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Surfaces, Interfaces, and Catalysis; Physical Properties of Nanomaterials and Materials

Increased Acid Dissociation at the Quartz/Water Interface Shivam Parashar, Dominika Lesnicki, and Marialore Sulpizi J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.8b00686 • Publication Date (Web): 10 Apr 2018 Downloaded from http://pubs.acs.org on April 10, 2018

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The Journal of Physical Chemistry Letters

Increased Acid Dissociation at the Quartz/Water Interface Shivam Parashar,† Dominika Lesnicki,‡ and Marialore Sulpizi∗,‡ †Department of Chemical Engineering, Indian Institute of Technology Roorkee, India. ‡Institute of Physics, Johannes Gutenberg University Mainz, Staudingerweg 7, 55099 Mainz, Germany E-mail: [email protected] Phone: +49 6131 39 23641. Fax: +49 6131 39 25441

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The Journal of Physical Chemistry Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract As shown by a quite significant amount of literature, acids at the water surface tends to be "less" acid, meaning that their associated form is favored over the conjugated base. What happens at the solid/liquid interface? In the case of the silica/water interface we show how the acidity of adsorbed molecules can instead increase. Using a free energy perturbation approach in combination with electronic structure -based molecular dynamics simulations, we show how the acidity of pyruvic acid at the quartz/water interface is increased of almost two units. Such increased acidity is the result of the specific microsolvation at the interface and in particular of the stabilization of the deprotonated form by the silanols, on the quartz surface, and the special interfacial water layer.

Graphical TOC Entry Pyruvic acid

pKa = -1.85

Quartz 0001

2


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Introduction The acid dissociation constants of molecules in bulk aqueous solution are routinely determined using techniques like potentiometric titration, voltammetry, and electrophoresis. 1 A more complicated task is to measure dissociation constants at interfaces since the signal originating from bulk molecules typically overwhelms that from surface molecules. The advent of interface selective vibrational spectroscopy techniques, capable to probe the molecular structure of the nanometric layer of a liquid interface, has recently permitted to selectively address properties of molecules at interfaces, also providing information on the degree of proton dissociation. Pioneering interface selective spectroscopic studies of acid/base pairs have shown that the surface favors the neutral form of the acid/base pair in comparison to the bulk. 2 For instance, using second harmonic generation (SHG) and vibrational Sum Frequency Generation (VSFG), it has been shown for phenol and carboxylic acids that the neutral acid species is favored over the anionic conjugate base. 3–5 Similarly, it was found for molecules containing an acid ammonium group that the neutral amine base species was favored over the cationic quaternary ammonium acid. 6,7 Nitric acid, known as a strong acid in bulk aqueous solution was also investigated at the water/air surface. Its dissociation does not occurs at the water surface while generally occurs in the first and second surface layers depending on the acid’s orientation and its solvation. 8–11 Amino acids, such as L-alanine and L-proline studied by VSFG present a reduced acid dissociation at the water surface. Higher pH values are required to induce the dissociation of carboxylic acid groups of molecule at surface. 12 Tahara and coworkers have evaluated the pH at model biological membranes (lipid/water interfaces), which substantially deviates from the bulk pH. The pH at the lipid/water interface is higher than that in the bulk when the head group of the lipid is positively charged, whereas the pH at the lipid/water interface is lower when the lipid has a negatively charged head group. 13 Now the question is what happens instead at the solid/liquid interface? The solid surface may contain hydrophilic groups (such as silanols in the case of quartz and silica), as well as 3



