Effect of Oxidation Level on the Interfacial Water at the Graphene Oxide–Water Interface: From Spectroscopic Signatures to Hydrogen-Bonding Environment

The interfacial region of the graphene oxide (GO)-water system is nonhomogenous due to the presence of two distinct domains: an oxygen-rich surface and a graphene-like region. The experimental vibrational sum-frequency generation (vSFG) spectra are distinctly different for the fully oxidized GO-water interface as compared to the reduced GO-water case. Computational investigations using ab initio molecular dynamics were performed to determine the molecular origins of the different spectroscopic features. The simulations were first validated by comparing the simulated vSFG spectra to those from the experiment, and the contributions to the spectra from different hydrogen bonding environments and interfacial water orientations were determined as a function of the oxidation level of the GO sheet. The ab initio simulations also revealed the reactive nature of the GO-water interface.


I. INTRODUCTION
Graphene oxide (GO), whether a single layer or a few layers of exfoliated sheets from graphite oxide, has recently received a lot of attention in the literature due to a range of potential applications. 1−35 GO consists of graphene sheets with oxygenated groups, and a number of studies have revealed a wide range of oxygen functional groups, such as hydroxyls and epoxides, 11 carboxylic acids, or sulfonates groups, 6,36 on these sheets as well as how these groups are arranged on the surface. 37−41 A key question that arises is how, depending on their number and partitioning, these oxygen functional groups can favor or prohibit reactions at the GO-liquid interface in aqueous media. To probe interfaces, several surface-specific techniques can be used such as environmental scanning electron microscopy (ESEM), secondary ion mass spectrometry (SIMS), Auger electron spectroscopy (AES), etc. 42−46 One method, vibrational sum-frequency generation (vSFG), 47,48 has received a lot of attention for characterizing interfaces experimentally 49−57 and in conjunction with simulations. 51,52,58−62 The synergy between vSFG experiments and molecular simulations allows for an in-depth probing of the interface, permitting a finer molecular interpretation of the underlying interfacial region. In this paper, an analysis of the graphene-oxide-water interface by ab initio molecular dynamics (AIMD) at different levels of oxidation was performed to provide insight on the effect of the different structural domains of graphene-oxide (organic, aromatic rich regions vs oxygenrich hydrophilic regions) on the interfacial water structure. Furthermore, the effect of the oxidation level of the GO sheet on the water structure was also studied. These results are put into perspective with the experimental vSFG spectra of these systems as a function of oxidation level, thereby not just confirming the accuracy of said ab-initio methods but also providing insight into the molecular origins of the spectral signatures in the experimental vSFG spectra. This paper is divided into four sections. Both the computational and experimental methods are outlined in Section II, the results are described and discussed in Section III, and the conclusions are presented in Section IV.

II. MATERIALS AND METHODS
II.a. Ab Initio MD Setup. The graphene oxide sheets in this study consist of a single layer composed of 180 carbon atoms (to have an ∼22.0 × 21.2 Å graphene sheet) and a varying number of oxygen functional groups. The GO 4/1 and GO 2/1 sheets were constructed based on the work of Sinclair et al. 41 The former consists of 24 epoxide groups and 20 hydroxyl groups for a ratio C/O of 4.09 for the former, while 50 epoxide groups and 40 hydroxyl groups were introduced for a ratio of C/O of 2.00 for the latter case. The GO/water interface was generated using the packmol software 63 by adding 265 water molecules on one side of the GO sheet generating a solvent layer having a thickness of 20 Å. With the moltemplate software, 64 parameter files for both systems were created using the OPLS-AA 65 force field for the GO sheet along with the SPC/E 66 force field for water. A 70 Å thick layer of vacuum is added in the z-direction (direction perpendicular to the interface) for both sets of systems resulting in a box of dimensions 22.0 × 21.2 × 104.0 Å. All simulations were performed using periodic boundary conditions (PBC). For the classical molecular dynamics (MD) simulations, long-range electrostatic interactions were evaluated using the particleparticle particle-mesh (PPPM) 67 method based on the Ewald summation method with a cutoff of 12.0 Å, while the Lennard-Jones interactions used a simple cutoff at 12.0 Å. All water bonds and angles were constrained using the SHAKE algorithm. 