Article pubs.acs.org/JPCC
Simulated Structure and Nonlinear Vibrational Spectra of Water Next to Hydrophobic and Hydrophilic Solid Surfaces Sandra Roy and Dennis K. Hore* Department of Chemistry, University of Victoria, Victoria, British Columbia, V8W 3V6, Canada S Supporting Information *
ABSTRACT: Molecular dynamics simulations have been used to study the structure of water molecules adjacent to solid hydrophobic and hydrophilic surfaces. The hydrophobic surfaces resemble self-assembled monolayers with methyl termination, whereas the hydrophilic surfaces are terminated with hydroxyl groups. The resulting water structure is characterized by its density profile, order parameters, and molecular tilt-twist distribution as a function of distance from the surface. In both cases, results are compared to those obtained in bulk water and also to the vapor− water interface. To make a deeper connection to experimental studies, we have applied a frequency-domain approach to calculate the nonlinear vibrational spectra of the O−H stretching response. We have observed that, despite the sharp atomic discontinuity imposed by the surface, water next to a hydrophobic surface is similar in structure and spectral response to what is observed for the more diffuse vapor−water interface. At the hydrophilic surface, water ordering persists for a greater distance from the surface, and therefore the spectral response accumulates over a greater depth. In the strongly hydrogen bonded side of the spectrum, this is seen as an increased nonlinear susceptibility. However, in the energy region of the uncoupled O−H oscillators we demonstrate that the low experimental signal is likely not due to an absence of those species but instead a net cancellation of the microscopic response due to opposing water orientations over a distance well within the experimental coherence length.
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INTRODUCTION The structure of water adjacent to solid surfaces is of fundamental importance to a wide range of fields as diverse as catalysis,1,2 chemical separations,3−5 and the biocompatibility of implant materials.6−9 In each of these application areas, surface-adsorbed water plays a central role in selectively sequestering some molecules to the surface while inhibiting the adsorption of others. Once molecules in solution have adsorbed to the solid surface, interfacial water plays a further role in governing the conformation and orientation of the adsorbed state. Yet, despite the recognized importance of water at the solid−aqueous interface, these water molecules have received little attention compared with water and solutes in the bulk solution phase. A large part of the disparity has resulted from the difficulty in probing interfacial water species with sufficient specificity. For example, grazing incidence techniques have penetration depths on the order of micrometers. Absorption-based techniques employing evanescent waves (such as ATR-IR spectroscopy10,11) probe a depth of hundreds of nanometers to a few micrometers depending on the wavelength of the probe light. These length-scales are orders of magnitude larger than the depth of the interface as determined by molecular simulations. In fact, prior to the last two decades, computer simulation was one of the only methods that could comment on structural aspects of adsorbed water layers in the presence of bulk water. Recently, however, nonlinear optical spectroscopy has made a significant mark in this field. Under the electric dipole approximation, techniques based on even orders of the susceptibility χ(n) will not generate a response from molecules that are arranged in centrosym© 2012 American Chemical Society
metric environments. As an example, second harmonic generation (SHG) relies on χ(2) ≠ 0, and therefore only those molecules with a net polarity to their orientation can participate in the SHG process.12−14 The nondegenerate version of this experiment, sum-frequency generation (SFG) spectroscopy, is particularly attractive for studying interfacial water species as it enables one of the pump lasers to be in the mid-IR, and tuned over the O−H stretching frequencies from 2800 to 3800 cm−1.15,16 This permits interfacial water molecules to be further classified according to their hydrogen bonding environment, as increasing coordination produces a greater red shift in the spectra. There have been many SFG studies of neat water at solid surfaces including those of water adjacent to mineral,17−25 metal,26,27 self-assembled monolayer,28,29 and polymer30−33 surfaces. Some of this work has been summarized in review articles.6,34−37 Recently, phaseresolved SFG experiments have been able to produce real and imaginary spectra of χ(2) over IR energies of interest.38−43 Details of the complex spectra have been well-studied, particularly for the water−vapor interface.44−47 A few phasedresolved studies of water next to solid surfaces have also been reported.24,48 Such studies have numerous benefits, such as more clearly identifying resonant features in the imaginary χ(2) spectrum, nonresonant background-free imaginary χ(2), and more discerning features in the otherwise broad O−H stretching frequency region. Another advantage is that, in a Received: June 28, 2012 Revised: October 3, 2012 Published: October 19, 2012 22867
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readily achieved in experiments. We then compare our results obtained at both solid surfaces with those from experimental studies.