ions, which can influence the dissociation constant. Can the situation effectively be reversed? Are hydrophilic surface enhancing the acid dissociation? Experimental investigation of acid/ base equilibrium at "buried" solid/liquid interface are more difficult. The group, e.g. of V. Grassian has been extensively studying adsorption and dissociation of strong and weak acids on silica particles, 14,15 however it is challenging for such experiments to quantify a change in the acidity upon adsorption at the solid/liquid interface. Some recent computational studies in the group of R.B. Gerber have evidenciated fast deprotonation of HCl and H2 SO4 on quartz surface covered by a water monolayer, 16,17 although, again, a quantitative measument of the acidity on such surface (and in comparison to liquid bulk conditions) was not provided. The group of D. Marx has recently addressed with accurate free energy calculations, also including nuclear quantum effects, the issue of acid dissociation in HCl-water clusters, and has shown that, a minimum of four water molecules is needed to stabilize the fully dissociated solvent-shared ion pair at low-temperature and thus to create the smallest droplet of acid. 18 In order to answer the question if adsorption at the solid/liquid interface can enhance acid dissociation, we will discuss in details the dissociation of pyruvic acid, the simplest α-keto acid, at silica/water interface. Pyruvic acid plays a key role in the intricate chemistry of the atmosphere as intermediate in the oxidative channels of isopropene and of secondary organic aerosols. 19 Silica is the main component of mineral dust particles in the atmosphere, and reactions on its surface, in presence of variable levels of humidity, and also including proton dissociation, have a direct impact on radical concentration and the ability of dust particles to serve as cloud condensation nuclei or ice nuclei. 20 Noticeably, the dissociation constant of pyruvic acid (bulk pKa 2.5) is close to the point of zero charge of α-quartz surface, 21,22 therefore pyruvic acid and silanols may compete for protons at the quartz surface. For example, we have shown that on the quartz 0001 surface two species of silanols exists, with the most acidic one, represented by the out-of-plane silanols presenting a pKa of 5.6. 21 Similarly at the amorphous silica/ water interface we also found that some convex geminals groups, as well as some type of vicinals are very acid with pKa of 2.9 and 2.1, respectively, 23 4


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therefore very close to the pKa of bulk pyruvic acid of 2.5. Anticipating our results, we find that pyruvic acid acidity is enhanced at the quartz/water interface, of almost two units. This result is quite interesting, since it goes in the opposite direction of what normally found for acids at the water/vapor interface. As we will explain in details in this Letter, such increased acidity is the results of the specific micro-solvation around the acid/abase groups and, in particular, of the stabilization of the conjugated base by the silanols groups on the quartz surface. In order to obtain a detailed microscopic understanding of the interface pKa variations, molecular modeling at the atomistic level is required. In particular, using ab initio molecular dynamics simulations, the acidity constants will be computed using the reversible proton insertion/deletion method 24,25 that we already applied to a wide range of chemical groups, also at solid/liquid interface. 21,23,26,27 Since our approach permits to explicitly take into account the solvent and its specific interaction with the molecule as well as with the surface, we will be able to pin down the origin of the pKa changes in terms of molecular orientation and local hydrogen bond strength. The inclusion of the full electronic structure will permit to address anharmonicity and polarization effects, which cannot be easily incorporated in a simpler empirical force field approach. We compute the pKa difference between the acid at the interface and the acid in the bulk, using a thermodynamics integration which transforms the acid into its conjugated base. We consider the α-quartz 0001 surface in contact with water in the neutral, fully hydroxilated form. As schematically shown in Fig.1 we actually transform a model system which contains the acid (AH) at the interface and the conjugated base (A-) in the bulk (left panel in Fig.1) into a system which contains the base (A-) at the interface and the acid (AH) in the bulk (right panel in Fig.1). The difference in pKa ’s between interface and bulk (∆pKa = pKaI − pKaB ) is then given

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AH =

A-

AH

AH

A-

A- =

(a) E0

(b) E1

Figure 1: The model used for the calculation of ∆pKa value. On the left side the protonated form of pyruvic acid (AH) and the deprotonated form (A− ) are shown. Schematic view of the simulation setup (a) the initial state with protonated acid (AH) at the interface and deprotonated acid (A-) in the bulk. (b) the final state with the acid in the bulk (AH) and the deprotonated acid (A-) at the interface.

by the following equation:

∆pKa = pKaI − pKaB =

(∆dp AAH )I − (∆dp AAH )B , ln10kB T

(1)

where (∆dp AAH )I,B is the deprotonation free energy for interface (I) and bulk (B), respectively, and can be calculated with the thermodynamic integration approach. We remand the reader to the Supplementary Information for all the details of the method implementation. DFT based Born-Oppenheimer molecular dynamics (DFTMD) simulations were performed using Becke exchange 28 and Lee, Yang and Parr 29 correlation functionals. All calculations have been carried out with the freely available DFT package CP2K/Quickstep which is based on the hybrid Gaussian and plane wave method. 30 Analytic Goedecker-Tecter-Hutter pseudopotentials, 31,32 a TZV2P level basis set for the orbitals and a density cutoff of 280 Ry were used. Dynamics were conducted in the canonical NVT ensemble with a timestep of 0.5 fs using the CSVR thermostat with the target temperature of 330 K to avoid the glassy behavior of BLYP water and a time constant of 1 ps. A periodic orthorhombic box of dimensions 19.64×17.008×43.5 Å is considered (see Supplementary Material for details