68 An initial geometry minimization was performed followed by a 500 ps equilibration run (with a time step of 0.5 fs) in the NVT ensemble (where N indicates the number of particles in the system, V indicates the system volume, and T indicates the absolute temperature of the system) with the temperature set to 300 K with a Nose-Hoover thermostat 69,70 and a time constant of 50 fs −1 . A production run was performed in the same ensemble for 1 ns with a time step of 0.5 fs. Snapshots were extracted every 200 ps, resulting in five snapshots for each system. For each snapshot, and for both systems, geometry optimization and cell relaxation were done using the CP2K 71,72 program with the L-BFGS algorithm. 73 The force evaluations were done at the density functional theory (DFT) level with the revPBE 74,75 functional and the empirical D3 76 dispersion, with a DZVP-MOLOPT-SR 77 basis set and GTH pseudopotentials. 78−80 The c cell parameter was kept fixed at 70.0 Å, giving a vacuum layer 40.0 Å thick, and PBC were applied in all directions using a periodic Poisson solver for electrostatics. For each optimized geometry, a 25 ps long NVT simulation at 300 K with a time step of 0.5 fs was then performed with the canonical sampling through a velocity rescaling (CSVR) thermostat 81 and a 100 fs −1 time constant. The position and velocities were extracted every 1 fs, and the first 5 ps of each trajectory were discarded as equilibration. The total sampling for both the GO 2/1 and GO 4/1 case was 100 ps (5 × 20 ps).
II.b. Preparation of the Graphene Oxide Samples. A large-area oligo-layered GO flake solution having a concentration of 5 mg mL −1 was purchased from NewMater Nanotechnology Co. Ltd. Transparent sapphire circular disks with flat surfaces (surface roughness <1.0 mm) were acquired from Meller Optics, Inc. These disks had an area of 20.27 cm 2 (diameter of 5.08 cm) and a thickness of 0.33 nm. To attain a conformal graphene flake layer onto the substrate, a diluted solution of GO flakes was prepared by mixing the 5 mg mL −1 graphene oxide with methanol and water with a weight ratio of 1:1740:100 (graphene oxide/methanol/water). The dilute solution was spin-coated onto the transparent sapphire substrate at 3000 rpm for 45 s. Prior to the deposition of the solution on the substrate for spin coating, 1 psi of nitrogen flow was applied to the surface of the sapphire substrate from nearly normal incidence. Two more identical samples were prepared, and these samples were treated thermally to reduce graphene oxide on the sapphire substrate. The thermal reduction of graphene oxide thin film was conducted at 300°C in a nitrogen-filled chamber for 10 min for one sample and 6 h for another sample. The successful reduction of the GO film was evident by the film color change and the vSFG results (vide supra). Figure 1 depicts the scheme to prepare thin GO/ rGO (where rGO indicates reduced graphene oxide) films on transparent sapphire substrates.
II.c. Experimental vSFG Setup. A picosecond scanning vibrational sum frequency generation spectrometer (EKSPLA), which has been described in previous works, 82,83 was used to perform the vSFG experiments. Briefly, the vSFG spectrometer is a commercial setup that uses a 532.1 nm visible beam and a tunable infrared beam overlapped spatially and temporally at the sample surface. The angle of incidence is 35°and 31°for the visible and the IR beams, respectively. The spatial resolution of the setup is ∼6 cm −1 . An SSP polarization geometry (where S, S, and P refer to the polarization of sum frequency, visible, and IR photons, respectively) was used. In all experiments, each scan was obtained with an increment of 8 cm −1 and an average over 300 laser shots per point. The energy of the visible beam is typically ∼200 μJ, and that of the IR beam is ∼180 μJ. The SFG photons were detected using a high-gain low-noise photomultiplier (Hamamatsu R585), which is integrated into the Ekspla system. The voltage of the photomultiplier tube (PMT) was set at 1400 V. The vSFG signal is normalized with respect to the visible and IR pulse energy.
