Applications: Aqueous Interfaces

  • Akihiro Morita
Part of the Lecture Notes in Chemistry book series (LNC, volume 97)


This chapter presents recent applications of the computational SFG analysis for aqueous interfaces. Aqueous interfaces are relevant to a variety of fields in chemistry and engineering, and have been extensively investigated by SFG spectroscopy. Nevertheless, their hydrogen-bonding network and complicated vibrational coupling hinder simple intuitive interpretation of the observed spectra. The aid of MD simulation to analyze the complicated SFG spectra is actually quite powerful. This chapter introduces the results of analysis for various aqueous interfaces led by the author’s group and others, including water, ice, electrolyte aqueous solutions, water-oil and water-membrane interfaces.


O–H stretching Vibrational coupling Interface thickness Ion segregation Electric double layer 

Water and aqueous interfaces have been extensively studied by the SFG spectroscopy, and computational analysis of their SFG spectra has been particularly developed [32, 36, 61, 76, 96]. Water has its characteristic three-dimensional network structure of hydrogen bonds, and the hydrogen-bond structure gives rise to a number of peculiar properties of liquid water [3, 39]. Therefore, it is an intriguing issue to understand the hydrogen-bonding structure of water surface, and to reveal the structural difference from that of bulk water and its implications [44]. The interface structure is of fundamental importance to interfacial properties and heterogeneous reactions at water surface.

One important advantage of applying the SFG spectroscopy to aqueous interfaces is the availability of the O–H stretching vibrational band. The O–H stretching band in 3000–3800 cm−1 region is fairly easy to measure technically by SFG spectroscopy, and its frequency and intensity are sensitive indicators of the hydrogen-bond strength. Selective detection of the O–H stretching band of interfacial water provides quite useful information on the interfacial structure of water.

On the other hand, SFG spectra of aqueous interfaces pose a challenge to interpretation. The O–H stretching vibration of water involves various kinds of vibrational couplings, both intramolecular and intermolecular, which complicate the spectral assignment. Just as an example, two equivalent O–H vibrations of a single isolated water molecule are coupled and split into symmetric and antisymmetric vibrational modes, which have orthogonal transition dipole moments. Therefore, the single water molecule exhibits two different directions of transition moments. We could not determine the orientation of the molecule from the observed direction of transition moment unless we know the character of the vibrational mode. In condensed phase, the water O–H moieties are coupled by the hydrogen bonds, and consequently the vibrational modes are delocalized among intermolecular O–H moieties. Such delocalized vibrations are often beyond our intuitive understanding. To properly assign the observed O–H vibrations in relation to the interface structure, theoretical analysis is particularly required.

Here we summarize the current status of the theoretical analysis of SFG spectra of water and aqueous interfaces. We discuss the surfaces of liquid water, ice, and electrolyte solutions. Besides the air-aqueous interfaces, liquid/liquid (water/oil) and water/monolayer interfaces are also treated. The knowledge described below should be regarded as fundamentals for future progress. In this chapter, we discuss the SFG spectra of O–H stretching region in the SSP polarization, the most commonly employed geometry, unless otherwise noted.

9.1 Water Surface

The vibrational spectra of water surface have been computationally analyzed by a number of researchers [4, 10, 13, 29, 52, 56, 57, 62, 73, 74, 80, 81, 103, 110]. Here we briefly show some basic information of water surface derived from the computational analysis of the SFG spectra.

Historical perspective

The SFG spectrum of water surface in the O–H stretching region was first reported by Shen and co-workers [14], and subsequently studied by other groups including Shultz and Richmond [88, 94] in the pioneer stage of SFG spectroscopy. Since then the water surface is one of the most intensively studied surfaces by SFG [9, 93]. The spectral shape has been shown in Fig.  1.1 in Chap.  1, which apparently consists of two bands, a sharp band at 3700 cm−1 and a broad one at 3000∼3600 cm−1. We note that the spectral lineshapes reported in early period [14, 88, 94] were noticeably different from each other. This problem of disagreement has been resolved by the progress of spectroscopy, and Fig.  1.1 is currently considered to be the established intensity spectrum of liquid water in the O–H stretching region.

First MD calculation of the water SFG spectrum was carried out by Morita and Hynes on the basis of the energy representation in Sect.  4.1 [57]. The calculated SFG spectrum of water surface reproduced the two-band structure in the O–H stretching region. The computation predicted the Im[χ(2)] spectrum that the sharp band at 3700 cm−1 has a positive amplitude of Im[χ(2)] while the broad band at 3000∼3600 cm−1 has a negative sign (see Figs.  8.2a and 9.1). As we have argued in Sect.  4.2, the sign of the Im[χ(2)] spectrum in the SSP polarization is indicative of the orientation of the transition dipole for the O–H stretching vibration. The positive sign at 3700 cm−1 indicates upward O–H orientation with H pointing to the vapor, while the negative sign at 3000∼3600 cm−1 implies downward O–H orientation. Subsequently the phase-sensitive or heterodyne-detected SFG measurement confirmed the band shape of the Im[χ(2)] spectrum [40, 66, 105].1 The prediction of the Im[χ(2)] spectral features is the first successful demonstration of the computational analysis in the SFG spectroscopy.
Fig. 9.1

MD analysis of surface thickness in SFG spectroscopy. (Left panel a) density profile of water surface as a function of \(\hat {z}\) in blue. The varying surface regions \(\hat {z} > z^{\text{thres}}\) are shown with orange bars. (Right panel b) convergence behavior of calculated Im[χ(2)] spectrum with expanding the interface region \(\hat {z} > z^{\text{thres}}\) [57]. (Reprinted from Ref. [57], Copyright 2012, with permission from Elsevier)

Thickness of surface sensitivity

One important and general concern in the SFG spectroscopy is to find the depth of detection in the interface region. As we have argued in Chap.  1, the SFG is sensitive to the interface where the inversion symmetry is broken. The SFG-active region of interface may depend on the system in question. In molecular liquids such as water, the broken symmetry arises from anisotropic molecular orientation near the interface, whereas the bulk material has random and isotropic orientation. The MD simulation is able to investigate molecular orientation with varying depth, and thereby answer the question about the spatial origin of surface sensitivity.