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of the system preparation). For each simulation, an equilibrium trajectory of 5 ps and an additional production run of 20 ps was used for the ∆pKa calculation. For both bulk and interface the most stable Tce isomer was considered. At the interface the acid is stabilized in a configuration with the heavy atoms plane parallel to the quartz surface. The acid remains localized within the first adsorbed layer of water, as shown by the position of the center of mass in Fig. 3 of the SI. In the protonated form the binding between pyruvic acid and the surface silanols is not direct, but mediated by a water bridge (see for example a snapshot from the simulation in Fig. 4 (b)). Additionally the methyl group of pyruvic acid also accommodates on the hydrophobic patch on the quartz surface (see Fig. 2 for a top view perspective). Such binding configuration is quite stable along the simulation trajectory as shown by the time traces reported in Fig. 2. Essentially pyruvic acid acid cannot freely diffuse at the interface, but remains quite strongly localized.

Figure 2: Top view of the (0001) α-quartz interface where the pyruvic acid is located (position in Å). Dots represent the average position of the Si (yellow), O (red) and H (black) atoms from the quartz interface. The lines represent the time traces (position as function of time) of the center of mass (cyan), the methyl group (magenta), the oxygen (red) and hydrogen (black) atoms from the pyruvic acid and the oxygen atom (blue) from the water bridge. From our calculation we find that the interfacial pyruvic acid is more acidic than the one 7



in the bulk by 1.84 pKa units. The easier deprotonation at the quartz/water interface can be understood through an analysis of the solvation structure around both protonated and deprotonated species. In particular we will discuss the solvation structure in terms of radial distribution functions and coordination numbers, specifically defined for the solid/liquid interface as described in the Supplementary Material. 3

3

(a)

(b)

HAH - Ow HAH - Ow

OA_ - Hw OA_ - Hw OA_ - HSi

2

1

0 0

1

2

4

6

8

6

4

rdf

2

rdf

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0 0

2

2

r (Å)

4

6

0 8

r (Å)

Figure 3: Radial distribution functions between (a) the hydrogen atom of the protonated pyruvic acid (HAH ) and the oxygen atoms of the water solvent (Ow ) (acid in bulk in black, acid at the interface in red), (b) the oxygen atom of the deprotonated pyruvic acid (OA− ) and the hydrogen atoms of the water solvent (Hw ) (conjugated base in bulk in black, at the interface in red. The rdf between OA− and the silanol proton (HSi ) is also reported (red dashed line, y axis values readable on the right). In the protonated form the solvation structure around the OH group is similar when comparing bulk and interface. In both cases the OH group donates a relatively strong hydrogen bond, which however is slightly shorter at the interface (red line in Fig. 3, position of the first peak at 1.61 Å) than in the bulk (black line in Fig. 3, position of the first peak at 1.71 Å). This first observation would suggest that at the interface the proton is more keen to leave its oxygen. Such a difference in the local solvation is the result of the different water behavior in the bulk and at the interface. At the interface the interaction with the hydrophilic surface renders the water molecules in the first adsorbed monolayer quite special. Such waters have indeed much slower orientational and diffusion dynamics than those in bulk 8


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(a)

(b)

(c)

(d)

Figure 4: The H-bonds formed between the protonated/deprotonated pyruvic acid and the surrounding atoms: (a) protonated acid in the bulk water, (b) protonated acid at the interface, (c) deprotonated acid in the bulk water and (d) deprotonated acid at the interface. Color code: Si, yellow; C, blue; O, red, H, white.

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water. As a result the hydrogen bond established between the interfacial water molecule and the OH group of pyruvic acid has a life time, larger than 20 ps, which even exceeds the simulation length. When we compare the behavior of the conjugated base (at the interface and in the bulk) we also notice interesting differences. Indeed while in the bulk the conjugated base is stabilized accepting hydrogen bonds from water (with an average number of Hbonds in the first shell of 2.64), at the interface it is stabilized by hydrogen Hbonds from water (on average 1.87), but additionally also by accepting hydrogen bonds from a surface silanol (on average 0.58). The hydrogen bond established with the silanol (dashed red line in Fig.3) is shorter (1.69 Å) than that accepted by water (continuous red line in Fig.3(b), position of the first peak at 1.85 Å). The shorter hydrogen bond is due to specific properties of the OH group in the silanols. As we have already shown in our previous work, 21,23 silanols may have acidity constants as low as 5, substantially lower than water, in turn establishing stronger hydrogen bonds than water. The silanols have therefore a special role in stabilizing the conjugated base and therefore in favoring the deprotonated form of pyruvic acid at the interface. The solvation behavior observed for pyruvic acid at the quartz/water interface is certainly not unique, and indeed a similar mechanism for the conjugated base stabilization could be in place also for other acids at hydroxilated interfaces. Of course the propensity to localize at the interface is strongly depending on the degree of hydrophilicity and hydrophobiticity of the acid as well as that of the solid surface.