phase-resolved SFG experiment, the real and imaginary component of a particular element of χ(2) is related to the absolute orientation of the water molecule, thereby revealing whether the water oxygen atom or hydrogen atoms are directed toward the interface. Despite these recent advancements, it remains challenging to relate the experimental observables to structural features of the interfacial water molecules. Vibrational SFG spectroscopy offers a unique combination of sensitivity and specificity in this regard, but it is difficult to gain structural insight from spectra alone. For this reason, significant attention has been paid to interfacial water over the past several decades, by ab initio techniques,49,50 molecular dynamics,51−60 and Monte Carlo simulations.61−66 As techniques for modeling interfacial water continue to develop, it becomes especially interesting to compare the results to those of SFG spectroscopy in whichever manner permits. For example, the degree of hydrogen bonding as calculated from the simulation snapshots may be compared with the experimental frequency distribution of O−H vibrations; the order parameters calculated from the Cartesian coordinates may be compared with the intensity of the experimental spectral features. Over the past decade, however, it has been possible to generate model SFG spectra from the simulations, thereby providing a direct link between structure and experimental observables. The first such technique was described in 2000 by Morita and Hynes,67 and has since been applied to a variety of vapor and liquid phases adjacent to water.68−73 In their energy representation of the SFG spectrum, the instantaneous forces on each atom were used as an indicator of the condensed-phase O−H frequency red shift from the vacuum value, and also as a measure of the perturbation of the molecule’s transition dipole moment. In 2002, Morita and Hynes introduced a different procedure for calculating the SFG spectrum, one based on a time-domain treatment.74 In analogy with bulk IR absorption spectra calculated from the Fourier transformation of the dipole autocorrelation, here the SFG spectrum arises from the transform of the polarizability-dipole moment correlation. This method is generally favored for two reasons. It does not require a priori knowledge of the vibrational dephasing time (reciprocal width of the homogeneous line width in a Lorentzian representation of an O−H oscillator). Also, anharmonic contributions may readily be included by modification of the force field. This development has been improved by Morita and others in recent years.75−81 Skinner’s group has used molecular simulations to assign spectral features based on the hydrogen-bonding character of individual water molecules.47,82 All of these methods for generating SFG spectra have been rigorously compared to experimental spectra of the vapor−water interface74,75,77 including isotopic dilution experiments.44,71,83 In this work, we use molecular dynamics simulations to study the structure of water adjacent to a solid hydrophobic and hydrophilic surface, and compare our results to those obtained at the more diffuse water−vapor interface and in the bulk water phase. We then apply Morita’s frequency-domain approach to calculate SFG spectra for the water response at these interfaces. Because the frequency-domain approach arrives at water properties through coupling the two constituent O−H oscillator, this provides an opportunity to comment on the nature of the water molecule through the coupling constants. All of our analyses are performed as a function of distance from the interface, thereby performing a depth-profiling that is not
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BACKGROUND We now describe details of the MD simulations, including our method of evaluating the water contact angles, calculation of the order parameters used to access the degree to which specific regions from the surface are structured, calculation of the second-order susceptibility tensor elements and their variation with the IR probe frequency in an SFG experiment. Simulation Details. Surfaces with different hydrophilicity and hydrophobicity behavior have been created. The solid surface was to mimic organic self-assembled monolayers (SAM). The solid substrate consisted of straight chains of OPLS/AA methylene united atoms assembled in a hexagonal fashion, with lattice constants a = 4.38 Å and c = 1.60 Å as in ref 61. In the case of the hydrophobic surfaces (12 centers spanning 17.6 Å), the terminal atom was an OPLS/AA methyl united atom. For the hydrophilic surfaces, hydroxyl termination was added to the 10-atom chains resulting in an overall length of 18.2 Å. The OH groups were oriented 71.5° from the surface normal and with a randomized azimuth about the normal. A previous Monte Carlo study by Janeček et al.61 investigated the effect of the azimuthal angle of surface OH groups on the hydrophobicity of the surface and determined that randomly distributed frozen OH groups resulted in the same water contact angle as freely rotating OH groups. For the sake of cheaper computation, we have therefore fixed the azimuth of the surface OH groups after their initial randomly generated orientation. We have thereby studied three different interfaces with water: water vapor, solid substrate with no and full hydroxyl coverage. The simulation box dimension was 39.45 × 37.96 × 100 Å3. The substrate was placed in contact with 1980 SPC/E water molecules. These waters initially occupied ∼40 Å along the z axis, so enough void (ca. 40 Å) was available at the top of the simulation box to allow a vapor−water interface to equilibrate. This avoided the need for pressure coupling, both at the vapor−water and solid−water interface. This was an important consideration since pressure coupling would consider all water molecules in the system and may have perturbed the surface water structure that we wish to observe. Considerable attention has been paid to the choice of water model employed for interfacial studies and the subsequent generation of SFG spectra. Detailed investigations may be found in the literature using SPC,74,84 SPC/E,67 TIP4P,82 POL3,68 E3B,82 CRK,81 and PD85 models. Reproducing experimental imaginary χ(2) spectra (more details below) at IR energies below 3250 cm−1 remains a current challenge.86 We chose SPC/E because it provided reasonable agreement with experimental isotopic dilution studies in the high-frequency region of the Im[χ(2)] spectra. D2O/HOD/H2O data reveal a strong shoulder on the red side of the uncoupled O−H vibration.87 A comparison of spectra generated from SPC/E, TIP4P, and E3B water models shows that SPC/E captures this feature the best.82 However, as a result of the inability of SPC/ E to produce Im[χ(2)] > 0 in the 3000 cm−1 region, we have restricted our discussion to IR energies in the range 3300−3800 cm−1. More details and comparison with experimental data will be provided in the Discussion. Temperature was kept at 300 K with the help of Berendsen temperature coupling. Simulations were carried out with a 3D periodic boundary condition and the surface atoms were kept fixed in space. Electrostatic 22868
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interactions were handled by particle mesh Ewald with a realspace equivalent cutoff of 12 Å; van der Waals interactions were cutoff at 12 Å. Minimization was followed by a 1 ns equilibration step. MD simulations were carried out for 10 ns while sampling atomistic forces and positions each 50 fs. Order Parameters. Order parameters are useful as a quantifiable means to assess the degree to which water molecules are oriented in specific regions of the interface. We define the molecular frame axes as follows: c is along the dipole moment, a is orthogonal to c in the molecular plane, and b is orthogonal to the molecular plane. The Euler angles θ, ψ, and ϕ, defining the orientation of the water molecule with respect to the surface, are defined as follows. We start with the molecular axes c, a, and b aligned with the space axes z, y, and x, respectively. We then perform a rotation of the molecule by an angle θ along the x axis, followed by a rotation of ψ around the molecular c axis and, finally, a rotation of ϕ around the z axis (part b of Figure 1).