The detected depth by SFG spectroscopy can be readily examined with MD simulation. As illustrated in Fig. 9.1, we introduce a depth coordinate \(\hat {z}\) which is normal to the interface and that the interface is located at \(\hat {z} \approx 0\). We tentatively set a region at the surface z > zthres, and calculate a χ(2) spectrum of the system in that restricted region. This calculation is feasible by MD simulation. By gradually lowering the threshold zthres and expanding that region, we can observe the convergence behavior of the calculated χ(2). Figure 9.1 shows the results of such analysis. The figure tells us that the positive band at 3700 cm−1 originates from the region of \(\hat {z} > -3 \; {\AA }\), since the band amplitude reaches the convergence up to the region. This result evidences that this positive band at 3700 cm−1 comes from the top monolayer of the water surface, again supporting the free O–H exposed to the air. On the other hand, the negative band at 3000∼3600 cm−1 converges at about \(\hat {z} > - 9 \; {\AA }\), indicating that the band of hydrogen-bonded O–H is attributed to a few top monolayers of the water surface. This analysis confirms the remarkably acute selectivity of SFG spectroscopy in the monolayer scale.

Analysis of hydrogen-bonded O–H band:

The broad band at 3000∼3600 cm−1 is attributed to hydrogen-bonded O–H, due to the substantial red shift of frequency. However, further detailed assignment of this band has invoked a number of studies and often confusions. As seen in the experimental SFG spectrum of water (left panel of Fig.  1.1), this broad band appears to have two sub-bands, one at about 3200 cm−1 and the other at about 3400 cm−1. The two sub-bands are often called “ice-like” and “liquid-like” bands, respectively, in analogy with these spectra of the corresponding bulk materials. The O–H band at 3200 cm−1 is obviously seen in the infrared and Raman spectra of ice [79], while the band at 3400 cm−1 is seen in liquid water [16]. However, the physical origin of these two sub-bands in the SFG spectrum is still controversial. An intuitive understanding of the two sub-bands comes from the picture that the water surface is a mixture of ice-like water and liquid-like water. This idea of two-state mixture model has a long history in bulk water [16], though there is no consensus to support this idea with microscopic investigation by MD simulation or other means.

Bonn and co-workers proposed an alternative assignment of the two-band structure that the two sub-bands are due to Fermi splitting of O–H stretching vibrational states by the H–O–H bending overtone [98, 99]. Their argument is supported by the experiment of H-D isotope dilution. By replacing H2O with HOD, they observed that the two sub-bands merge into one. This implies that the two-band structure should originates from vibrational coupling rather than the structure, since the isotope dilution little affects on the structure of nuclei.

As we argued in the beginning of this chapter, a main challenge in analyzing O–H vibration stems from extensive intra- and inter-molecular vibrational couplings, which delocalize the O–H vibrations and complicates the relation to the molecular orientation. To disentangle the O–H vibrations, the H-D isotope dilution offers a useful means. The isotope dilution preserves the structure of nuclei, while it effectively eliminates the intra- and inter-molecular couplings among nearby O–H bonds. Therefore, the observed spectrum approaches that of assembly of isolated O–H bonds in dilute conditions, and the ideal picture about the relation of O–H orientation and Im[χ(2)] in Sect.  4.2.1 becomes increasingly reliable in the spectral analysis.

The two sub-bands at 3200 and 3400 cm−1 are widely seen in the O–H bands of a variety of aqueous systems, though they exhibits varying spectral lineshapes and relative intensities. These O–H band shapes of various aqueous systems are likely influenced by inhomogeneous species as well as vibrational couplings. Previous time-resolved SFG measurements confirmed that the O–H band includes comparable homogeneous and inhomogeneous widths[8, 25, 51]. Comprehensive understanding of those band shapes is one of the principal aims of the further SFG analysis of water surface.

Bend vibration

Most SFG studies on water surface have dealt with the O–H stretching vibrations. The O–H stretching vibration is easy to measure and provides rich information on hydrogen-bonding environment, whereas the spectral analysis is complicated. There are some attempts to analyze other modes of the SFG spectrum, such as bend and libration [46, 60, 64, 75]. Here we discuss the bend mode in the SFG spectrum of water.

The SFG measurement of the bend band was first carried out by Benderskii and co-workers [108], and subsequently the heterodyne measurement of the bend band was reported by Kundu et al. [47]. The measured Im[χ(2)] spectrum revealed a positive band over the bend frequency region, though a previous simulation by Nagata et al. had predicted a bipolar shape of the Im[χ(2)] band [60]. The qualitative disagreement between the simulation and experiment was elucidated by further theoretical analysis [47], concluding that the bend band of SFG is actually dominated by the χIQB term of bulk quadrupole origin discussed in Chap.  7. The sign of Im[χ(2)] in the bend region is therefore insensitive to the molecular orientation at surface.

We note in passing that the role of quadrupole contribution on SFG spectra was also found in benzene [45, 50], as discussed in Sect.  10.2. Systematic investigation of the quadrupole effect on various systems is desired.