The graphene oxide film grown on an alumina substrate was placed in a precleaned (thorough rinsing with detergent and a copious amount of ion-exchanged nanopure deionized water followed by drying with compressed N 2 and finally UV/ozone cleaned (Novascan Technologies) for 15 min) home-built Teflon sample cell that was designed to allow for the The Journal of Physical Chemistry B pubs.acs.org/JPCB Article introduction of an aqueous solution without moving the sample surface. Laboratory-equilibrated deionized water (pH ≈ 6) was used for the experiments. The schematic experimental geometry is shown in Scheme S1 in the Supporting Information. II.d. Surface-Specific Velocity-Velocity Correlation Function from Simulations. In this study, the surfacespecific velocity-velocity correlation function (ssVVCF) formalism proposed by Otho et al. 84 was used. The method is described in detail in ref 84, and here just a brief description of the method is presented. In the case of just the IR spectrum, the IR response function (from the fluctuation−dissipation theorem) is related to the time derivative dipole−dipole correlation function. 85 The molecular dipole moment in turn is related to the permanent dipole moment of the molecule and the transition dipole moment of the normal mode. The latter is determined by multiplying the transition dipole by the normal mode vector in the molecular frame. Finally, the molecular dipole moment is converted to the lab frame through a rotational matrix that is applied to both the permanent and transition dipole moments in the molecular frame. The O−H stretch response is the one under consideration and can be considered to be decoupled from librational motion. The latter is dominated by the dynamics of the permanent dipole moment, while the O−H stretch response is dominated by the transition dipole moment. Since the main contribution to the O−H stretch normal mode is the O−H vector, 86 the normal mode vector in the laboratory frame can be replaced by the bond vector resulting in a simplified description for the IR response to the O−H stretch that is proportional to the O−H stretch velocity autocorrelation function. A similar reasoning was applied by Otho et al. for the SFG response function (which now also includes the polarizability tensor), connecting both the IR and SFG response to essentially different velocityvelocity type correlation functions.
χ xxz (ω) is the resonant component of the second-order susceptibility (where z is the direction perpendicular to the interface) and can be written as where Q(ω) is the harmonic quantum-correction factor 87 and is given by with kT 1 β = and T is the temperature set to 300 K. ℏ is the reduced Planck's constant and k is the Boltzmann constant. The non-Condon effects were taken into account by the frequency-dependent transition dipole moment and the frequency-dependent transition polarizability (μ(ω) and α(ω), respectively) parametrized in the work of Corcelli where ω, in (3) and (4), is specifically expressed in cm −1 . Finally, χ xxz ssVVCF (ω) is given by where i and j are the ith and jth oscillators, respectively. rż ,i OH is the z component of the velocity of the ith oscillator, and r j OH ÷◊ ÷ȧ nd r j OH ÷◊ ÷ are, respectively, the velocity vector and the displacement vector of the jth oscillator. r ij is the distance between the ith center of mass and the jth center of mass of the respective oscillators, and g(r) is a switching function: This switching function controls the cross-correlation terms between two oscillators: an r ij cutoff at 2.0 Å ensures only intramolecular coupling terms. The time correlation was evaluated for a t max of 10 ps. A smoothing Hann window function, f(t), was applied to the Fourier transform of the time correlation function.
The parameter τ was set to 0.50 ps. Additional details including other switching functions that were used are given in the Supporting Information.

III. RESULTS AND DISCUSSION
III.a. Average Water Density Fluctuations from the Instantaneous Water Interface. To characterize the interface between the GO sheet and the water, the Willard-Chandler instantaneous interface 90 was employed, as it provides a robust definition of the interfacial region. The ratio of the water density to the bulk density of water as a function of the distance to the instantaneous water interface is reported in Figure 2. Well-defined water layers, based on the minima in the density distributions in Figure 2, can be seen. This type of layering has also been seen for water next to other solid interfaces in studies performed by Gaigeot et al. 91,92 In the GO 4/1 case three distinct layers of water, namely, L1, L2, and L3, with increasing distance from the instantaneous interface are seen. A fourth layer, L0, is only present in the case of GO 2/1 , in the negative distance region (on the other side of the instantaneous interface) and corresponds to a small number of waters "trapped" on the GO sheet by the oxygen functional groups. Between the GO 2/1 and GO 4/1 , the major difference for the density resides in the L1 layer, which is more structured for GO 4/1 due to a sharper peak, as well as the presence of an L0 layer solely in the case of GO 2/1 .