Table 1. Limiting Cases for the Order Parameters Defined in Eq 1 and Eq 2
1 ⟨3cos2 θ − 1⟩ 2
1 ⟨5cos3 θ − 3cos θ ⟩ 2 and a single twist order parameter S3θ =
Sψ =
⟨sin 2 θ cos ψ ⟩ ⟨sin 2 θ ⟩
S2θ
S3θ
Sψ
0 1 0 −1
0 1 −0.5 1
0 1 0 −1
0
1 0 −1 0
1/3 ZCOM 2−4/3(3 + cos θc) ⎛ 1 − cos θc ⎞ = ⎜ ⎟ R0 2 + cos θc ⎝ 2 + cos θc ⎠
(3)
where zCOM is the corrected center of mass, R0 is the radius of the free droplet, and θc is the contact angle. The radius of the free droplet was calculated from its 0.5 g/mL density contour. This treatment resulted in a contact angle of 30 ± 3° for the hydrophilic surface, in agreement with results of other simulations.59 Results of 155 ± 3° were obtained for the hydrophobic surface, also consistent with what has been observed for other solid hydrophobic surfaces.51,89 Calculation of Nonlinear Susceptibility Tensor Elements. The second-order susceptibility tensor χ(2) is responsible for the magnitude and phase of the sum-frequency response through the generation of a second-order polarization P(2). This in turn radiates a field at the sum-frequency, ESF. The i component of the ESF vector at the point of detection is related to the element χ(2) ijk and the applied fields Evis,j and EIR,k through
We define three tilt angle order parameters based on the first three terms of a Legendre polynomial expansion following S0θ = 1
S 2θ =
S1θ
described above was performed but for a period of 1 ns. The change in the droplet shape can be correlated to its contact angle by88
Figure 1. (a) Sample and beam geometry for SFG experiments at the solid−water interface. When accessing the solid−water interface, it is customary to use a window or prism. The surface of the prism may be coated or functionalized in order to create the hydrophobic or hydrophilic material of interest. We consider that the positive z axis extends away from the bulk water phase. (b) Definition of the tile angle θ and twist angle ψ relating the molecular (a,b,c) frame to the surface (x,y,z) frame.
S1θ = ⟨cos θ ⟩
case isotropic θ = 0° θ = 90° θ = 180° ψ = 0° ψ = 90° ψ = 180° ψ = 270°
ESF, i ∝ Lii χijk(2) LjjEvis, jLkk E IR, k
(4)
where L are the local field corrections that account for the differences between the electric field magnitudes and phase in air and those at the aqueous surfaces. The subscripts i,j,k refer to any of the Cartesian lab frame coordinates x,y,z, where x and y are in the plane of the interface, and z is the surface normal as illustrated in part a of Figure 1. Eq 4 reveals that χ(2) is a rankthree tensor with 27 complex-valued elements. Owing to the isotropy in the azimuthal angle of adsorbed water molecules, and the nonresonant nature of their interaction with Evis, there are only 7 nonzero elements of χ(2). Of these, 3 are independent, so we take advantage of the improved statistics offered by averaging identical elements. 1 (2) (2) ) χ (2)⊥ ≡ (χxxz + χyyz (5a) 2
(1a) (1b) (1c)
(2)
Bounds of these four order parameters in limiting cases, along with their values for isotropic distributions of water molecules (bulk) are shown in Table 1. For our discussion to follow, it is instructive to note that S1θ and S3θ are polar order parameters, S(θ = 0°) ≠ S(θ = 180°), whereas S2θ is not sensitive to the molecular polarity. Also note that S2θ is capable of distinguishing perfect alignment at θ = 90° from an isotropic distribution. Water Contact Angles. Contact angle simulations have been performed to characterize the degree of hydrophobicity and hydrophilicity of the solid substrate studied. An 895molecule droplet of water was put on a 155.6 × 144.24 Å2 surface. The same equilibration and MD simulation as
χ (2) ≡ χ⊥(2) ≡ ⊥ (2) (2) χ⊥⊥⊥ ≡ χzzz
1 (2) (2) (2) (2) (χ + χzxx ) + χyzy + χzyy 4 xzx
(5b) (5c)
Here, x and y components are designated as those parallel to the surface, and z is perpendicular to the surface as shown in part a of Figure 1. In an experiment, the incident IR and visible pump beams are typically prepared in polarization states parallel (p) or 22869
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c1/c2 = +1; the high energy mode is the antisymmetric stretch with c1/c2 = −1. We refrain from using the terms symmetric and antisymmetric in the description of the condensed phase since hydrogen bonding greatly affects the nature of the coupling. Lab frame elements of the frequency-dependent secondorder susceptibility were then determined according to
perpendicular (s) to the plane of incidence, and either the s or p component of the reflected SF field is selected for detection. In the case where the IR beam is p-polarized, the visible beam is s-polarized, and the s-component of the SF is detected (commonly referred to as the ssp configuration), the elements (2) (2) χ(2) yyx and χyyz are probed. Because χyyx = 0 (it does not appear in eq (5)), such an experiment provides direct access to a single element of the second-order susceptibility tensor. If the experiment is configured for ppp polarizations, eight elements of χ(2) are probed, four of which are nonzero. In this case, the appearance of the spectra changes drastically with different angles of incidence of the visible and IR beams90−92 as a result of the geometric contributions to the L factors in eq 4. In this article, we have generalized the applicability of our results by describing the χ(2) elements directly as they appear in eq (5), thereby removing the influence of the experimental geometry. Sum-frequency spectra over the O−H stretching region were regenerated according to the procedure developed by Morita and Hynes.67 Briefly, the net force along the O−H bond vector was used as a measure of the red-shift of the low- (ω1) and high-energy (ω2) vibrational eigenmodes from those observed in the gas phase. We then set out to determine the eigenvalues (ωhigh and ωlow) and corresponding eigenvectors ([c1 c2]Thigh and [c1 c2]Tlow) of the matrix ⎡ ω1 V1,2 ⎤ ⎥ A=⎢ ⎢⎣ V1,2 ω2 ⎥⎦
χijk(2) (ωIR ) ∝
⎡ (∂α /∂r·∂μ /∂r ) ij low k
∑ ⎢⎢ N
⎣ ω low − ωIR − i Γ
+
(∂αij/∂r·∂μk /∂r )high ⎤ ⎥ ω high − ωIR − i Γ ⎥⎦
(9)
where N is the number of molecules considered, ωlow and ωhigh are the frequencies of the low- and high-energy eigenmodes, and the numerators in the above terms are the solutions to eq 7 determined separately for both eigenmodes. Note that in the numerator of eq 9, the subscript i refers to any of the lab frame Cartesian coordinates x, y, or z; in the denominator i = √−1, resulting in complex values of the χ(2) elements. We have fixed Γ = 15 cm−1 as that provided the best agreement with the experimental results.