9.2 Ice Surface

The structure of ice surface has been drawing wide attention for more than a century. Faraday suggested premelting of ice surface [15] below the freezing temperature, and subsequently a number of experiments using optical, magnetic or electrical means confirmed that the premelting layer is developed in several tens of nanometers at about T ≳−10C [79]. The SFG spectroscopy is powerful to selectively probe the microscopic hydrogen bonding environment at the ice surface. The experimental SFG spectrum of ice Ih basal surface is shown in Fig. 9.2. We notice the remarkably intense band at about 3200 cm−1 in the ice spectrum, much stronger than that of the water spectrum. The intensity further augments with lowering temperature [19, 113]. The origin of this remarkable band is understood with the help of MD analysis.
Fig. 9.2

(a, b) Schematic pictures of basal face of ice surface [71], where red and white symbols denote oxygen and hydrogen, and the bilayers are labeled with B1, B2, …, in order from the topmost layer to the bulk. In the magnified picture (b), upward and downward hydrogens of bilayer-stitching hydrogen bonds are colored in green and blue, respectively. (c, d) Experimental ice spectrum of SSP polarization at 232 K [113]. The inset (d) compares the ice and water spectra. (Reprinted with permission from Ref. [113]. Copyright 2001 by American Physical Society)

The intense band and its temperature dependence of the ice surface were reproduced by MD simulation [31, 35] using QM/MM calculation instead of the classical polarizable MD simulation. These authors found that the band intensity at 3200 cm−1 is substantially augmented by the charge transfer, and accordingly the classical model that omits the charge transfer effect could not sufficiently reproduce the remarkable intensity. The band intensity is sensitive to the local disorder of the tetrahedral ice structure as well as the charge transfer. The ordered ice structure facilitates delocalized O–H vibrations, which couple with the charge transfer and augment the band intensity. The large temperature dependence of the band intensity is elucidated with the sensitivity to the local disorder.

The intense band is mainly attributed to the bilayer-stitching O–H vibrations between the first (B1) and second (B2) bilayers of the ice surface in Fig. 9.2b. By looking at the panel (b), one may think that the signals from the upward O–H (green) and downward O–H (blue) vibrations should cancel each other in the ideal ice lattice. However, the MD analysis showed that the upward and downward O–H bonds between B1 and B2 layers are actually inequivalent because of more structural disorder in the B1 bilayer than that in B2, and the broken symmetry near the surface causes the strong SFG signal [71]. The larger disorder in the B1 layer is indicative of the surface premelting in the atomic level, and the premelting develops toward deeper bilayers with increasing temperature [92].

The above interpretation of the intense SFG band should be examined in comparison with experimental measurement of the Im[χ(2)] spectrum. However, experimentally reported lineshapes of the Im[χ(2)] spectrum are under serious controversy at present [68, 71, 97], though those of the SFG intensity spectrum agree. Otsuki et al. [71] and Smit et al. [97] reported a negative main band of the Im[χ(2)] spectrum, which is in accord with previous theoretical studies [11, 31, 35, 112], whereas Nojima et al. [68] experimentally reported a positive band. This problem of Im[χ(2)] spectrum should be resolved to establish the spectrum. There remain some important issues to be elucidated in relation to the SFG spectrum of ice, including the proton ordering near the ice surface [68, 102, 112] and the contribution of bulk signal in SFG [95, 112].

9.3 Electrolyte Solution Surfaces

Understanding of electrolyte aqueous solution surfaces has been remarkably advanced in this century [43, 89, 115]. In early days of the twentieth century, people believed that water surface is generally void of ions, on the basis of surface tension measurements [21, 84] and the theory of dielectrics [70]. This picture appears to be consistent to intuitive idea that ions prefer to be strongly hydrated in the interior of bulk rather than to expose themselves to the air. This intuitive picture was challenged in 2001 with MD simulation by Jungwirth and Tobias [42]. They predicted that some anions, such as I or Br, rather prefer to be exposed to the air as shown in Fig. 9.3. This prediction stimulated experimental studies of electrolyte solution surfaces by various means, including SFG, SHG and photoelectron spectroscopies [43, 72, 77]. The SFG spectroscopy played one of the leading roles to unveil the surface structures in combination with MD analysis [18, 32, 36, 41]. Such studies became a prototype of close collaboration of SFG experiment and MD simulation. Here we focus on the findings brought by the MD analysis of SFG spectroscopy.
Fig. 9.3

MD snapshots (left) and density profiles (right) of NaX (X = F, Cl, Br, I) aqueous solution surfaces [42]. (Reprinted with the permission from Ref. [42]. Copyright 2001 American Chemical Society)

9.3.1 Halide Ions: Surface Segregation

The MD simulation predicts the order of surface preference to be I > Br > Cl > F, indicating that larger anions (e.g. I) exhibit surface preference while smaller ones (F) are buried into the bulk liquid (see Fig. 9.3). In response to the MD prediction, SFG measurements of NaX (X = F, Cl, Br, I) aqueous solutions were carried out in 2004 by Liu et al. [49] and Raymond et al. [85]. While the two groups reported analogous spectra of NaX solutions, their interpretations were contradictory about the essential issue whether the observed SFG spectra support the surface preference of I and Br. This ambiguity clearly indicates the need of MD analysis to draw definite interpretation from the SFG spectra.

