Water Orientation at the Calcite-Water Interface

Mineral-water interfaces play an important role in many natural as well as technological fields. Fundamental properties of these interfaces are governed by the presence of the interfacial water and its specific structure at the surface. Calcite is particularly interesting as a dominant rock-forming mineral in the earth’s crust. Here, we combine atomic force microscopy, sum-frequency generation spectroscopy, and molecular dynamics simulations to determine the position and orientation of the water molecules in the hydration layers of the calcite surface with high resolution. While atomic force microscopy provides detailed information about the position of the water molecules at the interface, sum-frequency generation spectroscopy can deduce the orientation of the water molecules. Comparison of the calcite-water interface to the interfaces of magnesite-water, magnesite-ethanol, and calcite-ethanol reveals a comprehensive picture with opposite water orientations in the first and second layer of the interface, which is corroborated by the molecular dynamics simulations.


Molecular dynamics simulations
e mineral slabs in ethanol as well as the simulation parameters, such as equilibration times and force elds, are the same as those in reference 6. Additionally, we performed molecular dynamics of calcite and magnesite in water. For those simulations, we added 1000 water molecules to a simulation box with either calcite or magnesite. As in the other simulations, the box size was increased in order to accommodate the liquid molecules. We used the exible water model SPC/Fw. (7) e simulations were performed with LAMMPS (8), using the velocity Verlet algorithm (9) as the integrator. Electrostatics were calculated with the particle-particle-particle-mesh (P3M) method. (10) e simulations were performed at 300 K with Nosé-Hoover thermostats (11)(12)(13) with a damping factor of 0.1 ps. Nosé-Hoover barostats (11) were used only in one stage of the equilibration, in the direction perpendicular to the surface, at 1 atm and with a damping factor of 1 ps. We used a timestep of 1 fs for the simulations.
Hydrogen bond and dipole orientation analysis were done with the MDAnalysis (14) so ware. e criteria utilized to identify hydrogen bonds were: a maximum distance of 0.3 nm between water oxygen and carbonate oxygen (donor and acceptor atoms respectively) and a donor-hydrogenacceptor angle of 150 degrees. e same criteria were used in the ethanol simulations, where the donor was the oxygen from the hydroxy group. e analyses were conducted in the production run of 10 ns a er the equilibration.

Sum frequency generation spectroscopy
For the SFG spectroscopy the setup described in reference (15) was used. e angle of the incoming visible and infrared light was 56°and 40°with the surface normal, respectively. (15) As samples we used a polished single-crystal magnesite window (square shape, 12x12 mm, thickness 1.5 mm) from SurfaceNet GmbH and a polished single-crystal calcite window (circular shape, diameter 25 mm, thickness 2 mm) from Korth Kristalle GmbH. For the SFG experiments the samples have to be polished as otherwise the light will sca er. erefore, unfortunately, we could S 2 not use cleaved substrates which is the more common preparation method for these materials.
Both samples are uniaxially birefringent and have been cut such that the (10.4) plane is exposed For calcite-water interfaces, the acquisition time was typically chosen to be one hour (3600 s). All other sample systems were measured with shorter acquisition time in the order of minutes.
All spectra presented in this manuscript are background-corrected SFG intensity spectra. All spectra are normalized with respect to the acquisition time. In most cases, an additional normalization has been performed using a reference spectrum obtained from the mineral-gold interface of a goldcoated magnesite and a gold-coated calcite sample, respectively.
While the calcite sample was optically clear, the magnesite sample had visible cracks and optical impurities (due to the fact that it is a natural sample, as opposed to the synthetic calcite). erefore, the absolute intensity of the magnesite spectra varied greately (by approximately a factor in the order of 5, depending on where the visible and infrared light travelled through the crystal).