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RESULTS Water at a Solid Hydrophobic Surface. Density and order parameter for water at the solid hydrophobic surface is presented in Figure 2. The density shows a depletion zone of
(6) −1
where V1,2 = 49.5 cm is situated between the gas-phase symmetric and antisymmetric energies. If l,m,n are considered to be any of the molecular frame Cartesian coordinates a,b,c, then values of the polarizability tensor ∂αlm/∂r and dipole moment vector ∂μn/∂r are those calculated in ref 67, where r is the individual O−H bond vector. For each molecule in the simulation, these properties were first projected into the i,j,k lab frame according to ∂αij ∂r
∂μ k ∂r
∂αlm R(θ1 , φ1 , ψ1) ∂r1 ∂α + c 2 R(θ2 , φ2 , ψ2)T lm R(θ2 , φ2 , ψ2) ∂r1
= c1R(θ1 , φ1 , ψ1)T
= c1
∂μn ∂r1
R(θ1 , φ1 , ψ1) + c 2
∂μn ∂r2
R(θ2 , φ2 , ψ2)
(7a)
(7b)
where θ, φ, and ψ are the Euler angles that rotate each of the O−H bonds (r1 and r2) into the lab frame via the transformation operator ⎡(x·̂ a)̂ (x·̂ b)̂ (x·̂ c )̂ ⎤ ⎢ ⎥ R = ⎢(y ̂·a)̂ (y ̂ ·b)̂ (y ̂ ·c )̂ ⎥ ⎢ ⎥ ⎢ ⎥ ̂ ̂ ̂ ̂ ( ) ( ) ( ) z a z b z c · · · ̂ ̂ ⎣ ⎦
Figure 2. (a) Water density profile across the water−hydrophobic solid interface, (b) order parameters S1θ in red, S2θ in blue, S3θ in green, and Sψ in black. In both plots, the vertical dashed line indicates the position of the uppermost aliphatic atom, and serves as a reference for the distance scale; positive values of distance tend toward the bulk water phase. The regions labeled A−C were selected for subsequent analysis based on the trends and signs of the order parameters.
(8)
whose elements are the scalar product of the unit vectors in the molecular l,m,n axes and the lab frame i,j,k axes. In the case of the rank-two tensor ∂α/∂r, the transformation also requires application of the transposed operator RT. The coefficients c1 and c2 couple the two O−H oscillators to form the low- and high-energy vibrational eigenmodes, so eq (7) provides the labframe α and μ derivatives for a water molecule. In the gas phase, the low energy eigenmode is the symmetric stretch with
around 2 Å, as has been seen before in the literature.51 Two distinct orientations can be seen in the order parameter plot, as indicated by a generally positive Sψ near the interface that becomes negative near the bulk. This is due to a flip in the overall water orientation with respect to the normal. At the point Sψ changes sign, around 3 Å, we can see a shoulder in the plot of S1θ and S3θ and also in the density. This was the deciding 22870
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Figure 3. Results of structure, hydrogen bonding, water species analysis, and nonlinear vibrational spectra obtained for water adjacent to a solid hydrophobic surface. The rows are labeled A−C according to the density and order parameter regions defined in Figure 2. The first column shows the tilt and twist (θ and ψ as defined in part b of Figure 1) histograms for all water molecules found in this region of the interface. Darker regions indicate lower populations; the white regions indicated the highest population. The second column shows the OH frequency shift with respect to an uncoupled oscillator in the gas phase at 3707 cm−1. This is plotted as a difference in population ΔP with respect to results obtained in the bulk water sample. Data for the low-energy eigenmodes (red), high-energy eigenmodes (blue) are separated; the combination is plotted in black. The plots in the third column are histograms of the water molecule nature, as defined by the difference between ⟨|2c1c2|2⟩ in the region of interest and those values obtained in the bulk water phase. The results for the low energy modes are plotted in red, high energy modes in blue, and the population(2) weighted average in black. The final column shows the imaginary component of the nonlinear susceptibility tensor elements: χ(2) ∥∥⊥ in blue; χ∥⊥∥ in red, and χ(2) ⊥⊥⊥ in black.