Acknowledgement This work was supported by the Deutsche Forschungsgemeinschaft (DFG) TRR146, project A4. All the calculation were performed on the supercomputer of the High Performance Computing Center (HLRS) of Stuttgart (grant 2DSFG).

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Supporting Information Available • Theory on the pKa calculation using thermodynamics integration • Simulation details • Vertical energy gaps • Radial distribution function in presence of an interface

References (1) Reijenga, J.; van Hoof, A.; van Loon, A. Development of Methods for the Determination of pKa Values. Anal. Chem. Insights 2013, 8, 53. (2) Eisenthal, K. Liquid Interfaces Probed by Second-Harmonic and Sum-Frequency Spectroscopy. Chem. Rev. 1996, 96, 1343–1360. (3) Miranda, P.; Du, Q.; Shen, Y. Interaction of water with a fatty acid Langmuir film. Chem. Phys. Lett. 1998, 286, 1–8. (4) Rao, Y.; Subir, M.; McArthur, E. A.; Turro, N. J.; Eisenthal, K. B. Organic Ions at the Air/Water Interface. Chem. Phys. Lett. 2009, 477, 241–244. (5) Tang, C. Y.; Huang, Z.; Allen, H. C. Binding of Mg2+ and Ca2+ to Palmitic Acid and Deprotonation of the COOH Headgroup Studied by Vibrational Sum Frequency Generation Spectroscopy. J. Phys. Chem. B 2010, 114, 17068–17076. (6) Zhao, X.; Ong, S.; Wang, H.; Eisenthal, K. B. New method for determination of surface pKa using second harmonic generation. Chem. Phys. Lett. 1993, 214, 203–207. (7) Wang, H.; Zhao, X.; Eisenthal, K. B. Effects of Monolayer Density and Bulk Ionic Strength on Acid-Base Equilibria at the Air/Water Interface. J. Phys. Chem. B 2000, 104, 8855–8861. 11



(8) Shamay, E. S.; Buch, V.; Parrinello, M.; Richmond, G. L. At the Water’s Edge: Nitric Acid as a Weak Acid. Journal of the American Chemical Society 2007, 129, 12910– 12911, PMID: 17915872. (9) Kido Soule, M. C.; Blower, P. G.; Richmond, G. L. Nonlinear Vibrational Spectroscopic Studies of the Adsorption and Speciation of Nitric Acid at the Vapor/Acid Solution Interface. The Journal of Physical Chemistry A 2007, 111, 3349–3357, PMID: 17419597. (10) Wang, S.; Bianco, R.; Hynes, J. T. Depth-Dependent Dissociation of Nitric Acid at an Aqueous Surface: Car-Parrinello Molecular Dynamics. The Journal of Physical Chemistry A 2009, 113, 1295–1307, PMID: 19173580. (11) Wang, S.; Bianco, R.; Hynes, J. T. Dissociation of nitric acid at an aqueous surface: Large amplitude motions in the contact ion pair to solvent-separated ion pair conversion. Phys. Chem. Chem. Phys. 2010, 12, 8241–8249. (12) Strazdaite, S.; Meister, K.; Bakker, H. J. Reduced Acid Dissociation of Amino-Acids at the Surface of Water. Journal of the American Chemical Society 2017, 139, 3716–3720, PMID: 28177623. (13) Kundu, A.; Yamaguchi, S.; Tahara, T. Evaluation of pH at Charged Lipid/Water Interfaces by Heterodyne-Detected Electronic Sum Frequency Generation. J. Phys. Chem. Lett. 2014, 5, 762–766. (14) Tang, M.; Larish, W. A.; Fang, Y.; Gankanda, A. n.; Grassian, V. H. Heterogeneous Reactions of Acetic Acid with Oxide Surfaces: Effects of Mineralogy and Relative Humidity. The Journal of Physical Chemistry A 2016, 120, 5609–5616, PMID: 27322707. (15) Fang, Y.; Tang, M.; Grassian, V. H. Competition between Displacement and Dissociation of a Strong Acid Com pared to a Weak Acid Adsorbed on Silica Particle Surfaces: The Role of Adsorbed Water. The Journal of Physical Chemistry A 2016, 120, 4016– 4024, PMID: 27220375. 12


