Disentangling Sum-Frequency Generation Spectra of the Water Bending Mode at Charged Aqueous Interfaces

The origin of the sum-frequency generation (SFG) signal of the water bending mode has been controversially debated in the past decade. Unveiling the origin of the signal is essential, because different assignments lead to different views on the molecular structure of interfacial water. Here, we combine collinear heterodyne-detected SFG spectroscopy at the water-charged lipid interfaces with systematic variation of the salt concentration. The results show that the bending mode response is of a dipolar, rather than a quadrupolar, nature and allows us to disentangle the response of water in the Stern and the diffuse layers. While the diffuse layer response is identical for the oppositely charged surfaces, the Stern layer responses reflect interfacial hydrogen bonding. Our findings thus corroborate that the water bending mode signal is a suitable probe for the structure of interfacial water.


I. INTRODUCTION
The bending mode of H 2 O has a characteristic frequency around 1550−1700 cm −1 . This mode has been probed using vibrational spectroscopies, because it reports on the local structure of the hydrogen-bond network in water; when water is strongly (weakly) hydrogen-bonded, the frequency of the bending mode is blue-shifted (red-shifted). 1,2 Probing the bending mode of water has several advantages over probing the O−H stretch mode. Whereas the O−H stretch mode of water cannot be spectrally distinguished from other molecules containing OH-groups, the H−O−H water bending mode is specific to water. 3−8 Also, the vibrational coupling between bending modes has a limited impact on its spectral response, 3,9 in sharp contrast to the O−H stretch mode. 10,11 Furthermore, understanding the bending mode is essential to unveil the vibrational energy transfer from the O−H stretch mode of water and the amide mode of proteins to the local heat, 12−16 because the bending mode is believed to be an essential intermediate step to receive excess vibrational energy and release it to the local heat. 9,17−21 The H−O−H bending mode of specifically interfacial water molecules has been probed with sum-frequency generation (SFG) spectroscopy. 3,22−28 Although SFG spectroscopy is surface-specific, the precise origin of the SFG signal has been highly debated. So far, three distinct contributions have been proposed, from interfacial dipoles, bulk quadrupoles, and interfacial quadrupoles. 29,30 The dipole contribution refers to the first-order term of the second-order susceptibility, and a number of research groups have analyzed and interpreted the experimental and simulated SFG data of the bending mode based on the dipole mechanism. 22−24,31−33 The bulk quadrupole mechanism was proposed by Tahara, Morita, and coworkers in 2016, in which the first-order dipole term is masked by a higher-order term. 27 More recently, in 2020, a new set of the bending mode SFG spectra demonstrated the frequency shift of the bending mode due to the interaction of water with lipids/surfactants. Because the frequency shift cannot be accounted for via the bulk quadrupole mechanism, Tahara and co-workers proposed that the bending mode SFG signal is generated by the higher-order term arising from the interface (interfacial quadrupole mechanism). 28 Clarifying this apparent contradiction by unveiling the origin of the SFG signal is important, because the different assignments of the origin of the signal lead to different interpretations of the bending mode of waterand thereby of the structure of interfacial water. If the χ bend (2) signal arises from the dipole mechanism, it provides information on the molecular orientation of the interfacial water molecules. 34 If the signal arises through the interfacial quadrupole mechanism, one cannot obtain orientational information. 35,36 Currently, the bulk quadrupole mechanism is not supported by any experimental data. The remaining two mechanisms, dipole mechanism and interfacial quadrupole mechanism, can be identified from the sign of the H−O−H bending mode (χ bend (2) ) at the charged interfaces. If χ bend (2) is governed by the dipole mechanism, the sign of the Im(χ bend (2) ) signal changes with the sign of the surface charge. If χ bend (2) is governed by the interfacial quadrupole mechanism, the sign of the Im(χ bend (2) ) signal is positive, irrespective of the sign of the surface charge. 36 Extracting the χ bend (2) contribution at the charged interfaces is, however, not straightforward because the water signal at these interfaces arises not only from the oriented water molecules in the Stern layer (χ bend (2) term) which is invariant to the solution's salt concentration, but also from those oriented along the interfacial electric field in the diffuse layer (χ bend (3) term) ( Figure  1a,b). 37 This interfacial field and the magnitude of the χ bend (3) contribution has been examined by varying the bulk electrolyte concentration. 38−40 However, the χ bend (3) contribution is controversial: Reference 26 indicated a substantial χ bend (3) contribution, leading to the flipping of the sign of the Im(χ bend (2) ) peak due to the change of the negatively and positively charged interfaces (dipole mechanism), while ref 28 showed that the χ bend (3) contribution is negligible, leading to the positive Im(χ bend (2) ) peak irrespective of negatively or positively charged interfaces (interfacial quadrupole mechanism).