III.b. Hydrogen Bond Analysis of the Interfacial Waters. The hydrogen bond network of the waters was analyzed for both cases. A naming scheme for the different hydrogen bonding classes of water based on the work of Skinner et al. 93 was used here. A water is defined as residing in a hydrogen-bonding class N a , where N is the total number of hydrogen bonds (see Scheme S2 for definition of a hydrogen bond) a water molecule is involved in, and the subscript a refers to the number of hydrogen bonds involving the H atoms of the water under consideration: a is S for a single donor water, D is for a double donor water, and T and Q are for triple and quadruple donor waters, respectively. Water−Water hydrogen bonds are considered as well as water-oxygenbearing groups hydrogen bonds. Figure 3 shows the percentage of hydrogen-bonding classes for all water within the L0 ( Figure  3a) and L1 (Figure 3b) layers for GO 2/1 and the L1 layer for GO 4/1 . The composition of the L0 layer is very different from Although double donors are the most common in both L0 and L1, the waters in L0 tend to accept fewer hydrogen bonds. This point is reinforced by the second major class present in L0, namely, 4 T , which like 3 D has only one acceptor hydrogen bond (the same goes for 2 S and 5 Q ). This can be explained by a specific orientation of the water molecule in this L0 layer, where a water oxygen is less readily accessible to other waters (or hydroxyl groups) to accept hydrogen bonds, but its hydrogens are available to donate hydrogen, a point that will be discussed further. Additionally, in this layer ∼92% of the water molecules present are engaged in a hydrogen bond with an oxygen-bearing group of the GO: this is due to a higher number of oxygenated defects and due to the "trapped" position of the water. Approximately 44% of these waters are both donating and accepting from an oxygen-bearing group.
For the L1 layer, compared to GO 4/1 , GO 2/1 tends to have GO 2/1 with fewer 3 D (−8.6%) and 4 D (−2.5%) waters compared to GO 4/1 , while having a greater number of 3 S (+2.9%) waters. Additionally, GO 2/1 has a larger percentage of waters with, overall, four or a higher number of total hydrogen bonds that are double or triple the donor (4 T , +0.8%, 5 D , +1.8%, and 5 T , +2.4%). Additionally, overall one can see an increase of single donors (+3.3%) and triple donors (+4.0%) at the expense of the double donors (−9.0%). Between GO 4/1 and GO 2/1 there is an increase in the number of waters engaged in hydrogen bonds (donating or accepting) with an oxygen-bearing group (+6.4%), the most increase comes from the waters accepting at least one hydrogen bond from an oxygen-bearing group (+9.8%) or both accepting and donating one (+6.0%). Compared to the L0 layer, in the L1 layer for GO 2/1 , only 8.3% of the waters are both accepting and donating to an oxygen-bearing group.
To summarize, the L1 layer, for both systems, has 4 D as the major class, with the second one being 3 D . GO 2/1 sees a small decrease in 4 D and a bigger one in 3 D , but its number of highly hydrogen-bonded waters (4 T , 5 D , 5 T ) is greater than GO 4/1 , due to an increase of waters engaged in hydrogen bonds (donating or accepting) with an oxygen-bearing group (+6.4%).
III.c. Interfacial Water Orientation. To have a better understanding of the orientation of the water molecules around the interface between the graphene oxide sheet and water, the orientation of the water molecules was examined. Figure 4 shows the joint distribution of the θ DW /θ HH angles for water molecules in layer L1 for GO 2/1 (Figure 4a) and GO 4/1 (Figure 4b) and in layer L0 for GO 2/1 (Figure 4c), as well as the definition of the two relevant angles chosen, θ DW ( Figure  4d) and θ HH (Figure 4e). In the Supporting Information, the distribution for each trajectory is given, and the results are shown to be consistent with the overall distribution ( Figures  S1 and S2).
For the GO 2/1 L1 layer, two main orientations are present: one with values ranging from 50°to 55°and from 135°to 140°for θ DW and θ HH , respectively, corresponding to an orientation shown in Figure 5a, with one hydrogen pointing away from the instantaneous interface. The second orientation ranges from 120°to 125°and from 140°to 145°for θ DW and For the GO 4/1 L1 layer, the distribution shows a major peak in the region from 50°to 55°for θ DW and from 140 to 145°for θ HH (a representative structure is shown in Figure 5a). A new minor peak is present around values ranging from 90°to 95°f or both θ DW and θ HH (a representative structure is shown in Figure 5c), where both OH bonds are almost parallel to the instantaneous interface, slightly pointing toward it. The region with values from 145°to 150°and from 115°to 120°for θ DW and θ HH , respectively, is significantly diminished compared to those for GO 2/1 . Finally, GO 2/1 presents the same number of OH bonds pointing away and toward the interface, whereas, in GO 4/1 , most of them are pointing away from the interface or are almost parallel to it.