The MD simulation of NaI solution predicts the surface preference of I, and also reproduces the perturbed SFG spectrum of NaI solution from that of pure water. The role of NaI on the spectral perturbation is manifested in the Im[χ(2)] spectrum more clearly than the intensity spectrum (∼|χ(2)|2). Figure 9.4a shows the Im[χ(2)] spectrum of NaI solution [40], where the amplitude of Im[χ(2)] is shifted to the positive direction compared to that of the pure water in 3100∼3500 cm−1, and the perturbed Im[χ(2)] spectrum is well reproduced by the MD simulation in Fig. 9.4b [28].
Fig. 9.4

(a) Experimental Im[χ(2)] (SSP) spectra of 2 M NaI solution (red) and pure water (black) [40], (b) Calculated Im[χ(2)] spectra [28] by Eq. ( 5.27), and (b) the inset shows the self parts by Eq. ( 5.27). (c) Dipole-dipole correlation schemes of I and water at surface. μz − μz (SSP) cancels the Im[χ(2)] amplitude, while μy − μy (SPS) augments. (Reprinted with permission from Ref. [40]; Copyright 2008 by American Physical Society. Reprinted with the permission from Ref. [28]; Copyright 2007 American Chemical Society)

Electric double layer

The perturbation of electrolyte on the surface structure and SFG spectra is generally understood by the electric double layer picture, as illustrated in Fig. 9.5. This idea was applied to the SFG analysis by Shultz and co-workers [94], and has been widely utilized as a basic picture for qualitative understanding of spectral perturbation. In the case of NaI solution, the I anion comes closer to the surface than the Na+ cation, and thus these ions form an electric double layer near the surface with an upward electric field (left panel of Fig. 9.5). Consequently the water molecules in the double layer orient their dipole upward, which gives rise to the positive perturbation on the Im[χ(2)] spectra. In fact, the positive perturbation of Im[χ(2)] was observed by experiment and MD simulation, indicative of the surface preference of I more than Na+. On the other hand, if cations comes closer to the surface than anions, a reverse electric double layer should be formed and result in negative perturbation on Im[χ(2)] (right panel). We will see such examples in other electrolyte solutions, including HCl solution [26, 36].
Fig. 9.5

Two types of electric double layer formation at electrolyte interfaces and their perturbation on Im[χ(2)] spectra

This fundamental picture of spectral perturbation is widely valid for electrolyte solution surfaces, since the electric double layer is generally formed at electrified interfaces. Previous MD studies have shown that even a small charge separation of ions causes sensitive perturbation on the SFG spectra [23, 38]. We occasionally encounter SFG spectra of electrolyte solutions which are not readily interpreted with this picture. Such exceptional cases offer further specific insight into the spectra and structure, as we find some examples below.

Validity of \({\boldsymbol {\chi ^{(2)}}} \approx N \cdot \overline {\alpha ^{(2)}}\):

In the above paragraph we argued that the positive perturbation of Im[χ(2)] is indicative of the surface preference of I more than Na+. When we evaluate the perturbation on the spectral amplitude quantitatively, further insight is obtained into the mechanism of SFG spectra for electrolyte solution surfaces. The amplitude of χ(2) is conventionally presented with Eq. ( 3.41),
$$\displaystyle \begin{aligned} \chi _{pqr}^{(2)} \approx \sum_{l=1}^N \alpha^{(2)}_{l, pqr} = N \cdot \overline{\alpha^{(2)}_{pqr}}, \end{aligned} $$
on the basis of an assumption that the nonlinear susceptibility χ(2) is the sum of hyperpolarizabilities α(2) of constituent molecules. Equation ( 3.41) implies that χ(2) is governed by two factors, number density N and orientational order \(\overline {{\boldsymbol {\alpha }}^{(2)}}\). The electric double layer orients the water molecules, as illustrated in Fig. 9.5, and thus enhances the orientational average \(\overline {\alpha ^{(2)}_{pqr}}\). This interpretation is qualitatively in accord with the above picture of electric double layer.
However, the actual enhancement of the χ(2) amplitude is significantly smaller than that predicted by Eq. ( 3.41) in the SSP polarization. χ(2) is expressed by Eq. ( 5.27),
$$\displaystyle \begin{aligned} \chi _{pqr}^{(2),\text{res}}(\Omega, \omega_1, \omega_2) = \frac{i \omega_2}{k_B T} \int_{0}^{\infty } dt \left\langle {{A}_{\text{eff},}}_{pq}(t){{M}_{r}}(0) \right\rangle \exp (i \omega_2 t), \end{aligned} $$
$$\displaystyle \begin{aligned} {A}_{\text{eff},pq} (t) = \sum_{l=1}^{N} {\alpha }_{\text{eff}, pq}(l, t) \quad {M}_{r} (0) = \sum_{m=1}^{N} \mu_{\text{eff}, r} (m, 0). \end{aligned} $$
On the other hand, Eq. ( 3.41) represents the χ(2) as the sum of molecular hyperpolarizabilities \({\boldsymbol {\alpha }}^{(2)}_l\), and accordingly corresponds to in the form of time correlation function. We notice that Eq. ( 5.27) includes only the self correlation (l = m) of Eq. ( 5.27). Equation ( 5.27) should be regarded as an approximation of Eq. ( 5.27) by omitting the intermolecular correlation (lm).

The calculated Im[χ(2)] spectra of NaI solution by Eqs. ( 5.27) and ( 5.27) are compared in panels (b) and (b) of Fig. 9.4, respectively. The perturbation of NaI (red lines) from pure water (black) exhibits noticeable differences in the two panels. The self correlation of Im[χ(2)] spectrum in panel (b) exhibits a remarkable positive amplitude (red line), because of the orientational order of water molecules induced by the electric double layer. However, the Im[χ(2)] amplitude of NaI (red line) in panel (b) shows a rather modest perturbation to the positive direction. The difference between (b) and (b) indicates that Eq. ( 5.27) or Eq. ( 3.41) overestimates the positive perturbation on χ(2). The deviation is obviously attributed to the cross correlation among neighbor molecules (lm) in Eq. ( 5.27). The cross correlation is illustrated in Fig. 9.4c in the case of SSP polarization, where the z-component dipole is relevant through the \(\chi ^{(2)}_{yyz}\) element (see Eq. ( 3.49)). In the NaI solution surface, the induced z-component dipoles of different molecules tend to correlate anti-parallel, which thereby suppresses the total amplitude of dipole. This correlation effect becomes obvious in SFG spectra including surface-active and very polarizable species, such as I.