is making the fewest number of hydrogen bonds. The other hydrogen of the same molecule has the necessary geometry to participate in more H-bonds, and is seen to contribute more toward red-shifted populations at the surface. The same trend continues, but with diminished population difference when moving toward the bulk water phase (regions B and C). The coupling constants c1 and c2, as defined in eq 7, provide information on the nature of the vibrational modes and their localization. We have followed the same treatment as outlined by Morita67 for the vapor−water interface in calculating the degree of delocalization ⟨|2c1c2|2⟩. We note that nature of the modes can be readily obtained by determining ⟨2c1c2⟩ in that values closer to +1 will indicate symmetric-like stretching, whereas values tending toward −1 indicate antisymmetric-like behavior. However, as Morita identified, a shortcoming of ⟨2c1c2⟩ is that value of zero can represent either a mode that has equal contributions of symmetric and antisymmetric character or one that is completely localized (uncoupled OH oscillators). For this reason, it is more useful to plot ⟨|2c1c2|2⟩. Although the magnitude squared does not preserve the sign of 2c1c2, we know this information because we calculate the high- and low-energy eigenmodes separately (eq 9). In the third column of Figure 3, we plot Δ⟨|2c1c2|2⟩, the difference between the delocalization in the bulk water phase and that found for our defined regions of the interface. Because the water environments are similar, this representation allows the surface features to be more easily identified. Results for low-energy modes are plotted in red, high energy modes in blue, and the population-weighted average in black. The water structure at the surface (regions A and B) is dominated by uncoupled OH oscillators. One of these OH pairs has a very small frequency shift due to its inability to form H-bonds. This peak in the population (column 2) corresponds to a frequency of approximately 3750 cm−1. However, we do not observe a corresponding feature in the Δ⟨|2c1c2|2⟩ plot
factor to limit region A there; the end of region B was dictated by the change in sign of the first and third tilt order parameters. When looking at tilt-twist histograms (first column in Figure 3), two important water structures stand out in the region closest to the interface. The dominant orientation in region A shows a 120° tilt and 0° twist. This corresponds, as has been seen in the literature, to having one (uncoupled) hydrogen sacrificing hydrogen-bonding opportunities to the surface, thereby permitting the rest of the water sites to maximize possible hydrogen bonds.52,53 Region B is dominated by water molecules nearly parallel to the plane of the interface (θ ≈ ψ ≈ 90°). Finally, this is the only population that remains visible in region C, albeit slightly shifted toward θ > 90°. This geometry may be understood on the basis of hydrogen bonding between the successive layers, as has been observed for diffuse hydrophobic interfaces.93 The population maxima are much less pronounced in region C as the interface is rapidly becoming bulk-like. This is consistent with all 4 order parameters approaching zero at ∼8 Å from the surface (part b of Figure 2). Cartoons of the various water orientations and intramolecular geometries corresponding to these regions appear in part a of Figure S4 of the Supporting Information. The second column in Figure 3 shows the difference in population between water molecules in the bulk compared to those in the surface regions, as a function of the OH frequency shift from the gas phase value of 3707 cm−1. Data for the low energy eigenmodes are plotted in red, high energy modes in blue, and the combined population in black. In all three cases, negative values of ΔP indicate that the population at those frequencies at the surface is less than what is found in the bulk phase; ΔP > 0 indicates an enhanced population at the interface. In the region (A) closest to the surface, the hydrogen that is pointing toward the surface shows a high population in the low frequency shift region, as expected since this OH group 22871
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mode character analysis can mostly be described in the same way as for the solid hydrophobic interface, where two water orientations dominate as observed in Figure S3 of the Supporting Information. As we have followed Morita’s frequency-domain treatment to arrive at the coupling constants and SFG spectra using the same (SPC/E) water model, we verified that we have reproduced their results for the vapor−water interface. The only difference here is that the results we display for the coupling constants in Figure S3 of the Supporting Information are the differences, Δ⟨|2c1c2|2⟩ obtained in surface regions and the bulk water phase. The χ(2) spectra agree with those calculated by Morita and are also remarkably similar to what we observe at our solid hydrophobic surface. Comparison with homodyne (nonphase resolved) SFG experiments is difficult as the appearance of the spectra is extremely sensitive to the nonresonant contribution to |χ(2)|2. Because the nonresonant contribution is real, the imaginary spectra are more readily compared. This has been the subject of many recent discussions.36,86 All of the heterodyne experimental SFG data44 agree with Im[χ(2)] > 0 for the uncoupled O−H oscillator near 3700 cm−1, Im[χ(2)] crossing zero near 3600 cm−1 to take on negative values as the hydrogen-bonding environment is observed to be increasingly red-shifted. A second zero-crossing occurs near 3150 cm−1; O− H oscillators that are more red-shifted than 3150 cm−1 are observed with Im[χ(2)] > 0. Early attempts to simulate the vapor−water SFG spectra were unable to reproduce Im[χ(2)] > 0 in the 3000 cm−1 region. Recent attempts have been able to predict the correct sign of Im[χ(2)] for the most hydrogenbonded region but with varying magnitudes compared to the SFG amplitude in other regions of the spectrum. Water at a Solid Hydrophilic Surface. When water has been placed in contact with the hydrophilic surface, the results show a far more complicated behavior than observed with either of the hydrophobic surfaces. To begin, by simply inspecting the density and order parameters in Figure 4, evidence of many different structures can be realized. The density shows high and low regions with almost no depletion zone, as is typical for hydrophilic surfaces.57 As a result of this complexity, we have chosen six regions for analysis. The end of region A was decided according to the change of sign of the tilt and twist order parameters. All order parameter show strong ordering in that first interfacial region. Region B was chosen by identifying the maximum in the density profile but still includes two distinct orientations because Sψ has a positive and negative feature there. This change of sign is accompanied by a kink in the S3θ plot. Because the delimitation of those two structures is not clear, they were placed in the same region. The third region (C) analyzes the shoulder present in the density plot near 2 Å. This region show a fairly high degree of orientation for both Sψ and S1θ. This corresponds to a low average degree of twist degree and a high degree of tilt orientation. In the same way, regions D, E, and F were chosen according to order parameter signs, density peaks, and overall trend. The results of all the regions are shown in Figure 5. The first region (A) has a low density but strongly oriented water molecules. The orientation of 120° tilt and 90° twist corresponds to both hydrogens pointing toward the bulk at an angle. This is likely to promote some hydrogen bonding from the water oxygen to the surface hydrogen atoms. This orientation would be the most favorable in certain regions of the surface where two surface OH groups from the substrate are directed toward to each other to H-bond with oxygen lone