Here, using collinear heterodyne (HD)-SFG, we measure the H−O−H bending mode of water at the positively charged lipid (1,2-dipalmitoyl-3-trimethylammonium propane, DPTAP) and negatively charged lipid (1,2-dipalmitoylsnglycero-3-phospho-glycerol, DPPG) interfaces. We unambiguously establish that the χ bend (3) contribution is non-negligible and determine its spectrum. The careful extraction of the Im(χ bend (2) ) signal, by varying the electrolyte concentration, reveals that the sign of the Im(χ bend (2) ) signal is opposite at the water−DPTAP and water−DPPG interfaces. We highlight the importance of the homogeneous sampling of the water−lipid interface, which could be achieved by rotating the sample in the collinear HD-SFG setup.
II. METHODS II.A. Sample Preparation. We dissolved DPPG (sodium salt) and DPTAP (chloride salt) purchased from Avanti Polar Lipids in a mixture of 90% chloroform (Fischer Scientific, stabilized with amylene, >99%) and 10% methanol (VWR Chemicals, 99.8%) at a concentration of 4.3 × 10 −4 mol/L. Sodium chloride (Sigma-Aldrich, >99.5%) was baked in an oven for 8 h at 650°C. We used D 2 O (>99.9%), which was purchased from Sigma-Aldrich. H 2 O was obtained from a Milli-Q machine (resistance >18.2 MΩ cm). We prepared the sodium chloride solutions with their concentrations of 1 M and 0.1 mM. We chose the concentrations of 0.1 mM and 1 M to see the spectral deformations in both imaginary and real parts due to the complex χ bend (3) term, as is seen in what follows. The 20 mL sodium chloride solutions were poured into a Teflon trough with an 8.0 cm diameter. We then deposited ∼50 μL DPTAP and DPPG solutions onto the H 2 O and D 2 O solutions using a click syringe. The surface pressure of the DPTAP and DPPG monolayers was measured with a commercial surface tension meter (Kibron, Inc., Helsinki, Finland) and was determined to be ∼44 ± 3 mN/m and 19 ± 3 mN/m, respectively. The surface area per lipid was estimated to be ∼44 Å 2 and ∼52 Å 2 for DPTAP and DPPG, respectively. 41,42 The prepared samples were equilibrated for at least 40 min. For both HD-SFG and HD-SHG measurements, the trough was rotated to avoid the lipid monolayer distortion due to heat accumulation. 43 The speed of the sample at the laser irradiation spot was ∼1.0 cm/s.