SPS polarization

The SPS spectra of aqueous systems could provide complementary information to the SSP spectra. However, the SPS spectra have been less explored than SSP, because the signal intensity is generally weak and the analysis is less intuitive. The SPS spectra are associated to the \(\chi ^{(2)}_{yzy}\) element, which involves the y-component dipole. Since the relevant dipole is parallel to the interface, the mechanism of SPS spectra is not interpreted in terms of up/down dipole orientation of surface species. To understand the SPS spectra even in qualitative sense, the MD analysis is often required.

In the SPS polarization, the correlation effect discussed above has an opposite influence on the χ(2) amplitude, as illustrated in Fig. 9.4c. In contrast to the z-component dipole in SSP, the induced y-component dipoles in SPS tend to correlate parallel in the electric double layer and thus enhance the total χ(2) amplitude for the SPS polarization. The constructive effect of dipole correlation in the SPS case has been demonstrated by MD calculation and consistently elucidated the experimental spectrum [28]. The SPS spectrum of NaI solution provides another decisive evidence for the electric double layer formation by Na+ and I.

9.3.2 Buried Ions: F, SO\(_4^{2-}\)

In contrast to the ions in the preceding subsection, some other ions are repelled from the water surface and buried, in accord with the traditional picture of interfacial ions. MD simulation predicts that F and SO\(_4^{2-}\) are typical examples of such buried ions. One may expect that such buried electrolytes little perturb the surface structure, since these ions do not penetrate into the topmost layer. Yet the SFG spectroscopy can report perturbed SFG spectra for some of these electrolyte solutions, which implies the water surface is still perturbed by the ions. The mechanism of spectral perturbation and surface structure are elucidated with the help of MD analysis.

Figure 9.6a shows the computational [23] and experimental [17, 49] SFG spectra of NaF and Na2SO4 solutions. We find that the NaF (blue) and Na2SO4 (red) solution spectra are noticeably different. NaF little perturbs the SFG spectrum of neat water (black), whereas Na2SO4 obviously enhances the SFG intensity. These differences illustrate that specific effects on the surface are present among such buried ions. The reason of the spectral difference is understood as follows.
Fig. 9.6

(a) SFG spectra of 0.016 mole fraction (≈0.9 M) NaF (blue) and 1M Na2SO4 (red) solutions in comparison with that of pure water (black). Upper panels are calculated results [23], while lower panels are experimental [17, 49]. (b) Density profiles of ions and water along the depth coordinate \(\hat {z}\). The density of each species is normalized with that in the bulk. (c) \(\langle \cos \theta \rangle \) profiles of water orientation for pure water (gray), Na2SO4 (red) and NaF solutions (blue). The definition of the tilt angle θ is illustrated in the inset. (Reprinted with the permission from Refs. [17, 23, 49]. Copyright 2012, 2004, 2005 American Chemical Society)

Panels (b) and (c) show the calculated density profiles and water orientation, respectively, of the NaF and Na2SO4 solution surfaces. The density profiles in (b) confirm that all the present ions of Na+, F and \(\mathrm {SO}_4 ^{2-}\) are repelled from the topmost layer of the surface. By comparing the density profiles of NaF and Na2SO4 solutions in panel (b), we find that the NaF solution (left) exhibits almost overlapping profiles of Na+ and F ions, whereas the Na2SO4 solution (right) shows slight but significant difference in the Na+ and \(\mathrm {SO}_4^{2-}\) profiles. In the Na2SO4 solution, \(\mathrm {SO}_4^{2-}\) is more repelled from the surface than Na+, arguably because SO\(_4^{2-}\) is a divalent ion. Consequently, charge separation between Na+ and \(\mathrm {SO}_4^{2-}\) generates an electric double layer in a deep region by a few monolayers from the surface (\(\hat {z} \sim -5 \; {\AA }\)).

The effect of electric double layer in the Na2SO4 solution is manifested in the orientational profile of water in panel (c). This panel displays the \(\langle \cos \theta \rangle \) profile as a function of the depth coordinate \(\hat {z}\), where θ is the tilt angle of the water dipole from the surface normal. Near the Gibbs dividing surface of water (\(\hat {z} \approx 0 \; {\AA }\)), all the \(\langle \cos \theta \rangle \) profiles of pure water (black), Na2SO4 solution (red), and NaF solution (blue) show negative and nearly identical shapes. This feature means that the water orientation of the top layer is little perturbed by the buried ions. However, we see a negative \(\langle \cos \theta \rangle \) region in a deeper region \(\hat {z} \approx -5 \sim -10 \; {\AA }\) for the Na2SO4 solution (red dashed). This feature is a consequence of the electric double layer of Na+ and \(\mathrm {SO}_4^{2-}\) formed in that region. Further MD analysis confirmed that the enhanced SFG intensity in the Na2SO4 solution originates from the perturbed water orientation of the negative \(\langle \cos \theta \rangle \) in that deep region, and the perturbed Im[χ(2)] band of Na2SO4 solution was confirmed by the heterodyne detected SFG measurement [107].

In summary, the SFG signals of water originate from the surface region where the isotropic orientation is broken, and the electric double layer formation of electrolytes is a typical cause to perturb the water orientation. The above cases of NaF and Na2SO4 solutions exemplify that the SFG spectroscopy is sensitive to the perturbed water orientation induced by slight charge separation, even when the charge separation arises from a somewhat deep region from the topmost layer. The perturbed SFG spectra of electrolyte solutions may reflect the structural change in a deeper region than the topmost layer of the water surface.