indicating that these molecules have roughly the same delocalization as in the bulk. This effect is due to the fact that any water molecule showing this frequency shift in bulk, will also have its stretching vibrations localized on one of the OH groups. The other OH group of the same molecule at the surface is significantly red-shifted, yet localized as a result of the asymmetry in the H-bonding environments on either side of this rather sharp interface. This is why we see a negative deviation from the bulk in the degree of delocalization on the low energy side of the Δ⟨|2c1c2|2⟩ spectra in regions A and B. The other water molecule is parallel to the interface, thus maximizing hydrogen bonding with the oxygen from the first water molecule. We note the small positive peak at 3750 cm−1 resulting from the relative paucity of uncoupled oscillators in the bulk. The second orientation with θ ≈ ψ ≈ 90°, more prominent in region B, has more equivalent hydrogens and this can be seen as greater delocalization. However, as a result of the water orientation in region A, the geometry is not ideal to maximize the hydrogen bonds. These broken H-bonds appear around 3550−3600 cm−1. Approaching the bulk phase in region C, we observe similar behavior, but with the difference between surface and bulk roughly an order of magnitude less pronounced. The right-most column in Figure 3 shows the spectra (2) calculated for the Im[χ(2) ∥∥⊥] in blue, Im[χ∥⊥∥] in red, and ] in black. Imaginary components were determined Im[χ(2) ⊥⊥⊥ according to eq 9, as they are more descriptive of interfacial structure than |χ(2)| (or |χ(2)|2), and more revealing of the resonances than Re[χ(2)]. To facilitate comparison between different regions of the interface, spectra were normalized so that the maximum response in any region was set to unity. We note that the response is not normalized to the number of molecules, as the SFG response should increase with either increased orientation or population of oriented molecules. Starting with the region closest to the surface (A), we note that although there are two distinct populations, it is primarily the out-of-plane molecules that contribute to the SFG response. Moving into region B, the population of in-plane water molecules is enhanced, and yet we observe a very similar shape in the SFG spectra. In region C, as the water becomes less ordered (part b of Figure 2), we expect the SFG response per molecule to decrease. However, this is a very large region of the interface (density profile in part a of Figure 2), and so the collective response is responsible for the majority of the SFG signal. In this region, we note that the zero-crossing of Im[χ(2) ∥∥⊥] is red-shifted by ∼100 cm−1 compared to regions closer to the surface. In addition, the relative amplitudes of the positive and negative features are comparable. This is in contrast to the greater amplitude observed at higher frequencies closer to the surface. Comparison with the Vapor−Water Interface. The focus of our study is the solid−water interface; we have included results for the vapor−water interface for comparison and bench-marking purposes. The density and order parameter profiles obtained for the vapor−water interface are shown in Figure S2 of the Supporting Information. The density displays a monotonic transition from bulk to vapor values. The primary difference between this superhydrophobic vapor interface and the solid surface is in the extent of the interface, defined by either the density or order parameters. The vapor−water interface extends over ∼8 Å, whereas the density and structural variation of water at the solid hydrophobic surface occurs over ∼6 Å. The results of the tilt-twist histograms, populations, and 22872
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overall higher population than bulk in the higher frequency region. This will have a large positive contribution in the χ(2) response in the hydrogen bonded region. The OH group not interacting with the surface will show a lower frequency shift and will probably be more localized. One main feature that stands out in the degree of delocalization graph in the two first region (parts A and B of Figure 5, third column), in most of the spectral range, the OH oscillators are more localized than bulk. This agrees with the fact that the first layer of water orientation depends mostly on the interaction with surface hydroxyl making the OH modes more localized. One OH interacting with the surface hydroxyl will exhibit greater H-bonding and have lower energy, whereas the other OH oscillator will have a lesser redshift but still display a localized feature. It is this orientation that causes the overall negative deviation from bulk both in regions A and B for the Δ⟨|2c1c2|2⟩ graph. The water molecules having both hydrogens down and both hydrogens up are likely the cause of the slightly positive deviation of the delocalization at low frequency. Molecules contributing to hydrogen bonding come predominantly from the one hydrogen facing the surface at angle. This is why we again see a positive peak in the low frequency ∥∥⊥ spectral response. The other four regions (C−F) have the same overall trend that is roughly opposite to what has been observed in the first two regions (second and third columns of Figure 5). In those regions approaching the bulk water phase, the water orientation is dictated by regions closer to the interface, where the water cannot participate in as much hydrogen bonding than in the bulk. This is largely because of the orientation of the previous layer that does not favor a hydrogen bonding geometry. One does notice that favorable dipolar interactions are achieved, as evidenced by the tilt-twist histograms and in agreement with similar studies.93 Such features are also evident in the lowerthan-bulk population at higher frequency shifts. The few strong hydrogen bonds are fairly localized compared to the bulk due to the less organized layers closer to the interface. The water molecules then prefer having two broken hydrogen bonds with neighboring molecules showing a higher delocalization at higher frequency. Moving away from the interface from one region to another, the difference from the bulk slowly fades. Because the water structures display a large variety here, it is no surprise that their contribution to the χ(2) ∥∥⊥ spectral response is fairly different and often contradictory to what is observed in the more ordered regions (regions D and E). However, because the magnitude of the response is smaller, the contributions from these water molecules will not significantly affect the overall trend.
Figure 4. (a) Water density profile across the water−hydrophilic solid interface. (b) Order parameters S1θ in red, S2θ in blue, S3θ in green, and Sψ in black. In both plots, the vertical dashed line at 0 Å indicates the position of the surface hydroxyl group H atom, and serves as a reference for the distance scale; positive values of distance tend toward the bulk water phase. The regions labeled A−F were selected for subsequent analysis based on the trends and signs of the order parameters and oscillations in the density profile.
pairs. This would explain why the density of this water orientation is relatively low, as shown in region A of part a of Figure 4. Because the degree of H-bonding is high, we can see a positive deviation of the overall population at higher frequency shift. Both high and low energy OH modes have a higher population at high frequency shift illustrating that both modes contribute. Because both OH groups are in the same environment and it is mostly the oxygen lone pairs that contribute to the hydrogen bonding, the modes are highly coupled, and thus we see a higher-than-bulk delocalization of the modes around 3200 cm−1. The resultant χ(2) response is expected to show a slight negative contribution in ∥∥⊥ (ssp) because water hydrogens are pointing toward the bulk. However, the other orientation present in this and the adjacent region has a stronger positive contribution. Cartoons illustrating intramolecular water geometries and orientations with respect to the surface are shown in part b of Figure S4 of the Supporting Information. The second region (B) has a high population of water occupying multiple orientations. These include water oriented with both hydrogens directed toward the surface and another with hydrogens directed toward bulk. Perhaps the most interesting is the curved tilt-twist population. This orientation changes from 60° to 90° tilt and from 0° to 60° twist. This feature is interesting because the commonality between those orientations is actually the orientation of one of the hydrogens at an angle toward the surface. (This is also present in region A.) That implies that the OH bonds here orient themselves to hydrogen bond with the oxygen of the surface, whereas the rest of the molecule optimizes its orientation with respect to the surrounding molecules while maintaining this constraint. The frequency shift supports this interpretation by again having an
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DISCUSSION Comparison of All Interfaces Studied. The results of the entire interface (the sum of all the regions) are presented in Figure 6 for the three different systems. The frequency shift population and the mode delocalization are again a comparison with bulk water values. Looking at the vapor−water and hydrophobic surface response, the frequency shift is significantly different than the bulk. This is caused by the first regions having significant populations in low hydrogen bonding environments. Consequently, there is a lower population in the highly frequency shifted region. In contrast, it can be noted that the hydroxylated surface frequency shift population does not show a significant difference from the bulk water phase. This is caused by regions having a high degree of hydrogen bonding near the surface, together with by lesser hydrogen 22873
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Figure 5. Results of structure, hydrogen bonding, water species analysis, and nonlinear vibrational spectra obtained for water adjacent to a solid hydrophilic surface. The rows are labeled A−F according to the density and order parameter regions defined in Figure 4. Data appearing in the four columns are plotted with the same descriptions as appear in the caption to Figure 3.