In this study, we used the charged lipids of DPPG and DPTAP with the CO groups. The CO stretch mode contributions interfere with the H−O−H bending mode of water, 26 which may potentially complicate the interpretation on the SFG spectra. The other choices which have been commonly used for generating the charged surfaces are the surfactants without the CO groups, such as sodium dodecyl sulfate (SDS) and cetyltrimethylammonium bromide (CTAB). 24,44 However, SDS and CTAB have critical micellar concentrations of ∼0.1 mM to 1 mM, much higher than DPPG and DPTAP. In fact, for stable SFG measurements, researchers have used 1 mM−10 mM concentrations of SDS and CTAB. 44−46 Such high SDS and CTAB bulk concentrations prohibit fine control of charge screening by sodium chloride to tune the χ bend (3) contribution, which requires concentrations down to 0.1 mM. The bulk concentrations of the DPPG and DPTAP samples were ∼1 μM, much smaller than the 0.1 mM salt concentration. For DPPG and DPTAP, one can control the ionic strength with the salt concentration, allowing us to uncover the χ bend (3) contribution, unlike SDS and CTAB. II.B. HD-SFG Measurements. The HD-SFG measurements were performed on a collinear beam geometry using a Ti:Sapphire regenerative amplifier (Spitfire Ace, Spectra-Physics, centered at 800 nm, ∼40 fs pulse duration, 5 mJ pulse energy, 1 kHz repetition rate). The visible and IR beams were first focused into a 20 μm-thick y-cut quartz plate to produce sum-frequency signal serving as local oscillator (LO). These beams were then collinearly passed through an 8 mm CaF 2 plate for the phase modulation and focused on the sample surface at an angle of 45°. The SFG signal from the sample interferes with the SFG signal from the LO, generating the SFG interferogram. The SFG interferogram was dispersed in a spectrometer and detected by an EMCCD camera. The complex χ eff (2) spectra were obtained via the Fourier analysis of the interferogram and normalization by a z-cut quartz crystal. The measurements were performed with ssp (denoting s-, s-, and p-polarized SFG, visible, and IR beams, respectively) polarization combination. The details of the HD-SFG setup can be found in the Supporting Information.
Note that the HD-SFG measurement for the rotating sample is challenging because the height of the sample fluctuates due to the rotation of the sample, causing phase modulations. The height fluctuation of our samples had a standard deviation of 1.7 μm, which will cause ∼6°phase error with a typical noncollinear SFG setup. 47 In this work, we used a collinear HD-SFG geometry, which is much less sensitive to the height change than the noncollinear HD-SFG setup, and thus the phase error for the rotating sample is <1.7°. 48−50 Such a collinear HD-SFG setup is thus very suitable for HD-SFG measurements of rotating samples.
II.C. HD-SHG Measurements. A pulsed Yb:KGW (ytterbium-doped potassium gadolinium tungstate) laser system (Pharos, Light Conversion Ltd.) was used, generating pulses with a wavelength of ∼1030 nm, a pulse duration of roughly 210 fs, a repetition rate of 1 MHz, and a pulse energy of 15 μJ. The pulse energy was reduced to 300 nJ. After passing through y-cut quartz to generate the LO signal, and fused silica plates for phase modulation, the fundamental beam was focused onto the sample surface. All the measurements were performed with s-in/p-out polarization combinations. The incident angle of the incoming beam was set to 45°relative to the surface normal. The generated second harmonic generation (SHG) signal was dispersed in a spectrograph and detected by an EMCCD camera.

Contribution.
Figures 1c,f display the complex SFG susceptibility (χ eff (2) ) at the D 2 O−DPTAP and H 2 O−DPTAP interfaces with two different salt concentrations. First, we focus on the Im(χ eff (2) ) spectra at the D 2 O−DPTAP interface. For D 2 O, the bending mode is shifted to ∼1200 cm −1 , outside the studied frequency window, so that these measurements serve as a reference. For all the salt concentrations, the spectra commonly show a large positive peak at ∼1720 cm −1 and a relatively small negative peak at ∼1740 cm −1 . These peaks are attributed to the CO stretch mode. 51 A striking change of the spectra with increasing salt concentration is the elevation of the baseline (frequencyindependent nonresonant contribution). We then turn our respectively, where χ (2),NR represents the nonresonant contribution, χ CO (2),R (ω) denotes the resonant contribution from the CO stretch mode. c, Φ, κ, and Δk z denote ion concentration, the surface potential, the inverse of the Debye length, and the mismatch of the wave-vectors along the surface normal in the reflected SFG configuration, respectively. 