9.3.3 Acid

In the surface of acid solutions, the excess hydronium (H3O+) cations preferentially reside on the topmost surface of water. This microscopic behavior was predicted by MD simulation [58, 78]. It has been long known experimentally that the surface tension of acid solutions becomes smaller than that of neat water [84], implying a positive surface excess from the thermodynamic view. The relation to the microscopic surface structure of acid solutions and their SFG spectra is analyzed in the following.

HCl, HI (strong acid) solution surfaces

Figure 9.7 displays the calculated and experimental SFG spectra of strong acid solutions, HCl and HI [26, 58].2 The SFG spectra of acid solutions are generally characterized with two features: (i) reduced intensity of the free O–H band at about 3700 cm−1 and (ii) enhanced intensity of hydrogen-bonding O–H, particularly in 3200 cm−1 region. These characters are consistently elucidated by the MD analysis of SFG spectra.
Fig. 9.7

SFG spectra and orientation for acid solution surfaces. (a) calculated SFG spectra of pure water (black), 1.1 M HCl (blue) and 1.1M HI (red) [26]. The inset shows the experimental spectra by Mucha et al. [58]. (b) \(\langle \cos \theta \rangle \) profile of water orientation. (Reprinted with the permission from Refs. [26, 58]. Copyright 2007, 2005 American Chemical Society)

(i) The amplitude of the free O–H band is reduced in the acid solutions, essentially because the H3O+ covers the water surface and decreases the density of free O–H at the topmost layer. (ii) The increased intensity of hydrogen-bonding O–H band is understood from the electric double layer picture. As illustrated in the right panel of Fig. 9.5, the H3O+ layer at the topmost surface and the counter anions located below form an electric double layer. The double layer orients the water molecules toward the bulk liquid, resulting in negative perturbation on \(\langle \cos \theta \rangle \). This pertubation augments the negative \(\langle \cos \theta \rangle \) at water surface, since the pure water surface has intrinsic negative \(\langle \cos \theta \rangle \) orientation at the top layer \(\hat {z} = -3 \sim 0 \; {\AA }\) (see right panel of Fig. 9.7). Therefore, the enhanced water orientation of negative \(\langle \cos \theta \rangle \) by the acid perturbation augments the negative Im[χ(2)] amplitude and the SFG intensity in the hydrogen-bonded O–H frequency region.

H2SO4 solution surface

Sulfuric acid solution surface is relevant to heterogeneous atmospheric chemistry, as it is the main chemical component of sulfate aerosols, ubiquitously present in troposphere and stratosphere. The SFG measurement of sulfuric acid solution was performed in early stage of SFG spectroscopy [2, 83]. The observed spectra showed that the SFG intensity decreases in concentrated solutions (mole fraction x ≳ 0.2) and the whole O–H band eventually vanishes with increasing x. This behavior posed confusing interpretations for the surface structure.

This system poses an additional challenge in interpretation besides the strong acid solutions discussed above. Sulfuric acid undergoes two-step ionization: The first ionization is considered to be strong enough (pKa1 ≪ 0), whereas the second ionization (pKa2 ≃ 1.9 [20]) is not as strong as the first one. In such cases that the acid dissociation is not complete, the local composition of the ion species at the interface could be different from that in the bulk, since the interface is a less polar environment than the bulk. The ion dissociation at interface may be sensitive to the depth or other conditions, and coupled to the interface structure and SFG spectra. These uncertainties make such surfaces challenging to understand. The collaboration of SFG spectra and MD analysis can provide valuable information on the surface structure and ion composition.
Since we could not determine the local ion composition a priori, we assumed typical cases (a–c) about acid dissociation (9.1), where
  1. (a)

    Same pKa1,2 in Eq. (9.1) holds for surface as well, (HSO\(_4^-\) dominant, SO\(_4^{2-}\) present)

  2. (b)

    Second ionization is suppressed at surface (pKa2 ≫ 0), (no SO\(_4^{2-}\))

  3. (c)

    First ionization is also suppressed (pKa1 ≫ 0), (only neutral H2SO4)

and predicted the SFG spectra in each case by MD simulation. Figure 9.8 displays the MD results in comparison with the experiments [2, 33] to see whether the experimental features in O–H and S–O bands are consistently reproduced by MD predictions. We first find that case (a) would lead to excessively strong hydrogen bonding O–H signal, arguably because the presence of divalent anions (SO\(_4^{2-}\)) too much augments the electric double layer. Therefore, case (a) is not likely to be the proper case. On the other hand, case (c) shows the main S–O band at 1150 cm−1 in the SSP spectrum, which is assigned to the neutral H2SO4, while the experimental main S–O band as well as cases (a) and (b) arises at 1050 cm−1 from \(\mathrm {HSO_4^-}\). Therefore, case (c) is not the proper case either. The combination of SFG measurement and MD simulation thereby conclude that the first dissociation is facile at the surface, whereas the second dissociation to form \(\mathrm {SO}_4^{2-}\) is substantially more suppressed at the surface than in the bulk [30, 33, 53].
Fig. 9.8

Predicted SFG spectra of O–H and S–O bands of 0.2x sulfuric acid solution in comparison with experimental ones (top panels [2, 33]). In O–H spectra (center column), blue symbols refer to sulfuric acid solution, and black ones for pure water. In S–O spectra (right coloumn), SSP (purple) and SPS (red) combinations are displayed. MD calculations were performed in each case of three assumptions (a)–(c) about local acid dissociation, discussed in the text. Shadowed panels show obviously inconsistent spectra with experiments. (Reproduced from Ref. [33] with permission from the PCCP Owner Societies. Reprinted with the permission from Ref. [2]; Copyright 1997 American Chemical Society.) (∗)Top right panel shows experimental S–O spectra for 0.29x solution

9.3.4 Base

The surface preference of hydroxide (OH) anion remains a controversial and active issue both theoretically and experimentally [1]. Previous MD simulation studies reported different conclusions about its surface preference, which arguably depend on the methods and conditions. Direct experimental measurement of surface OH species is also challenging. What information can be extracted from the SFG spectra of basic solutions [104, 106]? Here we summarize the implications drawn from the MD analysis of the Im[χ(2)] spectrum.