For the GO 2/1 L0 layer, the joint distribution is shown in Figure 4c, and only one orientation is seen, with θ DW ranging from 170°to 175°and a θ HH value from 90°to 95°( Figure  5d). This configuration has both hydrogens pointing toward the instantaneous surface, which combined with the fact that in L0 water molecules are situated between the graphene sheet and the instantaneous interface, makes these hydrogens effectively pointing away from the graphene sheet.
III.d. vSFG Spectra of the Graphene Oxide-Water Interface. As mentioned in the Introduction, the vSFG spectroscopic technique is highly surface-specific due to its dependence on χ (2) , the second-order nonlinear susceptibility, and is thus zero in a centrosymmetric environment. 47,48 The experimental intensity (SSP polarization) I ssp ∝ |χ xxz (2) | 2 , where χ (2) = χ (2),R + χ (2),NR , with the two terms being the resonant (χ (2),R ) and nonresonant (χ (2),NR ) parts, respectively. At a fixed visible frequency, the nonresonant term is constant. 94 However, it should be pointed out that there could be a small χ (3) contribution to the experimental intensity, 95,96 which was neglected in this work and will be examined in future work.
In Figure 6a, the experimental spectra of the water-GOsapphire interface obtained by SSP polarization are reported. For the unreduced system, there is a major peak in the highfrequency region at 3700 cm −1 and a very broad intensity within the 3200−3500 cm −1 range with a minor peak at 3375 cm −1 . In the literature, this peak around 3700 cm −1 is typically attributed to dangling OH bonds pointing toward the air− water interface 50,53,59,97−99 or the graphene−water interface, 100 whereas the range between 3200 and 3500 cm −1 is typically attributed to hydrogen-bonded OH bonds (from water and hydroxyl groups) whether pointing away from or toward the interface. 50,53,59,97−99,101−103 After 10 min of reduction, one can see the disappearance of the 3700 cm −1 peak, a growth of a peak around 3500 cm −1 , and a specific peak growing at 2900 cm −1 , which can be attributed to methine groups resulting from the reduction of the graphene oxide. 104 After 6 h of reduction, the system presents no major difference with the system after 10 min of reduction. One would expect that the more oxidized graphene oxide would present fewer highfrequency intensities at the interface due to the presence of more oxygen-bearing groups available for hydrogen bonding, resulting in a lower number of weak or free OH oscillators: this is not the case, thereby underlining the need for molecular simulations of these two systems to obtain insight on the local structure of these interfaces.
A simulated spectrum can be obtained via the surface specific velocity-velocity correlation function formalism proposed by Otho et al. 84 from molecular dynamics simulations. Here the resonant component of the secondorder susceptibility was calculated. This method ensures a fast convergence, thus preventing the need for very long sampling trajectories. Figure 6b shows the simulated |χ xxz (2),R | 2 spectra,  where only the OH oscillators from the water (no contribution from GO hydroxyl groups) within 11 Å of the instantaneous interface (to avoid the other interface, namely, the air−water present in the simulation) are taken into account. The simulated spectra with confidence intervals are given in the Supporting Information ( Figure S3). The spectrum from the air−water interface can be found in Figure S4 in the Supporting Information and reproduces the experimental spectrum of air−water interface from the literature, further validating the functional used in the AIMD simulations. These simulated systems, compared to the experimental one, possess no sapphire support for the graphene oxide sheet, and any interpenetrated waters between the substrate and GO are absent. 100 For GO 2/1 , the peaks are slightly red-shifted (100 cm −1 ) 105 compared to the experimental results, with a major peak at 3600 cm −1 and a neighboring shoulder at 3300 cm −1 . Most of the low-frequency range (lower than 3200 cm −1 ) is absent in the simulated vSFG spectra from GO 2/1 . A possibility is that this region is different due to the noninclusion of any OH bonds from any hydroxyl groups, which can form hydrogen bonds (and thus appear in this low-frequency range) with other nearby oxygen-bearing groups (alkoxides, epoxides, hydroxyls) as well as water, as seen in previous experimental 106 and theoretical 107,108 vSFG studies on mineral-water interfaces. Nevertheless, the dominant features present in the experimental vSFG spectra are well-represented.
