−3.5 Å is due to protons from the surrounding silanols, whereas for the isolated (black line) the peak originates from water molecules. Leung et al.15 have also explored the influence of H-bonding between Q2 silanols at the (100) β-cristobalite surface, where the surface is composed of Q2 silanols sharing intramolecular H-bonds with bond lengths of 1.70 Å in vacuum.31 pKa = 7.6 was calculated. The possibility of forming an H bond was then eliminated by replacing the OH group by a H atom, so creating an isolated Q2 silanol. The pKa was consequently found to increase to 8.9, so that Leung et al. concluded that H-bonding was responsible only for a small decrease of the pKa. In particular, the simple removal of a hydrogen bond around the Q2 silanols at the (100) β-cristobalite surface could not produce a difference of 4 units between different Q2 sites and therefore could not explain a bimodal character of that surface. However, in comparing our result to the cristobalite, one should also take into account the role of the surface flexibility. Indeed, Musso et al.32 pointed out that for (100) cristobalite, the formation of Hbonds between surface OH groups induces a large variation in the flexible Si−O−Si angles with a sizable rearrangement of the structure across the whole layer thickness. It was also found that the layer thickness strongly influences the number of Hbonds formed by the silanols on the surface.32 So one could speculate that H-bond formation on cristobalite (100) is energetically more expensive than on quartz (0001) and amorphous silica, leading to a poorer associated base stabilization. Certainly, the amorphous surface is more flexible than crystalline surfaces, so that relaxation to maximize H-bond formation should be easier.

Corresponding Author

*M. Sulpizi. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Johannes Luetzenkirchen and Alvaro Cimas for useful discussions and careful reading of the manuscript. Computer time from HRLS (Hermit) is greatly acknowledged (project number 2DSFG).

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REFERENCES

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