Figure 9.9 displays the calculated and experimental Im[χ(2)] spectrum of NaOH solution in comparison with that of neat water. The Im[χ(2)] spectrum of NaOH solution shows remarkable features of perturbation. The Im[χ(2)] band at 3300–3600 cm−1 shifts to the positive direction, whereas the Im[χ(2)] band at 3000–3200 cm−1 to negative [106]. These opposite perturbations in different frequency regions are not interpreted with the electric double layer picture, and imply some other mechanism beyond the double layer picture.
Fig. 9.9

(Left) calculated and experimental Im[χ(2)] spectra of pure water (black) and 1.2 M NaOH solution (red). Both MD calculation [24] and experiment [106] show the opposite perturbations on the Im[χ(2)] amplitude at about 3400 and 3100 cm−1 regions. (Right) illustration of the first solvation shell of OH and the electric double layer. (Reprinted with the permission from Refs. [24, 106]. Copyright 2014, 2008 American Chemical Society)

The MD simulation of NaOH solution reproduces the opposite perturbations, and elucidates the whole mechanisms by analyzing the perturbed spectrum [24]. To summarize the mechanisms, the electric double layer formed between OH and Na+ brings the positive perturbation to the main O–H stretching band at 3300–3600 cm−1, since OH comes slightly closer to the surface than Na+. On the other hand, the negative perturbation at 3000–3200 cm−1 originates from the water in the first solvation shell (FSS) of OH, as we discuss below.

This contribution of FSS is general in the electrolyte solutions, and we briefly explain the mechanism in Fig. 9.10. In a case of an anion, the FSS includes water molecules that orient their dipoles toward the anion, as illustrated in panel (a), and consequently the upward and downward orientations co-exist in the whole FSS. When the ions with their FSS are distributed in the surface region (panel (b)), the net contribution of the topmost, downward contribution remains while the other contributions cancel each other. This mechanism is common with the χIQB mechanism of the quadrupole contribution in Chap.  7 (see detailed discussion in Appendix A.1).3 We note that the FSS is regarded to form a quadrupole with a pair of opposite dipoles.
Fig. 9.10

(a) Illustration of the first solvation shell (FSS, green) around an anion OH. (b) Distributed ions with FSS in the surface region. (c) Net dipole orientation generated from the FSS water [24]. One may consider that the topmost, downward orientation remains while the other contributions cancel. Alternatively, if one considers a FSS as a quadrupole of opposite dipoles, the net downward contribution emerges at an arbitrary threshold \(\hat {z}_{\text{thres}}\)

The mechanism of FSS is clearly manifested in OH, since the FSS component appears in a particularly low-frequency region at 3000–3200 cm−1 and is separated from the main O–H band. From the above discussion, we can readily understand that the FSS of anions have generally negative Im[χ(2)] contributions while the FSS of cations have positive Im[χ(2)] contribution. The feature of the FSS evidences that the OH anions retain the first solvation shell and do not preferentially expose themselves at the surface.

9.4 Oil/Water Interfaces

Oil/water interfaces are relevant to various phenomena, such as micelle formation, extraction, membrane transport, sensors, and phase transfer catalysis. Microscopic understanding of oil/water interfaces has been pursued with various experimental techniques [48, 55] as well as MD simulation [5, 6, 12, 82]. A main challenge of investigating oil/water interfaces lies in difficulties of selective detection of interfacial molecules with sufficient spatial resolution. The interface-sensitive nonlinear spectroscopy is able to probe buried oil/water interfaces with excellent selectivity as long as it is accessible by light. The SHG was applied to reveal detailed polarity environment in the vicinity of the liquid-liquid interfaces [100, 101]. The collaboration of vibrational SFG spectroscopy and MD analysis is powerful to reveal the details of the oil/water interfaces.

Typical and fundamental examples of oil/water interfaces were studied by Richmond and co-workers [55, 109, 111]. Figure 9.11a shows the SFG spectra of carbon tetrachloride (CCl4)/water and 1,2-dichloroethane (DCE)/water interfaces in comparison to that of air/water interface. We find that the CCl4/water spectrum retains the two-band structure that resembles air/water, while the spectrum of DCE/water interface becomes structureless and weaker. The apparent spectral difference may allow various interpretations. The MD analysis can clarify the interpretation of the spectra in relation to the structure of oil/water interfaces.
Fig. 9.11

(a) Experimental SFG spectra of neat water/vapor (black), water/CCl4 (blue) and water/1,2-dichloroethane (DCE, red) interfaces [55, 109, 111]. (b) Calculated Im[χ(2)] spectra of the three interfaces [34]. (c) Illustration of free O–H at water/DCE interface. (d) Calculated Im[χ(2)] spectra by restricting the water molecules having free O–H bonds at the interfaces. The free O–H band at CCl4/water is little perturbed, while that at DCE/water interface is more red shifted and broadened. (Reprinted with the permission from Ref. [34]. Copyright 2012 American Chemical Society)

The MD simulation of the SFG spectra was performed [34], which well reproduced the distinct SFG spectra of CCl4/water and DCE/water interfaces. The MD simulation allows for direction observation of interfacial water structure. However, the MD showed rather similar structure of interfacial water at CCl4 and DCE in terms of the density profile or orientation of water molecules, irrespective of the apparently distinct SFG spectra reproduced. The mechanism of the noticeable spectral differences becomes clearer in the calculated Im[χ(2)] spectra in Fig. 9.11b. Comparing the Im[χ(2)] spectra of the two oil/water interfaces, we find that the spectra in the H-bonding region below 3600 cm−1 not much different, which is consistent to the direct MD observation that the density and orientation of surface water are analogous at CCl4/water and DCE/water interfaces. However, we find that the free O–H band in 3600–3700 cm−1 is particularly suppressed in the DCE/water interface.