directly pointing toward the bulk (parallel to the surface normal) and participates in a significant degree of hydrogen bonding. The same behavior is then observed for the Im[χ(2) ∥∥⊥] of the water at the solid hydrophobic surface. For the hydrophilic surface, the nonlinear response in the ∥∥⊥ spectrum is quite different. Here, the sum of many different contributions from the various regions of the interface (shown in Figure 5) result in a mostly overall positive contribution throughout the spectrum. We do see a small negative contribution above 3550 cm−1. The results obtained for this surface cannot be easily explained on the basis of a single water orientation, as in the case of the hydrophobic surface. The overall positive feature in the SFG spectrum does suggest that most hydrogen bonding originates from molecules with a hydrogen atom pointing toward the interface. For completeness, we have calculated two additional elements of the lab/ surface-frame nonlinear susceptibility, Im[χ(2) ∥⊥∥] (shown in part d of Figure 6) and Im[χ(2) ] (shown in part e of Figure 6). ⊥⊥⊥ The ∥⊥∥ elements are directly related to the experimental sps results, and ⊥⊥⊥ is one contribution to the ppp spectrum. The other contributions to ppp are represented by the other two elements we calculate, but must be weighted by factors that depend on the experimental conditions (angles of incidence of the pump beams). We have mentioned that it is particularly
bonding regions at deeper layers of the interface (Figure 5). Also, the presence of an appreciable hydrogen bonding environment near the surface the interaction is more similar to that in the bulk water phase than for the hydrophobic surfaces. This causes the bulk difference of the frequency shift population to be significantly less for the hydrophilic interface compare to hydrophobic interface. In the overall mode delocalization, we notice in the hydrophobic surface (and vapor−water interface), that a higher degree of delocalization is found around 3500 cm−1, coming from molecules oriented parallel to the surface. The other major feature is a more localized mode in the hydrogen bonded region, which comes from the other hydrogen of the molecule with uncoupled OH. As for the hydroxylated surface we can notice almost no difference from the bulk. This is again caused by different surface regions having contrasting hydrogen bonding behaviors. If we look at Im[χ(2) ∥∥⊥] of the vapor−water interface (part c of Figure 6), we can notice an overall positive contribution in the low hydrogen bonding region (above 3550 cm−1). This feature is coming from the uncoupled OH that is pointing toward the interface. The other feaure, a negative contribution in the higher hydrogen bonding region, comes from a hydrogen pointing toward the bulk. This feature originates from the other hydrogen of the surface molecule, where the hydrogen is 22874
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In a recent study, Zhang et al. compared the Im[χ(2)] spectrum of water obtained at a superhydrophobic SH fractal film (water contact angle ∼165°) with that from a partially silanated nanoporous silica surface (water contact angle ∼120°).48 Both systems show a strong contribution with Im[χ(2)] > 0 for the uncoupled O−H oscillator near 3707 cm−1, in agreement with the spectra that we have calculated from our simulations. The experimental data then switches sign so that Im[χ(2)] < 0 for IR energies 3300−3650 cm−1. This is in reasonable agreement with our simulated spectra, save for the position of the zerocrossing which is about 100 cm−1 red-shifted in our case. It is interesting to note that, despite the more compact nature of the solid−water interface (majority of the density change within ∼4 Å) compared to the vapor−water interface (diffuse density distribution over ∼8 Å), the SFG spectra are remarkably similar, both in the case of experiments and simulations. In an MD simulation study of water confined between two alkane thiol surfaces, Layfield et al. examined the structure of water as a function of the distance from the surface.56 For the water molecules nearest the surface, they found that one O−H group is directed parallel to the surface normal, pointing toward the bulk. This corresponds to the same depth probed in our region A, and agrees with our results. Janecek et al.61 correlated the depletion zone with the hydrophilicity of an atomistic surface. Their results show that a hydrophilic surface has a depletion zone significantly smaller than an hydrophobic surface, which also agrees with our results. In the same study, the authors have also isolated a water species immediately adjacent to their surface that directs one O−H bond along the surface normal (θ ≈ 60° in our tilt angle convention). This was found to be a low-population species that exists before the first maximum in the density profile. Solid Hydrophilic Surface. In an experimental study of water at the crystalline quartz surface, Ostroverkhov et al. have obtained phase-resolved SFG spectra as a function of pH and have thereby extracted Im[χ(2)].24 It is particularly valuable to compare our simulated spectra with their results obtained at pH 1.5 since we model a fully hydroxylated surface with net neutral charge and the pHzc of quartz is about 2.5. The experimental Im[χ(2)] spectra show very low intensity around 3700 cm−1 (where the hydrophobic surfaces display uncoupled OH oscillators) and then Im[χ(2)] > 0 until the IR energy drops below 3200 cm−1, after which Im[χ(2)] < 0. Very similar results were obtained in a later study of the water-fused silica surface, both in the case of smooth surfaces and those with nanoporous overlayers.48 The results of our simulation also show almost no intensity in the 3700 cm−1 region. Part c of Figure 6 (solid green curve) shows the Im[χ(2) ∥∥⊥] spectra, for comparison with the ssp polarized spectra obtained in the experimental studies. This is particularly interesting as we have demonstrated that significant contributions to Im[χ(2)] arise around 3700 cm−1 from various depths throughout the interfacial region (Figure 5). However, the opposite signs of the contributions results in a very small SFG signal in this region. At IR energies greater than 3550 cm−1 our simulations indicate Im[χ(2)] < 0. The experimental results show Im[χ(2)] > 0, but the intensities are very low in both cases. For IR energies less than 3550 cm−1, both experimental results and our simulated spectra have large positive components of Im[χ(2)] under the conditions of these beam polarizations/χ(2) tensor elements. The experimental data again changes sign for ωIR < 3150 cm−1; however, this is outside of the region of applicability of the SPC/E water model in our current study.