26 (ω). Here, we assumed negligible NQEs on the spectral shape, in analogy with previous work. 28 We will discuss the validity of this assumption in the following. Figure 3 panels a and b show the subtracted spectra (ΔIm(χ eff (2) (ω,c)) = Im (χ eff,H 2 O (ω,c)) − Im (χ eff,D 2 O (ω,c))) of the DPTAP and DPPG samples, respectively. The ΔIm-(χ eff (2) (ω,c)) response in the 1580−1630 cm −1 frequency region decreases for the DPTAP sample, when the salt concentration increases from c = 0.1 mM to 1 M. On the other hand, the ΔIm(χ eff (2) (ω,c)) response in the 1580−1630 cm −1 frequency region increases for the DPPG sample. The changes of the ΔIm(χ eff (2) (ω,c)) spectra with varying salt concentration signify the non-negligible ΔIm(χ bend (3),R (ω) contribution. We further calculated the spectra ΔΔIm(χ eff (2) (ω)) = ΔIm(χ eff (2) (ω,c = 0.1 mM)) − ΔIm(χ eff (2) (ω,c = 1 M)), which reflect the c ( ) ( ) κ − Δ contribution (again under the assumption of negligible NQEs). The data are shown in Figure 3c,d for the DPTAP and DPPG samples, respectively. The ΔΔIm(χ eff (2) (ω)) spectra showed a positive 1580−1670 cm −1 contribution for the DPTAP sample and a negative contribution for the DPPG sample. The ΔΔIm(χ eff (2) (ω)) contribution in the ω < 1650 cm −1 region is more apparent than that in the ω > 1650 cm −1 region, where 1650 cm −1 is a typical H−O−H bending mode frequency. The prominent The positive and negative ΔΔIm(χ eff (2) (ω)) contributions for the DPTAP and DPPG samples indicate that the ΔΔIm-(χ eff (2) (ω)) signal is governed by the varies with the sign of the surface charge due to the surface potential of Φ(c), the flipping of the sign for ΔΔIm(χ eff (2) (ω)) for the positively charged DPTAP and negatively charged DPPG surface provides direct evidence for the χ bend The current finding is at odds with that in ref 28 in which the H−O−H bending mode contribution is unchanged upon the addition of the salt. The reason for such a discrepancy may be attributable to the lipid monolayer formation. A lipid monolayer is easily displaced from the laser spot as a result of the heat accumulation due to continued laser irradiation. 43 Because we used the rotating trough, such heat accumulation can be avoided.
This hypothesis can be confirmed by investigating the SFG signature of the CO stretch mode at the H 2 O−DPTAP and D 2 O−DPTAP interfaces. First, the ratio of the CO stretch peak amplitude vs the H−O−H bending mode amplitude in the Im(χ eff (2) ) spectrum at the H 2 O−DPTAP interface is much larger in this work than that reported in ref 28. This implies that the coverage of the DPTAP is higher in this work than in ref 28. Furthermore, the CO peak frequency is ∼1730 cm −1 in the intensity |χ eff (2) | 2 spectra at the D 2 O−DPTAP interface in refs 51 and 26, as well as our measurement (see Supporting Information), while the CO peak is located at ∼1740 cm −1 in ref 28. Because the lower surface coverage of DPTAP results in the blue-shift of the CO stretch peak, 51 the 1740 cm −1 CO peak observed in ref 28 indicates that the coverage of the DPTAP is likely strongly reduced in the probed region. With decreasing surface coverage of DPTAP, the surface charge decreases, lowering the impact of the χ bend (3) contribution on the SFG spectra. Note that very recently, Bakker and coworkers also pointed out that too small a surface charge leads to negligibly small dipolar contribution of the bending mode in ref 44.
III.B. Determination of χ bend (2) and χ bend (3) Spectra. The above result of the significant χ bend (3) contribution manifests that the χ bend (2) and χ bend (3) contributions are entangled in the measured χ eff (2) spectra. Thus, disentangling the χ bend (2) contribution from the χ bend (3) contribution requires fitting of the spectra. Here, before carrying out the fitting, we verify the assumption that the NQE is negligible between the H 2 O and D 2 O samples. In fact, the different nonresonant background between the H 2 O and D 2 O samples can be seen in the nonzero ∼1800 cm −1 region of ΔIm(χ eff (2) (ω,c)) of the DPTAP and DPPG samples as well as the SDS data in ref 28. Because the nonresonant contribution critically affects the inferred amplitude of the H− O−H bending mode signal, we checked whether the NQEs differentiate the nonresonant background of the H 2 O and D 2 O samples at the water−DPTAP interface by using HD-SHG spectroscopy. The amplitudes and phases obtained in the HD-SHG measurements are plotted in Figure 4 panels a and (2) (ω), as the Stern layer contribution is largely independent of the ionic strength and thus is insensitive to the salt concentration. Furthermore, the parameters for the CO stretch modes were identical between H 2 O and D 2 O samples. The global fitting provides the robust estimation of the χ bend (2) (ω) and χ bend (3) (ω) contributions. The details of the fitting functions and obtained parameters can be found in the Supporting Information.