The perturbation on the free O–H band is understood in the following manner. The free O–H of water at oil/water interface actually interacts with adjacent oil molecules, as illustrated in Fig. 9.11c. The “free” O–H at DCE/water interface is more perturbed than that at CCl4/water because of larger polarity of DCE than CCl4. As a consequence, the positive Im[χ(2)] band of “free” O–H is substantially red shifted and broadened for the DCE/water interface, as evidenced in Fig. 9.11d. The red-shifted free O–H band of DCE/water interface overlaps with the negative Im[χ(2)] band of the H-bonding O–H, and cancel the intensity. The apparent spectral difference between CCl4/water and DCE/water interfaces is attributed to the local interaction of water and oil molecules at the interfaces, rather than qualitatively distinct structure of molecular orientation.

9.5 Water at Monolayers

Amphiphilic molecules tend to form various self assembled structures in/on water, such as Langmuir monolayer, micelle and lipid bilayers. Such structures generally include interfaces of water and amphiphilic molecules, and their interfaces govern the stability of these structures. The interfaces of phospholipid membranes have been drawing particular attention by SFG spectroscopy [41], as the lipid membranes define the boundary of cells, control mass transport, and thereby play vital roles of living functions [7, 63]. A number of MD studies in relation to the SFG spectroscopy have been performed to aim at selective detection and understanding of water structure in contact with those amphiphilic monolayers [37, 38, 59, 69, 86, 87, 90, 91].

One of the basic concepts of the water structure is the flip-flop model of water orientation in Fig. 9.12. The orientational structure of water molecules is determined by the net charges of the monolayer molecules. When the monolayer molecules are negatively charged, such as sodium dodecyl sulfate (SDS, \(\mathrm {C}_{12} \mathrm {H}_{25} \mathrm {SO}_4^- \cdot \mathrm {Na}^+\)), the water molecules take upward orientation and leads to positive Im[χ(2)] band. On the other hand, if the monolayer is positively charged, such as cetyltrimethylammonium bromide (CTAB, C16H33N+(CH3)3 ⋅Br), the water takes downward orientation and shows negative Im[χ(2)] band. The reversal of the Im[χ(2)] band of water O–H stretching is experimentally verified in Fig. 9.12 [65]. We notice that this mechanism is essentially common with the electric double layer picture in Fig. 9.5.
Fig. 9.12

Water structure near negatively and positively charged monolayer. The O–H band of Im[χ(2)] spectrum changes its sign [65]. (Reprinted with permission from Ref. [65]. Copyright 2009, American Institute of Physics)

In a case that the amphiphilic molecules are neutral, the SFG spectra of water interface are not amenable to the simple flip-flop model. Biological membranes include various neutral but zwitterionic phospholipid molecules, such as phosphatidylcholine (POPC) and dipalmitoylphosphatidylcholine (DPPC). Figure 9.13 displays an illustration of the water/POPC interface (left panel) and the experimental [54] and calculated [37] Im[χ(2)] spectra (right). The polar head group of POPC includes a positively charged choline (−N+(CH3)3) and a negatively charged phosphate (\(-\mathrm {PO}_4^-\)), which form a zwitterionic molecule. The experimental Im[χ(2)] spectrum of the water/POPC interface shows a positive main band at 3300 cm−1 and a positive minor band at 3580 cm−1. Another, related experimental Im[χ(2)] spectrum of water/DPPC also shows a quite similar lineshape [22]. The MD analysis revealed that the main positive band at 3300 cm−1 is assigned to the water molecules between the choline and phosphate groups, labeled “NP”. The positive sign of this “NP” band is understood from the electric double layer of the charged groups. The minor band at 3580 cm−1 is attributed to the water molecules penetrating to the ester group, labeled “NPO”. This O–H band is located in a higher frequency region due to weaker hydrogen-bonding environment. The water molecules attached to the choline group, labeled “N”, do not show up clearly in the Im[χ(2)] spectrum, but they contribute to the dip between the two positive bands.
Fig. 9.13

(Left) Illustration of water/phosphatidylcholine (POPC) interface, where the polar head group of POPC is classified to choline (N, red), phosphate (P, blue) and ester oxygen (O, green). (Right) Experimental [54] (orange) and calculated [37] (black) Im[χ(2)] spectra of water/POPC interface. Experimental spectrum of water/DPPC (open circles) [22] is also shown. (Reprinted with the permission from Refs. [37, 54]; Copyright 2012, 2016 American Chemical Society. Reproduced from Ref. [22] by permission of John Wiley & Sons Ltd)


  1. 1.

    Early phase-sensitive SFG experiments reported a positive tail of Im[χ(2)] at around 3000 cm−1 region [40, 66, 105]. That feature is considered to be an artifact of phase calibration at present [67, 114].

  2. 2.

    Note that the present MD simulation employed the point polarizable model [27] instead of CRK. Therefore, the spectra and structure may not coincide with those of the CRK model in other parts.

  3. 3.

    One may wonder that the net dipole in the FSS cancel and thus no signal is generated. Even though one considers the FSS of an ion as a quadrupole consisting of opposite dipoles, as illustrated in Fig. 9.10b, the net negative contribution still remains at an arbitrary threshold \(\hat {z}_{\text{thres}}\). This mechanism is same with the χIQB term of the quadrupole contribution in Appendix A.1.


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Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  • Akihiro Morita
    • 1
  1. 1.Tohoku UniversitySendaiJapan

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