Figure 6. Comparison of all systems studied with the vapor−water interface (combined regions A−C) results in red, hydrophobic solid surface (combined regions A−C) in blue, and hydrophilic solid surface (combined A−F) in green. (a) Difference in the frequency distribution of the interfacial population with respect to that in bulk water; (b) difference in the overall mode character ⟨|2c1c2|2⟩ between water at the surfaces and bulk water; (c) real (dashed lines) and imaginary (solid (2) (2) lines) spectra of χ(2) ∥∥⊥, (d) χ∥⊥∥, and (e) χ⊥⊥⊥.
valuable to compare with phase-resolved SFG spectra (as will be done in the following section), as the imaginary components of χ(2) are free of nonresonant contributions to the line shape, thereby revealing the vibrational modes more clearly. However, there are very few experimental results for water ssp Im[χ(2)] at solid surfaces, and none in sps and ppp configurations. Nevertheless, we show our ∥⊥∥ and ⊥⊥⊥ results for comparison with future experimental studies. Comparison with Other Studies. Solid Hydrophobic Surface. Despite all of the experimental attention on water structure at solid surfaces, there have been very few phaseresolved SFG studies to reveal Im[χ(2)].24,48 This is in part due to the challenge associated with measuring the phase shift at a buried interface where the beams must travel through a dispersive phase in order to reach the solid−water interface.94 22875
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A molecular dynamics study by Ho et al. examined the structure of water adsorbed on β-crystalobite SiO2.57 Depending on the position within the lattice at which the face was cut, different densities, geometries, and orientations of the crystal OH groups were present to interface with water molecules. For low density surfaces, the hydroxyl groups always make an angle of 71.5° to the surface normal (as in our case), independent of the azimuthal angle of the surface-O bond. In the case of higher density cuts, the surface-O bond is not parallel to the surface normal, and therefore the OH vector tilt angle is a function of the surface-O azimuth. These two situations result in drastically different water density profiles as a function of distance from the surface. The results obtained for the low density surface are in agreement with the results we present in part a of Figure 4 and those obtained in other simulations.54,62 For an amorphous surface, or an experimental crystalline surface with multiple faces and/or steps exposed, it is reasonable to assume that the structure may be intermediate between the cases of the highand low-density OH cases. This may account for some of the minor variability between our calculated SFG spectra and those measured at the quartz and fused silica surfaces. Chen et al. used phase-sensitive SFG spectroscopy to study water structure adjacent to phospholipids with different headgroups.43 Although this system is not a planar hydrophilic surface, there is an interesting point of comparison with our results. As a result of our fixed 71.5° surface OH tilt angle, we have the partial negative charges (associated with the oxygen atoms) confined to a single plane. Likewise, the partial positive charges (associated with the hydrogen) atoms are confined to another plane, closer to the water, as indicated by the vertical dashed line at 0 Å in Figure 4. In some headgroups, there are more spacer atoms between the PO−4 group and the N(CH3)+3 group (DPPC) or NH+3 (DPPE) than with other headgroups. As a result, despite some flexibility in the headgroup torsional angles, the positive and negative charges are located in distinct planes with respect to the surface normal. In such cases, the water SFG spectrum displays Im[χ(2)] > 0 over the entire OH stretching region.
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ASSOCIATED CONTENT
S Supporting Information *
Results obtained for the vapor−water interface, for comparison with those presented for the solid hydrophobic-water interface. Graphical descriptions of water orientations and intramolecular water arrangements are also provided to assist in the interpretation of the tilt-twist histograms for all interfaces studied. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We thank the Natural Sciences and Engineering Research Council of Canada for support of this science with a Discovery Grant. Computers were purchased with support from the University of Victoria. Kailash Jena provided assistance in debugging early versions of the code that generated the SFG spectra. Kuo-Kai Hung provided a utility that enabled extracting coordinates from GROMACS binary file formats. We thank Paul Covert for insightful discussions related to experimental SFG spectra of water at hydrophilic mineral surfaces.
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REFERENCES
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CONCLUSIONS We have studied the structure of water next to solid hydrophobic and hydrophilic surfaces using atomistic molecular dynamics simulations. Interfacial water molecules were characterized according to their tilt-twist histograms, frequency of the O−H group vibrations, and nature of the water molecule as determined by the intramolecular O−H coupling constants. Each of these characteristics were assessed as a function of distance from the surface, and compared to results at the water−vapor interface and bulk water phase. We have made the connection to a sensitive experimental measure of interfacial water structure by simulating the nonlinear vibrational response of these systems from 3300−3800 cm−1. Our findings revealed that water adjacent to hydrophobic surfaces is remarkably similar to water near hydrophobic liquid or vapor phases, despite the relatively compressed features observed in a thinner interfacial region. At hydrophilic surfaces, our results account for the lack of signal in the 3600−3700 cm−1 region observed experimentally. However, we are able to illustrate that this is not due to a paucity of O−H oscillators with this energy, rather water molecules with uncoupled oscillators are oriented in opposing directions at different depths within the interfacial region, thereby leading to an effective cancellation of the macroscopic response. 22876
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dx.doi.org/10.1021/jp309744s | J. Phys. Chem. C 2012, 116, 22867−22877