For the GO 4/1 case, the |χ xxz (2),R | 2 shows the characteristic loss of the high-frequency dominant peak at 3600 cm −1 , consistent with the experimentally reduced GO, and gains three peaks at 3450, 3300, and 3150 cm −1 and a broad region below 3200 cm −1 , which means that, for GO 4/1 , OH bonds from water also account for this region, suggesting a strong hydrogen-bonding environment not only due to hydroxyl groups. Once again, the simulated spectrum for GO 4/1 qualitatively reproduces the main features of the experimental vSFG spectrum. To get further insight into the interface, the resonant imaginary component, Im χ xxz (2) , which is equal to Im χ xxz (2) , since typically the nonresonant part is real, 109 was examined. The sign of the imaginary part reflects the direction of the transition dipole (i.e., OH bond) with respect to the interface: 109 a positive sign for Im χ xxz (2) corresponds to a bond with the H atom pointing upward (away from the interface), and a negative sign corresponds to an OH bond with H pointing downward (toward the interface). Figure 7a,b shows the imaginary component Im χ xxz (2) for the GO 2/1 and GO 4/1 interfaces, and the component for each layer is reported, corresponding to the depth from the interface, and as expected the L1 layer, in both systems, is the major contributing component to Im χ xxz (2) . For GO 2/1 , the spectrum of the L0 layer has a negative broad region from ∼3100 to ∼3600 cm −1 . This is in keeping with the angle distribution in Figure 4c, where all the water molecules The Journal of Physical Chemistry B pubs.acs.org/JPCB Article are pointing away from the graphene-oxide sheet toward the instantaneous surface/interface. This broad negative range is consistent with Figure 3a, where the majority (80%) of water molecules are double (or more) donors, presenting very few "free" or weakly hydrogen-bonded OH bonds and are oriented away from the interface. When looking at the L1 layer, GO 2/1 shows a negative region from ∼3200 to ∼3500 cm −1 and a sharper positive region at ∼3600 cm −1 , which are in keeping with the angle distribution in Figure 4a, where the water presents both orientations: one with the water oriented with the H of the OH bond pointing away from the instantaneous interface (Figure 5a) thereby contributing to the negative region in the imaginary spectrum and another one with, this time, an OH bond with the H pointing toward (Figure 5b) the GO sheet and the instantaneous interface (contributing to the positive peak at higher frequencies).
For the L1 layer of GO 4/1 (Figure 4b), Im χ xxz (2) presents a major broad negative peak centered at ∼3400 cm −1 , a small positive peak at ∼3700 cm −1 , and a small positive component in the low-frequency region (less than 3000 cm −1 ). This is consistent with the angle distribution with most waters having an OH pointing away from the surface (Figure 4b and Figure  5a).
For further insight, Im χ xxz (2) is reported in Figure 7c,d for each major water hydrogen-bond class in the L1 layer for GO 2/1 and GO 4/1 , respectively. The 4 D class of water, which is the major class for both systems, gives rise to markedly different spectra in the two cases. Additionally, the other two hydrogen-bonding classes that contribute to the spectrum of GO 2/1 are 3 D and 5 T , whereas for the GO 4/1 case the only other major contribution apart from 4 D waters is from the 3 D waters.
The θ DW /θ HH joint distribution for the 4 D waters in the L1 layer for the two GO interfaces ( Figure S5a,b) clearly shows a broad distribution for the GO 2/1 case, while for the GO 4/1 case the waters are predominantly such that one OH bond points away from the interface with the other parallel to the interface ( Figure 5a) with a minor peak with the waters almost parallel to the interface but pointing slightly toward the interface. This is in keeping with the Im χ xxz (2) spectra for the 4 D waters in the L1 layer, which has large positive and negative contributions for the GO 2/1 case, whereas the positive contribution is considerably dampened in the GO 4/1 case. The 3 D waters also show a broad distribution ( Figure S5c,d) for the GO 2/1 case, whereas for the GO 4/1 case the waters are oriented with one OH pointing away from the interface and the other parallel to the interface or a minor peak with waters almost parallel but pointing slightly away from the interface. This again reflects the features of the Im χ xxz (2) spectra for the two interfaces with a positive and negative region for the GO 2/1 case but only a negative region for the GO 4/1 case. The 5 T case ( Figure S5e,f) has waters for both interfaces essentially oriented with one OH pointing toward the interface and the other parallel to the interface corresponding to an essentially strong positive feature in the spectrum.