Crystal orientation in SFG experiments
Both calcite and magnesite are minerals with a symmetry described by the space group R3c. (17) Both minerals are uniaxially birefringent. e optical axis is the c-axis, which is oriented perpendicular to the plane spanned by the oxygen atoms of the carbonate groups. (16,17)  Incoming light perpendicular to the optical axis First, we discuss the case used in the experiment: e incoming light propagates in a direction perpendicular to the optical axis. If the incoming light is s-polarized, the electric eld vector is perpendicular to the optical axis. e light travels through the mineral according to the principal ordinary refractive index¯o: If the incoming light is p-polarized, the polarization is approximately parallel to the optical axis of calcite and magnesite. In this case, the light travels through the mineral according to a refractive S 5 index that depends on the angle between the incident ray and the optical axis according to 1 where¯e is the principal extraordinary refractive index.
In the experiments, the crystals were mounted so that the angle between incoming light is approximately perpendicular to the optical axis ( ≈ 90°), with the optical axis inside the plane of incidence. For = 90°, p-polarized incoming light travels through the mineral according to¯e.
In the experiments, the displacement of the delay stage Δ = Δ /2 is adjusted: For calcite a delay di erence of 0.215 mm and for magnesite a delay di erence of 0.160 mm was obtained when switching the polarization of the visible beam from P to S (i.e., switching from PPP to SSP). e small discrepancy with respect to the calculated values might arise from an additional delay introduced by the polarizer. Should the infrared and visible light be focused on the mineralair boundary (i.e. the upper boundary), no change in delay would be expected when switching from SSP to PPP.
Incoming light parallel to the optical axis For illustrative purposes, let us assume the crystals were mounted so that the angle between the incoming light and the optical axis is approximately zero (this is not the orientation used in the experiments). If the incoming light is s-polarized, the polarization is perpendicular to the optical axis. If the incoming light is p-polarized, the polarization is also perpendicular to the optical axis.
In both cases, the light travels through the mineral according to the " ordinary" refractive index o .
Importantly, the speed of light inside the medium is equal for s-polarized and p-polarized light. For a mineral orientation rotated by 180°, this behavior was con rmed: no delay change was necessary when switching from PPP to SSP.
where it was assumed that the interfacial refractive index is given by the refractive index of the second medium, i.e. water or ethanol. As the mineral surfaces are not isotropic, measurements using SSP polarization combination are sensitive to the and elements. Here, we assume that the in uence of the anisotropy is small and may not even be projected on the solvent molecules. us, for simplicity we consider here in the discussion only the component. Under this assumption, the SFG intensity for the SSP polarization combination is proportional to  index of refraction for a wavelength larger than 2170 nm has been found in literature. erefore, a value of for a wavelength of 2170 nm is used for the IR wavelength of 3333 nm. is assumption is corroborated by an index of refraction that is insensitive to the wavelength in the region of e results for the proportionality factor ssp is presented below for the mineral-liquid interfaces presented here, as well as for the mineral-gold interfaces used for normalization. Importantly, the order of magnitude is similar for all cases.

Peak fi ing
We ed a simpli ed model for the complex second-order susceptibility (2) to our experimental intensity data using the following expression: (24) S 9 is model includes a wavenumber-independent non-resonant contribution 0 0 and two resonant (Lorentzian) peaks centered around the wavenumbers 1 and 2 with a full width at half maximum of 2Γ 1 and 2Γ 2 in the intensity spectrum, respectively.
In the resulting t for the magnesite-ethanol interface (Fig. S 3), the wavenumbers are 3220 cm −1 and 3420 cm −1 . e phase shi of the ed non-resonant signal is -53°.
Supporting Figure  To exclude that the absence of the signal for pure water in contact with calcite is due to interference e ects as explained in Ref. 25, we have performed an SFG experiment with 1 mM NaCl solution.
Clearly, Figure S 4 shows that also at 1 mM NaCl solution the signal is still absent. As such, we conclude that the absence of the signal for pure water is not caused by interference e ects.

Magnesite
Additional SFG spectra taken at the magnesite-water interface at di erent concentrations of sodium chloride are shown in Figure S 5.