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(16) Murdachaew, G.; Gaigeot, M.-P.; Halonen, L. r.; Gerber, R. B. First and second deprotonation of H2SO4 on wet hydroxylated (0 001) alpha-quartz. Physical Chemistry Chemical Physics 2014, 16, 22287–22298. (17) Murdachaew, G.; Gaigeot, M.-P.; Halonen, L.; G˜erber, R. B. Dissociation of HCl into Ions on Wet Hydroxylated (0001) Îś-Quartz. The Journal of Physical Chemistry Letters 2013, 4, 3500–3507. (18) Pérez de Tudela, R.; Marx, D. Acid Dissociation in HCl-Water Clusters is Temperature Dependent and Cannot be Detected Based on Dipole Moments. Phys. Rev. Lett. 2017, 119, 223001. (19) Reed Harris, A. E.; Pajunoja, A.; Cazaunau, M.; G˜ratien, A.; Pangui, E.; Monod, A.; Griffith, A., Elizabeth C. an d Virtanen; Doussin, J.-F.; Vaida, V. Multiphase Photochemistry of Pyruvic Acid under Atmospheric Conditions˙The Journal of Physical Chemistry A 2017, 121, 3327–3339, PMID: 28388049. (20) Cwiertny, D. M.; Young, M. A.; Grassian, V. H. Chemistry and Photochemistry of Mineral Dust Aerosol. Annual Review of Physical Chemistry 2008, 59, 27–51, PMID: 18393675. (21) Sulpizi, M.; Gaigeot, M.-P.; Sprik, M. The silica–water interface: how the silanols determine the surface acidity and modulate the water properties. Journal of chemical theory and computation 2012, 8, 1037–1047. (22) Leung, K.; Nielsen, I. M. B.; Criscenti, L. J. Elucidating the Bimodal Acid-Base Behavior of the Water-Silica Interface from First Principles. Journal of the American Chemical Society 2009, 131, 18358–18365, PMID: 19947602. (23) Pfeiffer-Laplaud, M.; Costa, D.; Tielens, F.; Gaigeot, M.-P.; Sulpizi, M. Bimodal Acidity at the Amorphous Silica/Water Interface. The Journal of Physical Chemistry C 2015, 119, 27354–27362. 13



(24) Sulpizi, M.; Sprik, M. Acidity constants from vertical energy gaps: density functional theory based molecular dynamics implementation. Phys. Chem. Chem. Phys. 2008, 10, 5238–5249. (25) Costanzo, F.; Sulpizi, M.; R.G., V.; Sprik, M. The oxidation of tyrosine and tryptophan studied by a molecular dynamics normal hydrogen electrode. J. Chem. Phys. 2011, 134, 244508. (26) Tazi, S.; Rotenberg, B.; Salanne, M.; Sprik, M.; Sulpizi, M. Absolute acidity of clay edge sites from ab-initio simulations. Geochimica et Cosmochimica Acta 2012, 94, 1 – 11. (27) Pfeiffer-Laplaud, M.; Gaigeot, M.-P.; Sulpizi, M. pKa at Quartz/Electrolyte Interfaces. The Journal of Physical Chemistry Letters 2016, 7, 3229–3234, PMID: 27483195. (28) Becke, A. D. Density-functional exchange-energy approximation with correct asymptotic behavior. Phys. Rev. A 1988, 38, 3098–3100. (29) Lee, C.; Yang, W.; Parr, R. G. Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density. Phys. Rev. B 1988, 37, 785–789. (30) VandeVondele, J.; Krack, M.; Mohamed, F.; Parrinello, M.; Chassaing, T.; Hutter, J. Quickstep: Fast and accurate density functional calculations using a mixed Gaussian and plane waves approach. Computer Physics Communications 2005, 167, 103 – 128. (31) Goedecker, S.; Teter, M.; Hutter, J. Separable dual-space Gaussian pseudopotentials. Phys. Rev. B 1996, 54, 1703–1710. (32) Hartwigsen, C.; Goedecker, S.; Hutter, J. Relativistic separable dual-space Gaussian pseudopotentials from H to Rn. Phys. Rev. B 1998, 58, 3641–3662.

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