Closer examination of the hydrogen bonds of the 4 D waters that are within the first maxima of the L1 region (distance from the instantaneous surface is less than or equal to the first peak, 1.75 Å for GO 2/1 , 1.25 Å for GO 4/1 ) show some interesting features (see the Supporting Information for the definition of the r-α pair). For the OH D donor vectors pointing toward the interface (θ OH ≥ 110°), the joint distribution of the hydrogen-bond distance (r) and hydrogen-bond angles (α) (Figure 8a) show significant deviation from the bulk water case ( Figure S6) for GO 2/1 with larger angles and longer distances, suggesting that these hydrogen bonds are much weaker than the case of bulk water and hence are much less red-shifted. This effect is less pronounced for the GO 4/1 case (Figure 8b), and coupled with the fact that these orientations are far fewer in the GO 4/1 case, the positive feature at high frequencies is considerably dampened.
From this decomposition analysis, one can see that, in addition to the differences in the distribution of the hydrogenbonding classes of water, the interfacial waters at the GO 2/1and GO 4/1 -water interfaces are oriented differently depending on the oxidation level of the graphene-oxide sheet resulting in very different vSFG spectra. The combined analysis of the orientation and hydrogen-bonding environment gives substantial insight into the type of interaction with water and the graphene-oxide surface. The 5 T class, increasing only by 2.4% between GO 4/1 and GO 2/1 and accounting for less than 10%, becomes the second most-dominant feature of the spectra for GO 2/1 , and the 3 D class decreasing from 24.9% to 16.3% in GO 2/1 , still being the second most-populous class, is not a dominant feature any more in the vSFG spectra. The 4 D class, varying from 44.5% to 42.0%, drastically changes its contribution to the vSFG spectra between GO 4/1 and GO 2/1 .
III.e. Reactivity of the GO-Water Interface. The AIMD simulations reveal several spontaneous epoxide (Figure 9a) opening events forming a charged pair of an alkoxide ion and a  Figure S7 in the Supporting Information shows that the hydrogen bonds formed by water with the alkoxide are very strong (unlike the other oxygenated groups) leading to red-shifts in the OH spectra. The alkoxide ions can abstract a proton from a neighboring hydroxyl group forming a hydroxyl group and a new alkoxide, resulting in the shuttling of the alkoxide along the sheet. Furthermore, reactive events in which the alkoxide extracts a proton from water forming a hydroxyl group are also seen ( Figure 9c). This could also be the origin of the positive red-shifted region in the water spectrum of GO 4/1 , since the OH group of the reactive water has a partial hydroxyl group character. Interestingly, the decomposition of the imaginary spectrum of water O-Hs in the L1 layer that participate or do not participate in hydrogen bonds with the GO surface shows that the O−H waters that are involved in hydrogen bonds (specifically donor hydrogen bonds) give rise to this redshifted feature (see Figures S8 and S9) in GO 4/1 . The hydroxide ion that is formed can then attack the carbocation forming another hydroxyl group (Figure 9d). These ringopening events that create alkoxide species result in carbocations that are stabilized by the graphene-rich regions that are present in GO 4/1 . Hence it is unsurprising that, for GO 4/1 , the ratio of alkoxide to oxygen-bearing groups is 0.066, and for GO 2/1 , it is only 0.030, and hence reactive events are more likely in the GO 4/1 case due to the two separate domains. Future studies will further examine these reactive events.

IV. CONCLUSION
This paper demonstrates that the orientation and the hydrogen-bonding class of water molecules plays a major role in the vSFG spectra and sheds light on the interactions specific to this interface. The ab initio MD simulations are in good agreement with the experiments, highlighting the fact that the DFT method used here is adequate for this system and details how the water molecules are adapting to the different levels of oxidation of the graphene-oxide sheet. It also provides insight into the interpretation of experimental spectra at a molecular level. A highlight of this work is the fact that this surface is reactive, with epoxide opening and alkoxide shuttling as well as proton abstraction events from interfacial waters, which will be the focus of future studies. All authors have given approval to the final version of the manuscript.

Notes
The authors declare no competing financial interest.