The obtained fits are plotted in the solid lines of Figures 1(c−f) and 2, while the χ bend (2) (ω) and χ bend (3) (ω)Φ(c) spectra obtained from the fit are shown in Figure 5. The inferred Im(χ bend (2) (ω)) and Im(χ bend (3) (ω)Φ(c)) spectra are negative and positive for the DPTAP samples, while these are positive and negative for the DPPG samples. The mechanism of the opposite sign of the χ bend (2) (ω) and χ bend (3) (ω)Φ(c) contributions was previously explained using ab initio calculations. 26 The term causes a line shape modulation of Im(χ bend (3) (ω)-Φ(c)) spectra in the low concentration regime (red dotted lines in Figure 5), giving rise to the low frequency contribution in the frequency region of less than ∼1650 cm −1 , as discussed above. We would like to stress that the opposite signs of the Im(χ bend (2) (ω)) peak at the positively charged DPTAP and the negatively charged DPPG interfaces reveal that the H−O−H bending mode SFG feature arises from the dipole rather than from the quadrupole contribution.
The peak frequencies of the χ bend (2) (ω) contribution at the H 2 O−DPTAP and H 2 O−DPPG interfaces were 1672 ± 10 and 1652 ± 2 cm −1 , respectively. Since a higher bending mode frequency indicates a stronger hydrogen bond, 1 the peak frequencies indicate that a water molecule in the vicinity of the DPTAP interface has stronger hydrogen bonding than those at the DPPG interface. This trend is consistent with the O−H stretch data of the DPTAP and DPPG interface; the HD-SFG spectra show that the H 2 O−DPTAP interface (center-of-mass frequency of 3360 cm −1 ) shows a slightly lower frequency than the H 2 O−DPPG interface (3390 cm −1 ). 55 The slightly higher frequency of the H 2 O molecules near the PO 4 − part of the phospholipid can be rationalized by previous simulation data. 56 This qualitative agreement between interfacial water stretch and bend frequencies substantiates the conclusion that the χ bend (2) (ω) response originates from the interfacial dipole. As such, the χ bend (2) (ω) peak contains information on the hydrogen bond structure of the interfacial water molecules.
The χ bend (2) (ω) contribution has a peak frequency of 1650 cm −1 and a full-width at half-maximum (fwhm) of ∼60 cm −1 . Since the χ bend (3) (ω) contribution reflects the bulk properties, the peak frequency and fwhm of the χ bend (3) (ω) spectra can be compared with the IR and Raman spectra of the water bending mode. Indeed, these values are very comparable to the 1644 cm −1 peak frequency and ∼70 cm −1 fwhm of the IR spectrum of the water bending. 9

IV. CONCLUSIONS
We performed the HD-SFG measurement of the H−O−H bending mode of water at the water-positively charged DPTAP and water-negatively charged DPPG interfaces. Our data show that the χ bend (3) (ω) contributions are not negligible at the charged interface. The sign of the Im(χ bend (2) (ω)) spectrum at the water−DPTAP interface is negative, whereas the sign of the Im(χ bend (2) (ω)) spectrum at the water−DPPG interface is positive. The change of the peak sign indicates that the bending mode signal arises from the dipole mechanism. Furthermore, we discussed the obtained frequency for the Im(χ bend (2) (ω)). The sensitivity of the peak frequency at the different interfaces indicates that the bending mode of the interfacial water molecules can be a reporter for the hydrogen bonding structure at the interfaces.
The Journal of Physical Chemistry B pubs.acs.org/JPCB Article Further details for the experimental methods; discussion on frequency variations of the CO stretch mode between different research groups; fitting procedures; comparison of HD-SHG and HD-SFG data; phaseaccuracy of HD-SFG measurements (PDF)